Microscopic Mechanisms and Evolution Models of Crack Development in an Expansive Soil under Conditions of Rainfall Evaporation Cycles

Abstract

Expansive soil is a special soil type that undergoes volume expansion during hygroscopicity and volume contraction during dehumidification. In this study, the effects of rainfall–evaporation cycles on the microscopic pores and cracks of expansive soils under different rainfall intensities were analyzed by simulating light rainfall, medium rainfall, and high-temperature drought environments using nuclear magnetic resonance (NMR) technology and image processing methods. The results showed that the micropores and small medium pores of the expanded soil gradually evolved into macropores during the cycling process, especially under stronger rainfall conditions. In addition, as the number of cycles increased, the expanded soil showed irrecoverable pore changes, which ultimately led to the scattering damage of the soil. By processing the surface crack images of expansive soils, the process of crack development was categorized into four stages, and it was found that the evaporation cycle of medium rainfall intensity caused the main cracks of expansive soils to develop more rapidly. A quantitative relationship model between the average crack width and the number of cycles as well as porosity was constructed, and the regression coefficient of determination R² reached 0.98, 0.96, and 0.84, respectively. This study simulates the effects of real rainfall conditions on expansive soils and investigates the mechanism and evolution of cracks in expansive soils, which is of great theoretical and practical significance.

1. Introduction

Expansive soils are noteworthy for their significant volume changes in response to moisture fluctuations. These soils, rich in clay minerals like montmorillonite, expand upon water absorption and contract upon water loss [1]. They are widespread in various regions globally, notably in arid and semi-arid areas such as Texas and California in the United States, Australia, China’s Loess Plateau, and parts of India. Research indicates that in these regions, the cyclical expansion and contraction of expansive soils due to moisture dynamics can jeopardize the stability of foundations, thereby posing risks to roads, buildings, and other infrastructure [2]. Therefore, an in-depth understanding of the modeling of crack formation and evolution in expansive soils is essential for preventing and solving related engineering problems.

Over the past decades, numerous researchers have endeavored to investigate the mechanisms and evolutionary patterns of cracking in expansive soils [3,4,5]. Currently, various experimental methods exist for determining the soil pore structure, such as mercury intrusion porosimetry [6], CT scanning [7], and electrical resistivity tomography [8]. By analyzing the relationship between water flow and volume change within cracks in expansive soils, Ito [9] investigated the expansion contraction mechanism of soils. Additionally, Zheng [10] analyzed the stability of expansive soil tunnels by simulating the process of the unsaturated infiltration and hygroscopic expansion of expansive soils under precipitation conditions using temperature and seepage fields using FLAC3D Version 6.0 technology. Huo [11] proposed a stability analysis method for expansive soil slopes with filled fissures by performing triaxial tests on expansive soils with fissures filled with gray-green clay and unfilled expansive soils. Dai [12] investigated the seepage field and stability evolution characteristics of fissured expansive soil slopes under rainfall by numerical simulation. Moreover, after conducting numerous wet and dry cycling tests, Estabragh [13] discovered irreversible expansion and contraction deformations in the same soil samples under different loading pressures. These deformations occurred during the wet and dry cycling process. Furthermore, some scholars have examined the formation of cracking patterns in expansive soils subjected to wet and dry cycling conditions. Tang [14] used a non-invasive method combining X-ray computed tomography (CT) and digital image processing techniques to study the evolution of drying crack networks in compacted cohesive soils. Ribeiro [15] estimated inert soil crack characteristics under field conditions using artificial neural networks. Zhu [16] obtained the fracture parameters of gangue powder-amended expansive soil by MATLAB and Image J software. The roughness and microporosity characteristics of the soil samples were revealed using laser confocal 3D microscopy and mercury penetrometer. Li [17] analyzed digital images of surficial fissured expansive soils with different water contents based on binarization and fractal dimension methods. Nevertheless, traditional experimental methods and observations frequently fail to provide comprehensive information due to the complexity of the cracking process in expansive soils and the micro-scale variations. Hence, it is imperative to explore novel methodologies for studying the microscopic mechanisms and evolutionary models of cracking in expansive soils.

In recent years, nuclear magnetic resonance (NMR) and image analysis have emerged as vital tools for studying the cracking of expansive soils [18,19]. Dong [20] employed NMR tests to monitor the alterations in the pore structure of expansive soils during multiple wet and dry cycles, as well as to investigate the mathematical relationship between the pore structure and swelling deformation. Shi [21] utilized NMR relaxation to examine the modifications in the pore size distribution of expansive soils during dewatering and shrinkage. The NMR technique can provide information about the cracking mechanism by monitoring the moisture movement within the microstructure of expansive soils [22,23,24]. NMR techniques can be employed to explore the interrelationship between moisture and soil microstructures, thus uncovering the microscopic mechanisms of cracking in expansive soils [25,26]. Image analysis is another crucial research method for obtaining the morphological characteristics of soil cracking and investigating the evolutionary pattern of the cracking process through the analysis of microscopic images of soil samples [27]. Image analysis techniques can furnish detailed image information and quantitatively characterize the morphological features of the cracking process through the utilization of image processing and analysis algorithms [28,29]. However, in this study, photographic techniques were employed to capture images of soil cracks that occurred after evaporation during the rainfall cycle. Subsequently, these captured images of soil cracks were processed and analyzed using Image-Pro Plus (IPP) software [30,31] to investigate the developmental pattern of soil cracks under rainfall cycle evaporation.

