Introduction

Developing a correct understanding and description of the anisotropic behavior of undisturbed loess is among the important problems in geotechnical engineering in loess areas. Cagauan and Uehara (1965) defined the anisotropy of soil as the degree of orientation of soil particles and limited it to the optical anisotropy of natural undisturbed soil units. However, for most natural clays, the clay minerals are usually elongate or tabular, and they are always present in the soil as large and small aggregates, with large aggregates capable of containing smaller aggregates (e.g., microaggregates), which continues until soil is formed (Shi et al. 1998). The microfabric formation of the arrangement of clay grains and aggregates in the soil may be related to the directional dependence, i.e., anisotropy, of the macroscopic physical properties. These anisotropic features are also manifested in various aspects, such as elastic anisotropy (Graham and Houlsby 1983; Lonardelli et al. 2007), thermodynamic anisotropy (Hueckel and Pellegrini 1996), magnetic anisotropy (Sun et al. 1995; Wang et al. 1995; Lagroix and Banerjee 2002), strength anisotropy (Liang et al. 2016; Zhang et al. 2017), deformation anisotropy (Cairncross and James 1977; Karlsson and Karstunen 2017; Xu et al. 2018), and permeability anisotropy (Leroueil et al. 1990; Chapuis and Gill 1989; Henderson and Pena 2017; Hong et al. 2019). Therefore, the study of the soil microfabric (or POGA) is an important perspective for studying the macroscopic anisotropy of soil.

Many pioneering studies on clay grain aggregates and their microfabric orientation indicate that the microfabric is an important cause of soil anisotropy (Cagauan and Uehara 1965; Morgenstern and Tchalenko 1967a, b; Lafeber 1967; Matalucci et al. 1969, 1970a, b; Tovey 1973; Osipov and Sokolov 1978; Hartley 1990; Hicher et al. 2000; Magaldi et al. 2002; Zhao et al. 2018). Although many attempts have been made to explain the orientation of grain aggregates or microfabrics via polarizing microscopy (Lafeber 1967), X-ray diffraction (XRD) (Brewer and Haldane 1957; Curtis et al. 1980; Zevin and Viaene 1990), scanning electron microscopy (SEM) (Matalucci et al. 1969, 1970a, b; Edil and Krizek 1975), and nuclear magnetic resonance (NMR) (Özarslan and Basser 2008), a quantitative description has not been provided. Tovey (1980) Tovey et al. (1989, 1992a, b; Tovey and Krinsley 1992) presented an index to quantitatively measure and evaluate the orientation of the soil grains and fabric by using an image processing technique, i.e., the index of anisotropy (Ia). Later, Shi et al. (1995, 1998) and Shi (1996) introduced Shannon entropy and proposed two methods for evaluating the order extent of the soil fabric: probability/alignment entropy (Hm) and frequency distribution function. A soil microanisotropy evaluation system has basically been formed (the Tovey-Shi evaluation system), and Shi et al. (1998) used this evaluation system to evaluate the orientation of compacted soil microfabric and its application in a micromechanical model. Wang et al. (2008a, 2010) and Wang (2009) applied the Ia to study the problem of particle orientation in pollutant barrier material and roadbed compacted clay by ArcGIS software. Tang et al. (2012) quantitatively analyzed the orientation of micropores before and after freezing of Shanghai silty clay. Zhang et al. (2017) used Hm to evaluate the strength anisotropy of undisturbed loess and the orientation mechanism of soil particles in Xining, China. Obviously, the Tovey-Shi evaluation system of soil microanisotropy is helpful for understanding the macroscopic anisotropy behavior of soil.

Chinese loess is a kind of aeolian sedimentary clay formed in arid and semiarid climate. Under the alternation of cold and warm paleoclimates, the stratigraphic profile shows distinct anisotropy. In the process of sedimentation and consolidation of the natural soil layer, the transport rate of soil particles and the structural units composed of these particles is slow, and the growth rate of the overlying soil pressure is lower than that of the solidification bonding between particles. Therefore, loess aggregates are often oriented and constitute structural anisotropy. This structure is also an important reason for the anisotropy of the physical properties of loess. In this paper, the orientation characteristics of soil aggregates are reflected by quantitative data, such as the roundness (R), orientation angle (θ), and Ia and Hm, contained in SEM photographs of loess in horizontal and vertical directions with different burial depths, and the anisotropic nature of the loess microfabric is revealed. Undoubtedly, it is of great significance to understand the soil anisotropic behavior from the POGA and promote research on the soil structure.

