Variations in Microstructure and Collapsibility Mechanisms of Malan Loess across the Henan Area of the Middle and Lower Reaches of the Yellow River

Abstract

The Henan area of the middle and lower reaches of the Yellow River is situated within the third sedimentary loess area, positioned as the southeasternmost segment within the transitional belt connecting the Loess Plateau with the North China Plain. Addressing concerns related to loess collapse, landslides, and subgrade settlement across various regions attributable to the collapsible nature of Malan loess in western Henan, this study undertook collapsibility testing of undisturbed Malan loess in the province. The different mechanisms of loess collapsibility in different regions were explained from the microstructure by using the indoor immersion-compression test double-line method, scanning electron microscope (SEM), and particles and cracks analysis system (PCAS). The relationship between quantitative factors of microstructure and collapsibility of loess was analyzed by linear regression analysis. The findings indicate that under identical overburden pressure and immersion conditions, the collapsibility of Malan loess in western Henan diminishes progressively from west to east. Microstructural tests were conducted on various loess specimens using scanning electron microscopy, revealing that the distribution of loess particles is notably concentrated in the Xingyang and Gongyi areas, leading to a reduction in pore area compared to the Shanzhou and Mianchi areas. While the Mianchi and Shanzhou areas exhibit a loose arrangement of loess particles, those in Xingyang and Gongyi are comparatively denser. Analysis of microstructural images through the particles and cracks analysis system elucidated that the pore arrangement in the Gongyi and Xingyang areas is more stable than in the Mianchi and Shanzhou areas. Additionally, there is a gradual concentration in particle distribution, accompanied by an increase in agglomeration degree. According to the analysis and comparison of microstructure and quantitative parameters of four groups of loess samples before and after collapsibility, it is revealed that the change mechanism underlying loess collapsibility in various regions of western Henan primarily stems from the external factors influencing the microstructural alterations within the loess. The microstructural determinants contributing to collapsibility changes in different regions encompass three principal aspects: Firstly, modifications in the grain morphology of the Malan loess skeleton in western Henan are notable. Secondly, variations in the internal pore characteristics of loess microstructure are observed. Thirdly, disparities exist in the interconnections between soil particles. The findings of this research hold significant worth for improving construction safety and geological hazard prevention within the Loess region of western Henan.

1. Introduction

China harbors the most extensive loess deposits globally, spanning geographically from west to east across a northwestern dry inland basin, a central loess plateau, and an eastern region characterized by hills and plains. The loess deposits in western Henan Province, situated within the upper and lower reaches of the Yellow River, are notable for their widespread distribution, significant outcrop thickness, and a well-defined evolutionary sequence of loess-paleosol strata. This area not only holds important meaning in studying the formation and evolution of the Yellow River, but also serves as a focus for investigating paleoclimate changes since the Quaternary [1,2]. During the period spanning 17–23 July 2021, Henan Province experienced an unprecedented historic heavy rainstorm. This event precipitated urban waterlogging, river floods, and landslides in various cities, leading to substantial casualties and property damage. Notably, locations such as Luoyang witnessed numerous incidents of road collapses and structural damage to houses due to the collapsible nature of loess, significantly endangering lives and property [3].

After the loess is soaked in water under a certain pressure, the structure of the loess is destroyed rapidly and additional subsidence is produced, which is called collapsibility. Loess shows robust stability under low water content conditions. However, the suction and bond strengths of the loess in question are subject to alteration upon encountering moisture and external loading, which in turn results in an increase of collapsibility [4,5,6,7,8,9,10]. Concurrently, the collapsibility of loess often triggers a cascade of geological hazards, including collapses and landslides, posing severe threats to human lives and property safety. Therefore, the investigation of loess collapsibility has remained a focal point for researchers in the field of geotechnical engineering [11]. Since the 1960s, the continual advancement and refinement of observation techniques, such as scanning electron microscopy (SEM) and computer-based research methodologies, have significantly improved researchers’ understanding of the microstructural intricacies of loess. In particular, insights into the pore distribution and soil particle connectivity within loess have been deepened [12,13,14]. For example, Wang conducted a study utilizing SEM imaging to investigate the variation in pore area during loess collapsibility, successfully establishing a logarithmic relationship between pore area and collapsibility coefficient [15]. Liu examined changes in particle morphology, pore size, and pore area throughout the process of loess collapsibility, proposing a comprehensive mechanism for loess collapsibility that integrates relevant parameters and material composition [16,17,18]. Several researchers have studied the internal mechanisms underlying loess collapsibility by developing quantitative models of its three-dimensional microstructure [19,20,21,22,23]. Gao and Fang investigated the microstructural changes in loess before and after collapsibility through SEM tests, revealing a linear relationship between pore area and collapsibility [24,25]. Jiang employed SEM testing to compare the microstructure of loess in its natural and remolded states, highlighting alterations in the connectivity mode between soil particles in remolded loess [26].

