Circular Vertical Shaft Is Planned To Have Finished

A circular vertical shaft is planned to have a finished, inside diameter of 26 ft in an underground hard rock mine. Rock properties are: Co = 27,400 psi, To = 1,840 psi, E = 6.19(106 psi), ν = 0.22, γ = 159pcf. The premining stress state relative to compass coordinates is: SE = 600 + 0.3h, SN = 200 + 0.4h, SV = 1.12h, where E, N, V refer to compass coordinates (x=east, y = north, z = up), h is depth in ft, stress is in psi, and compression is positive. Premining shear stresses are nil relative to compass coordinates. Properties of concrete are: Compressive strength = 5,500 psi, tensile strength = 550 psi, Young’s modulus = 5.5(106) psi, Poisson’s ratio = 0.25. Find: The concrete liner thickness in the vicinity of a water bearing cavernous dolomite where the pressure in the undisturbed ground is 210 psi. Note: The maximum allowable compression in the concrete is 3,500 psi.

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