liquefaction analysis for a single piled foundation by dr. lu chihwei moh and associates, inc. date:...

Liquefaction Analysis For a Single Piled Foundation

By

Dr. Lu ChihweiMoh and Associates, Inc.

Date: 11/3/2003

Back ground

During earthquake

Structural damage

Pile foundationUpper structure

Large bending moments

Inertia moment Kinematic moment

Liquefaction

Pile

U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003

Lu Chihwei


Lu Chihwei

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

Damage to piles

Damage on upper structure

Earthquake

Progressive damage

Waves de-amplified

Occurrence of liquefaction

Displacement

Liquefied layer

Unliquefied layer

Lateral flow of ground

Large displacementBefore Liquefaction

Illustration of the interaction between soils and a pile foundation


Lu Chihwei

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 (san

d layer+clay layer)


Lu Chihwei

-My

-Mc

Φｃ Φｙ Φ u

Mc

My

Mu

-Φｃ-Φｙ

-My

-Mc

Φｃ Φｙ Φ u

Mc

My

Mu

-Φｃ-Φｙ

M- relation (Conventional way)

Axial force on M- relation has to be neglected.


Lu Chihwei

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 Compressive strength of concrete fc (kN/m2) 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 Young’s Modulus of steel E (kN/m2) 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 Yielding strength of steel Ys (kN/m2) 3.8E5 Degrading parameter of steel s 0.80 Density of steel s (t/m

3) 7.80 Density of concrete c (t/m

3) 2.50

Axial force (kN)The pile used in the simulation

M- relation of the pile

Dead load of the pile head in single pile foundation is 1250KN and in the group pile foundation is 1753 KN

0

1800

3600

5400

7200

9000

0 0.003 0.006 0.009 0.012 0.015

0-1500-3000

-4500-1162-1753.3

Mom

ent (

KN

*m)

Curvature (1/m)

Ceacking stage Yeilding stageElastic

22

2

nL

EIPc

=68131 kNBuckling

k


Lu Chihwei

Sand layer

Clay layer

Dense, Loose & Medium dense sand, Reclaimed soil

Two-Layer ground

A cyclic elasto-plastic model (Oka, 1999)based on a nonlinear kinematic hardening rule

A cyclic elasto-viscoplastic model (Oka, 1992) based on a nonlinear kinematic hardening rule

Clay layer

Sand layer


Lu Chihwei

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

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 0.8 0.8 0.420 1.4

Coefficient of permeability k (m/s) 1.5x10-5 3.0 x 10-5 3.0 x 10-5 2.0 x 10-4 1.0x10-9

Compression Index 0.020 0.03 0.03 0.01 0.100

Swelling index 0.002 0.002 0.003 0.001 0.020

Stress Ratio of Failure State M*f 1.10 1.00 0.80 1.19 1.31

Stress Ratio at Maximum Compression M*m 0.85 0.80 0.70 0.91 1.28

Normalized Shear Modulus G0 /’m0 1980.0 1060.0 500.0 2140.0 300.0

Hardening Parameter B0*, B1

*, Cf for sand

B0*, Bs

*, Bt* for clay

8500, 85, 0 4000, 400, 0 2500, 25, 0 5500, 55, 0 500, 50, 0

Shear Wave Velocity Vs (m/s) 180

(’0=102 KN/m2)

134

(’0=102 KN/m2)

92

(’0=102 KN/m2)

190

(’0=102 KN/m2)

127

(’0=138 KN/m2)

Sand

Control parameter of anisotropy Cd 2000 2000 2000 2000 -

Parameter of Dilatancy D0, n 1.0, 2.5 1.0, 2.0 1.0, 1.0 1.0, 4.0 -

Reference Value of Plastic Strain Pr 0.008 0.003 0.001 0.002 -

Reference Value of Elastic StrainEr 0.09 0.035 0.005 0.01 -

Clay

Viscoplastic Parameter C01 (1/s) - - - - 5.5x10-6

Viscoplastic Parameter C02 (1/s) - - - - 7.8x10-7

Viscoplastic Parameter m0’ - - - - 14


Lu Chihwei

1 10 1000.1

0.2

0.3

0.4

Dense sandLoose sand

Medium sandReclaimed soil

Number of cycles

Str

ess

rati

o (

/' m

o)

Liquefaction strength curves of different sandy soils

Dr=50% Toyoura Sand: N=20, Stress Ratio=0.13(Oka 2001)


Lu Chihwei

The Governing Equation

Based on Biot’s soil-water coupling theory

u-p formulation

Momentum equation

Continuity equation

Constitutive equation

Definition of effective stress

: Density of total phase : Nominal stress tensor

: Acceleration vector : Body force vector

: Density of fluid phase : Unit weight of water

: Coefficient of permeability : Pore water pressure

'ijij

'ijd D


Lu Chihwei

Discretization of Governing Equations

Space discretization

Time discretization

u-p formulation

FEM

Newmark’s β method


Lu Chihwei


Lu Chihwei

Shaking direction

x y

z

o

-8

-4

0

4

8

0 2 4 6 8 10

Acc

eler

atio

n (m

/sec

2 )

Time (sec)

Input wave


Lu Chihwei

-1

-0.5

0

0.5

1

0 2 4 6 8 10

Loose sandMedium sand

Dense sandReclaimed soil

E.S.D

.R (1-'

v/'

v0)

Time (sec)

-0.1

0

0.1

0.2

0.3

0.4

0 2 4 6 8 10

Loose sandMedium sand

Dense sandReclaimed soil

Excess Pore Water Pressure Ratio (u/'

m)

Time (sec)

11111111

A

m

11111111

A

m

11111111

A

v

Effective Stress Decreasing Ratio

(a) At the center of sand soil (b) At the center of clay layer

Liquefaction takes place completely

Sand

Clay

)''