The microstructure of loess evolves during its deposition and subsequent soil formation processes. This evolution is influenced by various geological environmental conditions and the geological history of the region. Consequently, the microstructural characteristics of loess exhibit considerable variation across different layers and regions. Previous studies have extensively employed scanning electron microscopy and image processing technology to examine undisturbed loess samples. For example, Deng et al. utilized serial sectioning methods to investigate the pore size distribution of loess across distinct regions of the Loess Plateau [27]. Wang et al. analyzed Jinzhong loess to compare variations in pore distribution under various soaking conditions employing pressurized mercury techniques [13]. Most of the previous studies on loess collapsibility were limited to the use of individual methods. There is no comprehensive use of the above methods. The limitations of the single method have led to the lack of comprehensive and accurate research results. In addition, previous studies had focused too extensively on the collapsibility of loess depth and individual factors, while research on the collapsibility of Malan loess on the spatial scale is still lacking. In particular, there is still a significant gap in the study of collapsibility of Malan loess in western Henan. Addressing this gap necessitates the integration of micro-testing methodologies and fracture image recognition techniques to comprehensively elucidate the intricacies of loess collapsibility variations.

In this study, Malan loess from four distinct regions of Henan Province—namely Shanzhou, Mianchi, Gongyi, and Xingyang—underwent analysis by indoor water-immersed compression testing, complemented by scanning electron microscopy (SEM) and the particles and cracks analysis system (PCAS) [28]. This investigation aims to elucidate the variation patterns of loess collapsibility across western Henan Province from west to east and to clarify the mechanisms underlying the differences in loess collapsibility within the region. By integrating the findings regarding microstructural changes, this study offers a reliable theoretical foundation for subsequent projects in western Henan Province pertaining to this matter.

2. Sampling and Methodology

2.1. Test Soil

The analyzed loess samples were taken from the western part of Henan Province. Through field investigation, Malan loess in western Henan is concentrated in the Shanzhou, Mianchi, Gongyi, and Xingyang areas (Figure 1). The soil from the sampled area predominantly manifests characteristics of loess silty clay, characterized by relatively uniform particle distribution, absence of distinct bedding, and well-developed vertical joints. The relevant physical property indicators of loess across different regions are presented in

Table 1. Physical parameters of the loess samples.

Sampling Site	Specific Gravity	Natural Moisture Content %	Liquid Limit %	Plastic Limit %	Plasticity Index	Natural Density g/cm3	Dry Density g/cm3
Shanzhou	2.71	9.1	28.7	17.9	10.8	1.51	1.34
Mianchi	2.70	13.2	29.5	18.4	11.1	1.62	1.40
Gongyi	2.70	14.6	32.8	20.2	12.6	1.63	1.42
Xingyang	2.71	17.4	29.3	17.7	11.6	1.76	1.53

. To ensure uniformity in the overlying pressure applied, and that the obtained soil sample is least affected by unnecessary external factors, consistent depths of approximately 3 m were maintained while collecting soil samples from various areas. Each undisturbed soil sample underwent meticulous trimming and was encased in a protective layer of film, with foam added outside the plastic film to protect the sample during handling.

2.2. Sample Preparation and Test Methods

The collapsibility testing instrument utilized in this study comprises a WG single-lever consolidation instrument. Additionally, the microstructure analysis was conducted using the JSM-7800F electronic scanning microscope (Japan Electronics Co., Ltd., Amagasaki, Japan).

2.3. Indoor Water-Immersed Compression Test

In this test, the collapsibility of loess samples was assessed using the double-line method [29]. The collapsibility test commenced with an initial pressure of 50 kPa, with increments of 50 kPa added at each level. Upon reaching 200 kPa, increments of 100 kPa were subsequently applied until a pressure of 400 kPa was achieved. Two specimens are required for each set of tests, one of which is kept at a certain moisture content and the other is completely submerged under a vertical stress of 25 kPa. As shown in Figure 2. The test concluded when the readings of the two settlements did not exceed 0.01 mm.

