Modeling the runout behavior of the July 23rd, 2015 Cancia debris-flow event using two numerical models

. On 23 July 2015, a typical volume-enlarging debris flow was triggered by heavy rainfall that occurred 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 performance of different numerical methods when simulating the same debris-flow event. The results showed the following: (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 the field 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.


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 to simulate the runout behaviors of the debris flow. These models can be easily divided into two groups: continuum models [2,3] and discrete particle models [4,5]. At present, continuum models are regarded as a better choice due to the difficulty of accounting for the pore pressure in discrete particle models. Therefore, depth-averaged models derived from the principles of continuum mechanics are still the mainstream approach for 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 into balance equations, which extends the application range of the depth-averaged models. Among them, some models tried to consider entrainment using empirical law 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 been developed to address this limitation [6,13,14].
In this paper, we briefly introduce two depthaveraged numerical methods and review the July 23 * Corresponding author: zhitian.qiao2@unibo.it debris-flow event in Section 2. Section 3 compares and discusses the differences between simulated results and the field investigations and finally, some conclusions are presented in Section 4.

The July 23 rd , 2015 debris-flow event
The Cancia debris-flow channel is located on the southwestern 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 area. As depicted in Fig. 1a, the Salvella basin provides a huge source of abundant material. Two sub-basins confluence at the upper retention basin (1340 ma.s.l, Fig.  1c). The monitoring station is located at the elevation of 1665 m (Fig. 1b) and the Cancia village is located at the toe 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, this region went through a short and intense rainfall with the maximum 5min rainfall intensities 106 mm/h -1 recorded by the rain gauge, which produced a runoff able to entrain 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 the upper 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 the lower retention basin. Based on the field measurements, the total volume of the deposits increased compared with the initial volume. It means that this motion was accompanied by entrainment process that deepening the channel. The entrainment and deposition distribution of this event is obtained by comparing pre-and post-event DEM (Fig. 2) and the detailed information can be found in [15].

Governing equations
DAN3D is a three-dimensional numerical model for the dynamic analysis of rapid flow slides, debris flows, and rock avalanches. In this model, the flow is simplified as an incompressible equivalent fluid. This method uses the continuous Lagrangian approach for integrating the governing 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: where is the bulk density of the debris mass and the erodible material, ℎ is the bed-normal flow depth, and are the local flow velocities, and is the bednormal entrained depth, ⁄ represents the entrainment rate of material, and are the components of the acceleration of gravity in the x and y directions, respectively, is the bed-normal stress, and , , and 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 the landslide with entrainment phenomenon has a two-layer structure consisting of a thick sliding mass layer and a thin 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 is given by: where ℎ is the flow depth parallel to the z axis; and are the average flow velocities in the x and y directions, respectively; is the relative elevation of the sliding surface and varies due to entrainment. Similar to ⁄ in Eq. (1), ⁄ represents the entrainment rate of material in Shen's model.
The momentum balance equations of Shen's model are given by: The terms on the left side of Eq. (5) and Eq. (6) indicate the change rate of the total momentum in the soil column. The first two terms on the right side represent the momentum change rate due to the convection. The last second term refers to the momentum change rate contributed by the external force (supporting force N, lateral pressure P and basal resistance S).

Computational model
The preparation of input files for modeling is based on the DEMs with 2.5 m resolution. The source depths are approximately calculated by subtracting the post-from the pre-event DEM and manually filtering out the invalid data outside the simulation area. And then the initial sliding surface elevations are generated by subtracting the isolated source depths from the pre-event DEM. The computational region is 1600 m in the x https://doi.org/10.1051/e3sconf/202341505019 , 05019 (2023) E3S Web of Conferences 415 DFHM8 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 to cover the entire flow area.

Fig. 3. A 2D contour map of the simulation area.
Four groups of simulations were conducted to investigate the influence of entrainment and different numerical models on the July 23 debris flow event. The detailed simulation configurations are listed in Table 1. The physical parameters used in these simulations are given in Table 2. Among these parameters, the two Voellmy resistance parameters are determined by trial and error for a good fit in terms of flow depth. Table 2. Physical parameters of debris materials.

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 occurred on July 23, 2015. However, lateral bank overflows were observed in both models in comparison with the field investigation ( Fig. 2) because the no-entrainment model treats debris flow events as a unique surge of large volume.

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 the field survey and the numerical simulation. All results indicate that the deposition of material mainly occurs in the two retention basins. Instead, other areas exhibit the character of erosion. Although three subplots show a similar erosion and deposition pattern, there are some noticeable differences. In the simulation, most of the materials 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, the maximum value (7.49 m) observed in the field is in the upper basin rather than the lower basin. According to the monitored flow boundary of the July 23 event, the DAN3D model produces greater lateral propagation.  Fig. 5c) are selected along the channel to investigate the local significance of the erosion-deposition dynamics (Fig. 6). In section A-A', entrainment deepens the channel bed and with a maximum erosion depth of around 6 m in the field observation. The numerical results also perform a similar 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 and numerical 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, and Shen's model shows larger maximum flow depth than the DAN3D model. Like the upper retention basin, abundant sediments fill up the lower basin (section D-D').

Conclusions
Two typical models, namely Shen's model and the DAN3D model, are used to simulate the run-out process of the July 23rd debris flow event. Both models perform reasonably well, giving satisfactory accuracy of the final erosion-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 the inundated area both by exaggerating the final deposit and producing unrealistic channel overflows.