Consider a medium width vein (50 ft, 15.2 m) dipping 65? and mined by overhand mechanized cut

Question:

Consider a medium width vein (50 ft, 15.2 m) dipping 65? and mined by overhand mechanized cut and fill (MCF) with a level interval of 200 ft (61 m) as shown in the sketch.

(a) Derive a bolting formula algebraically for bolt safety factor assuming n bolts per hole using cable of capacity Tb (lbf, kN) force in ore (rock) having specific weight ? (pcf, kN/m3) while bolting on a square pattern with spacing S (ft, m).

(b) Layout a cable bolt pattern specifying bolt length, spacing, and angle using one 5/8-in., 25 ton (1.6 cm, 224kN) bolt per hole.