The test soil sample had dimensions of 3000 mm² in area and 20 mm in height. Initially, collapsibility tests were conducted on undisturbed loess under natural water content conditions across various regions. Subsequently, four moisture gradients of Malan loess, with water contents of 6.79%, 12.50%, 18.56% and 24.61% were prepared. The soil samples were adjusted to different moisture states using either the titration method or the air-drying method. During the humidification process, the amount of water required to reach a specific water content was calculated. The water was evenly applied to both ends of the soil sample enclosed within the ring knife. The fresh-keeping film was wrapped around the moisturizing cylinder, and after allowing it to stand for three days, both ends were flattened. The water content of the soil sample was measured in accordance with geotechnical testing standards to ensure uniformity across samples used in the test. The prepared soil samples were stored in a humidor as shown in the Figure 3.

Utilizing the compression curve outlined in the Chinese national standard (GB/T50123-2019) [30], the collapsibility coefficient of each sample group was computed. The formula for the calculation is defined as follows:

$${\delta }_S={\displaystyle \frac{h_P-h_P^{\prime }}{h_0}}$$

where ${\delta }_s$ represents the collapsibility coefficient; $h_P$ denotes the height of the sample following stabilization under a specific stress level; $h_P^{\prime }$ indicates the height after stabilization of submerged deformation at a particular stress level; and $h_0$ is the original height of the specimen.

ASTM D2435-03 [31] and D5333-03 [32] can be used to achieve essentially the same test results for the collapsibility test of loess. In the ASTM D2435-03 test standard, the test steps of loess collapsibility are specified in detail. The D5333-03 test method covers the determination of the magnitude of one-dimensional collapse that occurs when loess is inundated with fluid. In the ASTM D5333-03 test method, the formula for determining the coefficient of collapsibility of loess is consistent with that in the Chinese national standard (GB/T50123-2019). The Chinese national standard (GB/T50123-2019) is similar to the American standard (ASTM D2435-03 and D5333-03) in the process of collapsible compression test for loess. Therefore, the results have a certain accuracy.

2.4. Microscopic Test

The fundamental steps of this micro-test are outlined below:

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Preservation and preparation of microscopic samples: Soil samples used for microscopic analysis were sequentially numbered from 1 to 20. A small segment was extracted from the middle portion of each numbered sample and trimmed to dimensions of 20 mm × 1 mm × 1 mm (length × width × height). Before SEM imaging, the samples underwent two preparatory steps: drying and gold coating.

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Acquisition of microscopic images: The prepared microscopic loess samples were positioned beneath a scanning microscope to capture images of loess before and after immersion under natural conditions and at varying water contents.

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Processing of microscopic images: The microscopic images obtained from the scanning microscope underwent parameter calculation and classification utilizing the PCAS program. Subsequently, data extraction and analysis of the microstructural images of loess in its natural state, as well as pre- and post-immersion states with different initial water contents were conducted. Comparative analyses were performed to discern trends in parameters, such as pore area ratio, average shape coefficient, probability entropy, and distribution fractal dimension.

2.5. Characteristics of Loess Collapsibility

2.5.1. Characteristics of the Loess Collapsibility Curve in Various Regions

Following the results of the indoor water-immersed compression tests, the wetting coefficients of the four groups under differing pressures were calculated individually (Figure 4). Through comparison and analysis of the collapsibility curve characteristics, it was observed that the variation trend in loess collapsibility with increasing overlying pressure can be broadly categorized into three stages: In the initial stage, the deformation of loess collapsibility undergoes significant changes and manifests rapid development with the increase of overburden pressure. Evidently, the loess undergoes compaction under the combined influence of external loading and moisture, leading to an escalation in damage deformation due to structural instability. During the second stage, a noticeable deceleration in the rate of collapsible deformation becomes apparent. This observation suggests that following the first stage, despite continued increments in external loading, the soil structure gradually densifies and stabilizes. The third stage is exclusive to the Mianchi and Shanzhou areas, wherein the magnitude of collapsible deformation manifests a trend of continuous development. This phenomenon demonstrates that the loess in the Shanzhou and Mianchi regions is comparatively loose, offering ample space for structural disruption, whereas the loess in the Gongyi and Xingyang areas demonstrates greater density and stability. With the increase of overburden pressure, the wetting coefficient has a significant increase. The overburden pressure shows a good positive correlation with the wetting coefficient. This proves that the external load is an important factor affecting the soil subsidence, which means that the original macroporous structure of the soil is gradually destroyed under the action of load and the pore ratio decreases gradually.

