Experimental investigation on the interaction between rapid dry gravity-driven debris flow and array of obstacles

Abstract

Arrays of obstacles are a potentially effective measure to manage a channel landslide run-out deposit. In this research, three kinds of debris sands with different particle sizes, 0.25–0.5 mm, 1–2 mm and 2–5 mm respectively, are investigated in a 4.28-m-long chute with a fixed incline angle of 40°. Structure from motion (SfM) and other novel image analysis techniques are proposed to analyse the deposits’ characteristics, including time histories. These allow measuring accurately the run-out distance, width, 3D topography and area of the deposits which are used to assess the effectiveness of the obstacles to manage run-out deposits efficiently. Experimental results reveal that particle size has a significant impact on the final deposition because they effectively behave as three different rheology characteristics: viscous (fine), frictional (medium) and collisional (coarse). The observations show emerging shape properties that are characterised, as well as surprising behaviours when considering time histories such as the non-monotonic area growth in fine, or viscous, landslides. Other phenomena such as airborne particle jets are observed for the coarse particle size, representing a collisional-type flow. In practical terms, the experiments show that when designing protection barriers, a compromise is needed between length, width and depth of deposition and that this can only be decided based on the structure to be protected.

Appendix. Image processing

I. Topography of the deposit

A 3D topographical map of the deposited material was reconstructed using the software Context Capture. The software uses structure from motion (SfM), where a series of images are captured around the debris depositions to form the basis for the 3D reconstruction. The positions and orientations of the camera in each photograph are recovered from known control points in the object. Once recovered, a point cloud can be built from multiple observations by using common points between photographs. For a full explanation, SfM is fully described in Westoby et al. (2012).

It is important to note though that the resulting point cloud is to an arbitrary scale and therefore needs to be scaled to the real-world scale. This was achieved by using the known dimensions of a grid printed on the surface of the run-out plate. The reconstructions were carried out using between 100 and 130 images in NEF format captured with a NIKON D7000 with a fixed focal length.

The accuracy of the reconstructed 3D maps was checked using the known height of the obstacles installed on the run-out plate as shown in Fig. 13. Checks were not done in DAL because the obstacles were totally buried due to their reduced height. On the other hand, checking the accuracy against the RA and DAH arrangements was considered sufficient as the material, lighting and all other conditions remained the same in the DAL case. The accuracy results are shown in Table 5. The heights of the piles are in the range of 78.56–81.87 mm or − 1.80% to + 2.34% from the actual 80-mm height. The worst-case scenario shows therefore an error of 4.68 mm. The average measurement and accuracy are respectively 80.25 mm and 0.31% (or 0.62 mm).

Fig. 13

Reconstructed 3D maps in case of Obstacle1-Fine

Table 5 Reconstructed accuracy of the context capture

II. Area of the deposit

In order to determine the area of the debris flow, the deposition was measured using a binarization process of images in camera C1 in Matlab as shown in Fig. 14, where we are taking the OF Coarse case as an example.

Fig. 14

Whole process of the image segmentation (OF-Coarse)

At first, the original image (Fig. 14a) was cropped to the area of interest (Fig. 14b) removing surrounding objects. Then, the effect of the ambient light was effectively removed by a matrix operation where the pixel value matrix of the current image subtracts the first image’s directly to get a pre-processed image (Fig. 14c).

After that, a binarizing threshold was determined by trial-and-error by comparing the contoured line of the reconstructed images to the final image. The binarization of the image was implemented by the function im2bw and the chosen threshold values for all cases are listed in Table 6. The resulting image had holes due to the high threshold used to remove other areas, as shown in Fig. 14d that were filled using the function imfill (Ithresh, ‘hole’) as shown in Fig. 14e. Then, the small scattered points, representing isolated grains in Fig. 14e were removed using the function imopen to obtain the final segmentation shown in Fig. 14f. Moreover, the edge of the segmented deposition was finally smoothed using imopen in the shape of a disk with the diameter of 3 pixels.

Table 6 Thresholds used for binarization

III. Length and width of deposit

In order to measure the length and width of the depositing area, two critical characteristics of the deposition, the pixel distribution along a designated line in images obtained by camera NIKON D7000 was used to detect the boundary of the deposition accurately. Although the previous segmentation could have provided the same, it requires trial and error and therefore, this novel method was chosen to provide repeatability in the detection method between all the different runs. The process is shown in Fig. 15 for the DAL-fine case as an example. The figure shows the original photograph and the selected Observation window that covers the deposition boundary at its final position. The latter is selected by hand with the only condition that the window must include the boundary. First, a Matlab code is used to rectify the image as shown in Fig.15b, i.e. create a view perpendicular to the camera principal axis so that undistorted measurements can be taken. The four white circles marked in the images are reference points and were picked to form a rectangle using the grid in the deposition area. The grid gives their position which is then used for the image rectification.

Fig. 15

Determination method of a deposition’s boundary. a Original image. b Rectified image. c Calculation of the front boundary (X_fb) in observation window

Figure 15c shows the grey pixel value versus length for points along the red Designated line shown in Fig. 6a and b, over the distance defined in the detailed window calculated using the Matlab function, improfile. The red line in Fig. 15c represents the backbone line of the original pixel distribution shown as a blue solid line. It clearly shows two distinct zones: one with deposited material and greater grey pixel values and one without material. The boundary of the deposit is then identified by the change in grey pixel value from the outside (P_gout) to the inside of the deposition material (P_gin) and is detected at the grey pixel value of 0.5ΔP (where ΔP = P_gout - P_gin). This intersects the backbone line at a value of x_fb in the x-axis shown in the figure as D′. In order to turn the graph distance to the experiment’s dimensions from the Observation window, a control point (X_c) and the starting point of the designated line (X₀) are used.

IV. Measurement of natural angle of repose

The natural angle of repose was measured as shown in Fig. 16a. A funnel is installed on a fixed top plate with a fixed height. The deposit disk whose diameter is 10cm is installed on the ground plate and keeps vertical aligned with the axis of the funnel. Before the test, the fixed top plate should keep horizontal, which was calibrated by a levelling instrument and 4 adjustable columns. In addition, a plumb line checked the vertical relation between funnel and deposit disk, see Fig. 16b. Final deposit was displayed in Fig. 16c and the angle’s measurement was shown in Fig. 16d. In order to reduce the operational errors, each test was repeated 5 times and obtained the average as the final value.

Fig. 16

Measurement procedure of natural angle of repose. a Measuring device. b Vertical calibration. c Final deposit. d Measurement