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Comprehensive microstructural characterizations of 1-D consolidated kaolinite samples with fabric tensors and pore elongation factors
Accepted Manuscript Comprehensive microstructural characterizations of 1-D consolidated kaolinite samples with fabric tensors and pore elongation factors
Jun Kang Chow, Zhaofeng Li, Yu-Hsing Wang PII: DOI: Reference:
S0013-7952(17)31733-7 https://doi.org/10.1016/j.enggeo.2018.10.016 ENGEO 4975
To appear in:
Engineering Geology
Received date: Revised date: Accepted date:
29 November 2017 10 April 2018 24 October 2018
Please cite this article as: Jun Kang Chow, Zhaofeng Li, Yu-Hsing Wang , Comprehensive microstructural characterizations of 1-D consolidated kaolinite samples with fabric tensors and pore elongation factors. Engeo (2018), https://doi.org/10.1016/j.enggeo.2018.10.016
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ACCEPTED MANUSCRIPT
Comprehensive microstructural characterizations of 1-D consolidated kaolinite samples with fabric tensors and pore elongation factors. JK CHOW, Z Li and YH WANG
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Submitted to Engineering Geology
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Jun Kang CHOW Research Student, Department of Civil and Environmental Engineering The Hong Kong University of Science and Technology, HKSAR, China. Email: [email protected]
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Zhaofeng LI Research Student, Department of Civil and Environmental Engineering The Hong Kong University of Science and Technology, HKSAR, China. Email: [email protected]
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Yu-Hsing WANG Professor, Department of Civil and Environmental Engineering The Hong Kong University of Science and Technology, HKSAR, China. Email: [email protected]
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Corresponding author: Yu-Hsing WANG Professor Department of Civil and Environmental Engineering The Hong Kong University of Science and Technology HKSAR, China. Email: [email protected], Tel: (852) 2358-8757, Fax: (852) 2358-1534
Abstract: 299 Text: 5124 Figures: 17
ACCEPTED MANUSCRIPT ABSTRACT In this paper, through micromechanical analyses, the microstructural responses of kaolinite samples subjected to 1-D consolidation were quantitatively analyzed. Using a tailor-made, 3D-
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printed oedometer in preparing samples subjected to different loading levels, the applied loading
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was maintained during the freezing process of the sample in order to preserve the fabric
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associations for the subsequent characterizations using Mercury Intrusion Porosimetry (MIP) and Scanning Electron Microscopy (SEM). At least 3000 particles were identified in each sample to
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provide representative data for the micromechanical analyses. Besides, the voids and solids (particles and aggregates) were separated using proper binary images; the voids of the irregular
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shapes were further described using an equivalent ellipse. With the boundary established
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between the intra- and inter-aggregate pores based on the MIP results, the quantitative SEM
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analyses further revealed that the inter-aggregate pores exhibit a significantly large area fraction and therefore dominate the deformation responses. Fabric tensors were used to further quantify
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the directional behavior of the voids and particles. In addition, to provide complementary
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information and to further understand the associated deformation mechanism, the shape evolution of the inter-aggregate pores was examined, also based on the SEM images. All the
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findings further describe the compression process of the inter-aggregate pores during the collapse of the card-house structure formed by the aggregates. As the vertical stress increases, the cardhouse structure is gradually compressed; hence, the enclosed inter-aggregate pores that are initially elongated vertically are compressed into a rounder shape. For those pores which are initially aligned horizontally, they are further compressed and become more elongated in the horizontal direction. Ultimately, the inter-aggregate pores gradually align in the horizontal
ACCEPTED MANUSCRIPT direction, and the associated pore shape becomes flattened. The particles that form the aggregates also unavoidably follow the same trend, to also align in the horizontal direction.
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Keywords: fabric tensor, pore size distribution, inter-aggregate pores, 3D printing technique,
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average elongation factor.
ACCEPTED MANUSCRIPT 1
INTRODUCTION
The microstructural characterizations of clays in response to different conditions, such as the stress state and history and pore fluid properties, are always challenging as the interactions
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among the different fabrics, which are relevant to the properties of the particles, particle groups
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(aggregates) and pores, are much more complicated in clays than in sand and silt (e.g., Terzaghi
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et al. 1996; Palomino and Santamarina 2005). Tremendous effort therefore has been devoted to gain insights into this topic, mainly based on the morphological properties of clays, i.e., the
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shape, size and orientation of the fabric components that are quantified using different porosimetry and microscopy techniques (e.g., Delage et al. 1982; Delage and Lefebvre 1984;
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Griffiths and Joshi 1989; Hicher et al. 2000; Sivakumar et al. 2002; Kanayama et al. 2009; Cui
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and Jia 2013; Sasanian and Newson 2013; Yu et al. 2016).
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Published results have demonstrated the particular responses of clays when subjected to loading. For instance, the associated deformation is primarily governed by the compression of
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the inter-aggregate pores, while the intra-aggregate pores remain almost unchanged (e.g. Delage
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and Lefebvre 1984; Griffiths and Joshi 1989; Hicher et al. 2000; Wang and Xu 2007; Kanayama et al. 2009; Yu et al. 2016). In response to the applied loading, the aggregates, which enclose the
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intra-aggregate pores, move as whole units (e.g., Delage et al. 1982; Wang and Xu 2007), suggesting that the mechanical responses of clay are controlled by aggregate-to-aggregate interactions rather than by particle-to-particle interactions (e.g. Anandarajah et al. 1996; Kuganenthira et al. 1996; Yu et al. 2016). Nevertheless, some underlying problems and limitations in these previous studies on the microstructural characterizations of clay remain unsolved up to this moment. First, unloading the soil sample is unavoidable when preparing specimens for the subsequent microstructural characterizations. Although the rebound effect
ACCEPTED MANUSCRIPT during stress release was observed (Delage and Lefebvre 1984), such an effect is hitherto neglected and is considered to cause negligible effect to the characterizations (e.g., Cetin 2004; Hattab and Fleareau 2011). Second, quite often, different measurement techniques for complementary microstructural characterizations are applied; however, these different
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measurements are normally not carried out on the same sample. Hence, one may argue about and
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doubt the representation of associated analyses. Third, most of the previously published results
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are mainly based on the results of Mercury Intrusion Porosimetry (MIP) tests, with supplemented information based on brief and qualitative Scanning Electron Microscopy (SEM) analyses (e.g.,
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Delage and Lefebvre 1984; Kanayama et al. 2009; Romero 2013; Wang et al. 2013); quantitative
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analyses on the fabric of the soil samples were not performed in general. Even though quantitative analyses on the particle orientation can be found in few published results (Hicher et
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al. 2000; Cetin 2004; Hattab and Fleureau 2010; Hattab and Fleureau 2011), studies on the pore
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related fabric are still rare. As discussed in Tovey et al. (1992a), quantitative fabric studies have been constrained in the past due to several reasons: (i) lack of sophisticated image processing
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and analysis packages to meet the needs of geotechnical engineers and soil scientists; (ii)
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difficulty in achieving adequate discrimination between different components of the soil fabric;
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and (iii) requires tedious and detailed data processing work for the large amount of data. As emphasized in Tovey et al. (1992b), quantification of clay microstructure is seen as particularly important, as it enhances the qualitative observations by providing more objective data for interpretation. Therefore, we take the initiative to tackle the aforementioned problems in the current microstructural characterizations of clays. The first stage in this study is to prepare high-quality, load-preserved fabric 1-D consolidated clay samples, following the practical guide proposed in Chow and Wang (2017), and using a tailor-made, 3D-printed oedometer, for the
ACCEPTED MANUSCRIPT subsequent microstructural characterizations. Moreover, the same sample is used in both SEM analyses and MIP tests to facilitate meaningful analyses. In each of the SEM images taken, the associated position and orientation are controlled, and the number of the images used in the analyses is maximized to enhance the statistical representation. After the high-quality and
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representative clay samples are prepared, the second stage of this study is to seek a better way to
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quantitatively characterize the fabric from the SEM images, aiming for a better and more
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comprehensive demonstration of the responses of clay when subjected to 1-D consolidation. In this context, we resort to micromechanical analyses with fabric tensors, developed for granular
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media. These analyses have been proven effective in quantifying the microstructural orientation-
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related characteristics of granular media in a tensorial form (e.g., Kanatani 1984; Oda and Iwashita 1999; Li and Li 2009; Kang et al. 2012; Fu and Dafalias 2015). In addition, to
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comprehend the microstructural characterizations, the shape evolution of the inter-aggregate
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pores is also examined based on the SEM images.
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This paper is organized in the following order. It begins with experimental details on how to prepare the high-quality, load-preserved fabric 1-D consolidated kaolinite samples for
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microstructural analyses. Then, details of the tests for the microstructural analyses, i.e., the MIP
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and SEM tests, are delineated. Afterwards, the experimental results are presented and discussed, including the deformation characteristics during 1-D consolidation, measurements of the poresize distribution by the MIP technique, and fabric characterizations based on the SEM images (in terms of particle-based/void-based fabric tensors and the elongation factor of the pores). Finally, the particular responses and deformation mechanism of a kaolinite sample during 1-D consolidation is illustrated based on the experimental findings on the associated microstructural responses.
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SAMPLE PREPARATION FOR MICROSTRUCTURAL ANALYSES
Speswhite kaolin (from Imerys Minerals Ltd., UK) was used in this study, with most of the particle sizes being smaller than 2 Β΅m. The specific gravity and surface area (based on Brunauer-
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Emmett-Tell theory) of Speswhite kaolin are 2.6 and 14 m2/g, respectively. The sample
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preparations followed the guide proposed in Chow and Wang (2017), as illustrated in Fig. 1, to
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prepare high-quality load-preserved fabric samples that can faithfully capture the conditions at the original loading state. In the following section, the sample preparation work, which mainly
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includes the processes of (i) slurry-consolidation, (ii) 1-D consolidation and (iii) specimen
Slurry-consolidation
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2.1
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preparation for microstructural analyses, are described in detail.
