Time-dependent axial deformation of concrete: Development of a fractional calculus-based constitutive model

Abstract

Modeling the time-dependent behavior of concrete has long been a traditional challenge in the field of structural engineering. In current structural engineering, concrete time-dependent models for shrinkage and creep often rely on empirical or semi-empirical regression analysis of experimental data, lacking physical significance and showing deviations in practical applications. Fractional calculus (FC) constitutive models, as compared to traditional integer-order calculus models, demonstrate exceptional capabilities in describing time-dependent behavior of structures. FC-based models enable a more accurate capture of material and structural behavior over extended time scales. In this study, a theoretical model for the stress-strain-time relationship of concrete members is developed using a FC constitutive model. This model possesses a more practical physical expression, which significantly reduces the number of required parameters in time-dependent concrete models, and achieves better fitting results. The accuracy of this model is verified by several experimental data, and two key factors affecting the time-dependent deformation of concrete are initially selected for regression analysis using several different models. Thereafter, a unified theoretical calculation formula is derived, characterized by its simplicity and suitability for practical engineering applications. The impact of coupling beams on the axial deformation of adjacent vertical members within the structural system is also considered, and a comprehensive quantitative analysis of the effect of coupling beam stiffness is conducted.