AllPile
Version 7
User’s
Manual
Volume 1 and 2
CivilTech Software
CivilTech
Software
2015
All the information, including technical and engineering data, processes, and
results, presented in this program have been prepared according to recognized
contracting and/or engineering principles, and are for general information
only. If anyone uses this program for any specific application without an
independent competent professional examination and verification of its
accuracy, suitability, and applicability by a licensed professional engineer,
he/she does so at his/her own risk and assumes any and all liability resulting
from such use. In no event shall CivilTech be held liable for any damages
including lost profits, lost savings, or other incidental or consequential
damages resulting from the use of or inability to use the information
contained within.
Information in this document is subject to change without notice and does not
represent a commitment on the part of CivilTech Corporation. This program
is furnished under a license agreement, and the program may be used only in
accordance with the terms of the agreement. The program may be copied for
backup purposes only.
The program or user’s guide shall not be reproduced, stored in a retrieval
system, or transmitted in any form or by any means, electronic, mechanical,
photocopying, recording, or otherwise, without prior written consent from
CivilTech Corporation.
Copyright 2014 CivilTech Software. All rights reserved.
Simultaneously published in the U.S. and Canada.
Printed and bound in the United States of America.
Published by
CivilTech Software
Web Site: http://www.civiltech.com
CivilTech Software
TABLE OF CONTENTS
VOLUME 1
CHAPTER 1 INTRODUCTION .................................................................. 4
1.1
1.2
1.3
ABOUT ALLPILE .......................................................................................................................................... 4
ABOUT THE MANUAL................................................................................................................................... 4
ABOUT THE COMPANY................................................................................................................................. 4
CHAPTER 2 INSTALLATION AND ACTIVATION ................................................................... 5
2.1
INSTALLATION AND RUN.............................................................................................................................. 5
CHAPTER 3 OVERVIEW .............................................................................................................. 8
3.1
PROGRAM OUTLINE ..................................................................................................................................... 8
3.2
PROGRAM INTERFACE.................................................................................................................................. 9
3.3
PULL-DOWN MENUS.................................................................................................................................. 10
3.3.1
FILE .................................................................................................................................................... 10
3.3.2
EDIT ................................................................................................................................................... 10
3.3.3
RUN .................................................................................................................................................... 11
3.3.4
SETUP ................................................................................................................................................. 11
3.3.5
HELP................................................................................................................................................... 11
3.4
SPEED BAR ................................................................................................................................................ 12
3.5
SAMPLE AND TEMPLATES .......................................................................................................................... 12
CHAPTER 4 DATA INPUT............................................................................................................ 13
4.1
INPUT PAGES ............................................................................................................................................. 13
4.2
PILE TYPE PAGE ........................................................................................................................................ 13
4.2.1
PROJECT TITLES ................................................................................................................................. 14
4.2.2
COMMENTS ........................................................................................................................................ 14
4.2.3
UNITS ................................................................................................................................................. 14
4.3
PILE PROFILE PAGE .................................................................................................................................... 15
4.4
PILE PROPERTIES PAGE............................................................................................................................... 17
4.4.1
PILE PROPERTY TABLE ....................................................................................................................... 17
4.4.2
ADD TIP SECTION ............................................................................................................................... 18
4.4.2
ADD TIP SECTION ............................................................................................................................... 19
4.4.3
PILE SECTION SCREEN ........................................................................................................................ 19
4.4.4
EFFECTIVE AREA AND TOTAL AREA ................................................................................................... 22
4.4.5
SHALLOW FOOTING ............................................................................................................................ 23
4.5
LOAD AND GROUP ..................................................................................................................................... 25
4.5.1
SINGLE PILE ........................................................................................................................................ 25
4.5.2
GROUP PILES ...................................................................................................................................... 27
4.5.3
TOWER FOUNDATION ......................................................................................................................... 29
4.6
SOIL PROPERTY PAGE ................................................................................................................................. 30
4.6.1 SOIL PROPERTY TABLE ............................................................................................................................. 31
4.6.2
SOIL PARAMETER SCREEN .................................................................................................................. 33
4.7
ADVANCED PAGE ...................................................................................................................................... 35
4.7.1
ZERO RESISTANCE AND NEGATIVE RESISTANCE (DOWNDRAG FORCE) .............................................. 35
4.8
UNITS OF MEASURE ................................................................................................................................... 38
CHAPTER 5 RESULTS .................................................................................................................. 39
5.1
PROFILE ..................................................................................................................................................... 39
5.2
VERTICAL ANALYSIS RESULTS .................................................................................................................. 39
5.2.1
DEPTH (Z) VS. S, F, Q .......................................................................................................................... 40
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LOAD VS. SETTLEMENT ...................................................................................................................... 41
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CAPACITY VS. LENGTH ....................................................................................................................... 41
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T-Z CURVE .......................................................................................................................................... 42
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Q-W CURVE ........................................................................................................................................
42
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SUBMITTAL REPORT ...........................................................................................................................
43
.
SUMMARY REPORT.............................................................................................................................
43
5.2.2
5.2.3
5.2.4
5.2.5
5.2.6
5.2.7
5.2.8
DETAIL REPORT .................................................................................................................................. 43
5.2.9
EXPORTING TO EXCEL ........................................................................................................................ 44
5.2.10 FIGURE NUMBER ................................................................................................................................ 44
5.3
LATERAL ANALYSIS RESULTS .................................................................................................................... 44
5.3.1
DEPTH (Z) VS. YT, M, P AND PRESSURES ............................................................................................. 44
5.3.2
LOAD (P) - YT, M ................................................................................................................................ 45
5.3.3
DEPTH VS. YT ...................................................................................................................................... 46
5.3.4
DEPTH VS. M ...................................................................................................................................... 46
5.3.5
P-Y CURVE.......................................................................................................................................... 47
5.3.6
SUBMITTAL REPORT ........................................................................................................................... 47
5.3.7
SUMMARY REPORT............................................................................................................................. 47
5.3.8
COM624S OUTPUT/INPUT................................................................................................................... 47
5.3.9
EXPORTING TO EXCEL ........................................................................................................................ 48
5.3.10 FIGURE NUMBER ................................................................................................................................ 48
5.4
STIFFNESS [ K] RESULTS ............................................................................................................................ 48
5.5
PREVIEW AND PRINT SCREEN .................................................................................................................... 49
5.6
ERRORS AND TROUBLESHOOTING.............................................................................................................. 50
CHAPTER 6 SETUP ....................................................................................................................... 52
6.1
SETUP SCREEN........................................................................................................................................... 52
6.2
PULL-DOWN MENU: SETUP ....................................................................................................................... 52
6.3
SPEED BAR ................................................................................................................................................ 53
6.4
TABBED PAGES .......................................................................................................................................... 53
6.4.1
REPORT FORMAT PAGE ...................................................................................................................... 53
6.4.2
MATERIALS PAGE ............................................................................................................................... 54
6.4.3
PILE TYPE PAGE ................................................................................................................................. 56
CHAPTER 7 SAMPLES ................................................................................................................. 58
7.1
SAMPLES.................................................................................................................................................... 58
VOLUME 2
SEE PAGE 59 FOR Table of Contents
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. 1 INTRODUCTION
CHAPTER
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1.1 About AllPile
.
The program AllPile for Windows analyzes pile load capacity efficiently and
accurately. AllPile can handle all types of piles: drilled shaft, driven pile,
auger-cast pile, steel pipe pile, H-pile, timber pile, tapered pile, bell pile,
shallow foundation, etc. You can define new pile types and input customized
parameters based on local practices and experience. The program is capable
of performing the following calculations:
 Lateral capacity and deflection

Static and cyclic conditions
 Vertical capacity and settlement

Negative and zero friction
 Group vertical and lateral analysis

Shallow footing
 FHWA SHAFT program

Tower foundation
The lateral calculation directly uses COM624S, which is the same method as
FHWA’s COM624P. It is comparable with Ensoft’s Lpile®. 1 In our tests, AllPile
provided the same results as COM624P2 and Lpile. AllPile is compatible with all
Windows operating systems, such as 98/NT/2000/ME/XP.
Lpile is a registered trademark of Ensoft, Inc. COM624P is a public-domain software downloadable free
from the U.S. Federal Highways Administration web site.
1.2
About the Manual
Volume 1:

Describes how to install, activate, and start the program (Chapters 2 and 3).

Describes each input and output parameters (Chapter 4 and 5).

Describes customization of the program and how to set up calculation
methods and parameters (Chapter 6).

Provides typical examples for using the software (Chapter 7).
Volume 2:
Introduces the theory and methods of calculation used in the program (Users
should be somewhat familiar with pile design theory) (Chapter 8).
If you have questions or problems, please view the Chapter 9 before
1.3
About the Company
CivilTech Software employs engineers with experience in structural,
geotechnical, and software engineering. CivilTech has developed a series of
engineering programs that are efficient, easy to use, engineering-oriented,
practical, and accurate. The CivilTech Software program series includes
Shoring Suite Plus, LiquefyPro, AllPile, SuperLog, and lab testing programs.
These programs are widely used in the U.S. and around the world. For more
information, please visit our web site at www.civiltech.com.
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. 2 INSTALLATION
CHAPTER
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AND
. ACTIVATION
2.1
Installation and Run
USB key:
If you have CivilTech
USB key, the
program is inside the
key.
Introduction of USB key

Civiltech USB key functions the same way as a USB flash drive,
(or called memory sticks or jump drive), but with a special chipset
inside. It has a memory of 128 MB, and USB 2.0 connectivity. The
key is compatible with Windows 2000, Xp, 7, 8 and higher, but
may not work with Windows 98 (You need to install USB driver
for Win98).

Insert the key into any USB port in your computer. If you do not
have an extra USB port, you should buy a USB extension cord
(about $10-$20)

Wait until the small light on the back of the USB key stops
flashing and stays red. This means that Windows has detected the
USB key. A small panel may pop up that says “USB mass storage
device found”, you can either close this panel or click “OK”.

Do not remove the key while the light is blinking, as that will
damage the key. You can remove the key only during the following
situations:
1. Your computer is completely turned off, or
2. You have safely ejected the key from the system. You can do
this by going down to the Windows task bar, finding the icon
that says “Unplug or Eject Hardware” (usually located at the
bottom right-hand side of the screen) and clicking on that. It
will then tell you when it is safe to remove the hardware.
Running the Program within the Key.

No installation is required.

After you insert the key, use Windows Explorer (or click My
Computer) to check the USB drive (on most computers, it is either
called D:, E:, or F:). You will find some files inside. There is a
folder called “/Keep” inside. Do not change, remove, or delete this
folder or the files inside, or else your key will become void.

You will find a folder called “/AllPile7”. Open this folder and find
AllPile.exe. Double click this program to run AllPile from your key.

You can also create a new folder, save and open your project files
directly to and from your key. There should be enough room on the
5
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.key for your files.
.
 .The manual is also located in the key in the root directory. Double.click on the file to open it. You need Adobe PDF to read this file,
.which is downloadable free of charge from Adobe’s website.
.(http://www.adobe.com)

The USB key cannot be plugged in a network server and used by
many stations. It may damage the USB key.
Running the Program from your Hard Disk:
No USB key:
If you received the
program from email
or from download…

You can also run the program from your hard disk; the program
may run a little bit faster from your hard disk.

There is a file called al_setup.exe in the root directory of the key.
Double-click on the file to start installation.

The installation process will help you to install the program on
your local hard disk. Installation to network drive or disk is not
recommended. The program may not work properly.

The installation will create a shortcut on your desktop. Click the
icon to start the program.

You still need to plug the USB key into the USB port to run the
program. It will automatically detect the USB key.

The key activation status can be checked from Help manual under
Activation.
Installation:
The installation file is called al_setup.exe. Click it will start up the
installation process automatically. The installation process will help you to
install the program on your local hard disk and create a shortcut on your
desktop.
Activation:

Follow the instruction from Email we sent to you to open Activation
panel.

The CPU number is shown on the panel. This is a unique number for
your computer, which must be reported to CivilTech by email. The
email can be found on our web side: http://www.civiltech.com.

An Activation Code will email back to you after we verify you have
purchased the program.

Input the Activation Code in the Activation Pane, and then close the
program.

Click the icon to start the program, which has full function now.
6
Download Manual
from Internet
.
.
.
.
.
. updated manual for AllPile can be downloaded from our
The most
. (www.civiltech.com/software/download.html). Click on
Web site
AllPile.Manual link to open the manual, (you must have Adobe
Acrobat. Reader to open the file). Then, save the PDF file onto your
hard drive.
Quitting the
Program
From the File menu, select [Exit] or Ctrl+X.
Input Firm and User From the Help menu, select Firm and User. Once the panel pulls
Name
out, enter in your firm’s name and the user’s name. This information
will be printed in the report.
About Program
From the Help menu, select About. This will provide you with the
version of the program. Click anywhere on the screen to exit back to
the program.
Note: The program is not compatible for networking. You cannot
install the program on your network server and run it from
workstations. The program is one copy per license, which can only be
installed in one workstation.
Problem, Questions & Answers and Troubleshooting
If you encounter any problems, please save your data file and send us an email with the input files
for each module. Most time, telephone call cannot solve the problem. Attached input files and
email can solve the problem quickly. Email: support@civiltech.com. Please review Chapter
9, Questions & Answers before contact us.
If you need administrative assistance such as USB problem, please email your request to
sales@civiltech.com
7
Formatted: Bullets and Numbering
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CHAPTER
3 OVERVIEW
.
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3.1 Program Outline
.
AllPile operations can be divided into three main steps (Figure 3-1).
SStteepp 11,, D
Daattaa IInnppuutt
Pile Profile
Soil Property
Pile Section
Head and Loading
Group Conditions
SStteepp 22,, C
Caallccuullaattiioonn
Profile and K
Vertical Analysis
Lateral Analysis
SStteepp 33,, VVeerrttiiccaall A
Annaallyyssiiss
SStteepp 33,, LLaatteerraall A
Annaallyyssiiss
Charts and Graphics
Charts and Graphics
Export to Excel
Export to Excel
Submittal Report
Submittal Report
Summary Report
Summary Report
Detail Report
Com624 Output/Input
Figure 3-1. Program Flow
8
Step 1.
Input Data
Step 2.
Execute
Calculation
Step 3.
View and Print
Results
3.2
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Enter. information into the tabbed input pages (Figure
3-2)..This step is described in detail in Chapter 4.
.
.
Press either the [Vertical Analysis] button or the
.
[Lateral] button after inputting all the required data.
The [Profile] button provides the profile of the pile and
soil information. The [K] button calculates the stiffness
of pile.
After Step 2., select the reports and charts you want
from the result panel. See Chapter 5 for details.
Program Interface
AllPile’s program interface has three main components (Figure 3-2):
1. (Top) Pull-down menus of standard Windows type commands
2. (Second row) Speed bar with shortcut command buttons and
samples.
3. Input pages, six tabs to open the desired data input page
The first two rows are described below. The input pages are described in
detail in Chapter 4.
Pull-down menus
Speed bar
Input pages
Figure 3-2. Main Components of Program Interface
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3.3 Pull-Down Menus
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Figure 3-3. File Pull-Down Menu
HINT: You can use the F key such as F4, F5, F10 to execute functions.
3.3.1
3.3.2
File
New
Create a new data file.
Open
Open an existing file. A dialog box with a list of files
will open on the screen. Select the file you want and
open or click on Cancel to return to program.
Save (F10)
Save the file you are working on (save your open files
periodically to avoid losing data in case of a system
crash). If the file is untitled, the program will
automatically switch to the “Save as” command and ask
you to provide a file name.
Save As
Save a new untitled file or change the file name or
location of the file you are working with.
Save Current
Path
Select this option to make the program "remember" the
current path. When you open the program next time, it
will automatically go to this path to find your data files.
Historical file
list
Lists the five most recent files you used. You can click
on any one of them to open the file instantly.
Exit
Exit the program. You will be prompted to save any open
files.
Edit
The edit menu will be functional when the Pile Properties Table is active
(Figure 4-4) or Soil Property Table is active (Figure 4-10).
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Insert row .
.
Insert
.
duplicate row
.
Clear row
.
Delete row
Insert a blank row in the table
Insert a row with the same data as the row selected
Clear (delete) the data in the selected row and create a
blank row
Delete the selected row from the table and shift next row
up
HINT: Select a row by clicking any cell in the row. The selected cell will
be highlighted in blue.
3.3.3
Run
The Run menu gives options for executing the program’s analyses. If you
have not entered enough data to run the program, it will not execute.
3.3.4
Profile (F4)
Generate profile with information
Vertical Loading(F5)
Run vertical analysis only
Lateral Loading (F6)
Run vertical and lateral analyses
Stiffness, K (F7)
Run Stiffness anlysisanalysis
Setup
The Setup menu allows you to enter the material properties for the piles and
the properties of different pile types.
Open Setup
Open the Setup Options screen to set
parameters related to pile properties
Close Setup
Close Setup Screen and return to program
interface without saving changes
Save Setup
Save your changes in settings
Restore Saved Setup
Clear the screen and reload the previous saved
setting
Clear the screen and reload the default settings
Restore Default Setup
Print Setup Data
3.3.5
Open Notepad to view and print the setup data.
It is only enabled when you are in Setup
Screen.
Help
Help/Manual (F1)
Open the help manual
Activation
Check status of USB key or Activation. You
can activate program if not yet activated.
Firm and User
Input firm and user name
11
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Display information about the version of your
About
.
program.
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3.4 Speed Bar .
.
The speed bar provides seven short-cut buttons for certain commands and a
quick pull down manual containing examples of pile designs. Figure 3-4
shows the buttons and their corresponding commands.
New
Save
Profile
Open
Exit
Lateral analysis
Vertical analysis
Stiffness
Samples from pull-down list
Figure 3-4. Speed Bar
3.5
Sample and Templates
The pull-down list has 30 samples to illustrate how to use the program.
These examples can also be used as templates, in which users can modify
these examples and save it as a different file name. The original examples
cannot be overwritten. The samples starting with E are in English units and
M for metrics unit.
12
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CHAPTER
4 DATA INPUT
.
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4.1 Input Pages.
The input pages of AllPile are categorized into six tabbed pages (see Figure
4-1). These pages and their relative input parameters are listed below:
4.2
A. Pile Type page
Input pile type and general information about
the project
B. Pile Profile page
Input pile orientation and positioning
C. Pile Properties page
Input pile section data
D. Loadd and Group
Input pile head, load, and pile group conditions
E. l Properties page
Input subsurface conditions
F. Advanced page
Input analysis criteria
Figure 4-1. Pile Type Input Page
Page A, Pile Type
Page
As shown in Figure 4-1, you can select the pile type that best suits your
condition and design criteria. There are twelve different pile types to choose
from the pile type list.
13
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1. Drilled .pile diameter less than or equal to 24 inches, such as auger cast
2. Drilled .pile diameter is more than 24 inches, such as drilled shaft or pier
.
3. Shaft using US FHWA SHAFT methods of analysis
.
4. Driving.steel pile with opened end, such as H-pile or open-end pipe. For
plugged condition or friction inside of pile, refer to 4.4.4 of this chapter
and Chapter 8, Section 8.7. You can add a tip section to specify partially
open/close.
5. Driving steel pipe with closed end including pipe with shoe on the tip
6. Driving concrete pile: such as pre-cased circular or square concrete pile
7. Driving timber pile: tapered pile with small tip and large top
8. Driving jetted pile: soils are jetted during driving
9. Micropile: is a pressure-grouted small-diameter pile, also called mini-pile.
10. Uplift anchor: frictionless steel bar with grouted ends (uplift only)
11. Plate, Screw, and Helical: frictionless steel bar with concrete or steel
plates at the end (uplift only)
12. Shallow footing, spread footing for shallow foundations
NOTE: The parameters of each pile type can be customized in the Setup
Screen (Chapter 6).
4.2.1
Project Titles
The project title and subtitle can be input in these two boxes. The text will
appear in the report. The location and font can be customized in the Setup
screen described in Chapter 6.
4.2.2
Comments
The Comments box is for additional comments or descriptions of the project.
You can choose to include this message in the profile section of the report by
checking the Show text in Profile page.
4.2.3 Units
Select between English or Metric units to be used throughout the program. If
you change the units after input of data, the data you have entered will
automatically convert to the units specified. However, the data will not be
exactly the same after some truncation during conversion.
14
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4.3 Page B, Pile. Profile Page
.
This page presents pile profile information as shown in Figure 4-2. The
.
diagram on the left side reflects the information you input on the right side.
.
Figure 4-2. Pile Profile Input Page (H>0)
P is horizontal load at top of pile.
Q is vertical load at pile top. For batter pile, Q is axial load.
M is moment load at top of pile.
L is projected length of pile in vertical direction.
H is top height above ground * (see Hint below).
As is surface angle, limited up to 30 degree.
Ab is batter angle of pile, limited up to 30 degree.
HINT: You can enter pile data using either the interactive sliding bar or
typing the numbers into the text boxes followed by [Enter]. Changes will be
reflected in the profile on the left immediately.
* If H exceed the limits of sliding, you should type data directly in the text
box.
15
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1 Pile Length (L)
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.
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2. Top Height (H)
The total length of the pile, including above and
below ground. Zp is called pile depth measured
from pile top. Zs is called soil depth measured
from ground surface. For better pile, L is
projected length in vertical direction. The actual
pile length will be longer than L (See Item 4
Batter Angle).
The distance from the top of the pile to the ground
surface. A negative value indicates the pile is
buried below the ground surface (see Figure 4-3).
The sliding bar can also be used to select the
desirable elevation.
H is the distance from top of pile to ground
surface:
H > 0 Pile top above ground (Figure 4-2)
H = 0 Pile top at ground surface
H < 0 Pile top under ground (Figure 4-3)
For better pile, H is projected height in vertical
direction. (See Item 4 Batter Angle).
3. Surface Angle (As)
If the ground surface is sloped, input the slope (in
degrees) here. It is limited to 30 degree.
NOTE: Due to the limitations of the original
COM624, the friction angle of any soils should
be larger than the slope angle input here.
Cohesive soil with zero or small friction angle in
any layers cannot be associated with sloped
ground surface.
4. Batter Angle (Ab)
If the pile is battered, input the batter angle here. It
is limited to 30 degree.
The friction angle of any soils should be larger
than the batter angle. For batter pile, L is
projected length in vertical direction. The actual
length is L/COS(Ab). The actual top height is
H/COS(Ab).
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Figure 4-3. Pile Profile with H<0
4.4 Page C, Pile Properties Page
4.4.1 Pile Property Table
The table on the Pile Properties Page (Figure 4-4) allows you to choose the pile
property. Ten different sections can be defined along the length of the pile. If
the pile has a uniform section, you only need to input the first row. You should
input all the data through the Pile Section Screen shown in Figure 4-5 by
clicking on the buttons of the Pile Property Table Figure 4-4.
Click button to
open Pile Section
screen.
Figure 4-4. Pile Properties Page and Pile Property Table
17
Zp – Pile
Depth
.
.
.
. the distance from the top of the pile to the start of the following
Input
. having different pile properties (NOT from the ground surface).
section
. first row is always zero.
The
.
. Zp is measured from top of pile. Zp=0 is at pile top. Zs is
Note:
.
measured
from ground surface. Zs=0 is at ground surface.
Pile Data
Input
Press the button in this column to select details from the Pile Section
screen (Figure 4-5). You should input all the pile property data on the
Pile Section screen instead of on the Pile Properties table.
Width
Width of the pile section, or the pile diameter for a circular pile.
A’
Effective area of the pile section.
Perimeter
Perimeter of the pile section.
Inertia*
Effective moment of inertia of the pile.
E
Elastic modules of outside materials.
W
Weight of the pile section for uplift calculation. It is per foot or meter.
At*
Total or Gross Area of the pile section.
* - See section of 4.4.3, Effective Area and Total Area.
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4.4.2 Add Tip Section. (Input page C. Item 2)
. add an optional tip section at the bottom of pile. The area is
This button will
based on the.outside perimeter of the pile. Users can modify the data, which
is only for tip. resistance calculation. If tip section is not added, then program
assumes the .tip section is the same as the last section, which uses effective
area.
The tip section screen is different from the overall section screen as shown in
Figure 4-5. A tip section uses total area, A, instead of the effective Area, A’.
For more details, refer to “4.4.3 Effective Area and Total Area” section of
this chapter. For tip section input, users can choice to input their own
ultimate bearing pressure (capacity) or let the program generate its’ own. If
users define their own ultimate capacity, the program will directly use the
value for analysis without modification in the calculation.
4.4.3 Pile Section Screen
The Pile Section screen is for inputting pile material and size for the
particular section of the pile. Some of the fields in this window are the same
as the fields shown on the Pile Property table, you can input or change these
properties in either place.
Described below are seven general steps for inputting section properties.
When you are done, press [Apply] button to save the data. If you press
[Cancel], the data will not be saved and the Pile Property table (Figure 4-4)
will not be changed. If you have selected Shallow foundation as the pile type,
you will get the shallow foundation window for parameters input instead of
the one below. Refer to Section 4.4.4.
Step 1
Step 2
Step 3
Step 6
Step 4
Step 8
Step 5
Step 7
Step 9
Figure 4-5. Pile Section Screen
19
Step 1 .
.
.
.
.
Select Pile Shape
.
The shape of.the pile can be square/rectangular, circular/octangular, or Hshaped. The.internal configuration of the pile can be solid (one material),
. or circular space inside), or different material on the skin than
hollow (square
on the inside..
If you select H-pile, you can also input the pile designation, such as W24X94.
Then select strong or weak axis (used for lateral analysis). Strong axis means
the lateral load is acting in the same direction as the pile axis (X-X). Next,
press [Get Properties] and the program will search the database and get the
corresponding properties for the H-pile. If no match is found, the program
will select the closest size pile or give a warning message.
Step 2.
Select Outside Skin Materials
Select the outside skin material from the materials list. Skin material affects
the result for vertical analysis. The parameter of each material can be modify
in setup screen. The E of the outside materials are used for E input.
Step 3.
Steel-Rough
Specially treated rough surface
Steel-Smooth
Steel pipe or H-pile with normal surface
Concrete-Rough
Concrete cast directly against the soil such as augercast piles
Concrete-Smooth
Concrete cast in steel casing with smooth surface or
pre-cast concrete pile
Grouted
Cement with high grouting pressure during
installation such as tie-back anchor or micro pile
Post-Grouted
Grouting twice or more with higher grouting
pressure
Timber (Tapered)
Timber pile with large top and smaller tip (users
should define the start depth and the start diameter,
then the end depth and the end diameter)
Plastic
Pile with plastic surface
No-friction Steel
No friction, or frictionless part of pile, such as the
unbound length of tieback anchor
Sf = Soil Cohesion
The ultimate side resistance (adhesion) equals to soil
cohesion. Users can directly input C as adhesion in
Input Page E.
Select Inside Materials
The inside of the pile can be:
= Outside
The same material as the outside skin
Hollow
No material inside
Steel
Reinforcement bar in concrete
Concrete
Steel pipe filled with concrete
20
.
.
.
.
Step 4. Diameter Variation .
Allows users .to define the section changing along the length of the pile.
. For most pile with straight shaft, which section has no
Straight
. changes.
.
Step 5.
Belled
For belled pile. You need to input two sections to define
a bell. Input the diameter where the bell starts and select
the [Belled] feature. Input a large diameter at where the
bell ends and select the [Straight]. (Refer to sample 3 &
4)
Tapered
For timber pile or any tapered pile. A tapered pile starts
off with a large diameter at the top and a smaller diameter
at the bottom of the pile. Select [Tapered] feature at the
top of the pile with a larger diameter. Select [Straight] in
the next section with a smaller diameter (Refer sample 12)
Plate
For steel or concrete uplift plate. Select [Plate] at the
depth where the plate is to be located. (Refer to sample
17 & 18)
Reduction Factors or Adhesion
 If material of the pile is concrete, users can input reduction factor to reduce
the moment of inertia due to cracking of the concrete (30% is typically used).
 If metal is grouted or post-grouted section (Anchor or micro-pile), then
adhesion (bound strength between soil and grout) can be inputted in this field.
Step 6.
Wall thickness or Bar number and size. This step only generates data for Step 7.
If the section is pipe (Outside is steel and Inside is hollow), wall thickness
can input here. If the outside material is concrete or grout, the program will
allow you to input the Bar Size and Bar Number.
Bar Size
Based on ASTM standard reinforcement bars
Bar Number
Number of bars in the pile
After input in step 6, press 6
to run calculation and define Step 7.
Step 7. Percentage of Inside Materials of Total Area, and Total Area
If inside materials are different from outside materials, use the sliding bar to
select the percentage of different material on the inside as a proportion of the
total area of the section. 100% means the inside materials make up the entire
pile section. The total area, At, is automatically calculated based on width of
pile. But users can also directly input in step 7.
Step 8a. Width of Pile
Input width of pile section as follows:
Square section
Input side width
Circular section
Input diameter
21
.
.
.
.
Rectangular. section Input square root of (long side x short side)
.
Input average diameter
Octagon section
.
Press [Get Properties] button to get data.
H-pile
.
.
Step 8b. Effective Area, Perimeter, I, E, G
After inputting the pile section width, press 8
parameters. These parameters are:
to calculate the other
At
Total gross area, which is the area defined by the outside
perimeter. Please refer to section 4.4.4 below and Chapter
8.
A’
Effective area, which is different from the total area (for HPile, the effective area is the steel section area)
Perimeter
Perimeter of section
I’
Effective moment of inertia
E
Elastic modulus of outside materials.
Weight
Weight of the section per unit length
Note: Pressing 8
button will calculate the other parameters
automatically based on width. You can also modify the data directly.
Step 9.
Close Screen
If you are satisfied with your data, press [Apply] to close the screen and post
the data to the Pile Property table (Figure 4-4). [Cancel] closes screen but
does not save the data.
Hint:
If you already have data in Pile Property Table (Fig 4-4) and do not
want data to be overwritten by Pile Section Screen (Fig 4-5), then you
should click on [Cancel]
You also can directly input or modify the data in Pile Property Table
(Fig 4-4) after close Pile Section Screen (Fig 4-5).
4.4.4 Effective Area and Total Area
For pile analysis, the effective area and total area is used according to the pile
type. The effective area (A’) defined by the outside and inside areas and , is
commonly used in pile shaft compression calculations, whereas, the total area
(A) defined by the outside perimeter, is used for tip resistances calculations.
 H-Pile (A > A’):
A = width x height
A’= is the steel net area
22
.
.
.
. with steel bar (A < A’, Econcrete is used for input as outside
 Concrete Pile
.
materials):
.
. area of the pile
A = section
.
E
A'  A .  A 
Steel
Concrete
Steel
EConcrete
 Steel Hollow Pipe Pile (A> A’, Esteel is used for input as outside
materials):
A = Total outside circular area
A’ = Net area of Steel
For open pipe piles, tip area is A’,
For close pipe piles, tip area is A
 Steel Pipe Pile Filled with Concrete (A>A’, Esteel is used for input as
outside materials):
A = total outside circular area
A'  Asteel  Aconcrete 
Econcrete
Esteel
The same relations are used for the moment of Inertia (I) and (I’).
For more information, please read Chapter 8, Section 8.7
4.4.5
Shallow Footing
If you have selected shallow footing as pile type, the pile section screen will
be as shown in Figure 4-6.
23
.
.
.
.
.
.
.
.
.
Figure 4-6. Shallow Foundation Screen
Listed below are the items to be inputted:
Depth of
Footing (L)
This value is inputted in the pile profile Page B.
Shape
Select the shape of footing base. D is the width. B is the
length. The lateral force acts perpendicular to B. B can
be larger or smaller than D. For strip footing, input B=1ft
or 1 meter.
Thick (Th)
The thickness of the footing used to calculate its’ weight
Distance to
Hard Layer
(Ha)
If a hard layer exists below the base of the footing within
four times D, settlement will be significantly reduce.
Users can leave this box blank or input 999 if Ha is at
great depth or there is no hard layer. When this field is
left blank, the program will automatically search for a
hard layer. The program will consider a soil layer to be
hard if the Nspt > 50.
Weight
Weight per unit depth (per foot or meter). Same as the
weight in pile properties screen
Area
The total area of the base
Base Friction
Factor
Factor required to calculate the friction against sliding at
the base of the footing.
Cast-in-place footing (rough): factor of 0.6 to 1 (typical
value is 0.7)
Pre-cast with small surface: factor of 0.3 to 0.6 (typical
24
.
.
.
. value 0.4 is used)
.
.
.
4.5 Load and Group
.
You can start. off by selecting the pile configuration that most fits the
analysis. Select single pile, group pile or tower foundation analysis (Figure
4-6) from the tabs on the left side of the panel.
Step 2. Input
Loading
Step 3.
Cyclic
Condition
Select from
Single,
Group pile or
Tower
Foundation
Step 4. %
Supported
by Pile Cap
Step 1.
Select Head
Condition
Step 5.
Distribution
Load
Figure 4-6. Group/Head/Load Page (Single Pile)
4.5.1
Single Pile
Click on the Single Pile tab if you want to perform analysis of one pile, then
follow the steps below:
Step 1 .
Head Conditions for Single Pile
Single Pile has six possible head conditions as shown in Figure 4-6, click on
the condition that best suits your project. The conditions are described
below:
1. P, M
The head of the pile can freely rotate under
lateral shear load P and moment M.
2. P, M=0
This condition is a special case of condition 1
where moment M is zero. Only lateral shear
load (P) is acting on the pile (commonly called
free-head condition).
25
.
.
.
.
.
.
. M
3. P=0,
.
.
Shear load is zero and only moment is acting on
the pile top, a special case of condition 1.
4. P, St
St is the top rotation in degrees. Input St to
force the pile head to rotate to a certain degree.
5. P, St=0
Commonly called fixed-head, there is no
rotation in the pile head, since St=0. Moment
will be generated at the pile head.
6. P, Kms
Kms is head rotation stiffness in moment per
unit slope (useful for some structural analyses).
Input Kt along with P. If Kms=0, then it is the
same as condition 2 above (P, M=0).
NOTE: All the conditions can be combined with vertical load (Q).
Step 2.
Load Conditions for Single Pile
Based on the head conditions, there are many combinations of loads. The
program automatically selects load combinations based on the head condition
selected. Possible loads are:
Vertical load (Q) – Downward and uplift working load at pile top. Input a
negative value for uplift load. The program will calculate both downward and
uplift capacity in the vertical analysis. For batter pile, Q is axial load.
Shear load (P) – Lateral working load at pile top. Positive value of P is from
left to right, and negative value is from right to left.
Moment (M) – Working moment on the pile head. A positive value if M is
clockwise and a negative value if M is counterclockwise.
Torsion (T) – Torsion generated at the pile cap. Twisting of the pile cap due
to external load.
Slope (St) – The known slope angle at the pile head. Negative value is
clockwise and positive value is counterclockwise (unit is deflection/length).
Stiffness (Kms or Kt) – The rotation stiffness Kms or Kt is the ratio of
moment/slope (M/St). Negative value is clockwise and positive value is
counterclockwise (unit is the same as M).
Step 3
Cyclic Conditions
Select Static or Cyclic shear load. If the load is cyclic, specify the number of
cycles in the No. of Cycles box (between 2 and 500).
NOTE: The cyclic condition only applies to lateral analysis, not vertical.
Step 4
Percentage Load Supported by Pile Cap
You can adjust the amount of vertical load carried by the pile cap. For 0%
load supported by the pile cap, the entire load is transfer to the pile therefore
26
Step 5
.
.
.
.
dissipated by. the pile at greater depth. For 100% load supported, the entire
load is supported
. by the pile cap.
Note: To be .conservation using 0% is recommended.
.
Distributed lateral loads
.
To distribute load along the length of the pile press the [Input Load] button
to open the panel shown in Figure 4-7. In the Distributed Load table, enter the
following information:
Z
The starting point of the distributed load, z is the distance
from the pile top.
Pq
Pq is distributed load along pile length at the z location.
B
B is the width of the pressure.
Note: To apply the distributed load, the check box above the [Input Load]
button must be checked. You cannot only apply distributed load without a
shear load on pile top. You can move some load to top as shear load.
The following examples illustrate how data are to
be inputted in the table:
Example 1:
A signal post is 6ft wide and 8ft high above
ground. A pile 1.2 ft in diameter supports it
below ground. Wind pressure is 1.5 ksf. You
can input z=0 ft, pq=1.5ksf, B=6 ft in the first
row, and z=8 ft, Pq=0, and B=1.2ft in the second
row.
Example 2:
If a lateral pressure load of 1 kip per square foot
(1 ksf or 1 kip/ft2) acting on a 2ft high pile shaft
(dia = 1.5 ft), you can input z=2ft Pq=1ksf and
B=1.5ft.
Example 3:
Figure 4-7. Distributed Load
4.5.2
If a lateral load of 1kip per linear foot (1 kip/ft) is
acting on the pile diameter (diameter = 1.5 feet),
you should input Pq=1 ksf and B=1.
Group Piles
Group analysis lets you select two head conditions under compressive, shear,
moment, and torsion loading with unlimited number of piles. The analysis
provides settlement, rotation, and lateral movement of the pile cap under
these loadings. You can select the head condition that best fits your
condition.
27
.
.
.
.
.
.
.
.
.
Step 3. Input
Loads
Step 4. Cyclic
Condition
Step 5. % Load
Supported by
Cap
Step 2. Head
Condition
Step 1. Group
Layout
Figure 4-8. Pile No. & Loading Page
Step 1
Group Pile Layout
Assuming the lateral load (P) is acting in X direction, as shown in Figure 4-8,
the following data are required for group configuration:
Step 2
Number of Columns
(Nx)
Input number of piles in X direction
Column Spacing (Sx)
Input pile spacing in X direction measured
from center of piles
Number of Rows (Ny)
Input number of piles in Y direction
(perpendicular to the page)
Row Spacing (Sy)
Input pile spacing in Y direction measured
from center of piles
Head Conditions for Group Piles
The piles within a group have two possible head conditions as shown on
Figure 4-8.
Step 3
1. Free Head
Referred to as Free Head condition. The top of
each pile can freely rotate. Pin or hinge
connections are assumed between pile cap and
piles.
1. Fixed Head
Referred to as Fix Head, there is no rotation in
the pile head. The pile and pile cap are fixed.
Moment will be generated at the pile head.
Load Conditions for Group Piles
Four load conditions apply to a set of group piles:
28
.
.
.
. (Q) – Downward and uplift working load at pile cap, equally
Vertical load
.
distributed to. all piles in the group. Input a negative value for uplift load.
Lateral load. (P) – Lateral working load at pile cap. Positive value of P is
. and negative value is from right to left. Load will be
from left to right,
distributed to. all piles in the group based on their lateral stiffness.
Moment (M) – Moment generated at the pile cap. Positive value of P is
clockwise and a negative value is counterclockwise. There are no moments
at the tip of each pile individually due to the fixation of head by the pile cap.
Step 4
Cyclic Conditions
Select Static or Cyclic shear load. No. of Cycles (between 2 and 500). Only
for lateral analysis
Step 5
Percentage of Load Supported by Pile Cap
You can adjust the amount of vertical load carried by the pile cap. For 0%
load supported by the pile cap, the entire load is transfer to the pile therefore
dissipated by the pile at greater depth. For 100% load supported, the pile cap
supports the entire load.
Note: To be conservative using 0% is recommended.
4.5.3
Tower Foundation
Tower foundation analysis is similar to the other analyses, where you get to
specify a head condition under compression, shear, moment, and torsion. It is
assumed all piles have equal spacing in x and y direction. You can choose
from fix head, free head or no pile cap. The users will also be asked to input
the number of piles they want for the analysis (up to 4 piles).
Step 3
Step 2
Step 4
Step 1
Figure 4-9. Tower Foundation Screen
Step 1
Step 5
Select Head Condition
Select from the three head condition as described below:
29
.
.
.
.
Free Head .
.
Fixed Head .
.
.
No Cap
Step 2
Top of the pile can freely rotate. Pin or hinge
connections are assumed between pile caps and piles.
There are no rotation in the pile cap. Piles and pile cap
are fixed. Moment will be generated at the pile head.
There is no pile cap to connect each pile.
Load Conditions for Group Piles
Four load conditions apply to a set of group piles:
Vertical load (Q) – Downward and uplift working load at pile cap, equally
distributed to all piles in the group. Input a negative value for uplift load.
Shear load (P) – Lateral working load at pile cap. Positive value of P is from
left to right, and negative value is from right to left. Load will be distributed
to all piles in the group based on their lateral stiffness.
Moment (M) – Moment generated at the pile cap. Positive value of P is
clockwise and a negative value is counterclockwise. There are no moments
at the tip of each pile individually due to the fixation of head by the pile cap.
Step3
Cyclic Conditions
Select Static or Cyclic shear load. No. of Cycles (between 2 and 500). This
information is for lateral analyses only.
Step 4
Pile Number
The total number of piles under a tower.
Step 5
Pile Spacing
The spacing between piles are assumed to be equal. Spacing has to be input
in inches or cm. It is assumed x and y direction have the same spacing.
4.6 Soil Property Page
The Soil Property page (Figure 4-10) allows you to input water and soil
information in four easy steps.
30
.
.
.
.
4.6.1 Soil Property Table
.
.
.
.
.
You must have
a separate
layer at water
table location.
Input total unit weight above GWT, and
buoyant unit weight below GWT
Figure 4-10. Soil Property Page
Step 1
Ground Water Table (GWT)
First, users need to input depth of ground water table (GWT). The depth is
the distance from ground surface to GWT. If the water table is deeper than
the pile tip or at great depth, leave the box blank.
HINT: Input the water table depth before completing the Soil Property
table. Leave the box blank if there is no water or water is at great depth.
Step 2
Soil Property Input
You can input up to ten layers, if the GWT exist within a layer, you must
break the layer into two layers at the water table location. The total unit
weight should be use for soil above the GWT, but the buoyant unit weight
should be used for soil below the GWT. You should input all the data
through the Soil Parameter screen shown in Fig. 4-11.
Zs-Soil Depth
Input the top depth of the soil layer. The top is the
distance from ground surface to the top of the layer. The
depth of the first row (layer) is zero. The top of the
second layer is the bottom of the first layer. The top depth
of the last layer is defined as the last row. The bottom
depth of the last layer is undefined, assuming it extends to
a great depth.
Note: Zp is measured from top of pile. Zp=0 is at pile
top. Zs is measured from ground surface. Zs=0 is at
ground surface.
Soil Data
Press the [Click to Open] button in the cell to open the
31
Input
G
.
.
.
.
.
.
.
.
.
Soil Parameter screen (see next section).
HINT: It is recommended to input all soil parameters
to the Soil Parameters screen (Figure 4-11).
Unit weight of soil. If the soil is under the water table,
buoyant weight must be input. (This is why it is necessary
to divide a layer into two if the GWT sits within this
layer.) Buoyant weight is the total unit weight of the soil
minus the unit weight of the water.
HINT: Input total unit weight above GWT and
buoyant weight below GWT.
Phi
Friction angle of soil.
C
Cohesion of soil.
K
Modulus of Subgrade Reaction of soil (for lateral analysis
only). If you only run vertical analysis, you don’t have to
input this value (Refer to Ch.8 for description).
e50 or Dr
If soil is silt, rock, or clay, e50 is strain at 50% deflection
in p-y curve (only used for cohesive soil in lateral
analysis) (Refer to Ch.8). If soil is sand, Dr is the relative
density from 0 to 100 (%). It is for reference only and is
not used in the analysis.
Nspt
Standard Penetration Test (SPT) or N value, the number
of blows to penetrate 12 inches in soil (304.8 mm) with a
140-lb (622.72 N) hammer dropping a distance of 30
inches (0.762 m). Corrected SPT (N1) should be used. If
you do not have N1, use SPT instead.
Type
Number of Soil Type defined in Soil Parameter screen
HINT: for more detail on k and e50, refer to Chapter 8, Lateral Analysis.
Step 3
Surface Elevation
It is optional to input a value in this field. If an elevation is inputted, the
depth of the pile is shown on the left side and the elevation is shown on the
right side of the chart.
32
.
.
.
.
.
.
.
.
.
Step 1 Select
Soil Type
Step 2 Adjust
N(spt) slide bar
Step 3 Fine
tuning other
parameters
Links
Link Nspt to other
parameters
Figure 4-11. Soil Parameter Screen
4.6.2 Soil Parameter Screen
The Soil Parameter screen (Figure 4-11) is for inputting or modifying the soil
parameters. The program provides correlation between N value (SPT value)
and the other parameters (refer to Chapter 8 for details). You can move the N
sliding bar to modify all the parameters or move each bar individually.
The following steps show how to use this screen.
Step 1
Step 2
Step 3
Step 4
Select material: soft clay, stiff clay, silt, sand or rock
(including concrete) and p-y input.
Move the Nspt bar to the desired value. If the LINK check
box is checked the other bars will move correspondingly. If
the box is unchecked, the other parameters will not be
affected when moving the Nspt slide bar.
Fine tune the other sliding bars to get parameters that best
suits your geology. Changes will not affect the other values if
you alter the slide bars of other parameters other than N value.
If you are finished with the input process, close the screen by
clicking [APPLY]. The data will be display on the Soil
Property table. (If you press [Cancel], the data will not be
posted.)
NOTE:


