Lateral Earth Pressure - Elements of Soil Mechanics - page 191

Fig. 7.9 Passive earth pressure for a cohesionless soil with a horizontal upper surface.

7.4.2 Sloping soil surface

The directions of the principal stresses are not known, but we assume that the passive pressure acts paral-
lel to the surface of the slope. The analysis gives:

cos β + (cos

2

β − cos

2

φ ′ )

K p = cos β

cos β − (cos

2

β − cos

2

φ ′ )

7.4.3 Rankine's assumption on wall friction

The amount of friction developed between a retaining wall and the soil can be of a high magnitude (par-
ticularly in the case of passive pressure). The Rankine theory's assumption of a smooth wall with no fric-
tional effects can therefore lead to a significant underestimation (up to about a half) of the true K p value.
The theory can obviously lead to conservative design which, although safe, might at times be over-safe
and lead to an uneconomic structure.

7.5 Rankine's theory: cohesive soils

7.5.1 Effect of cohesion on active pressure

Consider two soils of the same unit weight, one acting as a purely frictional soil with an angle of
shearing resistance, φ ′ , and the other acting as a cohesive-frictional soil with the same angle of shearing
resistance, φ ′ , and an effective cohesion, c ′ . The Mohr circle diagrams for the two soils are shown in
Fig. 7.10.
At depth, h, both soils are subjected to the same major principal stress

′ =

σ γ

h . The minor principal 1

stress for the cohesionless soil is σ 3 but for the cohesive soil it is only ′ σ 3c , the difference being due to the ′

cohesive strength, c ′ , that is represented by the lengths AB or EF.