Numerical procedures of ‘enriched finite element method (or EFEM)’ are introduced in this paper for analyzing interaction between fully grouted bolts and rock mass. In EFEM, an element that is intersected by a rock bolt at any arbitrary direction is called ‘enriched’ element. Nodes of an enriched element have additional degrees of freedom to determine displacements and stresses of the bolt rod. Decoupling of rock bolt and elastoplastic behaviour of rock mass has also been incorporated into the EFEM procedures. The results of this method are compared with those of pull-out test results. In addition, a numerical example of a bolted tunnel is provided to demonstrate the efficacy of the proposed method for practical applications.


Presently, rock reinforcement technique (rock-bolting) is used in almost all types of underground structures due to its performance, cost-effectiveness, and safety. The structures reinforced by bolts are, in general, very reliable and long lasting. In general, rock bolts reinforce rock masses through restraining the deformation within rock masses [1] and reduces the yield region around the excavation boundary. Small displacements are normally sufficient to mobilize axial bolt tension by shear stress transmission from the rock mass to the bolt surface. Grouted bolts have been successfully applied in a wide range of rock mass qualities especially in poor rock mass and found to be often more economical and more effective than mechanical rock bolts. Owing to their grouting effect on improvement of rock mass, grouted rock-bolts have been widely used in tunneling and mining applications under difficult ground condition. In rock mechanics many literatures have been dedicated to characterize the behaviour of the single grouted rock bolt by analytical as well as numerical procedures [1–7]. The computational procedures of a rock mass reinforcement made by grouted rock bolts follow one of the two categories:

  1. the equivalent model where the strong heterogeneities due to the discrete reinforcing elements are substituted by an equivalent homogeneous medium and

  2. the discrete rock bolt model, where each reinforcing element is represented with a certain detail.

The proposed EFEM scheme falls into the second category but, unlike a classical FEM model where the edges of the solid rock elements must be aligned with the rock bolts [8], the bolting pattern can intersect the solid elements. This modelling enhancement, that could simplify model set up, is allowed by formulating the problem of rock bolt-rock mass interaction in the context of the Enriched Finite Element Method (EFEM). EFEM generalizations have been introduced in this decade [9; 10] to address different kind of problems like those in structural and fracture mechanics and of flow with phase interface. EFEM often involves a local enrichment of the numerical approximation by adding new variables to the typical FEM variables, to improve problem solution. In this study, a concept of "enriched element" [9] has been introduced in which only the nodes of the rock element intersected by the rock bolt at any arbitrary direction are enriched.

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