## 3 Result and Discussion
### Fractal Dimensions  
The fractal dimensions of porous materials reflect the self-similar structures of pores and the development degree of pore structures. Their values range from 2 to 3 [39; 40]. The smaller the fractal dimension is, the stronger the homogeneity is, and the larger the fractal dimension is, the more complex and inhomogeneous the pore structure is. In this paper, the fractal dimensions of micro pores (D\({}_{1}\)), meso pores (D\({}_{2}\)) and macro pores (D\({}_{3}\)), were analyzed, respectively, to study the fractal dimensions of sandstone more closely. Segmented fractal dimensions were calculated according to Equation (4) by the range of pore radii (T\({}_{2}\)). Fractal dimensions and correlation coefficients of sandstone under different F-T cycles and acid solutions are listed in Table 2.  
Among the fractal dimensions of pores with various sizes, they show different value ranges. For micro pores, it is worth noting that their fractal dimensions range from \(-\)0.285 to 1.099, which is not within the value ranges from 2 to 3, which indicates that micro pores do not obey the fractal theory [41]. As most of the water contained inside micro pores is absorbed water and film water, their statuses are quite different from moveable water contained in meso pores and macro pores. Therefore, the small pore realm associated with very small T\({}_{2}\) values may not be self-similar to the large pore systems and cannot be described by the fractal models in Equation (4). Therefore, fractal dimensions D\({}_{2}\) and D\({}_{3}\) are mainly analyzed in this paper. To display the variation trend of dimensions intuitively, the fractal dimensions of sandstone immersed in an acid solution after different F-T cycles are shown in Figure 6.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline
**PH** & **F–T Cycles** & **D\({}_{1}\)** & **R\({}^{2}\)** & **D\({}_{2}\)** & **R\({}^{2}\)** & **D\({}_{3}\)** & **R\({}^{  
Figure 6b presents the variation trend of D2 versus F-T cycles. D2 value ranges from 2.639 to 2.738, which indicates that meso pores are complex and heterogeneous. The D2 shows an increasing trend with F-T cycles increase, while it grows slowly before 20 F-T cycles and grows fast after 20 F-T cycles. It indicates that, although the coupled effect of F-T weathering and acid erosion degraded meso pores, it did not enhance the complexity and heterogeneity of meso pores significantly within 20 cycles. After 20 F-T cycles, D2 grows faster, meso pores become more and more evident in samples, and they are more complex and heterogeneous. It is worth noting that the D2 of sandstone treated by acid solution with pH equals to 2.8 and 4.2 grow faster before 20 F-T cycles, which can be explained as acid erosion accelerating the complication and heterogeneity of samples. As Figure 6c shows, the D3 value ranges from 2.841 to 2.979, which shows an increased trend overall, except for 20 F-T cycles. The increased trend of D3 reveals that macro pores become more complex inside sandstone with F-T cycle increase. In terms of the D3 drop, it is related to the macro porosity drop, which happened at 20 F-T cycles, shown in Figure 5c. It is caused by the first peel off of sandstone on the surface of the sample. As the macro pores are more distributed on the surface, when the surface of samples peeled off, macro pores on the surface were also eliminated; therefore, macro pores are relatively distributed homogeneously, causing the drop in D3. Dimensions of samples in different acidic solutions under 40 F-T cycles are plotted in Figure 6d to reveal the influence of acid  
Figure 6: Segmented fractal dimensions of sandstone immersed in acid solutions after different F–T cycles: (**a**) micro-pore dimension D1; (**b**) meso-pore dimension D2; (**c**) macro-pore dimension D3; (**d**) D2 and D3 of samples in different acidic solutions under 40 F–T cycles. solution on dimensions.