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題名 | 變分法與突變理論在邊坡穩定分析方法上之應用 |
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作者 | 鄭魁香; 蔣偉寧; | 書刊名 | 高苑技術學報 |
卷期 | 2 1993.02[民82.02] |
頁次 | 頁1-11 |
分類號 | 441.103 |
關鍵詞 | 邊坡穩定分析; 變分法; 突變理論; Landslide stability analysis; Variational calculus; Catastrophe theory; |
語文 | 中文(Chinese) |
中文摘要 | 邊坡穩定分析方法除了基於FEM的位移法和破壞機率法外,仍以極限平衡理論的各種切片法為邊坡穩定分析方法的要項。切片法至少有兩個明顯的缺點。第一:各種切片法以比較所得出之最小安全係數之臨界破壞面,並非是邊坡滑動破壞整體機置之最小安全係數。第二,極限平衡理論的本身並不能充份說明邊坡滑動破壞的實際機置。 本文針對上述兩個缺點採取了如下的改進。首先,使用變分法 (Variational calculus) 中求極值曲線的性質,恰可將安全係數定義為邊坡破壞滑動面曲線的函數,由安全係數函數之極值化條件,可求出整體系統之最小安全係數與任意之臨界破壞滑動面。其次,在考慮整體破壞機置的基礎上,本文引用了突變理論(Catastrophe theory),作為邊坡突然破壞(山崩)的基礎理論。文中,除了導出系統之控制方法 (即臨界點方程) 外,尚導出邊坡破壞之特徵關係方程 (C-R equation)。最後,並以實例作應用上之比較說明,間接支持了突變理在邊坡穩定分析應用上之可行性。 |
英文摘要 | The slice method, according to limited equilibrium theony is the most essential of analitical method about slope stability, besides the finite element and the probability of failure method. But the silce method has two crisp problems about the slope stability, one is that the factor of safety is not the smallest factor of the landslide mechanism, the other is that the theory of limited equilibrum is not the true mechanism of the landslise. In this paper, we use the varlationol calculus which can find the extrame value properties to get the general safety factor equation about any landslide plane of critical failure, and then, we find that the Catastrophe theory can be the fundamental theory about the mechanism of landslide. In addition to establish the governing equation about the critical point, the characteristic relation equation is also obtained by us. Finally, we do the exercise about the actual example, and this method is proved reasonable and probable. |
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