A hierarchical linear elastic boundary element solver for lenticular ore bodies

[摘要] South Africa is involved in huge mining operations deep in the earth's crust. Stressesinduced by these mining operations may cause seismic events or rockbursts to occur, whichcould damage infrastructure and put miners' lives at risk. The effect of different mininglayouts are modelled and used by engineers to make design decisions. The frequency atwhich models are updated and integrated with the decision making process is not optimal.These large mining layouts can not be modelled adequately using domain methods, butthey are particularly well suited for the boundary element method (BEM).This work focuses on the theory and background needed for creating a linear elasticstatic stress boundary element solver suited to South African mining layouts. It startswith linear elastic theory and subsequently describes the physical continuum, governingequations and the fundamental solutions which are an integral part of the BEM. Kelvin'ssolution cannot be applied to crack-like excavations, therefore the displacement discontinuitykernels, which are very well suited to model fractures, are derived. The derivationis approached from both the direct and indirect BEM's perspectives. The problem iscast as a boundary integral equation which can be solved using the BEM. Some of thedifferent specializations of the BEM are discussed. The major drawback of the BEM isthat it produces a dense influence matrix which quickly becomes intractable on desktopcomputers. Generally a mining layout requires a large amount of boundary elements,even for coarse discretization, therefore different techniques of representing the influencematrix are discussed, which, combined with an iterative solver like GMRES or Bi-CG,allows solving linear elastic static stress models.

[发布机构] Stellenbosch University