X-ray measurements of granular flows

(1)

X-ray measurements of granular flows

Ana Costa Conrado

(2)

This master’s thesis is submitted under the master’s programme Computational Science, with programme optionMechanics, at the Department of Mathematics, University of Oslo. The scope of the thesis is 60 credits.

The front page depicts a section of the root system of the exceptional Lie groupE8, projected into the plane. Lie groups were invented by the Norwegian mathematician Sophus Lie (1842–1899) to express symmetries in differential equations and today they play a central role in various parts of mathematics.

(3)

Abstract

Detailed motion of granular flows is difficult to describe since there is no access with intrusive techniques. Moreover traditional PIV/PTV with a light sheet is also difficult due to light scatter or opacity of the granules. This is the case with e.g., deformable slides and slumps, as well as sediment transport due to wave inundation. The former is important in relation to, for instance, tsunamis and is related to ongoing research at the NGI (two PhD students at the department).

The latter is important with respect to erosion of shorelines and reworking of sand dunes. On the other hand, Lagrangian trajectories within granulated flows can be measured by Xray and the Hydrodynamics Laboratory facilitates the required instruments. It is proposed in this project to investigate the possibility to measure velocities of particles in the core of a slide, and in other granulated flows, using X-ray tomography and tracking.

(4)

(5)

Acknowledgements

Special thanks to Prof Geir Kleivstul Pedersen and Prof Atle Jensen for the subject and supervision.

Thanks to Olav Gundersen.

Thanks to Laila Egbeocha Andersland, Jon Alexander Pirolt, Martin Sebastian Gyllengahm, Richard Andre Fauli, Reyna Guadalupe Ramirez de la Torre, Bin Hu.I am grateful to the Department of Geosciences, especially to Anne Claire Fouilloux, Hans Peter Verne, Kjetil Bakke, and Arnstein Orten.

(6)

(7)

List of Figures

1.1 Inside a plastic box, in the right sector, some marbles made of glass, and one larger white sphere. In the left compartment, glass spheres with tungsten wires inserted. Glass spheres were manufactured with three different thicknesses of tungsten wires, 0.5 mm, 0.23 mm, 0.19 mm. . . 4 2.1 glass spheres. X-ray source energy 52 kV, x-ray current 6 mA,

exposure time of 360 ms. Images from 16 January, 2019 . . . 10 2.2 K-means clustering of pixels in image from 2.1b after removing

background pixels. Based on [FCN18] . . . 10 2.3 Attenuation length of different materials with respect to the Photon

Energy (source: [XRa19])). Poly(methyl 2-methylpropenoate) ((C5O2H8)n) (PMMA) is also known as acrylic, acrylic glass, or plexiglass. Silicon dioxide (SiO2) gives origin to glass by melting [Cal97; Chi86]. C3H6represents the repeating unit of polypropylene (PP), a polymer [Cal97]. . . 11 2.4 Grains with and without tungsten wire tested in the x-ray machine.

The tungsten wire is 0.19 mm thick (see for specifications Table 2.1).

Exposure time of 40 ms. . . 12 2.5 Box with 10 cm width and a 40° slope with green peas inside the

x-ray machine. . . 13 2.6 Box with 5 cm width and a 15° slope with green peas inside the

x-ray machine. . . 14 2.7 Outside the x-ray machine, the rope to pull the lifting gate and

start the slide. . . 14 3.1 Top view of slide of green peas with one tracer tested in the x-ray

machine, from 13 December 2019. The W wire is 0.19 mm thick.

The images are captured at 155 frames per second, with exposure time of 6.45 ms, 80 kV, 5 mA, and a 2x2 pixel binning. The box is 10 cm wide and the inclination is 40°. . . 18 3.2 Side view of slide of green peas with one tracer tested in the x-ray

machine, from 13 December 2019. The tungsten wire is 0.19 mm thick. The images are captured at 155 frames per second, with exposure time of 6.45 ms, 80 kV, 5 mA, and a 2x2 pixel binning.

The box is 10 cm wide and the inclination is 40°. . . 18

(10)

List of Figures

3.3 Top view of slide of green peas with one tracer tested in the x-ray machine, from 18 December 2019. The tungsten wire is 0.19 mm thick. The images are captured at 141 frames per second, with exposure time of 7.09 ms, 70 kV, 5.7 mA, and a 2x2 pixel binning.

The box is 10 cm wide and the inclination is 15°. . . 19 3.4 Side view of slide of green peas with one tracer tested in the x-ray

machine, from 18 December 2019. The tungsten wire is 0.19 mm thick. The images are captured at 141 frames per second, with exposure time of 7.09 ms, 64 kV, 5.7 mA, and a 2x2 pixel binning.

The box is 10 cm wide and the inclination is 15°. . . 20 3.5 Partial program window of tracking application processing experi-

ments from 03 January 2020, top view. The images were captured at 190 frames per second, with exposure time of 5.26 ms, 80 kV, 5 mA, and a 4x4 pixel binning. After 0.15 s. . . 21 3.6 Partial program window of tracking application processing experi-

ments from 03 January 2020, top view. The images were captured at 190 frames per second, with exposure time of 5.26 ms, 80 kV, 5 mA, and a 4x4 pixel binning. After 0.7 s. . . 24 3.11 Rotation with respect to time for the tracking box. Tracking

application processing experiments from 03 January 2020, top view.

