J. Cent. South Univ. (2019) 26: 938-954

DOI: https://doi.org/10.1007/s11771-019-4062-2

Use of X-ray computed tomography to study structures and particle contacts of granite residual soil

SUN Yin-lei(孙银磊)^{1, 2}, TANG Lian-sheng(汤连生)^{1, 2}

1. School of Earth Sciences and Engineering, Sun Yat-sen University, Guangzhou 510275, China;

2. Guangdong Provincial Key Laboratory of Mineral Resources and Geological Processes,Guangzhou 510275, China

Central South University Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Abstract: A small problem about soil particle regularization and contacts but essential to geotechnical engineering was studied. The soils sourced from Guangzhou and Xiamen were sieved into five different particle scale ranges (d<0.075 mm, 0.075 mm≤d<0.1 mm, 0.1 mm≤d<0.2 mm, 0.2 mm≤d<0.5 mm and 0.5 mm≤d<1.0 mm) to study the structures and particle contacts of granite residual soil. The X-ray micro computed tomography method was used to reconstruct the microstructure of granite residual soil. The particle was identified and regularized using principal component analysis (PCA). The particle contacts and geometrical characteristics in 3D space were analyzed and summarized using statistical analyses. The results demonstrate that the main types of contact among the particles are face-face, face-angle, face-edge, edge-edge, edge-angle and angle-angle contacts for particle sizes less than 0.2 mm. When the particle sizes are greater than 0.2 mm, the contacts are effectively summarized as face-face, face-angle, face-edge, edge-edge, edge-angle, angle-angle, sphere-sphere, sphere-face, sphere-edge and sphere-angle contacts. The differences in porosity among the original sample, reconstructed sample and regularized sample are closely related to the water-swelling and water-disintegrable characteristics of granite residual soil.

Key words: X-ray computed tomography; granite residual soil; reconstruction; regularization; particle contact

Cite this article as: SUN Yin-lei, TANG Lian-sheng. Use of X-ray computed tomography to study structures and particle contacts of granite residual soil [J]. Journal of Central South University, 2019, 26(4): 938–954. DOI: https://doi.org/10.1007/s11771-019-4062-2.

1 Introduction

Granite residual soil, which is composed of dispersive particles that interact with one another in complex manners, is widely distributed in southern China [1]. Because of the water-disintegration and water-swelling characteristics, the particle distribution, mineral composition, morphology, structures and particle contacts are the main elements that affect the fabric and mechanical properties of granite residual soil [2, 3], which are difficult to study at the microscale. Accurate information on the particle structures and contacts among the particles is essential for determining the evolution of micro-mechanics of granite residual soil [4, 5].

As a small but essential problem, soil particle regularization and contacts are more crucial to geotechnical engineering. Few studies have focused on the structures of granite residual soil compared to other soils, e.g., sandy soil, soft soil, and loess [6–9]. ZUO et al [10] applied structural equation modelling (SEM) to investigate the relationship between microstructure and engineering properties. WANG [11] systematically studied the microstructures and pores of granite residual soil and found that edge-face contacts were the major constituent of the soil structure. SHI [12] proposed the probability entropy to describe the microstructural changes in the compaction process. IRFAN [13] proposed a weathering model of granite residual soil to modify the material and mass weathering schemes commonly adopted in Hong Kong to characterize granite residual soil in engineering. HU et al [14] studied the changing rule of the microstructures in different engineering environments. WU [15] analyzed the structures of granite residual soil, which included the particle scale and microstructures, and classified the granite residual soil. TANG et al [16] proposed a brittle-elasto-plastic model from the microscale of granite residual soil based on the accumulation mode. LI et al [17] investigated the granite residual soil with SEM and observed fine granular structures. Because of the limitation of the testing apparatus, studies on the structures of granite residual soil have been restricted at the 2D scale to microscopes and SEM. Few studies have reported on the particle contacts of granite residual soil.

