GRLWEAP™ Fundamentals
Frank Rausche, Garland Likins
2011, Pile Dynamics, Inc.
CONTENT
• Background and Terminology
• Wave Equation Models
– Hammer
– Pile
– Soil
• The Program Flow
– Bearing graph
– Inspector’s Chart
– Driveability
Some important developments in
Dynamic Pile Analysis
1800s
1950:
1970:
1976:
1980s:
1986:
1996, 2006:
Closed Form Solutions & Energy Formulas
Smith’s Wave Equation
CAPWAP
WEAP, TTI
(mainframes)
GRLWEAP
(PC’s)
Hammer Performance Study
FHWA Manual updates
WEAP = Wave Equation Analysis of Piles
WAVE EQUATION OBJECTIVES
• Smith’s Basic Premise:
– Replace Energy Formula
– Use improved pile model (elastic pile)
– Use improved soil model
(elasto-plastic static with damping)
– Allow for stress calculations
• Later GRLWEAP improvements:
– realistic Diesel hammer model (thermodynamics)
– comparison with pile top measurements
– development of more reliable soil constants
– driveability and inspectors’ chart options
– residual stress analysis option
GRLWEAP Application
• WHEN?
– Before pile driving begins
– After initial dynamic pile testing ( refined )
• WHY?
– Equipment selection or qualification
– Stress determination
– Formulate driving criterion
• Blow count calculation for desired capacity
– Capacity determination
from observed blow count
Some WEAP Terminology
• Hammer
• Hammer assembly
• Hammer efficiency
Ram plus hammer assembly
All non-striking hammer components
Ratio of Ek just before impact to Ep
•
•
•
•
•
All components between hammer and pile top
Weight of driving system
Protects hammer - between helmet and ram
Protects pile - between helmet and pile top
Generally the striker plate + hammer
cushion+helmet
Driving system
Helmet weight
Hammer cushion
Pile cushion
Cap
• Pile damping
• Soil damping
• Quake
Damping of pile material
Damping of soil in pile-soil interface
Pile displacement when static resistance
reaches ultimate
Some WEAP Terminology
• Bearing Graph
Ult. Capacity and max. stress vs. blow count
for a given penetration depth
• Inspector’s Chart
Calculates blow count and stresses for given
ult. capacity at a given penetration depth
as a function of stroke/energy
• Driveability analysis
Calculate blow count and stresses
vs. depth based on static soils analysis
•
•
•
•
Static Resistance to Driving
Ratio of long term to EOD resistance
Ratio of SRD to long term resistance
Setup occurring during a limited driving
interruption
SRD
Soil set-up factor
Gain/loss factor
Variable set-up
THE WAVE EQUATION MODEL
• The Wave Equation Analysis calculates the
movements (velocities and displacements) of
any point of a slender elastic rod at any time.
GRLWEAP Fundamentals
• For a pile driving analysis, the “rod” is
Hammer + Driving System + Pile
• The rod is assumed to be elastic(?) and
slender(?)
• The soil is represented by resistance
forces acting at the pile soil interface
GRLWEAP - 3 Hammer Models
External Combustion Hammer Modeling
Cylinder and upper frame =
assembly top mass
Ram guides for assembly stiffness
Drop height
Ram: A, L for stiffness, mass
Hammer base =
assembly bottom mass
External Combustion Hammers
Ram Model
Ram segments
~1m long
Combined RamH.Cushion
Helmet mass
External Combustion Hammers
Combined Ram Assembly Model
Ram segments
Assembly segments
Combined RamH.Cushion
Helmet mass
Diesel Hammer Combustion Pressure Model
•
•
•
•
Compressive Stroke, hC
Cylinder Area, ACH
Final Chamber Volume, VCH
Max. Pressure, pMAX
PrecompressionCombustionExpansionpressures from
thermodynamics
Ports
hC
DIESEL PRESSURE MODEL
Liquid Injection Hammers
Open
Expansion
Port
Pressure
Compression
pMAX
Time
Program Flow – Diesel Hammers
Fixed pressure, variable stroke
Setup hammer,
pile, soil model
Downward =
rated stroke
Calculate pile and
ram motion
Find upward
stroke
Downward =
upward stroke
Next Ru?