Materials and image processing

Site description and soil sampling

Chinese loess is famous for its wide distribution, large thickness, complete stratigraphic development, and continuous sedimentary time, and it is mainly distributed between 30°N and 49°N and 75°E and 127°E. The Loess Plateau is most developed from 34°N to 39°N and has a distribution area of approximately 630,000 km2. The research site at Yan’an is located in the middle of the Loess Plateau (Fig. 1b), which belongs to an arid-semiarid climate in the midlatitude zone. The upper layer of the late Quaternary aeolian loess was formed approximately 5~10 ka from the present and has a deposition thickness of approximately 10~30 m (Fig. 1c). Because the shallow loess is still underconsolidated and less disturbed by consolidation, the soil particles inherit more of the shape of the initial accumulation. Therefore, we selected shallow loess to study the characteristics of POGA.

Fig. 1
figure 1

Regional investigation and sampling process: (a) distribution of loess in China and prevailing wind direction of the Loess Plateau (Zhang et al. 2010); (b) location of Yan’an; (c) engineering site; (d) depth survey; (e) excavation of block samples; and (f) manual sampling and marking and sealing of the samples

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The loess used in the experiment was obtained from a fresh section of the Cutting Hills and Filling Land project for the Phase I Project in the Yan’an New Area. The soil samples were manually cut at depths of 2 m, 4 m, 6 m, 8 m, and 10 m below the surface (Fig. 1d). Large cubic clods were excavated from the section (Fig. 1e), and they were then cut into cylindrical soil columns, loaded into a metal bucket, and filled with crushed soil in situ to prevent breakage. The orientation was calibrated by compass, and the score was marked on the top of the soil column. The sample information was recorded on the label, and then the container was sealed with plastic tape and returned to the laboratory (Fig. 1f). The particle size distribution of the soil samples was determined using a laser particle size analyzer, and the soil was classified by the particle size (Fig. 2a and Table 1). The basic properties of the same soil have been published by Li and Li (2017) and Hong et al. (2019), and the values are shown in Fig. 2b and Table 1.

Fig. 2
figure 2

Soil description: (a) particle size distribution and classification and (b) properties of the Yan’an Malan loess

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Table 1 Basic properties of the samples
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ω is the natural moisture content; ρ is the natural density; e is the porosity ratio; WP is the plastic limit; WL is the liquid limit; IP is the plaster index

Specimen preparation and photo collection

SEM is an effective method for studying the microstructure of soil. SEM surveys have also been widely used to study the POGA. However, the preparation of soil microsamples is a relatively complex process, and the quality of sample preparation directly determines whether the SEM photos can truly reflect the microfabric characteristics of the soil. Generally, soil microsamples can be divided into two categories according to the observed surface conditions. (a) The first category is relatively flat surfaces (Fig. 3a), such as splitting/fracture surfaces (Delage and Lefebvre 1984; Hicher et al. 2000; Liu et al. 2011; Hattab et al. 2013; Nguyen et al. 2014). Although the authors attempt to prepare a flat observation surface, this method will inevitably lead to the separation of some particles from the original section (Wang 2009), and it will also disturb the adjacent microfabric. In addition, the observation surface of the split/fracture surface under the microscope is uneven, and the microscopic photographs have a certain field depth. Therefore, the particle/pore boundary is difficult to define, which makes the postprocessing of SEM photographs more difficult and leads to deviations in microscopic statistics. (b) The second category is solid-sliced surfaces (Fig. 3b). In addition to the relatively time-consuming curing process, this method almost completely avoids the disadvantages of the first method, and its advantages are obvious; therefore, it is also widely used in soil microstructure research (e.g., Morgenstern and Tchalenko 1967a, b; Lafeber 1967; Matalucci et al. 1969, 1970a, b; Liu et al. 2015; Li and Li 2017; Li et al. 2018).

Fig. 3
figure 3

Comparison of two microsamples under the microscope: (a) splitting/fracture surfaces and (b) solid-sliced surfaces

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Therefore, the solid-sliced sample preparation method was adopted in this study. The impregnating solution of the curing treatment was prepared with epoxy resin (cementing agent), acetone (diluent), ethylenediamine (curing agent), and dibutyl phthalate (plasticizer) at a volume ratio of 60:30:4:1. The specific operation steps of the curing treatment have been published by Li and Li (2017) and Li et al. (2018) to study the loess microstructure. The preparation process of the microsamples and image acquisition using a Quanta FEG 450 scanning electron microscope are shown in Fig. 4.

