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Probabilistic Model for Critical Crack Angle of Reinforced Concrete Beams

DOI：

 作者 单位 E-mail 余波 广西大学 gxuyubo@gxu.edu.cn 陈冰 广西大学 唐睿楷 广西大学 万伟伟 广西大学

钢筋混凝土（RC）梁的传统临界斜裂缝倾角计算模型无法综合考虑剪跨比、混凝土强度、配筋率、配箍率等重要因素的影响，而且属于确定性计算模型，导致计算精度有限、离散性较大。鉴于此，本文综合考虑上述重要因素及其不确定性的影响，研究建立了RC梁临界斜裂缝倾角计算的概率模型。首先基于修正压力场理论，建立了RC梁临界斜裂缝倾角的确定性计算模型；然后引入剪跨比修正系数，并综合考虑主观不确定性和客观不确定性因素的影响，结合贝叶斯理论和马尔科夫链蒙特卡洛法（MCMC），建立了RC梁临界斜裂缝倾角计算的概率模型；最后通过与试验数据和传统确定性计算模型的对比分析，验证了该模型的有效性和适用性。分析结果表明，该概率模型不仅可以合理描述临界斜裂缝倾角的概率分布特性，而且可以校准传统确定性计算模型的计算精度和置信水平，还可以根据预定的置信水平确定临界斜裂缝倾角的概率特征值，具有良好的计算精度和适应性。

Traditional models for critical crack angle of reinforced concrete (RC) beams are generally deterministic models and exhibit low computational accuracy and large fluctuation, due to the fact that they do not take into account the influences of various important parameters such as shear span ratio, concrete strength, reinforcement ratio and stirrup ratio. In order to overcome the above limitations, a probabilistic model for critical crack angle of RC beam was established in this study. The deterministic model for critical crack angle of RC beam was proposed based on the modified compression field theory (MCFT) first. Then, a probabilistic model of critical crack angle for RC beam which takes into account the influences of both aleatory and epistemic uncertainties was developed by combining with the Bayesian theorem and the Markov Chain Monte Carlo (MCMC) method. Finally, the applicability and efficiency of the proposed probabilistic model were validated by comparing with the experimental data and traditional deterministic models. Analysis results show that the proposed probabilistic model can not only describe the probabilistic distribution characteristics of critical crack angle, but also can provide a benchmark to calibrate the confidence level of traditional deterministic models and provide an efficient way to determine the characteristic values of critical crack angle with different confidence levels.
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