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High Strain Pile Testing with the Pile Driving
Analyzer System® (PDA)and CAPWAP®
PDA Wave Mechanics 1
Outline
• Introduction
– Measurement Evaluation
– Forces and Stresses in Pile
– Integrity
– Bearing capacity
– Examples
• Summary
• Problems
PDA Wave Mechanics 2
Measuring strain and acceleration
at one point
Strain transducer Accelerometer
PDA Wave Mechanics 3
Alternative force transducer or F=ma
For F=ma or top load cell
testing, accelerometers must
be attached to pile top.
PDA Wave Mechanics 4
PDA testing and data acquisitionPDA testing and data acquisition
After securely
attaching sensors to
pile, it is important to
input the pertinent
and latest calibration
values in PDA
PDA Wave Mechanics 5
Measurements on a follower, nearshore
PDA Wave Mechanics 6
The Pile Driving Analyzer - Model 8G
• Measures force and
velocity, usually near
the pile top, but also
at other locations
such as the pile toe.
• Determines Case
Method resistance,
iCAP®, energy
transferred to pile
and stresses in pile
PDA and CAPWAP 7
Site Link® for Remote Monitoring
Reduces travel cost and scheduling problems
Site Link® for Remote Monitoring
Reduces travel cost and scheduling problems
PDA and CAPWAP 8
Acceleration and Strain vs. TimeAcceleration and Strain vs. Time
Accelerometers, one on each
side; acceleration, velocity,
displacement
Strain Transducers, one on
each side; yield strain, stress
and average force
PDA Wave Mechanics 9
●
Compressive stresses, forces: FMX, CSX, CSI
PDA Wave Mechanics 10
●CSX = 233 MPa (33.8 ksi)
FMX = 1280 kN
●CSX = 233 MPa (33.8 ksi)
FMX = 1280 kN
●
● ●CSI = 245 MPa (35.5 ksi)
For H-piles, Load Cell or F=ma Measurements: no CSI
PDA Wave Mechanics 11
Compressive stresses, forces: FMX, CSX, CSI
Force, Velocity, DisplacementForce, Velocity, Displacement
FMX
DMX = ½ max (d1 + d2)
DFN = ½ (d1 fin + d2 fin)
d2(t) = ∫v2(t) dt
d1(t) = ∫v1(t) dt
d1 max
PDA Wave Mechanics 12
d1 fin
d2 fin
Pile top force and velocity from PDAPile top force and velocity from PDA
We are measuring the total force and the total velocity
We plot both together using Z to scale velocity
We are measuring the total force and the total velocity
We plot both together using Z to scale velocity
F(t) = ½ A E [ε1(t) + ε2(t)]
v(t) = ½ [v1(t) + v2(t)] Z
PDA Wave Mechanics 13
Fu = - vu (EA/c)Fu = - vu (EA/c)
u = - vu (E/c)u = - vu (E/c)
εu = - vu / cεu = - vu / cεd = vd / cεd = vd / c
d = vd (E/c)d = vd (E/c)
Fd = vd (EA/c)Fd = vd (EA/c)
If wave travels
“downwards”
If wave travels
“upwards”
PDA Wave Mechanics 14
Superposition of WavesSuperposition of Waves
Fd=ZvdFd=Zvd
Downward Waves
Fu=-ZvuFu=-Zvu
Upward Waves
F = Fd + Fu
v = vd + vu
PDA Wave Mechanics 15
Wave Down and Wave Up from F and Zv
Fd=½(F+Zv) Fu=½(F-Zv)
Fd or Wd; Fu or Wu
Fd1 or Wd1
Fd2 or Wu2
PDA Wave Mechanics 16
If we know wave up and wave down
We can calculate
Pile forces at other locations
If we know wave up and wave down
We can calculate
Pile forces at other locations
The force at any point along the pile length can be
determined from the superposition of the forces in
the upward traveling and downward traveling waves
The force at any point along the pile length can be
determined from the superposition of the forces in
the upward traveling and downward traveling waves
F = Fu + FdF = Fu + Fd
PDA Wave Mechanics 17
L
2L/ct = 0 L/c
Upward
Wave
Upward
Wave
Downward
Wave
Downward
Wave
Wave Superposition for Force below SensorsWave Superposition for Force below Sensors
X
Fd1
Fu2
Fx = Fu2 + Fd3
Fd3
2x/c
PDA Wave Mechanics 18
TopToe
t3
Tension Stress Calculation – Wave-UpTension Stress Calculation – Wave-Up
Point of max tension
min Fu
min Fu
PDA Wave Mechanics 19
Pile Damage: BTA, LTD
LTD
•A reduction of pile impedance (Z)
above the pile toe causes a tension
reflection before 2L/c
•The time at which the tension
reflection arrives at the gage location
indicates the depth to Z-reduction:
LTD = (tdamage / 2) c
•The magnitude of the Z-reduction is
calculated with the -formula
PDA Wave Mechanics 21
t1
t3
Fu,1 = ½(Ft3-Zvt3)
Fd,1 = ½(Ft1+Zvt1)
Damage Example
PDA Wave Mechanics 22
PDA Capacity Monitoring
The 1965 (Phase 1) equation was based on a
rigid body model: Ru = F(to) - mp a(to)
Time to is time of zero velocity – no damping
to
PDA Wave Mechanics 23
But then we derived the 1968 Case Method
Resistance Waves
L/c
L
x
Ri
-½Ri
RB
RB
Upward traveling wave at time 2L/c:
Fu,2 = -Fd,1 + ½Ri + ½Ri + RB
RTL = Fu,2 + Fd,1
Fd,1
-Fd,1
½Ri
PDA Wave Mechanics 24
½Ri
RD = Jv vtoe = Jc Z vtoeRD = Jv vtoe = Jc Z vtoe
Calculated Damping Component
The Case Method
uses the pile toe velocity for damping calculations; it is
affected by shaft and toe soil resistance!
Calculated Damping Component
The Case Method
uses the pile toe velocity for damping calculations; it is
affected by shaft and toe soil resistance!
