Suppose that entries and crosscuts are 45 ft wide and that pillars are square and 45 ft wide, as in Problem 6.3. Laboratory properties are the same as in Problem 6.1; depth and specific weight of overburden are also the same as in Problem 6.1. In addition, a joint set is present in the mine. Joint set dip is 68◦; dip direction is 54◦ clockwise from North.

(a) Find the joint shear strength necessary to just prevent joint slip within a typical pillar.

(b) If the joint is cohesion less and obeys a Mohr–Coulomb slip criterion, what joint friction angle is needed to just prevent slip?

(c) If the joint is frictionless, what cohesion is necessary?