Geomechanics and Ground Control · Geomechanics · 2 marks · Numerical answer
A rock obeys Mohr–Coulomb τ=7.5+0.84σn in MPa. In triaxial failure with confinement 5 MPa, find shear stress on the failure plane in MPa, to two decimals.
The envelope gives cohesion c = 7.5 MPa and friction angle φ = arctan(0.84). Let R be the Mohr-circle radius; its centre is C = σ₃+R. Tangency to the failure envelope requires R = c cosφ + C sinφ. Therefore R = (c cosφ+5 sinφ)/(1−sinφ). The shear coordinate of tangency is τ = R cosφ = 19.2253 MPa, or 19.23 MPa. The confining pressure is not the normal stress on the inclined failure plane.
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