Question $340$ marks

It is proposed to construct a $3$ m square pad foundation to support a $\backslash (1,350\backslash$mathrm$\{$kN$\}\backslash )$ column load at a depth of $1$ m below ground. The ground investigation consisted of Shell $\backslash$& Auger boreholes with in$-$situ Standard Penetration Tests $($SPT$\text{'}$s$)$ and Plate Bearing Tests at formation level.

The following information was gathered from the ground investigation:

$-\backslash (0-5\backslash$mathrm$\{$~m$\}\backslash )$ : Medium dense glaciofluvial gravelly SAND

$-$ Average SPT N$-$value $\backslash (=31\backslash ).$

$-$ Poisson's ratio $\backslash (=0\mathrm{.}25\backslash )$

$-\backslash (5\backslash$mathrm$\{$~m$\}-20\backslash$mathrm$\{$~m$\}\backslash )$ : Strong Granite bedrock

$-$ The results of a plate$-$bearing test using a $0\mathrm{.}760$ m diameter plate conducted at formation level are given on the Table and graph below.

$($a$)$ Given the ground investigation information above estimate the likely settlement of the proposed foundation using two different approaches $24$ marks

$($b$)$ It has been proposed to increase the loadings of some of the columns within the structure by $\backslash (50\backslash \%\backslash )$ while retaining the foundation size. Briefly outline the comments you would make to a structural engineer regarding this proposal with respect to the following:

$-$ Total settlement. $4$ marks

$-$ Differential settlement. $4$ marks

$-$ Settlement vs$.$ time. $8$ marks

Note: Negative values indicate plate movement downward