Transcript A Liquefaction Analysis of Structure- Group Pile

Liquefaction Analysis For a Single Piled
Foundation
By
Dr. Lu Chihwei
Moh and Associates, Inc.
Date: 11/3/2003
U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003
Back ground
Pile
During earthquake
Structural damage
Upper structure
Pile foundation
Large bending moments
Inertia moment
Kinematic moment
Liquefaction
Lu Chihwei
U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003
Lu Chihwei
U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003
Lu Chihwei
U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003
Lu Chihwei
U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003
Guidelines for Foundation Design in Japan
(2001)
• Before Liquefactionー Upper Structure
• After Liquefactionー Upper Structure and
Ground Deformation
• Flow Failureー Ground Deformation due to
Lateral Flow
Lu Chihwei
U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003
Illustration of the interaction between soils and a pile foundation
Earthquake
Before Liquefaction
Occurrence of liquefaction
Damage on upper structure
Displacement
Lateral flow of ground
Large displacement
Waves de-amplified
Liquefied layer
Damage to
piles
Progressive
damage
Unliquefied layer
Lu Chihwei
U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003
Key points
•Nonlinear behavior of soils (A cyclic elasto-plastic model for sand and a
cyclic elasto-viscoplastic model for clay)
•Nonlinear behavior of piles (Axial Force Dependent Model)
•3-Dimensional liquefaction analysis
•A series of calculations on a single-pile foundation installed in a 2-layer ground (sand
layer+clay layer)
Lu Chihwei
U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003
Mu
Mc
My
-Φ ｙ
-Φ ｃ
Φｃ
Φｙ
Φu
-Mc
-My
M-F relation (Conventional way)
Axial force on M-F relation has to be neglected.
Lu Chihwei
U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003
Axial force (kN)
The pile used in the simulation
Elastic Ceacking stage
-4500
-1162
-1753.3
Yeilding stage
9000
Moment (KN*m)
k
Young’s Modulus of concrete Ec (kN/m2)
2.5E7
Poisson’s Ratio of concrete c
0.25
Diameter of pile D (m)
1.5
2
Compressive strength of concrete fc (kN/m ) 36000.00
Tensile strength of concrete ft (kN/m2)
3000.00
Parameter of concrete 
0.50
Parameter of concrete 
4.00
Parameter of concrete 
4.00
Parameter of concrete  c
0.50
Degrading parameter of concrete  c
0.20690
2
Young’s Modulus of steel E (kN/m )
2.1E8
Poisson’s Ratio of steel  s
0.20
Diameter of reinforcement d (m)
0.029
Number of reinforcement N
24
Overburden of concrete dc (m)
0.150
2
Yielding strength of steel Ys (kN/m )
3.8E5
Degrading parameter of steel  s
0.80
3
Density of steel s (t/m )
7.80
3
Density of concrete c (t/m )
2.50
0
-1500
-3000
7200
5400
3600
1800
0
0
0.003 0.006 0.009 0.012 0.015
Curvature (1/m)
M-F relation of the pile
Buckling Pc 
 2 EI
2
L
n 2 =68131 kN
Dead load of the pile head in single pile foundation is
1250KN and in the group pile foundation is 1753 KN
Lu Chihwei
U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003
Two-Layer ground
Sand layer
Clay layer
Sand layer
Clay layer
A cyclic elasto-plastic model (Oka, 1999)
based on a nonlinear kinematic hardening rule
Dense, Loose & Medium dense sand, Reclaimed soil
A cyclic elasto-viscoplastic model (Oka, 1992)
based on a nonlinear kinematic hardening rule
Lu Chihwei
U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003
Constitutive law of sands based on finite deformation theory
Cyclic Elasto-plastic constitutive model by Oka et al.(1992, 1999)
Ⅰ Non-linear kinematic hardening rule
Ⅱ Non-associated flow rule
Ⅲ Overconsolidation boundary surface
Ⅳ Generalized flow rule
Ⅴ Consideration of strain dependency of shear stiffness
Lu Chihwei
U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003
The soils used in the simulation
Dense Sand
Medium Dense Sand
Loose Sand
Reclaimed Soil
Soft Clay
Density  (t/m3)
2.0
2.0
2.0
2.0
1.7
Void Ratio e0
0.6
1.5x10
Coefficient of permeability k (m/s)
Compression Index 
Swelling index 
Stress Ratio of Failure State M
*
f
Stress Ratio at Maximum Compression
Normalized Shear Modulus G0 /
