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A hierarchical linear elastic boundary element solver for lenticular ore bodies
Thesis (MSc (Mathematical Sciences. Applied Mathematics))--University of Stellenbosch, 2007.
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| Format: | Thesis |
| Language: | English |
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Stellenbosch : University of Stellenbosch
2008
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| _version_ | 1867614136854118400 |
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| access_status_str | Open Access |
| author | Zietsman, Christiaan Abraham |
| author2 | Du Plessis, J. P. |
| author_browse | Du Plessis, J. P. Zietsman, Christiaan Abraham |
| author_facet | Du Plessis, J. P. Zietsman, Christiaan Abraham |
| author_sort | Zietsman, Christiaan Abraham |
| collection | Thesis |
| dc_rights_str_mv | University of Stellenbosch |
| description | Thesis (MSc (Mathematical Sciences. Applied Mathematics))--University of Stellenbosch, 2007. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/1686 |
| institution | Stellenbosch University (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:47:15.075Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2008 |
| publishDateRange | 2008 |
| publishDateSort | 2008 |
| publisher | Stellenbosch : University of Stellenbosch |
| publisherStr | Stellenbosch : University of Stellenbosch |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/1686 A hierarchical linear elastic boundary element solver for lenticular ore bodies Zietsman, Christiaan Abraham Du Plessis, J. P. University of Stellenbosch. Faculty of Science. Dept. of Mathematical Sciences. Applied Mathematics. Dissertations -- Applied mathematics Theses -- Applied mathematics Mine safety -- Mathematical models Mining engineering -- Mathematical models Boundary element methods -- Mathematical models Thesis (MSc (Mathematical Sciences. Applied Mathematics))--University of Stellenbosch, 2007. South Africa is involved in huge mining operations deep in the earth's crust. Stresses induced by these mining operations may cause seismic events or rockbursts to occur, which could damage infrastructure and put miners' lives at risk. The effect of different mining layouts are modelled and used by engineers to make design decisions. The frequency at which 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, but they are particularly well suited for the boundary element method (BEM). This work focuses on the theory and background needed for creating a linear elastic static stress boundary element solver suited to South African mining layouts. It starts with linear elastic theory and subsequently describes the physical continuum, governing equations and the fundamental solutions which are an integral part of the BEM. Kelvin's solution cannot be applied to crack-like excavations, therefore the displacement discontinuity kernels, which are very well suited to model fractures, are derived. The derivation is approached from both the direct and indirect BEM's perspectives. The problem is cast as a boundary integral equation which can be solved using the BEM. Some of the different specializations of the BEM are discussed. The major drawback of the BEM is that it produces a dense influence matrix which quickly becomes intractable on desktop computers. Generally a mining layout requires a large amount of boundary elements, even for coarse discretization, therefore different techniques of representing the influence matrix are discussed, which, combined with an iterative solver like GMRES or Bi-CG, allows solving linear elastic static stress models. 2008-04-15T09:03:25Z 2010-06-01T08:30:42Z 2008-04-15T09:03:25Z 2010-06-01T08:30:42Z 2007-12 Thesis http://hdl.handle.net/10019.1/1686 en University of Stellenbosch 2221369 bytes application/pdf application/pdf Stellenbosch : University of Stellenbosch |
| spellingShingle | Dissertations -- Applied mathematics Theses -- Applied mathematics Mine safety -- Mathematical models Mining engineering -- Mathematical models Boundary element methods -- Mathematical models Zietsman, Christiaan Abraham A hierarchical linear elastic boundary element solver for lenticular ore bodies |
| title | A hierarchical linear elastic boundary element solver for lenticular ore bodies |
| title_full | A hierarchical linear elastic boundary element solver for lenticular ore bodies |
| title_fullStr | A hierarchical linear elastic boundary element solver for lenticular ore bodies |
| title_full_unstemmed | A hierarchical linear elastic boundary element solver for lenticular ore bodies |
| title_short | A hierarchical linear elastic boundary element solver for lenticular ore bodies |
| title_sort | hierarchical linear elastic boundary element solver for lenticular ore bodies |
| topic | Dissertations -- Applied mathematics Theses -- Applied mathematics Mine safety -- Mathematical models Mining engineering -- Mathematical models Boundary element methods -- Mathematical models |
| url | http://hdl.handle.net/10019.1/1686 |
| work_keys_str_mv | AT zietsmanchristiaanabraham ahierarchicallinearelasticboundaryelementsolverforlenticularorebodies AT zietsmanchristiaanabraham hierarchicallinearelasticboundaryelementsolverforlenticularorebodies |