Dep

Course:SoilDynamics

Module4:DynamicEarthPressure

Module 4:- Dynamic Earth Pressure Theory

1 General

2 Pseudo-Static method.

3 Pseudo-Static analysis.

4 Displacement Analysis.

Course:SoilDynamics


LECTURE 1

Course:SoilDynamics


DYNAMIC EARTHPRESSURE THEORY:

The retaining walls are subjected to dynamic earth pressure in seismic zones, the

magnitude of which is more than the static earth pressure due to ground motion.

For the safe and economic design of retaining structures, correct estimation of earth

pressure onretaining structures, sheet pilewalls, braced excavation etc. is very

important.

For the analysis and design of retaining walls in earthquake-prone zones, accurate

estimation of dynamic earth pressures is very important.

Conventional methods either use pseudo-static approaches of analysis even for

dynamic cases or a simple single-degree of freedom model for the retaining wall–soil

system.

Due to its complexity in analysis,under dynamic condition and/or under seismic

loading, the problem is no doubt challenging.

The recent devastating earthquakes in India, like the Kashmir Earthquake in 2005, and

theBhuj Earthquake in 2001 have added important dimensions to this problem, as in

the hilly regions, retaining structures are of utmost importance.

Among the theories available till date for the estimation of seismic earth pressure, the

Mononobe–Okabe (1926, 1929) method,which is the pioneeringwork in this field, is

commonly used.

Two approaches namely: Mononobe-Okabe (1929), is the modification of Coulomb’s

theory, and Kapila (1962) is the modification of Culmann’s graphical construction are

well known approaches to obtain dynamic earth pressure considering only Φ soil.

Course:SoilDynamics


Thereafter, a general solution for the determination of total (static plus dynamic) earth

pressure for a c-Φ soil has been developed by Prakash and Saran, 1966 and Saran

andPrakash, 1968 considering horizontal backfill surface and horizontal seismic

coefficient.

Course:SoilDynamics



1 General




Course:SoilDynamics


LECTURE 2

Course:SoilDynamics


PSEUDO-STATIC METHOD:

In this method, the dynamic force is replaced by an equivalent static force.

Some of the Pseudo-static methods are:

o Modified Swedish Circle Method

o Modified Taylor’s Method.

This method is applicable for both total and effective stressslope stability

analyses.

The method ignores cyclic nature of earthquake.

It assumes thatadditional static force is applied on the slope due to

earthquake.

Earthquake subjects sliding mass in general to vertical as well

as horizontalpseudo staticforces.

Since vertical pseudo static force on sliding mass has very little effect on

its stability,it is ignored.

Based on the results of field exploration and laboratory testing, unit

weight of soil orrock can be determined.

Course

BASIC C

MONON

in

F

co

fa

m

:SoilDyna

CONCEPT

NOBE-OKA

Modif

ncorporating

igure shows

ohesionless

ailure plane w

making an an

amics

:

ABE THEO

fied classica

g the effect o

s a wall of he

soil with uni

which is inc

ngle i with ho

ORY(1929):

al Coulomb’s

of inertia forc

eight H and i

it weight w a

clined toverti

orizontal.

Module

s theory for e

ce.

inclined vert

and angle of

ical by an an

e4:Dynam

evaluating d

tically at an

f shearing re

ngle θ. The b

micEarthP

dynamic eart

angle α reta

sistance φ.B

backfill is inc

Pressure

th pressure b

ining

BC1 is the tria

clined and

by

al

Course

F

fo

(i)

(i

di

(i

(i

(v

T

ea

T

:SoilDyna

F

(

or the failur

orces:

i) W1 weight

ii) Earth pres

irection.

iii) Soil react

iv) Horizonta

v) Vertical in

They gave th

arthpressure

They also con

o Effect

o Effect

o Partia

amics

Fig.(a) Forc

(c) Dynamic

re condition

t of the wedg

ssure P1, inc

tion R1, incl

al inertia for

nertia force =

hedifferent r

e.

nsidered the

t of Uniform

t of Saturatio

ally Submerg

ces acting on

(b) For

earth pressu

the soil we

ge acting at c

clined at an a

ined at an an

rce (W1αh) ac

=W1αvacting

relations for

following fa

m Surcharge.

on on Latera

ged backfill.

Module

n failurewed

rce Polygon

ure versus w

edge ABC, i

centre of gra

angle δ to no

ngle φ to the

cting at the c

g at the centr

r the compu

actors :

al Dynamic E

e4:Dynam

dge in active

wedge angle θ

is in equilibr

avity of ABC

ormal to the

e normal on t

centre of gra

re of gravity

utationof dyn

Earth Pressu

micEarthP

state

θ plot

rium under

C1.

wall in the

the face BC1

avity of the w

y of the wedg

namic active

ure.

Pressure

the followin

anticlockwis

1.

wedge ABC1

ge ABC1.

e and passiv

ng

se

1.

ve

Course:SoilDynamics



1 General




Course:SoilDynamics


LECTURE 3

Course:SoilDynamics


PSEUDO-STATIC ANALYSIS:

In pseudo static analysis, a surface of sliding is assumed and a quantitative estimate of

the factor of safety is obtained by examining the equilibrium conditions at the time of

incipient failure and compare the strength necessary to maintain limiting equilibrium

with the avalaible strength of soil.

