Geotechnical Engineering

DHARM

452 GEOTECHNICAL ENGINEERING

Pressure Passive resistance case

(force on wall)

Active

pressure case

P (earth pressure at rest)o

Pp

Pa

Away from the backfill O Toward the backfill

Direction of movement

Pressure

Fig. 13.4 Relation between lateral earth pressure and movement of wall
Very little movement (about 0.5% horizontal strain) is required to mobilise the active
pressure; however, relatively much larger movement (about 2% of horizontal strain for dense
sands and as high as 15% for loose sands) may be required to mobilise full passive resistance
(Lambe and Whitman, 1969). About 50% of the passive resistance may be mobilised at a move-
ment comparable to that required for the active case.

In a later sub-section (13.6.1), it will be shown that the failure planes will be inclined to
horizontal at (45° + φ/2) and (45° – φ/2) in the active and passive cases, respectively. This
means that the width of the sliding wedge at the top of the wall will be H cot (45° + φ/2) and H
cot (45° – φ/2) for active and passive cases, respectively, H being the height of the wall. For
average values of φ, these will be approximately H/2 and 2H. The strains mentioned by Lambe
and Whitman (1969) will then amount to a horizontal movement at the top of the wall of
0.0025 H for the active case and 0.4 H to 0.30 H for the passive case.

This agrees fairly well with Terzaghi’s observation (Terzaghi, 1936) that a movement of
0.005 H of the top of the wall, or even less, is adequate for full mobilisation of active state. (In
fact, Terzaghi’s experiments in the 1920’s indicated that even 0.001 H is adequate for this).

There are two reasons why less strain is required to reach the active condition than to
reach the passive condition. First, an unloading (the active state) always involves less strain
than a loading (passive state). Second, the stress change in passing to the active state is much
less than the stress change in passing to the passive state. (Lambe and Whitman, 1969).

The other factors which affect the lateral earth pressure are the nature of soil —cohe-
sive or cohesionless, porosity, water content and unit weight.
The magnitude of the total earth pressure, or to be more precise, force on the structure,
is dependent on the height of the backfilled soil as also on the nature of pressure distribution
along the height.

13.4 Earth Pressure at Rest

Earth pressure at rest may be obtained theoretically from the theory of elasticity applied to an
element of soil, remembering that the lateral strain of the element is zero. Referring to
Fig. 13.5 (a), the principal stresses acting on an element of soil situated at a depth z from the
surface in semi-infinite, elastic, homogeneous and isotropic soil mass are σv, σh and σh as
shown. σv and σh denoting the stresses in the vertical and horizontal directions respectively.