QUESTION $1($LO $4$: Slope Stability$)$

$1\mathrm{.}1($a$)$ The diagram shows a $10$ m deep multi$-$layer cutting constructed to a slope of $\backslash (45^\{\backslash$circ$\}\backslash ).$ It is decided to assess the safety factor against shear failure along a circular slip circle having a radius of $15$ m and a centre of rotation $15$ m directly above the toe of the cutting as shown in the diagram.

Given the following information, calculate the factor of safety against shear failure along the specified slip circle:

$-$ Material A: $\backslash (\backslash$phi$=0\backslash ),$ Cohesion $30$ kPa ; Unit weight $\backslash (18\backslash$mathrm$\{$kN$\}/\backslash$mathrm$\{$m$\}^\{3\}\backslash )$

$-$ Material B: $\backslash (\backslash$phi$=0\backslash ),$ Cohesion $40$ kPa ; Unit weight $\backslash (20\backslash$mathrm$\{$kN$\}/\backslash$mathrm$\{$m$\}^\{3\}\backslash )$

$-$ Centroid of $\backslash ($ W$\_\{\backslash$mathrm$\{$A$\}\}\backslash )$ is $10\mathrm{.}5$ m from the vertical through the centre of rotation.

$-$ Centroid of $\backslash ($ W$\_\{$B$\}\backslash )$ is $6\mathrm{.}2$ m from the vertical through the centre of rotation.

$-$ Disregard the effect of tension crack formation.

$($b$)$ Suppose the entire embankment in Question $1\mathrm{.}1($a$)$ consisted over its entire depth of $10$ m of Material A only. Calculate the factor of safety against shear failure along the same slip circle.

$1\mathrm{.}2($a$)$ Determine the safety factor for the embankment in $1\mathrm{.}1($b$)$ above using the stability chart for the $\backslash (\backslash$phi$=0\backslash )$ case. Comment on possible reasons for a discrepancy, if any, in the safety factor values obtained from the calculations in $1\mathrm{.}1($b$)$ and $1\mathrm{.}2($a$).$

$($b$)$ For the embankment in $\backslash (1\mathrm{.}2($a$)\backslash )$ above, assume all the input parameters are unchanged but in addition the soil also has an angle of internal friction $\backslash (\backslash$phi$=20^\{\backslash$circ$\}\backslash ),$ determine the safety factor for the embankment using the stability chart for $\backslash (\backslash$mathrm$\{$c$\}-\backslash$phi $\backslash )$ soils $($in the FRD handout$).$ Round answer to $1$ dp $.$

$($c$)$ Comment on possible reasons for a discrepancy, if any, in the safety factor values obtained from the calculations in $1\mathrm{.}2($a$)$ and $1\mathrm{.}2($b$).1\mathrm{.}3($a$)$ Describe three possible reason$($s$)$ why an increase in water content can promote instability of an embankment.

$($b$)$ State, with reasons, what will be the effect on the safety factor calculated in $1\mathrm{.}1($b$)$ above $($no calculations required$)$ if tension cracks were formed during a drought and which are filled with water following the first rains. QUESTION $2($LO $6$: Consolidation$)$

$2\mathrm{.}1($a$)$ A sand layer of thickness $1$ m overlies a clay layer of thickness $2$ m $($refer diagram$).$ A circular foundation of diameter $2$ m is located on top of the clay layer and exerts a total load of $200$ tonnes $($including self$-$weight$)$ on the surface of the clay. The water table coincides with the top of the clay.

The results of a consolidation test on a representative sample of the clay are attached in the form of a void ratio vs$.$ stress graph. Calculate the primary consolidation settlement, in $\backslash (\backslash$mathbf$\{$m m$\}\backslash ),$ of the foundation.