PDA Wave Mechanics 25
Jv … viscous damping factor [kN/m/s]
Jc … the dimensionless Case Damping Factor
vtoe = (2Fd1 – RTL)/Z based on wave mechanics
Case Method Static Resistance
Rstatic= RTL - RD
Rstatic= Fu,2 + Fd,1 - Jc(2 Fd,1 – Fd1 – Fu,2)
Rstatic= (1 – Jc)Fd,1 + (1 + Jc )Fu,2
Total Resistance = Static + Dynamic ResistanceTotal Resistance = Static + Dynamic Resistance
PDA Wave Mechanics 26
Fd,1 = 5,450 kN
Fu,2 = 2,730 kN
Rstatic = (1 – Jc) Fd,1+ (1 + Jc) Fu,2Rstatic = (1 – Jc) Fd,1+ (1 + Jc) Fu,2
RTL = 5,450 + 2,730 = 8,180 kN
For example with Jc= .3
Rstatic = (1 - .3) 5,450 + (1 + .3) 2,730 = 7,350 kN
RTL = 5,450 + 2,730 = 8,180 kN
For example with Jc= .3
Rstatic = (1 - .3) 5,450 + (1 + .3) 2,730 = 7,350 kN
PDA Wave Mechanics 27
Maximum Case Method Resistance, RXiMaximum Case Method Resistance, RXi
t1 t2
2L/c
Calculates Rstatic
at all times after
the first velocity
peak
Selects the
maximum Rstatic
for JC= 0.i
Calculates Rstatic
at all times after
the first velocity
peak
Selects the
maximum Rstatic
for JC= 0.i
PDA Wave Mechanics 28
Shaft and Toe Resistance
2L/ct = 0 L/c
L
x
R
-½R
RB
½R
RB
Fd,1 -Fd,1
½R
PDA Wave Mechanics 29
Ri - Wave upRi - Wave up
R
½R
PDA Wave Mechanics 30
An Example: PDA Capacity Results
End of Driving
PDA Wave Mechanics 31
PDA Capacity Results
Restrike; Blow No. 1
PDA Wave Mechanics 32
Restrike Blow No. 2
PDA Wave Mechanics 33
Restrike, blow No. 4
PDA Wave Mechanics 34
PEBWAP for and End Bearing Pile
20x0.5” OEP; LG = 22.3 m; D46-32; 0.6 mm/bl; JC = 0.3
0
1500
3000
4500
6000
7500
0 5 10 15
Resistance-kN
Toe Displacement - mm
Total Resistance Static Resistance
Static Resistance = Total Resistance – Damping Factor * Toe Velocity
PDA and CAPWAP 35
THE CAPWAP METHODTHE CAPWAP METHOD
1 Set up pile and soil model and assume
Rshaft and Rtoe
1 Set up pile and soil model and assume
Rshaft and Rtoe
Rshaft
Rtoe
5 If no satisfactory match: Go to Step 25 If no satisfactory match: Go to Step 2
4 Adjust Rshaft and Rtoe4 Adjust Rshaft and Rtoe
3 Compare WUC with measured WUM3 Compare WUC with measured WUM
2 Apply measured WDM to pile model at top and
calculate complementary WUC
2 Apply measured WDM to pile model at top and
calculate complementary WUC
WUM
WDM
WUC
PDA and CAPWAP 36
First try (poor)
Final match (good)
Adjustments
CAPWAP is an
Iterative Process
PDA and CAPWAP 37
Seg. i
∆Li
Ri
Fdo
i
Fdn
i
Fun
i
Fuo
i
Rdi
Rui
The Pile is divided in Np
uniform pile segments of
approximately 1 m length.
Segment lengths are chosen
for equal time increment
∆t = ∆Li/ci.
Each Segment has:
impedance Zi,,= EiAi/ci ,
mass mi = Zi ∆t and
stiffness ki = Zi/∆t .
The Pile Model
PDA and CAPWAP 38
The Combined CAPWAP Pile and Soil ModelThe Combined CAPWAP Pile and Soil Model
Soil segment length:
LSi = Nfac Li
Soil segment length:
LSi = Nfac Li
Spring (static resistance)
Dashpot (dynamic resistance)
Spring (static resistance)
Dashpot (dynamic resistance)
t
t
t
t
t
t
t
Pile Model:
Impedance Zi
= EiAi/ci
Pile Segment
Length Li
Wave Travel
time in Pile
t = Li/ci
Pile Model:
Impedance Zi
= EiAi/ci
Pile Segment
Length Li
Wave Travel
time in Pile
t = Li/ci
PDA and CAPWAP 39
Rui, qi
Rt, qt
Ji
JT Shaft Resistance,
Ns times
Shaft Resistance,
Ns times
tG
The Basic
CAPWAP
Soil Model
The Basic
CAPWAP
Soil Model
End
Bearing
End
Bearing
PDA and CAPWAP 40
mt
Rui, qi
Rt, qt
Ji
JT
JSK
JBT
Add Radiation Damping
Inertia Resistance
Add Radiation Damping
Inertia Resistance
tG
ms
mPL
Some
CAPWAP
Soil Model
Extensions
Some
CAPWAP
Soil Model
Extensions
mSP
PDA and CAPWAP 41
Signal Matching ExampleSignal Matching Example
PDA and CAPWAP 42
First Trial Analysis (Lousy Match)First Trial Analysis (Lousy Match)
Input F
Matching F
Input F
Matching v
or
Input v
Matching F
or
PDA and CAPWAP 43
Working with Wave-UpWorking with Wave-Up
RU = 782 kips
RT = 68 kips
JS/JT = .05/.15 s/ft
(JCS/JCT = .75/.22)
QS/QT = .10/.12”
RU = 782 kips
RT = 400 kips
RU = 782 kips
RT = 600 kips
RU = 782 kips
RT = 705 kips
JS/JT = .45/.02 s/ft
QS/QT = .10/.12”
PDA and CAPWAP 44
Working with Wave-UpWorking with Wave-Up
RU/RT = 782/705 kips
JS/JT = .45/.02 s/ft
(JCS/JCT = .75/.22)
QS/QT = .10/.12”
RU/RT = 782/705 kips
JS/JT = .30/.05 s/ft
(JCS/JCT = .50/.76)
RU/RT = 782/702 kips
JS/JT = .29/.05 s/ft
(JCS/JCT = .50/.76)
Prev.
