published_or_final_version / abstract / toc / Computer Science and Information Systems / Master / Master of Philosophy

Call number: LD2668 .T4 1986 R57 / Master of Science / Mechanical and Nuclear Engineering

The traditional design methodologies for tunnel and underground excavations are divided in to three categories: Empirical, Analytical, and Observational approaches, whereas in the last years the Numerical approach has strongly become popular both for the intrinsic simplicity of the software packages and their ability to manage problems unsolvable with the classic methods. In this thesis, the underground openings have been analyzed using constitutive models other than the Mohr-Coulomb theory. FLAC is used for the analysis and the software has been implemented to include the Polyaxial Strength Criterion. The details of the modifications made in the software are presented and the results are compared with the Singh's elasto-plastic stress distribution in squeezing grounds. The applicability of the Polyaxial Strength Criterion has been therefore extended to all the numerical suites designed for geo-mechanical purposes (FEM, FDM, …) and the obtained results compared to the observations of deformation and radial squeezing pressure of the instrumented tunnels in the Chibro-Khodri underground power station. This study will develop better comprehension of the behavior of the underground openings and also provide a useful tool to the designers in the planning stages. / Thesis (Ph.D.)-University of KwaZulu-Natal, Durban, 2012.

Many practical problems in the field of engineering become so complex that they may be effectively solved only with the aid of a computer. An effective solution depends on the use of an efficient algorithm. Plotting root locus diagrams is such a problem. This thesis presents such an algorithm. Root locus design of feedback control systems is a very powerful tool. Stability of systems under the influence of variables can be easily determined from the root locus diagram. For even moderately complex systems of the type found in practical applications, determination of the locus is extremely difficult if accuracy is required. The difficulty lies in the classical method of graphically determining the location of points on the locus by trial and error. Such a method cannot be efficiently applied to a computer program. The text presents an original algorithm for plotting the root locus of a general system. The algorithm is derived using the combined methods of complex variable algebra and numerical analysis. For each abscissa desired a polynomial is generated. The real roots of this polynomial are the ordinate values for points on the root locus. Root finding methods from numerical analysis enable the solution of the problem to be one of convergent iteration rather than trial and error. Among the material presented is a computer program for solution of the general problem, an example of a completely analytic solution, and a table of solutions for more simple systems. The program inputs are the coefficients of the open loop transfer function and the range and increments of the real axis which are to be swept. The output lists the real and imaginary components of all solution points at each increment of the sweep. Also listed are the magnitude and angle components of the solution point and the value of system gain for which this is a solution. For less complex problems, the method can be applied analytically. This may result in an explicit relation between the real and imaginary components of all solution points or even in a single expression which can be analyzed using the methods of analytic geometry. As with any advance in the theory of problem solving, the ideas presented in the thesis are best applied in conjunction with previous solution methods. Specifically, an idea of the approximate location of the root locus can be obtained using sketching rules which are well known. The method presented here becomes much more efficient when even a rough approximation is known. Furthermore, the specific locations of system poles and zeros are not required, but can be helpful in planning areas in which to search for solutions.