Cohesionless Soils

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

i < f

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

tan i < ( g_b /g_sat ) tan f

where

i = slope of ground surface
f = angle of internal friction of soil

g_b , g_sat = unit weights, Ib/ft³ (kg/m³)

Cohesive Soils

A slope in a cohesive soil is stable if

H < (C/gN)

where
H = height of slope, ft (m)

C = cohesion, lb/ft² (kg / m² )
g = unit weight, lb/ft³ (kg / m³ )
N = stability number, dimensionless

For failure on the slope itself, without seepage water,

N =(cos i)² (tan i - tan f )

Similarly, with seepage of water,

N = (cos i)²[ tan i - ( g_b/ g_sat ) tan f ]

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