N
Strokes
match?
N
Output
Potential / Kinetic Energy
EP = WR h
(potential or rated energy)
EK = ½ mR vi2
(kinetic energy)
EK = ηEP
(η - hammer efficiency)
WR
vi W
R
vi = 2g h η
Max ET = ∫F(t) v(t) dt
“Transferred Energy” EMX
ETR = EMX/ ER = “transfer ratio”
WP
h
GRLWEAP hammer efficiencies
•The hammer efficiency reduces the
impact velocity of the ram; reduction
factor is based on experience
•Hammer efficiencies cover all losses
which cannot be calculated
•Diesel hammer energy loss due to
precompression or cushioning can be
calculated and, therefore, is not covered
by hammer efficiency
GRLWEAP diesel hammer efficiencies
Open end diesel hammers:
0.80
(uncertainty of fall height, friction, alignment)
Closed end diesel hammers:
0.80
(uncertainty of fall height, friction, power assist,
alignment)
Other ECH efficiency recommendations
Single acting Air/Steam hammers:
0.67
(fall height, preadmission, friction, alignment)
Double acting Air/Steam/Hydraulic:
0.50
(preadmission, reduced pressure, friction, alignment)
Drop hammers winch released:
0.50
(uncertainty of fall height, friction, and winch losses)
Free released drop hammers (rare):
(uncertainty of fall height friction)
0.67
GRLWEAP hydraulic hammer
efficiencies
Hammers with internal monitor:
0.95
(uncertainty of hammer alignment)
Hydraulic hammers (no monitor):
0.80
Power assisted hydraulic hammers:
0.80
(uncertainty of fall height, alignment, friction, power assist)
If not measured, fall height must be assumed
and can be quite variable – be cautious !
VIBRATORY
HAMMER MODEL
VIBRATORY HAMMER MODEL
FL
Bias Mass with Line Force
m1
Connecting Pads
Oscillator with eccentric
masses, me, radii, re and
clamp
m2
2-mass system with vibratory force
FV = me 2 re sint
FV
GRLWEAP Hammer data file
Hammer-Driving System-Pile-Soil Model
Hammer:
(Masses and
Springs)
Pile:
Driving System:
Cushions (Springs)
Helmet (Mass)
Soil:
Driving System Modeling
The Driving Systems Consists of
– Helmet including inserts to align hammer and pile
– Hammer Cushion to protect hammer
– Pile Cushion to protect concrete piles
GRLWEAP Driving System Help
GRLWEAP Driving System Help
GRLWEAP Pile Model
To make realistic calculations possible
• The pile is divided into N segments
– of approximate length ∆L = 1 m (3.3 ft)
– with mass
m = ρ A ∆L
– and stiffness
k = E A / ∆L
– there are
N = L / ∆L pile segments
• Divide time into intervals
(typically 0.1 ms)
Computational Time Increment, ∆t
∆t is a fraction (e.g. ½ ) of the critical time, which is ∆L/c
Time
∆tcr
∆L
∆t
L/c
Length
Driving system
model
(Concrete piles)
Hammer Cushion: Spring
plus Dashpot
Helmet + Inserts
Pile Cushion + Pile Top:
Spring + Dashpot
Non-linear springs
Springs at material interfaces
Hammer interface springs
Cushions
Helmet/Pile
Splices with slacks
Non-linear (cushion) springs
• Parameters
Compressive
Force
• Stiffness, k = EA/t
• Coefficient of Restitution, COR
• Round-out deformation,δr , or
compressive slack
• Tension slack, δs
δs
k
δr
k /COR2
Compressive
Deformation
Hammer cushion
Pile cushion
Material
Modulus
(ksi)
Material
Modulus
(ksi)
Aluminum
Micarta
350
Plywood
30 new
75 used
Conbest
280
Oak
60
(transverse)
Hamortex
125
Nylon
175-200
Oak
(parallel)
750
The Pile and Soil Model
Mass density, 
Modulus, E
X-Area, A
Mass mi Stiffness ki
∆L= L/N  1m
Spring (static resistance)
Dashpot (dynamic resist)
Soil Resistance
• Soil resistance slows pile movement and
causes pile rebound
• A very slowly moving pile only encounters
static resistance
• A rapidly moving pile also encounters dynamic
resistance
• The static resistance to driving may differ from
the soil resistance under static loads
–
–
–
–
Pore pressure effects
Lateral movements
Plugging for open profiles
Etc.
