Zsaki, A.M. and J.H. Curran, Automatic geometry optimization for stress analysis of underground excavations, NUMOG IX Ninth International Symposium on Numerical Models in Geomechanics, 25-27 August 2004, Ottawa, Canada
ABSTRACT: The computation of stresses around underground excavations in a mine operation is a task that is often repeated as the mining progresses, amounting to considerable time for both model development and analysis. The distribution of stress is often evaluated using numerical techniques such as the finite element or the boundary element method. Since the general mine model often contains more detailed geometry than required, the resulting solution has higher numerical accuracy than warranted by the limited nature of other input parameters, such as rock mass properties. This paper presents an automated method of generating meshed model geometries used of numerical stress analysis by considering the effect of each excavation at region of interest. Using principles of continuum mechanics, and techniques from computer graphics it is possible to simplify or optimize the mesh while maintaining the accuracy of analysis results. The method is equally applicable to two or three dimensional boundary and finite element analysis. As an illustration of application of the method, an excavation-sequencing scenario modeled using three-dimensional boundary elements is analyzed and the quality of resulting solution is assessed using error estimators.
Zsaki, A.M. and J.H. Curran, Parallel computation of field Quantities in an underground excavations analysis code, 5th NARMS and 17th TAC Conference 2002, Toronto, Ontario, Canada
ABSTRACT: The boundary element method (BEM) is a widely used numerical technique for computing stresses and displacements on the boundary of underground excavations and in the surrounding domain. The BEM has a great potential for parallel implementation resulting in a drastic reduction in time spent computing results. This paper focuses on the development of parallel algorithms for the evaluation of field quantities, such as stresses and displacements, in a modern analysis code. Most of the previous research has been in the area of designing parallel algorithms for the solution of the system of equations arising from the BEM discretisation. However, in most practical analysis scenarios the evaluation of field quantities is more time consuming than the solution of the linear system of equations. Presented are two algorithms, which were tested on representative examples to evaluate the speedup and efficiency gained from the parallel implementation running on an off-the-shelf cluster of PC workstations commonly found in a typical consulting office environment.
Zsaki, A.M. and M. Paraschivoiu, A Non-overlapping domain decomposition for the Stokes problem, ASME Fluids Engineering
Division Summer Meeting 2002, Montreal, Quebec, Canada
ABSTRACT: A domain decomposition method with Lagrange multipliers for the Stokes problem is described. The dual system associated with the pressure Lagrange multiplier is solved with the Uzawa iterative procedure. Each iteration of the Uzawa procedure involves an inversion of a Laplacian will if performed with the finite element tearing and interconnecting FETI method. Numerical tests are performed by solving the driven cavity problem. An analysis of the number of outer iterations and an evaluation of the cost of the inner iterations are reported.
Zsaki, A. and J.H. Curran, Automatic meshing of underground excavations with emphasis on prismatic tunnels, 38th US Rock Mechanics Symposium 2001, Washington DC, U.S.A., pp. 1526-1533
ABSTRACT: The result of any finite element analysis is dependent on the quality of the finite element mesh of the domain analyzed. In rock engineering, particularly in excavations for tunneling projects, the investigation of the rock mass behavior in front of and around the excavations is important for support analysis and proper design. This paper introduces an automated technique of mesh generation for finite element analysis used in analysis of tunnels with prismatic cross-sections. The methodology of the approach is presented with emphasis on practical considerations of excavation sequencing. Examples generated by the method are presented along with validation of the generated mesh using a finite element package.
Innovative techniques in large-scale stress analysis of underground excavations
ABSTRACT: The successful operation of underground mines is dependent on the accurate forecast of the effects of continuously excavating stopes and mining infrastructure. Failures due to high stresses can easily cost tens of millions of dollars or even halt mining. The efficient evaluation of possible excavation sequencing scenarios requires the use of modern numerical stress analysis tools due to the complexity of geology and excavation geometry present in the mine model. Since the number of elements in a model is directly related to computation time, the analysis of the large models of mines requires considerable time and computational resources given the constraints imposed by the day-to-day operation cycle of a mine. The data-limited nature of problems characterizing models in geomechanics introduces uncertainty into the solution, limiting achievable accuracy. Since models contain a large number of excavations in a large volume of space, the interaction of excavations is limited to their intermediate vicinity. Also, the determination of the field quantities, such as stresses and displacements, in the rock mass requires significant computational time, often measured in days or weeks. To address the issue of reducing the computation times associated with large-scale analysis in geomechanics, the research contained in this thesis proposes a unified continuum-mechanics based framework of mesh optimization. The framework is independent of the stress analysis method employed and the dimension of the problem. It is capable of removing geometric detail from the model while improving the quality of the mesh and drastically reducing the computation time and resources required. In addition, the framework, as a concept, is applicable to other disciplines such as heat transfer and groundwater flow. The application of the framework creates models with solutions comparable to the results obtained from the full model, while the error in the approximate solution is less than the error arising from the inherent uncertainty in the input parameters. To address post-processing issues, a parallel algorithm was developed to reduce the long times involved in the computation of field quantities in a boundary element analysis. The algorithm harnesses the computing capabilities of networked workstations achieving considerable speedups even over common network connections.
Non-circular slope stability analysis using the Generalized Wedge Method with modifications and extensions for application in rock engineering
The stability of a slope, either natural or artificial, is of considerable importance. The purpose of this thesis is to find a method that is suitable to analyze slopes using a non-circular failure surface, where the failure mechanism is governed by structural weaknesses of the slope material. The Generalized Wedge Method was modified and extended to handle the requirements posed by rock slopes. The method was updated and several features were added to improve the application to stability analysis problems. Once implemented, the method was tested on a large number of test problems to validate its accuracy with success. The modified method was found to be accurate in modeling and analyzing problems commonly encountered in rock slope engineering.
Finite element modeling, analysis and structural design of circular reinforced concrete tanks
ABSTRACT: This Thesis is a research study conducted to gain more understanding of the applicability of The Finite Element method for analyzing circular reinforced concrete tanks and to implement structural design using computer programs written by the author. The thesis gives an insight into the basic theory behind the finite element method of analysis with a special focus on its application using computers. The analysis and design of circular reinforced concrete tanks by the conventional method outlined by the Portland Cement Association was used successfully in the past, however with the advent of high power computers, the finite element method of analysis has became more and more popular method in order to establish a higher precision in analysis. In this thesis different tanks were analyzed by both methods to verify the computer solution, and there are two complete structural designs of tanks included. The thesis is intended for the student or engineer with basic understanding of finite element modeling and analysis, but with appropriate knowledge of structural analysis and mechanics.
