Example Problems

Example Problem 1: An infinite slope consisting of uniform sand (friction angle $\phi' = 30^\circ$) is inclined at an angle of $20^\circ$ to the horizontal. Determine the Factor of Safety for completely dry conditions, and compare it to the conditions with steady groundwater seepage parallel to the slope face. Assume $\gamma_{sat} = 20\text{ kN/m}^3$ and buoyant unit weight $\gamma' = 10\text{ kN/m}^3$.

Example Problem 2: An infinite slope with an angle of $25^\circ$ consists of a saturated clayey soil. The soil properties are $c = 15 \, kPa$, $\phi = 22^\circ$, and saturated unit weight $19 \, kN/m^3$. The water table is at the ground surface, so seepage occurs parallel to the slope. Calculate the factor of safety against sliding along a potential failure plane at a depth of $4 \, m$.

Example Problem 3: A cutting is to be made in a purely cohesive clay soil with a cohesion of $40 \, kPa$ and a unit weight of $18 \, kN/m^3$. The slope angle is $60^\circ$. According to Taylor's stability charts, the stability number for a slope angle of $60^\circ$ is $0.16$. Calculate the critical height of the slope.