Problem $3)(6$ points$)$ You are hired as a geotechnical engineer. Your subcontractor $($a geotech lab firm$)$ performed $3$ unconsolidated undrained triaxial tests and $1$ unconfined compression test on in total $4$ in$-$situ clay samples, which were obtained from the same depth $(10$ ft below ground surface$)$ during your geotech drilling program. The saturated unit weight of the clay is also determined in the same lab as $120$ pcf $.$ The ground water table during the geotech field investigation program was observed at the ground surface. If the first triaxial test had a cell pressure of $1000$ psf and a major principial stress of $3000$ psf at failure:

a$)$ What is the deviatory stress at failure at the second triaxial test if the cell pressure for this test was $2000$ psf $?(1$ point$)$ b$)$ What is the minor principal stress at the third triaxial test if the major principal stress at failure for this test was $5000$ psf $?(1$ point$)$ c$)$ What is the undrained shear strength of this clay? $(1$ point$)$ d$)$ What is the expected unconfined compression pressure to fail the same in$-$situ clay during the performed unconfined compression test? $(1$ point$)$ e$)$ What is the sensitivity number of this clay, if a remolded sample is prepared from the same clay and an additional unconfined compression test was performed on the remolded sample, which showed an unconfined compression pressure of $\backslash (\backslash$mathrm$\{$qu$\}=1000\backslash$mathrm$\{$psf$\}\backslash )?(1$ point$)$ f$)$ What is the assumed OCR number of the in$-$situ clay $($without the need of running a consolidation test$),$ if the following equation can be used to estimate it for your preliminary design purposes? $(1$ point$)$

$-\backslash (\backslash$mathrm$\{$Cu$\}=0\mathrm{.}25\backslash )*$ effective overburden stress $*$ OCR

Cu : Undrained shear strength

For the questions a$)$ to e$)$ of Problem $3,$ use the conceptual thinking with the help of a not$-$to$-$scale Mohr's circle drawing only $($like we did in the lecture $21).$ The use of any equation or scaling any value off the Mohr's circle will get no credit for the a$)$ to e$)$ portion of the problem.