Simulating two-phase debris flows in HEC-RAS at Hummingbird

. Debris flows are typically modelled as a single homogeneous surge due to lack of data to support more complex model development and due to lack of time and funding for the practitioner and the communities they aim to support. Coarse debris flows are typically characterized by a coarse front, followed by a muddy slurry, that is then followed by a hyperconcentrated flow phase with lesser sediment concentrations. Presented herein is the modelling for a debris flow hazard assessment for Hummingbird Creek, British Columbia, Canada. Model calibration best matched the observed debris flow deposit when the coarse front and hyperconcentrated flow were modelled separately in two phases allowing for separate flow rheologies to be used for the front and the tail of the debris flow, and allowing for deposition between phases. Further research is needed to understand when simulation of two-phase flow may be most representative, particularly when no calibration data is available.


Introduction
Debris flows are a complex mixture of water, sediment, and often large woody debris, trucks, parts of buildings. Their behaviour is governed by both fluid and solid mechanics [1] which are ideally modelled using multiphase flow models. However, those require detailed inputs that are rarely available making them impractical to many practitioners [2,3]. Equivalent fluid models where the behaviour of the material is assumed to be relatively homogeneous and can be represented by a single rheology is used instead. Previous work has demonstrated that, once a model is calibrated, getting the volume right is more important than any individual rheological parameter or modelling software [4].
Coarse debris flows typically occur as one or more surges where each surge is characterized by a coarse front that drives the peak discharge, followed by a muddy slurry, that is then followed by a hyperconcentrated flow phase with lesser sediment concentration [5]. A debris flow surge is hence neither spatially nor temporally classified as a homogeneous fluid. Does this matter for a debris flow hazard assessment?
A debris-flow hazard assessment looks to answer two main questions: (1) How frequent are debris flow events and how large can they be? (i.e., the frequency-magnitude relationship) and (2) what is the intensity and extents of each modelled debris-flow scenario? [6]. The modelling component attempts to answer the second question, as the impact intensity and runout extents can be used to estimate building damage in hazard assessments [7].
Presented herein is a case study of the modelling work completed for a debris flow hazard assessment at Hummingbird Creek located on Mara Lake in British

Precedence
Field measurements taken at the Illgraben debris flow catchment in Switzerland [8] and at Gardia Creek in Italy [9] demonstrate that the fluid density and fluid behavior of a debris flow is highly variable within a single surge with the front of the surge exhibiting the greatest shear stresses. Previous modelling studies have demonstrated that events occur that cannot be replicated by modelling a single homogeneous surge. One such example is Neff Creek located in the Birken-D'Arcy valley approximately 140 km north-northwest of Vancouver, BC, Canada. The Neff Creek watershed is considered a transport limited (supply-unlimited) watershed with abundant sediment sources in as talus slopes. In significant rainfall or runoff events, the talus can be mobilized. Neff Creek experienced a debris flow event in 2015 that was characterized by multiple surges causing intense erosion in the proximal and medial zones of the fan [10]. In the modelling of Neff Creek, a Monte Carlo method was used to randomly divide the event volume into four stages and randomly select an input hydrograph for each of these stages [2]. Deposition was allowed to occur between each stage. It was found that simulations that considered deposition during an event resulted in greater lateral spreading, shorter overall runout distances, and thicker flow depths and deposits in key areas. For Neff Creek, the results matched the observed event more closely when variable inflow was coupled with deposition between surges [2].

Case Study: Hummingbird Creek
On July 11, 1997, a large debris flow occurred at Hummingbird Creek damaging roads and buildings in the community of Swansea Point (the fan-delta of Hummingbird Creek and Mara Creek). Approximately 92,000 m 3 was deposited on the fan-delta during this event and it had an estimated peak discharge of 1000 m 3 /s [11]. The distribution of deposits following the event is shown in Figure 1 below and was used in model calibration. Note the zone of thicker deposits near the fan apex. The event occurred following long-term high antecedent precipitation and was initiated from a 25,000 m 3 debris avalanche 2.4 km upstream of the fan apex. Channel entrainment rates were estimated at 28 m 3 /m [11].

