A $120-ft$ diameter cylindrical tank with an empty weight of $190,000lb($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

undrained shear strength $s_u=1000l\frac{b}{f}{t}^2$ and $y=118l\frac{b}{f}{t}^3,$ and the groundwater table is at a depth of

$5$ ft $.$ Using Terzaghi's 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 the tank is spread uniformly across the bottom of the tank.