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The clay sample was prepared from a slurry state, following the method described in Wang and Siu (2006). The kaolinite powder was first mixed with deionized water, in an amount about two
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times the liquid limit (LL) (LL = 65% as measured by Yu et al. 2016), i.e., ~1.3 kg of water was mixed with 1 kg of dry kaolinite powder. The kaolinite slurry was then poured into a long tailor-
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made consolidometer of 80 mm in diameter and 400 mm in height, taking particular care to
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avoid the entrapment of air bubbles. A vertical pressure of ~60 kPa was applied for consolidation, and double drainage was used during the process. When the vertical settlement converges to a steady value, the slurry consolidation is considered finished. After slurry consolidation, the kaolinite sediment was carefully taken out and trimmed for the 1-D consolidation tests. As shown in Fig. 1a, the central part of the sediment, which was believed to be less affected by the boundary conditions, was used for preparing the testing samples. Several cylindrical samples
ACCEPTED MANUSCRIPT with of size ~8 mm in height and 12 mm in diameter were then extracted from this sediment using a sharp trimmer for the subsequent 1-D consolidation tests.
2.2
1-D consolidation tests
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To preserve the fabric associations of the clay samples at the original loading state during rapid
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freezing (a step prior to freeze drying, which is presented later), as shown in Fig. 1b, a newly
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invented 3D-printed oedometer was used to conduct the 1-D consolidation tests; The printing material is VeroWhitePlusFullCure 835, and details of this tailor-made device are given in Chow
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and Wang (2017). The trimmed cylindrical sample (~8 mm in height and 12 mm in diameter)
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was placed in the sample cell, which was then positioned in the sample container that was filled with water, to maintain the degree of saturation. Weight holders containing lead shot were used
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to provide the dead load for 1-D consolidation. To determine the deformation of the sample,
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image-based measurements, i.e., Particle Image Velocimetry (PIV) and close-range photogrammetry techniques (White et al. 2003), were used. A digital camera (Canon EOS 7D,
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Canon U.S.A. Inc., USA) equipped with a timer controller (Canon TC-80N3, Canon U.S.A. Inc.,
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USA) was used to continuously capture high-resolution images (5184 Γ 3456 pixels) for the subsequent PIV analyses in order to determine the deformation. Four 1-D consolidation tests, up
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to maximum vertical pressures of ππ£β² = 30, 100, 200 and 250 kPa, were carried out according to ASTM D2435 (ASTM 2011) using the 3D-printed oedometer. In each consolidation test, loading was applied incrementally for four different levels, with an increment ratio of approximately 1. For instance, if the target maximum vertical pressure was 100 kPa, the loading increments were 12.5 kPa, 25 kPa, 50 kPa, and 100 kPa.
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Specimen preparation for microstructural analyses
After the 1-D consolidation tests, together with the load applied, the whole 3D-printed oedometer containing the consolidated kaolinite sample was submerged and frozen in a Dewar
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flask that contained liquid nitrogen for preserving the soil structure. This aimed at avoiding
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unloading effects that may alter the actual fabric associations, as happened in the test samples
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documented in most of the published results. Afterwards, still in a frozen condition, the cylindrical sample was taken out from the sample container and then cut into half using a sharp
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razor blade. This treatment, on the one hand, created a vertical observation plane on one half of the sample to facilitate the taking of meaningful SEM images; on the other hand, the remaining
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half of the sample could be used in the MIP test to obtain complementary information from the
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same sample regarding the pore-size distribution.
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Right after cutting, the frozen sample was snugly placed in a 3D-printed covered square container (see Fig. 1c) to maintain a known orientation and to protect the sample from any
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external disturbance. The whole container, with the cover removed and the frozen kaolinite
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sample placed inside, was then placed in a freeze dryer (Edwards Super Modulyo, Edwards Limited, UK) operating at a temperature of ~ -50Β°C, for at least 48 hours. Freeze drying allowed
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the removal of water by sublimation so the capillary effect was minimized, and therefore the fabric of the kaolinite sample was preserved.
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DETAILS OF MICROSTRUCTURAL CHARACTERIZATIONS
In performing the microstructural characterizations, MIP analyses were carried out to determine the pore-size distribution of the kaolinite samples subjected to different consolidation pressures. The morphological features of the kaolinite samples, i.e., the spatial distribution of the particles
ACCEPTED MANUSCRIPT and voids, were then visually examined by the SEM technique and characterized using the fabric tensors. Full details of each step mentioned are presented in this section.
3.1
Mercury Intrusion Porosimetry (MIP) test
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For each kaolinite sample, the MIP analyses were carried out according to ASTM D4404-10
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(ASTM 2010). As mentioned in Section 2.3, half of the sample was used in the MIP test. The
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equipment used was Micromeritics AutoPore IV 9500 V1.04 (Micromeritics Instrument Corporation, USA), with a maximum injection pressure of 210 MPa. The injection pressure, P,
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and the pore diameter, D (assuming a cylinder of a constant radius) are related as follows
β4πΎ cos π π
(1)
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π·=
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(Washburn 1921):
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where Ξ³ is the surface tension of the mercury (0.485 N/m at room temperature) and ΞΈ is the
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contact angle. An advancing contact angle of 162Β° was used, as suggested by Penumadu and Dean (2000), and therefore the smallest pore diameter could be measured was ~0.01 ΞΌm
Scanning Electron Microscopy (SEM) imaging and analyses
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3.2
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according to equation (1).
3.2.1 SEM imaging
After gold coating the vertical observation plane of the kaolinite sample, SEM images were taken with a JSM-6390 scanning electron microscope (JEOL USA, Inc., USA). A magnification factor of Γ7000, accelerating voltage of 20 kV and working distance of 10 ~ 14 mm were used to capture high-resolution SEM photographs. Sequential imaging was performed, starting from the
ACCEPTED MANUSCRIPT top left corner of the observation plane, and about 20 to 30 SEM photographs of size 9.14 οm ο΄ 6.85 οm (1280 ο΄ 960 pixels) were taken for further analyses. 3.2.2 Identification of the particles and voids based on the SEM photographs
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As shown in Fig. 2a, the kaolinite particles can be observed in the SEM photographs as narrow
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grey strips. These particles were then manually traced and marked with red lines to identify the
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length and orientation, as suggested in several studies (e.g., Cetin 2004; Hattab and Fleureau 2010), and were used subsequently in characterizing the directional distribution of the particles.
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In each sample, about 20 ~ 30 SEM photographs were taken from the observation plane, and in
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each SEM photograph, approximately 150 ~ 300 particles were identified. Hence, sufficiently large numbers of particles, i.e., at least 3000 particles, were analyzed, aiming at providing
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representative results. This was also in agreement to the suggestion given by Barton (1974)
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where at least 400 ~ 500 measurements are required to provide a good representation of a fabric
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component.
Next, in order to better quantify the voids, as shown in Fig. 2b, the raw photographs were
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first converted into binary images, in which the voids and solids (particles and aggregates) were
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represented by black and white, respectively. Through a number of trials, a threshold light (TL) intensity, TL = 34, was determined as the optimal threshold level, TLoptimal, to convert the SEM photographs into the binary images. As shown in Fig. 3, the TLs = Β±5 of TLoptimal give similar values to the number and area of voids obtained, showing that the chosen TLoptimal is satisfactory for the subsequent analyses. Then, the region-based method, which uses the moment of a shape in estimating the bestfitted ellipse, was adopted to describe the voids of irregular shapes using an equivalent ellipse
ACCEPTED MANUSCRIPT (e.g., Mulchrone and Choudhury 2004; Gonzalez and Woods 2010). According to Mulchrone and Choudhury (2004), this method is less dependent on the irregularities of the voids, and therefore is suitable for dealing with the voids captured by the SEM technique in this study. The built-in function in MATLAB was utilized to complete the data processing on the pixelated
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images of the voids, and details of the involved algorithms are given in Gonzalez and Woods
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(2010). In the data processing, the neighborhood connectivity was set as 8-connectivity to
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determine whether the void was connected. Finally, the properties of the equivalent ellipse used to describe the voids, such as area, lengths of the major and minor axes, orientation of the major
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3.2.3 Calculation of the fabric tensors
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axis, and eccentricity, were calculated.
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Fabric tensors are frequently used to concisely quantify the directional probability distribution of different classes of microstructural entities for particulate media (e.g., Kanatani 1984; Li and Li
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2009). In addition, the magnitudes/sizes of the microstructural entities are considered to play an
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influential role in determining the anisotropy of the soil properties. Therefore, it is reasonable to βweightβ the directional measurement with a weighting function to fairly reflect the contribution
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of each entity with a different magnitude, as suggested by Fu and Dafalias (2015). In this context,
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the second order weighted fabric tensors F proposed by several researchers (e.g., Satake 1983; Fu and Dafalias 2015), were used herein and are given in a discrete setting as follows: π
π
πΉ = β π€π π§π β π§π / β π€π π=1
(2)
π=1
where nk is the unit vector, β is the tensor product, π€π is the weighting function, and N is the total number of the unit vectors. The fabric tensors obtained from the two-dimensional SEM
ACCEPTED MANUSCRIPT Μ and the anisotropy images can be further described using the major principal direction ππ intensity factor, Ξ± = FI β FII, where FI and FII are the major and minor principal components, Μ is the mean orientation of the elements respectively (e.g., Fu and Dafalias 2015). Note that ππ being quantified, and is measured with respect to the horizontal plane, and the counter-clockwise
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rotation is considered as the positive direction. In this study, the fabric tensors were constructed
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based on the orientation of the major axis of the particles and voids, and simply termed particle-
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based and void-based fabric tensors, respectively, in the following discussion. Also, for each
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type of fabric tensor, the corresponding major-axis length of the particles or the voids was chosen as the weighting function.
EXPERIMENTAL RESULTS AND DISCUSSION
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The deformation characteristics of kaolinite samples subjected to 1-D consolidation at different
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loading stages is presented first. Then, the microstructural characterizations of kaolinite samples
Deformation characteristics of 1-D consolidation
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4.1
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based on the MIP and SEM analyses are discussed in detail.
Fig. 4a presents the corresponding consolidation curves of the kaolinite samples. All the data
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points from four different 1-D consolidation tests, with different maximum consolidation pressures, are shown; the consistent responses of the samples tested suggest similar properties were exhibited by all the samples. According to the graphical method suggested by Casagrande (1936), the pre-consolidation pressure is determined as ~55 kPa.
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Evolution of the pore-size distribution in response to 1-D consolidation
Fig. 4b presents the MIP analyses of the kaolinite samples subjected to different 1-D consolidation pressures. For comparison, the sample after slurry-consolidation, referred to as the
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initial state, is also presented. With an increase in the vertical stress, ππ£β² , it is observed that the
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dominant pores, i.e., the peaks of the distribution curve, shift to a smaller size, indicating the
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gradual collapse of the pores upon compression. To facilitate the discussion on the associated microstructural changes in the next section, as indicated in Fig. 4b, a boundary between the inter-
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and intra-aggregate pores is established based on the supporting evidence provided below.