PDA and CAPWAP 45
Working with Wave-UpWorking with Wave-Up
RU/RT = 782/702 kips
JS/JT = .29/.05 s/ft
(JCS/JCT = .50/.76)
RU/RT = 765/686 kips
JS/JT = .28/.06 s/ft
(JCS/JCT = .48/.82)
RU/RT = 765/686 kips
JS/JT = .26/.07 s/ft
(JCS/JCT = .44/.97)
QS/QT = .06/.12”
Unloading Parameters
Pretty good match: let’s quitPretty good match: let’s quit
PDA and CAPWAP 46
CAPWAP Help FeaturesCAPWAP Help Features
HC
CAPWAP Variable Help
HC
CAPWAP Variable Help
HR
CAPWAP Resistance
vs Displacement Help
HR
CAPWAP Resistance
vs Displacement Help
PDA and CAPWAP 47
CAPWAP’s
Static Pile and
Soil Model
CAPWAP’s
Static Pile and
Soil Model
kshaft, I = Ru,i
/qi
ktoe, i
Ru, i
kp, i
Rtoe, i
Q
u
1
uto
e
PDA and CAPWAP 48
CAPWAP Static AnalysisCAPWAP Static Analysis
The final static
load
displacement
curve is from a
t-z and q-z
analysis
The final static
load
displacement
curve is from a
t-z and q-z
analysis
PDA and CAPWAP 49
CAPWAP Static
Analysis
Options
CAPWAP Static
Analysis
Options
Smoothing
User Capacity
Uplift Test
Extrapolation
Failure Criteria
Smoothing
User Capacity
Uplift Test
Extrapolation
Failure Criteria
PDA and CAPWAP 50
Standard OutputStandard Output
PDA and CAPWAP 51
Comprehensive CAPWAP ReportComprehensive CAPWAP Report
• “Blow Count” is
from Direct Input in
CAPWAP or from
PDA-W
• “Job Information”
provides for other
information input
EX1; BENT 17-2; Pile: EX-1 Test: 04-Sep-1991 16:15:
D36-23; silt; 16"PSC; Blow: 1171 CAPWAP(R) 2013
Beta Version - Pile Dynamics OP: xxx yyyy
Analysis: 28-May-2013
-2500
0
2500
5000
kN F Msd
V*Z Msd
5 105 ms
-600
0
600
1200
kN
15 L/c
Wup Msd
Wup Cpt
Pile Type: Steel
Pile Size: 12 H Pile
Pile Installed: 03-Mar-2013 13:04
CAPWAP Capacity: 2677.1 (kN)
at Toe: 376.1 (kN)
Set at Yield: 16.897 (mm)
Blow Count: 200 b/m
Length: 22.0 (m)
Length Bl. gage: 21.9 (m)
Penetration: 21.0 (m)
Inclination: 10 (degree)
Hammer: Delmag:D36-23
Rated E: 119.3 (kJ)
Transfered E: 30.9 (kJ)
Max C Stress Top: 26.2 (MPa)
Max C Stress Pile: 26.7 (MPa)
Max Ten. Stress: -0.89 (MPa)
0 750 1500 2250 3000
0.0
7.0
14.0
21.0
28.0
Load (kN)
Displacement(mm)
0.00
5.00
10.00
15.00
20.00
25.00
DepthbelowGrade(m)
Sand
Sand
Clay
Sand
SPT N
bl/30cm
66
qu
kPa
1000.0
CAPWAP
kPa
160.0
Soil
Description
Blow Count
b/m
221
PDA and CAPWAP 52
EX2; CLARK; SOFT-ROCK; Pile: EX-2 Test: 02-Jun-1993
MKT DE 70B, HP 14 X 89; Blow: 627 CAPWAP® 2003-1
GRL Engineers, Inc.
CAPWAP FINAL RESULTS
Total CAPWAP Capacity: 764.6; along Shaft 79.5; at Toe 685.1 kips
ft ft kips kips kips kips/ft ksf s/ft in
764.6
1 6.7 4.2 2.0 762.6 2.0 0.30 0.06 0.255 0.060
2 13.5 11.0 1.0 761.6 3.0 0.15 0.03 0.255 0.060
3 20.2 17.7 1.0 760.6 4.0 0.15 0.03 0.255 0.060
4 26.9 24.4 1.0 759.6 5.0 0.15 0.03 0.255 0.060
5 33.7 31.2 2.0 757.6 7.0 0.30 0.06 0.255 0.060
6 40.4 37.9 3.0 754.6 10.0 0.45 0.10 0.255 0.060
7 47.1 44.6 4.0 750.6 14.0 0.59 0.13 0.255 0.060
8 53.8 51.3 18.6 732.0 32.6 2.76 0.59 0.255 0.060
9 60.6 58.1 1.0 731.0 33.6 0.15 0.03 0.255 0.060
10 67.3 64.8 1.0 730.0 34.6 0.15 0.03 0.255 0.060
11 74.0 71.5 1.0 729.0 35.6 0.15 0.03 0.255 0.060
12 80.8 78.3 4.9 724.1 40.5 0.73 0.16 0.255 0.060
13 87.5 85.0 39.1 685.1 79.5 5.80 1.24 0.255 0.060
Avg. Skin 6.1 0.94 0.19 0.255 0.060
Toe 685.1 503.31 0.066 0.120
Soil Model Parameters/Extensions Skin Toe
Case Damping Factor 0.437 0.971
Unloading Quake (% of loading quake) 99 100
Reloading Level (% of Ru) 100 100
Unloading Level (% of Ru) 78
CAPWAP match quality: 2.88 (Wave Up Match)
Observed: final set = 0.050 in; blow count = 240 b/ft
Observed: final set = 0.009 in; blow count = 1323 b/ft
Summary
Table Output
Summary
Table Output
Ri, qi, Ji
PDA and CAPWAP 53
EX2; CLARK; SOFT-ROCK; Pile: EX-2 Test: 02-Jun-1993
MKT DE 70B, HP 14 X 89; Blow: 627 CAPWAP® 2003-1
GRL Engineers, Inc.
EXTREMA TABLE
Pile Dist. max. min. max. max. max. max. max.
Sgmnt Below Force Force Comp. Tens. Trnsfd. Veloc. Displ.
