# Research on Rock Strength Test Based on Electro-Hydraulic Servo Point Load Instrument
## 4 Results and Discussion
### Effect of Loading Rate and Rock Sample Size on \(I_{\text{s(50)}}\)
#### 4.3.1 Effect of Loading Rate on \(I_{\text{s(50)}}\)  
From the results of the preliminary tests, it is known that the loading rate and loading method affect the damage load, which is closely related to \(I_{\text{s(50)}}\), so it is especially important to consider the effect of loading rate on \(I_{\text{s(50)}}\). Figure 7 shows the relationship curves between \(I_{\text{s(50)}}\) and loading rate for the three rock samples solved using different methods. From the overall trend, the \(I_{\text{s(50)}}\) of different sizes of the three rock samples increased with the increase in loading rate, except for individual specimens due to the heterogeneity of the rock sample itself or the error of the test operation.  
For the three rock samples with different sizes, the effect of loading rate on \(I_{\text{s(50)}}\) solved by different methods was analyzed and it was found that the curve shape changed as the size decreased. Taking \(I_{\text{s(50)}}\) for fine-crystalline granite as an example, when the sizes are \(50^{3}\), \(40^{3}\), \(30^{3}\), and \(20^{3}\) mm\({}^{3}\), the increase in \(I_{\text{s(50)}}\) is larger in the loading-rate range 0.1-0.5 kN/s, and the growth rates of \(I_{\text{s(50)}}\) are 0.076, 0.051, 0.048, and 0.150, respectively, while in the loading-rate range 0.5-1.0 kN/s, the growth rates of \(I_{\text{s(50)}}\) are 0.031, 0.062, 0.023, and \(-0.019\). This indicates that the effect of rate on \(I_{\text{s(50)}}\) varies in different loading-rate ranges when the rock sample size is different, and the overall performance is that the growth rate of \(I_{\text{s(50)}}\) is smaller in the larger loading-rate range than that in the smaller loading-rate range, but the effect of loading rate on \(I_{\text{s(50)}}\) is almost linearly increasing for the rock sample of size \(40^{3}\) mm\({}^{3}\).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Time** & **Method** & **Relationship Formula** & **Note** \\ \hline [PERSON], [PERSON] [29] and & Correction method & \(I_{\text{s(50)}}=F\)\(I_{\text{s1}}\) & \(F\) is the correction factor; \(D\) is the loading-point spacing \\ [PERSON], [PERSON] et al. [30] & Method I & \(F=0.2717+0.01457D\), \(D<55\) mm & (mm); \(D_{e}\) is the equivalent \\  & & \(F=0.754+0.058D\), \(D\geq 55\) mm & diameter (mm); \(P\) is the \\ [PERSON], [PERSON] et al. [21] & ISRM method & \(I_{\text{s(50)}}=F\)\(I_{\text{s1}}\) & point load breaking load (N); \\  & Method II & \(I_{\text{s}}=P/D_{e}^{2}\) & \(I_{s}\) refers to the uncorrected \\  & & \(F=(D_{e}/50)^{0.45}\) & point load strength value \\ [PERSON] et al. [31] & Traditional method & \(\text{lg}I_{\text{s(50)}3}=0.256+\text{lg}I_{\text{s2}}-1.008\exp(-0.0274D)\) & (N/mm\({}^{2}\)); \(W\) is the \\  & Method III & \(I_{\text{s(50)}}=P/D^{2}\) & minimum section width or \\ Ministry of & Engineering rock & \(I_{\text{s(50)}4}=I_{\text{s}}K_{d(50)}K_{f}\) & average width through the \\  & & \(I_{\text{s(50)}4}=I_{\text{s}}K_{d(50)}K_{f}\) & two loading points (mm); \\  & & \(I_{\text{s(50)}}=P/D^{2}\) & \(K_{d(50)}\) is the size effect \\  & & \(K_{d(50)}=1.2828(\text{lg}W^{0.6954})\) & correction factor; \(K_{f}\) is the \\  & & \(K_{f}=0.3161\exp(2.3034((D/W+\text{lg}(D/W))/2))\) & shape effect correction factor \\ \hline \hline \end{tabular}
\end{table}
Table 4: Method of solving the standard point load strength.