New database for the estimation of dynamic coefficient of friction of snow

Rakesh K. Aggarwal; Ranjan Das; Hemendra S. Gusain

doi:10.1515/geo-2022-0639

Artikel Open Access

New database for the estimation of dynamic coefficient of friction of snow

Rakesh K. Aggarwal , Ranjan Das und Hemendra S. Gusain

Veröffentlicht/Copyright: 31. Mai 2024

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Abstract

Knowledge of the Coulomb dynamic coefficient of friction of snow is a vital input parameter for the estimation of run-out distance, velocity, forces, and lateral spread of the snow avalanches in the hilly regions. This parameter is defined as the ratio of the wall shear force to the normal force components of an avalanche. Avalanches are one of the most devastating natural hazards. So, the proper understanding of avalanche flow parameters is vital for the people and the infrastructure in the mountainous regions of the world. Notwithstanding the utmost significance of the Coulomb friction parameter, a few measurements are available for this parameter. In the present work, based on 32 measurements carried out from 2017 to 2020, a new database for the shear force and normal force components of the avalanches and derived values of the dynamic coefficient of friction between the chute steel surface and the flowing snow are presented. The measurements were carried out using a three-component piezoelectric load cells-based dynamometer which in turn was installed on the 12° slope of a 61-m long snow chute, located in the Pir Panjal Himalayan range of India. Based on all the measurements, the average value of the dynamic coefficient of friction for snow-steel surface is estimated to be 0.113 with a standard deviation of 0.032. The results have been exhibited to be in accordance with the published literature. It is expected that the present database will be highly significant for the validation and improvement of avalanche dynamics models especially for high-density wet snow conditions. Further, shear force and normal force components data may be useful for the designing of snow sheds in mountainous regions.

Keywords: dynamometer; shear force; normal force; dynamic coefficient of friction; snow chute

