钢筋混凝土柱抗弯承载力的概率模型与校准分析

为了克服传统确定性抗弯承载力模型和校准方法无法合理考虑不确定性所存在的缺陷,分别建立了钢筋混凝土(RC)柱的概率抗弯承载力模型与概率校准方法。首先,基于RC柱正截面受弯承载力的基本假定,结合偏心受压RC柱的截面内力平衡条件,分别建立了大(小)偏心受压RC柱的确定性抗弯承载力模型;然后,综合考虑固有不确定性和认知不确定性的影响,分别建立了大(小)偏心受压RC柱概率抗弯承载力模型的解析表达式,进而结合贝叶斯理论和MCMC法确定了概率模型参数的后验分布信息,从而建立了RC柱的概率抗弯承载力模型;最后,基于概率抗弯承载力模型所确定的概率密度函数、置信区间和置信水平,提出了传统确定性抗弯承载力模型的概率校准方法。研究结果表明,所建立的概率抗弯承载力模型不仅可以合理描述RC柱抗弯承载力的概率分布特性,而且可以校准传统确定性抗弯承载力模型的计算精度和置信水平。

Probabilistic model and calibration of flexure strength of reinforced concrete columns

A probabilistic model and a calibration method for flexure strength of reinforced concrete (RC) columns were proposed to overcome the disadvantage that traditional deterministic flexure strength models and calibration methods cannot rationally consider the influence of uncertainties.Based on the basic assumption of flexure strength analysis of RC members,deterministic flexure strength models for large (small) eccentric compression RC columns were established firstly according to the force balance condition of eccentric compression RC columns.Then analytical expressions for probabilistic flexure strength models of RC columns were developed by considering the influences of both aleatory and epistemic uncertainties.Subsequently,probabilistic models were established by determining the posterior distribution information of probabilistic model parameters based on the Bayesian theory and the Markov Chain Monte Carlo(MCMC)method.Finally,probabilistic calibration methods of traditional deterministic flexure strength models were proposed based on the probability density function,confidence interval and confidence level determined by the proposed probabilistic models.Analysis results show that the probabilistic flexure strength models not only can reasonably describe the probabilistic characteristics of flexure strength,but also provide an efficient way to calibrate the accuracy and confidence level of traditional deterministic flexure strength models of RC columns.