Fig. 4
figure 4

Microsample preparation process and SEM photo collection: (a) sample drying and cutting small cylinders; (b) impregnating the sample under low pressure generated by a vacuum pump; (c) cutting off the excess part of the specimen; (d) Transferring the specimen to the impregnation mold; (e) lapping and polishing the impregnated sample with sandpaper and polishing agent, respectively; (f) filming the SEM photo by the Quanta FEG 450; and (g) obtaining SEM photos

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Image postprocessing

Graphic vectorization is one of the basic functions of ArcGIS, which was used to process the SEM photographs and has been used in the study of the microstructure pore/particle fractals of cohesive soil (Wang et al. 2004, 2007) and three-dimensional reconstruction and visualization (Wang et al. 2008b) and orientation of clay particles (Wang et al. 2008a, 2010; Wang 2009). Wang et al. also provided a detailed introduction on the use of ArcGIS to process SEM photographs (Wang et al. 2008a, 2010; Wang 2009) and used SEM photographs with high and low undulation (split/fracture surface) to study the soil microstructure features. In this study, ArcGIS 10.2 (ESRI 2013) software was used as a vectorization tool to process the solid-sliced SEM images to study the POGA in the same profile with depth.

The image postprocessing flow is shown in Fig. 5. The ArcGIS vectorization tool is used to convert the SEM image into vector polygons. Classification was conducted according to the particle size (Fig. 1a), and incomplete particles along the edges of photos were removed. The area, perimeter, maximum diameter (dmax), minimum diameter (dmin), and θ of each particle were statistically obtained. The rose pattern of the POGA is drawn according to the θ, and the long axis (Dmax) and the short axis (Dmin) as well as the principal θ of the best fitting ellipse of the rose chart were obtained by using the standard deviation ellipse principle of the ArcGIS toolbox.

Fig. 5
figure 5

ArcGIS image postprocessing flow: (a) original SEM image; (b) using ArcGIS to convert SEM images into vector polygons and classify the polygons; (c) extracting morphological data of the particles, including the area, perimeter, maximum diameter, and minimum diameter; (d) drawing standard deviation ellipse of particles; (e) obtaining the orientation angle; (f) plotting the azimuth rose diagram; and (g) determining the general direction and anisotropy parameters of soil using a standard deviation ellipse

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Statistical methods

Roundness (R)

R is a shape factor that is a widely used two-dimensional shape measurement method and an important indicator of particle shape. For a circle, its R has a maximum value of 1, and for a shape with a low ratio area (A) to perimeter (P), such as a narrow or thin shape or a rough-edged shape, its R value is less than 1 (Arasan et al. 2011). Cox (1927) initially defined a two-dimensional R, which is easy to measure according to the concept of three-dimensional objects’ sphericity. That is, R is the degree to which the ratio of the area to the circumference approaches the same ratio for a circle, and its expression is shown in Eq. (1):

$$ R=\frac{4\pi A}{P^2} $$
(1)

Anisotropy index

To reflect the overall orientation of the soil microfabric, Tovey (1980) defined Ia as the ratio of the principal axis to the minor axis of the optimal fitting ellipse of the rose diagram of the soil fabric orientation distribution and used this ratio to reflect the degree of soil fabric anisotropy (Dmax/Dmin). Later, Tovey et al. (1989) improved the above definition as (1 dmin /Dmax), which was used by Tovey and Krinsley (1990) and Tovey et al. (1992a, b) to perform a directional analysis of fine minerals and micropores in soil and sediments. Shi et al. (1995, 1998), Shi (1996) and Wang et al. (2008a) applied this improved formula to study the orientation of clay microscopic fabric (grain or pore). Therefore, the definition of Ia adopted in this study is shown in Eq. (2):

$$ {I}_{\mathrm{a}}=\frac{d_{\mathrm{max}}-{d}_{\mathrm{min}}}{d_{\mathrm{max}}}\times 100\% $$
(2)

