Problem $1(15$ points$)$

$($a$)$ Sketch the failure surface and name the zones suggested by Terzaghi. Also, state two assumptions made in deriving the Teraghir's bearing capacity equation.

$($b$)$ Draw the pressure distribution under the foundation for an eccentrically loaded foundation with one$-$way eccentricity. State the equations for minimum and maximum pressures $-q_{\text{m}\text{i}\text{n}}$ and $q_{\text{m}\text{a}\text{x}}.$

$($c$)$ Under what condition will the minimum pressure $(q_{\text{m}\text{i}\text{n}})$ under an eccentrically loaded foundation $($one$-$way eccentricity$)$ be equal to zero? Sketch the pressure distribution for this case.