In addition, the study concentrated on cement slurry about the relationship between capillary porosity and compressive strength under different _w/c_ ratios is not clear. Recently, micro-CT has become a popular technique widely used in evaluating the microstructure property of cementitious materials due to its simple and non-destructive characteristics and short test time. [PERSON] et al. [21] began to study the internal damage characteristics of Portland cement hydration products based on micro-CT in 1997 and found that the research and application of micro-CT in the field of cement concrete has increased dramatically. Micro-CT was initially used to investigate the internal structure of cement such as pore types (pores and damages) [22], pore shapes [23; 24; 25; 26], and pore network [27; 28]. The statistical and morphological analyses based on micro-CT provide a new view of the cement microstructure because they can provide a realistic 3D geometry [29]. With rapid computer technology developing, numerical approaches have drawn great attention from lots of scholars. Many kinds of cement hydration models have been established gradually, such as the Jennings-Johnson model [30], HYMOSTRUC3D model [31; 32; 33], Navi-Pignat model [34], CEMHYD3D model [35], DuCOM model [36], uic model [37], HydratiCA model [38], THAMES model [39], Park's model [40], Thermodynamic modeling [41], etc. The above hydration models provide a new solution for the study on microstructure evolution and hydration mechanism of cement-based materials. In this paper, the HYMOSTRUC3D model was selected to simulate the hydration process and the microstructure development of cement slurry. Instead of using a certain characteristic particle size to represent its real particle size distribution, the HYMOSTRUC3D model [31; 32; 33] can consider the continuous particle size distribution of cement particles. The HYMOSTRUC3D model is a function of the clinker composition, particle size distribution of cement, _w/c_ ratios of cement paste, and temperature in which the hydration of cement particle is controlled by the strict stereological principle and chemical reaction kinetics principle. The three-dimensional structure of cement slurry can be reconstructed, and the dynamic hydration process of cement slurry can be displayed with the visualization software Para View. Compared with other hydration models, the HYMOSTRUC3D model is more rigorous and powerful. The model was first proposed to calculate the hydration rate of cement particles, during which the hydration process was divided into two stages (phase boundary reaction stage and diffusion-controlled reaction stage) based on the hydration rate parameters \(k_{0}\) and \(\delta_{\text{tr}}\). Since then, the HYMOSTRUC3D model has been developed dramatically. Up to now, the HYMOSTRUC3D model has been used to simulate many properties of cement-based materials and blended cement-based materials, including the mechanical properties [31; 42], microstructure [32], the autogenous shrinkage [33], the transport properties [43], the tensile strength and stiffness [44] of cement-based materials. Hence, the HYMOSTRUC3D and micro-CT models were selected to study the effects of the _w/c_ ratio on pore structure evolution and strength development of cement slurry. The relationships between cement clinker, hydration products, porosity, compressive strength, etc. with _w/c_ ratios (0.40, 0.44, 0.50) and hydration times (1, 3, 7, 28, 140 days) were obtained from the cement slurry hydration kinetics model established on the HYMOSTRUC3D model [33], and the simulated results were compared with the measured results (mechanical tester and micro-CT). Moreover, the relationship between the compressive strength and capillary porosity was established by the mathematical prediction models (Balshin function, Ryshkewitch function, Schiller function [45; 46], and linear function), and the residuals of those mathematical models were analyzed. The evolution mechanisms of pore structure were discussed via SEM.