## 4 Conclusions  
A new CRAMM is proposed, which can accurately model the pore structure in concrete by setting the total porosity, pore gradation, pore size, and sub-porosity of each gradation segment. According to the CVM, 25 mesoscopic concrete specimens with the same aggregate structure and different pore structures are established, and the effects of total porosity, sub-porosity of each pore gradation segment, average pore radius and PSSA on the concrete failure process, elastic modulus, tensile strength, and peak strain are studied. The following conclusions can be drawn. The failure process of concrete specimens with and without pores under uniaxial tensile loading is very similar, but the pore structure demonstrates different characteristics, especially that the damage inside the cement mortar is more localized. The damage first germinates from the periphery of the specimen and then expands to the center of the specimen, and the existence of pores accelerates the expansion process. The existence of pores does not change the phenomenon that the most severely damaged area in concrete is ITZ before the internal stress reaches the ultimate stress. The pore structure has an important influence on the initiation and propagation direction of macroscopic cracks, which must pass through pores and ITZ. Both linear and exponential functions can fit well the relationship between elastic modulus and PSSA and the relationship between elastic modulus and total porosity, but the exponential function fits better. For specimens with the same aggregate structure and total porosity, the elastic modulus increases with the increase of the macropore content and is basically not affected by the average pore radius. The exponential function can fit well the relationship between total porosity and tensile strength, and the quadratic polynomial function can fit well the relationship between PSSA and tensile strength. For specimens with the same aggregate structure and total porosity,  
Figure 27: Stress\(-\)strain curves of elliptical pore specimen 1-ellipse and specimen 1-2-S. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Mechanical Properties** & **1-Ellipse** & **1-2-S** \\ \hline Modulus (MPa) & 29,118 & 29,879 \\ Strength (MPa) & 2.740 & 3.001 \\ Peak strain (\(10^{-3}\)) & 0.1843 & 0.1925 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: The mechanical properties of Specim 1-ellipse and Specim 1-2-S.  
there is no clear functional relationship between the tensile strength and the sub-porosity of different gradation segments, and the tensile strength is basically not affected by the average pore radius. The peak strain has an increasing trend with the increasing total porosity, which is more sensitive to pore space distribution and secondary porosity than total porosity. Peak strain is more sensitively affected by pore space distribution and sub-porosity. The effect of average pore radius and PSSA on peak strain has no obvious regularity. Based on the GRA, the effects of the pore structure parameters listed in this paper on the elastic modulus and tensile strength of concrete are very close in sequence. For pores with a radius in the range of 0.15-0.8 mm, the smaller the pores, the greater the effect of their porosity on the elastic modulus and tensile strength, and the less effect on the peak strain. Total porosity is the primary factor affecting elastic modulus and tensile strength, but is only a secondary factor affecting peak strain. The research has drawn some valuable conclusions, although some further work is needed. Firstly, this study adopts a 2D assumption to save computational cost, but due to the 3D random anisotropic distribution of aggregates and pores, the effect of the three dimension on pore structure and mechanical properties should be considered by extending the established model to 3D conditions. Secondly, the influence of pore structure on the mechanical properties of concrete under complex loads such as dynamic and temperature should be studied.