An in situ stress field between 3,000 ft and 3,500 ft is fit to the formulas v

An in situ stress field between 3,000 ft and 3,500 ft is fit to the formulas σv = 1.125h, σH = 3,500 + 0.33h, σh = 3,500 + 0.33h where the stresses are in psi and the depth h is in ft. Stresses σv, σH, σh are principal stresses in the vertical and horizontal directions. The weakest rock along the proposed shaft route has an unconfined compressive strength of 8,000 psi and a tensile strength of 750 psi. A circular, concrete liner is planned below 3,500 ft for a shaft with an outside diameter of 18 ft. If the liner is one foot thick and the concrete properties are: E = 5.0 million psi, ν = 0.20, γ = 156pcf, Co = 4,500 psi and To = 450 psi, determine what uniform radial stress would just cause the liner to fail, assuming the concrete follows a Mohr–Coulomb criterion.