A line-to-volume contact algorithm for modeling the complex bond-slip behavior of grouted bolts in rock mass

Abstract

Timely installation of rock bolts is essential in tunneling through weak surrounding rock to prevent rapid deformation behind the excavation face. However, understanding the support mechanism of rock bolts remains a challenge, primarily due to the highly nonlinear bond-slip behavior at the bolt-rock interface. This difficulty is further compounded by the large disparity in cross-sectional dimensions between the bolt and the surrounding rock mass. This study presents a novel and efficient finite element contact algorithm to simulate the interaction between rock bolts and the surrounding rock. Unlike conventional methods that establish direct contact constraints, our approach introduces relative displacement as the new degree of freedom (DOF) based on the dual Lagrange multiplier method. This new DOF is subsequently employed in the discretization of contact constraints and contact virtual work. The formulation enables direct integration of existing constitutive models for the bolt-rock interface, which are typically expressed in terms of relative slip displacement. In addition, it improves numerical stability by avoiding the saddle-point problems and spurious stress oscillations commonly observed in traditional contact formulations. Moreover, this method accommodates non-conforming meshes, enabling the rock bolt to be meshed separately and arbitrarily assembled into the mesh of the rock mass, thus enhancing the flexibility of numerical modeling. The accuracy and efficiency of our method are first validated against existing methods. Subsequently, the developed algorithm is applied to perform a detailed analysis of the mechanical response and support mechanism of rock bolts during tunnel excavation.