Transcript Case Method Introduction -

GRL
Dynamic Pile testing with the
Pile Driving Analyzer®
© 1998 Goble Rausche Likins and
Associates and Dr. Julian Seidel
GRL
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Summary
History of Dynamic Pile Testing
Measuring stress waves
Fundamentals of Wave Mechanics
The Case Method (Pile Driving Analyzer)
– Capacity
– Stresses
– Integrity
– Hammer performance
GRL
History of Dynamic
Pile Testing/Analysis
18th Century:
Closed Form Solutions
Late 19th Century:
Engineering News Formula
1920’s:
First Strain Measurements
1950:
Smith’s Wave Equation Program
1964:
Case Project began under Dr. G.G. Goble
1968:
Pile Driving Analyzer ® (PDA)
1970:
CAPWAP ®
1972:
Pile Dynamics, Inc. founded
1976:
WEAP program
1977:
Saximeter
1982:
Hammer Performance Analyzer
1986:
Hammer Performance Study
1989:
Pile Integrity Testing (PIT)
1996:
FHWA Manual
1998:
Pile Installation Recorders (PIR)
1999:
Remote PDA
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1-D Wave Theory
• Hammer causes a downward travelling
stress-wave to enter the pile
• Soil resistance causes stress-wave
reflections
• Stress in pile can be represented by
1-dimensional Wave Theory
• These stress-waves can be measured
and identified with measurement of
force and velocity near the pile top
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Newtonian Collision Analogy
v1
m1
m2
v1
W1
W2
Pile is a longitudinally-distributed mass
Hammer is a concentrated mass
“Rigid body” motion assumption is not reasonable
“Rigid body” motion assumption is reasonable
Motion is dominated by stress-wave effects
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Impact on elastic rod
time = dt
dL
F
Compressed Zone
Stress, s = F/A
Wavespeed, c = dL/dt
Cross-sectional area, A
Elastic modulus, E
Mass density, r
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Particle Velocity
dL
FF
F
dx
dx = F dL
EA
Particle Speed
Wave Speed
v = dx = F dL = F c
dt EA dt
EA
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Wavespeed
a = dv = d Fc
dt dt EA
v=Fc
EA
F = ma
= dL Ar a
dL
F1 = dL
c2 =A Er F1 c
c
dt
rE A
Cross-sectional area, A
Mass density, r
SI US
GRL Force, velocity, stress and
strain
Particle Speed
Wave Speed
Pile Impedance
v = d x = F dL = Fc
dt
EA dt
EA
F=s=vE
A
c
F = EAv
c
= Zv
s=e=v
E
c
SI US
GRL
Force and Velocity
Measurements
Accelerometer
2W
W
Strain transducer
GRL Measuring stress waves
Strain transducer
Accelerometer
GRL
Strain Transducer
C
T
F = sA = e EA
C
T
C
T
C
T
C
T
T
C
Strain Transducer
Resistance strain gages connected
in Wheatstone bridge configuration
GRL
Accelerometers
Piezo-electric
Accelerometer
Piezo-resistive
Accelerometer
strain gage
mass
spring
mass
cantilever
quartz
crystal
v =  a.dt
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Sign Conventions
Force:
•Compression -
positive (+)
•Tension -
negative (-)
Velocity:
•Downward -
positive (+)
•Upward-
negative (-)
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Infinite Pile
Compressive
stress-wave
x = constant
F(x,t)
v(x,t)
MotionWavespeed,
down pile
=c+
Compression
= +ve
F = EAv
c
= Zv
Cross-sectional area, A
Elastic modulus, E
GRL Time domain - infinite pile
Exponential
Decay
F = EAv
c
GRL
Finite pile with free end
+
+F
incident force wave
reflected in opp. sense
-F
Free End : F = 0
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Direction of Motion
Downward Travelling (incident) Waves
TOP
TOE
V
C
Force
+
Velocity
+
V
T
Force
F= Zv
-
Velocity
-
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Direction of Motion
Upward Travelling (reflected) Waves
TOP
TOE
V
C
Velocity
-
V
Velocity
+
F=-Zv
Force
+
T
Force
-
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Finite pile with free end
FF+,, v+
x = constant
+
incident wave pushes pile down
reflected tension wave pulls pile down
Free End : v doubled
+
+v
+v
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Time Domain - free pile
response response
time = 2L/c
time = 2L/c
Zv
Characteristic tension
response - velocity
increases relative to force
F
SI
US
Finite pile on rigid base
+
+v
incident wave pushes pile down
reflected wave pushes pile up
-v
Fixed End : v = 0
GRANITE
GRL
Finite pile on rigid base
vv+,, F+
x = constant
+C
incident wave pushes pile down
+F
+F
+C
reflected wave pushes pile up
Fixed End : F doubled
GRANITE
GRL
GRL
Time domain - pile on rigid
base
response response
time = 2L/c
time = 2L/c
F
Characteristic compression
response - force increases
relative to velocity
Zv
SI
US
GRL
Separation of Waves
Downward Waves
Upward Waves
F=F½(F+Zv)
=Zv
FF
½(F-Zv)
=
=-Zv

F = F+ F
E=mc2
SI
US
v = v+ v
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Waves example (SI)
• At impact a 300mmx6mm wall Grade 250 steel
pipe pile achieves a peak velocity of 5.34 m/s,
10m above ground level. At time 2L/c later,
the force and velocity are measured at 1620
kN and -2.67 m/s. What are the upward and
downward waves at impact and 2L/c later?
Answer
• EA/c = 210,000x5542x10-3/5120= 227 kNs/m
• At impact Fd = 227x5.34 = 1214 kN; Fu = 0 kN
• At 2L/c Fd = ½(1620+227x-2.67) = 507 kN
• At 2L/c Fu = ½(1620-227x-2.67) = 1113 kN

