CVE $362$ Soil Mechanics HOMEWORK $2$

Problem $1.$

A clayey specimen is subjected to loading and unloading along the path $ABCDEF.$ The Compression Index $($Cc$)$ and Recompression Index $($Cs$)$ are provided below. The initial void ratio at point $A$ is given as $e_A($value provided below$).$ Calculate the void ratios at points B$,$ C$,$ D$,$ E$,$ and F $($the effective stress for each point is provided below$).$ Assume that the effective stress at point $B$ corresponds to the overconsolidation stress. Present the calculated void ratios in both tabular and graphical form $($plot the graph of $e-log({}^{\text{'}})).$

${}_A^{\text{'}}=,55\mathrm{.}0K\frac{N}{m^2}{}_B^{\text{'}}=,K\frac{N}{m^2}{}_{C^{\text{'}}}=200\mathrm{.}0K\frac{N}{m^2}{}_D^{\text{'}}=,84\mathrm{.}0K\frac{N}{m^2}$

${}_E^{\text{'}}={132\mathrm{.}0}_K\frac{N}{m^2},{}_F^{\text{'}}={242\mathrm{.}0}_K\frac{N}{m^2},C_c=,C_s={0\mathrm{.}028}_{?}$

$e_A=1\mathrm{.}03$

Problem $2.$

An embankment for a road, with a thickness of $H_{em},$ is to be constructed over an existing soil layer with a thickness of H $.$ To accelerate the consolidation process and reduce settlement during the road's use, a preloading soil layer is added and will be removed once the consolidation process is complete $($see Figure $1).$ Calculate the settlement of the clay layer before and after the removal of the preloading soil layer. Laboratory consolidation tests were performed on a specimen collected from the middle of the clay layer, and the results are provided in Figure $2.$

Figure $1$

${}_A^{\text{'}}=,40\mathrm{.}0K\frac{N}{m^2},e_A=,1mn$

${}_B^{\text{'}}=,82\mathrm{.}0K\frac{N}{m^2},e_B=0\mathrm{.}975$

${}_C^{\text{'}}=,265\mathrm{.}0K\frac{N}{m^2}{e}_C=$