The earthquake forces are considered as equivalent static forces which are obtained by

multiplying the weight of the sliding wedge with seismic coefficients.

In the pseudo-static analysis, the peak ground acceleration is converted into a pseudo-

static inertia force and applied as a horizontal incremental gravity load.

Only dependent on the maximum amplitude, not on the frequency of ground motion.

It assumes relative movements of the wall and soil, large enough to induce a limit or

failure state in the soil, and hence full mobilization ofearth pressure is assumed in the

analysis.

Recently, researchers like Saran & Gupta (2003); Choudhary & Singh (2006) also

proposed the pseudo-static force-based methods to estimatethe seismic-active earth

pressure behind a retaining wall.

Even under static condition, the partial mobilization of earth pressure is more

common than the full mobilizationof earth pressure depending on the displacement of

the wall.

Pseudo static analysis is used for simple slope design to account for seismic forces.

• stability is related to the resisting forces (soil strength) and driving forces (inertial forces)

• seismic coefficient (kh) to represent horizontal inertia forces from earthquake

• seismic coefficient is related to PGA

• insufficient to represent dynamics of the problem.

Course:SoilDynamics


In actual analysis, a lateral force acting through centroid of sliding mass

is applied which acts in out of slope direction. This pseudo-static lateral

force Fhis calculated as follows :

Fh= m a = Wa/g = Wamax/g =khW

o Where, Fh=horizontal pseudo-static force acting through centroid of

sliding mass inout of slope direction. For two dimensional analysis, slope is

usuallyassumed to have unit length.

o m = t o t a l m a s s o f s l i d e m a t e r i a l .

o W = t o t a l w e i g h t o f s l i d e m a s s .

o a = acc e l e r a t i on ,

max i mu m ho r i zo n t a l a cce l e r a t i on a t g round su r f ace

du e to earthquake. ( =amax)

o amax=p eak g round acce l e r a t i o n .

o amax / g = s e i s m i c c o e f f i c i e n t .

Consequently, weight of sliding mass, W can be readily calculated.

On the other hand, selection of seismic coefficient takes considerable experience and judgement.

Certain guidelines regarding selection of seismic coefficient is as follows:

o Higher the value of peak ground acceleration, higher the value of kh

o khis also determined as function of earthquake magnitude.

o When both items are considered, khshould never be greater than amax / g.

o Sometimes local agencies suggest minimum value of seismic coefficient.

o For small slide mass, kh= amax.

o For intermediate slide mass, kh= 0.65 amax / g

o For large slide mass, kh= 0.1 for sites near faults generating 6.5 magnitude earthquake and ,kh= 0.15 for sites near faults generating 8.5 magnitude earthquake.

o kh= 0.1 for severe earthquake, = 0.2 for violent and destructive earthquake and = 0.5 for catastrophic earthquake

Course: Soil Dynamics Module 4: Dynamic Earth Pressure


1 General





LECTURE 4


DISPLACEMENT ANALYSIS:

There are very few methods available to compute displacements of rigid retainingwalls during earth-quakes.

Theseare :(i) Richard-Elms Model based on Newmark's Approach(ii) Solution in pure Translation(iii) Solution in pure rotation(iv) Nadim-whitmanmodd(v) Saran-Reddy-Viladkar Model

Displacement analysis is used to estimate the amount of permanentdisplacementsuffered by a slope due to strong ground shaking.

The adverse earthquake forces usually consists of a few cycles lasting for a very short

duration less than half a minute in most cases.

If the average shear resistance falls below the shear stress on a surface through the

slope, then only small displacement can't take place in such small duration force.

Further, the reversal of the acceleration will arrest the displacement till the next

adverse cycle.

The strength of soil under short duration dynamic load is not effected significantly.

Keeping this in view, the criterion for design should be based on the allowable

displacement rather than the limiting equilibrium.

Concept of Yield Acceleration:

Newmark (1965), defined the yield acceleration as the acceleration which drops the

dynamic factor of safety of the slope to unity.

Figure shows a slope of height Hand inclined to horizontal by an angle ϕ. ABM

represents a circular sliding wedge with its center at C.


Fig. Static Condition

In static condition , this wedge is in equilibrium under three forces,

o Weight W of the wedge acting at its e.g. in vertical downward direction

o ∑τs. ds along the arc AB. τsis the shear strength of the soil given by:

τs= c + σn tanϕ

where c = Unit cohesion of slope material

φ = Angle of internal friction of slope material

σn = Normal stress on the portion ds of the arc.

o ∑ σn.ds

If Fs represents the Static factor of safety, then,=R. .sFs=

.ds

W b


Fig. Seismic Condition

Let during earthquake, acceleration of magnitude ψ. g is generated, in the

direction making an angle ψwith vertical. ψand g are respectively the seismic

coefficient and acceleration due to gravity.

As shown in Fig. below, the stability of the slope, in this case can be analysed

by taking an additional force ψ. W.

If Fd represents the Dynamic factor of safety, then,

.

R. .dF =d . W h

ds

W b

τ d, is dynamic strength of soil.

There are others as well such as :

o Rigid Plastic Approach for Determining Displacement.

o Goodman and Seed's Approach.

Dep

Documents

Transcript of Dep