*
M*m
’
m0
0.8
-5
3.0 x 10
0.8
-5
3.0 x 10
0.420
-5
2.0 x 10
1.4
-4
1.0x10-9
0.020
0.03
0.03
0.01
0.100
0.002
0.002
0.003
0.001
0.020
1.10
1.00
0.80
1.19
1.31
0.85
0.80
0.70
0.91
1.28
1980.0
1060.0
500.0
2140.0
300.0
8500, 85, 0
4000, 400, 0
2500, 25, 0
5500, 55, 0
500, 50, 0
*
Hardening Parameter B0 , B1 , Cf for sand
B0*, Bs*, Bt* for clay
Shear Wave Velocity Vs (m/s)
(
180
KN/m2)
’
0=102
(
134
KN/m2)
’
0=102
(
92
KN/m2)
’
0=102
(
190
KN/m2)
’
0=102
(
127
KN/m2)
’
0=138
Sand
2000
2000
2000
2000
-
1.0, 2.5
1.0, 2.0
1.0, 1.0
1.0, 4.0
-
r
0.008
0.003
0.001
0.002
-
E
r
0.09
0.035
0.005
0.01
-
Viscoplastic Parameter C01 (1/s)
-
-
-
-
5.5x10-6
Viscoplastic Parameter C02 (1/s)
-
-
-
-
7.8x10-7
Viscoplastic Parameter m0’
-
-
-
-
14
Control parameter of anisotropy Cd
Parameter of Dilatancy D0, n
Reference Value of Plastic Strain 
P
Reference Value of Elastic Strain
Clay
Lu Chihwei
U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003
Liquefaction strength curves of different sandy soils
Dense sand
Loose sand
Medium sand
Reclaimed soil
Stress ratio (/'mo)
0.4
0.3
0.2
0.11
10
Number of cycles
100
Dr=50% Toyoura Sand:
N=20, Stress Ratio=0.13
(Oka 2001)
Lu Chihwei
U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003
The Governing Equation
Based on Biot’s soil-water coupling theory
u-p formulation
Momentum equation
Constitutive equation
Definition of effective stress


Continuity equation
d ij' D
 ij

 ij'
: Nominal stress tensor
: Density of total phase
: Body force vector
: Acceleration vector
: Unit weight of water
: Density of fluid phase
: Pore water pressure
: Coefficient of permeability
Lu Chihwei
U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003
Discretization of Governing Equations
Space discretization
FEM
Time discretization
Newmark’s β method
u-p formulation
Lu Chihwei
U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003
Lu Chihwei
8
2
Acceleration (m/sec )
U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003
Input wave
4
Shaking direction
0
-4
-8
11m
80 ton
0
2
z
x
4
6
Time (sec)
8
10
8m
10 m
Sand Layer
y
o
10 m
Clay Layer
20m
Segment 15
78m
Segment 7
Lu Chihwei
U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003
σ'
Effective Stress Decreasing Ratio ESDR ≡1 - ( m σ ' )
m0
Excess Pore Water Pressure Ratio EPWPR u  '
v
Sand
Clay
Dense sand
Reclaimed soil
1
1
1
1
1
1
1
1
A
Loose sand
Medium sand
A
A
1
1
1
1
1
1
1
1
1
1
1
E.S.D.R (1-'mv/'mv0)
1
0.5
0
-0.5
-1
0
2
4
6
Time (sec)
8
(a) At the center of sand soil
Effective Stress Decreasing Ratio
10
Excess Pore Water Pressure Ratio (u/ 'vm)
Liquefaction takes place completely
Loose sand
Medium sand
Dense sand
Reclaimed soil
0.4
0.3
0.2
0.1
0
-0.1
0
2
4
6
Time (sec)
8
10
(b) At the center of clay layer
Excess Pore Water Pressure Ratio
Lu Chihwei
U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003
Top of pier
Surface
Sand
Clay
Dense sand
Medium sand
Dense sand
Medium sand
Loose sand
Reclaimed soils
15
2
Accleration (m/sec )
2
Accleration (m/sec )
15
10
5
0
-5
-10
-15
Loose sand
Reclaimed soils
0
6
4
Time (sec)
2
(a)
Top of the pier
8
10
10
Medium sand and reclaimed soil
5
0
-5
-10
-15
Loose sand
0
2
4
6
Time (sec)
(b)
8
10
Ground surface
Acceleration responses
Lu Chihwei
U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003
Top of pier
Surface
Sand
Clay
Dense sand
Medium sand
Loose sand
Reclaimed soils
Dense sand
Medium sand
0.8
Displacement (m)
Displacement (m)
0.8
0.4
0
-0.4
-0.8
Loose sand
Reclaimed soils
0
2
4
6
Time (sec)
(a)
8
Top of the pier
10
Medium sand and reclaimed soil
0.4
0
-0.4
Loose sand
-0.8
0
2
4
6
Time (sec)
(b)
8
10
Ground surface
Displacement responses
Lu Chihwei
U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003
Pile head
b7
Sand
Clay
9000
4500
0
-4500
-9000
Dense sand
Medium sand
Loose sand
Reclaimed soils
Bending moment (KN*m)
Bending moment (KN*m)
Dense sand
Medium sand
0
2
4
6
Time (sec)
8
10
9000
Loose sand
Reclaimed soils
Medium sand and reclaimed soil
4500
0
Loose sand
-4500
-9000
0
2
4
6
Time (sec)
8
10
(b) Lower segment (b7)
(a) At pile heads
Bending moments
Lu Chihwei
