$($a$)$ For a pile$/$shaft in clay soil, draw conceptually the pile$/$shaft deflection, soil reaction, bending moment, and shear diagrams for free headed and fixed headed long flexible piles.

Free Headed

deflections

soil reaction

bending moment

shear

Fixed Headed

deflections

soil reaction

bending moment

shear

b$)$ Determine the horizontal displacement of a square pile of $0\mathrm{.}5m$ width and $15m$ long when the applied horizontal load equals $100kN($consider free head$).$ Consider the pile made of concrete and the soil modulus constant is constant and equal to $80$MPa.