Probabilistic Models And Calibration Analysis For Shear And Flexure Strength Of Reinforced Concrete Columns

Reinforced concrete(RC)columns(including frame and pier columns)are important vertical load-bearing and lateral resistance components of engineering structures such as buildings and bridges,which have an important impact on the safety of engineering structures.When the shear strength and flexure strength of RC columns are not adequately provided,RC columns would fail with typical failure modes such as flexure failure,flexure-shear failure and shear failure,which may lead to local damage or overall collapse of engineering structures.As a result,it not only affects the serviceability of engineering structures,but also leads to serious threat to the safety of engineering structures.Therefore,it is great significance to accurately analyze and predict the shear strength and flexure strength of RC columns for the bearing capacity design and safety assessment of engineering structures.Due to the mechanism of bearing capacity for RC columns is complex and there are numerous influencing factors,various bearing capacity models have been developed based on different model assumptions and experimental databases.However,traditional bearing capacity models of RC columns belong to the deterministic models,which can not reasonably consider the influences of the aleatory uncertainties inherent in the material properties,geometric size,and structural construction details of RC columns and the epistemic uncertainties that arise from lack of knowledge,introduction of various model assumptions,limited experimental data,and omission of some influential factors.As a result,it is difficult to describe the probabilistic distribution characteristics of bearing capacity for RC columns reasonably.Meanwhile,the accuracy and applicability of traditional bearing capacity models of RC columns change markedly under different conditions,since they were developed based on different experimental databases,influential factors or model assumptions.Therefore,it is necessary to calibrate the accuracy and applicability of traditional bearing capacity models of RC columns.However,traditional calibration methods can only evaluate the accuracy and applicability of deterministic models based on model error,and cannot reasonably consider the influences of aleatory uncertainties and epistemic uncertainties,as well as the confidence levels of deterministic models.Therefore,it is necessary to develop the probabilistic bearing capacity models involving both aleatory and epistemic uncertainties,and to propose the probabilistic calibration method for bearing capacity models of RC columns based on the probabilistic bearing capacity models.Hence,the main objectives of this dissertation are to develop probabilistic models of shear and flexure strength of RC columns,as well as the probabilistic calibration method for existing traditional deterministic bearing capacity models.Major contents of this dissertation are as follows:(1)A theoretical shear strength model for RC columns was established first based on the truss-arch model,by taking into account the condition of force equilibrium of the truss model as well as the condition of deformation compatibility between the truss model and the arch model.Then a simplified model for shear strength of RC columns was developed by simplifying the shear strength contribution coefficients of concrete,transverse reinforcement and arch action based on statistical analysis of 38 sets of experimental data.Analysis results show that the simplified model not only can rationally describe the shear strength contributions of concrete,transverse reinforcement and arch action,but also has high accuracy and convenience,which provides an accurate and efficient simplified model for shear strength analysis of RC columns.(2)Based on the experimental data of 58 shear-critical columns and 250 flexure-critical columns(including 200 sets of large eccentric columns and 50 sets of small eccentric columns),probabilistic shear and flexure strength models which involve both epistemic and aleatory uncertainties were developed by combining with Bayesian theory and Markov Chain Monte Carlo(MCMC)method based on DRAM algorithm.Then the empirical probabilistic distribution function and statistical characteristics(including mean and standard deviation)of shear strength and flexure strength for RC columns were determined based on the proposed probabilistic models.Analysis results show that the developed probabilistic shear and flexure strength models not only have good accuracy and applicability,but also can rationaly describe the probabilistic characteristics of shear and flexure strength for RC columns.Meanwhile,it provides the theoretical basis for the probabilistic limit state design and probabilistic safety assessment of RC columns.(3)Based on the probabilistic characteristics of shear and flexure strength for RC columns such as probabilistic density function,confidence interval and confidence level,the probabilistic calibration methods were presented to evaluate the accuracy and confidence level of traditional deterministic shear and flexure strength models.Analysis results show that the accuracy of traditional shear strength models of RC columns changes markedly under different conditions,due to the shear mechanism of RC columns is complex and there are numerous influencing factors.Generally,SL 191-2008 model,ACI 318 model,CSA-A23.3-04 model and FEMA 273 model underestimate the shear strength of RC columns,while Priestley model overestimates the shear strength of RC columns.Meanwhile,the accuracy of CEN-2005 model,Sezen model,GB 50010-2010 model and Pan model are relatively good.Although various flexure strength models for RC columns were developed beased on the similar model assumptions,the accuracy of different deterministic flexure strength models change markedly under different conditions due to the fact that different models established by considering the different influencing factors and experimental data.Generally,ACI 318 model underestimates the flexure strength of RC columns,while EN 1992-1-1 model overestimates the flexure strength of RC columns.Meanwhile,the accuracy of GB 50010-2010 model is relatively good.