The images were captured at 190 frames per second, with exposure time of 5.26 ms, 80 kV, 5 mA, and a 4x4 pixel binning. . . 25 3.12 Displacement in horizontal direction in pixels with respect to time

for the tracking box. Tracking application processing experiments from 03 January 2020, top view. The images were captured at 190 frames per second, with exposure time of 5.26 ms, 80 kV, 5 mA, and a 4x4 pixel binning. . . 26 3.13 Displacement in verical direction in pixels with respect to time

for the tracking box. Tracking application processing experiments from 03 January 2020, top view. The images were captured at 190 frames per second, with exposure time of 5.26 ms, 80 kV, 5 mA, and a 4x4 pixel binning. . . 27 viii

(11)

List of Figures 3.14 Partial program window of tracking application processing experi-

ments from 03 January 2020, side view. The images were captured at 190 frames per second, with exposure time of 5.26 ms, 80 kV, 5 mA, and a 4x4 pixel binning. After 0.11 s. . . 27 3.15 Partial program window of tracking application processing experi-

ments from 03 January 2020, side view. The images were captured at 190 frames per second, with exposure time of 5.26 ms, 80 kV, 5 mA, and a 4x4 pixel binning. After 1 s, finished. . . 28 3.16 Partial program window of dense optical flow application processing

experiments from 03 January 2020, top view. The images were captured at 190 frames per second, with exposure time of 5.26 ms, 80 kV, 5 mA, and a 4x4 pixel binning. After 0.12 s. . . 28 3.17 Partial program window of dense optical flow application processing

experiments from 03 January 2020, top view. The images were captured at 190 frames per second, with exposure time of 5.26 ms, 80 kV, 5 mA, and a 4x4 pixel binning. After 0.76 s. . . 32

(12)

(13)

List of Tables

2.1 Specifications of the tungsten wire 2000919636 . . . 12

(14)

(15)

CHAPTER 1 Introduction

Landslides often begin with a sudden sliding, but also a gradually increasing seeping, in water saturated scree¹ and is triggered as a rule in slopes steeper than 25°, according to the Norwegian Water Resources and Energy Directorate (NVE) [NVE; NVEjordskred].

Landslides can generate tsunamis with wavelengths that are significantly lower than those generated by submarine earthquakes , where the dispersive effects are more important [Gli+13]. The amplitude of the waves generated depends on the volume and and configuration of the landslide, and can become much larger than tsunami waves generated by submarine earthquakes [Fri01;

Vir+15].

Granular material can be defined as any material composed of many individual solid particles, irrespective of the particle size [Ned92]. Grains can behave like a solid (in a sand pile), a liquid (when poured from a silo) or a gas (when strongly agitated) [JFP06; JNB96]. A continuum description of granular flows would be of considerable help in predicting natural geophysical hazards or in designing industrial processes [JFP06]. During an avalanche, one of the most important phenomena concerning granular systems is the transition from a static equilibrium to a granular flow [AT01].

1.1 Literature

experimental techniques

[Wak+18] conducted experiments with a silo model and granular material (Seramis material). Seramis is a highly porous, processed, particulate clay composed of kaolinite, illite, and quartz, which has very high water retention qualities. Larger grain size tracer Seramis particles were selected and previously infiltrated with NaOH, which gave them a higher X-ray absorption and yet having similar size and density with overall particles. An algorithm for image processing was developed, tracking particle movements (measuring individual particle velocities, lateral movement and 3D rotations, using ultrafast X-ray tomography (image resolution of 5.00×10⁻⁴s). In most industrial products, granular materials are often required to flow under gravity in various kinds of silo shapes and usually through an outlet in the bottom. There are several

1large, loose stones on the side of a mountain [CambridgeDict]

(16)

1. Introduction

interrelated parameters which affect the flow, such as internal friction, bulk and packing density, hopper geometry, and material type.

[Hei11] provides an overview of x-ray imaging for multiphase flow. X-ray imaging is one family of noninvasive measurement techniques used extensively for product testing and evaluation of static objects with complex structures.

X-rays can also be used to visualise and characterise multiphase flows.

Granular flow

[Bab+18] tested different granular materials for X-ray tomography; materials of biological origin presented best contrast ratio. Contrast ratio is important for image segmentation (watershed method). The granular materials of biological origin, i.e. short grain white rice and sorghum, presented similar material and mechanical properties, e.g. density, compressibility, friction properties and elastic properties, which compete with properties of classical glass materials.

The macroscopic and microscopic frictional properties of plant materials were found to fit well with prediction of gravitational flow including rolling friction component.

[JFP06] proposed a new constitutive relation for dense granular flows, inspired by analogy and recent numerical and experimental work. They tested three-dimensional model through experiments on granular flows on a pile between rough sidewalls, in which a complex flow pattern develops. Without any fitting parameter, the model gave quantitative predictions for the flow shape and velocity profiles. Results support the idea that a simple visco-plastic approach can quantitatively capture granular flow properties, and could serve as a basic tool for modelling more complex flows in geophysical or industrial applications. Simple visco-plastic rheology presented represents a minimal model that quantitatively captures the basic features of granular flows important in many applications. This model could help to take into account more accurately the complex yield features specific to granular matter.

[MH10] used mixed nuts (almonds, cashews, walnuts, and crushed walnut shell sifted to a size range of 500 - 600 µm) as particles to study the Brazil nut effect. The tracer particle was designed to emulate a Brazil nut while also being easy to track. The Brazil nut effect is a phenomenon in which large, dense objects migrate to the top of a bed of granular media when exposed to vibration. An example of this phenomenon is finding Brazil nuts on the top of a can of mixed nuts. The same phenomenon can be observed in almost any granular system. In this project, the Brazil nut problem was examined through the use of stereoscopic X-ray imaging.

Ambient humidity can cause serious disruptions by creating clumps of particles that are more or less mobile [Dur00]. Wet sand can be fairly cohesive, whereas dry sand crumbles apart. The smaller the particles, the greater this perturbation; since capillary forces are then apt to be of the same order of magnitude as the gravitational forces that would otherwise largely determine the behaviour of these objets.

[Dur00] highlights as well the importance of the micromechanical interations of the particles in dry granular media, not only between themselves but also with the walls of the container. The overall properties of dry granular media depends strongly on the fundamental mechanical characteristics of their constituents.

How local energy is dissipated determines how granular materials behave. This 2

(17)

1.2. Hypotheses leads to the analysis of the physics of interactions between solids in relative motion. The role of friction and collision between two and more particle is discussed further.