Accurate characterizations of the soil structures from 2D to 3D were essentially impossible by thin-sectioning methods and microscopic imaging technology [18]. Advancements in technology have facilitated the quantification of soil characteristics, e.g., the distributions of pores and aggregates. The X-ray computed tomography (CT) method was successfully applied in the medical field [19], which provided inspiration for the field of geological science [20, 21]. As a non-destructive technique, the X-ray CT method offers an effective means of visualizing the spatial shapes of soil components, soil behaviours and processes. BECKERS et al [22] studied capillarity, considering the particles as spheres. Within the past ten years, the X-ray micro computed tomography (μ-CT) method has been widely applied to study particle shapes and pore characteristics in many fields [23, 24]. However, no previous studies have applied the X-ray CT method to granite residual soil, which is widely distributed in southern China.

In this paper, granite residual soils from Guangzhou and Xiamen were sieved into five different ranges of particle scale (d<0.075 mm, 0.075 mm≤d<0.1 mm, 0.1 mm≤d<0.2 mm,0.2 mm≤d<0.5 mm and 0.5 mm≤d<1.0 mm) and reconstituted into samples with homogeneous particles. The X-ray μ-CT method was applied to reconstruct the microstructure of granite residual soil. The particle identification and regularization methods were introduced based on principal component analysis (PCA), and the microstructures and contacts among the particles were analyzed and summarized by determining the locations of neighbouring particles.

2 Materials and methods

2.1 Materials

Two types of granite residual soils were obtained from Zengcheng, Guangzhou, and Haicang District, Xiamen, China (Figures 1(a) and (b), respectively). The representative bulk samples of granite residual soils in this study were oven dried at 105–110 °C to a constant mass, allowed to cool to the ambient laboratory temperature (25°C), disaggregated and sieved to obtain the fraction that passed through a 2 mm sieve. The dispersed size distributions of the soil particles are shown in Figure 1.

2.2 Sample preparation

Considering the experimental resolution of the CT equipment, after the sand, silt and clay particles were mixed together, the sand particles were clearly observed at a certain resolution, whereas the silt and clay particles were not clearly detected at this resolution. Therefore, five diameter size ranges of samples were studied: d<0.075 mm, 0.075 mm≤d< 0.1 mm, 0.1 mm≤d<0.2 mm, 0.2 mm≤d<0.5 mm and 0.5 mm≤d<1.0 mm. A small amount of deionized water was added to the samples to prepare the micro-scanning specimen (the soil particles remained dispersive but were aggregated by the cementation). The homogeneous particles were hierarchically compacted in the compaction test apparatus. Then, a PEEK tube was inserted into the compacted sample (Figure 2) and frozen for 1 min with liquid nitrogen. Next, the samples were immediately moved to a freeze-drier for 24 h (with a vacuum degree of over 90% and temperature under –45°C).

Figure 1 Size distributions of soil particles that passed through 2 mm sieve:(The red and blue numbers represent the mass percentage of granite residual soil from Guangzhou and Xiamen, respectively)

Figure 2 Sample preparation process and sizes of micro-scanning specimen (For particle sizes below 0.1 mm, the diameter of the PEEK tube was 1 mm; for other particle sizes, the diameter of the PEEK tube was 3 mm)

2.3 CT scanning and image reconstruction

The μ-CT scanning experiments were completed with X-ray imaging and biomedical application beam line (BL13W1) at the Shanghai Synchrotron Radiation Facility (SSRF) in China. The photon energy was set to 19.5 keV, and the exposure time was 0.5 s. The resolutions for scanning the sand, silt and clay samples were 3.25, 3.25 and 0.325 μm, respectively. The distances between the sample and detector were 10 and 20 cm for the resolutions of 0.325 and 3.25 μm, respectively. The aggregates were held in a PEEK tube, which was fixed on a rotary stage. The sample was rotated from 0° to 180° with intervals of 0.25°, as shown in Figure 3. The obtained raw synchrotron μ-CT (SMT) images must be pre-processed for the phase retrieval and slice reconstruction using the Pitre software, which was supplied by the SSRF [25], as shown in Figure 3. The 3D reconstruction of the sample was performed with the visualization software Avizo (version 8.0, VSG, France) [26].

2.4 Particle regularization

2.4.1 Particle identification

The raw SMT images were imported into the visualization software Avizo (Figure 4(a)) [27]. The anisotropic diffusion filter algorithm was performed to de-noise the SMT images, whereas the boundary geometry of the particle was preserved and the contrast of the particle boundary was enhanced. To conveniently and effectively identify the particles, each voxel, which is a component of the entire particle, was compared as a cube with six face-centred neighbours [27]. Meanwhile, the voxel value was diffusing until the difference did not exceed the limiting threshold value, which was controlled by the parametric adjustment and error analysis. Finally, the image was smoother after the de-noising process, and the particle boundary between adjacent particles or different media was sharper (Figure 4(b)).

