Figure $2$ illustrates a direct shear test on a sample of clean sand at an initial relative

density of Dr$=65\%.$ Figure $2($a$)$ shows the test and sample configuration and Figure $2($b$)$ shows

the conditions $$at failure$($defined as maximum obliquity $\backslash$sigma $1/\backslash$sigma $3).$ The sample is dry.

a$)$ What is the peak friction angle based on this test?

b$)$ Determine the magnitudes and orientations of $\backslash$sigma $1$ and $\backslash$sigma $3$ at failure. Draw a simple figure to

illustrate your answer.a$.$ Direct shear test

b$.$ Conditions on the failure

plane at failure

Figure $2$: Direct Shear Test