Shear Strength Applications in Plastic and Limit Equilibrium - Unsaturated Soil Mechanics in Engineering Practice - page 622

Figure 12.54 Components of active earth pressure showing limits of integration.

Integrating the above equation gives an equation which
takes on an extended form of the active force equation for
saturated soils:

angle of internal friction of 22 ◦ , and a φ b angle of 14 ◦ .As
the matric suction is increased from 0 to 100 kPa on the 8-
m-high wall, the total active pressure is reduced from 206
to 35 kN/m, respectively. In other words, matric suction in
the soil has a large influence on the active force against a
retaining wall.
The matric suction in a soil may not remain at a constant
value with time, and therefore, the active force against the
wall may vary. The highest force will occur when the matric
suction goes to zero. Even higher earth pressures are exerted
on the wall if water is allowed to collect in back of the wall.
The results illustrate the importance of maintaining matric
suction in the soil. At the same time, it is readily recognized
that it may be difficult to ensure the permanency of matric
suction in the soil.
Equations for the active earth force can also be written
for other situations. Let us consider the case where matric
suction decreases linearly with depth. The water table is
assumed to be 1m below the base of the wall. The negative

(H 2 y t )

N φ H

2 c

y t

ρg
N φ

−

P A = − −

2

u w ) tan φ b
N φ

2 (u a −

− (H − y t ) (12.59)

The active force decreases as matric suction increases.
It is possible to reach a condition where the active force
is zero. This situation is referred to as an unsupported
excavation.
Equation 12.59 assumes that the soil density is a con-
stant with respect to depth. Figure 12.55 illustrates a typical
active earth force against a retaining wall as a function
of the matric suction of the soil. Two heights of wall are
considered (i.e., 8 and 12 m). The density of the soil is
assumed to be 1800 kg/m 3 . The shear strength parameters
of the soil are an effective cohesion of 5 kPa, an effective

Figure 12.55 Active earth force when matric suction is constant with respect to depth and other
variables are as designated.