1、翻译部分英文原文Modelling of fully grouted rock bolt based on enriched finite element methodDebasis Deb a,n, Kamal C. Das b（Department of Mining Engineering, India；b Department of Mathematics, India）Abstract：Analysis of mechanical behaviour of rock mass reinforced by fully grouted rock bolt is introduced ba
2、sed on the enriched finite element method (EFEM). A solid element intersected by a rock bolt along any arbitrary direction is defined asenrichedel ement and it has additional degrees of freedom at each node for estimating displacements and stresses in bolt rod. Numerical procedures of EFEM are devel
3、oped to form enriched stiffness matrix using constitutive relations of rock mass, properties of bolt rod and grout material and orientation of the bolt. Decoupling of rock bolt and elasto-plastic behaviour of rock mass has been incorporated into the EFEM procedures. Released displacement of rock mas
4、s prior to bolt installation has also been considered in the procedures to provide realistic solution. The results of this method are verified with an analytical pull-out test model. In addition, a numerical example of a bolted tunnel is provided to demonstrate the efficacy of the proposed method fo
5、r practical applications.Keywords: EFEM Grouted rock bolt Decoupling Released displacement MohrCoulomb yield criterion Supported tunnels1 .IntroductionRock bolts have been widely used as the primary support system to stabilize the rock masses around tunnel, underground mine galleries, slopes and oth
6、ers structures 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. Axial load distribution along a fully grouted passive rock bolts shows that a neutral point exists on
7、 the bolt rod where shear stress at the interface between the bolt and grout material vanishes. The pickup length is 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
8、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 devel
9、oped along a bolt rod are analytically formulated by many researchers 1,2. Considering a bolt density factor, Indraratna and Kaiser 3 established an analytical model for the design of boltgrout interactions around a circular tunnel according to the elasto-plastic law. Cai et al. 4 derived an analyti
10、cal solution of rock bolts for describing the interaction behaviours of rock bolt, grout material and rock mass using shear lag model (SLM). Brady and Lorig 5 numerically analyzed the interactions of boltgrout in MohrCoulomb media using the finite difference method (FDM) technique and showed that ra
11、dial displacement and yielded region reduced due to the installation of grouted bolts around a circular tunnel.Limited works have been published for analysis of the interaction between fully grouted rock bolt installed in elasto-plastic rock mass using the finite element method. A few literatures de
12、al with finite element procedure involving combination of decoupled rock bolts and elasto-plastic rock mass 6,7. In this study, the concept of enriched element 8 has been introduced in which a bolt can intersect a regular element at any arbitrary direction. Each node of an “enriched element” has add
13、itional degrees of freedom to determine displacements and stresses of the bolt rod. The stiffness of an enriched element comprises constitutive properties of rock mass, physical andmaterial properties of bolt and grout, orientation of bolt and bore hole diameter. The enriched element can be applied
14、for analysis of elasto-plastic rock mass as well as decoupling of the bolt and/or both. Released displacement of rockmass, often signifying the delay in bolt installation, is an important factor of bolt performance. In this study, a released displacement factor has been incorporated into the EFEM pr
15、ocedures to provide realistic solution of displacements and stresses in rock mass as well as in bolt rod. MohrCoulomb yield criterion has been applied to determine the onset of yielding of rock mass. Decoupling at boltgrout interface has been modelled based on the peak shear strength of the grout ma
16、terial. For verification of the proposed method, results of pull-out test presented by Li and Stillborg 1 are compared with those obtained from the numerical models. This method has also been applied to evaluate rock mass behaviour and bolt performance for a circular bolted tunnel. Results presented in this paper show the efficacy of the proposed method, which can easily be applied for practical applications.2. Finite e
