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KHRI- Webinar( 23-05-2020)-Analysis of Pile Foundations under Earthquake Case Studies by Prof. Subhadeep Banerjee(IITM) - Sankar V AD, KHRI.pdf
1. ANALYSIS OF PILE FOUNDATIONS UNDER EARTHQUAKE – CASE STUDIES
Geotechnical Engineering Division
Department of Civil Engineering
Indian Institute of Technology Madras
Chennai 600 036, India
SUBHADEEP BANERJEE
Associate Professor
1
2. WHAT WE HAVE TODAY…
How to model seismic clay-pile-raft interaction
physical modeling
numerical simulations
How to estimate material properties of clay subjected
to cyclic loading?
How to estimate maximum pile bending moment pile
under seismic condition?
Case studies
2
4. Earthquake considerations for pile foundations
• During earthquakes, these pile foundations may
experience additional loading.
• In cities having thick marine clay deposit , pile foundations
are extensively used to achieve the required bearing
capacity.
• In most cases, pile foundations are not designed for
earthquake resistance.
• Many failure of pile-raft foundation due to the combination
of liquefaction of the deep sandy soil strata along with the
stiffness degradation of the top 10-15m soft clay layer
during the 1985 Mexico, 1999 Chi Chi, 2001 Bhuj, 2004
Boxing day and 2015 Nepal earthquakes .
4
5. How to handle a geotechnical problem ?
Courtesy: Burland (1987)
Acquire land.
Reconnaissance of the site.
Geologic history.
Detail survey and leveling.
Schedule detail soil testing.
Field: SPT, Borehole, plate load
test etc.
Laboratory: Index property,
strength, compressibility etc.
Modeling:
physical: not always possible
analytical: difficult for complex
problem
numerical: FEM, BEM, FDM
etc.
9. • MTS make biaxial shaking table
• Table size: 3 m x 3 m
• Simulation frequency: 0-50 Hz
• Maximum payload: 10 tonnes
• Maximum longitudinal displacement:
±250 mm
• Maximum linear acceleration (max
payload): 1g
Photograph of the shaking table
Schematic diagram of the table and actuators
1g-Shaking table
9
10. A laminar box with length of 1.5 m, width of 1 m and
depth of 1.2 m was fabricated using Aluminum tube
sections of 50 mm x 50 mm
The laminar box can support a maximum lateral
deflection of ±150 mm
Lamina
r shear
box
M24 HSS
bolts
Lifting
hook
Provision
for shear
pin
Photograph of the laminar shear box
Laminar box
10
11. 11
1-g Scaled Model Tests Using Shaking Table
11
Prototype
scale
Model
scale
Laminar
shear box
Shaking
table
12. 12
Preparation of clay bed
Polystyrene
sheet
Polystyrene sheet as
absorbent material
Laminar box placed on the
shaking table
14. Input Motion
A series of 14 sinusoidal signals with frequency
varying from 0.1 Hz to 30 Hz was applied
20 cycles of each frequency was applied
Input acceleration varied from 0.04 m/s2 to 0.1
m/s2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0 10 20 30
Feedback/Command
Frequency (Hz)
• Calibration run was performed
before the actual test to get the
Feedback/command ratio at
various frequencies
• Input amplitude was modified to
get the desired amplitude
14
15. Length λ
Mass
density
1 Acceleration 1
Force λ3
Stress λ Strain 1
Stiffness λ2
Modulus λ EI λ5
Time λ1/2
Frequency λ−1/2 Shear wave
velocity
λ1/2
• It is not feasible to attain true
similarity for soil-pile interaction
by applying the dimensional
analysis or similitude theory
• A geometric scale factor of 30
was chosen for the present study
0.18
m
0.20
m
0.25
m
0.35 m
Piled Raft and Pile Group
• A 7 m x 7 m raft with four piles of
