Consider a narrow vein overhand stope using cut and fill, as shown in the sketch. Cemented, hydraulic sand fill of modulus Ef is placed in the stope as mining proceeds up dip in a rock mass of modulus Er.?

(a) Develop a formula for crown pillar safety factor assuming uniform closure across the vein, whether across fill, open area, or un-mined ore.?

(b) If the vein is vertical, vein width is 4.6 m, level and raise intervals are 53.3 m, stope strike length is 53.3 m, Ef = 172 MPa, Er = 689 MPa, rock compressive strength is given by a size effects formula C_p = C_1?(0.78+0.22Hp/Wp)?and C₁ = 193 MPa; fill cohesion and angle of internal friction are 2.07 MPa and 35?, respectively, then determine pillar width measured down dip when failure impends. Note: the premining vertical stress in kPa 24.4d where d is depth in meters; the horizontal premining stresses are equal and equal to twice the vertical premining stress.

Fill Ore Crown Pillar Lo Ore Fill Sill Pillar Width Width (a) Overhand advance (b) Underhand advance