Effects of Paleosol on the Collapsibility of Loess Sites under Immersion Test Conditions

Abstract

The existence of multiple layers of red paleosol within loess strata presents a unique challenge due to its high hardness, which resists settlement deformation upon exposure to water. This attribute significantly influences the subsidence measurements of the loess strata. Despite this, the current literature lacks reports on the control effect of paleosol on collapsibility, leading to a deficiency in the theoretical basis for scientifically selecting collapsibility in these strata. This paper seeks to bridge this gap by examining the differences in self-weight collapsibility under various conditions, both indoor and outdoor, across different paleosol layers and strata. The analysis is grounded on statistical results derived from immersion tests conducted in the Loess Plateau. Moreover, the research zeroes in on two test sites in Xi’an, conducting extensive immersion tests and considering measurements such as water diffusion, changes in water content, soil pressure, and cumulative collapsibility under different test conditions. The study probes into the influence of paleosol layers on water infiltration and their role in controlling total weight collapse. The final results suggest that the presence of a paleosol layer inhibits collapsibility transfer to the lower layer and restricts water infiltration, thereby reducing total collapsibility. Discrepancies between measured and calculated collapsibility values showed a positive correlation with the number of paleosol layers. This research offers valuable insights into the collapsibility mechanism of paleosol-loess strata.

1. Introduction

Loess is a distinctive sedimentary deposit formed during the Quaternary period, exhibiting unique internal structures and external morphological features [1,2]. This sediment is widely distributed globally, with a notable presence in central and western China (Figure 1) [3]. Despite its unique natural characteristics, when used as a building material and supporting layer, loess is susceptible to sudden drops in strength and significant increases in deformation under the influence of factors such as rainfall and irrigation [4,5]. The collapsibility of loess in the Loess Plateau poses unique challenges for the sustainable operation of infrastructure. These challenges make resource development and the continuous progress of various projects in the Loess region more difficult [6]. As the western development progresses, engineering endeavors in loess regions are bound to encounter collapsibility issues, posing significant challenges to site selection and the safe operation of constructed facilities [7]. The classification of site collapse is a fundamental engineering aspect related to collapsible loess. Due to the failure to accurately assess the type of collapse in loess sites, it is not uncommon to eliminate collapsibility in advance and cause hazards in engineering construction (Figure 1). Therefore, accurate wet collapsibility assessments aid in the planning and maintenance of more durable and environmentally friendly infrastructure, thereby promoting sustainable development in the Loess Plateau.

In the study of the collapsibility characteristics of loess, two primary methods are commonly employed: indoor uniaxial or triaxial compression tests and on-site immersion tests. Indoor tests are preferred for their simplicity and controllability, while on-site immersion tests provide accurate and reliable results at the cost of being expensive and time-consuming. Despite indoor tests being more prevalent in projects, they often yield results that differ from immersion tests. This disparity has led geological scientists to conduct extensive research [8]. In efforts to enhance the accuracy of indoor tests, researchers such as Xing [9] and Mi et al. [10] have proposed single-line and double-line methods based on centrifugal model tests for measuring the moisture content of loess. However, these methods still exhibit some errors when compared to field tests. Shao [11] introduced different correction coefficients for various stratigraphic depths and modified the starting threshold value of the self-weight collapsibility coefficient through a comparison involving a substantial number of field tests and indoor tests. Nevertheless, the correlation between indoor and field test results in the Guan Zhong area was not thoroughly investigated. Moreover, alternative theoretical methods have been suggested, such as assigning different correction coefficients to different strata and employing neural networks for determination. However, these theoretical approaches have not yielded satisfactory results in post-processing.

The layered distribution of loess and paleosol, which interact with each other, forms the primary structure of the loess layer [12]. Due to different depositional environments, there are notable variations in the physical and mechanical properties between paleosol and loess. Research by Lei [13] on late Pleistocene loess in the southern Loess Plateau revealed that the paleosol structure was denser, and its mechanical properties were superior to those of the loess. Subsequent studies [14,15] have further validated this observation. In field immersion tests, some scholars have observed the unique collapsibility characteristics of loess–paleosol interactive strata. For instance, Li [16] conducted a large-area water immersion test on Q₂ loess and found significant differences in the collapsibility characteristics of foundation soil compared to general self-weight collapsible loess. However, there is a lack of corresponding data to support this research. Nevertheless, this study opens up a new research direction for analyzing the disparities between indoor and outdoor test results. Zhao [17] conducted a study on the water migration patterns in loess-paleosol strata and identified the inhibitory effect of the paleosol layer on vertical water infiltration. However, their investigation did not extensively explore the mechanisms by which this water barrier property of paleosol influences subsidence.

