A smooth, vertical retaining wall is 6.0 m high ($H$) and retains a dry, horizontal backfill of sand. The sand has a unit weight ($\gamma$) of $18.5 \text{ kN/m}^3$ and an effective friction angle ($\phi'$) of $32^\circ$. Calculate the total Rankine active lateral force per meter length of the wall and locate its point of application.

A 3.0 m high smooth retaining wall pushes into a sandy soil, developing full passive earth pressure. The sand has a unit weight ($\gamma$) of $19 \text{ kN/m}^3$ and an effective friction angle ($\phi'$) of $32^\circ$. Determine the passive earth pressure coefficient ($K_p$) and the total passive force ($P_p$) per meter length of the wall.

A retaining wall has a vertical back face ($\theta = 90^\circ$) and retains a backfill that is inclined at an angle of $\alpha = 10^\circ$ to the horizontal. The soil properties are $\phi' = 30^\circ$ and $\gamma = 18 \text{ kN/m}^3$. The wall friction angle is $\delta = 20^\circ$. Determine the Coulomb active earth pressure coefficient ($K_a$) and the total active force ($P_a$) on a 5.0 m high wall.

A 4.0 m high retaining wall retains dry sand ($\phi' = 35^\circ$, $\gamma = 17 \text{ kN/m}^3$). The wall is located in a seismic zone with a peak horizontal ground acceleration coefficient $k_h = 0.20$. Vertical acceleration is ignored ($k_v = 0$). Calculate the seismic active coefficient $K_{ae}$ and the total dynamic active force $P_{ae}$, assuming zero wall friction ($\delta = 0$) and a vertical wall ($\theta = 90^\circ$) with flat backfill ($\alpha = 0$).

A 6-meter-high concrete gravity retaining wall was constructed to support a hillside next to a new highway. The design accounted for active earth pressure from a granular backfill but omitted a functional weep hole or drainage pipe system.

A deep temporary excavation for a commercial basement was stabilized using a braced sheet pile wall. The wall was designed to handle the active earth pressure of the adjacent soil profile.