# Research on Rock Strength Test Based on Electro-Hydraulic Servo Point Load Instrument
## 4 Results and Discussion
### The Internal Stress State of Rock Samples under Different Loading Rates  
Japanese scholars such as [PERSON] and [PERSON] [11] made and processed epoxy resin into spheres, squares, and rectangles for point load tests, and used three-dimensional photoelastic tests to monitor the stress state during the whole process of point load tests. The results showed that the stress state of the three models near the loading axis is basically the same. Later, [PERSON] et al. and [PERSON] and [PERSON] [23; 24] also conducted theoretical studies on the internal stress state of cylindrical specimens in axial and radial point-loading tests. [PERSON] et al. [10] compared the stress distribution in the sphere and cylinder under axial and radial point loads, and showed that if the dimensions of the sphere and cylinder are similar, the stress distribution within the sphere and cylinder along the loading-axis direction is similar in terms of magnitude and distribution pattern. Thus, the analysis of the stress state and damage mechanism of axial point load tests of cylindrical samples is also applicable to square rock samples. According to the stress distribution on the loading axis of the specimen after the surface of the semi-infinite body is subjected to the normal concentrated force \(F\) of the Boussinesq problem and combined with [PERSON]'s principle, ignoring the influence of the specimen boundary, the stress magnitude at the midpoint of the loading axis as the origin, the vertical axis as the loading axis, and the horizontal axis is the stress magnitude axis, a right-angle coordinate system is established, and the stresses produced by the upper and lower two compressive stresses \(F\) on the loading axis are superimposed to obtain the compressive and tensile stresses at a point \(z\) on the loading axis [25; 26; 27; 28]:  
\[\sigma_{\rm c}=\frac{3F}{2\pi a^{2}}[(\frac{a^{2}}{(a-z)^{2}}+\frac{a^{2}}{(a +z)^{2}})] \tag{1}\]  
\[\sigma_{\rm t}=-\frac{F}{2\pi a^{2}}\times\frac{1-2\mu}{\sqrt{2}}[\frac{a^{2} }{(a-z)^{2}}+\frac{a^{2}}{(a+z)^{2}}] \tag{2}\]  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Loading Rate (kN/s)**} & \multirow{2}{*}{**Fine**} & \multirow{2}{*}{**Fine**} & \multirow{2}{*}{**Fine**} & \multirow{2}{*}{**Course**} & \multirow{2}{*}{**Crystalline**} & \multirow{2}{*}{**Granite**} & \multirow{2}{*}{**Sillstone**} & \multirow{2}{*}{**Sillstone**} & \\ \cline{3-3} \cline{8-12}  & & & & & & & & & & & & \\ \hline
0.1 & 34.82 & 25.16 & 16.38 & 7.33 & 24.76 & 16.91 & 12.11 & 6.17 & 11.68 & 8.18 & 5.37 & 2.75 \\
0.5 & 37.37 & 26.43 & 17.07 & 8.28 & 26.08 & 18.54 & 12.16 & 6.75 & 12.32 & 8.38 & 5.62 & 2.83 \\
1.0 & 38.8 [PERSON]'s ratio \(\mu\) of fine-crystalline granite, coarse-crystalline granite and siltstone were 0.200, 0.185, and 0.180, respectively, as measured by an indoor uniaxial compression test, and the distribution of tensile and compressive stresses on the loading axis of the rock sample point load could be analyzed by substituting Equations (1) and (2). The stress distribution states of three rock samples of different sizes under different loading rates were plotted, with the vertical axis coordinate scale being the ratio of the coordinate \(z\) of the corresponding point to the height \(a\) of the rock sample, and the horizontal axis coordinate scale being \(F/(2\pi a^{2})\). The plotted results are shown in Figure 6.  
Analyzing the stress distribution states of the three rock samples under different loading rates, it was found that most of the areas inside the rock samples were subject to tensile stresses. The tensile and compressive stresses on the loading axes showed an increasing trend with the increase in rate; the difference in stress distribution of the rock samples due to the rate was mainly reflected in the compressive stresses, and the compressive stresses were more affected by the rate near the center of the loading axes.