Figure $1$ shows a cross$-$section through an excavation in a deep sand deposit. The site engineer determined that the exaction is too deep for a cantilever sheet pile to perform as an economical option and recommended to prop a smaller thickness sheet pile wall by using wooden struts that are spaced $3$ m along the length of the wall. You are the office design engineer and are given the sketch below and asked to determine the following:

i$.$ The distribution of the lateral pressure over the wall height. $(10$ pts $)$

ii$.$ The total force that the retaining wall must resist. $(10$ pts $)$

iii. The loads $($in $kN)$ carried by the individual upper and lower props. $(10$ pts $)$

Figure $1$