臺灣博碩士論文加值系統

本文基於圓柱形孔穴擴張理論，探討孔穴外圍土壤之徑向應力及應變關係，對有限邊界孔穴外圍土壤之徑向應力-變形關係進行推導。
文章以孔穴擴張理論分別針對黏土及非黏性材料進行分析，並假設孔穴外圍土壤之應力-應變關係為線彈性-純塑性。黏性土壤於塑性狀態遵守Tresca降伏準則，當土壤形成塑性環時，變形前後體積保持不變；而非黏性材料則符合莫爾-庫倫降伏準則，孔穴未擴張時土壤處在等應力狀態，且在彈性區可採用小應變理論來分析；另外將土壤膨脹角引入塑性環的大應變中，並利用無窮級數的迭代運算，求得膨脹性土壤之大應變孔穴擴張關係；當土壤形成塑性環時，則利用非對應塑性流動法則導出應力與變形之關係。
研究結果顯示：(1)初始孔穴半徑大小不影響孔穴擴張行為，即孔穴邊界比固定，土壤參數固定，其徑向應力-應變關係的結果皆相等，因此本研究適用於任何尺寸大小之孔穴。(2)土壤參數固定，樁與樁之間距較小者，孔穴半徑達一定之膨脹比時，其所對應之徑向應力比愈大。樁距達一定的孔穴半徑倍數時，徑向應力-應變關係與無限邊界結果相同。(3)初始徑向應力、土壤剪力模數、膨脹角及摩擦角愈大，孔穴半徑達一定之膨脹比所需之徑向應力也愈大，隨著孔穴擴張膨脹比增加則徑向應力比增量也愈大。

A theoretical analysis, based on cylindrical cavity expansion theory, is developed for pressure-expansion relationship around cavity in soils. Expansion behavior of a cavity in finite boundary condition is the distinctive features of this study. The analytical process can be applied to the interpretation of the cone penetration test and the load-settlement estimation of granular column.
In the paper, analytical solution is presented for the expansion cavities of both clay and sand in elastic-perfectly plastic soils. Tresca yield criterion is adopted for clay so that the volume remains unchanged as the soil becomes plastic. Mohr-Coulomb yield criterion with a non-associated flow rule is used to represent plastic behavior of the sand. For the case of cylindrical cavity expansion, the axial or vertical stress is assumed to be the intermediate stress and plane strain conditions in the axial direction are assumed.
Load-strain investigations are demonstrated in the first phase of the study. Parametric studies over the influence factor of Young’s modulus, Poisson’s ratio, the initial in situ stress, cavity radius, angle of friction and angle of dilation are introduced as the second part of the study. Finally, the analytical limit pressure can then be obtained.

目錄..................................................I
表目錄................................................IV
圖目錄................................................V
符號說明...........................................XIII
第一章 緒論...........................................1
1-1 前言..........................................1
1-2 研究動機與目的.................................1
1-3 研究方法......................................2
1-4 研究內容......................................2
第二章 文獻回顧.......................................3
2-1 土壤在彈性範圍內之圓柱形孔穴擴張理論.........3
2-2 大地工程上黏土材料之孔穴擴張理論.............4
2-3 大地工程上非黏土材料之孔穴擴張理論............8
2-4 砂土中圓錐貫入試驗...........................21
2-5 孔穴擴張理論之應用...........................21
2-6 砂樁.........................................22
第三章 理論分析模式之建立.............................25
3-1土壤在彈性範圍內之孔穴擴張行為................25
3-1-1 孔穴外為無限邊界土壤應力在彈性範圍之
孔穴擴張行為...............................28
3-1-2 孔穴外為有限邊界土壤應力在彈性範圍之
孔穴擴張行為................................30
3-2 黏性土壤於塑性範圍內之孔穴擴張行為...........33
3-2-1 無限邊界於塑性範圍內之孔穴擴張行為.........33
3-2-2 有限邊界於塑性範圍內之孔穴擴張行為.........39
3-3 非黏性土壤應力達塑性時之孔穴擴張行為.........48
3-3-1 孔穴外為無限邊界之孔穴邊界恰達塑性時
之擴張行為.................................49
3-3-2 孔穴外為有限邊界之孔穴邊界恰達塑性時
之擴張行為.................................50
3-4 非黏性土壤形成塑性環後之孔穴擴張行為.........50
3-4-1 孔穴外為無限邊界之土壤形成塑性環時
孔穴擴張行為...............................51
3-4-2 孔穴外為有限邊界之土壤形成塑性環時
孔穴擴張行為...........................62
第四章 理論分析結果與討論.............................75
4-1 黏性土壤....................................75
4-1-1 有限邊界之徑向應力-應變關係................76
4-1-2 孔穴初始半徑對徑向應力-應變關係之影響......78
4-1-3樁間距對外圍土壤之徑向應力與應變關係的影響..78
4-1-4初始現地應力對孔穴擴張行為之影響............95
4-1-5 土壤剪力模數對孔穴擴張行為之影響...........100
4-2 非黏性土壤...................................106
4-2-1 非黏性土壤之有限邊界徑向應力-應變關係......106
4-2-2 孔穴初始半徑對徑向應力-應變關係之影響......109
4-2-3 樁間距對外圍土壤之徑向應力-應變關係的影響..109
4-2-4 初始現地應力對孔穴擴張行為之影響...........126
4-2-5 土壤剪力模數對孔穴擴張行為之影響...........130
4-2-6 土壤的膨脹角對孔穴擴張行為之影響...........135
4-2-7 土壤的摩擦角對孔穴擴張行為之影響...........140
4-3 極限應力.....................................145
4-3-1 摩擦角對極限應力之影響.....................145
4-3-2 膨脹角對極限應力之影響.....................148
4-3-3 柏松比對極限應力之影響.....................148
4-3-4 土壤剪力模數對極限應力之影響................150
第五章 結論與建議.....................................157
5-1 結論.........................................157
5-2 建議..........................................159
參考文獻..............................................161
附錄 A............................................169
附錄 B..........................................171
附錄 C...........................................178
附錄 D...........................................182

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