A Novel Multi-Scale Model for Predicting the Elastic Modulus of Cement Paste Suffering from Sulfate Attack

In this study, the cement paste under sulfate attack was divided into three scales, and a novel multi-scale model was established through a four-step homogenization framework to predict the macroscopic elastic modulus of the corroded cement. Firstly, X-ray diffraction (XRD) was conducted to obtain the micro-phase types of the corroded cement paste. Secondly, the nanoindentation technique was used to measure the mechanical parameters of the nanoindentation points. Thirdly, the energy spectrum spectrometer (SEM-EDS) and the linear difference method were utilized to calculate the volume fractions of microscopic solid phases on each nanoindentation point. Subsequently, based on the above works, a four-step homogenization framework was proposed by integrating Mori-Tanaka (MT) method, Self-consistent (SC) method and Voigt Parallel Model to promote the transformation of the elastic modulus of cement paste from microscale to macroscale. Finally, the predicted values of the macroscopic elastic modulus were compared with the results of the uniaxial compression test and the nanoindentation test. The results show that [[EQUATION]] and [[EQUATION]] are 0.50% and 0.22%, respectively. [[EQUATION]] and [[EQUATION]] are 1.95% and 1.06%, respectively. The relative error value is within the allowable error range. It is shown that the novel multi-scale model with a four-step homogenization framework, proposed in this paper, can effectively predict the macroscopic elastic modulus of cement paste suffering from sulfate attack.