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Three-dimensional microstructure characterization of loess based on a serial sectioning technique
Engineering Geology 261 (2019) 105265
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Three-dimensional microstructure characterization of loess based on a serial sectioning technique
T
⁎
Tingting Weia,b, Wen Fana,b,c, , Ningyu Yua,b, Ya-ni Weia,b a
School of Geology Engineering and Geomatics, Chang'an University, No.126 Yanta Road, Xi'an 710054, Shaanxi, China Key Laboratory of Western China's Mineral Resources and Geological Engineering, Ministry of Education, No.126 Yanta Road, Xi'an 710054, Shaanxi, China c China Electronic Research Institute of Engineering Investigations and Design, Xi'an 710054, Shaanxi, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Loess Three-dimensional microstructure Serial sectioning technique Quantitative analysis
Loess has a loose metastable structure that easily collapses during wetting and loading. Microstructure analysis is essential for a better understanding of the engineering properties of loess; however, two-dimensional (2D) methods cannot fully demonstrate the geometric microstructural characteristics of loess particles. The threedimensional (3D) loess microstructure is reconstructed based on an improved serial sectioning technique. Point, edge and face contacts are observed from the 3D reconstructed microstructure of natural loess. The 3D microstructural features of particles and pores are also quantitatively studied by analyzing statistical parameters, including the equivalent diameter, sphericity, aspect ratio and orientation index. The particle size distribution (> 10 μm) obtained from the microstructural analysis is validated via a comparison with the results of a laser particle size analysis. In total, 92% of the particles have a sphericity that lies between 0.5 and 0.9, and the aspect ratio of 93% of the particles is between 0.3 and 0.7. Additionally, 67% of the particles are oriented from 0° to 45°, whereas approximately 64% of the pores (> 2 μm) are oriented from 45° to 90°. Each 3D parameter has a unique value and can reflect the true spatial morphology of the particles, avoiding the influence of the observation angle and section. The 3D characterization of the loess microstructure will provide insights into the underlying collapse mechanisms and could provide realistic 3D parameters for use in numerical simulations.
1. Introduction Loess is Quaternary aeolian silt that has a global distribution, especially in semi-arid and arid regions. Loess mantles about 631,000 km2 of China, and the greatest bulk accumulation of loess on earth is the well-known Loess Plateau (Derbyshire, 2001). The metastable structure of loess is characterized by high porosity, meta-stable packing and weak cementation (Assallay et al., 1997; Yuan and Wang, 2009; Juang et al., 2019). These typical structures are susceptible to water (Juang et al., 2019; Li et al., 2016); hence, frequent wettinginduced landslides, collapses, debris flows and other geological disasters have occurred on the Loess Plateau in China, and they have killed many people, destroyed many buildings and buried thousands of acres of farmland (Duan et al., 2016; Wei et al., 2017). The mechanical behavior of loess is often controlled by the microstructures (Jiang et al., 2014). Some researchers have claimed that loess collapsibility is dominated by its porosity, cementation bond, particle contact relations and pore forms (Fang et al., 2013; Liu et al., 2016; Luo et al., 2018). The cementation, contact and orientation of particles play a vital role in
⁎
loess strength (Jiang et al., 2014; Li et al., 2019a; Matalucci et al., 1970). Therefore, accurate loess microstructure interpretations are critical for understanding loess collapsibility and other engineering behaviors. Two-dimensional (2D) image observation is the most direct and earliest method in the study of loess microstructure. As early as the middle of the last century, low precision optical microscopy was used to qualitatively observe large pores and particles. For example, the macropores of 11 Malan loess samples were found to be irregular in shape and variable in size in different locations (Zhu, 1963). Since the 1970s, high-precision scanning electron microscopy (SEM) has been used to observe the microstructure, reveal the collapsible mechanism and analyze the macromechanical behaviors of loess. Fang et al. (2013) suggested four types of particle contact relations, i.e., direct point contact, direct face contact, indirect point contact and indirect face contact. Jiang et al. (2014) proposed that the cementation bonds play important roles in loess strength and that the breakage of these bonds is influenced by stress path and confining pressure. Liu et al. (2016) combined X-ray diffraction with SEM to observe loess microstructure on
Corresponding author at: School of Geology Engineering and Geomatics, Chang'an University, No.126 Yanta Road, Xi'an 710054, Shaanxi, China. E-mail addresses: [email protected] (T. Wei), [email protected] (W. Fan).
https://doi.org/10.1016/j.enggeo.2019.105265 Received 10 February 2018; Received in revised form 13 August 2019; Accepted 13 August 2019 Available online 14 August 2019 0013-7952/ © 2019 Published by Elsevier B.V.
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including the density (1.82 g/cm3), water content (15.3%), liquid limit (33.7%), plastic limit (16.8%) and saturation (0.58). The loess particle size distribution obtained by a laser particle analyzer is also described in Table 1. The mineral composition of the loess is shown in Table 2.
the Loess Plateau and elaborated that the wetting-induced collapse was primarily attributed to the abundance of weakly cemented, unsaturated, porous pure clay and clay-silt mixture aggregates. 2D qualitative observations or quantitative analyses have greatly contributed to the study of the loess microstructure, especially the contact relationship between particles, cementation, and elemental compositions at different loess skeleton locations. However, 2D image results often give different results for pores and particles when observed from different angles and sections (Zhao and Wang, 2015). Since the 1980s, mercury intrusion porosimetry (MIP) has been applied to porosity and pore size distribution measurements. Naturally collapsed and consolidated loess does not have pore spaces larger than 3.5 μm in diameter, whereas in laboratory consolidated samples, 15% of the pore volume presents pore spaces larger than 3.5 μm in diameter (Rendell, 1988). Loading and wetting mainly constrict pores larger than 100 μm under a net stress of 110 kPa, which results in a more uniform pore size distribution and a less pronounced hysteresis (Ng et al., 2016). MIP can reflect the pore size and volume variations of loess during loading or wetting, although realistically, the pore size results obtained by MIP do not reflect the true distribution (Lange et al., 1994) and cannot visualize the pore structure. With the development of observation technology, 3D image acquisition has been made possible. The most commonly used technology is computed tomography (CT), which has been applied to obtain the 3D internal structure of geotechnical materials. The CT scanning technique can detect spatial geometric characteristics, such as the size, orientation and channel of pores and the morphology, size, and orientation of particles. The 3D microstructure can reflect the true morphologies of particles and pores. Zhao et al. (2017) studied the relationship between the aggregate microstructure and its role in the vegetative restoration of loess by CT with a resolution of 3.25 μm and showed that the fractal dimension was more sensitive for monitoring the quality of soil structure. Li et al. (2018) investigated the 3D pore structure of Malan loess at a resolution of 59 μm by quantifying the geometric parameters, and the results revealed a strong anisotropy. Despite these efforts, our current understanding of the underlying collapse mechanisms of loess remains controversial or incomplete, and studies on loess engineering properties from 3D microstructure are rare. The objective of this paper is to reconstruct and quantify the 3D loess microstructure based on improved resin impregnation and serial sectioning techniques. An experimental program was successfully developed that included sample preparation, serial image acquisition, image processing and 3D microstructure analysis. Qualitative description and quantitative analysis were carried out to characterize the 3D microstructural features of loess. The characterization of 3D loess microstructure provides insights into the underlying collapse mechanisms and could provide realistic parameters for numerical simulation and theoretical modeling.