No. Gages Stress Stress Energy
ft kips kips ksi ksi kip-ft ft/s in
1 3.4 586.4 -24.4 22.549 -0.937 23.53 11.7 0.738
2 6.7 588.7 -24.1 22.635 -0.927 23.40 11.6 0.725
4 13.5 585.7 -22.1 22.520 -0.849 22.79 11.5 0.699
6 20.2 587.3 -21.1 22.583 -0.810 22.30 11.4 0.670
8 26.9 590.1 -19.6 22.691 -0.753 21.73 11.2 0.637
10 33.7 594.8 -18.4 22.870 -0.706 21.02 11.0 0.600
11 37.0 592.6 -17.0 22.787 -0.653 20.42 10.9 0.579
12 40.4 598.9 -17.2 23.029 -0.661 20.09 10.8 0.559
13 43.8 596.6 -15.3 22.940 -0.590 19.39 10.6 0.539
14 47.1 607.0 -16.4 23.339 -0.629 19.05 10.4 0.518
15 50.5 602.3 -15.2 23.161 -0.585 18.21 10.2 0.496
16 53.8 608.4 -15.4 23.393 -0.592 17.79 10.0 0.473
17 57.2 568.4 -7.2 21.857 -0.276 15.45 9.9 0.449
18 60.6 576.1 -17.7 22.152 -0.682 14.91 9.8 0.423
19 63.9 589.0 -27.0 22.650 -1.039 14.16 9.7 0.394
20 67.3 624.9 -35.8 24.028 -1.376 13.38 9.6 0.363
21 70.7 668.4 -42.0 25.701 -1.613 12.39 9.4 0.329
22 74.0 718.3 -48.2 27.622 -1.852 11.36 9.2 0.293
23 77.4 756.7 -54.5 29.095 -2.095 10.14 8.8 0.255
24 80.8 785.1 -61.7 30.188 -2.371 8.94 8.1 0.216
25 84.1 793.0 -61.2 30.492 -2.355 7.59 6.8 0.178
26 87.5 806.4 -63.8 31.007 -2.451 6.21 5.3 0.140
Absolute 87.5 31.007 (T = 27.2 ms)
87.5 -2.451 (T = 44.2 ms)
CASE METHOD
J = = 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
RS1 830.3 799.1 767.8 736.6 705.3 674.1 642.9 611.6 580.4 549.2
RMX 862.6 839.8 821.8 808.3 795.0 782.0 769.8 757.8 745.7 733.7
RSU 836.4 805.8 775.2 744.6 713.9 683.3 652.7 622.1 591.4 560.8
RAU= 595.0 (kips); RA2= 757.7 (kips)
Current CAPWAP Ru= 764.6 (kips); Corresponding J(Rs)= 0.21; J(Rx)=0.64
ft/s ft/s kips kips kips in in kip-ft kips
11.95 0.00 554.8 587.9 587.9 0.747 0.054 23.7 709.9
Numerical
Output
Numerical
Output
Case Method
Extrema
PDA and CAPWAP 54
TAMPA DRILLED SHAFT TESTING
PDA and CAPWAP 55
Instrumentation
PDA and CAPWAP 56
CAPWAP Results for several blows
0
5000
10000
15000
20000
25000
0 10 20 30 40
Displacement (mm)
Load(kN)
Toe Top
APE 750; 60 ton ram (2.4% of test load = 2470 tons). Four blows; 4.5 ft drop; 6 ft dia. shafts;
(under pier) in limestone
see: Rausche, Likins, Hussein, (2008). GSP #180, ASCE
Proposed failure criterion for dynamic tests for the cumulative toe
displacement:
D/60
60 ton ram was 2.4% of failure load
2500 ton failure load
72” dia shaft; Cooper Marl
Large diameter shaft in soil
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0 1000 2000 3000 4000 5000 6000
PileTopDisplacement(in)
Pile Top Load (Kips)
Blow 3 = 2.5 FT Stroke Blow 4 = 4.0 FT Stroke
Blow 5 = 5.0 FT Stroke Elastic Line
PDA and CAPWAP 58
CAPWAP Comparisons
with Static Load Tests – H-Pile
H-pile 14x73 (356 x 109);
Penetration 45 m
Soil: Silts and clays with N<15
for depths < 30 m, then clays
and silts with 40<N<100 to 45 m.
Hammer: D30-32
EOD: 8 mm set/blow
BOR: 5 mm set/blow
EOR: 15 mm set/blow
0
500
1000
1500
2000
2500
0 20 40 60 80 100
Displacement (mm)
Load(kN)
Top
Toe
SLT
CAPWAP 21-day Restrike (Blow 2): Ru=2060 kN; (Blow 25): Ru=1600 kN
Static Load Test (48 days): 2000 kN; Rausche, Likins, Hussein, 2008.
PDA and CAPWAP 59
Florida Drilled ShaftFlorida Drilled Shaft
Diameter:
• to 20 ft (6.1m) 28” (710mm)
• to 44 ft (13.4m) 24” (610mm)
• Soil: Shaft: Sand
Toe: Soft Limestone.
• Hammer: 10 tons
Hussein et al., 1992
6.1 m
13.4 m
Toe 2
Toe
Shaft
Shaft
Note:
Toe 2 treatment much simplified in
CAPWAP 2014
PDA and CAPWAP 60
Florida Drilled Shaft: Class A PredictionFlorida Drilled Shaft: Class A Prediction
• Required Rult:
1000 kips (4450 kN)
• Static and dynamic
tests indicate a
capacity less than
760 kips (3380 kN),
depending on criterion
3560 kN
• Offset Criterion yields
650 kips (2890 kN)
from static and
dynamic test.
PDA and CAPWAP 61
CAPWAP Correlation:
Automatic Procedure
CAPWAP Correlation:
Automatic Procedure
PDA and CAPWAP 62
CAPWAP Correlation:
Radiation Damping Model
CAPWAP Correlation:
Radiation Damping Model
PDA and CAPWAP 63
Combined Data Bases of GRL 1996
and from Stress Wave Conferences
Mean: 0.98; COV: 0.17; N = 303
Likins and Rausche, 2004
PDA and CAPWAP 64
CAPWAP Critique - iCAP Features
• CAPWAP is Non-unique?
Just one result!
• CAPWAP is Slow?
Real time result!
• CAPWAP needs Experience?
Done by PDA Operator!
PDA and CAPWAP 65
iCAP Application
• When?
– During Monitoring
– During Restrike
– During Reanalysis
• When Not?
– When pile and/or soil properties are not well known
– Problem data which lead to poor matches
• How?
