BWBN Restoring Force Model-based Hysteresis Simulation Research Of Reinforced Concrete Columns

Reinforced concrete(RC)columns,as the main load-bearing and lateral resistance components of hydraulic structures such as hydropower stations and aqueducts,will not only occur ductile flexure failure but also occur flexure-shear or shear failure due to insufficient stirrup configuration under earthquake repeated load action.Considering various uncertainties in engineering practice,it is necessary to establish a unified restoring force model that can describe different failure modes by the probabilistic method,so as to carry out seismic demand analysis under the probabilistic framework,which is adapted to the probabilistic method of seismic fragility analysis.Therefore,the RC columns with flexure,flexure-shear,and shear failure are taken as the research objects in this paper,the Bayesian probabilistic theory is introduced to consider the aleatory and epistemic uncertainties,and the inelastic restoring force model and hysteresis loop prediction of RC columns are studied.The main research contents are as follows:(1)The Bouc-Wen-Baber-Noori model,known simply as BWBN model,which can effectively describe the typical hysteresis characteristics of RC columns,such as two degradation effects of stiffness and strength degradation as well as pinching effect,is selected as the unified restoring force model for different failure modes and the backward Euler numerical method is employed to solve the BWBN model.(2)Based on the PEER-Structural Performance Database,the cyclic loading test results of the 240 rectangular RC columns and 133 spiral RC columns with different failure modes are selected as the dataset.Considering various uncertainties,the Bayesian theory-based improved DE algorithm is employed to establish an identification method of the BWBN model and its control parameters of RC columns.The probability distribution and statistical values of the BWBN model parameters of RC columns under different failure modes are calculated and analyzed,and the accuracy and efficiency of this method are checked through the dataset.The results show that this method can identify the restoring force model and its parameter distribution accurately.(3)The probabilistic relationship between the RC column parameters and the BWBN model control parameters is established by using the Bayesian neural network(BNN)introducing uncertainty,and then the hysteresis loops of RC columns are predicted through the BWBN model.The results indicate that the BWBN model control parameters can be predicted via inputting the RC column parameters into the trained BNN,and the corresponding hysteresis loops can be obtained by substituting these parameters into the BWBN model through a numerical solution.The method is universally applicable to rectangular and spiral RC columns with different failure modes and is convenient for engineering applications.