Abstract The assessment of structural capacity against collapse is conducive to the optimal design of new structures as well as checking the safety of existing structures. However, the evaluation cannot be typically carried out by means of destructive tests on prototype or reduced scale structures. In this regard, the numerical models that adequately represent the prototype structures can be alternatively used. Specifically, both the nonlinearities and randomness as well as their coupling effect of materials need to be represented in a unified manner in structural analysis. The present paper aims at providing an effective approach to incorporate the stochastic nature of damage constitutive relationships in collapse analysis and assessment of concrete structures subjected to earthquake ground motions. Within the framework of stochastic damage mechanics, the spatial variability of concrete is represented by a two-scale stationary random fields. The concept of covariance constraint is introduced to bridge the two-scale random fields such that the scale-of-fluctuation of the random material property is satisfied at both scales. Random damage evolution induced structural collapse analysis is achieved via the nonlinear stochastic finite element method. To address the randomness propagation across scales, the probability density evolution method is employed. By exerting the absorbing boundary condition associated with an energy-based collapse criterion on the generalized probability density evolution equation, the anti-collapse reliability of concrete structures can be evaluated with fair accuracy and efficiency. Numerical investigation regarding an actual high-rise reinforced concrete frame-shear wall structure indicates that the random damage evolution of concrete dramatically affects the structural nonlinear behaviors and even leads to entirely different collapse modes. The proposed method provides a systematic treatment of both uncertainties and nonlinearities in collapse assessment of complex concrete structures.

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受随机损伤演化影响的混凝土结构的基于能量的倒塌评估

摘要 结构抗倒塌能力评估有利于新结构的优化设计和现有结构的安全性检验。然而，评估通常不能通过对原型或缩小规模的结构进行破坏性测试来进行。在这方面，可以替代地使用充分代表原型结构的数值模型。具体而言，材料的非线性和随机性及其耦合效应需要在结构分析中以统一的方式表示。本文旨在提供一种有效的方法，将损伤本构关系的随机性纳入地震地震作用下混凝土结构的倒塌分析和评估中。在随机损伤力学的框架内，混凝土的空间变异性由两尺度平稳随机场表示。引入协方差约束的概念来桥接两尺度随机场，使得随机材料属性的波动尺度在两个尺度上都得到满足。随机损伤演化引起的结构倒塌分析是通过非线性随机有限元方法实现的。为了解决跨尺度的随机性传播问题，采用了概率密度演化方法。通过在广义概率密度演化方程上应用与基于能量的倒塌准则相关的吸收边界条件，可以以相当准确和有效的方式评估混凝土结构的抗倒塌可靠性。对实际高层钢筋混凝土框架-剪力墙结构的数值研究表明，混凝土的随机损伤演化显着影响结构的非线性行为，甚至导致完全不同的倒塌模式。所提出的方法提供了对复杂混凝土结构倒塌评估中的不确定性和非线性的系统处理。