lecture 08 lep

GEOTECHNICAL AND FOUNDATION ENGINEERING

Lateral Earth Pressure

Course Instructor : Syed Zishan Ashiq

Week No. 08

May 2015

Mirpur University of Science & Technology Mirpur AJK Department of Civil Engineering

Learning Objectives

1. Learn about key concepts:

2. Place in context of Mohr Circle analysis

• At rest, active and passive earth pressure

• Lateral earth pressure coefficients

Lateral Earth Pressure

(R.P. Weber)

(R.P. Weber)

??

??

Water Pressure and Soil Pressure

Consider “at-rest” (geostatic) condition Consider hydrostatic condition

Anisotropic

sx

sz

sz sx ≠ sz sx > Isotropic

Earth Pressure Coefficient “At Rest”

sx

sz

K0 = Coefficient of Lateral Earth Pressure at Rest

For normally consolidated soil (Jaky, 1944):

For over-consolidated soil (Meyerhoff, 1976):

In general:

X

Z

Y

Calculate lateral total stress (sx) at z = 5 m if K0 = 0.5

sx

(M. Budhu)

What is a Lateral Earth Pressure?

7

• We can calculate σv’

• Now, calculate σh’ which is the horizontal stress

σh‘/ σv‘ = K

• Therefore, σh‘ = Kσv‘ (σV‘ is what?)

σv’

σh’

H

There are three states of lateral earth pressure

Ko = At Rest

Ka = Active Earth Pressure (wall moves away from soil)

Kp = Passive Earth Pressure (wall moves into soil)

Passive is more like a resistance

σv

σh

z

H

Coefficients of Lateral Earth Pressure

Active and Passive Limit Conditions

Ka = Coefficient of Active Earth Pressure

(Wall Moving Away from Backfill)

Active Failure Condition

movement Active

Failure

Wedge

(45+f/2)

Kp = Coefficient of Passive Earth Pressure

(Wall Moving Toward Backfill)

Passive Failure Condition

movement Passive

Failure

Wedge

(45 -f/2)

movement

Passive Failure

Consider Mohr’s Circles… sx decreases until failure

sx increases until failure

movement

Active

Failure

Active Earth Pressure - in granular soils

As the wall moves away from the soil,

sh’ decreases till failure occurs.

A

sv’

sh’

z

wall movement

sh’

Active state

K0 state

Active Earth Pressure - in cohesive soils

Follow the same steps as for granular soils. Only difference is that c 0.

AvAactiveh KcK 2']'[ ss

Everything else the same as for granular soils.

2

'45tan

'sin1

'sin1

..

'sin1

'sin1''

2 f

f

f

f

fss

a

xz

K

so

Pole Point

45f/2

Active Failure

45f/2

Rankine Active Failure Surface

14

Passive Earth Pressure - in granular soils

B

sv’

sh’

As the wall moves towards the soil,

sh’ increases till failure occurs.

wall movement

sh’

K0 state

Passive state

15

Passive Earth Pressure - in cohesive soils

Follow the same steps as for granular soils. Only difference is that c 0.

PvPpassiveh KcK 2']'[ ss

Everything else the same as for granular soils.

Rankine Passive Failure Surface

2

'45tan

'sin1

'sin1

..

'sin1

'sin1''

2 f

f

f

f

fss

p

zx

K

so

Pole Point

45f/2

Passive Failure

Rankine’s Earth Pressure Theory

i. Assumes smooth wall

ii. Applicable only on vertical walls

PvPpassiveh KcK 2']'[ ss

AvAactiveh KcK 2']'[ ss

Evolution of lateral stress with wall movement…

Active Failure at Ka

Passive Failure at Kp

Stationary (at rest) Movement toward

backfill

Movement away

from backfill

Ka < K0< Kp

Essential Points

1) Coefficient of Lateral Earth Pressure at Rest

2) Active Earth Pressure Coefficient:

3) Passive Earth Pressure Coefficient:

4) Active slip planes at 45˚ + f’/2 to horizontal

5) Passive slip planes at 45˚ - f’/2 to horizontal

6) More wall movement (inward) required for passive failure than active (outward) failure

20

Retaining Walls - Applications

Road

Train

Retaining Walls - Applications

basement wall

High-rise building

Gravity Retaining Walls

cobbles

cement mortar plain concrete or

stone masonry

They rely on their self weight to support the backfill

Cantilever Retaining Walls

They act like vertical cantilever, fixed to the ground

Reinforced; smaller section than gravity walls

Design of Retaining Wall

1

1

2 2

3 3

toe

toe

Wi = weight of block i

xi = horizontal distance of centroid of block i from toe

Block no.

- in granular soils

Analyse the stability of this rigid body with vertical walls (Rankine theory valid)

1

1

2 2

3 3

PA

PA

PP PP S

S toe

toe R

R y y

Safety against sliding along the base

tan }.{

A

iP

slidingP

WPF

H

h

soil-concrete friction

angle 0.5 – 0.7 f

to be greater

than 1.5

PP= 0.5 KPh2 PA= 0.5 KAH2

1

1

2 2

3 3

PA

PA

PP PP S

S toe

toe R

R y y

Safety against overturning about toe

H/3

}{3/

A

iiP

goverturninP

xWhPF

H

h

to be greater

than 1.5

Thank you for listening