## 3 Results  
### Tensile Strength and Deformation Characteristic  
In the Brazilian test, a circular disk is diametrically compressed along its diameter, resulting in a constant tensile stress perpendicular to the loading direction in the central part of the specimen. According to the maximum tensile stress criterion, the formula for calculating the tensile strength \(\sigma_{t}\) (MPa) is [9; 13]:  
\[\sigma_{t}=\frac{2P}{\pi Dt}=0.636\frac{P}{Dt} \tag{1}\]  
where \(P\) is the failure load (N), and \(D\) and \(t\) are the diameter and thickness of the specimen respectively (mm). However, it is believed that rock material properties and load conditions can generate a significant effect on the determination of indirect tensile strength and fracturing of rocks [38]. In other words, an invalid Brazilian test may occur because of some certain internal or external factors mentioned in the introduction. In fact, crack initiation occurring away from the disk center was observed in some rock specimens in this study. Therefore, the results from this standard formula may not present well the actual tensile strength of some rock materials, and the equation herein is mainly used for the purpose of comparison. According to the experimental data, the Brazilian test results are listed in Table 2. The tensile strengths of all specimens are calculated by Equation (1), while the brittleness index (BI), which is commonly used to characterize the failure behavior of rocks, is determined by the ratio of the uniaxial compressive strength to average tensile strength [50]. For a better comparison, the average tensile strength of each rock type under different loading conditions is plotted in Figure 3. As can be seen from Figure 3, the loading method has a significant influence on the tensile strength of rocks. The average tensile strength determined by the Type III test is the highest among the three test types for all rock types, while the Type II test is the lowest. It can also be found that the tensile strength determined by the Type I test is similar to the Type III test. The above experimental results are mainly related to the contact area between the specimen and the platens, and its size depends on the disc material, jaw material and load level. In fact, curved platens (Type III) have the highest contact area, and the rod platens (Type II) have the lowest. Figure 2: (**a**) A typical speckled pattern of specimen WS3-1; and (**b**) experimental setup for the Brazilian test. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Specimens No. ** & **D/mm** & **t/mm** & **\(P_{\text{max}}\)/kN** & **\(\sigma_{\text{t}}\)/MPa** & **Mean/MPa** & **BI** \\ \hline WS1-1 1  & 48.98 & 25.09 & 4.54 & 2.35 & \\ WS1-2 & 49.08 & 25.09 & 4.26 & 2.20 & 2.32 & \\ WS1-3 & 49.09 & 25.09 &  
Figure 4 presents the load-displacement curves of representative tests of each rock type under different loading configurations. It can be observed that the loading force rises linearly before the peak (except for the initial loading stage) and drops rapidly at the peak, which indicates that little damage occurs inside the specimen during the loading process. In other words, the tested specimens undergo little plastic deformation during the loading process. When the input energy reaches a critical level, it is released abruptly via fracture formation [51; 52]. In addition, it can be found that specimens tested by the Type I specification, undergoing less displacement, show a similar stiffness to those of the Type III specification when the slope is at the linear elastic stage. Moreover, it should be noted that the Type II test shows the lowest stiff response to load, i.e., specimens tested using the Type II specification exhibit the highest vertical displacement for the same loading force, which can be observed from the green horizontal dotted line in Figure 4a. Likewise, the other four rock types show similar performances.