– Just turn it on
• Notes:
– iCAP can be run directly from CAPWAP-2014 for non-
uniform piles
– iCAP is no CAPWAP; differences must be expected;
review is recommended
66PDA and CAPWAP 66
Summary
• PDA Testing During Driven Pile installation,
called monitoring, checks driving stresses, pile
integrity, resistance at the time of testing
• Performing a resike test after waiting yields a
dynamic load test.
• Case Method closed form measurements
together with stress wave considerations yield
information on
– dynamic stresses
– pile integrity
– bearing capacity
PDA Wave Mechanics 67
The End
Questions?
PDA Wave Mechanics 68
The Second End
No more questions?
PDA Wave Mechanics 69

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Pda capwap - frank rausche

  • 1. High Strain Pile Testing with the Pile Driving Analyzer System® (PDA)and CAPWAP® PDA Wave Mechanics 1 Outline • Introduction – Measurement Evaluation – Forces and Stresses in Pile – Integrity – Bearing capacity – Examples • Summary • Problems PDA Wave Mechanics 2
  • 2. Measuring strain and acceleration at one point Strain transducer Accelerometer PDA Wave Mechanics 3 Alternative force transducer or F=ma For F=ma or top load cell testing, accelerometers must be attached to pile top. PDA Wave Mechanics 4
  • 3. PDA testing and data acquisitionPDA testing and data acquisition After securely attaching sensors to pile, it is important to input the pertinent and latest calibration values in PDA PDA Wave Mechanics 5 Measurements on a follower, nearshore PDA Wave Mechanics 6
  • 4. The Pile Driving Analyzer - Model 8G • Measures force and velocity, usually near the pile top, but also at other locations such as the pile toe. • Determines Case Method resistance, iCAP®, energy transferred to pile and stresses in pile PDA and CAPWAP 7 Site Link® for Remote Monitoring Reduces travel cost and scheduling problems Site Link® for Remote Monitoring Reduces travel cost and scheduling problems PDA and CAPWAP 8
  • 5. Acceleration and Strain vs. TimeAcceleration and Strain vs. Time Accelerometers, one on each side; acceleration, velocity, displacement Strain Transducers, one on each side; yield strain, stress and average force PDA Wave Mechanics 9 ● Compressive stresses, forces: FMX, CSX, CSI PDA Wave Mechanics 10 ●CSX = 233 MPa (33.8 ksi) FMX = 1280 kN
  • 6. ●CSX = 233 MPa (33.8 ksi) FMX = 1280 kN ● ● ●CSI = 245 MPa (35.5 ksi) For H-piles, Load Cell or F=ma Measurements: no CSI PDA Wave Mechanics 11 Compressive stresses, forces: FMX, CSX, CSI Force, Velocity, DisplacementForce, Velocity, Displacement FMX DMX = ½ max (d1 + d2) DFN = ½ (d1 fin + d2 fin) d2(t) = ∫v2(t) dt d1(t) = ∫v1(t) dt d1 max PDA Wave Mechanics 12 d1 fin d2 fin
  • 7. Pile top force and velocity from PDAPile top force and velocity from PDA We are measuring the total force and the total velocity We plot both together using Z to scale velocity We are measuring the total force and the total velocity We plot both together using Z to scale velocity F(t) = ½ A E [ε1(t) + ε2(t)] v(t) = ½ [v1(t) + v2(t)] Z PDA Wave Mechanics 13 Fu = - vu (EA/c)Fu = - vu (EA/c) u = - vu (E/c)u = - vu (E/c) εu = - vu / cεu = - vu / cεd = vd / cεd = vd / c d = vd (E/c)d = vd (E/c) Fd = vd (EA/c)Fd = vd (EA/c) If wave travels “downwards” If wave travels “upwards” PDA Wave Mechanics 14
  • 8. Superposition of WavesSuperposition of Waves Fd=ZvdFd=Zvd Downward Waves Fu=-ZvuFu=-Zvu Upward Waves F = Fd + Fu v = vd + vu PDA Wave Mechanics 15 Wave Down and Wave Up from F and Zv Fd=½(F+Zv) Fu=½(F-Zv) Fd or Wd; Fu or Wu Fd1 or Wd1 Fd2 or Wu2 PDA Wave Mechanics 16
  • 9. If we know wave up and wave down We can calculate Pile forces at other locations If we know wave up and wave down We can calculate Pile forces at other locations The force at any point along the pile length can be determined from the superposition of the forces in the upward traveling and downward traveling waves The force at any point along the pile length can be determined from the superposition of the forces in the upward traveling and downward traveling waves F = Fu + FdF = Fu + Fd PDA Wave Mechanics 17 L 2L/ct = 0 L/c Upward Wave Upward Wave Downward Wave Downward Wave Wave Superposition for Force below SensorsWave Superposition for Force below Sensors X Fd1 Fu2 Fx = Fu2 + Fd3 Fd3 2x/c PDA Wave Mechanics 18
  • 10. TopToe t3 Tension Stress Calculation – Wave-UpTension Stress Calculation – Wave-Up Point of max tension min Fu min Fu PDA Wave Mechanics 19 Pile Damage: BTA, LTD LTD •A reduction of pile impedance (Z) above the pile toe causes a tension reflection before 2L/c •The time at which the tension reflection arrives at the gage location indicates the depth to Z-reduction: LTD = (tdamage / 2) c •The magnitude of the Z-reduction is calculated with the -formula PDA Wave Mechanics 21
