A rectangular foundation, $10\backslash$times $2$ m$2,$ is to carry a total uniform pressure of $400$ kPa and is to be founded at a depth of $1$ m below the surface of a saturated sand of considerable thickness. The bulk unit weight of the sand is $18$ kN$/$m$3$ and standard penetration tests carried out below the water table indicate that the deposit has an average N value of $15.$If the water table occurs at the proposed foundation depth, determine a value for the settlement of the centre of the foundation. $($Use De Beer and Martens$$ method.$)$