CIVIL ENGINEERING FORMULAS

192 CHAPTER EIGHT

STABILITY OF SLOPES

Cohesionless Soils

A slope in a cohesionless soil without seepage of water is stable if

(8.25)

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

(8.26)

where islope of ground surface
angle of internal friction of soil
b,satunit weights, lb / ft^3 (kg / m^3 )

Cohesive Soils

A slope in a cohesive soil is stable if

(8.27)

whereHheight of slope, ft (m)
Ccohesion, lb/ft^2 (kg / m^2 )
unit weight, lb/ft^3 (kg / m^3 )
Nstability number, dimensionless

For failure on the slope itself, without seepage water,

(8.28)

Similarly, with seepage of water,

(8.29)

When the slope is submerged, is the angle of internal friction of the soil
andis equal to b. When the surrounding water is removed from a submerged
slope in a short time (sudden drawdown), is the weighted angle of internal
friction, equal to (b/sat), and is equal to 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

N(cosi)^2 tani

b

sat

tan 

N(cosi)^2 (tan itan)

H

C

N

tani

b

sat

tan 

i