0.75m diameter and 18m length was
chosen as the prototype
• Model scale pile diameter=0.025 m
• Model scale pile length=0.6 m
Pile
group
Piled
raft
Single
pile
0.25
m
Similitude law
15
16. Parallel Plate Test to determine Flexural Rigidity
Stiffness of plastic pipes can be determined using the ASTM D-
2412 parallel plate load test
Specimen length: 150±3 mm
Loading rate : 0.5 mm/min
𝐸𝐼 = 0.149𝑟3
(𝐹
∆𝑦)
16
Model Pile Foundation
0
5
10
15
20
25
30
35
40
45
50
0 2 4 6 8 10
Force/unit
length
(N/m)
Displacement (mm)
Load deflection curve for PVC specimen
Acrylic and PVC specimens
Material E (Gpa)
cPVC 1.72
PVC 2.65
Acrylic 2.08
17. Acceleration was measured at 10
location using 5 piezoelectric and
5 inductive type accelerometers
Strain gauges (120 Ω TML make)
were attached to one pile each of
the piled raft and pile group
models
Two separate data acquisition
system, MGC plus and QuantumX
were used
17
Instrumentation
Accelerometer
Strain gauge
18. 18
Recorded Acceleration Response
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
1 10 100 1000
Fourier
amplitude
Frequency
Raw
signal
• Steady state amplitude was used to
compute transfer functions
• Bandpass filter was applied to
condition the signals
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
0 1 2 3 4 5
Acceleration
(m/s
2
)
time (s)
5Hz
Base
Clay mid
level
-6
-4
-2
0
2
4
6
0 0.5 1 1.5 2 2.5
Acceleration
(m/s
2
)
time (s)
10Hz
Base
Clay mid
level
24. Pile used for the study
900 mm and 500 mm prototype diameter
Three different pile materials:
1. Solid steel piles
2. Hollow steel piles
3. Hollow steel piles in-filled with plain
cement concrete
Essentially six types of EI of piles is
considered.
13 m prototype length
Strain gauges at different
locations along the pile length
24
26. 13.25
0.9 m diameter piles
25
12.50
7.50
5.5 14.25
PLAN
10
A1
A4
A3
Raft
Kaolin Clay
Model for pile-raft test
Accelerometers
3
2.5m
spacing
Strain gauges
A2
Sand
ELEVATION
All dimensions are prototype values and in m.
26
28. Raft
Pile
Clay
Figure 22: Half-model of the pile-clay raft domain in ABAQUS
Numerical simulation for the centrifuge tests
To reduce the computational time a 3D half-model was used
Input motion: Acceleration time history as measured in centrifuge test
20-noded brick element
The analyses were carried out incorporating the hyperbolic-hysteretic
clay behaviour via the user-defined subroutine in ABAQUS ver 6.7
28
29. Hyperbolic backbone
curve
Hyperbolic relation to
express the non-linear
stress-strain relation below
the state boundary surface
Modeling of cyclic
behaviour of soils: Masing
rules
Modeling of stiffness
degradation index of
backbone curve
Proposed model has been incorporated as a material subroutine
(UMAT) in ABAQUS
-100
-80
-60
-40
-20
0
20
40
60
80
100
-0.01 -0.005 0 0.005 0.01
Shear strain (%)
q (kPa)
Hyperbolic
Backbone
curve
Gmax
G
Hyperbolic-Hysteretic Soil model
G
q
G
G
G
G
G
f
s 2
max
max
)
)
(
3
1
(
29
Banerjee, S. and Malek, Sardar (2020). Assessment of a Hyperbolic Model for
Undrained Cyclic Shearing of Remoulded Clay. Journal of Engineering Mechanics,
ASCE, 146(7), DOI: 10.1061/(ASCE)EM.1943-7889.0001780.
30. Beam
How to measure bending moment from 3D brick elements?
Pile
(20 noded
brick)
• As the piles were modeled using solid elements, the
bending moments could not be directly obtained from the
ABAQUS output.
• This limitation may be overcome by adding a column of
very flexible beam elements along the discretized pile
axis.
