Laboratory Manual
CEE121 Introduction to Civil and Environmental
Engineering Measurements
Carlton L. Ho, P.E.
Department of Civil and Environmental Engineering
University of Massachusetts Amherst
Amherst, MA 01003
Spring 2005
[Reference: University of Massachusetts Amherst (2005). Laboratory Manual CEE121
Introduction to Civil and Environmental Engineering Measurements. Dept. of Civil and
Environmental Engineering, University of Massachusetts Amherst, Amherst, MA.]
TABLE OF CONTENTS
Page
1. INTRODUCTION
1.1
2. ENGINEERING UNITS
2.1
3. REPORTING ENGINEERING MEASUREMENTS
3.1
- Accuracy and Precision
- Significant Figures
- Rounding of Numbers
4. PREPARATION OF ENGINEERING LABORATORY REPORTS
- Report Grading
- Report Guidelines
- Model Report
4.1
1.0 INTRODUCTION
Welcome to the CEE Measurements class. In this class you will learn how to conduct some
common civil and environmental engineering measurements. This is a "hands-on" course. With
the guidance of the course professor and teaching assistants you will conduct 10 sets of
experiments that primarily cover basic laboratory measurements and surveying. This manual
serves as a guide for preparation of your laboratory reports. It contains background information
on engineering units, reporting engineering measurements, and guidelines on how to prepare a
laboratory report.
The format for preparation of your engineering reports is similar to that developed by the
department for the junior year laboratory classes and also used in the CEE111 class.
2.0 ENGINEERING UNITS
We will conduct measurements in this course using both the traditional English system and Le
Système International d'Unités (SI). However, the SI system is the preferred system of units for
many of your CEE classes and you should know it well. The following is a guide to the SI
system from the American Society for Testing and Materials.
ASTM (1999) Annual Book of ASTM Standards. ASTM, West Conshohocken, PA.
2.1
3.0 REPORTING ENGINEERING MEASUREMENTS
The document on the following pages from the American Society for Testing and Materials
(ASTM 1999. Annual Book of ASTM Standards. ASTM, West Conshohocken, PA) is a guide for
reporting engineering measurements including: difference between precision and accuracy,
significant digits, and rounding numbers.
There are two important issues regarding significant figures:
1. Conducting calculations with appropriate significant figures. See the following document for
the rules to follow.
2. How to report laboratory data to the appropriate number of significant figures. When making
laboratory measurements you must pay attention to the number of significant figures you record
the data to. This depends on the accuracy and precision of your measurements. Once you decide
this, all subsequent calculations with your measurements must follow the rules of significant
figures.
3.1
4.0 PREPARATION OF ENGINEERING LABORATORY
REPORTS
There are many styles and formats for preparing engineering reports. The following are
guidelines for preparing your CEE121 engineering laboratory reports. Also included in this
section is the grading system that will be used to evaluate your reports.
All reports must be prepared in their entirety using a personal computer, this includes using a
word processor for text (e.g., Word, etc.), a graphics program for plotting data (e.g., Excel,
SigmaPlot, etc.), a spreadsheet program for data reduction (e.g., Excel), and a drawing program
for sketches (e.g., AutoCad, etc.). All text is to be doubled spaced (except where noted below)
using a 12 point font (engineering reports are often single spaced but we need room to write
comments). Most reports are prepared using Times New Roman font. Keep in mind that you are
preparing a professional engineering report that must be of the highest quality both in terms of
technical content and presentation.
4.1 LABORATORY REPORT GUIDELINES
The following is to be used as a guide for preparing all laboratory reports in this course. The
actual style of each report may vary depending on the specific assignment being conducted.
See attached Model Report "Results of Direct Shear Tests Conducted on Ottawa Sand" as an
example of a report prepared in general accordance with these instructions.
Outline:
1. Cover Letter of Transmittal. The cover letter of transmittal is the official means of
transmitting the report to your client. Describe what the report is for, indicate that the work was
done in accordance to accepted engineering practices (in CEE121 that would be mostly in
accordance to the instructions provided to you in the laboratory) and urge your client to contact
you with any questions or concerns. All members of your group are to sign the letter.