  • 11. t1 t3 Fu,1 = ½(Ft3-Zvt3) Fd,1 = ½(Ft1+Zvt1) Damage Example PDA Wave Mechanics 22 PDA Capacity Monitoring The 1965 (Phase 1) equation was based on a rigid body model: Ru = F(to) - mp a(to) Time to is time of zero velocity – no damping to PDA Wave Mechanics 23 But then we derived the 1968 Case Method
  • 12. Resistance Waves L/c L x Ri -½Ri RB RB Upward traveling wave at time 2L/c: Fu,2 = -Fd,1 + ½Ri + ½Ri + RB RTL = Fu,2 + Fd,1 Fd,1 -Fd,1 ½Ri PDA Wave Mechanics 24 ½Ri RD = Jv vtoe = Jc Z vtoeRD = Jv vtoe = Jc Z vtoe Calculated Damping Component The Case Method uses the pile toe velocity for damping calculations; it is affected by shaft and toe soil resistance! Calculated Damping Component The Case Method uses the pile toe velocity for damping calculations; it is affected by shaft and toe soil resistance! PDA Wave Mechanics 25 Jv … viscous damping factor [kN/m/s] Jc … the dimensionless Case Damping Factor vtoe = (2Fd1 – RTL)/Z based on wave mechanics
  • 13. Case Method Static Resistance Rstatic= RTL - RD Rstatic= Fu,2 + Fd,1 - Jc(2 Fd,1 – Fd1 – Fu,2) Rstatic= (1 – Jc)Fd,1 + (1 + Jc )Fu,2 Total Resistance = Static + Dynamic ResistanceTotal Resistance = Static + Dynamic Resistance PDA Wave Mechanics 26 Fd,1 = 5,450 kN Fu,2 = 2,730 kN Rstatic = (1 – Jc) Fd,1+ (1 + Jc) Fu,2Rstatic = (1 – Jc) Fd,1+ (1 + Jc) Fu,2 RTL = 5,450 + 2,730 = 8,180 kN For example with Jc= .3 Rstatic = (1 - .3) 5,450 + (1 + .3) 2,730 = 7,350 kN RTL = 5,450 + 2,730 = 8,180 kN For example with Jc= .3 Rstatic = (1 - .3) 5,450 + (1 + .3) 2,730 = 7,350 kN PDA Wave Mechanics 27
  • 14. Maximum Case Method Resistance, RXiMaximum Case Method Resistance, RXi t1 t2 2L/c Calculates Rstatic at all times after the first velocity peak Selects the maximum Rstatic for JC= 0.i Calculates Rstatic at all times after the first velocity peak Selects the maximum Rstatic for JC= 0.i PDA Wave Mechanics 28 Shaft and Toe Resistance 2L/ct = 0 L/c L x R -½R RB ½R RB Fd,1 -Fd,1 ½R PDA Wave Mechanics 29
  • 15. Ri - Wave upRi - Wave up R ½R PDA Wave Mechanics 30 An Example: PDA Capacity Results End of Driving PDA Wave Mechanics 31
  • 16. PDA Capacity Results Restrike; Blow No. 1 PDA Wave Mechanics 32 Restrike Blow No. 2 PDA Wave Mechanics 33
  • 17. Restrike, blow No. 4 PDA Wave Mechanics 34 PEBWAP for and End Bearing Pile 20x0.5” OEP; LG = 22.3 m; D46-32; 0.6 mm/bl; JC = 0.3 0 1500 3000 4500 6000 7500 0 5 10 15 Resistance-kN Toe Displacement - mm Total Resistance Static Resistance Static Resistance = Total Resistance – Damping Factor * Toe Velocity PDA and CAPWAP 35
  • 18. THE CAPWAP METHODTHE CAPWAP METHOD 1 Set up pile and soil model and assume Rshaft and Rtoe 1 Set up pile and soil model and assume Rshaft and Rtoe Rshaft Rtoe 5 If no satisfactory match: Go to Step 25 If no satisfactory match: Go to Step 2 4 Adjust Rshaft and Rtoe4 Adjust Rshaft and Rtoe 3 Compare WUC with measured WUM3 Compare WUC with measured WUM 2 Apply measured WDM to pile model at top and calculate complementary WUC 2 Apply measured WDM to pile model at top and calculate complementary WUC WUM WDM WUC PDA and CAPWAP 36 First try (poor) Final match (good) Adjustments CAPWAP is an Iterative Process PDA and CAPWAP 37
  • 19. Seg. i ∆Li Ri Fdo i Fdn i Fun i Fuo i Rdi Rui The Pile is divided in Np uniform pile segments of approximately 1 m length. Segment lengths are chosen for equal time increment ∆t = ∆Li/ci. Each Segment has: impedance Zi,,= EiAi/ci , mass mi = Zi ∆t and stiffness ki = Zi/∆t . The Pile Model PDA and CAPWAP 38 The Combined CAPWAP Pile and Soil ModelThe Combined CAPWAP Pile and Soil Model Soil segment length: LSi = Nfac Li Soil segment length: LSi = Nfac Li Spring (static resistance) Dashpot (dynamic resistance) Spring (static resistance) Dashpot (dynamic resistance) t t t t t t t Pile Model: Impedance Zi = EiAi/ci Pile Segment Length Li Wave Travel time in Pile t = Li/ci Pile Model: Impedance Zi = EiAi/ci Pile Segment Length Li Wave Travel time in Pile t = Li/ci PDA and CAPWAP 39
  • 20. Rui, qi Rt, qt Ji JT Shaft Resistance, Ns times Shaft Resistance, Ns times tG The Basic CAPWAP Soil Model The Basic CAPWAP Soil Model End Bearing End Bearing PDA and CAPWAP 40 mt Rui, qi Rt, qt Ji JT JSK JBT Add Radiation Damping Inertia Resistance Add Radiation Damping Inertia Resistance tG ms mPL Some CAPWAP Soil Model Extensions Some CAPWAP Soil Model Extensions mSP PDA and CAPWAP 41
  • 21. Signal Matching ExampleSignal Matching Example PDA and CAPWAP 42 First Trial Analysis (Lousy Match)First Trial Analysis (Lousy Match) Input F Matching F Input F Matching v or Input v Matching F or PDA and CAPWAP 43
