Volume 6 – Geotechnical Manual, Site Investigation and Engineering ...

Chapter 7 RETAINING WALL
p a = K a p 0= K a γ z (7.7)
p a = K p p 0 = K p γ ζ (7.8)
where
p 0
= Effective overburden pressure (unit length)= γh
pa = Active lateral earth pressures (unit length)
pp = Passive lateral earth pressures (unit length)
z = Depth below the ground surface
h = Depth of tension crack (clayey soil only)
Z
H
p a =rZ tan 2 (45- Ø ) 2
P p =rZ tan 2 (45+ Ø ) 2
(a)
Z
ß
ß
p a =rZK o
p p =rZK p
K a = cosß β β
β β
K a = cosß β β
β β
K a = 1 K p
Z
2c tan (45°- Ø )
2c tan (45+ Ø ) 2
2
Z
p a = rZ tan 2 (45- Ø )-2c 2 tan(45°-Ø) P p = rZ tan 2 (45+ Ø )+2c 2 tan(45+Ø)
2
2
(b)
Figure 7.6 Triangular Lateral Force Distribution By Rankine Theory (a) For Granular Soil (b) For
Cohesive Soil With Tension Crack Depth ‘H’ (Active Case)
For non- granular (c’ – φ ‘) soils, the lateral pressures are :
P a = K a γz – 2cK a (7.9)
P p = K p γz + 2cK p (7.10)
c = Cohesive strength of soil
Theoretically, in soils with cohesion, the active earth pressure behind the wall becomes negative
from the ground surface to a critical depth z where γh is less than 2c′ √ K a . This critical depth is
referred to as the “tension crack.” The active earth pressure acting against the wall within the depth
of the tension crack is assumed to be zero. Unless positive drainage measures are provided, water
infiltration into the tension crack may result in hydrostatic pressure on the retaining structure and
should be full added to the lateral earth pressure.
March 2009 7-7