Geotechnical Engineering

DHARM

LATERAL EARTH PRESSURE AND STABILITY OF RETAINING WALLS 459

σv at a depth z below the surface = γ.z

Assuming that the wall yields sufficiently for the active conditions to develop,

σh = Ka. σv = Ka. γ.z,

where Ka =

1

1

−

+

sin

sin

φ

φ = tan

(^2) (45° – φ/2)
The distribution of the active pressure with depth is obviously linear, as shown in
Fig. 13.7 (b).
For a total height of H of the wall, the total thrust Pa on the wall per unit length of the
wall, is given by:
Pa =
1
2
KH^2
aγ ...(Eq. 13.10)
This may be taken to act at a height of (1/3)H above the base as shown, through the
centroid of the pressure distribution diagram.
The appropriate value of the unit weight γ should be used.
13.6.3 Passive Earth Pressure of Cohesionless Soil
Let us again consider a retaining wall with a vertical back, retaining a mass of cohesionless
soil, the surface of which is level with the top of the wall, as shown in Fig. 13.8 (a).
z
H Cohesionless soil(unit weight : )g Pp
KHpg
H/3
Kzpg
(a) Retaining wall with cohesionless
backfill (moving towards the fill)
(b) Passive pressure
distribution with depth
Fig. 13.8 Passive earth pressure of cohesionless soil—Rankine’s theory
σv at a depth z below the surface = γ.z
Assuming the wall moves towards the fill sufficiently to mobilise the full passive resist-
ance,
σh = Kp.σv = Kp.γ.z,
where Kp =
1
1

• −
  sin
  sin
  φ
  φ = tan
  (^2) (45° + φ/2)
  The distribution of passive pressure (resistance) with depth is obviously linear, as shown
  in Fig. 13.8 (b).
  For a total height H of the wall, the total passive thrust Pp on the wall per unit length of
  the wall is given by: