Problem $1-$ You will use your solution to this problem in a later homework assignment. A site consists of a $20$ ft thick layer of CL material with the water table located at the ground surface. Below the CL soil is a thick layer of SW soil. A single undisturbed Shelby tube sample was taken at the mid$-$height of the CL soil layer as shown by the shaded square symbol below.

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A foundation is to be composed of nine square footings arranged in a $33$ square pattern $($shown below$).$ The footings are square with a side length of $5$ ft $.$ The center to center spacing each way is $10$ ft $.$ The construction sequence involves forming the footings, placing rebar, and then pouring concrete. The footings rest on the original ground surface.

The uniformly distributed bearing pressure on each side and corner footing is $3,000$ pounds per square foot $($psf$),$ and the bearing pressure on the center footing is $4,400$ psf$.$ Assume the footings are placed at the ground surface.

Determine the stress increase $({}_v)$ at a depth of $10$ ft below the ground surface at points located: $($a$)$ below the center of the center footing and $($b$)$ below the center of a corner footing. Consider the foundation loads to be point loads and use

Foundation plan

the Boussinesq point load equation. Do not neglect the contribution of the other side and corner footings in each stress increase calculation. Suggestion: Program the point load equation into Excel or your calculator.