Flow-type landslides Impacting V-shaped Diversions: Physical Modelling

. In rural and sparsely populated areas, government issued pamphlets often recommend the construction of V-shaped diversions to protect personal property from flow-type landslides hazards, including debris flows. V-shaped diversions are advantageous because they attract low impact forces and runup heights due to their oblique impact angle. However, current design approaches are empirical, so it is unclear what resisting forces and wall heights are required. In this extended abstract, details of a new experimental setup and some preliminary results are presented. It is envisioned that findings from this study will help to shed light on scientific-based recommendations to design V-shaped diversions to enhance the resiliency of mountain communities globally.


Introduction
Flow-type landslides, including debris flows, snow avalanches, and granular flows, surge downslope under the influence of gravity and have been reported to cause fatalities and damage to infrastructure globally [1,2,3].
In rural areas, government-issued pamphlets recommend property owners to construct V-shaped diversions as personal protection against flow-type landslide hazards [3,4]. Owing to an oblique impact orientation between a V-shaped diversion and a flow, the resisting force and runup heights are lower compared to an orthogonal impact orientation. This means that Vshaped diversions do not require designs that are bulky. Despite the high engineering value of V-shaped diversions, they are designed empirically. For example, Fig. 1. shows a conceptual schematic diagram of a Vshaped diversion [5]. It is recommended that the deflector angle should be "such that the area enclosed by the retaining walls is greater than the desired level area", and "grade beam should extend two feet below the slope surface and be provided with three feet of freeboard". Besides these recommendations, it is recommended that the design of diversions should follow the procedures for other retaining structures [5]. Evidently, conventional retaining structures and Vshaped diversions subjected to oblique dynamic loading are fundamentally different [6]. However, there is no guidance on the design wall height against runup and an optimised diversion angle to reduce the impact force [7,8].
In this study, a new experimental setup, along with its instrumentation and modelling procedures is presented. Then, some preliminary results are shown. It is expected that the findings from this study will help to progress towards scientific-based design guidance for V-shaped diversions to empower vulnerable communities in mountainous regions to protect themselves from debris flow hazards.  Figure 2 shows the new experimental model developed for this study. It consists of a flume, which has a length of 1.5 m, a width of 0.2 m, and a depth of 0.3 m. The flume consists of a 0.3 m long container for storing the geomaterial initially at the upstream end. The inclination of the flume is selected to be = 35° to generate high energy flows on obstacles [9,10].

Methodology
The diversions are designed with three different diversion angles (i.e., 30°, 60°, 120°) while keeping the distance d between the two side walls constant. A Froude number Fr of 6 is selected to model supercritical flow [11,12].

Instrumentation
Top-and side-view cameras (i.e., 240 frames per second at a resolution of 1920×108) are mounted around the model to capture the flow and impact behaviour. A load cell is sandwiched between a fixed joint and a frontal diversion wall. Laser cartography is adopted to measure the spatiotemporal changes in flow height. This method makes use of refracted laser beams and the shadow bar technique to capture dynamic changes in the flow height. The laser beams pass through vertically placed cylindrical lens and are then refracted to a surface [13]. The height difference is proportional to the difference between the original reference line and the distorted line, which needs to be calibrated using a standard object with a known height beforehand. The contour of the thickness can then be deduced from the captured images [14]. This method has been successfully evaluated by Mcdonald and Anderson in 1996 [15].

Modelling procedures
In each model test, the model diversion is installed on an unchannelised board with dimensions of 1.0 m by 1.0 m to enable the impact behaviour to be studied. The diversion is affixed orthogonally to an inclined clear board with a fixed joint behind the V-shaped walls. High-speed cameras are then mounted around the model. Geomaterial is prepared in the storage container at the upstream end of the flume. The material is retained by a gate, which is released by lifting it vertically. The granular material used in the test is the Toyoura sand. A total mass of 10 kg is prepared, and then the flume is inclined to the target angle. Afterwards, the granular material is released from the container. The flow accelerates down the flume under the influence of gravity and impacts the model diversion. Figure 3 shows the impact behaviour as captured by the top camera. Grids on the board are spaced at an interval of 100 mm. The apex of the model diversion is placed 200 mm downstream from the mouth of the flume. The flow impacts the diversion (i.e., = 30°, and d = 100 mm).

Preliminary results
It can be observed that oblique shocks form when the granular flow impacts the diversion. The shock angle at quasi-steady state is approximately 80°. At the apex of the diversion wall, the granular material is observed to jump and form a stagnation point. The observed impact can be used to evaluate analytical formulations for predicting the runup height and impact force.

Summary
Diversion structures are more compact alternatives compared to traditional rigid barriers because they deflect the flow material to reduce the impact force and runup height. The described experimental model setup in this extended abstract will be used to optimise the the diversion angle, impact force, and wall height for a wide range of flow types. It is envisioned that findings from this study can be used to rationalise the design of Vshaped diversions for vulnerable communities globally.