3. 2D image acquisition based on serial sectioning 3.1. Sample preparation Loess samples with each side measuring 4 cm were dried by the freeze-drying method. The pore size of loess is much smaller than that of sand and ranges from several nanometers to hundreds of microns. Even resin with relatively low viscosity has difficulty entering loess pores. Thus, acetone, an organic solvent, was used to dissolve the resin and keep the mixture flowing. The loess pores were filled with an epoxy resin mixture that does not modify the soil microstructure (Fitzpatrick, 1984; Liu et al., 2016). A vacuum resin-injection apparatus (Fig. 2b) was assembled to remove the air from the pores and infuse the prepared epoxy resin mixture into the pores. The sample was placed inside a clean cup and transferred into the vacuum chamber (Fig. 2b), which maintained a vacuum pressure of 0.09 MPa. Then, the valve of the split funnel was opened to drip the mixture solution into the cup drop by drop until the liquid level exceeded the sample top surface by at least 1 cm (Liu et al., 2016). Following this step, the sample cup was removed and sealed with plastic film to prevent acetone volatilization, thus ensuring that the epoxy resin mixture sufficiently fills the pores. After a week, the sealed sample cup was opened to let the acetone volatilize, and approximately one month later, the resin reached the required hardness. 3.2. Grinding and polishing The serial sectioning technique was successfully used in the 3D reconstruction of Ottawa sand (Lu, 2010). During the experimental process, the loss of particles depends on the removed thickness, wheel speed and abrasiveness. Silt is the main particle in loess, the experimental procedures and parameters in sand are not applicable to loess. Therefore, the technique was modified through a series of trial tests to ensure the accurate application in loess. A combination of grinding and polishing (MultiPrep™ Precision Polishing System in Fig. 2d) was used to grind and polish a specimen to have an approximate mirror surface (Fig. 2c). Grinding by emery paper was initially performed to remove large bulges on the sample surface. Then, the sample was polished by different specification abrasives in turn. Next polishing began with the removal of the surface texture generated during the previous polishing. A high wheel speed will damage the sample surface and lead to some small particle losses, and a low wheel speed means a long polishing time. Finally, the most suitable wheel speed was determined to be 200 r/min.
2. Study area and sample 3.3. Image acquisition The south Jingyang Plateau is located on the right bank of the Jinghe River in Jingyang County, Shaanxi Province, China (Fig. 1a). The total area of the south Jingyang Plateau is approximately 70 km2, and the altitude is from 420 m to 490 m, with terrain higher in the east and lower in the west. Since 1976, > 80 landslides have been induced, killing a total of 31 people and burying thousands of acres of farmland, especially in the village of Zhai-tou (Duan et al., 2016). The sliding surface of the Zhai-tou landslide is located at a depth of approximately 20 m. Therefore, the loess sample in this study was taken 2 m inside the back wall of the Zhai-tou landslide at a depth of 20 m. Fig. 1b shows the stratigraphic profile of the sampling site. To reduce the disturbance to loess samples, samples were manually collected as a large cube volume of 40 × 40 × 40 cm using a sharp cutter and small shovel and then tightly encased in 5 layers of plastic wrap to avoid water loss. Table 1 shows the physical properties,
The images were captured with an optical microscope manufactured by Leica (Fig. 2e) with a size of 1100 μm × 814 μm and a resolution of 0.424 μm/pixel. By looping the polishing and image acquisition, 250 2D serial images were generated (Fig. 2f). 3.4. Removal thickness The removal thickness should consider the loess particle size to avoid particle loss and retain as many small particles as possible. Considering the image precision of 0.424 μm and the detectable object of 2 μm, 5 min of polishing was set as the standard, and a removal thickness of 1.2 μm is the average value of all layers. Each thickness was measured by calculating the altitude of the shallow pyramid-shaped pits before and after repolishing (Fig. 2g-2i). 2
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Fig. 1. Loess Plateau of north China and location of the sampling site (Fig. 1a after Derbyshire, 2001 and Luo et al., 2018). (a) Location of the study site on the Loess Plateau, and (b) stratigraphic profile of the sampling site.
Fig. 3b shows particles larger than 2 μm in yellow, with dark yellow representing independent particles and light yellow representing particles that cannot be segmented into individual particles accurately.
4. 3D microstructure reconstruction 4.1. Aligning The serial images present translation and rotation of up to 20 pixels and 2°, respectively. The alignment is based on the position of the same object in any two adjacent images. The manual method was chosen first to adjust the large translation and rotation, and the automatic aligning method was then used to optimize the results.
4.3. Representative elementary volume analysis (REV) The computation duration and complexity are dependent on the size of the reconstructed volume. Therefore, it is necessary to extract a REV that is small enough to ensure computational efficiency and large enough to represent the properties of loess. To ensure the representativeness of the REV, the effect on porosity was analyzed at thirteen different size subvolumes, which were concentrically extracted from the same stack of images. The average porosity was computed from three subvolumes of each size. The variance was used here for estimating the discreteness and variability. The formula of variance is as follows:
4.2. Segmentation 4.2.1. Image preprocessing and binarization Colour images were first converted to gray-level images (Fig. 3a). The nonlocal means filter, which determines the new value for the current pixel by comparing the neighborhoods of all pixels in a given image with the neighbours of the current pixel, was applied to eliminate noise and smooth the images (while preserving the edges and details). Then, the global threshold method and visual recognition were adopted, in which the gray images were binarized by selecting an appropriate threshold to separate the pores and particles, with particles in yellow and pores in black (Fig. 3b).
S2 =
1 n
n
∑1 −
_ (x i − x )2 ,
(1)
n
where x = ∑1 x i / n ; S2 is the variance, with a greater value corresponding to greater data variability; n represents the number of subvolumes in each size; and xi is the porosity of subvolumes. The porosity is strongly affected by the subvolume size, and the variance decreases as the subvolume size increases (Fig. 4). The loess sample porosity obtained from physical tests is 42%. For the smallest subvolume (2003 voxels), the average porosity is 46%, and the variance is 0.95%, which is because a small subvolume exactly covers several large pores, resulting in greater porosity. At 7003 voxels, the porosity tends to be stable (40%) and a variance of 0.018% is reasonable; thus, a subvolume of 7003 voxels is large enough to be unaffected by the size and location of the subvolume. Therefore, the cube with a side length of 700 pixels is an optimal REV in this study and used for geometric
4.2.2. Particle and pore segmentation Pore segmentation was performed via watershed transformation. Some particles were connected with others via narrow bridges between particles. An erosion algorithm was proposed to eliminate the narrow bridges between particles and some small unrecognizable spots, and dilation was used to compensate for the body shrinkage caused by erosion. The precision of the images captured by the optical microscope is 0.424 μm, which limits the minimum detectable objects to 2 μm. Table 1 Physical properties of loess. Density ρ/(g/cm3)
Water content ω/%
Porosity n/%
Saturation Sr
Liquid limit WL/%
Plastic limit WP/%
Grain-size distribution (%) Clay (< 2 μm) Silt (2–60 μm) Sand (> 60 μm)
1.82
15.3
0.42
0.58
33.7
16.8
3
14
81
5
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Table 2 Mineral composition of loess. Quartz
Illite
Plagioclase
Calcspar
Chlorite
Potassium feldspar
Dolomite
Hornblende
37.0%
21.5%
14.1%
13.8%
5.2%
3.8%
3.4%
1.2%
Fig. 2. Experimental process. (a) Sample preparation and resin-injection, (b) serial sectioning procedures, and (c) removal thickness determination.
global form of particles, and it ranges from 0 to1. A maximum value of 1 indicates a perfect spherical particle, and as the value decreases, the particle becomes irregular or ellipsoidal.
computations in further quantitative analyses. 4.4. Quantitative parameters (1) The 3D porosity is defined as the total number of pore voxels within the volume divided by the total number of voxels in the volume. (2) The equivalent diameter (EqD) is related to the object volume and is expressed as follows:
EqD =
3
6⁎Volume3d π
S=
Asp A
3
=
36πV 2 , A
(3)
where V and A are the volume and surface area of the particle, respectively, and Aspis the surface area of a sphere whose volume is equal to that of the particle. (4) The aspect ratio (As) measures the difference between the short axis and long axis of particles (aspect ratio = short axis/long axis). (5) The object orientation is determined according to two angles in space, where φ [0°-90°] is the angle between the horizontal plane and
(2)
where Volume3d is the volume of the object. (3) The sphericity (S) is an overall shape parameter, referred to as a
Fig. 3. (a) Gray micrograph of loess, (b) binary image of pores and particles, with independent particles in dark yellow, indivisible particles in light yellow, and pores in black, and (c) reconstructed 3D loess particles. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) 4
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Fig. 4. REV analysis using three stacks of loess sample images.
the particle long axis (pore channel) and θ [0°-180°] is the direction of the long axis (pore channel) projected onto the horizontal plane.