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As noted, published results have shown that the intra-aggregate pores are related to the entrapped and constricted porosity and therefore the volume of intra-aggregate pores remains
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almost unchanged in response to consolidation and shearing (e.g., Delage and Lefebvre 1984;
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Griffiths and Joshi 1989; Romero et al. 1999; Wang and Xu 2007; Kanayama et al. 2009). Based on this supporting finding, the range of pore-size where all samples subjected to different loading
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show a similar distribution is considered as the intra-aggregate pore range. Hence, the pore-size
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of ~0.14 ΞΌm is categorized as the upper boundary of the intra-aggregate pores in the following discussion; this value is also similar to the finding in Yu et al. (2016) for a Speswhite kaolin
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sample. Also, with respect to the total volume of voids, it is observed that the percentage of the inter-aggregate pores (i.e., pore size above 0.14 ΞΌm) decreases from ~87.5% (initial state) to ~82.5% (subjected to 1-D consolidation at 250 kPa). Nevertheless, as observed from the SEM images, the sizes of the two types of pores actually vary over a wide range. Hence, the boundary should lie within a range of pore diameters, depending on the condition of the samples, rather than a precise and single value. Herein, for simplicity, a definite value, i.e., 0.14 ΞΌm, is used as the boundary between the intra- and inter-aggregate pores herein.
ACCEPTED MANUSCRIPT The quality of all the pore-size measurements in this study is demonstrated in Table 1 by comparing the total intrusion volume (per gram) in the MIP test and the measured water content. Note that a total intrusion volume of 0.681 ml/g corresponds to a water content of 68.1%. The results shown in Table 1, according to Nagaraj et al. (1990), generally suggest a good quality of
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pore-size measurement in this study, where the size of pores is within the measurement range of
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the MIP equipment as well as the existence of non-interconnected voids and bottle-neck effects
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are considered as negligible in this study [similar to the findings reported by Delage and
Microstructural characterizations based on the SEM images
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4.3
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Levebvre (1984), and Griffiths and Joshi (1989)].
In this section, the results of the quantitative microstructural analyses based on the SEM images
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are discussed. Changes of the particle-based and void-based fabric tensors are presented first,
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followed by the evolution of the pore shapes. As described previously, about 20-30 SEM images
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were taken for each sample to provide representative characterizations. 4.3.1 Evolution of the directional distribution of particles and voids and their associated
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fabric tensors
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Fig. 5 presents the statistical analysis of the particles, based on all the SEM images taken, in response to different 1-D consolidation pressures, ππ£β² . As shown in Fig. 5a, the particle orientation is gradually towards the horizontal direction as ππ£β² increases. This tendency is further examined and quantified using the particle-based fabric tensors as presented in Fig. 5b, where the distribution of the associated anisotropy intensity factor, πΌπ , obtained from each SEM image, is shown. Note that the sample size P (i.e., number of SEM images taken), mean Β΅ and standard deviation Ο of the distribution of πΌπ are also specified in the figure for reference. The normal
ACCEPTED MANUSCRIPT distribution is chosen as it fits the experimental data more closely, according to the KolmogorovSmirnov test. At ππ£β² = 30 kPa, the distribution of πΌπ is wide with a low peak value. This indicates that the arrangement of particles at this consolidation state in the sample exhibits a wide range of forms, i.e., from a random distribution to an oriented arrangement along the major
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principal direction; the whole sample is less uniform in terms of the particle arrangement. As ππ£β²
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increases, a narrower distribution of Ξ±p associated with a higher Β΅ and a lower Ο is obtained,
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Μ . suggesting that the particle orientations tend to converge to the major principal direction, ππ,π
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To put it another way, the whole sample gradually becomes more uniform in terms of the particle arrangement as ππ£β² increases. This behavior can be better viewed in a summary figure, i.e., Fig.
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Μ , which is also summarized in Fig. 7a, is randomly distributed at ππ£β² = 7a. The evolution of ππ,π
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30 kPa, and then gradually becomes closer to ~0Β°, i.e., perpendicular to the loading direction, as ππ£β² increases. These results provide additional quantitative evidence to that based on the
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experimental observations (e.g., Hicher et al. 2000; Hattab and Fleureau 2011) and numerical
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simulations (e.g., Anandarajah 2000), i.e., the structural anisotropy of the particles becomes
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more pronounced as the 1-D consolidation pressure increases. Fig. 6 presents the statistical analysis of the voids subjected to different 1-D consolidation
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pressures. In addition, a summary of the associated anisotropy intensity factor of the void-based Μ , is given in Fig. 7b. fabric tensor, πΌπ£ , and the major principal direction of the voids, ππ,π£ Coincidentally, like the particle orientation behavior, the void orientation also becomes more uniform and tends to be in the horizontal direction as ππ£β² increases. These observations can be attributed to the collapse of the flocculated structure (a card-house like structure) during 1-D consolidation (further discussed next).
ACCEPTED MANUSCRIPT Although the particle orientation-based fabric tensors can quantitatively describe how the particles make an adjustment in response to 1-D consolidation, the orientation determined is associated with the particles rather than the aggregates that contain the particles. However, the responses to loading mainly occur through the aggregate-to-aggregate interactions in clayey soils
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(e.g. Delage and Lefebvre 1984; Griffiths and Joshi 1989; Hicher et al. 2000; Wang and Xu 2007;
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Kanayama et al. 2009; Yu et al. 2016). In addition, the void-based fabric tensors provide no
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information regarding the pore-shape features during pore rotation. Hence, to tackle these issues,
inter- and intra-aggregate pores, are carried out.
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further analyses of the SEM images, particularly considering the individual contribution of the
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4.3.2 Evolution of the microstructural features of voids
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To distinguish the responses of the inter- and intra-aggregate pores (voids), the number fraction,
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ππ , and the area fraction, π΄π , are therefore defined as: number of the specific type of pores observed total number of pores observed
(3)
π΄π =
cross sectional area of the specific type of pores observed total cross sectional area of pores observed
(4)
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ππ =
where π = 1, 2 represents the inter- and intra-aggregate pores, respectively. In addition, the equivalent diameter of a void, defined as the diameter of a circle with the same area as the void, is considered comparable to the mean pore diameter obtained in the MIP test and is therefore used to categorize the voids as inter- or the intra-aggregate pores. Figs. 8a-d presents the summaries of the pore features of kaolinite sample after 1-D consolidation at ππ£β² = 30, 100, 200 and 250 kPa, respectively. As shown in the figures, the cross-
ACCEPTED MANUSCRIPT sectional area occupied by the inter-aggregate pores is found to be much larger than that of the intra-aggregate pores (i.e., π΄1 >> π΄2 ), although the number of the intra-aggregate pores observed is greater (i.e., π2 > π1 ). This further verifies that the inter-aggregate pores are dominant in the loading response, and therefore the orientation of the voids observed in Fig. 6a is mainly
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contributed by the behavior of the inter-aggregate pores. Note that the corresponding major-axis
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length of the voids is used as the weighting function when calculating the fabric tensor.
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As the inter-aggregate pores are shown to be dominant in the loading response, the
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associated changes in the pore features are examined to further reveal the deformation mechanism during 1-D consolidation. The average elongation factor πΈπ_β , measured between
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angles g and h (in degrees), which is similar to the shape descriptor suggested by Mollon and
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Zhao (2012), is therefore introduced: π
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πΈπ_β
1 ππ΅ = β π ππ΄
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π=1
(5)
where N is the total number of pores, and ππ΄ and ππ΅ are respectively the major- and minor-axis
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lengths of the equivalent ellipse that describes the voids. To ease the presentation, the term E,
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instead of πΈπ_β , is used in the following discussion, unless the range of pore orientation degrees is required to be specified. In general, E = 1 means that the pores are perfectly round whereas E β 0 indicates that the pores are very elongated. The E value is calculated in intervals of 10 degrees of void orientation. For example, as shown in Fig. 8a, for all the voids with an orientation between 90ο°-80ο°, the average elongation factor E is 0.50. To facilitate discussion, the corresponding ellipse that matches the calculated E value is also plotted in the figure as a reference, and the associated orientation also represents the
ACCEPTED MANUSCRIPT pore orientation. Among all the loading stages, it is found that E exhibits a minimum value for those pores aligned horizontally (ΞΈ β 0Β°; termed case I) and a maximum value for those pores aligned vertically (ΞΈ β -90Β° or 90Β°; termed case II). As ππ£β² increases, the minimum value of E decreases (case I) and the maximum value of E increases (case II). That is, for case I, subsequent
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loading further compresses and then elongates the pores which are initially aligned horizontally
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and therefore E decreases with an increase in ππ£β² . On the other hand, for case II, subsequent
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loading gradually compresses the card-house structure and the aggregates reposition by moving downwards. Hence, the associated pores, which are initially elongated vertically, are compressed
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into a rounder shape and therefore E increases with an increase in ππ£β² . Ultimately, regardless of
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the initial conditions of the pores, it is believed that all the pores tend to elongate along the horizontal plane when the pressure is sufficiently high. The results shown in Figs. 8a-d also
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reveal that as ππ£β² increases, all the inter-aggregate pores gradually concentrate to align in the
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horizontal direction and the associated pore shape gradually becomes flattened with a lower E
Demonstration of the fabric evolution during 1-D consolidation
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value.
Summarizing the previously analysed results and discussion, the fabric evolution of kaolinite soil
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during 1-D consolidation can be demonstrated as shown in Fig. 9. Note that the orientation of the voids and the corresponding average elongation factor illustrated in the figure at each consolidation stage are based on the values obtained from Figs. 8a-d, as marked by an arrow, i.e., E80Β°_90Β° = 0.50 at ππ£β² = 30 kPa, E60Β°_70Β° = 0.58 at ππ£β² = 100 kPa, E40Β°_50Β° = 0.45 at ππ£β² = 200 kPa and E0Β°_10Β° = 0.32 at ππ£β² = 250 kPa. Initially as ππ£β² = 30 kPa, the flocculated (card-house-like) structure, which encloses the inter-aggregate pores elongating in the vertical direction, remains
ACCEPTED MANUSCRIPT stable. When ππ£β² increases beyond the pre-consolidation pressure, i.e., ππ£β² = 100 kPa in this case, each aggregate moves as a unit and the associated movement subsequently disrupts the stability of the card-house structure. The card-house structure gradually collapses and therefore the enclosed pores are compressed. With further increasing of ππ£β² up to 200 kPa, the aggregates
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progressively adjust themselves to align towards the horizontal plane, as do the particles
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contained in the aggregates. Finally, at ππ£β² = 250 kPa, such an orientation tendency in the
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horizontal direction becomes more pronounced. As shown in Fig. 9, the pores also rotate,
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accompanied with rearrangement of the aggregates and gradually becoming aligned to the horizontal direction. The scenarios illustrated in Fig. 9 also simply explain the consistent trend
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between the particle orientation and void orientation, as observed in Figs. 7a and 7b. Nevertheless, further investigations are needed to identify the structure of the aggregates based
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on the SEM images. Further, it should be noted that the conclusion drawn here only applies to
CONCLUSIONS
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5
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kaolinite clay and may not be applicable to other types of clay minerals, such as montmorillonite.
