$(25$ points$)$

Initially, total vertical stress and suction at mid$-$depth of a $3\mathrm{.}5m-$thick Onderstepoort clay are ${}_{vo}=45$kPa and $u_{s}o=3,000$kPa, respectively $($Figure $8).$ Compute heave or settlement if $($independent situations$)$:

a$.$ Total vertical stress increases to $200$kPa while suction remains unchanged.

b$.$ Suction decreases to $500$kPa but total vertical stress remains unchanged.

c$.$ Total vertical stress increases to $100$kPa while suction decreases to $1000$kPa.

d$.$ Total vertical stress increases to $100$kPa and suction decreases to $200$kPa.

Also, determine:

e$.$ Swelling pressure against a structure that completely prevents heave while suction decreases to $500$kPa.

f$.$ Swelling pressure against a structure that allows $3\%$ beave while suction decreases to $500$kPa.

g$.$ If suction decreases to $200$kPa, how much heave should be allowed to limit the swelling pressure to $300$kPa.

Compute:

h$.C_w$ between ${}_v$ of $200$ to $1,000$kPa, at $u_s=200$kPa.

i$.C_m$ between $u,$ of $200$ to $1,000$kPa at ${}_r=200$kPa.