This study was supported by the General Research Fund No. CityU 11213517 from the Research Grant Council of the Hong Kong SAR, Research Grant No. 51779213 from the National Science Foundation of China, and the BL13W beamline of the Shanghai Synchrotron Radiation Facility (SSRF).

1. Designing the experiment well in advance
<ol>
	<li>Determine test material, particle size, sample size and sample initial porosity. 
	NOTE: Leighton Buzzard sand with a diameter of 0.15~0.30 mm and a sample size of 8 x 16 mm (Diameter x Height) is used as an example to demonstrate the protocol of this study. Other sands such as Fujian sand, Houston Sand, Ottawa sand and Caicos ooids, etc. and similar sample sizes can also be used.</li>
	<li>Choose an appropriate detector (Figure 1<...

High-spatial resolution X-ray micro-CT and advanced image processing and analysis techniques have enabled the experimental investigation of the mechanical behavior of granular soils under shear at multi-scale levels (i.e., at macro-scale, meso-scale and grain-scale levels). However, CT image-based meso- and grain-scale investigations require the acquisition of high-spatial resolution CT images of soil samples during loading. The most challenging aspect of this process is perhaps the fabrication of a miniature triaxial lo...

It is widely recognized that the macro-scale mechanical properties of granular soil, such as stiffness, shear strength and permeability, are critical to many geotechnical structures, for example, foundations, slopes and rock-fill dams. For many years, on-site tests and conventional laboratory tests (e.g., one-dimensional compression tests, triaxial compression tests and permeability tests) have been used to evaluate these properties in different soils. Codes and standards for testing soil mechanical properties have also been developed for engineering purposes. While these macro-scale mechanical properties have been intensively studied, the grain-scale mechanical behavior (e.g., particle kinematics, contact interaction and strain localization) that governs these properties has attracted much less attention from engineers and researchers. One reason is the lack of effective experimental methods available to explore the grain-scale mechanical behavior of soils.
Until now, most of the understanding of the grain-scale mechanical behavior of granular soils has come from discrete element modeling1 (DEM), because of its ability to extract particle-scale information (e.g., particle kinematics and particle contact forces). In earlier studies of using DEM techniques to model granular soil mechanical behaviors, each individual particle was simply represented by a single circle or sphere in the model. The use of such over-simplified particle shapes has led to the over-rotation of particles and thereby a lower peak strength behavior2. To achieve a better modeling performance, many investigators have used a rolling resistance model3,4,5,6 or irregular particle shapes7,8,9,10,11,12 in their DEM simulations. As a result, a more realistic understanding of particle kinematic behavior has been acquired. Aside from particle kinematics, DEM has been increasingly used to investigate grain contact interaction and to develop theoretical models. However, because of the requirement to reproduce real particle shapes and the use of sophisticated contact models, DEM requires extremely high computational capability in the modeling of granular soils with irregular shapes.
Recently, the development of optical equipment and imaging techniques (e.g., the microscope, laser-aided tomography, X-ray computed tomography (CT) and X-ray micro-tomography (&#956;CT)) has provided many opportunities for experimental examination of the grain-scale mechanical behavior of granular soils. Via acquisition and analysis of soil sample images before and after triaxial testing, such equipment and techniques have been utilized in the investigation of soil microstructures13,14,15,16,17,18,19. More recently, in situ tests with X-ray CT or &#956;CT have been increasingly used to investigate the evolution of void ratio20, strain distribution21,22,23,24, particle movement25,26,27,28, inter-particle contact29,30,31 and particle crushing32 of granular soils. Here, &#8220;in situ&#8221; implies X-ray scanning conducted at the same time as loading. In contrast to general X-ray scanning, in situ X-ray scanning tests require a specially fabricated loading apparatus to deliver stresses to soil samples. With the combined use of the loading apparatus and X-ray CT or &#956;CT device, CT images of the samples at different loading stages of the tests can be acquired non-destructively. Based on these CT images, particle-scale observations of granular soil behavior can be acquired. These CT image-based particle-level observations are extremely helpful to verify numerical findings and to gain novel insights into the grain-scale mechanical behavior of granular soils.
This article aims to share the details of how an X-ray in situ scanning test of a soil sample can be carried out, using an exemplary experiment that observes particle kinematics, strain localization and inter-particle contact evolution within a soil sample. The results show that X-ray in situ scanning tests have a great potential to explore the grain-level behavior of granular soils. The protocol covers the choice of X-ray &#956;CT device and the preparation of a miniature triaxial loading apparatus, and detailed procedures to carry out the test are provided. In addition, the technical steps for using image processing and analysis to quantify the particle kinematics (i.e., particle translation and particle rotation), strain localization, and inter-particle contact evolution (i.e., contact gain, contact loss and contact movement) of the soil are described.

