## 2 Experimental Methods
### High-Speed Loading Machine with Two Load Cells for Dynamic Force Measurement  
In the present experiments, a specially-developed high-speed testing machine is used as a dynamic loading apparatus, as shown in Figure 4. The most significant feature of this machine is that it supplies a constant loading rate in the speed range of 0.1-20.0 m\(\cdot\)s\({}^{-1}\) with control precision of 0.1 m\(\cdot\)s\({}^{-1}\). The nominal strain rate is in the range of 2-400 s\({}^{-1}\) if a 5-cm edge length cubic specimen is used. A universal testing machine can never supply such high strain rates. Moreover, the Instron impact machine can supply loading force up to 160 kN, so large-sized specimens can be used. The SHPB system can carry out experiments at very high strain rates, but the size of specimens which it used is limited, usually not larger than one centimeter in length, so effects of air bubbles and grain boundaries cannot be considered. Compared to the SHPB system, the Instron high-speed loading machine is able to load larger specimens, avoiding the drawbacks of losing some intrinsic characteristics of ice when using too small-sized specimens. The Instron high-speed loading machine applies a servo control mechanism, hydraulic drive, and possesses a maximum actuator stroke of up to 600 mm. The actuator experiences acceleration, uniform speed, and slowdown three movement stages when loading. Actuator needs to travel a certain distance to accelerate to reach a pre-setting loading rate. The key to make ice specimen compressed at a pre-setting loading rate is to set the distance between platen and upper-surface of ice greater than that needed to reach the pre-setting loading rate, so the crosshead could contact with ice specimen at the pre-setting loading rate from the beginning of compression. The specimen is held for a very short time from beginning loading to finishing loading, so if the specimen is destroyed at uniform-speed movement stage, the specimen is regarded as being subject to uniform loading (as shown in Figure 5). \(\varepsilon_{\mathrm{np}}\) denotes the nominal ultimate strain, \(\dot{\varepsilon}_{\mathrm{n}}\) denotes the nominal strain rate, and \(\sigma_{\mathrm{c}}\) denotes the compressive strength; then, we have:  
\[\varepsilon_{\mathrm{np}}=\frac{\delta_{\mathrm{p}}}{h}=\frac{v\cdot\Delta t}{h} \tag{1}\]  
\[\dot{\varepsilon}_{\mathrm{n}}=\frac{\varepsilon_{\mathrm{np}}}{\Delta t}= \frac{v}{h} \tag{2}\]  
\[\sigma_{c}=\frac{F_{\mathrm{P}}}{A} \tag{3}\]  
where \(\delta_{\mathrm{p}}\) is the peak deformation of ice specimen, \(h\) is the height of specimen, \(v\) is the loading rate of the actuator, \(\Delta t\) is the sustaining time from the start of loading to reaching peak load, \(F_{\mathrm{P}}\) is the peak load, and \(A\) is the cross-sectional area of specimen. In this article, the term nominal strain is used to refer to the ratio of displacement increment obtained from actuator to original height of sample,  
Figure 3: Three types of ice specimens: (**a**) Non-speckle specimen (transparent specimen); (**b**) pure-white specimen; and (**c**) white-black speckle specimen. All of them are cubes with an edge length of 5 cm. and the term nominal strain rate is used to refer to the ratio of nominal strain to corresponding time interval. Both terms are related to deformation recorded by testing machine. In dynamic mechanical experiments, if the loading rate is too high, it is likely to form non-uniform stress due to the inertial effect. The loading rate should be lower than a threshold rate which is related to specimen length and material mechanical properties if we want to obtain the compressive strength at moderate rates. There are some theoretical formulas to consider the inertial effects [22; 23], while ice mechanics are so complex that theoretical formulas may be invalid sometimes. Instead, a two-load-cell system is used for force measurement. The dynamic load cell has a natural frequency of 37 kHz and a force capacity of 50 kN.