seismic earth pressures under restrained...

ICTPA 24th Annual Conference & NACGEA International Symposium on Geo-Trans May 27- 29, 2011 Los Angeles, CA U.S.A.

Seismic Earth Pressures under Restrained Condition

Fred Yi, PhD, PE

Chief Engineer

C.H.J., Incorporated

Table of Contents

• Introduction

• Review of Previous Studies

• Purpose of This Study

• Pseudostatic Numerical Simulation

– FEM Modeling

– Sample Results

– Seismic Earth Pressures of Restrained Walls

• Pseudostatic Seismic Coefficient, kh

• Static Design vs. Seismic Design

• Conclusions & Recommendations

May 27- 29, 2011 Los Angeles, CA U.S.A.ICTPA 24th Annual Conference & NACGEA International Symposium on Geo-Trans


Introduction

• Seismic Earth Pressure (SEP) – a classic but unresolved problem

– Studies since 1920’ (Okabe, 1926, Mononobe& Matsuo, 1929)

– Seismic earth pressure for non-yielding wall (Wood, 1973)

– Seismically Induced Earth Pressures for LRFD Seismic Design of Retaining Structures -Transportation Research Board’s 4 years & $850k project since 2010

TRB Research Project


Introduction

• The fact

– Lew, M., Sitar, N. and Al Atik, L. (2010). “Seismic Earth Pressures: Fact or Fiction.” Proceedings of the Earth Retention

Conference 3, Geo-Institute of ASCE, Bellevue, WA.



Introduction

• Main unresolved problems

– Existing SEP formula may be too conservative

– SEP distributions – normal triangular, inverted triangular, parabolic

– Seismic vs. pseudostatic – confusion in pseudostatic seismic coefficient, kh

REVIEW OF PREVIOUS STUDIES



Review of Previous Studies

• Cantilever Wall (Flexible / Yielding)

– Okabe (1924), Mononobe & Matsuo (1929)

– Seed & Whitman (1970)

– …

• Restrained Wall (Stiff / Non-yielding)

– Wood (1973)

– Ostadan (1998, 2004)

• Most recent

– Atik & Sitar (2007, 2008, 2010)

– Maleki & Mahjoubi (2010)


Mononobe-Okabe (M-O) Method

• Okabe (1926), Mononobe & Matsuo (1929)


Seed & Whitman (1970)

Φ≠35⁰ Φ=38⁰

Seed & Whitman (1970)

kh0 0.1 0.2 0.3 0.4

Φ=30ºM-O KAE

0.33 0.4 0.49 0.63 0.89

Ka+3/4kh0.33 0.405 0.48 0.555 0.63

Φ=33ºM-O KAE

0.29 0.36 0.44 0.57 0.78

Ka+3/4kh0.29 0.365 0.44 0.515 0.59

Φ=35ºM-O KAE

0.27 0.33 0.41 0.53 0.72

Ka+3/4kh0.27 0.345 0.42 0.495 0.57

Φ=38ºM-O KAE

0.24 0.29 0.37 0.48 0.58

Ka+3/4kh0.24 0.31 0.39 0.46 0.54

by Fred Yi, 2/16/2011

or

Wood (1973)


Ostadan (1998, 2004)


Atik & Sitar (2007, 2008, 2010)


Maleki & Mahjoubi (2010)


Purpose of This Study

• This study intends to solve

– Effects of soil strength parameters

– Effects of base conditions

– Relationship between kH and PGA

– A simple equation for engineers


PSEUDOSTATIC NUMERICAL SIMULATION



Pseudostatic Simulation by FEM

• Soil property

– Elastoplastic

– Mohr-Coulomb failure criteria (c=0, Φ)

• Boundary conditions

– Rigid base model

• Wall movement = 0 & deflection = 0

– Non-rigid base model

• Wall movement & deflection = 0

• Wall movement ≠ 0, deflection = 0


FEM model

• Rigid base, Restrained Rigid Wall

H

5H

Gravity

kH

Fixed in X Fixed in X

Changed to Fixed in Y

Fixed in XY


FEM model

• Non-Rigid base, Restrained Rigid Wall

5H

H

Fixed in X

Fixed in X

Changed to Fixed in YFixed in XY

Fixed in X

Gravity

kH


FEM model

• Non-Rigid base, Rigid Wall

5H

HGravity

kH

Fixed in X

Fixed in X

Changed to Fixed in YFixed in XY

No rotation

Lateral Stress (psf)


