邊坡破壞之Manifold數值模擬

Abstract

邊坡穩定分析一直是土木界歷久彌新的課題，從以前的切片法透過假設條件消除靜不定數來求解，到運用極限平衡法經由試誤法找出極限破壞面，到現今隨著電腦運算速度提升而越形重要的數值模擬方法，如有限元素法、邊界元素法、以及不連續變形分析法等等，種種方法其目的都是要找出穩定性最低之邊坡破壞滑動面以及延此滑動面之破壞安全係數。然而許多自然界的材料如土壤、岩石等並非連續體，以及受限於上述數值方法的方法學，對於不連續體大應變以及動態的邊坡破壞滑動總有其拘限性。 本論文致力於探討連續體過渡到不連續塊體的破裂行為，以石根華所提出的流形法Numerical Manifold Method為基本工具，採用工程界最常用的摩爾庫侖破壞準則來修改，可模擬塊體在不同的應力條件下裂縫的產生及延伸，進而探討現地自然邊坡漸進式破壞的破壞機制、作為破壞案例的數值模擬分析，預期能將此結果分析作為工程界設計與施工的參考。

The analysis of slope stability has long been an intriguing issue for civil engineers. In an attempt to obtain a unique solution for an indeterminate slope stability problem, many methods have been proposed. These techniques include the method of slices, and more recently as the computer capability improves, numerical simulations such as the finite element, boundary element, and discontinuous deformation methods. The goal of these stability analyses is to search for a potential failure surface within a slope that has the minimum safety factor and the value of this safety factor itself. Natural materials such as soils and rocks are inherently discontinuous, the above techniques have limitations in simulating these discontinuities and the phenomenon of deformation and sliding of a mass that contains discontinuities. A technique of numerically simulating the breakage of a continuous material and transformation into a set of discontinuous blocks has been developed in this thesis. Using the Mohr-Coulomb failure criteria and the numerical manifold method developed by Genhua Shi, the development and propagation of fractures within a continuous material can be simulated. The thesis describes details of this numerical technique and its applications in slope stability analyses.