Multiscale lattice Boltzmann-finite element modelling of chloride diffusivity in cementitious materials. Part I: Algorithms and implementation

Abstract

Chloride diffusivity in cementitious materials depends on both the environmental conditions and the evolution of their underlying microstructures over a wide range of length scales. Part I of this two-part investigation presents the algorithms and implementation of a hybrid lattice Boltzmann-finite element method that combines the advantages of lattice Boltzmann method and finite element method to estimate the chloride diffusivity in cementitious materials. Lattice Boltzmann method is used as micro-scale solver to predict the time-dependent chloride diffusivity in cement paste and interfacial transition zone (ITZ), the microstructures of which are generated from the HYMOSTRUC3D model. Finite element method is selected as meso-scale solver for estimating the chloride diffusivity in mortar and concrete, which are modelled as three-phase composites consisting of aggregate, matrix and ITZ, respectively. The upscaling between the micro-scale and meso-scale simulations is accomplished by using the volume averaging technique. The representative elementary volume (REV) of cementitious materials at a lower scale is determined with a numerical-statistical approach. Chloride diffusivity in the REV of cementitious materials at a lower scale is considered as input to predict the chloride diffusivity in cementitious materials at a higher scale. The developed multiscale lattice Boltzmann-finite element modelling scheme enables to acquire a meso-scale solution, i.e. chloride diffusivity, while still capturing the micro-scale information. The simulation results and validation are presented in detail in Part II.