Specifically, the collapsibility coefficient in the Mianchi and Shanzhou areas exceeds 0.07 under a 200 kPa load, classifying it as a strongly collapsible loess. The initial collapse pressure of Malan loess in the four regions is different, that is, the minimum external pressure required for obvious collapse of loess is different. The initial collapse pressure of loess in Xingyang is greater than 75 kPa, which is 95 kPa and 126 kPa, respectively. The initial collapse pressure of loess in Mianchi area is 55 kPa, and the initial collapse pressure of loess in the Shanzhou area is less than 50 kPa. Notably, the collapsibility coefficient in the Shanzhou area reaches 0.15, indicating particularly high collapsibility. Conversely, the collapsibility coefficient of loess in the Gongyi and Xingyang areas hovers around 0.5, categorizing it as a moderately collapsible loess.

The overall trend across the loess in the western part of the Henan Province indicates a gradual attenuation from northwest to southeast. To delve deeper into comprehending the patterns and mechanisms underlying the collapsibility of Malan loess in western Henan, it becomes imperative to investigate factors such as the initial water content, microstructural characteristics of the loess, and changes in microscopic quantitative parameters before and after soaking.

2.5.2. Characteristics of the Loess Collapsible Curve under Different Initial Moisture Content

Four sets of undisturbed soil samples sourced from Shanzhou, Mianchi, Gongyi, and Xingyang were prepared according to the methodology outlined in Section 2.3 to achieve varying water contents. Subsequently, indoor water-immersed compression tests were carried out to examine the characteristics of the collapsibility curve under different initial water contents. The results are summarized as follows:

A critical external factor influencing loess collapsibility is the initial water content of the soil samples. Figure 5 illustrates the relationship curve between the collapsibility coefficient and the overburden pressure across various regions and initial water content levels. A comprehensive analysis across different regions reveals a negative correlation between the initial moisture content and the collapsibility coefficient. Specifically, as the initial moisture content increases, the collapsibility coefficient decreases, and saturated loess remains stable without collapsing. Conversely, increased initial water content compromises the stable structure of the loess soil under its own weight or external loads, resulting in a weakened or nonexistent collapsibility. The loess wetting curve clearly consists of two parts: a sharp growth part and a gradual stabilization part, corresponding to the above concept of initial water content and external load affecting loess collapsibility. The maximum value of the wet subsidence coefficient is 0.142 in Shanzhou Mianchi, 0.135 in Gongyi, and 0.103 in Xingyang. The wetting coefficient of Xingyang loess specimens increases relatively slowly with the overlying pressure.

2.5.3. Characteristics of the Loess Collapsibility Curve under the Same Initial Water Content

To investigate the collapsibility of loess across four regions under uniform initial water content conditions, the loess samples with an initial water content of 6.79%—representing the highest collapsible deformation—are selected for comparative analysis.

Upon analysis of Figure 6, it is evident that under uniform initial moisture content and overburden pressure conditions, the collapsibility coefficient of the loess is most pronounced in the Shanzhou area and least pronounced in Xingyang. As discussed in the previous paragraph, initial water content exerts a significant influence on loess collapsibility. However, even with consistent initial water content, disparate levels of collapsibility persist among the regions. The change curves of loess moisture subsidence in different regions are basically consistent with the change curves under natural water content. It should be noted that there is still a trend of slow growth of loess wetting coefficients in the four regions after the 300–400 kPa stage, which is different from the above change curves. The wetting coefficients of Shanzhou, Mianchi, Gongyi and Xingyang were 0.158, 0.127, 0.094 and 0.072, respectively. The initial collapse pressure of Malan loess in the four regions is lower than that under natural water content. The initial pressure of loess collapsibility in Xingyang is 85 kPa, and the initial pressure of loess collapsibility in the three areas of Mianchi, Gongyi, Shaanxi is less than 50 kPa. In summary, the initial water content of the soil sample has a significant effect on the collapsibility of the loess, which is basically consistent with the collapsibility of the loess plateau studied by Liu [16,17,18].

To better comprehend the fundamental reasons for the divergence in loess collapsibility between the four regions of western Henan, further analysis of loess microstructure using techniques such as micro-electronic scanning mirrors is warranted.

