A $3m$ deep excavation will be supported by a cantilever sheet pile. The foundation soil is dense sand, but it is assumed that the pile tip penetrates impermeable soil so hydrostatic pore pressure can be used. A surcharge of $10$kPa is applied at the ground level. The water table is at the ground surface and dredge line as shown. Use ${}_w=10k\frac{N}{m^3}$ for your calculations.

a$)$ Using a factor of safety of $2\mathrm{.}0$ for $K_p,$ check if $D^{\text{'}}=5m$ is safe or not $($no need to iterate for other $D^{\text{'}}).$

b$)$ Calculate the maximum bending moment.