A circular vertical shaft is planned to have a finished, inside diameter of 5.8 m in an underground hard rock mine. Rock properties are: Co = 163.5 MPa, To = 10.21 MPa, E = 36.48GPa, ν = 0.27, γ = 25.63kN/m3. The premining stress state relative to compass coordinates is: SE = 2,414 + 4.53h, SN = 2,897 + 7.92h, SV = 25.34h, where stresses are in kPa, h=depth in m, E, N, V refer to compass coordinates (x = east, y = north, z = up) and compression is positive. Premining shear stresses are nil relative to compass coordinates. Properties of concrete are: Compressive strength=39.6 MPa, tensile strength = 2.93 MPa, Young’s modulus = 32.76GPa, Poisson’s ratio = 0.25. Find:
(a) The unlined shaft wall safety factors in tension and compression at a depth of 1,295 m,
(b) Concrete liner thickness in the vicinity of a water-bearing formation where the pressure in the undisturbed ground is 0.621 MPa. The maximum allowable compression in the concrete is 24.14 MPa.