A 5.0 m high cantilever retaining wall retains a horizontal sandy backfill ($\gamma = 18 \text{ kN/m}^3, \phi' = 30^\circ, c' = 0$). The base of the wall is 3.5 m wide ($B$). The total vertical force ($\sum V$) acting on the base (including wall weight and soil on the heel) is $420 \text{ kN/m}$. The net resisting moment about the toe ($\sum M_R - \sum M_O$) is $580 \text{ kN}\\cdot\text{m/m}$. Check the bearing pressure if the allowable bearing capacity is $200 \text{ kPa}$.

A cantilever retaining wall is subjected to a total overturning moment ($\sum M_O$) of $150 \text{ kN}\\cdot\text{m/m}$ from lateral earth pressure. The resisting moment ($\sum M_R$) provided by the weight of the wall and the soil resting on the heel is $400 \text{ kN}\\cdot\text{m/m}$. Calculate the Factor of Safety against overturning and determine if it is acceptable.

The same retaining wall from the previous example experiences a total horizontal driving force ($\sum F_D$) of $120 \text{ kN/m}$. The total vertical force ($\sum V$) acting on the base is $300 \text{ kN/m}$. The base of the wall rests on a soil with an interface friction angle $\delta = 25^\circ$ and base adhesion $c_a = 0$. Determine the Factor of Safety against sliding.

A retaining wall base has width $B = 4.0 \text{ m}$. The calculated maximum bearing pressure is $q_{max} = 180 \text{ kPa}$. The foundation soil is a stiff clay with an undrained cohesion $s_u = c = 100 \text{ kPa}$, friction angle $\phi = 0$, and unit weight $\gamma = 19 \text{ kN/m}^3$. The base is embedded $D_f = 1.0 \text{ m}$. Using Terzaghi's bearing capacity equation ($N_c = 5.7, N_q = 1.0, N_\gamma = 0$ for $\phi = 0$), calculate the Factor of Safety against bearing capacity failure.

A Mechanically Stabilized Earth (MSE) wall was constructed using geogrid reinforcement to support a highway ramp. The design assumed a specific tensile strength for the geogrid and a specific pullout resistance based on the frictional properties of the gravel backfill.

Two retaining wall designs are proposed for a 4-meter high soil retention project. Option A is an L-shaped wall (no heel, long toe). Option B is an inverted T-shaped wall (long heel, shorter toe).