Problem $3$:

An anchored sheet$-$pile bulkhead is shown in Figure below Let $L_1=2m,L_2=6m,l_1=1m,=16k\frac{N}{m^3},{}_{\text{s}\text{a}\text{t}}=18\mathrm{.}86k\frac{N}{m^3},{}^{\text{'}}=32,$ and $c=27k\frac{N}{m^2}.$

a$.$ Determine the theoretical depth of embedment, $D.$

b$.$ Calculate the anchor force per unit length of the sheet$-$pile wall.

Use the free earth support method.

c$.$ Calculate section modulus of the sheet pile