• The flexural rigidity of these elements may be
prescribed a value obtained by scaling down the actual
pile stiffness by a factor of 106, so that they will freely
adopt the deformed pile shape without interfering with its
structural response.
(EI)beam = (EI)pile / 106
• In this way, the bending moments along the actual pile
may be obtained by simply multiplying the computed
beam moments by the same scaling factor of 106.
(M)pile = (M)beam x 106
30
31. To simulate laminar box movements, linear multi-point constraints were
applied to the two vertical faces normal to the earthquake motion, so that
points on opposite ends of the domain and at the same depth move in unison
with each other.
Laminar box
Simulated
in ABAQUS
Laminar rings simulated by tie nodes
Model description
31
32. (a) Computed and measured accelerations
at Top of the Raft (A4)
(b) Computed and measured accelerations
at Clay Surface (A3)
Acceleration response
Centrifuge test
Numerical simulation
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0 5 10 15 20 25
Time (sec)
Acceleration
(m/s^2)
Centrifuge test
Numerical simulation
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0 5 10 15 20 25
Time (sec)
Acceleration
(m/s^2)
Centrifuge test
Numerical simulation
32
33. 0
0.2
0.4
0.6
0 1 2 3 4
Period (sec)
Spectral
Acceleration
(a) Computed and measured accelerations
at Top of the Raft (A4)
(c) Computed and measured response
spectra at Top of the Raft (A4)
(b) Computed and measured accelerations
at Clay Surface (A3)
(d) Computed and measured response
spectra at Clay Surface (A3)
Acceleration response
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0 5 10 15 20 25
Time (sec)
Acceleration
(m/s^2)
Centrifuge test
Numerical simulation
0
0.2
0.4
0.6
0.8
0 1 2 3 4
Period (sec)
Spectral
Acceleration
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0 5 10 15 20 25
Time (sec)
Acceleration
(m/s^2)
Centrifuge test
Numerical simulation Numerical simulation
Centrifuge test
33
34. 0
2
4
6
8
10
12
14
-1000 0 1000 2000 3000 4000
Depth
below
the
bottom
of
pile-raft
(m)
Bending moment(kNm)
Bending moment response
0
2
4
6
8
10
12
14
-1000 0 1000 2000 3000 4000
Depth
below
the
bottom
of
pile-raft
(m)
Bending moment(kNm)
Centrifuge test
Numerical
Centrifuge test
Numerical
Centrifuge test
Numerical
Large earthquake
(ab=0.1g)
Medium earthquake
(ab=0.07g)
Small earthquake
(ab=0.022g)
0
2
4
6
8
10
12
14
-1000 0 1000 2000 3000 4000
Depth
below
the
bottom
of
pile-raft
(m)
Bending moment(kNm)
Computed and measured maximum bending moment envelope for three different
scaled earthquakes and different added mass (0.9m solid steel piles).
(a) Added mass = 368 tonnes (b) Added mass = 605 tonnes (c) Added mass = 863 tonnes
34
35. Half-model for single pile
Half-model for 3x4 pile group
Half-model for 3x2 pile group
Half-model for 2x1 pile group
Beyond these we have to rely on numerical simulations alone
Physical Model for Large Pile-groups
35
36. There is an “active segment”, which depends upon the flexural stiffness of the pile.
0
2
4
6
8
10
12
14
-200 0 200 400 600 800 1000
Depth
(m)
Bending moment (kNm)
0
2
4
6
8
10
12
14
-2000 -1000 0 1000 2000 3000 4000
Depth
(m)
Bending Moment (kNm)
Added mass=368 t; large eq
Added mass=605 t; large eq
Added mass=863 t; large eq
Added mass=368 t; large eq
Added mass=605 t; large eq
Added mass=863 t; large eq
Added mass=368 t; large eq
Added mass=605 t; large eq
Added mass=863 t; large eq
0
2
4
6
8
10
12
14
-200 0 200 400 600 800 1000
Depth
(m)
Bending moment (kNm)
10mm-368ton-largeEQ (hollow steel)
10mm-605ton-largeEQ (hollow steel)
10mm-863ton-largeEQ (hollow steel)
10mm-368ton-largeEQ (concinfilled)
10mm-605ton-largeEQ (concinfilled)
10mm-863ton-largeEQ (concinfilled)
Added mass=368 ton-largeEQ
Added mass=605 ton-largeEQ
Added mass=863 ton-largeEQ
0.5 m dia piles 0.9 m dia piles
Let us re-look one more time….
