A large vertical shaft is planned for an underground hard rock mine. Laboratory tests on core from exploration drilling show that

Co = 148.3, To = 10.6, E = 43.10GPa, G = 17.24GPa,

γ = 22.78kN/m3 while premining stress measurements can be fit to the formulas SE = 1,379 + 6.8h, SN = 4,138 + 20.4h, SV = 24.9h where E,N, V refer to compass coordinates (x = east, y = north, z = up), stress is in kPa, depth h is in m, and compression is positive.

Premining shear stresses are nil relative to compass coordinates. Find:

(a) the most preferable shape of shaft (elliptical, rectangular, or ovaloidal) when the cross section is 4.5 × 9.0 m and

(b) The resulting factors of safety with respect to compression and tension at a depth of 854 m.