Nspt is corrected SPT (N1). The soil properties linked to Nspt value
are only recommendations. Users should use their engineering
judgment to adjust the parameters. If users do not have corrected
N1, Nspt is OK.
Users should input the water table first. The properties related to
Nspt value are different above and below the water table.
33
p-y Curve Input
.
.
.
. have a known properties (for example, C=5 ksf), users
 If the users
. N bar until the known properties reaches its value (In the
can move
.
example,. let C reach to 5 ksf).
.
. the p-y curve for the soil type or use the system default pYou can customize
y relation. From the Soil Parameter Screen, check the p-y input box on the
upper right corner of the panel. Then click on [Input p-y curve]. The p-y
input screen is shown in Figure 4-12. If you would like to modify the p-y
curve from the previous layer, it can be copied by clicking on the [Copy
from previous row] button. The values will be amplified if the users enter a
multiplier in the Copy Factor field.
Figure 4-12. Users define p-y Input
After you are satisfied with the entry, clicking on [Show Graphical Curve]
will give you the corresponding curve. Click [Apply] to accept the data
inputted or click [Cancel] to exit screen without accepting changes.
NOTE:
The system will generate a p-y curve based on the k and e50 value selected on
the soil parameter screen. Once the users input their preferred p-y curve
values and the box is checked, the k and e50 will be ignored in the analysis. If
p-y is inputted and the box is unchecked, the program uses the default p-y.
34
.
.
.
.
.
.
4.7 Advanced Page
.
This page allows users to assign analysis parameters. More details are
.
outlined in the following sections.
.
Figure 4-13. Advanced Page
4.7.1
Zero Resistance and Negative Resistance (Downdrag
Force)
1a. Zero Resistance
The program handles zero resistance on the Advanced page (Figure 4-13). If
a pile has a section that does not develop side resistance, this section has
“zero resistance”. For example, a free anchor length of tieback anchor and a
smooth caisson section of micropile are considered as zero resistance zones.
If a pile penetrates through a cave, the cave portion is considered as a zero
resistance zone. Up to two zero resistance zones can be defined in each case.
To specify the zone of zero resistance, you must enter the soil depth (Zs) of
the zone measured from the top of the soil in (feet/meter). Zero resistance
includes side and tip resistance.
HINT: You must check the left boxes to make the zone(s) be included in
the calculation. See Chapter 8 for details.
1b. Negative Resistance
If soils in the upper layers have significant settlement, the pile will
experience downdrag force. This area is called negative resistance. The
program handles negative resistance on the Advanced page (Figure 4-13). Up
to two negative resistance zones can be defined.
35
.
.
.
. effective factor, K . It ranges from 0 to 1 depending on the
“Factor” is the
.
impact of soil. settlement on the pile shaft. If the factor equals 1, then the
negative friction
to the friction in the downward capacity analysis. If
. is0, equal
the factor equals
then
there
is no friction between pile and soils. It is the
.
same as zero.friction. If the pile has a smooth surface and the soil has small
settlement, K is in the range of 0 to 0.3. If the pile has a rough surface and
neg
neg
the soil has a large settlement, K neg is 0.3 to 0.6.
HINTS:
1. If Kneg = 0, there is no resistance between the pile and the soil, i.e., it
is the same as zero resistance.
2. Kneg should be a positive value rather than using a negative value.
3. You must check the check box on the left side so that the calculation
will take into account the negative resistance.
4. The negative resistance only applies to downward side resistance, not
tip resistance. The induced downdrag force reduces the pile capacity
in the analysis.
1c. Auto determine Kneg
Users can click the button to let the program determine the K neg value. Users
need to input ground settlement at the top of negative zone. The settlement is
calculated by the users based on surcharge loading on the ground surface. In
Fig. 4.14, users need to calculate and input the ground settlement due to
surcharge loading or water table changes. AllPile will calculate the pile
settlement. If the ground settles more than pile, there is downdrag force and
negative resistance. If there is less settlement, there is not downdrag force and
negative resistance. AllPile will determine the neutral point internally and
therefore, Kneg is cal ululated.
Pile settlement calculated by Allpile
Ground settlement calculated by users
Ground has more
settlement than pile:
Negative Resistance
Figure 4-14.
Negative
Resistance
Neutral Point
Ground has less
settlement than pile: Nonegative resistance
36
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2. Zero Tip Resistance
.
If users do not .want the tip resistance included in the vertical capacity, this box
can be checked.
.
.
3. Define Tip Stratum
.
Tip resistance calculation is based on the soil properties at pile tip. There may
be several very thin layers under the tip. If the stratum is not defined (as zero),
the first layer below the tip will control the results. Users should define a
stratum thick enough to include all the influence layers. 10 times pile diameter
is recommended. This will provide more reasonable results and also smooth the
pile capacity vs. pile length curve. For shallow footing, 4 times footing width is
recommended. If a hard stratum is defined in footing property screen, the Tip
Stratum is limited to the hard stratum.
4. Analysis Parameters
For advanced users they can customize analysis parameters listed below:
FS for Downward
The factor of safety for downward capacity, including side resistance
and tip resistance.
FS for Uplift
The factor of safety for uplifting, including side resistance and the
weight of the pile.
Load Factor
The factor that is multiplied into the vertical load and lateral load.
Critical Depth as
Ratio of Diameter
The effect of overburden pressure increase with depth. The critical
depth to which the pressure becomes constant is defined by the
diameter of the pile.
Note: A critical depth of 20D is recommended
Limit of Max
Resistance
A limit can be applied to the side and tip resistance.
Allowable
Deflection
The vertical settlement and lateral deflection limit. If any one of
these values is exceeded, a warning message will be displayed.
Group Reduction
Factor Rside and
Rfront
In lateral group analysis, pile lateral capacity is reduced by existence
of a pile in front and a pile on side (based on spacing). Users can
input factor in addition to program calculated Rside and Rfront.
Note: If no limits to these values enter “9999”
Methods of Settlement Analysis
There are two methods for settlement analysis to choose from.
Vesic Method
Method based on Vesic’s publication in 1977.
Reese Method
Method based on Reese and O’Neil publication in 1988.
Define p-y and t-z Output Depths
Sometimes users might require p-y and t-z curves to be plotted out. Since the curves are
different at different depths, users can define the depths at which the curves are to be
generated. If the table is left blank, the program will automatically generate curves at
depths of equal intervals.
37
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4.8 Units of Measure
.
Table 4-1 Units of Measure
.
.
Input Page of
Item
Symbol
English Unit
Program
Pile Profile
Pile Property
Pile Number
and Loading
Distribution
Load
Group Pile and
Tower
Foundation
Soil Property
Pile length
Height (Pile top to
ground)
Surface slope angle
Batter angle
From pile top
Width
Area of section
Perimeter of section
Moment of inertia
Modulus of elasticity
Weight of pile section
Vertical Load
Shear (Lateral Load)
Moment
Torsion
Lateral Slope
Stiffness
From pile tip
Pressure
Width
% cap
Number of columns
Column spacing
Number of rows
Row spacing
Water table depth
from surface
Unit weight
Friction
Cohesion
Modulus of subgrade
reaction
Soil strain or
Relative density
SPT Value
Metric Unit
L
H
feet (ft)
feet (ft)
m
m
As
Ab
Z
D
A
Pi
I
E
Wi
Q
P
M
T
St
Kt
Z
Pq
B
Kcap
Nx
Sx
Ny
Sy or S
GWT
degrees
degrees
feet (ft)
inches (in)
square inches (in2)
in
in4
kip/in2
kip/ft
Kip
kip
kip-ft
kip-ft
in/in
kip-ft/in/in
Ft
kip/ft2
ft
percent
-in
-in
Degrees
Degrees
m
cm
cm2
cm
cm4
MN/m2 (MPa)
KN/m
KN
KN
kN-m
kN-m
cm/cm
kN-m/cm/cm
M
kN/m2 (kPa )
M
percent
-cm
-cm
G
Phi ()
C
k
ft
lb/ft3
degrees
kip/ft2
lb/in3
m
kN/m3
degrees
kN/m2 (kPa )
MN/m3
E50
Dr
Nspt
percent
percent
--
Percent
Percent
--
38
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CHAPTER
5 RESULTS
.
.
5.1 Profile
.
The Profile function provides the pile profile and soil conditions (Figure 5-1).
This report also presents soil parameters as well as foundation material
properties input by users. The report can be printed for references.
Figure 5-1. Profile Screen
5.2
Vertical Analysis Results
Clicking on [Vertical Analysis] will display a panel that allows you to choose
the different types of result from the analysis. For this analysis all lateral load
components are ignored and only vertical load is considered. Figure 5-2
shows the several choices available for vertical analysis.
Figure 5-2. Vertical Analysis Results Panel
39
5.2.1
.
.
.
.
Depth (z) vs.
. s, f, Q
The program.provides four diagrams in this report, as shown in Figure 5-3.
. is explained below. (All the data is based on ultimate loading
Each diagram
condition.) .
.
Vertical stress (overburden stress) in the soil
V Stress (S)
adjacent to the pile. The stress increases with
depth (z) to a certain point and then becomes
constant. This is because the overburden stress
has a maximum limit. This limit can be
modified on the Advanced page.
Skin Friction (f)
Upward and downward side resistances are the
combination of friction and adhesion from
soils.
Axial Force (Q)
Downward capacity and uplift are combined in
one graph. The left portion of the graph defines
the ultimate uplift capacity of the pile, whereas,
the right side of the graph defines the ultimate
downward (compression) capacity.
Figure 5-3. Depth vs. s, f, Q
40
5.2.2
.
.
.
.
.
Load vs. Settlement
.
. this button, you will get a graph of compression load vs.
By clicking on
settlement of.the pile/pile group. Three immediate settlement curves will be
. of the side is in blue, whereas, settlement of the tip is in
plotted. Settlement
red. Adding the two curves together will result in the total settlement, the
black line on the graph. Note that the peak of side resistance is at a different
location from peak of tip resistance.
Figure 5-3. Vertical Load vs. Settlement Plot
5.2.3
Capacity vs. Length
Press the [Capacity – Length] button to get the two diagrams shown on
Figure 5-4. One is the downward capacity (Qd) versus pile length (L). The
other is the uplift capacity (Qu) versus pile length (L). The start and end
lengths can be specified in the two boxes below the button. Users can also
choose to generate graphs for ultimate capacity or allowable capacity by
checking the corresponding box below the button. The Factor of Safety can
be defined on the advanced page.
NOTE: This function only works for a single section pile. If the pile has
more than one section, the resulted graph does not represent the actual
condition.
41
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.
.
Figure 5-4. Capacity vs. Length
5.2.4
t-z Curve
When clicked on the [t-z curve] button, a t-z curve will be generated (Figure
5-5). This curve gives the skin friction along the depth of the pile. It is a
function of relative movement between soil and pile. The t-z function can
generate t-z curves at various depths. Users can define the depths at which
these curves are to be generated on the Advanced page.
Figure 5-5. Skin Friction vs. Side Movement
5.2.5
q-w Curve
The q-w curve plots the tip settlement against the tip resistance. Figure 5-6
shows a plot of such curve.
42
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.
.
Figure 5-6. Tip Resistance vs. Tip Movement
5.2.6
Submittal Report
The formatted submittal report gives soil and pile physical parameters used in
the analysis, as well as the calculated results for vertical analysis in an
organized fashion. Presented here are the most important information
required for pile design.
5.2.7
Summary Report
Summary report provides on unformatted summary of calculated results. The
report is opened in Windows Notepad.
HINTS:
5.2.8

In the Notepad page, you can copy and paste data to other
Windows programs, such as Word. The tabulated data are tab
delimited, so they can be processed in Excel using Data/text to
columns function. To export data directly to Excel, see
"Exporting to Excel" below.

If the report text is wrapped in Notepad, you can improve
readability by selecting a smaller font by opening [Font] under
the Format menu. We recommend using Courier New font size
8.
Detail Report
The calculation report presents the details of the calculation so that the users
can check the correctness of the calculation and also understand how it is
done. It is viewed in Notepad or Wordpad (for larger files).
43
5.2.9
.
.
.
.
Exporting to
. Excel
.
If you have Microsoft
Excel 97 or 2000 installed on your computer, clicking
. will launch a pre-designed Excel file called “AllPile.xls”. If
on this button
.
your Excel program
has an option called Virus Macro Protection, you will see
. when AllPile launches Excel. You should check the [Enable
a dialogue box
Macros] option to allow the operation to be continued.
After the Excel file is opened, on the first sheet (Data), there is a button
called [Update Vertical Data]. Press this button to update data from AllPile.
Then you can view graphics presented in the next few sheets. You can edit
the graphics to customize your report, but do not change the structures and
the settings of the Data sheet.
All the instructions are presented in the Excel file.
5.2.10
Figure Number
The figure number box allows you to input a figure/plate number or page
number so that you can insert the graphic into your own report. The number
you entered will be displayed on anyone of the above-mentioned report. The
format of the report and the company name and logo can be modified in the
Setup/Options screen (refer to Chapter 6 for detail).
5.3
Lateral Analysis Results
The lateral analysis results panel (Figure 5-7) provides several choices.
Figure 5-7. Lateral Analysis Results
5.3.1
Depth (z) vs. yt, M, P and Pressures
The program provides 3 diagrams in the report, as shown in Figure 5-8.
Deflection (yt)
Lateral deflection along the depth (z)
44
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.
Moment (M)
.
Shear (P) .
.
. Pressures
Soil Lateral
.
Bending moment in the pile shaft
Shear force in the pile shaft. It equals the lateral
load applied at the pile head.
Lateral pressures between soils and pile. Users
can check it with passive pressure of the soils.
Figure 5-8. Depth vs. yt, M, P and Pressures
5.3.2
Load (P) - yt, M
Click this button to get the two diagrams shown in Figure 5-9.
Lateral load (P) vs. head
deflection (yt)
The diagram shows the pile head deflection
under the lateral load at pile head.
Lateral load (P) vs. maximum
moment (Mmax)
The diagram presents the maximum moment in
the pile shaft under the lateral load at pile head.
45
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.
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.
.
Figure 5-9. Lateral Load vs. Deflection & Moment
5.3.3
Depth vs. yt
A series of deflection curves at increasing loading. The loading conditions of
the different curves are presented on the table at the lower left corner of the
report (Figure 5-10).
Figure 5-10. Depth vs. Deflection
5.3.4
Depth vs. M
A series of bending moment curves at increasing loading. Loading conditions
are outlined in a chart at the lower left corner of the report (Figure 5-11).
46
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.
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.
.
.
.
Figure 5-11. Depth vs. Moment
5.3.5
p-y Curve
A series of p-y curves at different depths. The depths are defined on the
Advanced page.
5.3.6
Submittal Report
A report generated by the program that contains the most critical information
for design. It extracts calculation results from Com624S Output and
summarizes the information in this report.
5.3.7
Summary Report
Summary Report provides a summary of calculated results. The report is
saved and opened in Windows Notepad. If the file is too large, Windows will
automatically open the report in Wordpad instead of Notepad.
HINTS:
5.3.8

In the Notepad page, you can copy and paste data to other Windows
programs, such as Word. However, the tabulated data are spacing
delimited, so they are not suitable for Excel. To export data to Excel,
see "Exporting to Excel" below.

If the report text is wrapped in Notepad, you can improve readability
by selecting a smaller font by opening [Set Font] under the Edit
menu. We recommend using Courier new font size 8.
Com624S Output/Input
The lateral analysis is performed by uses the revised version of Com624S
program embedded in AllPile. You can view a typical Com624S output report
47
.
.
.
. button. You can also view the Com624S input file by pressing
by pressing the
.
the Com624 .Input button.
.
HINTS:
.
 If the program encounters some errors and cannot produce results,
.
you should review the Com624 output. You can also directly run
Com624P using the input file by the program.

5.3.9
Com624 program and example files can be downloaded from the
AllPile Section in CivilTech’s website.
Exporting to Excel
If you have Microsoft Excel 97 or 2000 installed on your computer, clicking
on this button will launch a pre-designed Excel file called “AllPile.xls”. After
the Excel file is opened, on the first sheet (Data) there is a button called
[Update Lateral Data]. Press this button to update data from AllPile. You
can view graphics presented on the next few sheets. You may edit the
graphics, but do not change the structures or settings in the Data sheet. All
instructions are presented in the Excel file.
5.3.10
Figure Number
The figure number box allows you to input a figure/plate number or page
number so that you can insert the graphic into your own report. The format of
the report and the company name and logo can be modified in the
Setup/Options screen (refer to Chapter 6 for details).
5.4
Stiffness [ K] Results
The stiffness analysis results panel (Figure 5-12) provides several choices.
The results provide most stiffness for the analysis of upper structures. They
are:

Kqx - Secant Stiffness: Vertical load vs. Vertical movement
(settlement)

Kpy - Secant Stiffness: Lateral Shear vs. Lateral movement
(deflection)

Kps - Secant Stiffness: Lateral Shear vs. Slope (rotation). Clockwise
is negative

Kmy - Secant Stiffness: Moment vs. Lateral movement (deflection)

Kms - Secant Stiffness: Moment vs. Slope (rotation). Clockwise is
negative
The are also two pile head conditions to let users select:
48
.
.
.
.
 Free.Head – The pile head is not restrained. The pile can free rotate.
The .stiffness will be lower.
. Head – The pile head is restrained by upper structure or pile
 Fixed
cup. .The pile cannot free rotate. The stiffness will be higher.
.
Figure 5-12. Stiffness Analysis Results
Summary Report provides a summary of calculated results. The report is
saved and opened in Windows Notepad. If the file is too large, Windows will
automatically open the report in Wordpad instead of Notepad.
5.5
Preview and Print Screen
The Preview and Print screen toolbar is shown below (Figure 5-13). The
functions of all the buttons are described in the following text.
Figure 5-13. Preview Screen
The buttons are:
Close
Close Preview
Page Height
Zoom to the page height
Page Width
Zoom to the page width
Zoom In
Enlarge the image
49
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.
.
Zoom Out .
Printer .
.
Printer Setup
.
.
5.6
Reduce the image
Send to printer
Set up printer. For some Windows system, this
button has not function or removed.
Clipboard
Copy the graphics to Windows Clipboard. Users can
paste the graphics to any Windows program such as
MS-Word, PowerPoint, and Excel.
Save
Save graphics to a Windows metafile, which can be
opened or inserted by other drawing programs for
editing.
Close
Close Preview
Errors and Troubleshooting
Report Layout
If the font, logo, and title are missing or misplaced in the report, most likely
the setup file is damaged, or the setting parameters are out of range. You
should open the Setup menu and restore to the manufacturer’s settings.
Please refer to chapter 6.
Vertical Analysis
The program will check most input for errors before calculation. Typical
errors are:

Total unit weight instead of buoyant unit weight under water table.
Buoyant unit weight should be input under water table.

No data in pile properties such as width, area, I, and E.

No data in soil properties such as G, Phi, and C.

Setup file is damaged, or the setting parameters are out of range. You
should open the Setup menu and check the values.
Lateral Analysis
The program uses a pre-processor of COM624S to perform lateral analyses.
The codes within the program have been re-written to solve most of the
problems when initiating COM624 in the previous version of this program.
The problems that are related to execution or limitations of COM624 are:

No COM624 output file! - Com624 computation encountered an error
and the program did not produce output file.

Error in Com624 computation! No Depth-yt data! - Com624 computation
encountered an error and the program did not produce Depth-yt.

Error in Com624 computation! No p-yt data! - Com624 computation
encountered an error and the program did not produce p-yt.
50
.
.
.
.
If any one of.the above warnings is encountered, please check the data. Most
of the cases are
. related to excessive calculated deflection, which exceeds the
allowable y ..This causes COM624 to terminate the calculations. The problem
occurs when.the pile is too flexible, soils are too soft, or load is too large.
.
 Pile too flexible
– If the I and E of the pile section are too small,
t
COM624 stops.

Soils are too soft or loose – If Phi or K is too small for sandy soils and C
or e50 is too small for cohesive soils, COM624 stops.

Load is too large – If P, M, or yt is too large, COM624 stops.

Large surface slope angle or batter angle – If the surface or batter angle is
larger than the soil friction angle, COM624 stops.

Large H – If the distance between pile top and ground surface is too
large, COM624 stops.
HINT: view the COM624 OUTPUT report to get the error message.
51
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CHAPTER
6 SETUP
.
.
6.1 Setup Screen
.
The setup screen has important parameters to run the analysis. (Figure 6-1). It
can be accessed by selecting [Open Setup] from the Setup pull-down menu.
Figure 6-1. Setup Screen
The setting of the program is saved in the system. Users can choose to
change these settings as they wish. After making the necessary changes to
the setting, you could make this your default setting by clicking on [Save
Setup]. If you make changes on the setup screen but would like to restore
your default setting, click on [Restore Saved Setup] on the Setup pull-down
menu. If you require to restore the manufacturers setting, click on [Restore
Default Setup] on the Setup pull-down menu. After you are satisfied with
the settings, you can return to the program by clicking on [Close Setup].
NOTE: With the same input data, if you get results different from the
previous results. It is possible the Set up parameters for the two runs are
different. You need to check the Set up data of the two runs.
6.2
Pull-Down Menu: Setup
Open Setup
Open setup screen.
Close Setup
Close the setup screen without saving the new settings.
Save Setup
Save the new settings and not close the screen
Restore Saved
Setup
Restore the saved settings
Restore Default
Setup
Restore the manufacturer settings
Print Setting
Summarize setting information in Notepad format
52
.
.
.
.
which allows you to print
.
.
6.3 Speed Bar ..
The speed bar
. has two buttons:
6.4
Save Setup
Save the modified settings
Close Setup
Close the setup screen and return to the program
Tabbed Pages
The three tabbed pages are summarized below. Each page is described in
detail in this chapter.
6.4.1
1. Report Format
Customize graphical output (reports)
2. Materials
Configure pile materials
3. Pile Type
Configure pile type and method code
1. Report Format Page
You can customize the format of the output report by designating the position
of each item. The location of each item are position based on coordinates,
where (0,0) is located at the upper left corner of the page. Positive X is in the
direction to the right, and positive Y is in the direction vertically downwards.
The units of measurements are in inches or centimeters.
The items listed in the rows are as follows:
Logo
The logo shown in the report can be a bmp, gif, or jpeg
file. Double click the row to specify the file path. The
width of the logo can be changed on the right most
column (W) in inches or centimeters.
Firm Title 1
Your company name is presented here. X and Y define
the coordinates. Double click the row to select text font.
Firm Title 2
You may enter a company subtitle here. X and Y define
the coordinates. Double click the row to select text font.
Figure Number
The page or figure number in the report. X and Y define
the coordinates. Double click the row to select text font.
The page number shown in the table is a dummy. The
actual text in the report is from the Lateral Analysis
Result or Vertical Analysis Result panel.
Project Title 1
This row specifies the location and font of the project
title. X and Y define the coordinates. The text shown in
the table is a dummy. The actual text in the report is
from the Pile Type page.
& Project Title 2
53
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.
Options:
.
.
Show all titles,
and logos in.
Graphics .
.
Show Pile and
Soil parameters
in Graphics
Turns on and off all the titles and logo in graphical
report. It is useful for copying and pasting to other
Windows programs.
Turns on and off all pile and soil parameters in Profile
graphical report.
Show Pile and
Soil Description
in Graphics
Turns on and off all pile and soil descriptions in Profile
graphical report.
Including Input
Information in
Report
The input data will be shown in the text Report
Preview Button:
Clicking on the [Preview] button will allow you to see the template of the
graphical report.
6.4.2
2. Materials Page
This page sets the properties for the pile materials. The Materials Page
(Figure 6-2) has two tables. The first table is the materials for the outside skin
of the pile. The second table is inside materials of the pile.
Figure 6-2. Materials Page
Each material in the table has four properties that can be customized:
Skin Friction
Angle  or
Defines the skin friction, , between granular soils and
the pile.
54
.
.
.
.
Faction K .
.
.
.
.
f

If you input a value > 2, the program will recognize
it as skin friction ()

If you input a value ranging from 0.1 to 2, the
program recognizes it as Kf . The program
multiplies Kf by the soil internal friction,  to get
the skin friction, :
 = Kf  
Where, Kf – friction factor (0.1 ~ 2)
NOTE: Internal friction, , is the friction between
granular soil particles. Skin friction, , is the skin
friction between soil and pile.  is not the same as  - usually  is less than .
Adhesion Ca or
Factor Kc
Defines the adhesion, Ca, between cohesive soils and
the pile.
If you input a value >2, the program recognizes it as
adhesion, Ca.
If you input a factor (range 0.1 to 2), the program
recognizes it as Kc. The program multiplies Kc by the
soil cohesion, C, to get the adhesion, Ca:
Ca = Kc KaC
Where,
Ka – adhesion factor (0.1 ~ 2). Users define it.
Ka – adhesion ratio (0.1 ~ 1.5). Program defines it
based on pile type and C (See Chapter 8).
Ka can be set to 1. It will bypass Ka calculation. This
option is in a check box of this page.
NOTE: Cohesion, C, is the shear strength between
cohesive soils. Adhesion, Ca, is the shear resistance
between soil and pile. Ca is not equal to C. Usually
Ca is less than C.
E
Defines elastic modulus of pile materials.
G
Specifies unit weight of pile materials.
The second table is the materials properties of the inside of the pile. For
example, a steel pipe pile filled with concrete has outside materials = steel
and inside materials = concrete. A concrete pile with steel bars has outside
materials = concrete and inside materials = steel. The material properties can
be customized:
E
Defines elastic modulus of inside pile materials.
G
Specifies unit weight of inside pile materials.
Check Box for Ka=1: See explanation of Ca and Kc above.
55
6.4.3
.
.
.
.
.
.
3. Pile Type. Page
. page is shown in Figure 6-3. The table in this page defines the
The Pile Type
pile type and.method code. The pile types listed in this table is the same list
on the Pile Type input page (Figure 4-1).
Figure 6-3. Pile Type Setup Page
Kdown
Figure 6-2. Pile Type Page
The horizontal to vertical stress ratio for calculations of
downward (compression) capacity. You can modify the
factor based on your experience. See Chapter 8.
Kdown=Vertical Stress/Horizontal Stress
Driven pile (displacement pile): K down>=1
Drilled pile (no-displacement pile): Kdown<1
Kup
The horizontal to vertical stress ratio for calculations of
uplift capacity. You can modify the factor based on
your experience. See Chapter 8.
Kup=Vertical Stress/Horizontal Stress
Driven pile (displacement pile): K up>=1
Drilled pile (no-displacement pile): Kup<1
Method Code
This column is for the program’s internal use. This
should not be changed by users. A code including
five letters to define the calculation method for each
pile type. Each letter is explained below:
56
.
.
.
.
.
.
.
.
.
1st
Pile installation method:
D – Driven pile (displacement pile)
N – Drilled pile (no-displacement pile)
2nd
Downward calculation method:
A,B,C … - reserved for different methods
O – No calculation
3
rd
Uplift calculation method:
A,B,C … reserved for different methods
O – No calculation
4
th
Tip resistance calculation method:
A,B,C … reserved for different methods
O – No calculation
5
th
Lateral calculation method:
A – COM624S method
O – No calculation
57
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.
.
.
CHAPTER... 7 SAMPLES
.
7.1 Samples
.
Samples with different soil conditions and pile types are included in the program. These
examples are intended to demonstrate the capabilities of the program and allow users to
learn more about the input process and other key functions. The samples include:
1. Auger Cast Concrete Pile
2. Drilled Shaft No Bell
3. Drilled Shaft with Bell
4. FHWA SHAFT Method with Bell
5. Driving Steel Pipe, Close Ended
6. Driving Steel Pipe, Open Ended
7. Driving Steel H Pile, Open Ended
8. Driving Steel Pile in Sloped Ground
9. Driving Steel Pile with Battered Angle
10. Driving Concrete Pile with Battered Angle
11. Driving Concrete Pile with Stinger
12. Driving Timber Pile with Battered Angle
13. Driving Jetted Pile
14. Micropile with Pressure Grout
15. Uplift Anchor based on Soil Strength
16. Uplift Anchor based on Bound Strength
17. Uplift Plate in Shallow Mode
18. Uplift Plate in Deep Mode
19. Shallow Foundation
20. COM624 Sample 1, One Soil
21. COM624 Sample 2, Five Soils
22. COM624 Sample 3, in Butter Angle
23. COM624 Sample 4, P-Y Input
24. COM624 Sample 5, Sloped Ground
25. Group Steel Piles
26. Group Auger Cast Piles
27. Group Pre-cast Concrete Piles
28. Tower Mono-Pile
29. Tower with 3 Piles
30. Tower with 4 Piles
Please open the sample files stored in the program and run them to see the input and
output data. The samples are in English units. For Metric (SI) units, open the sample
then choose metric on the Pile Type page.
58
Volume 2
.
.
.
.
.
.
.
.
.
CHAPTER
8
CALCULATION THEORY
.
CHAPTER 8 CALCULATION THEORY
Detailed in this chapter:
 The theories behind the
program
 The equations and methods that
are use to perform the analyses.
59
.
.
.
.
.
.
. CONTENTS
.
.
CHAPTER 8 CALCULATION
THEORY ........................ 60
8.1
GENERAL PILES......................................................................................................................... 61
8.1.1 VERTICAL ANALYSIS ................................................................................................................. 61
8.1.2 LATERAL ANALYSIS .................................................................................................................. 73
8.1.3 TORSION ANALYSIS ................................................................................................................... 73
8.2
DRILLED SHAFT ANALYSES .................................................................................................. 77
8.2.1 VERTICAL ANALYSIS ................................................................................................................ 77
8.2.2 LATERAL ANALYSIS .................................................................................................................. 82
8.3
SHALLOW FOOTING ANALYSES............................................................................................ 83
8.3.1
VERTICAL ANALYSIS................................................................................................................ 83
8.3.2
CAPACITY FOR COMBINED LOADING........................................................................................ 86
8.3.3 SETTLEMENT FROM VERTICAL LOAD ....................................................................................... 88
8.3.4
ROTATION FROM MOMENT ...................................................................................................... 89
8.4
UPLIFT PLATE .......................................................................................................................... 91
8.4.1 SHALLOW MODE ....................................................................................................................... 91
8.4.2
DEEP MODE ............................................................................................................................. 92
8.5
UPLIFT ANCHOR....................................................................................................................... 95
8.6
SOIL PARAMETERS AND CORRELATIONS.......................................................................... 95
8.6
SOIL PARAMETERS AND CORRELATIONS.......................................................................... 96
CHAPTER 9 QUESTIONS ANG ANSWERS
98
APPENDIX A SYMBOLS AND NOTATIONS
APPENDIX B UNITS CONVERSIONS
60
.
.
.
.
CHAPTER 8 ..CALCULATION THEORY
.
8.1 GENERAL PILES
.
.
8.1.1 Vertical Analysis
This program uses procedures described in the Foundations & Earth
Structures, Design Manual 7.02, published by Department of Navy, Naval
Facilities Engineering Command.
8.1.1.1 Downward (Compression) Load Capacity Calculation
Ultimate downward capacity can be determined by the following equations:
Qdw = Q tip + Qside
Where
Qdw = ultimate downward capacity
Q tip = ultimate tip resistance
Qside = ultimate side resistance
Ultimate tip resistance:
Qtip = Atip ∙ qult = Atip ∙ (Nq Sv + Nc C)
Where
Atip = area of pile tip
qult= ultimate end bearing pressure
Sv = vertical stress in soil (overburden pressure)
Nq = bearing factor for cohesionless soils. It is a function of
friction shown in Table 8-1.
Nc = bearing factor for cohesive soils. It is a function of z/B
(depth/width) shown in Table 8-2.
C – soil cohesion at tip
Table 8-1. Bearing Capacity Factor, Nq

Nq
Nq
(Internal friction)
(Displacement
pile)
(Non-Displacement
pile)
26
11.0
5.6
28
15.2
7.6
30
21.0
10.3
31
24.6
12.1
32
29.1
14.2
33
34.5
16.9
61
.
.
.
.
34
.
.
35
.
36
.
.
37
41.3
20.3
49.9
24.6
60.9
30.1
75.0
37.1
38
93.0
46.1
39
116.1
57.7
40
145.4
72.3
Table 8-2. Bearing Capacity Factor, Nc
z/B
Nc
(Depth/Width)
0
6.3
1
7.8
2
8.4
3
8.8
4
9
>4
9
Ultimate side resistance:
Q side =  Sf Pi l =  (f0 + Ca) Pi l
Where
Sf = side resistance
f0 = skin friction of cohesionless soil
Ca = adhesion of cohesive soil
Pi = Perimeter of pile section
l = segment of pile
Skin friction of cohesionless soil:
f0 = Sh tan(δ) = Kdown ∙ Sv ∙ tan(δ)
Where K down 
Sh
Sv
or
S h  K down  S v
Sv = vertical stress in soil
Sh = horizontal stress in soil
Kdown = ratio of Sh/Sv which is defined in the table of Setup.
62
.
.
.
.
δ. = skin friction between soil and pile. It is a function of pile skin
For steel pile, δ = 20 -30 . For concrete pile, δ = K
. materials.
. K is friction factor ranging from 0.1 to 1. K can be
. defined
in the table of Setup.
.
.
o
o
f
f
Adhesion of cohesive soil:
f
Ca = Kc ∙ Ka ∙ C
Where C = shear strength of cohesive soil (cohesion)
Kc = adhesion factor ranging from 0.1 to 1, defined in the
table of Setup.
Ka = Adhesion ratio, Ca/C, which is a function of C shown
in Figure 8-1. If Ka =1 is check in Setup Page2, then
calculation in Fig. 8-1 is bypassed. Users can input
Kc to define Ca.
Adhesion Ratio Ka
1.5
1.25
All Piles
Ratio Ka=Ca/C
1
Concrete Pile
0.75
0.5
0.25
0
0
1000
2000
3000
4000
Cohesion C, Psf
Figure 8-1. Adhesion Ratio, Ka
63
.
.
.
.
Limited Depth of side resistance and end bearing
.
Experience. and field evidence indicate that the side friction and end
bearing increase
. with vertical stress S up to a limiting depth of
embedment.
. Beyond this limiting depth (10D to 20D, B = Pile width), there
is very little
. increase in side friction and end bearing. Penetration Ratio,
:
v
PR, is used to define the limiting depth. PR = 20 is commonly used for both
side friction and end bearing. The values can be changed on the Advanced
page.
PRtip = (z/D)tip, Penetration ration for calculation of end bearing.
PR f = (z/D)f, Penetration ration for calculation of side friction.
Where
z = depth
D = average pile width
The limitation of side friction and end bearing also can be expressed as
absolute value for both cases. The values can be changed in the table of
Advanced Page.
q_limit, Limit of end bearing pressure.
f0_limit, Limit of sum of side friction and adhesion.
Allowable downward capacity can be determined by the following equation:
Qallw _ d 
Qtip
FS _ tip
Where

Qside
FS _ side
Qtip = ultimate tip resistance
Qside = ultimate side resistance
FS_tip = factor of safety for tip resistance, defined in the
table of Advanced Page.
FS_side = factor of safety for side resistance in
downward direction, defined in Advanced Page.
8.1.1.2 Zero Side Resistance
In some cases, a portion of the pile does not have contact with soils. For
example, soils have gaps, or the pile passes through an underground basement
or tunnel. Side resistance cannot be developed in this portion. Therefore the
concept of zero friction can be used. It includes both zero friction and zero
adhesion. Two zero-resistance zones can be input in the program.
8.1.1.3 Zero Tip Resistance
In special conditions, users do not want to include the tip resistance in pile
capacity. These conditions include peat or soft soils at pile tip. Or the pile tip
64
.
.
.
. point. Users can include the depth of the pile tip in the zero
has a very sharp
. For example, if the pile tip is at a depth of 35 feet, users can
resistance zones.
.
set a zero resistance
zone from 35 to 36 feet. The tip resistance will be zero in
.
the calculation.
.
.
8.1.1.4 Negative Side Resistance
Piles installed through compressive soils can experience “downdrag” forces
or negative resistance along the shaft, which results from downward
movement (settlement) of adjacent soil. Negative resistance results primarily
from consolidation of soft deposits caused by dewatering or fill placement.
The downdrag force is the sum of negative friction and adhesion. It does not
include tip resistance. It only effects downward capacity, not uplift capacity.
Two zero- and two negative-resistance zones can be input in the program. If
the same zone is defined as both a zero-resistance and negative-resistance
zone, the program considers the zone as a zero-resistance area.
Downdrag Force from Negative Friction:
Q neg = Kneg ∙ (f0) Pi l = Kneg ∙ (Sf + Ca) Pi l
Where
Q neg = Downdrag force from negative side friction
Kneg = Negative side friction factor. It ranges from 0 to 1
depending on the impact of settlement of the soil to the pile shaft.
Sf = side resistance
f0 = skin friction of cohesionless soil
Ca = adhesion of cohesive soil
Pi = Perimeter of pile section
l = segment of pile
8.1.1.5 Maximum Settlement Calculation at Ultimate Vertical Resistance
Based on Vesic’s recommendation (1977), the settlement at the top of the pile
consists of the following three components:
Settlement due to axial deformation of pile shaft, Xs
l
A' E
Qtip = tip ultimate resistance
X s  (Qtip  Qside )
Where
Qside = side ultimate resistance
∆l = pile segment
A’ = effective pile cross sectional area
E = modulus of elasticity of the pile
The equation is different from what shown in DM-7. This equation uses numerical integration,
which is more accurate then the empirical equation in DM-7.
Settlement of pile point caused by load transmitted at the point, X pp
65
.
.
.
.
.
.
.
.
.
X pp 
Where
C p Qt
Bq ult
Cp = empirical coefficient depending on soil type and method of
construction. It is defined in Table 8-3 below.
B = pile diameter
qult= ultimate end bearing pressure
Table 8-3. Typical Value of Cp for Settlement Analysis
Soil Type
Driven Piles
Drilled Piles
Sand
0.03
0.135
Clay
0.025
0.045
Silt
0.04
0.105
Settlement of pile point caused by load transmitted along the pile shaft, X ps
X ps 
Where
C s Qs
Le qult
Le = embedded depth
qult= ultimate end bearing pressure
Qs = side resistance
C s  (0.93  0.16
Where
z
)C p
B
z/B = depth / pile width
(Note: NAVY DM-7 has typo mistake in the equation)
Total settlement of a single pile, Xtotal
Xtotal = (Xs+Xpp+Xps)
66
.
.
.
.
8.1.1.6 Relationship Between. Settlement and Vertical Load
Vertical load.and settlement relation can be developed from t-z (side load vs
. and q-w (bearing load vs base settlement) curves. The t-z
shift movement)
. the relation between side resistance and relative movement
curve represents
. shaft. The t-z curve can vary at different depth and in
within soil and
different soils. The q-w curve represents the relation between tip resistance
and base movement of the shaft.
t-z and q-w Relation
Generally, t-z and q-w relations require a considerable amount of
geotechnical data from field and laboratory tests, which are not always
available for engineers. AllPile uses the following procedures to determine
the amount of settlement:
1. First, calculate ultimate side resistance and ultimate tip resistance of
shaft using the methods introduced in 8.1.1.5.
2. Find relationships between settlement and load transfer ratios
(developed resistance against ultimate resistance) using the
corresponding charts in Fig 8-2 – 8-5
3. Integrate both side and tip resistances, as well as elastic
compression of shaft body, to obtain total vertical resistance as a
function of settlement.
4. From the relationships between settlement and load transfer ratios,
we can develop t-z and q-w curve.
Typical settlement against load transfer ratios are shown in Figures 8-2
through 8-5 proposed by Reese and O’Neal (1988). Figure 8-2 and 8-3
represent the side load transfer ratio for cohesive soils and cohesionless
soils/gravel respectively. Figure 8-4 and 8-5 represent the end bearing load
transfer ratio for cohesive soils and cohesiveless soils respectively.
Figure 8-2.
Normalized load
transfer relations
for side resistance
in cohesive soil
(Reese and O'Neill,
1989)
67
.
.
.
.
.
.
.
.
.
Figure 8-3 Normalized load transfer relations for side resistance
in cohesionless soil (Reese and O'Neill, 1989)
Figure 8-4. Normalized load transfer relations for base
resistance in cohesive soil (Reese and O'Neill, 1989)
68
.
.
.
.
.
.
.
.
.
Figure 8-5. Normalized load transfer relations for base
resistance in cohesionless soil (Reese and
O'Neill, 1989)
Two Options for Settlement Analysis
In Advanced Page, AllPile provides two options for developing loadsettlement relation.
Option 1:
The load transfer ratio is based on diameter of shaft (D s) or base
diameter of shaft (Db) if it is different from the former, i.e. shafts
with bell. This option is recommended for larger-size shafts.
Option 2:
The load transfer ratio is based on the calculated settlement from
Vesic's method as described in Section 8.1.1.5. This option yields a
closer match between settlement calculation of Vesic’s method. It is
recommended for smaller diameter piles.
69
.
.
.
. vs. Settlement
Total, Side and Tip Resistance
.
. the vertical load is distributed in to side resistance and tip
Figure 8-6 shows
. chart from results of program shows that side resistance
resistance. The
. settlement, while tip resistance develops at large settlement.
develops at small
The ultimate.value of the two cannot simply be added together. That is why
tip resistance requires large Factor of Safety to get allowable capacity.
Figure 8-6.
Total, Side and Tip Resistance vs. Settlement
Capacity at Allowable Settlement
AllPile provides two methods to determine Qallow. One is defined by Factor of
Safety presented in Section 8.1.1.1. The other method is defined by
allowable settlement.
Calculate Qallow based on allowable settlement. Depending on the amount of
allowable settlement X allow, then back-calculate Qallow based on the
relationship between Xallow and load. Xallow can be defined on Advanced Page.
8.1.1.7 Uplift Load Capacity Calculation
Ultimate uplift capacity can be determined by the following equations:
Qup = Qw + Qside
Where
Qw = weight of pile
70
.
.
.
. = ultimate side resistance
Q
.
.
.
Q = ∑W ∆l
.
. = weight of pile section in unit length
Where W
side
w
i
i
∆l = segment of pile
Q side =  Sf Pi∙l =  (f0 + Ca) Pi l
Where Sf = side resistance
f0 = skin friction of cohesionless soil
Ca = adhesion of cohesive soil
l = segment of pile
Pi = Perimeter of pile section
f0 = Kup ∙Sv tanδ
Where K up 
Sh
Sv
or
S h  K up  S v
Sv = vertical stress in soil
Sh = horizontal stress in soil
Kup = ratio of Sh/Sv which is defined in the table of Setup
δ = skin friction between soil and pile. It is function of pile side
materials. For steel pile, δ = 20o-30o. For concrete pile, δ = KfФ.
Kf is a friction factor ranging from 0.1 to 1. K f can be defined in in
the table of Setup.
Ca = Kc ∙ Ka ∙ C
Where
C = shear strength of cohesive soil (cohesion)
Kc = adhesion factor ranging from 0.1 to 1, defined in the table of
Setup.
Ka = Adhesion ratio, Ca/C, which is a function of C shown in
Figure 8-1.
Allowable Uplift Capacity can be determined by following equations:
Qallw _ U 
Qw
Q
 side
FS _ w FS _ up
Where
Qw = weight of pile
71
.
.
.
. = ultimate side uplift resistance
Q
.
. = factor of safety for pile weight, defined in the table of
FS
.
Advanced
Page.
.
FS = factor of safety for side resistance for uplift, defined in
.
the table of Advanced Page.
side
_w
_up
8.1.1.8 Batter Shaft Capacities Calculation
The capacities of batter is from vertical capacities then adjusted by its batter
angle:
Q batter = cos  ∙ Q vertical
Where
 = Batter angle of shaft
Q = vertical capacities including downward and uplift
8.1.1.9 Group Vertical Analysis
In most cases, piles are used in groups as shown in Figure 8-7, to transmit the
load to each pile. A pile cap is constructed over group piles. The analysis can
be divided into four steps.
Figure 8-7 Group Pile for Vertical Analysis
Step 1. Calculate Capacity of Individual Pile, Qsingle
Qsingle can be calculated using the methods mentioned in above sections.
Qsingle includes side resistance and tip resistance.
Step 2. Calculate Capacity of a Pile Block, Qblock
Qblock is calculated using single pile method including side and tip resistance.
The block has the following dimensions:
Bx = (nx-1) ∙ Sx + D
By = (ny-1) ∙ Sy + D
L is the same as the length of each individual pile
72
.
.
.
.
Step 3. Calculate the Group Efficiency, η
.
.
Q .

nQ .
.
block
sin gle
Where
n = total number of pile. n = nx ∙ ny
Qsingle = capacity of individual pile
Qblock = capacity of block pile
η = group efficiency
Step 4. Determine the Capacity of Group Pile, Qgroup
If η ≥ 1, then Qgroup = n ∙ Qsingle
If η < 1, then Qgroup = Qblock
8.1.1.10 Settlement Analysis for Group Pile
Suggested by Vesic (1969), the settlement for group pile can be estimated
based on settlement of a single pile (DM7-7.2-209):
X group  X sin gle 
Where
B'
D
B' = smallest dimension between Bx and By (see Step 2 above)
D = diameter of a single pile
8.1.2
Lateral Analysis
AllPile directly uses COM624S calculation methods for lateral analysis. For
details on COM624, please refer to the FHWA publications, FHWA-SA-91048, COM624P – Laterally Loaded Pile Program for the Microcomputer,
Version 2.0, by Wang and Reese (1993). In that publication, Part I provides a
User’s Guide, Part II presents the theoretical background on which the
program is based, and Part III deals with system maintenance. The appendices
include useful guidelines for integrating COM624 analyses into the overall
design process for laterally loaded deep foundations.
COM624 Manual
You need to read COM624 manual to understand the lateral analysis.
User's Manual Publication Number: FHWA-SA-91-048.
http://www.civiltech.com/downloads/com624A.pdf
http://www.civiltech.com/downloads/com624B.pdf
http://www.civiltech.com/downloads/com624C.pdf
73
.
.
.
.
8.1.2.1 Lateral Deflection Calculation
.
Here is brief.introduction to the program. COM624S uses the four nonlinear
.
. dY
dY
EI
.Q
RP 0
(1)
4
dZ
2
4
dZ 2
q
differential equations to perform the lateral analysis. They are:
Where Q = axial compression load on the pile
Y = lateral deflection of pile at depth of Z
Z = depth from top of pile
R = soil reaction per unit length
E = modules of elasticity of pile
I = moment of inertia of the pile
Pq = distributed load along the length of pile
EI (
d 3Y
dY
)  Q( )  P
dZ
dZ
Where
P = shear in the pile
Where
M = bending moment of the pile
(2)
dY
 St
dZ 2
d Y
EI ( 2 )  M
dZ
(4)
(3)
Where St = slope of the elastic curve defined by the axis of pile
Figure 8-8 Graphical Presentation of AllPile
Results
74
.
.
.
. program solves the nonlinear differential equations
The COM624S
.
representing .the behavior of the pile-soil system to lateral (shear and
moment) loading
conditions in a finite difference formulation using Reese’s
. analysis.
p-y method of
For each set of applied boundary loads the program
.
performs an .iterative solution which satisfies static equilibrium and achieves
an acceptable compatibility between force and deflection (p and y) in every
element.
Graphical presentations versus depth include the computed deflection, slope,
moment, and shear in the pile, and soil reaction forces similar to those
illustrated in Figure 8-8.
Figure 8-9 Group Pile for Lateral Analysis
8.1.2.2 Group Lateral Analysis
Typical group layout is shown in Fig. 8-9. Due to the group effect, the lateral
capacity of individual piles cannot be fully developed. Deduction factors are
applied to the soil reaction, and then lateral analysis is performed for individual
piles.
Step 1. Calculate Deduction Factor Rside and Rfront
Assuming the lateral load P is in X direction. Please note that R front is not the
same as Rside.
Table 8-4. Deduction Factor Rfront
Sx
Rfront
>8D
1
8D
1
6D
0.8
75
.
.
.
.
4D.
3D.
.
<3D.
.
0.5
0.4
0.4
Table 8-5. Deduction Factor Rside
Sy
Rside
>3D
1
3D
1
2D
0.6
1D
0.3
<1D
0.3
Note: D = pile diameter
Reference: FHWA HI 97-013
Step 2. Reducing Soil Lateral Resistance by Applying the Deduction Factors from Step 1
Combine the reduction factors and apply them to p-y curve for lateral analysis.
Step 3. Calculate P-yt (the Lateral Capacity and Deflection) of Each Individual Piles
Calculate the lateral capacity of each pile and get P-Yt curve for all piles.
Step 4. Get Lateral Capacity of group piles
After P-Yt curve for each pile is constructed. The Pgroup is the sum of Psingle for
individual piles at the same deflection under one pile cap.
Pgroup = ∑Psingle
y group = y single
8.1.3 Torsion Analysis
Allpile calculates the Ultimate side resistance for vertical analysis (Section
8.1.1.1). It assumes the vertical side resistance is equal to horizontal side
resistance.
The torsion resistance is integration of (Side resistance * Pile diameter /2 * Pile
circumference) * Pile length.
76
.
.
.
.
.
.
8.2 DRILLED SHAFT
ANALYSES
.
Drilled shafts are normally used in
.
deep foundation to transfer vertical
.
load through weak soils to stronger
soils or rocks at depth. Since it is
often used to carry a relatively large
vertical load over a good depth of
soils, typical diameter of drilled shaft
ranges from 4 ft (1.2 m) to 20 ft (6
m). In most cases, the aspect ratio of
a drilled shaft, or its length divided by
its diameter, should not exceed 30.
This program uses procedures
described in the Drilled Shafts:
Construction Procedures and Design
Methods (FHWA-IF-99-025)
published by FHWA in August 1999.
Figure 8-10. Drilled Shaft
8.2.1
Vertical Analysis
8.2.1.1 Downward (Compression) Load Capacity Calculation
Ultimate downward capacity can be determined by the following equations:
Qdw = Q tip + Qside
Where
Qdw = ultimate downward capacity
Q tip = ultimate tip resistance
Qside = ultimate side resistance
Ultimate tip resistance ( Qtip ):
Base in cohesive soils [Su  0.25 MPa (5,200psf)]
Qtip = q ult Ab
Where
qult = ultimate bearing pressure
Ab = base area
If Z (depth of base)  3Db (diameter of base):
qult = 9 C
or qult = Nc* ∙C
[If C  96kPa (1tsf)]
[If C < 96kPa (1tsf)]
77
.
.
.
. C (or S ) = undrained shear strength below base
.
. N * = modified bearing capacity factor for cohesive soils. It
. can be assumed to be a function of S in UU triaxial
. compression as shown in Table 8-6.
.
Where
v
c
u
Table 8-6. Modified Bearing Capacity Factor, Nc*
C
Nc*
(Undrained Shear Strength)
(Bearing Capacity Factor)
24kPa (500psf)
6.5
48kPa (1000psf)
8.0
96kPa (2000psf)
9.0
If Z (depth of base) < 3Db (diameter of base):
qult 
2
Z 
1 
 N c * Su
3  6 Db 
Base in cohesionless soils (NSPT  50)
In Metric unit:
qult (kPa) = 57.5 ∙ NSPT
In English unit:
qult (tsf) = 0.6 ∙ NSPT
Where
NSPT = blow count per 0.3m or 1ft of penetration in the Standard
Penetration Test. If N>51, 50 is used.
Base in rocks [0.25MPa (2.5tsf) < C < 2.5MPa (25tsf)]
If embedment in rock  1.5B (diameter of base):
qult = 5 ∙ C = 2.5 ∙ qu
If embedment in rock < 1.5B (diameter of base):
qult = 4 ∙ C = 2.0 ∙ qu
Where
qu = unconfined compressive strength below base
*Attention: The two equations above were developed for drilled shafts sitting on or
embedded in good quality bedrock with RQD close to 100%. If rock is jointed or fractured,
please consult geotechnical engineer for correct procedures to calculate tip resistance.
Ultimate side resistance ( Qside ):
Q side =  f0 ∙ l ∙ Pi
78
.
.
.
.
f. = skin friction
. = segment of pile
l
.
P. = perimeter of pile
.
Where
0
i
Shaft in cohesive soils [Su  0.25 MPa (5,200psf)]
f0 =  ∙ C
 = 0.55
(for Su / Pa  1.5)
 Su

