A hierarchical linear elastic boundary element solver for lenticular ore bodies
Date
2007-12
Authors
Zietsman, Christiaan Abraham
Journal Title
Journal ISSN
Volume Title
Publisher
Stellenbosch : University of Stellenbosch
Abstract
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.
Description
Thesis (MSc (Mathematical Sciences. Applied Mathematics))--University of Stellenbosch, 2007.
Keywords
Dissertations -- Applied mathematics, Theses -- Applied mathematics, Mine safety -- Mathematical models, Mining engineering -- Mathematical models, Boundary element methods -- Mathematical models