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  • 學位論文

西部麓山帶砂岩彈性組成律之研究及應用

指導教授 : 鄭富書

摘要


若利用有限元素法數值分析的方式,常透過適當之簡化與假設來進行數值分析。一般對於岩石材料之變形,現有有限元素法數值分析常採等向性線彈性模式配合Drucker-Prager或Mohr-Columb塑性組成模式描述麓山帶砂岩變形行為。然而此類模式往往無法反映麓山帶砂岩之真實變形特性如:(1)體積應力作用下,非線性彈性變形及塑性應變閉鎖情形;(2)剪應力作用下,剪應力與彈性體積應變偶合行為;(3) 橢圓帽狀塑性勢能面之存在。 由於忽略掉此剪脹效應將錯估岩石的變形性,為了描述此剪脹的特性,本研究採用高階格林非線性彈性組成律模式。並將此彈性組成律模式應用於有限元素法程式ABAQUS上,根據此高階格林非線性彈性組成律模式推導出其增量形式的切線勁度矩陣後並加以驗證,驗証後再將此切線勁度矩陣撰寫於有限元素法程式ABAQUS中之副程式以便應用於有限元素法之數值分析上。 在開始進行工程案例分析之前,先以單元素進行數值三軸試驗以驗証自行撰寫的有限元素法ABAQUS副程式的正確性,以檢核有限元素分析是否可以描述此麓山帶砂岩彈性組成律模式,而由單元素分析的結果與實驗資料比對結果顯示,此數值模式可適切的描述麓山帶砂岩的彈性變形行為。最後本研究亦分別考慮隧道、基礎、邊坡案例進行應用上的分析,將分析結果與線彈性組成律比較,探討此模式的適用性,以隧道分析結果顯示使用線彈性模式分析所得變形量14.6cm太小過於保守,而使用麓山帶砂岩非線性彈性組成律模式分析所得變形量28.75cm較線彈性模式分析所得變形量為大,也較線彈性模式更接近真實的隧道變形量。

並列摘要


The numberic method of finite element is mostly based on the applicable simplification and hypotheses as to proceeding the simulation analysis. Generally speaking, the present finite element method adopts the isotropic-linear model, assisted by the plastic model of Drucker-Prager or Mohr-Columb to simulate the deformation of rock materials, and also applies them to describe the deformation behaviors of western foothill sandstones. However, this kind of model is hard to represent the realistic deformed characters of western foothill sandstones, such as (1) the nonlinear elastic deformation and plastic strain closure condition under volumetric stress effect, (2) the coupling behavior between shear stress and elastic volumetric strain under shear stress effect, and (3) the existence of elliptical plastic potential surface. It would be inaccurate to estimate the rock deformation when ignoring the shear dilation effect, thus this research utilizes the advanced Green nonlinear elastic component model to describe the characters of shear dilation. To apply it to finite element method of ABAQUS program, the tangent stiffness matrix was deduced based on certain model, ensuing by its verification and coding the subroutine belonging to ABAQUS to proceed the further analysis. Before analyzing the engineering construction cases, single element was applied to triaxial test to verify the accuracy of the subroutine, and to inspect if the material model is proper to describe the elastic component model of western foothill sandstone. According to the result comparisons of single element analysis and testing data, this model presents its appropriateness for represent the elastic deformation behavior of western foothill sandstone. Besides, this model is also applied to analyze the tunnel, foundation or slope cases to testify its application. Moreover, the results are compared with the ones of linear elastic method, which reveals a more reasonable condition.

參考文獻


[42] 鄭富書、黃燦輝、林銘郎 (2000),台灣隧道工程老問題之新探討-軟岩之力學特性,地工技術,第79期,第81-90頁
[43] 蔡立盛 (2000),粗顆粒砂岩三軸實驗技術改善-以木山層砂岩為例,國立台灣大學土木工程學研究所碩士論文。
[1] D, R. J. OWEN and E. HINTON (1980), Finite elements in plasticity : Theory and Practice.
[3] Desai, C. S., Somasundram, S. and Frantziskonis, G. (1986), A hierarchical approach for constitutive modeling of geologic materials. Int. J. Rock Mech. Mining Sci. & Geomech. Abstr., 10, 225-257.
[4] Desai, C. S. and Salami, M .R. (1987a), A constitutive model and associated testing for soft rock. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 24, 299-307.

被引用紀錄


廖俊逸(2008)。砂岩受剪引致異向軟化及依時組成模式初探〔碩士論文,國立臺灣大學〕。華藝線上圖書館。https://doi.org/10.6342%2fNTU.2008.00462

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