E3S Web of Conferences 415, 05019 (2023)
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https://doi.org/10.1051/e3sconf/202341505019

Modeling the runout behavior of the July 23rd, 2015 Cancia
debris-flow event using two numerical models
Zhitian Qiao1*, Matteo Berti1, Wei Shen2, and Tonglu Li2
1Department of Biological, Geological and Environmental Science, University of Bologna, Via Zamboni 67, 40126 Bologna, Italy
2Department of Geological Engineering, Chang’an University, Yanta Road No. 126, 710064 Xi’an Shaanxi, China

Abstract. On 23 July 2015, a typical volume-enlarging debris flow was triggered by heavy rainfall thatoccurred a few days before the event. The available data corresponding to this event is obtained from detailed
field investigations conducted before and after the event, as well as the monitoring station installed in June
2014. This study aims to reproduce the July 23 debris-flow event using two different numerical methods,
analyse the influence of entrainment on the runout behavior of the debris flow and compare the performanceof different numerical methods when simulating the same debris-flow event. The results showed thefollowing: (1) The expanded inundated area and unrealistic overflowing were observed in the scenario
without entrainment while the simulation that takes entrainment into account presented more perfect results.
It illustrates that entrainment is a non-negligible factor for the simulation of these volume-enlarging debris
flows. (2) Two models considering the entrainment performed a good match between the simulation and thefield survey. However, some noticeable differences can be observed in terms of the erosion-deposition
distribution because different numerical schemes were adopted in the two models. Specifically, the DAN3D

code always gives higher mobility and larger lateral spreading relative to the Shen model.

1 Introduction
Debris flows are common types of fast-moving
landslides and are known as one of the most hazardous
disasters in mountainous regions around the world [1].
Plenty of numerical models have been developed tosimulate the runout behaviors of the debris flow. Thesemodels can be easily divided into two groups:
continuum models [2, 3] and discrete particle models [4,5]. At present, continuum models are regarded as abetter choice due to the difficulty of accounting for thepore pressure in discrete particle models. Therefore,
depth-averaged models derived from the principles ofcontinuum mechanics are still the mainstream approachfor debris flow simulations [6, 7].
For that type of volume-enlarging debris flow [8, 9],
the entrainment cannot be ignored to accurately predict
the final magnitude of debris flows [10]. Currently,
many researchers have integrated the entrainment intobalance equations, which extends the application rangeof the depth-averaged models. Among them, somemodels tried to consider entrainment using empiricallaw where there is a proportional relationship between
the flow velocity, v, and the flow depth, h [11, 12],which provides a simple way to estimate the volume
increasing during the entrainment process but is unable
to explain the physical mechanism of the entrainment.
Other process-based entrainment models have beendeveloped to address this limitation [6, 13, 14].
In this paper, we briefly introduce two depthaveraged numerical methods and review the July 23

debris-flow event in Section 2. Section 3 compares anddiscusses the differences between simulated results andthe field investigations and finally, some conclusions arepresented in Section 4.

2 Materials and methods
2.1 The July 23rd, 2015 debris-flow event
The Cancia debris-flow channel is located on thesouthwestern slope of Mount Antelao (3264 ma.s.l.) in
the dolomitic region of the eastern Italian Alps. There
are two basins, Salvella and Bus de Diau, in the study

Fig. 1. Overview of the Cancia debris-flow channel.

* Corresponding author: zhitian.qiao2@unibo.it© 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, 05019 (2023)
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area. As depicted in Fig. 1a, the Salvella basin provides
a huge source of abundant material. Two sub-basinsconfluence at the upper retention basin (1340 ma.s.l, Fig.
1c). The monitoring station is located at the elevation of1665 m (Fig. 1b) and the Cancia village is located at thetoe of the fan and is protected by the lower retention
basin (1000 ma.s.l, Fig. 1d).
The July 23 event is a typical well-documented
debris flow and entrainment case. At approximately
2:05 P.M. on July 23, 2015, the time-lapse video records
the arrival of fast-flowing debris. Before the event, thisregion went through a short and intense rainfall with themaximum 5min rainfall intensities 106 mm/h-1 recordedby the rain gauge, which produced a runoff able toentrain the material laying within the debris channel bed.
As reported by the video, the lag time between rainfall
onset and debris flow occurrence was 20 min. The solidliquid front of debris flow formed upstream of the giant
rock, and then propagated downstream until reached theupper retention basin where the solid part of the mixture
mostly stopped, a part of the material continued to flow
downstream, finally, the debris flow reached in thelower retention basin. Based on the field measurements,
the total volume of the deposits increased comparedwith the initial volume. It means that this motion wasaccompanied by entrainment process that deepening thechannel. The entrainment and deposition distribution ofthis event is obtained by comparing pre- and post-event
DEM (Fig. 2) and the detailed information can be foundin [15].

