E3S Web of Conferences 415, 05006 (2023)
DFHM8

https://doi.org/10.1051/e3sconf/202341505006

Simulating two-phase debris flows in HEC-RAS at Hummingbird
Creek, British Columbia, Canada
Kathleen Horita1*
1BGC Engineering Inc., Vancouver, V6Z 0C8, Canada

Abstract. 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 thecommunities 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 sedimentconcentrations. 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 mostrepresentative, particularly when no calibration data is available.

1 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 solidmechanics [1] which are ideally modelled using multiphase flow models. However, those require detailed
inputs that are rarely available making them impracticalto many practitioners [2,3]. Equivalent fluid models
where the behaviour of the material is assumed to berelatively homogeneous and can be represented by asingle rheology is used instead. Previous work has
demonstrated that, once a model is calibrated, getting thevolume 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 temporallyclassified 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 eventsand how large can they be? (i.e., the frequency-magnituderelationship) and (2) what is the intensity and extents ofeach modelled debris-flow scenario? [6]. The modellingcomponent attempts to answer the second question, as theimpact intensity and runout extents can be used toestimate 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

Columbia (BC), Canada. We have used a doublehydrograph, with different rheological characteristics foreach surge, to test whether this method produces a better
calibration more akin to observations.

2 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 behaviorof a debris flow is highly variable within a single surgewith the front of the surge exhibiting the greatest shear
stresses. Previous modelling studies have demonstrated
that events occur that cannot be replicated by modelling asingle 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 sedimentsources 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 wascharacterized by multiple surges causing intense erosionin the proximal and medial zones of the fan [10]. In themodelling of Neff Creek, a Monte Carlo method was used
to randomly divide the event volume into four stages andrandomly select an input hydrograph for each of thesestages [2]. Deposition was allowed to occur between eachstage. 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, theresults matched the observed event more closely when

* Corresponding author: khorita@bgcengineering.ca© The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0(https://creativecommons.org/licenses/by/4.0/).

E3S Web of Conferences 415, 05006 (2023)
DFHM8

https://doi.org/10.1051/e3sconf/202341505006

variable inflow was coupled with deposition between
surges [2].

front and the other 50% with the muddy tail. The peakdischarge of 1000 m3/s was associated with the coarse
front as previous work has shown the coarse front to havethe 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].

3 Case Study: Hummingbird Creek
On July 11, 1997, a large debris flow occurred atHummingbird Creek damaging roads and buildings in thecommunity of Swansea Point (the fan-delta ofHummingbird Creek and Mara Creek). Approximately
92,000 m3 was deposited on the fan-delta during thisevent and it had an estimated peak discharge of 1000 m3/s
[11]. The distribution of deposits following the event isshown in Figure 1 below and was used in model
calibration. Note the zone of thicker deposits near the fanapex. The event occurred following long-term highantecedent precipitation and was initiated from a
25,000 m3 debris avalanche 2.4 km upstream of the fanapex. Channel entrainment rates were estimated at28 m3/m [11].

Q = 0.0059V0.94(1)

The flow hydrographs were approximated by atriangular 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 thesediment volume estimated to be carried by the coarse
surge and muddy afterflow (50% of the 92,000 m3 each).
The coarse front was modelled first, and the terrain
modified to absorb the coarse front deposit. The muddyafterflow was then run over the terrain that included thedeposition 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 wellas the velocities near the fan apex estimated by Jakob etal. [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 anddebris flow module of HEC-RAS (HydrologicEngineering 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 bydynamic 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 thefan apex (grey in Figure 1) and match the inundation anddeposition extents (hatched in Figure 1).
Given the two distinct deposits seen in Figure 1, it washypothesized 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

Fig. 2. Calibration of the depths and inundation extents for thecoarse front. The black outline matches the observed
deposition from Figure 1. The terrain contour interval is 5 m.

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-magnituderelationship for Hummingbird Creek, extract impactintensities, and develop a composite hazard map for thefan-delta and the community.

