Question $440$ marks

A deep layer of saturated normally consolidated CLAY is to be loaded by a square foundation with a stress of $100$ kPa $.$

A series of conventional consolidated undrained triaxial compression tests were carried out on undisturbed samples of saturated CLAY taken at a depth of $3$ m below ground level $($BGL$),$ from the CLAY layer, and gave the following results.

$($a$)$ Determine the shear strength parameters $(\backslash ($ c$\_\{$u$\}\backslash )$ and $\backslash (\backslash$phi$\_\{$u$\}\backslash ))$ in terms of total stress. $..15$ marks

$($b$)$ Determine the shear strength parameters $(\backslash (\backslash$mathrm$\{$c$\}^\{\backslash$prime$\}\backslash )$ and $\backslash (\backslash$phi$^\{\backslash$prime$\}\backslash ))$ in terms of effective stress. $10$ marks

$($c$)$ Prior to loading the effective stress from where the sample was taken was $30$ kPa $.$ Calculate the horizontal effective stress at this depth

$($i$)$ before placement of the $100$ kPa loading of the foundation

$($ii$)$ after the excess pore water pressure due to the $100$ kPa loading has dissipated. $\mathrm{.}6$ marks

$($d$)$ Plot the $\backslash ($ q $\backslash )$ vs$.$ p $\text{'}$ graph including the failure envelope, and use it to determine whether the $100$ kPa loading will induce long term failure in the CLAY layer. Other methods also acceptable.. $9$ marks