GRL Waves - pile on rigid base
F,Zv
F = ½(F - FZv)
F = ½(F + Zv)
Zv
GRL
Time of reflection
x
R
Total travel distance = 2x
SI
Wavespeed = c
Reflection from resistance at x
arrives at pile-top at time 2x/c
US
GRL
Typical pile response
toe response time = 2L/c
start of toe response
timing and amount of
separation is a function
of location and extent
of soil resistance
response from shaft only
response from pile base
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Typical pile response
F=½(F+Zv)
F

exponential decay
returning compressive
reflections lift pile-top
force….
...and slow the pile-top
down relative to the
“no resistance” pile
toe response time = 2L/c
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Typical pile response
F=½(F-Zv)
F=½R
Rshaft @ 2F@ 2L/c
toe response time = 2L/c
upward travelling wave
before 2L/c is related to
the cumulative shaft
resistance
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Typical pile response
Upward wave - isolates
response from pile/soil
Q. Why may it be preferable to view data as F , F ?
Downward wave - isolates input
from driving system
SI
US
GRL
Shaft resistance (SI)
Problem: Make an approximate estimate of the
pile shaft resistance.
2340kN; 3.34 m/s
1420kN
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•
•
-1.32m/s
Answer:
Z = 2340/3.34 = 700 kNs/m
Rshaft @ 2 x Fé@ 2L/c
Rshaft @ 2x ½(1420-700x-1.32) = 2344 kN

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Conclusion
• Pile driving events can be evaluated using
1-D Wave Mechanics principles
• Stress-waves cause changes in force and
particle velocity
• Force and velocity are related by the pile
impedance
• Waves travelling both up and down a pile
can be separated by F and V measurement
• Soil resistance causes reflections which
can be interpreted to determine extent and
location of resistance
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Case-Goble Capacity
A pile is struck at time t1.
The impact force generates a wave F(down,t1)
L
F(,t1)
F(,t2)
The impact wave returns to the pile top at time
t2 = t 1+ 2L/c together with all resistance waves
GRL The Case Method Equation
At time t2 = t1 + 2L/c the upward traveling waves
arriving at the pile top include the reflection of the
initial impact wave plus the sum of all resistances:
F(,t2) = - F(,t1) + R
Or, rearranging we solve for the resistance:
R = (F2 -v2Z)/2 + (F1 +v1Z)/2
where R is the total pile resistance,
mobilized at a time L/c after t1.
GRL The Case Method Equation
R = ½(F1 + Zv1 + F2 - Zv2)
F1 and v1 are pile top force and velocity at time 1
F2 and v2 are pile top force and velocity at time 2
Time 2 is 2L/c after Time 1: t2 = t1 + 2L/c
R is the total pile resistance
present at the time of the test,
and mobilized by the hammer impact.
GRL
Case-Goble Static
Resistance
Total Resistance = Static + Dynamic
Rstatic= R - Rdynamic
Need to estimate Rdynamic
(Estimate it from pile velocity)
Jc = ?
SI US
GRL
Case Damping Factor
• To calculate static from total resistance, a
viscous damping parameter, Jv , is
introduced
Rd = Jv v
• Non-dimensionalization leads to the Case
Damping Factor, Jc:
Jc = Jv  Z  Rd = Jc Z v
Jc = ?
GRL
Case-Goble Static
Resistance
Total Resistance = Static + Dynamic
Rstatic= R - Rdynamic
Rs = (1-Jc)[F1+ Zv1]/2 + (1+Jc)[F2 - Zv2]/2
Jc = ?
SI US
Case Damping Factor
Values for RMX
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0
0.2
0.4
0.6
0.8
1.0
Gravel
0.3
0.4
Sand
0.4
0.5
Reducing
Grain Size
Increasing
Damping factor
Silt
0.5
0.7
Clay
0.7
1.0

1000 days
100 days
1 day
capacity
GRL
10 days
Restrike testing - fine
grained soils
Restrike testing generally undertaken 1 to 10 days after installation
log time
Mobilized Resistance
Ultimate Resistance
Displacement for
full mobilization
Mobilized Resistance
Maximum test
displacement
Resistance, R
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Displacement, x
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Resistance:
Rules for good correlation
•Need to Mobilize Capacity
(sufficient set per blow)
• Account for time dependent strength changes
Setup - Capacity increase
Relaxation - Capacity decrease
Therefore, restrike test pile after sufficient wait
using a sufficiently large impact weight
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Capacity Results
• GRLWEAP
• by numerical analysis of assumed
pile/hammer/soil prior to installation
• Case Method
• measured by PDA during installation
• CAPWAP
• by numerical analysis of measured
PDA data after installation
GRL
The Pile Driving Analyzer
calculates ...
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… PDA Results
• Case Method Bearing Capacity
• Pile Stresses
• Compressive at Top
• Bending at Top
• Tension Below Top
• Compressive at Bottom
• Pile Integrity (Beta)
• Transferred Energy
GRL
PDA RESULTS vs
GRLWEAP
• CAPACITY
– PDA:
from force and velocity records
– GRLWEAP: from analysis and blow count
• TOP STRESSES
– PDA:
directly measured
– GRLWEAP: from analysis and blow count
• Note:
Max. Compressive Stress does NOT
always occur at Pile Top