 1.5 
 Pa

  0.55  0.1
(for 1.5  Su / Pa  2.5)
Where  = shear strength reduction factor
Pa = atmospheric pressure = 101kPa or 2.12ksf
Shaft in cohesionless soils (NSPT  50)
f0 =  ∙ C
In sand:
 = 1.5 - 0.245 [Z(m)]0.5
[If NSPT  15 B/0.3m]
or  = NSPT /15 ∙ {1.5 - 0.245 [Z(m)] }
0.5
[If NSPT < 15 B/0.3m]
Where  = empirical factor which varies with depth
Sv = effective vertical stress at depth Z
Z = depth where side resistance is calculated
Attention:
- Z must be converted to meter before calculating .
- Range of : 0.25    1.2
Shaft in rocks [0.25MPa (2.5tsf) < C < 2.5MPa (25tsf)]
 qu 
f0  0.65  Pa 
 Pa 
Where
0.5
qu = unconfined compressive strength at depth where side
resistance is calculated
Pa = atmospheric pressure = 101kPa or 2.12ksf
8.2.1.2 Uplift Load Capacity Calculation
Ultimate uplift capacity can be determined by the following equations:
Qup = Qw + Q'side + Q'b
79
Shaded area = A'b
.
.
.
. = weight of pile
Where Q
.
. = ultimate side resistance against uplift
Q'
.
Q' = ultimate bell resistance against uplift (Q' is only calculated
. for belled shafts in cohesive soils)
.
w
side
b
b
Qw = ∑Wi ∙ ∆l
Where
Wi = weight of pile section in unit length
∆l = segment of pile
Q' side =  k ∙ Qside
Where
k = coefficient of uplift resistance
k=1
(for cohesive soils)
 k = 0.75
(for cohesionless soils)
 k = 0.7
(for rocks)
Qside = ultimate side resistance in compression in Section 8.2.1.1
If a belled drilled shaft is used
Q'b = Nu ∙ C ∙ A'b
Where
(for cohesive soils only)
Nu = bearing capacity factor for uplift
= 3.5 Z/Db or 9 (whichever is smaller)
Z = depth of drilled shaft
Db = diameter of base/bell
C (or Su) = undrained shear strength
A'b = area of bell base - area of shaft body ("Donut" area)
Attention: Belled shaft is not recommended for cohesionless soil
and is too difficult to be constructed in rock layer. Therefore, Q'b
will not be considered in those two types of earth material.
Bell
Shaded area = A'b
Shaft body
Figure 8-11 Top View of Donut
80
.
.
.
.
.
.
8.2.1.3 Exclusion Zones
.
According to. the SHAFT manual, the exclusion zones do not contribute side
resistance for. drilled shaft as shown in Figure 8-10.
Exclusion zones in the calculation of Downward Capacity :

For straight shafts: Top 5' and bottom one diameter of shaft

For belled shafts: Top 5' belled section and one diameter of stem (D s)
Exclusion zones in the calculation of Uplift Capacity :

For straight shafts: Top 5'

For belled shafts: Top 5', entire belled section and two diameter of
stem (Ds) calculated from top of belled section
8.2.1.3 Group Vertical Analysis
Bg =
Min. width of group
In most cases, shafts are used in group as shown in Figure 7-10, to transfer
the load to each shaft. A cap is constructed over group shafts. The analysis
can be divided into four steps.
Ds = Diameter of shaft
Figure 8-12 Group Shaft for Vertical Analysis
Step 1. Calculate Capacity of Individual Pile, Qsingle
Qsingle can be calculated using the methods mentioned in above sections.
Qsingle includes side resistance and tip resistance.
Step 2. Calculate Minimum (Shortest) Dimension of Shaft Block, Bg
Bg = (Nx-1) ∙ Sg + Ds
Where
Nx = number of shafts on the short side of the group
Sg = shaft spacing
Ds = diameter of drilled shaft
Step 3. Calculate the Group Efficiency, η

Bg
Ds
81
.
.
.
. = minimum width of shaft group
Where B
.g
. s = diameter of drilled shaft
D
.
Step 4. Determine the Capacity of Group Pile, Q
.
Q
= η ∙ Q.single
group
group
8.2.2
Lateral Analysis
Lateral analysis for drilled shafts at single or group conditions are identical to
that for drilled or driven piles. User can refer to Section 8.1.2 for the theories
and the calculation procedures used in lateral analysis.
82
.
.
.
.
.
.
8.3 SHALLOW FOOTING
ANALYSES
.
Shallow foundations are designed to transfer
.
vertical load to soils at relatively shallow depths.
.
Typical shallow foundations include spread
footings, strip footings, and mats. The bearing
capacity of shallow foundations is influenced by
a number of factors, which will be covered in the
next section. Shallow foundations are often
subject to lateral loading or eccentricity. The
stability of shallow foundations against
eccentricity is controlled primarily by the ability
to withstand overturning. AllPile uses procedures
and recommendations given in Principles of
Foundation Engineering, Brooks/Cole
Engineering Division, Braja M. Das., 1984, as the
primary references for shallow foundation
analyses.
Figure 8-13. Shallow Footing
8.3.1
8.3.1.1
Vertical Analysis
Vertical (Compression) Load Capacity Calculation
Ultimate downward capacity (q ult) can be determined by the following
equation:
qult = c N c s c d c i c g c + q N q sq d q i q g q + 0.5  D N  s  d  i  g 
Where
c = cohesion
q = effective stress of soil at foundation base
 = unit weight of soil
D = width or diameter of foundation
N = bearing capacity factors
s = shape factors
d = depth factors
i = load inclination factors
g = ground inclination factors
a.) Bearing Capacity Factors (N):
N c  N q  1cot 


N q  tan 2  45  e  tan 
2

83
.
.
.
.
N.  2N  1 tan 
.
 Ds  N 
s  1 
.

b.) Shape Factor (s):
 Dl  N 
.
.

q
q
c
c
 Ds 
sq  1  
 tan 
 Dl 
 Ds 
s  1  0.4 
 Dl 
Where, Ds = Sort side of Footing
Dl = Long side of footing
c.) Depth Factor (d):
For shallow foundations, in which embedment to footing width ratio
(L/D)  1: L – Depth, D - Width
L
d c  1  0.4 
 D
d q  1  2 tan  1  sin  
2
L
D
d  1
For deeper foundations, in which L/D > 1:
L
d c  1  0.4 tan 1  
 D
L
2
d q  1  2 tan  1  sin   tan 1  
 D
d  1
Where, tan-1 (L/D) is in radius
Al
d.) Load Inclination Factor (i):
A 

ic  iq  1  l 
 90 
2
84
.
.
.
.  A
. i  1  
.  
.
.
Where, A is inclination of load in degree. A = tan (P/Q) is in radius.
.
l

-1
l
l
P = Shear Load, Q = Vertical Load
e.) Ground Inclination Factors (g) (Reference: Foundation Design
Principles & Practices, Donald P. Conduto, p.176):
A 

g c  1  s 
 147 
g c  g   1  0.5 tan As 
5
Where, As is angle of slope in degree.
f.) Battered Footing Reduction Factors (kbat):
As
Ab
k bat  cos Ab 
Where, Ab is angle of battered footing against
vertical axis in degree.
*Attention: Unlike other factors, kbat is not applied to the equation of
ultimate downward capacity (qu) directly. It will be put into the
calculation when the total ultimate downward capacity (Qu) is
calculated. Detail about Qu is given below.
Total ultimate downward capacity (Q u) represents the total bearing capacity
against compression over the area of footing base. It can be determined by
the following equations:
Net Ultimate Bearing Capacity (qnet):
qnet = qu - q
Where, qu = ultimate bearing capacity
q = overburden soil pressure
Total Ultimate Bearing Capacity (Qult):
Qult = (qnet x kbat) A
Where, kbat = battered footing reduction factor
A = base area of footing
85
.
.
.
.
Allowable downward
capacity (Q
.
equation: .
.
.Q  Q
F .S .
.
allow) can be calculated by the following
ult
allow
8.3.2
8.3.2.1
Capacity for Combined Loading
Vertical (Compression) Load (Q) Only
If there is only a vertical load, Q, without any lateral loading, i.e. shear loads
and bending moment, the Factor of Safety of the shallow foundation can be
calculated using the equation below:
F .S . 
Q ult
Q.
Where, Qult = ultimate bearing capacity
Q = total vertical load
Users can also check the ratio between Q and the allowable bearing capacity,
Qallow, to see if the shallow foundation is considered stable. If Q > Q allow, the
foundation is insufficient.
8.3.2.2
Vertical Load With Moment (Q + M)
Typical lateral loads on the foundation include bending moment (M) and
shear load (P) as illustrated in the next diagram. In this section, we will study
the procedures used to determine footing capacity against the combination of
vertical load and bending moment (Q+M).
Eccentricity (e) will be generated by the moment and vertical load (see Figure
8-12):
e
M
Q
a.) If e  D/6, the pressure on the foundation can be determined by:
Q
6M
 2
DB D B
Q
6M
q min 

DB D 2 B
q max 
86
.
.
.
. D = width of foundation base in lateral load direction
Where,
.
.
B = length of foundation base in the other direction
.
.
.
Reaction pressure
at the base of the foundation distributed in a trapezoid
pattern across the full width (D) of the foundation.
b.) If e > D/6, then:
q max 
4Q
4 BD  2e 
q min  0
Reaction pressure at the base of the foundation is distributed in a triangular
pattern across the effective width (D') of the foundation.
D'  D  2e
Due to the distribution of reaction pressure, a new ultimate bearing
capacity called, qult', has to be recalculated using the same procedures as
mentioned in Section 8.3.1.1, but based on D' instead of D.
To calculate the Factor of Safety:
F .S . 
q ult '
q max
or
F .S . 
Q ult '
Q
Where, Qult' = qult'  D'  B
8.3.2.3
Vertical Load With Shear Load (Q + P)
The shear load (P) has two impacts to the shallow foundation calculation:
1. It generates load inclination  Al = tan-1 (P/Q)  which affects vertical
bearing capacity calculation (see Section 8.3.1.1).
2. Footing base sliding calculation becomes necessary. The sliding
resistance (Pf) can be calculated by the following equation:
Pf  k f (W  Q)
87
.
.
.
. Where, k = base friction factor for cast-in-place foundation
.
.
k is close to tan ( = angle of internal friction)
.
k = 0.3-0.8 is recommended
.
.
W = weight of footing and the soil above
f
f
f
Factor of Safety against sliding can be calculated by:
F .S . 
8.3.3
Pf
P
Settlement From Vertical Load
If only vertical load is applied to the shallow foundation, the elastic
settlement (X0) of the footing can be calculated using the equation below:
X0 
Dsq 0
Es
(1   2 )
Where, q0 = pressure under working load
Q
Area
q0 
or
q0 
qu
F .S .
Ds – Short side of footing
Dl – Long side of footing
 - Poisson ratio;  = 0.3 is recommended for general
soil conditions
Es - Young's modulus
Es = 766NSPT
for cohesionless soils
Es = 375C
for cohesive soils
Where, NSPT = blow count over 12" of soil
C = undrained cohesion of soil
 = Settlement factor for flexible foundation, which is a
function of Dl/Ds (footing shape ratio)
[Note 1] X0 is the elastic settlement at the center of a footing. If there is soft
clay underneath the footing, consolidation settlement, which is timedependent, should be considered. AllPile does not include calculation of
consolidation settlement as it is not within the scope of the program.
[Note 2] AllPile assumes that a hard layer of soil, i.e. rock or intermediate
geomaterials (IGMs) is in great depth from the base of footing. If H a, the
distance between footing base and hard soil, is over 4 times the footing width
(D), the actual elastic settlement will not change considerably.
If Ha is less than 4D, the elastic settlement can be calculated based on the
following equation:
X 0 ' X 0
Ha
4D
( H a  4)
88
.
.
.
. Where, X ' = actual elastic settlement when Ha < 4D
.
.
X = elastic settlement based on H > 4D
.
H = distance between bottom of footing and hard soil
.
.
0
0
a
a
If user does not define Ha, AllPile will automatically search for the closest
hard soil stratum with NSPT  50 based on user's input in the Soil Property
page.
8.3.4
Rotation From Moment
The maximum settlement and rotation for a footing under both vertical and
lateral loads can be determined by the following procedures:
1. Calculate eccentricity and effective width (D') based on section 8.3.2.2.
2. Determine the ultimate capacity (Q'ult) under moment and vertical load
from Section 8.3.2.2
3. Determine the Factor of Safety under both moment and vertical load
F .S .1 
Qult
Q
4. Calculate the ultimate capacity under vertical load only (see Section
8.3.2.1)
5. Get Qallow (v) under vertical load only
Qallow (v) 
Qult (v)
F .S .1
6. Calculate X0 under Qallow (v) based on Section 8.3.3
7. Determine the maximum settlement and rotation using the equations
below:
2
3

e
e
e 
X max  X 0 1  2.31   22.61   31.54  
 D
 D
 D  

2
3

e
e
e 
X e  X 0 1  1.63   2.63   5.83  
 D
 D
 D  

Qult (v)
89
.
.
.
. Where, X = settlement at edges of footing
.
.
X = settlement under point of vertical load
.
(vertical load may not apply to center of footing)
.
e = eccentricity
.
max
e
Rt = Rotation of Footing
*Note: These equations are only valid if e/D  0.4


 X max  X e 
Rt ( Rotation )  sin 

 D e 
 2

1
90
8.4
.
.
.
.
.
.
UPLIFT PLATE
.
Uplift plates are commonly used as a ground anchors to stabilize structures
.
that are subject to shear loads or moments. Due to its characteristics, uplift
.
plate only provides uplift resistance against pull out, and has no bearing
capacity. Uplift plate calculation can be divided into two modes:

Shallow mode if L (= embedment)  Lcr

Deep mode if L > Lcr
Where Lcr = critical depth in uplift resistance calculation
For cohesionless soils, Lcr is defined in Figure 8-14; for
cohesive soils, Lcr can be determined using the
following equations:
Lcr = D (0.107 Cu + 2.5)
Lcr  7D
Where Cu = undrained cohesion in kPa
Q
Q
L
Lcr
L
Shallow Mode
L-Lcr
Deep Mode
Figure 8-14
8.4.1
Critical Depth of Uplift Plates
Shallow Mode
For Cohesionless Soils
Uplift capacity (Quplift) can be determined by the following equation:
Quplift  Bq  A  L  W
91
.
.
.
. Where, A = area of plate
.
.
W = weight of plate
.
B = breakout factor
.
.
 L
L
q

Bq  2  K u ' tan  m   1  1
D
 D




Where, D = width of plate
Ku' = uplift factor, equal to 0.9 in general
 = internal angle of friction of soil
m = shape factor coefficient, a function of 
and is defined in figure 8-15
For Cohesive Soils
Uplift capacity (Quplift) can be determined by the following equation:
Quplift  C u  Bc  L A  W
Where, Bc = breakout factor, can be determined using
the Figure 7-14 on page 78
Cu = undrained cohesion in kPa
A = area of plate
W = weight of plate
8.4.2
Deep Mode
For Cohesionless Soils
Uplift capacity (Quplift) in deep mode can be determined by the following
equation:
Quplift  Q' plate Q' skin
Where, Q'plate = uplift capacity calculated in shallow
mode
Q'side = side resistance developed in the portion
of (L - Lcr)
92
.
.
.
.
.
.
.
.
.
14
12
Critical Depth (Lcr)
10
y = 2.596E-06x4 - 1.168E-04x3 + 3.505E-03x2 + 1.907E-02x + 1.229E+00
Lcr/D
8
6
4
2
0
0
5
10
15
20
25
30
35
40
45
50
Phi (deg)
Figure 8-15 The relationship between critical
depth (Lcr) and friction angle of soil (Phi)
Shape Factor Coefficient (m)
0.8
0.7
y = 5.370E-07x4 - 6.389E-05x3 + 3.218E-03x2 - 6.363E-02x + 4.618E-01
0.6
m
0.5
0.4
0.3
0.2
0.1
0
20
25
30
35
40
45
50
Phi (deg)
Figure 8-16 The relationship between shape factor
coefficient (m) and friction angle of soil (Phi)
93
.
.
.
.
.
.
.
.
.
Breakout Factor Bc
1.2
1
y = 0.6818x4 - 1.493x3 + 0.085x2 + 1.7209x + 0.0034
Bc/9
0.8
0.6
0.4
0.2
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
L/D over Lcr/D
Figure 8-17 The relationship between breakout
factor (Bc) and the ratio of embedment against
critical depth
94
1
.
.
.
.
.
8.5 UPLIFT ANCHOR
.
Uplift anchors have the same function as uplift plates, though they use a
.
completely different mechanism. Unlike uplift plates, which develop bearing
.
capacity generated from its base plate against the soil mass on top of the plate
.
to resist uplift forces, uplift anchors generates the majority of the uplift
resistance through adhesion and friction along their grouted section. An uplift
plate can be divided into two portions.

The top section, formed by uncovered steel bar which extends from
the ground surface to the top of the grout, is typically called Free
Length (Lf). Friction developed in this section is neglected.

The bottom section is the grouted portion of the uplift anchor with a
diameter of D. The total side resistance generated in this section is
based on the adhesion of the grout and the bonded length (L b).
The amount of adhesion is developed on grout pressure. The higher the grout
pressure, the higher the adhesion that can be achieved from the bonded
length. Post-grout also helps to generate higher adhesion.
Q uplift  D  L b  C a
Where, Lb = bonded length
Ca = adhesion input by user
Q
STEEL BAR
Lf
GROUT
Lb
D
Figure 8.18
Uplift anchor
95
.
.
.
.
.
8.6 SOIL PARAMETERS
AND CORRELATIONS
.
There are a number of references in the industry that present the correlations
.
between soil parameters. The soil parameters function is useful if users only
.
have a few parameters available and want to estimate the others to complete
.
the calculation. However, one should bear in mind that these correlations are
from various sources, references, and statistical results of different soil types
under different conditions. The actual value may be different from the
estimate given by the correlation. Users should make their own judgment
based on local experience and local soil conditions and adjust the values
accordingly.
Following are the references used to form the soil correlation in the program:
Table 8-6. General Soil Parameters for Sand
Compactness
SPT*
Relative Density
Friction
Unit Weight
Moist
Submerged
Very Loose
Loose
Medium
Dense
Very Dense
Dr

Unit
-%
Deg
0-4
0-15
<28
4-10
15-35
28-30
10-30
35-65
30-36
30-50
65-85
36-41
>50
85-100
>42


pcf
pcf
<100
<60
95-125
55-65
110-130
60-70
110-140
65-85
>130
>75
Symbol
N SPT
*SPT -- Standard Penetration Test
Reference: Steel Sheet Piling Design Manual, USS, 1975, p.12
Table 8-7. General Soil Parameters for Clay
Consistency
SPT
UCS*
Shear Strength
Unit Weight
Saturated
Very Soft
Soft
Medium
Stiff
Very Stiff
Hard
Symbol
NSPT
qu
Cu
Unit
-pcf
psf
0-2
0-500
0-250
2-4
500-1000
250-500
4-8
1000-2000
500-1000
8-16
2000-4000
1000-2000
16-32
4000-8000
2000-4000
>32
>8000
>4000