This article starts from the statistics of a large number of on-site immersion tests conducted in the Loess Plateau area, aiming to analyze the differences between indoor and outdoor self-weight subsidence in different sites. In contrast to previous theoretical studies, the focus of this article is on the control effect of the paleosol layer on the subsidence amount. Based on two large-scale water immersion tests in Xi’an, combined with geotechnical engineering surveys and dynamic monitoring methods, data such as the cumulative settlement amount, settlement section shape, and water infiltration patterns of different strata were obtained. Through the analysis of these data, we strive to shed light on the mechanisms by which paleosol strata influence land subsidence. Comprehending the stability and permeability of soil paves the way for the adoption of more sustainable strategies in architectural design and infrastructure development. Our goal is to furnish more dependable and pragmatic insights into the issue of subsidence in engineering construction within loess regions and to provide more efficacious guidance for sustainable building practices. This endeavor assists in enhancing our understanding of sustainability principles in the context of geographical spatial planning.

2. Materials and Methods

2.1. Geological Survey of the Study Area

The on-site immersion tests examined in this study are primarily located in the Loess Plateau region of China. This region spans from 34° to 38.5° north latitude and 102° to 112° east longitude. The topographic elevation gradually decreases from northwest to southeast. The topographic elevation gradually decreases from northwest to southeast. The specific terrain changes are shown in Figure 2.

The distribution of loess in this area is continuous, with a significant thickness of stratum development [18]. The region experiences a semi-arid continental monsoon climate, with average annual temperature and precipitation decreasing from southeast to northwest. The average annual precipitation ranges from 140 mm to 737 mm, while the average annual temperature ranges from −3 °C to 15 °C. As Xi’an is situated in the southeastern part of the Loess Plateau, it has the most developed paleosol with a substantial thickness [19]. Two on-site immersion test sites were selected in Xian Ning East Road, Xi’an, Shaanxi Province (test site 1: longitude 109.06°, latitude 34.24°), and Chang’an District, Xi’an, Shaanxi Province (test site 2: longitude 109.94°, latitude 34.15°) (Figure 3). Both test sites fall within the warm temperate sub-humid continental climate zone. The summer season is influenced by the southeast monsoon, resulting in concentrated rainfall from July to September, often in the form of heavy rain. The meteorological information of Xi’an over the years is shown in

Table 1. Summary table of the main meteorological data of Xi’an Meteorological Station.

Information	Multi-Year Average	Annual Maximum	Annual Minimum
Temperature (°C)	13.7	41.8	−9.3
Humidity (%)	63.2	93.4	41.8
Precipitation (mm)	604.0	883.2
Evaporation (mm)	406.9	1512
Wind speed (m/s)	1.6	15.2

. Winter, on the other hand, is influenced by the northwest monsoon, leading to dry and cold conditions. The stratigraphy of the region includes layers such as mixed fill: mixed fill (Q₄^ml), new loess (Q₃^eol), paleosol (Q₃^el), old loess (Q₂^eol), and paleosol (Q₂^el). Due to the continuous evolution of regional geomorphic units and intense modern tectonic activities, this area is prone to disasters such as ground fractures.

2.2. Research Method

In the Loess Plateau, several scholars have conducted in situ immersion experiments of varying scales [16,20,21,22,23,24,25,26,27,28]. However, due to the high cost of testing, poor reproducibility, and other factors, it has become crucial to perform a comparative analysis of the test data obtained from these different sites. Therefore, this paper aimed to conduct a statistical analysis of the results of large-scale field flooding tests in the Loess Plateau area. By comparing the measured and calculated self-weight collapse in different regions, the characteristics of self-weight collapse in different regions and the differences between the measured and calculated values will be revealed. Additionally, to better understand this difference, the test sites were classified based on the presence or absence of paleosol layers and the different number of layers. Through this classification study, this paper aimed to provide a more detailed understanding of the collapsibility of loess under different geological conditions and offer more nuanced information for comprehending the collapsibility mechanism of loess.

