# Shape Effect and Accuracy Analysis of Rock Tensile Strength Test
## 3 Comparison and Analysis of the Accuracy Between Direct Tension and Brazilian Splitting Tests
### Test Results and Analysis  
For the standard cylindrical specimens, during the field tests, the uneven attachment of the loading blocks on both ends leads to stress concentration on the end faces during loading, resulting in eccentric errors. In contrast, no such errors exist in the numerical simulation; thus, the direct tensile tests of the standard cylindrical specimens are not further analyzed. The standard tensile strength values presented below are derived from the results of the tensile tests of the simulated standard cylindrical specimens [1; 30; 31; 32; 33; 34]. Figure 6 presents the results of the numerical simulation of disc splitting, including stress distribution contour maps at different time points for the disc's end face and the Y-Z cross-section. As shown in the figure, ignoring the stress concentration effect at the loading point, the maximum tensile stress initially occurs at the centre of the disc's end face. This is because, during the loading process, the centre of the disc's end face experiences the most concentrated stress due to the loading effect. This position is a potential initiation site \begin{table}
\begin{tabular}{l l l} \hline \hline
**Specimen Shape** & **Diameter Range/mm** \\ \hline Dumbbell-shaped specimen with curved-transition surface & 45–55 \\ Dumbbell specimen with linear-transition surface & 45–55 \\ \hline \hline \end{tabular} Note: Take one piece for every 1 mm in diameter.  
\end{table} 
Table 4: Test plan arrangement. for cracks. Subsequently, the region of maximum tensile stress expands from the centre of the cross-section along the Y-axis toward the loading point, ultimately resulting in a spindle-shaped stress distribution. The stress distribution contour map of the Y-Z cross-section shows that the maximum tensile stress region of the disc extends from the centre of the end face along the Z-axis toward the specimen centre, i.e., the origin of the spatial coordinates. Based on the above analysis, it can be concluded that the crack initiation point of the disc-splitting test is at the centre of the cross-section, with the crack subsequently expanding toward the loading point and the specimen centre, ultimately penetrating the entire specimen. Figure 7 presents a line chart comparing the tensile strength data obtained from the disc-splitting numerical simulation test with the actual tensile strength values of the specimen. It can be seen that, with the height\(-\)to\(-\)diameter ratio fixed at 2.0, the tensile strength of the specimen decreases as the disc diameter increases. In addition, there is a slight discrepancy between the tensile strength values measured in the disc-splitting test and the specimen's actual tensile strength values. In these numerical simulation tests, two dumbbell-shaped specimens were used, both subjected to direct tensile loading at both ends. The main difference lies in the shape and angle of the transition region between the central effective test area and the two end grips. Consequently, these two dumbbell-shaped specimens were considered as one type for the purpose of analysis. Figures 8 and 9 illustrate the X-Z cross-sectional stress distribution contours at three different time points, as well as the final fracture results, for dumbbell-shaped specimens featuring an arc transition and a straight transition with a 63\({}^{\circ}\) inclination under a load applied along the positive Z-axis. It can be observed that, during tensile loading, the zone of maximum tensile stress first appears at the junction between the arc  
Figure 6: Disc stress distribution contour map. transition and the central effective test area. The stress concentration then propagates in an X-shaped pattern toward the specimen's centre, ultimately forming crescent-shaped stress concentration zones on both sides of the central effective test region. From a three-dimensional perspective, these zones manifest as bowl-shaped areas of maximum tensile stress on either side. As shown in the final fracture images, the specimen's fracture surface is ultimately bowl-shaped.