pcf
<100
100-120
100-130
120-130
120-140
>130
*UCS -- Unconfined Compressive Strength
Reference: Steel Sheet Piling Design Manual, USS, 1975, p.12
96
.
.
.
.
k and e50:
.
. that are particularly important for lateral pile analysis—
There are two parameters
. Reaction (k) and Soil Strain (E ). Modulus of subgrade
Modulus of Subgrade
. equation Es = k x in COM624S analysis, where Es is the
reaction is used in the
secant modulus on a. p-y curve and x is the depth below ground surface. The value of
50
k describes the increase in Es with depth. Please note that the k-value is not the same
as the coefficient of vertical subgrade reaction used to calculate elastic settlements
of shallow foundations. It is also different from the coefficient of lateral subgrade
reaction used in elastic pile analysis. (For more detail and example, please refer to
NAVY DM7, 2-235. COM624S uses nonlinear differential analysis.) On the other
hand, the soil strain E50 parameter is only applicable for clay soil and is obtained by
either lab testing or by correlation. The input value E50 represents the axial strain at
which 50% of the undrained shear strength is developed in a compression test. The
following two tables demonstrate the correlation of k and E50 with other soil
parameters for different soil type:
Table 7-8. Modulus of Subgrade Reaction (k) vs NSPT for Sand
Compactness
Loose
Medium
Dense
Symbol
NSPT
Unit
--
4-10
10-30
30-50
(Dry)
k
(Saturated)
k
kN/m3
pci
kN/m3
pci
6790
25
5430
20
24430
90
16300
60
61000
225
33900
125
SPT
MSR*
*MSR -- Modulus of Subgrade Reaction
Reference: Handbook on Design of Piles and Drilled Shafts Under lateral Load,
US Department of Transportation, 1984, p.64
Table 7-8. Modulus of Subgrade Reaction (k) and Soil Strain (E50)
vs NSPT for Clay
Consistency
Soft
Medium
Stiff
Very Stiff
Hard
Symbol
NSPT
Unit
--
2-4
4-8
8-16
16-32
>32
Shear Strength
Cu
kPa
psf
12-24
250-500
24-48
500-1000
48-96
1000-2000
96-192
2000-4000
192-383
>4000
MSR*
Static Loading
k
Cyclic Loading
k
kN/m3
pci
kN/m3
pci
%
8140
30
--2
27150
100
--1
136000
500
54300
200
0.7
271000
1000
108500
400
0.5
543000
2000
217000
800
0.4
SPT
Soil Strain
E50
Reference: Lateral Load Piles, Lymon C. Reese, p.97
97
.
.
.
.
.
CHAPTER 9 QUESTIONS
& ANSWERS
.
I can not change printer .
. you can't change printer within program.
For some Windows operation system,
.
If you want to change printer, you need to do followings:
1. Close the program.
2. In Windows, click Start; go to Setup, Printers & Devices
3. Select the printer you want, make it default printer. Close the panel.
4. Open the program again. Then send to print.
How to make a PDF file?
You need to install PDF writer such as Adobe PDFwriter (or CurePDF, DoPDF). It is installed in your
computer as one of your printers. To print PDF file, you need to do followings:
1. Close the program.
2. In Windows, click Start; go to Setup, Printers & Devices
3. Find the PDF writer you installed before, make it as default printer. Close the panel.
4. Open the program again. Then send to printer. The PDF write will ask you where to save the file.
Input the path to save the PDF file.
Input Error
If you are in a country other than US, you may use decimal symbol “,” instead “.”
Our software must use "." for decimal symbol.
You need got to Windows Control panel, Open "Regional and Language Options"
Select Number Tab, change Decimal symbol from “,” to "."
Buttons in input screen shifted or not aligned
For some computers, the buttons may not be aligned with column in the table. You may do followings
to improve it:
1. Go to Windows Control Panel,
2. Open Display,
3. Try different Screen resolutions and Fonts size. Most of time, you can fix the problem.
Can I use Allpile to design shoring wall?
No! You need to use shoring software such as our ShoringSuite program for shoring wall.
Allpile is for pile in symmetrical condition surrounded by soils. Shroing is for excavation support.
Above excavation base, half section of pile is to retain soils and another half section of pile is opened to
air without soils. Below base, it is symmetrical surrounded by soil. Allpile uses soil-structural
interactive method. The soil pressure is mobilized by pile pushing. More pile deflection toward soils,
more pressure is mobilized. The pressures are calculated by program based on soil-structural
interaction. There is no concept of active and passive pressure. The pressure diagram of Allpile is
different from shoring pressure diagram; therefore, the shear and moment are different. Shoring uses
equilibrium method. All active pressure and passive pressure are pre-defined and inputted regardless
pile deflection. Pressures are increased with depth at constant ratio (so called equivalent fluid density)
The loading for Allpile is mainly acting on pile top as concentrated force (Vertical and lateral loads).
The loading for Shoring is mainly from soil pressures and surcharge above excavation base as
distributed pressures. The calculated moment and deflection may be significant different between the
two programs. For example, at excavation base, based on shoring method, the passive pressure starts
from zero (it increasing with ratio of Kp*gamma). In Allpile, The pressure has maximum value
because the deflection is large at the base. You may input active pressure above base. But you cannot
control passive pressure below base.
98
.
.
.
.
Shoring program uses arching for passive pressure. Allpile does not allow to input arching.
.
How the program convert.Nspt to other soil parameters?
The program used Tables 7-8 in. page 99 from Nspt to get the other soil parameters.
.
.
Does Nspt need to be corrected?
Yes. You need to input corrected SPT such as N1. If you only have field SPT, it is OK to use them
directly, because Tables 7-8 are based on statistic data. It is not so accurate.
How does Allpile calculate the batted pile?
1. Convert the force from perpendicular to ground to perpendicular to pile.
2. Use sloping ground equation. Page 357, PDF file C of com624 manual.
3. Convert calculated deflection from perpendicular to pile to perpendicular to ground
Why I get less or equal deflection for negative batted Pile?
If you rotate the profile (drawing) count-clockwise to a degree equal to better angle, the pile becomes a
vertical pile and the ground surface is up-sloped. The sloped ground surface should increase the lateral
resistance of ground. However, there is not too many studies of this situation, some exports suggest
ignoring the effect of the up-slope.
The lateral load is parallel to ground. It has two components. One is a lateral load perpendicular to pile.
One is an axial load as a vertical load to pile. The lateral load (perpendicular to pile) causes
perpendicular deflection to pile. The vertical load (axial load) causes uplift along pile axis. Since uplift
movement is not reliable, it is ignored in the calculation. Only perpendicular deflection converted to
horizontal deflection. Therefore, The final deflection is equal to a vertical pile.
How to apply Load Factors?
Allpile is calculation and analysis program. It can be used for any code and load factors. You can
apply factors in loading before input the program. You also can apply factors in ultimate results after
running the program. You can apply LRFD load factors in Page F, Table 4, Raw 4.
Can Allpile anylize irregular pile group
Allpile is only for symmetrical layout with total pile in even number. The spacing should be the same
in one direction. X and Y spacing can be different. If you have two types of piles, for example, batted
piles in different direction. You can run two analyses, then average the results. If you have 7 piles, you
can run two cases: 6 piles and 8 piles then average the results.
How can seismic condition be considered in lateral analysis?
Seismic condition can be considered in lateral analysis in page D. Input number of cyclic
from 2 to 50
How to apply cyclic loading?
For cyclic loading, Please see Manual Com624B.pdf, page 289. Unfortunately, there is not too many
information about cyclic loading in the manual of Com624. There are two ways to consider the pile
under cyclic loading:
1. Input cyclic loading and normal soil strength. Our experience is No. of cyclic =50 for seismic
condition.
2. Input reduced soil strength and static loading.
Can users define the bearing capacity instead of the program
calculated ones?
99
.
.
.
.
. in page C. Please click Item 2, add a tip section.
Users can define the bearing capacity
. and input the bearing capacity in Item 7. Users can
Then open the pile section screen
also easily set bearing capacity. to zero in page F, Item 2.
.
What are the differences .between Drilled Shafts and SHAFT (US FHWA
methods) in pile type?
Drilled Shafts have two types: One type is for diameters less than 24 inches; the other is for
diameters larger than 24 inches. The calculation methods are the same for both types, but the
parameters are different. Please review the parameters in Setup screen. SHAFT uses calculation
methods recommended by US FHWA. It mainly uses SPT for bearing capacity. Some side
resistances are ignored in exclusion zone. SHAFT is a more conservative method.
How many layers of soil can I input?
Up to 10 layers of soil. If you have more than 10 layers of soil, you need
to combine two or three similar layers to one layer. Here are some
examples: If you have the following layers:
2m thick with SPT=5, 3m thick with SPT=12, 1m thick with SPT=7.
You can combine them into one layer: 6m thick with
SPT=(5x2+12x3+7x1)/6=8.8
Can Allpile design the reinforcement?
No. You need to estimate the reinforcement first and input to the program, and then the program
calculate the capacity of pile and the moment in the pile. Using the Max. Moment, you can design the
reinforcement based on concrete design code. Sometime, you may need concrete design software.
There are some software can help you.
1. Enercalc http://www.enercalc.com/products.html
2. PCA software http://www.structurepoint.org/soft/soft_profile.asp?l_family_id=30
Open End Pile with Plugged CondItions
For diving pile, users can select between open-end pile and close-end pile in Page A, Item 1.
In open-end pile program uses effective area (A' - the area of steel tube) for tip resistance calculation.
In close-end pile, program uses total gross area (At - the area base on outside diameter) for tip
resistance calculation.
In both types, you always can add a tip section (Page C, Item 2), and then specify a tip area you want in
following steps:
1. Select open-end pile or close-end pile in Page A, Item 1.
2. Create a tip section in Page C, Item 2.
Input a tip area (Here we call it as A_plug).
You need estimate A_plug based on soil type, local experience and knowledge of piles.
A_plug always falls between A and A'
If pile is fully plugged, use A_plug=At
If pile is not plugged, use A_plug=A’
The easy way is using A_plug=(A+A')/2
If it is more plug and more friction inside, A_plug close to At.
If it is less plug and less friction inside, A_plug close to A'.
The side resistance calculation outside pile is the same between two types of piles.
Why the tip resistance is diffrent from my hand calulation?
You need to set Input Page F, Item 3 to zero.
100
.
.
.
.
APPENDIX A .. SYMBOLS AND NOTATIONS
Symbol
Description
English
Metric
.
S
Vertical stress in
ksf
kN/m
. soil (overburden pressure)
.
S
Horizontal stress in soil
ksf
kN/m
2
v
2
h
qult
Ultimate end bearing
ksf
kN/m2
Sf = f0 +Ca
Side resistance, combination of skin friction and
adhesion
ksf
kN/m2
f0
Skin friction from cohesionless soils (ultimate)
ksf
kN/m2
Ca
Adhesion from cohesive soils (ultimate)
ksf
kN/m2
FS_work
Factor of safety at working load condition
--
--
FS_side
FS for side resistance in downward calculation
--
--
FS_up
FS for side resistance in uplift calculation
--
--
FS_tip
FS for tip resistance in downward calculation
--
--
FS_w
FS for weight of pile in uplift calculation
--
--
Qtip
Vertical tip resistance
kip
kN
Qup
Uplift ultimate capacity
kip
kN
Qdw
Downward (compression) ultimate capacity
kip
kN
Qneg
Load from negative friction
kip
kN
Qwork
Vertical work load or design load applied to pile
kip
kN
Qallw_u
Allowable uplift capacity
kip
kN
Qallw_d
Allowable downward capacity
kip
kN
Qgroup
Vertical capacity of group pile
kip
kN
Qsingle
Vertical capacity of single pile
kip
kN
Qplate
Vertical uplift capacity of plate or bell
kip
kN
dz or dl
Pile segment
ft
m
Kbat
Factor for battered pile
Rt
Base rotation
R,Rside or Rfront
--
--
degree
degree
Group reduction factor
--
--
yt or y
Lateral deflection
in
cm
x
Vertical settlement
in
cm
Lcr
Critical depth in uplift analysis
ft
m
101
.
.
.
.
APPENDIX B .. UNITS CONVERSIONS
.
English to Metric
Metric to English
.
.
1 ft = 0.3048 m
1 m = 3.281 ft
1 in = 2.54 cm = 25.4 mm
1 cm = 0.3937 in
1 lb = 4.448 N
1 mm = 0.03937 in
1 kip = 4.448 kN
1 N = 0.2248 lb
1lb/ft2 = 47.88 N/m2
1 kN = 224.8 lb = 0.2248 kip
1 kip/ft2 = 47.88 kN/m2 = 47.88 kPa
1 N/m2 = 20.885 x 10-3 lb/ft2
1lb/ft3 = 0.1572 kN/m3
1 kN/m2 = 1 kPa = 20.885 lb/ft2 = 20.885 x 10-3 kip/ft2
1lb/in3 = 271.43 kN/m3
1 kN/m3 = 6.361 lb/ft3 = 0.003682 lb/in3
Note: In some places of the program, “kp” is used instead “kip” due to limited spaces.
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User Manual for PileAXL
User Manual for PileAXL
A Program for Single Piles under Axial Loading
By Innovative Geotechnics Pty Ltd
2017/3/19
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User Manual for PileAXL
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User Manual for PileAXL
Chapter 1. Introduction
PileAXL is a program developed by Innovative Geotechnics for single piles under axial loading (compression
or tension) for both onshore and offshore geotechnical problems. Both bored piles and driven piles can be
analysed by the program. The program computes the ultimate and factored pile capacities for a range of
pile lengths together with the short-term pile load settlement curve for a specific pile length under the axial
load at the pile head. It is a useful tool for pile foundation design by both structural and geotechnical
engineers. Some of the important features and benefits are summarised as follows:
•
Analysis methods for driven piles include (1) American Petroleum Institute Method (API RP2A), (2) U.S.
Army Corps of Engineers Method (USACE), (3) Imperial College Pile Method (ICP) and (4) User-defined
method;
•
Offshore driven pile foundations can be analyzed by the built-in API method, ICP Method, Fugro
Method and UWA method included in PileAXL program;
•
Analysis methods for bored piles or drilled shafts include (1) FHWA Clay, (2) FHWA Sand, (3) FHWA
Gravelly Sand, (4) FHWA Gravels, (5) FHWA Rational Beta Method (Kulhawy and Chen 2007) and (5)
General rocks based on the recommendations from FHWA publication entitled "Drilled Shafts:
Construction Procedures and LRFD Design Methods" (FHWA-NHI-10-016);
•
Advanced options are available in the program to consider the effects of upper and lower soil layers on
ultimate end bearing resistance within the layered soils;
•
Automatic generation of nonlinear T-Z curves and Q-W curves for various soil types such as cohesive
soils, cohesionless soils and rocks according to the pile installation type;
•
Various cross section types such as circular section, rectangular section, steel H-section, steel pipe
section, octagonal section and user-defined section are available in the program. Plugged and
unplugged options are available to the steel H-section and steel pipe section;
•
Two different design approaches are available in PileAXL: (1) Allowable stress design and (2) Load
resistance factor design. Partial factor of safety or resistance factors can be specified by the users for
ultimate shaft resistance (compression), ultimate shaft resistance (tension) and ultimate end bearing
resistance for the design to be consistent with the current common design approaches;
•
The program allows the users to apply additional reduction factor to the internal shaft resistance of the
unplugged steel pipe section to consider the effects of driving disturbance; and
•
Short pile lateral capacity analysis based on Broms method for soils and Hong Kong Geoguide method
for rocks (only available under standalone or flexible license).
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User Manual for PileAXL
Chapter 2. Start the new file
When PileAXL program is started, the following dialog (Figure 2-1) will firstly appear, which enables the user
to choose (1) Start a new project or (2) Open an existing project.
Figure 2-1 Project start dialog in PileAXL
Once the option of “Start a new project” is selected, a default new project with two soil layers is
automatically created. The default file name is “Newfile.AXL”. The corresponding file path is shown on the
top title bar of the program. The ground profile and general program interface is loaded and shown in
Figure 2-2.
Figure 2-2 Default analysis file of PileAXL
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User Manual for PileAXL
If “Open an existing project” button is clicked, then the file selection dialog will be invoked as shown in
Figure 2-3 where the user will be able to open the existing PileAXL analysis file with the file type of AXL.
Figure 2-3 Analysis file selection dialog for PileAXL
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User Manual for PileAXL
Chapter 3. Project Title Information Input
The project title information can be input by the users with clicking the “Title” icon from the toolbar or
clicking “Project Title” menu item from the main “Define” menu of the program. Figure 3-1 shows the
general layout of “Title” dialog. The following information can be input by the user for the project:
•
Project Title;
•
Job Number;
•
Design Engineer;
•
Client; and
•
Description.
Figure 3-1 General layout of “Project Title” Dialog
The following items are created by the program for the user’s reference and cannot be changed by the user
from this dialog:
•
Date – the creation date of the project file. The date will also be updated when the project file is
changed and saved.
•
File name – the full file name with the directory path; and
•
File path – the directory path of the program.
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User Manual for PileAXL
Chapter 4. Analysis Option Input
Various analysis options can be input by the users with clicking the “Analysis Option” icon from the toolbar
or clicking “Analysis Option” menu item from the main “Define” menu of the program. Figure 4-1 shows the
general layout of “Analysis Option” dialog. This dialog provides the user with different analysis options as
described below for five groups: (1) “Control Parameters”; (2) Axial Capacity Design Approach; (3) Plug
Setting (Driven Pile Only); (4) End Bearing in Layered Soils (Advanced Option) and (5) "Units of Input and
Analyses" group.
Figure 4-1 General Layout of Analysis Option Dialog for PileAXL
"Control Parameters" group lists the main control parameters for the analysis:
•
Number of pile elements: This is the number of pile elements used in the analysis. The pile length will
be equally divided into elements with the specified number.
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User Manual for PileAXL
" Axial Capacity Design Approach " group lists the main control parameters for the partial factor of safety or
resistance factors adopted in the analysis for pile compression capacity:
•
Partial factor of safety or resistance factor for shaft resistance: This is the partial factor of safety or
resistance factor of the ultimate shaft resistance. It is usually less than 1.0 for resistance factor and
greater than 1.0 for factor of safety;
•
Partial factor of safety or resistance factor for end bearing resistance. This is the partial factor of safety
or resistance factor of the ultimate end bearing resistance. It is usually less than 1.0 for resistance factor
and greater than 1.0 for factor of safety;
•
Partial factor of safety or resistance factor for shaft resistance in tension: This is the resistance factor of
the ultimate shaft resistance. It is usually less than 1.0 for resistance factor and greater than 1.0 for
factor of safety.
"Plug Settings" group lists the main control parameters for the plug settings of driven pile analysis:
•
Plugged condition for steel open-ended piles: This is for the condition where a plugged toe is formed
under the pile bottom when the steel open-ended piles are driven into the target toe depth. The
ultimate bearing capacity is calculated based on the gross section area and only ultimate shaft
resistances along the external pile shaft area are considered;
•
Unplugged condition for steel open-ended piles: This is for the condition where an unplugged toe is
formed under the pile bottom when the steel open-ended pies are driven into the target depth. The
ultimate end bearing capacity is calculated based on the section area and ultimate shaft resistance both
along internal and external pile shaft areas are considered. If this option is selected, then an additional
reduction factor can be applied to the internal shaft resistance in order to consider the potential
disturbing effects on the internal friction during driving.
Figure 4-2 Plug settings for steel open-ended driven piles
"End Bearing in Layered Soils" group lists the control parameters for the ultimate end bearing calculation
within the layered soils based on the approaches recommended in Meyerhof (1976), Meyerhof and Sastry
(1978) and Matsui (1993).
Two different empirical depth parameters for upper and lower layers can be input by the user: (1) empirical
depth parameter for the upper layer X1 and (2) empirical depth parameter for the lower layer X2. Those
two parameters control the effects of upper and lower soil layers on the current soil layer when the
ultimate end bearing capacity is calculated. The graph in Figure 4-3 shows the general distribution of the
ultimate end bearing resistance within the layered ground profile. Those parameters generally range from 3
to 6 pile diameters. In PileAXL, the default value is 0 which means that no layering effects are considered for
pile capacity and settlement analysis.
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User Manual for PileAXL
Figure 4-3 Plug settings for steel open-ended driven piles
"Units of Input and Analyses" group provides two unit options in the program.
•
SI Units: This is to select SI Units in the program. It the default option in the program.
•
English Units: This is to select English Units in the program.
13
User Manual for PileAXL
Chapter 5. Pile Properties and Load Input
The inputs for the pile properties including different installation and cross section types can be accessed
from the built-dialog at the left side on the main program interface as shown in the figure below.
Figure 5-1 General Layout of Pile Type and Cross Section Dialog
Both driven and bored piles are supported by PileAXL and the following cross section types can be used in
the pile capacity and settlement analysis:
Driven Piles:
•
Circular Section;
•
Rectangular Section;
14
User Manual for PileAXL
•
Octagonal Section;
•
H Section;
•
Pipe Section; and
•
User-defined Section
Bored Piles or Drilled Shaft:
•
Circular Section;
•
Rectangular Section; and
•
User-defined Section
Figure 5-2 Cross Section Types in PileAXL
Note that the rectangular section for bored piles or drilled shafts enable the users to analyse the barrette
piles which are usually adopted for large axial loads.
Apart from the section type properties, the pile length, pile top level, Young’s modulus of the pile material,
loading type (compression or tension) and axial force at the pile head can be readily input by the users from
this dialog.
15
User Manual for PileAXL
Chapter 6. Soil Layers and Properties Input
PileAXL offers an innovative and straightforward interactive way to create multiple soil layers with various
relevant parameters in the program. Soil layer input dialog can be invoked through clicking "Soil Layers and
Properties" item under "Define" menu or clicking "Soil Layers and Properties" icon from the toolbar.
Soil layers can be added, inserted or deleted through "Add", "Insert" and "Delete" buttons. The layer colour
also can be adjusted or updated by clicking "Colour" button. In the current version, maximum 50 soil layers
can be defined by the user. Layer name also can be defined by the user through text input. The available
material types from “Soil Layers and Properties” input dialog include: (1) Null material; (2) Cohesive soils; (3)
Cohesionless soils and (4) Rocks. For each material type, different analysis methods for ultimate shaft
resistance and ultimate end bearing resistance can be selected through "Advanced" tab except for Null
materials which are mainly used to model the pile cantilever (free length) section above or below water. In
another word, free length or cantilever pile length is defined through adopting a soil layer with Null
material properties at the ground surface. Once "Null Material" type is selected, the "Advanced" tab will be
disabled.
Input of soil layers and properties mainly consists of two parts:
(1) Basic soil parameters on "Basic" Tab such as soil layer thickness, total unit weight, groundwater status
(above or below ground water table), undrained shear strength for cohesive soils, effective friction angle for
cohesionless soils and unconfined compressive strength for rocks. For cohesive soils and rocks, the strength
increment with the layer depth also can be specified through "Strength Parameters - Advanced" option. The
strength increment is automatically set to zero if the default option is selected.
(2) Advanced soil parameters related to different pile capacity analysis approaches on "Advanced" Tab.
The available pile capacity analysis models depend on the soil type which the user select and are listed
below for different soil types and pile installation types:
Driven Piles:
•
Cohesive Soils: API Method, USACE Method, ICP Method and User Defined Method.
•
Cohesionless Soils: API Method, USACE Method, ICP Method and User Defined Method.
Bored Piles:
•
Cohesive Soils: FHWA Method, User Defined Method.
•
Cohesionless Soils: FHWA Method, Rollins’s Gravelly Sand Method, Rollins’s Gravel Method, Rational
Beta Method and User Defined Method.
•
Rock: General Rock Method and User Defined Method
Detailed descriptions about the different pile capacity analysis methods adopted by PileAXL and the input
parameters required are presented in Appendix A.
Figure 6-1 shows the soil layer and property input for the layer with “Null” material type. Since it is a layer
with “Null” material type, the “Advanced” tab is disabled with grey colour and cannot be clicked. If the
check box of “Input Layer below Water Table” is ticked, this means that the layer with “Null” material type
16
User Manual for PileAXL
is under the water table – cantilever or free length within the water. If the check box is unticked, the input
soil layer thickness represents the cantilever or free length within the air.
Figure 6-1 Soil Layers and Properties Input for “Null” material type
Figure 6-2 shows the soil layers and properties input of the cohesive soils for the basic parameters. Three
different strength options are available in PileAXL: (1) undrained shear strength for cohesive soils, effective
friction angle for cohesionless soils and unconfined compressive strength for rock; (2) SPT-N for all material
types and (3) Cone Tip Resistance for all material types.
Figure 6-2 Soil Layers and Properties Input for “Cohesive” material type
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User Manual for PileAXL
The first option is the basic option and the values input into the second and third options will be converted
into the basic option parameters during the analysis. An advanced parameter for the strength increase with
the depth is provided for cohesive soil and rock material types. As for the cohesionless soils, if the cone tip
resistance option is adopted, then the strength increase parameter with the depth is also available to the
cone tip resistance.
Figure 6-3 shows a typical advanced parameter input dialog for the cohesive soils. Different analysis
methods can be selected from this dialog to calculate the ultimate shaft and end bearing resistances. The
available t-z and q-w curve options are also presented on the dialog. In the current version, the best
suitable t-z and q-w curve options are automatically selected by the program according to the soil type and
pile installation type.
Figure 6-3 Soil Layers and Properties Input for the cohesive soils – Advanced Parameters
Clicking different layer within the layer list will display the corresponding basic parameter. The program will
save the input parameters into the internal memory when the “OK” or “Apply” button at the bottom or “X”
button at the top right corner is pressed. The ground profile will be automatically updated once the soil
layer input is updated and saved. If “Copy Graph” item under the “File” menu is clicked or the “Copy to
Clipboard” toolbar button on the right side of the program interface is pressed, then the input ground
profile can be copied into the clipboard and then pasted into the report if required. A sample of the copied
ground profile graph with the analysis results is shown in Figure 6-4.
The users can use “Display Option” dialog as shown in Figure 6-5 to select or deselect display items: (1)
General input information and (2) Analysis results for the ground profile plot.
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User Manual for PileAXL
Figure 6-4 Typical Ground Profile after Soil Layer Input
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User Manual for PileAXL
Figure 6-5 Display options for ground profile plot
The option of negative skin friction is available in PileAXL if the users want to consider the effects of
negative skin friction on the axial capacity and settlement of the pile. The following input dialog –
Downdrag Option for negative skin friction can be accessed by clicking “Downdrag Option” menu under the
“Define” menu.
Figure 6-6 Downdrag option in PileAXL
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User Manual for PileAXL
The input of negative skin friction is based on the soil layer in PileAXL. Once the checkbox from the first
column is ticked, then “NSF Option” column will change from “No” to “Yes” and the input cell for downdrag
force then becomes editable – from which the user can manually enter the magnitude of the downdrag
force from that layer. The default value for downdrag force is 0. The program will ignore the contribution of
shaft and end bearing resistances from that soil layer when the axial capacity is assessed. The downdrag
force if entered will be added to the pile head axial loading as defined previously in Figure 5-1 for the
settlement calculation.
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User Manual for PileAXL
Chapter 7. Reviewing Soil Layer Input Parameters
PileAXL provides the user with the option of reviewing soil layer input parameters. Soil layer input summary
dialog can be invoked through clicking "Soil Layer Input Summary" option under "Define" menu or "Soil
Layer Input Summary" icon from the left toolbar. The invoked summary table is shown in Figure 7-1 which
enables the user to review the detailed soil layer parameter inputs into the analysis and spot the input
errors if any.
Figure 7-1 Soil layer input summary table for an example
22
User Manual for PileAXL
Chapter 8. Reviewing Pile Input Parameters
Similar to soil layer input parameters, pile input summary table can be opened through clicking "Pile Input
Summary" option under "Define" menu or pressing "Pile Input Summary" from the left toolbar. It
summaries the values of pile input parameters from the user. Multiple columns for different pile segments
can be shown if more than one pile segment is used. The dialog as shown in Figure 8-1 enables the users to
review the input parameters related to the pile type, section type, section dimension, material stiffness, top
connection conditions, bending stiffness and pile batter.
Figure 8-1 Pile input summary table for an example
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User Manual for PileAXL
Chapter 9. Run Analysis
Running the analysis file with the input parameters created from the previous steps can be invoked by
clicking "Run Analysis" option under "Analyze" menu or clicking “Run Analysis” icon from the top toolbar.
The invoked running message dialog as shown in Figure 9-1 details the analysis information and the analysis
result status.
The warning messages if any will be displayed under the progress bar to show the likely cause of the
problem. Clicking "OK" button will close the dialog and the user will be able to access the various analysis
results if the analysis run is successful. Otherwise, the user will need to review the input file to find out why
the analysis cannot be successfully completed.
Figure 9-1 Run Analysis Message Box for an example
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User Manual for PileAXL
Chapter 10. Viewing Analysis Results
PileAXL provides an easy way to access various detailed analysis results through "Analysis Results" Output
Dialog as shown in Figure 10-1. The User can view almost all analysis results plotted against the pile length.
Clicking the corresponding radio button enables the User to switch different analysis result plots
conveniently. Soil layers with the specified layer colours and boundaries are also shown in the graph to help
the user to know the relative position of the results to the soil layers.
Figure 10-1 Analysis Results Dialog of PileAXL
This “Analysis Results” Output Dialog can be invoked by clicking “Analysis Results” icon from the left toolbar
and the analysis results which are available for viewing from this dialog include:
•
Distribution of the ultimate unit shaft resistance with the pile length;
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•
Distribution of the ultimate total shaft resistance with the pile length;
•
Distribution of the ultimate end bearing resistance with the pile length;
•
Distribution of the ultimate total pile capacity (ultimate total shaft resistance plus ultimate end bearing
resistance) with the pile length;
•
Combined plot of the ultimate total shaft resistance, ultimate end bearing and ultimate total pile
capacity against the pile length;
•
Distribution of the factored total shaft resistance with the pile length;
•
Distribution of the factored end bearing resistance with the pile length;
•
Distribution of the factored total pile capacity (ultimate total shaft resistance plus ultimate end bearing
resistance) with the pile length;
•
Combined plot of the factored total shaft resistance, ultimate end bearing and ultimate total pile
capacity against the pile length;
•
Distribution of the effective vertical stress with the pile length;
•
Distribution of the pile weight with the pile length;
•
Distribution of the ultimate tension capacity; and
•
Distribution of the factored tension capacity.
The above results can also be viewed by clicking the corresponding items under the “Display” menu. In
addition to the plotting results, PileAXL also provides the detailed analysis results in the excel-like table
format if “Display Results” button is pressed. It is convenient for the user to go through each analysis result
at different depths. The tabulated results can be also easily copied into the third-party software for further
process if required.
PileAXL also enables the user to copy or print the relevant results on the graph. This can be done by clicking
“Copy Graph” or “Print Graph” on the bottom of the “Analysis Results” Dialog. The copied graph can be
easily pasted into the third-party application for reporting purpose. A sample of the copied and pasted
result graph is shown in Figure 10-2 for an example.
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Figure 10-2 Copied result graph (combined Plot – Ultimate) for an example
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Chapter 11. Viewing T-Z Curves
In PileAXL, once the analysis is successfully completed, the user can access the various analysis results. The
dialog for t-z curve plot can be invoked by clicking the "T-Z Curve Plot" option under "Display" menu or “T-Z
Curve Plot” from the toolbar.
Figure 11-1 “T-Z Curve Plot” dialog for an example
T-Z curves for all the nodes can be selected and viewed by the user through T-Z Curve Plot Dialog as shown
in Figure 11-1. Plot or update the T-Z curve plots can be done through the following steps:
•
Step 1: Tick the check box for the pile node number where you want to view the results. Note that
multiple node points can be selected;
•
Step 2: Click the "Plot/Update" button at the bottom of the table to update the T-Z curve plots.
For each node point listed in the table, other relevant information such as Depth, Level, Ultimate Unit Shaft
Resistance, and T-Z model type are also displayed for the user's information. The background colour of row
in the table follows the colour of the soil layer.
If required, detailed T-Z curve results can be accessed through clicking the button of "Results Table" under
the summary table. A new window with gird-type outlook as shown in Figure 11-2 will be invoked with "z"
settlement (mm or inch) and "fs" mobilised shaft resistance (kPa or lbs/ft^2) for the selected node points
along the pile length.
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Figure 11-2 Tabulated T-Z Curve results for an example
PileAXL enables the user to copy or print the relevant results on the graph. This can be done by clicking
“Copy Graph” or “Print Graph” on the bottom of the “Analysis Results” Dialog. The copied graph can be
easily pasted into the third-party application for reporting purpose as shown in Figure 11-3.
Figure 11-3 Copied T-Z curves graph for an example
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Chapter 12. Viewing Q-W Curves
In addition to T-Z curves, the user also can access Q-W curve information once the analysis is successfully
completed in PileAXL. The dialog for Q-W curve plot can be invoked by clicking the "Q-W Curve Plot" option
under "Display" menu or “Q-W Curve Plot” from the toolbar. The invoked “Load Deflection Curve for Pile
Base” dialog is shown in Figure 12-1.
Figure 12-1 “Q-W Curve Plot” dialog for an example
The option of “Q-W Curve Plot” shows the relationship between the end bearing resistance and pile toe
settlement. If required, the tabulated results as shown in Figure 12-2 for the load and deflection curves at
the pile base will be presented in the Excel-like table format through clicking the button of "Display Results"
under the graph.
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Figure 12-2 Tabulated Q-W Curve results for an example
PileAXL also enables the user to copy or print the relevant results on the graph. This can be done by clicking
“Copy Graph” or “Print Graph” on the bottom of “Load Deflection Curve for Pile Head” dialog. The copied
graph can be easily pasted into the third-party application for reporting purpose. A sample of the copied
and pasted result graph is shown in Figure 12-3.
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Figure 12-3 Copied Q-W Curve Plot for an example
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Chapter 13. Pile Axial Load Settlement Curves
The dialog for pile settlement curve plot can be invoked by clicking the "Axial Load Settlement Curve"
option under "Display" menu or “Axial Load Settlement Curve” icon from the toolbar. Figure 13-1 shows the
“Axial Load Settlement Curve” dialog for an example.
Load-settlement curve is generated by the program for the specified axial loading at the pile head.
Preliminary estimations on the ultimate shaft resistance, ultimate end bearing resistance and ultimate axial
pile capacity are carried out by the program and the results are shown on the load-settlement curve graph.
Since the load settlement curve covers a much wider settlement range in order to present a more complete
picture, the pile head settlement corresponding to the input axial load is shown on the graph with the
arrow pointing to the right axis. The arrow pointing to the bottom axis shows the input axial load at the pile
head.
Figure 13-1 “Axial Load Settlement Curve” dialog for an example
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If required, the tabulated results as shown in Figure 13-2 for the load and settlement curve at the pile head
will be presented in the Excel-like table format through clicking the button of "Display Results" under the
graph.
Figure 13-2 Tabulated axial load settlement curve results
PileAXL also enables the user to copy or print the axial load settlement curve results on the graph. This can
be done by clicking “Copy Graph” or “Print Graph” on the bottom of “Load Deflection Curve for Pile Head”
dialog. The copied graph can be easily pasted into the third-party application for reporting purpose. A
sample of the copied and pasted result graph is shown in Figure 13-3.
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Figure 13-3 Copied axial load pile settlement curve
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Chapter 14. Axial Load Transfer Curves
In addition to the axial load and settlement curve at the pile head, PileAXL also provides with the user the
distribution of axial load transfer along the pile shaft once the analysis is successfully completed.
The dialog for the axial load transfer curve plot can be invoked by clicking the "Axial Load Distribution vs.
Depth" option under "Display" menu or “Axial Load Distribution Curve Plot” from the toolbar. The invoked
“Axial Load Transfer Curve” dialog is shown in Figure 14-1. The axial load transfer curve is plotted against
the elevation or depth. The more advanced option for the axial load transfer curve is presented in PileAXL
program where 5 different curves corresponding to the different axial loads at the pile head are provided.
Figure 14-1 “Axial Load Transfer Curve” dialog for an example
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Chapter 15. Short Pile Lateral Capacity Analysis
In additional to the estimation of axial capacity and settlement under the axial loading at the pile top,
PileAXL provides a simple and powerful tool to determine the capacity of the short piles under later force
and bending moment applied at the pile head in accordance with Broms method for cohesionless and
cohesive soils and Hong Kong Geoguide method for rocks.
The dialog for short pile lateral capacity analysis can be invoked by clicking the "ShortPileLAT" option under
"Tool" menu from the toolbar. The invoked dialog is shown in Figure 15-1.
Figure 15-1 “Axial Load Transfer Curve” dialog for an example
The input parameters required for short pile lateral capacity analysis are as follows:
•
Pile Diameter;
•
Effective Soil Unit Weight;
•
Undrained Shear Strength. This is for cohesive soils only;
•
Effective Friction Angle. This is for cohesionless soils only;
•
Unconfined Compressive Strength. This is for rocks only;
•
Applied Horizontal Force at the pile head, H. The applied force should be the factored force for ULS
(Ultimate Limit State);
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•
Applied Bending Moment at the pile head, BM. The applied force should be the factored force for ULS
(Ultimate Limit State); and
•
Geotechnical Resistance Reduction Factor. Note that this factor is also defined as Geotechnical Strength
Reduction Factor in some other Limit State Design Standards and is in general less than 1.0.
Clicking the button of “Analyze” will run the short pile lateral capacity analysis and the result summary will
be displayed under “Analysis Results”. Graphical output is also presented on the right side of the dialog.
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APPENDICES
Appendix A. T-Z curves for axial force analysis
A.1 Cohesive Soils
A.1.1 Driven Piles
A.1.1.1 API Method
For the cohesive soils, the following equations as recommended in API (2000) are adopted to calculate the
ultimate shaft resistance, 𝑓𝑠 and ultimate end bearing resistance, 𝑓𝑏 :
𝑓𝑠 = 𝛼𝑐𝑢
𝛼 = 0.5𝜓 −0.5 where 𝜓 ≤ 1.0
𝛼 = 0.5𝜓 −0.25 where 𝜓 ≥ 1.0
𝜓 = 𝑐𝑢 /𝑝𝑜′
𝑓𝑏 = 9𝑐𝑢
𝑐𝑢 is undrained shear strength and 𝑝𝑜′ is effective overburden pressure at the point in question. The
following t-z and q-w curves is adopted in PileAXL for the cohesive soils of driven piles.
Figure A.1-1 t-z curve adopted for the cohesive and cohesionless soils – driven piles (after API 2000)
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Figure A.1-2 q-w curve adopted for the cohesive and cohesionless soils – driven piles (after API 2000)
Figure A.1-3 shows the basic parameter input of API method for cohesive soils. The basic strength
parameter is undrained shear strength.
Figure A.1-3 Basic soil parameter input of API method for cohesive soils
If SPT-N or Cone Tip Resistance option is adopted, then the input values will be converted into the
undrained shear strength in the analysis through the following equations:
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𝑐𝑢 = 5×𝑁 (𝑘𝑃𝑎)
𝑐𝑢 =
𝑞𝑐 − 𝑝𝑜′
𝑁𝑘
where N is SPT-N value (blow counts), 𝑞𝑐 is the cone tip resistance and 𝑁𝑘 is the conversion constant and
adopted to be 16 in the program.
Figure A.1-4 shows the advanced parameter input of API method for cohesive soils. If the option of
“Resistance Parameter (Default)” is ticked, then the adhesion parameter 𝛼 will be determined by the API
method based on the effective overburden pressure and varies with the depth. If the option is unticked,
then the default adhesion parameter 𝛼 will be constant and equal to 0.5. The default maximum shaft
resistance and end bearing resistance are 1000 kPa and 90000 kPa, respectively in PileAXL. In the current
version, once the API method is adopted, then both t-z and q-w curves will be based on the API method
and no other options are available.
Figure A.1-4 Advanced soil parameter input of API method for cohesive soils
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A.1.1.2 USACE Method
For the cohesive soils, the following equations as recommended in USACE (1991) are adopted to calculate
the ultimate shaft resistance, 𝑓𝑠 and ultimate end bearing resistance, 𝑓𝑏 :
𝑓𝑠 = 𝛼𝑐𝑢
𝑓𝑏 = 9𝑐𝑢
𝑐𝑢 is undrained shear strength and 𝛼 is the adhesion factor which can be determined from Figure A.1-5
based on the value of undrained shear strength.
Figure A.1-5 Variation of the adhesion factor with the undrained shear strength (after USACE, 1991)
The t-z curve for USACE method is based on the recommendation by Coyle and Reese (1966) in the
following table.
Table A.1-1 T-z curve for USACE method based on the recommendation by Coyle and Reese (1966)
Load Transfer/Ultimate Load Transfer
Settlement (inch)
0
0
0.18
0.01
0.38
0.02
0.79
0.04
0.97
0.06
1.00
0.08
0.97
0.12
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0.93
0.16
0.93
>0.20
The q-w curve for USACE method is based on the concept of Skempton (1951) which predicts the load in
end bearing of a pile in clay as a function of the pile tip movement. The following equations are adopted in
PileAXL:
𝑓𝑏−𝑚𝑜𝑏 = 𝑓𝑏 (
𝑤 0.5
) ≤ 𝑓𝑏
2𝐷𝜀50
where 𝑓𝑏−𝑚𝑜𝑏 is the mobilised end bearing resistance, D is the pile diameter, w is the pile toe movement,
𝑓𝑏 is the ultimate end bearing resistance and 𝜀50 is the strain factor ranging from 0.005 to 0.02. In PileAXL,
a value of 0.01 is adopted for the strain factor for all cohesive soils.
Figure A.1-6 shows the basic parameter input of USACE method for cohesive soils.
parameter is undrained shear strength.
The basic strength
Figure A.1-6 Basic soil parameter input of USACE method for cohesive soils
If SPT-N or Cone Tip Resistance option is adopted, then the input values will be automatically converted
into the undrained shear strength in the analysis as described in A.1.1.1. Figure A.1-7 shows the advanced
parameter input of USACE method for cohesive soils. If the option of “Resistance Parameter (Default)” is
ticked, then the adhesion parameter 𝛼 will be determined by the USACE method based on the value of
undrained shear strength (Figure A.1-5). If the option is unticked, then the default adhesion parameter 𝛼
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will be constant and equal to 0.5. The default maximum shaft resistance and end bearing resistance are
1000 kPa and 90000 kPa, respectively in PileAXL. In the current version, once the USACE method is adopted,
t-z curve is based on the recommendations from Coyle and Reese (1966) and q-w curve is based on the
concept of Skempton (1951).
Figure A.1-7 Advanced soil parameter input of USACE method for cohesive soils
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A.1.1.3 ICP Method
ICP Method is an empirical pile design method which was proposed by Jardine and Chow (1996) in Imperial
College, UK. The main feature of this method is that the calculation of ultimate shaft resistance and end
bearing resistance is mainly based on the cone tip resistance from the cone penetration tests (CPT).
Figure A.1-8 General procedure of calculating the ultimate shaft resistance for cohesive soils based on ICP method
If the user inputs other strength parameters for soils such as undrained shear strength or SPT-N values
instead of the cone tip resistance value, those strength parameters will be automatically converted into the
equivalent cone tip resistance value in the analysis using ICP method.
Figure A.1.8 shows the general procedure of calculating the ultimate shaft resistance based on ICP method
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for cohesive soils. Figure A.1.9 shows the general procedure of calculating the ultimate end bearing
resistance based on ICP method for cohesive soils.
In the current version, once the ICP method is adopted for cohesive soils, t-z curve will be generated based
on the recommendations from Coyle and Reese (1966) and q-w curve will be generated based on the
concept of Skempton (1951).
Figure A.1-9 General procedure of calculating the ultimate end bearing resistance for cohesive soils based on ICP
method
Figure A.1-10 shows the basic parameter input of ICP method for cohesive soils. The basic strength
parameter is the con tip resistance. Figure A.1-11 shows the advanced parameter input of ICP method for
cohesive soils. The required input parameters for ICP method for cohesive soils in PileAXL are (1) Yield
Stress Ratio, YSR; (2) clay strength sensitivity index, St and interface friction angle at failure (Phi-f). One set
of nominal default values (YSR=2, St=5 and Phi-f=25) are available in PileAXL when the option of “Resistance
Parameters (Default)” is ticked.
Similar to USACE method, t-z curve is based on the recommendations from Coyle and Reese (1966) and q-w
curve is based on the concept of Skempton (1951).
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Figure A.1-10 Basic soil parameter input of ICP method for cohesive soils
Figure A.1-11 Advanced soil parameter input of ICP method for cohesive soils
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A.1.1.4 User Defined Method
For the User Defined Method, the basic soil parameter input dialog is the same as the previous method.
Note that the input strength parameters on the basic soil parameter dialog will not be used to calculate the
ultimate shaft resistance and end bearing resistance as those values are directly input into the program
through the advanced soil parameter input dialog as show in Figure A.1-12.
Similar to USACE and ICP methods, t-z curve is based on the recommendations from Coyle and Reese (1966)
and q-w curve is based on the concept of Skempton (1951).
Figure A.1-12 Advanced soil parameter input of User Defined method for cohesive soils – Driven Piles
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A.1.2 Bored Piles / Drilled Shafts
A.1.2.1 FHWA Method
For the cohesive soils, the following equations as recommended in FHWA manual (O’Neill and Reese 1999)
are adopted to calculate the ultimate shaft resistance, 𝑓𝑠 and ultimate end bearing resistance, 𝑓𝑏 :
𝑓𝑠 = 𝛼𝑐𝑢
𝛼 = 0.55 for 𝑐𝑢 ⁄𝑝𝑎 ≤ 1.5
𝛼 = 0.55 − 0.1(𝑐𝑢 ⁄𝑝𝑎 − 1.5) for 1.5 ≤ 𝑐𝑢 ⁄𝑝𝑎 ≤ 2.5
where 𝑐𝑢 is undrained shear strength and 𝑝𝑎 is the atmospheric pressure.
𝑓𝑏 = 𝑁𝑐 𝑐𝑢
𝐿
𝑁𝑐 = 6.0 (1 + 0.2 ( ))
𝐷
Noted that 𝑓𝑏 cannot be greater than 3800 kPa for bored piles within the cohesive soils according to
O’Neill and Reese (1999) and 𝑁𝑐 cannot be greater than 9.0. The following t-z and q-w curves are adopted
in PileAXL for the cohesive soils of bored piles.
Figure A.1-13 t-z curve adopted for the cohesive soils – bored piles (FHWA,1999)
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Figure A.1-14 q-w curve adopted for the cohesive soils – bored piles (FHWA,1999)
The basic soil parameter input dialog of cohesive soils for bored piles or drilled shafts is the same as the
driven pile as shown previously, for example, in Figure A.1-6. The advanced soil parameter dialog is shown
in Figure A.1-15.
Figure A.1-15 Advanced soil parameter input of FHWA method for cohesive soils – Bored Piles or Drilled Shafts
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The default adhesion factor 𝛼 depends on the distribution of the undrained shear strength within the soil
layer and is not a constant value when the option of “Resistance Parameter (Default)” is ticked. If this
option is unticked, the default value provided by the program is 0.55 which is constant though the clay layer.
In PileAXL, for the bored piles or drilled shafts, t-z and q-w curves are based on the recommendations from
FHWA (1999) as shown in Figure A.1-13 and Figure A.1-14.
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A.1.2.2 User Defined Method
For the User Defined Method, the basic soil parameter input dialog is the same as the previous method.
Note that the input strength parameters on the basic soil parameter dialog will not be used to calculate the
ultimate shaft resistance and end bearing resistance as those values are directly input into the program
through the advanced soil parameter input dialog as show in Figure A.1-16.
Figure A.1-16 Advanced soil parameter input of User Defined method for cohesive soils – Bored Piles or Drilled
Shafts
In PileAXL, for the bored piles or drilled shafts, t-z and q-w curves are based on the recommendations from
FHWA (1999) as shown in Figure A.1-13 and Figure A.1-14.
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A.2 Granular Soils
A.2.1 Driven Piles
A.2.1.1 API Method
For the granular soils, the following equations as recommended in API (2000) are adopted to calculate the
ultimate shaft resistance, 𝑓𝑠 and ultimate end bearing resistance, 𝑓𝑏 :
𝛽 = 𝐾 tan 𝛿
𝑓𝑠 = 𝛽𝑝𝑜
𝑓𝑏 = 𝑁𝑞 𝑝𝑜
where K is the coefficient of lateral pressure and usually assumed to be 0.8 for open-ended pipe pile with
unplugged toe or 1.0 for plugged or close end pipes, 𝛿 is the friction angle between the soil and pile, 𝛽 is
the shaft friction factor, 𝑁𝑞 is the bearing capacity factor and 𝑝𝑜 is the effective overburden pressure.
The following table is adopted in PileAXL for the values of interface friction angle, 𝛿 and bearing capacity
factor, 𝑁𝑞 .
Table A.2-1 Design parameters for cohesionless soils (after API 2000)
The t-z and q-w curves shown in Figure A.1-1 and Figure A.1-2 are adopted in PileAXL for the granular soils
of driven piles. Figure A.2-1 shows the basic parameter input of API method for cohesionless soils.
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The basic strength parameter is the effective friction of angle. If SPT-N or Cone Tip Resistance option is
adopted, then the input values will be automatically converted into the effective friction angle in the
analysis based on the following equations:
𝜙 ′ ≅ tan−1 [𝑁⁄(12.2 + 20.3×𝑝𝑜′ /𝑝𝑎 )]0.34
or
𝜙 ′ ≅ tan−1 [0.1 + 0.38× log(𝑞𝑐 ⁄𝑝𝑜′ )]
where N is SPT-N value (blow counts), 𝑞𝑐 is the cone tip resistance and 𝑝𝑎 is the atmosphere pressure
(101.3 kPa).
Figure A.2-2 shows the advanced parameter input of API method for cohesionless soils.
Figure A.2-1 Basic soil parameter input of API method for cohesionless soils – Driven Piles
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Figure A.2-2 Advanced soil parameter input of API method for cohesionless soils – Driven Piles
If the option of “Resistance Parameter (Default)” is ticked, then the shaft friction factor 𝛽 and bearing
capacity factor 𝑁𝑞 will be determined by the API method based on the input effective friction angle. If the
option is unticked, then the shaft friction factor and end bearing capacity factor can be input by the user.
The default maximum shaft resistance and end bearing resistance are 1000 kPa and 90000 kPa, respectively
in PileAXL.
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A.2.1.2 USACE Method
For the granular soils, the following equations as recommended in USACE (1991) are adopted to calculate
the ultimate shaft resistance, 𝑓𝑠 and ultimate end bearing resistance, 𝑓𝑏 :
𝛽 = 𝐾 tan 𝛿
𝑓𝑠 = 𝛽𝑝𝑜
𝑓𝑏 = 𝑁𝑞 𝑝𝑜
where K is the coefficient of lateral pressure, 𝛿 is the friction angle between the soil and pile, 𝛽 is the
shaft friction factor, 𝑁𝑞 is the bearing capacity factor based on Figure A.2-3 and 𝑝𝑜 is the effective
overburden pressure. The calculation of the effective overburden pressure is based on the concept of
critical depth in USACE method. The effective overburden pressure used to calculate the ultimate shaft
resistance and end bearing resistance remains constant below the critical depth. The critical depth varies
between 10 to 20 pile diameters (B), depending on the relative density of the sand according to the
following table.
Table A.2-2 Recommended critical depth for cohesionless soils (after USACE 1991)
Sand Density
Critical Depth
Loose
10B
Medium Dense
15B
Dense
20B
USACE (1991) recommends the values of the friction angle between the soil and pile based on the effective
friction angle of the soil in the following table.
Table A.2-3 Recommended interface friction angle for cohesionless soils (after USACE 1991)
Pile Material
Interface Friction Angle, 𝜹
Steel
0.67∅ ~ 0.83∅
Concrete
0.67∅ ~ 0.83∅
Timber
0.80∅ ~ 1.00∅
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The recommended coefficient of lateral pressure, K is provided in the table below. Kc is the coefficient of
lateral pressure for the pile under compressive loading and Kt is the coefficient of lateral pressure for the
pile under tension loading.
Table A.2-4 Recommended coefficient of lateral pressure for cohesionless soils (after USACE 1991)
Soil Type
Kc
Kt
Sand
1.00 ~ 2.00
0.50 ~ 0.70
Silt
1.00
0.50 ~ 0.70
Clay
1.00
0.70 ~ 1.00
Noted that the input parameter in PileAXL is the shaft friction factor 𝛽 instead of two separate parameters
such as the coefficient of lateral pressure and interface angle of friction.
Figure A.2-3 Bearing capacity factor for cohesionless soils – Driven Piles (after USACE 1991)
The basic parameter input dialog for USACE method is the same as API method (Figure A.2-1) for
cohesionless soils. The advanced parameter input dialog for USACE method is shown in Figure A.2-3. The
only difference is that t-z curve based on Coyle and Sulaiman (1967) and q-w curve based on Vijayvergiya
and Mosher (1984) are adopted for USACE method.
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Figure A.2-4 Advanced soil parameter input of USACE method for cohesionless soils – Driven Piles
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A.2.1.3 ICP Method
The third method for the cohesionless soils of driven piles is ICP Method proposed by Jardine and Chow
(1996) in Imperial College, UK. The main feature of this method is that the calculation of ultimate shaft
resistance and end bearing resistance is mainly based on the cone tip resistance from the cone penetration
tests (CPT). If the user inputs other strength parameters for cohesionless soils such as effective friction
angle or SPT-N values instead of the cone tip resistance value, those strength parameters will be
automatically converted into the equivalent cone tip resistance value in the analysis using ICP method for
cohesionless soils.
Figure A.2-5 General procedure of calculating the ultimate shaft resistance for cohesionless soils based on
ICP method (after Jardine et al. 2005)
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Figure A.2-6 General procedure of calculating the ultimate end bearing resistance for cohesionless soils
based on ICP method (after Jardine et al. 2005)
Figure A.2.4 shows the general procedure of calculating the ultimate shaft resistance based on ICP method
for cohesionless soils. Figure A.2.5 shows the general procedure of calculating the ultimate end bearing
resistance based on ICP method for cohesionless soils. The basic parameter input dialog for ICP method is
the same as API or USACE method (Figure A.2-1) for cohesionless soils. The advanced parameter input
dialog for USACE method is shown in Figure A.2-6. The only advanced parameter for ICP method is Phi-cv,
𝛿𝑐𝑣 which is the interface friction angle between piles and soils. The default value is 29 degree but it is
subject to the change by the user if the option of “Resistance Parameters (Default)” is selected. T-z curve
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based on Coyle and Sulaiman (1967) and q-w curve based on Vijayvergiya and Mosher (1984) are adopted
for ICP method for cohesionless soils.
Figure A.2-7 Advanced soil parameter input of ICP method for cohesionless soils – Driven Piles
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A.2.1.4 Fugro Method
Fugro Method is a modification of ICP method and was developed as part of a research project for API by
Fugro in 2004.
The ultimate unit shaft resistance in compression is expressed as:
′
𝜎𝑣𝑜
𝑓𝑠 = 0.08 ∙ 𝑄𝑐 ∙ ( )
𝑃𝑎
0.05
ℎ −0.90
∙ ( ∗)
𝑅
′
where 𝑄𝑐 is cone tip resistance, 𝜎𝑣𝑜
is effective vertical stress at the depth of consideration, 𝑃𝑎 is the
atmosphere pressure, h is the pile length minus the depth of consideration and 𝑅∗ is the equivalent radius
which is calculated as √𝑅𝑜2 − 𝑅𝑖2
for open-ended steel pipe section (𝑅𝑜 is the outside radius and 𝑅𝑖 is
the inside radius) and R for closed-ended piles. The minimum value of (h/R*) is 4 in the calculation.
For tension, the ultimate unit shaft resistance is expressed as:
′
𝜎𝑣𝑜
𝑓𝑠 = 0.045 ∙ 𝑄𝑐 ∙ ( )
𝑃𝑎
0.15
ℎ −0.85
∙ ( ∗)
𝑅
Note that the minimum value of (h/R*) is 4 in the calculation.
̅̅̅𝑐 )
The ultimate end bearing resistance is calculated as a direct function of average cone tip resistance (𝑄
over ± 1.5 diameters near the pile toe and area ratio, Ar which is calculated as 1 − (𝐷𝑖 ⁄𝐷𝑜 )2 where Di is
the inner diameter and Do is the outside diameter. The equation for the ultimate end bearing resistance
calculation is as follow:
̅̅̅𝑐 ⁄𝑃𝑎 )0.5 ∙ 𝐴𝑟 0.25
𝑓𝑏 = 8.5 ∙ (𝑄
The basic parameter input dialog for Fugro method is the same as API or USACE method (Figure A.2-1) for
cohesionless soils. If the user inputs other strength parameters for cohesionless soils such as effective
friction angle or SPT-N values instead of the cone tip resistance value, those strength parameters will be
automatically converted into the equivalent cone tip resistance value in the analysis using Fugro method for
cohesionless soils. The advanced parameter input dialog for Fugro method is shown in Figure A.2-8. Noted
that no additional soil parameters such as interface friction angle between piles and soils are required as
input for this method.
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Figure A.2-8 Advanced soil parameter input of Fugro method for cohesionless soils – Driven Piles
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A.2.1.5 UWA Method
UWA Method is developed by UWA in 2005 for the assessment of the axial capacity of driven offshore piles
in siliceous sand at the request of API piling sub-committee. The ultimate shaft resistance can be expressed
as:
𝑓𝑠 =
𝑓 ′
′ )
(𝜎 + ∆𝜎𝑟𝑑
tan 𝛿𝑐𝑣
𝑓𝑐 𝑟𝑐
′
where 𝛿𝑐𝑣 is the interface friction angle between piles and soils, 𝜎𝑟𝑐
is the radial effective stress after
′
installation and equalization, ∆𝜎𝑟𝑑 is the increase in radial stress due to loading stress path and 𝑓⁄𝑓𝑐 is
equal to 1 for compression and 0.75 for tension.
The radial effective stress after installation and equalisation is given as:
ℎ
′
𝜎𝑟𝑐
= 0.03 ∙ 𝑄𝑐 ∙ 𝐴𝑟,𝑒𝑓𝑓 0.3 [max( , 2)−0.5 ]
𝐷
where 𝑄𝑐 is cone tip resistance, 𝐴𝑟,𝑒𝑓𝑓 is effective area ratio and h is the relative distance above the pile
tip (pile length minus the depth of consideration).
The effective area ratio is calculated as:
𝐷𝑖 2
𝐴𝑟,𝑒𝑓𝑓 = 1 − 𝐼𝐹𝑅 ( )
𝐷𝑜
where IFR is the incremental filling ratio and is calculated as the minimum of 1 and (𝐷𝑖 ⁄1.5)0.2 , 𝐷𝑖 is the
inner pile diameter and 𝐷𝑜 is the outside pile diameter. The change in the radial stress during pile loading
is expressed as:
′
∆𝜎𝑟𝑑
= 4𝐺
∆𝑟
𝐷
𝑄𝑐 ⁄𝑃𝑎
𝐺 = 𝑄𝑐 ∙ 185 ∙ ( ′
)
(𝜎𝑣𝑜 ⁄𝑃𝑎 )0.5
−0.7
where ∆𝑟 is usually taken as 0.02 mm.
̅̅̅𝑐 )
The ultimate end bearing resistance is calculated as a direct function of average cone tip resistance (𝑄
over ± 1.5 diameters near the pile toe and effective area ratio, 𝐴𝑟𝑏,𝑒𝑓𝑓 which is calculated as 1 −
𝐹𝐹𝑅(𝐷𝑖 ⁄𝐷𝑜 )2 where Di is the inner diameter, Do is the outside diameter and FFR is the final filling ratio
which is calculated as the minimum of 1 and (𝐷𝑖 ⁄1.5)0.2 . The equation for the ultimate end bearing
resistance calculation is as follow:
̅̅̅𝑐 (0.15 + 0.45𝐴𝑟𝑏,𝑒𝑓𝑓 )
𝑓𝑏 = 𝑄
The basic parameter input dialog for UWA method is the same as API or USACE method (Figure A.2-1) for
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cohesionless soils. If the user inputs other strength parameters for cohesionless soils such as effective
friction angle or SPT-N values instead of the cone tip resistance value, those strength parameters will be
automatically converted into the equivalent cone tip resistance value in the analysis using Fugro method for
cohesionless soils. The advanced parameter input dialog for Fugro method is shown in Figure A.2-9.
Figure A.2-9 Advanced soil parameter input of UWA method for cohesionless soils – Driven Piles
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A.2.1.6 User Defined Method
For the User Defined Method for cohesionless soils, the basic soil parameter input dialog is the same as the
previous method (such as Figure A.2-1). Note that the input strength parameters on the basic soil
parameter dialog will not be used to calculate the ultimate shaft resistance and end bearing resistance as
those values are directly input into the program through the advanced soil parameter input dialog as show
in Figure A.2-10.
Similar to USACE and ICP methods, t-z curve based on Coyle and Sulaiman (1967) and q-w curve based on
Vijayvergiya and Mosher (1984) are adopted for User Defined method for cohesionless soils.
Figure A.2-10 Advanced soil parameter input of User Defined method for cohesionless soils – Driven Piles
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A.2.2 Bored Piles
A.2.2.1 FHWA Method - Sand
For the cohesionless soils, the following equations as recommended in FHWA manual (O’Neill and Reese
1999) are adopted to calculate the ultimate shaft resistance, 𝑓𝑠 for sand:
𝑓𝑠 = 𝛽𝜎𝑧′
𝛽 = 1.5 − 0.245𝑧 0.5 where 0.25 ≤ 𝛽 ≤ 1.5
where z is the depth below the ground surface, 𝜎𝑣′ is the effective overburden pressure and 𝜙 is the
effective friction angle of the sand. The calculation of the ultimate end bearing resistance, 𝑓𝑏 based on the
effective friction angle is carried out by the following equations:
𝑓𝑏 = 0 for 𝜙 ≤ 30°
𝑓𝑏 = 1530 𝑘𝑃𝑎 for 30° ≤ 𝜙 ≤ 36°
𝑓𝑏 = 3830 𝑘𝑃𝑎 for 36° ≤ 𝜙 ≤ 41°
𝑓𝑏 = 4300 𝑘𝑃𝑎 for 41° ≤ 𝜙
Alternatively, if SPT-N value is adopted, then the ultimate end bearing resistance is calculated as follows:
𝑓𝑏 = 0.0575×𝑁 (𝑀𝑃𝑎) for 𝑁 ≤ 75
𝑓𝑏 = 4.3 (𝑀𝑃𝑎) for 𝑁 > 75
where N is the SPT-N value (Blow Counts). If the cone tip resistance is selected as the basic strength
parameter, then the input value will be automatically converted into the effective friction angle for
cohesionless soils in the analysis.
The basic parameter input dialog for FHWA method for cohesionless soils (bored piles or drilled shafts) is
shown in Figure A.2-11. The advanced parameter input dialog is shown in Figure A.2-12. T-z (Figure A.2-13)
and q-w (Figure A.2-14) curves recommended in FHWA manual (O’Neill and Reese 1999) for granular soils
are adopted.
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Figure A.2-11 Basic soil parameter input of FHWA method for cohesionless soils – Bored Piles or Drilled Shafts
Figure A.2-12 Advanced soil parameter input of FHWA method for cohesionless soils – Bored Piles or Drilled Shafts
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Figure A.2-13 t-z curve adopted for the granular soils – bored piles (FHWA, 1999)
Figure A.2-14 q-w curve adopted for the granular soils – bored piles (FHWA, 1999)
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A.2.2.2 FHWA Method – Gravelly Sand
For the cohesionless soils, the following equations as recommended in FHWA manual (O’Neill and Reese
1999) are adopted to calculate the ultimate shaft resistance, 𝑓𝑠 for gravelly sand:
𝑓𝑠 = 𝛽𝜎𝑧′
𝛽 = 2.0 − 0.15𝑧 0.75 where 0.25 ≤ 𝛽 ≤ 1.8
where z is the depth below the ground surface and 𝜎𝑣′ is the effective overburden pressure. The
procedures of calculating the ultimate end bearing resistance, t-z and q-w curves are the same as FHWA
Method – Sand.
Figure A.2-15 Advanced soil parameter input of FHWA method for gravelly sand – Bored Piles or Drilled Shafts
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A.2.2.3 FHWA Method – Gravel
For the cohesionless soils, the following equations as recommended in FHWA manual (O’Neill and Reese
1999) are adopted to calculate the ultimate shaft resistance, 𝑓𝑠 for gravel:
𝑓𝑠 = 𝛽𝜎𝑧′
𝛽 = (3.4)×𝑒 −0.085×𝑍 where 0.25 ≤ 𝛽 ≤ 3.0
where z is the depth below the ground surface and 𝜎𝑣′ is the effective overburden pressure. The
procedures of calculating the ultimate end bearing resistance, t-z and q-w curves are the same as FHWA
Method – Sand.
Figure A.2-16 Advanced soil parameter input of FHWA method for Gravel – Bored Piles or Drilled Shafts
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A.2.2.4 FHWA Method – Rational Beta
For the cohesionless soils, the following equations as recommended in Chen and Kulhawy (2002) as
described in FHWA-NHI-10-016 (2010) are adopted to calculate the ultimate shaft resistance, 𝑓𝑠 for
granular materials:
𝑓𝑠 = 𝛽𝜎𝑧′
𝛽 = 𝐾𝑜 (
𝜎′
𝐾𝑜 = (1 − sin ∅′ ) ( 𝑝′ )
𝜎𝑣
𝐾
) tan ∅′
𝐾𝑜
sin ∅′
where tan ∅′ ≤ 𝐾𝑝 tan ∅′
𝜎𝑝′
≈ 𝑛(𝑁60 )𝑚
𝑝𝑎
where 𝜎𝑝′ is the effective vertical preconsolidation stress, n and m are the empirical constants for
correlating SPT values with 𝜎𝑝′ as suggested by Mayne (2007) and Kulhawy and Chen (2007). The default
values in PileAXL are 0.47 for n and 0.8 for m. The procedures of calculating the ultimate end bearing
resistance, t-z and q-w curves are the same as FHWA Method – Sand.
Figure A.2-17 Advanced soil parameter input of Rational Beta method for granular soils – Bored Piles or Drilled
Shafts
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A.2.2.5 User Defined Method – Granular Soils
For the User Defined Method, the basic soil parameter input dialog is the same as the previous method.
Note that the input strength parameters on the basic soil parameter dialog will not be used to calculate the
ultimate shaft resistance and end bearing resistance as those values are directly input into the program
through the advanced soil parameter input dialog as show in Figure A.2-18.
Figure A.2-18 Advanced soil parameter input of User Defined method for granular soils – Bored Piles or Drilled
Shafts
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A.3 Rock – Only available to bored piles or drilled shafts
A.3.1 General Rock
Only bored piles are considered for general rock. If the rock material is selected in the lateral analysis for
driven pile, then this rock material is automatically converted to an “equivalent” cohesive soil material with
high undrained shear strength (half of the unconfined compressive strength) in the pile settlement and axial
capacity analysis.
A.3.1.1 Ultimate Shaft Resistance and End Bearing Resistance
For general rock material in PileAXL, the following equation are adopted to calculate the ultimate shaft
resistance, 𝑓𝑠 and ultimate end bearing resistance,𝑓𝑏 :
𝜎𝑐 𝛽
𝑓𝑠 = 𝑝𝑎 ∙ 𝛼 ( )
𝑝𝑎
𝑓𝑏 = 𝑁𝑐 𝜎𝑐
where α and β are empirical factors determined from the various load tests, σc is the unconfined
compressive strength of intact rocks in the unit of MPa and 𝑁𝑐 is the bearing capacity factor for the rock
which is assumed to be 2.5 in PileAXL. Kulhawy and Prakoso (2005) reviewed the database of the currently
existing methods of predicting ultimate shaft resistance and suggested that β can be adopted as 0.5 for all
practical purposes. As for the empirical factor, α, a default value of 0.63 is considered to be close to the
lower bound to 90% of the published data for normal rock sockets in PileAXL.
A.3.1.2 t-z curve for rock
The following hyperbolic relationship for t-z curve as recommended by O’Neill and Hassan (1998) is
adopted in the program to calculate the mobilised shaft resistance 𝑓𝑠−𝑚𝑜𝑏 based on the pile settlement z:
𝑓𝑠−𝑚𝑜𝑏 =
𝑧
2.5𝐷 𝑧
+
𝐸𝑚
𝑓𝑠
where D is the pile diameter and 𝐸𝑚 is the elastic modulus of the rock mass. The following relationship
proposed by Rowe and Armitage (1984) is adopted to calculate the elastic modulus of the rock mass based
on the unconfined compressive strength of rocks:
𝐸𝑚 = 215√𝜎𝑐
A.3.1.3 q-w curve for rock
According to Pells (1999), for massive and intact rock, the load-displacement behaviour is linear up to
bearing pressures of 2 to 4 times the UCS. For jointed rock mass, the load-displacement behaviour is linear
up to 0.75 to 1.25 times the UCS. Baguelin (1982) suggested using the following equation for the linear
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load-displacement relationship for end bearing up to a specific maximum displacement at which the
ultimate bearing resistance is mobilised:
σb = sb ∙
4Eb
π(1 − υb 2 )D
in which Eb is elastic rock modulus at the pile toe; sb is pile toe displacement; υb is Poisson’s ratio (0.25
is adopted in the program); D is the pile diameter and σb is the mobilised end bearing pressure at the pile
toe. This elastic-plastic relationship is adopted in PileAXL.
The basic parameter input dialog for General Rock method for rocks (bored piles or drilled shafts) is shown
in Figure A.3-1. The advanced parameter input dialog is shown in Figure A.3-2. T-z curve based on the
method by by O’Neill and Hassan (1998) and q-w based on the recommendation from Baguelin (1982) are
adopted.
Figure A.3-1 Basic soil parameter input of General Rock Method – Bored Piles or Drilled Shafts
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Figure A.3-2 Advanced soil parameter input of General Rock Method – Bored Piles or Drilled Shafts
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A.3.2 User Defined Method for Rock
For the User Defined Method, the basic soil parameter input dialog is the same as the previous method.
Note that the input strength parameters on the basic soil parameter dialog will not be used to calculate the
ultimate shaft resistance and end bearing resistance as those values are directly input into the program
through the advanced soil parameter input dialog as show in Figure A.3-1. Slightly different from the user
defined method for soils, two additional parameters will need to be provided for the rock: (1) Elastic
modulus, Er-m and (2) Poisson’s ratio, Mu-m as shown in the figure below.
Figure A.3-4 Advanced soil parameter input of User Defined method for rocks – Bored Piles or Drilled Shafts
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Appendix B. Examples
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Example B.1 Steel pipe pile driven into clay and sand layers
This example involves a single 1800 mm diameter steel pipe pile of 65 m long driven through interbedded
clay and sand layers and into the dense sand layer. The water table is located at the ground surface. The
wall thickness of the steel pipe pile is 20 mm. Figure B.1-1 shows the ground profile with the pile length and
loading conditions for this example. Axial force applied at the pile head is 20000 kN.
Figure B.1-1 Ground profile with the pile length and loading conditions for Example 1
Note that the cantilever portion of the pile is modelled with using a layer with “Null” material type in
PileAXL program. If the cantilever portion is within the water such as driven piles used for offshore projects,
the user only needs to make sure that this special “Null” layer is under water table in the soil layer input. In
this example, since the first 5 m cantilever portion is within the water, the first layer – which is the layer
with “Null” material type under the water table. The water table is shown as a thicker blue line in the
ground profile as shown in the figure. Cone tip resistance is adopted as the basic strength parameter for the
clay and sand layers. The steel pipe pile is assumed to be plugged. ICP method is adopted for both clay and
sand layers.
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Figure B.1-2 Combined plot of the pile capacity results for Example 1
Figure B.1-2 shows the combined plot of the pile capacity results for Example 1 which includes the
distribution of ultimate total shaft resistance, ultimate end bearing resistance and ultimate pile total
capacity. Figure B.1-3 shows the pile axial load vs settlement relationship for this example.
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Figure B.1-3 Pile axial load and settlement relationship for Example 1
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Example B.2 Bored pile socketed into strong granite
This example involves a 600 mm diameter reinforced concrete bored pile installed through multiple sand
and clay layers and socketed into strong granite layer. The water table is located at the ground surface.
Figure B.2-1 shows the ground profile with the pile length and loading conditions for this example. Axial
force applied at the pile head is 2121 kN.
Figure B.2-1 Ground profile with the pile length and loading conditions for Example 2
For this example, FHWA Clay model is used to model the clay layers and FHWA Sand model is used to model
the sand layers. The strong granite layer is modelled with General Rock model in PileAXL. The pile length is
35.9 m.
Figure B.2-2 shows the combined plot of the pile capacity results for Example 2 which include the
distribution of ultimate total shaft resistance, ultimate end bearing resistance and ultimate pile total
capacity. Figure B.2-3 shows the pile axial load vs settlement relationship for this example.
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Figure B.2-2 Combined plot of the pile capacity results for Example 2
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Figure B.2-3 Pile axial load and settlement relationship for Example 2
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Example B.3 Bored pile socketed into weak siltstone – Singapore Case
This example involves a 1.4 m diameter reinforced concrete bored pile installed through fill, soft marine clay,
firm clay and dense clayey silt layers and socketed into weak siltstone in Singapore (Leung 1996). The water
table is assumed to be located at the ground surface. Figure B.3-1 shows the ground profile with the pile
length and loading conditions for this example. The maximum axial force applied at the pile head during the
testing is 20000 kN.
Figure B.3-1 Ground profile with the pile length and loading conditions for Example 3
The pile length in this case is 16 m and the analysis results from PileAXL will be compared with the testing
results as reported in Leung (1996). Figure B.3-2 shows the combined plot of the pile capacity results for
Example 3 which include the distribution of ultimate total shaft resistance, ultimate end bearing resistance
and ultimate pile total capacity. Figure B.3-3 shows the pile axial load vs settlement relationship for this
example. The comparison results between the testing results and predictions by PileAXL are presented in
Figure B.3-4.
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Figure B.3-2 Combined plot of the pile capacity results for Example 3
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Figure B.3-3 Pile axial load and settlement relationship for Example 3
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25000
Pile Top Load (kN)
20000
15000
10000
Testing Results from Leung (1996)
PileAXL
5000
0
0
2
4
6
8
10
12
14
16
18
Pile Head Settlement (mm)
Figure B.3-4 Comparisons between testing results and the predictions by PileAXL for Example 3
It can be seen from Figure B.3-4 that the load settlement curve predicted by PileAXL for this case is
reasonably close to the one recorded during the testing. It is noted that the results from PileAXL are on the
conservative side.
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CHAPTER 2. Consideration of AllowableStress Design and LRFD Design
CHAPTER 2 – ASD and LRFD Designs – 2-2
2.1
Introduction
A factor of safety represents the reserve capacity which a foundation or structure has against collapse
for a given set of loads and design conditions. Uncertain design parameters and loads, require a higher
factor of safety than required when the design parameters are well known. Designers should have a high
level of confidence in the soil and pile parameters and the analysis. Therefore, uncertainty in the analysis
and design parameters should be minimized rather than usage of a high factor of safety.
In the United States, many design engineers use a combination of the factor of safety method for
geotechnical analysis of the foundation. The factor of safety method is often referred to as the Allowable
Stress Design (ASD) method and also termed the global approach. The engineer will consider all of the
factors at hand, including such things as the quality of the subsurface investigation, the statistical nature of
the loading, and the expected competence of the contractor, and an overall factor of safety is selected for
individual piles and for the group of piles.
In recent years the concept of load and resistance factor design has been used widely in structural
engineering (referred to as LRFD method) and is termed the component approach. The LRFD method was