Probability/alignment entropy

The Ia reflects the overall distribution of the cohesive soil microfabric to a certain extent, but it does not reflect the orderliness of the body of the fabric unit. Shi et al. (1995, 1998) and Shi (1996) introduced Shannon entropy to reflect the orderliness of the arrangement of the microscopic structural units of the clay, called Hm (probability entropy or alignment entropy). Liu et al. (2011) and Zhang et al. (2017) also used this index to quantitatively evaluate the degree of order of microscopic pores in clay materials. Hm is defined as shown in Eq. (3):

$$ {H}_m=-\sum \limits_{i=1}^n\frac{m_i}{M}\bullet \frac{\ln \left({m}_i/M\right)}{\ln n}=-\sum \limits_{i=1}^n{P}_i\bullet {\log}_n{P}_i $$
(3)

where Hm is the probability entropy of the arrangement of cohesive soil structural units, mi is the number of particles in the i-th azimuthal zone, M is the total number of particles, and n is the number of azimuthal zones equally divided in the direction of the unit arrangement. The arrangement direction is 0°–180°, which is equally divided into 10° sections, with n = 18. Pi is the probability that the structural unit occurs in a certain azimuth.

Results and discussion

Variation in the roundness (R) with depth and its correlation with anisotropy

Many kinds of R classifications of particles have been developed according to different research purposes and research methods (Russell and Taylor 1937; Krumbein 1941; Powers 1953; Alshibli and Alsaleh 2004; Al-Rousan et al. 2007; Arasan et al. 2011). Based on the R value of Eq. (1), the R classification of Powers (1953) will be adopted in this paper. Powers believes that the angular group in the Russell and Taylor (1937) five-group classification should be subdivided and that a set composed of very angular particles should be added; therefore, the R of the particles can be divided into six categories.

Figure 6 shows that the rounded particle content is dominant in both vertical and horizontal soil aggregates. In the horizontal direction, the content of very angular, angular, and subangular particles changed little as the depth increased (by approximately 2.5%, 5%, and 10%, respectively), while the content of subrounded and rounded grains decreased slightly, and the number of well-rounded particles increased slightly. In the vertical direction, the variation in the angular and subangular grain contents was similar to the variation in the horizontal direction with increases in depth, and the contents were approximately 5% and 10%, respectively. The study of Zhang et al. (2017) also showed that undisturbed loess particles are mainly round or elliptical particles that are parallel to the natural sedimentary surface, which is consistent with the results of this study.

Fig. 6
figure 6

Roundness classification and its variation with depth: (a) parallel to the depositional plane (horizontal direction) and (b) perpendicular to the depositional plane (vertical direction)

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Relative frequency percentages of silt, fine sand, and medium sand grains in the various R classes of the aeolian sediments at different depths in horizontal and vertical directions studied are presented in histograms (Fig. 7). In the medium sand group, approximately 60~90% of the grains are rounded and well rounded, 10%~25% are subrounded, while very few are subangular, angular and very angular. In the fine sand group, approximately 55~75% of the grains are rounded and well rounded, 16~28% are subrounded, and approximately 10% are subangular, angular, and very angular. In the silt group, 55~63% of the grains are rounded and well rounded, approximately 18~25% are rounded, and approximately 20% are subangular, angular, and very angular. All of the studied sediments of silt and fine sand have a unimodal distribution with an R class that varies from rounded to angular. However, obvious differences are recognized between histograms of the R classes of the various size fractions. However, mainly subcircular, circular, and very circular sediments were observed, and these shapes mainly depended on the size fraction. Little variation was observed in the frequency distribution of the R classes of medium sand (less than 2%).

Fig. 7
figure 7

Histograms of the relative frequency percentages of the roundness classes in the grain-size fractions of the studied sediments. The abscissa is the roundness classification: 1 very angular, 2 angular, 3 subrounded, 4 subrounded, 5 rounded, and 6 well rounded. The number in the first column represents the depth of the soil, H represents the horizontal direction, and V represents the vertical direction

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Although R cannot directly reflect the anisotropy of the soil, it can control the anisotropy through the morphology, physical properties, contact mode, and POGA. Related studies have also shown that the shape of the particles during the deposition process seriously affects the contact pattern, orientation and anisotropy of the soil particles under the action of gravity (Matalucci et al. 1969). Moreover, round particles have greater shear stiffness (Manne and Devarakonda 2016) and lower stress state sensitivity than particles with other shapes (Cho et al. 2006). Thus, elongated particles in particular present more pronounced anisotropy than angular or round particles (Nouguier-Lehon et al. 2003).

