Course
Year
Version
: S0484/Foundation Engineering
: 2007
: 1/0
Session 11 – 12
LATERAL EARTH PRESSURE
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 compressed
sufficiently to mobilize its shear strength and the passive pressure
develops.
AT REST EARTH PRESSURE
q
Jaky, Broker and Ireland  Ko = M – sin ’
Sand, normally consolidated clay  M = 1
Clay with OCR > 2  M = 0.95
v =  . z + q
z
Broker and Ireland
Ko = 0.40 + 0.007 PI , 0  PI  40
Ko = 0.64 + 0.001 PI , 40  PI  80
v
h
h
K
v
At rest, K = Ko
Sherif and Ishibashi  Ko =  +  (OCR – 1)
 = 0.54 + 0.00444 (LL – 20)
 = 0.09 + 0.00111 (LL – 20)
LL > 110%   = 1.0 ;  = 0.19
ACTIVE EARTH PRESSURE
ACTIVE EARTH PRESSURE
RANKINE ACTIVE EARTH PRESSURE
1 = 3 . tan2 (45+/2)+2c.tan (45+/2)
a = v . tan2(45-/2) – 2c . tan (45-/2)
a = v . Ka – 2cKa
Ka = tan2 (45 - /2)
ACTIVE EARTH PRESSURE
Note :
z = 0  v = 0 ; a = -2cKa
z = H  v = H
The tensile stress decreases with depth
and becomes zero at a depth z = zc or
zcKa – 2cKa = 0
and
2c
zc 
 Ka
zc = depth of tensile crack
ACTIVE EARTH PRESSURE
RANKINE ACTIVE EARTH PRESSURE FOR INCLINED BACKFILL
Ka  cos 
Pa 
1
cos   cos 2   cos 2 
cos   cos 2   cos 2 
2
.

.
H
.Ka
2
(for granular soil, c = 0)
For c- soil
 a  zK a  zK a ' cos 
where :

c
1 
2
Ka ' 
2 cos   2  cos  sin  
2
cos  
 z 
2




c 2
c

2
2
2
2
4 cos  cos   cos   4  cos   8  cos  sin  cos     1

 
 z 
 z 


ACTIVE EARTH PRESSURE
COULOMB 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
Ka 
sin 2 (  )

sin(    ). sin(    ) 
2
sin . sin   1 

sin(



).
sin(



)


2
ACTIVE EARTH PRESSURE
COULOMB’S ACTIVE EARTH PRESSURE WITH A SURCHARGE ON THE
BACKFILL
PASSIVE EARTH PRESSURE
RANKINE PASSIVE EARTH PRESSURE
PASSIVE EARTH PRESSURE
RANKINE PASSIVE EARTH PRESSURE
p= v . tan2(45+/2) + 2c . tan (45+/2)
PASSIVE EARTH PRESSURE
RANKINE PASSIVE EARTH PRESSURE
Kp = tan2 (45 + /2)
h = v . Kp + 2cKp
PASSIVE EARTH PRESSURE
COULOMB PASSIVE EARTH PRESSURE
Kp 
sin2 (  )

sin(   ). sin(   ) 
sin2 . sin   1 

sin(   ). sin(  ) 

Pp = ½ Kp .  . H2
2
LATERAL EARTH PRESSURE DUE TO
SURCHARGE
2q
a 2b

.
nH a 2  b 2


2
a > 0,4
4q
a 2b

.
nH a 2  b 2


2
a  0,4
q
0,203b
 .
H 0,16  b 2


2
LATERAL EARTH PRESSURE DUE TO
SURCHARGE

q
  sin . cos 2
H
q
P  H2  1 
90
 b' 
1  tan 1  
H
 a'b' 
 2  tan 1 

 H 
R  a' b' 90   2 
2
H 2  2  1   R  Q   57,30a' H
z
2H 2  1 
Q  b'2 90  1 
PURPOSE OF LATERAL EARTH
PRESSURE
• STABILITY ANALYSIS GRAVITY WALL
AGAINST
– SLIDING
– OVERTURNING
PURPOSE OF LATERAL EARTH
PRESSURE
PURPOSE OF LATERAL EARTH
PRESSURE