Problem $1$:

Figure below shows a cantilever sheet pile wall penetrating a granular soil. Here, $L_1=4m,L_2=8m,=16\mathrm{.}1k\frac{N}{m^3},{}_{\text{s}\text{a}\text{t}}=18\mathrm{.}2k\frac{N}{m^3},$ and ${}^{\text{'}}=32.$

What is the theoretical depth of embedment, $D?$

For $30\%$ increase in $D,$ what should be the total length of sheet piles?

What is the theoretical maximum moment of sheet pile?