Geomechanics and Ground Control · Ground Control · 2 marks · Multiple choice
A circular tunnel of radius a=3 m receives t=0.3 m shotcrete after5 mm radial convergence. Shotcrete has σc=20 MPa,Ec=15 GPa,ν=0.25. Its capacity is $p_{max}=\sigma_c[1-(a-t)^2/a^2]/2$. Its stiffness is $$k=\frac{E_c[a^2-(a-t)^2]}{(1+\nu)[(1-2\nu)a^2+(a-t)^2]}.$$ Which support-reaction line fits?
Capacity is10[1−(2.7/3)²]=1.9 MPa. Stiffness k≈1740.46 MPa relates support pressure to relative convergence u/a, so slope versus u is k/a≈0.580 MPa/mm. Starting at u=5 mm, capacity is reached near8.28 mm. That slope and endpoint match Q, B, rather than the steeper P or shallower R,S.
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