Thin overburden is scrapped to expose fresh bedrock at the site of a planned shaft. A 0-45-90 strain gauge rosette is bonded to the bedrock after a five inch square portion of the surface is ground smooth. The 0-gauge is oriented N30E. A 6-inch diameter coring bit is then used to relieve the in situ strains by over coring the gauge. Final readings after over coring are: ε(0) = 1,000 μ in./in., ε(45) = 500 μ in./in., ε(90) = 3,000μin./in. where the strain meter reads tension as positive.

(a) If Young’s modulus is 2.4 million psi and Poisson’s ratio is 0.20, what is the state of strain and the state of stress at the gauge site relative to compass coordinates?

(b) What is the best orientation of a 10 × 20 ft rectangular shaft at this site?

(c) What unconfined compressive and tensile strengths (Co, To) are needed to ensure safety factors of 2 and 4 in compression and tension, respectively?