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In this study, the microstructural responses of kaolinite samples subjected to 1-D consolidation were quantitatively characterized by means of micromechanical analyses based on SEM images,
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in addition to the pore-size distribution determined by the MIP test. The salient findings are summarized as follows. Unlike most published results, the applied loading was maintained at different loading stages during rapid freezing of the sample, in order to preserve the fabric associations not affected by the unloading effects of the subsequent characterizations. This was achieved using the newly invented 3D printed oedometer. In addition, for each sample at different loading stages,
ACCEPTED MANUSCRIPT at least ~3000 particles were identified manually to provide representative sampling for micromechanical analyses. By using appropriate binary images, the voids and solids (particles and aggregates) were separated; and the region-based method was adopted to further describe voids of irregular shape using an equivalent ellipse.
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With a definitive boundary established between the intra- and inter-aggregate pores based on the MIP results, the quantitative SEM analyses further reveal that the inter-aggregate pores
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exhibit a significantly large area fraction and therefore dominate the deformation responses.
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Μ and the Based on the analyses of the fabric tensors, in terms of the major principal direction ππ anisotropy intensity factor Ξ±, it is found the particles tend to align horizontally in response to the
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increased consolidation pressure. Interestingly, the void fabric exhibits a similar orientation
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tendency. To provide complementary information and further understand the deformation mechanism of kaolinite clay subjected to 1-D consolidation, the shape evolution of the inter-
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aggregate pores by means of the elongation factor, E, (E = 1 represents pores that are perfectly
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round whereas E β 0 indicates the pores are very elongated) was examined, also based on the SEM images. It is found that E exhibits a minimum value for those pores aligned horizontally
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and a maximum value for those pores aligned vertically. As the consolidation pressure ππ£β²
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increases, the minimum value of E decreases and the maximum value of E increases. These findings can be attributed to the compression process of the inter-aggregate pores during the collapse of the card-house structure formed by the aggregates. As ππ£β² increases, the card-house structure of kaolinite clay is compressed, and the aggregates reposition by moving downwards. Hence, the enclosed inter-aggregate pores, which are initially elongated vertically, are compressed into a rounder shape and therefore E increases. Following the same tendency as for card-house collapsing, the pores which are initially aligned horizontally are further compressed
ACCEPTED MANUSCRIPT and become more elongated in the horizontal direction, and therefore E decreases as ππ£β² increases. Ultimately, the inter-aggregate pores gradually concentrate to align in the horizontal direction and the associated pore shape gradually becomes flattened with a lower E value. The particles that form the aggregates also unavoidably follow the same trend and align in the
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horizontal direction. Lastly, it is important to reiterate that similar microstructural characterizations could be
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carried out for other geotechnical testing, e.g., direct shear and triaxial tests, to enhance the
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statistical representation of the result, provided that the applied loadings are maintained in
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preparing the specimens for the subsequent microstructural characterizations.
ACKNOWLEDGMENTS
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This research was supported by the Hong Kong Research Grants Council (project no. T22-
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603/15N) and Hong Kong PhD Fellowship Scheme (HKPFS). The authors are grateful to the
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reviewers for their valuable comments.
ACCEPTED MANUSCRIPT REFERENCES Anandarajah, A. (2000). Numerical simulation of one-dimensional behaviour of a kaolinite. GΓ©otechnique. 50(5), 509-519. Anandarajah, A., Kuganenthira, N. and Zhao, D. (1996). Variation of fabric anisotropy of
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kaolinite in triaxial loading. Journal of Geotechnical Engineering, 122, 633-640.
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ASTM D2435 (2011). Standard test methods for one-dimensional consolidation properties of
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Barton, C.M. (1974). The micromorphological soil-investigation work of Dr. Lafeber. In Soil microscopy. Edited by Rutherford, G.K. The Limestone Press, Kingston. Ont., 1-19.
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Casagrande, A. (1936). The determination of the pre-consolidation load and its practical significance. In Proceedings of the international conference on soil mechanics and foundation
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engineering, Harvard University, 3, 60-64. Cetin, H. (2004). Soil-particle and pore orientations during consolidation of cohesive soils.
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Engineering Geology, 73, 1-11.
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Chow, J.K. and Wang Y.H. (2017). Preparation of high-quality load-preserved fabric clay samples for microstructural characterizations: a pragmatic guide featuring a 3D-printed
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oedometer. Geotechnical Testing Journal, 40(5), 891-905. Cui, Z. and Jia, Y. (2013). Analysis of electron microscope images of soil pore structure for the study of land subsidence in centrifuge model tests of high-rise building groups. Engineering Geology, 164, 107-116. Delage, P. and Lefebvre, G. (1984). Study of the structure of a sensitive Champlain clay and of its evolution during consolidation. Canadian Geotechnical Journal, 21(1). 21-35.
ACCEPTED MANUSCRIPT Delage, P., Tessier, D. and Marcel-Audiguier, M. (1982). Use of the Cryoscan apparatus for observation of freeze-fracture planes of a sensitive Quebec clay in scanning electron microscopy. Canadian Geotechnical Journal, 19, 111-114. Fu, P. and Dafalias, Y.F. (2015). Relationship between void- and contact normal-based fabric tensors for 2D idealized granular materials. International Journal of Solids and Structures, 63,
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68-81.
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Gao, Y. and Wang, Y.H. (2014). Experimental and DEM examinations of K0 in sand under
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different loading conditions. Journal of Geotechnical and Geoenvironmental Engineering ASCE, 140(5), DOI: 10.1061/(ASCE)GT.1943-5606.0001095.
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Gonzalez, R.C. and Woods, R.E. (2010). Digital image processing (3rd edition, International edition), Pearson Education, Inc., Upper Saddle River, New Jersey.
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Griffiths, F.J. and Joshi, R.C. (1989). Change in pore size distribution due to consolidation of clays. GΓ©otechnique, 39(1), 159-167.
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Hattab, M. and Fleureau, J.M. (2010). Experimental study of kaolin particle orientation
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mechanism. GΓ©otechnique, 60(5), 323-331.
Hattab, M. and Fleureau, J.M. (2011). Experimental analysis of kaolinite particle orientation
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during triaxial path. International Journal for Numerical and Analytical Methods in Geomechanics, 35, 947-968.
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Hicher, P.Y., Wahyudi, H. and Tessier, D. (2000). Microstructural analysis of inherent and
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induced anisotropy in clay. Mechanics of Cohesive-frictional Materials, 5(5), 341-371. Kanatani, K.I. (1984). Distribution of directional data and fabric tensors. International Journal of Engineering Science, 22(2), 149-164. Kanayama, M., Ohira, T., Ogawa, Y., Higashi, T., Ohtsubo, M. and Nakano, A. (2009). Variation of microstructure with consolidation proceeding for sand-clay mixed soils. Journal of the Clay Science Society of Japan, 48(1), 1-8. Kang, D.H., Yun, T.S., Lau, Y.M. and Wang, Y.H. (2012). DEM simulation on soil creep and associated evolution of pore characteristics. Computers and Geotechnics, 39, 98-106.
ACCEPTED MANUSCRIPT Kuganenthira, N., Zhao, D. and Anandarajah, A. (1996). Measurement of fabric anisotropy in triaxial shearing. GΓ©otechnique, 46(4), 657-670. Li, X. and Li, X.S. (2009). Micro-macro quantification of the internal structure of granular materials. Journal of Engineering Mechanics, ASCE, 135(7), 641-656. Mollon, G. and Zhao, J. (2012). Fourier-Voronoi-based generation of realistic samples for
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discrete modelling of granular materials. Granular Matter, 14, 621-638.
Mulchrone, K.F. and Choudhury, K.R. (2004). Fitting an ellipse to an arbitrary shape;
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implications for strain analysis. Journal of Structural Geology, 26, 143-153. Nagaraj, T.S., Vatsala, A. and Srinivasa, B.R. (1990). Discussion on Change in pore size
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distribution due to consolidation of clays. GΓ©otechnique, 40(2), 303-309.
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Oda, M. and Iwashita, K. (1999). Mechanics of granular materials: An introduction, A.A. Balkema, Netherlands.
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Palomino, A.M. and Santamarina, J.C. (2005). Fabric map for kaolinite effects and pH and ionic
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concentration on behavior. Clays and Clay minerals, 53(3), 211-223. Penumadu, D. and Dean, J. (2000). Compressibility effect in evaluating the pore-size distribution of kaolin clay using mercury intrusion porosimetry. Canadian Geotechnical Journal, 37, 393-
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Romero, E., Gens, A. and Lioret, A. (1999). Water permeability, water retention and microstructure of unsaturated compacted Boom clay. Engineering Geology, 54, 117-127.
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Romero, E. (2013). A microstructural insight into compacted clayey soils and their hydraulic properties. Engineering Geology, 165, 3-19. Sasanian, S. and Newson, T.A. (2013). Use of mercury intrusion porosimetry for microstructural investigation of reconstituted clays at high water contents. Engineering Geology, 158, 15-22. Satake, M. (1983). Fundamental quantities in the graph approach to granular materials. Mechanics of granular materials: New models and constitutive relations, 9-19.
ACCEPTED MANUSCRIPT Sivakumar, V., Doran, I.G. and Graham, J. (2002). Particle orientation and its influence on the mechanical behaviour of isotropically consolidated reconstituted clay. Engineering Geology, 66, 197-209. Terzaghi, K., Peck, R.B. and Mesri, G. (1996). Soil mechanics in engineering practice, John Wiley & Sons, Inc., Hoboken, New Jersey.
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Tovey, N.K., Krinsley, D.H., Dent, D.L. and Corbett, W.M. (1992). Techniques to quantitatively
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study the microfabric of soils. Geoderma, 53, 217-235.
of some types of soil fabric. Geoderma, 53, 179-200.
