**4. Results**

The experimental observations from the micro-CT analysis are presented in this section. Distribution of snow grains is given in Section 4.1. Section 4.2 presents the changes in snow microstructure with respect to the applied load. Microstructural parameters for the discretized sections of the snow volume are presented in Section 4.3.

#### *4.1. Distribution of Snow Grains*

Some examples of the complex 3D morphology of the investigated natural dry snow are presented in Figure 4. The snow sample was composed of ice crystals with significant variations in shape and size. However, moving through the cross sections, the most dominated shapes are needles, capped columns and dendrites, see Figure 4a–c.

**Figure 4.** 3D images of snow grains distribution: (**a**) scan of the whole investigated snow volume; (**b**) scan of the snow volume across a cross-section and selection of two individual grains; (**c**) slightly deeper cross-section than the one shown in Figure 4b, to focus on the individual grains; (**d**) structure of two individual snow grains. Red arrows in Figure 4 represent an example of the described hollow core structure.

There was no possibility for snow grains to grow into different shapes during the scanning time as the snow temperature was kept constant at –15 ◦C. In addition, there was no presence of water in the pore space between ice crystals. These natural ice crystals observed to be completely non-isotropic in shape and size. A number of the ice crystals observed to have a deep hollow core (see-through tunnel) with variable dimensions (Figure 4d). To study the nature of this hollow core further, two individual ice crystals of different shapes are selected. The structure of these two crystals can be seen at two successive cross-sections in Figures 4b,c. The presented crystals (Figure 4) appeared to have hollow core with closed tip at one end (Figure 4d, the tip was cut). The width of the presented ice crystals was approximately 0.85 mm , and the diameter of the tunnel ranges from 0.06 mm to 0.22 mm Moreover, pore volume of blue and yellow colored crystals (from Figure 4d) was approximately 0.092 mm<sup>3</sup> and 0.051 mm3, respectively. One can observe in Figure 4 that a significant number of snow grains have the described hollow core structure, and some examples are shown by red arrows in Figures 4a–c.

#### *4.2. Displacement of Snow Grains*

Figures 5 and 6 show the displacement and strain fields between unloaded state (0 MPa) and the loaded states at 0.3 MPa (Figures 5b and 6b), 0.6 MPa (Figures 5c and 6c) and 0.8 MPa (Figures 5d and 6d). The spatial resolution of the DVC analysis is limited to the size of the correlation window (sub volume), which is 32 × 32 × 32 voxels. Hence, the DVC analysis is not carried out at granular level, for individual grain tracking.

**Figure 5.** The DVC results for the snow sample at three loaded states, 0.3 MPa, 0.6 MPa and 0.8 MPa. w refers to the displacement in z-direction within the investigated volume. Figure 5a represents the displacement field at unloaded state. Figure 5b,c,d represent the displacement fields between unloaded state and loaded states 0.3 Mpa, 0.6 Mpa and 0.8 Mpa, respectively. Arrows indicate the direction of the displacement field and dashed black lines in Figure 5c,d represent the moving punch.

**Figure 6.** Normal strain fields with respect to the applied stress and dashed black lines in Figure 6c,d represent the moving punch. Figure 6a represents the strain field at unloaded state. Figure 6b,c,d represents the strain fields between unloaded state and loaded states 0.3 Mpa, 0.6 Mpa and 0.8 Mpa, respectively.

One can observe in Figure 5 that the measured displacement field at all the loaded states exhibit similar feature of upward compression (in z-direction). This is expected due to the position of the moving punch. In addition, overall displacement of snow volume appeared to be increasing as the applied stress increases, especially close to the moving punch. However, larger amount of deformation can be observed at the center of the sample (in radial direction) compared to the boundaries. This phenomenon may be due to the smaller punch diameter than the sample holder.

Snow grains close to the fixed punch appeared to be insensitive to the applied stress at least up to 0.8 MPa, as no significant displacement is observed, see Figure 5. This may be due to the boundary condition imposed by the fixed punch. At 0.8 MPa of applied stress, significant deformations may be due to breakage of bonds between ice crystals and re-distribution of ice crystals. However, strain fields in Figure 6 shows that the deformations were fairly distributed through out the whole volume where parts of the snow volume experience positive strain field (tensile) while other parts experience negative stain field (compression). One can observe that there is also a part of the snow volume which experiences almost zero deformation. However, tracking of individual grains due to compression needs to be studied further.

Figure 7 shows the reconstructed grayscale images of the investigated snow volume at four loading states. Four cross-cuts per loading state are presented so that, behavior of ice crystals can be observed close to the fixed punch (top layer, XY-plane, Figure 7a), in the center of the snow volume (XY-plane, Figure 7b), close to the moving punch (bottom layer, XY-plane, Figure 7c), and center cross-section in z-direction (XZ-plane, Figure 7d). The internal features of the snow volume in Figure 7 are very extensive, therefore four crystals from each image are selected to describe general observations. Note that, the selected cross-cuts for a respective loading were correspond to the same cross-cut (slice), to avoid the rotational effects and to ensure that the observed solid movements of grains are solely due to compression tests.

