Lateral Earth Pressure - Elements of Soil Mechanics - page 183

Chapter 7

Lateral Earth Pressure

7.1 Earth pressure at rest

Consider an element of soil at some depth, z below ground surface. We saw in Chapter 3 that the vertical
total stress, σ 1 acting at that point is caused by the total weight acting above. In the case of a homogenous
soil with no surface surcharge, σ 1 is due to the weight of the material above ( = γ z) as shown in
Fig. 7.1.
A lateral stress, σ 3 acts at the point and is equal to the vertical stress multiplied by the coefficient
of earth pressure , K. In this case the coefficient is the coefficient of earth pressure at rest , denoted
by K 0 .
It has been shown experimentally that, for granular soils and normally consolidated clays, K 0 ≈ 1 − sin φ ′
(Jaky, 1944 ).
Eurocode 7 actually relates K 0 to the overconsolidation ratio and states that K

′ ×

= − ( sin ) φ OCR for 0

soils with not very high values of overconsolidation ratio and a horizontal ground surface.

7.2 Active and passive earth pressure

Let us consider the simple case of a retaining wall with a vertical back (details of wall design and
construction are given in Chapter 8) supporting a cohesionless soil with a horizontal surface (Fig. 7.2) .
Let the angle of shearing resistance of the soil be φ ′ and let its unit weight, γ , be of a constant value.
Then the vertical stress, σ 1 acting at a point at depth below the ground surface will be equal to γ × the
depth:

Behind the wall, at depth h, the vertical stress, σ 1 = γ h.
In front of the wall, at depth d, the vertical stress, σ 1 = γ d.

If the wall is allowed to yield (i.e. move forward slightly), it is clear that the soil behind the wall will
experience a reduction in lateral stress (it will expand slightly), whilst the soil in front will compress slightly
and thus experience an increase in lateral stress. This shows that, in addition to the at rest state, soil can
exist in two states. In expansion, the soil is in an active state, and in compression, the soil is in a passive
state.
We can say therefore (in this example), that the soil behind the wall is in an active state and thus, the
pressure that the soil is exerting on the wall is active pressure . By contrast, the soil in front of the wall is
in a passive state and so the pressure that the soil is exerting on the wall is passive pressure .
As with the at-rest condition described in Section 7.1, the lateral earth pressure acting at some
depth is equal to the vertical stress (pressure) multiplied by the appropriate coefficient of earth pressure.
We can now introduce the coefficient of active earth pressure , K a and the coefficient of passive earth
pressure , K p .