Shear Strength Applications in Plastic and Limit Equilibrium - Unsaturated Soil Mechanics in Engineering Practice - page 618

Figure 12.46 Components of active earth pressure distribution when soil has tension cracks
and matric suction decreases linearly with depth.

Figure 12.47 Mohr circle construction for passive earth pressure case.

where: where

sin φ / 1 sin φ or N φ = tan 2 ( 45 φ / 2 ) .

c + u w ) tan φ b ].

N φ = 1 − + +

c = total cohesion [i.e., c = (u a −

Rearranging Eq. 12.51, the horizontal stress can be writ-
ten as

12.3.10 Coefficient of Passive Earth Pressure
The coefficient of passive earth pressure can be written as
the ratio of the net horizontal pressure to the net vertical
pressure. Dividing Eq. 12.53 by the net vertical pressure
gives the passive earth pressure coefficient:

sin φ cos φ

u a ) 1

+

σ h − u a = (σ v −

sin φ −

2 c (12.52)

1 − 1 − sin φ

Similar trigonometric functions to those used in the active
pressure analysis can be used to rewrite Eq. 12.52:

2 c N φ
σ v −

u w ) tan φ b N φ
σ v −

2 (u a −

K p = N φ +

u a +

(12.54)

u a

2 c N φ

σ h − u a = (σ v − u a )N φ +

Equations 12.43 and 12.54 show that both active and
passive earth pressure coefficients vary with overburden
pressure.

u w ) tan φ b N φ + 2 (u a − (12.53)