Keywords

1 Introduction

Geophysical hazardous granular flows such as landslides, debris flows, and rock avalanches commonly occur in mountainous areas, causing massive lives and economic losses each year [7, 6]. Accurate measurement of such granular flows, focusing on some key parameters like flow velocity and particle size, can greatly help disaster prevention and mitigation. It is also an important basis for studying the dynamics between a granular flow and a structure, especially for the design of hazard defense structures [4]. Some measuring methods to extract granular-flow velocity consisted of placing tracer particles in the flows and using image processing methods, including the particle image velocimetry (PIV), the particle tracking velocimetry (PTV), the laser speckle velocimetry (LSV), etc. The traditional PIV technology [1] belongs to the Euler method, which employs laser irradiation to view tracer particles dispersed in the flows, and performs correlation calculation on two adjacent image frames. This method has high calculation accuracy, but its operation is complicated [11, 15]. In contrast, the PTV method belongs to the Lagrangian method [10], calculating the velocity by measuring the length of the particle optical trajectory under an exposure time interval. This method has strong real-time performance and the operation is simple [2], but the accuracy is relatively lower compared to the PIV algorithm. The LSV method is generally applied to dense granular flow. The original pixels of particle are replaced by speckles, and the flow velocity is then determined by using the two adjacent speckle images. Therefore, this method is only suitable for measuring an averaged flow velocity of the directional flow field [12].

With the development of technology, the digital image processing method shows great potential for measuring the granular flows in the laboratory and the field [5, 13]. Image processing technologies are commonly utilized with modern computers to analyze and process flow images, and quickly generate the required images through the use of digital combinations. Digital image processing, in particular, can filter out two-dimensional array pixels, generating the final image that is required by using image compression, image restoration, image transformation, chromaticity reconciliation and some other methods [3].

The aim of this study is to investigate the flow velocity and particle size of dry dense granular flow impacting on an obstacle. First, a small-scale laboratory chute experiments were performed with quartz-glass material. The cameras were used to record images of granular flow moving and impacting on a cylindrical structure. Second, on the basis of the video material recorded during experiments, the grayscale processing, the binarization and other digital image processing technologies were utilized to identify granular-flow velocity. In addition, the generative adversarial network (GAN) for image processing was also used to identify particle size in granular shock area upstream of the obstacle generated when granular flow impacts on the obstacle surface.

2 Methods

2.1 Experimental Set-Up

Laboratory chute experiments were performed with quartz-glass particles impacting on a cylindrical obstacle varying in radius Rc [5], using an experimental chute facility at the Institute of Mountain Hazards and Environment, Chinese Academy of Sciences, Chengdu, China. The experimental chute system consists of three functional parts, including the top start-up area, the flowing reach in the middle, and the bottom collection box. The top of the chute is a hopper that is made of plexiglass, which is 0.6 m in length, 0.8 m in width and 0.4 m in height (a total volume of 0.192 m3). The total length of the flowing area of the chute system with a rectangular cross-section is 2.5 m, the channel width is 0.8 m, and the transparent side walls are 0.35 m in height, all of which are made of plexiglass material. A hollow cylindrical barrier that is made of aluminum (Fig. 1a), 280 mm high and 10 mm thick, with a radius Rc ranging from 60 to 140 mm, was installed in the middle of the flow reach and 780 mm away from the chute outlet.

Fig. 1
A 2-part image. Part a is an experimental setup of a granular flow test of the chute facility. Part b is quartz-glass grains.

a Experimental set-up of the chute facility using for granular flow test. b Quartz-glass grains used in the experiments

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During the experiment, the first step is to store the granular materials in the top hopper, and a gate system controls the flow rate of the particles into the chute channel with an inclination angle θ, and the granular flow continues to flow down and impact on the cylinder. The cameras (GOPRO) are installed just above and on the side of the chute to obtain experimental videos for further analysis, with a maximum resolution of 4 k and a frame rate of 240 fps.

2.2 Granular Material

The granular material used in this study was quartz-glass particles as mentioned above, with particle shape approximately ellipsoid, an average diameter ranging from 1.7 mm to 4.0 mm, and the colored in blue and transparent (see Fig. 1b). During the test, the initial granular mass was 100 kg and the density was tested as 1646 kg/m3. Find more information about the granular material (e.g. internal friction angle, cohesion and friction between the particles and the chute bed) used for impact experiments in Chen et al. [5]. For different experimental runs, they were controlled by the parameters θ and Rc.

2.3 Image Processing Methods

In this study, the image processing methods used for the analysis of granular-flow velocity and particle size include the grayscale processing, the image binarization, and the image erosion and dilation. The flow chart of the image processing is presented in Fig. 2.

Fig. 2
A flowchart of image processing from the original image to corrosion and dilation of images with images counterpart in each step from a to d.

