2014-01-012024-05-17https://scholars.lib.ntu.edu.tw/handle/123456789/682840摘要：根據我們最近的研究成果，發現 Vanmarcke 隨機場理論與其衍生的演算法（local averaging subdivision LAS 演算法），應用於有限元素模擬土壤剪力強度空間變異性時， 會導致誤導的分析結果。關鍵的問題在於此理論和演算法的基本假設：一區間的整體 剪力強度，是該區間內剪力強度的空間變異平均值。此假設雖然符合直覺，但我們發 現這個假設一般而言是不正確的，而且在某些應力狀態和空間變異方向的組合下，此 假設可能造成非常誤導的分析結果。 因此，本研究將系統性地探討這一研究議題。我們的研究目標包括(a)進一步了解此 問題的嚴重程度，(b)發展一個新理論和新演算法，取代Vanmarcke 理論和LAS 演算法， (c)了解在新理論和新演算法下，針對諸多大地工程議題（如考慮土壤空間變異之擋土 結構，淺基礎，邊坡穩定）的隨機有限元分析的結論，是否與Vanmarcke 理論和LAS 演算法的結論有顯著不同。<br> Abstract: Based on our recent investigations, it is found that a well known theory (Vanmarcke’s theory) and the resulting algorithm (the local averaging subdivision LAS algorithm) can produce misleading results when they are implemented in finite element analysis (FEA) to simulate spatial variability of soil shear strengths. The key issue is in the fundamental assumption made in the theory and the algorithm – the overall shear strength of a region is the average of the spatially variable shear strength over that region. Although intuitive, this assumption is found to be in general incorrect and, moreover, to be extremely misleading in certain combinations of stress state and spatial variability orientation. Therefore, this research is proposed to further explore this issue in a more systematic manner. The goal is to find how serious this issue can be, to derive a new theory and a new algorithm to replace Vanmarcke’s theory and the LAS algorithm, and to investigate whether the new theory and algorithm would produce significantly different conclusions from Vanmarcke’s theory and the LAS algorithm when the new framework is implemented in random field FEA for geotechnical subjects such as retaining structures, shallow foundations, and slope stability subjected to spatial variability.土壤剪力強度空間變異性不確定性可靠度分析soil shear strengthspatial variabilityuncertaintyreliability analysis