The composite element concept is introduced in this paper firstly, then the explicit hollow rock bolt element model is developed which comprises rock material, bolt material, bolt-rock interface. The main advantage of the new model is that it can be incorporated into the conventional finite element analysis, and the mesh generation of the bolted rock structures becomes relatively more convenient and feasible. More important, the radial expansion and compression effects as well as the common shear/tension effects along the axis can all be simulated, therefore the model provide a framework to predict the shear/tensile and the fascinated(staved) failure phenomena of the hollow bolt in the reinforced jointed rock structures.


The "Swellex" bolt is a hollow metallic bolt which is completely connected to the rock masses. In the FEM analysis of such supported rock structures, it is essential to formulate a bolt element which can simulate the radial expansion and compression effects besides the common shear tension effects along the axis. Aydan(I989) developed a three-dimensional bolt element with 8 nodal points. Two of these are connected to the bolt, whereas the six others are connected to the rock masses. The number of nodes in the two-dimensional case is reduced to six. Swoboda & Marence(l992) modified the Aydari's formulation, assigning different coordinates for the bolt nodes and the nodes of rock-grout interfaces. Chen & Egger (l997) also developed a two dimensional explicit model of bolt element with 6 nodes, of which two are connected to the bolt, whereas the four others are connected to the rock mass. For the hollow bolt, Stillborg(I986) proposed a two dimensional model in which two set of trusses parallel to the bolt axis and one set of trusses perpendicular to the bolt axis. Giani & Ferrero (1994) used the model in the FEM calculation for a tunnel, from which the difference in bolting efficiency between passive, fully grouted and the "Swellex " bolt dependent on the rock mass cohesion has been analyzed. All of the above explicit bolt element models have the same characteristics: they are conventional elements which have definite nodes, and some of these nodes should be the common nodes of the nearby rock material elements. Consequently, the existence of the bolts of large quantity will impose very strong restraints on the finite element mesh generation. What will be described in the following is the general principle of the composite element concept which has been implemented in the solid and grouted bolt element model(Chen et al., 2002), then an explicit hollow bolt element model inbedded within a conventional element of rock material is developed. In the formulation the bolt-rock interface is taken into account, and the radial expansion and compression effects as well as the common shear/tension effects along the axis are simulated, too.

2.1 The concept of composite element and sub-element

Suppose an in-homogenous domain shown in the Figure containing two sub domains which have different mechanical characteristics.

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