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系統識別號 U0026-1508201210543600
論文名稱(中文) 含兩相非混合、可壓縮並具有黏滯性流體之孔彈性介質於固定載重下壓密理論與數值研究
論文名稱(英文) A Theoretical and Numerical Study on Consolidation Behaviors of A Poroelastic Medium Containing Two Immiscible, Viscous, Compressible Fluids Subject to Constant External Loadings
校院名稱 成功大學
系所名稱(中) 水利及海洋工程學系碩博士班
系所名稱(英) Department of Hydraulics & Ocean Engineering
學年度 100
學期 2
出版年 101
研究生(中文) 黃鈺涵
研究生(英文) Yu-Han Huang
學號 n88971033
學位類別 博士
語文別 中文
論文頁數 135頁
口試委員 指導教授-羅偉誠
口試委員-蔡長泰
口試委員-陳主惠
口試委員-周憲德
口試委員-譚義績
中文關鍵字 孔彈性理論  固定壓力  壓密  總沉陷量  土壤基質統體模數  有效黏滯係數 
英文關鍵字 Poroelasticity theory  Constant loading  Consolidation  Total settlement  Bulk modulus of solid matrix  Effective dynamic viscosity parameter 
學科別分類
中文摘要 本研究應用孔彈性理論方程式及兩種非混合流體之應力-應變本構關係,推導出含兩相非混合流體之彈性孔隙介質的壓密理論。假設土體表面施加垂直固定壓力,透過拉普斯轉換求得排水與不排水之四種不同上下邊界情況,以及濕潤性與非濕潤性流體之孔隙水壓與壓密沉陷量的一維解析解。為量化分析非飽和土壤之壓密行為,本文數值模擬十一種不同質地非飽和土壤為例,其孔隙由兩種非混合之流體(空氣-水)所填滿,另外再針對林肯砂土及哥倫比亞細砂質壤土,探討孔隙間不同流體組合(空氣-水、油-水、空氣-油)之變化,分別模擬三種不同初始飽和度及四種邊界條件,以無因次孔隙水壓及土壤總沉陷量結果圖相互比較討論其壓密行為。
根據結果得知,相同孔隙間流體組合不同質地之土壤,皆發現初始飽和度值越小,則無因次孔隙水壓消散越快,且最快到達壓密沉陷穩定。探討不同土壤質地受壓後之變化,以砂土含量較高之土壤的壓力消散為最快,而壓力消散最慢為黏土含量較高之土壤,此與土壤孔隙介質滲透係數有關;然而土壤總沉陷量之比較,以黏土含量較高之土壤總沉陷量為最大,而沉陷量最小為砂土含量較高之土壤,其背後的物理機制與土壤基質統體模數有關。
對於相同土壤性質不同孔隙間流體組合的探討,發現土壤之消散快慢與流體之黏滯係數、相對滲透係數、滲透係數及流體密度皆有關係,因此流體的組合對於壓密沉陷之影響較為複雜,且須考慮的因子較多,依目前結果得知無因次孔隙水壓隨飽和度變化的曲線趨勢與Lo et al. (2005)所提出之有效動力黏滯係數之曲線趨勢非常相似。
在此探討未飽和土壤之邊界條件、土壤質地及孔隙間流體性質對未飽和土壤沉陷行為的影響。主要針對未飽和土壤推導沉陷理論並進行數值模擬討論,應可對於固定壓力下發生土壤沉陷的模擬提供參考價值與助益。
英文摘要 In this study, a theoretical analysis of consolidation behaviors for a poroelastic medium containing two immiscible, compressible, viscous fluids is presented based on the theory of poroelasticity and the linear stress-strain relationship. Using Laplace transformation, we derive the analytical solution of the excess pore pressure of the wetting and non-wetting fluids as well as soil settlement for different drained and undrained boundaries under a constant external load. To quantitatively investigate the consolidation process of an unsaturated porous medium, a numerical study is carried out to determine the dimensionless pore water pressure and soil settlement for eleven different soil texture classes whose pore space is simultaneously occupied by air and water as illustrative examples. Moreover, we examine the effect of the mixture of immiscible fluids using Lincoln sand and Columbia fine sandy loam saturated either air-water, oil-water, or air-oil. Then, three different initial saturations and four boundary conditions are selected to model the dimensionless pore water pressure and soil settlement.
Our numerical results show that the dimensionless pore water pressure dissipates faster at low water saturation, in which soil settlement also tends to achieve stable faster. In addition, it is also revealed that soils with high sand content respond to the external load the fastest, followed by high silt content and high clay content. Lastly, soil settlement is found to be the greatest in soils with high clay content, followed by high silt content and high sand content, the dominant factor of which is mainly due to the bulk modulus of solid matrix.
For the same soil texture with different pore fluid mixtures, the dimensionless excess pore pressure dissipation speed is related to the coefficient of viscosity, relative permeability coefficient, permeability coefficient, and material density; therefore, the effect of pore fluid mixture on soil consolidation is more complicated so that more factors need to be considered. It is also observed that an effective dynamic viscosity parameter is a crucial physical parameter that possesses the similar trend to the dimensionless pore pressure with respect to water saturation.
In the current study, we have made a first but important step in exploring the impact of the boundary conditions, soil texture, and pore fluid properties on the consolidated process of unsaturated soils. Our result should be able to offer reference and benefit for a better understanding of the consolidated behavior of an unsaturated elastic porous medium under a constant loading subject to different boundaries conditions in various soil textures.
論文目次 目錄
中文摘要 Ⅰ
英文摘要 Ⅱ
誌謝 Ⅳ
目錄 Ⅴ
表目錄 Ⅶ
圖目錄 Ⅷ
符號說明 ⅩⅥ
第一章 緒論 1
1-1 研究動機 1
1-2 文獻回顧 2
1-3 研究目的及方法 8
1-4 本文架構 9
第二章 研究理論 10
2-1 孔彈性理論方程式 10
2-2 應力-應變關係式 12
2-3 控制方程式 13
2-4 初始條件 17
2-5 邊界條件 17
第三章 數值模擬 25
3-1 土壤種類與質地 25
3-2 保水曲線 32
3-3 水力傳導函數 32
3-4 傅立葉級數展開解 33
第四章 結果與討論 39
4-1 相同流體條件不同土壤質地之比較 39
4-1-1 邊界條件的影響 39
4-1-2 初始飽和度的影響 40
4-1-3 土壤質地的影響 40
4-2 相同土壤質地不同流體條件之比較 42
4-2-1 邊界條件的影響 42
4-2-2 初始飽和度的影響 43
4-2-3 土壤質地的影響 44
4-2-4 流體性質的影響 44
第五章 結論與建議 126
5-1 結論 126
5-2 建議 129
參考文獻 130
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