Rheological Model of DMFC Rockbolt and Rockmass in a Circular Tunnel

In this paper, the time evolutions of the mechanical characteristics of a discretely mechanically or frictionally coupled (DMFC) rockbolt and surrounding rockmass are studied. A conceptual model is developed to analyze the interaction between the DMFC rockbolt and rockmass, and analytical solutions are presented for a tunnel supported with DMFC rockbolts. The formulation is based on the following assumptions: (1) a deep tunnel with a circular cross-section; (2) an axisymmetric problem, i.e., having a lateral pressure coefficient K _a = 1; (3) homogeneous and isotropic ground; (4) small deformations; (5) rockbolts simulated as two cylindrical surfaces and oppositely distributed forces, i.e., one at the head and the other at the bolt bond; and (6) viscoelastic material assumptions, i.e., a one-dimensional viscoelastic model for the rockbolt and a three-dimensional viscoelastic model for the rockmass. The analytical solutions of the rheological model are obtained by assuming the constitutive models of the rockmass and rockbolt in terms of a Maxwell model and Maxwell model (M–M), Kelvin model and Kelvin model (K–K), and Kelvin model and Maxwell model (K–M). The analytical solutions of the M–M model are compared with the results obtained from numerical simulations with FLAC3D. The analytical solutions are in good agreement with the numerical results in the case of small rheological rock deformation and close bolt arrangement. Furthermore, the variation of the axial force along the rockbolt and the evolution of stress and displacement in the rockmass are closely related to the rheological parameters and support parameters.