accepted formally in 1994 by the American Association of State Highway and Transportation Officials
(AASHTO) as a standard.
The design of a foundation is controlled by geotechnical performance when the soils are weak and
the foundation will fail in a geotechnical mode such as bearing capacity under vertical loading, bearing
failure under lateral loading and/or overturning, or when foundation displacements (vertical, lateral, or
rotational) are larger than tolerably limits for the structure above the foundation. The design of the
foundation is controlled by structural performance when the foundation will fail as a structural member due
to lack of structural capacity in bending moment and/or shear before geotechnical failure modes can develop.
Plainly, the engineer aims to prevent a failure of the structure. However, the precise definition of
failure may be difficult, leading to possible misunderstandings in communicating with the owner and others.
Therefore, the need for the structure to perform as expected over its service life needs to be understood by
all relevant parties. Limit states are defined as those conditions under which a structure or its components
no longer perform an intended function. Whenever a structure or a part of a structure fails to satisfy one of
its designated operational criteria, it is said to have reached a limit state.
The two limit states of interest for most foundations are (1) strength limit state (ultimate limit state),
and (2) serviceability limit state. Strength limit states pertain to structural safety and collapse. For driven
piles under axial load, the strength limit state is typically taken to be the ultimate axial capacity of the pile
driven in a soil strata. Serviceability limit states pertain to conditions under which performance
requirements under normal service loads are exceeded. Such conditions might include movement and
elastic shortening of driven piles. Serviceability limit states are typically checked using all specified or
characteristic service loads (without any factors).
2.2
The Allowable Stress Design (ASD)
Engineers have traditionally used a global factor of safety for the design of piles, giving careful
consideration to all pertinent parameters influencing behavior. The value in the use of such an overall factor
is that the engineer may use judgment to select relevant parameters. For example, the shear strength of the
soil may be chosen more liberally or more conservatively, depending on the entire character of the design.
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CHAPTER 2 – ASD and LRFD Designs – 2-3
Examples of the use of global factors of safety for various geotechnical structures have been discussed by
many geotechnical engineers. One issue on the strength limit state of the ASD method is the choice of the
factor of safety (FS) to be used for the foundation design.
FS = R/Q
(2.1)
where
R = mean value of resistance, and
Q = mean value of load (or the nominal applied load)
The choice of factor of safety for use in foundation design in the United States is usually based on
several factors, including consideration of impact of failure on the public well being, redundancy in the
foundation system, and the availability of information from load tests.
Pile static analysis will yield results of ultimate pile capacity, which includes the soil resistance from
the side friction and from the tip bearing. The ultimate pile capacity from the soil resistance is generally
referred to “geotechnical pile capacity.” The allowable geotechnical pile capacity is selected by dividing
the ultimate geotechnical pile capacity by a factor of safety as shown in Equation (2.2).
Qa = Ru/FS = (Rs + Rt)/FS
(2.2)
where
Qa = allowable pile capacity, lb (kN);
Ru = ultimate soil resistance, lb (kN);
Rs = ultimate side resistance, lb (kN);
Rt = ultimate tip resistance, lb (kN);
FS = factor of safety;
In static analysis methods, the factor of safety ranges from 2 to 4 and has primarily depended upon
the reliability of the particular static analysis method with consideration of the following items:
1.
The level of confidence in the input parameters (this is a function of the type and extent of the
subsurface exploration and laboratory testing of soil and rock materials).
2.
Variability of the soil and rock.
3.
Method of static analysis.
4.
Effects of the proposed pile installation method.
5.
Level of construction monitoring (static load test, dynamic analysis, wave-equation analysis.)
While the range in static analysis factors of safety varies from 2 to 4, most of the static analysis
methods recommend a factor of safety of 2.5 to 3.0. However, use of factor of safety equal to 2.0 is usually
allowed if a load test of similar foundation is performed at the project site. If a load test is performed during
the design phase of a project, any questions regarding foundation capacity and stiffness can be answered
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CHAPTER 2 – ASD and LRFD Designs – 2-4
and the resulting knowledge be utilized in design. The factors of safety in Table 2.1 are presented based
on various control methods of pile installations.
Construction Control Method
Static load test with wave equation analysis
Dynamic analysis with wave equation analysis
Indicator piles with wave equation analysis
Wave-equation analysis
Factor of Safety
2.0
2.25
2.5
2.75
Table 2.1 Recommended factor of safety for the ASD design
Serviceability limit states are typically checked using all specified or characteristic service loads
without any factors. The serviceability limit states are typically varied with the functions of the super
structures.
2.3
Load and Resistance Factor Design (LRFD)
The allowable stress design is familiar to most foundation designers. However, it suffers from the
shortcoming that all uncertainty is lumped into one global factor of safety that is difficult to evaluate
functionally reliability of the foundation. The functional reliability of the foundation involves the
variability of the soil and rock properties and pattern and quality of soil and rock sampling, as well as the
accuracy of the design model and quality of construction. While it is difficult to arrive at a global factor of
safety that addresses all of these effects, each of the component uncertainties can be analyzed individually
and incorporated into a load and resistance design method, which considers the load and resistance
components separately.
The LRFD specifications of AASHTO present methods of modifying the component loads and the
component resistances. The basic equation is shown below.
Rr
∑ (ηiγ i Qi ) ≤ φ Rn =
(2.3)
where
ηi = factors to account for ductility, redundancy and operational importance;
γi = load factor;
Qi = force effect, stress or resultant;
φ = resistance factor;
Rn = nominal (ultimate) resistance; and
Rn = factored resistance.
Several features of the LRFD method are similar to the method of partial safety factors. The engineer,
in obtaining a solution to Equation (2.3), must estimate the loads and load combinations that may be
imposed on the structure, and estimate the ultimate resistance available to resist the loading.
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2.3.1
Loads addressed by the LRFD specifications
A large number of types of loads are considered in the LRFD specifications, including dead load of
structural components and nonstructural attachments; dead load of wearing surface and utilities; horizontal
load from earth pressure; load from earth surcharge; vertical load from earth fill; load from collision of a
floating vessel; load from collision of vehicles; load from an earthquake; ice load; vertical load from
dynamics of vehicles; load from the centrifugal force of vehicle traveling on a curve; load from the braking
of vehicles; live load from vehicles; live load from surcharge; live load from pedestrians; load from water
pressure in fill; load from currents in stream; loads due to changes in temperature of structure; wind load
on structure; and wind load on vehicles. Each of the types of loads is discussed (NHI, 1998) and some
guidance is given in making the computation of magnitude of the load.
A number of basic load combinations (called limit states) are identified by AASHTO for use in
design. The combinations are grouped into Strength (I, II, III, IV, V), Service (I, II, III), Extreme Event (I,
II), and Fatigue. Table 2.2 and Table 2.3 summarize the recommended load factors, which are directly
related to a pile foundation.
Table 2.2 Recommended load factors for live loads from ASSHTO 2010
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Table 2.3 Recommended load factors for permanent loads from ASSHTO 2010
2.3.2
Resistances addressed by the LRFD specifications
The principal emphasis of the LRFD specifications in regard to resistance resides in the
determination of values of geotechnical parameters. National Cooperative Highway Research program
Project NCHRP 24-17, “LRFD Deep Foundations Design,” was initiated to provide (1) recommended
revisions to the driven pile and drilled shaft portions of Section 10 of the AASHTO LRFD Bridge Design
Specification and (2) a detailed procedure for calibrating deep foundation resistance factors. The American
Association of State Highway and Transportation Officials (AASHTO) recently issued an updated Load
and Resistance Factor Design (LRFD) design guide specification (AASHTO 2010). The AASHTO
specifications are traditionally observed on all federally-aided projects in the United States and generally
viewed as a national code of U.S. highway practice.
The ultimate geotechnical capacity of a pile is called “nominal resistance” in the AASHTO LRFD
code. The nominal resistance for driven piles in general can be predicted based on the following methods.
• static analysis
• dynamic formula
• wave-equation analysis
• dynamic load testing
• static load testing
The dynamic formula, wave-equation analysis, dynamic load testing, and static load testing are
commonly based on the performance data collected during pile installation or pile-loading tests. Therefore,
the reduction factors recommended for each method have been established and are easy for verification.
Table 2.4 presents the recommended reduction factors from ASSHTO 2010 for the above methods.
Estimating Method for Pile Nominal Capacity
Dynamic formula (Engineering News Record)
Dynamic formula (FHWA modified Gates method)
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Reduction factors
0.1
0.4
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Wave equation analysis, without pile dynamic
measurements or load test, at the end of driving
conditions only
Dynamic testing (2% of piles)
Static testing or 100% dynamic testing
Static testing plus 2% dynamic testing
0.4
0.65
0.75
0.8
Table 2.4 Recommended reduction factors for the LRFD design (ASSHTO 2010)
Static analysis is the most-commonly used method for engineers to estimate the nominal resistance
of driven piles, based on the soil parameters obtained from the soil investigation. However, this method is
largely based on empirical equations for side resistance and tip resistance of various soil layers, soil strength,
and pile types. With a number of variables being involved in the static-analysis method, the LRFD
reduction factors have to be derived carefully based on each parameter from a broad range of field test data.
The resistance factors on axially-loaded piles for the limit-state geotechnical strength were recommended
by AASHTO as shown in Table 2.5. The newly recommended strength-reduction factors as a function of
a given reliability index ( β ) for the static-analysis method based on the extensive studies from NCHRP
24-17 are listed in Table 2.6 for reference.
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Table 2.5 Resistance factors for geotechnical strength limit state for axially loaded
piles (ASSHTO 2010)
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Table 2.6 Strength reduction factors recommended by NCHRP
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2.3.3
Comments on the LRFD Design
The AASHTO LRFD Specifications are written based on probabilistic limit-state theory with several
listed load combinations. The advantages of a probability-based LRFD specification are:
• A more uniform level of safety throughout the system;
• Measure of safety will be a function of the variability of loads and resistance;
• Designers will have an estimate of the probability of meeting or exceeding the design
criteria during the design life;
• The potential exists to place all structural materials and methods of construction on
equal footing;
• A realistic rational framework for future development of the specification will be
available;
• Proponents of future changes in materials and construction techniques will be asked to
provide the same measure of reliability that all current materials and construction
methods will be asked to meet;
• Designers will have a better understanding of where and how uncertainties of load and
resistance models are accounted for, and will be able to relate past performance.
The disadvantages of basing a specification on this philosophy include an increased design effort, as
it is realistic to expect that a greater number of load and resistance factors will be available. However, the
designer will need little or no knowledge of reliability theory.
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CHAPTER 3. Computational Methods of
Axial Pile Capacity
CHAPTER 3 – Methods for Pile Capacity – 3-2
3.1
Basic Equation of Analytical Method
The ultimate capacity of the pile for compression loading is computed by use of the following
equation.
Qd = Qf+ Qp = fAs + qAp
(3.1)
where
Qf = skin friction resistance, lb (kN);
Qp = total end bearing, lb (kN);
f = unit load transfer in skin friction (normally varies with depth), lb/ft2 (kPa);
q = unit load transfer in end bearing (normally varies with depth), lb/ft2 (kPa); (Note: for
computations of end bearing on all methods APILE uses an average of soil properties
within 1.5 pile diameters above and below the pile tip);
Ap = gross end area of pile, ft2 (m2); and
As = side surface area of pile, ft2 (m2).
Equation (3.1) is used at each pile increment as it penetrates into the ground. While Equation (3.1)
is generally accepted, there is no general agreement on the methods of obtaining f and q. As noted earlier,
the user is urged to make use of several recommendations in the literature and use judgment in making a
final design. Alternately, a special study can be made for a specific site.
3.2
American Petroleum Institute (API) Method
The use of the equations of statics to compute the geotechnical capacity of piles is well established
and numerous procedures have been suggested. Most of the methods employed herein are presented by the
American Petroleum Institute (API) in their manuals on recommended practice (RP). The API procedures
in RP2A have been adopted by a number of organizations.
The API procedures for clay are based essentially on the use of undrained shear strength and are
largely empirical. The API procedure for sand is also strongly empirical but effective-stress techniques are
naturally employed because no excess pore water pressures are assumed.
3.2.1
Skin Friction in Cohesive Soil
The 1986 method of the American Petroleum Institute (API) for computing the skin friction in
cohesive soil is based on various types of clays. For normal, consolidated, highly-plastic clays, API Method
1 (1986) was generally used. For other types of clay, API Method 2 (1986) was recommended for design.
Further research studies have led API RP 2A (1987) to combine Method 1 and Method 2 into a
Revised API method. The current API RP 2A (2014) is still the same revised method introduced in 1987
for computations of ultimate side friction and tip resistance, but adding new recommendations on t-z and
Q-w curves. The APILE program uses the recommendations from the latest API RP 2A (2014).
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3.2.1.1 API Method 1
The following brief statement from API RP2A (1986) presents Method 1.
For highly-plastic clays, such as those found in the Gulf of Mexico, f may be equal to c for underconsolidated and normally-consolidated clays. For over-consolidated clays f should not exceed 1 kips per
square foot (48 kPa) for shallow penetrations or c equivalent to normally-consolidated clay for deeper
penetrations, whichever is greater.
In general:
Q f = f As
(3.2)
where
Qf = axial load capacity in skin friction, lb (kN);
f = unit skin friction resistance (adhesion), lb/ft2 (kPa); and
As = side surface area of pile, ft2 (m2).
The above Equation (3.2) may be written more properly as:
L
Q f = ∫ f x dAs
o
(3.3)
where
Qf = axial load capacity in skin friction, lb (kN);
L = penetration of pile below ground surface, ft (m);
fx = unit resistance in clay at depth x, measured from ground surface, lb/ft2 (kPa); and
As = side surface area of pile, ft2 (m2).
This API provision is for highly-plastic clays, such as those found in the Gulf of Mexico, and the
method of obtaining fx is shown in Figure 3.1Values of fx recommended by API RP2A (1986).
The step-by-step computational procedure is:
1.
Construct diagram showing undrained shear strength as a function of depth. API suggests use of
unconfined compression or miniature vane tests, and judgment should be employed in regard to the
use of other data.
2.
Construct diagram showing the maximum fx. The estimated value of shear strength of normally
consolidated clay may be obtained from the following expression:
cn p= k=
f ( PI )
c
(3.4)
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CHAPTER 3 – Methods for Pile Capacity – 3-4
where
cn = undrained shear strength of normally consolidated clay,
p = undrained shear strength = γx
γ = effective unit weight of soil; and
kc = constant.
The constant kc has been shown by Skempton and others to be a function of the plasticity index, PI.
As a reference, some engineers suggested that kc should be taken as 0.25 for Gulf of Mexico soils on the
basis of their local experience. The unit weight of the soil, total or submerged depending on location of the
water table, should be obtained from a study of data from the soil borings at the site.
3.
Select a pile of a given geometry.
4.
Select an incremental length of the pile, extending from the ground surface to some depth. The
length to be used is selected on the basis of the variations in the diagrams prepared in Steps 1 and 2.
5.
For the incremental depth being considered in Step 4, obtain a value of the average shear strength
from the diagram prepared in Step 1.
6.
Compare the value obtained in Step 5 with the value of ( f x )max for the same depth obtained from the
diagram prepared in Step 2. The smaller of the values is to be used in computing load capacity of
the pile.
7.
The value of f x obtained in Step 6 shall be used with the appropriate surface area of the side of the
pile to compute the load capacity of the first increment. Equation (3.2), appropriately modified, can
be used.
8.
The second increment of pile penetration can be selected, with the top of the second increment being
the bottom of the first increment.
9.
Steps 5 through 7 should be repeated.
10. The loads obtained for each of the two increments can be added to obtain the total axial load
capacity of the pile in skin friction for the two increments considered.
11. Other increments are selected until the total length of the pile (see later section for procedure for
obtaining end bearing) is taken into account.
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Figure 3.1 Values of fx recommended by API RP2A (1986)
3.2.1.2 API Method 2
The following brief statement from API RP2A (1986) presents Method 2.
For other types of clay, f should be taken equal to c for c less or equal to 1/2 kips per square foot (24
kPa). For c in excess of 1/2 kips per square foot (24 kPa) but less than or equal to 1.5 tons per square foot
(72 kPa) the ratio of f to c should decrease linearly from unity at c equal to 1/2 kips per square foot (24 kPa)
to 1/2 at c equal to 1.5 kips per square foot (72 kPa). For c in excess of 1.5 kips per square foot (72 kPa), f
should be taken as 1/2 of c.
The detailed explanation of the application of Method 2 is shown in the following section.
f x = α x cx
(3.5)
where
fx = unit resistance in clay at depth x, measured from ground surface;
αx = a coefficient that is a function of cx; and
cx = undrained shear strength at depth x.
A recommendation of values for α is shown in Figure 3.2. This referenced graphics follows that f
may be taken equal to c for undrained shear strengths of 0.5 kips per square foot or less, and equal to 0.5 c
for values of c equal to or greater than l.5 kips per square foot. A linear variation is used for values of c
between 0.5 and l.5 kips per square foot.
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Figure 3.2 Values of α recommended by API RP2A (1986)
The step-by-step computation procedure is:
1.
Same as Step l in Method l.
2.
Same as Step 3 in Method 1.
3.
Select an incremental length of pile (see Step 4 in Method l).
4.
Obtain a value of c for the incremental length from the diagram prepared in Step l.
5.
Enter Figure 3.2 with value of c obtained in Step 4 and obtain α .
6.
Compute the unit skin friction resistance (unit load transfer) f x by use of Equation (3.5).
7.
Compute the load capacity of the first incremental length of the pile by use of Equation (3.2) as
appropriately modified.
8.
Select a second increment and repeat Steps 4 through 7.
9.
Add load computed for first two increments.
10. Select other increments of length until the length of pile is taken into account.
3.2.1.3 Revised API Method (1997-2014)
New releases of the API Recommended Practice 2A (RP 2A) have proposed a revised equation for
the coefficient α. The factor, α, recommended by API RP 2A (2014) can be computed by the following
equations:
α = 0.5ψ −0.5 if ψ ≤ 1.0
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α = 0.5ψ −0.25 if ψ > 1.0
With constraint that α ≤ 1.0
(3.6)
Where
ψ = c / p for the depth of interest;
p = effective overburden pressure; and
c = undrained shear strength of soil.
As a reference, Figure 3.3 presents a comparison between a-factors calculated from 1986 and 1987
API RP 2A recommendations. The comparison can only be made for a specific depth because the
overburden stress will change with depth; hence, for a given value of c the value of c / p will change.
Comparisons shown in Figure 3.3 are for depth where p is 0.5, 1.0, and 2.0 Ton/ft2. Careful study of
Figure 3.3 indicates that for normally consolidated clay, where c / p is equal approximately to 0.25, the
revised method yields higher values of α than does Method 2. The revised method yields higher values of
α at the depth where p is equal to 2.0 Ton/ft2 (80 to 100 ft) except for heavily overconsolidated clay. The
revised method yields lower values of α where it is equal to 0.5 T/ft2 (20 to 25 ft) than does Method 2.
Figure 3.3 Comparison between α factors from 1986 and 1987 API RP2A
recommendations
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CHAPTER 3 – Methods for Pile Capacity – 3-8
The step-by-step computation procedure is identical with that for Method 2 except that Equations
(3.6) are used in Step 5 instead of using Figure 3.2.
3.2.2
End Bearing in Cohesive Soil
The recommendations of API RP 2A (1987-2014) for end bearing in clay are as follows: “For piles
end bearing in clay, q in 1b/ft2 (kPa) should be equal to 9c. If the strength profile below the pile tip is not
uniform, then the c utilized should reflect appropriate adjustment.” This recommendation is consistent with
that suggested by many other investigators.
The API recommendation in equation form is as follows, along with a suggestion for modifying the
value of c:
Q p = qAp
(3.7)
q=9c
(3.8)
where
Qp = axial load capacity in end bearing;
q = unit end bearing resistance;
c = undrained shear strength at tip of pile, taken as the average over a distance of 1.5 diameters
above and below the tip of the pile; and
Ap = cross-sectional area of tip of pile.
3.2.3
Skin Friction in Cohesionless Soil
Experimental results that are available for driven piles in sands show a considerable scatter for values
of skin friction and end bearing. The scatter is likely due to the influence of methods of installation on soil
properties and the state of stress. The following recommendations for computing unit values of skin friction
and end bearing for piles in sand are consistent with the state of the practice; however, the user should use
such values with caution. Pile-load tests are recommended if feasible.
The API RP 2A (1987-2014) recommendations for side resistance for pipe piles in cohesionless soil
(sand) are given in the following sections.
f = k (tan δ ) po = β po
(3.9)
where
β = k (tan δ ) = dimensionless shaft friction factor (introduced in 2010) to avoid confusion with
other nomenclature in the API RP-2A code, the multiplication of k times tan δ produce
the same results as the values proposed for the new beta coefficient.
k = coefficient of lateral earth (ratio of horizontal to vertical normal effective stress), a value of
k = 0.8 was recommended for open-ended pipe piles, that are driven unplugged, for
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CHAPTER 3 – Methods for Pile Capacity – 3-9
loadings in both tension and compression. A value of k = 1.0 was recommended for full
displacement piles.
p = effective overburden pressure at the point in question; and
o
δ = the friction angle between the soil and the pile wall. In the absence of data on δ, Table 3.1
is used internally by APILE for siliceous soil. APILE computes δ = φ − 5o (in degrees)
based on user’s inputted value of friction angle (φ). The limiting f is interpolated linearly
within APILE for intermediate values of δ in Table 3.1.
Equation (3.9) implies that the value of f increases without limit; however, Table 3.1 presents
guidelines for limiting values.
Limiting f ,
δ , degrees
kips/ft2 (kPa)
Very loose to medium,
sand to silt
15
1.0 (47.8)
Loose to dense,
sand to silt
20
1.4 (67.0)
Medium to dense,
sand to sand-silt
25
1.7 (83.1)
Dense to very dense,
sand to sand-silt
30
2.0 (95.5)
Dense to very dense,
gravel to sand
35
2.4 (114.8)
Soil
Note: APILE computes δ = φ − 5o and f is interpolated linearly for intermediate δ values.
Table 3.1 Guidelines for side friction in siliceous soil
3.2.4
End Bearing in Cohesionless Soil
For end bearing in cohesionless soils, API recommends the following.
q = po N q
(3.10)
Where
q = unit end bearing resistance;
p = effective overburden pressure at the pile tip; and
o
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Nq = bearing capacity factor.
The API publication points out that many soils do not fit the description of those in the tables and
that the design parameters are not suitable for these soils. Examples are loose silts, soils containing large
amounts of mica or volcanic grains, and calcareous sands. These latter soils are known to have substantially
lower design parameters. Drilled and grouted piles may have higher capacities than driven piles in
calcareous soils.
Equation (3.10) implies that the value of q increases without limit; however, Table 3.2 presents
guidelines for limiting values.
Soil
Nq
Limiting q ,
2
kips/ft (MPa)
Very loose to medium,
sand to silt
8
40 (1.9)
Loose to dense,
sand to silt
12
60 (2.9)
Medium to dense,
sand to sand-silt
20
100 (4.8)
Dense to very dense,
sand to sand-silt
40
200 (9.6)
Dense to very dense,
gravel to sand
50
250 (12.0)
Table 3.2 Guidelines for tip resistance in siliceous soil
3.3
Revised Lambda Method
The Lambda Method was developed for clay layers as indicated in the referenced papers in this
section. When the subsurface consists of more than 25% of sand strata, the user should not rely on the
results based on Lambda Method.
3.3.1
Skin Friction in Cohesive Soil
Vijayvergiya and Focht (1972) proposed the following equation for computing the resistance in skin
friction:
Q f = λ ( pm + 2cm ) As
(3.11)
where
Qf = axial load capacity in skin friction;
λ = a coefficient that is a function of pile penetration;
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pm = the mean vertical effective stress between the ground surface and the pile tip;
cm = the mean undrained shear strength along the pile; and
As = side surface area of pile.
A curve, giving λ as a function of pile penetration, was presented. Kraft, et al (1981) made a further
study of data and revised the method of obtaining λ . The following equations were employed.
For normally consolidated soils,
=
λ 0.178 − 0.16 ln π 3
(3.12)
For over-consolidated soils,
=
λ 0.232 − 0.032 ln π 3
(3.13)
where
π 3 = (π B f max ( L2e ) / ( AEU ))
(3.14)
B = pile diameter;
fmax = peak soil friction (taken as the mean undrained shearing strength);
Le = embedded pile length;
A = cross-sectional area of pile material;
E = modulus of elasticity of pile material; and
U = pile displacement needed to develop the side shear (taken as 0.1 inch).
In the absence of consolidation data, Kraft, et al., considered the clay to be over-consolidated if the
undrained shear strength divided by the overburden stress was equal to or larger than 0.10. The value of
the lower limit of λ was taken as 0.110.
The step-by-step computation procedure is outlined below.
1.
Construct diagram showing undrained shear strength as a function of depth.
2.
Construct diagram showing vertical effective stress as a function of depth.
3.
Select a pile of a given geometry.
4.
Select a pile penetration for computation of the axial load capacity in skin friction.
5.
Use diagram constructed in Step 1 and compute cm .
6.
Use diagram constructed in Step 2 and compute pm .
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7.
Obtain value of λ from Equations (3.12) through (3.14).
8.
Substitute values of λ , pm , and cm , along with the value of As , into Equation (3.11) and compute
Qf .
9.
Select a different pile penetration and repeat Steps 5 through 8 to obtain pile capacity Q f as a
function of pile penetration.
3.3.2
End Bearing in Cohesive Soil
The Lambda Method is a modified method that has been mostly used by offshore engineers for
transfers in skin friction. The Lambda method does not propose equations for the tip resistance. For that
reason, the APILE program uses the API equations of tip resistance (described in Section 3.2.2)when the
Lambda Method is selected by the user.
3.3.3
Skin Friction in Cohesionless Soil
Sand layers are not part of the Lambda Method. In the Lambda Method any sand layer in the model
is thus converted to an “equivalent” clay by using the following equation:
Equivalent cx = effective stress * Ko * tan(phi)
(3.15)
After this conversion, the APILE program uses the equations for skin friction in cohesive soils from
the Lambda Method (previously described in Section 3.3.1).
The “Equivalent cx" in Equation (3.15) stands for the undrained shear strength at depth x, which is a
similar term as the user-inputted undrained shear strength of clay layers. The term “ cm ” in Equation (3.11)
is the mean undrained shear strength along the pile. The APILE program calculates internally the averaged
cm based on the “Equivalent cx" at the top and the bottom of each pile increment.
After calculating the mean averaged undrained strength cm based on the “Equivalent cx", APILE
also assumes that the term fmax in Equation (3.14) is equal to cm because the mean undrained shear
strength is recommended to be the peak soil friction in the computation of π3.
The computations used for this section are rational but it should be emphasized that the Lambda
Method was only developed for clay layers. When the subsurface consists of more than about 25% of sand
strata, the user should not rely on the results from the Lambda Method.
3.3.4
Tip Resistance in Cohesionless Soil
As mentioned earlier, the Lambda Method is a modified method that has been mostly used by
offshore engineers for transfers in skin friction in clay layers. The Lambda method does not propose
equations for sand layers. For that reason, the APILE program uses the API equations of tip resistance
(previously described in Section 3.2.4) when the Lambda Method is selected by the user.
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3.4
U.S. Army Corps of Engineers (USACE) Method
3.4.1
Pile in Cohesionless Soil
3.4.1.1 Skin Friction
For design purposes, USACE established that the skin friction of piles in sand increases linearly to
an assumed critical depth (Dc) and then remains constant below that depth. The critical depth varies
between 10 to 20 pile diameters or widths (B), depending on the relative density of the sand. The reference,
the critical depths criteria used by APILE for sand is included in Table 3.3. Intermediate values are
interpolated linearly within the program.
Sand Density
Critical Depth
Dc
Loose
φ ≤ 33°
10 B
Medium Dense
33° < φ ≤ 36°
15 B
Dense
φ > 36°
20 B
Table 3.3 Guidelines for Critical Depth (Dc) in Sands
The unit skin friction acting on the pile shaft may be determined by the following equations:
f s = Kσ v' tan δ
σ v' = γ ' D for D < Dc
σ v' = γ ' Dc for D ≥ Dc
Qs = f s As
(3.16)
where
K = lateral earth pressure coefficient (Kc for compression piles and Kt for tension piles);
σ v' = effective overburden pressure;
δ = angle of friction between the soil and the pile (reference values of δ are provided in Table
3.4 but APILE uses the average value of δ for each range defined in Table 3.4);
γ' = effective unit weight of soil;
D = depth along the pile at which the effective overburden pressure is calculated;
Dc = critical depth (reference for Dc is provided in Table 3.3); and
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As = side surface area of pile.
Pile Material
Steel
Concrete
Timber
δ
δ
(recommended range)
(used inside APILE)
0.67φ to 0.83φ
0.90φ to 1.00φ
0.80φ to 1.00φ
0.75φ
0.95φ
0.90φ
Table 3.4 Sample Values of δ
Values of K for piles in compression (Kc) and piles in tension (Kt) are provided in
Table 3.5. Table 3.4 and Table 3.5 present ranges of values of δ and K based upon
experience in various soil deposits. These values should be selected for design
based upon experience and pile load test. It is not intended that the designer would
use the minimum reduction of the φ angle while using the upper range K values.
Kc
Soil Type
Kt
Sand
1.00 to 2.00
0.50 to 0.70
Silt
1.00
0.50 to 0.70
Clay
1.00
0.70 to 1.00
Note: The above do not apply to piles that are prebored, jetted, or installed with a
vibratory hammer. Picking K values at the upper end of the above ranges should
be based on local experience. K , δ , and N q values back calculated from load
tests may be used.
Table 3.5 Sample Values of K (Kc and Kt)
For steel H-piles, As should be taken as the block perimeter of the pile and δ should
be the average friction angle of steel against sand and sand against sand ( φ ). It
should be noted that Table 3.5 is general guidance to be used unless the long-term
engineering practice in the area indicates otherwise. Under prediction of soil
strength, parameters at load test sites have at times produced back-calculated
values of K that exceed the values in Table 3.5. It has also been found both
theoretically and at some test sites that the use of displacement piles produces
higher values of K than does the use of non-displacement piles. Values of K that
have been used satisfactorily but with standard soil data in some locations are as
presented in Table 3.6.
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Soil Type
Displacement Piles
Non-Displacement Piles
Compression
Tension
Compression
Tension
Sand
2.00
0.67
1.50
0.50
Silt
1.25
0.50
1.00
0.35
Clay
1.25
0.90
1.00
0.70
Note: Although these values may be commonly used in some areas they should not
be used without experience and testing to validate them.
Table 3.6 Common Values for Corrected K (Kc and Kt)
3.4.1.2 End Bearing
For design purposes the pile tip bearing capacity can be assumed to increase linearly to a critical
depth (Dc) and then remain constant. The same critical-depth relationship used for skin friction can be used
for end bearing. The unit tip bearing capacity can be determined as follows:
q = σ v' N q
σ v' = γ ' D for D < Dc
σ v' = γ ' Dc for D ≥ Dc
(3.17)
Where
q = unit end bearing resistance;
σ v' = effective overburden pressure;
γ' = effective unit weight of soil;
Nq = bearing capacity factor (reference for Nq is provided in Figure 3.4); and
D = depth along the pile at which the effective overburden pressure is calculated; and
Dc = critical depth (reference for Dc is provided in Table 3.3).
For steel H-piles the tip area of the pile should be taken as the area included within the block
perimeter. A curve to obtain the Terzaghi-Peck (1967) bearing capacity factor Nq (among values from
other theories) is shown in Figure 3.4. To use the curve one must obtain measured values of the angle of
internal friction ( φ ) which represents the soil mass.
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Figure 3.4 Bearing Capacity Factor Nq from Terzaghi-Peck (1967)
3.4.1.3 Tension Capacity
The tension capacity of piles in sand is calculated as follows with Equation (3.16)
while using the K values for tension from Note: The above do not apply to piles
that are prebored, jetted, or installed with a vibratory hammer. Picking K values
at the upper end of the above ranges should be based on local experience. K , δ ,
and N q values back calculated from load tests may be used.
Table 3.5:
Qult = Qs (Tension ) = f s As
(3.18)
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3.4.2
Piles in Cohesive Soil
3.4.2.1 Skin Friction
Although called skin friction, the resistance is due to the cohesion or adhesion of the clay to the shaft
of the pile:
f s = ca
ca = α c
Qs = f s As
(3.19)
where
ca = adhesion between the clay and the pile;
α = adhesion factor; and
c = undrained shear strength of the clay from a quick Q test.
The values of α as a function of the undrained shear are given in Figure 3.5. An alternate procedure
developed by Semple and Rigden (1984) to obtain values of α which are especially applicable for very long
piles is given in Figure 3.6 where:
α = α1 α 2
(3.20)
And
fs = α c
(3.21)
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Figure 3.5 Values of α versus undrained shear strength
Figure 3.6 Values of α1 and α2 applicable to very long piles
3.4.2.2 End Bearing
The pile unit-tip bearing capacity for piles in clay can be determined from the following equations:
q=9c
(3.22)
Q p = qAp
(3.23)
where
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q = unit end bearing resistance;
c = undrained shear strength at tip of pile, taken as the average over a distance of 2 diameters
below the tip of the pile;
Qp = axial load capacity in end bearing; and
Ap = cross-sectional area of tip of pile.
However, the movement necessary to develop the tip resistance of piles in clay soils may be several
times larger than that required to develop the skin-friction resistance.
3.4.2.3 Compression Capacity
By combining the skin friction and the tip bearing capacity, the ultimate compression capacity may
be found as follows:
Qult = Qs + Q p
(3.24)
3.4.2.4 Tension Capacity
The tension capacity of piles in clay may be calculated as:
Qult = Qs (Tension ) = f s As
(3.25)
3.4.2.5 S-Case Shear Strength
The pile capacity in normally consolidated clays (cohesive soils) should also be computed in the
long-term S shear strength case. That is, develop an S-Case shear strength trend and proceed as if the soil
is drained. The computational method is identical to that presented for piles in granular soils, and to present
the computational methodology would be redundant. It should be noted, however, that the shear strengths
in clays in the S-Case are assumed to be φ > 0 and c = 0 . Some commonly used S-Case shear strengths
in alluvial soils are reported in Table 3.7.
Soil Type
Consistency
Angle of Internal
Friction (deg)
Fat Clay (CH)
Very Soft
13 to 17
Fat Clay (CH)
Soft
17 to 20
Fat Clay (CH)
Medium
20 to 21
Fat Clay (CH)
Stiff
21 to 23
Silt (MH)
25 to 28
Note: The designer should perform testing and select shear strengths. These general data
ranges are from test on specific soils in site specific environments and may not represent the soil in
question.
Table 3.7 S-Case Shear Strength for Alluvial Soils
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3.5
Federal Highway Administration (FHWA) Method
3.5.1
Introduction
A single pile derives its load-carrying ability from the frictional resistance of the soil around the shaft
and the bearing capacity at the pile tip:
Q = Qs + Q p
(3.26)
Q p = q p Ap
(3.27)
where
and
L
Qs = ∫ f sCd dz
o
(3.28)
in which
Qs = axial load capacity in skin friction;
Qp = axial load capacity in end bearing;
qp = bearing capacity at pile tip;
Ap = area of pile tip;
L = length of pile in contact with soil;
fs = ultimate skin resistance per unit area of shaft;
Cd = effective perimeter of pile; and
z = depth coordinate.
3.5.2
Point Resistance
The point bearing capacity can be obtained from
q p = c Nc + q Nq +
γB
Nγ
2
(3.29)
Where Nc, Nq and Nγ are dimensionless parameters that depend on the soil friction angle φ. The
term c is the cohesion of the soil, q is the vertical stress at pile base level, B is the pile diameter (or
width), and γ is the unit weight of the soil.
For end bearing in cohesive soils, the following equation is recommended:
Q p = Ap c N c
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Values of Nc are suggested between 7 and 16, though a value of Nc=9 is usually used.
For end bearing in cohesionless soils, the FHWA method uses the following:
Qp = Ap q α t N q'
(3.31)
where
N q′ = bearing capacity factor from Figure 3.7 and
αt = dimensionless factor dependent on the depth-width relationship of the pile (Figure 3.7).
Meyerhof (1976) recommended limiting values for tip resistance in cohesionless soils, which are
shown in Figure 3.8. These reduction values are automatically calculated and used by APILE internally
within the program (cannot be avoided by specification of higher unit end bearing by user).
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Figure 3.7 Chart for Estimating the α Coefficient and the Bearing Capacity Factor N’q for
FHWA Method
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Figure 3.8 Relationship between maximum unit pile point resistance and friction angle
for cohesionless soils (after Meyerhof 1976)
3.5.3
Side Friction
The ultimate skin resistance per unit area of shaft is calculated as follows:
f s = ca + σ h tan(δ )
(3.32)
where
ca = pile-soil adhesion;
σh = normal component of stress at pile-soil interface, and
δ = pile-soil friction angle.
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The normal stress σh is related to the vertical stress σv as σ h = K σ v , where K is a coefficient of
lateral stress. Substituting into Equation (3.32) produces the following result:
f s = ca + Kσ v tan(δ )
(3.33)
For cohesive soils, Equation (3.32) reduces as follows:
f s = ca
(3.34)
where the adhesion ca is usually related to the undrained shear strength σu in the following equation:
ca = α σ u
(3.35)
where α is an empirical adhesion coefficient that depends mainly upon the following factors: nature
and strength of the soil, type of pile, method of installation, and time effects. Figure 3.9 presents the α values used by the APILE program as suggested by Tomlinson (1980).
For cohesionless soils, Equation (3.32) reduces to:
f s = ca + Kσ v tan(δ ) ≅ Kσ v tan(δ )
(3.36)
because ca is either zero or small compared to K σv tan (δ ) .
The main difficulty in applying the effective stress approach lies in having to predict the normal
effective stress on the pile shaft σ h = K σ v .
Nordlund (1963, 1979) developed a method of calculating skin friction based on field observations
and results of several pile load tests in cohesionless soils. Several pile types were used, including timber,
H, pipe, monotube, etc. The method accounts for pile taper and for differences in pile materials.
Nordlund (1963, 1979) suggests the following equation for calculating the ultimate skin resistance
per unit area:
f s = Kδ C f pd
sin(ω + δ )
cos(ω )
(3.37)
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Figure 3.9 Adhesion factors for driven piles in clay (α method) (after Tomlinson, 1980)
Combine Equations (3.28) with (3.37) to calculate the frictional resistance of the soil around the pile
shaft as follows:
L
Qs = ∫ Kδ C f pd
0
sin(ω + δ )
Cd dz
cos(ω )
(3.38)
which simplifies for non-tapered piles ( ω = 0 ) as follows:
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L
Qs = ∫ Kδ C f pd sin(δ )Cd dz
0
(3.39)
in which
Qs = axial load capacity in skin friction;
Kδ = coefficient of lateral stress at depth z;
Cf = correction factor for Kδ when δ ≠ φ ;
pd = effective overburden pressure;
L = length of pile in contact with soil;
δ = pile-soil friction angle;
ω = angle of pile taper, in degrees, equal to deviation from vertical (less than 90 degrees);
Cd = effective perimeter of pile; and
z = depth coordinate.
To avoid numerical integration, computations are performed for pile segments within soil layers of
the same effective unit weight and friction angle. With such conditions, Equation (3.39) becomes
n
Qs = ∑ Kδ iC fi pdi sin(δ i )Cdi Di
i =1
(3.40)
where
n = number of segments; and
Di = thickness of single segment.
Figure 3.10 through Figure 3.13 provide values of Kδ for various values of φ when δ = φ (after
Nordlund, 1979), while Figure 3.14 includes a correction factor to be applied to Kδ when δ ≠ φ. Figure
3.15 provides the relationship δ/φ for different pile types and sizes.
Figure 3.16 shows the correction factor of field SPT N-values for the influence of effective
overburden pressure, and Figure 3.17 shows a correlation between SPT N values and φ.
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/ft.
/ft.
/ft.
Figure 3.10 Design curves for evaluating Kδ for piles when φ = 25° (after Nordlund,
1979)
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/ft.
/ft.
/ft.
Figure 3.11 Design curves for evaluating Kδ for piles when φ = 30° (after Nordlund,
1979)
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/ft.
/ft.
/ft.
Figure 3.12 Design curves for evaluating Kδ for piles when φ = 35° (after Nordlund,
1979)
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/ft.
/ft.
/ft.
Figure 3.13 Design curves for evaluating Kδ for piles when φ = 40° (after Nordlund,
1979)
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Figure 3.14 Correction factor Cf for Kδ when φ ≠δ (after Nordlund, 1979)
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Figure 3.15 Relationship of δ/φ and pile displacement, V, for various types of piles
(after Nordlund, 1979)
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Figure 3.16 Chart for correction of N-values in sand for influence of effective
overburden pressure(after FHWA, 1993)
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Figure 3.17 Relationship between standard penetration test values and φ or relative
density description (after Peck, Hanson, and Thornburn)
3.5.4
Recommended FHWA Approach for Downdrag
When soil moves downward relative to the pile, it creates a drag force on, and therefore within, the
pile. The downward soil movement creates the potential for downward pile movement. This downward
pile movement is referred to as downdrag. The drag force and/or the downdrag movement may be large or
small, but for practical consideration they always exist primarily due to the contrasting stiffness between
the pile and the surrounding geomaterials as well as due to soil disturbance and soil stress changes caused
by pile installation.
The recent FHWA Publication FHWA-NHI-16-009 titled Design and Construction of Driven Pile
Foundations – Volume 1 (FHWA, 2016) introduced an approximate method for downdrag design (Siegel
el al., 2013). The recommended approach is based on the neutral plane method developed by Fellenius
(1991), and modified by Siegel et al. (2013). These references indicate that the determination of drag
force and its effect on the structural resistance should be considered in the structural strength limitstate analysis. Determination of the downdrag movement, since it contributes to pile-head settlement,
should be part of a geotechnical service limit-state analysis.
Negative shaft resistance occurs as the soil moves downward relative to the pile. The accumulation
of negative shaft resistance with depth produces the drag force on the pile. There exists a depth along the
pile where the sum of the permanent load on the pile plus the negative shaft resistance is equal to the positive
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shaft resistance on the pile plus the toe resistance. This depth is the location of the neutral plane. The
maximum drag force and the maximum axial compression stress in the pile occur at the neutral plane.
Figure 3.18 illustrates the changes that occur as the pile approaches the geotechnical strength limit
state. Note that the location of the neutral plane moves up the pile toward the ground surface. This results
in a reduction in the magnitude of the negative shaft resistance as well as the drag force in the pile. At the
geotechnical strength limit state, geotechnical failure, all shaft resistance is positive as the entire pile is
moving downward relative to the soil during plunging failure.
Figure 3.18 Change in neutral plane, negative shaft resistance, and drag force during
transition to geotechnical strength limit (after Geotechnical Manual from Minnesota
DOT).
Siegel et al. (2013) proposed a downdrag design approach using the neutral plane method within the
LRFD framework. This approach is the FHWA recommended design method for downdrag. It does not
treat the drag force as an additional load that must be supported. Rather, drag force is a settlement
consideration in the geotechnical service limit state and is a structural consideration in the pile structural
limit state. The approach recognizes that drag force develops on all piles, regardless of soil and loading
conditions.
The information necessary to implement the downdrag analysis procedure includes:
• Unfactored structural loads to determine the permanent load.
• Defined subsurface stratigraphy with appropriate parameters for all layers.
• Soil behavior models to characterize load-deformation response, (instrumented load
tests, or t-z and Q-w models).
• Information on fill placement including amount, lateral extent, and timeline.
In the recommended approach, all loads and resistances should be unfactored. The use of factored
loads or factored resistances will distort load-transfer relationships and lead to erroneous predictions of
settlement and drag force.
The step by step procedure for downdrag analysis from the FHWA (2016) recommendation can be
summarized below.
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STEP 1 Assume soil consolidation and ground settlement will occur.
STEP 2 Using an appropriate static analysis method for the pile type and subsurface conditions, determine
the nominal shaft, mobilized toe, and total mobilized resistance as a function of pile penetration
depth.
STEP 3 Select the pile toe elevation for analysis.
STEP 4 Develop the axial load and resistance versus depth diagram at the selected pile toe elevation.
Plot the accumulated shaft resistance versus depth (ΣRs) from Step 2 on the load and resistance
diagram. Program APILE provides this diagram as one of the standard output plots for FHWA
analyses.
Determine the unfactored permanent load on the pile. Add the unfactored permanent load to the
accumulated shaft resistance versus depth. This is indicated by the line in Figure 3.19. This
graph is also calculated (interactively with user) by APILE for FHWA analyses.
Figure 3.19 Axial load and resistance plot of unfactored permanent load plus
cumulative shaft resistance vs depth (after Siegel et al. 2013).
Subtract the sum of the accumulated shaft resistance at a given depth from the nominal resistance
at the selected the pile toe elevation (Rn - ΣRs). Plot this resistance on the load and resistance
diagram. This is denoted by dashed lines in Figure 3.20. The curves a, b, and c, in Figure 3.20
represent the total mobilized resistance based on the shaft resistance plus a mobilized toe
resistance of 100%, 50%, and 0% of the nominal toe resistance, respectively. These curves are
also provided by APILE for FHWA analyses.
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Figure 3.20 Axial load and resistance plot of unfactored permanent load plus
cumulative shaft resistance vs depth (after Siegel et al. 2013).
STEP 5 Determine the location of the neutral plane, the magnitude of the maximum axial compression
load in the pile, and the magnitude of the drag force.
For the example given in Figure 3.20, the neutral plane occurs at depth A, B, or C, depending on
the magnitude of the mobilized toe resistance. If 100% of the toe resistance is mobilized, the
neutral plane occurs at a depth of 30 feet (point A), the maximum axial load in the pile is 80 tons,
and the drag force is 40 tons (80 tons – 40 ton permanent pile head load). Conversely, if no toe
resistance is mobilized, the neutral plane occurs at a depth of 20 feet (point C), the maximum
axial load in the pile is 60 tons, and the drag force is 20 tons (60 tons – 40 ton permanent pile
head load).
STEP 6 Check the structural strength limit state due to loading conditions including drag force.
The factored structural resistance of the pile in the strength limit state in axial compression, Pr,
must exceed the factored permanent load and factored drag force per Equation (3.41).
1.25(Qd) + γp (DF) < Pr
(3.41)
where
Qd = permanent load on pile (kips);
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𝐷𝐷F = drag force on pile (kips);
γp = load factor for drag force in neutral plane analysis;
Pr = factored axial compression resistance of pile (kips).
An AASHTO load factor for drag force, γp, determined by static analysis methods using the
neutral plane procedure is not yet available. Therefore, local calibration is required for
implementation of this approach. The Minnesota DOT has adopted a load factor of 1.1 for drag
force with the neutral plane downdrag procedure while a local calibration effort is in progress.
This load factor was based on an equivalent minimum factor of safety 1.5 for material strength
evaluation. This step is not implemented in APILE but can be done by the user outside the
program using provided results.
STEP 7 Calculate the settlement due to downdrag with respect to the neutral plane.
The factored structural resistance of the pile in the strength limit state in axial compression, Pr,
must exceed the factored permanent load and factored drag force per Equation (3.41).
Calculate the thickness of compressible soil, tsoil, beneath the neutral plane.
tsoil = (Dil) - Dnp
where:
tsoil = thickness of compressible soil beneath neutral plane (feet).
𝐷𝐷il = depth from reference to top of incompressible layer (feet).
Dnp = depth from reference to neutral plane (feet).
Determine settlement due to downdrag from stress increase.
Sdd = tsoil (γp ∆σ /Es )
where:
Sdd = settlement due to downdrag (feet).
tsoil = thickness of compressible soil beneath neutral plane (feet).
γp = load factor for downdrag.
∆σ = increase in vertical stress.
Es = elastic modulus of in-situ soil.
It should be noted that effective stress changes such as approach fill placement after pile driving
will alter the plot of the permanent load plus cumulative shaft resistance. This will in turn alter
the location of the neutral plane, the maximum compression force in the pile, the magnitude of
the drag force, and calculated settlement due to downdrag. Similarly, changes in the permanent
load to be applied to the pile or changes in the pile toe elevation will also alter the analysis results.
This step is not implemented in APILE but can be done by the user outside the program using
provided results.
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3.6
Norwegian Geotechnical Institute (NGI) Method
3.6.1
Introduction
The computation of axial capacity for offshore piles has traditionally been based on the API method.
After results of tests of high quality from driven piles in dense sand under axial loading became available
to the participants in the Euripides project, new methods, which directly correlated with Cone Penetration
Test (CPT) cone resistance, have been developed. Over the last 10 years, the Norwegian Geotechnical
Institute (NGI) built a database with well-documented results from tests of driven piles in sand. Their
studies on comparison of results from various methods of soil investigation and on results of field tests of
piles under axial loading has led to a new method of computation, as presented below.
3.6.2
Pile in Cohesionless Soil
3.6.2.1 Side Friction
To compute the capacity of a driven pile in sand under axial load (Clausen et al, 2005), the following
soil parameters are needed as a function of depth for each of the sand layers:
1.
Unit weight.
2.
Porewater pressure.
3.
Relative density.
In contrast to clay, undisturbed samples of sand cannot be obtained except by use of extraordinary
measures, such as freezing. Therefore, estimates of the relative density must be based upon results from
some type of in-situ test. Example of such tests are SPT (standard penetration test), CPT (cone penetrometer
test), PMT (pressuremeter test) or observed pile driving resistance. For most offshore projects, CPTs are
routinely carried out as a part of a normal program of site investigation. For some of the older pile tests in
NGI’s database, the site investigations only include SPT results. Because the computation method proposed
in the following is linked to CPT results, one needs a conversion between SPTs and CPTs. The approach
used to obtain this conversion was to:
1.
Calibrate the NGI-99 method against results from the high-quality pile tests with CPT results.
2.
Find the SPT to CPT conversion that gives the best agreement between the observed capacity, and
the capacity calculated by the NGI-99 method for the pile tests with SPTs only.
Carrying out Step 2 above resulted in the following simple expressions:
N corr = N meas (0.77)(log10 (1915 kPa / σ 'vo ))
(3.42)
qc = 2.8( N corr )(σ atm )
(3.43)
where
Ncorr = is the corrected SPT N-value, Peck et al (1974);
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Nmeas = is the measured SPT N-value;
σ’vo = is the vertical effective stress;
σatm = is the atmospheric reference pressure (100 kPa); and
qc = is the computed cone-tip resistance.
The NGI calculation method uses the following relationship between the CPT tip resistance qc and
the sand relative density Dr:
Dr = 0.4ln{qc / [22(σ 'vo σ atm )0.5 ]}
(3.44)
It should be noted that for very dense sands at a shallow depth, the above equation may result in Dr
> 1.0. Such a result is not considered to be unrealistic, and should be used in the computations (Clausen et
al, 2005).
The local unit skin friction on a driven pile in sand, τskin is given by:
τ skin ( Z ) = ( Z / Z tip )(σ atm )( FDr )( Fsig )( Ftip )( Fload )( Fmat )
(3.45)
τ skin ( Z ) > 0.1(σ 'vo )
(3.46)
where
Z = is the depth below the ground surface;
Ztip = is the depth of tip of pile;
σ’vo = is the vertical effective stress;
σatm = is the atmospheric reference pressure (100 kPa);
FDr 2.1( Dr − 0.1)0.17 ;
=
Fsig = (σ 'vo / σ atm )0.25
;
Ftip = 1.0 for a pile driven open-ended, Ftip = 1.6 for a close-ended pile;
Fload = 1.0 for tension, Fload = 1.3 for compression; and
Fmat = 1.0 for steel, Fmat = 1.2 for concrete;
The relative density Dr to be used for FDr is the value computed at the depth Z. It should be noted
that the ratio Z/Ztip leads to a “friction fatigue” effect, i.e. as the pile is driven deeper the local unit skin
friction at depth Z goes down.
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3.6.2.2 End Bearing
The end bearing (tip resistance) acting against a pile driven closed-ended is given by:
σ tip = 0.8(qc ) / (1 + Dr2 )
(3.47)
The end bearing acting against a pile driven open-ended is taken as the smallest of the values of
coring tip resistance and the plugged tip resistance. The coring tip resistance is computed by assuming a
stress of qc acting against the pile wall, and an internal pile/plug unit skin friction taken as 3 times the
external skin friction. The higher value of inside friction is caused by arching near the pile tip. The plugged
tip resistance of an open-ended pile is computed as:
Coring Tip Resistance
σ tip = (qc )
(3.48)
Plugged Tip Resistance
σ tip = 0.7 (qc ) / (1 + 3Dr2 )
(3.49)
3.6.3
Pile in Cohesive Soil
3.6.3.1 Side Friction
The design equations for ultimate unit side friction according to the NGI method are given below
(Karlsrud et al, 2005).
For ψ < 0.25:
NC
)( suref ) (α NC )(ψ NC )(σ 'vo )
τ skin (α
=
=
(3.50)
τ skin = ( β NC )(σ 'vo )
(3.51)
where
ψ = is the stress ratio = ( sudss ) / (σ 'vo ) ;
suref = undrained referenced shear strength, is the shear strength from the UU test;
sudss = is the shear strength from the DSS test;
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α = (τ skin ) / ( suref ) (see Figure 3.21);
β NC = 0.08(lp − 10%)0.3 ;
lp = plastic index; and
σ 'vo is the vertical effective stress.
For 0.25 < ψ < 1.0:
τ skin = (α )( suref )( Ftip )
(3.52)
If
τ skin < ( β min )(σ 'vo ) then use τ skin = ( β min )(σ 'vo ) . Where β min = 0.06(lp − 12%)0.33
The value of α can be computed by linear interpolation between ψ = ψNC and ψ = 1.0 in Figure
3.21. The recommended Ftip in clay is dependent on whether the pile tip is closed-ended or open-ended.
The Ftip factor is taken as 1.0 for a pile driven open-ended. The following equation may be used to compute
Ftip for a closed-ended pile.
Ftip ,closed
= 0.8 + 0.2 (ψ 0.5 )
1.0 < Ftip ,closed < 1.25
(3.53)
For ψ > 1.0:
τ skin = (α NC )( suref )( Ftip )
α = 0.5ψ −0.3
(3.54)
3.6.3.2 End Bearing
The design equation for ultimate end bearing in clay, according to the NGI method, for closed-ended
or plugged cases is taken as 9 times the undrained reference shear strength.
σ tip = 9 ( suref )
(3.55)
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Figure 3.21 α values recommended by NGI method
3.7
Imperial College (ICP/MTD) Method
3.7.1
Introduction
Jardine and Chow (1996) of Imperial College, U.K., developed an empirical pile design method,
which is commonly referred as the MTD (Marine Technology Directorate) method (1996). Offshore
engineers recently also refer to the MTD method as ICP (Imperial College Pile) method because the Marine
Technology Directorate in U.K. no longer operates (Jardine et al 2005).
The major feature of this method is that the ultimate unit friction and pile end bearing are directly
correlated with Cone Penetration Test (CPT) cone resistance. Another noticeable feature is that both unit
friction and end bearing are highly dependent on pile geometry.
3.7.2
Pile in Cohesionless Soil
3.7.2.1 Side Friction
The design equations for ultimate unit side friction according to the ICP/MTD method are expressed
in Table 3.8.
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Note: Above recommendations apply to (i) silica sands, (ii) piles with circular cross-sections (iii) capacities
available in ‘first-time’ slow maintained loading tests conducted around ten days after driving.
Table 3.8 Procedures for side friction capacity calculations in sand (MTD Method,
from Jardine et al 2005)
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3.7.2.2 End Bearing
The design equations for ultimate unit side friction in cohesionless soil according to the MTD method
are expressed in Table 3.9.
Table 3.9 Procedures for end bearing calculations in sand (MTD Method, from Jardine
et al 2005)
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3.7.3
Pile in Cohesive Soil
3.7.3.1 Side Friction
The design equations for ultimate unit side friction in cohesive according to the MTD method are
expressed in Table 3.9.
Table 3.10 Procedures for long-term side friction capacity calculations in clay (MTD
Method, from Jardine et al 2005)
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CHAPTER 3 – Methods for Pile Capacity – 3-47
Yield Stress Ratio (YSR) shown in Table 3.9 is defined as the vertical effective yield stress (σ’vy) to
the vertical in situ effective stress (σ’vo). OCR (over-consolidation ratio) is defined as the vertical maximum
pre-consolidation effective stress (σ’vc) to the vertical in situ effective stress (σ’vo). YSR is also named as
apparent OCR in some literature, but generally YSR is greater than OCR.
3.7.3.2 End Bearing
The design equations for ultimate unit side friction in cohesive soil according to the MTD method
are expressed in Table 3.11.
Table 3.11 Procedures for long-term end bearing calculations in clay (MTD Method,
from Jardine et al 2005)
The alternative methods outlined in Table 3.11 represent provisional best estimates and the tentative
plugging criterion given in Step J1 is wholly empirical. Further research is required to explore the basic
mechanisms of internal shaft friction development and plugging. However, the remaining uncertainties are
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unlikely to have a major impact on practical design and the lower limit recommendation given in Step J3
should offer safe estimates for Qb.
3.8
Fugro Method
3.8.1
Introduction
Numerous recent comparison of pile load test results and axial pile capacities predicted according to
the recommendations of API RP 2A for piles in sand have proven that API RP 2A method may tend to be
conservative for relatively short piles in very dense sand, while it may tend to be un-conservative for relative
long piles driven into loose sands. Various design methods have been developed during recent years, which
suggest that considerably more accurate predictions of capacities can be made through direct correlation of
pile friction and end bearing with the results of in-situ cone penetration test (CPTs). CPTs have been
routinely performed as part of offshore soil investigations during the last decades, and have been found to
be repeatable and to give a continuous soil profile with an indication for soil type, behavior and strength.
Fugro was retained by American Petroleum Institute to conduct a study on “Axial Pile Capacity
Design Method for Offshore Driven Piles in Sand” in 2004 (see Fugro Report No. P1003, submitted to the
American Petroleum Institute). The objective of this study is to provide the API Geotechnical Resource
Group (RG7) with data and information needed to improve pile design criteria and to propose an improved
design method for axially loaded, open-ended, offshore driven pipe piles in sands. Fugro predicted the pile
capacity at locations of the qualified pile load tests with the current API and ICP/MTD (Jardine and Chow,
1996) design criteria. Comparison of API and ICP/MTD design criteria with database test results enabled
Fugro to proposed a new design method for prediction of axial capacity of driven pipe piles in sand.
3.8.2
Pile in Cohesionless Soil
3.8.2.1 Side Friction
The design equations for ultimate unit side friction in sand according to the Fugro method use the
similar format as the ICP/MTD method, i.e.:
In Tension:
f t / qc = a (σ 'v / pa )b (h / R*)c if (h / R*) > N
(3.56)
In Compression:
f c / qc = a (σ 'v / pa )b (h / R*)c if (h / R*) > N
(3.57)
where
ft = unit skin friction in tension at depth z;
fc = unit skin friction in compression at depth z;
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σ’v = effective vertical soil stress at depth z;
pa = atmospheric reference pressure (100 kPa);
h = distance from depth z to pile tip;
R* = effective pile radius = ( R)( DR 0.5 ) ;
DR = 1 − ( Di / Do ) 2 = displacement ratio;
Di = inner pile diameter at pile tip;
Do = D = outer pile diameter at pile tip;
R = pile outer radius = 0.5 D ; and
a, b, c and n = empirical constants.
The above equations have similar format as the design equations recommended by ICP/MTD method
with the following two exceptions:
1.
The additional term representing increase in radial effective stress during shearing in MTD method
was omitted.
2.
The term tan(δcv) representing the (pre-installation) sand-steel interface friction angle was also
neglected.
First, n was assumed to equal to 4. The empirical constants, a, b, and c were determined through
statistical analyses of test piles in the data base until a good fit between predicted and observed friction
capacity was obtained.
This resulted in the following formulae:
In Tension:
f t / qc = 0.045 (σ 'v / pa )0.15 (h / R*) −0.85 if (h / R*) ≥ 4
(3.58)
In Compression:
f c / qc = 0.08 (σ 'v / pa )0.05 (h / R*) −0.90 if (h / R*) ≥ N
(3.59)
f c / qc = 0.08 (σ 'v / pa )0.05 (h / R*) −0.90 (h / 4 R) if (h / R*) < N
(3.60)
The above design equations for unit friction result for typical pipe piles in average unit friction in
tension being in the order of 70 to 80 percent of the average unit friction in compression.
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3.8.2.2 End Bearing
For practical design purpose Fugro developed a formula, which calculates the end bearing at 10%
pile tip displacement and not the whole load-displacement curve. The following equation for end bearing
in sand was considered:
qeb / pa = a (qc / pa )b (σ 'v / pa )c ( Do ) d ( DR)e
(3.61)
where
qeb = unit end bearing at depth z;
qc = average cone resistance from 1.5 D above and 1.5 D below pile tip;
σ’v = effective vertical soil stress at depth z;
pa = atmospheric reference pressure (100 kPa);
Do = D = outer pile diameter at pile tip;
R = pile outer radius ( = 0.5 D); and
a, b, c, d and e = empirical constants.
Regression analyses (linear and logarithmic) were performed on the end bearing data for open and
closed-ended piles and constants c and d were assigned to be zero. The following simple relation for unit
end bearing is recommended:
qeb / pa = 8.5(qc / pa )0.5 ( DR)0.25
(3.62)
It is noted that the above equation suggests that the ultimate end bearing is proportional to the square
root of cone resistance and not linear to cone resistance like in most CPT-based design equations. One
qualitative explanation might be that the ultimate end bearing as defined by Fugro is possibly more a
measure of soil stiffness at the pile tip than of the ultimate strength of soil.
3.8.3
Pile in Cohesive Soil
The design equations for ultimate unit side friction in clay is not provided by Fugro method and the
same equations recommended by the ICP/MTD method are used in computation by APILE software.
3.9
University of Western Australia (UWA) Method
3.9.1
Introduction
Lehane, Schneider, and Xu from the University of Western Australia (UWA), Perth, at the request
of the American Petroleum Institute (API) piling sub-committee, conducted a review of methods for the
assessment of the axial capacity of driven offshore piles in siliceous sand in 2005. They developed an
extended database of static load tests and evaluated the existing API recommendations (API-2000) and
three Cone Penetration Test (CPT) based methods namely: Fugro-04, MTD-05 (ICP-05), and NGI-04. A
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new design method, referred to as UWA-05, emerged following the evaluation exercise and is the described
in the paper (Lehane et al 2005).
3.9.2
Pile in Cohesionless Soil
3.9.2.1 Side Friction
The design equations for ultimate unit side friction in sand according to the NGI method use a similar
format to the ICP/MTD method, i.e.:
=
τ f ( f / f c ) (σ 'rc + ∆ σ 'rd )b tan(δ cv )
(3.63)
where
σ 'rc = 0.03 qc ( Ars *)0.3[max(h D , 2)]−0.5 ;
2
Ars *= 1 − IFR ( Di2 D ) ;
IFRmean = min[1, ( Di 1.5)0.2 ] in which Di is in meter;
∆ σ 'rd = 4Go ∆y D
in which
τf = unit skin friction at depth z;
δcv = constant volume interface friction angle;
σ’rf = radial effective stress at failure;
∆σ’rd = change in radial stress due to loading stress path (dilation);
f / fc = 1 for compression and = 0.75 for tension;
∆ y = dilation (assumed for analyses = 0.02 mm, same as for ICP/MTD);
Go =
qc 185 − (qcN ) −0.75 with q = (q P ) / (σ ' P )0.5
cN
c
ref
vo
ref
Di = inner pile diameter at pile tip;
D = Do = outer pile diameter at pile tip;
Pref = reference pressure (100 kPa); and
σ’vo = in situ vertical effective stress.
For full scale offshore piles, as IFR = 1 and the dilation term (∆σ’rd) can be ignored, the UWA-05
formulations simplify to:
τ f = ( f / f c ) 0.03 qc ( Ars *)0.3[max (h D , 2)]−0.5 tan(δ cv )
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(3.64)
3.9.2.2 End Bearing
Similar to Fugro’s proposal, the unit end bearing capacity (qb0.1) is defined as the tip resistance at
10% pile tip displacement. For a closed-ended pile, with a diameter D, the total base resistance is given as:
Qb = (qb 0.1 )(π / 4) D 2
(3.65)
where
qb 0.1 = 0.6 (qc ,avg )
;
Qb = total end bearing;
Qc,avg = average cone resistance from 1.5 D above and 1.5 D below pile tip; and
D = outer pile diameter at pile tip.
For open-ended pipe pile, a relatively consistent relationship between qb0.1 for a pipe pile and the
CPT qc value becomes apparent when the effects of sand displacement close to the tip during pile driving
are account for. The installation effect is best described by the incremental filling ratio (IFR) measured
over the final stages of installation and is referred as the final filling ratio (FFR). As the FFR approaches
zero, qb0.1approaches that of a closed-ended pile with the same outer diameter.
The displacement induced in the sand in the vicinity of the base is most conveniently expressed in
the terms of the effective area ratio Ard*. The ratio (Ard*) depends on the pile’s (D / t) ratio (outer diameter
to wall thickness) and FFR value, and varies from unity for a pile installed in a fully plugged mode to about
0.08 for a pipe pile installed in a coring mode with (D / t) of 50.
Qb = (qb 0.1 )(π / 4) D 2
=
qb 0.1 (0.15 + 0.45 Ard *) (qc ,avg )
Ard *= 1 − FFR ( Di2 D 2 )
FFR = min[1, ( Di 1.5) 2 ] in which Di is in meter;
(3.66)
Where
Qb = total end bearing;
Qc,avg = average cone resistance from 1.5 D above and 1.5 D below pile tip;
Di = inner pile diameter at pile tip; and
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D = outer pile diameter at pile tip.
3.9.3
Pile in Cohesive Soil
The design equations for ultimate unit side friction in clay is not provided by UWA method and the
same equations recommended by the ICP/MTD method are used in computation by APILE software.
3.10 Punch Through Commentary on End Bearing
API-RP-2A-WSD (2014) has some recommendations for piles tipped in cohesionless layers with
adjacent layers of lower strength. Table 3.2 can be used if the pile achieves a penetration of two to three
diameters or more into the cohesionless layer and if the pile tip is at least three diameters above the bottom
of the layer to prevent punch through. Where these pile tip penetrations are not achieved, some modification
in the tip resistance of Table 3.2 may be necessary. Where adjacent layers are of comparable strength to
the layer of interest, the proximity of the pile tip to the layer interface is not a concern.
From API Pile Foundation Design Commentary (Annex C), the use of cone penetration data (qc)
averaged between 1.5D above to 1.5D below the pile tip level should generally be satisfactory in presence
of weaker clay layers near the pile tip, provided that qc does not vary significantly. It is recommended to
reduce the end bearing component if the pile tip is within a zone up to +/- 3D from weak layers. If averaging
of qc data is applied to this +/- 3D zone, the combined effects can be unduly cautious and such results
should be critically reviewed.
To prevent punching into layered weak soils, pile tip capacity based on the averaged tip resistance
between 1.5D above and 1.5D below the tip is adopted by default in APILE for every computation method
(not just API). However, APILE also provides to expert users the control options to eliminate this averaging
or to increase the averaging from the default of +/-1.5D to the larger +/-3D averaging lengths.
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CHAPTER 4. References for Load Transfer
t-z and Q-w Curves
CHAPTER 4 – Load-Transfer (t-z and Q-w) Curves – 4-2
4.1
Mechanics of Load Transfer
While the mechanics of load transfer from a deep foundation (pile) to the supporting soil is not well
understood and is the subject of many investigations, some general aspects of the mechanics are known and
are presented here to provide a useful tool for analysis.
A typical load-settlement curve for a deep foundation is shown in Figure 4.1. The vertical dashed
line in the figure is the load which causes plunging; that is, the load which will cause continued settlement
of the pile with no further increases in load. If the load is increased to some value Qp at point P, the gross
settlement is represented by the horizontal dotted line to point P. If the load is then released, there is some
rebound as indicated by the light solid line, with the net settlement being defined as the settlement at zero
load after unloading. The manner in which the load is distributed from the pile to the supporting soil is of
interest. A typical curve of the distribution of load along the length of an axially loaded deep foundation is
shown in Figure 4.2. The slope of the curve indicates the rate of load transfer from the foundation to the
soil.
Figure 4.1 Typical load-settlement curve
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Figure 4.2 Typical distribution of load along the length of an axially-loaded pile
Some insight into the problem of the mechanics of load transfer from a deep foundation may be
obtained by considering the idealized load-distribution and load-settlement curves in Fig. 4.3. Figure 4.3a
shows the results of loading a pile which rests on an unyielding surface in which all the load is transferred
by tip resistance and none by side resistance. The load-distribution curves for loads of QT1 and QT2 show
a constant load in the pile regardless of depth. The load-settlement curve for such a case is also shown.
The settlement, or movement at the top of the pile, can be obtained by computing the compression in the
pile from basic principles of mechanics. The load-settlement curve will be a straight line, as shown, if the
effective stiffness of the pile is constant with depth.
Figure 4.3b shows a similar pile but in this instance its tip is assumed to be resting on an elastic
surface which yields linearly with the applied load. The load-distribution curves remain unchanged, as
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shown. However, the settlement of the top of the pile is now made up of two quantities: (1) compression
in the pile due to the applied load and (2) the settlement of the pile tip.
Figure 4.3 Idealized load-distributed and load-settlement curves for an axially-loaded
pile
Figure 4.3c shows the case where the soil produces a uniform shaft resistance with no tip resistance.
The load-distribution curves are triangular, as indicated. The load versus settlement is again linear and
made up of the compression in the pile due to the triangular distribution of load and the settlement of the
tip of the pile.
While of interest, none of these idealized models represents the true behavior of the axially-loaded
deep foundation. A real pile has some combination of all the factors plus non-uniform and nonlinear
behavior. A more realistic model is shown in Figure 4.4. Figure 4.4a shows the free body of a pile in
equilibrium where the applied load QT is balanced by a tip load QB plus side loads R. A mechanism is
shown in Figure 4.4b that can be used to illustrate the deformations in the pile. The pile has been replaced
by an elastic spring. Representing the soil is a set of nonlinear springs spaced along the pile, with one
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CHAPTER 4 – Load-Transfer (t-z and Q-w) Curves – 4-5
spring depicting the soil behavior beneath the pile tip. The ordinate t of the curves is load transfer and the
abscissa z is the shaft movement (Figure 4.4c).
No load is transferred from shaft to soil unless there is a downward movement of the shaft. This
downward movement is dependent on the applied load, on the position along the pile, on the stress-strain
characteristics of the pile material, and on the load transfer-movement curves along the pile shaft and at the
pile tip. To solve the problem of the distribution of load along the pile for a given applied load and the
determination of downward movement at any point along the pile, a nonlinear differential equation must
be solved.
Figure 4.4 Mechanical model of an axially-loaded pile
The differential equation can be obtained by considering an element from the shaft as shown in
Figure 4.5. The unit strain is:
dwz Qz
=
dz
EA
(4.1)
where
wz = movement of the pile at point z;
Qz = load in the pile at point z;
E = Modulus of elasticity of the pile material; and
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A = cross-sectional area of the pile.
Figure 4.5 Element from an axially-loaded pile
From Equation (4.1):
Qz = EA
dwz
dz
(4.2)
Differentiating Eq. (4.2) with respect to z,
dQz
d 2 wz
= ( EA) z
dz
dz 2
(4.3)
If the load transfer from the pile to the soil at point z, in force per unit of area, is defined as fz, then
dQz = f z C dz
(4.4)
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where, C is the circumference of the pile at point z, and
dQz
= fz C
dz
(4.5)
Solving Equations (4.3) and (4.5) simultaneously,
( EA) z
d 2 wz
= fz C
dz 2
(4.6)
The load transfer can be expressed as a function of the pile movement wz, as follows:
f z = β z wz
(4.7)
where, βz a function which depends on depth z and pile movement wz.
Equation (4.7) is substituted into Eq. (4.6) to obtain the desired differential equation:
d 2 wz
− η β z wz =
0
dz 2
(4.8)
where
η=
C
EA
(4.9)
If η and β are constants, a closed-form solution can be obtained for Eq. (4.8). However, since β
cannot normally be a constant, the closed-form solution is of little importance and will not be presented.
Referring to Figure 4.6, a convenient solution to the nonlinear differential equation, Equation (4.8),
is obtained by writing the equation in finite-difference form and using numerical techniques. Equation (4.8)
becomes:
 ∆wz 
 ∆wz 

