A ground reaction curve (GRC) of a 3 m radius unlined circular tunnel is shown in the figure. The tunnel is supported by 300 mm thick shotcrete lining. The uniaxial compressive strength (\( \sigma_c \)), modulus of elasticity (\( E_c \)) and Poisson’s ratio (\( \nu \)) of shotcrete material are 20 MPa, 15 GPa, and 0.25 respectively. The maximum capacity (\( p_{{max}} \)) of the lining and its stiffness (\( k \)) are given as: \[ p_{{max}} = \frac{1}{2} \sigma_c \left( 1 - \frac{(a - t)^2}{a^2} \right) \] \[ k = \frac{E_c (a^2 - (a - t)^2)}{(1 + \nu)\left[(1 - \nu) a^2 + (a - t)^2\right]} \] where \( a \) = radius of the unlined tunnel and \( t \) = thickness of the lining. If the lining is constructed after 5 mm radial deformation, the support reaction is best represented by the line shown in the figure.
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When dealing with ground reaction curves (GRC), the support pressure and radial deformation are key factors. Identifying the correct line requires understanding the deformation at which the tunnel lining is applied.
Step 1: Understand the ground reaction curve (GRC).
The GRC typically shows the relationship between radial deformation and support pressure. For a tunnel with shotcrete lining, the support reaction depends on the radial deformation and the stiffness of the lining. Step 2: Identify the deformation at which the lining is constructed.
The problem specifies that the lining is constructed after a radial deformation of 5 mm. This means we need to look for the point on the GRC that corresponds to 5 mm of deformation. Step 3: Analyze the graph.
In the graph provided, the curve corresponding to the 5 mm deformation is best represented by the line labeled \( R \). Step 4: Conclusion.
Thus, the support reaction for a 5 mm radial deformation is best represented by line \( R \). Answer: The correct option is \( \boxed{R} \).