2.6. Microstructure

The microstructure of loess primarily comprises three components: structural units (including individual minerals, aggregates, and clusters), cements (comprising clays and organic matter), and pores [33]. The morphology of the skeleton particles predominantly consists of granular particles, with a minor presence of condensed block particles. The formation and augmentation of agglomerate particles contribute to the attenuation of loess collapsibility. The connection patterns among skeleton particles can be categorized into four modes: direct point contact, indirect point contact, direct surface contact, and indirect surface contact [34]. The distinction between direct and indirect contact modes primarily arises from their varying sensitivity to force and water, with point contact connections being more prone to damage and collapsibility compared to surface contact connections. Pores within loess exhibit diverse characteristics, including large pores, overhead pores, intergranular pores, and intragranular pores. Among these, large pore overhead pores and overhead pores [35] exert a more pronounced influence on collapsibility. The pore distribution depends on the arrangement of the soil particles. When the particles are loosely arranged, the pore distribution is dominated by large pores or overhead pores. When the loess collapses, the soil particles are arranged relatively compactly, and the pore distribution is concentrated in tiny pores.

2.7. Image Analysis of Loess Microstructure in Different Regions

Figure 7 depicts the SEM images of loess samples from all four regions before and after immersion in water. The microstructure of the loess before and after soaking in the same area was compared. It was found that the number of macropores in the soil samples decreased sharply after immersion. The connection mode of the soil particles changes and the connection of particles after immersion gradually changes from point–point contact to point–surface contact or surface–surface contact. At the same time, the arrangement of the soil particles also changed. Before collapse, the soil samples were mainly overhead pores. After the occurrence of collapsibility, although the overhead pores exist in a small amount, the intergranular pores increase sharply. Comparative analysis of the microstructure of the loess in these regions reveals variations in the quantity of pores, pore distribution, and pore connectivity. Notably, the number of macropores and overhead pores in Malan loess diminishes gradually from west to east in western Henan, accompanied by a denser arrangement of loess particles in the eastern regions. Furthermore, the connection between loess skeleton particles in the Mianchi and Shanzhou areas primarily consists of point contact or point–surface contact, whereas surface contact predominates in the Gongyi and Xingyang loess. The morphology of particles within the microstructure of the loess varies across different regions. In the Shanzhou area, the microstructure reveals predominantly granular soil particles, interspersed with clusters formed by a small quantity of fine particles. Similarly, across western Henan, the particles of loess remain predominantly granular from west to east, albeit with a gradual emergence of agglomerated particles. For instance, in Xingyang loess (Figure 7g,h), the morphology of skeleton particles tends to exhibit a smoother profile, with fewer aggregates formed through aggregation, compared to loess in the western regions. Additionally, the number of intergranular pores in the Xingyang and Gongyi loess is notably lesser than that observed in the Mianchi and Shanzhou loess. In summary, the pore size has a great influence on the collapsibility of loess, which is basically consistent with the conclusion of loess collapsibility and pore size in the Jinzhong area studied by Wang [13].

Based on the SEM image, it can be inferred that as the natural water content increases, water immersion induces a reduction in the connection strength among skeleton particles, resulting in the destabilization and disintegration of the overhead pore structure within the loess. At the same time, under the influence of upper soil pressure, soil compaction occurs, leading to an augmentation in structural strength and consequently, a diminishing trend in collapsibility across western Henan from west to east. The mechanism underlying the collapsibility change of Malan loess can be summarized as follows: In the Mianchi and Shanzhou areas, Malan loess primarily consists of granular particles, rendering it susceptible to damage. The presence of large pores and overhead pores facilitates collapsibility, while the connection mode of skeleton particles is significantly impacted by external factors. Conversely, in the Xingyang and Gongyi areas, the loess skeleton particles exhibit relatively denser characteristics, with fewer large pores and overhead pores. Moreover, the particle connection mode has been compromised by water immersion and is less susceptible to external factors.

2.8. Image Analysis of Loess Microstructure under the Same Initial Water Content

As previously noted, the natural water content is recognized to affect the collapsibility of loess. To further elucidate the mechanism underlying the variation in collapsibility of Malan loess in western Henan, a comparative analysis of the microstructure before and after collapse was conducted by maintaining uniform natural moisture content across different regions. Figure 8 presents four sets of SEM images depicting loess with identical initial moisture content across the four regions. Given that varying initial moisture contents exhibit consistent patterns of loess collapsibility within the study area, this section exclusively examines the SEM characteristics of loess with an initial moisture content of 6.79% before and after soaking.