To explore the natural migration patterns of soil moisture and understand the developmental characteristics of self-weight collapse in loess, as well as the role of paleosol layers in this process, this study executed two sets of on-site inundation tests for comparative analysis. Test site 1, lacking seepage holes, was juxtaposed with test site 2, which was equipped with seepage holes. Firstly, a detailed investigation of the test site was conducted using geotechnical engineering survey methods to understand the distribution characteristics of various layers and the physical mechanical properties of the loess at the site. Moisture sensors were then embedded in various layers, considering the stratigraphic structure, to measure the changes in moisture content during the inundation process. Subsequently, the test results underwent a meticulous comparative analysis, focusing on the settlement of different layers during the self-weight collapse and the dynamic changes in moisture content in each layer throughout the entire process. These observations were then utilized to elucidate the influence of paleosol layers on the mechanism of self-weight collapse. This study employed the simple supported beam model from elastoplastic mechanics to provide a theoretical framework for interpreting the observed phenomena. The integration of field tests, geotechnical surveys, and theoretical models allows for a comprehensive exploration of the complex interplay between soil moisture migration, self-weight collapse, and the role of paleosol layers in the intricate geological processes within the loess strata.

In this research, circular test pits were meticulously constructed at two specific locations, guided by the determined lower limit depth of site weight collapse derived from geotechnical engineering surveys. Test point 1 featured a test pit with a diameter of 20 m, while test point 2 boasted a larger test pit with a diameter of 30 m. Both test pits shared a uniform depth of 50 m. To account for the diverse stratigraphic conditions, present at each test point, a thoughtful arrangement of measuring points was implemented. These points included shallow and deep marking points, moisture sensors, seepage holes, and soil pressure boxes, with specific details available in Figure 4. Notably, test point 2 was configured with six evenly distributed seepage holes, strategically positioned 7 m from the center of the test pit, facilitating controlled water infiltration. The seepage holes are drilled using a drilling machine, and the holes are filled with medium-coarse sand to promote water infiltration. Conversely, test point 1 did not incorporate any seepage holes.

Throughout the test, a comprehensive set of observations and measurements were conducted, including settlement observations, soil moisture content assessments, and soil pressure monitoring. To ensure efficient data collection, a remote automated data collection system was utilized. This system improved the accuracy and timeliness of data acquisition, enabling thorough analysis of the test results and providing valuable insights into the behavior of the site under investigation. Specific information regarding the sensors can be found in

Table 2. Main parameters of the sensors used in the experiment.

Information	Moisture Content Sensor	Soil Pressure Sensor
Product model	RS-SD-N01	DP-TGH
Measuring range	0–100%	0–10 MP
Accuracy	2%FS	0.5%FS
Resolution	0.1%	0.01%FS

.

3. Results

3.1. Statistical Result

For simplicity, we defined the ratio of measured self-weight collapse settlement to collapse settlement as β₀. The presented statistical data in

Table 3. Statistical summary of on-site trial pit inundation test results.

