Lateral Earth Pressure - Elements of Soil Mechanics - page 202

Example 7.8: Coulomb K a

Determine Coulomb's K a value for φ ′ = 20°, δ = 10°, β = 0°, ψ = 90°, c ′ = 10 kPa,
c w = 10 kPa.

Solution:

{ } =

2

cosec 90 ° sin 70 °

K

a =

0 4467 .

sin 100 sin 30 sin 20 / sin 90

° + ° ° °

Hence the K a value for horizontal pressure = 0.4467 × cos 10° = 0.44.

10
10

=

K ac = 2 0 44 1 . + . 1 88

In part (b) of Example 7.10, the values of K a and K ac are obtained via Table 7.1. It is
interesting to compare the answers with those found in this example.

Fig. 7.19 Determination of line of action p a .

7.6.4 Point of application of total active thrust

When using the Culmann line construction, the magnitude of P a is obtained directly from the force
diagram. Its point of application may be assumed to be where a line drawn through the centroid of the
failure wedge, and parallel to the failure plane, intersects the back of the wall. (See Fig. 7.19. )

7.7 Coulomb's wedge theory: passive earth pressure

7.7.1 Granular soils

With the assumption of a plane failure surface leading to a wedge failure, Coulomb's expression for K p
for a granular soil is: