Question $1$

$($a$)($i$)$ A typical Mohr circle and failure envelope are shown in Figure $1$ below. The angle $$

the failure plane inclination to the horizontal. Derive an expression for $$ as a function of $\frac{O}{}.$

Figure $1$: A typical Mohr circle and failure envelope

$($ii$)$ What are the major differences of test procedures for consolidated drained triaxial test and

unconsolidated undrained triaxial test?

$($ii$)$ Describe why drawing Mohr$-$circles is not required when determining shear strength

parameters using direct shear test.

$($b$)$ A specimen of dry sand with $\frac{O}{}=36$ was tested in triaxial compression under a cell pressure

of $100$ kPa $.$

$($i$)$ Draw the Mohr circle and failure envelope representing the condition above on the provided

graph paper on Page $7($top$).$

$($ii$)$ Determine the angle of the failure plane to the horizontal, and normal and shear stresses on

the failure plane using the Mohr circle diagram drawn above.