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2013
Frank Rausche
Pile Dynamics, Inc.
The Case Method and the
Pile Driving Analyzer® (PDA)
Outline
• Testing Objectives
• Hardware
– Standard
– Wireless testing
– Remote testing
• Methods
– Stresses
– Integrity
– Capacity
• Examples
• Summary
PDPI June 2013 – Case Method 2
Testing Objectives: Economical Load Testing D
yna
mic
Tes
tin
g
Sta
tic
Test
ing
PDPI June 2013 – Case Method 3
Testing Objectives: Installation Monitoring Stresses, Integrity, Resistance, Energy (Case Method)
PDPI June 2013 – Case Method 4
Basically We
Have to Measure
Pile Top Force and
Velocity
and Process Data with the
Pile Driving Analyzer®
PDPI June 2013 – Case Method 5
Measuring Strain and Acceleration (need to do it on opposite pile sides)
Strain transducer Accelerometer
PDPI June 2013 – Case Method 6
PDA testing data acquisition
• Need Minimum 2 strain measurements per pile to
compensate for bending
PDPI June 2013 – Case Method 7
Mounting the sensors
PDPI June 2013 – Case Method 8
Measurements on cylinder piles
PDPI June 2013 – Case Method 9
Wireless testing components using
smart sensors
Transmitter
PDPI June 2013 – Case Method 10
Strain and Acceleration Sensors
PDPI June 2013 – Case Method
Wir
ele
ss
Un
der
Wate
r
11
Sensor Installation/Protection
H-piles Pipe piles
PDPI June 2013 – Case Method 12
Lofting pile into leads
PDA
PDPI June 2013 – Case Method 13
Concrete Piles
PDPI June 2013 – Case Method 14
Smart and Wireless Sensors
Make for Happy Testers
PDPI June 2013 – Case Method 15
SiteLink and Wireless Testing
PDPI June 2013 – Case Method 16
PAX - SiteLink Connect Operation
• PDA is being operated by office engineer
• Office computer acts as a remote keyboard and monitor
• PAX is used with PDA-L
• Data resides on PAX until downloaded
PDPI June 2013 – Case Method 17
• No traveling/scheduling cost/delays/issues
• Immediate analysis and quick report submittal
• Increased efficiency of test engineer
• Remote supervision of inexperienced personnel avoids errors
SiteLink Advantages
PDPI June 2013 – Case Method 18
Measurements on a follower, nearshore
PDPI June 2013 – Case Method 19
Basic Strain and Acceleration Measurements
ε1(t), ε2(t), one strain on each side
a1(t), a2(t), one acc. on each side
PDPI June 2013 – Case Method 20
Standard Presentation
F = ½ (S1 + S2 ) (EM * AR)
PDPI June 2013 – Case Method
v = ½ ∫(a1 + a2 ) dt
Fu = ½ (F - vZ)
Fd = ½ (F + vZ)
21
Maximum Force, FMX
PDPI June 2013 – Case Method 22
●CSX = 233 MPa (33.8 ksi) ●
● ●CSI = 245 MPa (35.5 ksi)
Calculated at Bottom: CSB = 264 MPa (38.2 ksi)
PDPI June 2013 – Case Method
Compresisve Stress Results At Gage Location (CSX and CSI) and at Bottom (CSB)
23
Calculating Tension Stresses Below Pile Top From Force in Wave-down and Wave-up
Fd
Fu
F
vZ
PDPI June 2013 – Case Method 24
L
Upward
Wave
Downward
Wave
Wave Superposition for Force Below Sensors
x
Fd1
Fu2
Fx = Fu2 + Fd3
Fd3
2x/c t = 0
2L/c
L/c
PDPI June 2013 – Case Method 25
Tension Stress Calculation (Wave-Up)
Fu
Fd
Max. Tension - up
Minimum Compression - down
x
PDPI June 2013 – Case Method 26
Tension Stress Maximum and Distribution
t3
top toe
Point of max tension
Max. Tension Wave Up
Equal
PDPI June 2013 – Case Method 27
Another Tension Stress Example
top toe
PDPI June 2013 – Case Method 28
Pile Damage: BTA, LTD
•A pile impedance reduction
(damage?) causes a tension
reflection before 2L/c
•The time at which the tension
reflection arrives at the gage