When a container filled with granular material is tilted beyond a certain angle, the resulting flow involves only a few layers near the free surface [Dur00].

Any flow takes place in sheets. The mean velocity of the particles decreases rapidly with depth. The discussion applies to avalanche flow.

Object tracking

[BK08] declares that the Meanshift algorithm is not distracted by far-away points. The continuously adaptive mean shift (CamShift) algorithm in high- speed vision extraction is better than other algorithms in terms of displacement extraction of high-frequency vibration [ZCG19]. The CamShift offers real time, high efficiency, high accuracy, and robustness. It applies the Meanshift with new scaled search window and previous window location [OpenCV.js].

1.2 Hypotheses

In the present study, we aimed at solving the following scientific question:

• How are the velocity profiles of particles flowing down a certain inclination along an inclined wall?

• How are the linear and rotational velocities of the particles?

We assumed that the particles could be made of glass. Marbles (glass spheres) could be used as particles in a granular flow. Tracers would be Tungsten (W)² wires inside similar glass spheres of the same size as the usual marbles. Tungsten is more visible in x-ray images than glass.

Figure 1.1 shows conventional glass marbles and glass spheres with tungsten wire inside. Another reason for the choice of glass for the granular material is its density higher than water. The experiments should lead to the study of the motion of flowing granular material in water. The first experiments should be in air.

The use of x-ray measurements is justified by the interest in capturing the movement of a particle in the middle of the flow. It is interesting to be able to register the motion of a tracer far from the side walls, where there is friction with the particles.

In traditional PIV (particle image velocimetry) the tracer is passive. Here, the tungsten wire is an active tracer, the particle with the wire inside should move with the rest of the particles.

1.3 Outline

The rest of the text is organised as follows:

Chapter 2 presents the methods used.

2Tungsten, also called Wolfram, is a chemical element with the symbol W and atomic number 74. Atomic mass is 183.85 [Cal97]

(18)

1. Introduction

Figure 1.1: Inside a plastic box, in the right sector, some marbles made of glass, and one larger white sphere. In the left compartment, glass spheres with tungsten wires inserted. Glass spheres were manufactured with three different thicknesses of tungsten wires, 0.5 mm, 0.23 mm, 0.19 mm.

Chapter 3 consists of results of the x-ray measurements, the object tracking and optical flow applications.

Chapter 4 deals with the conclusion and suggestions for future work.

Appendix A features where the code used and the raw data have been published.

4

(19)

PART I

The First Part

(20)

(21)

CHAPTER 2 Method

2.1 X-ray

X-rays are electromagnetic waves with wavelengths in the 10 nm to 6×10⁻³nm range, or with frequencies between 3×10¹⁷ Hz and 5×10¹⁹Hz. The energy of the photons ranges between 1.2×10³ eV and 2.4×10⁵eV [AF72]. X-rays can be produced when high-energy electrons strike a metal target and are used as diagnostic tools in medicine to see bone structure and as treatments for certain cancers.

X-rays were discovered completely by accident by Wilhelm Röntgen in 1895 and can be used to identify inner structures, not only in medical imaging, but also in nondestructive testing (NDT) [Rön95] for materials or objects, where the aim is to analyse (nondestructively) the inner parts that are undetectable to the naked eye [Hel13].

X-ray computed tomography (CT), or "computerized tomography" or

"computed axial tomography" (CAT), is used to noninvasively and nonintrusively obtain cross-sectional images of objects, including the internal structure.

Noninvasive method of acquiring images does not require the use of sensors and it does interfere with the measurement object [Gre+07]. Bin Hu [Hu+05]

describes the application of the algorithm to the three-phase (oil, water, air) slug flow in pipelines and the principle and operation of the X-ray system. In X-ray CT, the X-rays are transmitted through the measured object and measured after they pass through the object. The X-rays penetrate through the object and their intensity is measured by a detector array placed on the opposite side of the source. In order to take projections from multiple directions, the source and detector must be rotated around the object. A material’s linear attenuation coefficient,µ, is a measure of the degree to which X-rays are attenuated when passing through a differential length of material,dL, as defined by

dI

I =−µ dL (2.1)

where Iis the final intensity of an X-ray beam, the X-ray energy recorded by a detector. For an object with uniform composition and path length (or thickness) L, the final intensity of an X-ray beam with initial intensityI0 is

I=I0e^{−µ L}, (2.2)

which is Beer-Lambert law [PPP07]. X-ray intensity attenuates exponentially with penetration thickness and different materials have different attenuation.

(22)

2. Method

As the light propagates across the medium, there can be an exchange of energy between the light and the atoms in the medium. The linear absorption coefficient (or loss coefficient or linear attenuation coefficient)µcharacterises the spatial rate of change of the irradianceI [PPP07]. Linear attenuation coefficients (µ) are proportional to the density of the material and generally increase with the atomic number [97]. The linear absorption coefficient µof the material for x-rays is a constant for a given wavelength [KA74]. Equation (2.2) can be rewritten in terms of themass absorption coefficient ^µ_ρ, if divided and multiplied in the exponent by the densityρof the material

I=I0e⁻⁽^µ^ρ^{)µ L} (2.3)

The mass absorption coefficient ^µ_ρ is independent of the physical and chemical state of the material, in contrast to the linear attenuation coefficientµ, which is not. Therefore, the linear absorption coefficient for a given x-ray beam is much greater in water than in steam or in a stoichiometric mixture of oxygen and hydrogen, whereas the mass absorption coefficient ^µ_ρ remains the same for all three material states. This characteristic of the mass absorption coefficient

µ

ρ distinguishes x-rays from visible light. Diamonds are transparent to light, while carbon as graphite is a strong absorber; both, however, present the same mass absorption coefficient for x-rays.