District	Location	Self-Weight Settlement/cm		Test Pit Dimension/m	β0	Data Source
		Measured Value	Calculated Value
Gansu	Lanzhou Anning District	18.5	11.2	10 × 10	1.65	[29]
	Lanzhou Donggang	87	50.1	Ellipse 15 × 13	1.73	[29]
	Lanzhou Feijiaying	11.9	5.8	4 × 4	2.05	[25]
	Lanzhou Gongjiawan	63.5	36	12 × 11.8	1.76	[30]
	Lanzhou Heping Town	231.5	128.8	Φ40	1.80	[28]
	Lanzhou Chengguan District	34.5	22.1	Ellipse 15 × 13	1.56	[26]
	Lanzhou Shajingyi	12.5	9.1	14 × 14	1.37	[29]
	Lanzhou Wanchuan River	78.4	36.25	15	2.16	[31]
	Qingyang Xialaochi in Gansu	63.6	47	Φ20	1.35	[27]
	Gansu Yongdeng	135.2	43.6		3.1	[21]
	Lanzhou Xigu	93	50.1	Φ20	1.85	[29]
	Lanzhou Xigu Cotton Factory	86	23.2	15 × 15	3.71	[29]
	Lanzhou Yuzhong Fanjiawo	53.9	64	20 × 40	0.84	[32]
	Lanzhou Xinzhuangling	39.7	69.1	Φ15	0.57	[29]
Ningxia	Guyuan in Ningxia	128.8	103.4	Φ15	1.24	[29]
	Guyuan County Qiyin	103.1–115.7	163.0–261.1	110 × 70	1.58–2.25	[29]
	Ningxia Yanghuang Pump	261.1	140.5	110 × 70	1.86	[33]
Shannxi	Baoji in Shaanxi	34.4	28.5	20 × 20	1.21	[25]
	Sanyuan in Shaanxi	20.7	21.2	10 × 10	0.97	[29]
	Weinan Heyang	47.7	36.5	10 × 10	1.31	[34]
	Weinan-Xiancheng Intercity Railway	4.6	19.7	Φ16	0.23	[35]
	Weinan Pucheng Power Plant	6.5	65.1	Φ20	0.01	[16]
	Weinan Tongguan County	16.2	17.55	Φ25	0.92	[24]
	Fuping Zhangqiao in Shaanxi	20.7	23	10 × 10	0.9	[36]
	Xi’an Hongqing River	11.1	18.7	Φ20	0.59	[20]
	Xi’an University of Finance and Economics	0.21	44.5	Φ30	0.05	[29]
	Xi’an Jiaotong University	0.81	10.1	10 × 10	0.08	[30]
	Xi’an Rongjiazhai	7.8	18	Φ23	0.43	[37]
	Xi’an Beijiao Xujia Village	3.8	13.7	Φ10	0.27	[29]
	Xi’an Xianning East Road	1	15.8	25 × 18	0.06	[29]
	Xi’an Huangqutou	7.41	19	Φ20	0.39	[38]
	Xi’an Gaowangdui Village	0	11.2	Φ25	0	[39]
	Xi’an Yangcun	0.2	18.2	Φ25	0.01	[39]
	Xi’an Yuedenge	5.1	19.9	Φ26	0.26	[38]
	Xianyang Beiyuan Buli Village	55.4	34.6	Φ20	1.60	[10]
Hebei	Fanshan in Hebei	21.3	44.8		0.47	[25]
	Zhangjiakou in Hebei	10.5	88.7	Φ11	0.12	[29]
Shanxi	Yicheng	1.9	4.2	10 × 10	0.45	[16]
	Yuci Haojiagou	84.85	103.5	Φ10	0.82	[40]
	Shanxi Aluminum Plant Phase I	5.7	9.6	12 × 12	0.6	[41]
	Shanxi Aluminum Plant Phase II	3.06	11	12 × 12	0.28	[41]
	Taiyuan	3.6	18.6	Φ10	0.19	[29]
	Ruyi Cheng in Yuncheng,	30.42	53.22		0.57	[42]
Henan	Lingbao in Henan	1.3	5.5	7 × 7	0.24	[43]
	Zhangwan Township in Shan County	19.3	58.8	Ellipse 32 × 28	0.33	[44]
	Xiyuan Township in Lingbao City	10.4	34.2	Ellipse 39 × 33	0.30	[44]
	Guxian Town in Lingbao City	47.7	50.9	Φ35	0.94	[44]
	Yuling Town in Lingbao City	59.3	38	Φ20	1.56	[44]
	Guxian Town in Yanshi City	2.7	4.4	Φ25	0.61	[44]
Qinghai	Xining Datong	40	24.3	15 × 15	1.65	[29]
	Xining Nanchuan	65	40.9	32 × 53	1.59	[29]
	Ledu in Qinghai	98.2	62		1.58	[44]
	Lanchong in Qinghai	101.4	58	12 × 12	1.75	[23]
Xizang	Northeastern Edge of the Qinghai-Tibet Plateau	21.9	40.6		0.54	[45]
Xinjiang	Yili in Xinjiang	352.9	215.3		1.64	[46]

outline the results of flooding tests conducted in the Loess Plateau. The table comprises details such as the dimensions of the submerged test pit, the measured and calculated values of self-weight collapsibility, and the measured β₀. This comprehensive information spans across various provinces, providing valuable insights into the performance and behavior of the studied strata under flooding conditions.