1 Introduction

Although it is obvious that several materials include rheological parameters, there is no material of wide engineering implication that under usual situations exhibits the perplexing complexities found in the snow [1]. The lack of sufficient experimental data for the Coulomb dynamic friction coefficient for the flowing snow μ _k has caused significant conjecture about the frictional behavior for snow avalanches, involving the true usage of constitutive relationships applied for simulating snow avalanches. Currently, most of the researchers and practitioners across the world are estimating the value of this snow dynamic friction coefficient μ _k through the back-analysis for the real avalanche sites or small-scale snow chutes by the application of various avalanche dynamics models, e.g., Schaerer [2], Martinelli et al. [3], McClung and Schaerer [4], Ancey and Meunier [5], Verma et al. [6], Kocyigit and Gurer [7], Naaim et al. [8], Ligneau et al. [9], and Sanz Ramos et al. [10]. However, these studies lack the objectivity and the physical basis in the selection of optimum μ _k values. It can be asserted here that a real understanding of the flowing avalanches will be possible only when all major parameters influencing avalanche dynamics models are equally validated with the measurements. Further, the knowledge of shear force and normal force components of a snow avalanche from which the dynamic coefficient of friction μ _k is evaluated is equally important for the design of snow sheds in the mountainous regions. These snow sheds play a vital role in protecting the people and vehicles from avalanche hazards. A limited number of studies have been done in the past to measure shear and normal force components of the avalanches which lead to the subsequent evaluation of the values of μ _k. To elaborate, Casassa et al. [11] obtained values of μ _k by sliding snow blocks over the natural avalanche slopes. They reported relatively much higher values of friction coefficient in the range of 0.57–0.84, for the snow density ρ _s varying from 60 to 340 kg m⁻³; temperature T of snow varying from −10.2 to −2.2°C, and a large spectrum of snow grains varying from new snow to artificially compacted snow. Gleason [12] estimated a coefficient of static friction in the range of 0.53–1.76, between the snow layers with the aid of a piece of roughened plastic with a known mass fixed on a 10 cm × 10 cm portion of plyboard. Temperature T of the snow varied from −8.0 to −0.5°C during the experiments. However, the author did not provide any information on the dynamic coefficient of friction of snow μ _k. Kern et al. [13] measured basal shear force and velocity profile on a 34 m long and 2.5 m wide chute. The authors measured the basal snow shear stress on the rubber mats with the piezo force gauges as ≈ 794 kPa. However, the authors did not provide any information for the μ _k values. From the experiments conducted on a 34-m-long Snow Chute, Tiefenbacher, and Kern [14] estimated effective μ _k for wet snow of mean density ρ _s ≈ 400 kg m⁻³ on a rubber matted surface as 0.72 from the measured shear force and calculated normal force values. This value is considerably higher due to taking into account the internal friction processes within the snow. Further, the authors presented the analysis in their research based on scant measurements. Platzer et al. [15] measured shear force, normal force, and coefficient of dynamic friction μ _k for wet, dry, and slush snow flows based on 42 experiments. The authors used force plates of size 0.68 m × 0.68 m, covered with roughened aluminum sheets in their experiments. They used wet snow of density varying from 380 to 597 kg m⁻³; dry snow density varying from 211 to 364 kg m⁻³; and slush density varying from 556 to 700 kg m⁻³. They did most of the measurements on wet snow and obtained μ _k values in the range of 0.330.53. Further, they observed that dry snow avalanches have lower μ _k values than wet avalanches and slush flows. The authors found that the measured coefficients of friction are much higher than the Swiss guideline’s suggestions which needs further investigation. Platzer et al. [16] estimated values of μ _k varying from 0.22 to 0.55 between the dry snow and the rubber mat surface. The authors found the basal shear to be the main frictional behavior responsible for slowing down the avalanche flows. As an important deduction from their studies, they did not find the velocity dependency for μ _k values in contrast to several other proposed constitutive models for the basal friction related to snow avalanches. A few research studies have also been done in the past for the estimation of μ _k between the snow and the ski sliders made of plastic, aluminum, and steel surfaces [17,18]. In a recent study, Dong et al. [19] carried out a series of experiments to estimate the shear force, normal force, and dynamic friction coefficient for rock-ice avalanches. The authors found ice content and melt water as the most significant parameters affecting the values of the dynamic friction coefficient. However, due to large variations in the operating conditions, these studies cannot be fully applied in the simulation of avalanche flows. So, it can be summarized here that the limited research studies carried out in the past for the estimation of the dynamic friction coefficient of snow μ _k are not comprehensive in nature and cannot be used in the simulation of all types of avalanche flows under wide varying conditions of snow temperature, density, surface type, and the avalanche speeds. The present experimental study was undertaken, for the generation of a new experimental database for the shear force and normal force components of an avalanche and the dynamic coefficient of friction of snow μ _k between the steel surface and snow, for the high-density wet snow on a 61-m-long snow chute located in the Pir Panjal Himalayan range of India. The main motivation behind these experiments was to apply the measured μ _k values in the validation of an avalanche dynamics model which is under development [20]. With the availability of experimental μ _k values, uncertainty in the model simulations is expected to be reduced. Even though the present data does not encompass the entire domain of full-scale flows, 32 experimental runs included in the current work offer further understanding of the frictional mechanisms at basal shear layers of the snow avalanches. It is expected that the present force and friction coefficient database for high-density wet snow avalanches can be applied in any snow-bound area of the world for the refinement in avalanche dynamics studies and snow shed designs.

2 Methodology

Figure 1 illustrates the flowchart followed for the measurement of the dynamic friction coefficient of snow μ _k. The detailed methodology is given in the following subsections:

Figure 1

Flowchart showing the main steps followed in executing the experiments for the measurement of dynamic coefficient of friction of snow μ _k.

2.1 About the measurement system

The measuring system for the dynamic coefficient of friction of snow μ _k consists of a ‘Kistler’ make 9255B model dynamometer, a 20 m long charge cable, an eight-cable junction box, four-channel amplifiers, and data acquisition and display units (Figure 2). The dynamometer comprises four number piezoelectric force sensors which are three component types and mounted under heavy preload between two plates of size 260 mm × 260 mm. Each sensor comprises three pairs of quartz plates, one for sensing the force along z-direction, whereas the other two sensing force along x and y-directions. The input avalanche force can be split into three orthogonal components. Positive or negative charges are obtained at the connections based on the force direction. Positive charges produce negative voltages at the output of the charge amplifier and vice-versa. The dynamometer has a rigidity >2.0 kN µm⁻¹ and a significantly high natural frequency of ≈ 2.0 kHz. The measuring accuracy of the system is ±0.5%. The fine resolution of ±0.25% enabled the minimum dynamic changes in the force measurements. The dynamometer was calibrated in the factory premises of Kistler Instrumente AG, Switzerland. The dynamometer has a measuring sensitivity of −8.0 pc N⁻¹ for the net shear force of the flowing avalanche F _x (N) in the x-direction and F _y (N) in the y-direction. For net normal force F _z (N) in the z-direction, the dynamometer has a sensitivity of 3.7 pc N⁻¹. Further, the output signals of the dynamometer are sent to two, four-channel charge amplifiers which convert the dynamometer charge signals into output voltages proportional to the forces sustained. The proportionate voltages generated are acquired and displayed on two laptops in real time.

