Abstract: Numerical analysis is an important research method to avoid the shortcomings of experiments and to realize theoretical expectations. Based on the mesoscale numerical test method, the established intergranular failure mode-based three-dimensional meso-fracture theoretical analysis model of concrete is modified. The adopted numerical model of concrete is composed of mortar, interfaces and aggregates, which is consistent with the theoretical model. In order to simulate the mechanical behaviors of ordinary strength concrete, the plastic damage constitutive model is used to characterize the mechanical properties of mortar and interfaces, and aggregates are set as elastic spheres. A self-designed aggregate placement program is used to establish standard cubic specimens of three-dimensional model concrete with cross-sectional dimensions of 100 mm (1-graded), 150 mm (2-graded), 300 mm (3-graded) and 450 mm (4-graded). The theoretical model is improved by the splitting tensile loading numerical tests of standard cubic specimens under different interfacial strength conditions. A semi-theoretical and semi-empirical modified calculation formula for predicting the splitting tensile strength of different graded concrete is established. Compared with the results of numerical and physical tests, the modified theoretical model can effectively represent the variation of the macroscopic mechanical properties of concrete with the mechanical and structural properties of meso-component materials. The proposed theoretical model modification method based on overlapping effect analysis and structural effect analysis can lay a foundation for the subsequent establishment of semi-theoretical and semi-empirical prediction formula of concrete mechanical properties upon modified fracture analysis model.