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UBC Theses and Dissertations

Derivation of an equivalent boundary method for ground-support interaction problems Mitelman, Amichai


This thesis presents a novel approach termed ‘Equivalent Boundary’ (EB) for the analysis of ground-support interaction problems. The basic idea of the proposed method is to simplify these problems by representing the ground as analogous structural entities. Similar to the convergence-confinement method, increased efficiency is attained by focusing on the ground-support boundary, rather than simulating a great portion of the surrounding ground, as is required in finite-element models. Within this thesis, a number of different ground-support problems are addressed: room and pillar mines, vertical circular shafts, and tunnels. Different structural analogues are chosen for each problem according to the nature of each problem: the pillar is represented by a spring, the shaft by a ring, and the tunnel by a series of beam elements. Expressions for the stiffness of the structural analogues are derived. Subsequently, the unsupported ground displacements are used as an input; based on these, the displacements, internal forces, and factor of safety of the supported ground can readily be computed. All results have been validated against numerical models. For the tunnel problem, a methodology for the analysis of circular tunnels in elastic ground is derived. The underlying assumption of the traditional convergence-confinement approach is that the tunnel is subjected to a hydrostatic stress field, a simplification which poses considerable practical limitations. Within the proposed method, the case of a tunnel subjected to a non-uniform stress field can be addressed. Subsequently, the methodology is further modified to address two more complex conditions: 1) a circular tunnel in plastic ground, and 2) a non-circular horseshoe shaped tunnel in elastic ground. Due to the efficient computational process, the method developed in this thesis is well-suited for probabilistic analyses that require a large number of iterations. A methodology for the cost estimation of tunnel support based on the construction method is presented. A practical example is used to demonstrate the advantages of the EB method developed in this thesis. Additionally, this methodology constitutes a useful stand-alone concept, which can be implemented using other available tunnel analysis methods.

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