  • 22. Working with Wave-UpWorking with Wave-Up RU = 782 kips RT = 68 kips JS/JT = .05/.15 s/ft (JCS/JCT = .75/.22) QS/QT = .10/.12” RU = 782 kips RT = 400 kips RU = 782 kips RT = 600 kips RU = 782 kips RT = 705 kips JS/JT = .45/.02 s/ft QS/QT = .10/.12” PDA and CAPWAP 44 Working with Wave-UpWorking with Wave-Up RU/RT = 782/705 kips JS/JT = .45/.02 s/ft (JCS/JCT = .75/.22) QS/QT = .10/.12” RU/RT = 782/705 kips JS/JT = .30/.05 s/ft (JCS/JCT = .50/.76) RU/RT = 782/702 kips JS/JT = .29/.05 s/ft (JCS/JCT = .50/.76) Prev. PDA and CAPWAP 45
  • 23. Working with Wave-UpWorking with Wave-Up RU/RT = 782/702 kips JS/JT = .29/.05 s/ft (JCS/JCT = .50/.76) RU/RT = 765/686 kips JS/JT = .28/.06 s/ft (JCS/JCT = .48/.82) RU/RT = 765/686 kips JS/JT = .26/.07 s/ft (JCS/JCT = .44/.97) QS/QT = .06/.12” Unloading Parameters Pretty good match: let’s quitPretty good match: let’s quit PDA and CAPWAP 46 CAPWAP Help FeaturesCAPWAP Help Features HC CAPWAP Variable Help HC CAPWAP Variable Help HR CAPWAP Resistance vs Displacement Help HR CAPWAP Resistance vs Displacement Help PDA and CAPWAP 47
  • 24. CAPWAP’s Static Pile and Soil Model CAPWAP’s Static Pile and Soil Model kshaft, I = Ru,i /qi ktoe, i Ru, i kp, i Rtoe, i Q u 1 uto e PDA and CAPWAP 48 CAPWAP Static AnalysisCAPWAP Static Analysis The final static load displacement curve is from a t-z and q-z analysis The final static load displacement curve is from a t-z and q-z analysis PDA and CAPWAP 49
  • 25. CAPWAP Static Analysis Options CAPWAP Static Analysis Options Smoothing User Capacity Uplift Test Extrapolation Failure Criteria Smoothing User Capacity Uplift Test Extrapolation Failure Criteria PDA and CAPWAP 50 Standard OutputStandard Output PDA and CAPWAP 51
  • 26. Comprehensive CAPWAP ReportComprehensive CAPWAP Report • “Blow Count” is from Direct Input in CAPWAP or from PDA-W • “Job Information” provides for other information input EX1; BENT 17-2; Pile: EX-1 Test: 04-Sep-1991 16:15: D36-23; silt; 16"PSC; Blow: 1171 CAPWAP(R) 2013 Beta Version - Pile Dynamics OP: xxx yyyy Analysis: 28-May-2013 -2500 0 2500 5000 kN F Msd V*Z Msd 5 105 ms -600 0 600 1200 kN 15 L/c Wup Msd Wup Cpt Pile Type: Steel Pile Size: 12 H Pile Pile Installed: 03-Mar-2013 13:04 CAPWAP Capacity: 2677.1 (kN) at Toe: 376.1 (kN) Set at Yield: 16.897 (mm) Blow Count: 200 b/m Length: 22.0 (m) Length Bl. gage: 21.9 (m) Penetration: 21.0 (m) Inclination: 10 (degree) Hammer: Delmag:D36-23 Rated E: 119.3 (kJ) Transfered E: 30.9 (kJ) Max C Stress Top: 26.2 (MPa) Max C Stress Pile: 26.7 (MPa) Max Ten. Stress: -0.89 (MPa) 0 750 1500 2250 3000 0.0 7.0 14.0 21.0 28.0 Load (kN) Displacement(mm) 0.00 5.00 10.00 15.00 20.00 25.00 DepthbelowGrade(m) Sand Sand Clay Sand SPT N bl/30cm 66 qu kPa 1000.0 CAPWAP kPa 160.0 Soil Description Blow Count b/m 221 PDA and CAPWAP 52 EX2; CLARK; SOFT-ROCK; Pile: EX-2 Test: 02-Jun-1993 MKT DE 70B, HP 14 X 89; Blow: 627 CAPWAP® 2003-1 GRL Engineers, Inc. CAPWAP FINAL RESULTS Total CAPWAP Capacity: 764.6; along Shaft 79.5; at Toe 685.1 kips ft ft kips kips kips kips/ft ksf s/ft in 764.6 1 6.7 4.2 2.0 762.6 2.0 0.30 0.06 0.255 0.060 2 13.5 11.0 1.0 761.6 3.0 0.15 0.03 0.255 0.060 3 20.2 17.7 1.0 760.6 4.0 0.15 0.03 0.255 0.060 4 26.9 24.4 1.0 759.6 5.0 0.15 0.03 0.255 0.060 5 33.7 31.2 2.0 757.6 7.0 0.30 0.06 0.255 0.060 6 40.4 37.9 3.0 754.6 10.0 0.45 0.10 0.255 0.060 7 47.1 44.6 4.0 750.6 14.0 0.59 0.13 0.255 0.060 8 53.8 51.3 18.6 732.0 32.6 2.76 0.59 0.255 0.060 9 60.6 58.1 1.0 731.0 33.6 0.15 0.03 0.255 0.060 10 67.3 64.8 1.0 730.0 34.6 0.15 0.03 0.255 0.060 11 74.0 71.5 1.0 729.0 35.6 0.15 0.03 0.255 0.060 12 80.8 78.3 4.9 724.1 40.5 0.73 0.16 0.255 0.060 13 87.5 85.0 39.1 685.1 79.5 5.80 1.24 0.255 0.060 Avg. Skin 6.1 0.94 0.19 0.255 0.060 Toe 685.1 503.31 0.066 0.120 Soil Model Parameters/Extensions Skin Toe Case Damping Factor 0.437 0.971 Unloading Quake (% of loading quake) 99 100 Reloading Level (% of Ru) 100 100 Unloading Level (% of Ru) 78 CAPWAP match quality: 2.88 (Wave Up Match) Observed: final set = 0.050 in; blow count = 240 b/ft Observed: final set = 0.009 in; blow count = 1323 b/ft Summary Table Output Summary Table Output Ri, qi, Ji PDA and CAPWAP 53
