Geotechnical Engineering

DHARM

510 GEOTECHNICAL ENGINEERING

(c) If the friction angle between the material of the base of the wall and the foundation
soil is δ′, the requirement of safety against sliding is that the obliquity of the reaction R be less
than δ′. This may be expressed:

T

N

< tan δ′ ...(Eq. 13.79)

or T < N tan δ′

or T < μ. N ...(Eq. 13.80)

where μ is the coefficient of friction (= tan δ′) between the base of the wall and the foundation

soil. Further, one may insist on a margin of safety by demanding a certain minimum factor of

safety against sliding, ηs (greater than unity), expressed as follows:

ηs =

μ.N

T

...(Eq. 13.81)

This means that the frictional resistance to sliding is compared with the horizontal

component of the thrust, which tends to cause sliding of the wall over its base.

If passive resistance is considered, the factor of safety against sliding should be greater

than two. However, more commonly, the passive resistance is ignored and it is required that

the factor of safety against sliding be 1.5 or more.

(d) For the wall to be safe against overturning, the reaction R must cross the base of the

wall (that is x >/ b). If the requirement of no tension is satisfied, complete safety against over-

turning is automatically assured.

The factor of safety against over turning, η 0 , is expressed:

η 0 =

Restoring moment

Overturing moment

...(Eq. 13.82)

These moments are taken about the toe of the wall. The force Pah causes an overturning

moment for the wall about the toe, while the forces W, Pav, and Pph cause a restoring moment.

In this case η 0 is given by:

η 0 =

W(bx P bx Pz

Pz

av ph

ah

−+ − + 122

1

)( )

. ...(Eq. 13.83)
It is recommended that this value be not less than 1.5 for granular soils and 2.0 for
cohesive soils, if passive pressure is ignored. However, if passive pressure is also considered,
this should be more than these specified values.

13.8.3Influence of Yield of Wall on Design

The strain conditions within the failure wedge depend upon the nature of the yield of the wall.

The distribution of lateral earth pressure with depth may be shown to be highly dependent on

the strain conditions within the failure wedge and hence on the nature and extent of the yield

of the wall.

Figure 13.52 (a) represents the case where a wall is prevented from yielding. It is then

subjected to ‘earth pressure at rest’. The light gridwork represents planes that are initially

horizontal and planes on which slip may occur, if an active case is reached. This gridwork is

used to illustrate strains that occur in cases discussed later. The earth pressure distribution in