3.1.1. Collapsibility Partition Results

Figure 5 illustrates the results of inundation tests conducted in the Loess Plateau region. Figure 5a shows the statistical division of the measured β₀ in the immersion test in the Loess Plateau. Figure 5b–e presents both measured and calculated values of self-weight collapse, along with their ratio, distinguished by different regions. In Figure 5a, it can be seen that the measured β₀ was generally distributed by region, and it showed a trend of increasing gradually from east to west. To delve deeper into these differences and their relationship with specific provinces, the data were segregated accordingly. Figure 5b underscores a substantial number of inundation tests conducted in Gansu Province. Notably, the measured values of self-weight collapse in Gansu were considerably higher than the calculated values, resulting in a ratio greater than 1. In some instances, this ratio reached as high as 4, indicating that the measured self-weight collapse in certain Gansu areas is nearly four times that of the calculated values. Similar patterns were observed in Qinghai (Figure 5c), where the measured values were approximately 1.6 times the calculated values, aligning with the correction factors outlined in current standards. Conversely, Shaanxi and Henan exhibited different trends. In Shaanxi (Figure 5d), unlike Gansu and Qinghai, the measured self-weight collapse consistently fell below the calculated values. In Henan (Figure 5e), the ratio of measured to calculated values predominantly ranged between 0.3 and 0.9. Interestingly, Shaanxi featured some specific cases where, in numerous inundation tests, the calculated values of self-weight collapse significantly exceeded the measured values, leading to a ratio close to 0. This suggests that in these areas, measured collapse was minimal or absent, while calculated values imply the presence of collapse. Such cases were found to be relatively rare in other regions. These observed differences may be influenced by geological and soil layer characteristics, warranting further in-depth research for a comprehensive explanation. Understanding these variations is crucial for refining models and standards, ensuring accurate predictions of self-weight collapse in different regions of the Loess Plateau.

3.1.2. Effect of Paleosol on Collapsible Quantity

This study investigated the influence of paleosol on the discrepancy between indoor and outdoor tests through an analysis of field test results from different strata. The occurrence of paleosol layers varied across distinct geomorphological units, leading to stratification based on the number of paleosol layers. These categories include non-paleosol, single-layer paleosol, double-layer paleosol, and multi-layer paleosol, with the self-weight collapsibility of each category calculated accordingly. Consistent patterns were observed among sites with similar strata, and representative sites were chosen for detailed examination. The outcomes are illustrated in Figure 6, where the map encompasses various regions. The collapsibility values, both calculated and measured, under the non-paleosol, single-layer paleosol, double-layer paleosol, and multi-layer paleosol layers were plotted from left to right, corresponding to the depth. The left side of the map provides a visual depiction of the stratigraphic conditions at the site. It became evident from the figure that the difference between the measured and calculated curves arose with the presence of paleosol in the stratum, and this difference gradually intensified with an increase in the number of paleosol layers. As shown in Figure 6a, it is obvious that when there was no paleosol layer in the stratum, the two curves were relatively close, and the difference was not obvious. Figure 6b reflects the site immersion test of a single-layer paleosol and the calculation of self-weight collapsibility, with the calculated collapsibility of this type being larger than that of the field test. The trends of the two curves were basically the same before the appearance of the paleosol layer, and there was an obvious inflection point on the measured curve at the top of the paleosol layer. After this point, there was almost no collapsibility in the paleosol layer and its lower strata, but there was a certain amount of collapsibility in the calculation curve. Figure 6c also shows the same trend, and the inflection point of the measured curve also appeared above the first layer of paleosol. When the first layer of paleosol appeared, there was almost no collapsibility in the lower stratum, but the calculated curve obtained by laboratory tests still had collapsibility. Figure 6d reflects the site immersion test and the calculation of self-weight collapsibility in the presence of multi-layer and thick paleosol, and the interlayer between multi-layer paleosol and loess. The calculated collapsibility of this type was larger than that measured by the field immersion test, and the measured collapsibility value of the field immersion test was close to 0, that is, non-self-weight collapsibility. In summary, these findings emphasize that the presence of paleosol layers impacted self-weight collapsibility, leading to observable differences between the measured and calculated values.

3.2. Test Result

3.2.1. Effect of Paleosol on Collapsible Quantity

Figure 7 illustrates the variation in the vertical permeability coefficient of soil layers and the changes in water content with depth before and after flooding at different test points. At test point 1, where no water injection hole was present, the vertical permeability coefficient of the paleosol layer was smaller than that of the upper stratum. The permeability coefficients of the paleosol layer, middle layer, and lower layer continued to decrease. The junction between the paleosol layer and the loess layer had a smaller vertical permeability coefficient, resulting in a larger increase in water content at this interface. In this test point, the soil moisture content in the depth range of 0–23 m was 17.01–23.03% before flooding. After prolonged and extensive flooding, the soil moisture content increased by 3.97–12.38%. The maximum change occurred in the depth range of 0.5–11.0 m, with an increase of 7.62–13.02%. The soil moisture content in the paleosol layer and the lower transitional section increased relatively less, growing by 3.97–8.39%. This indicates significant variations in the self-weight collapsibility of the soil at different depths in the absence of water injection holes. For test point 2, which had multiple water injection holes, the presence of these holes facilitated easier penetration of water into the deeper layers, resulting in a more extensive variation in soil moisture content. The soil moisture content before flooding ranged from 14.50 to 26.60%, and after flooding, it increased by 2.13–15.29%. The variation in soil moisture content in the paleosol layer remained relatively small, while other layers exhibited relatively consistent changes. This suggests that the presence of water injection holes can alter the path of water infiltration, leading to more widespread changes in soil moisture content, especially in deeper layers.

