Multiscale Reliability Analysis Of FRP Bridge Structures With Probabilitic And Non-Probabilistic Uncertainties

FRP structures are increasingly used in bridge engineering,but they usually have conservative designs due to the lack of understanding of their reliability comparing with those made of traditional construction materials.The reason is that,on the one hand,due to the hierarchical characteristics of its geometry,uncertainties exist in parameters at various length scales.On the other hand,the data for precisely determining statistics of some variables are insufficient with limited applications of FRP in bridges,and they should be treated as non-probabilistic variables.Traditional probability-based reliability analysis method relies on precise probability information of random variables,which cannot be applied for FRP bridges due the aforementioned reasons.Therefore,it is necessary to develop a novel uncertainty quantification method to simultaneously consider variations at various length scales and sources.The development enables to precisely evaluate the reliability performance of the bridge under complicated uncertainty environment thereby providing theoretical fundamentals for the design and analysis of FRP bridges.In this thesis,uncertainty quantification methods FRP bridge structure are studied as follows:(1)On the microscale,considering uncertainties in the material properties of constituent materials of FRP,namely fibre and matrix,the representative volume element(RVE)is taken from the FRP with periodically distributed fibres in matrix.The effective elastic properties of the FRP are analyzed by a classical homogenization method based on the mean field theory,i.e.Mori-Tananka method.It is then combined with the perturbation-based stochastic finite element method to consider uncertainties,and the particle swarm optimization(PSO)algorithm together with interval analysis are used to deal with interval variables.The development enables to determine upper and lower bounds of mean value and standard deviation of effective elastic properties of FRP composites.(2)On the macroscale,to quantify uncertainties in laminated FRP composite structural components,the relationship between the mechanical properties of laminated FRP components and the material properties of constituents is established first through the classic lamination theory and Mori-Tanaka method.It is then integrated with advanced uncertainty quantification methods to consider both random and interval uncertainties.Based on the polynomial chaos expansion(PCE)theory and the orthogonal Chebyshev polynomials,a surrogate model for the effective stiffness and strength of FRP structural component is proposed,and it is used to determine the upper and lower bounds of probability density of failure probability under axial tension.(3)By embedding the first-order second moment method(FOSM)of probability analysis into the gradient projection method of interval analysis,the cross-scale propagation of uncertainty is realized by means of the derivative relationship between the finite element analysis results of macro structure and the uncertainty parameters of meso scale.A novel reliability analysis method suitable for FRP structure under multiscale mixed uncertainty is proposed,and a theoretical example is given to demonstrate the efficiency and accuracy of the method.(4)With application to the Gao Liang Jian gate area working bridge,fully considering uncertainties in both macro-and microscale parameters,limit state functions for structural performance controlled by displacement and stress are established respectively,which are then solved by the proposed reliability analysis method.The comparative analysis of interval variable processing methods is carried out,which shows that unreasonable uncertainty processing methods will lead to misjudgment of structural reliability.