2. Cover page. The cover page for each lab report should include the title of the report, the
person, company or agency the report is prepared for and their address; the person, company or
agency the report was prepared by and their address; and the date.
This is page "i" of the report but do not put the number on this page.
3. Executive Summary. On its own page, preceding the main body of the report, is an executive
summary. This is one of the most important sections of a technical report. It offers the reader a
summary of what is contained in the report. The executive summary should be concise (limit to
one page) and should briefly summarize the objectives (why did you do the lab?), materials
(what did you test?), methods (what standard methods were used? what modifications were
made.), most important results and significance of the results.
4.1
This is page "ii" of the report, numbered bottom center, using lowercase roman numerals in 12point font.
NOTE: you are NOT required to prepare an Executive Summary for CEE121.
4. Table of Contents. List each section title and the page it appears on.
This is page "iii" of the report. Title heading is "TABLE OF CONTENTS", top center of the
page.
5. List of Tables with page numbers. List of Table titles with the page number each table
appears on. Tables are presented either in the main body of the report as close as possible after
the first reference to the table or at the end of the main body of the report.
This is page "iv" of the report (or next number in sequence if Table of Contents is greater than 1
page). Title heading is "LIST OF TABLES", top center of the page.
6. List of Figures with page numbers. List of Figure titles with the page number each figure
appears on. Figures are presented either in the main body of the report as close as possible after
the first reference to the figure or at the end of the main body of the report following the figures.
This is page "v" of the report (or next number in sequence). Title heading is "LIST OF
FIGURES", top center of the page. If the List of Tables and List of Figures are short they can be
placed on one page.
7. List of Symbols. Alphabetical order, English first followed by Greek. Give definition and
units.
This is page "vi" of the report (or next number in sequence). Title heading is "LIST OF
SYMBOLS", top center of the page.
Examples:
T = temperature [°C]
u = pore water pressure [kPa]
α = angle [° or radians]
δ = displacement [mm or m]
8. Introduction. The main body of the report begins with an introduction of 1-2 paragraphs. A
proper introduction will present enough information so that the reader can understand the
purpose of the report and the significance of the processes or phenomena being measured.
This is page 1 of the report, numbered bottom center, using Arabic numbers in 12-point font
(with all previous pages being numbered using lower case roman numerals e.g., i, ii, iii, iv, v,
etc.).
It is also section "1.0 INTRODUCTION", left justified, of the report. This and all subsequent
pages do not contain a title. Instead, they will consist of sequentially numbered sections. See the
format section for more details.
4.2
9. Objectives/Purpose. The objectives define the purpose of the report. It states what you
desire to accomplish and/or prove. Note that there is a difference between the Objective and the
Method used to reach that objective. The objectives statement should be approximately one
paragraph in length and be clear and concise.
10. Background. In some reports, a background section will be included to review such items as
past work and/or relevant theory that the reader should note.
NOTE: you are NOT required to prepare a Background section for CEE121.
11. Test Equipment and Samples Materials. If relevant, describe the equipment and sample(s)
used for testing, how and when the samples were obtained, and how they were stored prior to
testing.
12. Methods of Investigation. In your own words describe the general procedure for each test
performed during the lab so that the reader understands what you did. Include technique, order of
events, etc. Do not make this section too long. These should not be detailed instructions. The
procedure summary should be concise and to the point. If a published standard (e.g., American
Society for Testing and Materials) was used then reference the standard (give number and full
title) followed by a summary of the major steps conducted for the procedure and note any
variations from the standard.
13. Presentation of Results. Gives a description of the results. This is a factual presentation of
the results, i.e., what did you measure, observe, calculate, etc. Include primary figures, tables,
graphs and equations used for calculations. Refer to all figures and tables in the text. When
appropriate, specific details should be included in a separate Appendix. Show sample
calculations wherever necessary in an Appendix; this includes any data that was reduced using a
spreadsheet. Ensure that the results are organized and presented in a logical sequence. Answer
specific questions listed in the instructions for the laboratory.
