Quantitative Research and Characterization of the Loess Microstructure in the Bai Lu Tableland, Shaanxi Province, China

Loess is a special geotechnical material with strong structural properties, and the microstructural characteristics of loess significantly influence its macroscopic physical features, mechanical properties, and catastrophic behavior. In this paper, serial samples were extracted from the continuous loess and paleosol strata of the Bai Lu tableland; with these samples, the optical microscopy-based serial sectioning method was adopted to study the quantitative characterization and variation in the loess microstructure. -reedimensional characteristics and quantitative parameters of the particles, pores, and throats of the loess were obtained. -e results indicate that the volume, Eq-Radius, and major-minor axis ratio of the loess particles satisfy third-order, third-order, and secondorder Gaussian distributions, respectively. -e Eq-Radius of the loess pores and throats satisfies a first-order Gaussian distribution, and the throat channel length satisfies a gamma distribution.With increasing stratum depth, the particles becomemore flattened, the throat radii become larger and the pore channels become slenderer. -e variation in fitting parameters and the correlations between the macrophysical and mechanical properties of loess were then explored. -e study of the microstructure of loess contributes to a better understanding of the catastrophic behavior of loess and the physical mechanism of geologic hazards in this area.


Introduction
Loess generally shows a high strength when dry, but under conditions of soaking, the skeleton of loess weakens rapidly, which would result in the collapse of loess, settlement of loess ground, and instability of a loess slope [1][2][3]. As a special geotechnical material, loess is known for its strong structure, water sensitivity, and seismic vulnerability, among which the water sensitivity and seismic vulnerability essentially originate from its structural properties. Microstructural characteristics are the most dominant factors controlling the structural properties of loess and can directly influence the engineering properties and macroscopic mechanical behavior of loess [4,5]. As a granular material, the deformation and failure of loess begins with shear deformation and slippage among particles; on the other hand, the mechanical properties of loess are dominated by its microstructure [4,6,7]. e microstructure of loess mainly consisted of pores, particles, and connections, which control the contact system and force chains in the loess and then dominate the macrophysical and mechanical properties of loess [8]. e study of the microstructure of loess contributes to a better understanding of the catastrophic behavior and physical mechanism of loess geologic hazards.
Scientists and engineers have long noticed the importance of microstructure for the determination of loess engineering properties [9,10], and considerable efforts have been made to explore the microstructure of loess. ese studies mainly focus on the following aspects: (1) investigation of loess microstructural characteristics and variations among different regions and geological ages, (2) classification of loess microstructure and determination of the corresponding microstructural parameters, (3) evolution of loess microstructure under specific conditions, and (4) microscopic mechanism of typical loess geologic hazards.
Due to the variation in material provenance, sedimentary geological environment, and history, the microstructural characteristics and parameters vary from loess to loess. e structural characteristics of Malan loess in the midstream area of the Yellow River, which were studied using the oil immersion method, were described earlier in terms of the loess microstructure [9,11]. Subsequently, increasingly more studies have been presented. Loess samples from various regions, depths, and geological ages were extracted to study the pore sizes, particle characteristics, and cementations, as well as the types of loess microstructures [2,[12][13][14][15][16][17][18]. Mercury intrusion porosimetry (MIP) and scanning electron microscopy (SEM) are the most widely adopted techniques in such studies, and the investigations have mainly concentrated on the determination of the plane morphology, two-dimensional characteristics of the loess pores and particles, and corresponding microstructural parameters [19].