FEM Results


Passive EP

At-rest EP




FEM Results


Passive EP

At-rest EP




FEM Results


Lateral Displacement (ft)


Seismic Earth Pressure


0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.1 0.2 0.3 0.4 0.5

∆P

0E/γH

2

Seismic Coefficient, kH

Rigid Base

φ=30⁰

φ=33⁰

φ=35⁰

φ=38⁰




0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.1 0.2 0.3 0.4 0.5

∆P

0E/γH

2


Non-Rigid Base, Restrained Wall

φ=30⁰

φ=33⁰

φ=35⁰

φ=38⁰




0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.1 0.2 0.3 0.4 0.5

∆P

0E/γH

2


Non-Rigid Base, Rigid Wall

φ=30⁰

φ=33⁰

φ=35⁰

φ=38⁰



0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.1 0.2 0.3 0.4 0.5 0.6

∆P

0E/γH

2

Pseudostatic Seismic Coefficient, kH

Rigid base, Restrained rigid wall

Non-Rigid base, Restrained rigid wall

Non-Rigid base, Rigid wall

Wood (1973)


Seismic Earth Pressures of Rigid Walls





Distribution of Seismic Earth Pressure

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 2 4

z/H

(∆P0E)/(P0)H/1.17kH


kh=0.1

kh=0.2

kh=0.3

kh=0.4

kh=0.5

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 2 4

z/H

(∆P0E)/(P0)H/1.02kH


kh=0.1

kh=0.2

kh=0.3

kh=0.4

kh=0.5

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 2 4

z/H

(∆P0E)/(P0)H/1.15kH


kh=0.1

kh=0.2

kh=0.3

kh=0.4

kh=0.5

0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.1 0.2 0.3 0.4 0.5 0.6

Th

rust

Po

int

, z/H

Pseudostatic Seismic Coefficient, kH




Thrust Point of Seismic Earth Pressure


PSEUDOSTATIC SEISMIC COEFFICIENT, kh



Seismic Coefficient (kH)

• Confusion:

– kH=PGA

• Seed & Whitman (1970)

• FEMA 450 (kH=SDS/2.5)

• HCHRP Report 611

• FHWA-NHI-10-024

– kH=PGA/2

• ASSHTO LRFD Bridge Design Specification, 2010

• Kramer (1996), kH=(1/3 ~ ½) PGA

• What should it be?

What should kh be?

• The magic number of 0.65


Idriss & Boulanger (2008), Soil Liquefaction During Earthquakes, EERI MNO-12

Data by Atik & Sitar (2008)


Atik & Sitar (2008), Experimental and Analytical Study of the Seismic Performance of Retaining Structures,University of California, Berkeley

PGA ∆Kae kH

0.4 0.05 0.02

0.5 0.16 0.07

0.6 0.26 0.11

0.7 0.37 0.16

0.8 0.48 0.21

kh = 0.47PGA - 0.1675

kh = 0.46PGA - 0.113

-0.09

0.01

0.11

0.21

0.31

-0.2

0

0.2

0.4

0.6

0.8

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

kh


Examination of an earthquake record

• Acceleration records

• Velocity time history

• Displacement time history

-4

0

4

0 5 10 15 20 25 30 35 40

Accele

ration

(m/s

2)

Time (sec)

El Centro Earthquake Record (N-S)

-0.4

-0.2

0

0.2

0.4

0.6

0 5 10 15 20 25 30 35 40

Velo

city (m

/s)

Time (sec)


-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0 5 10 15 20 25 30 35 40

Dis

tance (m

)

Time (sec)



Earthquake record, cyclic and pseudostatic

• Irregular time history of earthquake records

• Cyclic loading in laboratory testing

• Pseudostatic seismic coefficient

-2

-1

0

1

2

0 5 10 15 20 25 30 35 40

Accele

ration

(m/s

2)