The Soil Model
Segment
i-1
RIGID SOIL
SURROUNDING
SOIL/PILE
INTERFACE
ki-1,Rui-1
Ji-1
ki,Rui
Segment
Ji
i
ki+1,Rui+1
Segment
i+1
Ji+1
Smith’s Soil Model
Total Soil Resistance
Rtotal = Rsi +Rdi
Segment
i
ui
vi
Fixed
Shaft Resistance and Quake
Rsi
-Rui
Rui
qi
qi
Recommended Shaft Quake
( qi )
ui
2.5 mm; 0.1 inches
Recommended Toe Quakes, qt
Non-displacement
piles
Displacement piles
0.1” or 2.5 mm
D/120: very dense/hard
soils
0.04” or 1 mm on
hard rock
qt
D/60: softer/loose soils
qt
D
u
Rut R
Smith’s Soil Damping Model (Shaft or Toe)
Rd = RsJs v
Pile
Segment
Fixed
reference
(soil around
pile)
velocity v
dashpot
Smith damping factor,
Js [s/m or s/ft]
Rd = RuJs v
Smith-viscous damping
factor Jsvi [s/m or s/ft]
Alternative Soil Models
Coyle-Gibson Results (1968)
Sand
Clay
Recommended damping factors
after Smith
Shaft
Clay:
Sand:
Silts:
Layered soils:
0.65 s/m or 0.20 s/ft
0.16 s/m or 0.05 s/ft
use an intermediate value
use a weighted average
Toe
All soils:
0.50 s/m or 0.15 s/ft
Numerical treatment:
Force balance at a segment
Force from upper spring, Fi
Resistance force, Ri
Mass mi
(static plus damping)
Weight, Wi
Force from lower spring, Fi+1
Acceleration: ai = (Fi – Fi+1 + Wi – Ri) / mi
Velocity, vi, and Displacement, ui, from Integration
Wave Equation Analysis calculates displacement of
all points of a pile as function of time.
Calculate displacements:
uni = uoi + voi t
mi-1
uni-1
Fi, ci
Calculate spring displacement:
ci = uni - uni-1
Calculate spring forces:
mi
uni
Fi = ki ci
mi+1
k = EA / ΔL
uni+1
Set or Blow Count Calculation from
Extrapolated toe displacement
R
Maximum Set
Calculated
Ru
Extrapolated
Set
Final Set
Quake
Blow Count Calculation
• Once pile toe rebounds,
max toe displacement is known,
example: 0.3 inch or 7.5 mm
• Final Set = Max Toe Displacement – Quake
= 0.3 – 0.1 = 0.2 inch
= 7.5 - 2.5 = 5 mm
• “Blow Count” is Inverse of “Final Set”
BCT = 12 / 0.2 = 60 Bl / ft
BCT = 1000 / 5 = 200 Bl / m
Alternative Blow Count Calculation
by RSA
• Residual Stress Analysis is also called
Multiple Blow Analysis
• Analyzes several blows consecutively with
initial stresses, displacements from static
state at end of previous blow
• Yields residual stresses in pile at end of
blow; generally lower blow counts
RESIDUAL STRESS OPTION
BETWEEN HAMMER BLOWS, PILE AND SOIL STORE ENERGY
Set for 2 Blows
Convergence:
Consecutive Blows
have same
pile compression/sets
COMPUTATIONAL PROCEDURE
Smith’s Bearing Graph
• Analyze for a range of capacities
– In: Static resistance distribution assumed
– Out: Pile static capacity vs. blow count
– Out: Critical driving stresses vs. blow count
– Out: Stroke for diesel hammers vs. blow count
Bearing Graph:
Required Blow Count
For required capacity
Find minimum blow count
Bearing Graph:
Capacity Determination
Find indicated capacity
For observed blow count
Program Flow – Bearing Graph
Input
Model hammer &
driving system
Model Pile
Distribute Ru
Set Soil Constants
Time Increment
Increase Ru
Static Analysis
Ram velocity
Dynamic Analysis
• Pile stresses
• Energy transfer
• Pile velocities
Increase
R u?