<table>
	<tbody>
		<tr>
			<td>Confining pressure offering device</td>
			<td>GDS</td>
			<td>STDDPC</td>
			<td></td>
		</tr>
		<tr>
			<td>De-aired water</td>
			<td>N/A</td>
			<td>N/A</td>
			<td>Water de-aired in the lab</td>
		</tr>
		<tr>
			<td>Leighton Buzzard sand</td>
			<td>Artificial Grass Cambridge</td>
			<td>Drained Industrial Sand 25 kg</td>
			<td>Can be replaced with different soils</td>
		</tr>
		<tr>
			<td>Miniature triaxial loading device</td>
			<td>N/A</td>
			<td>N/A</td>
			<td>The miniature loading device is specially fabricated by the authors</td>
		</tr>
		<tr>
			<td>Silicon grease</td>
			<td>RS company</td>
			<td>RS 494-124</td>
			<td></td>
		</tr>
		<tr>
			<td>Synchrotron radiation X-ray micro CT setup</td>
			<td>Shanghai Synchrotron Radiation Facility Center (SSRF)</td>
			<td>13W1</td>
			<td>The triaxial testing is carried out at the BL13W beam-line of the SSRF</td>
		</tr>
		<tr>
			<td>Vacuum pump</td>
			<td>Hong Kong Labware Co., ltd.</td>
			<td>Rocker 300</td>
			<td></td>
		</tr>
	</tbody>
</table>

visualization of failure and the associated grain-scale mechanical behavior of granular soils under shear using synchrotron x-ray micro-tomography

The rapid development of X-ray imaging techniques with image processing and analysis skills has enabled the acquisition of CT images of granular soils with high-spatial resolutions. Based on such CT images, grain-scale mechanical behavior such as particle kinematics (i.e., particle translations and particle rotations), strain localization and inter-particle contact evolution of granular soils can be quantitatively investigated. However, this is inaccessible using conventional experimental methods. This study demonstrates the exploration of the grain-scale mechanical behavior of a granular soil sample under triaxial compression using synchrotron X-ray micro-tomography (&#956;CT). With this method, a specially fabricated miniature loading apparatus is used to apply confining and axial stresses to the sample during the triaxial test. The apparatus is fitted into a synchrotron X-ray tomography setup so that high-spatial resolution CT images of the sample can be collected at different loading stages of the test without any disturbance to the sample. With the capability of extracting information at the macro scale (e.g., sample boundary stresses and strains from the triaxial apparatus setup) and the grain scale (e.g., grain movements and contact interactions from the CT images), this procedure provides an effective methodology to investigate the multi-scale mechanics of granular soils.

Figure 5 depicts the particle kinematics results of a Leighton Buzzard sand (LBS) sample at a 2D slice during two typical shear increments, I and II. Most of the particles are successfully tracked and their translations and rotations are quantified following the above protocol. During the first shear increment, neither particle displacements nor particle rotations show clear localization. However, a localized band is developed in both the particle displacement map and particle rotation map d...

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Visualization of Failure and the Associated Grain-Scale Mechanical Behavior of Granular Soils under Shear using Synchrotron X-Ray Micro-Tomography

The protocol describes procedures to acquire high-spatial resolution computed tomography (CT) images of a granular soil during triaxial compression, and to apply image processing techniques to these CT images to explore the grain-scale mechanical behavior of the soil under loading.

The rapid development of X-ray imaging techniques with image processing and analysis skills has enabled the acquisition of CT images of granular soils ...