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Tovey, N.K., Smart, P., Hounslow, M.W. and Leng, X.L. (1992). Automatic orientation mapping
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Wang, Q., Cui, Y., Tang, A.M., Barnichon, J., Saba, S. and Ye, W. (2013). Hydraulic conductivity and microstructure changes of compacted bentonite/sand mixture during
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hydration. Engineering Geology, 164, 67-76.
Wang, Y.H. and Siu, W.K. (2006). Structure characteristics and mechanical properties of
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kaolinite soils. I. Surface charges and structural characterizations. Canadian Geotechnical
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Journal, 43(6), 587-600.
Wang, Y.H. and Xu, D. (2007). Dual porosity and secondary consolidation. Journal of
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Geotechnical and Geoenvironmental Engineering, ASCE, 133(7), 793-801. Washburn, E.W. (1921). Note on a method of determining the distribution of pore sizes in a
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porous material. In Proceedings of the National Academy of Sciences of the United States of
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America, 115-116.
White, D.J., Take, W.A. and Bolton, M.D. (2003). Soil deformation measurement using particle image velocimetry (PIV) and photogrammetry. GΓ©otechnique, 53(7), 619-631. Yu, C.Y., Chow, J.K. and Wang, Y.H. (2016). Pore-size changes and responses of kaolinite with different structures subject to consolidation and shearing. Engineering Geology, 202, 122-131.
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Table 1
Comparisons of the total intrusion volume per gram in the MIP tests and the measured water content.
Samples
Total intrusion volume in Measured water content (%)
After compression at 100 kPa
0.559
After compression at 200 kPa
0.525
After compression at 250 kPa
0.508
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0.643
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After compression at 30 kPa
68.8
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0.681
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Initial state
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the MIP tests (ml/g)
64.6 56.8 52.9 51.2
ACCEPTED MANUSCRIPT LIST OF FIGURES Summary of the important features in each step of sample preparations for microstructural analyses: (a) slurry-consolidation; (b) 1-D consolidation; and (c) specimen preparations for microstructural analyses (after Chow and Wang 2017).
Fig. 2
Selected SEM images to illustrate the identification of the microstructure of the kaolinite samples: (a) particle identifications by the hand tracing method; and (b) void identifications by the binary segmentation method (black and white represents voids and particles, respectively).
Fig. 3
The number and area of voids identified while using different threshold level (TL) to convert the SEM photographs to binary images.
Fig. 4
The soil responses after 1-D consolidation at different pressures: (a) the consolidation curves of kaolinite samples; and (b) the pore-size distribution of the kaolinite samples.
Fig. 5
The statistical analysis of the particles of kaolinite samples after 1-D consolidation: (a) the overall direction distribution of particles; and (b) the distribution of the anisotropy intensity factor of particle-based fabric tensors.
Fig. 6
The statistical analysis of the voids of kaolinite samples after 1-D consolidation: (a) the overall directional distribution of voids; and (b) the distribution of the anisotropy intensity factor of void-based fabric tensors.
Fig. 7
A summary of the major principal direction and anisotropy intensity factor obtained from (a) the particle-based fabric tensors; and (b) the void-based fabric tensors.
Fig. 8
A summary of the pore features of kaolinite sample after 1-D consolidation at (a) 30 kPa; (b) 100 kPa; (c) 200 kPa; and (d) 250 kPa.
Fig. 9
Demonstration of the fabric evolution during 1-D consolidation. Note that the orientation of voids and its corresponding average elongation factor used for each consolidation stage are as specified in Figs. 8a β d.
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ACCEPTED MANUSCRIPT HIGHLIGHTS The microstructural responses of kaolinite are quantitatively analysed.
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Load-preserved, high quality kaolinite samples are prepared for analysis.
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Fabric tensors are used to quantify the direction distribution of fabrics.
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The shape evolution of inter-aggregate pores is examined.
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Figure 1
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Jun Kang Chow, Zhaofeng Li, Yu-Hsing Wang PII: DOI: Reference:
S0013-7952(17)31733-7 https://doi.org/10.1016/j.enggeo.2018.10.016 ENGEO 4975
To appear in:
Engineering Geology
Received date: Revised date: Accepted date:
29 November 2017 10 April 2018 24 October 2018
Please cite this article as: Jun Kang Chow, Zhaofeng Li, Yu-Hsing Wang , Comprehensive microstructural characterizations of 1-D consolidated kaolinite samples with fabric tensors and pore elongation factors. Engeo (2018), https://doi.org/10.1016/j.enggeo.2018.10.016
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ACCEPTED MANUSCRIPT
Comprehensive microstructural characterizations of 1-D consolidated kaolinite samples with fabric tensors and pore elongation factors. JK CHOW, Z Li and YH WANG
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Submitted to Engineering Geology
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Jun Kang CHOW Research Student, Department of Civil and Environmental Engineering The Hong Kong University of Science and Technology, HKSAR, China. Email: [email protected]
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Zhaofeng LI Research Student, Department of Civil and Environmental Engineering The Hong Kong University of Science and Technology, HKSAR, China. Email: [email protected]
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Yu-Hsing WANG Professor, Department of Civil and Environmental Engineering The Hong Kong University of Science and Technology, HKSAR, China. Email: [email protected]
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Corresponding author: Yu-Hsing WANG Professor Department of Civil and Environmental Engineering The Hong Kong University of Science and Technology HKSAR, China. Email: [email protected], Tel: (852) 2358-8757, Fax: (852) 2358-1534
Abstract: 299 Text: 5124 Figures: 17
ACCEPTED MANUSCRIPT ABSTRACT In this paper, through micromechanical analyses, the microstructural responses of kaolinite samples subjected to 1-D consolidation were quantitatively analyzed. Using a tailor-made, 3D-
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printed oedometer in preparing samples subjected to different loading levels, the applied loading
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was maintained during the freezing process of the sample in order to preserve the fabric
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associations for the subsequent characterizations using Mercury Intrusion Porosimetry (MIP) and Scanning Electron Microscopy (SEM). At least 3000 particles were identified in each sample to
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provide representative data for the micromechanical analyses. Besides, the voids and solids (particles and aggregates) were separated using proper binary images; the voids of the irregular
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shapes were further described using an equivalent ellipse. With the boundary established
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between the intra- and inter-aggregate pores based on the MIP results, the quantitative SEM
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analyses further revealed that the inter-aggregate pores exhibit a significantly large area fraction and therefore dominate the deformation responses. Fabric tensors were used to further quantify
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the directional behavior of the voids and particles. In addition, to provide complementary
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information and to further understand the associated deformation mechanism, the shape evolution of the inter-aggregate pores was examined, also based on the SEM images. All the
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findings further describe the compression process of the inter-aggregate pores during the collapse of the card-house structure formed by the aggregates. As the vertical stress increases, the cardhouse structure is gradually compressed; hence, the enclosed inter-aggregate pores that are initially elongated vertically are compressed into a rounder shape. For those pores which are initially aligned horizontally, they are further compressed and become more elongated in the horizontal direction. Ultimately, the inter-aggregate pores gradually align in the horizontal
ACCEPTED MANUSCRIPT direction, and the associated pore shape becomes flattened. The particles that form the aggregates also unavoidably follow the same trend, to also align in the horizontal direction.
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Keywords: fabric tensor, pore size distribution, inter-aggregate pores, 3D printing technique,
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average elongation factor.
ACCEPTED MANUSCRIPT 1
INTRODUCTION
The microstructural characterizations of clays in response to different conditions, such as the stress state and history and pore fluid properties, are always challenging as the interactions
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among the different fabrics, which are relevant to the properties of the particles, particle groups
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(aggregates) and pores, are much more complicated in clays than in sand and silt (e.g., Terzaghi
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et al. 1996; Palomino and Santamarina 2005). Tremendous effort therefore has been devoted to gain insights into this topic, mainly based on the morphological properties of clays, i.e., the
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shape, size and orientation of the fabric components that are quantified using different porosimetry and microscopy techniques (e.g., Delage et al. 1982; Delage and Lefebvre 1984;
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Griffiths and Joshi 1989; Hicher et al. 2000; Sivakumar et al. 2002; Kanayama et al. 2009; Cui
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and Jia 2013; Sasanian and Newson 2013; Yu et al. 2016).
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Published results have demonstrated the particular responses of clays when subjected to loading. For instance, the associated deformation is primarily governed by the compression of
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the inter-aggregate pores, while the intra-aggregate pores remain almost unchanged (e.g. Delage
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and Lefebvre 1984; Griffiths and Joshi 1989; Hicher et al. 2000; Wang and Xu 2007; Kanayama et al. 2009; Yu et al. 2016). In response to the applied loading, the aggregates, which enclose the
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intra-aggregate pores, move as whole units (e.g., Delage et al. 1982; Wang and Xu 2007), suggesting that the mechanical responses of clay are controlled by aggregate-to-aggregate interactions rather than by particle-to-particle interactions (e.g. Anandarajah et al. 1996; Kuganenthira et al. 1996; Yu et al. 2016). Nevertheless, some underlying problems and limitations in these previous studies on the microstructural characterizations of clay remain unsolved up to this moment. First, unloading the soil sample is unavoidable when preparing specimens for the subsequent microstructural characterizations. Although the rebound effect
ACCEPTED MANUSCRIPT during stress release was observed (Delage and Lefebvre 1984), such an effect is hitherto neglected and is considered to cause negligible effect to the characterizations (e.g., Cetin 2004; Hattab and Fleareau 2011). Second, quite often, different measurement techniques for complementary microstructural characterizations are applied; however, these different
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measurements are normally not carried out on the same sample. Hence, one may argue about and
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doubt the representation of associated analyses. Third, most of the previously published results
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are mainly based on the results of Mercury Intrusion Porosimetry (MIP) tests, with supplemented information based on brief and qualitative Scanning Electron Microscopy (SEM) analyses (e.g.,
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Delage and Lefebvre 1984; Kanayama et al. 2009; Romero 2013; Wang et al. 2013); quantitative
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analyses on the fabric of the soil samples were not performed in general. Even though quantitative analyses on the particle orientation can be found in few published results (Hicher et
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al. 2000; Cetin 2004; Hattab and Fleureau 2010; Hattab and Fleureau 2011), studies on the pore
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related fabric are still rare. As discussed in Tovey et al. (1992a), quantitative fabric studies have been constrained in the past due to several reasons: (i) lack of sophisticated image processing
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and analysis packages to meet the needs of geotechnical engineers and soil scientists; (ii)
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difficulty in achieving adequate discrimination between different components of the soil fabric;
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and (iii) requires tedious and detailed data processing work for the large amount of data. As emphasized in Tovey et al. (1992b), quantification of clay microstructure is seen as particularly important, as it enhances the qualitative observations by providing more objective data for interpretation. Therefore, we take the initiative to tackle the aforementioned problems in the current microstructural characterizations of clays. The first stage in this study is to prepare high-quality, load-preserved fabric 1-D consolidated clay samples, following the practical guide proposed in Chow and Wang (2017), and using a tailor-made, 3D-printed oedometer, for the
ACCEPTED MANUSCRIPT subsequent microstructural characterizations. Moreover, the same sample is used in both SEM analyses and MIP tests to facilitate meaningful analyses. In each of the SEM images taken, the associated position and orientation are controlled, and the number of the images used in the analyses is maximized to enhance the statistical representation. After the high-quality and
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representative clay samples are prepared, the second stage of this study is to seek a better way to
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quantitatively characterize the fabric from the SEM images, aiming for a better and more
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comprehensive demonstration of the responses of clay when subjected to 1-D consolidation. In this context, we resort to micromechanical analyses with fabric tensors, developed for granular
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media. These analyses have been proven effective in quantifying the microstructural orientation-
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related characteristics of granular media in a tensorial form (e.g., Kanatani 1984; Oda and Iwashita 1999; Li and Li 2009; Kang et al. 2012; Fu and Dafalias 2015). In addition, to
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comprehend the microstructural characterizations, the shape evolution of the inter-aggregate
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pores is also examined based on the SEM images.