N
Choose first Ru
Calculate Blow
Count
Output
PURPOSE OF ANALYSIS
• Preliminary Equipment Selection
– Hammer OK for Pile, Capacity
– Includes stress check
• Driving Criterion
– Blow Count for Capacity and Stroke
OUTPUT REVIEW
• Blow Counts Satisfactory?
• Stresses Less Than Allowable?
• Economical Hammer, Pile?
If not, consider reanalyzing with different
hammer system, pile size.
INSPECTOR’S CHART
Constant capacity – analyze with variable energy or stroke
OK
Bad
Question for Driveability:
WHAT IS RU DURING DRIVING?
• We call it Static Resistance to Driving (SRD),
because we lose shaft resistance during driving.
• Will we regain resistance by Soil Set-up
primarily along shaft (may be 10 x in clay)
• Driveability requires analyze with full loss of
set-up (or with partial loss of set-up for a short
driving interruption)
Set-up factors
Soil Type
Setup Factor
Clay
2
Silt – Clay
1
Silt
1.5
Sand – Clay
1.2
Fine Sand
1
Sand - Gravel
1
Thendean, G., Rausche, F., Svinkin, M., Likins, G. E., September, 1996.
Wave Equation Correlation Studies. Proceedings of the Fifth International
Conference on the Application of Stress-wave Theory to Piles 1996:
Orlando, FL; 144-162.
For Driveability:
Static capacity changes
Set-up Time
Remolding
energy
Ru
Ru/SF
Ru/SF
Time
Driving
Waiting Time
Re-Drive
• Set-up factor, SF
• Capacity increases (Set-up) after driving stops
• Capacity decreases (Remolds) during redrive
Program Flow – Driveability
Input
Calculate Ru
for first gain/loss
Model hammer &
driving system
Analysis
First depth of
analysis
- soil model Pile length and
model
Increase Depth
Next G/L
Increase
G/L?
N
Increase
Depth?
