The water table at a site is at 5 m below the ground level, and it is required to excavate to this level. The soil profile consists of a thick bed of sand where the unit weight is 17.0 kN/m³ above the water table and 20.0 kN/m³ below the water table. The friction angle of the sand is 37°. The walls of the excavation will be supported by a cantilever sheet pile.

a. How deep would you drive the sheet piles? Use the simplified approach discussed in Section 18.8, with factor of safety of 1.5 on the passive resistance.

b. Determine the maximum bending moment in the sheet piles and the required section modulus for the sheet-pile section, assuming an allowable stress of 190 MN/m².