$12\mathrm{.}20$ Foundation engineers are often challenged by the ex$-$

istence of soft compressible soils at the construction

site. Figure $12\mathrm{.}44$ shows a soil profile with a silty sand

$(=17k\frac{N}{m^3}$;${}_{\text{r}\text{a}\text{t}}=19\mathrm{.}2k\frac{N}{m^3})$ underlain by high

plasticity clay $({}_{\text{s}\text{a}\text{x}}=18\mathrm{.}8k\frac{N}{m^3})$ and a peat layer

$({}_{\text{s}\text{a}\text{t}}=15k\frac{N}{m^3}),$ followed by dense sand. To expedite

consolidation and minimize future settlement, an additional

$1\mathrm{.}75m$ thick fill material, compacted to a unit weight of

$20\mathrm{.}1k\frac{N}{m^3},$ will be placed on top of the silty sand layer. The

plan area of the fill is $8m8m.$ The fill load will be left

in place for $18$ months, after which construction will begin

with the fill becoming part of the permanent foundation.

Undisturbed samples collected from the clay and organic

layers had the following properties.

a$.$ Estimate the total consolidation settlement under the ac$-$

tion of the fill load. Consider both the clay and peat layers

to be normally consolidated.

b$.$ Estimate the time for $99\%$ primary consolidation in each

layer. Are the layers singly or doubly drained? Explain.

c$.$ Estimate the secondary compression in each layer at the

end of $18$ months.

d$.$ What will be the total settlement at the end of $18$ months?

e$.$ What is the remaining excess pore water pressure at point

A two months after the application of the fill load?

f$.$ Determine the effective stress at point A two months after

the application of the fill load.

g$.$ A piezometer was installed at point $A$ to monitor the pore

water pressure. What should be the piezometer reading

$(u_{\text{p}\text{i}\text{e}\text{s}\text{o}\text{m}\text{e}\text{t}\text{e}\text{r}})$ two months after the fill load was applied?