**1. Introduction**

The three-dimensional (3D) arrangemen<sup>t</sup> of ice crystals and pores, i.e., the microstructure of snow, changes with time due to exchanges of matter between the ice crystals. Although the link between the snow microstructure and its physical properties has been addressed for a long time [1,2], it is still difficult to characterize the snow microstructure and its evolution over time. Two common approaches used to characterize the 3D microstructure of snow are serial sectioning [3,4] and X-ray computed microtomography (micro-CT) imaging [5,6]. The micro-CT is a technique for non-destructive 3D imaging of internal microstructures [7]. Based on the acquired 3D data it is possible to make a quantitative analysis of internal features such as porosity, cracks, grains, fibres etc., as well as material deformation and strain [8]. In addition, the micro-CT enables the evolution of a material microstructure to be studied in both temporal and spatial domain.

The micro-CT method has been used by many researchers for more than ten years to visualize the snow microstructure. However, the 3D quantitative analysis of displacement of snow grains during compaction is limited. Schleef and Löwe [9] addressed the influence of external mechanical stress on isothermal densification and specific surface area (SSA) of snow, using the micro-CT measurements. They reported that evolution of the snow SSA is independent of the snow density, while snow densification increases with increasing external stress. Kaempfer and Schneebeli [10] investigated the isothermal metamorphism of fresh snow at different temperatures for nearly one year. They deduced snow microstructural parameters from the tomographic images, which describe the structural information related to grain boundaries. Pinzer et al. [11] performed time-lapse micro-CT experiments on snow metamorphism under a static temperature gradient. They observed the structural evolution and mass transfer within snow through ice grains. Ebner et al. [12] further observed the snow metamorphism exposed to an advective airflow and reported that saturated airflow has no influence over grains coarsening rate. Wang and Baker [13] investigated the snow microstructure evolution under compression tests, based on the X-ray micro-CT imaging. They also performed analysis of SSA, structure model index and structure thickness. One of their findings from interrupted compression tests was that the SSA of snow decreased more rapidly than the determined values of SSA. Kerbrat et al. [14] and Hagenmuller et al. [15] proposed image processing techniques to determine snow properties such as density and SSA based on the micro-CT measurements. They emphasized that the retrieval method of these snow properties is sensitive to the voxel size (10 μm for their experiments), especially for fresh snow. Wiese and Schneebeli [8] performed the micro-CT measurements of snow microstructure under the influence of settlement at constant temperature gradient. Their observations show an increase in density, strain and viscosity over time due to settlement induced via external loading. All these investigations have larger focus on microstructural parameters, and smaller focus on structural changes in a snowpack at granular level due to compaction. Further, Schleef et al. [16] observed the impact of various levels of compression on the microstructure of snow, which is similar to the presented study. The major focus of their study was on the dependence of density and SSA to the applied stress using a microcompression device. However the presented study focuses on the characteristics of individual ice crystals under external loading. A high quality tomographic data with spatial resolution of 4.3 μm was carried out in this study to observe the microstructural features of snow grains with respect to applied stress.

The purpose of this initial study is to analyze the 3D images of snow grains during compression tests induced via in-situ uniaxial load. The presented analysis of the micro-CT measurements focuses on displacement and strain fields based on digital volume correlation (DVC) [17] and porosity distribution of the investigated snow volume. Microstructural parameters such as density and SSA have been calculated for various load stages from the tomography data. The investigated snow volume is prepared from a freshly fallen low density snow that was collected right after precipitation. Section 2 focuses on experimental arrangemen<sup>t</sup> and measurement procedure. Section 3 describes the applied techniques, which are DVC and porosity analysis. Section 4 details the observations of the study and discussions of the observed results are given in Section 5. A summary including conclusions are presented in Section 6.

## **2. Experimental Procedure**

#### *2.1. Micro-CT System with In-Situ Load Module*

Snow sampling and scanning were performed at the micro-CT lab, Luleå University of Technology, Sweden. The 3D images of snow microstructure were obtained using a ZEISS Xradia 510 Versa (Carl Zeiss X-ray Microscopy, Pleasanton, CA, USA). The Xradia 510 Versa can achieve 0.7 μm of true spatial resolution with minimum achievable voxel size of 0.07 μm. The components of the micro-CT system are a sealed microfocus X-ray tube, 4-axis sample stage, a photo detector and a load stage, see Figure 1a. The system is equipped with a Deben CT5000TEC temperature (Deben UK Limited, Bury Saint Edmunds, UK) controlled load stage with a 500 N load cell. The Xradia 510 Versa can be operated at tube voltage range of 30–160 kV with maximum output of 10 W.

