Geomechanics and Ground Control · Ground Control · 2 marks · Numerical answer
A circular tunnel of radius 3 m is in a hydrostatic field of 15 MPa. Rock E=5 GPa and ν=0.25. Find uniform boundary support pressure in MPa needed to limit radial displacement to 4 mm, to two decimals.
For the elastic circular-opening model, inward boundary displacement is u=a(1+ν)(p₀−pi)/E. Use consistent units: u=0.004 m, a=3 m and E=5000 MPa. Rearranging gives pi=15−0.004×5000/[3×1.25]=9.66667 MPa, or 9.67 MPa. Greater support pressure reduces the pressure difference causing convergence.
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