Evaluate the active vertical and horizontal stress if a disc core of $5\mathrm{.}6$ cm diameter taken at a depth of $900$ m in an Indian limestone$.$ The triaxial test done on a sample of the same rock resulted in a failure load of $2000$ kg$.$ The unit weight of rock $=2475$ kg m$-3$ and the poison$$s ratio is $0\mathrm{.}41.$ The governing insitu horizontal stress relation is given by $220+2$S$0$ where S$0$ is the stress.