$(25\%)$ Problem $4.$ In Figure P$4,$ the soil is sandy with an internal friction angle of $32.$

There is a $4m4m$ concrete foundation sitting on the ground surface bearing a

concentrated load of $Q=16,000kN.$ A strong earthquake occurs, applying a horizontal

force $E$ to the foundation that causes the sliding failure between the foundation and the soil

at Point A$.$

a$)$ Schematically draw a 'zoomed$-$in view' of the element shown at Point A$,$ then show

the state of stress on only the horizontal plane;

b$)$ Only 'schematically' draw the Mohr circle for the element $($i$.$e$.,$ there is no need to

accurately draw the Mohr circle$).$

c$)$ Using formulas, find the force of earthquake causing the element of soil at Point A

to fail in sliding.

d$)$ Find the state of stress on the vertical plane of the element at Point A$,$ and draw it

'zoomed$-$in view' of the element;

e$)$ Find the values of major and minor principal stresses: