## 4 Analysis of Results
### Size Effect of the Mechanical Properties of Basalt Blocks
#### 4.1.3 Size Effects of Strength Criterion  
Figure 12 shows the strength variation curves of basalt samples with different sizes containing hidden cracks under uniaxial and triaxial compression. Figure 12a shows the relationship between the compressive strength of the basalt and the sample size under various confining pressures. The UCS of basalt decreases from 303.06 MPa to 52.53 MPa as the sample size increases from 25 mm to 500 mm, reflecting a reduction rate of approximately 82.67% and indicating a significant strength reduction trend. The obtained REV size is relatively large, approximately 500 mm, highlighting a notable size effect. However, with an increase in the confining pressure to 30 MPa, the compressive strength of basalt decreases from 442.75 MPa to 246.33 MPa as the sample size increases from 25 mm to 500 mm, resulting in a reduction rate of approximately 44.36%. Hence, the strength reduction trend weakens, and the obtained REV size is smaller, approximately 150 mm, indicating a less significant size effect. Thus, the rise in the confining pressure mitigates the strength size effect of basalt to a certain extent. Figure 12b shows the relationship between the compressive strength of basalt and confining pressure under different sample sizes. The compressive strength of intact basalt with smaller sizes increases from 303.06 MPa to 442.75 MPa as the confining pressure increases from 0 MPa to 30 MPa, demonstrating an approximately linear increasing trend. This behavior aligns with the linear strength criterion, such as the MC strength criterion. However,  
Figure 12: Compressive strength of different-sized basalt samples with hidden cracks under different confining pressures. (**a**) Relationship between sample size and compressive strength; (**b**) relationship between confining pressure and compressive strength. the compressive strength of basalt blocks with larger size (i.e., 500 mm) increases from 52.53 MPa to 246.33 MPa as the confining pressure increases from 0 MPa to 30 MPa; therefore, the linear increasing trend is weakened, which approximates to a nonlinear strength criterion such as the Hoek-Brown (HB) strength criterion. Consequently, as the sample size increases, the strength criterion of basalt transitions from linear to nonlinear [44]. Based on the obtained variation trend in the UCS of basalt containing hidden cracks with the increase in the sample size, a prediction model for basalt strength considering the size effect is proposed, as expressed in Equation (1). Moreover, this strength size effect model is integrated into the classical HB strength failure criterion for intact rocks, as expressed in Equation (2). This integration results in the establishment of a strength failure criterion for basalt containing hidden cracks that accounts for the size effect, as expressed in Equation (3). In these equations, \(\text{UCS}_{d}\) and \(\text{UCS}_{d50}\) represent the UCS of rock samples of arbitrary diameters and a diameter of 50 mm, respectively, and \(d\) represents the sample size. \(\sigma_{1}\) and \(\sigma_{3}\) denote the maximum and minimum (confining pressure) principal stresses, respectively; \(\sigma_{\text{ci}}\) represents the uniaxial compressive strength of the intact rock; and \(m\) is the rock material constant. It is worth noting that this study serves as a preliminary exploration and attempt on the rock strength criterion considering the size effect, due to the necessary simplification of the numerical model. Therefore, further systematic exploration in this area will be conducted using various methods. \[\text{UCS}_{d}=\text{UCS}_{d50}(\frac{d}{50})^{-0.36} \tag{1}\]  
\[\sigma_{1}=\sigma_{3}+\sigma_{\text{cl}}(m\frac{\sigma_{3}}{\sigma_{\text{ci }}}+1)^{0.5} \tag{2}\]  
\[\sigma_{1}=\sigma_{3}+\text{UCS}_{d50}(\frac{d}{50})^{-0.36}(m\frac{\sigma_{3 }}{\text{UCS}_{d50}(\frac{d}{50})^{-0.36}}+1)^{0.5} \tag{3}\]  
In summary, as the confining pressure increases, the size effect on the strength of basalt is somewhat mitigated.