When the absorbing material is a chemical compound, alloy, or solid solution instead of a single element, its mass absorption coefficient is calculated from those of its constituent elements and the composition. The calculation of ^µ_ρ for silicon dioxide (SiO2) will serve as illustration. For a wavelengthλ= 0.5609Å (AgKα), the mass absorption coefficients of silicon and oxygen are 3.28cm²/g and 0.740cm²/g, respectively (see [KA74, Appendix V]). The atomic weights of silicon and oxygen are 14 and 16. ThusSiO2 is 14/(14 + 2×16) = 0.304Si, and 2×16/(14 + 2×16) = 0.700 O. Therefore,

µ

ρ

SiO₂

= 0.304µ ρ

Si

+ 0.700µ ρ

O

= 0.304×3.28 + 0.700×0.740

= 1.51cm²/g

(2.4) For tungsten, the mass absorption coefficient ^µ_ρ is 53.0 cm²/g for a wavelengthλ= 0.5609Å (AgKα).

X-ray imaging may be mainly classified into radiography, stereography, and computed tomography (CT) [Hei11]. Radiography produces a static image after the exposure. Radiography is the act of obtaining a shadow image of an object using penetrating radiation such as X-rays orγ-rays [Car95].

Stereographic measurement methods use information from two 2D projections to calculate the 3D location of features in an object [Doe92]. This can be accomplished by analyzing two images of an object which are taken at different positions either due to a rotation or translation of the sample. Alternatively, with two identical source/detector pairs like those found in [HGJ08], and using appropriate software controls for the two CCD cameras, two image projections can be acquired simultaneously [Hei11].

In CT, the reconstruction produces a two-dimensional cross-sectional image of an object showing internal details [Hei11]. Tomography literally means “the picture of a slice” [Car95].

8

(23)

2.1. X-ray The energy (penetrating power) of X-rays is controlled by a voltage applied across the anode, and by a current applied to the filament in the cathode [Raf18].

X-ray wavelength

X-rays are short-wavelength and high-energy beams of electromagnetic radiation [Zol14]. The low wavelength limit of X-ray radiationλin nm is

λ=1.2398×10³

V (nm) (2.5)

whereV is the acceleration voltage of electrons expressed in volts. Or forλin Å

λ=12398

V (2.6)

For a tube operating at a peak voltageV = 52 kV, the wavelength of the x-ray radiation isλ= 0.023842 nm = 0.23842 Å¹

materials/absorptions

In Figure 2.1b, the tungsten wires are not visible. This shows the top view.

The side view (Figure 2.1a) shows only two of the three boxes. The three boxes had together six layers of glass spheres. There were three glass spheres with tungsten wire of 0.5 mm thickness. The diameter of the glass spheres was approximately 16 mm. Clustering the intensity of pixels to detect the tungsten wire would not help to see it (Figure 2.2).

calculating the exponentials from Equation(2.3) Tungsten wire in glass spheres

Densityρ_SiO₂ ofSiO₂ is 2.2 g cm⁻³.

µ

ρ

SiO₂

ρSiO₂ = 1.925cm²/g×2.2g/cm³= 4.24cm⁻¹ (2.7) Passing through one glass sphere of 16 mm of diameter, the exponential is

µ

ρSiO₂

SiO2

ρSiO₂×D= 1.925cm²/g×2.2g/cm³×16mm= 6.78 (2.8) The fraction transmitted is for 16 mm of SiO2

fraction transmitted = I I0 =e

−

µ

ρSiO2

SiO2

ρ_SiO₂×D

=e^−6.78= 1.1×10⁻³ (2.9) Density ofW is 19.3 g cm⁻³.

µ

ρ_W

W

ρ= 53.0cm²/g×19.3g/cm³= 1022.9cm⁻¹ (2.10)

10.1 nm = 1 Å, where Å stands for ångström.

(24)

2. Method

(a) glass spheres from the side (b) glass spheres in top view Figure 2.1: glass spheres. X-ray source energy 52 kV, x-ray current 6 mA, exposure time of 360 ms. Images from 16 January, 2019

original image from x-ray

30000 40000 50000 60000

('2', ' clusters')

0

1 ('3', ' clusters')

0 1

0 1 2

('5', ' clusters')

0 1 2 3

0 1 2 3 4

('9', ' clusters')

0 1 2 3

4 ('10', ' clusters')

0 1 2 3

4 ('11', ' clusters')

0 1 2 3

4 ('12', ' clusters')

0 1 2 3 4 5 6 7 K-Means Clustering

Figure 2.2: K-means clustering of pixels in image from 2.1b after removing background pixels. Based on [FCN18]

Passing through one wolfram/tungsten wire of 0.5 mm, the exponential is

µ

ρ

W

ρ_WL= 53.0cm²/g×19.3g/cm³×0.5mm= 51.145 (2.11) The transmitted intensity is

I

I₀ =e(^µρ)WρWL=e^−51.145= 6.1377×10⁻²³ (2.12) Solving the equation for the number of glass spheres n, the intensity transmittedIrelative to the initial I0

I

I0 =e⁻(^µρ)_SiO₂^ρ^SiO2×D×n−(^µρ)_W^ρ^W^L=e−130.38079n−95.6315 (2.13)

Grains: chickpeas and green peas

Another solution to increase the contrast between tracer (tungsten wire) and particles was to consider a different particle material for the experiments. Simple 10

(25)

2.1. X-ray

Figure 2.3: Attenuation length of different materials with respect to the Photon Energy (source: [XRa19])). Poly(methyl 2-methylpropenoate) ((C5O2H8)n) (PMMA) is also known as acrylic, acrylic glass, or plexiglass. Silicon dioxide (SiO2) gives origin to glass by melting [Cal97; Chi86]. C3H6 represents the

repeating unit of polypropylene (PP), a polymer [Cal97].

choice was to try biological materials, such as grains. Two types of grains were tested: roasted chickpeas and dry green peas. Both grains were compared with respect to their contrast in the x-ray machine (Figure 2.4), difference in weight, difficulty of inserting the wire, and how they behaved in the first experiments.