2

E3S Web of Conferences 415, 05006 (2023)
DFHM8

https://doi.org/10.1051/e3sconf/202341505006

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 ora distinct coarse and muddy afterflow deposit are
hypothesized in the following list. More research isneeded 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 tosediment 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 sedimentaccumulation in headwaters, or sudden landslide
failure)- Entrainment (does it bulk through erosion andscour 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 relentlesschallenge to refine our attempts at representing thisvariability to better support the communities we live inand work for.

Fig. 3. Calibration of the depths and inundation extents for themuddy afterflow. The black outline matches the observed
deposition from Figure 1. The terrain contour interval is 5 m.
Table 1. Calibrated rheology for each hydrograph
Sediment
Concentration

DynamicViscosity(Pa·s)

Yield
Strength(Pa)Coarse
Front

50%

15000

Muddy
Afterflow50%

1100

I would like to thank my esteemed colleagues at BGC who havetaken the time to teach me as much as they know about debris
flows with particularl thanks to Carie-Ann Lau, Matthias Jakob,and Hamish Weatherly for their guidance with the Hummingbird
Creek hazard assessment. Thank you to Sophia Zubrycky andHazel Wong for their encouragement and stoke, and finally toAndrew Mitchell for the endless discussion on any idea I may
have and for numerous references.

4 Discussion

References

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 torepresent 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 theremainder of the debris flow (no examples). At Neff
Creek and Hummingbird Creek, calibration events wereavailable to help guide the modelling and multiplehydrograph method. The challenge in moving forward isin how to decide on the number of hydrographs, sedimentconcentrations, and rheology in the absence of calibration
events?
Hummingbird Creek is a gentle-over-steep watershedmeaning 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 thatthe plateau in the upper watershed has more water storage
and could contribute to more dilute afterflow orsubsequent surges. Mountain channels, such as Neff
Creek, that exhibit distinct surges are hypothesized tohave 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

R. Iverson, Reviews of Geophysics, 35, 3, 245-296,(1997)
2. A. Mitchell, S. Zubrycky, S. McDougall, J. Aaron,
M. Jacquemart, J. Hübl, R. Kaitna, and C. Graf, Nat.
Hazards Earth Syst. Sci, 22, 1627-1654 (2022)
3. S. McDougall. Can. Geotech. J., 54, 5 (2014)
4. K. Barnhart, R. Jones, D. George, B. McArdell, F.
Rengers, D. Staley, and J. Kean. JGR Earth Surf.
126, 12, e2021JF006245 (2021)
5. O. Hungr, Earth Surf. Process. Landforms 25, 483495 (2000)
6. M. Jakob, Env. Eng. Geosci. XXVII, 2, 153-166(2021)
7. M. Jakob, D. Stein, and M. Ulmi, Nat. Hazards, 60,241-261 (2012)
8. B. McArdell. Int. J. Eros. Control. Eng. 9, 4 (2016)
9. G. Nagl, J. Hübl, and R. Kaitna. Earth Surf. Process.
Landforms, 45, 1764-1777 (2020)
10. C. Lau, Simon Fraser University Master Thesis,(2017)
11. M. Jakob, D. Anderson, T. Fuller, O. Hungr, and D.
Ayotte, Can. Geotech. J. 37, 1109-1125 (2000)
1.

3

E3S Web of Conferences 415, 05006 (2023)
DFHM8

https://doi.org/10.1051/e3sconf/202341505006

12. M. Bovis, M. Jakob, Earth Surf. Proc. Land., 24,1039-1054 (1999)
13. L. Marchi, F. Cazorzi, M. Arattano, S. Cucchiaro,
M. Cavalli, and S. Crema, Nat. Hazards Earth Syst.
Sci., 21, 87-97 (2021)
14. J. Kean, S. McCoy, G. Tucker, D. Staley, and J.
Coe, J. Geophys. Res. Earth. Surf., 118, 2190-2207(2013)
15. M. Piantini, F. Gimbert, H. Bellot, and A. Recking,
Earth Surf. Dynam., 9, 1423-1439 (2021)

4