Many studies have shown that the R of soil particle aggregates can indicate tectonic disturbances and reflect the sedimentary history of soil (Powers 1953) and it also has a controlling effect on the macroscopic physical properties of soil (Nouguier-Lehon et al. 2003; Ting et al. 1995; Kock and Huhn 2007; Alan et al. 2007; Li 2013; Li et al. 2013b). Among these properties, the relationship between the particle’s R and internal friction angle is important. The R of sand has a good linear relationship with the internal friction angle (Cho et al. 2006; Sivakumar et al. 2002; Santamarina and Cho 2004; Rousé 2005; Rousé et al. 2008), and clay-gravel mixed soil also has a similar linear relationship (Li 2013; Li et al. 2013b). However, for natural aeolian sediments, anisotropy was generated during the deposition process, and the POGA after deposition will also be affected by the positive correlation of the overburden pressure (Meade 1965), which will lead to a further increase in the directional dependence of the macroscopic physical properties of the soil.

Orientation angle change with burial depth

Since the directional orientation of the unit is mirror symmetrical within the range of 0–360°, only the orientation of the units in the range of 0–180° must be statistically analyzed. The 0–180° range is divided into 18 azimuths of 10° each, and the frequency of the particles in each section is determined. The degree of orientation of the micro unit in each subarea is determined to obtain an azimuth rose diagram that reflects the directional distribution of the units.

At all depths horizontal and vertical to the photomicrograph of the rose diagram, the grain aggregates have a certain degree of preferred orientation (Fig. 8).

Fig. 8
figure 8

Horizontal and vertical orientation angle rose diagram and its frequency distributions at different depths (m represents the burial depth, H represents the horizontal direction, and V represents the vertical direction)

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Horizontal direction

The histograms of the preferred orientation of the five horizontal micrographs have a distinct bimodal distribution, although this bimodal distribution remains to be further interpreted (Matalucci et al. 1969). Nevertheless, the preferred direction of the Yan’an Malan loess to the particles is generally between 130° and 150° (N40°W and N60°W), and the probability in this range is greater than 50%, although the maximum probability is only 56.82% (Fig. 8a, c, e, g, i). However, this phenomenon of uniformity of more than 50% at all depths likely indicates that the particles followed a certain regularity in the deposition process, which is similar to the aeolian genesis of Chinese loess. Many studies on Quaternary loess indicate that Chinese loess is the product of dust accumulation from the East Asian winter monsoon during the Quaternary glacial periods (Jing 1980; Li 1986; Wang 1987; An et al. 1991a, b; Pang 1999; Zhang 2001). The main provenance of this dust is Southern Mongolia and the adjacent Gobi and desert areas (Rutter 1992; Sun 2004), and it is mainly carried by near-surface winds (generally below 3000 m) (Zhang 2001; Sun 2004). In particular, the Late Pleistocene loess strongly reflects the close relationship with the Quaternary East Asian paleomonsoon (winter monsoon) climate (Fig. 1a) (Teng and Shen 1995; Ding and Yu 1995; Lu and An 1997, 1998; Sun et al. 1995; Pang 1999; Zhao et al. 2002; Xu et al. 2006; Zhang et al. 2010). This finding is mainly due to the cold climate of the Quaternary glacial period and the difference in the thermal properties between the land and sea, which led to a stronger winter monsoon than summer monsoon in East Asia. At that time, the Mongolian-Siberian region had low temperatures and high air pressure; the pressure gradient was larger, and the wind was stronger than those in the surrounding area. The winter monsoon controlled the climate in northern China for 8–9 months (Ding and Yu 1995). The front could reach the Yangtze River Basin (Pang 1999) and was capable of carrying a large amount of dust deposits over the Loess Plateau (Jing 1980). The summer monsoon in East Asia comes from the ocean. During the Quaternary, the East Asia region was generally hot, the temperature difference was small, the pressure gradient was small, and the East Asian summer monsoon circulation was very weak, and its activity range was limited to the south of the southern margin of the Loess Plateau (Sun et al. 1996). In addition, the summer monsoon’s effect on East Asia was also very short (Ding and Yu 1995) because of the Quaternary glacial climate, which was dry and with little rain; therefore, dry deposition was the main process of dust settlement in the loess area (Zhang 2001). Therefore, a large amount of accumulated loess could be preserved and continued to thicken (Jing 1980; Sun et al. 1996), which preserve the orientation of the particles to some extent (Sun et al. 1995). The direction of the long axis of the particles when the dust material was stacked was parallel to the dominant wind direction (Reading 1978; Sun et al. 1995; Wang et al. 1995). The East Asian winter monsoon prevailed in the Malan loess deposit period in the Loess Plateau, which coincided with the phenomenon that the particles were distributed horizontally in the slices at all depths. Although it is a weak fit, this result does not completely obscure the fact that the horizontal orientation of the particles likely occurred due to the paleowind direction. Matalucci et al. (1969) studied microscopic photographs of Vicksburg loess and former Vicksburg loess in Mississippi, USA, and showed that the preferred orientation of silt-sized particles preserved the local paleowind direction quite well. Lagroix and Banerjee (2002) also confirmed that the loess fabric in Alaska well recorded the paleowind changes in that area. In addition, this weak coincidence phenomenon (or bimodal distribution of the preferential orientation of particles) may also be due to the local variation in sedimentary wind direction caused by topography, atmospheric turbulence, or other meteorological factors (Matalucci et al. 1969; Wang et al. 1995). Obviously, for the aeolian loess in the Loess Plateau, where the climate is not conducive to the development of loam formation (Lagroix and Banerjee 2002), the loess of POGA in this region should also provide a good indication of the paleowind. If this rule can be verified by loess sections in different areas of the Loess Plateau, then it will be of great significance for both the genesis of loess and the study of paleoclimate.