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This paper is organized in the following order. It begins with experimental details on how to prepare the high-quality, load-preserved fabric 1-D consolidated kaolinite samples for
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microstructural analyses. Then, details of the tests for the microstructural analyses, i.e., the MIP
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and SEM tests, are delineated. Afterwards, the experimental results are presented and discussed, including the deformation characteristics during 1-D consolidation, measurements of the poresize distribution by the MIP technique, and fabric characterizations based on the SEM images (in terms of particle-based/void-based fabric tensors and the elongation factor of the pores). Finally, the particular responses and deformation mechanism of a kaolinite sample during 1-D consolidation is illustrated based on the experimental findings on the associated microstructural responses.
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SAMPLE PREPARATION FOR MICROSTRUCTURAL ANALYSES
Speswhite kaolin (from Imerys Minerals Ltd., UK) was used in this study, with most of the particle sizes being smaller than 2 Β΅m. The specific gravity and surface area (based on Brunauer-
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Emmett-Tell theory) of Speswhite kaolin are 2.6 and 14 m2/g, respectively. The sample
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preparations followed the guide proposed in Chow and Wang (2017), as illustrated in Fig. 1, to
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prepare high-quality load-preserved fabric samples that can faithfully capture the conditions at the original loading state. In the following section, the sample preparation work, which mainly
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includes the processes of (i) slurry-consolidation, (ii) 1-D consolidation and (iii) specimen
Slurry-consolidation
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2.1
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preparation for microstructural analyses, are described in detail.
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The clay sample was prepared from a slurry state, following the method described in Wang and Siu (2006). The kaolinite powder was first mixed with deionized water, in an amount about two
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times the liquid limit (LL) (LL = 65% as measured by Yu et al. 2016), i.e., ~1.3 kg of water was mixed with 1 kg of dry kaolinite powder. The kaolinite slurry was then poured into a long tailor-
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made consolidometer of 80 mm in diameter and 400 mm in height, taking particular care to
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avoid the entrapment of air bubbles. A vertical pressure of ~60 kPa was applied for consolidation, and double drainage was used during the process. When the vertical settlement converges to a steady value, the slurry consolidation is considered finished. After slurry consolidation, the kaolinite sediment was carefully taken out and trimmed for the 1-D consolidation tests. As shown in Fig. 1a, the central part of the sediment, which was believed to be less affected by the boundary conditions, was used for preparing the testing samples. Several cylindrical samples
ACCEPTED MANUSCRIPT with of size ~8 mm in height and 12 mm in diameter were then extracted from this sediment using a sharp trimmer for the subsequent 1-D consolidation tests.
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1-D consolidation tests
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To preserve the fabric associations of the clay samples at the original loading state during rapid
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freezing (a step prior to freeze drying, which is presented later), as shown in Fig. 1b, a newly
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invented 3D-printed oedometer was used to conduct the 1-D consolidation tests; The printing material is VeroWhitePlusFullCure 835, and details of this tailor-made device are given in Chow
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and Wang (2017). The trimmed cylindrical sample (~8 mm in height and 12 mm in diameter)
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was placed in the sample cell, which was then positioned in the sample container that was filled with water, to maintain the degree of saturation. Weight holders containing lead shot were used
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to provide the dead load for 1-D consolidation. To determine the deformation of the sample,
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image-based measurements, i.e., Particle Image Velocimetry (PIV) and close-range photogrammetry techniques (White et al. 2003), were used. A digital camera (Canon EOS 7D,
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Canon U.S.A. Inc., USA) equipped with a timer controller (Canon TC-80N3, Canon U.S.A. Inc.,
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USA) was used to continuously capture high-resolution images (5184 Γ 3456 pixels) for the subsequent PIV analyses in order to determine the deformation. Four 1-D consolidation tests, up
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to maximum vertical pressures of ππ£β² = 30, 100, 200 and 250 kPa, were carried out according to ASTM D2435 (ASTM 2011) using the 3D-printed oedometer. In each consolidation test, loading was applied incrementally for four different levels, with an increment ratio of approximately 1. For instance, if the target maximum vertical pressure was 100 kPa, the loading increments were 12.5 kPa, 25 kPa, 50 kPa, and 100 kPa.
ACCEPTED MANUSCRIPT 2.3
Specimen preparation for microstructural analyses
After the 1-D consolidation tests, together with the load applied, the whole 3D-printed oedometer containing the consolidated kaolinite sample was submerged and frozen in a Dewar
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flask that contained liquid nitrogen for preserving the soil structure. This aimed at avoiding
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unloading effects that may alter the actual fabric associations, as happened in the test samples
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documented in most of the published results. Afterwards, still in a frozen condition, the cylindrical sample was taken out from the sample container and then cut into half using a sharp
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razor blade. This treatment, on the one hand, created a vertical observation plane on one half of the sample to facilitate the taking of meaningful SEM images; on the other hand, the remaining
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half of the sample could be used in the MIP test to obtain complementary information from the
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same sample regarding the pore-size distribution.
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Right after cutting, the frozen sample was snugly placed in a 3D-printed covered square container (see Fig. 1c) to maintain a known orientation and to protect the sample from any
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external disturbance. The whole container, with the cover removed and the frozen kaolinite
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sample placed inside, was then placed in a freeze dryer (Edwards Super Modulyo, Edwards Limited, UK) operating at a temperature of ~ -50Β°C, for at least 48 hours. Freeze drying allowed
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the removal of water by sublimation so the capillary effect was minimized, and therefore the fabric of the kaolinite sample was preserved.
3
DETAILS OF MICROSTRUCTURAL CHARACTERIZATIONS
In performing the microstructural characterizations, MIP analyses were carried out to determine the pore-size distribution of the kaolinite samples subjected to different consolidation pressures. The morphological features of the kaolinite samples, i.e., the spatial distribution of the particles
ACCEPTED MANUSCRIPT and voids, were then visually examined by the SEM technique and characterized using the fabric tensors. Full details of each step mentioned are presented in this section.
3.1
Mercury Intrusion Porosimetry (MIP) test
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For each kaolinite sample, the MIP analyses were carried out according to ASTM D4404-10
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(ASTM 2010). As mentioned in Section 2.3, half of the sample was used in the MIP test. The
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equipment used was Micromeritics AutoPore IV 9500 V1.04 (Micromeritics Instrument Corporation, USA), with a maximum injection pressure of 210 MPa. The injection pressure, P,
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and the pore diameter, D (assuming a cylinder of a constant radius) are related as follows
β4πΎ cos π π
(1)
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π·=
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(Washburn 1921):
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where Ξ³ is the surface tension of the mercury (0.485 N/m at room temperature) and ΞΈ is the
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contact angle. An advancing contact angle of 162Β° was used, as suggested by Penumadu and Dean (2000), and therefore the smallest pore diameter could be measured was ~0.01 ΞΌm
Scanning Electron Microscopy (SEM) imaging and analyses
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3.2
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according to equation (1).
3.2.1 SEM imaging
After gold coating the vertical observation plane of the kaolinite sample, SEM images were taken with a JSM-6390 scanning electron microscope (JEOL USA, Inc., USA). A magnification factor of Γ7000, accelerating voltage of 20 kV and working distance of 10 ~ 14 mm were used to capture high-resolution SEM photographs. Sequential imaging was performed, starting from the
ACCEPTED MANUSCRIPT top left corner of the observation plane, and about 20 to 30 SEM photographs of size 9.14 οm ο΄ 6.85 οm (1280 ο΄ 960 pixels) were taken for further analyses. 3.2.2 Identification of the particles and voids based on the SEM photographs
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As shown in Fig. 2a, the kaolinite particles can be observed in the SEM photographs as narrow
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grey strips. These particles were then manually traced and marked with red lines to identify the
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length and orientation, as suggested in several studies (e.g., Cetin 2004; Hattab and Fleureau 2010), and were used subsequently in characterizing the directional distribution of the particles.
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In each sample, about 20 ~ 30 SEM photographs were taken from the observation plane, and in
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each SEM photograph, approximately 150 ~ 300 particles were identified. Hence, sufficiently large numbers of particles, i.e., at least 3000 particles, were analyzed, aiming at providing
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representative results. This was also in agreement to the suggestion given by Barton (1974)
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where at least 400 ~ 500 measurements are required to provide a good representation of a fabric
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component.
