Two consolidated drained $($CD$)$ triaxial tests were conducted on a dense, angular sand at the same void ratio. Test A had a confining pressure of $100$ kPa $,$ while the confining pressure for test B was $400$ kPa $.$ At failure, the maximum deviator stress, ${}_1-{}_3,$ for tests A and B were $400$ and $1700$ kPa $,$ respectively.

a$)$ Plot the Mohr's circles for both tests$/$specimens at failure.

b$)$ Assuming c$\text{'}=0,$ determine $\text{'}$ for each test$/$specimen$.$

c$)$ Determine the orientation of the failure plane for each test$/$specimen; sketch the sample with principal stresses at failure and the failure plane indicated.

d$)$ Calculate the shear and normal stress on the failure plane for both tests. Is it the same as the maximum shear stress on the sample? Why or why not?

e$)$ Use the failure stresses for each test$/$specimen and perform a linear regression of the two failure stresses in order to obtain the overall$/$average effective friction angle for the dense sand. The effective cohesion intercept should be close to zero, but you could force it to be zero by using a third data point in your regression at $(0,0).$ What is the effective friction angle for the dense sand?