Figure 3 Schematic illustration of an axial micro computed tomography system (μCT) and image pre-processing

Figure 4 Steps of particle identification process:

To distinguish the particles and surrounding medium (air), the SMT image should be segmented while creating a binary image with the interactive threshold adjustment function of Avizo. The voxel values of different media were assigned as 0 (air) and 1 (solid particle). After the de-noising process, the residual micropores and noise fragments between the particles and different media were further eliminated in morphology operations. Without affecting the particle surface, the Fill Holes function of Avizo was applied to fill the micropores [26]. The noise fragments were removed with the open command, which was programmed with MATLAB (R2013a). After a series of treatments, the binary images show the particles, surrounding medium, and contacts among the particles to the scale of the image resolution (Figure 4(c)). To label each particle, the air medium that surrounded solid particles was removed using the watershed, distance transform and numerical reconstruction algorithms of Avizo. Then, each solid particle was labelled with a different colour from 1 to the total number of particles (Figure 4(d)). To assess the treating precision, the image was masked and compared with the binary image (Figure 4(c)), which accurately represented the morphology of each particle [27]. The labelled particle had identical voxel values, and every voxel occupied one cubical “point” in the 3D space. Experimental experience has indicated that the 3D voxels better compose the particle morphology for high-resolution or high-quality SMT images.

2.4.2 Particle parameters

The 3D reconstruction and regularization of particles are critical for studying the structures and particle contacts of granite residual soil, which can improve the mechanical properties of the soil. As the essential particle parameters, the centre, sizes and orientation of the particles were accurately quantified using PCA, which was proposed by ARCHIBALD et al [28]. All voxel information of the labelled particle was imported into MATLAB as a 3D matrix. With the loop iteration, the spatial locations of the particle voxels were collected and stored in an n×3 matrix, where n is the total number of voxels for a certain particle.

The particle was composed of numerous cubic voxels (the voxel values were identical), and the cubes were directly arranged face-face, edge-edge and angle-angle. For a random cube not on the particle surface, 6, 8 and 12 possible cubes absolutely contacted the faces, angles and edges of the objective cube, respectively [6]. The spatial locations of all particle voxels that were circumambient to each particle voxel were defined and could be searched to determine what, if anything, occupied them. After any type (face-face, edge-edge, or angle-angle) was not explored during the loop iteration, the cube was assessed as the situation on the particle surface. The volume was the sum of cubic voxels with identical values [29]. The locations of the particle centre in the x, y and z directions were calculated by summing the voxel locations in each direction.

                         (1)

                         (2)

                          (3)

where c_j, c_k and c_i are the global centres of mass of each particle f(i, j, k) in the x, y and z directions, respectively; V is the total voxel number of the particle.

The orientation and sizes of the particle play important roles in the regularization. To regularize the particle, three typical lengths of the 3D particle were determined using the PCA method, namely, the long, intermediate and short axes, which were orthogonal to one another and passed through the centre of mass of the particle. First, the long axis of the particle was determined with the voxel- exploring method from 0 to n. The extreme line segment between two given particles was determined, with the line segment passing through the particle centre. The long axes of a particle are the sum of the voxel cubes, which were distributed along the line segment. Second, the voxel cubes, which were distributed in the section perpendicular to the long axis and crossed the particle centre, were explored, and the extreme distance between two voxel cubes (the line segment that passes through the particle centre) was determined as the intermediate axis. Third, the voxel cubes, which were distributed in the section perpendicular to the long and intermediate axes and crossed the particle centre, were explored, and the extreme distance between two voxel cubes (the line segment that passed through the particle centre) was determined as the short axis. Finally, the long, intermediate, and short axes of a particle were determined as the length, width and thickness, respectively, of the cuboid-shaped regularization for the width- thickness ratio above 1.5. The orientation of the cuboid particle is the direction of the long axes, and the included angle (α) was determined using the angle (β=180°–α) between the normal vector of the long and intermediate axes and the normal vector of the x and y axes (Figure 5(a)). However, for width-thickness ratios near 1.0, the clump particle was regularized as a sphere, and the diameter was the average of the long, intermediate, and short lengths (Figure 5(b)).