14. Discussion of Results. This is your engineering interpretation of the results and their
significance. It is an important part of the report. Discuss the results, i.e., do they seem
reasonable, meet expectations, compare with published data whenever possible, etc. If problems
were encountered during testing and/or the results appear to be incorrect, discuss what the
problems were and their influence on the results. Answer specific questions listed in the
instructions for the laboratory.
15. Summary and Conclusions. You should summarize what you did, why, how, and results
obtained. The summary and conclusions is similar to the executive summary.
16. References. Provide citations for material borrowed from other authors. This includes
background information, published standards and standard methods. In general you should avoid
the use of direct quotes and put information in your own words. Stick with scientific journals
and textbooks and avoid articles from the popular press. Make sure that internet sources are
reputable (e.g. ASCE, EPA, professional organizations). Cite the material both where it appears
in the text and in the references section. Make sure references are complete, i.e., author(s), date,
4.3
title, full name of journal or book, Volume #, pages, etc. Make this section single spaced. There
are several formats for listing references. The method that is used by the American Society of
Civil Engineers is shown below:
Example citations in text:
One author: (Babcock 1995)
Two authors: (Babcock and Wilson 1995)
Three or more authors: (Babcock et al. 1995)
Example reference formats:
For your lab manual:
University of Massachusetts Amherst (2004). Laboratory Manual CEE121 Introduction to
Civil and Environmental Engineering Measurements. Dept. of Civil and Environmental
Engineering, University of Massachusetts Amherst, Amherst, MA.
For internet articles:
Author/editor (year) “Title of Electronic Work”. Online. Information supplier, site/path/file.
Access date.
For a book:
Knudsen, J.G. and Katz, D.L. (1958). Fluid Dynamics and Heat Transfer, McGraw Hill.
New York, NY.
For a journal article:
Norris, R.H. and Streid, D.D. (1940). “Laminar Flow Heat Transfer Coefficients for Ducts.”
Trans. Am. Soc. Mechanical Engineers, 5, 525.
17. Appendices. When relevant include sample calculations, detailed data tables and figures,
raw data sheets, etc.
Additional Notes:
1. Data sheets that are completed during lab session and those that involve simple calculations
may be completed in pencil and should appear in an appendix.
2. Number all sections consecutively starting with the Introduction as follows1.0 MAJOR SECTION TITLE -- all caps + bold
1.1 FIRST SUBSECTION -- all caps + bold
1.1.1 Second Subsection -- first letter cap, underline text + bold
3. Number pages bottom center using 12-point font.
4. When using tables and figures that are cut and paste from other publications make sure to
clearly identify the reference in the figure or table title as either (from xxxx - means you copied
the figure directly out of the reference) or (after xxxx - means you took the figure from the
reference but made some modifications). When taking other information from publications make
4.4
sure to reference the material. If you directly quote material from the literature then it must be
presented in quotations, i.e., " ….".
5. The axes of graphs should be scaled such that the curve(s) extend over the complete area of
the graph for greatest definition. All measured data points should appear as symbols on the graph
regardless of whether a line is fit to the data. Make proper use of legends, units, symbols, scale,
etc., in graphs. Keep all axes titles, tick labels etc. in 12 pt font size. Use Portrait layout as often
as possible.
Note: default settings in Excel make for poor quality graphs (in terms of presentation). See
attached for example of a poor quality Excel graph versus a good quality Excel graph, which can
be made with only a few changes to the default Excel settings.
6. Headings and data entries in tables should be of the same style and font size as that used for
the main text of the report (typically 12-point Times New Roman).
7. All tables and figures must have titles numbered in sequential order of how they are
referenced in the text (e.g., Table 1, Table 2, etc.). All table titles should be centered above the
table or below the figure in bold 12-point font size and of the same style font used for the main
text of the report (e.g., most often this is Times New Roman). For example,
Table 1. Summary of dimensions measured for aluminum part 1
- table follows title- figure followed by titleFigure 1. Schematic of aluminum part 1
8. Equations should be numbered sequentially and all variables fully described including units
directly after the equation and in the list of symbols.
k = q/iA
(1)
where:
k = hydraulic conductivity (m/s)
q = flow rate (m3/s)
i = hydraulic gradient (m/m)
A = area of specimen (m2)
4.5
5.2 REPORT GRADING SYSTEM
5.2.1. Laboratory Reports
Laboratory report grades will be based on technical content, presentation, and overall impression
of the report. Presentation is how well the report is prepared in terms of writing and editorial
issues including using proper format for page layout, figures, text, equations, pagination,
references, margins, grammar, spelling, etc. Technical content refers to the accuracy and
completeness of the material presented including proper description of methods of investigation,
reduction of data, equations and assumptions, discussion of results, conclusions from data,
evaluation of accuracy of results, etc. Overall impression is our assessment of the overall quality
of the report.