 −

 ∆z m +1  ∆z m −1
= η β m wm
2h
(4.10)
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Equation (4.1) can also be written in difference form as
Qi
 ∆wz 

 =
 ∆z i ( EA)i
(4.11)
Substituting the expressions from Eqs. (4.11) and (4.9) into Eq. (4.10), the following expression is
obtained assuming a constant EA:
Qm +1 − Qm −1 =
2 h C β m wm
(4.12)
Equations (4.11) and (4.12) are elementary, of course, but are sufficient to give a solution to the
problem of the axially loaded pile.
Figure 4.6 Segment of a load-distribution curve along an axially-loaded pile
Assuming that curves are available showing load transfer as a function of pile movement, a suggested
procedure for computing the load-settlement curve and a family of load-distribution curves is as follows:
1.
Assume a slight downward movement of the pile tip, refer to the corresponding load-transfer curve,
and obtain the resulting load on the pile tip.
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2.
Select the number of segments into which the pile is to be divided (some experimenting will indicate
the number required for acceptable accuracy) and consider the behavior of the bottom segment.
3.
Assume a load at the top of the bottom segment and compute the elastic compression in that
segment, using Eq. (4.11) written for that location. Employ the appropriate value of pile stiffness
under axial load (EA) for the segment.
4.
Use the assumed tip movement and the results of the computation in Step 3 to compute the
downward movement at the mid-height of the bottom segment.
5.
Refer to the appropriate curve showing load transfer versus movement and obtain the resulting unit
load transfer (bmwm in Eq. (4.12)).
6.
Use the Eq. (4.12) and compute the load at the top of the bottom segment.
7.
Repeat Steps 3 through 6 until the difference between successive computation of movement at that
segment is less than the tolerance that was selected.
8.
Compute, in a like manner, pile loads and movements for the other segments until the top of the pile
is reached. This will yield one point on the load-settlement curve and one of the family of loaddistribution curves.
9.
Select other assumed tip movements and repeat computations to produce the entire load-settlement
curve and the whole family of load-distribution curves.
The axial stiffness EA in a pile segment is assumed to be constant. However, EA can be different
from segment to segment such as for composite piles or tapered piles. The computation scheme described
in this document allows a different EA for each segment in computation. Because the convergence is
checked on the basis of each individual segment, there is no convergence problem during computation with
this scheme.
This outlined procedure has been used successfully as described in technical literature, and
limitations on use of the method involve the accuracy with which load-transfer curves can be predicted.
Thus, one of the principal aims of further research is the development of additional information on loadtransfer curves for deep foundations.
4.2
Experimental Techniques for Obtaining Load-Transfer Curves
With the completion of a field load test on an instrumented pile, curves such as shown in Figure 4.7a
and Figure 4.7b should be available. Figure 4.7a shows a load-settlement curve for the top of the pile. This
curve may be obtained by measuring the load with a load cell and the downward movement of the top of
the shaft with dial gages. Figure 4.7b shows a set of curves which gives load in the pile at various points
along its length for each of the applied loads. These data are obtained from instrumentation placed on or
inside the pile. Figure 4.7a and Figure 4.7b indicate that four loads were applied to the pile; however, in
the general case, several more loads would have been applied.
From the data in Figure 4.7a and Figure 4.7b, it is desired to produce a set of load-transfer curves
such as are shown in Figure 4.7d. Such curves can be produced for any desired depth. Figure 4.7c illustrates
the procedure for obtaining a point on one of the curves.
In this instance, the procedure is illustrated for obtaining load transfer at a depth z below the ground
surface. For a particular load-distribution curve, corresponding to a particular load Qz, the slope of the
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load-distribution curve is obtained at point z. In Figure 4.7c this slope is indicated as the quantity ∆Qz ∆ z .
To obtain the load transfer sz, the quantity is then divided by the pile circumference at the point z. Thus,
the load transfer t will have the units of force per square of length.
The downward movement of the pile corresponding to the computed load transfer may be obtained
as follows: (1) the settlement corresponding to the particular load in question is obtained from the curve
Figure 4.7a; (2) the shortening of the pile is computed by dividing the cross-hatched area, shown in Figure
4.7b, by the pile cross-sectional area times an effective modulus of elasticity; and (3) the downward
movement of the pile at point z is then computed by subtracting the shortening of the pile from the observed
settlement.
The above procedure enables one point on one load-transfer curve to be obtained. Other points can
be obtained by using the other load-distribution curves. In the same manner load-transfer curves can be
developed at the desired depths (see Figure 4.7d).
As can be readily understood, accurate load-settlement and load-distribution data are required.
Figure 4.7 Development of load transfer versus movement curves
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4.3
Load-Transfer Curves
The mechanical model presented in Figure 4.4 for obtaining the response of a single pile to axial
loading treats the load-transfer curves from the pile to soils with a set of nonlinear springs. The method
was first used by Seed and Reese (1957); other studies are reported by Coyle and Reese (1966), Coyle and
Sulaiman (1967), and Kraft et al. (1981). The method is characterized as the t-z method. In the t-z method,
the pile has been replaced by an elastic spring and the soil is replaced by a set of nonlinear mechanisms
along the pile and at the pile tip.
The acquisition of load-transfer curves from a load test requires that the pile be instrumented
internally for the measurement of axial load with depth. The number of such experiments is relatively small
and in some cases the data are barely adequate; therefore, the amount of information that can be used to
develop analytical expressions is limited.
The criteria of load-transfer curves used for the APILE program to calculate the relationship between
load and settlement are presented in the following sections.
4.4
Side-Resistance Curves in Cohesive Soil
Coyle and Reese (1966) examined the results from three, instrumented field tests and the results from
rod tests in the laboratory and developed a recommendation for a load-transfer curve. The curve was tested
by using results of full-scale experiments with un-instrumented piles. The comparisons of computed loadsettlement curves with those from experiments showed agreements that were excellent to fair. Table 4.1
presents the fundamental curve developed by Coyle and Reese.
An examination of Table 4.1 shows that the movement to develop full load transfer is quite small.
Furthermore, the curve is independent of soil properties and pile diameter. The maximum load transfer
calculated, based on the methods presented in earlier chapters, will be selected by the user for computing
the load-transfer curves.
Ratio of Load Transfer to
Movement (in.)
Maximum Load Transfer
0
0
0.18
0.01
0.38
0.02
0.79
0.04
0.97
0.06
1.00
0.08
1.00*
> 0.08
Table 4.1 Side resistance in cohesive soil
4.5
End-Bearing Curves in Cohesive Soil
The criteria of load-transfer curves used for the APILE program to calculate the relationship between
load and settlement are presented in the following sections. The work of Skempton (1951) was employed
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and a method was developed for predicting the load in end bearing of a pile in clay as a function of the
movement of the tip of the pile. The laboratory stress-strain curve for the clay at the base of the pile was
obtained by testing, or was estimated from values given by Skempton to laboratory strain ε50, at one-half
of the ultimate compressive strength of the clay. Skempton reported that ε50 ranged from 0.005 to 0.02.
Skempton further used the theory of elasticity to develop approximate equations for the settlement of a
footing (base of a pile) by use of laboratory stress-strain curves. His equations are as follows:
σ f 