36
37. What is active length?
0
2
4
6
8
10
12
14
-200 0 200 400 600 800
Depth
below
the
bottom
of
pile-raft
(m)
Bending moment (kNm)
Centrifuge tests
Numerical
Centrifuge tests
Numerical
Centrifuge tests
Numerical
0.5m hollow
steel piles
EI=242369 kNm2
0.9m hollow
steel piles
EI=2544292 kNm2
0.9m solid
steel piles
EI=6763309 kNm2
0
2
4
6
8
10
12
14
-1000 0 1000 2000 3000
Depth
below
the
bottom
of
pile-raft
(m)
Bending moment (kNm)
0.5 m hollow steel piles generate significant moments only along their upper segments of about 4
to 6m below the pile head.
This observation motivates the postulate that there is an “active segment”, which depends upon
the flexural stiffness of the pile.
Below the active segment, the pile experiences a small negative moment, which is typically no
more than 10% of the maximum fixed-head moment.
37
38. Dimensional Analysis
The factors influencing the bending moment in the pile,
i. Pile-Soil Stiffness: Rk =
la is the active length.
Assuming that the clay bed deforms largely by simple shearing over the
active pile length, its lateral stiffness may be characterized by πb2Gr2/la,
in which G is the shear modulus and b is a constant such that br is the
radius of an effective area of the ground which contributes to pile
support and is assumed herein to be a constant.
ii. Mass Ratio:
m is the mass of the raft and
ρ is the density of the soil.
iii. Ground motion loading: peak base acceleration (ab/g).
iv. Active Slenderness Ratio:
G
Eep
2
4
1
b
2
a
l
r
3
r
m
r
la
38
39. Best Fit Correlations: Active length
5
10
15
20
25
30
0.01 0.03 0.05 0.07 0.09
Active
slenderness
ratio
0.021
b
0.414
3
0.133
n
2
ep
g
a
ρr
m
r
c
E
Centrifuge tests
Numerical analysis
Equation (16)
R2 = 0.75
r
la
= 1400
133
.
0
2
n
ep
r
c
E
414
.
0
3
r
m
021
.
0
g
ab
1
39
40. y = 0.003x
R² = 0.9235
0
0.00005
0.0001
0.00015
0.0002
0.00025
0.0003
0.00035
0 0.02 0.04 0.06 0.08 0.1 0.12
Centrifugetests
Numerical
p
EI
r
M max
54
.
0
2
n
r
c
ep
E 91
.
0
g
b
a
4
.
0
3
r
m
031
.
1
r
p
l
Equation(17)
R2 = 0.927
analysis
Best Fit Correlations: Bending moment in stiff piles
lp ~< la
p
EI
r
M max
= 0.0007
54
.
0
2
n
ep
r
c
E
91
.
0
g
ab
4
.
0
3
r
m
031
.
1
r
lp
Active length can not be estimated;
l = length of pile (lp)
40
41. y = 3E-05x
R² = 0.84
0
0.0001
0.0002
0.0003
0.0004
0.0005
0.0006
0.0007
0 5 10 15 20
Centrifugetest
Numerical
p
EI
r
M max
70
.
0
2
n
ep
r
c
E
65
.
0
g
ab
85
.
0
3
r
m
005
.
1
r
la
Equation(18)
R2 = 0.84
analysis
Best Fit Correlations: Bending moment in flexible piles
lp > la
Active length can be estimated;
l = active length of pile (la)
p
EI
r
M max
= 3x10-5
7
.
