Coupling rheological model for end-anchored bolt and surrounding rock mass
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Graphical Abstract
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Abstract
A structural model for the coupling interaction of end-anchored rock bolt and rock mass is established by analyzing their long-term evolution mechanisms based on the following assumptions: (1) circular cross section; (2) deep tunnel; (3) ![]()
=1, i.e., axisymmetric problem; (4) homogeneous, isotropic and viscoelastic ground; (5) one-dimensional viscoelastic rock bolt; (6) the bolt forces are treated as two uniformly compressive distributed loads applied at both ends of the bolt. When the Maxwell model is chosen for describing the rheological behaviors of ground and rock bolt, the closed-form solutions are presented for a circular tunnel supported with end-anchored rock bolt. The analytical solutions are compared with the results obtained by the finite difference method through the secondary development of FLAC3D. The comparisons show that the analytical solutions provide reasonable results for the end-anchored rock bolt with low to moderate spacings. Under the same rock properties, tunnel geometry and construction and reinforcement characteristics, the analytical and numerical solutions of two tunnels are obtained respectively supported by the rock bolt with different viscosity coefficients. The research shows there is an eigenvalue for the viscosity coefficient of rock bolt with regard to the specific tunnel supported by end-anchored rock bolt. When the viscosity coefficient of rock bolt is larger than the eigenvalue, the axial force of bolt increases with the time, and the rock bolt will play an active part in engineering reinforcement continuously. When the distribution of rock bolts around the tunnel perimeter is linked to the far-field stresses and the material parameters are adapted to the ground, smaller convergence and reduced reinforcement stresses are possible. The proposed rheological model will be useful in predicting the time-dependent closure and the support load and in optimizing support design for tunnels.
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