A brown silty sand fill 5m thick was placed over a 15 m thick layer of compressible graysilty clay. Underlying the clay layer is impermeable rock. Assume for this problem thatthe settlement of the fill is small compared to the settlement of the silty clay layer.Properties of the over consolidated silty clay layer are;

Initial void ratio, eo = 1.1
Compression index, Cc = 0.36
Cr / Cc = 0.1
δꞌp/δꞌo =1.2
Saturated unit weight, γsat = 14.91 kN/m3
Coefficient of consolidation, cv = 0.858 m2/yr
Unit weight of silty sand fill, γsat = 19.62 kN/m3
The water table at the interface of the ground surface and fill.

Required
(a) Compute the consolidation settlement of the silty clay layer due to the weight of the 5m fill by taking the layer as a single layer (no sublayers).
(b) Compute the consolidation settlement of the silty clay layer due to the weight of the 5m fill by dividing the layer into five sub layers.
(c) Compute the time rate of settlement
(d) compute δꞌ(z) and plot δꞌ(z) when average degree of consolidation U = 70%
(e ) what are the values of (total) pore water pressures at the bottom and mid-depth of the silty clay layer after 20 years of the fill placement? [use the “exact” solution equation of the sine series for excess pore water pressures]