Geotechnical Engineering

DHARM

LATERAL EARTH PRESSURE AND STABILITY OF RETAINING WALLS 489

As usual, BC is the required rupture surface and Pa is given by the weight of the soil in
the triangle CGL or Pa = 1/2γx^2 sin ψ = 1/2γ x. n.
The construction is based on the principle that the location of the triangle CGL (whose
weight equals Pa) gets shifted proportionately to the shift in D, the point of intersection of the
backfill surface and the φ-line. Thus with the arbitrary location D 1 for D, AG gets shifted to
A 1 G 1 ; and this gives one the procedure required to locate the correct position of the triangle
CGL, the rupture surface BC, and the active thrust Pa for this situation.
(2) β equals φ:
When β exactly equal φ, the ground line and the φ-line are parallel and will meet only at
infinity. The points C and D, and the triangle CGL exist at infinity. However, the triangle CGL
can be constructed any where between the φ-line and the ground line. The construction is
shown in Fig. 13.31.

H

a

B y-line

f

A bf=

C

L M

G

y

Ground line

f-line

n

x

x

Fig. 13.31 Special case of Poncelet construction when β = φ

(i) Draw the ground line and the φ-line.

(ii) Draw the ψ-line BK through B at an angle ψ with the φ-line.

(iii) From any convenient point G on the φ-line, draw a line parallel to ψ-line to meet the

ground line in C.

(iv) With G as centre and GC as radius, draw an arc to cut the line in L.

(v) Join CL and drop CM perpendicular on to LG.

The value of Pa is given by

Pa = γ (∆CGL) =

1

2

1

2

γψγxxn^2 sin =.

Poncelet Construction for the Determination of Passive Resistance
The determination of Coulomb’s passive resistance graphically by the Poncelet construc-
tion is similar to that in the case of active thrust, except that the signs of the angles of internal
friction of soil and wall friction have to be reversed. Graphically, this is accomplished by con-
structing the position line at an angle of – (φ + δ) with the wall face, i.e., on to the opposite side
of the fill, as shown in Fig. 13.32. Likewise, the φ-line is to be drawn through the heel B at an
angle (– φ), i.e., below the horizontal.