探討空間變異性下Φ=0°土壤的整體剪力強度分佈形式

Vanmarcke (1977)提出在一區域之隨機場中，土壤性質的空間平均(Spatial Average)等於其固有平均值(Inherent Mean)，而其變異性大小為固有變異性(Inherent Variance) × 變異數折減因子(Variance Reduction Factor)。而後Fenton and Vanmarcke (1990)提出空間平均法應用於有限元素法(FEM)之分析中。而高炳勳(2012)根據空間平均的方式進行隨機場有限元素分析，對於在均勻的應力場下具有空間變異性土壤的整體剪力強度(Mobilized Shear Strength)之變異性與期望值，已提出了一套完整的數學模型，本研究將根據Ditlevsen (1966)所提出的數學模型更進一步提出在均勻的應力場下具有空間變異性土壤的整體剪力強度的機率分佈模型，希望能不用透過隨機場有限元素分析，來得到具有空間變異性土壤的整體剪力強度。除此之外，本研究也希望能運用提出的整體剪力強度分佈模型發展新的隨機場有限元素分析參數給定方式，因此會同時探討在隨機場中不同位置整體剪力強度的關聯性，最後將有限元素分析結果與前人所使用的空間平均方式進行比較。本研究將使用有限元素分析軟體為ABAQUS以及數學計算軟體MATLAB進行整體剪力強度的分析運算，並設定不同的應力狀態與空間變異性，檢驗本研究所提出的整體剪力強度分佈模型正確性。

關鍵字

隨機場；空間變異性；整體剪力強度；機率分布模型；有限元素分析

並列摘要

Vanmarcke (1977) showed that the spatial averaged property of a random field over a region has mean value identical to the inherent mean, while the variance is inherent variance multiplied by variance reduction factor. Furthermore, Fenton and Vanmarcke (1990) propose the method of simulating spatial average in finite element method. Kao (2012) proposes a set of equations to predict the mean value and variance of mobilized shear strength for spatially variable soil under uniform stress states. This study further advances the distribution model of 2-D mobilized shear strength. Complicated behavior of mobilized shear strength can be fitted satisfactorily with this model. Based on the distribution model, mobilized shear strength of soil with spatial variability can be simulated without the need of conducting random field finite element analyses. Another purpose of this study is to propose a new way in assigning material properties in random field finite element method analysis. Spatial averaging effect can be avoided during the properties assignment process with the new way introduced herein. Comparison of the results of the finite element method with the results of the previous studies are also presented.

並列關鍵字

random field ； spatial variability ； mobilized shear strength ； probability distribution ； finite element analysis

參考文獻

高炳勳 (2012). 在簡單應力狀態下探討具空間變異性土壤的整體剪力強度. 臺灣大學土木工程學研究所學位論文, (2012年).

Jha, S. K., and Ching, J. (2013). Simulating spatial averages of stationary random field using the Fourier series method. Journal of Engineering Mechanics, 139(5), 594-605.

Breysse, D., Niandou, H., Elachachi, S., and Houy, L. (2005). A generic approach to soil-structure interaction considering the effects of soil heterogeneity, Geotechnique, 55(2), 143-150.

Ching, J. and Phoon, K.K. (2013a). Mobilized shear strength of spatially variable soils under simple stress states, Structural Safety, 41, 20-28.

Ching, J. and Phoon, K.K. (2013b). Effect of element sizes in random field finite element simulations of soil shear strength, Computers and Structures (in press).

國際替代計量

探討空間變異性下Φ=0°土壤的整體剪力強度分佈形式

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