Next, in order to better quantify the voids, as shown in Fig. 2b, the raw photographs were
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first converted into binary images, in which the voids and solids (particles and aggregates) were
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represented by black and white, respectively. Through a number of trials, a threshold light (TL) intensity, TL = 34, was determined as the optimal threshold level, TLoptimal, to convert the SEM photographs into the binary images. As shown in Fig. 3, the TLs = Β±5 of TLoptimal give similar values to the number and area of voids obtained, showing that the chosen TLoptimal is satisfactory for the subsequent analyses. Then, the region-based method, which uses the moment of a shape in estimating the bestfitted ellipse, was adopted to describe the voids of irregular shapes using an equivalent ellipse
ACCEPTED MANUSCRIPT (e.g., Mulchrone and Choudhury 2004; Gonzalez and Woods 2010). According to Mulchrone and Choudhury (2004), this method is less dependent on the irregularities of the voids, and therefore is suitable for dealing with the voids captured by the SEM technique in this study. The built-in function in MATLAB was utilized to complete the data processing on the pixelated
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images of the voids, and details of the involved algorithms are given in Gonzalez and Woods
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(2010). In the data processing, the neighborhood connectivity was set as 8-connectivity to
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determine whether the void was connected. Finally, the properties of the equivalent ellipse used to describe the voids, such as area, lengths of the major and minor axes, orientation of the major
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3.2.3 Calculation of the fabric tensors
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axis, and eccentricity, were calculated.
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Fabric tensors are frequently used to concisely quantify the directional probability distribution of different classes of microstructural entities for particulate media (e.g., Kanatani 1984; Li and Li
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2009). In addition, the magnitudes/sizes of the microstructural entities are considered to play an
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influential role in determining the anisotropy of the soil properties. Therefore, it is reasonable to βweightβ the directional measurement with a weighting function to fairly reflect the contribution
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of each entity with a different magnitude, as suggested by Fu and Dafalias (2015). In this context,
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the second order weighted fabric tensors F proposed by several researchers (e.g., Satake 1983; Fu and Dafalias 2015), were used herein and are given in a discrete setting as follows: π
π
πΉ = β π€π π§π β π§π / β π€π π=1
(2)
π=1
where nk is the unit vector, β is the tensor product, π€π is the weighting function, and N is the total number of the unit vectors. The fabric tensors obtained from the two-dimensional SEM
ACCEPTED MANUSCRIPT Μ and the anisotropy images can be further described using the major principal direction ππ intensity factor, Ξ± = FI β FII, where FI and FII are the major and minor principal components, Μ is the mean orientation of the elements respectively (e.g., Fu and Dafalias 2015). Note that ππ being quantified, and is measured with respect to the horizontal plane, and the counter-clockwise
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rotation is considered as the positive direction. In this study, the fabric tensors were constructed
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based on the orientation of the major axis of the particles and voids, and simply termed particle-
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based and void-based fabric tensors, respectively, in the following discussion. Also, for each
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type of fabric tensor, the corresponding major-axis length of the particles or the voids was chosen as the weighting function.
EXPERIMENTAL RESULTS AND DISCUSSION
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4
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The deformation characteristics of kaolinite samples subjected to 1-D consolidation at different
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loading stages is presented first. Then, the microstructural characterizations of kaolinite samples
Deformation characteristics of 1-D consolidation
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4.1
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based on the MIP and SEM analyses are discussed in detail.
Fig. 4a presents the corresponding consolidation curves of the kaolinite samples. All the data
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points from four different 1-D consolidation tests, with different maximum consolidation pressures, are shown; the consistent responses of the samples tested suggest similar properties were exhibited by all the samples. According to the graphical method suggested by Casagrande (1936), the pre-consolidation pressure is determined as ~55 kPa.
ACCEPTED MANUSCRIPT 4.2
Evolution of the pore-size distribution in response to 1-D consolidation
Fig. 4b presents the MIP analyses of the kaolinite samples subjected to different 1-D consolidation pressures. For comparison, the sample after slurry-consolidation, referred to as the
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initial state, is also presented. With an increase in the vertical stress, ππ£β² , it is observed that the
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dominant pores, i.e., the peaks of the distribution curve, shift to a smaller size, indicating the
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gradual collapse of the pores upon compression. To facilitate the discussion on the associated microstructural changes in the next section, as indicated in Fig. 4b, a boundary between the inter-
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and intra-aggregate pores is established based on the supporting evidence provided below.
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As noted, published results have shown that the intra-aggregate pores are related to the entrapped and constricted porosity and therefore the volume of intra-aggregate pores remains
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almost unchanged in response to consolidation and shearing (e.g., Delage and Lefebvre 1984;
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Griffiths and Joshi 1989; Romero et al. 1999; Wang and Xu 2007; Kanayama et al. 2009). Based on this supporting finding, the range of pore-size where all samples subjected to different loading
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show a similar distribution is considered as the intra-aggregate pore range. Hence, the pore-size
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of ~0.14 ΞΌm is categorized as the upper boundary of the intra-aggregate pores in the following discussion; this value is also similar to the finding in Yu et al. (2016) for a Speswhite kaolin
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sample. Also, with respect to the total volume of voids, it is observed that the percentage of the inter-aggregate pores (i.e., pore size above 0.14 ΞΌm) decreases from ~87.5% (initial state) to ~82.5% (subjected to 1-D consolidation at 250 kPa). Nevertheless, as observed from the SEM images, the sizes of the two types of pores actually vary over a wide range. Hence, the boundary should lie within a range of pore diameters, depending on the condition of the samples, rather than a precise and single value. Herein, for simplicity, a definite value, i.e., 0.14 ΞΌm, is used as the boundary between the intra- and inter-aggregate pores herein.
ACCEPTED MANUSCRIPT The quality of all the pore-size measurements in this study is demonstrated in Table 1 by comparing the total intrusion volume (per gram) in the MIP test and the measured water content. Note that a total intrusion volume of 0.681 ml/g corresponds to a water content of 68.1%. The results shown in Table 1, according to Nagaraj et al. (1990), generally suggest a good quality of
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pore-size measurement in this study, where the size of pores is within the measurement range of
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the MIP equipment as well as the existence of non-interconnected voids and bottle-neck effects
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are considered as negligible in this study [similar to the findings reported by Delage and
Microstructural characterizations based on the SEM images
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4.3
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Levebvre (1984), and Griffiths and Joshi (1989)].
In this section, the results of the quantitative microstructural analyses based on the SEM images
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are discussed. Changes of the particle-based and void-based fabric tensors are presented first,
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followed by the evolution of the pore shapes. As described previously, about 20-30 SEM images
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were taken for each sample to provide representative characterizations. 4.3.1 Evolution of the directional distribution of particles and voids and their associated
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fabric tensors
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Fig. 5 presents the statistical analysis of the particles, based on all the SEM images taken, in response to different 1-D consolidation pressures, ππ£β² . As shown in Fig. 5a, the particle orientation is gradually towards the horizontal direction as ππ£β² increases. This tendency is further examined and quantified using the particle-based fabric tensors as presented in Fig. 5b, where the distribution of the associated anisotropy intensity factor, πΌπ , obtained from each SEM image, is shown. Note that the sample size P (i.e., number of SEM images taken), mean Β΅ and standard deviation Ο of the distribution of πΌπ are also specified in the figure for reference. The normal
ACCEPTED MANUSCRIPT distribution is chosen as it fits the experimental data more closely, according to the KolmogorovSmirnov test. At ππ£β² = 30 kPa, the distribution of πΌπ is wide with a low peak value. This indicates that the arrangement of particles at this consolidation state in the sample exhibits a wide range of forms, i.e., from a random distribution to an oriented arrangement along the major
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principal direction; the whole sample is less uniform in terms of the particle arrangement. As ππ£β²
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increases, a narrower distribution of Ξ±p associated with a higher Β΅ and a lower Ο is obtained,
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Μ . suggesting that the particle orientations tend to converge to the major principal direction, ππ,π
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To put it another way, the whole sample gradually becomes more uniform in terms of the particle arrangement as ππ£β² increases. This behavior can be better viewed in a summary figure, i.e., Fig.
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Μ , which is also summarized in Fig. 7a, is randomly distributed at ππ£β² = 7a. The evolution of ππ,π
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30 kPa, and then gradually becomes closer to ~0Β°, i.e., perpendicular to the loading direction, as ππ£β² increases. These results provide additional quantitative evidence to that based on the
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experimental observations (e.g., Hicher et al. 2000; Hattab and Fleureau 2011) and numerical
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simulations (e.g., Anandarajah 2000), i.e., the structural anisotropy of the particles becomes
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more pronounced as the 1-D consolidation pressure increases. Fig. 6 presents the statistical analysis of the voids subjected to different 1-D consolidation
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pressures. In addition, a summary of the associated anisotropy intensity factor of the void-based Μ , is given in Fig. 7b. fabric tensor, πΌπ£ , and the major principal direction of the voids, ππ,π£ Coincidentally, like the particle orientation behavior, the void orientation also becomes more uniform and tends to be in the horizontal direction as ππ£β² increases. These observations can be attributed to the collapse of the flocculated structure (a card-house like structure) during 1-D consolidation (further discussed next).
ACCEPTED MANUSCRIPT Although the particle orientation-based fabric tensors can quantitatively describe how the particles make an adjustment in response to 1-D consolidation, the orientation determined is associated with the particles rather than the aggregates that contain the particles. However, the responses to loading mainly occur through the aggregate-to-aggregate interactions in clayey soils
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(e.g. Delage and Lefebvre 1984; Griffiths and Joshi 1989; Hicher et al. 2000; Wang and Xu 2007;
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Kanayama et al. 2009; Yu et al. 2016). In addition, the void-based fabric tensors provide no
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information regarding the pore-shape features during pore rotation. Hence, to tackle these issues,
inter- and intra-aggregate pores, are carried out.
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further analyses of the SEM images, particularly considering the individual contribution of the
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4.3.2 Evolution of the microstructural features of voids
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To distinguish the responses of the inter- and intra-aggregate pores (voids), the number fraction,
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ππ , and the area fraction, π΄π , are therefore defined as: number of the specific type of pores observed total number of pores observed
(3)
π΄π =
cross sectional area of the specific type of pores observed total cross sectional area of pores observed
(4)
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CE
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ππ =
where π = 1, 2 represents the inter- and intra-aggregate pores, respectively. In addition, the equivalent diameter of a void, defined as the diameter of a circle with the same area as the void, is considered comparable to the mean pore diameter obtained in the MIP test and is therefore used to categorize the voids as inter- or the intra-aggregate pores. Figs. 8a-d presents the summaries of the pore features of kaolinite sample after 1-D consolidation at ππ£β² = 30, 100, 200 and 250 kPa, respectively. As shown in the figures, the cross-
ACCEPTED MANUSCRIPT sectional area occupied by the inter-aggregate pores is found to be much larger than that of the intra-aggregate pores (i.e., π΄1 >> π΄2 ), although the number of the intra-aggregate pores observed is greater (i.e., π2 > π1 ). This further verifies that the inter-aggregate pores are dominant in the loading response, and therefore the orientation of the voids observed in Fig. 6a is mainly
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contributed by the behavior of the inter-aggregate pores. Note that the corresponding major-axis
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length of the voids is used as the weighting function when calculating the fabric tensor.