  • 27. EX2; CLARK; SOFT-ROCK; Pile: EX-2 Test: 02-Jun-1993 MKT DE 70B, HP 14 X 89; Blow: 627 CAPWAP® 2003-1 GRL Engineers, Inc. EXTREMA TABLE Pile Dist. max. min. max. max. max. max. max. Sgmnt Below Force Force Comp. Tens. Trnsfd. Veloc. Displ. No. Gages Stress Stress Energy ft kips kips ksi ksi kip-ft ft/s in 1 3.4 586.4 -24.4 22.549 -0.937 23.53 11.7 0.738 2 6.7 588.7 -24.1 22.635 -0.927 23.40 11.6 0.725 4 13.5 585.7 -22.1 22.520 -0.849 22.79 11.5 0.699 6 20.2 587.3 -21.1 22.583 -0.810 22.30 11.4 0.670 8 26.9 590.1 -19.6 22.691 -0.753 21.73 11.2 0.637 10 33.7 594.8 -18.4 22.870 -0.706 21.02 11.0 0.600 11 37.0 592.6 -17.0 22.787 -0.653 20.42 10.9 0.579 12 40.4 598.9 -17.2 23.029 -0.661 20.09 10.8 0.559 13 43.8 596.6 -15.3 22.940 -0.590 19.39 10.6 0.539 14 47.1 607.0 -16.4 23.339 -0.629 19.05 10.4 0.518 15 50.5 602.3 -15.2 23.161 -0.585 18.21 10.2 0.496 16 53.8 608.4 -15.4 23.393 -0.592 17.79 10.0 0.473 17 57.2 568.4 -7.2 21.857 -0.276 15.45 9.9 0.449 18 60.6 576.1 -17.7 22.152 -0.682 14.91 9.8 0.423 19 63.9 589.0 -27.0 22.650 -1.039 14.16 9.7 0.394 20 67.3 624.9 -35.8 24.028 -1.376 13.38 9.6 0.363 21 70.7 668.4 -42.0 25.701 -1.613 12.39 9.4 0.329 22 74.0 718.3 -48.2 27.622 -1.852 11.36 9.2 0.293 23 77.4 756.7 -54.5 29.095 -2.095 10.14 8.8 0.255 24 80.8 785.1 -61.7 30.188 -2.371 8.94 8.1 0.216 25 84.1 793.0 -61.2 30.492 -2.355 7.59 6.8 0.178 26 87.5 806.4 -63.8 31.007 -2.451 6.21 5.3 0.140 Absolute 87.5 31.007 (T = 27.2 ms) 87.5 -2.451 (T = 44.2 ms) CASE METHOD J = = 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 RS1 830.3 799.1 767.8 736.6 705.3 674.1 642.9 611.6 580.4 549.2 RMX 862.6 839.8 821.8 808.3 795.0 782.0 769.8 757.8 745.7 733.7 RSU 836.4 805.8 775.2 744.6 713.9 683.3 652.7 622.1 591.4 560.8 RAU= 595.0 (kips); RA2= 757.7 (kips) Current CAPWAP Ru= 764.6 (kips); Corresponding J(Rs)= 0.21; J(Rx)=0.64 ft/s ft/s kips kips kips in in kip-ft kips 11.95 0.00 554.8 587.9 587.9 0.747 0.054 23.7 709.9 Numerical Output Numerical Output Case Method Extrema PDA and CAPWAP 54 TAMPA DRILLED SHAFT TESTING PDA and CAPWAP 55
  • 28. Instrumentation PDA and CAPWAP 56 CAPWAP Results for several blows 0 5000 10000 15000 20000 25000 0 10 20 30 40 Displacement (mm) Load(kN) Toe Top APE 750; 60 ton ram (2.4% of test load = 2470 tons). Four blows; 4.5 ft drop; 6 ft dia. shafts; (under pier) in limestone see: Rausche, Likins, Hussein, (2008). GSP #180, ASCE Proposed failure criterion for dynamic tests for the cumulative toe displacement: D/60
  • 29. 60 ton ram was 2.4% of failure load 2500 ton failure load 72” dia shaft; Cooper Marl Large diameter shaft in soil 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 0 1000 2000 3000 4000 5000 6000 PileTopDisplacement(in) Pile Top Load (Kips) Blow 3 = 2.5 FT Stroke Blow 4 = 4.0 FT Stroke Blow 5 = 5.0 FT Stroke Elastic Line PDA and CAPWAP 58 CAPWAP Comparisons with Static Load Tests – H-Pile H-pile 14x73 (356 x 109); Penetration 45 m Soil: Silts and clays with N<15 for depths < 30 m, then clays and silts with 40<N<100 to 45 m. Hammer: D30-32 EOD: 8 mm set/blow BOR: 5 mm set/blow EOR: 15 mm set/blow 0 500 1000 1500 2000 2500 0 20 40 60 80 100 Displacement (mm) Load(kN) Top Toe SLT CAPWAP 21-day Restrike (Blow 2): Ru=2060 kN; (Blow 25): Ru=1600 kN Static Load Test (48 days): 2000 kN; Rausche, Likins, Hussein, 2008. PDA and CAPWAP 59
  • 30. Florida Drilled ShaftFlorida Drilled Shaft Diameter: • to 20 ft (6.1m) 28” (710mm) • to 44 ft (13.4m) 24” (610mm) • Soil: Shaft: Sand Toe: Soft Limestone. • Hammer: 10 tons Hussein et al., 1992 6.1 m 13.4 m Toe 2 Toe Shaft Shaft Note: Toe 2 treatment much simplified in CAPWAP 2014 PDA and CAPWAP 60 Florida Drilled Shaft: Class A PredictionFlorida Drilled Shaft: Class A Prediction • Required Rult: 1000 kips (4450 kN) • Static and dynamic tests indicate a capacity less than 760 kips (3380 kN), depending on criterion 3560 kN • Offset Criterion yields 650 kips (2890 kN) from static and dynamic test. PDA and CAPWAP 61
  • 31. CAPWAP Correlation: Automatic Procedure CAPWAP Correlation: Automatic Procedure PDA and CAPWAP 62 CAPWAP Correlation: Radiation Damping Model CAPWAP Correlation: Radiation Damping Model PDA and CAPWAP 63
  • 32. Combined Data Bases of GRL 1996 and from Stress Wave Conferences Mean: 0.98; COV: 0.17; N = 303 Likins and Rausche, 2004 PDA and CAPWAP 64 CAPWAP Critique - iCAP Features • CAPWAP is Non-unique? Just one result! • CAPWAP is Slow? Real time result! • CAPWAP needs Experience? Done by PDA Operator! PDA and CAPWAP 65
  • 33. iCAP Application • When? – During Monitoring – During Restrike – During Reanalysis • When Not? – When pile and/or soil properties are not well known – Problem data which lead to poor matches • How? – Just turn it on • Notes: – iCAP can be run directly from CAPWAP-2014 for non- uniform piles – iCAP is no CAPWAP; differences must be expected; review is recommended 66PDA and CAPWAP 66 Summary • PDA Testing During Driven Pile installation, called monitoring, checks driving stresses, pile integrity, resistance at the time of testing • Performing a resike test after waiting yields a dynamic load test. • Case Method closed form measurements together with stress wave considerations yield information on – dynamic stresses – pile integrity – bearing capacity PDA Wave Mechanics 67
  • 34. The End Questions? PDA Wave Mechanics 68 The Second End No more questions? PDA Wave Mechanics 69