location indicates the depth to the
damage: LTD = (tdamage / 2) c
PDPI June 2013 – Case Method 29
2L/c t = 0 L/c
Z2
Fd2
Fu1
Fd,1
2x/c
Z1
A
B
FA = FB: Fu,1 + Fd,1 = Fd,2
vA = vB: vu,1 + vd,1 = vd,2
2nd equation: (Z2/Z1)(Z1vu,1 + Z1vd,1) = Z2 vd,2
with = Z2/Z1: (- Fu,1 + Fd,1) = Fd,2 = Fu,1 + Fd,1
= (Fu,1 + Fd,1) / (- Fu,1 + Fd,1)
x
PDPI June 2013 – Case Method 30
t1
t3
Fu,1 = ½(Fu,t3 - Zvt3)
Fd,1 = ½(Ft1+Zvt1)
Damage Assessment Example
PDPI June 2013 – Case Method 31
Resistance Waves
L/c
L
x
Ri
-½Ri
RB
½Ri
RB
Upward traveling wave at time 2L/c:
Fu,2 = -Fd,1 + ½Ri + ½Ri + RB
Fd,1 -Fd,1
½Ri
RTL = Fu,2 + Fd,1
Fu,2
Fd,1
PDPI June 2013 – Case Method 32
The Case Method Equation
RTL = Fd,1 + Fu,2
RTL is the total pile resistance:
Dynamic + static; shaft resistance + end bearing
RTL is mobilized during time 2L/c following time t1
PDPI June 2013 – Case Method 33
The Static Resistance is Total Resistance - Damping
RS= RTL – RD
Assuming RD = Jv v [kN/m/s][m/s]
Introducing: Jc = Jv / Z ….. Case Damping Factor
Then RD = Jc Z v
PDPI June 2013 – Case Method 34
Using pile toe velocity as representative vtoe = 2 Fd,1- RTL
Rstatic= RTL - Jc(2 Fd,1 – RTL)
Rstatic= (1 – Jc)Fd,1 + (1 + Jc )Fu,2
vtoe
PDPI June 2013 – Case Method 35
Rstatic = (1 – Jc) Fd,1+ (1 + Jc) Fu,2
F
= 5450 kN
F
= 50 kN
F
=2,820 kN
F
= 2,730 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
PDPI June 2013 – Case Method 36
Time of Fd,1
and Fu,2
t1 t2 2L/c
We calculate Rstatic at the time when it
gives the maximum
activated value
PDPI June 2013 – Case Method 37
R
Compressive upward wave
Fur = ½R; vur = -½R/Z
Tensile downward wave
Fdr = -½R; vdr = -½R/Z
R/2
R/2
Δx
x
Pile with shaft resistance:
Equilibrium and Continuity
PDPI June 2013 – Case Method 38
Shaft and Toe Resistance 2L/c t = 0 L/c
L
x
Rf
-½Rf
RB
½Rf
RB
Fd,1
-Fd,1 ½Rf
PDPI June 2013 – Case Method 39
Friction Pile Records
PDPI June 2013 – Case Method
Fd Fu
F
vZ
40
Wave-up Force Change Due to Friction
Rf
½Rf
PDPI June 2013 – Case Method 41
PDA Soil Resistance Results End of Driving
PDPI June 2013 – Case Method 42
PDA Soil Resistance Results Restrike; Blow No. 1
PDPI June 2013 – Case Method 43
Restrike Blow No. 2
PDPI June 2013 – Case Method 44
Restrike, Blow No. 4
PDPI June 2013 – Case Method 45
• Quick signal
matching
• Total Capacity
• Shaft vs end bearing
• Tension stresses
• Compression strs.
• Recommended Jc
• Match Quality
• Computed match
• Load test curve
• Distribution
Another Method of Capacity Calculation: iCAP®
(a subset of CAPWAP®)
Best Results on uniform driven piles!
iCAP :
Ru 493 kips
MQ 2.12
PDPI June 2013 – Case Method 46
PDPI June 2013 – Case Method
A Monitoring Example: Rigolet Bridge
47
Cylinder Piles 66” dia.
PDPI June 2013 – Case Method 48
PDA Measurements
including circumferential
strain measurements
PDPI June 2013 – Case Method 49
Cylinder Pile Data (EOD)
PDPI June 2013 – Case Method 50
Case Method Monitoring Results
PDPI June 2013 – Case Method 51
An Example: Wave equation + Testing
Water Table at 3 m or 10’ depth
Depth Description N qu
m (ft) kPa (ksf)
4 (13) Sand 6
8 (26) Sand 13
13.4 (44) Clay 180 (3.8)
22 (72) Clay with Sand Lenses 300 (6.2)
52 PDPI June 2013 – Case Method
GRLWEAP Static
Soil Analysis
• Based on “SA” analysis
using: • N-value
• qu
Ru = 1700 kN
Rshaft = 1200 kN
53 PDPI June 2013 – Case Method
Wave Equation analysis input
54 PDPI June 2013 – Case Method
Wave Equation analysis: Bearing Graph
08-Aug-2012GRL Engineers, Inc.
