Lateral active earth pressure can be calculated using the Rankine equation for

the drained case:

$\backslash$sigma $3=\backslash$sigma $1$Ka $2$c$$Ka

where c$$ is the drained cohesion and Ka is the coefficient of active lateral

earth pressure.

a$)$ Assuming that c$=0,$ use the Mohr circle construction together with the

Mohr$-$Coulomb failure envelope to prove that

Ka$=\backslash$sigma $3/\backslash$sigma $1=(1-$Sin$)/(1+$Sin$)$