3.2.2. Result of Formation Soil Pressure Change

Soil pressure at different depths and in different formations was monitored and statistically analyzed during the immersion test. The transfer relationship of soil pressure was obtained and is shown in Figure 8. The origin of the axis represents the initial soil pressure at different depths, allowing for the analysis of the change in soil pressure. Test site 1 consisted of a single layer of paleosol (Figure 8a). It can be observed that the soil pressure in the upper layer of the paleosol gradually increased with the injection of water, indicating significant susceptibility to collapse. This may result in ground settlement and the formation of cracks. However, the soil pressure in the paleosol layer initially increased slightly but then stabilized, suggesting that the paleosol layer experienced only minor deformation and played a supportive role in limiting the downward transfer of collapsibility. The soil pressure in the lower old loess stratum remained almost constant, indicating relatively minimal collapse deformation. This could be attributed to the support provided by the upper soil layer and the paleosol layer. The variation in soil pressure aligns with the measured depth of the collapsible soil layer.

At test site 2, the stratum was characterized by multiple layers of paleosol, as shown in Figure 7b. The soil pressure at this location increased with both depth and the amount of injected water. The first layer of paleosol experienced structural damage due to the additional overlying soil and the increased volume of injected water, resulting in variations in soil pressure corresponding to changes in water volume. As the water injection rate increased, the soil pressure in the second layer of paleosol initially increased slightly before stabilizing. This suggests that the second layer of paleosol underwent slight deformation in response to the increased water injection. At the same time, as water injection intensified, the soil pressure of the overlying Q₂ loess stratum initially rose and then decreased. However, the magnitude of this change was not significant, indicating that this process was primarily influenced by the infiltration of the upper water body and the deformation of the upper stratum. As water injection stopped, the collapsibility process of the Q₂ loess stratum concluded, leading to stable soil pressure. Meanwhile, the soil pressure in the upper paleosol gradually decreased, indicating an “unloading rebound” trend.

3.2.3. The Influence of Paleosol Layers on Settlement

Figure 9 presents the results of cumulative self-weight settlement and layered self-weight settlement at two test points. Specifically, Figure 9a,b illustrates the measured and calculated values of self-weight settlement obtained from on-site measurements and indoor experiments for test point 1. Figure 9c,d demonstrates the comparison between the measured and calculated values of layered self-weight settlement. At test point 1, where no water injection holes were installed and a single layer of paleosol existed from 11.5 to 15.2 m, it was evident from the figures that the self-weight settlement measured on site primarily occurred in the Q₃ loess above 11 m. The paleosol and the underlying strata experienced minimal self-weight settlement. This discrepancy between the measured and calculated values can be attributed to the water-blocking effect of the paleosol layer in the absence of water injection holes, preventing further infiltration of water. Consequently, the paleosol layer and the underlying loess did not undergo self-weight settlement, leading to the mismatch between the measured and calculated values.

At test point 2, equipped with multiple seepage holes, there are paleosol layers distributed at depths of 10–12.4 m, 20.2–22.6 m, and 23.5–25.2 m. The figure depicts a substantial disparity between the measured and calculated values in this stratum, where paleosol and loess are alternately distributed. On-site measurements showed minimal self-weight collapse, while the calculated curve still indicated a collapse of 31.4 cm. Furthermore, the collapsibility of the upper soil layer, as observed in the field measurements, did not equal the sum of the collapsibility and settlement of the lower soil layer. This discrepancy is mainly attributed to the fact that the measured curve decreased upon passing through the paleosol layer, resulting in a negative collapse quantity. In other words, the lower layer experienced collapsing, but this deformation was not transferred to the upper strata, possibly because the paleosol was relatively strong and did not undergo significant collapsing deformation [47].

