A block–particle–bar coupled algorithm to simulate tunnel excavation and support

During tunnel excavation, the stress of the surrounding rock is redistributed, leading to a local stress concentration around the tunnel. In addition, blasting excavation and other factors lead to a strength reduction of rock mass around the tunnel and eventually form a relaxation fracture zone (loosening zone). If supporting measures are not adopted in time during tunnel excavation, the rock strength in the loosening zone will be further reduced and eventually lead to overall instability and collapse. To simulate the bolt/cable supporting effect on the loosening zone and surrounding intact rock, a block–particle–bar coupling algorithm based on penalty springs is proposed. This coupling algorithm is based on the continuum–discontinuum element method (CDEM). CDEM is a dynamic, explicit solution algorithm based on a generalized Lagrange system. A strict controlling equation is established by the Lagrange energy system, and an explicit iterative solution of the dynamic relaxation method is used to realize a unified description of continuous and discontinuous media. The progressive failure of a solid is analyzed through the fracture of the bond between the blocks or particles. Using CDEM, the entire process of the solid from continuous deformation to fracture and movement can be simulated. In the block–particle–bar coupled algorithm, discrete particle clusters are adopted to represent the broken rock mass inside the loosening zone around the tunnel, block elements are used to represent the intact rock mass outside the loosening region, and bar elements are introduced to describe the supporting structures, such as bolts and cables. A contact coupling mode is adopted between particles and blocks, one normal spring and two tangential springs are constructed, and brittle Mohr–Coulomb fracture constitutive law and tensile fracture constitutive law are introduced to represent contact behavior. To realize the transmission of force and displacement, the interpolation coupling approach is adopted between the elements of bars and the elements of discrete particles or blocks. In this coupling mode, penalty springs S_gn and S_gs along and perpendicular to the axis of the bar, respectively, are established. S_gn and S_gs are mainly used to describe the pulling and pushing effect and the lateral compression effect between the bar and the surrounding rock, respectively. The coupling algorithm described in this paper is adopted to simulate the elastic field of a circular shield tunnel, rectangular tunnel reinforced by prestressed rock bolts, reinforcement of full-anchored rock bolts on surrounding rock, and the tunnel support effect in a jointed rock mass. The results of the four numerical cases show the accuracy and rationality of the coupling algorithm. Using this proposed algorithm, the progressive failure process of rock tunnels under high ground stress and the supporting process by lining and bolt (cable) can be accurately simulated.