5.2. Pore size distribution Pore size distribution (PSD) is one of the main factors that affects permeability and can indicate complex pore structural characteristics in far more detail than porosity alone. The PSD curves of loess as detected by MIP and serial sectioning are shown in Fig. 6. The MIP curve shows peaks of 2% and 10.2% at 0.026 μm and 4.5 μm, respectively. The serial sectioning curve shows a single peak of 12% at 13.5 μm, with values ranging from 2 μm to 40 μm. MIP systematically underestimates pore sizes due to the “ink bottle effect” (Lange et al., 1994), although this effect can be estimated from the MIP test when decreasing the pressure. Objects < 2 μm have a smaller gray level and are easily mistaken for pores, thus, the pore size is overestimated to a certain extent. Thus, the true PSD lies between the curves of MIP and serial sectioning.
5. Results 5.1. Particle size distribution Fig. 5 presents the percent passing curves of the particle size distribution from 10 μm to 50 μm as obtained by a laser particle analyzer and serial sectioning technique. All particles with a diameter of > 10 μm were clearly identified and accurately extracted in the 3D reconstructed microstructure. The following quantitative characterization of loess particles is based on this size group. Particles of 2 μm to 5 μm mainly occur in association with clay, and skeletal effects are not obvious in loess structural systems (Li et al., 2019b). Some of the particles from 5 μm to 10 μm are embedded in aggregates, which makes it impossible to accurately identify their boundaries. Because the reconstruction volume is small, fewer particles larger than 50 μm exist in the reconstruction range. Thus, the range of 10 μm - 50 μm is validated via comparison with the results of laser particle size analysis.
5.3. Particle morphology The particle morphology can reflect the loess formation mode and depositional history and influence the physical and mechanical properties. For example, the morphology defines the arrangement and
Fig. 5. Particle size distribution. 5
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Fig. 6. Pore size distribution.
Fig. 7. Particle morphology. (a) Sphericity and aspect ratio distributions, (b) sphericity vs. equivalent diameter, and (c) visualization of several typical loess particles.
to discuss the relationship between the particle size and the orientation angle. The contribution of each diameter group to each angle group is consistent with that of all particles in each angle group. Concluding that the orientation angle of natural loess particle is irrelevant to its diameter.
thereby affects the intergranular friction and movement mode of the particles (Cox and Budhu, 2008). When the sphericity is > 0.9, the aspect ratio is close to 0.8 and the particles are close to spherical (Fig. 7c). When the sphericity is < 0.5, the particles are obviously long strips (Fig. 7c). Fig. 7a shows that 92% of the loess particles have sphericity that lies in the range between 0.5 and 0.9, and the aspect ratio of 93% particles is between 0.3 and 0.7. For particles with the same equivalent diameter, they have different morphologies, the difference between the maximum and minimum sphericity is approximately 0.5 (Fig. 7b). Overall, the sphericities decrease as the equivalent diameter increases, showing that the smaller the particle diameter is, the greater the probability of approaching a sphere.
5.5. Pore orientation Pore orientation is determined by the channel that connects two adjacent pore bodies. Fig. 8c shows the pore orientation of natural loess, and approximately 64% of the pores are oriented from 45° to 90° (φ). At the beginning of sedimentation, a loess particle falls freely until it contacts another particle, thus forming a remarkable vertical pore structure (Assallay et al., 1997). With an increase in the overlying soil layer, the loess structure is compacted, the pores are still mainly in directions > 45° (φ). Because the vertical stress is uniform, the pore distribution in the horizontal direction is relatively random (Fig. 8c). The permeability test shows that the loess sample permeability in this study is greater in the vertical direction (2.8 × 10−5 cm/s) than in the horizontal direction (1.6 × 10−5 cm/s). We therefore conclude that the pore orientation plays a primary role in controlling the flow of liquid.
5.4. Particle orientation The particle orientation can not only reflect the current arrangement state but can also influence the slipping between particles. During loading, the particle arrangement and preferred orientation will change, which affects the internal fraction angle and subsequently affects the shear strength (Matalucci et al., 1970). The rose diagram of the particle orientation (Fig. 8b) shows that 67% of the particles are oriented between 0° and 45° (φ). During the process of loess deposition, the particles were distributed randomly in the horizontal direction (Fig. 8b), under the influence of gravity and overburden pressure, the angle φ of the particles gradually decreased. The distribution of particles with different diameters in each angle group (Fig. 8a) was plotted 6
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Fig. 8. Orientation. (a) Distribution of particles with different diameters in each angle group, (b) and (c) rose diagrams of particles and pores, respectively. φ is the angle between the horizontal plane and the particle long axis (pore channel), and θ is the direction of the long axis (pore channel) projected onto the horizontal plane. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
6. Discussion
could provide realistic skeletons for use in 3D numerical modeling (Fig. 9f).
6.1. Qualitative analysis of particles 6.1.2. Particle contact The contact relation is an important factor for determining whether particles will easily slip over each other. Four typical particle contact relations are obtained from 2D images according to the contact area and clay cementation thickness between particles: direct point and face contact and indirect point and face contact, (Fang et al., 2013). Point contact is rare in this sample, as observed from the 3D reconstructed microstructure. In addition, there is not only one contact relation between two particles, such as the case for particles in group b in Fig. 9, in which direct point contact coexists with indirect face contact. The connection between particles is a dynamic and balanced process.
6.1.1. Particle association Three skeleton units appear in the natural loess sample: individual silt or sand, clay-coated silt and aggregate (Fig. 9e - 9f). Clay acts as the main cement connecting all the skeleton particles together to form a stable open structure. A minority of the silt and sand particles occur individually. Most silt particles were coated by clay platelets or calcium carbonate to form clay-coated silts (Li et al., 2016, 2019a). Most aggregates consist of both silt and clay particles, while some are composed of purely clay particles (Liu et al., 2016). The size of aggregates varies from tens to hundreds of micrometers. The 3D particle associations
Fig. 9. Particle contact relation and association. (a-d) Four typical contact relations in loess, (e) basic association units of loess and (f) corresponding 3D structures. 7
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Unstable point contact, which is sensitive to force because of the small contact area, may be common in the initial stage of microstructure formation (Assallay et al., 1997). As the overlying stress increases, the number of point contacts gradually decreases. Edge contact and face contact relations are widely observed in this sample (Fig. 9a-9c). When subjected to force, direct face contact is relatively stable among these contact relations, and point and edge contacts are easier to dislocate to cause compression. Particles with indirect contact are typically thickly coated with clay at the point of contact, thus making them sensitive to water, and once the stress exceeds the residual strength of the cement wetted in water, the structure will collapse. The contact relations obtained from the 3D reconstructed microstructure can reflect the real contacts between particles in space and avoid the influence of the 2D observation angle and section. Based on the contact relation, we can study the displacement, stress state and contact stability of particles under external forces and water to explore the collapsibility and micro-failure mechanisms of loess. 6.2. Advantages of the serial sectioning technique in loess microstructure research In general, different loess microstructures are characterized using different techniques. In this paper, many 3D characteristics of loess can be revealed using the serial sectioning technique. The results based on the serial sectioning technique also have several advantages over those based on the thin-section and SEM methods. Compared with the thin-section method, which can provide 2D section images, the 3D microstructure based on the serial sectioning technique improves the accuracy of microstructure judgments. First, each particle exists in a 3D space and has a definite size, shape and orientation, while the thin-section technique often gives different results for one object if the images are captured from different angles and sections. For example, the 3D volume-based porosity was 40% and close to the porosity measured by the physical method, while the 2D porosity of 250 images varied from 25% to 52% (Fig. 10). The contact relation of particles in group b is indirect face contact, while direct point and indirect face contact are observed in section s1 (b) and s2 (b) respectively (Fig. 9b). Fig. 11 shows a particle characterized by quantitative parameters obtained from the 3D structure and eight thin sections. The orientation of s1 is 59.59°, whereas that of s3 is 153.79° (Fig. 11). The long axis difference between s6 and s4 is 42.64 μm, and the roundness difference between s4 and s8 is 0.34 (Fig. 11). Then, the existence of edge contact has been observed for the first time from the 3D microstructure of loess, which has been mistaken for point contact in the s1 (c) and s2 (c) sections (Fig. 9c). Compared with the SEM method, the serial sectioning technique provides a more effective method to quantitatively study the loess microstructure evaluations during wetting and loading. The silt particles of loess are often bonded to or coated by clay particles (Wei et al., 2019). SEM can be used to examine the skeleton grain shape after removing the attachments from surfaces. However, it is difficult to determine the current orientation and contact relations of loess particles after wetting and loading by SEM. 3D reconstructed microstructure based on serial sectioning can obtain the current orientation and contact relations of particles, providing better technical conditions for studying the loess collapse and compaction progress.