2.5 Particle contact determination

To accurately determine the type of contact among the particles, the 3D space was divided into eight quadrants with the Cartesian coordinate system. With the key coordinates and mass centre of cuboid and spherical particles, the command codes of the judging principle were developed using MATLAB, and the principles for assessing contacts among the particles are provided in Appendix.

3 Results and discussion

3.1 Image processing

Overall, 720 slices were obtained for each sample, and encouraging results were obtained for the majority of the slice images. A few original CT soil slice images exhibited poor contrast, as shown in Figure 6. After the pre-processes of phase retrieval and slice reconstruction, the images were clear enough to reconstruct the 3D structures of the samples. The slices of ten samples to reconstruct the 3D images in our proposal were of high quality.

Figure 5 Regularization process:(a_i =max(i^rot)–min(i^rot), b_j=max(j^rot)–min(j^rot), c_k=max(k^rot)–min(k^rot), where i^rot, j^rot and k^rot are 1D arrays to provide the particle’s voxel coordinates)

Figure 6 Image pre-processing:

3.2 Image reconstruction

Four 1-mm- and six 3-mm-diameter specimens of cylindrical granite residual soil were investigated with two spatial resolutions of 0.625 μm (particle sizes less than 0.1 mm) and 3.25 μm (particle sizes greater than or equal to 0.1 mm). The volume was visualized and analysed using the Avizo software package. Ten typical 2D slices were extracted from the 3D volumes and are presented in Figure 7. Small cubic volumes were extracted from the 3D volumes to clearly observe the morphology of particles less than 0.2 mm in size. The 2D and 3D images show the internal structures of the grains of the granite residual soil (dark blue) and gas (black).

Figure 7 Typical 2D slices extracted from 3D volumes (Grains of granite residual soil appear in dark blue, and black voids correspond to a less dense medium that is filled with gas. S: Sphere; A: Angle; F: Face)

Figure 7 illustrates the pores based on the 2D and 3D images. The high resolution helped us clearly observe the micropores and microparticles, which were significantly amplified. The Guangzhou soil had larger pores than the Xiamen soil for the same particle range. Compared to the particle sizes above 0.2 mm, the images of particles less than 0.2 mm in size illustrate that the solid particles were more densely packed and composed of sheet and plate structures. Figures 7(a2), (A2), (b2) and (B2) show that the main contact types among the particles were face-face, face-angle, face-edge, edge-edge, edge-angle and angle-angle contacts.

In addition, Figures 7(a₁), (A₁), (b₁) and (B₁) show that the systems were mixed with few spherical particles, and contacts between sheet and spherical particles were rare. The 2D and 3D images illustrate that the internal particles were composed of concave-convex clump and spherical structures when the particle size was larger than 0.2 mm. Figures 7(c₂), (C₂), (d₂) and (D₂) show that the samples were composed of the ten contact types. The sphere-sphere and sphere-face contacts are shown in Figure 7(e₁), the face-angle contact is shown in Fig. 7(E₁), and the face-face contact is shown in Fig. 7(d₁). The reconstruction results of X-ray μ-CT demonstrate the correct comparison with the SEM method in Figure 8.

3.3 Image regularization

In this study, the granite residual soils were rigorously sieved into different particle groups, and the internal structures and pore distributions of the samples were considered relatively uniform statistically. The particle structures and contacts were analysed using the regularized 3D reconstructions of the soil samples. For particle sizes greater than 0.2 mm, the regularized volumes (300×300×300 pixels) were sufficiently clear to use and analyse the internal structures and particle contacts. However, for particle sizes less than 0.2 mm, the representative cubic volumes (50×50× 50 pixels) of the regularized samples were collected to analyse the internal structures and particle contacts (Figure 9). Based on the method presented in the last section, the irregular particles in the granite residual soil were regularized as spherical or cuboid particles (Figure 9).

