DHARM

LATERAL EARTH PRESSURE AND STABILITY OF RETAINING WALLS 521

Ka for top layer =

130

130

1

3

−°

+°

sin =

sin

Ka for bottom layer =

120

120

049

−°

+°

=

sin

sin

.

Active pressure at 3 m depth – considering first layer

Kav 1

1

3

.σ= × × (^318) = 18 kN/m^2
Active pressure at 3 m depth – considering second layer
Kav 2 ..σ=049 3 18× × = 26.46 kN/m^2
Active pressure at the base of the wall :
KKaa 22 ×× + 318 × × 4524. = 26.46 + 0.49 × 4.5 × 24 = 79.38 kN/m^2
The pressure distribution with depth is shown in Fig. 13.57 (b).
Total active thrust, Pa, per metre run of the wall
= Area of the pressure distribution diagram

1
2
318 45 2646^1
2
×× + ×..+ × ×4 5 52 92..
= 27 + 119.07 + 119.07 = 265.14 kN
The height of the point of application of this thrust above the base of the wall is obtained
by taking moments, as usual.
z =
(. .. .)
.
27 5 5 119 07 2 25 11907 1 5
26514
×+ × + ×m
= 2.244 m
Example 13.10: Excavation was being carried out for a foundation is plastic clay with a unit
weight of 22.5 kN/m^3. Failure occurred when a depth of 8.10 m was reached. What is the value
of cohesion if φ = 0°?
φ = 0° γ = 22.5 kN/m^3
Failure occurs when the critical depth, Hc, which is^4 c N
γ φ

. is reached.

Since φ = 0, Nφ = tan^2 (45° + φ/2) = 1

4

22 5 1

1

c

. ×

× = 8.10

∴ Cohesion, c = 45.6 kN/m^2

Example 13.11: A sandy loam backfill has a cohesion of 12 kN/m^2 and φ = 20°. The unit weight
is 17.0 kN/m^3. What is the depth of the tension cracks?

Depth of tension cracks, zc, is given by

zc =

2 c

N

γ φ

. φ = 20°

∴ Nφ = tan (45° + φ/2) = tan 55° = 1.428