Problem $3$

In a consolidated drained $($CD$)$ axisymmetric triaxial test, a sand specimen is first isotropically consolidated to a total stress of ${}_3=450$kPa. With this value of ${}_3$ maintained constant, the specimen is next sheared with the drainage valve open. At failure, the principal stress difference $({}_1-{}_3)$ is equal to $1,121$kPa.

a$)$ Compute the major and minor principal stress at failure $($i$.$e$.,{}_{1_f}^{\text{'}}={}_{1_f}$ and ${}_{3_f}^{\text{'}}={}_{3_f}).$

b$)$ Next, determine the effective friction angle ${}^{\text{'}}.$

c$)$ The normal and shear stress acting on the failure plane $($i$.$e$.,{}_{ff}^{\text{'}}$ and ${}_{ff}).$

d$)$ What is the orientation of the failure plane $($i$.$e$.,{}_f)?$

e$)$ Finally, draw the Mohr circle associated with failure.