Figure 9 shows that cuboid particles dominated in the regularized samples for particle sizes less than 0.2 mm. In particularly, for particle sizes less than 0.075 mm, the contacts between cuboid particles are more common than the contacts between cuboid and spherical particles, e.g., the angle-angle, angle-edge, angle-face, face-face, face- edge, angle-edge and edge-edge contacts were abundant, whereas the sphere-sphere, sphere-face and sphere-edge contacts were rare because clay particles dominated the soil samples. The Xiamen samples had more spherical particles than the Guangzhou samples. The number of spherical particles increased when the particle size increased above 0.075 mm. Although most particles remained cuboid, the number of contacts between spherical and cuboid particles increased. When the particle size was greater than 0.2 mm, the majority of the particles in the granite residual soil were spheres. The contact distributions of the samples are shown in Figure 10. In both the Guangzhou and Xiamen samples, the major components of the granite residual soil (d<0.1 mm) were cubic particles, and the main contacts among the particles were angle-angle (A-A), angle-edge (A-E), angle-face (A-F), edge-edge (E-E), edge-face (E-F) and face-face (F-F). Because there were spherical particles, the samples had a small number of sphere-sphere, sphere-face, sphere-edge, and sphere-angle contacts. More spherical particles appeared in the Xiamen samples than in the Guangzhou samples.

Figure 8 SEM results of granite residual soil

Figure 9 Particle regularization of granite residual soil and main particle contacts of sample

However, for particle diameters larger than 0.1 mm, more spherical particles made more sphere-sphere, sphere-face, sphere-edge, and sphere-angle contacts than other types, particularly sphere-face contacts. With more widely distributed original particles (a width-thickness ratio greater than 1.5), the contacts between cubic particles (particularly angle-face and edge-edge types) were also the major parts in the samples. For particle sizes above 0.5 mm, the distribution of spherical contacts (sphere-sphere, sphere-edge, sphere-angle, and sphere-face) dominated the samples.

3.4 Porosity

The porosities of the original, reconstructed and regularized samples were tested with Mercury intrusion porosimetry (MIP), Avizo and MATLAB, respectively, and the results are shown in Figure 11. A small difference appeared between the original and reconstructed samples of Guangzhou soil. The granite residual soil composed of kaolinite was well water-swelled (Figure 12), which made the pore channel shrink, particularly for particle sizes below 0.1 mm. This expansibility caused the reconstruction to have a smaller porosity than the original sample. Meanwhile, considerable differences were observed between the reconstructed and regularized samples, and this trend increased with increases in the particle size. This phenomenon may be a consequence of more new fragments that formed because of the detachment along the convex parts of the particle that separates from the parent particles, which resulted from the water disintegration of granite residual soil (Figure 12).

During the regularization process, the extreme length of the original particle was applied as the length of the regular particle, and more spaces were occupied by the exceeding parts of the regularization, particularly for the particles with a width-thickness ratio greater than 1.5. However, more space of the pore channels is occupied if more particle fragments separate from the maternal particles. Consequently, regularized samples are significantly less porous than the original and reconstructed samples. (In this paper, we mainly study the structures and particle contacts; the changes before and after regularization will be investigated in future work.) The differences among the original, reconstructed, and regularized samples of Xiamen soil were larger than those of Guangdong soil, which indicates that the soil from Xiamen was more water-disintegrable than the soil from Guangzhou.

Figure 10 Distribution of particle contacts:

Figure 11 Porosities of original, reconstructed and regularized samples:

Figure 12 Changes before and after wetting:

3.5 Particle distribution

Figures 13 and 14 show the particle distributions of Guangzhou and Xiamen granite residual soil. In this work, the original soil particles were homogeneous to reconstitute the samples. After the reconstitution process, the soil particles were easily water-swelled and water-disintegrable, as noted in the previous section. The water- disintegrable characteristics made parts of the particles disintegrate into more fragments. In particular, for the soil with particles whose diameters were larger than 0.1 mm, smaller particles were clearly observed, e.g., Figure 13(a) shows that the dispersive particles of 0–0.5 mm in size were dominant in the reconstituted sample.

