Problem $3(20$ pts$)$

A sand with $\backslash$phi $=30$ degrees is sheared in a triaxial test with $\backslash$sigma $1=\backslash$sigma $3=20$ psi initially. Both $\backslash$sigma $1$

and $\backslash$sigma $3$ are increased, with $\backslash$Delta $\backslash$sigma $3=\backslash$Delta $\backslash$sigma $1/4.$ What is the maximum value of $\backslash$sigma $1$ reached during

the test?