For a slope stabilization project, if the undrained shear strength $(c_u)$ of the native soil

and the factor of safety $($FS$)$ against a rotational slide were estimated as $c_u=25$kPa and

$FS=0\mathrm{.}75,$ respectively, estimate the maximum spacing of the deep soil$-$lime mixing

columns with $50cm$ diameter to achieve a FS of $1\mathrm{.}3$ after mitigation if the shear strength

of the column is given as $200$kPa.

Hint: Estimate the composite undrained shear strength valid after the mitigation as a

function of the replacement ratio and native soil's and column's shear strength.