最弱路徑模型於空間隨機剪力強度問題中的校正

Calibration of Weakest-path Model for Problems with Spatially Variable Shear Strengths

陳映中(Ying-Zhong Chen)

指導教授 ： 卿建業

國立臺灣大學/工學院/土木工程學研究所/碩士(2019年)

https://doi.org/10.6342/NTU201902363

摘要

本研究探討土壤性質的空間變異性對各種大地工程案例的影響。經過前人研究發現，任意區域內的空間平均並不適用於受驅動強度所控制的極限狀態問題，而是需要沿臨界滑動曲線(critical slip curve, CSC)的特殊空間平均值。臨界滑動曲線並非任何規定的曲線，它能同時反映出弱帶以及該工程之力學機制、邊界條件，在本研究使用的最弱路徑模型(weakest-path model)之下，臨界滑動曲線被定義為n個互相獨立的潛在滑動曲線(potential slip curve, PSC)中最弱的ㄧ條，但由於有限元素分析(FEA)無法明確的找出沿著臨界滑動曲線上的空間平均值，取而代之的是均質化(homogenization)方法，藉由比較隨機場模型以及均質模型的反應(response)，將隨機場均質化成隨機變數。在本研究中，最弱路徑模型所扮演的角色是預測均質化的土壤性質，如此便可在沒有複雜的隨機有限元素分析(RFEA)之下預測土壤實際提供的強度。研究中的案例分為四類，包含邊界束制強、中、弱，以及無邊界束制，以上分別代表主動式擋土牆、開挖底部隆起及淺基礎承載力、土壤試體(軸向施以均佈位移)，以及土壤試體(頂部施以側向位移)，研究中發現，當潛在滑動曲線大致上遵守古典滑動曲線(classical slip curve)的軌跡時最弱路徑模型能有效的預測均質化土壤性質，不僅如此，在臨界關聯性長度現象(critical SOF)時亦表現良好，這使得最弱路徑模型更有意義。

關鍵字

空間變異性 ； 最弱路徑模型 ； 臨界關聯性長度 ； 均質化 ； 獨立潛在滑動曲線

並列摘要

This study explores the effects of spatial variability in soil properties on various geotechnical engineering cases. Previous studies have found that the spatial average in any region is not suitable for ultimate limit state problems that are governed by mobilized soil strength and that an average along the critical slip curve is needed. The critical slip curve is not a prescribed curve, it can reflect the weak region, mechanical mechanism and boundary conditions of the engineering. Among the weakest-path model in my study, critical slip curve is defined as the weakest-path of the n independent potential slip curves. However, the average along the critical slip curve can not be easily calculated by finite element analysis, an alternative approach, call homogenization, is used. Homogenize random fields into random variables through comparing the responses of heterogeneous cases and the responses of homogeneous cases. In this study, the weakest-path model plays the role of predicting the homogenized soil properties, so that the actual soil strength can be predicted without complex random finite element analysis. The cases in the study are divided into four types, strong boundary effect, medium boundary effect, week boundary effect, and boundaryless effect, represented separately active retaining wall, basal heave or bearing capacity, soil column (axial displacement at the top), and soil column (lateral displacement at the top). The study found that the weakest-path model can effectively predict the homogenized soil properties if the potential slip curve roughly follow the trajectory of the classical slip curve. Moreover, it also performs well in the phenomenon of critical scale of fluctuation, which makes the weakest-path model more meaningful.

並列關鍵字

spatial variability ； weakest path model ； critical scale of fluctuation ； homogenization ； independent potential slip curve

參考文獻

Allahverdizadeh, P., Griffiths, D. V. and Fenton, G. A. (2016). Influence of soil shear strength spatial variability on the compressive strength of a block. Georisk: Assessment and Management of Risk for Engineered Systems and Geohazard, Vol, 10, No. 1, 2-10.

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). Probability distribution for mobilized shear strengths of spatially variable soils under uniform stress states, Georisk, 7(3), 209-224.

Ching, J., Phoon, K.K. and Sung, S.P. (2017). Worst case scale of fluctuation in basal heave analysis involving spatially variable clays. Structural Safety, 68, 28-42.

Ching, J., Wu, T. J., Stuedlein, A. W. and Taeho Bong. (2018). Estimating horizontal scale of fluctuation with limited CPT soundings. Geoscience Frontiers, 9, 1597-1608..