## 5 Discussion  
### Size Effect of Rock Strength  
Generally, the size effect of the mechanical properties of rocks typically contains two aspects: absolute size effect and shape effect. In this study, the size effect refers to the absolute size effect of cuboid or cylindrical rock samples with a constant aspect ratio in the range of 2-2.5. Extensive studies have been performed on the rock mechanical property size effect, and some empirical formulae or theoretical expressions have been proposed to quantify this relationship, among which the most typical rock strength size effect relationship is the HB empirical formula. Therefore, the findings in this study were compared with existing literature data, such as the HB empirical formula and other research results, as shown in Figure 18, where \(\text{UCS}_{\text{d50}}\) and \(\text{UCS}_{\text{d}}\) represent the UCS of rock samples with a 50 mm diameter and an arbitrary diameter, respectively [47; 48; 49].  
There is a power function attenuation relationship between the UCS and rock sample sizes; that is, the UCS typically decreases gradually with an increase in the sample size. This decreasing trend is more significant at small sizes, and the U  
Figure 17: Progressive fracture process and failure mechanisms of the intact basalt rock mass during excavation in underground caverns. (**a**) Stress state change within the surrounding rock mass near excavation surface; (**b**) Crack evolution process within the surrounding rock mass near excavation face.  
Figure 18: Influence of specimen size on the UCS [47; 48; 49].  
when the sample size reaches a certain critical value. This critical sample size is called the REV, at which the obtained mechanical properties are considered the characteristics of the equivalent continuum. However, the HB formula mainly represents rocks with good homogeneity, where the UCS decreases relatively gradually with the increase in the sample size and tends to stabilize easily, resulting in a lower REV. This formula may overestimate the strength of rock samples that contain more micro-defects or are affected by temperature or weathering, such as amygdala basalt or heat-treated marble. For basalt with hidden cracks, the UCS change trend with the increase in the sample size is in good agreement with the HB model overall, while this downward tendency is more evident, leading to a higher power exponent and a larger REV size, that is, a more significant size effect of the rock strength, which is mainly due to the occurrence of hidden cracks in basalt (i.e., a significant heterogeneity).  
Therefore, there is no universal law or formula for the rock mechanical property size effect, which is strongly associated with defect types, defect distribution characteristics, and lithology. The relationship between the rock mechanical parameters and sample sizes is essentially the rock structural characteristic effect on the mechanical parameters with the change in the sample size; that is, the rock mechanical property size effect is essentially the structural problem of the rock itself. Hence, it is necessary to further explore the relationship between the rock structures and REV, or the corresponding mechanical parameters, and establish a quantitative formula that can comprehensively consider the various influencing factors, such as the lithology, defect types, and defect parameters, so as to determine the rock mechanical properties more accurately and reliably. In other words, as long as the geometric parameters of the defect structures in a rock or rock mass, such as the length, spacing, and density of structural planes, can be preliminarily determined, the REV size and corresponding mechanical parameters can be quickly obtained to better guide engineering practice.