Figure 2

Measuring system for shear force (F _x) and normal force (F _z) components of an avalanche.

2.2 Installation of the measurement system

The dynamometer mentioned earlier was installed on a vibration-proof fixture, at a distance of 0.5 m from the end of the 30° slope and ground-flushed with the 12° sloped section of a 61-m-long and 2-m-wide avalanche dynamics experimental facility, i.e., snow chute located at Dhundhi field research station, 20 km away from Manali, Himachal Pradesh, India. Dhundhi lies in the Pir Panjal Himalayan range of India. The 61 m length of the snow chute was designed keeping in view the sufficient fluidization of the released snow mass, attainment of significant avalanche velocities, dynamic similarity between the snow chute avalanches, and the real-scale avalanches. Further, the availability of a natural mountain slope of about 65 m length near the shelters also contributed to fixing this particular length of the snow chute. Elaborating further, the snow chute consists of a 5.5 m long snow hopper inclined at a 35° slope. This is similar to the formation zone of a natural avalanche. Then, there is a 13.5-m-long trapezoidal diverging–converging section (2 m × 4 m tapered) inclined at a 35° slope. This is meant for ensuring the fluidization of the released snow mass and acts like an extended portion of the formation zone of an avalanche. After this, there is a 22-m-long channel inclined at 30°. This is similar to the track zone of an avalanche. After this, there is an 8-m-long channel inclined at 12°. This channel is similar to the run-out zone of an avalanche. Lastly, there is a 12-m long test bed inclined at −1.8° reverse slope. This portion acts like an extended portion of the run-out zone of a natural avalanche. So, snow chute dimensions align with the natural avalanche slopes. Further, a 12° sloped section was selected for installing the dynamometer as practically, snow sheds are generally constructed at the conjunction of the end of the avalanche track zone and the roads or low sloped zone of the avalanche path.

In order that no side vibrations are transmitted to the dynamometer through the body of the snow chute, a uniform gap of 10 mm was provided all around the dynamometer which was afterward filled with a soft rubber gasket to prevent the ingress of snow. Figure 3(a) depicts a view of the snow chute at Dhundhi indicating the location of the snow friction coefficient μ _k measurement system. Figure 3(b) and (c) illustrate the details of the μ _k measurement system.

Figure 3

(a) A view of the snow chute at Dhundhi, Himachal Pradesh, India; (b) a close view of the dynamometer installed on 12^° slope of the snow chute; (c) a view of the data acquisition and display details of the snow dynamic coefficient of friction μ _k measurement system.

It is a well-known fact that the occurrence of snow avalanches happens to be gravity-based. The law of dynamic similitude necessitates the Froude number F _r = v _s/(gh)^1/2 of the avalanche flow to be the same while transforming at laboratory size. The F _r revealed, by the snow chute flow lies within ≈ 8–10, that nearly conforms with the F _r values revealed by the real-scale avalanches, thereby ensuring dynamic similarity between the experimental trials and the real avalanches [21]. Here, v _s (m s⁻¹) represents snow velocity, g (m s⁻²) is the acceleration due to gravity, and h (m) denotes flow depth of the avalanche. In the present experiments, v _s was estimated as ≈ 14–17 m s⁻¹ and h ≈ 0.35–0.42 m, from the videos of the snow chute flow.

2.3 Measurement/computation procedure

The acquired peak voltages from the dynamometer were converted into the equivalent force components by multiplying the voltage values with the respective force conversion factors. Each amplifier gives maximum output of 10 V corresponding to the maximum force. Keeping the expected force range in mind during the snow chute experiments, for acquiring force component values in the x-direction, 10 V was set to maximum force of 2 kN, i.e., 1 V = 200 N. Similarly, for acquiring force values in the z-direction, 1 V was set equal to 400 N. After getting the individual force components, the net forces were computed as elaborated below:

The net shear force of the flowing avalanche F _x (N) in the x-direction, i.e., along the avalanche flow direction, is computed as:

(1) F x = F x 12 + F x 34 ,

where F _x12 and F _x34 are the measured force components in the x-direction. The net shear force F _y in the lateral direction is not reported here as the snow chute flow is confined from the lateral sides.