4. Discussion

4.1. Water Diffusion Characteristics above and below Paleosol

The presence of paleosol significantly affects the vertical permeability coefficient of the soil. For example, at test point 1, the soil permeability coefficients decreased from 3.33 m/d, to 2.70 m/d, to 2.30 m/d in the upper, middle, and lower parts of the paleosol, respectively. At a depth of 8 m, when the distances from the center of the test pit were 12 m, 14 m, and 16 m, the infiltration times were observed to be the 5th day, 9th day, and 22nd day, respectively, indicating a certain lag in water diffusion. Additionally, the permeability coefficient decreased from 2.4 m/d to 0.7 m/d, suggesting that gravity influenced the process of water diffusion from top to bottom and from inside to outside. Water tends to diffuse preferentially along pores with a larger permeability coefficient, leading to soil infiltration. Once the pores are saturated, water starts to diffuse outward, eventually saturating the soil. At test point 2, due to the presence of seepage holes, a dominant channel from bottom to upward was created, and water diffused through this channel. This diffusion method implies that water first saturates the bottom of the soil in the form of a saturation front and then spreads upward. In contrast to the relatively water-isolated paleosol layer, stagnant water formed on top of the paleosol, and its infiltration mode gradually shifted from vertical penetration to horizontal penetration. Understanding the water diffusion patterns within the loess-paleosol stratigraphy is crucial for disaster risk reduction and mitigation on the Loess Plateau, as well as for achieving sustainable development in the region [48].

4.2. Collapsibility Mechanism of Soil under the Action of the Paleosol Layer

Up to this point, it can be considered that in the absence of a paleosol layer, the upper inundation tests gradually saturated the underlying stratum through continuous water injection. In this process, the saturation zone propagated downward along the lateral infiltration line, with a diffusion angle of approximately 40°, reaching the underlying stratum. The stratum underwent bending deformation under the influence of soil pressure and subsequent water injection. Due to the fact that the upper soil and water pressure were greater than the support force of the underlying stratum, the stratum settled in a strip-like form. Additionally, the gravitational and pressure components acting on the upper stratum unit exceeded the tensile strength of the soil, leading to the formation of ground cracks (Figure 10a).

When paleosol layers are present in the formation but have no advantageous channels, water seeps into the formation from top to bottom. The upper strata undergo subsidence, which is then transmitted to the top of the underlying paleosol layer. While the paleosol layer has some water-isolating effect, water continues to seep downward to a certain extent. During this process, the lower strata will continue to collapse under the force of the soil and the action of water, but the amount of collapse will be relatively small. Simultaneously, the paleosol undergoes slight deformation under the influence of different soil and water pressures, impeding the downward transmission of force. As a result, the loess above the paleosol layer becomes fully saturated and collapses, but the loess below does not experience complete saturation and subsidence. This phenomenon explains why, in certain water immersion tests, the measured curve of self-weight collapse exhibited an inflection point above the paleosol layer (Figure 10b).

When advantageous channels are present in the formation, water can rapidly permeate the entire formation via seepage holes and disperse within it. This water spreads vertically from top to bottom, bottom to top, and horizontally from inside to outside through these channels. The upper loess settled to the upper part of the paleosol layer in the manner shown in Figure 9a. Due to its low permeability and high strength, the paleosol layer undergoes only slight deformation under the influence of the upper soil and water pressure. It serves as a supporting layer, effectively preventing the transmission of force from continuing downward. When there are multiple paleosol layers, its performance becomes even better. Simultaneously, the lower stratum started to collapse and deform under the influence of water, and the upper paleosol was in contact with the lower loess layer due to deformation, which made them have equal soil pressure at a certain time. After the subsidence of the lower loess ended, the upper paleosol still maintained its original deformation but failed to continue to contact the lower loess. The two maintained a certain soil pressure, causing a cavity between the strata. Therefore, the amount of collapse produced by the lower loess layer cannot be transferred to the surface through the paleosol layer, resulting in the upper stratum not completely producing a collapse deformation equal to the sum of the amount of collapse in the lower layer. This also explains the phenomenon that the measured collapsibility is much smaller than the calculated value when there are multiple layers of paleosol in the formation (Figure 10c).

We used the simply supported beam model for explanation. Assume that its bending stiffness is EI, both ends are subject to the reaction force of the lower strata acting on A and B; the deformation height generated between the paleosol and the underlying stratum is denoted as H, D represents the influencing diameter of the subsidence in the test pit, q stands for the overlying soil water pressure, and S denotes the settlement of the lower part of the paleosol stratum under the load q (Figure 11).

