Seismic Analysis of Retaining Structures

Seismic Analysis of Retaining Structures

Nanjundaswamy P.Department of Civil Engineering

S J College of Engineering, Mysore

[email protected]

Retaining Walls

Where

Retaining Walls….

?

Road

Train

Retaining Walls….

Retaining Walls….

Retaining Walls….

Retaining Walls….

Retaining Walls….

highway

Retaining Walls….

Retaining Walls….

Retaining Walls….

ship

warehouse

sheet pile

Sheet PilesSheets of interlocking steel or timber

driven into the ground, forming a continuous sheet

Retaining Walls….

Retaining Walls….

Retaining Walls….

CofferdamSheet pile walls enclosing an area,

to prevent water seeping in

Retaining Walls….

Retaining Walls….

Tieback wall

Retaining Walls….

Retaining Walls….

Columbia Tower, Seattle, Washington

19

Shoring

propping and supporting the exposed walls to resist lateral earth pressures

Retaining Walls….

Retaining Walls….

Retaining Walls….

Retaining Walls….

Retaining Walls….

basement wall

High-rise building

Retaining Walls….

Retaining Walls….

Retaining Walls….

Retaining Walls….

Geogr i d-r ei nf or ced soi l RW al ong JR Kobe Li ne ( 1995)

Retaining Walls….

Reconstruction of the slope of embankment using GRS-RWs having a FHR facing for a

track of bullet trains (Shinkan-Sen)

Retaining Walls….

Retaining Walls….

Soil Nailing

Steel rods placed into holes drilled into the walls & grouted

Retaining Walls….

Soil Nailing

Retaining Walls….

Interlocking stretchers

and headers

filled with soil

Good drainage & allow plant growth.

CRIB WALL

Retaining Walls….

Retaining Walls….

Why ?

Poor Performance

Retaining walls Failures

Failures . . . .

Failures . . . .

Failures . . . .

Failures . . . .

Failures . . . .

Failures . . . .

MSE Wall Failure

Failure Mechanism

Tension Failure Pull Out Failure

Failure Mechanism . . . .

Failure Mechanism . . . .

Forces acting on retaining wall

L0

L

H

z

LELR

Sv`

45+/2

P2(live loads)P1

DSurcharge

+hs

Soil pressure

+hq

Surcharge pressure

=ht

Live load pressure

h

Total lateral pressure

Under Static Conditions

Static Earth Pressures

Two types

Active Earth Pressure

Passive Earth Pressure

Concept of Lateral Earth Pressures

v

v

hh

Conceptual Steps:

• Stick a thin plate through soil w/o causing any strain

• Assume we remove soil on left side w/o causing any strain on right side

• Assume we can move plate left or right

o

expansion n;compressio with

(-) (+)

Kp

Ka

Ko

“Passive State” -failure due to compression

“At Rest” - no strain

“Active State” -failure due to expansion

Static Earth Pressures . . . .

Classical methods

Coulomb Theory (1776)

Rankine Theory (1857)


C.A.Coulomb1736-1806

WJM Rankine1820-1872

Coulombs Earth Pressure Theory Isotropic & Homogeneous Rupture surface is plane Failure wedge is a rigid body Pressure surface is a plane Wall friction exists on the pressure surface 2 – D failure Cohesionless Force equilibrium of the failure wedge is determined. Force acting on the back of wall is due to the weight

of soil wedge above the planar failure surface. Failure plane is inclined to horizontal by α that

depends on Φ, β, δ & θ Frictional force on the failure surface causes the wall

movement


2

2

1HKP AA

2

2

2

)cos()cos(

)sin()sin(1)cos(cos

)(cos

AK

3

Hh

)cot()tan()tan(1

)cot()tan(1)cot()tan()tan(

)tan(tan

2

1

2

11

C

C

C

CA

Coulombs Earth Pressure Theory


Isotropic & homogeneous

Rupture surface is plane inclined at 45+Φ/2 for active case & 45-Φ/2 for passive case

Failure is 2 – D and is by shear

Wall is smooth & vertical

AA

A

KHP

K

2

22

22

2

1

coscoscos

coscoscoscos

Rankines Earth Pressure Theory

Static Pressures . . . .

Dynamic Response

Quite Complex Inherent variability

Uncertainty

Properties and behaviour of Soil

Response depends on Sub-soil

Backfill

Inertial and Flexural response of wall

Nature of input motion

Interaction between wall and soil

Dynamic Response . . . .

Current understanding come from

Model tests

• Shaking table tests

• Centrifuge tests

Numerical analyses Simplified Analysis (pseudo-static)

Simplified Dynamic Analysis (Sliding block model)

Dynamic Analysis

Finite Element Technique

Finite Difference Technique

Model Testing

To measure and understand the response of

ground at different locations under dynamic loading• Manual one directional shaking table

• Frequency 2 Hz

• Acceleration 0.5g

• Period 12 to 20 seconds

• Accelerometers• To measure the acceleration of ground

• Pore water pressure sensors• To measure pore water pressure variation

Model testing . . .

Model testing . . .

Model testing . . .

Model testing . . .

Model testing . . .

10

20100 140 160150130120110100908050 70604030

50

40

30

20

0 10 20

10

50

40

30

20

30 40 60 7050 80 90 100 110 120 130 150 160140

Deformation Pattern of Model Ground after Shaking

Responses recorded

Responses recorded

Model testing . . .

Typical Time histories of acceleration and excess pore water pressure

1 0 2 0 3 0

-3

0

3

T im e (s )

In p u t

-3

0

3

Ac

ce

lera

tio

n (

m/s

2)

Ex

ce

ss

PW

P (

kP

a)

A 3 - C a s e 1

-3

0

3 A 3 - C a s e 2

0

2 P 4 - c a s e 1

0

2 P 4 - c a s e 2

Processed records

Model testing . . .

Model testing . . .

Model testing . . .

Model testing . . .

Centrifuge

Model testing . . .

Centrifuge

Model testing . . .

Model testing . . .

Model testing . . .

Movie

Model testing . . .

Numerical Analysis

Pseudo Static Methods

• Pseudo-static seismic actions are added to the static problem as external forces

• Common in most codes

• Simple to use

• Relatively low computational & simpler boundary condition requirements

Pseudo Static Methods . . .

• Applied PS force is based on PGA and will not represent true dynamic nature of earthquake load on structure

• Does not consider the effects of

• Amplification

• Soil hysteric damping

• Development of cyclic pore pressures

Numerical Analysis . . .

Pseudo Dynamic Methods

• Processing and modeling requirements are lower

• Addresses the shortcomings of PS

• Does not consider the effects of

• Non-linear soil behaviour

• Soil hysteric damping

• Development of cyclic pore pressures


Dynamic Methods

• Mode of failure is not defined

• Any constitutive model to represent the soil behaviour

• Quite complex and requires many input parameters


The soil zones and the applied models in each zone


The selected finite difference mesh for numerical analysis by FLAC-2D.



Contours of the pore pressure ratio (Ru), at the end of analyses for SPT=20


Contours of the pore pressure ratio (Ru), at the end of analyses for SPT=40



13121110987654321100

200

300

400

500

600

700

800

900

Height of wall (m)

MSE (Metal)

Co

st (

dolla

rs/m

2) Mean Values

Thanks for Listening

Documents

Seismic Analysis of Retaining Structures