利用物質點法模擬與探討路面受壓之行為

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Title:	利用物質點法模擬與探討路面受壓之行為
Authors:	劉晏彤;Liu, Yen-Tung
Contributors:	土木工程學系
Keywords:	物質點法;廣義插值物質點法;降伏準則;路面受壓分析;車輪載重;Material Point Method;Generalized Interpolation Material Point Method;von Mises criteria;Drucker-Prager criteria;mechanical behaviors of pavement under wheel loads
Date:	2025-07-21
Issue Date:	2025-10-17 11:03:08 (UTC+8)
Publisher:	國立中央大學
Abstract:	長久以來，有限元素法（Finite Element Method, FEM）在固體力學問題的分析中廣泛應用並得到充分驗證，然而在面對複雜幾何結構與大變形問題時，常會遇到模型建構困難和網格重新分配等挑戰。近年來，物質點法（Material Point Method, MPM）因其模型建構彈性高，並能有效處理材料大變形與運動接觸等問題，逐漸成為探討複雜力學行為的熱門數值方法之一。本研究運用物質點法建構三維路面數值模型，以模擬路面受壓過程中土體內部之應力分佈與變形行為，探討不同參數條件下力學反應之異同。模型中包含路面上方質量塊，以及路面下方之底層、基層與路床，並透過調整土壤材料參數與加載方式，建立多組對照模擬案例。研究中首先考慮兩組材料模型：Model A為依土層分層設置之異質材料模型，Model B則視作均質土壤材料，作為探討材料參數設定對模擬穩定性與結果合理性之對照基準。在數值方法方面，比較傳統物質點法與廣義插值物質點法(Generalized Interpolation Material Point Method, GIMP)在應力傳遞行為之差異。在組成律方面，納入土壤受力分析常見之von Mises與Drucker-Prager降伏準則，分析其對塑性行為與應力分佈的影響。加載方式則分別探討自重加載與速度加載兩種條件對模擬行為之影響。本研究進一步透過應力-時間曲線與深度-應力曲線進行系統性比較，並將各物質點上之物理量輔以視覺化軟體進行呈現，強化模擬結果之可讀性與直觀呈現。本研究可證實物質點法應用於路面受壓行為研究之可行性與潛力，並為後續數值模擬提供分析依據，有助於提升相關工程研究之準確性與可靠性。;For decades, the Finite Element Method (FEM) has been widely applied and rigorously validated in the analysis of solid mechanics problems. However, when dealing with complex geometries and large deformation scenarios, FEM often faces challenges such as difficulties in model construction and the need for repeated mesh regeneration. In recent years, the Material Point Method (MPM), with its high flexibility in model development and its ability to effectively handle large deformations and material contact behaviors, has gradually emerged as a popular numerical method for analyzing complex mechanical phenomena. This study utilizes the Material Point Method to construct a three-dimensional numerical model aimed at simulating the stress distribution and deformation behavior within subgrade soils under surface loading conditions. The model consists of a mass block, surface layer, base layer, and original soil, with multiple comparative simulation cases created by adjusting soil material parameters and loading methods. Initially, two sets of material models are considered: Model A, a heterogeneous layered soil model based on stratified configurations, and Model B, a homogeneous soil model. These models serve as a comparative benchmark for evaluating the stability and rationality of material parameter settings. Regarding numerical techniques, this study compares the traditional MPM and the Generalized Interpolation Material Point Method (GIMP) in terms of their differences in stress transmission behavior. For constitutive modeling, both the von Mises and Drucker-Prager yield criteria are incorporated to investigate their influence on plastic behavior and stress distribution. In terms of loading approaches, both self-weight and velocity-based loading are examined to assess their effects on simulation results. The study further conducts systematic comparisons through stress–time and depth–stress curves and enhances the interpretability of simulation outcomes using Ovito for visual representation. The results demonstrate the feasibility and potential of applying MPM in simulating pavement compression behavior. This research provides valuable references for subsequent numerical modeling and contributes to improving the accuracy and reliability of related geotechnical engineering analyses.
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