Fig. 10. Porosity of 2D serial images.
For example, accurate quantitative interpretation of loess microstructure during wetting and loading will provide insights into the underlying collapse mechanisms. Cementation bonds stabilize the initial open structure, once the water content and external load exceed the critical value, the bonding strength would fail to support the soil fabric and the fundamental particle rearrangement occurs, transforming the initial stable open structure into a closed structure (Li et al., 2016, 2019b). The particle rearrangement is closely associated with the local porosity, morphology, contact relation and cementation (Liu et al., 2016). Based on these characteristics, the displacement, stress state and contact stability of particles under external load and water can be analyzed to explore the loess collapse mechanism, and along with the analysis of the quantitative parameters, these characteristics can be used to predict the collapse behavior of loess, and determine loess engineering sites that can be pretreated by suitable loading and wetting. Furthermore, microstructure evaluations during loading and wetting can guide compaction work in loess engineering sites. The compression of filling sites is used in many engineering construction sites on the Loess Plateau, such as Yan'an (Li et al., 2014). During the compaction process, the soil particles overcome the resistance between particles, produce displacement, reduce porosity and increase density. The stress state, movement and contact mode among particles during loading and wetting will be studied to determine the contact stability between particles and find the most stable arrangement states under different conditions to guide the compaction work of loess site. In addition, quantitative characterization of 3D loess microstructure could provide realistic parameters for numerical simulations. Porosity, particle size distribution, particle morphology and contact relation obtained by the 3D reconstruction method can be used to set porosity, form clumps and balls, and determine contact and coordination number for 3D modeling.
6.3. Engineering implications Loess is regarded as a problematic soil that raises different engineering problems in urgent need of solutions in engineering practice. The accurate interpretation of loess 3D microstructures can help to deepen the understanding of the behavioral mechanisms associated with different engineering problems. Such understanding is expected to provide suggestions for engineers in the design and construction of buildings and facilities built on loess deposits. 8
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Fig. 11. Quantitative characterization of a loess particle by thin-section and serial sectioning technique.
7. Conclusions
and theoretical modeling. The serial sectioning technique overestimates the pore size and cannot measure pores smaller than 2 μm. This method provides a new approach for pore structure research, and its limitation will be compensated for by improvement in the scanning accuracy. In future work, accurate interpretations of loess 3D microstructures during wetting and loading will also be developed to provide insights into the underlying collapse mechanisms, thereby providing guidance for the pretreatment of engineering sites.
The resin impregnation and serial sectioning techniques have been improved to make them suitable for loess 3D microstructure reconstruction. The particle association and contact of loess are qualitatively analyzed in space. Individual silt or sand, clay-coated silt and aggregates are the three types of particle associations. Point, edge and face contacts are observed from the 3D reconstructed microstructure of natural loess. The 3D microstructural features of particles and pores are quantitatively studied by analyzing statistical parameters that include the equivalent diameter, sphericity, aspect ratio and orientation index. The particle size distribution (> 10 μm) and total porosity obtained from microstructural analysis are validated by comparison with the results of the laser particle size analysis and physical test. A total of 92% of the loess particles have sphericity that lies between 0.5 and 0.9, and the aspect ratio of 93% of the particles is between 0.3 and 0.7. In total, 67% of the particles are oriented from 0° to 45°, whereas approximately 64% of the pores (> 2 μm) are oriented from 45° to 90°. Each 3D parameter has a unique value and can reflect the true spatial morphology of particles and pores, avoiding the influence of the observation angle and section. The 3D characterization leads to further insights into the natural loess microstructure and promotes the progress of loess microstructures research. The 3D parameters of loess microstructure are based on the 3D reconstructed structures and can reflect the true spatial morphologies of particles, thus providing realistic quantitative parameters, particle associations and contact relations for use in numerical simulations
Acknowledgments This study was sponsored by the National Natural Science Foundation of China (No. 41630634 and 41602281), the Fundamental Research Funds for the Central Universities (No. 310826161019), and the Project of Sanqin Scholar in Shaanxi (No. 2019ZDLSF07-0701). References Assallay, A.M., Rogers, C.D.F., Smalley, I.J., 1997. Formation and collapse of metastable particle packings and open structures in loess deposits. Eng. Geol. 48 (1–2), 101–115. https://doi.org/10.1016/S0013-7952(97)81916-3. Cox, M.R., Budhu, M.A., 2008. Practical approach to grain shape quantification. Eng. Geol. 96 (1), 1–16. https://doi.org/10.1016/j.enggeo.2007.05.005. Derbyshire, E., 2001. Geological hazards in loess terrain, with particular reference to the loess regions of China. Earth-Sci. Rev. 54 (1–3), 231–260. https://doi.org/10.1016/ S0012-8252(01)00050-2. Duan, Z., Peng, J.B., Wang, Q.Y., 2016. Characteristic parameter and formation mechanism of repeatedly failure loess landslides. MT Res. 34 (1), 71–76 (In Chinese). Fang, X.W., Shen, C.N., Li, C.H., et al., 2013. Quantitative analysis of microstructure characteristics of Pucheng loess in Shaanxi Province. Chin. J. Rock Mech. Eng. 32 (9),
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Luo, H., Wu, F.Q., Chang, J.Y., Xu, J.B., 2018. Microstructural constraints on geotechnical properties of Malan Loess: a case study from Zhaojiaan landslide in Shaanxi province. China Eng. Geol. 236, 60–69. https://doi.org/10.1016/j.enggeo.2017.11.002. Matalucci, R.V., Abdel-Hady, M., Shelton, J.W., 1970. Influence of grain orientation on direct shear strength of a loessial soil. Eng. Geol. 4 (2), 121–132. https://doi.org/10. 1016/0013-7952(70)90008-6. Ng, C.W.W., Sadeghi, H., Hossen, S.B., et al., 2016. Water retention and volumetric characteristics of intact and re-compacted loess. Can. Geotech. J. 53 (8), 1258–1269. https://doi.org/10.1139/cgj-2015-0364. Rendell, H.M., 1988. Comparison between naturally consolidated and laboratory consolidated loess. Eng. Geol. 25 (2), 229–233. https://doi.org/10.1016/0013-7952(88) 90028-2. Wei, Y.N., Fan, W., Cao, Y.B., 2017. Experimental study on the vertical deformation of aquifer soils under conditions of withdrawing and recharging of groundwater in Tongchuan region, China. Hydrogeol. J. 25, 297–309. https://doi.org/10.1007/ s10040-016-1498-4. Wei, T.T., Fan, W., Yuan, W.N., et al., 2019. Three-dimensional pore network characterization of loess and paleosol stratigraphy from South Jingyang Plateau, China. Environ. Earth Sci. 78 (11), 333. https://doi.org/10.1007/s12665-019-8331-z. Yuan, Z.X., Wang, L.M., 2009. Collapsibility and seismic settlement of loess. Eng. Geol. 105 (1), 119–123. https://doi.org/10.1016/j.enggeo.2008.12.002. Zhao, B., Wang, J.F., 2015. 3D quantitative shape analysis on form, roundness, and compactness with μCT. Powder Technol. 291, 262–275. https://doi.org/10.1016/j. powtec.2015.12.029. Zhao, D., Xu, M.X., Liu, G.B., et al., 2017. Quantification of soil aggregate microstructure on abandoned cropland during vegetative succession using synchrotron radiationbased micro-computed tomography. Soil Tillage Res. 165, 239–246. https://doi.org/ 10.1016/j.still.2016.08.007. Zhu, H.Z., 1963. Some characteristics of the granules and structure of the Malan loss in the middle reaches of the Yellow River. Sci. Geol. Sin. 4 (2), 88–100 (In Chinese).
