Numerical procedure based on finite element method (FEM) and finite difference method (FDM) for the analysis of bolt-grout interactions are introduced in this paper. The finite element procedure incorporates elasto-plastic concepts with Hoek and Brown yield criterion and has been applied for rock mass. Bolt-grout interactions are evaluated based on finite difference method and are embedded in the elasto-plastic procedures of FEM. The experimental validation of the proposed FEM-FDM procedures and numerical examples of a bolted tunnel are provided to demonstrate the efficacy of the proposed method for practical applications. 1. Introduction Rock bolts have been widely used as a primary support system to stabilize the rock masses around tunnel, underground mine galleries, slopes, and others structure made in rock masses. In general, rock bolts reinforce rock masses through restraining the deformation within rock masses [1] and reduces the yield region around the excavation boundary. During the last four decades, different types of rock bolts have been in practice, out of which fully grouted active/passive bolts were the most common types. For a fully grouted passive rock bolt installed in deformable rock masses, a neutral point exists on the bolt rod, where shear stress at the interface between the bolt and grout material vanishes. The pickup length is then defined as the length between free end from the tunnel boundary to the neutral point, and the shear stress along this bolt length drags the bolt towards the tunnel [1]. The bolt length between the neutral point and the other free end of the bolt (inside the rock mass) is designated as anchor length and the developed shear stress drags the bolt towards the rock mass or, in other words, anchors the bolt into the rock mass. Based on these concepts, shear stresses and axial loads developed in a bolt rod are analytically formulated by many researchers who consider the effect of faceplate at the free end of the bolt [1, 2]. Bolt grout interactions around a circular tunnel in Hoek and Brown medium have been formulated analytically considering a bolt density factor [3]. In their study, Indraratna and Kaiser [3] demonstrated that due to the installation of bolts, the Hoek and Brown parameters , , and uniaxial compressive strength of intact rock, , would change to new values , , and based on the bolt density factor which consists of bolt spacing, shear stress on the bolt grout interactions, tunnel radius, and bolt diameter. Considering different approaches to bolt performance, Stille [4] presented a closed form
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