Problem $4.(35$ points$)$

The foundation soil is a horizontally layered $1$D sand$/$clay soil mixture and the water table is at $1\mathrm{.}0$ m from the surface. Note the following:

$(1)$ The site conditions are given in Fig. A$.1($Elevation$)$ and Fig. A$.2($Plan$)$;

$(2)$ Columns are $30$ cm in diameter and carry loads of $600$ kN and $900$ kN ;

$(3)$ The combined rectangular mat is: width $B=3m$ and the length, $L$ is to be determined; $(4)$ The point C is at the middle of the clay layer;

$(5)$ Only $1$D loading conditions are to be considered $($i$.$e$.$ No correction for $2$D$/3$D loading is necessary$).$