Investigation Of Uncertainty Quantification Of Constitutive Parameters Of Concrete In Structures

Concrete is a kind of multi-phase composite material with cement as the main cementing material and various mineral components as the matrix.In engineering practice,due to the influence of various random factors,the concrete of different components,different floors or different structures exhibits great variation.For a component,due to the heterogeneity of concrete,there is spatial variation in the mechanical properties of concrete.Then how can we assign the values for the mechanical properties of concrete in a structure in numerical analysis? In most engineering practice,the mechanical properties of concrete with the same strength grade are usually taken as deterministic values.In this situation,the variability of the mechanical properties of concrete is not reasonably considered,and thus may result in unignorable bias.On the other hand,in many researches on the stochastic response analysis of concrete structures involving randomness in parameters,the mechanical parameters of concrete at different positions in a structure are taken as perfectly dependent or independent random variables,and the different parameters at the same position are taken as perfectly dependent variables.Again,this is quite different from the practical situation.In this paper,the variability and probabilistic dependence characteristics of the mechanical properties of concrete in structures are studied,and the complete probabilistic description and the corresponding simulation method for the constitutive parameters of concrete in structures are proposed.Firstly,at a certain point in a structure,the constitutive parameters of concrete are generally probabilistically dependent.The dependence configuration is essentially determined by the underlying physical mechanisms of concrete.In this paper,based on 329 test complete compressive stress-strain curves,the complete probabilistic description and the simulation method of the compressive constitutive parameters of concrete are proposed by adopting the copula function method.The results show that the dependence configuration of the constitutive parameters of concrete is nonlinear.And the generated complete curves by the proposed method agree well with the test curves at the level of second-order moments.At the level of sample,due to the constraint of dependence configuration,no abnormal complete curve is generated.The stochastic response analysis of a 6-story RC frame structure is conducted and the influence of the dependence configuration of the constitutive parameters of concrete on the structural stochastic response and reliability is studied.When concrete expands from a single point to a component,due to the heterogeneity of concrete,the physical and mechanical properties of concrete at different spatial positions are different.The spatial variability of concrete may affect the possible partially damaged area and failure mode of the component under loading.Therefore,a plain concrete slab is cast and the spatial variability of the physical and mechanical properties of concrete is studied by the rebound and core test.The test results show that the spatial correlation of the different constitutive parameters of concrete is similar and follows the exponential correlation coefficient function model.The correlation lengths of the constitutive parameters and rebound number are 0.44 m and 0.47 m,respectively.In addition,the size,shape and failure modes of specimens all have a certain influence on the complete compressive stress-strain curve.The compressive constitutive parameters of concrete in a component should be considered as a four-variate random field,and the dependence between random fields is nonlinear.If the correlation function or the power spectral density function is adopted to describe the dependence of the four-variable random field,deviation will be inevitably induced in the dependence configuration.Therefore,an approach by synthesizing the spatial correlation function and the multi-variate copula function(SCFVCF)is proposed in this paper.In the proposed method,the correlation function model is adopted to quantify the spatial dependence involved in the random field,and the copula function model is adopted to quantify the dependence configuration between random variables.For the simulation of samples,the spectral representation method and the conditional sampling method are incorporated.The results show that the proposed method can capture the spatial correlation and nonlinear dependence of the random field of the multiple constitutive parameters of concrete.Then the influence of the dependence configuration of the random fields on the failure modes and the hysteresis performance of an I-type shear wall is studied.In engineering practice,a normal distribution is suggested for the compressive strength of the concrete with the same strength grade.Actually,this distribution involves a combination of many factors.In other words,it is composed of many subdistributions.Actually,for a specific batch or a specific structure,the compressive strength of concrete does not satisfy this distribution but a sub-distribution.Therefore,in this paper,the variability of the mechanical properties of concrete in structures is divided into four hierarchies: structure,floor,component and representative volume element(RVE).Then a hierarchy model is adopted to quantify the randomness of concrete in structures.In order to study the influence of the variability of concrete in structures,the stochastic response analysis of a 6-story RC frame is conducted.On the basis of the aforementioned works,the stochastic response analysis of a22-story RC frame-shear-wall structure is conducted.The effectiveness of the complete probabilistic description model and the simulation method of the variability of concrete in structures is verified.The influence of the variability(including nonlinear dependence,spatial variability and the hierarchical variability)of the compressive constitutive parameters of concrete in structures on the structural response and reliability is studied.So far,from a point to a component,and then to a whole structure,the complete probabilistic description model of the compressive constitutive parameters of concrete in structures and the simulation method are established.The feasibility of the proposed method is also verified by an engineering structure.Finally,the main conclusions of this paper are made,and the investigations to be done in the future are briefly discussed.