Output
N
COMPUTATIONAL PROCEDURE
Driveability Analysis
• Analysis as the pile is penetrated
– Input capacity with depth (static analysis)
• Generates a driving record
– Predicts blow count with depth
– Stresses, (diesel stroke), with depth
Static Soil Analysis
Approximate for Bearing Graph:
– Percent Shaft Resistance
– Resistance Distribution
Detailed for Driveability
– Shaft Resistance vs Depth
– End Bearing vs Depth
– Set-up Factor
Driveability
PURPOSE OF ANALYSIS
• Preliminary Equipment Selection
– Hammer OK for Pile, Capacity
• Driving Criterion
– Blow Count for Capacity and stroke
• Driveability
– Acceptable Blow Count throughout
– Acceptable Stresses throughout
Co ntract No .:
P ro ject:
S tru cture Na me an d/o r No .:
P ile Drivin g Co ntracto r o r Su bco n tracto r:
Co un ty:
(Piles d riv en b y)
R
a
m
Pile Driving
and
Equipment
Data Form
Hammer
Man ufa cturer:
Mo d el No .:
Ham mer Type :
Se rial No .:
Man ufa cturers Max imu m Ra te d E ne rg y:
Stro ke a t Max imu m Ra te d E ne rg y:
Ran ge in O p era tin g E ne rg y:
to
Ran ge in O p era tin g S tro ke:
to
Ram W eigh t:
(kip s)
Mod ific atio ns:
(ft-lbs)
(ft)
(ft-lbs)
(ft)
Anvil
Striker
Plate
Weigh t:
Thickne ss:
(kips) Diam ete r:
(in)
(in )
Mate rial # 1
Hammer
Cushion
Ma te rial # 2
(fo r Co mp osite Cu shion )
Nam e:
Na me :
Area :
(in2 ) A re a:
Thickne ss/Plate :
(in)
Th ickn ess /P la te:
No. o f P la tes:
No . of Plate s:
Tota l Thickne ss of Ha mm er Cu sh ion :
Helmet
(Drive Head) Weigh t:
Pile
Cushion
(kips)
Mate rial:
Area :
(in2 )
No. o f S he ets:
Tota l Thickne ss of P ile Cus hio n:
Th ickn ess /S h ee t:
(in )
Pile Typ e:
Wall Th ickn ess:
Cro ss Se ctio na l Area :
(in )
Tap er:
(in 2) We ig ht/Ft:
Orde re d Le n gth :
Design Lo ad :
Ultim ate P ile Ca pa city:
(ft)
(kip s)
(kip s)
Pile
Descrip tion of S plice:
Driv ing Sh oe /Clo su re P la te De scriptio n:
Su bm itted By:
Telep ho ne No.:
(in 2)
(in)
Date :
Fax No .:
(in)
Required Input Data
• Hammer
– Model
– Energy level (stroke)
• Driving system
– Hammer cushion material (E, A), thickness
– Helmet weight (of entire assembly)
– Pile cushion material (E, A), thickness
(for concrete piles only)
Required Input Data
• Soil
(from Borings with elevations)
– Type of soils
– N-values vs depth
or other strength parameters
– Elevation of water table
Data Entry
•Resistance distribution
•Simple
•From soil input wizard
•For driveability
•Soil properties vs depth:
•Shaft unit resistance – requires calculation
•End bearing
- requires calculation
•Quakes and damping
•Set-up factor
•Analysis depths
Available Help - Indirect
GRLWEAP Help – Direct:
F3
Area calculator from any area input field.
Final Recommendation
• Perform sensitivity studies on parameters
• Plot upper and lower bound results
• Note: low hammer efficiency not always conservative
• Read the helps and disclaimers
•On screen or after printing them
• Compare results with dynamic testing
Summary
• There are 3 distinctly different hammer models
– External Combustion Hammer models
– Diesel hammer and pressure models
– Vibratory hammer model
• There are 3 components in driving system model
– Hammer Cushion
– Helmet and Inserts
– Pile Cushion (concrete piles only)
• Model Parameters can be found in
GRLWEAP Help Section or Hammer data file.
SUMMARY continued
• The wave equation analysis works with “Static
Resistance to Driving” (SRD) plus a Damping or
Dynamic Resistance
• Important analysis options include:
– Bearing Graph
– Inspector’s Chart
– Driveability Graph
• The whole package is geared towards standard
analyses; some research options exist
Summary: W.E. APPLICATIONS
• Design stage
– Preliminary hammer selection
– Selection of pile section for driveability
– Selection of material strength for driving
• Construction stage
– Hammer system approval
– Contractors use to select equipment
– One means of estimating blow count
– Inspector’s chart for variable hammer stroke
Summary: Purpose of analysis
Develop driving criterion
Final Set (Blow count) for a required capacity
Final Set as a function of energy/stroke
Check driveability
Final Set (Blow Count) vs. depth
Stresses vs. depth
Optimal equipment
To Minimize Driving Time