# Shape Effect and Accuracy Analysis of Rock Tensile Strength Test
## 2 Analysis of Shape Effects in Splitting Tests
### Numerical Simulation Validation  
This study systematically analyzes the shape effects caused by disc diameter by conducting similar simulation experiments in the laboratory, coupled with numerical simulations of disc specimens using the finite element analysis software ANSYS 19.0. The finite element method is widely applied in engineering mechanics, particularly in the analysis of complex loads and geometries, where it demonstrates significant advantages. Compared to traditional physical experiments, numerical simulations not only provide precise stress field distributions but also reveal the micro-mechanisms of material failure, without being constrained by physical testing conditions. Therefore, the numerical simulations using ANSYS software not only provide theoretical support for the experimental data but also offer insights into the in-depth analysis of the influence of disc diameter on shape effects.  
The material dimensions selected in the numerical simulation validation are the same as those in the similitude simulation test. The material was selected from the ANSYS material library, with a tensile strength of \(\sigma_{\text{t}}=5\) MPa. These material parameters meet the conventional experimental requirements in engineering rock mechanics and effectively simulate the stress response and failure modes of rock-like materials during the splitting process. However, due to limitations in processing accuracy during actual tests, the contact between the plate and the disc may not always remain perfectly tight [22]. This incomplete local contact may lead to stress concentration effects, thereby affecting the precision of the test results. Furthermore, the unique loading method of the test means that the traditional line load model may not fully reflect the actual failure conditions on the disc surface. Therefore, based on existing academic research, this study adopts a 20\({}^{\circ}\) curved surface loading method for numerical simulations [14], aiming to more accurately simulate the effect of actual loading conditions on disc failure, as shown in Figure 3. The curved surface loading method effectively simulates the nonlinear stress distribution between contact surfaces, avoiding potential stress calculation deviations that may arise from traditional methods.  
\begin{table}
\begin{tabular}{l l l l l l l l l l l} \hline \hline
**Diameter** & **Test 1** & **Test 2** & **Test 3** & **Test 4** & **Test 5** & **Test 6** & **Test 7** & **Test 8** & \
\begin{tabular}{l} **Standard** \\ **Deviation** \\ \end{tabular} &
\begin{tabular}{l} **Average** \\ **Value** \\ \end{tabular} \\ \hline
30 & 0.87 & Failed & Failed & Failed & 0.90 & 1.07 & 1.08 & 1.03 & 0.08 9 & 0.99 \\
40 & 0.79 & 0.85 & 0.85 & 0.76 & 0.84 & 0.83 & 0.70 & 0.95 & 0.06 7 & 0.82 \\
50 & 0.88 & 0.63 & Failed & 0.83 & Failed & 0.66 & 0.74 & 0.59 & 0.10 4 & 0.72 \\
70 & 0.67 & 0.72 & 0.70 & 0.75 & 0.67 & Failed & 0.58 & Failed & 0.05 4 & 0.68 \\
90 & 0.49 & 0.48 & 0.56 & 0.50 & Failed & 0.64 & 0.60 & 0.05 8 & 0.55 \\
110 & 0.55 & Failed & 0.41 & Failed & 0.52 & 0.54 & 0.41 & 0.43 & 0.06 0 & 0.48 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Similar simulation test results.  
Figure 3: Loading method.