Breakdown of the grading system is as follows (maximum = 20 pts):
1. Technical 60% (12 pts):
Introduction and Objectives - 1 pt.
Materials and Methods - 2 pts.
Presentation and Discussion of Results - 7 pts
Summary and Conclusions - 2 pts.
Score: __________
2. Presentation 30% (6 pts):
Cover letter
Spelling and grammar
Quality of writing
Page layout
Layout of graphs and Tables
Table of Contents, List of Tables, List of Figures, and pagination
References format
List of symbols
Format of equations
Correct use of units and significant figures
Score: __________
3. Overall Impression 10% (2 pts)
Final assessment of overall quality of report.
Score: __________
=========
Total Score: __________
4.6
5.2.2 Interpretation of Grades
The following describes each number grade based on grades from 0 to 100%.
Number
Grade (%)
90 - 100
Rating
Description of Grade
Excellent
Outstanding report in all respects
80 - 89
Very good
High quality report in nearly all respects
70 - 79
Good
60 - 69
Fair
59 and less
Poor
A quality report but with some deficiencies
Report lacking in several critical aspects; some key issues
were not addressed
Report has serious deficiencies
Due Dates and Late Policy:
Reports are due at the beginning of your laboratory section one week after the last laboratory
period unless otherwise instructed. Any report handed in after the start of laboratory on the due
date but before 5:00 p.m. will have 25% deduced from the grade. Any report handed in after 5:00
p.m. on the due date will have 50% deducted from the grade. No exceptions will be given
without a valid (e.g., medical emergency) and substantiated excuse.
Attendance for all laboratories is mandatory. Failure to attend a laboratory session without prior
approval or a valid emergency will result in a grade of zero for that lab.
4.7
MODEL REPORT
Thursday Morning Laboratory Section
CEE121 CEE Measurements
Dept. of Civil and Environmental Engineering
University of Massachusetts Amherst
Amherst, MA 01003
January 28, 2004
Professor Don J. DeGroot
CEE121 CEE Measurements
Dept. of Civil and Environmental Engineering
University of Massachusetts Amherst
Amherst, MA 01003
Dear Professor DeGroot:
We are pleased to submit herewith our Report “Results of Direct Shear Tests Conducted on
Ottawa Sand.” This note summarizes the results of the direct shear tests we conducted on the
samples of Ottawa Sand you provided us. All tests were conducted in general accordance with
the American Society for Testing and Materials standards.
This report completes our work for this laboratory. Should you have any questions please do not
hesitate to contact us.
