Geotechnical Engineering

DHARM

LATERAL EARTH PRESSURE AND STABILITY OF RETAINING WALLS 507

convenience in design, however, Pa is resolved into its horizontal component, Pah and its verti-
cal component, Pav. Let R represent the reaction from the foundation soil acting on the base of
the wall, which is also for convenience taken to be resolved into its horizontal component T
and its vertical component N. A passive resistance Pp which is usually small, may exist on the
side of the wall remote from the backfill as shown. Let its horizontal and vertical components
be Pph and Ppv respectively. Pp is often neglected in view of its relatively small magnitude.

Pph

Ppv

To e

z 2 Pp

b

x 1

x 2

T

R N x

e b/2 B

Pav

d

Pah

z 1

A

Heel

Pp T

R N

W

Pav

Pah

Pa

(a) Forces acting on a gravity retaining well (b) Force diagram

Pa

W

Fig. 13.50 Force system on a gravity retaining wall

For equilibrium of the wall under these forces, one may write

N = W + Pav – Ppv ...(Eq. 13.68)

and T = Pah – Pph ...(Eq. 13.69)

For any arbitrarily chosen section of the wall, W, Pa and Pp may be obtained and there-
fore N and T may be computed.

The eccentricity e of the force N relative to the centre of the base of the wall may be
computed by taking moments about B.

N. x = W. x 1 + Pavx 2 + Pah.z 1 – Ppv.b – Pph.z 2 ...(Eq. 13.70)
(Note: If Pp strikes the body of the wall and not the base slab, the appropriate lever arm
for Ppv with respect to B must be used).