# Shape Effect and Accuracy Analysis of Rock Tensile Strength Test
## 2 Analysis of Shape Effects in Splitting Tests
### Splitting Test Results  
The obtained load-displacement curve is shown in Figure 2. The basic mechanical parameters of rock-like materials are shown in Table 1.  
\begin{table}
\begin{tabular}{p{42.7 pt} p{42.7 pt} p{42.7 pt} p{42.7 pt} p{42.7 pt} p{42.7 pt} p{42.7 pt}} \hline \hline
**Density** **(g\(\cdot\)cm\({}^{-3}\))** & **Porosity** **(\%)** & **P-Wave Velocity (m\(\cdot\)s\({}^{-1}\))** & **Elastic Velocity (GPa)** & **Elastic Modulus (MPa)** & **Cohesion Friction Angle (\({}^{\circ}\))** & **Internal Friction** **Poisson’s Ratio** & **Uniaxial Compressive****Strength (MPa)** \\ \hline
2.3 & 20 & 3800 & 25 & 2 & 30 & 0.2 & 30 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Basic mechanical parameters of rocks.  
Figure 1: Split test disc specimen (**left**) and split result (**right**).  
By analyzing the load-displacement curve after the specimen splitting, it was found that the specimen exhibited good elastic characteristics with increasing pressure in the initial stage, which corresponds to the compaction stage. However, once the strength reaches its peak, the stress rapidly drops with almost no residual strength, exhibiting characteristics of brittle failure. Additionally, upon observing the fractured specimen, the cracks were found to propagate radially and gradually extended to the specimen's edge. This is due to the rapid propagation of the cracks without significant plastic deformation, which is typical of brittle fracture behaviour [19].  
The calculation of the splitting tensile strength is based on Equation (1) [20; 21]:  
\[\sigma_{\mathrm{t}}=\frac{2P}{\pi Dt} \tag{1}\]  
In the equation, \(P\) represents the maximum pressure at the point of splitting failure of the specimen, in units of N; \(D\) is the diameter of the disc specimen, in metres; and \(t\) is the thickness of the disc specimen, in metres. The tensile strength of the disc specimens in this similar simulation experiment, calculated using the above equation, is shown in Table 1.  
Some data in Table 2 show that the specimens exhibited poor fragmentation, and the actual failure surface deviated from the centreline of the specimen diameter (as indicated by the red circle in Figure 1 (right)). The measured tensile strength deviated significantly, making it unsuitable for use as valid experimental data, and was thus discarded. The data in Table 1 show that the standard deviation for each group is small, indicating low dispersion and high accuracy. This also confirms that, compared to field core sampling, the tensile strength of specimens made using similar material preparation techniques in the laboratory exhibits greater accuracy and consistency. Based on the average tensile strength values obtained from the experiments in Table 2, as the specimen diameter increases from 30 mm to 100 mm, the measured strength decreases by 17.17%, 27.27%, 31.31%, 44.44%, and 51.52%, respectively. This phenomenon is caused by the differing internal stress distributions in specimens of varying sizes. It is evident that the size effect of the specimen diameter on the test results cannot be ignored in the splitting test.  
Figure 2: Splitting load–displacement curve.