以有限元素法進行邊坡穩定分析之研究

A Study on Analysis of Slope Stability Using Finite Element Method

鄧子榆(Zeu-Yu Teng)

指導教授 ： 馮道偉 ； 馮道偉

中原大學/工學院/土木工程研究所/碩士(2001年)

https://doi.org/10.6840/cycu200100371

摘要

台灣地區地形陡峭，地勢高聳之山地佔全島面積之半，外加地質構造複雜且降雨集中，因此，邊坡穩定問題顯得格外重要。傳統上，對於邊坡穩定問題之分析以極限平衡法為主，然而，近三十年來，有限元素法之快速發展，已使得其成為較極限平衡法更為成熟且完整之分析方法。
本研究之主要目的在對於邊坡穩定相關之問題進行數值分析。研究中所採用之主要分析工具為「PLAXIS」有限元素程式，此程式為一大地工程之多功能分析程式。此外，為比較有限元素法與傳統極限平衡法之差異，本研究亦輔以PCSTABL5M程式進行相關之分析。主要的研究內容包括：1）邊坡滑動安全係數分析，在考慮不同之邊坡傾斜角與土壤參數等影響因子下，比較有限元素法與極限平衡法之分析結果；2）降雨對邊坡穩定之影響，探討邊坡土層於降雨情況下之有限元素分析；3）土釘擋土結構與邊坡穩定分析，探討土釘應用於邊坡穩定時之行為與機制；4）邊坡破壞滑動面之研究，比較有限元素法與極限平衡法分析所得之邊坡潛在滑動面，並提出一基於力學原理求取潛在滑動面位置之方法；5）針對士林碧溪附近之地滑整治區進行邊坡潛變分析之案例研究，並將數值分析結果與實際之觀測結果作一比較。
經由分析結果顯示：1）以有限元素法分析所得之邊坡安全係數與極限平衡法(Bishop Method)分析之結果頗為一致，且二者之差距僅介於1%~5%之範圍內；2）降雨分析方面，以有限元素法分析邊坡因降雨引致土壤凝聚力降低之情形時，發現當凝聚力降低至原始
值之某一比率時會產生邊坡滑動安全係數驟降之情形，此特性值可定義為”臨界凝聚力損失率”；3）對於土釘結構於邊坡穩定之分析時，根據不同土釘置入角度與長度可進行最佳化設計，並由施工過程邊坡網格變形情況與安全係數分佈，則可作為施工與設計時之參考；4）本研究採用PLAXIS程式分析之輸出應力資料，並配合Mohr-Coulomb破壞準則，以推估邊坡之可能潛在滑動面位置，由分析結果可概略地研判邊坡潛在滑動面之趨勢；5）對於案例之研究，以有限元素法分析邊坡潛變問題時可獲得頗為良好的趨勢，惟於數值模擬之過程中仍有許多影響因素無法於分析時一併考慮，因而致使其與實際觀測結果略有差距。

關鍵字

破壞滑動面 ； 有限元素法 ； 極限平衡法 ； 邊坡穩定 ； 臨界凝聚力損失率

並列摘要

In Taiwan, because of the steep topography, complicated geological structures and concentrated rainfall, therefore, the slope instability is always a serious problem. In practice, the majority of slope stability analyses are still performed by using limit equilibrium method (LEM). But recently, it is argued that the finite element method (FEM) of slope stability analysis is a more powerful method than the limit equilibrium method.
The objective of this thesis is to study problems of slope stability with numerical analysis. The finite element program PLAXIS is used to perform slope stability analysis and the results are compared with those from the limit equilibrium method. The topics in the thesis include : 1) the safety analysis of slope by FEM & LEM for different slope angles and soil parameters; 2) the influence of rainfall on slope stability, to simulate the rainfall mechanics more reasonable; 3) soil nailing in slope stability analysis, to study the behavior and mechanics for soil nailing which apply to the slope stability; 4) the analysis of slope failure by using the principle of material mechanics and use this method to estimate the location of failure plane; 5) creep analysis of slopes in Shih-Lin is for case study, and the numerical results were compare with the observed deformation from the inclinometer measurements.
The results of this study indicate that: 1) the safety factor of slopes which considered in this thesis is consistent with limit equilibrium method analysis, and the difference of results of the two methods is within the range of 1%~5%; 2) in rainfall analysis, a critical value of reduced cohesion due to the rainfall could be found while using finite element method, where it is defined as “critical reduction on cohesion”; 3) from the results of soil nailing analysis, we can understand relative behavior and mechanics of soil nailing, and these information could be extended to carry out the optimum design of soil nailing; 4) the proposed method for searching failure surface of slopes can offer a probable range to determine the potential failure surface of slopes; 5) the results of case study using PLAXIS indicate a similar tendency to the measured deformation of slopes.

並列關鍵字

finite element method ； limit equilibrium method ； slope stability

參考文獻

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