本研究主要研究混凝土材料之非線性行為，透過Darwin & Pecknold提出的等效單軸應變概念與Balan所提出的混凝土亞塑性模型(Hypo-plastic Model)，將混凝土材料中多軸互制行為轉化為多個單軸行為，簡化了混凝土在塑性行為分析中許多積分及複雜的數學計算，且也能得到相當好的結果。在傳統的塑性力學中，流動法則(Flow Rule)及硬化法則(Hardening Rule)為塑性材料模型中常用到的兩個法則，在亞塑性模型中雖然此兩個法則無使用，但其造成的影響卻直接表現於材料行為中。本研究使用之分析方式有別於傳統做法，使用塑性力學處理材料非線性問題，提出一個方法處理混凝土非線性行為。混凝土之亞塑性材料模型中主要分為兩個部分，分別為材料破壞曲面(Ultimate Surface)，及等效單軸應力應變曲線。本研究選用由Menetrey & Willam 修正 Willam-Warnke 之模型，成為Menetrey-Willam模型。同時，考慮到材料之三維壓力強度極限(Ultimate Strength)，加入帽蓋模型修正且提出封閉Menetrey-Willam模型，包含了子午線與帽蓋模型。在混凝土等效單軸應力應變曲線則是使用Saenz所提出的曲線公式，此公式僅需以一條方程式即可描述混凝土行為中之硬化段與軟化段，在數值模擬的使用上相當簡潔且方便。本研究之數值算例分別驗證了混凝土單軸、雙軸、三軸及高強度混凝土之三軸行為，在混凝土的三軸試驗中，因三個方向的應力加載，導致混凝土的強度提高，在研究中也提出修正破壞曲面的方式預測混凝土在三軸試驗的應力應變走向。

In this research, focus on non-linear behavior of concrete by using concept of “Equivalent Uniaxial Strain” proposed by Darwin & Pecknold and concept of “Hypo-plastic Model” proposed by Balan, concept of “Equivalent uniaxial strain” degenerate muti-axial which react upon each other into multiple uniaxial, also simplify mathematic calculation. Though, in traditional plastic mechanics, flow rule and hardening rule commonly use plastic material model, those rules are not used in hypo-plastic model. Method of this research is different from traditional way. Hypo-plastic model can be classified into two parts, one is “Ultimate Surface”, the other one is “Equivalent uniaxial strain envelope”. In regard of using ultimate surface model, choose Willam-Warnke which revised by Menetrey & Willam and named Menetrey-Willam Model. Meanwhile, in consideration of ultimate strength in tri-axial compress, we adding “Cap Model” to revise and named this model “Closed Menetrey-Willam” model, this contain both meridian and cap model. Second part of hypo- plastic model is using Equivalent uniaxial strain envelope of concrete proposed by Saenz. In this study, uniaxial, biaxial, tri-axial experiments are applied to verify analysis. Especially tri-axial loading test, because of loading path along three principal directions, strength of concrete will be lifted up to another level, in order to solve this, propose a method of revising failure surface to predict ultimate state in tri-axial loading test.

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