Session 11 – 12 LATERAL EARTH PRESSURE

Course : S0484/Foundation Engineering

Year : 2007

Version : 1/0

LATERAL EARTH PRESSURE

Topic:• General • Active earth pressure

– Rankine earth pressure– Coulomb earth pressure– Lateral earth pressure due to surcharge

• Passive earth pressure– Rankine earth pressure– Coulomb earth pressure

• Influence of ground water table

GENERAL

• Lateral earth pressure represents pressures that are “to the side” (horizontal) rather than vertical.

• Caused by soil self weight and or external load

• 3 categories:– At rest earth pressure– Active earth pressure– Passive earth pressure

AT REST EARTH PRESSURE

The at rest pressure develops when the wall experiences no lateral movement. This typically occurs when the wall is restrained from movement such as a basement wall that is supported at the bottom by a slab and at the top by a floor framing system prior to placing soil backfill against the wall.

ACTIVE EARTH PRESSURE

The active pressure develops when the wall is free to move outward such as a typical retaining wall and the soil mass stretches sufficiently to mobilize its shear strength.

PASSIVE EARTH PRESSURE

If the wall moves into the soil, then the soil mass is compressedsufficiently to mobilize its shear strength and the passive pressure develops.

AT REST EARTH PRESSURE

q

v

h

z v = . z + q

v

hK

At rest, K = Ko

Jaky, Broker and Ireland Ko = M – sin ’

Sand, normally consolidated clay M = 1

Clay with OCR > 2 M = 0.95

Sherif and Ishibashi Ko = + (OCR – 1)

= 0.54 + 0.00444 (LL – 20)

= 0.09 + 0.00111 (LL – 20)

LL > 110% = 1.0 ; = 0.19

Broker and IrelandKo = 0.40 + 0.007 PI , 0 PI 40Ko = 0.64 + 0.001 PI , 40 PI 80

ACTIVE EARTH PRESSURE

ACTIVE EARTH PRESSURE

Ka = tan2 (45 - /2)

1 = 3 . tan2 (45+/2)+2c.tan (45+/2)

a = v . tan2(45-/2) – 2c . tan (45-/2)

a = v . Ka – 2cKa

RANKINE ACTIVE EARTH PRESSURE

ACTIVE EARTH PRESSURE

Note :

z = 0 v = 0 ; a = -2cKa

z = H v = H

The tensile stress decreases with depth and becomes zero at a depth z = zc or

zcKa – 2cKa = 0

and

a

cK

cz

2

zc = depth of tensile crack

ACTIVE EARTH PRESSURE

RANKINE ACTIVE EARTH PRESSURE FOR INCLINED BACKFILL

1cossincos8cos4coscoscos4sincos2cos2cos

1'

:

22

2

22222

z

c

z

c

z

cK

where

a

22

22

coscoscos

coscoscoscosKa

Ka.H..Pa 22

1 (for granular soil, c = 0)

For c- soil

cos'aaa zKzK

ACTIVE EARTH PRESSURE

Assumptions:

-Fill material is granular soil

- Friction of wall and fill material is considered

- Soil failure shape is plane (BC1, BC2 …)

Pa = ½ Ka . . H2

2

2

2

)sin().sin()sin().sin(

1sin.sin

)(sinKa

COULOMB ACTIVE EARTH PRESSURE

ACTIVE EARTH PRESSURE

COULOMB’S ACTIVE EARTH PRESSURE WITH A SURCHARGE ON THE BACKFILL

PASSIVE EARTH PRESSURE

RANKINE PASSIVE EARTH PRESSURE

PASSIVE EARTH PRESSURE

p= v . tan2(45+/2) + 2c . tan (45+/2)

RANKINE PASSIVE EARTH PRESSURE

PASSIVE EARTH PRESSURE

Kp = tan2 (45 + /2)

h = v . Kp + 2cKp

RANKINE PASSIVE EARTH PRESSURE

PASSIVE EARTH PRESSURE

2

2

2

)sin().sin()sin().sin(

1sin.sin

)(sinKp

Pp = ½ Kp . . H2

COULOMB PASSIVE EARTH PRESSURE

LATERAL EARTH PRESSURE DUE TO SURCHARGE

222

2

ba

ba.

nH

q2

222

2

ba

ba.

nH

q4

22b16,0

b203,0.

H

q

a > 0,4

a 0,4

LATERAL EARTH PRESSURE DUE TO SURCHARGE

2cos.sinH

q

12H90

qP

12

122

H2

H'a30,57QRHz

H

'btan 1

1

H

'b'atan 1

2

22 90'b'aR

12 90'bQ

PURPOSE OF LATERAL EARTH PRESSURE

• STABILITY ANALYSIS GRAVITY WALL AGAINST– SLIDING– OVERTURNING

PURPOSE OF LATERAL EARTH PRESSURE

PURPOSE OF LATERAL EARTH PRESSURE