Problem $1$: as a contractor for a shallow foundation site, you noticed that the bearing capacity would not meet the design. What is your approach to increasing the bearing capacity of the soil without changing the design?

Your suggested solution $(5$ points$)$:

Rationale to support your solution $(5$ points$)$:

Problem $2(9-1$ from page $173)$: A strip of wall footing $3$ ft wide is located $3\mathrm{.}5$ ft below the ground surface. Supporting soil has a unit weight of $125$ pcf $.$ The results of laboratory tests on the soil samples indicate that the supporting soil's cohesion and angle of internal friction are $1200$ psf and $25,$ respectively. Groundwater was not encountered. Determine the foundation soil's allowable bearing capacity if a factor of safety of $3$ is used. $(10$ points: Provide full details of your work$)$

Problem $3(9-9$ from page $174)$: A square footing is to be constructed on a uniform thick deposit of clay with an unconfined compressive strength of $3$ ksf $.$ The footing will be located $5$ ft below the ground surface and is designed to carry a total load of $300$ kips $.$ The unit weight of the supporting soil is $128$ pcf$.$ No groundwater was encountered during soil exploration. Considering general shear, determine the square footing dimension, using a factor of safety of $3.(10$ points: Provide full details of your work$)$