A multilevel room and pillar metal mine is under consideration in flat strata striking N60E. Entries are planned on strike, crosscuts up, and down dip. Table 6.6 shows depths and material properties associated with the geologic column. Rock properties data were determined from laboratory testing on NX-core at an L/D ratio of two. Stress measurements indicate that the premining stresses relative to compass coordinates are: Sv = 1.1d, Sh = 300 + 0.3d, SH = 500 + 0.5d, where v = vertical, h = azimuth is 150?, H =azimuth is 60?, d =depth in ft, and stress units are psi. Three joint sets are present. Set 1 is vertical and strikes parallel to the strata. Set 2 strikes due north and dips 30? east; Set 3 also strikes due north, but dips 65? west. Joint properties for Mohr?Coulomb failure criteria are given in Table 6.7. Joint normal and shear stiffness (Kn, Ks) that relate normal stress and shear stress to corresponding displacements are also given in Table 6.7 as are the joint spacing?s (S). One mining plan calls for mining a lower B level 102 thick in high and low grade ore at a depth of 950 ft and an upper A level of high grade ore 18 ft thick at a depth of 921 ft.

(a) Assume there is no size effect on compressive strength, then determine the maximum possible extraction ratio based on ore strength (ignore joints).

(b) Assuming square pillars, show in plan and vertical section, the relationship between rooms and pillars in the two levels that would be dictated by rock mechanics and explain your recommendation.

(c) What safety factor would you recommend for pillars in the upper and lower mining horizons and why?

Depth = 950 ft Il ft Fabe Davis 14 ft Low grade Details of the gecloge column. Noce the depth to the bottom of the False Davis 43 ft High grade 25 ft Low grade 20 ft High grade Bonneterre dolomite Table 6.6 Rock properties, strata depths, and thickness El10 Cof 10) psi To( i02) psi Depth ft (thickness) psi psi 0 (60) 130.0 0.003 0.30 0.10 0.05 0.34 11.74 25.17 60 (50) 163.2 6.92 1191 49.0 1 10 (195) 167.2 10.65 0.31 16.12 7.34 27.33 53.1 305 (350) 170.8 12.09 0.26 26.87 12.28 32.67 59.2 162.5 655 (I 10) 7.58 0.32 23.76 12.85 34.30 51.5 12.05 765 (1 50) 161.3 5.35 0.21 19.61 37.67 49.3 166.3 915 (6) 6.75 0.31 29.26 9.35 43.67 49.0 Ore 10.07 921 (18) 218.7 8.75 0.30 18.27 18.50 60.4 3.79 5.21 939 (11) 152.0 0.22 7.30 6.80 36.0 950 (102) Ore 218.7 8.75 0.30 18.27 10.07 18.50 60.4 166.3 43.67 1,052 (163) 6.75 0.31 29.26 9.35 49.0 041 1215 (330) 12 146.2 3.94 11.24 7.90 31.00 42.3 13 167.2 10.65 0.31 16.12 7.34 27.33 53.1 1.545 (100) Table 6.7 Joint properties Property joint set c psi po Kn 10psilin. K, 100psilin. S t Set I Set 2 Set 3 0.0 35 10.0 30 20.0 25 1.76 2.31 3.29 0.56 3.14 0.92 25.3 4.7 6.1 3.