The numerical modelling of rockbolts in geomechanics by finite element methods
In tunnel excavation, the use of rockbolts has long been a popular means of reinforcement in rock masses to prevent the rock opening from caving in. The idea has evolved from the earliest form of rockbolt made of wood to the more up-to-date form of pre-tensioned or grouted steel rockbolts. A major breakthrough in the design of rockbolt models was made by Aydan (1989). This rockbolt element was modelled in coupled form, with one sub-element representing the steel bolt, and the other sub-element the grout. This representation was necessary to model the complex action in the continuous rock mass near the joint. In elasticity problems, the large displacement formulation of a beam element is derived from the fundamental theory, and the bending phenomenon of a thin rod is analysed by the finite element discretizations of the bar elements and the beam elements. Experiments show that the deformation characteristics of the latter representation resemble a more realistic life behaviour. Based on this finding, this thesis proposes a modification to Aydan's two-dimensional rockbolt element, with the beam elements discretising the steel bolt. The different mechanical responses of a perfectly elastic rockbolt are considered, and the large displacement formulation of the new rockbolt element is derived by combining those of Aydan's rockbolt element and the beam element. The mechanics of the Aydan element and the new rockbolt element are described, and their performances are compared in an identical situation. It is found that in the two two-dimensional examples used in this thesis, the modified element ensures the continuity of curvature of the rockbolt, and in general, can act as support across a discontinuity or joint between rock masses well. In conjunction with the displacement method in the finite element procedures, a conventional iteration solution procedure is first described to solve the nonlinear incremental stiffness equation. However, it is found that this procedure is cumbersome, and requires a large amount of comptutations. Some limited storage quasi-Newton minimization algorithms are considered as an alternative.