Problem $2[15$ Points$]$

Consider the soil pro$$le shown in Figure H$7-2.$ Each soil layer is homogeneous. The groundwater table is at the ground surface. Piezometers a$,$ b$,$ and c are installed at interfaces between layers as shown in Figure H$7-2.$ The measured elevation of $$uid in each piezometer, relative to its tip, is also shown. The datum is located at the elevation of point c$.$

The saturated unit weight for the upper sand layer, the soft clay, and the stiff clay are $20\mathrm{.}5,16\mathrm{.}8,$ and $18\mathrm{.}5$ kN$/$m$3,$ respectively.

$($a$)$ Determine the elevation head, pressure head, and total head at points a$,$ b$,$ and c$.[3$pts$]$

$($b$)$ Determine the vertical total stress, pore $$uid pressure, and vertical effective stress at points a$,$ b$,$ and c$.[3$ pts$]$

$($c$)$ Determine the ratio between the coef$$cient of permeability for the soft clay and the stiff clay,

i$.$e$.,$ ksoft$/$kstiff$.[3$ pts$]$

$($d$)$ Finally, assume that the location of the groundwater table drops to the elevation of point a$.$ Assume that all the unit weights remain unchanged and neglect capillary rise in the upper sand layer and the height of water in piezometer a drop to zero, and that in piezometer c remains at $18$ m$.$ The reading of piezometer b is deemed unreliable. Determine the vertical total stress, pore $$uid pressure, and vertical effective stress at points a$,$ b$,$ and c for the new location of the groundwater table. $[6$ pts$]$