The grains with tungsten wire through the diameter are approximately 10 % heavier.

Inserting the tungsten wire in a roasted chickpea is much easier and can be done with the force of the fingers. We could produce several tracers as seen in Figure2.4. Disadvantage of the roasted chickpeas was that they suffer more of friction with the walls of the box, once we tried the first slides in the x-ray machine.

Green peas had to be drilled or soaked in water to have the tungsten wire inserted through the diameter. When drilling dry green peas, sometimes they crack. First, some were drilled as they are, dry. Then, a tungsten wire was glued inside the hole. The hole was larger than the tungsten wire and, therefore, a small amount of glue was used.

Another procedure was tested. Some green peas were left to soak in water and then the tungsten wire was easily inserted through the diameter. Then they were slowly dried in about 40° Celsius. They do not return to their original size, they inflate and there was an empty space inside. They become larger than the rest. Larger particles suffer the Brazil nut effect in granular flow. Therefore, this procedure was not the best.

(26)

2. Method

(a) chickpeas, 43 kV, 4.7 mA, 20 May 2019.

(b) green peas soaked in water, 57 kV, 7.0 mA, 10 May 2019.

(c) green peas, 43 kV, 7.0 mA, 8 May 2019.

Figure 2.4: Grains with and without tungsten wire tested in the x-ray machine.

The tungsten wire is 0.19 mm thick (see for specifications Table 2.1). Exposure time of 40 ms.

Table 2.1: Specifications of the tungsten wire 2000919636

Dia 121.20 mg

Type HW61L/l

Lot G1411

Nw 358.2 g

Q’ty 590 m

Intensity 2560.7 Nmm⁻²

In 120.300 mg

Out 120.590 mg

Qc 28286

Date 2014-10-14

alternative: coating of Cu in paint (Soromap AF2 racing)

One idea was to paint green peas with "Soromap AF2 racing". This paint has a high copper (Cu) content according to the data sheet [Soromap]. This suggestion was not followed because of the disadvantage of not tracking the rotation of the tracer. Moreover, the amount of copper in the paint would not be more visible than the tungsten wire inside the grain.

12

(27)

2.2. Experimental set-up

Figure 2.5: Box with 10 cm width and a 40° slope with green peas inside the x-ray machine.

2.2 Experimental set-up

The device used in the laboratory provides horizontal and vertical views of the experiment, as in [Smi+18], similar to the system used in [Hu+05].

box, slope, lifting gate with rope

The experiment set-up consisted of 3D printed boxes with a slope inside and a removable wall (lifting gate). All parts were designed with software [Blender].

The first slope was 3D printed to 40°. This angle was determined following our assumption that under 40° nothing would happen in the experiments. This assumption was based on the warning from NVE [NVE] about landslides on slopes above 25° for particles with fluid. The first box was designed to be 10 cm wide (Figure 2.5). A second box was designed and 3D printed with 5 cm width (Figure 2.6).

When the x-ray machine is closed and turned on, the rope is hanging outside to be pulled after the filming is started from the computer. The rope and the door of the x-ray machine are seen in Figure 2.7.

2.3 Object Tracking

CamShift (continuously adaptive mean-shift) tracking was chosen to track the tracer. The CamShift allows to track the movement of an object that changes size from frame to frame in a video. The object can change in size as it moves closer to or further away from the camera or as it rotates. First, the feature distribution to represent an object (e.g. color, texture) is chosen, as well as a search window on the initial frame.

The CamShift function from OpenCV.js version 4.2.0 [OpenCV.js] was used with a tracking algorithm adapted from the tutorial [OpenCVCamShift]. In the mentioned tutorial, an image is converted from RGBA (red-green-blue-alpha)

(28)

2. Method

Figure 2.6: Box with 5 cm width and a 15° slope with green peas inside the x-ray machine.

Figure 2.7: Outside the x-ray machine, the rope to pull the lifting gate and start the slide.

14

(29)

2.4. Optical Flow to HSV (hue-saturation-value) colour space. Then, hue, saturation and value are used to qualify the object to be tracked.

Instead of HSV (hue-saturation-value) colour space, in a grayscale colour space delivered by the x-ray, only the feature V (value), or the pixel intensity, is available. Therefore, only V (value), or the pixel intensity of a grayscale image from the x-ray, is the feature to track.

The background in the x-ray image from the experiments is close to white in intensity. The tracers made of tungsten appear in darkest gray (close to black).

When there is good contrast between tracers and particles, a masking based on pixel intensity suffices to track the tracer.

In the video from the x-ray experiments, the challenge with CamShift algorithm was that the trackbox is dislocated to far-away points with dark shadows. The trackbox misses the tracer and sticks to some darker spots as the video runs, during the movement of the peas. The trackbox ends up very often on the border of the box in the top view. In the side view the trackbox wides up to englobe several green peas, because they appear dark, in similar intensity to the tungsten wire tracer. The walls of the box are almost as dark as the tungsten wire tracer. The CamShift is distracted by far-away points with similar pixel intensity since the algorithm allows for change in size and rotation of the tracked object.

To overcome this issue in the top view video, a solution was to reduce the size of the video frames removing the box walls from the region of interest to be tracked. This resulted in correct tracking the tracer.

2.4 Optical Flow

Optical Flow based on OpenCV.js ([OpenCVOpticalFlow]) with dense optical flow was performed on the videos of the experiments.

Lucas-Kanade method computes optical flow for a sparse feature set (corners detected using Shi-Tomasi algorithm). If the corner detection could detect only the tracers, the method would be more successful. This requires first a better preprocessing of the frames. Shi-Tomasi algorithm is based on Sobel operators [BK08].

Dense optical flow is a method where we associate some kind of velocity with each pixel in the frame or some displacement that represents the distance a pixel has moved between the previous frame and the current frame [BK08].

