剪切型钢筋混凝土柱抗剪承载力计算的概率模型

现有的钢筋混凝土（RC）柱抗剪承载力计算模型大多属于确定性模型，难以有效考虑几何尺寸、材料特性和外荷载等因素存在的不确定性，导致计算结果的离散性较大，且计算精度和适用性有限。鉴于此，该文结合变角桁架-拱模型和贝叶斯理论，研究建立了剪切型RC柱抗剪承载力计算的概率模型。首先基于变角桁架-拱模型理论，并考虑轴压力对临界斜裂缝倾角的影响，建立了剪切型RC柱抗剪承载力的确定性修正模型；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科夫链蒙特卡洛（MCMC）法，建立了剪切型RC柱的概率抗剪承载力计算模型；最后通过与试验数据和现有模型的对比分析，验证了该模型的有效性和实用性。分析结果表明，该模型不仅可以合理描述剪切型RC柱抗剪承载力的概率分布特性，而且可以校准现有确定性计算模型的置信水平，并且可以确定不同置信水平下剪切型RC柱抗剪承载力的特征值。

PROBABILISTIC MODEL FOR SHEAR STRENGTH OF SHEAR-CRITICAL REINFORCED CONCRETE COLUMNS

Traditional computational models for determining the shear strength of shear-critical reinforced concrete (RC) column are generally deterministic models, and exhibit large fluctuation, low computational accuracy, and poor applicability, due to the fact that they do not take into account the uncertainties of geometric conformation, material properties, and external loads. In order to overcome the above limitations, a probabilistic model for shear strength of shear-critical RC column was established based on the variable angle truss-arch model and Bayesian theory. Firstly, based on the variable angle truss-arch model, an improved deterministic computational model of the shear strength of an RC column was established by taking into consideration the influence of the axial load ratio on the critical crack angle. Then, a probabilistic computational model of shear strength for shear-critical RC columns which takes into account the influence of both epistemic and aleatory uncertainties was developed by combining the Bayesian theory and the Markov Chain Monte Carlo (MCMC) method. Finally, the applicability, accuracy, and efficiency of the proposed probabilistic computational model were validated by comparing with the experimental data and existing deterministic models. The results indicate that the proposed probabilistic computational model can describe the probabilistic characteristic of shear strength of shear-critical RC column reasonably. Meanwhile, the proposed probabilistic computational model provides a benchmark to calibrate the confidence level of traditional deterministic models. Furthermore, the proposed probabilistic computational model provides an efficient way to determine the characteristic values of shear strength of shear-critical RC columns with different confidence levels.