Sincerely yours,
Maurice Richard
Project Engineer
Henri Richard
Project Engineer
Enclosure (1)
MODEL REPORT
Results of Direct Shear Tests Conducted on Ottawa Sand
Prepared for
Don J. DeGroot
CEE121 Civil and Environmental Engineering Measurements
Department of Civil and Environmental Engineering
University of Massachusetts Amherst
Amherst, MA 01003
Prepared by
Maurice Richard and Henri Richard
Thursday Morning Laboratory Section
CEE121 Civil and Environmental Engineering Measurements
Department of Civil and Environmental Engineering
University of Massachusetts Amherst
Amherst, MA 01003
28 January 2004
TABLE OF CONTENTS
Page
TABLE OF CONTENTS ............................................................................................... ii
LIST OF TABLES .........................................................................................................iii
LIST OF FIGURES .......................................................................................................iii
LIST OF SYMBOLS ..................................................................................................... iv
1.0 INTRODUCTION..................................................................................................... 1
2.0 OBJECTIVES ........................................................................................................... 1
3.0 TEST MATERIALS ................................................................................................. 1
4.0 METHODS OF INVESTIGATION........................................................................ 2
5.0 PRESENTATION OF RESULTS ........................................................................... 3
6.0 DISCUSSON OF RESULTS.................................................................................... 5
7.0 SUMMARY AND CONCLUSIONS ....................................................................... 6
REFERENCES................................................................................................................ 7
Appendix A Tabulated Test Results and Sample Calculation ....................................... 11
Appendix B Original Data Sheets.................................................................................. 22
[Note: the Appendices are not included in this model report]
ii
LIST OF TABLES
Page
Table 1
Specimen Parameters and Test Results.......................................................... 8
LIST OF FIGURES
Figure 1
Figure 2
Figure 3
Shear Stress versus Horizontal Displacement................................................ 9
Volume Change versus Horizontal Displacement ......................................... 9
Peak Horizontal Shear Stress versus Vertical Consolidation Stress ............ 10
iii
LIST OF SYMBOLS
ENGLISH
Dr = relative density (%)
eo
= initial void ratio (-)
ec
= void ratio at the end of consolidation (-)
emax = maximum void ratio (-)
emin = minimum void ratio (-)
Vv = volume of voids (cm3)
Vs = volume of solids (cm3)
GREEK
∆Xh = change in horizontal displacement (mm)
∆Xv = change in vertical displacement (mm)
εv
= vertical strain (%)
φ'
= friction angle (°)
ρs = density of solids (Mg/m3)
σ'vc = vertical consolidation stress (kPa)
τh
= horizontal shear stress (kPa)
iv
1.0 INTRODUCTION
This report presents and discusses results of three direct shear tests conducted on
reconstituted samples of Ottawa sand. The tests were performed on 28 January 2004 at the
University of Massachusetts Amherst, Geotechnical Engineering Laboratories. The Ottawa sand
specimens were prepared to a dense condition, consolidated and then sheared with drained
conditions. The direct shear test forces a shear failure to occur on a horizontal plane in a soil
specimen contained in a split box, by sliding the two halves of the box relative to each other. The
test data measured in this laboratory were used to estimate the shear strength of the soil in terms
of the friction angle.
This report presents a summary of the test program and measured results. The report
includes information on the objectives, methods of investigation, and presentation and discussion
of test results.
2.0 OBJECTIVES
The purpose of this report is to evaluate the results of drained direct shear tests to
determine the shear strength parameters (φ' and c') of Ottawa sand. The objective of the
experiment was to measure the relationship between shear stress and vertical effective stress for
several specimens of reconstituted dense Ottawa Sand under drained conditions using a direct
shear apparatus.
3.0 TEST MATERIALS
The direct shear tests were conducted on a sample of uniformly graded Ottawa sand. The
sand was supplied in an air dry condition by the Ottawa Sand Co., Ottawa, Illinois in a 22.7 kg
1
bag. The manufacturer's data sheet lists the nominal gradation to be: 100 % passing a #40 sieve
and 100 % retained on a #200 sieve.
4.0 METHODS OF INVESTIGATION
The direct shear tests were conducted on Ottawa sand in general accordance with
American Society for Testing and Materials (ASTM) D3080 Standard Test Method for Direct
Shear Test of Soils Under Consolidated Drained Conditions (ASTM 1998) using an ELE Ltd.
Model DX-4 direct shear device. The basic test procedure consists of placing a soil specimen in a
square shear box, applying a vertical (normal) consolidation stress and subsequently shearing the
specimen by application of a horizontal shear force at a constant rate of deformation. The shear
box is split horizontally, forming a plane that allows for the top of the specimen to be displaced
relative to the bottom. During shear, measurements of the vertical displacement, horizontal
displacement, and horizontal shear force are made.
Key features of the specimen preparation and test procedures used for the three tests
conducted for this project are as follows:
1.
The Ottawa sand was placed into the 60 mm square direct shear box by allowing the
particles to free fall, from a height of about 15 cm. This "raining" technique was used to
obtain dense specimens. The final target height of each specimen was approximately 26
mm.
2.
