PROB.#$1.$ A gravity retaining wall is shown in Fig. $1.$ Calculate the factor of safety with respect to overturning and sliding. The following data is given:

Wall dimensions: $H=6m,x_1=0\mathrm{.}6m,x_2=2m,x_3=2m,x_4=0\mathrm{.}5m,x_5=0\mathrm{.}75m,x_6=0\mathrm{.}8m,D=1\mathrm{.}5m,=10$

Soil properties: ${}_1=16\mathrm{.}5k\frac{N}{m^3},{}_1=32,c_1=0,{}_2=18k\frac{N}{m^3},{}_2=22,c_2=40k\frac{N}{m^2}$

The unit weight of concrete is $23\mathrm{.}58k\frac{N}{m^3}.$ Use Rankine's active earth pressure in your calculation.

PROB.#$2.$ Solve Prob.#$1$ using Coulomb's active earth pressure in your calculation. Use $=\frac{2}{3}{}_1.$

PROB.#$3.$ A uniform surcharge of $30k\frac{N}{m^2}$ is placed on top of the backfill in Fig. $1.$ Calculate the factor of safety against failure in over t$$ning and sliding. Use Rankine's active earth pressure.