The distributions of reconstructed samples obtained with the non-destructive X-ray CT method accurately indicate the physical situations. However, the regularization and reconstruction had different distributions. Figures 13(b)–(e) show that the particle size of the regularization exceeded the maximum value (original value) because of the volume changes of the regularized particle. In Figure 13(c), 24% of the particles had diameters larger than 0.2 mm. The main reason is that the particles with sizes of 0.1–0.2 mm were tighter than the other particles, and small changes in volume made the regularized length larger than 0.2 mm. Different results were obtained for the Xiamen granite residual soil, as shown in Figure 14. Larger percentages of the particles that exceeded the original particle diameter can be observed in Figures 14(b)–(e), which explains why the Xiamen granite residual soil has stronger water- expansibility than the Guangzhou soil.

Figure 13 Particle distribution of different results of Guangzhou granite residual soil (Because of the homogeneity of the original particles, the original value was 100%):

4 Conclusions

This paper presented a method of 3D SMT image analysis to quantify the particle morphology and particle contacts. The mass centres, length and orientations of the individual particles were determined based on PCA. The long, intermediate and short axes of a particle were determined as the length, width and thickness, respectively, of the cuboid-shaped regularization for the width- thickness ratio above 1.5. When the width-thickness ratio of the particle was near 1.0, the clump particle was regularized as a sphere, and the diameter is the average of the long, intermediate, and short axes.

The main types of contacts among the granite residual soil particles are face-face, face-angle, face-edge, edge-edge, edge-angle and angle-angle contacts for particle sizes less than 0.2 mm. When the particle sizes are greater than 0.2 mm, the main contacts are face-face, face-angle, face-edge, edge-edge, edge-angle, angle-angle, sphere-sphere, sphere-face, sphere-edge and sphere-angle contacts. The X-ray μ-CT results are consistent with the SEM results.

Figure 14 Particle distributions of Xiamen granite residual soil (Because of homogeneity of the original particles, original value was 100%)

The water-swelling characteristics of granite residual soil make the pore channel shrink, and the reconstructions are less porous than the original sample, particularly for particles less than 0.1 mm. During the regularization process, the extreme length is applied in the cubic particle, and more spaces are occupied by the exceeded parts of the regularization, particularly for the particles with width-thickness ratios above 1.5. More spaces of the pore channels are occupied, which makes the regularization significantly less porous than the original and reconstructed samples. The differences among the original, reconstructed and regularized samples of Xiamen soil were larger than those of Guangdong soil, which indicates that the soil from Xiamen is more water-disintegrable than the soil from Guangzhou.

Appendix

1. Angle-angle contact (Figure 15(a))

1) Point C of particle 1 is determined as the origin of the Cartesian coordinates;

2) The distance from each point of particle 1 to point A₁ is larger than the distance from point C to A₁; the distance from each point of particle 2 to point C is larger than the distance from point A₁ to C;

3) The vector through point A₁ and perpendicular to face ABCD does not pass through face ABCD; point A₁ is located in quadrant II;

4) The vector through point O₁ and perpendicular to face ABCD does not pass through face ABCD; point O₁ is located in quadrant I, II, III, or IV.

2. Angle-edge contact (Figure 15(b))

1) Point C of particle 1 is determined as the origin of the Cartesian coordinates;

2) The distance from each point of particle 2 to edge CD is larger than the distance from point A₁ to edge CD, and the distance from each point of particle 1 to point A₁ is larger than the distance from edge CD to point A₁;

3) The vector through point O and perpendicular to face ABCD does not pass through face ABCD, and point A₁ is located in quadrant III;

4) The vector through point O₁ and perpendicular to face ABCD does not pass through face A₁B₁C₁D₁.

3. Angle-face contact (Figure 15(c))

1) Point C of particle 1 is determined as the origin of the Cartesian coordinates;

2) The distance from each point of particle 2 to face ABCD is larger than the distance from point A₁ to face ABCD;

3) The vector through point A₁ and perpendicular to face ABCD passes through face ABCD, and point A₁ is located in Quadrant IV;

4) The vector through point O₁ and perpendicular to face ABCD passes through face ABCD.

4. Edge-edge contact (Figure 15(d))

1) Point C of particle 1 is determined as the origin of the Cartesian coordinates;

2) The projection lines of edges CD and A₁D₁ are intersecting;

3) The distance from each point of Particle 2 to edge CD is larger than the distance from edge A₁D₁ to edge CD; the distance from each point of particle 1 to edge A₁D₁ is larger than the distance from edge CD to edge A₁D₁;

4) Points A₁ and D₁ are located in quadrants IV and III, respectively.