U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003
Distributions of sectional forces at the time when the maximum bending
moment occurred at the bottom of pier
Dense
Medium
Loose
Reclaimed
Dense
Medium
0
5
Sand Layer
10
15
Clay Layer
20
4
-5000
0
5000
1 10
Bendingmoment
Moment(kN*m)
(KN-m)
Bending
Depth (m)
Depth (m)
0
Loose
Reclaimed
5
Sand Layer
10
15
Clay Layer
20
-1200 -600
0
600 1200
Shear
ShearForce
force(KN)
(kN)
Lu Chihwei
U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003
Distributions of sectional forces of the end of seismic event (t=10 sec)
Dense
Medium
Dense
Medium
Loose
Reclaimed
5
0
Sand Layer
10
Depth (m)
Depth (m)
0
Loose
Reclaimed
Sand Layer
5
10
Clay Layer
15
15
20
-4500 -2250
0
2250 4500
Bending moment
Moment (kN*m)
(KN. m)
Bending
20
-600 -300
0
300 600
Bending
Moment
(KN-m)
Shear
force (kN)
Clay Layer
Lu Chihwei
U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003
a: At the time when maximum bending moment occurs at the bottom of the pier
b:At the largest displacement occurred at the ground surface
c:At the largest moment occurred at the low segment
d: At the end of simulation
Medium dense sand
Loose sand
a:
b:
c:
d:
0
0
Depth (m)
Depth (m)
5
10
Clay Layer
t=3.34 sec ESDR= -0.22
t=6.94 sec ESDR=0.90
t=7.71 sec ESDR=0.92
t=10 sec ESDR=0.97
0
Sand Layer
Sand Layer
15
a:
b:
c:
d:
t=3.16 sec ESDR= 0.25
t=4.14 sec ESDR=0.72
t=5.21 sec ESDR=1.00
t=10 sec ESDR=1.00
t=3.34 sec ESDR= -0.22
t=6.94 sec ESDR=0.90
t=7.71 sec ESDR=0.92
t=10 sec ESDR=0.97
Sand Layer
Sand Layer
5
10
15
5
10
15
Clay Layer
20
20
0
350
3000 6000 -700 -350
-6000 -3000 0
Shear force
Force(kN)
(KN)
(KN*m)
Moment(kN*m)
Bendingmoment
Bending
Shear
a:
b:
c:
d:
0
700
Depth (m)
t=3.16 secESDR= 0.25
t=4.14 sec ESDR=0.72
t=5.21 sec ESDR=1.00
t=10 sec ESDR=1.00
Depth (m)
a:
b:
c:
d:
Clay Layer
5
10
15
Clay Layer
20
20
-6000 -3000 0
3000 6000 -700 -350
350
0
Bending Moment
Bending
moment (KN*m)
(kN*m)
(KN)
Shear Force
Shear
force (kN)
700
Distributions of sectional forces
Lu Chihwei
U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003
a: At the time when maximum bending moment occurs at the bottom of the pier
b:At the largest displacement occurred at the ground surface
c:At the largest moment occurred at the low segment
d:At the end of simulation
e:At the time maximum acceleration occurred at the ground surface
Reclaimed soils case
t=3.25 secESDR= -0.28
t=6.90 secESDR=0.88
t=7.71 secESDR=0.90
t=10 sec ESDR=0.96
t=3.25 sec
t=6.90 sec
t=7.71 sec
t=10 sec
e:
a:
d:
ESDR=0.90
ESDR=0.96
Clay Layer
t=3.25 sec
t=6.55 sec
t=10 sec
0
Sand Layer
5
Depth (m)
10
e:
a:
d:
t=3.25 sec
t=6.31 sec
t=10 sec
0
Sand Layer
5
15
ESDR= -0.28
ESDR=0.88
0
Depth (m)
Depth (m)
0
a:
b:
c:
d:
10
15
5
Sand Layer
10
15
Clay Layer
Depth (m)
a:
b:
c:
d:
Dense sand case
5
Sand Layer
10
15
Clay Layer
Clay Layer
20
20
-6000 -3000 0
3000 6000 -700 -350
0
350
Bendingmoment
Moment(kN*m)
(KN*m)
Bending
Shear
Shear Force
force (KN)
(kN)
700
20
20
4
4
5000 1 10 1.5 10 -1500 -1000 -500
-5000 0
0
(KN*m)
Moment
Bending
(KN)
Force
Shear
Bending moment (kN*m)
Shear force (kN)
500
Distributions of sectional forces
Lu Chihwei
U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003
Conclusions
Reason
After
Liquefaction
Bending
moments on
Pile head
The inertia force from
upper structure
Decreases
Bending
moments on
Segment at
interface
Kinematic bending
moment due to ground
deformation and inertia
bending moment
Increases
Time (sec)
After the peak of
seismic waves,
before the
completion of
liquefaction
Lu Chihwei
U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003
In engineering practice:
1. How to feed back soil springs for structural design?
2. The ground line for design of superstructure shall be lowered
when ground liquefies.
3. The damping of waves on the ground surface due to liquefaction
4. Sectional force at the interface --- Relative stiffness between 2
layers--- How to apply them?
5. The damage due to lateral spread
Lu Chihwei
U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003
Thank you very much for your attention
Dr. Lu Chihwei
Moh and Associates, Inc.