GRLWEAP Version 2010GRLWEAP Example
08-Aug-2012GRL Engineers, Inc.
GRLWEAP Version 2010GRLWEAP Example
Com
pres
sive
Stre
ss (M
Pa)
0
4
8
12
16
20
Tens
ion
Stre
ss (M
Pa)
0
4
8
12
16
20
Blow Count (blows/.30m)
Ulti
mat
e C
apac
ity (k
N)
0 60 120 180 240 300 360
0
800
1600
2400
3200
4000
Blow Count (blows/.30m)
Stro
ke (m
)
0 60 120 180 240 300 360
0
1
2
3
4
5
DELMAG D 30-32
Ram Weight 29.37 kN
Efficiency 0.800
Pressure 9645 (99%) kPa
Helmet Weight 17.79 kN
Hammer Cushion 19259 kN/mm
Pile Cushion 1009 kN/mm
COR of P.C. 0.500
Skin Quake 2.500 mm
Toe Quake 10.160 mm
Skin Damping 0.650 sec/m
Toe Damping 0.500 sec/m
Pile Length
Pile Penetration
Pile Top Area
20.50
14.01
3716.12
m
m
cm2
Pile Model
Skin Friction
Distribution
Res. Shaft = 71 %
(Proportional)
For 1700 kN capacity we would expect 170 bl/m = 51 bl/0.3m
55 PDPI June 2013 – Case Method
Wave Equation analysis: Bearing Graph
At the statically predicted capacity of 1700 kN we would expect a
blow count of 51 bl/0.3m)
We would expect a transferred energy of 26 kJ at a stroke of 2.4 m
56 PDPI June 2013 – Case Method
08-Aug-2012GRL Engineers, Inc.
GRLWEAP Version 2010GRLWEAP Example
08-Aug-2012GRL Engineers, Inc.
GRLWEAP Version 2010GRLWEAP Example
Com
pres
sive
Stre
ss (M
Pa)
0
4
8
12
16
20
Tens
ion
Stre
ss (M
Pa)
0
4
8
12
16
20
Blow Count (blows/.30m)
Ulti
mat
e C
apac
ity (k
N)
0 60 120 180 240 300 360
0
800
1600
2400
3200
4000
Blow Count (blows/.30m)
Stro
ke (m
)
0 60 120 180 240 300 360
0
1
2
3
4
5
DELMAG D 30-32
Ram Weight 29.37 kN
Efficiency 0.800
Pressure 9645 (99%) kPa
Helmet Weight 17.79 kN
Hammer Cushion 19259 kN/mm
Pile Cushion 1009 kN/mm
COR of P.C. 0.500
Skin Quake 2.500 mm
Toe Quake 10.160 mm
Skin Damping 0.650 sec/m
Toe Damping 0.500 sec/m
Pile Length
Pile Penetration
Pile Top Area
20.50
14.01
3716.12
m
m
cm2
Pile Model
Skin Friction
Distribution
Res. Shaft = 71 %
(Proportional)
Wave Equation analysis: Bearing Graph At Refusal we would expect a 4000 kN capacity
57 PDPI June 2013 – Case Method
Wave Equation analysis: Bearing Graph
At refusal (1210 bl/m or 370 bl/ft) we would expect 4000 kN
capacity at a stroke of 2.5 m and a transferred energy of 26.8 kJ
Let’s check the analysis! 58 PDPI June 2013 – Case Method
• Measure force and motion near the pile top
• Calculate transferred energy, bearing capacity, stresses
PDA Testing + CAPWAP®
59 PDPI June 2013 – Case Method
GRLWEAP
at Refusal
1210
(370)
27
(20)
17.5
(2.5)
1.1
(0.15)
PDA Results and Comparison GRLWEAP
PDA Wave Equation Rated/Mean
Stroke in m
in ft
2.7
8.8
2.5
8.3
3.5
11.3
Transfer Ratio(%) 21 27 29
Blow
Count
Transf’d
Energy
Comp.
Stress
Tension
Stress
Bl/m
(Bl/ft)
kJ
(ft-kips)
MPa
(ksi)
MPa
(ksi)
Measured
by PDA
1460
(445)
21
(15.5)
13.5
(1.9)
2.4
(0.35)
60 PDPI June 2013 – Case Method
CAPWAP Results
Best Signal Match
• CAPWAP (Signal Matching) is a one-dimensional dynamic
analysis of the pile which uses the measured signals to determine
static and dynamic soil resistance values.
