Problem $1$:

Consider the data below in Fig. $8\mathrm{.}17($b$)$ of Holtz and Kovacs $(1981)($also shown in Figure $8\mathrm{.}22$ in Holtz, Kovacs and Sheahan, $2011)$ showing an interpreted profile of preconsolidation stress. Estimate the over$-$consolidation ratio at depths of about $\backslash (2\backslash$mathrm$\{$~m$\},6\backslash$mathrm$\{$~m$\}\backslash ),$ and $15$ m $.$ An areal fill of sand $($total unit weight is $\backslash (18\backslash$mathrm$\{$kN$\}/\backslash$mathrm$\{$m$\}^\{3\}\backslash ))$ is to be placed at this site in $0\mathrm{.}5$ m lifts; how many lifts of the fill can be placed before any of the clay layers would be expected to exhibit virgin compression?

Fig. $8\mathrm{.}17$ Overburden and preconsolidation stress profiles for Lake Champlain deposits $($Laurentian or Leda clays$)$ of Eastern Canada: $($a$)$ Saint$-$Alban, Qu$$bec$,$ test fills $($after Leroueil, et al$.,1978$a$)$; $($b$)$ C$.$ F$.$ S$.$ Gloucester test $($after Bozozuk and Leonards, $1972).$