ADAPTING AND CALIBRATING THE DAN3D DYNAMIC MODEL FOR NORTH AMERICAN SNOW AVALANCHE RUNOUT MODELLING

Jordan Aaron1, Michael Conlan2, Katherine Johnston2, Dave Gauthier2*, Scott McDougall1

1Department of Earth, Ocean and Atmospheric Sciences, The University of British Columbia, Vancouver, BC, Canada

2BGC Engineering, Vancouver, BC, Canada

ABSTRACT: Numerical dynamic snow avalanche simulations are now a key component in snow avalanche hazard and risk assessment, land use planning, and mitigation design. Advances in computer hardware have allowed for the development of three-dimensional simulations, in place of the traditional two or even one-dimensional models. The Swiss RAMMS model has emerged as the most widely used of these newer 3D approaches, and has the added advantage of applications to other geohazards such as rockfall and debris flow. Another model that was developed specifically for geohazards is Dan3D, originally developed for extremely rapid, flow-like landslides. In this paper we test the adaptation of Dan3D to the snow avalanche phenomena. We present three case studies and discuss the prospects and next steps toward validating and calibrating Dan3D for North American snowpack and terrain conditions, and consider applications to avalanche risk problems that are unique to this part of the world.

KEYWORDS: dynamic model, avalanche runout, three dimensions, deposit volume

1. INTRODUCTION

Avalanche dynamic models are an important component of avalanche hazard and risk assessments. One-dimensional models such as the PLK model (Perla et al. 1984), PCM model (Perla et al. 1982) and the Leading Edge Model (LEM) (McClung and Mears 1995) are often used in Canada and elsewhere. These models are simple to use but only analyse flowing avalanches down a path chosen by the user, which is often difficult to define in complex terrain (Jamieson et al., 2008). Such models also do not analyze more complex or realistic processes such as entrainment. For this reason, higher-dimensional models have recently been created to simulate avalanches, such as RAMMS (Christen et al., 2010).

This paper introduces the Dan3D model, a dynamic model that simulates avalanche motion over three-dimensional terrain. The model has been used in practical applications to forecast the motion of extremely rapid, flow-like landslides (e.g. Nicol et al., 2013); to date, the applicability of this model to snow avalanches has not yet been explored. The main obstacle to using Dan3D in this context is that its input parameters have not been calibrated for snow avalanches. Borstad

(2005) applied the two dimensional DanW model to snow avalanches. Borstad (2005) assumed that basal resistance is governed by the frictional rheology, and the simulation was run starting from the point of maximum velocity in the path- usually somewhere in the middle of the avalanche track. Reasonable results were obtained using this approach. As discussed below, in the present work we use the Voellmy rheology and simulate the avalanche from initial failure to deposition.

In this paper we back-analyse three snow avalanche case studies from western Canada. These cases demonstrate the applicability of Dan3D to model snow avalanches and provide a starting point for developing a database of calibrated cases. Once calibrated, Dan3D could be a useful tool for avalanche hazard and risk assessments, as it will be able to provide estimates of impact area, flow velocities and impact pressures.

2. DAN3D OVERVIEW

Dan3D is a fluid mechanics-based model originally developed to simulate the motion of extremely rapid, flow-like landslides (Hungr & McDougall, 2009). Dan3D can simulate anisotropic internal stress states, as well as entrainment of path material. The numerical method used to solve the governing equations is smoothed particle hydrodynamics, a technique that allows for the simulation of large displacements and bifurcations of the flow.

* Corresponding author address: Dave Gauthier, BGC Engineering, 600-372 Bay St, Toronto, ON; tel: 613-893-4920; fax: 416-649-0335; email: DGauthier@bgcengineering.ca

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A 2D slice showing the forces acting on each computational element is shown in Figure 1. Dan3D calculates landslide accelerations based on the gravitational force driving motion down the slope. The downslope component of the gravitational force is opposed by the basal resistance force. Internal pressure gradients caused by the inclination of the top surface and momentum expended entraining path material are accounted for in the model.

Figure 1: Forces acting on a slice of material in Dan3D. W is the weight, T is the basal resistance, P is the internal force and E is the inertial resistance due to entrainment.

The parameters that govern a Dan3D simulation can only be estimated based on previous successful calibrations of the model. The parameters that control the simulations are those that govern the basal rheology (used to calculate the T force in Figure 1). For all the cases presented here, the Voellmy rheology (Voellmy, 1955) is used to calculate the magnitude of this force, which is similar to the approach employed by RAMMS. The equation for this rheology is shown below.