 2 
qb = N c 
(4.13)
wb
B
= 2 ε 50
(4.14)
where
qb = failure stress in bearing at base of footing;
σf = failure compressive stress in the laboratory unconfined-compression or quick-triaxial test;
Nc = bearing capacity factor, (Skempton recommended 9.0);
B = diameter of footing or equivalent length of a side for a square or rectangular shape;
ε50 = strain measured from unconfined-compression or quick-triaxial test; and
wb = settlement of footing.
Stress-strain curves from a number of laboratory tests have been plotted on log paper and have been
found to plot approximately as a straight line. Many of the slopes have been approximately 0.5. Therefore,
in the absence of a laboratory stress-strain curve a parabola can be used to yield a stress-strain curve up to
the failure stress. The value of ε50 can be selected in consideration of whether the clay is brittle or plastic.
As an example of the use of the Skempton relationships, the following data were selected.
B = 30 in. (Atip = 4.91 ft2)
c = 780 lb/ft2
Select ε50 = 0.01
The basic equation for load versus settlement at the tip of the pile is as follows:
Q = Kb ( wb )
n
(4.15)
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where
Kb = a fitting factor;
If n is selected as 0.5, Kb can be evaluated as follows:
Qb
Qb
2
2
= [(9)(780)(4.91)] / 2.0
= 17, 230 lbs
wb50 = 2 b ε b50
=
= 0.60in
wb50 (2)(30)(0.01)
Substituting,
17, 230 = Kb ( 0.60 )
Kb = 22, 240
0.5
Then, the curve in Table 4.2 can be derived using Eq. (4.15). In this example, it is assumed that the
load will not drop as the tip of the pile penetrates the clay.
Tip Load, Qb
Tip Movement, wb
0
0
2200
0.01
4450
0.04
7000
0.10
12,100
0.30
17,230
0.60
24,500
1.20
34,460
2.40
34,460
10.00
Table 4.2 End bearing in cohesive soil (Skempton)
4.6
Side-Resistance Curves in Cohesionless Soil
Mosher (1984) studied the problem of the transfer of load in skin friction (side resistance) of axiallyloaded piles in sand. He recommended the use of the following equation and table (Table 4.3) for obtaining
t-z (load transfer curves) in granular soils.
f =
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w
1
1
+
w
Es f max
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CHAPTER 4 – Load-Transfer (t-z and Q-w) Curves – 4-14
(4.16)
where
f = unit load transfer, lb/ft2;
w = pile movement, in;
fmax = maximum unit load transfer, lbs/ft2; and
Es = soil modulus, lb/ft2/in.
Prior to making use of Eq. (4.16), the mixed dimensions should be noted.
Relative Density
Es, lbs/ft2/in.
φ, degrees
Loose
28-31
6,000-10,000
Medium
32-34
10,000-14,000
Dense
35-38
14,000-18,000
Table 4.3 End bearing in cohesive soil (Mosher)
4.7
End-Bearing Curves in Cohesionless Soil
Vijayvergiya and Mosher (1984) studied available literature, performed some careful experiments,
and proposed an equation for computing the load versus tip settlement for piles in sand. Vijayvergiya (1977)
gives the displacement function as:
1
 z3
q =   qmax
 zc 
(4.17)
where the maximum bearing capacity, qmax, is obtained by:
qmax = σ v N q
(4.18)
where σv is the effective vertical stress which is equal to the overburden pressure. The greatest
limitation of use of the maximum bearing capacity is its dependence on overburden pressure.
Vijayvergiya (1977) linked the critical displacement, zc to the width of the pile tip.
For
displacements, z, greater than the critical displacement, zc, the tip resistance is taken as being constant.
This is contrary to early statements in his paper, that for sands the tip resistance continued to increase with
displacement.
Mosher (1984) proposed another approach for defining the maximum tip resistance. The soil beneath
the tip is assumed to behave similarly to an elastic-plastic material with strain hardening, as shown in Figure
4.8. The yield point is then defined as the point of transition between elastic and plastic strain hardening
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CHAPTER 4 – Load-Transfer (t-z and Q-w) Curves – 4-15
behavior. The yield capacity of a pile has been assumed to be reached when the tip displacement is 0.25
inches. Substituting 0.25 inch in Vijayvergiya’s expression for displacement yields
13
q = ( 4 z ) qmax
(4.19)
This displacement function showed better agreement with field data. It was further altered to reflect
the field data for different densities:
Loose:
12
q = (4 z)
qmax
(4.20)
Medium:
13
q = ( 4 z ) qmax
(4.21)
Medium-Dense:
14
q = (4 z)
qmax
(4.22)
where the maximum yield tip resistance, qmax, is obtained from the method described in Chapter 3.
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Figure 4.8 Tip resistance vs. displacement relationship
4.8
Load-Transfer Curves Recommended by API RP 2A-WSD (2014)
Various empirical and theoretical methods are available for developing curves for axial load transfer
an pile displacement, (t-z) curves. Theoretical curves described by Kraft et al. (1981) may be constructed.
Empirical t-z curves based on the results of model and full-scale pile load tests may follow the procedures
in clay soils described by Coyle and Reese (1966) or granular soils by Coyle, H.M. and Suliaman, I. H.
“Skin Friction for Steel Piles in Sand”, Journal of the Soil Mechanics and Foundation Division, Proceedings
of the American Society of Civil Engineers, Vol.93, No. SM6, November 1967, p. 261-278. Additional
curves for clays and sands are provided by Vijayvergiya, V. N., Load Movement Characteristics of Piles,
Proceedings of the Ports ’77 Conference, American Society of Civil Engineers, Vol. II, p.269-284.
Curves developed from pile load tests in representative soil profiles or based on laboratory soil tests
that model pile installation may also be justified. Other information may be used, provided such
information can be shown to result in adequate safeguards against excessive deflection and rotation. API
summarized the available information from the technical literature and made the recommendation for t-z
curves and Q-w curves.
4.8.1
API Load-Transfer Curves for Side Resistance (t-z Curves)
In the absence of more definitive criteria, the t-z curves in Figure 4.9 and Table 4.4 are recommended
by API Recommended Practice 2A-WSD for non-carbonate soils. Figure 4.9 should be carefully
considered. Values of the residual adhesion ratio tres/tmax at the axial pile displacement at which it occurs
(zres) are a function of soil stress-strain behavior, stress history, pipe installation method, pile load sequence
and other factors.
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Sand: tres = tmax
1
Clay: tres = 0.9 tmax
tmax
0.8
Clay: tres = 0.7 tmax
t / tmax
0.6
Clay and Sand
0.4
0.2
0
0
1
2
z/zpeak
3
4
5
Figure 4.9 Pile load transfer (t-z) curves from API RP 2A-WSD
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z/zpeak
t/tmax
Clays
Sands
0.16
0.30
0.30
0.31
0.50
0.50
0.57
0.75
0.75
0.80
0.90
0.90
1.0
1.00
1.00
2.0
0.70 to 0.90
1.00
∞
0.70 to 0.90
1.00
Key:
z
zpeak
is the local pile axial deflection
is the displacement to maximum soil adhesion or unit skin
friction;
D
is the outside diameter;
t
is the mobilized soil-pile adhesion or unit shaft friction.
tmax= f(z) is the maximum soil adhesion or unit skin friction;
Table 4.4 Definition of t-z Curves from API RP 2A-WSD
A typical value for zpeak of one percent of the pile outer diameter (i.e. zpeak/D=0.01) is recommended
for routine design purposes. However, there is significant uncertainty on this value and ranges from 0.25%
to 2.0% of the pile diameter may be considered in cases where axial pile stiffness is critical for design.
The value of tres/tmax for clays can range from 0.70 to 0.90. Laboratory, in situ or model pile tests
can provide valuable information for determining values of tres/tmax and zres for various soils.
4.8.2
API Load-Transfer Curves for End Bearing (Q-w Curves)
The end bearing or tip load capacity should be determined as described in Chapter 3. However,
relatively large pile tip movements are required to mobilize the full end bearing resistance. A pile tip
displacement up to 10 percent of the pile diameter may be required for full mobilization in both sand and
clay soils. In the absence of more definitive criteria, the following curve (Table 4.5) is recommended for
both sands and clays, where:
z = axial tip deflection, in. (mm);
D = pile diameter, in. (mm);
Q = mobilized end-bearing capacity, lb (kN); and
Qp = total end bearing, lb (kN), computed according to Section 6.4.
The recommended curve is shown in Figure 4.10
Z/D
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CHAPTER 4 – Load-Transfer (t-z and Q-w) Curves – 4-19
0.002
0.25
0.013
0.50
0.042
0.75
0.073
0.90
0.100
1.00
∞
1.00
Table 4.5 Tip load-displacement curve data
Figure 4.10 Tip load-displacement curve
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CHAPTER 5. References for Special
Engineering Problems on Pile
Foundations
CHAPTER 5 – Special Engineering Problems on Pile Foundations – 5-2
5.1
Mechanics of Load Transfer
Program APILE computes the axial capacity as a function of depth of a driven pile in clay, in sand,
and in mixed-soil profiles based on the equations described earlier in this manual. The pile capacity
predicted by those semi-empirical methods may need to be adjusted for special site conditions and
installation methods. General references are provided in this chapter when some special conditions arise.
Most of the semi-empirical design methods for prediction of axial capacity of piles require internal
friction angles (φ) for calculating the side friction in sand layers, and the undrained cohesive strength for
calculating the side friction in clay layers. The design engineers should gather all the necessary soil
parameters based on the geotechnical investigation report prepared for the application site. The subsurface
can be divided into sub-layers based on the soil properties (cohesive or non-cohesive) with the associated
layer depth and soil parameters.
For non-cohesive soil (sand), the required soil parameters include soil unit weight, angle of internal
friction (φ), and the depth of the ground water table. If the angle of internal friction is not available from
the laboratory tests (direct shear tests), the blow counts (SPT-N) from the standard penetration test can be
used to determine the angle of internal friction. The relationship between SPT-N, φ, and Dr by Gibbs and
Holtz (1957) is used to derive the internal friction angles.
For cohesive soil (clay), the required soil parameters include soil unit weight, undrained cohesive
strength, and the depth of the ground water table. The undrained cohesion should be measured from the
laboratory tests (unconfined compression tests or triaxial unconsolidated-undrained tests) or shear vane
tests in the fields.
5.2
Piles Installed in Special Soils
The geotechnical engineer may encounter a soil that is unusual in character, especially if doing work
in an area where little is known about the existing soil. This section includes discussions of special
considerations for foundation design and construction due to the unique nature of particular soil conditions.
It should be noted that there can be other soil conditions that require special consideration that are not
included herein.
5.2.1
Liquefiable soils
One of the most dramatic causes of damage to structures during earthquakes has been the
development of liquefaction in deposits of saturated sand. High pore-water pressure arises due to ground
vibration, and the resulting upward flow of water frequently turns sand into a "quick" or liquefied condition.
The behavior of piles in deposits of liquefied soil is significantly different from piles installed in nonliquefied soils.
The factors affecting liquefaction of sands has been extensively investigated in the past three decades.
The understanding of the phenomenon has advanced to a degree that analytical procedures have been
formulated to predict liquefaction at a particular site. The design engineer should present the study of
liquefaction-potential analysis for the subject site in a seismic area. If the liquefaction potential is high in
some soil layers, the foundation should be designed accordingly based on the recommendations presented
in the local codes and engineering literature.
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As an example, in a recommendation by Federal Highway Administration (Publication No. FHWANHI-16-009), if the soils are found to be subject to liquefaction during the design event, the pile foundation
must be designed to accommodate the following resulting behavior: the loss of resistance in the liquefied
zone, the seismic induced loads, as well as the anticipated vertical and horizontal displacements, and the
resulting drag force. Alternatively, the liquefaction potential may be mitigated through groundimprovement techniques.
Pile foundations in liquefiable soils must penetrate through the zone of liquefaction and develop
adequate resistance in the underlying deposits. Evaluation of compression and uplift resistances during the
seismic event can be made by assigning residual strength properties to the liquefiable layers. Appropriate
residual strengths should be used to analyze axial and lateral loading.
Following a seismic event that induces soil liquefaction, the liquefied layer will generally consolidate
as pore water pressure dissipates. The location of the zone of liquefaction relative to the neutral plane is
very important, according to Fellenius and Siegel (2008).
If the settlement profile and magnitude caused by liquefied layers are known or assumed, the separate
TZPILE program from Ensoft can be used to analyze the pile capacity under downdrag based on soilstructure interaction techniques (i.e., relative movement between the soil and pile). Fellenius and Siegel
(2008) noted that the location of the zone of liquefaction relative to the neutral plane (as described in Section
5.6 of this Technical Manual) is very important. If liquefaction occurs in soil layers above the location of
the neutral plane before liquefaction, the liquefaction event will have limited effect on the pile. If
liquefaction occurs in soil layers located below the pre-liquefaction location of the neutral plane, it will
increase the axial compression load in the pile as well as result in additional pile settlement. The structural
design of the pile section and the settlement resulting from liquefaction occurring below the neutral plane
should be reevaluated in the design using programs like TZPILE. The pile foundation must be structurally
capable of supporting the increased drag force and the foundation settlement occurring after liquefaction
must be within the structure's performance criteria.
5.2.2
Calcareous Sands
Calcareous sands often consist of skeletal remains of marine organisms. Skeletal calcareous sand
grains are characterized by the presence of intra-particle voids that increase the tendency of these sands to
crush under stress. Particle crushing is more predominant under shear stresses than under isotropic
compression. Stresses in soil under deep foundations often reach the range where crushing becomes
significant. Calcareous sands crush more readily than silica sands. The presence of thin plate-like shell
fragments further increases the crushability of calcareous sands. The behavior of calcareous sands has been
observed to be markedly different from the silica sands. In particular, calcareous sands are fragile and
known to undergo considerable volume reduction, as a result of ‘crush-up’ when subject to compressive
stress. This unusual feature tends to have a major effect on the behavior of foundations in these materials.
Static pile load tests in calcareous sand strata have yielded very low skin friction values. Piles driven
in calcareous sand also have been found to encounter low driving resistance. Both these peculiar
phenomena have been attributed to particle crushing. The calcareous grains had crushed under the walls of
the pile and natural cementation in the deposit prevented the calcareous sand from exerting any significant
lateral stress against the walls of the pile. A stress-strain curve from the laboratory exhibits severe strain
softening. Thus, skin friction was low to non-existent with the large deformation during installation, and
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CHAPTER 5 – Special Engineering Problems on Pile Foundations – 5-4
the allowable end bearing on the piles was insufficient to provide adequate safety during the design load.
The engineer should design the pile foundation based on the lower-bound residual strength of calcareous
sands. Loading tests are important for engineers to derive the acceptable soil parameters for foundation
design.
5.2.3
Scouring/Erosion
Soil scouring is an estimate of the ability of soils to resist erosion, based on the physical
characteristics of each soil. Generally, soils with faster infiltration rates, higher levels of organic matter
and improved soil structure have a greater resistance to erosion. Past erosion has an effect on a soil’s
erodibility for a number of reasons. Many exposed subsurface soils on eroded sites tend to be more erodible
than the original soils, because of their poorer structure and lower organic matter.
As part of the geotechnical investigation, hydraulic studies should be conducted to predict the depth
of erosion if the site is subjected to flooding based on 50 years of records. The potential loss of the ground
cover due to erosion should be considered in the design of pile foundations. Soil erosion can be reduced
by planting vegetation, ground cover, shrubs and other plants. Roots from these plants will help to hold
soil in place on the ground; thus, soil will not be easily blown away due to wind, or be washed away from
rain. Constructing surface runoff barriers, such as edging made of bricks or stones, can help reduce soil
erosion by decreasing water runoff.
Figure 5.1 Illustration of long-term degradation, contraction scour, and local scour
There are two kinds of scour conditions (Figure 5.1) that the engineer should consider in design of
pile foundations. One type of scour is called “channel degradation and contraction” or “long-term scour,”
where the scour is widespread across the riverbed and the original ground surface or the riverbed are
changed/reshaped extensively from the flood. The other type of scour is known as “local” or “short-term
scour” around the pile, where the soils around and near the pile are lost during scour.
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For the long-term scour, the weight of soil within the scouring depth is not considered when
computing effective stress because the extensive soils are removed or lost. In APILE the user simply needs
to assume the new ground surface to be located at the estimated scouring depth.
For the case of local scour, the weight of the soil from the original ground surface may still be
considered in the effective stress computation. For this case, only the side friction on the pile within the
local scouring depth is ignored, which can be specified by the user in APILE.
5.2.4
Expansive soil
Expansive clay at a construction site, if not recognized, can lead to disastrous results on some
occasions. The existence of expansive clay causes an increase in the cost of the foundation. Clay expands
as it becomes wet and shrinks as it dries. Furthermore, moisture will collect when evaporation is cut off,
which can lead to soil swelling. Severe differential movement of the foundations on expansive clay can
sometimes be troublesome. Expansive soil movements are generally the greatest where semi-arid
environments exist, which lead to periods of extended drought followed by periods of extended rainfall.
For pile foundations it is common practice to extend piles through the active zone of expansive clay
with sufficient embedded length to resist the uplift forces on the shafts. The active zone should be identified
based on the weather conditions that affect seasonal moisture change, the presence of a groundwater table
or rock. The uplift force should be estimated based on the thickness of the active zone, and the estimated
adhesion on the pile shaft, which is often based on local experience.
5.2.5
Freezing soil
According to recent studies, 55 percent to 60 percent of the exposed land surface in the Northern
Hemisphere freezes and thaws seasonally. Freezing and thawing caused changes in soil structure and affect
the cycle of water on and below the land surface. The active layer of permafrost is the portion that thaws
in summer and re-freezes in winter. The importance of freezing and thawing processes in soils has long
been recognized. Much attention initially focused on the problems of frost heave because of its importance
in the construction and maintenance of roads, railroads, and oil pipelines. Furthermore, freezing of the soil
dramatically reduces infiltration into the subsurface, which results in more surface water runoff from
melting snow. This can lead to increased soil erosion, and even flooding.
In northern climates, the soil may remain permanently frozen, a condition termed permafrost. The
construction of light structures and other facilities in such regions is aimed at preventing the thawing of the
permafrost, since thawing can result in significant ground settlement.
The most important properties of frozen soils are: (1) shearing strength, (2) continuous strength and
deformation modulus of frozen soils, (3) heaving force, (4) the change in soil properties in freezing-thawing
cycles, and (5) settlement induced by thawing. The frost heave (ad-freeze) may adversely affect piles
embedded within shallow layers which are vulnerable to freeze/thaw action. The foundation engineers
should identify the frost depth based on the local experience, and estimate the ad-freeze forces as a part of
external loads on the foundation. The pile embedment needs to be sufficient below the frost depth to counter
the ad-freeze uplift forces in design consideration.
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5.3
Skin Friction on Taper Piles
If tapered piles are used, only the FHWA method in APILE has the option to take into account the
taper angle for computing the skin friction. All the other methods simply use the averaged straight-section
for computing the skin friction.
5.4
End Bearing
End bearing is computed by using the weighted average of end bearing over a distance of 1.5 pile
diameters above and below the tip of the pile. In using the results of such computations, however, the
designer should employ judgment in those cases where the total capacity in compression shows a sharp
decrease with depth.
In performing the computations to obtain the loads in end bearing for the general method, no
averaging is done. It is assumed that such averaging, if necessary, was done in assigning the unit endbearing values and that the computation increment is taken small enough so that averaging of skin friction
is unnecessary.
5.5
Soil Plug
If an open pipe is used as a pile, at and near the ground surface, analysis may show that a plug of soil
will be forced up the inside of the pile. Therefore, the end bearing capacity of the pile is computed by
adding resistance in skin friction along the inner surface plus the end bearing of material area only. In
computing resistance in skin friction along the inner surface of the pile, only the surface area of the thick
section (driving shoe) at the end of the pile will be considered within APILE. If the pipe pile is
homogeneous then APILE considers the inner side resistance in the surface area of the homogeneous pipe.
The load from the plug is compared to the load from end bearing over the full area of the base and the
smaller of the two values is used by APILE. If the smaller load is from the plug, an asterisk will be placed
in the end-bearing column in the output text file.
The length of the end section of the pile and the internal diameter of that section are input parameters
that allow the designer to make appropriate decisions concerning the development of a plug in the pile as it
is driven. The input of the remolded strength of clay layers also contributes to the flexibility of the decision
making. That is, the remolded strength may be used to compute the internal resistance to account for the
fact that the internal plug is highly disturbed as it enters the pile. If there is a length of pipe at the end of
the pile with a significantly greater thickness than the pipe above, the designer may decide that only that
thicker section will resist the skin friction as the plug moves up (since soil would be disturbed in the
transition to the thinner section).
The designer can also change the computation of the resistance from the plug by selecting the value
of the remolded shear strength of the clay that is inputted. If it is believed that the pile will plug early on,
the internal diameter can be made constant for the entire length and the length of the end section can be
made equal to the length of the pile. The same line of reasoning holds for a pile driven into sand except
that the unit skin friction for the interior of the pile is computed the same way as the unit skin friction for
the exterior of the pile.
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The CPT-based methods (NGI and MTD) recommend different coefficients for side friction and end
bearing for fully plugged piles and unplugged piles. The program will follow those recommendations based
on user selections in evaluation of the axial capacity of open-ended piles for each of NGI and MTD methods.
5.6
General Notes on Downdrag (Negative Skin Friction)
Piles will be subjected to downdrag when the soils in contact with the upper portion of the foundation
move downward relative to the movement of the piles under its external loading. The resulting downward
force from the near-surface soils will add to the force applied to the pile by the superstructure and can lead
to excessive settlement of foundation. It is of interest to note that, even though there is settlement of the
surface soils, downdrag will not develop if the pile moves downward under the applied dead and live loads
more than does the settling soil. Thus, the relative movements of the soil and pile are fundamental in regard
to the occurrence of downdrag.
The neutral plane is defined as a plane where the relative movement between the pile and the soil is
zero. Above the neutral plane, the settling soil will add load to the pile, and the load will be transferred to
the soil below the neutral plane. If the near-surface stratum is very weak and subjected to surface loading,
the neutral plane may conveniently be assumed to be at the surface of the strong layer if the soil in the
strong layer has negligible movement. The downdrag force may be computed by integrating the maximum
load transfer (negative friction) along the portion of pile above the neutral plane. The maximum
compressive load in the pile will be the sum of the downdrag and the external load applied at the top of the
pile. Structurally, the pile section would need to be designed based on that maximum load.
The predicted position of the neutral plane and the resulting negative skin friction may not be
accurate if pile movement is ignored in the analysis. A more prudent analysis accounts for the pile
movement, which includes the displacement needed to mobilize side and base resistance and the elastic
shorting of the pile under the action. The basic concept can be illustrated in Figure 5.2. A pile extends
through one of more strata of soil expected to undergo settlement, and into underlying soil layers not
expected to undergo settlement as shown in Figure 5.2a. The load transfer curves (t-z curves), in terms of
unit side friction and unit base resistance versus relative movement between the pile and soil are assumed
in Figure 5.2b.
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CHAPTER 5 – Special Engineering Problems on Pile Foundations – 5-8
Figure 5.2 Mechanics of downdrag development and the possible location of the
neutral plane
The relative movement of the pile under the downdrag action with respect to the soil is first assumed
to be as shown in Figure 5.2c, with the neutral plane selected at the interface between the upper
compressible soil and the underlying non-settling strata. A negative sign indicates the soil is moving
downward with respect to the pile (soil downdrag developed) and a positive sign indicates the pile is moving
downward with respect to the soil (soil resistance developed). With these assumptions, the distribution of
load along the pile length is shown in Figure 5.2d. It follows that the maximum load in the pile occurs at
the interface between the settling and non-settling strata (the initial assumed neutral plane). Considering,
however, that downdrag movement of the pile is necessary to mobilize the base resistance, and that the pile
also undergoes elastic shorting, the neutral plane cannot occur at the interface between the layers but must
move upward, as shown in Figure 5.2e. A revised distribution of load along the pile is shown in Figure
5.2f.
Any relative downward movement of the soil with the respect to the pile will result in some downdrag.
The initial assumed neutral plane serves as the starting point. In order to determine the depth of the neutral
plane accurately, the pile movement and the settlement of soils from the surcharge have to be calculated or
estimated in the downdrag analysis. The separate Ensoft program TZPILE has the capability to compute
the relative movement more precisely between the soil and the pile if the profile of soil settlement is known.
Users may also read the notes in Section 5.2.1 of this Technical Manual for applications of neutral plane in
liquefaction problems.
5.7
Pile Driveability
The pile must have sufficient driveability to overcome the soil resistance encountered during driving
to reach the specified pile penetration depth. If a pile section does not have sufficient stiffness and strength
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CHAPTER 5 – Special Engineering Problems on Pile Foundations – 5-9
for driving hammers available from the contractor, it will not be driveable to the desired pile penetration
depth. Piles can be damaged during installation by using an improper driving hammer. The wave-equation
analysis is commonly used to analyze the driving stresses and efficiency of pile installation by the selected
hammer. Generally, the limit of pile driveability is the maximum soil resistance a pile can be driven against
without sustaining damage or a refusal driving resistance with a properly selected driving system.
In evaluating the driveability of a pile, the soil disturbance during installation and the time dependent
soil strength changes should be considered. Both soil setup and relaxation can have effects on pile driving.
The soil resistance in clay may reduce 30% to 40% during initial driving because of soil remolding. The
APILE user should consider to apply different reduction/modification factors on the computed soil
resistance during evaluation of the pile axial capacity at various conditions: initial driving, restrike and
ultimate. The APILE program provides the user with an option for specifying the reduction/modification
factor on each soil layer.
In summary, a pile must satisfy two aspects of driveability. First, the pile must have sufficient
stiffness to transmit driving forces large enough to overcome soil resistance. Second, the pile must have
sufficient structural strength to withstand the driving forces without damage.
5.8
Time Effects on Pile Capacity
The soil is greatly disturbed when a pile is driven into the soil. The volume changes cause distortion
of the clay, changes in the structure of the clay, and usually results in loss of strength of the clay. The
volume changes during pile driving results in lateral deformations and there can be uplift and lateral
movement of piles previously driven. As the soil surrounding the pile recovers from the installation
disturbance, a time dependent change in pile capacity often occurs.
Frequently piles driven in saturated clays, and loose to medium dense silts or find sands gain some
capacity after driving has been completed. This phenomenon is generally recognized as soil setup.
Occasionally piles driven into dense saturated fine sands, dense silts, or weak laminated rocks such as shale,
will exhibit a decrease in capacity after the driving has been completed. This phenomenon is called
relaxation.
If an open-ended-pipe pile is driven into clay, a soil plug may or may not form during the pile driving
after a certain pile penetration and be carried down with the pile as the pile is driven farther. If the plug
does not form, the pile will behave as a non-displacement pile with heave and lateral displacement being
minimized. Pile driving in clay causes increases in total pressure and porewater pressure above the at-rest
pressures in the vicinity of the pile wall as the pile top passes a point. An additional effect of pile driving
is a shearing deformation of large magnitude as the pile wall moves past a particular point in the soil; at
present it is not clear whether all of the shearing deformation occurs at the interface between the pile and
the soil or whether or not some soil moves down with the pile.
5.8.1
Cohesive Soil
Because of the time required for excess porewater stress to dissipate in soils with low permeability,
there are significant effects with time on piles driven into saturated clays. There is an increase in axial
capacity with time of piles driven into clay. Engineers have long been aware that the piles "set up" with
time and that this effect can be quite dramatic. The state of stress the clay immediately after the pile driving
is such that there are excess porewater pressures which are undoubtedly maximum in the vicinity of the pile
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CHAPTER 5 – Special Engineering Problems on Pile Foundations – 5-10
wall, but measurements have shown that these excess porewater pressure extend several diameters and
perhaps many diameters away from the pile wall. There will be a relatively rapid decay of the excess
porewater pressures where gradients are high with the decay being an exponential function of time. Along
with the decay of excess porewater pressures is a movement of water in the clay with evidence indicating
that the flow of water is predominantly horizontal. The horizontal movement of water leads to a decrease
in water content at the pile wall; measurements have indicated that this change in water content is significant.
Along with the decrease in water content, there occurs an increase in the shearing strength of the clay. Part
of the strength increase may be also due to the thixotrophy of the clay.
5.8.2
Cohesionless Soil
The driving of a pile into sand or cohesionless soil, with the resulting vibration, causes the sand
deposit to decrease in volume sufficiently to allow the pile to penetrate. The volume decrease is frequently
such that a lowering of the ground surface occurs, particularly in the vicinity of the pile. While there are
little experimental data, there is a strong indication that the lateral vibration of a pile driven into sand results
in arching.
A particle of sand will move outward and downward. Lateral vibration causes a space to be created
that is slightly larger than the pile and arching reduces the lateral stress against the pile wall. Therefore,
the soil stresses against the wall of a pile in sand are usually much lower than passive pressures and can be
lower than the earth pressure at rest. If the sand is so dense that volume change cannot take place, the
driving resistance becomes extremely high and crushing of the sand grains will result.
The above points apply principally to a sand composed of quartz or feldspar; a pile driven into
calcareous sand will crush the sand and lateral earth pressures against the pile wall can be quite low,
especially if the calcareous sand is cemented. It is usually assumed that an open-ended-pipe pile driven
into quartz sand will plug; such may not be the case for calcareous sand. As for clay, the driving of a pile
into cohesionless soil will cause shearing deformation of a large magnitude at the pile wall, sand above a
clay can be moved downward, there will be residual stresses in the driven pile, and there will be a complex
state of stress in the soil surrounding the pile after the pile has been driven.
5.9
Battered Piles
Battered piles are used to resist large lateral loads when there is a large unsupported pile length or in
weak soils where there is little lateral support. Many offshore or marine structures are subjected to
overturning moments due to wind load, wave pressure, and ship impacts. Also, retaining walls are subjected
to horizontal forces and bending moments due to earth pressure. For foundations in such structures, usually
combinations of vertical and batter piles are used.
The ability to install driven piles on an angle, or batter, gives such piles a distinct advantage with
respect to their ability to carry lateral loads. Batter piles carry lateral loads primarily in axial compression
and/or tension while vertical deep foundations carry lateral loads in shear and bending. When subjected to
lateral loading, batter piles will therefore generally have a greater capacity and be subject to smaller
deformations than vertical piles of the same dimensions and material.
A pile driven on an angle is usually expressed as a batter ratio (horizontal to vertical). Example of
1:6 batter ratio is a 1-foot horizontal to 6-feet vertical, and sometimes the batter ratio is also expressed as a
batter angle between the pile axis and the vertical.
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CHAPTER 5 – Special Engineering Problems on Pile Foundations – 5-11
For computation of load transfer from batter piles, APILE takes into account the actual pile length
in each soil stratum as well as any additional overburden effect in certain soils.
Technical Manual (Rel. Aug/2023)
APILE v2023
APILE 2023 – User’s Manual
A Program for the Study
of Driven Piles
under Axial Loads
by
Shin Tower Wang
Jose A. Arrellaga
Luis G. Vasquez
for
ENSOFT, INC.
3003 W. Howard Lane
Austin, Texas 78728
United States of America
(Release Date: March 2024)
CHAPTER 5. Example Problems
CHAPTER 5 – Example Problems – 5-2
5.1
Introduction
This chapter presents several examples that were solved using APILE. In order to assure accuracy
from the computer results, some examples have been compared with the results from hand calculations.
The step-by-step hand calculations were carried out based on the procedures described in the accompanying
APILE Technical Manual. The users can have confidence in their results if limited amounts of hand
calculations can be done for comparisons. The studies in this chapter also provide guidance for the analysis
of axially loaded piles with APILE.
There are three types of output data provided by the computer. The first type is the output file which
contains formatted text that consists of an echo-print of the input data; the distribution of skin friction, end
bearing, and total capacity; and the final load-settlement curve. The second type of output presents the data
for a graphics file that allows the code to produce plots. All of the data are saved with ASCII format and
the user may access the files with any text editor.
Several problems are provided herein as examples of different applications that may be solved using
our computer program APILE. Each example focuses on a particular computational feature of the program.
Input files for each example are automatically copied to the APILE data directory during installation (<Root
Drive>\Ensoft\APILE2018-Examples).
Example problems provide the user information on input and output of various cases, and present a
quick tutorial for real-world applications. The user is encouraged to study these examples and, with
modifications, may even use them to solve similar problems. However, by no means can these limited
examples explore the full functions and features provided by APILE.
The main features of each example included with APILE are summarized as follows.
Example Problem 1 – Steel Pipe Pile
•
non-uniform soil deposit, two layers of sand and two layers of clay,
•
open-ended steel pipe pile,
•
example with English units, and
•
hand calculations with FHWA, USACE and API methods for verification.
Example Problem 2 – Offshore Steel Pipe Pile in Sand
•
sand layers with varying soil parameters,
•
open-ended steel pipe pile with internal plug computed within APILE,
•
example with S.I. units, and
•
hand calculations with API method for verification.
Example Problem 3 – Open-Ended Steel-Pipe Pile in Clay
•
clay layers with varying soil parameters,
•
open-ended steel pipe pile with internal plug computed within APILE, and
•
example with S.I. units.
Example Problem 4 – Prestressed Concrete Pile for Bridge Foundation
•
non-uniform soil deposit, one layers of stiff clay and one layer of sand,
User’s Manual (Rel. Mar/2024)
APILE v2023
CHAPTER 5 – Example Problems – 5-3
•
prestressed concrete pile,
•
example with S.I. units, and
•
hand calculations with API, FHWA, and USACE methods for verification (including
accounting for code-specified limiting values).
Example Problem 5 – FHWA Tapered Pile
•
sand layers,
•
tapered pile for FHWA method (other methods do not account for tapered pile effects),
•
example with English units,
•
hand calculations with FHWA method for verification (including accounting for codespecified limiting values).
Example Problem 6 – Uplift Pile Capacity
•
non-uniform soil layers, and
•
study uplift (tension) capacity of pile.
Example Problem 7 – CPT Based Method for Close-Ended Pile
•
non-uniform soil layers,
•
steel-pipe pile with closed end,
•
hand-calculation with NGI and MTD methods for verification, and
•
example with S.I. units.
Example Problem 8 – CPT Based Method for Open-Ended Pile
•
non-uniform soil layers,
•
steel pipe pile with open end,
•
hand-calculation with NGI and MTD methods for verification, and
•
example with S.I. units.
Example Problem 9 – LRFD Based Method
•
non-uniform sand layers,
•
steel pipe pile with closed end,
•
LRFD load factors and reduction factors, and
•
example with S.I. units.
Example Problem 10 – API Method on Battered Pile
•
non-uniform clay layers,
•
fully plugged, open ended steel pipe pile,
•
1.0H:1.5V pile batter,
•
hand-calculation with API method for verification, and
example with English units.
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APILE v2023
CHAPTER 5 – Example Problems – 5-4
Example Problem 11 – CPT to APILE
•
example for importing and interpreting CPT data into APILE,
•
mixed layers of sand and clay,
•
extra input of PI and YSR for CPT-based methods (NGI, MTD, Fugro and UWA), and
•
example of CPT data imported into APILE with English units.
User’s Manual (Rel. Mar/2024)
APILE v2023
CHAPTER 5 – Example Problem 1 – 5-1
5.2
Example Problem 1 – Steel Pipe Pile in Sand and Clay
This example is included to illustrate a common case in which a 10 in. diameter steel pile is subjected
to a vertical load. The soil deposit is not uniform, as shown in Figure 5.1. It is assumed that the pile is not
plugged.
The computational results from APILE for various methods in this example are compared with
approximate hand computations performed using a spreadsheet. Selected graphics outputted by APILE are
also presented along with the output text file. The user may select to eliminate the printing of capacity for
each increment length to shorten the length of the output text (see Section ).
Figure 5.1 General soil description of Example Problem 1.
5.2.1
Comparison of APILE Results with Hand Computations
This section contains some comparisons of the results obtained from hand computations against those
from the computer run in APILE for three different methods.
5.2.1.1 FHWA Method
a. Sand layer from 0 to 10 ft
Depth
(ft)
Inc.
(ft)
Avg.
Effect.
Stress
(psf)
Surface
Friction
Angle
δ (deg)
Coefficient
of Lateral
Stress
(kδ)
2
2
60
11.9
4
2
180
11.9
User’s Manual (Rel. Mar/2024)
Correction
Factor
(Cf)
Unit Side
Friction
(ksf)
Incremental
Side
Friction
(lbs)
1.15
0.56
7.968
41.72 0(1)
1.15
0.56
23.903
125.16 0(1)
APILE v2023
CHAPTER 5 – Example Problem 1 – 5-2
(1)
6
2
300
11.9
1.15
0.56
39.839
208.60
8
2
420
11.9
1.15
0.56
55.774
292.03
10
2
540
11.9
1.15
0.56
71.710
375.47
Summation:
876.1
APILE model is instructed to ignore top 5 ft
b. Clay layer from 10 to 20 ft
Depth
(ft)
Inc.
(ft)
12
2
Avg
Shear
Stress
(psf)
1000
Length/
Diameter
Ratio
Adhesion
Coefficient
(α)
Unit Side
Friction
(ksf)
12
1
1000
Incremental
Side
Friction
(lbs)
5236
14
2
1000
12
1
1000
5236
16
2
1000
12
1
1000
5236
18
2
1000
12
1
1000
5236
20
2
1000
12
1
1000
5236
Summation:
26180
c. Sand layer from 20 to 30 ft
Depth
(ft)
Inc.
(ft)
Avg.
Effect.
Stress
(psf)
22
2
1160
11.9
Coefficient
of Lateral
Stress
(kδ)
1.15
24
2
1280
11.9
26
2
1400
28
2
30
2
Surface
Friction
Angle
δ (deg)
Correction
Factor
(Cf)
Unit Side
Friction
(ksf)
Incremental
Side
Friction
(lbs)
0.56
154.043
806.57
1.15
0.56
169.979
890.01
11.9
1.15
0.56
185.914
973.45
1520
11.9
1.15
0.56
201.850
1056.88
1640
11.9
1.15
0.56
217.785
1140.32
Summation:
4867.23
d. Summary and Comparison with FHWA Method
Total side friction = 876+26,180+4,867 = 31,923 lbs vs. 32.0 kips (from APILE)
Total tip resistance = Ap σv α Nq = (0.104) (1700) (0.67) (64) = 7,582 vs. 7.7 kips (from APILE, using
Options > Control Options > Average Depth to Estimate Tip Resistance = 0 D for easy comparison
with hand calculations, whereas for design purposes it would be more applicable to select an average
resistance of +/- 1.5 D from pile tip).
5.2.1.2 USACE Method
a. Sand layer from 0 to 10 ft
User’s Manual (Rel. Mar/2024)
APILE v2023
CHAPTER 5 – Example Problem 1 – 5-3
Surface
Friction
Angle
δ (deg)
Coefficient
of Lateral
Stress
(kδ)
Depth
(ft)
Inc.
(ft)
Avg.
Effect.
Stress
(psf)
2
2
60
26.3
1.25
1
37.067
194.08 0(1)
4
2
180
26.3
1.25
1
99.691
521.98 0(1)
6
2
300
26.3
1.25
1
166.152
869.97
8
2
420
26.3
1.25
1
232.613
1217.96
10
2
540
26.3
1.25
1
299.074
1565.95
Summation:
3653.88
(1)
Correction
Factor
(Cf)
Unit Side
Friction
(ksf)
Incremental
Side
Friction
(lbs)
APILE model is instructed to ignore top 5 ft
b. Clay layer from 10 to 20 ft
Depth
(ft)
Inc.
(ft)
12
2
Avg
Shear
Stress
(psf)
1000
Length/
Diameter
Ratio
Adhesion
Coefficient
(α)
Unit Side
Friction
(ksf)
12
0.75
750
Incremental
Side
Friction
(lbs)
3927
14
2
1000
12
0.75
750
3927
16
2
1000
12
0.75
750
3927
18
2
1000
12
0.75
750
3927
20
2
1000
12
0.75
750
3927
Summation:
19635
c. Sand layer from 20 to 30 ft
Surface
Friction
Angle
δ (deg)
Coefficient
of Lateral
Stress
(kδ)
Depth
(ft)
Inc.
(ft)
Avg.
Effect.
Stress
(psf)
Correction
Factor
(Cf)
Unit Side
Friction
(ksf)
Incremental
Side
Friction
(lbs)
22
2
750
26.3
1.25
1
463.343
2426.06
24
2
750
26.3
1.25
1
463.343
2426.06
26
2
750
26.3
1.25
1
463.343
2426.06
28
2
750
26.3
1.25
1
463.343
2426.06
30
2
750
26.3
1.25
1
463.343
2426.06
Summation:
12130.31
d. Summary and Comparison with USACE Method
Total side friction = 3,654+19,635+12,130 = 35,419 lbs vs. 35.1 kips (from APILE)
Total tip resistance = Ap σv Nq = (0.104) (750) (47) = 3,666 vs. 3.7 kips (from APILE, using Options >
Control Options > Average Depth to Estimate Tip Resistance = 0 D for easy comparison with hand
User’s Manual (Rel. Mar/2024)
APILE v2023
CHAPTER 5 – Example Problem 1 – 5-4
calculations, whereas for design purposes it would be more applicable to select an average tip resistance of
+/- 1.5 D from pile tip).
5.2.1.3 API Method
a. Sand layer from 0 to 10 ft
Depth
(ft)
Inc.
(ft)
Avg.
Effect.
Stress
(psf)
2
2
60
30
Coefficient
of Lateral
Stress
(kδ)
0.8
4
2
180
30
6
2
300
8
2
10
2
(1)
Surface
Friction
Angle
δ (deg)
Correction
Factor
(Cf)
Unit Side
Friction
(ksf)
Incremental
Side
Friction
(lbs)
1
27.713
145.10 0(1)
0.8
1
72.000
376.99 0(1)
30
0.8
1
120.000
628.32
420
30
0.8
1
168.000
879.65
540
30
0.8
1
216.000
1130.98
Summation:
2638.95
APILE model is specified to ignore top 5 ft
b. Clay layer from 10 to 20 ft
Depth
(ft)
Inc.
(ft)
12
2
Avg
Shear
Stress
(psf)
1000
Length/
Diameter
Ratio
Adhesion
Coefficient
(α)
Unit Side
Friction
(ksf)
12
0.45
448.95
Incremental
Side
Friction
(lbs)
2350.70
14
2
1000
12
0.47
465.30
2436.32
16
2
1000
12
0.48
480.09
2513.76
18
2
1000
12
0.49
493.63
2584.64
20
2
1000
12
0.51
512.35
2682.65
Summation:
12568
c. Sand layer from 20 to 30 ft
1160
Surface
Friction
Angle
δ (deg)
30
Coefficient
of Lateral
Stress
(kδ)
0.8
2
1280
30
26
2
1400
28
2
30
2
Depth
(ft)
Inc.
(ft)
Avg.
Effect.
Stress
(psf)
Correction
Factor
(Cf)
Unit Side
Friction
(ksf)
Incremental
Side
Friction
(lbs)
22
2
1
535.783
2805.36
24
0.8
1
591.208
3095.57
30
0.8
1
646.634
3385.78
1520
30
0.8
1
702.060
3675.99
1640
30
0.8
1
757.486
3966.20
User’s Manual (Rel. Mar/2024)
APILE v2023
CHAPTER 5 – Example Problem 1 – 5-5
Summation:
16928.88
d. Summary and Comparison with API Method
Total side friction = 2,639+12,568+16,928 = 32,136 lbs vs. 32.2 kips (from APILE)
Total tip resistance = Ap σv Nq = (0.104) (1700) (40) = 7,072 vs. 7.0 kips (from APILE, using Options >
Control Options > Average Depth to Estimate Tip Resistance = 0 D for easy comparison with hand
calculations, whereas for design purposes it would be more applicable to select an average tip resistance of
+/- 1.5 D from pile tip).
5.2.2
Input and Output Data Files for Example 1
Users can read Section 2.1.1 (7) of this manual for reference on the location of placement of the input and
output data files for the example files installed with this program. The default installation directory is the
following: (Root Drive) c:\Ensoft\Apile2023-Examples. The input data files for all examples presented in
this manual are installed automatically with the program.
The input-data filename for Example 1 is the following:
Example 1 - Steel Pipe Pile in Sand and Clay.ap10d
The output-data filename for Example 1 is the following:
Example 1 - Steel Pipe Pile in Sand and Clay.ap10o
5.2.3
Graphical Results of Computer Analysis
The resulting plots of unit skin friction, accumulated skin friction, tip resistance, and total capacity
versus depth provided by the computer program based on different methods, may be seen in Figure 5.2,
Figure 5.3, Figure 5.4 and Figure 5.5 respectively.
Results of combined plots versus depth, shown in Figure 5.6, only contains the curves of skin friction,
tip resistance, and total capacity versus depth for the API RP 2A method specified under Data >
Computational Method > Method for Load Settlement.
User’s Manual (Rel. Mar/2024)
APILE v2023
CHAPTER 5 – Example Problem 1 – 5-6
Figure 5.2 Curves of Unit Skin Friction vs Depth for Example Problem 1.
Figure 5.3 Curves of Accumulated Skin Friction vs Depth for Example Problem 1.
User’s Manual (Rel. Mar/2024)
APILE v2023
CHAPTER 5 – Example Problem 1 – 5-7
Figure 5.4 Curves of Tip Resistance vs Depth or Example Problem 1.
Figure 5.5 Curves of Total Capacity vs Depth or Example Problem 1.
User’s Manual (Rel. Mar/2024)
APILE v2023
CHAPTER 5 – Example Problem 1 – 5-8
Figure 5.6 Combined Plots vs Depth based on API method for Example Problem 1.
User’s Manual (Rel. Mar/2024)
APILE v2023
CHAPTER 5 – Example Problem 2 – 5-9
5.3
Example Problem 2 – Offshore Steel-Pipe Pile in Sand
This example is included to illustrate a case of a pile on an offshore structure. The pile is a steel pipe
and in this example with on outside diameter of 1000 mm and inside diameter of 860 mm. The subsurface
condition mainly consists of cohesionless soils and the pile was driven to a depth of 33.3 meters. The
computer program APILE calculated 8,004 kN for the total bearing capacity (API RP-2A), which is similar
to the value of 8,187 kN that is obtained from simplified hand calculations. Soil data is provided in Table
5.1.
Layer
1
2
3
4
5
6
Depth
Soil Type
(m)
0
2
2
3
3
5
5
25
25
30.5
30.5
36
γ'
φ
3
(kN/m )
18.1
19
9.2
10.2
10.2
5.7
5.7
5.7
5.7
11.2
11.2
11.2
sand
sand
sand
sand
sand
sand
sand
sand
sand
sand
sand
sand
(Deg.)
33
37.5
37.5
39
39
30
30
30
30
40.5
40.5
40.5
Ko
Nq
0.46
0.39
0.39
0.37
0.37
0.5
0.5
0.5
0.5
0.35
0.35
0.35
32
40
40
40
40
20
20
20
20
40
40
40
Table 5.1 Soil Data for Example Problem 2
5.3.1
Hand Computations for API Method
The program output will be compared to the results from the following hand calculations.
5.3.1.1 Skin Friction
The general equation for skin friction is:
L
Q f = ∫ f x dAs
o
(5.1)
where
Qf = axial load capacity in skin friction, lb (kN);
L = penetration of pile below ground surface, ft (m);
fx = unit resistance at depth x, measured from ground surface, lb/ft2 (kPa); and
As = side surface area of pile, ft2 (m2).
At each increment,
User’s Manual (Rel. Mar/2024)
APILE v2023
CHAPTER 5 – Example Problem 2 – 5-10
f x As = (k (tan δ ) po ) As
f x As = k (tan(φ − 5))(∑ (γ h))(∑ π Dh)
(5.2)
Or,
f x As = ( Max Skin Friction)(∑ π Dh)
(5.3)
where
k = coefficient of lateral earth (ratio of horizontal to vertical normal effective stress), a value of
k = 0.8 was recommended for open-ended pipe piles, that are driven unplugged, for
loadings in both tension and compression. A value of k = 1.0 was recommended for full
displacement piles.
p = effective overburden pressure at the point in question;
o
δ = the friction angle between the soil and the pile wall. In the absence of data on δ, APILE
computes δ = φ − 5o (in degrees) based on user’s inputted value of friction angle (φ). The
limiting f is interpolated linearly within APILE for intermediate values of δ.
D = outside pile diameter.
Combining Eq. (5.1) and Eq. (5.2):
𝑸𝑸𝒇𝒇 = 𝒌𝒌(𝒕𝒕𝒕𝒕𝒕𝒕(∅ − 𝟓𝟓)) � 𝜸𝜸𝜸𝜸 � 𝝅𝝅𝝅𝝅𝝅𝝅
(5.4)
where k, ∅ and γ are averaged values.
Using the values from Table 5.1 we can make computations of ∑ 𝛾𝛾ℎ at various sample depths:
18.1+19
� ∗ 2 = 37.1 kN/m2
2
at 2m: ∑ 𝛾𝛾ℎ = �
9.2+10.2
� ∗ 1� + 37.1 = 46.8 kN/m2
2
At 3m: ∑ 𝛾𝛾ℎ = ��
10.2+5.7
� ∗ 2� + 46.8 = 62.7 kN/m2
2
At 5m: ∑ 𝛾𝛾ℎ = ��
Values of unit side resistance (fx) at various sample depths can be computed as follows:
0.46+0.39
33+37.5
� �𝑡𝑡𝑡𝑡𝑡𝑡 �
− 5�� (37.1)� = 9.20 kN/m2
2
2
At 2m, 𝑓𝑓2𝑚𝑚 = ��
0.39+0.37
37.5+39
� �𝑡𝑡𝑡𝑡𝑡𝑡 �
− 5�� (46.8)� = 11.66 kN/m2
2
2
At 3m: 𝑓𝑓3𝑚𝑚 = ��
0.37+0.50
39+30
� �𝑡𝑡𝑡𝑡𝑡𝑡 �
− 5�� (62.7)� = 15.43 kN/m2
2
2
At 5m: 𝑓𝑓5𝑚𝑚 = ��
User’s Manual (Rel. Mar/2024)
APILE v2023
CHAPTER 5 – Example Problem 2 – 5-11
We can now solve Eq. (5.4) at the various sample depths:
At depth of 2m:
𝑓𝑓
+𝑓𝑓
𝑄𝑄𝑓𝑓,2𝑚𝑚 = �� 2𝑚𝑚 2 0𝑚𝑚 � ∗ 𝜋𝜋𝜋𝜋ℎ� + 𝑄𝑄𝑓𝑓,0𝑚𝑚
9.20+0
� (𝜋𝜋 ∗ 1 ∗ 2)� + 0 = 28.89 kN
2
𝑄𝑄𝑓𝑓,2𝑚𝑚 = ��
At depth of 3m:
𝑓𝑓
𝑄𝑄𝑓𝑓,3𝑚𝑚 = �� 3𝑚𝑚
+𝑓𝑓2𝑚𝑚
� ∗ 𝜋𝜋𝜋𝜋ℎ� + 𝑄𝑄𝑓𝑓,2𝑚𝑚
2
11.66+9.20
� (𝜋𝜋 ∗ 1 ∗ 1)� + 28.89 = 61.65 kN
2
𝑄𝑄𝑓𝑓,3𝑚𝑚 = ��
At depth of 5m:
𝑓𝑓
+𝑓𝑓
𝑄𝑄𝑓𝑓,5𝑚𝑚 = �� 5𝑚𝑚 2 2𝑚𝑚 � ∗ 𝜋𝜋𝜋𝜋ℎ� + 𝑄𝑄𝑓𝑓,3𝑚𝑚
15.43+11.66
� (𝜋𝜋 ∗ 1 ∗ 2)� + 61.65 = 146.76 kN
2
𝑄𝑄𝑓𝑓,5𝑚𝑚 = ��
Following similar computations methods used in the sample depths above we can now compute
values for the remaining depths, with the results included in Table 5.2.
Depth
(m)
φ -5
(deg)
tan (φ -5)
γ(h)
Σ γ(h)
2
2
(kN/m ) (kN/m )
f
(kPa)
π (d)(h) π (d)(h)f
Qf
(kN)
2
30.25
0.58318
37.1
37.10
9.20
6.28
28.89
28.89
3
33.25
0.65563
9.7
46.80
11.66
3.14
32.76
61.65
5
29.5
0.56577
15.9
62.70
15.43
6.28
85.11
146.76
25
25
0.46631
114
176.70
41.20
62.83
1779.07
1925.82
30.5
30.25
0.58318
46.475
223.18
55.31
17.28
833.81
2759.63
33
35.5
0.71329
28
251.18
62.71
7.85
463.47
3223.10
Table 5.2 Hand Computations of Side Resistances for Example Problem 2
•
•
In table above the calculated f values were compared with the limiting values in the Technical
Manual. For each depth, the lower of the two values was used.
For this example, the program has produced output at 0.5-meter increments. Changing the depth
increment of the hand calculations to the 0.5-meter increment of depth will produce a more
accurate final result (with exact match to the results from the computer program).
5.3.1.2 Base Resistance
The general equation for end bearing in Sands is:
Q p = qAp
User’s Manual (Rel. Mar/2024)
APILE v2023
CHAPTER 5 – Example Problem 2 – 5-12
(5.5)
and
q = po N q
(5.6)
Where
Qp = axial load capacity in end bearing;
q = unit end bearing resistance;
Ap = cross-sectional area of tip of pile.
p = effective overburden pressure at the pile tip; and
o
Nq = bearing capacity factor.
To check soil plugging, calculate the average end bearing value from depth H to (H+3D) as follows:
H +1.5 D
∫ Qp ( x)dx
H −1.5 D
3D
(5.7)
Q p = ( Max.Unit End Bearing ) Ap
(5.8)
For an open-ended pipe pile for end bearing we must consider both a plugged and unplugged case.
The plugged and unplugged values are computed in the following sub sections.
5.3.1.3 Fully Plugged Case
For a fully plugged case the tip area is computed as follows:
𝑨𝑨𝒑𝒑 = 𝒇𝒇𝒇𝒇𝒇𝒇𝒇𝒇 𝒃𝒃𝒃𝒃𝒃𝒃𝒃𝒃𝒃𝒃𝒃𝒃 𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂 𝒐𝒐𝒐𝒐 𝒕𝒕𝒕𝒕𝒕𝒕 =
Combining Eq. (5.5) and (5.6):
𝝅𝝅 ∗ 𝑫𝑫𝟐𝟐
= 𝟎𝟎. 𝟕𝟕𝟕𝟕𝟕𝟕𝟑𝟑𝟑𝟑𝟑𝟑 𝒎𝒎𝟐𝟐
𝟒𝟒
𝑸𝑸𝒑𝒑 = 𝒒𝒒 𝑨𝑨𝒑𝒑 = �� 𝜸𝜸𝜸𝜸� 𝑵𝑵𝒒𝒒 𝑨𝑨𝒑𝒑
(5.9)
where γ is an averaged value and the calculated q values are compared with the limiting values
