A fill will be placed over the soil profile shown in Figure $1,$ which consists of sand, soft clay, and

another layer of sand. The proposed fill will be $2m$ thick and has an average unit weight of $20$

$k\frac{N}{m}3.$ The water table is located at a depth of $0\mathrm{.}5m$ below the existing ground surface. The

unit weight of sand below and above the water level is $18k\frac{N}{m}3.$ The clay has an average unit

weight of $17k\frac{N}{m}3.$ Clay exhibits "ordinary" stress$-$strain behavior. Consolidation tests on

several samples present the results shown in Figure $1.$ The results of monotonic single shear

$($DSS$)$ tests performed on samples extracted at a depth of $6m$ are presented in Table $1.$ Note

that these tests were executed in samples that were extracted in a way that maintains minimal

disturbance.

a$.$ Use the results of the DSS tests to develop a relationship that describes the variation of

su with consolidation stress and history $($OCR$).$ Do not assume $m=0\mathrm{.}8,$ but plot the

resistances obtained with the OCR, and fit a curve with the appropriate relationship to

determine the value of $"m."$

b$.$ Estimate the undrained resistance for the soil at a depth of $6m$ : $($i$)$ before placement of

the fill, $($ii$)$ immediately after placement of the fill, and $($ii$)$ when the clay has completely

consolidated after the placement of the filling. Note: Consider the changes in effective

vertical stress for these three scenarios.

c$.$ Draw a $v-$In$(\{$:$p^{\text{'}})$ scheme showing the critical state line, the isotropic consolidation line,

and show the history of the three samples used in the DSS test. Show points

corresponding to: $($i$)$ in$-$situ conditions $($before sampling$),($ii$)$ the maximum

consolidation stress in the DSS test, $($iii$)$ after unloading before cutting in undrained

conditions, and $($iv$)$ at the time of DSS test failure.

Figure $1$: Soil profile, pre$-$consolidation stress, and current stress with depth.

Table $1$: Results of simple shear tests.