(Solution) - An in situ stress field between 3 000 ft and 3 500 ft is fit -(2025 Original AI-Free Solution)

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An in situ stress field between 3,000 ft and 3,500 ft is fit to the formulas ?v = 1.125h, ?H = 3,500 + 0.33h, ?h = 3,500 + 0.33h where the stresses are in psi and the depth h is in ft. Stresses ?v, ?H, ?h 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, ? = 0.20, ? = 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.