in the Technical Manual. For each depth, the lower of the two values is used.
User’s Manual (Rel. Mar/2024)
APILE v2023
CHAPTER 5 – Example Problem 2 – 5-13
Using the values from Table 5.1 and Eq. (5.9) we calculate the following:
At depth 0m:
𝑄𝑄𝑝𝑝,0𝑚𝑚,𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 = 0 (𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑞𝑞 = 0)
At depth 2m:
18.1+19
� ∗ 2� ∗ 40 ∗ 0.785398 = 1165.5 𝑘𝑘𝑘𝑘
2
𝑄𝑄𝑝𝑝,2𝑚𝑚,𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 = ��
At depth 3m:
19+10.2
� ∗ 1� ∗ 40 ∗ 0.785398 = 1624.2 𝑘𝑘𝑘𝑘
2
𝑄𝑄𝑝𝑝,3𝑚𝑚,𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 = �37.1 + �
At depth 5m:
10.2+5.7
� ∗ 2� ∗ 20 ∗ 0.785398 = 1061.8 𝑘𝑘𝑘𝑘
2
𝑄𝑄𝑝𝑝,5𝑚𝑚,𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 = �37.1 + 14.6 + �
Following similar computations methods used in the sample depths above we can now compute
values for the remaining depths, with the results included in Table 5.3.
Depth
(m)
0
γ(h)
Σ γ(h)
2
2
(kN/m ) (kN/m )
0
0
Qp (plugged
(kN)
0
2
37.1
37.1
1165.53
3
14.6
51.7
1624.2
5
15.9
67.6
1061.86
25
114
181.6
2852.57
30.5
33
46.475
28
228.075
256.075
7165.19
7539.82
Table 5.3 Hand Computations of Fully Plugged End Bearing for Example Problem 2
•
•
•
In table above the calculated q values were compared with the limiting values in the Technical
Manual. For each depth, the lower of the two values was used (this is the case at the 33-m depth).
For this example, the program has produced output at a 0.5-meter increments. Changing the
depth increment of the hand calculations to the 0.5-meter increment of depth will produce a more
accurate final result (with exact match to the results from the computer program).
At user’s discretion, the APILE program can use averaged values of Qp over a length of 1.5 pile
diameter above and below the pile tip. This is done following Eq. (5.7).
5.3.1.4 Partially Plugged Case
For a fully unplugged case the tip area is computed as follows:
𝐴𝐴𝑝𝑝 = 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 =
𝜋𝜋 ∗ (𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 2 − 𝐷𝐷𝐷𝐷𝐷𝐷2 )
= 0.204518𝑚𝑚2
4
Adding the effect of side friction from a partial plug in the inner wall of the pile, the previous Eq.
(5.10) is now calculated as follows:
User’s Manual (Rel. Mar/2024)
APILE v2023
CHAPTER 5 – Example Problem 2 – 5-14
𝑸𝑸𝒑𝒑 = 𝒒𝒒 𝑨𝑨𝒑𝒑 = �� 𝜸𝜸𝜸𝜸� 𝑵𝑵𝒒𝒒 𝑨𝑨𝒑𝒑 + 𝑸𝑸𝒇𝒇,𝒊𝒊𝒊𝒊𝒊𝒊𝒊𝒊𝒊𝒊 𝒘𝒘𝒘𝒘𝒘𝒘𝒘𝒘
(5.10)
where γ is an averaged value and the calculated q values are compared with the limiting values
in the Technical Manual. For each depth, the lower of the two values is used.
Using the values from Table 5.1 and Eq. (5.10) we calculate the following:
At depth 0m:
𝑄𝑄𝑝𝑝,0𝑚𝑚,𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 = 0 (𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑞𝑞 = 0)
At depth 2m:
𝑄𝑄𝑓𝑓,𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤 = 𝜋𝜋𝜋𝜋ℎ𝑓𝑓 = 3.14 ∗ 0.86 ∗ 2 ∗
0+9.20
= 24.8 𝑘𝑘𝑘𝑘
2
𝑄𝑄𝑝𝑝,2𝑚𝑚,𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 = (37.1 ∗ 40 ∗ 0.204518) + 24.84 = 328.3 𝑘𝑘𝑘𝑘
At depth 3m:
𝑄𝑄𝑓𝑓,𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤,3𝑚𝑚 = (𝜋𝜋𝜋𝜋ℎ𝑓𝑓) + 𝑄𝑄𝑓𝑓,𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤,2𝑚𝑚 = �3.14 ∗ 0.86 ∗ 1 ∗
54.6 𝑘𝑘𝑘𝑘
𝑄𝑄𝑝𝑝,2𝑚𝑚,𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 = (51.7 ∗ 40 ∗ 0.204518) + 54.66 = 477.6 𝑘𝑘𝑘𝑘
9.20+12.88
� + 24.84 =
2
At depth 5m:
𝑄𝑄𝑓𝑓,𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤,5𝑚𝑚 = (𝜋𝜋𝜋𝜋ℎ𝑓𝑓) + 𝑄𝑄𝑓𝑓,𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤,3𝑚𝑚
12.88 + 16.64
= �3.14 ∗ 0.86 ∗ 1 ∗
� + 54.6 = 134.4 𝑘𝑘𝑘𝑘
2
𝑄𝑄𝑝𝑝,2𝑚𝑚,𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 = (67.6 ∗ 20 ∗ 0.204518) + 134.4 = 410.9 𝑘𝑘𝑘𝑘
Following similar computations methods used in the sample depths above we can now compute
values for the remaining depths, with the results included in Table 5.5.
Depth
(m)
0
γ(h)
Σ γ(h)
2
2
(kN/m ) (kN/m )
0
0
Qp (unplugged)
(kN)
0
2
37.1
37.1
328.35
3
14.6
51.7
477.61
5
15.9
67.6
410.92
25
114
181.6
2470.67
30.5
33
46.475
28
228.075
256.075
4328.26
4964.14
Table 5.4 Hand Computations of Partially Plugged End Bearing for Example Problem 2
•
In table above the calculated q values were compared with the limiting values in the Technical
Manual. For each depth, the lower of the two values was used.
User’s Manual (Rel. Mar/2024)
APILE v2023
CHAPTER 5 – Example Problem 2 – 5-15
•
•
For this example, the program has produced output at 0.5-meter increments. Changing the depth
increment of the hand calculations to the 0.5-meter increment of depth will produce a more
accurate final result (thus with exact match to the results from the computer program).
At user’s discretion, the APILE program can use averaged values of Qp over a length of 1.5 pile
diameter above and below the pile tip. This is done following Eq. (5.7).
5.3.1.5 Total Resistance
The total bearing capacity of the pile is given in Eq. (5.11). To determine the total bearing capacity
of the pile, the smallest value from the skin friction equations in Eq. (5.2) and Eq. (5.3) and the end bearing
equations in Eq. (5.7) and Eq. (5.8) must be used in Eq. (5.11).
QTotal = Q f + Q p
(5.11)
5.3.2
Comparison of APILE Results with Hand Computations
Table 5.5 contains a comparison of the results obtained from hand computations against those from
the computer run in APILE (for API Method).
Since Qp,pplugged < Qp,plugged at all depths then the values in Table 5.4 control the end bearing
capacity. Using the computed values from Table 5.2 and Table 5.4 we can find the total resistance displayed
in Table 5.5 along with comparisons against the computer run in APILE (API Method).
Depth
(m)
Qf
(kN)
Qp
(kN)
QT(Hand) QT(APILE)
(kN)
(kN)
2
28.89
328.35
357.24
349.30
3
61.65
477.61
539.26
497.10
5
146.76
410.92
557.68
561.70
25
1925.82
2470.67
4396.49
4257.70
30.5
2759.63
4328.26
7087.89
6877.90
33
3223.10
4964.14
8187.24
8003.90
Table 5.5 Comparison of Total Resistances for Example Problem 2
•
Some discrepancies are noticed between the rough hand calculations and the computed results
from APILE. If the user refines the computational depths to match the more accurate 0.5-meter
increments used by APILE, the hand computed values should then be much closer to the APILE
software calculations.
User’s Manual (Rel. Mar/2024)
APILE v2023
CHAPTER 5 – Example Problem 2 – 5-16
•
5.3.3
APILE model is using Options > Control Options > Average Depth to Estimate Tip
Resistance = 0 D for easy comparison with hand calculations, whereas for design purposes it
would be more applicable to select an average tip resistance of +/- 1.5 D from pile tip.
Input and Output Data Files for Example 2
Users can read Section 2.1.1 (7) of this manual for reference on the location of placement of the input and
output data files for the example files installed with this program. The default installation directory is the
following: (Root Drive) c:\Ensoft\Apile2023-Examples. The input data files for all examples presented in
this manual are installed automatically with the program.
The input-data filename for Example 2 is the following:
Example 2 - Large Steel Pipe Pile in Sand.ap10d
The output-data filename for Example 2 is the following:
Example 2 - Large Steel Pipe Pile in Sand.ap10o
5.3.4
Graphical Results of Computer Analysis
Resulting plots of accumulated skin friction, ultimate tip resistance, and ultimate total capacity versus
depth provided by the computer program may be observed in Figure 5.7, Figure 5.8 and Figure 5.9
respectively. Results of axial load versus short-term settlement are included in Figure 5.10.
Figure 5.7 Curves of Accumulated Skin Friction vs Depth for Example Problem 2.
User’s Manual (Rel. Mar/2024)
APILE v2023
CHAPTER 5 – Example Problem 2 – 5-17
Figure 5.8 Curves of Ultimate Tip Resistance vs Depth for Example Problem 2.
Figure 5.9 Curves of Ultimate Total Capacity vs Depth for Example Problem 2.
User’s Manual (Rel. Mar/2024)
APILE v2023
CHAPTER 5 – Example Problem 2 – 5-18
Figure 5.10 Curve of Axial Load vs Settlement for Example Problem 2.
User’s Manual (Rel. Mar/2024)
APILE v2023
CHAPTER 5 – Example Problem 3 – 5-19
5.4
Example Problem 3 – Steel Pipe Pile in Clay
5.4.1
Description
This example is included to show the response of a steel pile embedded in cohesive soils. The
modeled pile is 39 meters long and open-ended steel pipe, with an outer diameter of 500 mm and an inner
diameter of 480 mm. The soil data is given in Table 5.6. The bearing capacity was calculated by APILE,
using the API RP2A method. Because this pile is open ended, a plug of soil may be forced up the inside of
the pile. In this APILE model, the soil resistance from the plug is compared to the resistance from the endbearing over the full area of the base and the smaller of the two values is used (Data > Circular Pile
Section > Internal Pile Plug Calculated by Program).
Layer
1
2
3
4
5
Depth
(m)
Soil Type
0
4
4
10
10
20
20
36
36
40
clay
clay
clay
clay
clay
clay
clay
clay
clay
clay
C
γ'
(kN/m ) (kN/m2)
18.6
9.8
18.6
9.8
8.8
9.8
8.8
9.8
8.8
19.6
8.8
19.6
8.8
58.8
8.8
58.8
9
78.4
9
78.4
3
Table 5.6 Soil Data for Example Problem 3
5.4.2
Input and Output Data Files for Example 3
Users can read Section 2.1.1 (7) of this manual for reference on the location of placement of the input and
output data files for the example files installed with this program. The default installation directory is the
following: (Root Drive) c:\Ensoft\Apile2023-Examples. The input data files for all examples presented in
this manual are installed automatically with the program.
The input-data filename for Example 3 is the following:
Example 3 - Steel Pipe Pile in Clay.ap10d
The output-data filename for Example 3 is the following:
Example 3 - Steel Pipe Pile in Clay.ap10o
5.4.3
Graphical Results of Computer Analysis
The resulting plot of combined ultimate axial capacities versus depth provided by APILE may be
observed in Figure 5.11. Results of axial load versus short-term settlement are included in Figure 5.12.
User’s Manual (Rel. Mar/2024)
APILE v2023
CHAPTER 5 – Example Problem 3 – 5-20
Figure 5.11 Curve of Combined Plots vs Depth (ultimate) for Example Problem 3.
Figure 5.12 Curve of Axial Load vs Settlement for Example Problem 3.
User’s Manual (Rel. Mar/2024)
APILE v2023
CHAPTER 5 – Example Problem 4 – 5-21
5.5
Example Problem 4 – Prestressed Concrete Pile for Bridge
Foundation
This example is included to illustrate a modeling case that may be applicable for a simple bridge
foundation. The soil deposit consists of two sublayers as shown in Figure 5.13. The top layer is a 3-meter
stiff clay underlain by a medium dense to dense sand layer. One meter of the top clay layer is not considered
for axial friction (side resistance) transfers. The proposed pile for these foundations is composed of
prestressed concrete piles with 450 mm (18-in.) in outside diameter. The elastic modulus of the prestressed
pile is 25,000,000 kN/m2 (3,626,000 psi). Each pile is required to provide about 2000 kN for a service
load.
The APILE output for this example is shown in detail so the user can examine the increase in pile
capacity with depth. The user may elect to eliminate the printing of capacity for each increment length to
shorten the length of output.
Figure 5.13 Pile layout and soil conditions of Example Problem 4.
User’s Manual (Rel. Mar/2024)
APILE v2023
CHAPTER 5 – Example Problem 4 – 5-22
5.5.1
Hand Computations and Comparisons with APILE
The program output will be compared to the results from the following hand calculations.
5.5.1.1 API Method – Skin Friction
A. For the top Clay layer (ignoring friction on top 1 meter)
fAs (clay) = ( α ) ( c )*π *D* h
(5.12)
where
Avg. effective overburden pressure (p) is 18.9 * 1.5 = 28.35 kN/m2
α = (0.5)(c/p) - 0.25 = (0.5)(95/28.35)-0.25 = 0.37
fAs (clay) = (0.37) (95)*π *(0.45)* (3-1) = 99 kN
B. For the bottom Sand layer
fAs (sand) = ko*(Σγh)*tan (φ- 5)*π *D* h
(5.13)
where
Avg. effective overburden pressure (p) from 0 to 3 m
18.9 * 1.5 = 28.3 kN/m2
Avg. effective overburden pressure (p) from 3 to 5 m
18.9 * 3 + (9.1) (1) = 65.8 kN/m2
Avg. effective overburden pressure (p) from 5 to 10 m
18.9 * 3 + (9.1) (2) + (9.1) (2.5) = 97.6 kN/m2
Avg. effective overburden pressure (p) from 10 to 15 m
18.9 * 3 + (9.1) (7) + (9.1) (2.5) = 143.1 kN/m2
Avg. effective overburden pressure (p) from 15 to 20 m
18.9 * 3 + (9.1) (12) + (9.1) (2.5) = 188.6 kN/m2
Avg. effective overburden pressure (p) from 20 to 25 m
18.9 * 3 + (9.1) (17) + (9.1) (2.5) = 234.2 kN/m2
Computation of skin friction from each sub-layer based on API Method:
(5)
(3)
(4)
(2)
(1)
f
=
Avg.
s (3)*(4)
ko*tan (φ-5)
Total area
Depth
effective
< limiting
interval
(π *D* h)
ko= 1, φ = 36
stress
value (99.3)
3–5m
2.83 m2
65.8 kN/m2
0.6
39.5
2
5 – 10 m
7.07 m
97.6 kN/m2
0.6
58.6
2
2
10 – 15 m
7.07 m
143.1 kN/m
0.6
85.9
User’s Manual (Rel. Mar/2024)
(6)
fs A = (2)*(5)
111.8 kN
414.3 kN
607.3 kN
APILE v2023
CHAPTER 5 – Example Problem 4 – 5-23
15 – 20 m
20 – 25 m
7.07 m2
7.07 m2
188.6 kN/m2
234.2 kN/m2
0.6
0.6
99.3
99.3
ΣfAs =
702.1 kN
702.1. kN
2537.6 kN
5.5.1.2 API Method – End Bearing
The general equation for end bearing is:
Qp = (Nq) (σv) (Ap)
(5.14)
where
Ap (tip area) = (0.45) (0.45) (π./4) = 0.159 m2,
σv (effective stress at tip) = 18.9 *3 + (9.1) (22) = 258 kN/m2, and
Nq = 40.
Therefore:
Qp = (40) (258) (0.159) = 1641
Limiting Tip Resistance = 9,600 kPa (see Technical Manual)
Qp = (9600) (0.159) = 1526.4
5.5.1.3 API Method – Comparisons of APILE Results with Hand Computations
The total transfer in side resistance is provided by adding the results from Eq. (5.12) plus Eq. (5.13):
Qf = 99 + 2537.6 = 2636.6 kN which compares to 2659.6 kN computed by APILE
(APILE is more accurate since it divides the soil layers into smaller increments)
The transfer in end bearing is provided by the result from Eq. (5.14):
Qp = 1526.4 kN which compares to 1526.8 kN computed by APILE
5.5.1.4 FHWA Method – Skin Friction
A. For the top Clay layer (ignoring friction on top 1 meter)
fAs (clay) = ( α ) ( cu )*π *D* h
(5.15)
= ( 0.72 ) ( 95 )*π *(0.45)* (3-1)
= 193 kN
B. For the bottom Sand layer
fAs (sand) = ko*Cf*(Σγh)*sin (δ)*π *D* h
User’s Manual (Rel. Mar/2024)
APILE v2023
CHAPTER 5 – Example Problem 4 – 5-24
(5.16)
The average displaced volume per foot is π (0.45)2 /4 = 0.159 m3.per meter
For a precast concrete pile with V=1.71 ft3 per ft, δ = 0.9φ.
Computation of skin friction from each sub-layer based on FHWA Method:
(4)
(5)
(3)
(2)
(1)
ko *Cf *sin (δ)
fs = (3)*(4)
Avg.
Total area
Depth
effective
ko=2.1,δ =0.9φ
< limiting
interval
(π *D* h)
stress
value
(95.5)
Cf =0.95.
2
2
3–5m
2.83 m
65.8 kN/m
1.07
70.4
5 – 10 m
7.07 m2
97.6 kN/m2
1.07
104.4
10 – 15 m
7.07 m2
143.1 kN/m2
1.07
153.1
2
15 – 20 m
7.07 m
188.6 kN/m2
1.07
201.8
20 – 25 m
7.07 m2
234.2 kN/m2
1.07
250.6
ΣfAs =
(6)
fs A = (2)*(5)
199.2 kN
738.3 kN
1082.5 kN
1426.7 kN
1771.7 kN
5218.4 kN
5.5.1.5 FHWA Method – End Bearing
The general equation for end bearing is:
Qp = (α ) (Nq) (σv) (Ap)
(5.17)
where
Ap (tip area) = (0.45) (0.45) (π./4) = 0.159 m2,
σv (effective stress at tip) = 18.9 *3 + (9.1) (22) = 258 kN/m2,
Nq = 60,
α = 0.7, and
The limiting value from Meyerhof (1976) is 7258 kN/m2.
Qp = (0.7) (60) (258) = 9702 > 7258 kN/m2
Therefore the limiting value should be used for the bearing capacity.
Qp = (7258) (0.159) = 1154
5.5.1.6 FHWA Method – Comparisons of APILE Results with Hand Computations
The total transfer in side resistance is provided by adding the results from Eq. (5.15) plus Eq. (5.16):
Qf = 193 + 5218.4 = 5411.4 kN which compares to 5279.9 kN computed by APILE
(APILE is more accurate since it divides the soil layers into smaller increments)
The transfer in end bearing is provided by the result from Eq. (5.17):
Qp = 1154 kN which compares to 1154.4 kN computed by APILE
User’s Manual (Rel. Mar/2024)
APILE v2023
CHAPTER 5 – Example Problem 4 – 5-25
5.5.1.7 USACE Method – Skin Friction
A. For the top Clay layer (ignoring friction on top 1 meter)
fAs (clay) = ( α ) ( cu )*π *D* h
(5.18)
= ( 0.5 ) ( 95 )*π *(0.45)* (3-1)
= 134 kN
B. For the bottom Sand layer
fAs (sand) = ko*(Σγh)*tan (δ)*π *D* h
(5.19)
The skin friction in sand increases linearly to an assumed critical depth (Dc).
Dc = 20B for dense sand = 20 (0.45 m) = 9 m.
Effective overburden pressure (p) at 9 m
18.9 * 3 + (9.1) (6) = 111.3 kN/m2
Computation of skin friction from each sub-layer based on USACE Method:
(4)
(5)
(2)
(1)
k
*tan
(δ)
o
(3)
fAs =
Total area
Depth
Avg. effective stress
ko= 1.25, δ =
interval
(π *D* h)
(2)*(3)*(4)
0.95φ
3–5m
2.83 m2
65.8 kN/m2
0.85
158.3 kN
5–9m
6.65 m2
84.0 kN/m2
0.85
403.4 kN
2
111.3 kN/ m
9 – 25 m
22.62 m2
0.85
2139.9kN
(critical depth controls)
ΣfAs =
2701.6 kN
5.5.1.8 USACE Method – End Bearing
The general equation for end bearing is:
Qp = (Nq) (σv) (Ap)
(5.20)
where
Ap (tip area) = (0.45) (0.45) (π/4) = 0.159 m2,
σv (effective stress at Dc) = 18.9 *3 + (9.1) (6) = 111.3 kN/m2 (assuming Dc=9m but should be
computed based on Table in Technical Manual), and
Nq = 55 (approximate, from Figure in Technical Manual), so
Qp = (55) (111.3) (0.159) = 973 kN.
User’s Manual (Rel. Mar/2024)
APILE v2023
CHAPTER 5 – Example Problem 4 – 5-26
5.5.1.9 USACE Method – Comparisons of APILE Results with Hand Computations
The total transfer in side resistance is provided by adding the results from Eq. (5.18) plus Eq. (5.19):
Qf = 134 + 2701.6 = 2835.6 kN which compares to 2894.8 kN computed by APILE
(APILE is more accurate since it divides the soil layers into smaller increments)
The transfer in end bearing is provided by the result from Eq. (5.20):
Qp = 973 kN as compared to 991.3 kN computed by APILE
(APILE uses a better approximation than the hand computations for the critical depth Dc and for
the bearing capacity factor Nq for the USACE method)
5.5.2
Input and Output Data Files for Example 4
Users can read Section 2.1.1 (7) of this manual for reference on the location of placement of the input and
output data files for the example files installed with this program. The default installation directory is the
following: (Root Drive) c:\Ensoft\Apile2023-Examples. The input data files for all examples presented in
this manual are installed automatically with the program.
The input-data filename for Example 4 is the following:
Example 4 - Prestressed Concrete Pile.ap10d
The output-data filename for Example 4 is the following:
Example 4 - Prestressed Concrete Pile.ap10o
5.5.3
Graphical Results of Computer Analysis
The resulting plots of ultimate accumulated skin friction and ultimate tip resistance versus depth
provided by the APILE computer program may be observed in Figure 5.14 and Figure 5.15, respectively.
Note that the load-transfer curve of skin friction versus depth in Figure 5.14 starts from about the 1m depth (actually from the previous finite increment in some methods). This is because the program was
instructed to ignore skin friction at the top 1 meter.
User’s Manual (Rel. Mar/2024)
APILE v2023
CHAPTER 5 – Example Problem 4 – 5-27
Figure 5.14 Curve of Ultimate Skin Friction vs Depth for Example Problem 4.
Figure 5.15 Curve of Ultimate Tip Resistance vs Depth for Example Problem 4.
User’s Manual (Rel. Mar/2024)
APILE v2023
CHAPTER 5 – Example Problem 5 – 5-28
5.6
Example Problem 5 – Tapered Pile Capacity
Driven piles with a depth-variable circumference or perimeter over all of their length are called
tapered piles. They are usually installed using some type of impact hammer and have long been recognized
as the most cost effective driven pile alternative to use in applications calling for “friction piles”, especially
in coarse-grain soil condition (Peck 1958).
This example is included to illustrate an application in which a Raymond Uniform Tapered Pile
(made of steel) was considered for the deep foundation. The tapered pile has a diameter of 12 inches at the
pile tip and the taper angle is 0.5 degrees extending from the pile tip to the pile head. The length of the
proposed pile is 30 feet, which results in a diameter of 18.28 inches at the pile head.
The soil deposit consists of two sublayers as shown in Figure 5.16. The top layer is 18-ft loose sand
with the internal friction angle of 30 deg., underlain by a very dense sand layer with the internal friction
angle of 40 deg. The theory for extra load transfer from the angle of pile taper in sand layers is only
applicable by the FHWA method, which adopts the recommendations by Nordlund (1963, 1970).
Figure 5.16 Pile layout and soil conditions of Example Problem 5.
5.6.1
Hand Computations and Comparisons with APILE
The program output will be compared to the results from the following hand calculations.
User’s Manual (Rel. Mar/2024)
APILE v2023
CHAPTER 5 – Example Problem 5 – 5-29
Step 1. Compute effective stresses in the middle of soil layers:
Layer 1: 𝜎𝜎�𝑣𝑣0 = 𝑃𝑃𝐷𝐷 = 383.4 𝑝𝑝𝑝𝑝𝑝𝑝
Layer 2: 𝜎𝜎�𝑣𝑣0 = 𝑃𝑃𝐷𝐷 = 1130.4 𝑝𝑝𝑝𝑝𝑝𝑝
Step 2. Compute 𝛿𝛿�𝜙𝜙 for each one of the layers (pile segments):
Layer 1. Compute volume:
The depth of pile at middle of first layer is equal to 9 ft + 18 ft/2 = 21 ft
The increase of radius at 21 ft above the pile tip:
𝑡𝑡𝑡𝑡𝑡𝑡 =
𝑥𝑥
=> 𝑥𝑥 = ℎ ∙ tan 𝜔𝜔
ℎ
𝑥𝑥 = 21 𝑓𝑓𝑓𝑓 tan(0.5) => 0.1832642 𝑓𝑓𝑓𝑓
Diameter of pile at middle of first layer in inches
𝐷𝐷1 = 12 + 2 * 12 * x = 12 + 2 * 12 * 0.1832642 = 16.398341
𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉 =
�12
𝜋𝜋𝐷𝐷
𝜋𝜋∗16.3983412
𝑓𝑓𝑓𝑓 3
=
= 1.4666524
4
4∗144
𝑓𝑓𝑓𝑓
Compute 𝛿𝛿�𝜙𝜙 for layer 1 (interpolate linearly):
V = 1.4
V = 1.5
𝛿𝛿� = 1.159
𝜙𝜙
𝛿𝛿� = 1.184
𝜙𝜙
1.184
− 1.159
�𝛿𝛿�𝜙𝜙 − 1.159� =
(1.4666524 − 1.4)
1.5 − 1.4
(𝛿𝛿�𝜙𝜙)𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 #1 = 1.1756631
Layer 2. Compute volume:
The increase of radius at 6 ft above the pile tip
𝑥𝑥 = ℎ ∙ tan(𝑤𝑤) = 6 ∗ tan(0.5) => 0.0523612 𝑓𝑓𝑓𝑓
Diameter of pile at middle of second layer:
𝐷𝐷2 = 12" + 2 ∗ 12 ∗ 0.0523612 = 13.256669"
𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉 =
�22 𝜋𝜋13.2566692
𝜋𝜋𝐷𝐷
=
= 0.958509 𝑓𝑓𝑓𝑓 3 ⁄𝑓𝑓𝑓𝑓
4
4 ∗ 144
Compute 𝛿𝛿�𝜙𝜙 for layer 2 (interpolate linearly):
V = 0.9
V = 1.0
𝛿𝛿� = 1.025
𝜙𝜙
𝛿𝛿� = 1.053
𝜙𝜙
1.053 − 1.025
�𝛿𝛿�𝜙𝜙 − 1.025� =
(0.958509 − 0.9)
1.0 − 0.9
User’s Manual (Rel. Mar/2024)
APILE v2023
CHAPTER 5 – Example Problem 5 – 5-30
(𝛿𝛿�𝜙𝜙)𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 #2 = 1.0413825
Step 3. Compute values of Kδ for both layers:
Layer 1:
𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉 = 1.4666524 𝑓𝑓𝑓𝑓 3 ⁄𝑓𝑓𝑓𝑓
𝜙𝜙 = 30°
Interpolate linearly for 𝑤𝑤 = 0.5°:
V=1
Kδ = 2.928
V = 10
Kδ = 3.180
(𝐾𝐾𝛿𝛿 − 2.928) =
Layer 2:
3.18 − 2.928
[log(1.4666524) − log(1)]
log(10) − log (1)
𝐾𝐾𝛿𝛿𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 1 = 2.9699145
𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉 = 0.958509 𝑓𝑓𝑓𝑓 3 ⁄𝑓𝑓𝑓𝑓
𝜙𝜙 = 40°
For w = 0.5° and any volume between 0.1 and 10 ft3/ft the value of Kδ = 17.28.
𝐾𝐾𝛿𝛿𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 2 = 17.28
Step 4. Compute the correction factor (use same digitized curves as computer program):
Layer 1:
𝛿𝛿� = 1.1756631; 𝜙𝜙 = 30°
𝜙𝜙
CF = 1.0
𝛿𝛿� = 1
𝜙𝜙
CF = 1.03
𝛿𝛿� = 1.2
𝜙𝜙
(𝐶𝐶𝐶𝐶 − 1) =
Layer 2:
For 𝜙𝜙 = 38°
1.03 − 1
(1.1756631 − 1)
1.2 − 1
𝐶𝐶𝐶𝐶𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 1 = 1.0263495
𝛿𝛿� = 1.0413825; 𝜙𝜙 = 40°
𝜙𝜙
CF = 1.0
𝛿𝛿� = 1
𝜙𝜙
𝛿𝛿� = 1.2
𝜙𝜙
CF = 1.07
(𝐶𝐶𝐶𝐶 − 1) =
For 𝜙𝜙 = 42°
User’s Manual (Rel. Mar/2024)
1.07 − 1
(1.0413825 − 1)
1.2 − 1
𝐶𝐶𝐶𝐶𝜙𝜙=38 = 1.0144839
APILE v2023
CHAPTER 5 – Example Problem 5 – 5-31
CF = 1.0
𝛿𝛿� = 1
𝜙𝜙
𝛿𝛿� = 1.2
𝜙𝜙
CF = 1.09
(𝐶𝐶𝐶𝐶 − 1) =
Interpolate linearly for Φ = 40°
Step 5. Compute values of δ:
Layer 1:
Layer 2:
1.09 − 1
(1.0413825 − 1)
1.2 − 1
𝐶𝐶𝐶𝐶𝜙𝜙=38 = 1.0186221
𝐶𝐶𝐶𝐶Φ=40° 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 2 = 1.016553
𝛿𝛿𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 1 = 1.1756631 ∗ 30° = 35.269893°
𝛿𝛿𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 = 1.0413825 ∗ 40° = 41.6553°
Step 6. Compute friction contribution for each layer:
Layer 1
𝑄𝑄𝑠𝑠 = 𝐾𝐾𝛿𝛿 ∗ 𝐶𝐶𝐶𝐶 ∗ 𝑃𝑃𝐷𝐷 ∗ �
𝑄𝑄𝑆𝑆1 = 2.9699145 ∗ 1.0263495 ∗ 383.4 ∗
sin(𝛿𝛿 + 𝑤𝑤)
� ∗ 𝐶𝐶𝑑𝑑 ∗ Δ𝑑𝑑
cos 𝑤𝑤
sin(35.269893 + 0.5)
∗ 3.1415927 ∗ 16.398341 ∗ 18
cos(0.5)
𝑄𝑄𝑆𝑆1 = 52790.621 [𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝]
Layer 2
𝑄𝑄𝑆𝑆2 = 17.28 ∗ 1.016553 ∗ 1130.4 ∗
sin(41.6553 + 0.5)
13.25669
∗ 3.1415927 ∗
∗ 12
cos(0.5)
12
𝑄𝑄𝑆𝑆2 = 555037.24 [𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝]
Compute total frictional resistance:
𝑄𝑄𝑠𝑠 = 𝑄𝑄𝑆𝑆1 + 𝑄𝑄𝑆𝑆2 = 52.79[𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑘] + 555.04[𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑘] = 607.83[𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑘]
which compares to 575.5 kips computed by APILE
Step 7. Compute tip resistance contribution from FHWA method:
Qp = Ap q α t N q'
(5.21)
where
Ap
is the pile tip bearing area,
q
is the vertical stress at pile base level,
N q′ = bearing capacity factor (see figure in Technical Manual), and
User’s Manual (Rel. Mar/2024)
APILE v2023
CHAPTER 5 – Example Problem 5 – 5-32
αt = dimensionless factor dependent on the depth-width relationship of the pile (see figure in
Technical Manual).
𝐴𝐴𝑝𝑝 = π 𝐷𝐷𝑝𝑝2 /4 = 3.14 (12)2 /4 = 113.1 in2 = 0.785 ft2
q = 42.6 lb/ft3 x 18 ft + 60.6 lb/ft3 x 12 ft = 1494 lb/ft2
N q′ = 160
αt = 0.75
Qp = 140.7 kips which compares well to 140.8 kips computed by APILE
Step 8. Compute limiting tip resistance:
QL = 327.98 kips which is higher so not controlling
Step 9. Total static pile capacity is then
𝑄𝑄𝑇𝑇 = 607.83[𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑘] + 140.81[𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑘] => 748.64 𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑘 , which compares well to the 716.3 kips
obtained from the APILE model.
(APILE is more accurate since it divides the pile sections into smaller increments)
5.6.2
Input and Output Data Files for Example 5
Users can read Section 2.1.1 (7) of this manual for reference on the location of placement of the input and
output data files for the example files installed with this program. The default installation directory is the
following: (Root Drive) c:\Ensoft\Apile2023-Examples. The input data files for all examples presented in
this manual are installed automatically with the program.
The input-data filename for Example 5 is the following:
Example 5 - FHWA Tapered Pile.ap10d
The output-data filename for Example 5 is the following:
Example 5 - FHWA Tapered Pile.ap10o
5.6.3
Graphical Results of Computer Analysis
The resulting plots of ultimate total capacity versus depth provided by the computer program may
be observed in Figure 5.17. Figure 5.18 includes a plot of axial load versus settlement.
User’s Manual (Rel. Mar/2024)
APILE v2023
CHAPTER 5 – Example Problem 5 – 5-33
Figure 5.17 Curve of Combined Plots (Ultimate Total Capacity) vs Depth for Example
Problem 5.
Figure 5.18 Axial Load vs Settlement for Example Problem 5.
User’s Manual (Rel. Mar/2024)
APILE v2023
CHAPTER 5 – Example Problem 6 – 5-34
5.7
Example Problem 6 – Uplift Pile Capacity
5.7.1
Description
Piles may be subjected to loads in tension instead of compression. The tension capacity of piles
differs from the compression capacity of piles in both the side friction and end bearing. For piles under
tension the soil resistance is from the side friction only.
Some research recommends applying a reduction factor to the side friction when the pile moves
upward based on field experimental studies. This may be caused by less confining pressure from the soil
around the pile under tension. This example includes an arbitrary reduction factor of 0.8 for tension
capacity (under Data > Computational Method > Method for Pile Capacity > Type of Loading >
Tension).
A different reduction in side friction may be specified primarily to cover a distance near the shallow
depth. This example includes an arbitrary 4-meter exclusion of friction in the top soil layer (under Data >
Circular Pile Section > Zero-Friction Length from Ground).
The tension capacity of piles should also include the self-weight of piles. This is automatically
accounted within APILE according to the pile type/material selected by the user. The values computed by
APILE are included in a column in the output text file.
This example illustrates a common case for study of the tension capacity of a pipe pile. The soil
deposit consists of six sub-layers as shown in Table 5.7. The pile is a 60-m long, open-ended steel pipe,
with an outer diameter of 1000 mm and an inner diameter of 936 mm.
The output is shown in detail so the user can examine the increase in pile capacity with depth. The
user may elect to eliminate the printing of capacity for each increment length to shorten the length of output.
Layer
1
2
3
4
5
6
Depth
Soil Type
(m)
0
10
10
20
20
30
30
40
40
50
50
100
Clay
γ'
Cu
(kN/m3) (kN/m2)
0.1
4
20
φ
Ko
Nq
---
---
---
(Deg.)
Sand
9
---
34
0.6
20
Clay
6
200
200
---
---
---
Sand
9
---
36
0.6
30
Clay
9
350
350
---
---
---
Sand
9
---
38
0.6
30
Table 5.7 Soil data for Example Problem 6
User’s Manual (Rel. Mar/2024)
APILE v2023
CHAPTER 5 – Example Problem 6 – 5-35
5.7.2
Input and Output Data Files for Example 6
Users can read Section 2.1.1 (7) of this manual for reference on the location of placement of the input and
output data files for the example files installed with this program. The default installation directory is the
following: (Root Drive) c:\Ensoft\Apile2023-Examples. The input data files for all examples presented in
this manual are installed automatically with the program.
The input-data filename is the following:
Example 6 - Uplift Pile Capacity.ap10d
The output-data filename is the following:
Example 6 - Uplift Pile Capacity.ap10o
5.7.3
Graphical Results of Computer Analysis
The resulting plots of ultimate total capacity versus depth provided by the computer program may
be observed in Figure 5.19. The self-weight of the pile is included in the total capacity for the uplift (tensile)
capacity. Figure 5.20 includes a plot of uplift load versus uplift movement.
Figure 5.19 Curve of Ultimate Total Capacity vs Depth for Example Problem 6.
User’s Manual (Rel. Mar/2024)
APILE v2023
CHAPTER 5 – Example Problem 6 – 5-36
Figure 5.20 Curve of Axial Load vs Movement for Example Problem 6.
User’s Manual (Rel. Mar/2024)
APILE v2023
CHAPTER 5 – Example Problem 7 – 5-37
5.8
Example Problem 7 (Offshore Version) – CPT Based Methods for
Close-Ended Pile
Many of the existing semi-empirical methods for predicting the axial capacity of driven piles were
developed approximately two decades ago on the basis of an extended database of static-loading tests. The
soil properties and subsurface conditions were obtained primarily by conventional sampling methods and
testing equipment, including the Standard Penetration Test (SPT), field-vane test, and triaxial-undrained
(UU) tests using undisturbed soil samples, taken by the use of Shelby tubes.
Recently, the cone penetration test (CPT) has been widely used in subsurface exploration worldwide,
especially in the offshore industry. The American Petroleum Institute (API) conducted a review of CPTbased methods for assessment of the axial capacity of driven piles. Two CPT-based methods have been
studied and adopted by API as alternate design methods. Those two CPT-based methods that were selected
by API are: the NGI-99 method developed by the Norwegian Geotechnical Institute and the MTD method
developed by Imperial College in London (Richard Jardine et al, 2005).
The example included here are for the customers who purchased the offshore-version of APILE.
This example is for an offshore application and will focus on the axial capacity of closed-ended piles
predicted by different semi-empirical methods. Computed results from four CPT-based methods are
included for comparison. The pile is a 60-m long pipe with a closed end and with an outer diameter of
2134 mm and an inner diameter of 2044 mm. The soil deposit consists of six sub-layers and the soil
properties, including those from CPT tests, are shown in Table 5.8.
Layer
1
2
3
4
5
6
Depth
(m)
0
10
10
20
20
30
30
40
40
50
50
100
Soil Type
γ'
3
(kN/m )
Cu
2
(kN/m )
0.1
20
φ
(Deg.)
Ko
Nq
---
---
---
Clay
4
Sand
9
---
34
0.6
20
Clay
6
200
200
---
---
---
Sand
9
---
36
0.6
30
Clay
9
350
350
---
---
---
Sand
9
---
38
0.6
30
Qc
1
200
10,500
20,000
2,000
2,000
30,500
39,500
5,000
5,000
50,000
50,000
PI
YSR
50
2
---
---
20
3
---
---
15
3
---
---
Table 5.8 Soil data for Example Problem 7
5.8.1
Comparison of APILE Results with Hand Computations
Table 5.9 and Table 5.10 contains various comparisons of the results obtained from approximate
hand computations (spreadsheet) against those from the computer run in APILE for two different offshore
methods.
User’s Manual (Rel. Mar/2024)
APILE v2023
CHAPTER 5 – Example Problem 7 – 5-38
Layer
1
2
3
4
5
6
Depth
(m)
0
10
10
20
20
30
30
40
40
50
50
60
NGI METHOD
Soil Type
Total Skin Friction (kN)
Hand Calc
Computer
Clay
516
537
Sand
3,504
3,571
Clay
6,280
6,251
Sand
14,859
14,780
Clay
12,014
11,844
Sand
30,033
28,619
Table 5.9 Comparison of results for NGI Method in Example Problem 7
Layer
1
2
3
4
5
6
Depth
(m)
0
10
10
20
20
30
30
40
40
50
50
60
MTD METHOD
Soil Type
Total Skin Friction (kN)
Hand Calc
Computer
Clay
295
268
Sand
4,048
3,783
Clay
5,767
5,313
Sand
12,360
13,503
Clay
17,572
15,206
Sand
30,114
33,711
Table 5.10 Comparison of results for MTD Method in Example Problem 7
5.8.2
Input and Output Data Files for Example 7
Users can read Section 2.1.1 (7) of this manual for reference on the location of placement of the input and
output data files for the example files installed with this program. The default installation directory is the
following: (Root Drive) c:\Ensoft\Apile2023-Examples. The input data files for all examples presented in
this manual are installed automatically with the program.
The input-data filename is the following:
Example 7 - CPT Methods on Close Ended Pile.ap10d
User’s Manual (Rel. Mar/2024)
APILE v2023
CHAPTER 5 – Example Problem 7 – 5-39
The output-data filename is the following:
Example 7 - CPT Methods on Close Ended Pile.ap10o
5.8.3
Graphical Results of Computer Analysis
The resulting plots of total capacity from different empirical methods and axial load versus settlement
computed based on MTD method may be observed in Figure 5.21 and Figure 5.22.
Figure 5.21 Curves of Ultimate Total Capacity vs Depth for Example Problem 7.
User’s Manual (Rel. Mar/2024)
APILE v2023
CHAPTER 5 – Example Problem 7 – 5-40
Figure 5.22 Curve of Axial Load vs Settlement for Example Problem 7.
User’s Manual (Rel. Mar/2024)
APILE v2023
CHAPTER 5 – Example Problem 8 – 5-41
5.9
Example Problem 8 (Offshore Version) – CPT Based Method for
Open-Ended Pile
Many large offshore piles are driven with an open-ended tip. It is obvious that soil will be pushed
into the pile through the pile tip during pile driving, forming a soil plug inside the pipe pile. If the soil plug
develops excessive side friction on the inner wall at a certain depth, the soil plug may not be pushed further
into the pipe pile by driving. This condition is typically referenced as a fully plugged pile. On the other
hand, the soil plug may be pushed up continuously during pile driving because the friction developed on
the inner wall is not strong. In this case the pile tip is not fully plugged and it is usually referenced as an
unplugged pile.
The determination if the pile acts as a fully plugged pile or as an unplugged pile is a very complicated
task. One simple approach is described in the APILE Technical Manual. For unplugged conditions, the
total soil resistance at the tip is the sum of the side friction along the inner surface of the pile and the end
bearing from the metal area at the pile tip. If the pile is fully plugged, the soil resistance at the pile tip is
derived from end bearing over the full area of the base. Comparing the soil resistance at the tip, based on
the above two different conditions, the user may take the results from APILE with the smaller one for the
recommended tip resistance.
The total length of soil plug formed inside the pipe pile depends on the soil properties in each sublayer. In many cases the length of the soil plug may be less than 50% of the total pile penetration. The
MTD method (as well as other offshore methods) directly asks the user to determine the plug condition as
one of the required input parameters.
This example is included for the customers who purchased the offshore-version of APILE. This
example will focus on the axial capacity of open-ended, unplugged piles predicted by four CPT-based semiempirical methods (NGI, MTD, Fugro, and UWA methods) for an offshore application. The pile is a 60m-long pipe with an outer diameter of 2134 mm and an inner diameter of 2044 mm. The soil deposit
consists of six sub-layers and the soil properties, including Qc from the CPT tests, are shown in Table 5.11.
Notice that from the output text file from APILE, a pile plug fully develops (no asterisk in output
table) after 34 meters of pile penetration using the NGI Method and after 29 meters of pile penetration for
the MTD Method.
Layer
1
2
3
4
5
6
Depth
(m)
0
10
10
20
20
30
30
40
40
50
50
100
Soil Type
γ'
3
(kN/m )
Cu
2
(kN/m )
0.1
20
φ
(Deg.)
Ko
Nq
---
---
---
Clay
4
Sand
9
---
34
0.6
20
Clay
6
200
200
---
---
---
Sand
9
---
36
0.6
30
Clay
9
350
350
---
---
---
Sand
9
---
38
0.6
30
User’s Manual (Rel. Mar/2024)
Qc
1
200
10,500
20,000
2,000
2,000
30,500
39,500
5,000
5,000
50,000
50,000
PI
YSR
50
2
---
---
20
3
---
---
15
3
---
---
APILE v2023
CHAPTER 5 – Example Problem 8 – 5-42
Table 5.11 Soil data for Example Problem 8
5.9.1
Comparison of APILE Results with Hand Computations
Table 5.12 and Table 5.13 contains various comparisons of the results obtained from approximate
hand computations (spreadsheet) against those from the computer run in APILE for two different offshore
methods.
Depth
(m)
0
10
10
20
20
30
30
40
40
50
50
60
Layer
1
2
3
4
5
6
NGI METHOD
Soil Type
Total Skin Friction (kN)
Hand Calc
Computer
Clay
516
537
Sand
2,513
2,253
Clay
6,280
6,145
Sand
9,288
9,361
Clay
12,014
11,498
Sand
18,771
18,111
Table 5.12 Comparison of results for NGI Method in Example Problem 8
Layer
1
2
3
4
5
6
Depth
(m)
0
10
10
20
20
30
30
40
40
50
50
60
MTD METHOD
Soil Type
Total Skin Friction (kN)
Hand Calc
Computer
Clay
230
209
Sand
2,563
2,399
Clay
4,495
4,099
Sand
7,771
8,535
Clay
13,697
11,720
Sand
24,032
26,010
Table 5.13 Comparison of results for MTD Method in Example Problem 8
User’s Manual (Rel. Mar/2024)
APILE v2023
CHAPTER 5 – Example Problem 8 – 5-43
5.9.2
Input and Output Data Files for Example 8
Users can read Section 2.1.1 (7) of this manual for reference on the location of placement of the input and
output data files for the example files installed with this program. The default installation directory is the
following: (Root Drive) c:\Ensoft\Apile2023-Examples. The input data files for all examples presented in
this manual are installed automatically with the program.
The input-data filename is the following:
Example 8 - CPT Methods on Open Ended Pile.ap10d
The output-data filename is the following:
Example 8 - CPT Methods on Open Ended Pile.ap10o
5.9.3
Graphical Results of Computer Analysis
The resulting plots of the total capacity predicted by different methods and the axial load versus
settlement based on the NGI method may be observed in Figure 5.23 and Figure 5.24, respectively.
Figure 5.23 Curves of Ultimate Total Capacity vs Depth for Example Problem 8.
User’s Manual (Rel. Mar/2024)
APILE v2023
CHAPTER 5 – Example Problem 8 – 5-44
Figure 5.24 Curve of Axial Load vs Settlement for Example Problem 8.
User’s Manual (Rel. Mar/2024)
APILE v2023
CHAPTER 5 – Example Problem 9 – 5-45
5.10 Example Problem 9 – LRFD Method on Closed Pipe Pile
An example is presented from the National Highway Institute’s publication titled “Load and
Resistance Factor Design (LRFD) for Highway Bridge Substructures” (NHI, 2001) to illustrate a simple
example of driven piles as foundations based on the LRFD method. This example is included to
demonstrate the convenience of using APILE in the design of driven piles under axial loads based on the
new LRFD design procedures.
The proposed driven pile is a close-ended steel pipe pile with an outside diameter of 460 mm. The
wall thickness is 12.7 mm. The total length (penetration) below the original grade (without scouring) is 12
meters. The configuration and loading of the proposed bridge substructures are shown in Figure 5.25.
Figure 5.25 Bridge substructures configuration and loading for Example Problem 9.
5.10.1 Soil Profile and Properties
A generalized subsurface profile along the alignment of the bridge is shown in Figure 5.26. The
subsurface soils are predominated by fine sand and medium dense to dense sand. The soil density and
strength increase with depth.
User’s Manual (Rel. Mar/2024)
APILE v2023
CHAPTER 5 – Example Problem 9 – 5-46
The water table is at the 2 m below the existing ground surface. Soil properties for use in analysis
includes unit weight and the penetration resistance (SPT blow counts).
5.10.2 Loading Computations
The unfactored vertical loads on the pile group (substructure) shown in Figure 5.25 include:
DC (Dead load of structural components and non-structural attachments) = 4600 kN.
DW (Dead load of wearing surfaces and utilities) = 3900 kN.
LL (Vertical live load) = 3450 kN.
The total unfactored load (Q) is:
Q = DC + DW + LL
= 4600 kN + 3900 kN + 3450 kN
= 11950 kN
For the Strength I and Service I Limit States, the factor load is expressed as
� � η𝑖𝑖 𝛾𝛾𝑖𝑖 𝑄𝑄𝑖𝑖
Assume a typical structure such that ηi = 1.0. The load factors for Limit States of Strength I and
Service I are listed in Table 5.14.
Limit State
γDC
γDW
γLL
Strength I
1.25
1.25
1.75
Service I
1.00
1.00
1.00
Table 5.14 Summary of factored loads for Example Problem 9
User’s Manual (Rel. Mar/2024)
APILE v2023
CHAPTER 5 – Example Problem 9 – 5-47
Figure 5.26 General soil description of Example Problem 9
The total factored load effects are then calculated as follows.
For the Strength I Limit State:
∑η𝑖𝑖 𝛾𝛾𝑖𝑖 𝑄𝑄𝑖𝑖 = ηi [ γDC DC + γDW DW + γLL LL ]
= (1.0) [ (1.25) (4600 kN) + (1.50) (3900 kN) + (1.75) (3450 kN) ]
= 17638 kN
User’s Manual (Rel. Mar/2024)
APILE v2023
CHAPTER 5 – Example Problem 9 – 5-48
For the Service I Limit State:
∑ η𝑖𝑖 𝛾𝛾𝑖𝑖 𝑄𝑄𝑖𝑖 = ηi [ γDC DC + γDW DW + γLL LL ]
= (1.0) [ (1.0) (4600 kN) + (1.0) (3900 kN) + (1.0) (3450 kN) ]
= 11950 kN
5.10.3 APILE Estimated Axial Capacity of Single Pile from N60 SPT
Calculations of nominal side and base resistance were carried out in APILE (filename “Example 9 LRFD Method on Closed Pipe Pile - Initial.ap10d”). Table 5.15 shows the calculated ultimate side friction
and ultimate tip resistance for various methods and the values provided by the referenced publication (NHI,
2001). The NHI manual uses Meyerhof (1976) which provides low estimate of side friction rom SPT
values. The NHI manual also references the Field Tests from Vesic (1970) done on a test pile at the same
site. The FHWA results from APILE are close to those from the Vesic, 1970, field tests.
Methods
NHI 2001 (Meyerhof, 1976)
FHWA method
US ARMY method
API method
Field Test (Vesic, 1970)
Side Friction, kN
Tip Resistance, kN
445
1028
730
759
1180
1460
1267
1047
802
1900
Total Ultimate
Capacity, kN
1905
2295
1777
1561
3080
Table 5.15 Initial calculations of ultimate axial compressive capacity for Example 9
The factored axial resistance of a single pile is:
QR = φ Qult = φqp Qp + φqs Qs
The reduction factors for the computation methods based on SPTs are:
φqp = 0.45
φqs = 0.45
The reduction factors for the axial capacity of a driven pile based on a full-scale loading test are:
φqp = 0.8
φqs = 0.8
The factored side friction and tip resistance for the methods above (filename “Example 9 - LRFD
Method on Closed Pipe Pile - Final.ap10d”) and the result from the full-scale loading test are presented in
Table 5.16. Based on Strength I Limit State, the total factored load is 17638 kN. If the designer selects the
factored pile capacity based on FHWA method (Total Factored Capacity of 1033 kN), the substructure pile
group will need 17 piles. On the other hand, having a local site test (Vesic, Total Factored Capacity of
2464 kN) can reduce the pile group to 7 or 8 piles.
User’s Manual (Rel. Mar/2024)
APILE v2023
CHAPTER 5 – Example Problem 9 – 5-49
Methods
Side Friction, kN
NHI 2001 (Meyerhof, 1976)
FHWA method
US ARMY method
API method
Field Test (Vesic, 1970)
200
463
329
341
944
Tip Resistance, kN
657
570
471
361
1520
Total Factored
Capacity, kN
857
1033
800
702
2464
Table 5.16 Final calculations of factored axial compressive capacity for Example 9
5.10.4 Input and Output Data Files for Example 9
Users can read Section 2.1.1 (7) of this manual for reference on the location of placement of the input and
output data files for the example files installed with this program. The default installation directory is the
following: (Root Drive) c:\Ensoft\Apile2023-Examples. The input data files for all examples presented in
this manual are installed automatically with the program.
The input-data filenames are the following:
Example 9 - LRFD Method on Closed Pipe Pile - Initial.ap10d
Example 9 - LRFD Method on Closed Pipe Pile - Final.ap10d
The output-data filenames are the following:
Example 9 - LRFD Method on Closed Pipe Pile - Initial.ap10o
Example 9 - LRFD Method on Closed Pipe Pile - Final.ap10o
5.10.5 Graphical Results of Computer Analysis
The results of factored side friction, tip resistance, and total capacity versus depth provided by the
computer program for FHWA method were plotted together in Figure 5.27 and Figure 5.28 includes a plot
of axial load versus settlement. Based on Service I Limit States, the total factored load is 11950 kN on a
total of 17 piles. Therefore, each pile will take 703 kN, which will have an approximate settlement of 0.003
m as indicated in Figure 5.28.
User’s Manual (Rel. Mar/2024)
APILE v2023
CHAPTER 5 – Example Problem 9 – 5-50
Figure 5.27 Curve of LRFD Geotechnical Capacity (Factored Capacity) vs Depth for
Example Problem 9 (FHWA Method).
Figure 5.28 Curve of Axial Load vs Settlement for Example Problem 9.
User’s Manual (Rel. Mar/2024)
APILE v2023
CHAPTER 5 – Example Problem 10 – 5-51
5.11 Example Problem 10 – Battered Pile
Battered piles are used to resist large lateral loads when there is a large unsupported pile length or in
weak soils where there is little lateral support. Many offshore or marine structures are subjected to
overturning moments due to wind load, wave pressure, and ship impacts. Also, retaining walls are subjected
to horizontal forces and bending moments due to earth pressure. For foundations in such structures,
designers often evaluate the use of combinations of vertical and batter piles.
The ability to install driven piles on an angle, or batter, gives such piles a distinct advantage with
respect to their ability to carry lateral loads. Batter piles carry lateral loads primarily in axial compression
and/or tension while vertical deep foundations carry lateral loads in shear and bending. When subjected to
lateral loading, batter piles will therefore generally have a greater capacity and be subject to smaller
deformations than vertical piles of the same dimensions and material.
A pile driven on an angle is usually expressed as a batter ratio (horizontal to vertical). Example of
1:6 batter ratio is a 1-foot horizontal to 6-feet vertical, and sometimes the batter ratio is also expressed as a
batter angle between the pile axis and the vertical.
5.11.1 Soil Profile and Pile Properties
A generalized subsurface profile along the alignment of the bridge is shown in Figure 5.29. The
subsurface soils are predominantly soft to medium stiff and stiff normal consolidated clay nearby a coastal
area. The soil density and strength increase with the increase of soil depth. The water table is at the existing
ground surface. Soil properties for use in analysis include effective unit weight (γ’) and undrained shear
strength (c), which are presented in the soil profile.
Steel pipe piles with 24-in OD and wall thickness of 0.5 inches are considered for this application.
The pile will be installed with 1 to 1.5 batter ratio degrees (1.0H:1.5V), which represents a batter angle of
approximately 33.7 degrees (input into APILE). The total embedded pile length is 144 ft, which will
penetrate approximately 6 ft into the bottom stiff clay layer. The pile will be driven based on the specified
batter ratio with a close-ended pile tip. The API method is used for prediction of the axial compressive
capacity of the battered pile for this application. The total side resistance can also be considered as pullout capacity (under tension). Some applications may apply a reduction factor on the side friction for the
uplift (pull-out) capacity if the pile has short embedded length.
User’s Manual (Rel. Mar/2024)
APILE v2023
CHAPTER 5 – Example Problem 10 – 5-52
Figure 5.29 General soil description of Example Problem 10
5.11.2 Hand Computations and Comparisons with APILE
The program output will be compared to the results from the following hand calculations.
5.11.2.1 API Method – Skin Friction
Computations of side resistance were performed using a spreadsheet, with the following results:
The total side friction from the table above is approximately 641 kips vs. 633 kips from APILE.
User’s Manual (Rel. Mar/2024)
APILE v2023
CHAPTER 5 – Example Problem 10 – 5-53
5.11.2.2 API Method – End Bearing
The tip area (closed ended tip) = 3.14 ft2
The unit tip resistance = 9 (1500 psf) = 13,500 lbs/ft2 = 13.5 k/ft2
The total tip resistance = 13.5 (3.14) =42.4 kips vs. 42.4 kips from APILE.
5.11.2.3 API Method – Total Capacity
The total compressive capacity is approximately 683 kips using approximate hand computations and
675 kips from APILE. The total pull-out capacity, without applying a reduction factor, is 641kips for the
battered pile (based on approximate hand computations, 633 kips based on APILE results). For comparison,
if the pile is driven vertically without the batter to the same tip elevation (the pile tip at 6 ft into the bottom
clay layer), the compressive capacity will be only 582 kips.
5.11.3 Input and Output Data Files for Example 10
Users can read Section 2.1.1 (7) of this manual for reference on the location of placement of the input and
output data files for the example files installed with this program. The default installation directory is the
following: (Root Drive) c:\Ensoft\Apile2023-Examples. The input data files for all examples presented in
this manual are installed automatically with the program.
The input-data filename is the following:
Example 10 - API Method on Battered Pile.ap10d
The output-data filename is the following:
Example 10 - API Method on Battered Pile.ap10o
5.11.4 Graphical Results of Computer Analysis
The APILE results of factored side friction, tip resistance, and total capacity versus length along the
battered pile for the API method are plotted together in Figure 5.30. Axial load versus settlement is in
Figure 5.31.
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CHAPTER 5 – Example Problem 10 – 5-54
Figure 5.30 Curve of Combined Plots (Ultimate Total Capacity) vs Battered Length for
Example Problem 10.
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CHAPTER 5 – Example Problem 10 – 5-55
Figure 5.31 Axial Load vs Settlement for Example Problem 10.
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CHAPTER 5 – Example Problem 11 – 5-56
5.12 Example Problem 11 – CPT to APILE
This example is used to demonstrate various features for importing and processing of data files
obtained from cone penetration tests (CPT) into soil layers for APILE. Users may start with a new data file
(File > New) and select to import CPT data (Data > Import CPT Data) or users may open an existing
APILE model that needs to be modified with a new soil profile generated from imported CPT data. This
example describes importing into a new data file, but the process is similar for importing into an existing
file/APILE model.
5.12.1 Sample CPT Data
A soil testing agency that was contracted for the CPT test at a site provides the user with a CPT data
file and the information in Table 5.17. This is the only required information for importing and interpreting
the CPT data into APILE. The sample CPT data file ‘Example 11 - CPT-01 - Ensoft Site.cpd’ in included
within the files for this APILE example.
CPT File Name:
Example 11 - CPT01 - Ensoft Site.cpd
Column 1:
Column 2:
Column 3:
Column 4:
Column 5:
Cone:
Ground Water:
15 cm with Net Area Ratio = 0.80
15.8 ft during testing
Depth (m)
Qc (tsf)
Fs (tsf)
Pore Pressure (psi)
Inclinometer
(degrees)*
* This value/parameter is not currently used or necessary for importing or interpretation
Table 5.17 Summary of Sample CPT Data from Testing Agency
5.12.2 Importing & Interpreting CPT Data
Selection of Data > Import CPT Data for the sample CPT data file (Example 11 - CPT-01 - Ensoft
Site.cpd) using parameters from Table 5.17 above are displayed in Figure 5.32. Selecting the Import button
(lower right in Figure 5.32) provides a new screen similar to Figure 5.33.
Notice that the units in the screen are now consistent English units (Depth in feet and Qtip in psf),
since the new APILE data file was started with English units. If the user desires to have metric/SI units
then start the process again with a new APILE file and select SI Units (Options > Units > S.I. Units).
The user has to enter new soil layers (using the green + button), select soil types, select layer depths,
and enter the mechanical properties for the top and bottom of each soil layer. After close evaluations of the
different interpreted parameters from the CPT file, the user may reach similar modeling decisions as those
partially shown in Figure 5.34. The full set of parameters can be found by opening Example 11 (Example
11 - CPT to APILE.ap10d) and selecting Data > Soil Layers > Edit Soil Layers with CPT.
5.12.3 Pile Properties & Computation Methods
The pile data is not consequential for this example, but the model assumes a steel pipe pile with 24in OD and wall thickness of 0.5 inches with a length/penetration of 65 ft. The FHWA, USACE and API
methods are used for prediction of the axial compressive capacity, while the API method is used for the
load-settlement curves.
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CHAPTER 5 – Example Problem 11 – 5-57
In addition, this model also selects the NGI, MTD, Fugro and UWA methods (for the APILE
Offshore Version) since those are better associated to CPT-based parameters. For side resistance in
cohesive soils, these CPT methods also use two other variables (Plasticity Index in NGI and Yield Stress
Ratio in the other methods) which need to be provided by the soil investigation or computed by the user
outside APILE. This example uses the values shown in Table 5.18, but the user should read the applicable
sections in Chapter 3 of the APILE Technical Manual for notes regarding these variables.
In particular, the following reference is provided for the Yield Stress Ratio:
Yield Stress Ratio (YSR) is defined as the vertical effective yield stress (σ’vy) to the vertical
in situ effective stress (σ’vo). OCR (over-consolidation ratio) is defined as the vertical
maximum pre-consolidation effective stress (σ’vc) to the vertical in situ effective stress
(σ’vo). YSR is also named as apparent OCR in some literature, but generally YSR is greater
than OCR.
Layer
Depths (ft)
10.5
26.6
30.0
42.0
53.5
59.0
Clay
Clay
Clay
Plasticity
Index (%)
30
30
25
25
20
20
Yield Stress
Ratio
2.0
2.0
2.0
2.0
3.0
3.0
Table 5.18 PI and YSR for Example 11.
5.12.4 Input and Output Data Files for Example 10
Users can read Section 2.1.1 (7) of this manual for reference on the location of placement of the input and
output data files for the example files installed with this program. The default installation directory is the
following: (Root Drive) c:\Ensoft\Apile2023-Examples. The input data files for all examples presented in
this manual are installed automatically with the program.
The input-data filename is the following:
Example 11 - CPT to APILE.ap10d
The output-data filename is the following:
Example 11 - CPT to APILE.ap10o
5.12.5 Graphical Results of Computer Analysis
APILE results of unfactored total capacity versus length for the various computational methods are
plotted together in Figure 5.35. Axial load versus settlement is in Figure 5.36.
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CHAPTER 5 – Example Problem 11 – 5-58
Figure 5.32 CPT Data Import Parameters for Example 11
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CHAPTER 5 – Example Problem 11 – 5-59
Figure 5.33 Sample Blank Soil Data from Newly Imported CPT Data
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CHAPTER 5 – Example Problem 11 – 5-60
Figure 5.34 Sample Soil Data from Imported CPT for Example 11
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CHAPTER 5 – Example Problem 11 – 5-61
Figure 5.35 Ultimate Total Capacity vs Pile Length for Example Problem 11.
Figure 5.36 Axial Load vs Settlement for Example Problem 11.
User’s Manual (Rel. Mar/2024)
APILE v2023