Overall, despite uniform initial moisture content across the four regions, notable differences persist in the microstructure. When compared to the microstructure observed under natural water content conditions, the microstructure of the four sets of loess samples shows relatively consistent particle arrangement and pore distribution. In the Shanzhou area (Figure 8a,b), the arrangement of particles is predominantly characterized by trellis pores, indicating a looser arrangement of loess particles compared to the other three areas. While loess in the Xingyang and Gongyi areas shares similarities with Mianchi and Shanzhou in terms of being primarily composed of granular particles, a minor presence of condensed block particles is observed. Simultaneously, there was a decrease observed in the number of macropores and trellis pores, primarily within the inter-particle pores, while the connection mode of skeleton particles shifted from point contact to surface contact. Upon comparing the microscopic images before and after collapse, it was evident that the rearrangement of particles occurred during the collapse process, gradually filling the trellis pores with small pores. Despite reducing the natural water content of the loess in Xingyang and Gongyi, the microstructure of the loess in these areas still exhibited disparities compared to that in Mianchi and Shanzhou. This divergence in microstructure, attributed to macroscopic soil deformation, illustrates the gradual weakening of overall loess performance across western Henan from west to east. This further underscores the multifaceted influence of microstructural factors on the degree of loess collapsibility.

2.9. Quantitative Analysis of Loess Microstructure

To facilitate a comparative analysis of the quantitative microstructural parameters of loess across test groups, SEM images with a magnification of 500× were selected for quantitative analysis using the particles and cracks analysis system (PCAS) images. Given the grayscale nature of soil SEM images, threshold segmentation was employed to convert them into binary images (Figure 9). To minimize errors during analysis, the final threshold was determined by averaging multiple selected thresholds, typically three in number.

2.10. Quantitative Analysis of Loess Microstructure in Different Regions under Natural Conditions

Table 2. Quantitative parameters of microstructures in different regions.

Sampling Site	State of Soil Sample	Average Form Factor	Probability Entropy	Porosity Distribution Fractal Dimension	Pore Area Ratio
Shanzhou	Before soaking After soaking	0.398 0.357	0.991 0.988	2.8 2.5	39.21% 22.78%
Mianchi	Before soaking After soaking	0.388 0.355	0.987 0.985	2.6 2.2	35.86% 21.77%
Gongyi	Before soaking After soaking	0.342 0.323	0.984 0.983	2.2 1.9	17.86% 7.57%
Xingyang	Before soaking After soaking	0.343 0.329	0.979 0.977	1.9 1.5	16.15% 8.32%

presents the calculated quantitative parameters of the loess microstructure before and after soaking in different regions. Figure 10 illustrates the corresponding trends in these parameters. Quantitative analysis of the microstructure, based on the data presented in the tables and figures, yielded the following results:

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Average form factor. In this paper, the shape coefficient of the pore is defined as ${\mathrm{F}}_{\mathrm{i}}=\mathrm{S}/\mathrm{C}$. In the formula, C is the circumference of the circle with equal area to the image contact area, and S is the actual circumference of the image contact area. The value of the pore shape coefficient is between 0 and 1. The larger the value, the closer the pore shape is to the circle, and the smaller the value, the narrower the pore shape. The complexity of pore morphology makes the shape coefficient of a single pore to often show a large error, and the shape of a single pore cannot reflect the total pore characteristics of the soil. Therefore, the average shape coefficient is usually used to quantitatively describe the pore morphology of a soil. The formula for calculating the average shape coefficient is as follows:

$$F={\displaystyle \frac{1}{n}}\sum _{i=1}^n{F}_i$$

where $\mathrm{n}$ is the statistical number of particle contact points. Larger F-values indicate that the pore features are closer to circular, and vice versa for narrower and longer. A pore shape close to circular means that the larger the pore size, the looser the particle arrangement is. The average form factor serves as an indicator of pore shape. Results suggest that under the influence of overlying load and immersion, the soil’s pore structure undergoes a transformation, shifting from a predominantly wide and open configuration to one characterized by narrower and more constricted pores. This observation points to the gradual disappearance of larger pore structures. The aforementioned findings highlight the spatial variability in the microstructure of loess across western Henan, with a corresponding inconsistency in initial water content. Notably, the roundness of loess pores in all four regions shows a general decreasing trend before and after immersion. However, this decline is less pronounced in the Xingyang and Gongyi areas compared to Shanzhou and Mianchi. In particular, Shanzhou loess experiences the most significant reduction in pore roundness. This observation suggests that loess particles in the Xingyang and the Gongyi areas are arranged in a denser configuration, rendering their pore morphology less susceptible to alteration.

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Probability entropy [36]. This parameter serves as a measure of the orderliness of pore and particle distribution within the soil. Values closer to 0 indicate a more ordered and regular arrangement, while values approaching 1 signify greater disorder and irregularity. When the pore and particle distribution is more irregular, the soil is unstable and prone to collapsibility, and the probability entropy is larger. This parameter is calculated using the following formula:

$$H_m=-\sum _{i=1}^n{\displaystyle \frac{m_i}{M}}\times {\displaystyle \frac{\ln \left(m_i\times M)\right.}{\ln n}}$$

where $m_i$ represents the number of pores in the ith location of the n locations within the 0–180° range, $M$denotes the total number of pores.