𝑇 = (−𝜎𝑧 𝑓 + 𝜌𝑔𝑣2

𝜉)

(1)

where 𝜎𝑧 is the bed normal total stress, 𝜌 is the

density, 𝑔 is the gravitational constant, 𝑣 is the

avalanche velocity, 𝑓 is the friction coefficient and 𝜉 is the turbulence coefficient. The friction and turbulence coefficient are calibrated parameters.

The Voellmy rheology is a two-parameter rheology, with a frictional term and velocity-dependent term. It has been used in dynamic models of snow avalanches (e.g Voellmy, 1955; Christen et al., 2010). To use Dan3D, the user inputs a digital elevation model representing the

surface that the avalanche moves over (referred to here as the ‘path topography’) as well as the thickness and geometry of the release area (referred to here as the ‘slab’). Then, the friction and turbulence coefficients are input and the simulation is run. When calibrating Dan3D, these basal resistance parameters are systematically varied, either through trial and error or by an automated algorithm (Aaron et al., 2016), until the simulation results match field observations of impact area and deposit distribution.

3. MODEL RESULTS

In the present work, three downed avalanches are back-analyzed. These cases were selected because post-failure investigations resulted in reasonable estimates of slab volumes, flow areas, and deposit volumes. These estimates were obtained using photographs taken directly post-avalanche and from discussion with personnel that were present during their release or subsequent investigation. The calibrated basal resistance parameters for each of the case histories are summarized in Table 1, and important details of the individual analyses are presented in the following sections.

The avalanche path topography for all cases were obtained from the Geogratis database, which contains 1:50,000 scale digital elevation model (DEM) data for all of Canada. We believe that the use of this coarse elevation data is justified because the snowpack smooths topographic details, although the low resolution topography may result in the loss of some important features, such as roads.

3.1 Case 1: Grizzly

In March of 2012, a large natural avalanche occurred on the Grizzly Slide path in the Columbia Mountains near Rogers Pass. The avalanche overran the Trans-Canada Highway and deposited debris about 80 m wide and 1.5 m in average thickness. The avalanche runout zone as observed from the highway is presented in Figure 2. Due to poor visibility, there was substantial uncertainty associated with the slab geometry for this event. To account for this, a sensitivity analysis was performed to explore the effects of different slab geometries. In this sensitivity analysis only the slab area was varied. The simulation that best matched field observations is shown in Figure 3.

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Table 1: Volume and calibrated basal resistance parameters for the four analysed case histories.

Case Volume (m3) Friction Coefficient

Turbulence Coefficient (m/s2)

Mt Robson 320,000 0.22 1750

Grizzly 370,000 0.28 1000

Ross Peak 82,000 0.15 4000

South Rockies 28,000 0.29 1000

The runout distance was reproduced, however the avalanche simulated in DAN3D spread wider than was observed. The average thickness on the road is overestimated, likely due to uncertainties in the failed volume, as well as the fact that Dan3D currently neglects the densification of the avalanche deposit.

Figure 2: The 2012 Grizzly runout zone as observed from the Trans-Canada Highway.

Figure 3: Grizzly simulation results overlain on Google Earth. The red line shows the observed impact area, the grey outline shows the simulated impact area and the contours show final deposit depths. Background image data: Google Earth

3.2 Case 2: Ross Peak

Ross Peak is located in the Columbia Mountains approximately 10 km southwest of Rogers Pass. A large event occurred on this path on January 9, 2007. It was a Size 4 natural avalanche. The flow path of this avalanche was complex, due to the presence of a ridge parallel to the flow direction in the avalanche track. There was evidence of the avalanche running up and around this ridge (Figure 4). Both the slab and debris were dry. Photos taken in the days following the release of this avalanche provided realistic constraints on the geometry and thickness of the slab, flow path, and deposit volume. For this case a slab thickness of 1.6 m was used based on photographs of the source area taken immediately following the failure.

Figure 4: The Ross Peak avalanche track and runout zone, as viewed from a helicopter (Parks Canada Photo).

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The complex flow of the avalanche was well reproduced using Dan3D, as was the run-up on the ridge (Figure 5). Run-up features provide field constraints of the velocity of the flowing mass at a certain point and their reproduction by the model indicates that the simulated flow velocities match the field conditions. The runout distance of the deposit is slightly underestimated, likely due to inaccuracies in the path topography.

