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EXAMPLE <br />1) Desired pillar size - 100' X 100' <br />2) Desired center to center entry dimensions - 120' X 120' <br />3) Maximum overburden depth - 1200' <br />• Assumptions: <br />p = pillar width = 100' <br />1 = pillar lenyth = 100' <br />m = mining height = 13' <br />H = overburden depth = 1200' <br />X = density of overburden = 1.1 psi/ft. depth = 158 lb/ft3 <br />~ = anyle of internal friction = 40° <br />Tan 6=1+Sin~ <br />1 - Sin ~ <br />Cohesion = Uniaxial Strength (after Abel) <br />2 Tan B <br />T,A.L. = tributary area load (maximum load to be carried by one pillar) <br />_ (p + 20)(1 + 20) (~ )(H) <br />2000 <br />00 =compression strength (psi) at pillar ribside or cohesion strenyth <br />• = 600 ps i <br />off =horizontal pressure (psi) <br />_ [6.944 X 10'3 (X )(H)] <br />o„ =maximum stable vertical pillar stress (psi) <br />_ (oH Ta n B + oo ) <br />Y = distance into pillar at location of maximum stable pillar stress (ft .), <br />or to edge of confined core <br />= m In o„ <br />Tan B (Tan B-1) o0 <br />L = load carrying capacity of pillars (after Abel) <br />= 7,2 X lU-2 ov [Pl - PY - lY + 4 Y2)] <br />3 <br />(for rectangular pillars where 2 Y <P) <br />= 7.2 X lU-2 Oy [P2 - 2 PY + 4 Y2] <br />3 <br />• (for square pillars where 2Y <P) <br />Safety Factor = L <br />T.A.L. <br />