Equation (1) gives the maximum deflection (settlement) of the midpoint when the soil element is affected by the uniform load Q from the upper part.

$$w_{0MAX}=\frac{5q{L}^4}{384EI}$$

(1)

When the load $q\le \frac{384EIH}{5L^4}$, only the midpoint of the paleosol contacts the lower stratum. In this case, the contact length between the paleosol and the lower stratum is zero, and the strata at both ends of the lower part of the paleosol do not make contact: $R_A=R_B=qL/2$.

However, when the load $q>\frac{384EIH}{5L^4}$, section of the paleosol will be in contact with the lower stratum. Let us assume that the contact points are points C and D, and the contact length is represented by a. Due to symmetry, points C and D are equidistant from both ends of the lower part of the paleosol, and this distance is denoted as b. Due to the uniformly distributed load on segment AC and the concentrated forces acting at both ends, with the given conditions:$M_C=0w_A=H$ (upward).

Simultaneously, from $M_C=\frac{q{b}^2}{2}-R_{A}b=0$, it follows that $R_A=\frac{qb}{2}$.

Equation (2) determines the deflection of the free end by superposition method.

$$w_A=\frac{R_A{b}^3}{3EI}-\frac{q{b}^4}{8EI}=Hb=\sqrt[4]{\frac{24EIH}{q}}$$

(2)

Therefore, the contact length between paleosol and the lower layer can be calculated by Equation (2), as given by Equation (3):

$$a=L-2b=L-2\sqrt[4]{\frac{24EIH}{q}}$$

(3)

Equation (4) gives the reaction force provided by both ends of a paleosol:

$$R_A=R_B=\frac{qb}{2}=\frac{1}{2}\sqrt[4]{24EIH{q}^3}=\sqrt[4]{\frac{3EIH{q}^3}{2}}$$

(4)

Equation (5) gives the height of the cavity region:

$$H\prime =H+S=\frac{R_A{b}^3}{3EI}-\frac{q{b}^4}{8EI}+S$$

(5)

From the variation curve of earth pressure in Figure 8, we can see that the earth pressure on the paleosol layer increases first and then decreases. So far, it can be considered that if $q\le \frac{384EI{H}_{min}}{5L^4}$, it means that there is a cavity, which may cause a huge difference between the indoor calculated collapsibility and the measured value and then affect the accuracy of the evaluation of loess collapsibility. If $q>\frac{384EI{H}_{max}}{5L^4}$, there is no cavity, and there may be some difference between the indoor calculated collapse amount and the measured value. This can enhance previous explanations of the mechanisms behind on-site inundation tests in paleosols, enrich the theoretical achievements in this field, provide guidance for construction design in loess areas, and drive sustainable development in the region.

5. Conclusions

Through the analysis of immersion test results in different field zones and monitoring data from large-scale on-site immersion tests, the following conclusions were primarily drawn:

• The vertical permeability of the paleosol layer is generally lower than that of loess, which often prevents water from continuing to penetrate during the water logging stage. The water diffuses horizontally to a certain extent, so that a water-rich zone is often formed at the interface between the paleosol and the loess, and subsidence mainly occurs in the loess layer overlying the paleosol. As a result, the difference between the measured and calculated values of collapsibility shows a positive correlation with the number of paleosol layers.
• The existence of preferential channels alters the way water diffuses, causing water to move from the top to the middle instead of in a top-to-bottom direction. The presence of paleosol layers impedes the subsidence process, preventing the transfer of subsidence from the lower loess to the surface. This complexity reduces the accuracy of categorizing site subsidence.
• The measured β₀ value in the region showed a gradual increase from northwest to southeast. Notably, the extreme case of β in the Guanzhong area of Shaanxi was less than 0.01, a phenomenon closely tied to the presence of paleosol in the striatum. A cavity existed between the paleosol and the underlying stratum. The mechanical model outlines the conditions for this cavity’s existence, indicating that the cavity’s size is related to the upper load and the height of the collapsible area.

This research provides theoretical support for the development of the Loess Plateau region, especially in improving ground stability and preventing the settlement of infrastructure such as roads and buildings. By delving into the mechanisms behind loess subsidence, it offers reliable theoretical backing for future infrastructure planning and construction. This contributes to the region’s sustainable development goals by facilitating reliable technical support for future infrastructure development and planning, thereby aiding the long-term growth and stability of the Loess Plateau region.