Geomechanics and Ground Control · Geomechanics · 2 marks · Numerical answer
A circular tunnel is 100 m deep under rock of unit weight 27 kN/m³. Tangential stress at horizontal boundary A is 5 MPa. Find tangential stress at crown B in MPa, to two decimals.
Far-field vertical stress is 2.7 MPa. Kirsch’s horizontal-boundary relation gives 5=3σv−σh, so σh=3.1 MPa. At the crown, the tangential stress is 3σh−σv=9.3−2.7=6.6 MPa. Assume a circular unsupported opening in elastic ground with the shown principal-stress orientation.
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