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 15 ft, level and raise intervals are 175 ft, stope strike length is 175 ft, Ef = 25ksi, Er = 1,000ksi, rock compressive strength is given by a size effects formula C_p = C₁ (0.78+0.22Hp/Wp)?and C₁ = 28,000 psi; fill cohesion and angle of internal friction are 300 psi and 35?, respectively, then determine pillar width measured down dip when failure impends. Note: the premining vertical stress in psi is 1.1d?where d?is depth in ft; the horizontal premining stresses are equal and equal to twice the vertical premining stress.

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Time (min) 4.22 1.90 7.22 11.4 0.0 11.4 Head (in.) 36.0 30.0 24.0 12.0 18.0 30.5 91.4 76.2 61.0 45.7 (cm) Note The standpipe inside diameter is 0.5 in. (1.27 cm).