剪切型钢筋混凝土柱临界斜裂缝倾角的概率模型

对于剪切型钢筋混凝土(RC)柱,传统的确定性临界斜裂缝倾角模型难以有效考虑其材料参数、几何尺寸和边界约束条件等方面不确定性因素的影响,导致计算精度有限,且离散性较大。鉴于此,本文研究建立了剪切型RC柱临界斜裂缝倾角的概率模型。首先,基于变角桁架模型理论,建立了剪切型RC柱临界裂缝倾角的确定性模型;然后,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可夫链蒙特卡洛(MCMC)法,建立了剪切型RC柱临界斜裂缝倾角的概率模型,并推导了均值和方差的解析表达式,从而能够合理描述临界斜裂缝倾角的概率分布特性;最后,利用试验数据对比验证了该模型的有效性,并校准了现有确定性模型的置信水平,进而确定了不同置信水平下剪切型RC柱临界斜裂缝倾角的概率特征值。

Probabilistic model for critical diagonal crack angle of shear-critical reinforced concrete columns

Traditional models for critical diagonal crack angle of shear-critical reinforced concrete (RC) column are generally deterministic and exhibit low accuracy and large scatter,due to the fact that they do not consider the uncertainties of various influential factors,such as material parameters,geometric dimension and boundary constraints and so on.In order to overcome the above limitations,a probabilistic model for critical diagonal crack angle of shear-critical RC column was established in this study.The deterministic model for critical diagonal crack angle of shear-critical RC column was proposed based on the variable angle truss model first.Then,a probabilistic model for critical diagonal crack angle of shear-critical RC column which takes into account the influence of both epistemic and aleatory uncertainties was developed by combining with the Bayesian theory and the Markov Chain Monte Carlo (MCMC) method.Moreover,analytical expressions of the mean and variance of probabilistic critical diagonal crack angle were also derived.The accuracy and efficiency of the proposed probabilistic model were validated by comparing with the experimental data and existing deterministic models,which indicates that the proposed probabilistic model could describe the probabilistic characteristic of critical diagonal crack angle of the shear-critical RC column reasonably.Most importantly,the proposed probabilistic model provides not only a benchmark to calibrate the confidence level of traditional deterministic models,but also an efficient way to determine the characteristic values of critical diagonal crack angles of shear-critical RC column with different confidence levels.