岩石边坡模糊随机损伤可靠性研究

目的延拓非确定损伤理论研究以揭示损伤力学蕴涵的复杂机理.方法基于损伤、概率、模糊隶属度在0,1]区间上协调一致性,提出了模糊随机损伤力学观念;构造解释了3类损伤变量模糊性态及对应模糊映射分布,即降半分布、“秋千”分布和组合“秋千”分布,实现了随机损伤变量模糊化自适应生成与构建;依据扩张原理及随机损伤变量满足β概率分布,对模糊集上随机损伤变量的CDF、PDF积分修正,结合当量正态理论,将三类模糊随机损伤泛函引入本构方程,完成了模糊随机有限元可靠度与模糊随机损伤同步分析.结果分析表明,基于全面统计评价的初始损伤场建立,避免了常规损伤力学分析中试验及模型构造的困难.结论借助可靠度理论所得的模糊随机损伤力学模型,可全面揭示复杂工程对象在损伤模糊演变过程中具有的随机变异本质,实现局部损伤发育与结构宏观可靠度的耦合分析.

Rock Slope Reliability Studies Based on Fuzzy Stochastic Damage Theory

The objective of the research is to discover comprehensive damage evolution mechanism through the extension of uncertain damage theory. Fuzzy Stochastic Damage Mechanics development original model is introduced here to discover essentials of damage mechanics science with damage uncertainty＇ s proper expansion based on harmony of damage conception, probability, fuzzy degree of membership on 0,1 ] scale. Three damage variables＇ fuzzy definition status and corresponding fuzzy mapping distributions are formulated, namely, half depressed distribution, swing distribution, combined swing distribution, by which, stochastic damage variables＇ fuzzy process is realized during adaptive generation. Under expansion theory, CDF and PDF of fuzzy stochastic damage variables that submit to probabilistic distribution are adjusted. Damage model ,with equivalent normalization theory, is clarified by the introduction of three fuzzy stochastic damage functionals for constitutional model. And the reliability and fuzzy stochastic damage analysis are carried out on the basis of fuzzy stochastic finite element method. It shows that introduction of comprehensive statistical analytic initial damage field model can help avoid so many inconveniences on damage mechanics research as experimentation and numerical algorithm. Furthermore, the essential conclusion is that fuzzy-stochastic model of damage mechanics based on reliability theorem is an effective principle that can disclose comprehensively randomness of fuzzy evolution on complex structures＇ damage development. The coupled analysis of local material damage evolution and engineering macro-reliability can be realized.