Geotechnical Engineering

DHARM

LATERAL EARTH PRESSURE AND STABILITY OF RETAINING WALLS 453

sh

sv

sh

z

H

H

KHog

Po

Ground surface

(a) Stresses on element of

soil at depth z

(b) Pressure distribution for

a depthH

Fig. 13.5 Stress conditions relating to earth pressure at rest

The soil deforms vertically under its self-weight but is prevented from deforming later-

ally because of an infinite extent in all lateral directions. Let Es and ν be the modulus of

elasticity and Poisson’s ratio of the soil respectively.

Lateral strain, εh =

σ

υ

h σσ

s

v

s

h

EEEs

−+

F

HG

I

KJ

= 0

∴

σ

σ

υ

υ

h

v

=

()1−

...(Eq. 13.1)

But σv = γ. z, where γ is the appropriate unit weight of the soil depending upon its

condition. ...(Eq. 13.2)

∴σh =

υ

υ

γ

1 −

F

HG

I

KJ

..z ...(Eq. 13.3)

Let us denote

υ

1 −υ

F

HG

I

KJ

by K 0 , which is known as the “Coefficient of earth pressure at rest”

and which is the ratio of the intensity of the earth pressure at rest to the vertical stress at a

specified depth.

K 0 =

υ

1 −υ

F

HG

I

KJ

...(Eq. 13.4)

∴σh = K 0. γ.z ...(Eq. 13.5)
The distribution of the earth pressure at rest with depth is obviously linear (or of hydro-
static nature) for constant soil properties such as E, υ, and γ, as shown in Fig. 13.5 (b).