## 2 Generation of Mesostructures and Numerical Models
### Size Distribution of Pores  
Concrete is a typical porous material with pore sizes spanning micro, meso, and macro scales [34]. Statistics show that the porosity of ordinary concrete is generally no less than 8%, in which the porosity of pores with diameters between 53 and 106 nm is about 1%, and the porosity of pores with diameters larger than 106 nm is about 2 to 5% [35]. [PERSON] [36] found that it is unscientific to use total porosity to characterize the complex pore structure in concrete, and the pore size distribution also has an important impact on the strength of concrete. [PERSON] [37] used CT scanning technology to observe the spatial distribution and morphological characteristics of pores in the concrete and found that the pores are randomly generated and obey uniform distribution. [PERSON] [6] used the optical microscopic image analysis method, based on quantitative stereology, to obtain some parameters of pore structure in concrete, such as the pore size, pore gradation, and pore spatial distribution, and measured the compressive strength of the specimens with different pore structures. Based on the weakening degree of pores on the mechanical properties of concrete, [PERSON] divided the pores into harmless pores, small hazardous pores, medium hazardous pores, and large hazardous pores according to the pore size [38]. It is generally believed that small pores (<10 \(\upmu\)m) mainly affect the permeability and durability of concrete, while large pores (>200 \(\upmu\)m) affect the compressive strength of concrete [39; 40]. Based on a comprehensive evaluation of calculation cost and research purpose, only the pores with radii greater than 150 \(\upmu\)m are simulated, and the smaller pores are assumed to mix with the cement to form a uniform mortar. To simulate the pore structure in concrete more realistically, it is comprehensively determined based on the real observed data [6; 37; 41]. Based on [PERSON]'s experimental research experience [6], the pore structure established in this paper includes four pore gradations. Concrete models with total porosity of 0%, 1%, 2%, 3%, and 4% were established. The specimens with the same total porosity are divided into three categories according to the different pore structure types, namely, S-type specimens with a relatively large proportion of small pores, L-type specimens with a relatively small proportion of small pores, and M-type specimens with a moderate proportion of small pores. The sub-porosity of each gradation segment of pores set in the paper is within the range of the actual measured sub-porosity of the corresponding gradation in the literature [41] to ensure the rationality of the sub-porosity values. To study the influence of the spatial distribution of pores on the mechanical properties of concrete, the specimens with the same aggregate structure, total porosity, pore gradation, pore size, and sub-porosity of each gradation segment of pores but different pore spatial distribution are established. All established concrete specimens and related parameters are shown in Table 2, in which the average pore radius and PSSA are important parameters to describe the pore structure [42; 43].