1917–1925 (In Chinese). Fitzpatrick, E.A., 1984. Micromorphology of Soils. Chapman and Hall, New York. Jiang, M.J., Zhang, F.G., Hu, H.J., et al., 2014. Structural characterization of natural loess and remolded loess under triaxial tests. Eng. Geol. 181, 249–260. https://doi.org/10. 1016/j.enggeo.2014.07.021. Juang, C.H., Dijkstra, T., Wasowski, J., Meng, X.M., 2019. Loess geohazards research in China: advances and challenges for mega engineering projects. Eng. Geol. 251, 1–10. https://doi.org/10.1016/j.enggeo.2019.01.019. Lange, D.A., Jennings, H.M., Shah, S.P., 1994. Image-analysis techniques for characterization of pore structure of cement-based materials. Cement Concr. Res. 24, 841–853. https://doi.org/10.1016/0008-8846(94)90004-3. Li, P.Y., Qian, H., Wu, J.H., 2014. Accelerate research on land creation. Nature. 510, 29–31. Li, P., Vanapalli, S., Li, T.L., 2016. Review of collapse triggering mechanism of collapsible soils due to wetting. J. Rock Mech. Geotech. Eng. 8 (2), 256–274. https://doi.org/10. 1016/j.jrmge.2015.12.002. Li, Y.R., He, S.D., Deng, X.H., et al., 2018. Characterization of macropore structure of Malan loess in NW China based on 3D pipe models constructed by using computed tomography technology. J. Asian Earth Sci. 154, 271–279. https://doi.org/10.1016/ j.jseaes.2017.12.028. Li, P., Xie, W.L., Pak, R.Y.S., Vanapali, S.K., 2019a. Microstructural evolution of loess soils from the Loess Plateau of China. Catena. 173, 276–288. https://doi.org/10.1016/j. caten a.2018.10.006. Li, X.A., Li, L.C., Song, Y.X., et al., 2019b. Characterization of the mechanisms underlying loess collapsibility for land-creation project in Shaanxi Province, China-a study from a micro perspective. Eng. Geol. 249, 77–88. https://doi.org/10.1016/j.enggeo.2018. 12.024. Liu, Z., Liu, F.Y., Ma, F., et al., 2016. Collapsibility, composition, and microstructure of loess in China. Can. Geotech. J. 53 (4). https://doi.org/10.1139/cgj-2015-0285. Lu, Y., 2010. Reconstruction, Characterization, Modeling and Visualization of Inherent and Induced Digital Sand Microstructures. Diss.. Georgia Institute of Technology.
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Three-dimensional microstructure characterization of loess based on a serial sectioning technique
T
⁎
Tingting Weia,b, Wen Fana,b,c, , Ningyu Yua,b, Ya-ni Weia,b a
School of Geology Engineering and Geomatics, Chang'an University, No.126 Yanta Road, Xi'an 710054, Shaanxi, China Key Laboratory of Western China's Mineral Resources and Geological Engineering, Ministry of Education, No.126 Yanta Road, Xi'an 710054, Shaanxi, China c China Electronic Research Institute of Engineering Investigations and Design, Xi'an 710054, Shaanxi, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Loess Three-dimensional microstructure Serial sectioning technique Quantitative analysis
Loess has a loose metastable structure that easily collapses during wetting and loading. Microstructure analysis is essential for a better understanding of the engineering properties of loess; however, two-dimensional (2D) methods cannot fully demonstrate the geometric microstructural characteristics of loess particles. The threedimensional (3D) loess microstructure is reconstructed based on an improved serial sectioning technique. Point, edge and face contacts are observed from the 3D reconstructed microstructure of natural loess. The 3D microstructural features of particles and pores are also quantitatively studied by analyzing statistical parameters, including the equivalent diameter, sphericity, aspect ratio and orientation index. The particle size distribution (> 10 μm) obtained from the microstructural analysis is validated via a comparison with the results of a laser particle size analysis. In total, 92% of the particles have a sphericity that lies between 0.5 and 0.9, and the aspect ratio of 93% of the particles is between 0.3 and 0.7. Additionally, 67% of the particles are oriented from 0° to 45°, whereas approximately 64% of the pores (> 2 μm) are oriented from 45° to 90°. Each 3D parameter has a unique value and can reflect the true spatial morphology of the particles, avoiding the influence of the observation angle and section. The 3D characterization of the loess microstructure will provide insights into the underlying collapse mechanisms and could provide realistic 3D parameters for use in numerical simulations.
1. Introduction Loess is Quaternary aeolian silt that has a global distribution, especially in semi-arid and arid regions. Loess mantles about 631,000 km2 of China, and the greatest bulk accumulation of loess on earth is the well-known Loess Plateau (Derbyshire, 2001). The metastable structure of loess is characterized by high porosity, meta-stable packing and weak cementation (Assallay et al., 1997; Yuan and Wang, 2009; Juang et al., 2019). These typical structures are susceptible to water (Juang et al., 2019; Li et al., 2016); hence, frequent wettinginduced landslides, collapses, debris flows and other geological disasters have occurred on the Loess Plateau in China, and they have killed many people, destroyed many buildings and buried thousands of acres of farmland (Duan et al., 2016; Wei et al., 2017). The mechanical behavior of loess is often controlled by the microstructures (Jiang et al., 2014). Some researchers have claimed that loess collapsibility is dominated by its porosity, cementation bond, particle contact relations and pore forms (Fang et al., 2013; Liu et al., 2016; Luo et al., 2018). The cementation, contact and orientation of particles play a vital role in
⁎
loess strength (Jiang et al., 2014; Li et al., 2019a; Matalucci et al., 1970). Therefore, accurate loess microstructure interpretations are critical for understanding loess collapsibility and other engineering behaviors. Two-dimensional (2D) image observation is the most direct and earliest method in the study of loess microstructure. As early as the middle of the last century, low precision optical microscopy was used to qualitatively observe large pores and particles. For example, the macropores of 11 Malan loess samples were found to be irregular in shape and variable in size in different locations (Zhu, 1963). Since the 1970s, high-precision scanning electron microscopy (SEM) has been used to observe the microstructure, reveal the collapsible mechanism and analyze the macromechanical behaviors of loess. Fang et al. (2013) suggested four types of particle contact relations, i.e., direct point contact, direct face contact, indirect point contact and indirect face contact. Jiang et al. (2014) proposed that the cementation bonds play important roles in loess strength and that the breakage of these bonds is influenced by stress path and confining pressure. Liu et al. (2016) combined X-ray diffraction with SEM to observe loess microstructure on
Corresponding author at: School of Geology Engineering and Geomatics, Chang'an University, No.126 Yanta Road, Xi'an 710054, Shaanxi, China. E-mail addresses: [email protected] (T. Wei), [email protected] (W. Fan).
https://doi.org/10.1016/j.enggeo.2019.105265 Received 10 February 2018; Received in revised form 13 August 2019; Accepted 13 August 2019 Available online 14 August 2019 0013-7952/ © 2019 Published by Elsevier B.V.
