Lateral Earth Pressure - Elements of Soil Mechanics - page 192

H

F

E

G

φ '

45° −

φ '

2

c'

φ '

A B D

σ ' 3c σ ' 3 σ ' 1

H

φ '

45° +

2

90° − φ '

F

G

φ '

45° −

2

Fig. 7.10 The effect of cohesion on active pressure.

Consider triangle HGF:

φ

′ ′

φ

sin 45 °− cos 45 °−

HF
GH

HF
c

sin( 90

°− ′

φ
φ

)

2 2

=

′ =

= 2

′ φ ′

sin 45 °+ cos 45 °−

2 2

or

′

φ

= ′ HF 2 sin 45 °−

2

′ ′

Difference between σ 3 and σ 3c

HF

= EF =

′

φ

cos 45

°−

2

′

φ

sin 45 °−

′

φ

2

= ′ = ′ 2 c 2 c tan 45 °−

′

φ

2

cos 45 °−

2

Hence the active pressure, p a , at depth h in a soil exhibiting both frictional and cohesive strength and
having a horizontal upper surface is given by the expression:

′

φ

=

− ′ − ′ p = K h γ 2 c tan 45 °− K h γ 2 c K

a a a a

2