$-$ Problem $4$

Figure $4$ shows the soil profile at the Cherry Island landfill in Delaware. This profile consists of the following soil layers $\backslash (\{\}^\{1\}\backslash )$ :

Figure $4$: Soll prohle at Unerry Island Iandfill site in Delaware.

$-$ Dredge$/$Alluvium: The dredge consists primarily of sandy silty clay to clayey silt. The alluvium is comprised of clayey silts and silty clays with varying amounts of sand, organic matter silty sands. The saturated unit weight of the dredge$/$alluvium is $\backslash (97\mathrm{.}0\backslash$mathrm$\{$lb$\}/\backslash$mathrm$\{$ft$\}^\{3\}\backslash ).$

$-$ Columbia Formation: The Columbia Formation is comprised of poorly sorted, fine$-$tocoarse sand and gravel with silty sand, silty clay and clayey silt lenses of varying thickness. The saturated unit weight of the Columbia Formation is $\backslash (125\mathrm{.}0\backslash$mathrm$\{$lb$\}/\backslash$mathrm$\{$ft$\}^\{3\}\backslash ).$

$-$ Potomac Formation: The Potomac Formation consists of brownish red, stiff to hard, moderately to heavily overconsolidated, clayey silt to silty clay, with traces of fine sand. The saturated unit weight of the Potomac Formation is $\backslash (120\mathrm{.}0\backslash$mathrm$\{$lb$\}/\backslash$mathrm$\{$ft$\}^\{3\}\backslash ).$

Also present at the site is a layer of municipal waste that is roughly $220$ feet thick. The saturated unit weight of the municipal waste is estimated to be $\backslash (72\mathrm{.}3\backslash$mathrm$\{$lb$\}/\backslash$mathrm$\{$ft$\}^\{3\}\backslash ).$ Above the groundwater table, the moist unit weight of the municipal waste is estimated to be $\backslash (57\mathrm{.}3\backslash$mathrm$\{$lb$\}/\backslash$mathrm$\{$ft$\}^\{3\}\backslash ).$ Neglect any capillary rise in the municipal waste.

Determine the vertical total stress, pore pressure and vertical effective stress at the middepths of the three soil layers; i$.$e$.,$ at depths $\backslash (($z$)\backslash )$ of $\backslash (45\mathrm{.}0\backslash$mathrm$\{$ft$\},106\mathrm{.}5\backslash$mathrm$\{$ft$\}\backslash )$ and $181\mathrm{.}5$ ft $.$

$\backslash (\{\}^\{1\}\backslash )$ Report from Geosyntac Consultants to Delaware Solid Waste Authority, $2021.$

$-$ Problem $4$

At the site of the Cherry Island landfill, the soil profile at the Delaware River is shown in Figure $5.$ The saturated unit weight of the river sediments is $\backslash (95\mathrm{.}0\backslash$mathrm$\{$lb$\}/\backslash$mathrm$\{$ft$\}^\{3\}\backslash ).$ The saturated unit weights for the Columbia and Potomac formations are again $125\mathrm{.}0$ and $\backslash (120\mathrm{.}0\backslash$mathrm$\{$lb$\}/\backslash$mathrm$\{$ft$\}^\{3\}\backslash ),$ respectively.

Figure $5$: Soil profile at Cherry Island landfill site in Delaware.

a$)$ Assuming the groundwater table to be at the ground surface, determine the vertical total stress, pore pressure and vertical effective stress at the mid$-$depths of the three soil layers; i$.$e$.,$ at depths $\backslash (($z$)\backslash )$ of $\backslash (30\mathrm{.}0\backslash$mathrm$\{$ft$\},76\mathrm{.}5\backslash$mathrm$\{$ft$\}\backslash )$ and $151\mathrm{.}5$ ft $.$

b$)$ Repeat part $($a$)$ assuming that sea level rise causes the groundwater table to rise one $(1)$ foot above the ground surface. Note that buoyant unit weights will be present in the expressions for effective stress for all three soil layers.