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including the density (1.82 g/cm3), water content (15.3%), liquid limit (33.7%), plastic limit (16.8%) and saturation (0.58). The loess particle size distribution obtained by a laser particle analyzer is also described in Table 1. The mineral composition of the loess is shown in Table 2.
the Loess Plateau and elaborated that the wetting-induced collapse was primarily attributed to the abundance of weakly cemented, unsaturated, porous pure clay and clay-silt mixture aggregates. 2D qualitative observations or quantitative analyses have greatly contributed to the study of the loess microstructure, especially the contact relationship between particles, cementation, and elemental compositions at different loess skeleton locations. However, 2D image results often give different results for pores and particles when observed from different angles and sections (Zhao and Wang, 2015). Since the 1980s, mercury intrusion porosimetry (MIP) has been applied to porosity and pore size distribution measurements. Naturally collapsed and consolidated loess does not have pore spaces larger than 3.5 μm in diameter, whereas in laboratory consolidated samples, 15% of the pore volume presents pore spaces larger than 3.5 μm in diameter (Rendell, 1988). Loading and wetting mainly constrict pores larger than 100 μm under a net stress of 110 kPa, which results in a more uniform pore size distribution and a less pronounced hysteresis (Ng et al., 2016). MIP can reflect the pore size and volume variations of loess during loading or wetting, although realistically, the pore size results obtained by MIP do not reflect the true distribution (Lange et al., 1994) and cannot visualize the pore structure. With the development of observation technology, 3D image acquisition has been made possible. The most commonly used technology is computed tomography (CT), which has been applied to obtain the 3D internal structure of geotechnical materials. The CT scanning technique can detect spatial geometric characteristics, such as the size, orientation and channel of pores and the morphology, size, and orientation of particles. The 3D microstructure can reflect the true morphologies of particles and pores. Zhao et al. (2017) studied the relationship between the aggregate microstructure and its role in the vegetative restoration of loess by CT with a resolution of 3.25 μm and showed that the fractal dimension was more sensitive for monitoring the quality of soil structure. Li et al. (2018) investigated the 3D pore structure of Malan loess at a resolution of 59 μm by quantifying the geometric parameters, and the results revealed a strong anisotropy. Despite these efforts, our current understanding of the underlying collapse mechanisms of loess remains controversial or incomplete, and studies on loess engineering properties from 3D microstructure are rare. The objective of this paper is to reconstruct and quantify the 3D loess microstructure based on improved resin impregnation and serial sectioning techniques. An experimental program was successfully developed that included sample preparation, serial image acquisition, image processing and 3D microstructure analysis. Qualitative description and quantitative analysis were carried out to characterize the 3D microstructural features of loess. The characterization of 3D loess microstructure provides insights into the underlying collapse mechanisms and could provide realistic parameters for numerical simulation and theoretical modeling.
3. 2D image acquisition based on serial sectioning 3.1. Sample preparation Loess samples with each side measuring 4 cm were dried by the freeze-drying method. The pore size of loess is much smaller than that of sand and ranges from several nanometers to hundreds of microns. Even resin with relatively low viscosity has difficulty entering loess pores. Thus, acetone, an organic solvent, was used to dissolve the resin and keep the mixture flowing. The loess pores were filled with an epoxy resin mixture that does not modify the soil microstructure (Fitzpatrick, 1984; Liu et al., 2016). A vacuum resin-injection apparatus (Fig. 2b) was assembled to remove the air from the pores and infuse the prepared epoxy resin mixture into the pores. The sample was placed inside a clean cup and transferred into the vacuum chamber (Fig. 2b), which maintained a vacuum pressure of 0.09 MPa. Then, the valve of the split funnel was opened to drip the mixture solution into the cup drop by drop until the liquid level exceeded the sample top surface by at least 1 cm (Liu et al., 2016). Following this step, the sample cup was removed and sealed with plastic film to prevent acetone volatilization, thus ensuring that the epoxy resin mixture sufficiently fills the pores. After a week, the sealed sample cup was opened to let the acetone volatilize, and approximately one month later, the resin reached the required hardness. 3.2. Grinding and polishing The serial sectioning technique was successfully used in the 3D reconstruction of Ottawa sand (Lu, 2010). During the experimental process, the loss of particles depends on the removed thickness, wheel speed and abrasiveness. Silt is the main particle in loess, the experimental procedures and parameters in sand are not applicable to loess. Therefore, the technique was modified through a series of trial tests to ensure the accurate application in loess. A combination of grinding and polishing (MultiPrep™ Precision Polishing System in Fig. 2d) was used to grind and polish a specimen to have an approximate mirror surface (Fig. 2c). Grinding by emery paper was initially performed to remove large bulges on the sample surface. Then, the sample was polished by different specification abrasives in turn. Next polishing began with the removal of the surface texture generated during the previous polishing. A high wheel speed will damage the sample surface and lead to some small particle losses, and a low wheel speed means a long polishing time. Finally, the most suitable wheel speed was determined to be 200 r/min.
2. Study area and sample 3.3. Image acquisition The south Jingyang Plateau is located on the right bank of the Jinghe River in Jingyang County, Shaanxi Province, China (Fig. 1a). The total area of the south Jingyang Plateau is approximately 70 km2, and the altitude is from 420 m to 490 m, with terrain higher in the east and lower in the west. Since 1976, > 80 landslides have been induced, killing a total of 31 people and burying thousands of acres of farmland, especially in the village of Zhai-tou (Duan et al., 2016). The sliding surface of the Zhai-tou landslide is located at a depth of approximately 20 m. Therefore, the loess sample in this study was taken 2 m inside the back wall of the Zhai-tou landslide at a depth of 20 m. Fig. 1b shows the stratigraphic profile of the sampling site. To reduce the disturbance to loess samples, samples were manually collected as a large cube volume of 40 × 40 × 40 cm using a sharp cutter and small shovel and then tightly encased in 5 layers of plastic wrap to avoid water loss. Table 1 shows the physical properties,
The images were captured with an optical microscope manufactured by Leica (Fig. 2e) with a size of 1100 μm × 814 μm and a resolution of 0.424 μm/pixel. By looping the polishing and image acquisition, 250 2D serial images were generated (Fig. 2f). 3.4. Removal thickness The removal thickness should consider the loess particle size to avoid particle loss and retain as many small particles as possible. Considering the image precision of 0.424 μm and the detectable object of 2 μm, 5 min of polishing was set as the standard, and a removal thickness of 1.2 μm is the average value of all layers. Each thickness was measured by calculating the altitude of the shallow pyramid-shaped pits before and after repolishing (Fig. 2g-2i). 2
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Fig. 1. Loess Plateau of north China and location of the sampling site (Fig. 1a after Derbyshire, 2001 and Luo et al., 2018). (a) Location of the study site on the Loess Plateau, and (b) stratigraphic profile of the sampling site.
Fig. 3b shows particles larger than 2 μm in yellow, with dark yellow representing independent particles and light yellow representing particles that cannot be segmented into individual particles accurately.
4. 3D microstructure reconstruction 4.1. Aligning The serial images present translation and rotation of up to 20 pixels and 2°, respectively. The alignment is based on the position of the same object in any two adjacent images. The manual method was chosen first to adjust the large translation and rotation, and the automatic aligning method was then used to optimize the results.
4.3. Representative elementary volume analysis (REV) The computation duration and complexity are dependent on the size of the reconstructed volume. Therefore, it is necessary to extract a REV that is small enough to ensure computational efficiency and large enough to represent the properties of loess. To ensure the representativeness of the REV, the effect on porosity was analyzed at thirteen different size subvolumes, which were concentrically extracted from the same stack of images. The average porosity was computed from three subvolumes of each size. The variance was used here for estimating the discreteness and variability. The formula of variance is as follows:
4.2. Segmentation 4.2.1. Image preprocessing and binarization Colour images were first converted to gray-level images (Fig. 3a). The nonlocal means filter, which determines the new value for the current pixel by comparing the neighborhoods of all pixels in a given image with the neighbours of the current pixel, was applied to eliminate noise and smooth the images (while preserving the edges and details). Then, the global threshold method and visual recognition were adopted, in which the gray images were binarized by selecting an appropriate threshold to separate the pores and particles, with particles in yellow and pores in black (Fig. 3b).
