UBC Theses and Dissertations

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UBC Theses and Dissertations

A method for analysis of rock blocks with complex arbitrary geometries Santos, Jair


The volume, centre of mass, and inertia properties of a block of rock are important physical characteristics when calculating its stability. As a result, civil and geotechnical engineers often need to determine these properties, which are difficult to obtain due to the complex geometry of typical blocks. Currently, the volume of rock blocks with arbitrary geometries are calculated making use of approximations that include, but are not limited to, filling the total volume with tetrahedral blocks and adding up the units; slicing the block in smaller geometrically regular parts; creating profiles of the block, and other analogous methods. Very often, the shape of the blocks are represented by arbitrary polyhedra with any number of faces and vertices and a variety of methods can be used to potentially obtain properties of the block from a polyhedron. This thesis describes a new method to calculate the volume and centre of mass of a block of rock represented by a polyhedron, using vector analysis and linear programming, analytic geometry, integral calculus, structural geology and rock mechanics theory. Additionally, methods of computational geometry and algorithms are used to demonstrate the processes. The method calculates the volume as a single body improving accuracy that can be affected only by minor irregularities of the rock. It is more effective with the use of computer automation; therefore, technical aspects of the programming procedures will be outlined. The creation of automatic procedures to obtain the results is of great significance to the geotechnical engineering industry, since it will improve the accuracy of results and speed the development of projects. Consequently, this thesis will provide a base for future software development. The method is restricted to convex polyhedra, with at least one face exposed to the surface.

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Attribution-NonCommercial-NoDerivs 2.5 Canada