Vertical direction

The preferred orientation of particles in the five vertical micrographs is substantially within 45° of the ground level (Fig. 8b, d, f, h, j). With increases in depth, the compaction effect increases, and this orientation is more significant. This phenomenon obviously indicates that the particles tend to form a more stable planar structure under the action of gravity and compaction during the deposition process; that is, the maximum axial plane of the particles always tends to adjust or rotate perpendicular to the direction of the maximum principal stress (Cetin 2004; Nouguier-Lehon et al. 2003; Kock and Huhn 2007; Hattab and Fleureau 2011). Many researchers have also confirmed that this preferred orientation of particles plays an important role in the formation of anisotropic structures in clay. For example, the results of Cetin (2004) show that the overburden earth pressure may cause a certain degree of preferential orientation. When the overburden earth pressure is less than the maximum effective (preconsolidation) stress, only small preferential orientations and small changes in soil structure will be observed. When the earth pressure is loaded to a stress level greater than the preconsolidation stress, the soil structure is rearranged or orientated into a new more stable and compact structure, which tends to be perpendicular to the direction of the maximum principal stress, and as the load increases, the degree of preferential orientation will increase, thus forming an anisotropic structure. Curtis et al. (1980) argue that the preferred orientation of particles in clay-rich sediments is almost entirely from compaction strain, although the presence of nonplanar particles also prevents the development of nearby planar structures. Hattab and Fleureau (2011) believe that when the consolidation stress reaches a certain position (under the triaxial path), the rotation mechanism of the particles to the preferential plane becomes more important. Obviously, the preferred orientation of vertical particle agglomerates is caused by compaction strain of clay particles and rotation of nonplanar particles, and this phenomenon is consistent with the macroanisotropy behavior of clay, which is controlled to a large extent by the directional dependence of its microfabric. In particular, the POGA has a very significant influence on the anisotropic behavior of clay (Matalucci et al. 1970a, b; Edil and Krizek 1975; Sachan 2007; Li et al. 2013a).

Anisotropy index and entropy with burial depth

Equation (2) shows that the variation range of Ia can extend from 0 to 100%. When Ia = 0, the soil microfabric is random and isotropic overall. When Ia = 100%, the soil microfabric is distributed in the same orientation and completely anisotropic. According to Eq. (3), Hm is in the range of [0,1]. When Hm = 0, the soil microfabric unit has a certain orientation distribution, which shows that the unit body is oriented and that orderliness is the highest. When Hm = 1, the fabric unit probability is the same at each azimuth, indicating complete disorderliness or complete randomness. In other words, larger Hm values correspond to more anisotropic fabrics, while smaller Hm correspond to more isotropic fabrics.

Figure 9a shows that with an increase in depth, the Ia of the silt and fine sand in the horizontal direction is greater than zero, and except for the minimum at 4 m, the Ia at other depths is more than 10%, with a more significant Ia of up to 20.54% observed for fine sand. The total Ia of soil grains gradually increases, with a maximum value of 15.49%. In the vertical direction (Fig. 9b), the Ia of silt, fine sand, and total soil grains increases with the depth of the soil layer. The soil grains have a directional arrangement overall and the anisotropy is remarkable. This finding indicates that as the overburden pressure increases, the clay particles deform or rotate so that the long axis direction of the soil particles tends to be horizontal.

