MATHEMATICAL-MODELING OF CEMENT PASTE MICROSTRUCTURE BY MOSAIC PATTERN .1. FORMULATION

This paper develops a mathematical model using mosaic patterns to char acterize structural features of complex, multiphase, and multidimensio nal microstructures, such as those for cement paste. A multiphase micr ostructure can be characterized by m independent parameters; the first m - 1 parameters are equivalent to the volume fractions of the phases , while the final parameter describes the grain size, and thus, the sp atial arrangement of the microstructure. An evaluation procedure for t he parameters is given; they can be evaluated based on a 2D image, and then the 3D microstructure can be simulated by the present model. The relationship among the model parameters and material parameters, such as water-to-cement ratio and particle size distribution, are also est ablished.