0
2
n
ep
r
c
E
65
.
0
g
ab
85
.
0
3
r
m
005
.
1
r
la
41
42. 0
500
1000
1500
2000
2500
3000
3500
0 500 1000 1500 2000 2500 3000 3500
Predicted
bending
moment
Actual bending moment
Bending moment response:
Proposed relationship vs. Model tests
42
43. 0
5
10
15
0 5 10 15
Bending
moment
reported
in
past
studies
(MNm)
Bending moment computed from proposed relationship (MNm)
Meckering earthquake (1968)
Whittier earthquake (1987)
Newcastle earthquake (1994)
Bending moment response:
Proposed relationship vs. Poulos and Tabesh (1996)
43
44. 0
500
1000
1500
2000
2500
3000
0 500 1000 1500 2000 2500 3000
Predicted
bending
moment
(Nikalaou
et
al.,
2001)
Predicted bending moment (Proposed correlation)
Bending moment response:
Proposed relationship vs. Nikolaou et al. (2001)
44
46. Three-dimensional (3-D) numerical model of the field
pile lateral load test (Urano et al., 2011)
The analysis was carried out using ABAQUS ver 6.10
Soil Layer
Hypoelastic Soil Model
RCC or Steel pile groups and Raft
Linearly elastic materials
CASE STUDY 1:
Simulation of piles under lateral load
47. Details of Field Test
9500
3200
2000
2000
600
1.9 m thick Fill
1.5 m thick Loam
1.4 m thick Clay
2.1 m thick Clayey sand
0.9 m thick Sandy clay
0.55 m thick Clay
2.15 m thick Medium sand
Cement
injected layer
400 mm
dia Piles
Raft
2000
2000
3800
3800
Pile group configuration
Lateral load
48. Numerical Modeling
Structured mesh generated
20-noded quadratic brick elements (C3D20R)
- Reduced integration-type elements
3-noded quadratic space beam elements (B32)
Used symmetry
Assigned proper boundary conditions
49. 3D Soil-Pile-Raft Model in ABAQUS
Depth
(m)
Soil
Profile
Eo
(kN/m2)
1.9 Fill 69160
1.5 loam 66500
1.4 Clay 39900
2.1 Clayeysand 31920
0.9 Sandyclay 154280
0.55 Clay 154280
2.15 Medium sand 252700
Raft E (kN/m2)
= 2.5x107
Pile E (kN/m2)
= 3.9x107
53. -10
-8
-6
-4
-2
0
-200 -100 0 100 200
Depth
(m)
Bending moment (kNm)
Field
Analysis By Urano et
al.
Analysis By ABAQUS
Results and Discussion
Bending moment along the pile length
54. Pile–Raft–Reinforcement Body
Depth
(m)
Soil
Profile
Eo
(kN/m2)
1.9 Fill 69160
1.4 loam 66500
1.5 Clay 39900
2.1
Clayey fine
sand
31920
0.9 Sady clay 154280
0.55 Clay 154280
2.15
Medium
sand
252700
Pile, Raft and
Reinforcement Body
Modulus of Elasticity (E0) of Reinforcement Body 1.5x106 kN/m2
55. -10
-8
-6
-4
-2
0
-200 -100 0 100 200
Depth
(m)
Bending moment (kN-m)
With Reinforcement Body
Field
Analysis By Urano et al.
RB
Analysis By
ABAQUS
56. Mayoral et al (2009) reported recorded data from a bridge support
system in Mexico City, after the 2004 Guerrero Coast earthquake
(Mw=6.3; PGA=0.03g).
405m long Impulsora Bridge is located in the North Eastern part of
Mexico City.
Instrumented ‘Support 6’ is one among eight supports and
corresponds to the central portion of the bridge.
Box foundation and 77 RCC square friction piles of cross section
0.5x0.5m2 that extends to 30m depth-A Piled Raft foundation.
Load Sharing Piles : 85% & Raft : 15% (Mendoza & Romo,1998).
