Geotechnical Engineering

DHARM

494 GEOTECHNICAL ENGINEERING

H

Hs

HHss 11

G J

A¢

D

B Ks 2

K 1

C F

E

s 1

(90° – )

d

Fig. 13.35 Break in the backfill surface (After Taylor, 1948)
(iii) The total thrust on the wall for the actual cross-section with the backfill surface
ADE is obtained by another Poncelet construction. The irregular shape introduced by the break
is eliminated by replacing area ADB by the area BA′D as follows: The triangle BAD and BA ′D
have a common base BD; the altitudes are made equal by drawing AA′ parallel to BD, A′ being
on the line ED produced. The Poncelet construction with A′B as the wall face and A′E as the
backfill surface gives the thrust P.

(iv) AK 1 B represents the distribution of the thrust P 1 which is larger than the correct
thrust by (P 1 – P). The pressure distribution in the lower portion of the wall also may be
assumed to be linear without significant loss of accuracy.

Thus if (σ 1 – σ 2 ) is the final value of the pressure at B,

σ 2

2 1

×Hs = (P 1 – P)

or σ 2 =

(^21)
1
()PP
Hs
−
Thus, the final pressure distribution is given by the triangle AJG plus the trapezium
GJKB.
The moment of the thrust P about point B may be expressed as
M = PH 111 ssPPH
3
1
3 1
F cosδδ( ) cos
HG
I
KJ
−−F
HG
I
KJ
If the total thrust alone, and not the distribution of pressure, is of interest, step (iii) is
adequate. The thrust may be taken to act at approximately^1
3
H above the base.
13.7.7 Effect of Uniform Surcharge and Line Load
Uniform Surcharge
Let a uniform surcharge q per unit area act on the surface of the backfill as shown in Fig. 13.36.
The effect of surcharge is to increase the intensity of vertical pressure, thereby increas-
ing the lateral earth pressure.