Determination of loess microstructure types could provide more insight into the catastrophic characteristics and mechanical behavior of loess. On the basis of microscopic observations, a widely used classification of pores in loess was proposed according to pore size. Four types of pores, macropores, mesopores, fine pores, and micropores, were proposed, and the division thresholds were pore diameters of 0.032 mm, 0.008 mm, and 0.002 mm, respectively [20,21]. Loess microstructure was divided into 12 categories by Gao [22,23], mainly considering the forms of grains, modes of arrangement, and types of connection, and divided into 6 categories by Lei, considering the cementation strengths and pore types [20,21]. e influence of microstructure types on the stability of loess has been properly studied [24], and many conceptual microstructure models have been proposed to explore the mechanism of loess deformation and failure [14,[25][26][27], which has a great significance for the assessment of loess engineering. e engineering properties of loess are fundamentally controlled by their microstructure. Many scholars have devoted their work to exploring the relationship between the microstructural parameters and mechanical properties of loess, and a combination of microtests and macrophysicalmechanical experiments has been carried out [5,[28][29][30][31][32]. e achievements demonstrated that the variation in loess strength is directly related to the changes in microstructure and that cementation bonds play an important role in the strength and deformation behavior of loess [30]. ese studies paved the way for the establishment of disaster theory of loess on multiple scales of analysis. e importance of loess microstructure for the understanding of loess collapse and corresponding geohazards has been demonstrated by many recent efforts [3,[33][34][35][36][37][38][39]. Based on microstructure tests and analyses, the formation and development of loess microstructures during collapse were divided into five stages [1]. Many conceptual models have been proposed to elucidate the origin of loess collapsibility [25]. e contribution of the microstructure to the strength of compacted loess after soaking was explored [40], and the relationship of the collapse potential versus the microstructural parameters of the loess was qualitatively studied [41]. e relationship between loess microstructure and seismic subsidence and the relationship between microstructure and shear strength under freezing conditions were studied [42][43][44][45]. However, despite these efforts, the current understanding of the cause of collapsibility and the underlying mechanisms controlling loess collapse behavior remain controversial or incomplete.
Notably, the research quality and image resolution have been improving gradually with the development of new observation apparatuses and processing technologies, and the achievements reflect the shift from qualitative analysis to quantitative research. Most of these achievements are concentrated around the characterization of two-dimensional (2D) morphology, and very few researchers have studied the three-dimensional (3D) microstructural characteristics of loess. To date, optical and electron microscopy, nuclear magnetic resonance (NMR), and X-ray computed tomography (CT) are the most commonly used techniques used to obtain microscopic images of soil, among which optical and electron microscopy are generally used to obtain two-dimensional images [46][47][48]. NMR is more suitable for detecting pores in materials filled with water, and highenergy X-ray CT scanning can be used to obtain images with higher resolutions but is expensive and not easily accessible to most researchers in geotechnical engineering. With the advent of serial sectioning, microscopy-based image analysis can be used to create 3D microstructures [49]. It is feasible to obtain the 3D microstructure of loess by combining optical microscope scanning, serial sectioning, and 3D image reconstruction. Although the method of optical microscopybased serial sectioning has the disadvantage of being timeconsuming and laborious, it is inexpensive and easy to follow yet produces large, high-resolution area images, which can capture both short-range features (particles) and long-range features (localized zones) to enable a more comprehensive characterization of the soil microstructure.
e Bai Lu tableland is located in the southern Wei He Basin, Shaanxi Province, China, and is covered by a great thickness of loess with continuous loess-paleosol interbedded strata. Due to the approximate flat geography, the typical microstructural characteristics of aeolian loess in the tableland were preserved well. In this paper, Di Zhai village was chosen as the research site. Data collection and field investigation were performed to determine the geological conditions of the site. Engineering drilling was carried out to explore the loess and paleosol strata. Serial samples from various loess and paleosol strata were extracted. Field and laboratory tests were conducted to obtain the physical and mechanical parameters of the loess. e optical microscopybased serial sectioning method was adopted; the experiment method included sample preparation, observation, image processing, structure reconstruction, and quantitative index analysis. e characteristics of the loess particles and pores and the microstructural parameters were systematically studied. is work could provide a scientific basis for the study of loess catastrophic mechanics theory and the construction of projects in this area.