Time (sec)

0

0.2

0.4

0.6

0.8

1

0 5 10 15 20 25 30 35 40

Equiv

ale

nt k

H

(m/s

2)

Time (sec)

-4

0

4

0 5 10 15 20 25 30 35 40

Accele

ration

(m/s

2)

Time (sec)



Considering Energy Conservation: t=0~5 s

• Original acceleration record

• Equivalent Harmonic cyclic wave

• Equivalent Pseudostatic load

-4

-2

0

2

4

0 1 2 3 4 5 6 7 8 9 10

Accele

ration

(m/s

2)

Time (sec)

El Centro Earthquake Record4

-4

-2

0

2

4

0 1 2 3 4 5 6 7 8 9 10

Accele

ration

(m/s

2)

Time (sec)

-4

-2

0

2

4

0 1 2 3 4 5 6 7 8 9 10

Equiv

ale

nt k

H

(m/s

2)

Time (sec)

PGA=3.42m/s2

Amp=1.27m/s2, T=0.556sec

kH=0.81m/s2


Equivalent cyclic wave Amp & Pseudostatic kH

0

0.5

1

1.5

2

2.5

3

3.5

4

0 10 20 30 40

Accele

ration (m

/s2)

Time (sec)

PGA

Harmonic

Pseudostatic

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 10 20 30 40

Norm

alized A

mplitu

de (*/PGA)

Time (sec)

Harmonic

Pseudostatic


-2

-1

0

1

2

3

0 5 10 15 20 25 30

Dis

tance (m

)

Time (sec)

Kobe Earthquake (1995), Type111

-4

-2

0

2

4

0 5 10 15 20 25 30

Accele

ration

(m/s

2)

Time (sec)


-0.5

0

0.5

1

1.5

2

0 5 10 15 20 25 30

Velo

city (m

/s)

Time (sec)



Examination of an earthquake record

• Acceleration records

• Velocity time history

• Displacement time history


Equivalent cyclic wave Amp & Pseudostatic kH


0

0.5

1

1.5

2

2.5

3

3.5

0 10 20 30 40

Accele

ration (m

/s2)

Time (sec)

PGA

Harmonic

Pseudostatic

0

0.1

0.2

0.3

0.4

0.5

0.6

0 10 20 30 40

Norm

alized A

mplitu

de (/P

GA)

Time (sec)

Harmonic

Pseudostatic

Suggested kH – PGA relationship

• Essential Structures

• Other Structures


STATIC DESIGN VS. SEISMIC DESIGN



Static Design vs. Seismic Design

• Factor of safety for static design

• Factor of safety for seismic design

• Therefore, a statically designed structure can withstand a seismic load of


Upper Bound of PGA covered by static design

-

0.05

0.10

0.15

0.20

0.25

0.30

30 31 32 33 34 35 36 37 38 39

PG

A u

pp

er

bo

un

d (

g)

Frictional angular, φ (⁰)

Essential Structures (Rigid Base)

Others (Rigid Base)


Others (NonRigid Base, restrained)


Others (NonRigid Base, rigid wall)

CONCLUSIONS AND RECOMMENDATIONS


Conclusions

• The increment of SEP of rigid walls is independent of internal frictional angle of the backfill soils

• The ratio of the increment of SEP of rigid walls to γH2

depends only on kh and base conditions

• The increment can be expressed as

– ∆�� ∙ � ∙ � �

– �� 1.02��&�� 1.17�� ! ��

• Thrust point is lower than the middle point of the wall and can be conservatively taken as 0.45H

• Kh is significantly lower than PGA and can be conservatively taken as

– � � " ∙ #�$%&

– β � (�⁄ for essential structures

– " � (*⁄ ��+,��+�-.+-��


Recommendations

• Seismic Earth Pressures under Restrained Condition

• Thrust point=0.45H


Type of Structures/

Rigid Base Non-Rigid Base

Essential Structures 0.5 0.6

Other Structures 0.33 0.4

��

THANK YOU!


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