## 2 Experimental Methods
### Digital Speckle Correlation Method for Deformation Measurement  
In ice mechanics experiments, deformation of specimens is usually measured through measuring actuator displacement, conventional strain gauges, or an extensometer. Under creep and quasi-static conditions, these methods work well and were widely used; while these methods are not suitable for ice dynamic compression experiments due to restrictions resulting from material features of ice and their own limitations. Measuring actuator displacement is an indirect measurement, and nominal strain or strain-rate can be derived. The prerequisites are that the rigidity of the test machine is large enough and interfaces between the platens and specimen are perfect. The former prerequisite is easy to meet, but the latter prerequisite is not. It is difficult to use bond strain gauges on the surface of the ice specimen or freeze strain gauges in ice specimens; in addition, gauges may provide local reinforcement, which perturbs the stress field. The average strain can be obtained between two points by employing an extensometer, but the extensometer risks being damaged under dynamic loading. Furthermore, the inertia effect of the extensometer, itself, also affects the measurement results. In short, to measure the dynamic deformation of ice specimens requires applying a new feasible deformation measurement method. The digital speckle correlation method is an optical deformation measurement method which is based on gray-scale analysis of speckle images [18]. The basic principle is calculating the pixel displacement by matching speckles between the un-deformed image and the deformed image, and then deriving information of strain and strain-rate. Compared with the traditional electrical measurement methods (such as the use of strain gauges, extensometer, etc. ), the digital speckle correlation method breaks through the limitations of localized measurement, small deformation measurement, and contacting measurement, providing whole field information, large deformation measurement, and non-contacting measurement. Due to its non-contacting feature, deformation measurements of materials that cannot stick to strain gauges effectively can be achieved very well. Since it was put forward, the digital speckle correlation method has been developed into an important deformation measurement method in mechanical testing [24], such as biomechanical testing [25], mechanical testing of wood, rock, and composite materials [26; 27], as well as crack propagation and other practical applications fields [28; 29]. The digital speckle correlation method performs deformation measurement based on the correlation principle, as shown in Figure 6. The following steps should be taken to measure deformation by use of DSCM: First, select reference points in the reference image and determining an appropriate correlation subset zone with reference points located at the centers. Second, select appropriate correlation formulas for correlation computation to calculate pixel displacements of the reference points in the deformed images. There are many formulas that can be used for correlation computation [30]. A widely used cross-correlation formula is used:  
\[C(\mathrm{u},\mathrm{v})=\frac{\sum\sum\Bigl{[}\Bigl{(}f(x_{i},y_{j})-\overline {f}(x_{i},y_{j})\Bigr{)}\cdot\Bigl{(}g\Bigl{(}x^{\prime}_{i},y^{\prime}_{j} \Bigr{)}-\overline{g}\Bigl{(}x^{\prime}_{i},y^{\prime}_{j}\Bigr{)}\Bigr{)} \Bigr{]}}{\biggl{[}\sum\Bigl{(}f\bigl{(}x_{i},y_{j}\bigr{)}-\overline{f}\bigl{(} x_{i},y_{j}\bigr{)}\Bigr{)}^{2}\cdot\sum\sum\Bigl{(}g\Bigl{(}x^{\prime}_{i},y^{ \prime}_{j}\Bigr{)}-\overline{g}\Bigl{(}x^{\prime}_{i},y^{\prime}_{j}\Bigr{)} \Bigr{)}^{2}\biggr{]}^{1/2}} \tag{4}\]  
where \(f\) and \(g\) are gray-scale functions of the reference image and deformed image, respectively. \(\overline{f}\) and \(\overline{g}\) are average values of \(f\) and \(g\), respectively.