The net normal avalanche force F _z(N) is computed as the summation of force components in the z-direction, i.e., perpendicular to the plane of avalanche flow as given below:

(2) F z = F z 1 + F z 2 + F z 3 + F z 4 ,

where F _z1, F _z2, F _z3, and F _z4 are the measured force components in the z-direction.

Figure 4(a) and (b) illustrates the sample graphs acquired on the display screens for the voltage values corresponding to force components in the x, y, and z-directions. From these graphs, voltage values were obtained and converted into their equivalent force components, from which net force values were computed. In order to test the accuracy of the dynamometer, a person with known weight stood on its top surface and the corresponding F _z force computed from the acquired data. Agreement between both the two readings ensured that the dynamometer was properly calibrated. Dynamic coefficient of friction μ _k for the chute-steel surface was estimated from the following equation:

(3) μ k = F x F z .

Figure 4

Display of voltage values on the computer screens during an experiment at snow chute, Dhundhi, H.P., India corresponding to (a) shear force F _x, F _y components and (b) normal force F _z components.

3 Results and discussion

For carrying out the experiments, snow was filled inside the hopper of the snow chute to its maximum capacity of 11 m³ by shoveling from the neighboring unobstructed regions. Further, uniformity of the snow samples cut was ensured in the experiments. However, minor compaction of the snow occurred in the hopper during the shoveling of the snow. In case of all the experiments performed in the current work, average density of snow ρ _s for the snow occupied inside the hopper was taken. For measuring ρ _s, a 100 cm³ snow cylindrical sampler was gently pushed horizontally within the snowpack, excess snow was removed with a snow cutting plate, and then snow from the sampler was emptied on the surface of the electronic weighing machine by gently tapping on it. The weight of the snow measured in grams divided by the sample volume gave the snow density ρ _s. Before using this electronic machine for snow, it was tested for measuring the density of water. Since water density was measured with ±5.0% uncertainty, it can be confidently stated that present density measurements for snow are also with ±5.0% uncertainty. For obtaining force measurements, μ _k measurement system was switched on, reset, and run a few seconds before the release of snow from the hopper during each experiment. The moment avalanche hit the dynamometer, as explained in the previous paragraphs, F _x, F _y, and F _z force component graphs (in the form of voltage signals) were captured on the computer screens, saved, and afterwards, peak values of the force components at a particular instant extracted from these graphs. The main source of error is not resetting the data acquisition software, before the start of each experiment. Resetting ensures that no residual charge is left on the load cells. If this is not done, sometimes absurd values of the force are recorded, which have to be removed from the present database. The complete summary of the experiments conducted during the period 2017 to 2020 at Snow Chute, Dhundhi is given in Table 1. For clarity, it is mentioned here that the order of present shear force F _x and normal force F _z values is the same as that of Platzer et al. [15]. However, the range of variation of F _x values in the current experimental work is lesser as compared to that of Platzer et al. [15]. On the other side, the range of variation of the current normal force F _z values is more as compared to that of Platzer et al. [15]. Most probably, the reason for this deviation may be that Platzer et al. [15] used rubber mats on the chute surface in their experiments while in the present work, a steel surface has been used on the chute. Based on the experimental force data shown in Table 1, the average value of μ _k is estimated as 0.113. This database can be significant for improving and calibrating the avalanche dynamics models specifically for high-density wet snow conditions. Further, based on these measurements, the variation of shear force F _x and normal force F _z with snow density ρ _s is shown in Figure 5(a) and (b). Figure 5(a) shows the variation of shear force F _xwith the density of snow ρ _s. It can be noted that initially, there is an increase in the values of F _x with the increase in ρ _s but after attaining the value of ρ _s ≈ 500.0 kg m⁻³, there is a decrease in the value of F _xwith a further increase in the value of ρ _s. This is probably due to the fact that with the increase in the ρ _s values, snow grains coalesce together to form a smoother surface, and thus, shear friction decreases. This indirectly also implies that very high-density (>500 kg m⁻³) snow avalanches may cover much larger run-out distances as compared to low-density snow avalanches. However, as expected, the normal force F _z values increase with ρ _s values due to the increase of the vertical load on the load cells (Figure 5(b)). For the same reasons, the value of the snow dynamic coefficient of friction μ _kdecreases with the increase in the values of ρ _s with a coefficient of determination R ² ≈ 0.97 (Figure 6). However, based on back-analysis for a large number of avalanche events, Naaim et al. [8] found an increase in the values of the static snow friction coefficient up to a snow density ρ _s of 200 kg m⁻³. For values of ρ _s > 200 kg m⁻³, the authors did not observe any trend. However, the present database has got ρ _s values > 200 kg m⁻³. Current results are in good agreement with Mellor [1] who presented the value of μ _k for the steel and snow surface in the range of ≈ 0.12–0.32 under widely varying conditions of temperature T. Authors also noted that with the increase in temperature T of snow, there is a decrease in the values of μ _k and vice-versa. Contrary to this result, Platzer et al. [15] found values of μ _k for wet snow avalanches higher than the dry snow avalanches. Naaim et al. [8] also noticed an increase in the values of the snow friction coefficient with the increase in temperature T of snow. However, these authors found a decrease in the values of the friction coefficient with the increase in liquid water content. From these conflicting observations, it seems that the liquid water content seems to be playing the key role in increasing or decreasing the values of μ _k. Colbeck [17] postulated that three friction mechanisms: dry, lubricated, and capillary dominate between the snow and the ski slider at different water film thicknesses. The snow dynamic friction is high when the thickness of the water film is insufficient to prevent ploughing by solid-to-solid contacts. As the water film thickens and solid-to-solid interactions become less frequent, the slider has to overcome only the viscous resistance of the water film between the supporting snow grains and the slider and so the friction decreases. With a further increase in water film thickness, the capillary attraction between the snow grains and the slider increases and causes an increase in friction. Probably due to this reason, friction is high in the case of very wet snow. With further investigation, it is found that the present measured dynamic friction μ _k values are much lower than those obtained by Platzer et al. [15,16]. As pointed out earlier, the main reason for this seems to be the rubber mats that the authors used at the chute surface in their experiments. Present results are also in agreement with Verma et al. [6] who estimated a value of μ _k in the range ≈ 0.10–0.22 for wet snow of density in the range of 250–450 kg m⁻³, through the calibration of an avalanche dynamics model with the experimental values of avalanche velocity and run-out distance at snow chute, Dhundhi, India. However, the present research could not include the effect of avalanche speed on the value of μ _k in the experiments. Platzer et al. [16] also did not find any dependence of μ _k values on the avalanche speeds but Schaerer [2] found that μ _k varies inversely with the speed of the avalanche. Contrary to this observation, McClung and Schaerer [4] found that μ _k increases with the speed of the avalanche. Ancey and Meunier [5] found the dependence of μ _k on the avalanche speed in a complex manner. So, due to large variability in the observations, this aspect also needs further investigation.

