$(25$ points$)$

On a segment of a potential slip surface in Guadalix Red clay, total normal stress is $400$kPa, suction is $1,500$kPa, and shear stress is $700$kPa. The shear strength characteristics are given in Figure $9.$ Compute Factor of Safety of the segment against failure:

a$.$ For the existing condition.

b$.$ If suction decreases to $0$kPa, total normal stress remains at $400$kPa, and shear stress remains unchanged.

If the contribution of suction to shear strength of unsaturated Guadalix Red clay for $u$s$,$ values greater than $u_s$ is given by:

$b{u}_c^2(kPa)$

and for $u_s$ values less than $u_u$ is given by$,$

$u^{2}tan{}^2(kPa)$

where, assuming $a=0\mathrm{.}5$

$u_4=(\frac{b}{tan}{)}^2(kPa)$

c$.$ Using Figure $10$ and the equations given above, compute shear strength for total normal stress of $100$kPa, and $u,$ values of $0,50,100,$ and $150$kPa.