Figure 7e,i,m,q represent a cross-cut close to the fixed punch (top layers, XY-plane) at load states 0 MPa, 0.3 MPa, 0.6 MPa and 0.8 MPa, respectively. The selected crystals in these four images are named as A, B, C and D. Crystals A and B show that not all the crystals in this cross-cut experience displacement. The dendrite crystals in this case were almost unchanged in terms of shape and size. Crystals C and D experience grains breakage. Analysis of displacement field in Figure 5 show that this part of the snow volume experienced very small displacement. However, observation of individual ice crystals shows a small degree of grain displacement close to the fixed punch, which can be also seen from the strain fields in Figure 6.

*Materials* **2019**, *12*, 850

(**a**)Close to fixedpunch

(**e**) Height = 4.26 mm;Load=0 MPa

(**i**) Height = 4.26 mm;Load= 0.3 MPa

(**m**) Height = 4.26 mm; Load = 0.6 MPa

(**q**) Height = 4.26 mm; Load = 0.8 MPa

(**b**)Centerofthesample

(**f**) Height = 2.3 mm; Load = 0 MPa

(**j**) Height = 2.43 mm; Load=0.3 MPa

(**n**) Height = 2.64 mm; Load0.6MPa

=

(**r**) Height = 2.72 mm; Load = 0.8 MPa

(**c**) Close to moving punch

(**g**) Height = 0.43 mm; Load=0 MPa

(**k**) Height = 0.51 mm;Load=0.3MPa

(**o**) Height = 0.96 mm;

(**s**) Height = 1.18 mm;Load = 0.8 MPa

(**d**) Center cross-cut

(**h**) Load = 0 MPa

(**l**) Load = 0.3 MPa

(**p**) Load = 0.6 MPa

(**t**) Load = 0.8 MPa

**Figure 7.** Distribution of ice crystals at four slices of the investigated snow volume at a given load. Note that the compaction is applied from the bottom of the snow volume via moving punch and it is visible in Figure 7p,t.

Figure 7f,j,n,r represent a cross-cut (XY-plane) at the center of the snow volume at all load states. The selected crystals in these four images are named as A, B, C and D. Crystals A and B tend to move closer to each other and form well connected grains. Crystals C and D, experience re-distribution due to the formation of new crystals, and one can observe that crystals C and D moves out of the scan volume as the compaction increases.

Figure 7g,k,o,s represent a cross-cut (bottom layers, XY-plane) close to the moving punch at all load states. The selected crystals in these four images are named as A, B, C and D. Crystals A and B tend to experience breakage of grains bond due to compaction, while crystals C and D tend to form into new crystals. As this part of the snow volume experienced the compaction directly from the punch, crystals observed to be deformed significantly via bond breakage. This was already observed from the displacement field in Figure 5.

Figure 7h,l,p,t represent a center cross-cut (XZ-plane) in z-direction at all load states. The selected crystals in these four images are named as A, B, C and D. Crystals A, C and D tend to experience recrystalization as the applied stress increases. Moreover, one can observe the moving punch in Figure 7p,t. As the punch compact the snow surface, crystals tend to appear within the VOI (for example, crystal B).

#### *4.3. Porosity Measurements*

Figure 8 shows the calculated porosity distribution for the discretized sections of the snow volume and the whole volume. The straight lines in Figure 8 represent the average porosity values for the whole volume at a given load state. Note that the moving punch applied compaction from the bottom, as shown in Figure 3b,c. The calculated density and SSA are given in Table 1.

**Figure 8.** Porosity distributions for the discretized sections of the investigated snow volume. The calculated density values of the snow volume at each load state are given (in units kg m–3).


**Table 1.** Microstructural parameters under loading conditions.

One can observe that the porosity of the whole snow volume linearly decreases as the applied compression increases. Under compaction, the ice crystals tend to move closer resulting in densification where the ice crystals re-distribute into the pore space. Note that the moving punch is excluded from the data shown in Figure 8, which can be observed from the reduction of data points as the investigated snow volume experienced compaction.

There is a distinct vertical heterogeneity can be observed for the porosity distribution in the axial direction, see Figure 8. At an unloaded state, the initial snow sample exhibits a higher porosity (77.5%) at the bottom compared to the top (74.5%) of the sample. This may be due to the preparation of the snow sample. The sample holder was pushed straight into the dry natural snow and shaved off the excess snow from the top with a sharp spatula, producing a flat and smooth surface. The described sample preparation appeared to force the grains to move closer at the top of the sample holder, which resulted in around 3% of porosity variation between top and bottom layers.

At 0.3 MPa loading stage, this vertical heterogeneity in porosity distribution between the top (74%) and bottom (75%) layers was reduced to around 1%. This may be due to the initial compression, which forces the grains to re-arrange. Furthermore, there was more than 6 hours of settling process during the scan at unloaded state. It may also be possible that the bottom layers experience the weight of top layers due to settlement thus forcing the distribution of ice crystals into the pore space.

At 0.6 MPa and 0.8 MPa load stages, the vertical heterogeneity in porosity distribution between the top (73.5% & 71%, respectively) and bottom (70% & 67.5%, respectively) layers was then re-increased to around 3%. As described in Figure 7, snow grains at higher loads experience bond breakage and grain re-arrangement. Table 1 further shows that the overall density increases with compression while the SSA decreases.