Table 1

Summary of the measurements for shear force F _x and normal force F _z components of an avalanche during the period 2017–2020 at Snow Chute, Dhundhi, Himachal Pradesh, India

Date of experiment	Snow density, ρ _s(kg m⁻³)	Snow type^a	Temperature of snow T (°C)	Net shear force along the avalanche flow direction, F _x (N)	Net normal force perpendicular to the avalanche, flow, F _z (N)	Dynamic coefficient of friction between snow-steel interface (μ _k)
February 10, 2017	280	RG	−1.2	59.09	376.90	0.157
February 11, 2017	290	RG	−1.1	64.75	415.17	0.156
February 27, 2017	393	RG	−0.8	105.02	758.12	0.139
February 27, 2017	313	RG	−0.7	76.59	499.86	0.153
February 28, 2017	297	RG	0.5	68.53	441.44	0.155
February 28, 2017	373	RG	−1.3	84.29	559.46	0.151
February 29, 2017	330	RG	−0.7	99.77	698.85	0.143
March 4, 2018	467	MF	0.0	113.67	946.78	0.120
March 4, 2018	588	MF	0.0	91.30	1151.27	0.079
March 5, 2018	602	MF	0.0	85.78	1166.60	0.074
March 5, 2018	591	MF	−0.7	84.10	1170.66	0.072
March 6, 2018	606	MF	−0.5	69.86	1196.64	0.058
March 6, 2018	636	MF	−0.5	90.17	1154.70	0.078
March 6, 2018	622	MF	−0.3	76.85	1185.50	0.065
March 7, 2018	517	MF	−0.5	109.92	1046.93	0.105
March 7, 2018	458	MF	−0.4	113.53	926.42	0.123
March 9, 2018	457	MF	−0.5	114.60	924.11	0.124
March 11, 2018	571	MF	−0.5	97.18	1130.34	0.086
March 15, 2018	320	RG	−0.8	79.87	524.71	0.152
March 16, 2018	533	MF	−0.5	107.09	1074.32	0.100
March 17, 2018	493	MF	−0.5	112.69	1001.61	0.113
March 18, 2018	600	MF	0.0	77.80	1183.77	0.066
March 19, 2018	620	MF	0.0	86.61	1164.52	0.074
February 14, 2019	417	RG	−0.4	109.68	824.60	0.133
February 15, 2019	383	RG	−0.5	102.55	728.93	0.141
February 15, 2019	457	RG	−0.5	113.50	924.11	0.123
February 16, 2019	390	RG	−0.8	104.31	749.46	0.139
February 17, 2019	407	RG	−0.5	107.96	797.52	0.135
February 18, 2019	508	MF	−0.5	111.17	1030.53	0.108
March 5, 2020	510	MF	−0.4	105.60	1085.60	0.097
March 6, 2020	540	MF	−0.5	112.27	1034.24	0.109
March 7, 2020	596	MF	0.0	88.22	1160.24	0.076
Average value of μ _k						0.113
Standard deviation for μ _k						0.032
Maximum value of μ _k						0.157
Minimum value of μ _k						0.058