The image processing of granular flow using the grayscale processing, the image binarization, and the image erosion and dilation

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The grayscale processing of the experimental images refers to the process of converting a color image into a so-called grayscale image. The color of each pixel of a color image is determined by three monochromatic components, namely, red (R), green (G), and blue (B). Thus, such a pixel has a color variation range of more than 16 million (2553). The grayscale image is a special color image with the same three components R, G, and B, and the variation range of each pixel is 255. Grayscale images, like the color images, reflect the overall and local characteristics and distribution of luminance and chromaticity, but they can speed up calculations.

A threshold value Q (gray value) is used here for the image binarization. Comparing the gray value Q1 with Q at the target, if Q1 < Q, the value of Q1 becomes zero; otherwise, if Q1 > Q, then the value of Q equals to 255. By selecting an appropriate threshold to reflect the contour of the desired image, the gray value of the image after binarization is only zero or 255, making the contour features of the image more obvious and simplifying the image.

Image erosion and dilation are the most basic morphological operators in mathematical morphology. The following Eqs. (1) and (2) are used to represent the image erosion and dilation techniques, respectively:

$$A\Theta B = \left\{ {z\left| {\left( B \right)_{z} \cap A^{c} } \right. = \emptyset } \right\}$$
(1)

where \(A\Theta B\) indicates the corrosion of B on A; z is the set of all points; Ac is the complement of set A; \(\emptyset\) represents the empty set.

$$A \oplus B = \left\{ {z\left| {\left[ {\left( {\hat{B}} \right)_{z} \cap A} \right] \subseteq A} \right.} \right\}$$
(2)

where \(A \oplus B\) is the inflation of B to A; \(\hat{B}{ }\) is the image of B about the origin.

Image erosion and expansion technologies can quickly extract the outline of granular flow for each image frame. The specific operation processes are (1) select a convolution kernel of an appropriate size, and (2) perform image erosion and expansion processing on the binarized image. These processes can remove some noises, however, considering that the image is generally compressed, which results in a restored original shape.

2.4 Velocity Measurement Based on Moving Images

Based on the scale mark (with an accuracy of 1 mm) on the chute bed, the movement velocity of granular flow can be calculated, using the image frames captured by the camera that is set in the overhead view. In this paper, the digital image processing method is utilized to obtain an envelope of the granular-flow head, as presented by the red line in Fig. 3. It has been observed that the front part of granular flow generally shows the lighter color than that of the middle part, indicating some saltation particles in the front of granular flow [5]. Therefore, these saltation particles are not considered for the determination of the flow head envelope. Consequently, the determined envelope can be integrated to obtain a coverage area of granular-flow head, and the mean line of the flow head (see the blue dotted line in Fig. 3) is calculated according to the principle of area equivalence, as shown in Eq. (3).

$$\overline{X}_{h} = \frac{1}{W}\mathop \smallint \limits_{L}^{R} E_{h} {\text{d}}y$$
(3)
Fig. 3
A set of 3 overhead views of the granular flow in an experimental setup.

Measurement of the velocity using a time series of experimental images from an overhead view of the granular flow before impacting on the cylinder

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where \(\overline{X}_{h}\) is the coordinate of the mean line of the granular flow head; L and R are the upper and lower limits of the integral determined by the true left and true right boundaries of the chute, respectively; Eh represents the envelope of the flow head; W is the width of the chute.

The transport velocity u1 can be then determined as a ratio of the changes of \(\overline{X}_{h}\) between image frames (three frames were selected in this study) to the corresponding time interval, as seen in Eq. (4).

$$u_{1} = \frac{1}{m\Delta t}\mathop \sum \limits_{m}^{k} \left\| {\overline{X}_{h, k}^{t} - \overline{X}_{h, k}^{t - \Delta t} } \right\|$$
(4)

where \(\overline{X}_{h, k}^{t}\) is the coordinate value at time t; k = 1, 2;  We only considered to use the last three frames of images before  impacting, so m = 2; \(\Delta t\) = 1/60 s.

2.5 Particle Identification Using the Image Deblurring Method

Granular shock wave is formed ( with a thickness of standoff distance Dstandoff [6]) due to the disturbance of the cylindrical obstacle to the granular-flow field. In this study, the changes of the shock thickness at the steady state with changing obstacle size are also determined by analyzing the video frames, and the numbers particles within the shock influencing area in the flow direction is counted using the image processing method.

The granular flow has some saltation particles in the front during the movement and impact with the obstacle, leading to a blurring of images. Hence, we consider to use the generative adversarial networks (GAN) to make the moving images clearer, so as to better identify the particles. The GAN method can be expressed as [8]:

$$\begin{array}{*{20}c} {{\text{min}}} \\ G \\ \end{array} \begin{array}{*{20}c} {{\text{max}}} \\ D \\ \end{array} V\left( {D,G} \right) = E_{{x\sim P_{data} (x)}} \left[ {\log \left( {D\left( x \right)} \right)} \right] + E_{{z\sim P_{Z} (z)}} \left[ {\log \left( {1 - D\left( {G\left( z \right)} \right)} \right)} \right]$$
(5)

where D is the discriminator, G is the generator, e is the expectation, X is the real data, Pdata is the data distribution of the generator, z is the random noise, PZ is the a priori probability of the input noise, and the logarithmic function “log” has no specific base.