Experimental Method and Scheme
e Bai Lu tableland is located in the southern Wei He Basin adjacent to the northern Qin Ling Mountains, which is a strip terrain oriented southeast-northwest and divides the Ba and Chan rivers. According to the geological tectonic background and evolution history, the Bai Lu tableland was formed on river terraces with aeolian loess covers and was affected by fault activity and fluviatile erosion. e geologic conditions of the study area are presented in Figure 1. According to the strata data, the loess in the Bai Lu tableland has been depositing since the early Pleistocene, accumulating a thickness of approximately 65-126 m of a continuous loess-paleosol strata sequence. e Bai Lu tableland is a suitable site for studying the variation in microstructural characteristics of the loess-paleosol sequence.
An 80 m deep geological borehole was drilled in Di Zhai village, from which 8 layers of loess and 7 layers of paleosol were explored. e depth and thickness of every layer are presented in Figure 1. Samples were extracted from every layer, with which the physical parameters were tested and are presented in Table 1.
e optical microscopy-based serial sectioning method was adopted to study the 3D microstructure of the loess. e experiment and image reconstruction process mainly involved the following steps. (1) Sample preparation: a subcubic sample with a side length less than 1.0 cm was extracted from the loess sample and then saturated in a vacuum environment using a special liquid. e liquid is a mixture of epoxy resin, acetone, ethane diamine, and dibutyl phthalate, with constant volume ratios of 200 ml, 100 ml, 4 ml, and 2 ml. Acetone has a low consistency and can be easily volatilized; the mixed liquid was diluted and could easily infiltrate into the pores of the loess sample. Ethane diamine and dibutyl phthalate accelerate the solidification process and improve the hardness of the sample. Finally, the sample was prepared via secondary casting for polishing and observation. (2) Image capture: the sample was polished to obtain a smooth plane using Multiprep equipment, with which the polishing process could be controlled to a precision of 0.1 μm. e planar image of the sample with the resolution of 0.4 μm/pixel was observed using a Leica DM6000M microscope. e sample was then repolished to remove approximately 2 μm, which was controlled using the vertical displacement laser monitor and the polishing duration. A series of 2D images with a spacing of 2 μm were then obtained. (3) ree-dimensional (3D) structure reconstruction: all the slices were aligned and converted to extract the particles and pores, adopting the appropriate threshold via the changes of gray scale. Generally, the point of inflection for the colormap of gray intensity is selected as the threshold value. e 2D images were calibrated, and the 3D particle and pore morphologies were then reconstructed using Avizo software. (4) Quantitative analysis: the microstructural characteristics, parameters, and variations of various layers of loess were then analyzed using the statistical indexes of particles, throats, and pores. e experiment and image reconstruction processes are presented in Figure 2. Since the undisturbed samples of strata L7 and L8 were not extracted successfully, the microstructure study mainly focused in strata L1-S6.

Three-Dimensional Quantitative
Characteristics of Loess Particles e morphological characteristics of loess particles could be depicted by adopting the parameters volume (V), Eq-Radius , orientation, and major-minor axis ratio, among which the orientation was described by adopting the angles phi and theta, and the major-minor axis ratio was defined as W/L. e definitions of the characteristic parameters of a loess particle are presented in Figure 3.
Figures 4(a) and 4(b) present the distribution of quantitative probability versus the corresponding volume of the loess particle, in which the test data, fitting curve, and cumulative probability curve of loess L1 and paleosol S1 are presented, respectively. According to the figures, the experimental data could be fitted well by applying the thirdorder Gaussian distribution function. e fitting function can be expressed as formula (1), in which x P−V represents the particle volume and α1, α2, α3, b1, b2, b3, c1, c2, and c3 are the fitting parameters. According to the fitting condition, the correlation coefficient of fitting is approximately equal to 1.0. For loess L1, 60% of the loess particles have a volume smaller than 35 μm , 70% of the particles are smaller than 65 μm , and 80% of the particles are smaller than 215 μm ; for paleosol S1, the thresholds of 60%, 70%, and 80% correspond to 70 μm , 150 μm , and 415 μm , respectively. Consequently, it is obvious that the loess L1 of the Bai Lu tableland is finer than the paleosol S1.
(1) Figure 4(c) presents a comparison of the fitting curves of various layers of loess and paleosol, indicating that the deeper layer generally involves a larger proportion of small particles, while layer L3 shows a finer particle characteristic. Figure 4(d) shows the variation in the fitting parameters of the loess and paleosol layers. Although the fitting parameter α1 varies from layer to layer, the value of α1 for the paleosol is generally greater than that of the adjacent loess layer. e values of b and c tend to increase with increasing depth.
Figures 5(a) and 5(b) show the distribution characteristics of particle Eq-Radius for L1 and S1, and the experimental data also satisfy the third-order Gaussian distribution well. Figure 5(c) presents the variation in the fitting curves for various loess and paleosol layers. e distribution of the curves depicted that finer particles are generally enriched in the upper layers except L3. Figure 5(d) gives the variation in fitting parameters, which shows that the values of the parameters b3 and c3 generally decrease with the increase in depth.

