title of the thesis - Department of Geology - Queen's University
title of the thesis - Department of Geology - Queen's University
title of the thesis - Department of Geology - Queen's University
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4.2 Numerical Methods<br />
Phase 2 and Universal Distinct Element Code (UDEC) are two numerical stress analysis packages<br />
that were used to model and simulate stress on <strong>the</strong> 7400 Level. Phase 2 , developed by Rocscience<br />
(Rocscience Inc., 2005), is a continuum code that employs <strong>the</strong> finite element method. Using this<br />
program <strong>the</strong> model is discretized into a mesh <strong>of</strong> triangular elements and nodes (Fig. 4.1). When<br />
boundary conditions are applied, displacements are computed at each node. The displacements<br />
within elements are used to calculate strains for each element. Strain is <strong>the</strong>n translated into stress,<br />
integrating rockmass properties (Pande et al., 1990). The behaviour <strong>of</strong> both <strong>the</strong> continuum and<br />
discontinuities in this <strong>the</strong>sis is assumed to be governed by Mohr-Coulomb failure criteria.<br />
UDEC, developed by Itasca Consulting Group, Inc. (2000), is a<br />
discontinuum code that employs <strong>the</strong> distinct element method. A<br />
discontinuum model differs from <strong>the</strong> continuum model in that <strong>the</strong><br />
Figure 4.1: Schematic<br />
diagram <strong>of</strong> triangular<br />
elements and nodes.<br />
model is defined by contacts and interfaces that separate rigid and/or<br />
deformable blocks (Cundall and Hart, 1992; Hart, 2003). UDEC<br />
models use a continuum mesh inside blocks. Contacts are allowed to<br />
interact and deform (Jing, 2003).<br />
Unlike <strong>the</strong> finite element method, <strong>the</strong> UDEC model allows for<br />
evolving contact conditions. The model proceeds through a series <strong>of</strong> time steps – a feed-forward<br />
process where results from <strong>the</strong> previous iterations are used for <strong>the</strong> next. UDEC works by applying<br />
<strong>the</strong> force-displacement law at contacts and formulating and solving equations <strong>of</strong> motion<br />
(Newton’s second law) for <strong>the</strong> defined blocks (Hart, 2003). Using block properties, forces and<br />
displacements are translated into stress and strain for each bock. As strain is accumulated, <strong>the</strong>se<br />
quantities are recalculated and used as inputs for <strong>the</strong> next time step. As <strong>the</strong> model progresses, it<br />
recognizes block rotation, sliding contacts, block detachment and new interfaces between blocks<br />
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