(-1≡m0

mσ

σESDR

Excess Pore Water Pressure Ratio

Effective Stress Decreasing Ratio

Excess Pore Water Pressure Ratiov'

uEPWPR


Lu Chihwei

Acceleration responses

-15

-10

-5

0

5

10

15

0 2 4 6 8 10

Dense sandMedium sand

Loose sandReclaimed soils

Acc

lera

tion

(m/s

ec2 )

Time (sec)

-15

-10

-5

0

5

10

15

0 2 4 6 8 10



Acc

lera

tion

(m/s

ec2 )

Time (sec)(a) Top of the pier (b) Ground surface

Loose sand

Medium sand and reclaimed soil

Sand

Clay

Top of pierSurface


Lu Chihwei

Displacement responses

-0.8

-0.4

0

0.4

0.8

0 2 4 6 8 10



Dis

plac

emen

t (m

)

Time (sec)

-0.8

-0.4

0

0.4

0.8

0 2 4 6 8 10



Dis

plac

emen

t (m

)

Time (sec)(a) Top of the pier (b) Ground surface

Loose sand


Sand

Clay

Top of pierSurface


Lu Chihwei

-9000

-4500

0

4500

9000

0 2 4 6 8 10



Ben

ding

mom

ent (

KN

*m)

Time (sec)

-9000

-4500

0

4500

9000

0 2 4 6 8 10



Ben

ding

mom

ent (

KN

*m)

Time (sec)

(a) At pile heads (b) Lower segment (b7)

Bending moments

Loose sand


Sand

Clay

Pile head

b7


Lu Chihwei

-5000 0 5000 1 10420

15

10

5

0

Dense

Medium

Loose

Reclaimed

Bending Moment (KN-m)

Dep

th (

m)

Clay Layer

Sand Layer

Distributions of sectional forces at the time when the maximum bending moment occurred at the bottom of pier

-1200 -600 0 600 120020

15

10

5

0

Dense

Medium

Loose

Reclaimed

Shear Force (KN)

Dep

th (

m)

Clay Layer

Sand Layer

Bending moment (kN*m) Shear force (kN)


Lu Chihwei

Distributions of sectional forces of the end of seismic event (t=10 sec)

-4500 -2250 0 2250 450020

15

10

5

0

DenseMedium

LooseReclaimed

Bending Moment (KN m)

Dep

th (

m)

Clay Layer

Sand Layer

.-600 -300 0 300 600

20

15

10

5

0

Dense

Medium

Loose

Reclaimed

Bending Moment (KN-m)

Dep

th (

m)

Clay Layer

Sand Layer

Shear force (kN)Bending moment (kN*m)


Lu Chihwei

-700 -350 0 350 70020

15

10

5

0

t=3.16 sect=4.14 sect=5.21 sect=10 sec

Shear Force (KN)

Dep

th (

m)

Clay Layer

Sand Layer

a:b:c:d:

ESDR= 0.25

ESDR=0.72

ESDR=1.00

ESDR=1.00

-6000 -3000 0 3000 600020

15

10

5

0


Bending Moment (KN*m)

Dep

th (

m)

Clay Layer

Sand Layer

a:b:c:d:

ESDR= 0.25

ESDR=0.72

ESDR=1.00

ESDR=1.00

-6000 -3000 0 3000 600020

15

10

5

0



Dep

th (

m)

Clay Layer

Sand Layer

a:b:c:d:

ESDR= -0.22

ESDR=0.90

ESDR=0.92

ESDR=0.97

-700 -350 0 350 70020

15

10

5

0


Shear Force (KN)

Dep

th (

m)

Clay Layer

Sand Layer

a:b:c:d:

ESDR= -0.22

ESDR=0.90

ESDR=0.92

ESDR=0.97

Loose sand Medium dense sand

Distributions of sectional forces

a: At the time when maximum bending moment occurs at the bottom of the pierb: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

Bending moment (kN*m) Bending moment (kN*m)Shear force (kN) Shear force (kN)


Lu Chihwei

Reclaimed soils case Dense sand case

-700 -350 0 350 70020

15

10

5

0


Shear Force (KN)

Dep

th (

m)

Clay Layer

Sand Layer

a:b:c:d:

ESDR= -0.28

ESDR=0.88

ESDR=0.90

ESDR=0.96

-6000 -3000 0 3000 600020

15

10

5

0



Dep

th (

m)

Clay Layer

Sand Layer

a:b:c:d:

ESDR= -0.28

ESDR=0.88

ESDR=0.90

ESDR=0.96

-5000 0 5000 1 104 1.5 10420

15

10

5

0

t=3.25 sect=6.31 sect=10 sec


Dep

th (

m)

Clay Layer

Sand Layer

e:a:d:

-1500 -1000 -500 0 50020

15

10

5

0

t=3.25 sect=6.55 sect=10 sec

Shear Force (KN)

Dep

th (

m)

Clay Layer

Sand Layer

e:a:d:

Distributions of sectional forces

a: At the time when maximum bending moment occurs at the bottom of the pierb: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

Bending moment (kN*m) Bending moment (kN*m)Shear force (kN) Shear force (kN)


Lu Chihwei

Conclusions

Reason After

Liquefaction Time (sec)

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

After the peak of seismic waves,

before the completion of liquefaction


Lu Chihwei


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

Thank you very much for your attention

Dr. Lu Chihwei

Moh and Associates, Inc.


liquefaction analysis for a single piled foundation by dr. lu chihwei moh and associates, inc. date:...

Documents

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taiwan workshop

lu chihweiu

lu chihweimoh

lu chihweiguidelines

lu chihweiillustration

lu chihweithe soils

singlepile foundation