Page 258 - Civil Engineering Formulas

192 CHAPTER EIGHT

STABILITY OF SLOPES

Cohesionless Soils
A slope in a cohesionless soil without seepage of water is stable if
i (8.25)

With seepage of water parallel to the slope, and assuming the soil to be satu-
rated, an infinite slope in a cohesionless soil is stable if

b
tan i tan (8.26)
sat
where i slope of ground surface
angle of internal friction of soil
3
3
, sat unit weights, lb/ft (kg/m )
b
Cohesive Soils
A slope in a cohesive soil is stable if
C
H (8.27)
N
where H height of slope, ft (m)
2
2
C cohesion, lb/ft (kg/m )
3
3
unit weight, lb/ft (kg/m )
N stability number, dimensionless
For failure on the slope itself, without seepage water,
2
N (cos i) (tan i tan ) (8.28)
Similarly, with seepage of water,

b
2
N (cos i) tan i tan (8.29)
sat
When the slope is submerged, is the angle of internal friction of the soil
and is equal to . When the surrounding water is removed from a submerged
b
slope in a short time (sudden drawdown), is the weighted angle of internal
friction, equal to ( / ) , and is equal to .
b
sat
sat
BEARING CAPACITY OF SOILS
The approximate ultimate bearing capacity under a long footing at the surface
of a soil is given by Prandtl’s equation as