(30)

(31)

CHAPTER 3 Results

3.1 Experimental results

In this chapter the results of green peas sliding down a slope inside the boxes are presented. Tracking and optical flow algorithms are simulated with videos from the x-ray measurements.

The first experiments were run with 59 frames per second and 16.95 ms in a similar experimental set-up as in Figures 3.1 and 3.2. See Appendix A for publishing of raw data.

Figures 3.1 and 3.2 show some frames from the video of the experiment run on 13 December 2019. Figure 3.1 displays three frames of the top view from the box with one tracer. Figure 3.2 presents the corresponding frames in the side view of the box. On frame number 00574 (first images on top and side views, on both figures), the geen peas and the tracer are beginning to slide.

The tracer is visible on these first frames for both views. After some frames, the tracer disappears from the images and stops outside the image. In the top view (Figure 3.1), the bottom shows a dark shadow due to the box wall. In the side view (Figure 3.2), similar shadows are seen of the bottom of the box. The conclusion was that the grains were sliding too fast.

In Figures 3.3, and 3.4, some frames of the top and side views of the experiment are displayed, when the inclination was reduced to 15°. This was an attempt to reduce the speed of the grains. Using a lower angle, the tracer does not disappear completly as in Figures 3.2 and 3.1. Here, when we use 141 frames per second and 7.09 ms exposure time, the tracer is blurred in the images. The contrast between grains and tungsten wire is low, the tracking algorithm loses the tracer.

3.2 Tracking grains

The implementation of the CamShift allows opening a video and choosing an initial tracking window by clicking down, dragging, releasing on the first frame of the chosen video. The tracking window (or tracking box) englobes the object to be tracked, here the tracer. Three images appear on the screen after choosing a video file (from left to right): first a plotted image (canvas) of the first frame, second an image to plot the video frames (as canvas) and display the tracking window as the video is run, and third a video html. The first image, located above videoInput inscription, is used to check the pixel intensities and coordinates of the pixels in the first frame, and to select the tracking window

(32)

3. Results

(a) 00574. (b) 00598. (c) 00600.

Figure 3.1: Top view of slide of green peas with one tracer tested in the x-ray machine, from 13 December 2019. The W wire is 0.19 mm thick. The images are captured at 155 frames per second, with exposure time of 6.45 ms, 80 kV, 5 mA, and a 2x2 pixel binning. The box is 10 cm wide and the inclination is 40°.

(a) 00574. (b) 00598. (c) 00600.

Figure 3.2: Side view of slide of green peas with one tracer tested in the x-ray machine, from 13 December 2019. The tungsten wire is 0.19 mm thick. The images are captured at 155 frames per second, with exposure time of 6.45 ms, 80 kV, 5 mA, and a 2x2 pixel binning. The box is 10 cm wide and the inclination is 40°.

18

(33)

3.2. Tracking grains

(a) 01147. (b) 01170. (c) 01173.

(d) 01178. (e) 01179. (f) 01180.

Figure 3.3: Top view of slide of green peas with one tracer tested in the x-ray machine, from 18 December 2019. The tungsten wire is 0.19 mm thick. The images are captured at 141 frames per second, with exposure time of 7.09 ms, 70 kV, 5.7 mA, and a 2x2 pixel binning. The box is 10 cm wide and the inclination is 15°.

(34)

3. Results

(a) 01147. (b) 01170. (c) 01173.

(d) 01178. (e) 01179. (f) 01181.

Figure 3.4: Side view of slide of green peas with one tracer tested in the x-ray machine, from 18 December 2019. The tungsten wire is 0.19 mm thick. The images are captured at 141 frames per second, with exposure time of 7.09 ms, 64 kV, 5.7 mA, and a 2x2 pixel binning. The box is 10 cm wide and the inclination is 15°.

20

(35)

3.2. Tracking grains

Figure 3.5: Partial program window of tracking application processing experiments from 03 January 2020, top view. The images were captured at 190 frames per second, with exposure time of 5.26 ms, 80 kV, 5 mA, and a 4x4 pixel binning. After 0.15 s.

(seen as a green box in Figure 3.5, and subsequent Figures 3.6 to 3.10). Then, some options are available under the videoInput in order to mask out intensities in the grayscale that are not to be tracked. These intensities to be masked should be the higher intensities close to white¹ and all light gray intensities that do not correspond to the tracer.

It was also implemented the selection of a subwindow of the video. Then, only part of the frame is searched by the algorithm. This is a solution to remove the box walls. Such artifice works in the top view of the box. It removes dark areas that have similar intensity as the tracer. In Figure 3.5, after 0.15 s, the tracer is being followed by the red rectangle that englobes the tungsten tracer.

The masking of pixels according to intensity in grayscale reduces the tracked window from the initial green box in the initial frame kept on the left canvas (Figures 3.5 to 3.10). In Figures 3.5 to 3.10, the red square moves and rotates with the tracer.

After the whole video is run in tracking and the button Stop turns into Start again, the results of the rotation of the tracking box and the displacement of the centroid of the tracking box with respect to the time are plotted. These plots are displayed under the video html object (the third column in the html page application). Here the results of these plots are Figures 3.11, 3.12, and 3.13.

The movement seems to start after 0.4 s.

Figure 3.14 shows the failure of the side view tracking due to lack of contrast between grains of green peas and tungsten wire in the tracer. This is the screenshot of the program running after 0.11 s. The duration of the videos

1(in 8-bit grayscale, white is 255)

(36)

3. Results

(in top and side view) is 1 s. In the side view, there are more grains and they are concentrated in a row in the width, making the image darker. It becomes more difficult to mask with respect to pixel intensity. The algorithm finds again the tracer when the grains roll apart, dispersed in the length of the box, in Figure 3.15 by the end of the video of 1 s. The results for rotation and displacement are not reliable because of the observed behaviour in the beginning, in Figure 3.14, when the tracer is not tracked appropriately. The centre position and the rotation were wrong in Figure 3.14. These experiments show that the rolling down a slope of 15° takes less than 0.5 s.