When using the real data as input, the closer the value of D(x) is to one, the better the discriminator. While if the input is the generated data, it is expected that the closer the D(G(z)) value is to zero, the discriminator should be better. The two terms are combined to optimize the objective function of the discriminator. The larger the value of D(G(z)) when the generated data G(z) is input to the discriminator, the better the generator, indicating that the generated data is closer to the real data and minimizing the generator objective function [9]. Figure 4 shows the processed images of granular shock generated by the cylinder. In this study, particle number Np refers to only the number of surface particles arranged in the shock influencing area along the flow direction, as seen in Fig. 4c.

Fig. 4
A set of 3 images of the granular shock area. Part a has a standoff distance and part c contains the number of particles in the granular shock area.

a Original image of a granular shock. b Image after the GAN processing. c Counting of particles in granular shock area

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3 Results

According to the above-mentioned methods, the image processing programs used for our granular flow experiments were conducted with PYTHON [14], and in the following the summary statistics of calculated flow velocity u1 and counting of particles are presented under different experimental conditions.

3.1 Granular Flow Velocity

The granular flow velocity u1 increases strongly with increasing slope angle θ ranging from 30° to 38° (see Fig. 5). In addition, the variability of the measured velocity also grows with increasing θ.

Fig. 5
A box plot plots u subs 1 versus theta for velocity. The trend is upwards.

Granular flow velocity u1 measured by image processing method as a function of slope angle θ

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3.2 Particle Size Identification

According to the results of linear regression analysis, the R2 value of the linear model between the standoff distance Dstandoff and particle number Np is 0.86, which means that the thickness of a granular shock wave increases nearly linearly with increasing number of particles Np in the shock area for all obstacle sizes Rc (Fig. 6). The obstacle with the larger diameter tends to generate the greater value of Dstandoff.

Fig. 6
A dot plot plots the D subs standoff versus N subs p for R subs c equals 6, 8, 10, 12, and 14 centimeters.

Relationship between Dstandoff and particle number Np

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4 Discussions

The measured granular-flow velocity u1 using the image processing method is growing linearly with increasing slope angle θ (see Fig. 5), which is reasonable. This is due to the fact that the increased Y-component (flow direction) gravity acceleration generated by the greater slope angle accelerates granular flows, hence increasing the particle velocity. The variation of flow velocity for each slope angle θ is mainly considered to be caused by saltation particles in the front of granular flows on the chute bed. Relatively high agreement is observed between the calculated front envelope for the early flow stage and the mean line of the granular-flow head. However, the difference between the two increases with the development of granular flow. This is likely due to that the more saltating particles are produced during the acceleration process of the granular flow. Nevertheless, the image processing method still shows potential good applications for measuring granular-flow velocity. It is also worth noting that this method is possibly only suitable for measuring the surface velocity of granular flow. The velocity and displacement distance of the surface particles are considerably larger than those of the middle and bottom particles due to friction, also contributing to a variability in recognizing an envelope of the flow head.

The thickness of granular shock wave generated upstream of the cylinder is characterized as the value of the standoff distance Dstandoff, demonstrating a positive relationship with the number of particles Np in the shock area, as seen in Fig. 6. It can be calculated that the averaged particle size is about 3 mm, while the particle size range used in our experiments ranges from 1.7 mm to 4.0 mm, showing a good agreement. Note that both the standoff distance and the particle number were measured at the steady state of granular flow for each experimental run.

The granular shock thickness or the standoff distance can be used to characterize the shock intensity [5], demonstrating an inversely proportional to increasing Fr. Here we investigated the relationship between the number of particles Np in the shock area and Fr, as shown in Fig. 7. The value of Np decreases with increasing Froude number Fr ranging from about 6–12.5, trending to change less and approaching to a limit varying with obstacle size. This shows the effect of particle size on granular shock thickness possibly due to that a force chain is formed at the steady state, also providing a potential way to measure particle size of dense granular flow.

Fig. 7
A dot plot plots the N subs p versus F r for R subs c equals 6, 8, 10, 12, and 14 centimeters.

Counting of particle number Np as a function of Froude number Fr

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5 Conclusions

In this paper, controlled laboratory experiments were performed to study characteristics of granular flow moving and impacting on a cylinder varying in size. The experimental images were obtained with cameras and were analyzed through some image processing methods such as the grayscale processing, the image binarization, and the image erosion and expansion. Key parameters including the granular-flow velocity and particle number in the granular shock area were obtained.

The measured granular-flow velocity and its variability obtained using the image processing method increases with increasing slope angle. The calculated envelope shows a good agreement with the mean front line of granular flow head at the early stage. The thickness of granular shock wave formed upstream of the obstacle demonstrates a positive relationship with the number of particles in the granular shock area. Furthermore, this particle number decreases nonlinearly with increasing Froude number, approaching to a limit value. This finding could be helpful for the analysis and particle size identification of dense granular flow when impacting on an obstacle.