Question: A rectangular shaft 3 m wide by 6 m long is sunk vertically in ground where the state of premining stress is xx =

A rectangular shaft 3 m wide by 6 m long is sunk vertically in ground where the state of premining stress is σ_xx = 7.9, σ_yy = 14.2, σ_zz = 11.0, τ_xy = 1.5, τ_yz = 0, τ_zx = 0, with compression positive, x=east, y=north, and z =up, in MPa. Rock properties are: E = 31.0GPa, v = 0.20, C_o = 10³ MPa, T_o = 6.2 MPa. Find

(a) The most favorable orientation of the shaft and

(b) The safety factors in this orientation. Indicate by sketch where the peak stresses occur in cross section.

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