Geotechnical Engineering

DHARM

LATERAL EARTH PRESSURE AND STABILITY OF RETAINING WALLS 499

First, the line load is disregarded and Poncelet construction is carried through; the

failure plane BC is located and the thrust Pa 1 is determined. The distribution of pressure ABD

is obtained,

wherein BD = σ 1 = 2Pa 1 /Hs ...(Eq. 13.62)

Point A′ is then located on the backfill surface produced, the weight of the triangle of

soil being equal to q′. The distance AA′ (= a) is given by

q′ =

1

2

γaH. s ...(Eq. 13.63)

Now another Poncelet construction, starting from point A′, with unchanged ψ-line, is

performed to determine the failure plane AC′ and the total thrust Pa 2. The surcharge causes

an additional thrust of Pa 2 – Pa 1 , which has a distribution that is approximately as shown in
Fig. 13.40 (b). This is approximated with reasonable accuracy by a broken line.
Let the lines parallel to the failure planes BC and BC′, and passing through the point
the action of the line load q′, meet the wall face in E and E′, respectively. It may be assumed
that at point E, there is no effect of the line load and that the pressure is EF; that at point E′
the pressure caused by the line load has its maximum value σ 2 ; and, that at point B there is no
effect of the surcharge and that the pressure is BD.

Since^1

2 2

σ is the average pressure added over the height of the wall DE, σ 2 is defined by

the equation

Pa 2 – Pa 1 =^1

2 2

σ×Hs,

whence σ 2 =

(^221)
1
()PP
H
aa
s
−
...(Eq. 13.64)
The use of this equation allows the completion of the pressure distribution diagram
AFF′D.
The moment of this pressure diagram about the heel B of the wall, which may be re-
quired in the stability computations of the wall, is given by
MB =
1
3
1
123 112
PHas×+− +cosδδ(PPH Haass)( ) cos ...(Eq. 13.65)
13.7.8Lateral Earth Pressure of Cohesive Soil
The lateral earth pressure of cohesive soil may be obtained from the Coulomb’s wedge theory;
however, one should take cognisance of the tension zone near the surface of the cohesive backfill
and consequent loss of contact and loss of adhesion and friction at the back of the wall and
along the plane of rupture, so as to avoid getting erroneous results.
The trial wedge method may be applied to this case as illustrated in Fig. 13.41. The
following five forces act on a trial wedge:

1. Weight of the wedge including the tension zone, W.