Figure 5: Calibrated Dan3D results for Ross Peak overlain on Google Earth. The thick red line shows the observed impact area, the grey area shows the simulated impact area and the contours show final deposit depths. The slab volume used in the simulation was 82*103 m3. Background image data: Google Earth

3.3 Case 3: South Rockies

This case study examines an avalanche that occurred in the winter of 2012 in the southern portion of the Rocky Mountains of western Canada. It was a size 3 natural avalanche. This avalanche travelled around a bend in the path and left a relatively long, thin deposit in the track and runout zone (Figure 6). The average thickness of this deposit was approximately 0.5 m. Based on post-event photographs the slab was assessed to have an average thickness of 1.7 m and a total volume of 28,000 m3. Dan3D simulated the avalanche flow and deposit distribution well, including the thin deposit that stretches towards the release area (Figure 7).

Figure 6: The South Rockies avalanche as observed from the runout zone.

Figure 7: South Rockies simulation results overlain on Google Earth. The red outline shows the observed impact area, and the grey outline shows the simulated impact area. Background image data: Google Earth.

4. DISCUSSION

When calibrated, Dan3D can reproduce the bulk characteristics of the three case studies that have been back-analyzed. As demonstrated by the Ross Peak and South Rockies cases, the model can capture complex, three dimensional features of the flow such as bifurcations and run-up. The Ross Peak case demonstrates the sensitivity of the Dan3D results to the input topography of the avalanche path. Careful consideration should be given to how the snowpack smooths topographic features. The Grizzly case shows that deposit depths may be overestimated due to the neglect of the densification of the avalanche deposit.

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A-priori estimation of the parameters controlling the basal rheology is the biggest impediment to the routine use of Dan3D to simulate snow avalanches. These parameters vary substantially for the three cases analyzed. The Ross Peak and Grizzly case histories are located within 10 km of each other, but appear to have experienced very different resistance to movement. It is therefore unlikely that a single set of basal resistance parameters will be found that can adequately simulate all avalanches within a given area. Instead, the ultimate goal should be the creation of a database of calibrated cases, which captures the variability of basal resistance parameters. This database can then be used to run forward analyses in a probabilistic context.

5. CONCLUSIONS

The applicability of Dan3D to model snow avalanches has been explored through the back analysis of three case histories. The key findings of this work are:

Dan3D can reproduce the bulk characteristics of all the cases analysed

Simulation results are somewhat sensitive to the input path topography. Careful consideration is needed to properly represent how the snowpack can modify the topography that the avalanche moves over

Back-analysed parameters can vary substantially, so the use of Dan3D for practical projects requires local calibration and expert judgement

Work is ongoing to address and explore some of the issues noted above. Model results obtained using path topography derived from LiDAR will be compared to the results presented in this paper in order to better understand the influence of the input topography data. Additionally, we are investigating methods to include the densification of the avalanche deposit in Dan3D. Finally, future work will focus on analyzing more case histories to build a database of calibrated parameters, and linking these parameters to snowpack conditions. In its present state Dan3D can be used in practical applications, however site-specific calibration will be necessary. Expert judgement is needed to verify that simulation results are reasonable and Dan3D should be used in concert with other statistical and dynamic models, such as the one dimensional models mentioned above. If used in this way, Dan3D can be a useful tool to aid

experienced professionals in snow avalanche hazard and risk analyses.

ACKNOWLEDGEMENTS

We thank the Avalanche Control Service of Parks Canada at Rogers Pass, B.C. for providing data for the case studies. Funding for this work was provided in part by a graduate scholarship given by The Natural Sciences and Engineering Research Council of Canada, and scholarships given by the Department of Earth, Ocean and Atmospheric Sciences at The University of British Columbia.

REFERENCES

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Borstad, C., 2005: Dynamic modelling of extreme speed profiles of dry flowing avalanches. Masters of Applied Science Thesis, Department of Civil Engineering, The University of British Columbia, Vancouver, Canada.

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Hungr, O., and McDougall, S. 2009: Two numerical models for landslide dynamic analysis. Computers & Geosciences, 35(5) 978–992. doi:10.1016/j.cageo.2007.12.003

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Voellmy, A., 1955: Über die Zerstörunskraft von Lawinen (On breaking force of avalanches). Schweizerische Bauzeitung, 73, 212–285 (in German).

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