The tests were conducted in an open container that was used as a water bath for the
specimens. After application of the seating load, the zero reading on the vertical
2
displacement dial gauge was recorded and thereafter Town of Amherst tap water was
added to the water bath.
3.
The three tests were conducted at different final vertical (normal) consolidation stresses
of 100 kPa for Test DS-1, 200 kPa for Test DS-2, and 400 kPa for Test DS-3. The
consolidation stresses were applied in one increment. During consolidation, changes in
the height of the specimens were measured using the vertical displacement dial gauge.
Approximately 15 minutes was allowed to elapse between application of the vertical
consolidation stress and start of shear.
4.
All specimens were sheared at a constant rate of horizontal deformation equal to 0.25
mm/min. Free drainage was allowed to occur during shear. Periodic readings of vertical
displacement, horizontal displacement (using a dial gauge) and horizontal shear force
(using a proving ring) were recorded during shear. The tests were allowed to continue
until a definite peak horizontal shear resistance was reached.
5.
At the end of shear, the apparatus was disassembled and the specimen was collected and
placed in an oven to measure the mass of solids.
5.0 PRESENTATION OF RESULTS
Table 1 presents a summary of the results for the three tests. Tabulated data for the shear
portion of each test are in Appendix A. Original data sheets are in Appendix B.
The initial void ratio of each specimen was computed as
eo = Vv/Vs
(5.1)
where
eo = initial void ratio (-)
3
Vv = volume of voids (cm3)
Vs = volume of solids (cm3)
The volume of solids was computed using the oven dry mass of solids and an assumed density of
solids ρs = 2.65 Mg/m3 (Holtz and Kovacs 1981). The volume of voids was computed as the
difference between the measured total specimen volume and the computed volume of solids. The
initial void ratio for the specimens ranged from 0.544 to 0.561 which corresponds to initial
relative densities of 85 and 80 percent using a minimum void ratio emin = 0.5 and a maximum
void ratio emax = 0.8 (Lambe and Whitman 1969). The void ratio at the end of consolidation (ec)
was computed using the measured vertical deformation of the specimen at the end of
consolidation.
Figure 1 plots the measured shear stress versus horizontal displacement and Figure 2
plots the volume change versus horizontal displacement for the three tests. The data show an
increase in the shear stress with increasing horizontal displacement until the peak shear stress is
reached. Thereafter, the specimens exhibit a strain softening response. The increase in shear
resistance to the peak shear stress and subsequent strain softening response is more pronounced
with an increase in the consolidation stress. In terms of volume change, all three specimens
display an initial contraction followed by significant dilation that continues until the end of the
test. The magnitude of dilation tends to increase with a decrease in the consolidation stress while
the maximum rate of dilation appears to coincide with the peak shear resistance for all three
specimens.
Since the complete state of stress is not known in the direct shear device, i.e., only the
shear and normal stress on the horizontal plane is known, there is not enough information to
compute the Mohr circle of stress for the failure condition. It is therefore common to assume that
4
the horizontal plane is the failure plane (Lambe and Whitman 1969). With this assumption, it is
possible to compute the friction angle of the specimen as
φ' = tan-1(τh/σ'vc)max
(5.2)
where
φ' = friction angle (°)
τh = horizontal shear stress (kPa)
σ'vc = vertical consolidation stress (kPa)
Table 1 presents the values of (τh)max for the three tests and the corresponding values of φ'
which range from 42.7° to 43.8°. These results are plotted in Figure 3 together with a best fit
linear line to the three data points using an assumed cohesion intercept = 0. This line corresponds
to a friction angle of 43°.
6.0 DISCUSSION OF RESULTS
The initial relative densities of the three specimens vary somewhat (80 to 85%) but all
three specimens have a sufficiently high enough relative density to be considered a dense to very
dense sand (Lambe and Whitman 1969). The corresponding shear data, presented in Section 5,
show characteristics expected of a dense sand: (1) shear stress versus horizontal displacement
curves that display a distinct peak shear stress followed by strain softening; (2) an increase in the
consolidation stress results in a corresponding increase in the peak shear stress; and (3) initial
contraction followed by significant dilation during shear.