Following immersion, the probability entropy of loess across all four regions manifests an upward trend. Notably, Shanzhou loess possesses the lowest probability entropy prior to soaking, whereas Xingyang loess displays the highest. This finding implies a less ordered pore arrangement within Shanzhou loess compared to Xingyang loess, suggesting a greater degree of stability in the pore structure of the latter.

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Porosity distribution fractal dimension [37]. The distribution fractal dimension reflects the spatial distribution of objects. A smaller fractal dimension implies a more concentrated distribution of particles or pores. The pore distribution is more concentrated, which indicates that the particles are arranged closely, the intergranular pores increase, and the number of large pores decreases. The box-counting method is employed for calculation:

$$D_V=-\underset{r\to 0}{\lim }{\displaystyle \frac{\ln N\left(r\right)}{\ln r}}=-K$$

where $r$ represents the side length of the square box, $N\left(r\right)$ denotes the number of boxes containing objects, and $K$ indicates the linear slope.

Analysis of the fractal dimension reveals that the loess in Gongyi and Xingyang manifests a lower value compared to Mianchi and Shanzhou. Furthermore, all four regions demonstrate a decrease in fractal dimension following collapse. This observation suggests a weaker tendency towards dispersed and collectivized pore distribution in Xingyang and Gongyi loess. Conversely, Malan loess in Mianchi and Shanzhou displays a more concentrated pore distribution.

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Pore area ratio. This represents the proportion of pores within the soil as observed in the microscopic image. The value ranges from 0 to 1, with higher values indicating a greater abundance of pores. It provides enough space for the occurrence of loess collapsibility, and thus the collapsibility of the loess increases. Under the influence of external loads and water, the pore area of loess in all regions manifests a decreasing trend. Notably, Shanzou loess possesses a higher initial pore area ratio compared to the other three regions, and it also experiences the most rapid decline following immersion and external load application. This observation suggests that loess in the eastern part of western Henan has a denser skeletal particle arrangement compared to the western part. In conjunction with previous findings, it can be inferred that the naturally high water content of Malan loess in Gongyi and Xingyang contributes to the destruction of large pores and overhead pores between soil particles. Consequently, the reduction in pore area ratio after soaking is less pronounced in these areas compared to Mianchi and Shanzhou. Interestingly, the pore area ratio of Mianchi and Shanzhou loess after collapsibility remains higher than that of Gongyi and Xingyang loess before collapsibility.

The relationship between the loess collapsibility coefficient and the quantitative parameters of microstructure was compared by statistical linear regression analysis (Figure 11). It is found that there is a certain linear relationship between the four quantitative parameters and loess collapsibility.With the increase of average form factor, probability entropy, fractal dimension of porosity distribution and Pore area ratio, the collapsibility of loess increases linearly. The correlation coefficients R² of average form factor and probability entropy are 0.937 and 0.938, respectively. The correlation coefficient R² of the fractal dimension of porosity distribution and the proportion of pore area are 0.916 and 0.950, respectively. This finding indicates that the porosity area ratio has a greater relationship with collapsibility.

2.11. Quantitative Analysis of Loess Microstructure and Microstructural Changes under Uniform Initial Water Content across Different Regions

To enhance the accuracy of the analysis, loess samples from all four regions were subjected to testing under a controlled and uniform initial water content. Given that the general trends in loess collapsibility under identical initial water content conditions were largely consistent across the different regions, a group of samples exhibiting the most pronounced differences in collapsibility was selected for further investigation.

Table 3. Quantitative microstructural parameters of loess in different regions (ω = 6.79%).

Sampling Site	State of Soil Sample	Average form Factor	Probability Entropy	Porosity Distribution Fractal Dimension	Pore Area Ratio
Shanzhou	Before soaking After soaking	0.398 0.371	0.994 0.990	3.4 3.2	45.79% 30.28%
Mianchi	Before soaking After soaking	0.364 0.345	0.989 0.986	2.9 2.5	41.77% 27.78%
Gongyi	Before soaking After soaking	0.358 0.332	0.987 0.983	2.6 2.3	17.52% 8.77%
Xingyang	Before soaking After soaking	0.342 0.332	0.982 0.979	2.3 2.0	16.21% 7.52%

presents the quantitative microstructural parameters of loess samples with an initial water content of 6.79% before and after immersion. Figure 12 illustrates the changes in these micro-quantitative parameters for loess from different regions before and after soaking.

