A $120$ ft diameter cylindrical tank with an empty weight of $1,900,000lb$ is to be built on top

of a $2$ ft thick compacted gravel fill with a unit weight of $I30l\frac{b}{f}t3.$ The fill will be roughly the

same diameter as the tank. This tank is to be filled with water. The underlying soil is an

undrained clay with $su=1,000l\frac{b}{f}t2$ and $=118l\frac{b}{f}t3,$ 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.

Include the weight of the gravel fill in your computations and assume the weight of the water

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