# Experimental Study of Material Proportioning for Similar Modeling of Brittle Rocks
## 2 Materials and Methods
### Testing Methods and Evaluation Indicators  
This study used uniaxial compression tests and Brazilian splitting tests to measure the mechanical parameters of the specimens, as shown in Figure 3. The uniaxial compression test determines the compressive strength and elastic modulus of the analogous materials, while the Brazilian splitting test measures their tensile strength. During the loading process, the acoustic emission related to specimen fracture was simultaneously monitored. Figure 3: Mechanical testing of the analogous material specimens: (**a**) uniaxial compression test, (**b**) Brazilian splitting test, and (**c**) loading equipment and acoustic emission monitoring system. Figure 2: Partially prepared specimens: (**a**) standard cylindrical specimens and (**b**) Brazilian disc specimens. To develop rock simulation materials characterized by brittleness for use in large-scale true three-dimensional physical model experiments investigating the evolution process of rockbursts, it is essential to evaluate the rockburst tendency and brittleness of the materials in addition to identifying their fundamental mechanical parameters. Rockburst tendency refers to the activity and intensity with which rock is likely to experience a rockburst under specific conditions [30]. This tendency determines the rock's capacity to undergo rockburst failure. The rockburst tendency index, \(W_{\text{cf}}\)[31], is a widely used evaluation indicator for assessing rockburst tendency. In this study, \(W_{\text{cf}}\) was used as a criterion to determine whether the analogous materials exhibit rockburst potential. \(W_{\text{cf}}\) represents the ratio of the total input energy density prior to the peak to the failure energy density following the peak in the stress-strain curve obtained from the uniaxial compression test of a rock specimen. \(W_{\text{cf}}\) is defined as follows:  
\[W_{\text{cf}}=E_{1}/E_{2}, \tag{1}\]  
where \(E_{1}\) is the total input energy density calculated from the rising segment of the stress-strain curve during the uniaxial compression test and \(E_{2}\) is the failure energy density calculated from the descending segment of the stress-strain curve (see Figure 4). The energy density can be calculated by integrating the stress-strain curve of the specimen. The classification criteria for the rockburst tendency index, \(W_{\text{cf}}\), are as follows: \(W_{\text{cf}}\) < 1.0 indicates no rockburst tendency, 1.0 \(\leq W_{\text{cf}}\) < 2.0 indicates moderate rockburst tendency, and \(W_{\text{cf}}\)\(\geq\) 2.0 indicates strong rockburst tendency [32]. Currently, most scholars use the compressive strength-tensile strength ratio as a brittleness evaluation index. However, this ratio reflects the material's strength characteristics rather than its complete brittleness characteristics. It does not account for other parameters, such as residual strength, that influence the variations in rock brittleness. The sensitivity of the compressive strength-tensile strength ratio is insufficient to describe the brittleness differences among various rocks, and its range of variation is quite limited. This study introduces the rock brittleness index, \(B_{i}\)[33], to assess the brittleness of the analogous materials. The rock brittleness index, \(B_{i}\), consists of two components: the rate of stress drop after the peak and the ratio of the elastic energy released during failure to the total energy stored before the peak strength. The definition of \(B_{i}\) is as follows:  
\[B_{i}=\frac{\sigma_{\text{p}}-\sigma_{\text{r}}}{\varepsilon_{\text{r}}- \varepsilon_{\text{p}}}+\frac{\left(\sigma_{\text{p}}-\sigma_{\text{r}}\right) \left(\varepsilon_{\text{r}}-\varepsilon_{\text{p}}\right)}{\sigma_{\text{p}} \varepsilon_{\text{p}}}, \tag{2}\]  
where \(\sigma_{\text{p}}\) and \(\sigma_{\text{r}}\) are the peak strength and the residual strength, respectively, and \(\varepsilon_{\text{p}}\) and \(\varepsilon_{\text{r}}\) are the peak strain and the residual strain, respectively.