Advances in Civil Engineering
Figures 6(a) and 6(b) show the distributions of the major-minor axis ratio for loess particles from L1 and S1; these distributions exactly satisfied the second-order Gaussian distribution with a correlation coefficient up to 0.98. e probability density function in the distribution can be represented by adopting formula (2), where x (A−R) represents the major-minor axis ratio of the loess particles and α1, α2, b1, b2, c1, and c2 are the fitting parameters. According to the figures, the parameters α1, α2, b1, b2, c1, and c2 are regressed by applying the least squares method and are determined to be 0.1062, 011139, 1.837, 2.334, 0.337, and 0.6536 for loess L1 and 0.1283, 0.05716, 1.902, 2.599, 0.4602, and 0.8863 for paleosol S1. Figure 6(c) presents the variation in fitting curves for various loess layers and paleosol layers. e ratios of the major-minor axis length fall in the range of 1.0 to 4.0 for layers L1, S1, L2, S2, and L4, the range of 1.0 to 6.0 for layers L5 and S5, and the range of 1.0 to 8.0 for L6 and S6. Consequently, with increasing strata depth, loess particles generally become increasingly flattened.
(2)  value of loess particle orientation. e values of phi mainly fall in the ranges of 0-30°and 85-90°, which indicates that most of the loess particles were deposited with a gentle inclination and near-vertical orientation. According to Figure 7(a), the value of phi for the upper layer of soil is generally smaller when 0°< phi < 30°and larger when 85°< phi < 90°, which indicates that particles in the deeper layers of loess were more prone to be deposited horizontally. According to Figure 7(b), all the curves increase sharply near the angle theta � 90°, which indicates that the loess deposited with a predominantly eastward orientation, and the directionality characteristics are more obvious for the soil of the upper layer.    of voids control the structural, physical, and mechanical properties of loess, as well as its collapsibility, seismic subsidence, and other disaster-related behaviors. Based on the variation and influence of void morphology, we defined throats and pores to depict the void characteristics of loess quantitatively. e throat is defined as a narrow passage through loess pores and connects adjacent pores. e pores in loess could be generalized as a sphere with equal volume, with which the Eq-Radius of the pore was defined as the radius of the sphere, and the throat channel length was defined as the distance between adjacent pore centers. e definitions of the loess void characteristic parameters are presented in Figure 8, in which the chromatic aberrations are due to the visual effect induced by the shadow of threedimensional pores.

Three-Dimensional Quantitative Characteristics of Loess Voids
According to the experimental results, we extracted voids from images to build a 3D pore network, and the network was separated into many pores by throats. e distribution characteristics of the throat dimension generally directly dominated the connectivity and permeability of loess. e dimension of the throat could be described by adopting the parameter throat Eq-Radius, which was defined as the radius of a circle with equal area. e distribution of throat Eq-Radius in the loess is presented in Figure 9. e relationship of throat Eq-Radius and the corresponding quantity probability density satisfied a first-order Gaussian distribution well. e probability density function can be expressed as formula (3), in which x (T−R) represents the throat Eq-Radius and α1, b1, and c1 are the fitting parameters. Figures 9(a) and 9(b) show a comparison of the fitting curves versus the experimental data of layers L1 and S1, depicting that the parameters α1, b1, and c1 are 0.07191, 3.677, and 4.166, respectively, for loess L1 and 0.08427, 3.836 and 3.4, respectively, for paleosol S1, and that the correlation coefficient R is close to 1.0 in both cases.
(3) .0 μm for L1 to S6, respectively, and that the maximum throat Eq-Radius generally increases gradually with increasing stratum depth. According to the shape of the fitting curves, the curve of a deeper stratum tends to be wider, and the curve of a shallow stratum falls into a relatively tight bound, which indicates that the loess at a great depth has large pore throats. Figure 9(d) represents the variation in fitting parameters for various layers of soil, which depicted that the parameter α1 decreases with increasing stratum depth and that the parameters b1 and c1 show a contrary characteristic.
According to the definition, the throat channel length represents the distribution of the average pore length in the loess and is one of the most important structural parameters that can reflect the uniqueness of loess. e distribution of throat channel length versus the probability density is given in Figure 10  Advances in Civil Engineering the comparison of the experimental data and fitting curves of the loess L1 and paleosol S1, respectively. According to the figures, the distribution of throat channel length satisfies the gamma function well. e density function of the gamma distribution can be expressed as follows: where x (T−L) represents the throat channel length, α is a shape parameter, and β is a scale parameter. e Γ(α) function is a generalization of a factorial on a real number. e mean value μ and variance σ of the gamma distribution are given by the following formula: e fitting parameters are determined by adopting the least squares method. According to the results, the parameters α, β, μ, and σ are, respectively, determined to be 3.92611, 5.85606, 22.9523, and 134.18 for loess L1 and 3.77738, 5.62399, 21.2439, and 119.467 for paleosol S1. Figure 10(c) shows the distribution of channel length for various loess and paleosol layers. e curve of the upper layer generally shows a narrower and higher coverage area, as well as a larger peak with a smaller abscissa, which indicates that the pore channel becomes slenderer with increasing stratum depth. Figure 10(d) presents the variation in fitting parameters for various loess strata. According to the figure, the parameters α, β, and μ increase gradually with increasing stratum depth.
Similar to the determination of the quantitative microstructural parameters for throats, those for pore size could be described by adopting the parameter Eq-Radius of a sphere with an equal volume. Figure 11 gives the distribution characteristics of the pore Eq-Radius for the loess. e comparison of experimental data and fitting curves is presented in Figures 11(a) and 11(b), which shows that the relationship of pore Eq-Radius and probability density also satisfies the first-order Gaussian distribution well. e parameters α1, b1, and c1 could be regressed by adopting the least squares method and are, respectively, given as 0.1015, 6.256, and 5.689 for loess L1 and 0.1532, 6.71, and 3.587 for paleosol S1. e corresponding correlation coefficient R results are high. Figure 11(c) shows the distribution characteristics of the pore Eq-Radius for various layers, and Figure 11(d) gives the variation in the fitting parameters for various layers of loess and paleosol. e variations in the fitting curves and parameters for the pore size are similar to those for the throat.

