Shear Strength Applications in Plastic and Limit Equilibrium - Unsaturated Soil Mechanics in Engineering Practice - page 623

pore-water pressures are assumed to decrease in a hydro-
static manner:

A surcharge term must be included in Eq. 12.60 when the
soil has tension cracks to a depth y c . Figure 12.57 shows the
variation in the active earth force for the above example with
tension cracks 2m deep. The results show that when other
variables remain constant, tension cracks increase the active
earth force. In all of the above cases, the active earth force
corresponding to zero matric suction refers to a saturated
soil with zero pore-water pressures.
The point of application of the resultant force can be
computed by considering the line of action of the force
associated with each component of the active earth pressure
diagram. The point of application becomes lower on the wall
as the matric suction of the soil increases. The active earth
force is zero when the tension zone depth is equal to the
height of the wall. That is, the soil should stand without any
support if the height of the vertical excavation is less than
the tension zone depth.

ρg(H 2 y t ) 2 c (H

− − y t )

P A = − N φ

2 N φ

2 (u a − H

u w ) h tan φ b
N φ

H 2
2 D −

y t
2 D

− − y t −

(12.60)
Typical results using the above equation are shown in
Fig. 12.56. The soil properties and the heights of the wall are
the same as for the previous example. The results show that
when matric suction decreases linearly with depth (which
is often the case), the active earth force does not decrease
as rapidly with changing matric suction as when the suc-
tions are constant with depth. Equation 12.60 represents the
compressive components of the active force diagram.

Figure 12.56 Active earth force when matric suction decreases linearly to a water table that is
1m below base of wall.

Figure 12.57 Active earth force when soil has tension cracks and linear decrease in matric
suction to water table that is 1m below base of wall.