Q$.1$ 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$),225,340,450]]$

$(20\%)$

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 $75k\frac{N}{m^2}.[$ note: $=c^{\text{'}}+{}^{\text{'}}tan{}^{\text{'}}]$