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Stability Analysis of Slopes 
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The quantitative determination of the stability of slopes is necessary in a number of engineering activities, such as:
Quite a number of techniques are available for these analyses
The factor of safety is commonly thought of as the ratio of the maximum load or stress that a soil can sustain to the actual load or stress that is applied. Referring to Fig. given below the factor of safety F, with respect to strength, may be expressed as follows:
where τ_{ff} is the maximum shear stress that the soil can sustain at the value of normal stress of σ_{n}, τ is the actual shear stress applied to the soil.
Above equation may be expressed in a slightly different form as follows:
Two other factors of safety which are occasionally used are the factor of safety with respect to cohesion, Fc, and the factor of safety with respect to friction, Fφ.
The factor of safety with respect to cohesion may be defined as the ratio between the actual cohesion and the cohesion required for stability when the frictional component of strength is fully mobilised. This may be expressed as follows:
The factor of safety with respect to friction, Fφ, may be defined as the ratio of the tangent of the angle of shearing resistance of the soil to the tangent of the mobilised angle of shearing resistance of the soil when the cohesive component of strength is fully mobilised.
A further factor of safety which is sometimes used is FH, the factor of safety with respect to height. This is defined as the ratio between the maximum height of a slope to the actual height of a slope and may be expressed as follows:
where, C_{m} = Mobilized Cohesion
∅_{m} = Mobilized Friction Angle
C_{m} = C / F_{s} and tan∅_{m} = tan∅ / F_{s}
Factor of Safety w.r.t. Cohesion (f_{c})
and F_{c} = C / C_{m}
where, H_{c} = Critical depth
H = Actual depth
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