• Based on the static results, a simulated static test is performed
leading to a load-set curve, representation a (very) quick load test.
Measured Measured, F
and vZ
61 PDPI June 2013 – Case Method
CAPWAP Results
Best Signal Match
Load-Set
Curve
62 PDPI June 2013 – Case Method
CAPWAP Numerical Results Ru= 2100 kN Rshaft = 1110 kN Rtoe = 990 kN
63 PDPI June 2013 – Case Method
Summary of Capacities Based on EOD
Static
Analysis
Capacity
Actual
Blow
Count
Wave
Equation
Capacity
CAPWAP
Capacity
kN
(kips)
Bl/m
(Bl/ft)
kN
(kips)
kN
(kips)
1,700
(382)
1482
(445)
4,000
(900)
2,100
(470)
Check whether additional capacity can be gained with
time by doing a restrike test.
Pile is driven 6 inches after 24 hours waiting time.
Blow Count now is 300 Bl/m (90 bl/ft)
64 PDPI June 2013 – Case Method
Hammer Performance Results
End of Drive
PDA Wave Equation Rated/Mean
Stroke in m
in ft
2.7
8.8
2.5
8.3
3.5
11.3
Transfer Ratio(%) 21 27 (Refusal) 29
Beginnning of Restrike
PDA Wave Equation Rated
Stroke in m
in ft
3.3
10.7
2.5
8.3
3.5
11.3
Transfer Ratio(%) 35 26 (90 bpf) N/A
65 PDPI June 2013 – Case Method
Revisiting the Wave Equation Bearing Graph
At 300 bl/m or 90 bl/ft we would expect 2500 kN capacity
with again 26 kJ transferred energy and a stroke of 2.5 m
66 PDPI June 2013 – Case Method
Capacity Summary Based on EOD and BOR
Static
Analysis
Capacity
Actual
Blow
Count
Wave
Equation
Capacity
CAPWAP
Capacity
kN
(kips)
Bl/m
(Bl/ft)
kN
(kips)
kN
(kips)
End of
Driving
1482
(445)
4,000*
(900)
2,100**
(470)
Restrike
1,700***
(382)
300
(90)
2,500
(560)
2,550
570
67 PDPI June 2013 – Case Method
Capacity Summary Based on EOD and BOR
Static
Analysis
Capacity
Actual
Blow
Count
Wave
Equation
Capacity
CAPWAP
Capacity
kN
(kips)
Bl/m
(Bl/ft)
kN
(kips)
kN
(kips)
End of
Driving
1482
(445)
4,000*
(900)
2,100**
(470)
Restrike
1,700***
(382)
300
(90)
2,500
(560)
2,550
570
68 PDPI June 2013 – Case Method
Capacity and (LRFD) Safe Load Summary
Method
Nominal
Resistance
(kN)
Resistance
Factor, φ (AASHTO 2009)
Equivalent
F.S.
Safe Load
(kN)
Static
Formula 1700 0.40 (avg) 3.50 485
ENR
Gates
31,352
4,510
0.10
0.40
14.0
3.50
2,240
1,290
WE-EOD
WE-BOR
4,000
2,500
0.50
0.50
2.80
2.80
1,430
890
CW-EOD
CW-BOR
2,100
2,550
0.65
0.65
2.15
2.15
977
1,190
69 PDPI June 2013 – Case Method
Back-calculation of Hammer Efficiency
PDPI June 2013 – Case Method 70
Results from Wave Equation after Matching EOD and BOR Test Results
Quantity
EOID BOR
Normal or
CAPWAP GRLWEAP
Normal or
CAPWAP GRLWEAP
Hammer Efficiency (%) 80 50 80 73
Hammer Cushion
- Elastic Modulus (ksi) 550 275 550 550 Combustion Pressure
(%) 100 100 100 120
Pile Cushion
- Elastic Modulus (ksi)* 60 - 90 70 60 - 90 110
Pile Cushion
- Coeff. of Restitution 0.50 0.25 0.50 0.25
The hammer may have overheated at EOD after 4230 blows. and, therefore, had poor energy transfer.
PDPI June 2013 – Case Method 71
• The PDA processes pile top force and velocity records
according to the (closed form solution) Case Method;
results allow for assessment of • Pile Stresses
• Hammer Performance
• Soil Resistance
• Pile Integrity
• These results are diplayed in Real Time and, therefore,
allow for real time monitoring of the pile installation
• For Dynamic load testing Restrikes + CAPWAP are
usually necessary
• After PDA+CAPWAP the GRLWEAP analysis can be
refined
Summary
PDPI June 2013 – Case Method 72