3.3 Optical flow

Same video as used in Figures 3.5 to 3.10 for the top view of the experiments is used for the dense optical flow in OpenCV.js. The results are plotted in Figures 3.16 to 3.23.

22

(37)

3.3. Optical flow

(38)

3. Results

24

(39)

3.3. Optical flow

Figure 3.11: Rotation with respect to time for the tracking box. Tracking application processing experiments from 03 January 2020, top view. The images were captured at 190 frames per second, with exposure time of 5.26 ms, 80 kV, 5 mA, and a 4x4 pixel binning.

(40)

3. Results

Figure 3.12: Displacement in horizontal direction in pixels with respect to time for the tracking box. Tracking application processing experiments from 03 January 2020, top view. The images were captured at 190 frames per second, with exposure time of 5.26 ms, 80 kV, 5 mA, and a 4x4 pixel binning.

26

(41)

3.3. Optical flow

Figure 3.13: Displacement in verical direction in pixels with respect to time for the tracking box. Tracking application processing experiments from 03 January 2020, top view. The images were captured at 190 frames per second, with exposure time of 5.26 ms, 80 kV, 5 mA, and a 4x4 pixel binning.

Figure 3.14: Partial program window of tracking application processing experiments from 03 January 2020, side view. The images were captured at 190 frames per second, with exposure time of 5.26 ms, 80 kV, 5 mA, and a 4x4 pixel binning. After 0.11 s.

(42)

3. Results

Figure 3.15: Partial program window of tracking application processing experiments from 03 January 2020, side view. The images were captured at 190 frames per second, with exposure time of 5.26 ms, 80 kV, 5 mA, and a 4x4 pixel binning. After 1 s, finished.

Figure 3.16: Partial program window of dense optical flow application processing experiments from 03 January 2020, top view. The images were captured at 190 frames per second, with exposure time of 5.26 ms, 80 kV, 5 mA, and a 4x4 pixel binning. After 0.12 s.

28

(43)

3.3. Optical flow

(44)

3. Results

30

(45)

3.3. Optical flow

(46)

3. Results

32

(47)

CHAPTER 4 Summary and future work

Lack of contrast between the glass marbles and grains, and the tracer (tungsten wire) was a challenge when processing the images from the experiments to simulate landslides. The first effort in this work was to define the materials for the granular material and compare the absorption for x-rays with the material of the tracer (tungsten). The observations in the laboratory showed that glass marbles were not suitable to be used as granular material for the experiments with tungsten wires as tracer. Inserting tungsten wire inside grains, like green peas, resulted in better contrast in the x-ray measurements.

The first box to be the container was designed with 10 cm width and the first slope was designed to be 40°. The slope was reduced to 15°, because without water the grains roll down and the movement is fast. A second box was 3D printed with 5 cm width and the experiments were performed with an inclination of 15°.

Initially, the highest amount of pixels with lowest amount of frames per second (and highest exposure time for each frame) was the input given to the x-ray machine. This led to disappearance of the tracer during the sliding of grains. The grains rolled too fast, and the exposure time was too high.

When the frames per second increased and the exposure time decreased, the quality of the images improved and the tracers were visible in every frame.

Then, the tracer could be tracked in the frames with the CamShift tracking implemented for a limited amount of grains. In the width (5 cm), in the side view of the box, it is still challenging to mask the pixel intensities of the grains and track the tungsten wire tracer. Dense optical flow can show the velocities of the pixels in colours.

4.1 future work

The contrast between tracer and the particles of the granular material could be increased. This would allow the experiments with more particles. This is achieved by increasing the thickness of the tungsten wire inside the tracers.

Related to the tracking algorithm, one possible improvement to apply the CamShift with grayscale images is to preprocess the digital image to work with image gradients, edge detection instead [Mer15; Raf18]. It may be possible to reach a binarisation of the images where the tungsten tracer is visible and a dark shadow of green peas and box walls disappear. These resulting images should be implemented as input to the CamShift tracking algorithm. The velocities are

(48)

4. Summary and future work

still to be calculated from the displacements, calibrated and plotted in metres (instead of pixels) per second.

With respect to the optical flow algorithm, dense optical flow, can be further explored.

34

(49)

Appendices

(50)

(51)

APPENDIX A

Code and raw data used

The codes used and information about raw data are published on https://github.uio.no/anacos/xraytrc

(52)

(53)

Bibliography

[97] ASTM E1441-97: Standard for Computed Tomography (CT) Imaging. American Society for Testing and

Materials: West Conshohocken, PA, 1997.

[AF72] Alonso, M. and Finn, E.Física um curso universitário. Editora Edgard Blücher Ltda, 1972.

[AT01] Aranson, I. S. and Tsimring, L. S. “Continuum description of avalanches in granular media”. eng. In:

Physical review. E, Statistical, nonlinear, and soft matter physicsvol. 64, no. 2 Pt 1 (2001), p. 020301.

[Bab+18] Babout, L. et al. “Selection of material for X-ray tomography analysis and DEM simulations: comparison between granular materials of biological and non- biological origins”. In: Granular Matter vol. 20:38 (2018), pp. 1–14.

[BK08] Bradski, G. and Kaehler, A.Learning OpenCV, Com- puter Vision with the OpenCV Library. O’Reilly Media, 2008.

[Blender] blender.https://wwww.blender.org. 2019.

[Cal97] Callister, W. D.Materials science and engineering: an introduction. John Wiley & Sons, Inc., 1997.

[CambridgeDict] Cambridge dictionary.https://dictionary.cambridge.org. 2020.

[Car95] Cartz, L.Nondestructive Testing. ASM International, Materials Park, 1995.

[Chi86] Chiaverini, V.Tecnologia Mecânica. McGraw-Hill Ltda, 1986.

