Geomechanics and Ground Control · Geomechanics · 2 marks · Numerical answer
The circular tunnel shown has vertical far-field stress σ₀ and horizontal stress kσ₀. Boundary point A is on the horizontal radius; B is 45° above it. The tangential-stress ratio σθ(A)/σθ(B) is 2. Find k, to two decimals.
At the horizontal boundary, Kirsch’s relation gives σθ(A)=(3−k)σ₀. At 45°, the cos2θ term vanishes, giving σθ(B)=(1+k)σ₀. Hence (3−k)/(1+k)=2. Solve 3−k=2+2k to obtain k=1/3≈0.33. B is at 45°, not at the crown.
More Geomechanics questions
GATE 2023 MN Q50– Waves travel through the 100 mm long elastic isotropic cylindrical rock specimen from…
GATE 2023 MN Q51– A 100 mm high rock specimen with one horizontal joint is loaded vertically at 20 MPa as…
GATE 2023 MN Q53– A rock sample of mass 60 g displaces 27 g of brine. Brine specific gravity is 1.05. Find…
GATE 2022 MN Q32– Water seeps through a vertical sand column of area 4000 mm² and length 300 mm. Applied…
GATE 2022 MN Q40– A 50 mm diameter rock sample fails under 120 kN uniaxial compression on a plane inclined…
GATE 2021 MN Q30– A coal sample has moisture content 8.0% and bulk unit weight 15.6 kN/m³. Find dry unit…