Fig. 1. Distribution of debris deposits on the Hummingbird
Creek fan-delta in July of 1997 [9] The modelling software used was the 2D mud and debris flow module of HEC-RAS (Hydrologic Engineering Center-River Analysis System) version 6.1 developed by the United States Army Corps of Engineers (USACE). The non-newtonian flow rheology used was the Bingham rheology with flow resistance described by dynamic viscosity and yield strength. Initially the model was run using a single rheology, but the model results could not replicate the region of thicker deposits near the fan apex (grey in Figure 1) and match the inundation and deposition extents (hatched in Figure 1).
Given the two distinct deposits seen in Figure 1, it was hypothesized that the surge may best be represented by two rheologies: a coarse frictional front and a muddy afterflow. From Figure 1 and a back-analysis of the event by Jakob et al. [11], it was estimated that approximately 50% of the deposit volume was associated with the coarse front and the other 50% with the muddy tail. The peak discharge of 1000 m 3 /s was associated with the coarse front as previous work has shown the coarse front to have the greatest depth and therefore the greatest discharge [1,5]. The peak discharge of the muddy afterflow was estimated using a linear regression relationship between peak discharge, Q and sediment volume, V for muddy debris flows [12].
The flow hydrographs were approximated by a triangular hydrograph where the time to peak is 20% of the total flow duration [2,12]. The sediment concentration was assumed to be 50% by volume for both hydrographs and the flow duration was then calculated based on the sediment volume estimated to be carried by the coarse surge and muddy afterflow (50% of the 92,000 m 3 each). The coarse front was modelled first, and the terrain modified to absorb the coarse front deposit. The muddy afterflow was then run over the terrain that included the deposition from the first simulated flow surge. The model was calibrated to match the depth contours and runout extents shown in Figure 1 (Figure 2 and Figure 3), as well as the velocities near the fan apex estimated by Jakob et al. [11]. The calibrated rheologies for each hydrograph are shown in Table 1. These were applied to model the events for the entire spectrum of the frequency-magnitude relationship for Hummingbird Creek, extract impact intensities, and develop a composite hazard map for the fan-delta and the community.

Discussion
Results suggest that there is merit in modelling material variability and deposition during a presumed multi-phase event through splitting the flow and sediment volume into more than one hydrograph. The rationale may be to represent multiple surges (e.g., Neff Creek), represent different parts of a single surge (e.g., Hummingbird Creek), or to allow a debris basin to fill followed by the remainder of the debris flow (no examples). At Neff Creek and Hummingbird Creek, calibration events were available to help guide the modelling and multiple hydrograph method. The challenge in moving forward is in how to decide on the number of hydrographs, sediment concentrations, and rheology in the absence of calibration events? Hummingbird Creek is a gentle-over-steep watershed meaning it is characterized by a gentle plateau in the upper watershed that drains into a steeper channel below. Debris flows are most likely to initiate as oblique debris avalanches into the channel. One could hypothesize that the plateau in the upper watershed has more water storage and could contribute to more dilute afterflow or subsequent surges. Mountain channels, such as Neff Creek, that exhibit distinct surges are hypothesized to have stretches of channel that act as depositional zones where sediment accumulates until it oversteepens at its front and releases as a surge [14,15]. This pulsing behaviour was found to be more likely when the deposit had a bimodal grain size distribution [15].
Factors that may influence the likelihood of surges or a distinct coarse and muddy afterflow deposit are hypothesized in the following list. More research is needed to see if this list can be simplified to be of use to the typical practitioner in debris flow hazard assessments: -Volume of rainfall/runoff available relative to sediment availability (e.g., gentle-over-steep watersheds versus small watershed with single incised channel) -Material type (e.g., coarse versus fine fraction, well-graded or poorly graded, uniform versus bimodal distribution) -Initiating mechanism (e.g., slow sediment accumulation in headwaters, or sudden landslide failure) -Entrainment (does it bulk through erosion and scour or debulk as it moves down the channel) -Variability in the hydrograph and in the channel gradient that may encourage local deposition Debris flows are highly variable and it is a relentless challenge to refine our attempts at representing this variability to better support the communities we live in and work for.