𝜌𝜌𝜕(𝑣𝑥 ℎ)𝜕𝑡𝜏𝑧𝑥 − 𝜌𝑣𝑥𝜕𝑥+

𝜕𝑦= 𝜌ℎ𝑔𝑥 + 𝑘𝑥 𝜎𝑧 (−𝜕𝑏
𝜕𝑡+

𝜕ℎ
𝜕𝑥

𝜕𝑏
𝜕𝑡

𝜕(𝑣𝑥 ℎ)𝜕𝑡
𝜕(𝑣𝑦 ℎ)) + 𝑘𝑦𝑥 𝜎𝑧 (−𝜕ℎ𝜕𝑦𝜕ℎ𝜕𝑥)+(3)+𝜕(𝑣𝑥 ℎ)𝜕𝑥+𝜕(𝑣𝑦 ℎ)
𝜕𝑦+

𝜕𝑍
𝜕𝑡(4)

=0=−
=−

𝜕(𝑣𝑥2 ℎ)−𝜕𝑥𝜕(𝑣𝑥 𝑣𝑦 ℎ)𝜕𝑥𝜕(𝑣𝑥 𝑣𝑦 ℎ)−

𝜕𝑦2 ℎ)
𝜕(𝑣𝑦𝜕𝑦++𝑁𝑥 −𝑑𝑃𝑥 −𝑆𝑥

ℎ(5)

ℎ(6)

𝑚
𝑁𝑦 −𝑑𝑃𝑦 −𝑆𝑦𝑚The terms on the left side of Eq. (5) and Eq. (6)indicate the change rate of the total momentum in thesoil column. The first two terms on the right side
represent the momentum change rate due to theconvection. The last second term refers to themomentum change rate contributed by the external force(supporting force N, lateral pressure P and basal
resistance S).
2.2.2 Computational model
The preparation of input files for modeling is based onthe DEMs with 2.5 m resolution. The source depths areapproximately calculated by subtracting the post- fromthe pre-event DEM and manually filtering out theinvalid data outside the simulation area. And then theinitial sliding surface elevations are generated bysubtracting the isolated source depths from the pre-event
DEM. The computational region is 1600 m in the x(1)=0) + 𝑘𝑥𝑦 𝜎𝑧 (−where ℎ is the flow depth parallel to the z axis; 𝑣𝑥
and 𝑣𝑦 are the average flow velocities in the x and ydirections, respectively; 𝑍 is the relative elevation of thesliding surface and varies due to entrainment. Similar to𝜕𝑏⁄𝜕𝑡 in Eq. (1), 𝜕𝑍 ⁄𝜕𝑡 represents the entrainment rateof material in Shen’s model.
The momentum balance equations of Shen’s model
are given by:𝜕𝑡𝜕(𝑣𝑦 ℎ)𝜕𝑦𝜕𝑡𝜕𝑡

DAN3D is a three-dimensional numerical model for thedynamic analysis of rapid flow slides, debris flows, androck avalanches. In this model, the flow is simplified as
an incompressible equivalent fluid. This method uses
the continuous Lagrangian approach for integrating thegoverning equations in the depth direction. Furthermore,
the depth-integrated equations are deduced in a local
Cartesian coordinate system (x, y, z), the axis of z points
outward normal to the sliding surface. The governing
equations can be expressed as follows:𝜕(𝑣𝑥 ℎ)𝜕ℎ𝜕𝑏𝜕ℎ2.2.1 Governing equations+= 𝜌ℎ𝑔𝑦 + 𝑘𝑦 𝜎𝑧 (−where 𝜌 is the bulk density of the debris mass andthe erodible material, ℎ is the bed-normal flow depth, 𝑣𝑥
and 𝑣𝑦 are the local flow velocities, and 𝑏 is the bednormal entrained depth, 𝜕𝑏 ⁄𝜕𝑡 represents theentrainment rate of material, 𝑔𝑥 and 𝑔𝑦 are thecomponents of the acceleration of gravity in the x and y
directions, respectively, 𝜎𝑧 is the bed-normal stress, and𝑘𝑥 , 𝑘𝑦𝑥 , 𝑘𝑥𝑦 and 𝑘𝑦 are the stress coefficient.
The time term on the left side of Eq. (2) and Eq. (3)represents the variation of momentum fluxes per unit
basal area; the first four terms represent the momentum
fluxes due to the gravity, normal stress, transvers shear
stress and basal shear stress, respectively. The last term
refers to the momentum fluxes due to the entrainment.
By contrast, Shen’s model [7] assumes that thelandslide with entrainment phenomenon has a two-layer
structure consisting of a thick sliding mass layer and athin erodible mass layer. Although it is also a continuum
model, it is formulated in a Eulerian coordinate. In a
global Cartesian coordinate system, the mass balance isgiven by:

