Geotechnical Engineering

DHARM

LATERAL EARTH PRESSURE AND STABILITY OF RETAINING WALLS 523

Example 13.13: A smooth vertical wall 5 m high retains a soil with c = 2.5 N/cm^2 , φ = 30°, and
γ = 18 kN/m^3. Show the Rankine passive pressure distribution and determine the magnitude
and point of application of the passive resistance.

H = 5 m φ = 30° c = 2.5 kN/cm^2 = 25 kN/m^2

γ = 18 kN/m^3

Nφ = tan^245

30

2

F °+ ° 3

HG

I

KJ

=

Pressure at the base:

γH. Nφ = 18 × 5 × 3 = 270 kN/m^2

2 cNφ = 2 × 25 × 3 = 86.6 kN/m^2

Wall Pp

5m

270

86.6 kN/m^2

z=2m

86.6
(a) (b)
Fig. 13.59 Passive pressure of a c – φ soil (Ex. 13.13)
The distribution of the first component is triangular and that of the second component
is rectangular with depth and the pressure distribution is as shown in Fig. 13.59 (b).
The total passive resistance, Pp, on the wall per metre run is obtained as the area of the
pressure distribution diagram.

∴ Pp = 58661

2

×+××. 270 5 = 433.0 + 675.0 = 1,108 kN

The height of the point of application above the base is obtained by taking moments as

usual.

∴ z =

(/ /)433 5 2 675 5 3

1108

×+×

m = 2.00 m

Example 13.14: A retaining wall 9 m high retains granular fill weighing 18 kN/m^3 with level
surface. The active thrust on the wall is 180 kN per metre length of the wall. The height of the
wall is to be increased and to keep the force on the wall within allowable limits, the backfill in
the top-half of the depth is removed and replaced by cinders. If cinders are used as backfill
even in the additional height, what additional height may be allowed if the thrust on the wall
is to be limited to its initial value? The unit weight of the cinders is 9 kN/m^3. Assume the
friction angle for cinders the same as that for the soil.