## 3 Mechanical Experiment
### Analysis of the Experimental Results
#### 3.2.1 Different HDRs  
UCS  
Figure 6a illustrates that as the HDR increases, the UCS value displays a changing trend that is M shaped. The curve is fitted by two parts with a HDR of 0.6\(\sim\)1.2 and 1.2\(\sim\)2, and the fitting parameter is good, \(R^{2}\) is 0.918 and 0.99988, respectively in order to obtain the fitted Formula (3) for the UCS at each stage. When the HDR ranges from 0.6 to 1.2, \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**LR (mm\(\cdot\)min\({}^{-1}\))** & **HDR** & **SR (s\({}^{-1}\))** & **Load Condition** & **UCS (MPa)** & **Axial Peak Strain \(\epsilon\) (\%)** \\ \hline \multirow{8}{*}{0.8} & 0.6 & 4.44 \(\times\)10\({}^{-4}\) & Quasi-dynamic & 4.96 & 4.36 \\  & 0.8 & 3.33 \(\times\)10\({}^{-4}\) & Quasi-dynamic & 5.23 & 2.94 \\  & 1 & 2.67 \(\times\)10\({}^{-4}\) & Quasi-dynamic & 5.8 & 2.15 \\  & 1.2 & 2.22 \(\times\)10\({}^{-4}\) & Quasi-dynamic & 5.17 & 3.74 \\  & 1.4 & 1.90 \(\times\)10\({}^{-4}\) & Quasi-dynamic & 5.59 & 1.85 \\  & 1.6 & 1.67 \(\times\)10\({}^{-4}\) & Quasi-dynamic & 5.69 & 1.34 \\  & 1.8 & 1.48 \(\times\)10\({}^{-4}\) & Quasi-dynamic & 5.16 & 1.64 \\  & 2 & 1.33 \(\times\)10\({}^{-4}\) & Quasi-dynamic & 4.55 & 2.71 \\
0.1 & & 1.67 \(\times\)10\({}^{-5}\) & Static & 5.18 & 1.01 \\
0.2 & & 3.32 \(\times\)10\({}^{-5}\) & Static & 3.47 & 1.09 \\
0.5 & & 8.32 \(\times\)10\({}^{-5}\) & Static & 5.63 & 1.18 \\
1 & & 1.67 \(\times\)10\({}^{-4}\) & Quasi-dynamic & 6.16 & 1.97 \\
2 & 2 & 3.39 \(\times\)10\({}^{-4}\) & Quasi-dynamic & 5.40 & 1.47 \\
5 & & 8.30 \(\times\)10\({}^{-4}\) & Quasi-dynamic & 6.07 & 1.15 \\
10 & & 1.66 \(\times\)10\({}^{-3}\) & Dynamic & 5.23 & 1.32 \\
20 & & 3.32 \(\times\)10\({}^{-3}\) & Dynamic & 4.83 & 1.21 \\
50 & & 8.32 \(\times\)10\({}^{-3}\) & Dynamic & 6.68 & 1.27 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Experimental results on specimens with different HDRs and different LRs. Figure 5: Stress–strain curves of specimens with different HDR. (**a**) HDRs of 0.6–1; (**b**) HDRs of 1.2–1.6; (**c**) HDRs of 1.6–2. the UCS roughly tends to first increase fast and then decrease slowly. The maximum UCS, 5.8 MPa, during this stage is obtained when the HDR is 1. After passing the dividing line of a HDR of 1.2, the UCS curve shows a trend of first fast growth then reducing significantly. And the maximum value of the UCS, 5.69 MPa, in this interval is obtained at a HDR of 1.6. Additionally the UCS has a small error prediction range, indicating it is low dispersion. Therefore, within the HDR range of 0.6\(\sim\)2, UCS presents different change trends, and the maximum value is obtained at a HDR of 1. However, the UCS does not completely decrease with the increase in size; when the HDR ranges from 0.6 to 1, the UCS follows an increasing trend. This is not consistent with previous conclusions that as the size increases, UCS gradually decreases to stabilize [4; 6; 7; 10; 31]. However, this result seems to coincide with the conclusions of [PERSON] and [PERSON] [1; 20] that the UCS increases within a certain HDR range and gradually decreases when exceeding this range. \[\left\{ \begin{array}{l}y_{1}=-5.625x^{2}+10.725x+0.475\\ y_{2}=-4.80357x^{2}+14.53643x-5.34486\\ E_{1}=18.7875x^{2}-31.1875x+18.8125\\ E_{2}=12.01786x^{2}-39.59215x+33.87629\end{array} \right. \tag{3}\]  
where \(y_{1}\) is the UCS value when the HDR is 0.6\(\sim\)1.2, MPa; \(y_{2}\) is the UCS value when the HDR is 1.2\(\sim\)2, MPa; \(E_{1}\) is the peak axial strain when the HDR is 0.6\(\sim\)1.2, %; \(E_{2}\) is the peak axial strain when the HDR is 1.2\(\sim\)2, %; \(x\) is the HDR. Axial Peak Strain \(\varepsilon\)  
The peak strain is inversely proportional to the UCS, mainly due to the gap in the elastic modulus. Under the same compressive strength, as the elastic modulus increases, the peak strain decreases. As can be seen from Figure 5, when the HDR ranges from 0.6 to 1, the curve slope increases, the elastic modulus of the specimen gradually increases, and the peak strain gradually decreases.