This protocol allows to acquire particle scale data of granular soils using x-ray micro-tomography and develop a understanding of the micro-scale processes and mechanisms underlying the microscopic behavior of granular materials. The main advantage of this technique is that it provides a full access to the particle scale information of granular soils including particle morphology, microstructure, breakage, displacement, and rotation within the deformation of granular materials. This method can also be applied to the investigation of other types of stone-based natural or synthetic materials such as rocks, soil-rock mixture, concrete, ceramics, asphalt and even polymer composites.Begin with design of the experiment well in advance as described in the text protocol. Determine test material, particle size, sample size, and sample initial porosity. To prepare a soil sample on the board, first add a small amount of silicone grease around the lateral surface of the top end of the base plate.Then place a porous stone on its upper surface. Put a membrane around the lateral surface of the top end. Add a small amount of silicone grease on the contact surfaces between the two parts of the sample maker and place the sample maker on the base plate to allow the membrane to pass through it.Lock the sample maker. Create suction inside the sample maker through its nozzle using a vacuum pump. Fix the membrane to the lateral surface of its upper end.Ensure that the membrane is attached to the inner surface of the sample maker. Drop the test granular material from a certain height into the sample maker using a funnel until it is completely filled. The upper surface of the soil sample should be the same level as the upper edge of the sample maker.Place another porous stone on top of the soil sample. Apply some silicone grease around the lateral surface of a stainless steel cushion plate and place it on top of the porous stone. Remove the top side of the membrane from the sample maker and fix it to the cushion plate.Remove the suction inside the sample maker nozzle and create suction inside the valve on the base plate. Finally, remove the sample maker. A miniature dry sample is produced.Now, fix the confining cell on the base plate and fix the chamber top plate on the top of the confining cell. Affix the rest of the loading apparatus on the chamber top plate. Add a constant confining pressure of 25 kilopascals to the sample and remove the suction inside the sample.Gradually increase the confining pressure to a predetermined value using the confining pressure offering device. To scan a section of the sample, set the computed tomography or CT-scanner to image capture mode. Then, start the rotation stage to rotate the entire apparatus across 180 degrees at a predetermined constant rotation rate to capture CT projections of the sample at different angles.For a high-spatial resolution CT scanner, a full scan of the sample usually requires the sample to be scanned at several different heights. Apply an axial load on the sample with a constant loading rate. Here, a loading rate of 0.2 percent per minute is used.Users can set a different loading rate according to the experiment requirement. Pause the axial loading at a pre-determined axial strain. Wait until the measured axial force reaches a steady value, and carry out the next scan.Repeat these steps until the end of loading. We construct CT slices of the sample based on the CT projections after phase retrieval using the PITRE software. Load the projections into PITRE from the menu load image.Click the icon projection sinogram. Enter relevant parameters in the appeared window and click single to reconstruct a CT slice. Implement image filtering on the CT slices.An anisotropic diffusion filter is used to perform image filtering. Now, perform image binarization on the filtered CT slices. To do so, implement the image binarization by applying an intensity value threshold to the CT slices.This value is determined according to the intensity histogram of the CT slices using Otsu's method. Separate individual particles from the binarized CT slices using a marker-based watershed algorithm and store the results in a 3-D labeled image. Validate the results by comparing the calculated particle size distribution from the CT image to those from a mechanical sieving test.A matlab script is used to extract particle properties, including particle volume, particle surface area, particle orientation, and particle centroid coordinates. Intrinsic matlab functions are used to acquire these properties for each particle. Extract contact foxholes from the binarized CT slices by implementation of a logical and operation between the binary image of the CT slices and the binary image of watershed lines acquired from the implementation of the marker-based watershed algorithm.To quantify the strain field of the sample, use a grid-based method to calculate the strain field during any two consecutive scans, based on the particle translation and particle rotation. Analyze inter-particle contact evolution of the sample. Based on the extracted contact foxholes, the labeled images of particles, and the particle tracking results, analyze the branch vector orientation of the lost contacts and the gained contacts within the sample during each share increment.The stress-strain curve and a 2-D slice of a Leighton Buzzard sand sample under triaxial compression are shown. Displayed here are particle kinematics results at the 2-D slice during the test. Most of the particles are successfully tracked and their translations and rotations are quantified.A localized band is developed in both the particle displacement map and particle rotation map at the end of the test. Shown here is the normalized orientation frequency of branch vectors of gained contacts and lost contacts in the sample during the test. The lost contacts exhibit a clear directional preference towards the minor principle stress direction during the test.Calibration of the rotation axis as detailed in the text protocol is important because the successful reconstruction of CT slice not only relies on the appropriate positioning of the rotation stage. To avoid any ionized radiation to human bodies from the x-ray source, one needs to make sure all doors and windows of the scanning room are properly closed before each scan. Following a similar procedure, institute testing with x-ray diffraction or scattering can be performed.This provides a tool for measurement of inter-particle contact forces and their propagation within the forming granular materials. The acquired experimental data can be used for the development of advanced constitutive models of sand, considering their grain-scale mechanical behaviors, and for numerical modeling of sands under loading.

Visualization of Failure and the Associated Grain-Scale Mechanical Behavior of Granular Soils under Shear using Synchrotron X-Ray Micro-Tomography

Abstract