A sample holder (Figure 1b) was specifically designed to visualize material properties for the micro-CT experiments. This holder has a fixed punch made of brass, a Polymethyl methacrylate (PMMA) tube with inner and outer diameter of 6 mm and 10 mm, respectively. Further, a moving punch with diameter of 5.95 mm was made of aluminium. The diameter of the moving punch is slightly smaller than the inner diameter of the PMMA tube, in order to ensure a smooth and frictionless compression. The in-situ load stage was used to apply uniaxial stress to compact a snow volume via the moving punch, which means the compression is applied from the bottom, and both the punch plates have smooth and flat surface. The investigated snow sample was small enough such that it was not required to move the sample vertically during data acquisition.

Scout-and-ScanTM Control Software Control Software (Carl Zeiss X-ray Microscopy, Pleasanton, CA, USA) was used for reconstructing the scanned images. Quantitative analysis of microstructure (shape of crystals, porosity etc.) was obtained from 3D image analysis, using the software Dragonfly Pro (Carl Zeiss X-ray Microscopy, Pleasanton, CA, USA) (ORS).

**Figure 1.** Experimental arrangemen<sup>t</sup> of the micro-CT system: (**a**) the micro-CT consists of a sealed microfocus X-ray tube, 4-axis sample stage, a photo detector and a temperature controlled in-situ load stage; (**b**) the sample holder was 6 mm in diameter and 5 mm in height, note that the material visible in the sample holder is sugar; (**c**) selection of volume of interest (VOI) in the snow volume.

## *2.2. Snow Sampling*

An undisturbed natural dry snow block was collected right after latest precipitation outside of Luleå University of Technology (LTU), Sweden and ambient temperature was about –4 ◦C at the time of collection. The acquired snow block was immediately placed in a freezer held at –18 ◦C. Tools such as sample holder, spatula etc., that were required to prepare a final snow sample were also kept in the freezer. After the sample holder and tools were cooled down, a cylindrical snow sample was prepared using thermal insulated gloves, still being inside the freezer. Thereafter, the sample holder with snow sample was transferred quickly from the freezer to the in-situ load stage that was held at –15 ◦C. Surface of the snow sample was flattened using the moving punch to minimize the skewness of the applied load.

## *2.3. Data Acquisition*

The X-ray source voltage and current were set to 50 kV and 80 μA, respectively. Temperature of the in-situ load stage was maintained at –15 ◦C for all the measurements. To avoid the microstructural damage close to the edges, an interior VOI was defined for the DVC analysis, which corresponds to 4.4 mm in diameter and 3.9 mm in height, see Figure 1c. A total of 1601 projections of the investigated snow volume were recorded as the sample rotated over 360◦ in high resolution setting for a period of 6 h.

Prior to the scan, the snow sample was placed in the micro-CT chamber for 30 min to ensure thermal equilibrium for the sample and mount. Initially, a low resolution scan was carried out for 30 min to improve stability of the source and to check if the reconstruction is as expected. Thereafter, higher resolution scans of the snow volume were performed using the 4× objective and 4.4 mm field of view (FOV). In this case, the micro-CT reconstructs the spatial distribution of ice crystals and pore space with a resolution in terms of voxel size 4.3 μm at an exposure time of 12 s per projection.

Figure 2a shows a schematic representation of the loading profile, where micro-mechanical uniaxial compression tests on the snow sample were performed at four load states such as 0 MPa, 0.3 MPa, 0.6 MPa and 0.8 MPa. The load stage was used in a continuous mode where the compression was applied until the user-defined load was reached. The snow volume was scanned first at 0 MPa (unloaded state) and then subsequent scans were conducted at three load states. After each loading state, the snow sample was allowed to rest for 30 min prior to the scan.

**Figure 2.** Graphical representation of compression tests: (**a**) schematic representation of the applied loading profile; (**b**) real-time force and displacement data for 0.6 MPa loading profile. In Figure 2a, red circles represent the beginning of scanning, white circles represent the end of scanning and blue circles represent the relaxation time during respective load cycles.

Figure 2b shows the loading and displacement data for the load state of 0.6 MPa. Figure 2b shows rapid and large deformation of snow during the loading period due to grain rearrangements, however the load profile curve was steeper up to 0.35 MPa as the snow sample was already compacted up to 0.3 MPa during the previous load state. After 0.35 MPa, snow tends to resist the force up to 0.45 MPa where the snow structure breaks due to failure of cohesive bonds and recrystallization. The similar behavior can be observed when the force starts to increase up to 0.55 MPa. After reaching the desired load, the snow sample is set to relax for 30 min prior to the scan. During the load relaxation, the stress relaxed to a residual value of about 64 kPa after 30 min. Apparently the described global structural failures (see Figure 2b) during the load profile allow the ice crystals to move into more compact arrangements, which tend to strengthen the bonds between grains [18,19]. Furthermore, there was no scan performed during the relaxation phase, as this would create motion artefacts due to high resolution.
