Physical model investigation of the transition of a debris flow from the aerial to the water phase

. In order to study the phenomena of debris flow motion and deposition at the transition between a channel and an underwater storage area, experiments were carried out on a physical model. The current situation and the planned works were reproduced in two idealised 1:100 scale models. The experiments show that the flows experience an abrupt transition into water with the creation of a water wave and enter the lake undergoing a decrease in front velocity, but without creating upstream stagnation or local deposits due to the sudden phase change. Instead, the debris flows move to the lower part of the model, where they are deposited in the horizontal plane and in the lower parts of the conoid. The construction of a retention basin in the lake does not decisively influence the dynamics of the transition between the aerial and underwater phases. The results of the physical modelling provide indispensable data for the validation of the 3D numerical codes currently being tested.


Situation
The Steinlaui torrent in the municipality of Lungern, canton Obwalden (Switzerland), is known for its significant debris flow phenomena. These pose a considerable risk to the road infrastructure running along the eastern side of the Lungeren lake (Kanton Obwalden, 2016). In order to reduce the risk of debris flows, the construction of a new section of the national road and the associated bridge over the Steinlaui torrent includes the construction of a retention basin downstream of the paved channel that runs under the bridge. The basin is planned within the lake (ASTRA, 2017).

Aim of the work
The aim of the work is the analysis of the feasibility of the retention basin for debris flows within the lake. In particular, the flow and deposition phenomena of the debris flows entering the lake are to be studied. Among the issues raised with the project is the possible influence of the deposits in the basin on the upstream flow conditions, which could lead to a reduction of the hydraulic capacity near the bridges of the communication routes along the lake.
The experiments will provide a series of qualitative observations as well as quantitative data that will be used for the development and initial validation of the 2D and multiphase 3D numerical codes.

Physical model
The experiments are performed in an idealised 1:100 scale model that reproduces approximately 70 metres of channel and the storage area within the lake over a length of approximately 100 meters. The dimensions and geometry of the model are presented in the figure below.
The paved channel has a slope of 24%, a riverbed width of 12 meters and banks with a slope of 1:1. In contrast, the underwater cone has a slope of 33%. The planned retention basin for the debris flows is created with a 6-meter-deep ditch that extends from the edge of the lake for approximately 60 metres, and then reconnects with a horizontal plane to the current surface of the underwater conoid. The flow is generated by suddenly releasing the mixture placed in a vertical cylindrical tank with a circular outlet by opening the gate valve at the outlet. For the generation of the debris mixture with the desired dynamic characteristics (in particular peak flow, total volume and front propagation velocity), the outlet opening and the height of the mixture in the vertical cylinder are adjusted.
The debris mixture consists of fine mineral powder, sand, gravel and water. The mean grain size of the material used in the physical model is 3 mm, while the maximum grain size is 8 mm. The water content is varied between 20 and 30% to achieve the desired flow conditions.

Instrumentation
In the physical model, the debris flows entering the channel are measured by detecting the decrease in the level of the mixture in the vertical tank with a sonar sensor, the flow depths are measured over two sections of the channel by means of sonar sensors, and the velocity of the flow front along the entire model is measured by analysing the frames of the video footage (taken with a GoPro-Hero8® at a rate of 25 fps). Also the water wave developping on the basin surface after the impact of the debris flow is measured by a sonar sensor. An example of the measurements is shown in figure the following figure. All sonar sensors are of type BAUMER UNAM 18U6903/S14 with a sonic frequency of 380 kHz and a response time <10 ms.

Experiments
The experiments were carried out for the current geometry and for the design situation (with containment basin in the lake) by varying the volume of the melt, the maximum outflow and the speed of the melt front. A total of 42 experiments were carried out. The spectrum of flow front velocities analysed in the laboratory varies between 10 and 18 m/s, which corresponds to the velocities that can be expected for debris flows in steeply sloping channels such as the Steinlaui (J = 24%). The analysed runoff depths vary between 4 and 5 metres.

Observations and results
The experiments carried out show that the flows enter the lake with an abrupt transition generating a water wave on the lake surface and experiencing a decrease in front velocity, despite the increase in gradient from 24% to 33% between the channel and the subaqueous cone, without causing stagnation upstream. Both in the canal section and on the first part of the cone, velocities are high and range between 10 and 18 m/s in the canal and decrease to around 6-8 m/s on the underwater cone. However, no deposits are observed at the phase transition.
Most of the deposits are observed in the lower part of the model at the bottom of the lake as well as at the bottom of the cone.
The construction of a retention basin in the upper part of the underwater cone does not significantly condition the flow and deposit dynamics in the transition zone between the aerial and underwater phases of the debris flow.

Conclusions
The experiments on the physical model carried out proved to be extremely important for understanding the phenomena accompanying the transition of a debris flow from the air phase to the underwater phase, which had not previously been the subject of this type of research.
The idealised 1:100 scale model and the measuring instruments used also make it possible to generate fundamental quantitative results for the validation and calibration of the two-and three-dimensional numerical models currently being developed in our laboratory.
The assessment of the scale effects and the possibilities of the scalability of the data collected on the physical model at a scale of 1:100 is currently being researched through the study of the transport and the deposition phenomena of debris flow using a family of models (at scales of 1:100, 1:50 and 1:25).