2.2 Numerical models𝜕𝑡𝜕𝑡𝜏𝑧𝑦 − 𝜌𝑣𝑦Fig. 2. The elevation changes of Cancia debris flow channel
before and after event.

𝜕ℎ𝜕(𝑣𝑦 ℎ))+(2)2E3S Web of Conferences 415, 05019 (2023)
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direction and 1387.5 m in the y direction (Fig. 3). And
the minimum and maximum elevations of the simulation
area are 945.1 m and 1803.7 m, respectively. According
to the field investigations, the entrainment is assumed tocover the entire flow area.

investigation (Fig. 2) because the no-entrainment model
treats debris flow events as a unique surge of large
volume.

Fig. 3. A 2D contour map of the simulation area.

Four groups of simulations were conducted toinvestigate the influence of entrainment and differentnumerical models on the July 23 debris flow event. The
detailed simulation configurations are listed in Table 1.
Table 1. Configurations of different simulation groups.
SimulationgroupsNumericalMethods

ConsiderEntrainment

C1

Shen’s modelNo

C2

DAN3D modelNo

C3

Shen’s model

Yes

C4

DAN3D model

Yes

Fig. 4. Comparison between (a) Shen’s model and (b)DAN3D code in terms of flow depth.

A comparison between the observed and simulated
elevation changes pre- and post-event is shown in Fig.
5. Overall, there is a reasonable agreement between thefield survey and the numerical simulation. All results
indicate that the deposition of material mainly occurs in
the two retention basins. Instead, other areas exhibit thecharacter of erosion. Although three subplots show asimilar erosion and deposition pattern, there are somenoticeable differences. In the simulation, most of thematerials deposit in the lower basin, with a maximum
depth of approximately 7.35 m and 4.9 m respectively
for the Shen’s model and DAN3D code. Conversely, themaximum value (7.49 m) observed in the field is in theupper basin rather than the lower basin. According to themonitored flow boundary of the July 23 event, theDAN3D model produces greater lateral propagation.

The physical parameters used in these simulations
are given in Table 2. Among these parameters, the two
Voellmy resistance parameters are determined by trialand error for a good fit in terms of flow depth.
Table 2. Physical parameters of debris materials.
Parameters

Value

Frictional Resistance tan ∅𝑏

0.11

Basal Resistance 𝜉 (m/s2)

450Internal friction 𝜑 (°)

35

Bulk density (g/cm3)

2.04

3 Results and discussion
The simulated results of both numerical models without
entrainment are presented in Fig. 4. These simulation
results illustrate that both codes can reasonably simulate
the runout process of the debris flow event that occurredon July 23, 2015. However, lateral bank overflows wereobserved in both models in comparison with the field3

E3S Web of Conferences 415, 05019 (2023)
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4 Conclusions
Two typical models, namely Shen’s model and theDAN3D model, are used to simulate the run-out processof the July 23rd debris flow event. Both models performreasonably well, giving satisfactory accuracy of the finalerosion-deposit distribution, inundation area, and runout
distance comparing with the survey measurements.
However, the different numerical schemes adopted by
the two codes lead to some noticeable differences. For
this case, the DAN3D model always presents a greater
lateral spreading and a thinner depositional thickness
than Shen’s model. Additionally, entrainment is a
crucial process in reproducing the July 23rd debris flow
event. The simulations that do not take the entrainment
into account present imperfect results in terms of theinundated area both by exaggerating the final deposit
and producing unrealistic channel overflows.

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Fig. 5. The topography changes before and after the debris
flow event.

Furthermore, four different cross-sections (A-A’, BB’, C-C’ and D-D’ shown in Fig. 5c) are selected along
the channel to investigate the local significance of theerosion-deposition dynamics (Fig. 6). In section A-A’,entrainment deepens the channel bed and with amaximum erosion depth of around 6 m in the fieldobservation. The numerical results also perform asimilar erosive character but with a lower erosion depth.
In both field and numerical data, erosion is dominant in
the upper reach. In section B-B’, both field andnumerical results present a depositional character, but
simulation results show a lower maximum deposition
depth. The alternative erosion and deposition occur
down to the lower basin. When the materials approach
the lower retention basin (section C-C’), all situations
exhibit the evident deposition characteristics, andShen’s model shows larger maximum flow depth thanthe DAN3D model. Like the upper retention basin,abundant sediments fill up the lower basin (section DD’).

Fig. 6. Debris flow channel cross-sections comparing thepre- and post-event morphology.

4