56
CASE STUDY 2:
Seismic Response of an Instrumented Bridge Support
57. 57
Transverse (a) and longitudinal view (b) of Support 6
(Mayoral et al., 2009; Mendoza & Romo, 1998)
(b)
(a)
Seismic Response of an Instrumented Bridge Support
58. 58
A satellite image of the Impulsora bridge
Source : Map data- Google, INEGI (http://maps.google.com), viewed 4 May 2018
Seismic Response of an Instrumented Bridge Support
59. 59
Soil profile at the site
Seismic Response of an Instrumented Bridge Support
Soft clay
60. 60
Actual FE mesh for single pile
Connection of degrees of freedom
Modelling of Pile
61. 61
(a) FE model of piled raft and superstructure with piles modelled using brick elements,
(b) FE model of piled raft and superstructure with piles modelled using beam elements
(b)
(a)
Seismic Response of an Instrumented Bridge Support
62. 0.000
0.005
0.010
0.015
0.020
0.025
0.030
0.035
0 2 4 6 8 10 12
Sa(g)
Period (s)
Measured-bridge deck
Present study-bridge deck
62
0.000
0.005
0.010
0.015
0.020
0.025
0.030
0.035
0 2 4 6 8 10
Sa
(g)
Period (s)
Actual 60m
Computed RS
surface
Measured surface
Seismic Response of an Instrumented Bridge Support
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0 5 10 15
Sa(g)
Period (s)
Measured-foundation level
Present study- foundation
level
At ground level At raft
At bridge deck
63. The compressor, gear, motor, and
piping systems are placed on a
baseplate of size 8.7 m x 3.8 m
The operating speed of the
compressor is around 10000 rpm
while the motor operates at 1500rpm
The total equipment weight on the
foundation is 51.1 tonnes
The vertical load capacity for 500mm
diameter & 18 m long piles were
estimated to be 700 kN, and a 2x2
pile group was proposed for the
foundation
Dynamic lateral load tests were
conducted on single piles at the site
to estimate the stiffness, following IS
9716-1981 63
CASE STUDY 3:
Pile Supported Compressor Unit
64. To facilitate fixing of the
oscillator, a pile cap of
dimensions 0.75 m x 0.75 m x
0.75 m was cast on top of the
pile, without contact with
ground
64
0 250 500 750
Vs (m/s)
0
2
4
6
8
10
12
14
16
18
20
0 25 50 75
Depth
(m)
SPT N
0.5m
Depth
(m)
Description Unit
Weight
(kN/m3)
Liquid
limit
(%)
Plasticity
index
(%)
Water
content
(%)
Shear
Modulus
Gmax
(MPa)
Averag
e SPT N
Modulus
reduction
curve and
damping
curve
assigned*
0.0-2.5 Dark brown
silt
16.7 72 36 30 25.0 5 Vucetic and
Dobry (1991);
PI = 30
2.5-5.0 Black silty
clay
17.0 53 27 27 46.8 7 Vucetic and
Dobry (1991);
PI = 30
5.0-9.5 Black silts
with seams
of fine sand
17.5 - - 43 106.0 8 Seed and
Idriss (1970);
average
9.5-11.5 Black silty
clay with
seams of
fine sand
17.5 38 22 38 140.0 10 Vucetic and
Dobry (1991);
PI = 20
11.5-
14.0
Silty sand 18.0 - - 27 206.1 30 Seed and
Idriss (1970);
average
14.0-
16.0
Blackish
silty sand
18.0 - - 20 433.3 44
Idriss (1990),
upper range
16.0-
18.0
Clay with
sand
19.0 47 27 21 651.0 56
18.0-
20.0
Brownish
silty sand
19.8 - - - 741.2 60
Lateral dynamic load test on pile
66. A 3D finite element model is developed to simulate
the free and forced vibration response of the single
pile in layered soil.
The free vibration response of the pile was simulated
by applying an impulse at the center of the vertical
face of the pile cap.
