Problem $3-$ A very practical problem.

When working in urban environments, such as New York Metro, the most available building sites will be the sites of a former buildings or other developments in the past. Here, a site of a former material yard is being redeveloped into single level condominium and duplex housing, so the bearing pressure is low.

A sand layer is known to have been placed in the late $1800\text{'}$s to early $1900\text{'}$s to elevate the ground surface to above the clay surface and groundwater table. However, the method of fill placement is not known, and given that it was placed in the $1900\text{'}$s$,$ it is likely that any compaction was minimal. The subsurface investigation found that the spatial variation of average minimum N $-$values over the fill is between $10$ and $35b\frac{l}{f}t.$

We can assume that all consolidation resulting from placement of the sand is complete because the consolidating layer is relatively thin, the sand was placed many years ago, and the CL layer is doubly drained.

a$.$ Estimate the ultimate consolidation settlement $(S_c)$ on the centerline of the footings. The bearing pressure is $2,000psf(1$ tsf $)$ for all footings. Assume that the stress increase from one footing does not influence its neighbors because the footings are far apart $(4$B$).$

Sublayers are not needed for a thin consolidating layer. Immediate settlement $(S_i)$ is not an issue because the footings are resting on the sand layer.

b$.$ What is the range of total settlement, accounting for the SW layer compression?

c$.$ What is the potential maximum differential settlement and angular distortion between footings? If the structures are wood frame with flexible siding $($no brick or block$),$ is the potential settlement tolerable? The criterion for $\frac{}{l}$ is $0\mathrm{.}008$ or less.

d$.$ How long does it take after end of construction for consolidation of the CL layer to reach Uave $=90\%?$

e$.$ Is total and$/$or differential settlement a problem to be mitigated? Why or why nots?

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Plan view