DHARM

LATERAL EARTH PRESSURE AND STABILITY OF RETAINING WALLS 467

or σ (^3) c =
γ
φ φ
.
tan ( / ) tan( / )
zc
(^2452)
2
°+^452
−
°+
...(Eq. 13.22)

γ
φ φ
z
N
c
N
−^2 ...(Eq. 13.23)
where Nφ = tan^2 (45° + φ/2),called ‘flow value’.
The equation for σ (^3) c, or the lateral pressure for a cohesive soil, is known as Bell’s equation.
In fact, this may be also obtained from the relation between principal stresses expressed
by Eq. 8.36 by taking σ 1 = γz and σ 3 = σh as follows:
σ 1 = γz and σ 3 = σh as follows:
σ 1 = σ 3 Nφ + 2c Nφ
σ 1 = γz, σ 3 = σh
∴γz = σhNφ + 2c Nφ
or σh =
γ
φ φ
z
N
c
N
−^2 , as obtained earlier.
With the usual notation,
1
Nφ
= Ka for a cohesionless soil.
∴ σ (^3) c = σh = Kz
c
a N
γ
φ
−^2
At the surface, z = 0 and σh = – 2 cN/ φ ...(Eq. 13.24)
The lateral pressure distribution diagram is obtained by superimposing the diagram for
the first and second terms, as shown in Fig. 13.15.

+

H

2zc

zc

2c/ NÖ f

Cohesive

fill

K h = H/Naggf

Fig. 13.15 Active pressure distribution for a cohesive soil
The negative values of active pressure up to a depth equal to half of the so-called ‘criti-
cal depth’ indicate suction effect or tensile stresses; however, it is well known that soils cannot
withstand tensile stresses and hence, suction is unlikely to occur. Invariably, the pressure
from the surface in the tension zone is ignored.