A pillar in a hard rock, strata-bound, room, and pillar mine is transected by a small fault that dips 75? due east and strikes due north. The ore horizon dips due west 15? and also strikes due north. Depth to the pillar of interest is 1,230 ft (375 m). Overburden specific weight averages 158pcf (25.0kN/m3). Rock and joint properties are given in Table 6.3. The preexcavation stress is caused by gravity alone; the horizontal stress is estimated to be one-fourth the vertical stress before mining. Determine:

(a) The premining stress acting normal to the ore horizon and the shear stress acting parallel to the ore horizon at the depth of interest;

(b) The post mining pillar normal and shear stresses acting on the pillar;

(c) The maximum safe extraction ratio consistent with a pillar safety factor of 1.5 (ignores any size effect and neglect the joint);

(d) Joint shear strength needed for a safety factor of 1.5.

Property material Co psi (MPa) To psi (MPa) c psi (MPa) () Rock Joint 15,000(103) 1,500(10.3) 20 (0.14) 28