[Doe92] Doering, E. R. “Three-Dimensional Flaw Reconstruc- tion Using a Real-Time X-Ray Imaging System”. PhD thesis. Iowa State University, Ames, IA., 1992.

[Dur00] Duran, J.Sands, Powders, and Grains, An Introduction to the Physics of Granular Materials. Springer-Verlag New York, Inc., 2000.

(54)

Bibliography

[FCN18] Fouilloux, A., Conrado, A., and Nalvarte, G.Python for analyzing and visualizing spatio-temporal data.https:

//annefou.github.io/metos_python/. 2018.

[Fri01] Fritz, H. M. “Lituya Bay case: rockslide impact and wave run-up”. In:Sci Tsunami Hazards vol. 19, no. 1 (2001), pp. 3–22.

[Gli+13] Glimsdal, S. et al. “Dispersion of tsunamis: does it really matter?” In:Natural Hazards and Earth System Sciences vol. 13, no. 6 (2013), p. 1507.

[Gre+07] Green, C. et al. “Novel Application of X-ray Computed Tomography: Determination of Gas/Liquid Contact Area and Liquid Holdup in Structured Packing”. In:

Industrial & Engineering Chemistry Research vol. 46, no. 17 (2007), pp. 5734–5753.

[Hei11] Heindel, T. “A Review of X-Ray Flow Visualization With Applications to Multiphase Flows”. In:Journal of Fluids Engineering vol. 133 (7 2011).

[Hel13] Hellier, C. J.Handbook of Nondestructive Evaluation. McGraw Hill, New York, 2013.

[HGJ08] Heindel, T. J., Gray, J. N., and Jensen, T. C. “An X-Ray System for Visualizing Fluid Flows”. In:Flow Measurement and Instrumentation vol. 19 (2 2008), pp. 67–78.

[Hu+05] Hu, B. et al. “Development of an X-ray computed tomography (CT) system with sparse sources: application to three-phase pipe flow visualization”. In:Experiments in Fluids vol. 39, no. 4 (Oct. 2005), pp. 667–678.

[JFP06] Jop, P., Forterre, Y., and Pouliquen, O. “A constitutive law for dense granular flows”. In:Naturevol. 441 (2006), pp. 727–730.

[JNB96] Jaeger, H., Nagel, S., and Behringer, R. “Granular solids, liquids, and gases”. eng. In:Reviews of Modern Physics vol. 68, no. 4 (1996).

[KA74] Klug, H. P. and Alexander, L. E.X-Ray Diffraction Procedures for Polycristalline and Amorphous Materi- als. John Wiley & Sons, 1974.

[Mer15] Mery, D.Computer Vision for X-Ray Testing. Springer International Publishing, 2015.

[MH10] Morgan, T. B. and Heindel, T. “X-Ray Particle Tracking of Dense Particle Motion in a Vibration- Excited Granular Bed”. In: Digital Repository Iowa State University, 2010.

[Ned92] Nedderman, R. M.Statics and kinematics of granular materials. eng. Cambridge ; New York: Cambridge University Press, 1992.

40

(55)

Bibliography

[NVE] The Norwegian Water Resources and Energy Direc- torate.https://www.nve.no. 2019.

[NVEjordskred] Jordskred og flomskred.https://publikasjoner.nve.no/

faktaark/2013/faktaark2013_05.pdf. 2018.

[OpenCV.js] OpenCV.js.https://docs.opencv.org/4.2.0/. 2019.

[OpenCVCamShift] OpenCV, Meanshift and Camshift.https://docs.opencv.

org/master/df/def/tutorial_js_meanshift.html.

[OpenCVOpticalFlow] OpenCV, Optical Flow.https://docs.opencv.org/4.2.0/

db/d7f/tutorial_js_lucas_kanade.html.

[PPP07] Pedrotti, F. L., Pedrotti, L. M., and Pedrotti, L. S.

Introduction to optics. Upper Saddle River, NJ: Pearson Prentice Hall, 2007.

[Raf18] Rafael C. Gonzalez, R. E. W.Digital Image Processing. Pearson, 2018.

[Rön95] Röntgen, W. C. Eine neue Art von Strahlen: I Mit- teilung. In: Sitzungsbericht der Würzburger Physikal.- Medicin. Gesellschaft. Verlag und Druck der Sta- hel’schen K. Hof- und Universitäts-Buch- und Kun- sthandlung. Würzburg, 1895.

[Smi+18] Smith, L. et al. “X-ray measurements of plunging breaking solitary waves”. In: European Journal of Mechanics / B Fluidsvol. X (2018), pp. XX–XX.

[Soromap] Soromap,Data Sheet, PTFE Self-Polishing Matrix Antifouling AF2 Racing. https://www.soromap.com/

produit/ptfe-self-polishing-antifouling-af2-racing/ptfe- self-polishing-antifouling-af2-racing-xpr82146.html.

2019.

[Vir+15] Viroulet, S. et al. “Tsunami Waves Generated by Cliff Collapse: Comparison Between Experiments and Triphasic Simulations”. eng. In: (2015).

[Wak+18] Waktola, S. et al. “A new data-processing approach to study particle motion using ultrafast X-ray tomography scanner: case study of gravitational mass”. In:

Experiments in Fluidsvol. 59:69 (2018), pp. 1–14.

[XRa19] X-Ray Optics, T. C. for, ed. The Center for X-ray optics, X-Ray Interactions With Matter, The x-ray attenuation length of a solid.http://http://henke.lbl.gov/

optical_constants/atten2.html. 2019.

[ZCG19] Zhang, C. Y., Chen, L., and Gou, R. B. “High-speed vision extraction based on the CamShift algorithm”.

In:Cluster Comput vol. 22 (2019), pp. 555–564.

[Zol14] Zolotoyabko, E.Basic Concepts of X-Ray Diffraction. Wiley-VCH, 2014.

X-ray measurements of granular flows