Discussion
e correlation of the physical parameters (such as unit mass, water content, liquid limit, plastic limit, permeability coefficient, and shear wave velocity) and fitting parameters of the distribution function of the particles, pores, and throats of the loess was studied. e values of the permeability coefficient and shear wave velocity have obvious correlations with the fitting parameters of the loess pores and throats. e relationship between the physical properties and the fitting parameters is presented in Figure 12. According to the figures, the fitting parameters b1 and c1 of the Eq-Radius of the throats and pores and the fitting parameters of throat channel length decrease linearly with the increase in permeability coefficient and increase with the increase in shear wave velocity; meanwhile, the fitting parameter α1 of the Eq-Radius of the throats and pores shows   Figure 11: Distribution characteristics of pore Eq-Radius for loess: (a) probability density versus pore Eq-Radius of L1; (b) probability density versus pore Eq-Radius of S1; (c) distribution characteristics of pore Eq-Radius for various layers; (d) variation in fitting parameters for various layers of loess. Advances in Civil Engineering the reverse variation. Based on the above description, we propose that the macrophysical-mechanical properties of loess are quantitatively dominated by certain microstructural parameters of loess, and the quantitative correlation would be the next focus of our research. e microstructure of loess is mainly controlled by the parameters of the particles, pores, and cementation, as well as the structure model. Although the research method used in this study is available to analyze the three-dimensional quantitative characterization of particles and pores, it is difficult to investigate the cementation of particles. Consequently, the microstructurebased structure model of loess still needs to be generalized in the future.

Conclusion
e loess of the Bai Lu tableland involves a series of loesspaleosol interbedding strata, and the microstructural characteristics, physical features, and mechanical properties of this loess vary from layer to layer. As a special geotechnical material with strong structural properties, the microstructural characteristics significantly influence the macroscopic mechanical properties and catastrophic behavior of this loess. e study of the microstructure of loess contributes to a better understanding of the catastrophic behavior and physical mechanism of loess geologic hazards. e main conclusions can be summarized as follows: (1) e volume and Eq-Radius of the loess particles satisfy a third-order Gaussian distribution, and the major-minor axis ratio of the loess particles satisfies a second-order Gaussian distribution. In the Bai Lu tableland, the loess deposited with a predominantly eastward orientation, and the directionality characteristics are more obvious for the soil in the upper layer. With increasing stratum depth, the loess particles generally become increasingly flattened. (2) e Eq-Radius of the loess pores and throats satisfies a first-order Gaussian distribution, and the throat channel length satisfies a gamma distribution. With increasing stratum depth, the loess throat radii increase, and the pore channels become slenderer. (3) e fitting parameters of the distribution function obviously depend on the variation in the loess and paleosol strata, and the macrophysical-mechanical properties of the loess were controlled by certain microstructural parameters. (4) e quantitative correlation of the microstructural parameters and the physical and mechanical properties of loess will be the focus of our future work.

Conflicts of Interest
e authors declare that they have no conflicts of interest.