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Average form factor. Despite the uniform initial moisture content across the four regions, variations in soil particle morphology are still evident. Notably, the pore shape in Shanzhou appears smoother compared to Xingyang. Following immersion, the average shape coefficient of loess in all regions decreases, with the most rapid decline observed in Shanzhou. The trend aligns with the changes observed in the average shape coefficient of loess under natural water content conditions.

(2)

Probability entropy. Under the same initial water content, the probability entropy of the loess shows a gradual decrease from Shanzhou to Xingyang. This observation suggests a progressive increase in pore orderliness and a more stable arrangement distribution.

(3)

Porosity distribution fractal dimension. The fractal dimension of pore distribution in loess across the four regions remains largely consistent with that observed in the natural state, albeit with minor variations. The lower fractal dimension values in Xingyang and Gongyi indicate a more concentrated distribution of soil particles, suggestive of a condensed state.

(4)

Pore area ratio. The pore area ratio of loess in each region manifests a gradual decrease both before and after soaking and collapsibility, implying a corresponding increase in the area ratio occupied by particles. Xingyang loess displays the smallest pore area ratio, both before and after soaking compared to other regions, further supporting the notion of its denser soil structure.

(5)

The aforementioned data analysis suggests that while the consistency of loess water content does influence soil microstructure to a certain degree, the quantitative microstructural parameters nonetheless exhibit consistent patterns of change. Notably, the variation trends observed in loess from different regions under natural water content conditions are largely similar. This finding underscores the multifaceted nature of the factors governing loess collapsibility and provides further insight into the increased collapsibility of Shanzhou loess compared to the other three regions under identical initial water content conditions.

The relationship between the collapsibility coefficient of loess and the quantitative parameters of microstructure in different regions under the same initial moisture content is shown in the Figure 13. It is found that there is a certain linear relationship between the four quantitative parameters and loess collapsibility. It is basically consistent with the variation law of loess collapsibility under natural water content. The correlation coefficients R² of average form factor and probability entropy are 0.921 and 0.938, respectively. The correlation coefficient R² of the fractal dimension of porosity distribution and the proportion of pore area are 0.936 and 0.955, respectively. The influence of pore area ratio on loess collapsibility is still the strongest. This is basically consistent with the conclusion of the relationship between pore area and collapsibility studied by Gao and Fang.

3. Conclusions

This study employed a combination of indoor confined compression tests, scanning electron microscopy (SEM) imaging, and PCAS software (http://matdem.com/index.asp?lg=cn) to analyze the microstructure of the loess samples before and after collapse. The investigation revealed the following key insights into the microstructure and collapsibility mechanisms of Malan loess in different regions of western Henan Province:

(1)

Loess collapsibility in western Henan manifests a decreasing trend from west to east. Shanzhou loess possesses the highest collapsibility among the four regions, with a collapsibility coefficient of approximately 0.15, classifying it as a strongly collapsible loess. Conversely, Xingyang and Gongyi loess demonstrate weaker collapsibility, with a coefficient of around 0.05, indicative of medium collapsibility.

(2)

The initial water content of soil samples significantly affects loess collapsibility. A negative correlation is observed between the initial water content and the collapsibility coefficient across the four regions. This implies that the collapsibility gradually diminishes with increasing initial water content, and saturated loess does not exhibit collapse behavior. Even when the initial water content is consistent across the four sampling sites, variations in loess collapsibility persist, and the observed trends remain largely consistent with those under natural water content conditions.

(3)

The intensity of collapsibility of Malan loess in different regions is affected by the interaction of microstructure and internal and external factors. The differences of the pore size, the arrangement of particles, the contact form between particles and the arrangement of pores in the Malan loess are the fundamental reasons for the difference in loess collapsibility in different regions. When there are large pores, overhead pores, point particle contact forms and unstable pore arrangement in Malan loess, the collapsibility will be higher than in other Malan loess.

In this paper, the mechanism of collapsibility and microstructure change of undisturbed Malan loess in western Henan is studied by means of indoor immersion-compression tests and electron microscope scanning. It is of great significance to improve the construction safety and geological disaster prevention in the loess area of western Henan. However, due to the limitation of time and distance, the sampling area of Malan loess is reduced. In future research, we will sample and analyze the Malan loess in more areas. At the same time, the accuracy and professionalism of the characterization technology will be further improved.