The principal parameter desired in strength testing of sands is the friction angle, which
defines the Mohr-Coulomb failure criteria. In this test program, the same method was used to
5
prepare all of the samples and, as desired, approximately the same initial void ratio (and relative
density) was achieved for all of the tests (Table 1). For the same initial density, the friction angle
should be approximately the same for different consolidation stresses. Table 1 and Figure 3 show
that this is the case for the three tests giving an average friction angle of about 43°. The friction
angle of 43° is typical for dense sands as reported in the literature (e.g., Lambe and Whitman
1969, Holtz and Kovacs 1981).
7.0 SUMMARY AND CONCLUSIONS
This report presents the results of three direct shear tests conducted on reconstituted
samples of Ottawa Sand. The tests were conducted at the Geotechnical Engineering Laboratories,
University of Massachusetts Amherst, on 28 January 2004. The tests used a standard 60 mm
square direct shear apparatus and were conducted in general accordance with ASTM D3080
Standard Test Method for Direct Shear Test of Soils Under Consolidated Drained Conditions
(ASTM 1998). The three specimens were prepared for testing by allowing the sand to free fall
from a height of 15 cm into the direct shear box to achieve a high initial relative density. The
specimens were then consolidated to a different preshear vertical consolidation stress for each
test equal to 100, 200, and 400 kPa. Direct shear was conducted at a constant rate of strain of
0.25 mm/min until the specimens sheared beyond their peak horizontal shear resistance.
The initial void ratio for the three specimens ranged from 0.544 to 0.561, which
corresponds to initial relative densities of approximately 85 and 80 percent (Table 1). The
measured shear behavior for all three specimens is typical of that for dense sands, i.e., shear
stress versus horizontal displacement curves with a distinct peak shear stress followed by strain
softening (Figure 1) and initial contraction followed by significant dilation (Figure 2). Using the
6
assumption that the horizontal plane is the failure plane, the three tests give similar friction
angles ranging from 42.7° to 43.8° (Table 1). The best linear fit to the data, assuming a zero
cohesion intercept, is approximately 43° (Figure 3). This friction angle is consistent with that
reported in the literature (Lambe and Whitman 1969).
REFERENCES
ASTM. (1998). 1998 Annual Book of ASTM Standards, Volume 04.08 Soil and Rock (I): D420 D4914, West Conshohocken, Pennsylvania.
Holtz, R.D. and Kovacs, W.D. (1981). An Introduction to Geotechnical Engineering. PrenticeHall, Inc., Englewood Cliffs, New Jersey.
Lambe, T.W. and Whitman, R.V. (1969). Soil Mechanics. John Wiley & Sons, Inc., New York.
7
Table 1 Specimen Parameters and Test Results
Initial State
Test
No.
eo
Dr
(%)
DS-1
0.559
DS-2
DS-3
Consolidation
80
σ'vc
(kPa)
100
εv
(%)
0.36
0.561
80
200
0.544
85
400
At Peak Horizontal Shear Stress
0.553
∆Xh
(mm)
1.56
∆Xv
(mm)
0.234
τh
(kPa)
93.1
φ'
(º)
43.0
0.47
0.554
1.50
0.131
184.6
42.7
0.73
0.533
1.70
0.144
383.0
43.8
ec
Notes:
1. Dr computed using assumed emax = 0.8 and emin = 0.5
8
Shear Stress, τh (kPa)
400
300
200
100
0
DS-1
DS-2
DS-3
0
1
2
3
Horizontal Displacement, ∆Xh (mm)
Figure 1. Shear Sstress versus horizontal displacement
Volume Change, ∆Vol (mm3)
1500
DS-1
DS-2
DS-3
1000
500
dilation
0
contraction
-500
0
1
2
Horizontal Displacement, ∆Xh (mm)
Figure 2. Volume change versus horizontal displacement
9
3
500
DS-1
DS-2
DS-3
Peak Shear Stress, (τh)max (kPa)
400
300
200
φ' = 43 degrees
100
0
0
100
200
300
400
Vertical Consolidation Stress, σ'vc (kPa)
Figure 3. Peak horizontal shear stress versus vertical consolidation stress
10
500