Q$3.$ A $120-$ft diameter cylindrical tank with an empty weight of $1,900,000lb($including the

weight of the cylindrical mat foundation$)$ is to be built. The bottom of the mat will be at a

depth of $2$ ft below the ground surface. This tank is to be filled with water. The underlying

soil is an undrained clay with $s_g=1000$Ib$/$ft$^2$ and $=118lb/$ft$^2,$ and the ground water table

is at a depth of $5$ ft $.$ Assume that general shear failure occurs in soil.

Use Terzaghi and Vesic Equations, compute the maximum allowable depth of the water in

the tank that will maintain a factor of safety of $3\mathrm{.}0$ against a bearing capacity failure. Assume

the weight of the water and tank is spread uniformly across the bottom of the tank.