Pile was modeled using the central beam and rigid
link technique
Pile material behavior was assumed to be linear
elastic with a Young’s modulus value of 29 GPa,
poisons ratio of 0.2 and a unit weight of 25 kN/m3
An iterative equivalent linear analysis procedure is
followed whereby the analysis is repeated after each
step with updated shear modulus and damping in soil
elements
Modulus degradation and damping curves were
employed to arrive at strain dependent shear
modulus and damping ratio 66
Numerical Simulation
Central beam
Rigid beams
Pile cap
Near field soil
elements
67. 67
-0.00004
-0.00002
0
0.00002
0.00004
0.00006
0 0.1 0.2 0.3 0.4 0.5
Displacement
(m)
Time (s)
Experime
nt
Simulati
on
Error
(%)
Natural
frequency (Hz)
20.00 18.18 9.10
Damping ratio
(average)
0.127 0.120 5.5
• An impulse of 15Ns was found to
produce a maximum displacement
comparable to the displacement
observed during the field test
• A reasonable estimate of the natural
frequency of the pile soil system is
obtained
Damped natural frequency of the pile-soil system
Recorded free vibration response
Simulated free vibration response
Simulation of Free Vibration Test
68. The response of the
pile soil system was
evidently nonlinear
with resonant
frequency decreasing
with increasing
amplitude of exciting
force.
The simulation was
found to capture this
variation in resonant
frequencies.
68
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
5 10 15 20 25 30 35
Displacement
(mm)
Frequency (Hz)
e=32.8
e=49.2
e=65.5
e=82
Simulation e=32.8
Simulation e=49.2
Simulation e=65.6
Simulation e=82
Simulation of Forced Vibration Test
69. Varghese, Ramon, A. Boominathan, and Subhadeep Banerjee (accepted). Stiffness and Load Sharing
Characteristics of Piled Raft foundations Subjected to Dynamic Loads. Soil dynamics and Earthquake
Engineering, Elsevier.
Banerjee, S. and Malek, Sardar (2020). Assessment of a hyperbolic model for undrained cyclic shearing of
remoulded clay. Journal of Engineering Mechanics, ASCE, 146(7), DOI: 10.1061/(ASCE)EM.1943-
7889.0001780.
Varghese, Ramon, A. Boominathan, and Subhadeep Banerjee (2019). Seismic Response characteristics of
a piled raft foundation. Journal of Earthquake and Tsunami, World Scientific,
doi.org/10.1142/S1793431119500052.
Banerjee, S., Goh, S. H. & Lee, F. H. (2014). Earthquake-induced Bending Moment in Fixed Head Piles in
Soft Clay. Geotechnique, ICE, Vol. 64, No. 6, 431–446.
Banerjee, S., Minu Joy & Sarkar, D. (2016). Parametric study and centrifuge-test verification for amplification
and bending moment of clay-pile system subject to earthquakes. Geotechnical and Geological Engineering,
Springer , Vol. 34, No. 6, 1899-1908.
Ma Kang, S Banerjee, FH Lee, HP Xie (2012). Dynamic soil-pile-raft interaction in normally consolidated soft
clay during earthquakes. Journal of Earthquake and Tsunami, World Scientific, Vol.6, No.03, 1250031.
Subhadeep Banerjee & Omprakash N. Shirole (2013). Numerical Analysis of Piles under Cyclic Lateral
Load. Indian Geotechnical Journal, Springer, Vol. 44, No. 6, 436-448.
S Banerjee, SH Goh, FH Lee (2007). Response of soft clay strata and clay-pile-raft systems to seismic
shaking. Journal of Earthquake and Tsunami, World Scientific, Vol.1, No. 03, 233-255.
Varghese, Ramon, A. Boominathan, and Subhadeep Banerjee (2017). Substructure based Numerical
Simulation of Seismic Response of a Piled Raft System. Proceedings of 3rd International Conference on
Performance Based Design in Earthquake Geotechnical Engineering (PBD-III), Vancouver, Paper no. 195.
For further details please refer…
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