空間變異性土體於地工結構出口最大水力坡降的機率分佈

Abstract

由於礦物組成不均勻與受應力歷史差異等原因，即使在地質上看似均勻的土層中，土壤參數仍呈現一定程度的變異性。此種隨空間位置改變而產生的參數差異被稱為空間變異性 (Spatial variability)，是導致大地工程分析與設計結果產生不確定性的主要因素之一。在深開挖工程與土石壩等大地工程應用中，管湧破壞 (Piping failure) 為潛在之破壞機制，對整體結構安全評估具有關鍵影響。然而，目前多數設計規範並未充分考慮土壤參數的空間變異性，在部分情境下，若滲流出口存在低滲透係數之薄層土體，將導致出口處水力坡降顯著升高，進而引發管湧破壞。然而，傳統均質分析方法難以準確描述此類破壞行為，導致分析結果潛藏不可量化的風險與不確定性。 本研究針對滲透係數 (Permeability) 具空間變異性土體，探討在滲流作用下管湧破壞機率，並提出最弱路徑模型 (Weakest-path model, WPM)，用以描述最大出口水力坡降 (Maximum exit hydraulic gradient) 的機率分布。進一步地，藉由隨機有限元素分析 (Random finite element analysis, RFEA) 所得結果，對最弱路徑模型中各項參數進行校準與驗證。透過本研究發展之機率模型，結合模型參數回歸分析結果，能在大幅降低計算成本的前提下，快速且合理地估算管湧破壞機率，為未來實務工程提供兼具效率與可靠度之風險評估工具。

Due to the difference in mineral composition and variations in stress history, soil properties often exhibit a certain degree of variability, even within geologically uniform layers. This spatially dependent variability, known as spatial variability, is one of the primary sources of uncertainty in geotechnical analysis and design. In geotechnical applications such as deep excavations and earth dams, piping failure is a potential failure mechanism that plays a critical role in overall structural safety assessment. In certain cases, the presence of a thin layer of soil with low permeability at the seepage exit can lead to a significant increase in the hydraulic gradient, thereby triggering piping failure. Traditional homogeneous analyses are often incapable of accurately capturing such failure behaviors, resulting in unquantified risks and uncertainties in analysis results. This study focuses on evaluating the probability of piping failure under seepage conditions in soils with spatially variable permeability. A Weakest-path model (WPM) is proposed to describe the probabilistic characteristics of maximum exit hydraulic gradient. Furthermore, model parameters are calibrated and validated using results obtained from Random Finite Element Analysis (RFEA). By integrating the proposed probabilistic model with regression analysis of the calibrated parameters, the probability of piping failure can be estimated both efficiently and accurately. This approach significantly reduces the computational cost associated with RFEA while providing a reliable and practical tool for risk assessment in real-world geotechnical engineering projects.