Question 14.4: (After Koppula, 1984) Consider a cohesive slope of height, H...
(After Koppula, 1984)
Consider a cohesive slope of height, H inclined at 60° to the horizontal. Let the shear strength of the soil be given by a_{0}/ γ = 0.02 and c_{0} / γ H = 0.3. Determine the factor of safety, F_{s}, when the seismic coefficient A = 0 (no earthquake) and A = 0.4 g (strong earthquake), where g = the acceleration due to gravity (9.81 m/s²).
When \beta =60° and the seismic coefficient A=0, from Figure 14.12 we obtain the stability factor N_{1} =3.2, and from Figure 14.13 we obtain the stability factor N_{2} =5.3 . The factor of safety F, can be computed from Equation (14.29) as
F = N_{1}\frac{\alpha _{0} }{\gamma }+N_{2} \frac{c_{0} }{\gamma H} (14.29)
F=\left(3.2\right) \left(0.02\right) +\left(5.3\right) \left(0.3\right) =1.65
When the seismic activity is increased to 0.4 g, the values of N_{1} and N_{2} are found to be 2.0 and 2.75, respectively, and F is calculated as
F=\left(2.0\right) \left(0.02\right) +\left(2.75\right) \left(0.3\right) =0.87
