A room and pillar coal mine is contemplated at a depth of 533 m in strata striking

Question:

A room and pillar coal mine is contemplated at a depth of 533 m in strata striking due north and dipping 18? east. Entries are driven on strike, crosscuts up, and down dip. Mining height is 4.6 m measured from the floor; 0.5 m of low grade coal is left in the roof. Three joint sets are present. Set 1 is vertical and strikes east?west. Set 2 strikes due north and dips 60? east; Set 3 also strikes due north, but dips 35? west. The average overburden specific weight is 24.7kN/m³. Stress measurements indicate that the premining stresses relative to compass coordinates are: Sv = 23.8d, Sh = 4, 138 + 5.66d, SH = 345 + 17.0d, where v=vertical, h = east, H = north, d = depth in m, and stress units are kPa. Rock properties near the mining horizon are given in Table 6.10. These data were determined from laboratory testing on NX-core (5.4 cm diameter) at an L/D ratio of two. Joint properties for Mohr?Coulomb failure criteria are given in Table 6.11. Joint normal and shear stiffness (Kn, Ks) that relate normal stress and shear stress to corresponding displacements are also given in Table 6.11 as are the joint spacing?s (S). What extraction ratio is possible with no size effect on pillar strength and no joints present when a safety factor with respect to maximum shear stress of 1.75 is required? What is the maximum possible extraction ratio comment?