Question $1-$ Shear Strength $($Direct Shear Test$)$

A direct shear test was conducted on a soil sample with a cross$-$sectional area of $0\mathrm{.}005625m^2.$ The results are shown below:

$\backslash$table$[[$Normal force, N $($N$),250,500,750],[$Shear Force at failure, $T(N),225,340,450]]$

a$)$ Assume the area of the shear contact area remains the same during the test, plot a graph of shear stress against the normal stress $($in $k\frac{N}{m^2}).$

b$)$ Find the shear strength parameters c$\text{'}$ and $\text{'}$ from the graph.

c$)$ Estimate the shear strength of the sample when subject to an effective normal stress $({}^{\text{'}})$ of Note: $[$:$=c^{\text{'}}+{}^{\text{'}}tan{}^{\text{'}}\}$