Note: ^aFierz et al. 2009.The international classification for seasonal snow on the ground.

Figure 5

Variation of (a) shear force F _x(N) with snow density ρ _s (kg m⁻³), (b) normal force F _z (N) with snow density ρ _s (kg m⁻³).

Figure 6

Variation of dynamic coefficient of friction of snow μ _k with its density ρ _s (kg m⁻³).

4 Conclusion

In the current work, a limited set of experiments has been carried out for the measurement of shear force and normal force components of high-density wet snow avalanches on a small-scale. Based on these measured values, the average value of the dynamic coefficient of friction of snow μ _k has been estimated as 0.113 with a standard deviation of 0.032. Due to the dynamic similarity between the snow chute flow and the real avalanches, the measured force values and the estimated friction values can be extended for validating, calibrating the avalanche dynamics models, and improving the design accuracy of the avalanche control structures like snow sheds, etc., for the different mountain terrains. Practically, the present friction database has been successfully used in validating one avalanche dynamics model. However, the present work has certain limitations. There is a need to make the present friction measurement system more user-friendly by providing real-time storage of the experiments data on the computers. Further, in the present work, a dynamic friction coefficient for high-density wet snow has been obtained between the steel-snow interface. These data base may have limited applications in validating the avalanche dynamics models in the avalanche velocity range of ≈ 14–17 m s⁻¹. More experiments can be done in the near future to obtain a wider database for the snow dynamic friction coefficient by fixing surfaces of different materials on the bed of the snow chute. Further, in the present research, quantification of liquid water content was not done. So, in future experiments, there is a need to quantify the liquid content within the snow for getting better insight into the complex variation of μ _k. Further, the effect of variable avalanche speeds on the values of the dynamic coefficient of friction of snow needs to be extensively studied in the near future. In spite of all these limitations, the present work has vital importance for the snow-bound regions as carrying out experiments on the real avalanche sites for the measurement of friction and other parameters is quite hazardous and challenging.

Acknowledgements

The authors are grateful to the Director, Defence Geoinformatics Research Establishment (DGRE) for his generous support and inspiration in executing this work. Technical support of Sh. Ashwani Kumar, TO-C in carrying out the field experiments is duly acknowledged here. Special thanks are due to Sh. Hem Raj Sharma, TO-C for his technical support in troubleshooting the friction measurement system during the field experiments.

Funding information: This work was supported by DGRE (DRDO), Chandigarh, India.
Author contributions: RKA led the installation of snow dynamic coefficient of friction measurement on the snow chute at Dhundhi (H.P.), India. He also designed and executed the experiments. Further, RKA prepared the manuscript with contributions from RD and HSG. The authors applied the SDC approach for the sequence of authors.
Conflict of interest: The authors declare no conflict of interest.

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Received: 2023-11-19

Revised: 2024-04-07

Accepted: 2024-04-13

Published Online: 2024-05-31

This work is licensed under the Creative Commons Attribution 4.0 International License.

Artikel in diesem Heft

https://doi.org/10.1515/geo-2022-0639

Schlagwörter für diesen Artikel

dynamometer; shear force; normal force; dynamic coefficient of friction; snow chute

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