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As the inter-aggregate pores are shown to be dominant in the loading response, the
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associated changes in the pore features are examined to further reveal the deformation mechanism during 1-D consolidation. The average elongation factor πΈπ_β , measured between
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angles g and h (in degrees), which is similar to the shape descriptor suggested by Mollon and
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Zhao (2012), is therefore introduced: π
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πΈπ_β
1 ππ΅ = β π ππ΄
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π=1
(5)
where N is the total number of pores, and ππ΄ and ππ΅ are respectively the major- and minor-axis
CE
lengths of the equivalent ellipse that describes the voids. To ease the presentation, the term E,
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instead of πΈπ_β , is used in the following discussion, unless the range of pore orientation degrees is required to be specified. In general, E = 1 means that the pores are perfectly round whereas E β 0 indicates that the pores are very elongated. The E value is calculated in intervals of 10 degrees of void orientation. For example, as shown in Fig. 8a, for all the voids with an orientation between 90ο°-80ο°, the average elongation factor E is 0.50. To facilitate discussion, the corresponding ellipse that matches the calculated E value is also plotted in the figure as a reference, and the associated orientation also represents the
ACCEPTED MANUSCRIPT pore orientation. Among all the loading stages, it is found that E exhibits a minimum value for those pores aligned horizontally (ΞΈ β 0Β°; termed case I) and a maximum value for those pores aligned vertically (ΞΈ β -90Β° or 90Β°; termed case II). As ππ£β² increases, the minimum value of E decreases (case I) and the maximum value of E increases (case II). That is, for case I, subsequent
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loading further compresses and then elongates the pores which are initially aligned horizontally
IP
and therefore E decreases with an increase in ππ£β² . On the other hand, for case II, subsequent
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loading gradually compresses the card-house structure and the aggregates reposition by moving downwards. Hence, the associated pores, which are initially elongated vertically, are compressed
US
into a rounder shape and therefore E increases with an increase in ππ£β² . Ultimately, regardless of
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the initial conditions of the pores, it is believed that all the pores tend to elongate along the horizontal plane when the pressure is sufficiently high. The results shown in Figs. 8a-d also
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reveal that as ππ£β² increases, all the inter-aggregate pores gradually concentrate to align in the
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horizontal direction and the associated pore shape gradually becomes flattened with a lower E
Demonstration of the fabric evolution during 1-D consolidation
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4.4
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value.
Summarizing the previously analysed results and discussion, the fabric evolution of kaolinite soil
AC
during 1-D consolidation can be demonstrated as shown in Fig. 9. Note that the orientation of the voids and the corresponding average elongation factor illustrated in the figure at each consolidation stage are based on the values obtained from Figs. 8a-d, as marked by an arrow, i.e., E80Β°_90Β° = 0.50 at ππ£β² = 30 kPa, E60Β°_70Β° = 0.58 at ππ£β² = 100 kPa, E40Β°_50Β° = 0.45 at ππ£β² = 200 kPa and E0Β°_10Β° = 0.32 at ππ£β² = 250 kPa. Initially as ππ£β² = 30 kPa, the flocculated (card-house-like) structure, which encloses the inter-aggregate pores elongating in the vertical direction, remains
ACCEPTED MANUSCRIPT stable. When ππ£β² increases beyond the pre-consolidation pressure, i.e., ππ£β² = 100 kPa in this case, each aggregate moves as a unit and the associated movement subsequently disrupts the stability of the card-house structure. The card-house structure gradually collapses and therefore the enclosed pores are compressed. With further increasing of ππ£β² up to 200 kPa, the aggregates
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progressively adjust themselves to align towards the horizontal plane, as do the particles
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contained in the aggregates. Finally, at ππ£β² = 250 kPa, such an orientation tendency in the
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horizontal direction becomes more pronounced. As shown in Fig. 9, the pores also rotate,
US
accompanied with rearrangement of the aggregates and gradually becoming aligned to the horizontal direction. The scenarios illustrated in Fig. 9 also simply explain the consistent trend
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between the particle orientation and void orientation, as observed in Figs. 7a and 7b. Nevertheless, further investigations are needed to identify the structure of the aggregates based
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on the SEM images. Further, it should be noted that the conclusion drawn here only applies to
CONCLUSIONS
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5
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kaolinite clay and may not be applicable to other types of clay minerals, such as montmorillonite.
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In this study, the microstructural responses of kaolinite samples subjected to 1-D consolidation were quantitatively characterized by means of micromechanical analyses based on SEM images,
AC
in addition to the pore-size distribution determined by the MIP test. The salient findings are summarized as follows. Unlike most published results, the applied loading was maintained at different loading stages during rapid freezing of the sample, in order to preserve the fabric associations not affected by the unloading effects of the subsequent characterizations. This was achieved using the newly invented 3D printed oedometer. In addition, for each sample at different loading stages,
ACCEPTED MANUSCRIPT at least ~3000 particles were identified manually to provide representative sampling for micromechanical analyses. By using appropriate binary images, the voids and solids (particles and aggregates) were separated; and the region-based method was adopted to further describe voids of irregular shape using an equivalent ellipse.
IP
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With a definitive boundary established between the intra- and inter-aggregate pores based on the MIP results, the quantitative SEM analyses further reveal that the inter-aggregate pores
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exhibit a significantly large area fraction and therefore dominate the deformation responses.
US
Μ and the Based on the analyses of the fabric tensors, in terms of the major principal direction ππ anisotropy intensity factor Ξ±, it is found the particles tend to align horizontally in response to the
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increased consolidation pressure. Interestingly, the void fabric exhibits a similar orientation
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tendency. To provide complementary information and further understand the deformation mechanism of kaolinite clay subjected to 1-D consolidation, the shape evolution of the inter-
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aggregate pores by means of the elongation factor, E, (E = 1 represents pores that are perfectly
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round whereas E β 0 indicates the pores are very elongated) was examined, also based on the SEM images. It is found that E exhibits a minimum value for those pores aligned horizontally
CE
and a maximum value for those pores aligned vertically. As the consolidation pressure ππ£β²
AC
increases, the minimum value of E decreases and the maximum value of E increases. These findings can be attributed to the compression process of the inter-aggregate pores during the collapse of the card-house structure formed by the aggregates. As ππ£β² increases, the card-house structure of kaolinite clay is compressed, and the aggregates reposition by moving downwards. Hence, the enclosed inter-aggregate pores, which are initially elongated vertically, are compressed into a rounder shape and therefore E increases. Following the same tendency as for card-house collapsing, the pores which are initially aligned horizontally are further compressed
ACCEPTED MANUSCRIPT and become more elongated in the horizontal direction, and therefore E decreases as ππ£β² increases. Ultimately, the inter-aggregate pores gradually concentrate to align in the horizontal direction and the associated pore shape gradually becomes flattened with a lower E value. The particles that form the aggregates also unavoidably follow the same trend and align in the
IP
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horizontal direction. Lastly, it is important to reiterate that similar microstructural characterizations could be
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carried out for other geotechnical testing, e.g., direct shear and triaxial tests, to enhance the
US
statistical representation of the result, provided that the applied loadings are maintained in
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preparing the specimens for the subsequent microstructural characterizations.
ACKNOWLEDGMENTS
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This research was supported by the Hong Kong Research Grants Council (project no. T22-
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603/15N) and Hong Kong PhD Fellowship Scheme (HKPFS). The authors are grateful to the
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CE
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reviewers for their valuable comments.
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ACCEPTED MANUSCRIPT Kuganenthira, N., Zhao, D. and Anandarajah, A. (1996). Measurement of fabric anisotropy in triaxial shearing. GΓ©otechnique, 46(4), 657-670. Li, X. and Li, X.S. (2009). Micro-macro quantification of the internal structure of granular materials. Journal of Engineering Mechanics, ASCE, 135(7), 641-656. Mollon, G. and Zhao, J. (2012). Fourier-Voronoi-based generation of realistic samples for
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Table 1
Comparisons of the total intrusion volume per gram in the MIP tests and the measured water content.
Samples
Total intrusion volume in Measured water content (%)
After compression at 100 kPa
0.559
After compression at 200 kPa
0.525
After compression at 250 kPa
0.508
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0.643
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After compression at 30 kPa
68.8
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0.681
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Initial state
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the MIP tests (ml/g)
64.6 56.8 52.9 51.2
ACCEPTED MANUSCRIPT LIST OF FIGURES Summary of the important features in each step of sample preparations for microstructural analyses: (a) slurry-consolidation; (b) 1-D consolidation; and (c) specimen preparations for microstructural analyses (after Chow and Wang 2017).
Fig. 2
Selected SEM images to illustrate the identification of the microstructure of the kaolinite samples: (a) particle identifications by the hand tracing method; and (b) void identifications by the binary segmentation method (black and white represents voids and particles, respectively).
Fig. 3
The number and area of voids identified while using different threshold level (TL) to convert the SEM photographs to binary images.
Fig. 4
The soil responses after 1-D consolidation at different pressures: (a) the consolidation curves of kaolinite samples; and (b) the pore-size distribution of the kaolinite samples.
Fig. 5
The statistical analysis of the particles of kaolinite samples after 1-D consolidation: (a) the overall direction distribution of particles; and (b) the distribution of the anisotropy intensity factor of particle-based fabric tensors.
Fig. 6
The statistical analysis of the voids of kaolinite samples after 1-D consolidation: (a) the overall directional distribution of voids; and (b) the distribution of the anisotropy intensity factor of void-based fabric tensors.
Fig. 7
A summary of the major principal direction and anisotropy intensity factor obtained from (a) the particle-based fabric tensors; and (b) the void-based fabric tensors.
Fig. 8
A summary of the pore features of kaolinite sample after 1-D consolidation at (a) 30 kPa; (b) 100 kPa; (c) 200 kPa; and (d) 250 kPa.
Fig. 9
Demonstration of the fabric evolution during 1-D consolidation. Note that the orientation of voids and its corresponding average elongation factor used for each consolidation stage are as specified in Figs. 8a β d.
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ACCEPTED MANUSCRIPT HIGHLIGHTS The microstructural responses of kaolinite are quantitatively analysed.
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Load-preserved, high quality kaolinite samples are prepared for analysis.
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Fabric tensors are used to quantify the direction distribution of fabrics.
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The shape evolution of inter-aggregate pores is examined.
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