5. Edge-face contact (Figure 15(e))

1) Point C of particle 1 is determined as the origin of the Cartesian coordinates;

2) The distance from each point of particle 2 to face ABCD is not smaller than the distance from edge A₁D₁ to face ABCD;

3) Edge A₁D₁ is parallel to face ABCD;

4) Points A₁ and D₁ are located in quadrant IV; mass centre O is located in quadrant VII;

5) The vector through point O₁ and perpendicular to face ABCD passes through face ABCD.

6. Face-face contact (Figure 15(f))

1) Point C of particle 1 is determined as the origin of the Cartesian coordinates;

2) Mass centre O of particle 1 is located in quadrant VII;

3) The normal vector of plane ABCD through point O passes through face A₁B₁C₁D₁, whereas the normal vector of plane A₁B₁C₁D₁ through point O₁ passes through face ABCD;

4) The normal vector of face ABCD is parallel to the normal vector of face A₁B₁C₁D₁.

7. Sphere-angle contact (Figure 15(g))

1) Point C of particle 1 is determined as the origin of the Cartesian coordinates;

2) The distance from each point of particle 1 to the mass centre of particle 2 is larger than the distance from point C to the mass centre of Particle 2;

3) The mass centre of particle 2 is located in quadrant II.

8. Sphere-edge contact (Figure 15(h))

1) Point C of particle 1 is determined as the origin of the Cartesian coordinates;

2) The distance from each point of particle 1 to the mass centre of particle 2 is larger than the distance from edge CD to the mass centre of particle 2;

3) The mass centre of particle 2 is not located in quadrant IV.

Figure 15 Judging principle of contacts among particles

9. Sphere-face contact (Figure 15(i))

1) Point C of particle 1 is determined as the origin of the Cartesian coordinates;

2) The distance from each point of particle 1 to the mass centre of particle 2 is larger than the distance from face ABCD to the mass centre of particle 2;

3) The mass centre of particle 2 is located in quadrant IV.

10. Sphere-sphere contact (Figure 15(j))

The neighbouring particles are spheres.

Acknowledgement

The authors thank the Beam Line (BL13W1) of the Shanghai Synchrotron Radiation Facility (SSRF) for supporting the use of the radiation source.

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(Edited by YANG Hua)

中文导读

基于微观层析成像技术的花岗岩残积土颗粒接触方式研究

摘要：颗粒的接触方式以及颗粒的规则化处理对于研究岩土力学性质非常关键。本次研究中采集到了广州及福建地区的花岗岩残积土，在实验室条件下将其分别筛分成五种不同的粒组(d<0.075 mm,0.075 mm≤d<0.1 mm, 0.1 mm≤d<0.2 mm, 0.2 mm≤d<0.5 mm and 0.5 mm≤d<1.0 mm)，基于微观层析成像技术研究颗粒之间的接触方式。利用主成分分析法对组成颗粒的体素进行识别和搜索，确定颗粒的中心、方向及尺寸；基于笛卡尔空间坐标系，根据相邻颗粒关键位置的空间坐标，对其接触方式进行判定。结果显示，当花岗岩残积土颗粒粒径小于0.2 mm时，颗粒接触方式主要包含面-面、面-角、面-棱、棱-棱、棱-角、角-角接触；当颗粒粒径大于0.2 mm时，颗粒接触方式主要包含面-面、面-角、面-棱、棱-棱、棱-角、角-角、球-球、球-面、球-棱、球-角接触。土样的原始孔隙率、重建后的孔隙率及规则化后的孔隙率三者之间存在差异，这主要与花岗岩残积土遇水膨胀及崩解特性有关。

关键词：微观层析成像技术；花岗岩残积土；颗粒重建；颗粒规则化；颗粒接触

Foundation item: Projects(41572277, 41877229) supported by the National Natural Science Foundation of China; Project(2015A030313118) supported by the Natural Science Foundation of Guangdong Province, China;Project(201607010023) supported by the Science and Technology Program of Guangzhou, China

Received date: 2017-07-17; Accepted date: 2018-01-22

Corresponding author: TANG Lian-sheng, PhD, Professor; E-mail: eestls@mail.sysu.edu.cn; ORCID: 0000-0003-3635-7776