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系統識別號 U0026-0810201801342800
論文名稱(中文) 利用Laplace-Fourier轉換方法分析多含水層表面荷重引起之三維壓密問題
論文名稱(英文) Analyzing Three-dimensional Consolidation Problems of Multi-aquifers due to Surface Loadings by Laplace-Fourier Transform Method
校院名稱 成功大學
系所名稱(中) 土木工程學系
系所名稱(英) Department of Civil Engineering
學年度 106
學期 2
出版年 107
研究生(中文) 林彥呈
研究生(英文) Yen-Cheng Lin
學號 N66051451
學位類別 碩士
語文別 英文
論文頁數 47頁
口試委員 指導教授-林育芸
口試委員-黃忠信
口試委員-王雲哲
口試委員-黃銘智
中文關鍵字 三維壓密問題  表面荷重  多含水層  Laplace-Fourier轉換方法 
英文關鍵字 Three-dimensional consolidation problems  Surface loading  Multi-aquifer  Laplace-Fourier transform 
學科別分類
中文摘要 本文應用Vardoulakis和Harnpattanapanich所開發的方法來解決由表面荷重引起之三維壓密問題。 此方法(我們稱之為L-F法)是建立在Biot的孔隙彈性理論與位移函數在空間與時間轉換域的一般解上。 然而,由於一般解中的指數函數包含有深度 z 以及時間轉換後的變量 "s" ,因此當這兩個變量超出可計算範圍時,會出現數值上的困難。 本研究著重於發展數值技巧以改進L-F法在一些極端情況的使用,包括了:(1) 厚層問題、(2) 多含水/阻水層問題、(3) 極限時間下的壓密行為。 此外,本文也採用有限元素法(FEM)來驗證數值技巧在平面應變與三維下的準確度。 藉由兩種方法的比較,顯示本文提出之數值技巧成功地解決了關於指數函數的問題,同時也突顯出L-F法在效率上的優勢,尤其是對於三維的壓密問題。
英文摘要 This thesis applied the numerical procedure developed by Vardoulakis and Harnpattanapanich to solve three-dimensional consolidation problems caused by surface loading. This procedure (we call it the L-F method) is based on Biot’s poroelastic theory of soils and the general solution of the displacement functions in the transform spatial and time domains. Since the general solutions consist of exponential functions in terms of depth z and the transformed variable "s" of time, difficulties will occur when the components of exponential terms excess the numerical limits. This research focused on improving the L-F method to solve some extreme cases, including (1) thick-layer problems, (2) multi-aquifers/aquitards systems, and (3) limiting time consolidation behaviors. Additionally, finite element models were built to verify the results of our numerical method, and the verification was carried out in both plane-strain and 3D problems. The comparisons show that our numerical techniques successfully solve the difficulties related to exponential terms and the efficiency of the L-F method is better than the finite element method, especially for 3D problems.
論文目次 摘要 I
Abstract II
誌謝 III
Contents V
List of Figures VII
List of Tables IX
Notation X
Chapter 1 Introduction 1
Chapter 2 Theoretical Background 3
2.1 Poroeleastic Theory 3
2.2 Fundamental Solutions 5
2.2.1 Displacement functions for plane-strain problems 5
2.2.2 Displacement functions for 3-D problems 6
2.2.3 Fundamental solutions in the transform domain 6
2.3 Multi-layer System 8
2.3.1 Boundary and continuity conditions 8
2.3.2 The transfer matrix 10
2.4 Limiting Behaviors 13
2.4.1 Undrained condition 13
2.4.2 Drained condition 13
2.5 Numerical Inversion 14
2.5.1 Stehfest algorithm 14
2.5.2 Legendre-Gauss quadrature 14
Chapter 3 Numerical Techniques and FEM Models 16
3.1 Thick-layer Problems 16
3.1.1 Bounds on exponential functions 17
3.1.2 Sublayer method 19
3.2 Limiting Time Conditions 20
3.2.1 Small flow time 20
3.2.2 Large flow time 21
3.3 Numerical Fourier Inversion 22
3.4 Finite Element Models 23
3.4.1 Modeling 23
3.4.2 Meshing 24
Chapter 4 Numerical Results 26
4.1 Plane-strain Problems 26
4.1.1 Single-layer 26
4.1.2 Multi-layer 33
4.2 3-D Problems 35
4.2.1 Single-layer 35
4.2.2 Multi-layer 36
4.3 Comparison of Computational Time 41
Chapter 5 Conclusion 43
References 44
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[28] Weisstein, Eric W. "Laguerre-Gauss Quadrature." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Laguerre-GaussQuadrature.html
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