S2 =
1 n
n
∑1 −
_ (x i − x )2 ,
(1)
n
where x = ∑1 x i / n ; S2 is the variance, with a greater value corresponding to greater data variability; n represents the number of subvolumes in each size; and xi is the porosity of subvolumes. The porosity is strongly affected by the subvolume size, and the variance decreases as the subvolume size increases (Fig. 4). The loess sample porosity obtained from physical tests is 42%. For the smallest subvolume (2003 voxels), the average porosity is 46%, and the variance is 0.95%, which is because a small subvolume exactly covers several large pores, resulting in greater porosity. At 7003 voxels, the porosity tends to be stable (40%) and a variance of 0.018% is reasonable; thus, a subvolume of 7003 voxels is large enough to be unaffected by the size and location of the subvolume. Therefore, the cube with a side length of 700 pixels is an optimal REV in this study and used for geometric
4.2.2. Particle and pore segmentation Pore segmentation was performed via watershed transformation. Some particles were connected with others via narrow bridges between particles. An erosion algorithm was proposed to eliminate the narrow bridges between particles and some small unrecognizable spots, and dilation was used to compensate for the body shrinkage caused by erosion. The precision of the images captured by the optical microscope is 0.424 μm, which limits the minimum detectable objects to 2 μm. Table 1 Physical properties of loess. Density ρ/(g/cm3)
Water content ω/%
Porosity n/%
Saturation Sr
Liquid limit WL/%
Plastic limit WP/%
Grain-size distribution (%) Clay (< 2 μm) Silt (2–60 μm) Sand (> 60 μm)
1.82
15.3
0.42
0.58
33.7
16.8
3
14
81
5
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Table 2 Mineral composition of loess. Quartz
Illite
Plagioclase
Calcspar
Chlorite
Potassium feldspar
Dolomite
Hornblende
37.0%
21.5%
14.1%
13.8%
5.2%
3.8%
3.4%
1.2%
Fig. 2. Experimental process. (a) Sample preparation and resin-injection, (b) serial sectioning procedures, and (c) removal thickness determination.
global form of particles, and it ranges from 0 to1. A maximum value of 1 indicates a perfect spherical particle, and as the value decreases, the particle becomes irregular or ellipsoidal.
computations in further quantitative analyses. 4.4. Quantitative parameters (1) The 3D porosity is defined as the total number of pore voxels within the volume divided by the total number of voxels in the volume. (2) The equivalent diameter (EqD) is related to the object volume and is expressed as follows:
EqD =
3
6⁎Volume3d π
S=
Asp A
3
=
36πV 2 , A
(3)
where V and A are the volume and surface area of the particle, respectively, and Aspis the surface area of a sphere whose volume is equal to that of the particle. (4) The aspect ratio (As) measures the difference between the short axis and long axis of particles (aspect ratio = short axis/long axis). (5) The object orientation is determined according to two angles in space, where φ [0°-90°] is the angle between the horizontal plane and
(2)
where Volume3d is the volume of the object. (3) The sphericity (S) is an overall shape parameter, referred to as a
Fig. 3. (a) Gray micrograph of loess, (b) binary image of pores and particles, with independent particles in dark yellow, indivisible particles in light yellow, and pores in black, and (c) reconstructed 3D loess particles. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) 4
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Fig. 4. REV analysis using three stacks of loess sample images.
the particle long axis (pore channel) and θ [0°-180°] is the direction of the long axis (pore channel) projected onto the horizontal plane.
5.2. Pore size distribution Pore size distribution (PSD) is one of the main factors that affects permeability and can indicate complex pore structural characteristics in far more detail than porosity alone. The PSD curves of loess as detected by MIP and serial sectioning are shown in Fig. 6. The MIP curve shows peaks of 2% and 10.2% at 0.026 μm and 4.5 μm, respectively. The serial sectioning curve shows a single peak of 12% at 13.5 μm, with values ranging from 2 μm to 40 μm. MIP systematically underestimates pore sizes due to the “ink bottle effect” (Lange et al., 1994), although this effect can be estimated from the MIP test when decreasing the pressure. Objects < 2 μm have a smaller gray level and are easily mistaken for pores, thus, the pore size is overestimated to a certain extent. Thus, the true PSD lies between the curves of MIP and serial sectioning.
5. Results 5.1. Particle size distribution Fig. 5 presents the percent passing curves of the particle size distribution from 10 μm to 50 μm as obtained by a laser particle analyzer and serial sectioning technique. All particles with a diameter of > 10 μm were clearly identified and accurately extracted in the 3D reconstructed microstructure. The following quantitative characterization of loess particles is based on this size group. Particles of 2 μm to 5 μm mainly occur in association with clay, and skeletal effects are not obvious in loess structural systems (Li et al., 2019b). Some of the particles from 5 μm to 10 μm are embedded in aggregates, which makes it impossible to accurately identify their boundaries. Because the reconstruction volume is small, fewer particles larger than 50 μm exist in the reconstruction range. Thus, the range of 10 μm - 50 μm is validated via comparison with the results of laser particle size analysis.
5.3. Particle morphology The particle morphology can reflect the loess formation mode and depositional history and influence the physical and mechanical properties. For example, the morphology defines the arrangement and
Fig. 5. Particle size distribution. 5
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Fig. 6. Pore size distribution.
Fig. 7. Particle morphology. (a) Sphericity and aspect ratio distributions, (b) sphericity vs. equivalent diameter, and (c) visualization of several typical loess particles.
to discuss the relationship between the particle size and the orientation angle. The contribution of each diameter group to each angle group is consistent with that of all particles in each angle group. Concluding that the orientation angle of natural loess particle is irrelevant to its diameter.
thereby affects the intergranular friction and movement mode of the particles (Cox and Budhu, 2008). When the sphericity is > 0.9, the aspect ratio is close to 0.8 and the particles are close to spherical (Fig. 7c). When the sphericity is < 0.5, the particles are obviously long strips (Fig. 7c). Fig. 7a shows that 92% of the loess particles have sphericity that lies in the range between 0.5 and 0.9, and the aspect ratio of 93% particles is between 0.3 and 0.7. For particles with the same equivalent diameter, they have different morphologies, the difference between the maximum and minimum sphericity is approximately 0.5 (Fig. 7b). Overall, the sphericities decrease as the equivalent diameter increases, showing that the smaller the particle diameter is, the greater the probability of approaching a sphere.
5.5. Pore orientation Pore orientation is determined by the channel that connects two adjacent pore bodies. Fig. 8c shows the pore orientation of natural loess, and approximately 64% of the pores are oriented from 45° to 90° (φ). At the beginning of sedimentation, a loess particle falls freely until it contacts another particle, thus forming a remarkable vertical pore structure (Assallay et al., 1997). With an increase in the overlying soil layer, the loess structure is compacted, the pores are still mainly in directions > 45° (φ). Because the vertical stress is uniform, the pore distribution in the horizontal direction is relatively random (Fig. 8c). The permeability test shows that the loess sample permeability in this study is greater in the vertical direction (2.8 × 10−5 cm/s) than in the horizontal direction (1.6 × 10−5 cm/s). We therefore conclude that the pore orientation plays a primary role in controlling the flow of liquid.
5.4. Particle orientation The particle orientation can not only reflect the current arrangement state but can also influence the slipping between particles. During loading, the particle arrangement and preferred orientation will change, which affects the internal fraction angle and subsequently affects the shear strength (Matalucci et al., 1970). The rose diagram of the particle orientation (Fig. 8b) shows that 67% of the particles are oriented between 0° and 45° (φ). During the process of loess deposition, the particles were distributed randomly in the horizontal direction (Fig. 8b), under the influence of gravity and overburden pressure, the angle φ of the particles gradually decreased. The distribution of particles with different diameters in each angle group (Fig. 8a) was plotted 6
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Fig. 8. Orientation. (a) Distribution of particles with different diameters in each angle group, (b) and (c) rose diagrams of particles and pores, respectively. φ is the angle between the horizontal plane and the particle long axis (pore channel), and θ is the direction of the long axis (pore channel) projected onto the horizontal plane. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
6. Discussion
could provide realistic skeletons for use in 3D numerical modeling (Fig. 9f).
