Geotechnical Engineering

DHARM

LATERAL EARTH PRESSURE AND STABILITY OF RETAINING WALLS 495

Differential increase in the weight of any differential soil wedge

dW = – (γdA + qds cos β) ...(Eq. 13.54)

where dA = differential area of the differential soil wedge,

ds = differential length of the surface, and
β = the angle of surcharge.
This is under the assumption that q is the intensity of surcharge load per unit horizon-
tal area.

The negative sign in Eq. 13.54 indicates that as θ increases, the weight of the sliding soil
wedge decreases.

From the geometry of the figure,

dA =

1

2

Hdss′. ...(Eq. 13.55)

s 1 d

s 2

s 2

H

H¢s

a

W

Unit weight :g

Hs

ds

B

q

dq

W

dA

b s

q/unit area

(a) Backfill with surcharge (b) Pressure distribution

A

Fig. 13.36 Effect of uniform surcharge on earth pressure (Jumikis, 1962)

or ds =

2 dA

Hs′ ...(Eq. 13.56)

Substituting this into Eq. 13.54, one gets

dW = −+′

F

HG

I

KJ

=− +

′

F

HG

I

KJ

γβγ

β

dA

qdA

H

q

H

dA

ss

22

.cos

.cos

.

= – γ 1 .dA ...(Eq. 13.57)

where γ 1 = γ

β

+

′

F

HG

I

KJ

2 q

Hs

.cos

...(Eq. 13.58)

Thus, one can imagine that the effect of uniform surcharge may be taken into account

by using a modified unit weight γ 1 , which is given by Eq. 13.58, in the computation of the

weights of trail sliding wedges in the Culmann’s construction, or for γ in Eq. 13.46, if Poncelet’s