Fig. 9
figure 9

Variation in Ia with depth: (a) parallel to the depositional plane (horizontal direction) and (b) perpendicular to the depositional plane (vertical direction)

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Figure 10 shows that the vertical total Hm values of the different burial depths are smaller than the horizontal values and the order of the vertical grain arrangement is better than that of the horizontal direction. For silt and fine sand, the Hm is > 0.5 for silt and between 0.608 and 0.812 in both the horizontal and vertical directions. For fine sand, the Hm value of fine sand is less than that of silt, and the minimum Hm value is 0.382, which indicates that fine sand tends to be more anisotropic. Thus, fine sand is a good indicator of anisotropy (Matalucci et al. 1969).

Fig. 10
figure 10

Variation in Hm with depth

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Figure 11 shows that Ia and Hm vary with the natural water content. As the water content increases, Hm decreases gradually, Ia increases gradually, and disordered soil fabrics changes toward ordered fabrics (directional fabrics), although this change relationship is not linear (Shi et al. 1998). When the moisture content was <15.8%, Hm showed little change (Fig. 11a), although the vertical direction had higher Ia than the horizontal direction and the vertical direction had more obvious directional soil arrangement characteristics overall, which increased along with the water content. When the water content exceeded this value, Hm in the vertical and horizontal directions decreased rapidly, and Ia increased rapidly (Fig. 11a). In other words, the ordering of the soil fabric increased, the directional soil arrangement characteristics became more obvious overall, and the anisotropy became more significant.

Fig. 11
figure 11

Changes in Ia and Hm with the water content (w): (a) this study and (b) compared with Shi et al. (1998)

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Compared with Shi et al. (1998), who performed a one-dimensional compression test of highly plastic expansive clay, the variation in Ia and Hm of the undisturbed loess and the compacted clay was similar to the variation in the water content (Fig. 11b). The difference was only caused by the difference in the threshold water content and consolidation pressure determined by the soil properties. When the consolidation pressure and water content increased to a certain value, the orientation characteristics of clay particle agglomerates became more apparent (Shi et al. 1998), thus causing anisotropy in the soil (Sivakumar et al. 2002). In addition, the orderly degree of soil fabric more directly indicated the stress-strain state of the soil and the external forces acting on it. Therefore, further study on the variation in Ia and Hm with stress and strain will be of great significance for understanding the physical and chemical properties of fine-grained soil (Shi et al. 1998) because they reflect both the direction of the soil and the order of the soil fabric.

Summary and conclusions

Based on the above analysis results, the following conclusions can be drawn.

The statistical results of R show that the undisturbed loess grains are dominated by rounded grains in directions parallel and perpendicular to the natural sedimentary plane. Although R cannot directly reflect the anisotropy of the soil, it can control the anisotropy through the morphology, physical properties, contact mode, and POGA.

The anisotropy characteristics of undisturbed loess are controlled by the POGA, which was determined by the SEM microphotographs of horizontal and vertical slices at different depths and the ArcGIS standard deviation ellipse. The POGA of the vertical direction in Malan loess is basically parallel to the depositional direction, and a deeper burial depth leads to a more significant result. The azimuth angle range of the POGA in the horizontal directional is approximately 130°–150° (N40°W–N60°W), which may hold some significance for the paleowind direction. Similar studies in other sections of the Loess Plateau are needed to test the robustness of the results obtained herein.

The Ia and Hm parameters are used to characterize the direction of the soil and the order of the grains and aggregates, respectively. Regardless of the vertical or horizontal direction, the Ia of the soil increases with depth, meaning that the directionality of the soil becomes increasingly obvious and the anisotropic characteristics increase. The Hm value changes little with depth in the horizontal direction and decreases with depth in the vertical direction, and the orientation of the grains and aggregates is also better in the vertical direction.

Compared with highly plastic compacted clay, the Ia and Hm show similar changes. When the water content is lower than the threshold value, the anisotropy and order degree increase as the water content increases. When the water content is on the right side of the threshold value, the soil fabric has significant anisotropy and a directional arrangement.

The research method can also be applied for the study of pore characteristics in porous media.