6.1. Qualitative analysis of particles 6.1.2. Particle contact The contact relation is an important factor for determining whether particles will easily slip over each other. Four typical particle contact relations are obtained from 2D images according to the contact area and clay cementation thickness between particles: direct point and face contact and indirect point and face contact, (Fang et al., 2013). Point contact is rare in this sample, as observed from the 3D reconstructed microstructure. In addition, there is not only one contact relation between two particles, such as the case for particles in group b in Fig. 9, in which direct point contact coexists with indirect face contact. The connection between particles is a dynamic and balanced process.
6.1.1. Particle association Three skeleton units appear in the natural loess sample: individual silt or sand, clay-coated silt and aggregate (Fig. 9e - 9f). Clay acts as the main cement connecting all the skeleton particles together to form a stable open structure. A minority of the silt and sand particles occur individually. Most silt particles were coated by clay platelets or calcium carbonate to form clay-coated silts (Li et al., 2016, 2019a). Most aggregates consist of both silt and clay particles, while some are composed of purely clay particles (Liu et al., 2016). The size of aggregates varies from tens to hundreds of micrometers. The 3D particle associations
Fig. 9. Particle contact relation and association. (a-d) Four typical contact relations in loess, (e) basic association units of loess and (f) corresponding 3D structures. 7
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Unstable point contact, which is sensitive to force because of the small contact area, may be common in the initial stage of microstructure formation (Assallay et al., 1997). As the overlying stress increases, the number of point contacts gradually decreases. Edge contact and face contact relations are widely observed in this sample (Fig. 9a-9c). When subjected to force, direct face contact is relatively stable among these contact relations, and point and edge contacts are easier to dislocate to cause compression. Particles with indirect contact are typically thickly coated with clay at the point of contact, thus making them sensitive to water, and once the stress exceeds the residual strength of the cement wetted in water, the structure will collapse. The contact relations obtained from the 3D reconstructed microstructure can reflect the real contacts between particles in space and avoid the influence of the 2D observation angle and section. Based on the contact relation, we can study the displacement, stress state and contact stability of particles under external forces and water to explore the collapsibility and micro-failure mechanisms of loess. 6.2. Advantages of the serial sectioning technique in loess microstructure research In general, different loess microstructures are characterized using different techniques. In this paper, many 3D characteristics of loess can be revealed using the serial sectioning technique. The results based on the serial sectioning technique also have several advantages over those based on the thin-section and SEM methods. Compared with the thin-section method, which can provide 2D section images, the 3D microstructure based on the serial sectioning technique improves the accuracy of microstructure judgments. First, each particle exists in a 3D space and has a definite size, shape and orientation, while the thin-section technique often gives different results for one object if the images are captured from different angles and sections. For example, the 3D volume-based porosity was 40% and close to the porosity measured by the physical method, while the 2D porosity of 250 images varied from 25% to 52% (Fig. 10). The contact relation of particles in group b is indirect face contact, while direct point and indirect face contact are observed in section s1 (b) and s2 (b) respectively (Fig. 9b). Fig. 11 shows a particle characterized by quantitative parameters obtained from the 3D structure and eight thin sections. The orientation of s1 is 59.59°, whereas that of s3 is 153.79° (Fig. 11). The long axis difference between s6 and s4 is 42.64 μm, and the roundness difference between s4 and s8 is 0.34 (Fig. 11). Then, the existence of edge contact has been observed for the first time from the 3D microstructure of loess, which has been mistaken for point contact in the s1 (c) and s2 (c) sections (Fig. 9c). Compared with the SEM method, the serial sectioning technique provides a more effective method to quantitatively study the loess microstructure evaluations during wetting and loading. The silt particles of loess are often bonded to or coated by clay particles (Wei et al., 2019). SEM can be used to examine the skeleton grain shape after removing the attachments from surfaces. However, it is difficult to determine the current orientation and contact relations of loess particles after wetting and loading by SEM. 3D reconstructed microstructure based on serial sectioning can obtain the current orientation and contact relations of particles, providing better technical conditions for studying the loess collapse and compaction progress.
Fig. 10. Porosity of 2D serial images.
For example, accurate quantitative interpretation of loess microstructure during wetting and loading will provide insights into the underlying collapse mechanisms. Cementation bonds stabilize the initial open structure, once the water content and external load exceed the critical value, the bonding strength would fail to support the soil fabric and the fundamental particle rearrangement occurs, transforming the initial stable open structure into a closed structure (Li et al., 2016, 2019b). The particle rearrangement is closely associated with the local porosity, morphology, contact relation and cementation (Liu et al., 2016). Based on these characteristics, the displacement, stress state and contact stability of particles under external load and water can be analyzed to explore the loess collapse mechanism, and along with the analysis of the quantitative parameters, these characteristics can be used to predict the collapse behavior of loess, and determine loess engineering sites that can be pretreated by suitable loading and wetting. Furthermore, microstructure evaluations during loading and wetting can guide compaction work in loess engineering sites. The compression of filling sites is used in many engineering construction sites on the Loess Plateau, such as Yan'an (Li et al., 2014). During the compaction process, the soil particles overcome the resistance between particles, produce displacement, reduce porosity and increase density. The stress state, movement and contact mode among particles during loading and wetting will be studied to determine the contact stability between particles and find the most stable arrangement states under different conditions to guide the compaction work of loess site. In addition, quantitative characterization of 3D loess microstructure could provide realistic parameters for numerical simulations. Porosity, particle size distribution, particle morphology and contact relation obtained by the 3D reconstruction method can be used to set porosity, form clumps and balls, and determine contact and coordination number for 3D modeling.
6.3. Engineering implications Loess is regarded as a problematic soil that raises different engineering problems in urgent need of solutions in engineering practice. The accurate interpretation of loess 3D microstructures can help to deepen the understanding of the behavioral mechanisms associated with different engineering problems. Such understanding is expected to provide suggestions for engineers in the design and construction of buildings and facilities built on loess deposits. 8
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Fig. 11. Quantitative characterization of a loess particle by thin-section and serial sectioning technique.
7. Conclusions
and theoretical modeling. The serial sectioning technique overestimates the pore size and cannot measure pores smaller than 2 μm. This method provides a new approach for pore structure research, and its limitation will be compensated for by improvement in the scanning accuracy. In future work, accurate interpretations of loess 3D microstructures during wetting and loading will also be developed to provide insights into the underlying collapse mechanisms, thereby providing guidance for the pretreatment of engineering sites.
The resin impregnation and serial sectioning techniques have been improved to make them suitable for loess 3D microstructure reconstruction. The particle association and contact of loess are qualitatively analyzed in space. Individual silt or sand, clay-coated silt and aggregates are the three types of particle associations. Point, edge and face contacts are observed from the 3D reconstructed microstructure of natural loess. The 3D microstructural features of particles and pores are quantitatively studied by analyzing statistical parameters that include the equivalent diameter, sphericity, aspect ratio and orientation index. The particle size distribution (> 10 μm) and total porosity obtained from microstructural analysis are validated by comparison with the results of the laser particle size analysis and physical test. A total of 92% of the loess particles have sphericity that lies between 0.5 and 0.9, and the aspect ratio of 93% of the particles is between 0.3 and 0.7. In total, 67% of the particles are oriented from 0° to 45°, whereas approximately 64% of the pores (> 2 μm) are oriented from 45° to 90°. Each 3D parameter has a unique value and can reflect the true spatial morphology of particles and pores, avoiding the influence of the observation angle and section. The 3D characterization leads to further insights into the natural loess microstructure and promotes the progress of loess microstructures research. The 3D parameters of loess microstructure are based on the 3D reconstructed structures and can reflect the true spatial morphologies of particles, thus providing realistic quantitative parameters, particle associations and contact relations for use in numerical simulations
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