Coal mine entries are driven 20 ft (6.1 m) wide on strike at a depth of 1200 ft (366 m) in a coal seem that dips 15◦. Crosscuts are driven up and down dip and are also 20 ft (6.1 m) wide. The...

Coal mine entries are driven 20 ft (6.1 m) wide on strike at a depth of 1200 ft (366 m) in a coal seem that dips 15◦. Crosscuts are driven up and down dip and are also 20 ft (6.1 m) wide. The production pillars that are formed are twice as long in the strike direction as they are in the dip direction. Compressive strength of coal is estimated to be 2,000 psi (13.8 MPa); tensile strength is estimated at 350 psi (2.41 MPa). The premining stress state is considered to be attributable to gravity only, so the vertical stress is unit weight times depth and the horizontal stress is one-fourth the vertical stress. Assume that a Mohr–Coulomb failure criterion applies and that a safety factor with respect to compressive strength of 1.5 is required. Find the extraction ratio possible under these conditions, and then estimate the pillar safety factor with respect to shear strength. Neglect any size effect that may exist.