PLEASE DO PART E USING THE INSTRUCTIONS PROVIDED

A CU triaxial test $($axial compression$)$ on a specimen of saturated overconsolidated clay was carried out under a cell pressure of $\backslash (507\backslash$mathrm$\{$kN$\}/\backslash$mathrm$\{$m$\}^\{2\}\backslash ).$ Consolidation took place against a back pressure of $\backslash (204\backslash$mathrm$\{$kN$\}/\backslash$mathrm$\{$m$\}^\{2\}\backslash ).$ The principal stress difference at failure was $539$ kPa and the pore pressure reading at failure was $124$ kPa $.$ A companion drained test $($CD$)$ performed on an identical sample of the same clay at a consolidation pressure of $155$ kPa $($back pressure was zero$)$ shows that the friction angle of the sample is $19$ degrees.

$($a$)$ How much is the undrained cohesion $\backslash ((\backslash$mathrm$\{$Cu$\})\backslash )$ of the sample? $\backslash ((\backslash$mathrm$\{$kPa$\})\backslash )$

Your last answer was interpreted as follows: $269\mathrm{.}5$

$($b$)$ What maximum principal stress difference would you expect at failure for the companion CD test? $($hint: the cohesion of the sample is NOT zero!$)($kPa$)$

Your last answer was interpreted as follows: $318\mathrm{.}875$

$($c$)$ What maximum principal stress difference would you expect if the second test was performed by keeping $\backslash (\backslash$sigma$\_\{1\}\backslash )$ constant and reducing $\backslash (\backslash$sigma$\_\{3\}\backslash )($ie$.$ lateral extension test$)?($kPa$)$

Your last answer was interpreted as follows: $\backslash \backslash (162\mathrm{.}2396\backslash \backslash )$

$($d$)$ How much is the Skempton parameter $\backslash ($ A $\backslash )$ at failure $\backslash (\backslash$left$($A$\_\{$f$\}\backslash$right$)\backslash )$ for the first $($undrained$)$ test?

Your last answer was interpreted as follows: $-0\mathrm{.}1484$

$($e$)$ Assuming $\backslash (\backslash$mathrm$\{$A$\}\_\{\backslash$mathrm$\{$f$\}\}\backslash )$ is independent of the applied confining pressure for this sample, what maximum principal stress difference would you expect if the second test was performed undrained $($CU$)($assume zero back pressure$)?($kPa$)$

Part e$)$ is obtained by using simultaneous equations. The value A$\_(-)$f for part d$)$ is used to setup

the equation for part e$),$ with u$\_$f $/$ delta$\_$sigma$\_$final $=$ A$\_$f$.$ Note that this delta$\_$sigma$\_$final is

what we are trying to find. Using the Mohr circle of total stress, you can shift that circle using u$\_$f

to get the effective stress Mohr circle. Sigma$\_$dash$\_1$ and sigma$\_$dash$\_2$ values will then be in

terms of u$\_$f and delta$\_$sigma$\_$final which you can put in any of the Mohr$-$Coulomb criterion

equations and solve simultaneously.

Part e$)$ is obtained by using simultaneous equations. The value A$\_(-)$f for part d$)$ is used to setup

the equation for part e$),$ with u$\_$f $/$ delta$\_$sigma$\_$final $=$ A$\_$f$.$ Note that this delta$\_$sigma$\_$final is

what we are trying to find. Using the Mohr circle of total stress, you can shift that circle using u$\_$f

to get the effective stress Mohr circle. Sigma$\_$dash$\_1$ and sigma$\_$dash$\_2$ values will then be in

terms of u$\_$f and delta$\_$sigma$\_$final which you can put in any of the Mohr$-$Coulomb criterion

equations and solve simultaneously.