In this study, expansive soils from the Pingdingshan area in China were chosen for experimentation. A rainfall simulator and a constant temperature drying oven were employed to mimic natural moisture variations in expansive soils, replicating rainfall and evaporation processes, respectively. NMR and advanced photography techniques were utilized to capture and meticulously analyze the changes in pore size and the formation of soil cracks after these simulated rainfall and evaporation cycles. Subsequently, the soil crack images were processed and thoroughly examined using Image-Pro Plus software. This analysis revealed the pattern of soil crack development under the simulated conditions, laying the groundwork for constructing a corresponding evolutionary model. A deeper understanding of the micro-mechanisms and evolution patterns of crack formation in expansive soils can provide valuable insights for addressing soil cracking impacts in geotechnical engineering.

2. Materials and Methods

2.1. Materials

The soil samples utilized in this experiment were collected from an expansive soil slope located near the South-to-North Water Diversion Main Canal in Ye County, Pingdingshan City. The sampling point has a longitude of 113.15° E, and a latitude of 33.55° N, and the samples were collected at a depth of 1~1.5 m. The hard plastic brownish-red clay mainly consists of gray-green clay as a fill material.

Following the guidelines of GBT 50123-2019 [32] (Chinese standard), a suite of fundamental physical tests was conducted on the collected soil samples. The outcomes of these tests are presented in

Table 1. Basic physical indicators of swelling soil in Pingdingshan.

Natural Water Content/%	Dry Density/(g/cm3)	Liquid Limit/%	Plastic Limit/%	Plasticity Index	Maximum Dry Density/(g/cm3)	Optimum Moisture Content/%	Free Swelling Ratio/%
14.42	1.70	43.6	20.2	23.4	1.71	17.42	43.7

, while Figure 1 illustrates the particle size distribution. Based on ASTM D 2487-17e1 [33] standards, the analyzed soil samples are classified as low-plasticity clay.

2.2. Rainfall Simulation

To accurately simulate real rainfall conditions, it is essential to incorporate the concept of rainfall intensity. This study adhered to the GB/T 28592-2012 [34] (Chinese standard) for categorizing rainfall intensity levels, as detailed in

Table 2. Criteria for classifying rainfall intensity levels.

Rainfall Intensity Level	Total 24 h Precipitation/mm	Total 12 h Precipitation/mm	Simulated Rainfall Flow mL/h
light rainfall	0.1–9.9	≤4.9	12.5
medium rainfall	10.0–24.9	5.0–14.9	31.25
heavy rainfall	25.0–49.9	15.0–29.9	93.75
storm rainfall	50.0–99.9	30.0–69.9	187.5

. Accordingly, rainfall intensity was classified into four distinct levels: light rainfall, medium rainfall, heavy rainfall, and storm rainfall. Each of these intensity levels was methodically tested in the experiments. The flow rate corresponding to the median of the rainfall intensity class precipitation range was selected to replace that type of rainfall for the test, i.e., light rainfall corresponds to 5 mm, medium rainfall corresponds to 12.5 mm, heavy rainfall corresponds to 37.5 mm, and storm rainfall corresponds to 75 mm in a 24 h period.

The flow ranges corresponding to different rainfall intensities can be deduced based on Equation (1) and the criteria for classifying rainfall intensity.

$$Q={\displaystyle \frac{A\times p}{t}}$$

(1)

where Q is the required flow rate for simulating rainfall, mL/h; A is the cross-sectional area of the catchment, 60 cm²; p is the precipitation amount, cm; and t is the duration of rainfall, h.

The rainfall controller of the rainfall simulation device (refer to Figure 2) was calibrated to simulate rainfall at different intensities by adjusting the flow rate to the median value, based on the calculated flow range. The device is composed of three components arranged vertically: a water storage tank, a rainfall controller for simulating diverse rainfall conditions, and a container for holding the soil sample. The container is equipped with bottom holes to allow downward seepage of the soil sample.

2.3. Nuclear Magnetic Resonance Test

For the NMR porosity testing on the specimen blocks that underwent rainfall treatment, we used MesoMR12-060H-I NMR equipment. The basic performance parameters of the equipment include a magnetic field strength of 0.3 ± 0.05 T and a main frequency of 12.8 MHz. To ensure the provision of a uniform and stable main magnetic field, the magnet temperature was controlled to within 32 ± 0.01 °C.

The NMR technique used in this experiment was the CPMG pulse sequence (Carr Purcell Meiboom Gill, CPMG, Nottingham, UK) for the determination of the transverse relaxation time T₂, where TE = 0.8, NECH = 12,500, and TW = 4000. The principle of this NMR test relies on the relaxation mechanism of the hydrogen atoms in the process of leptonization, where the surface relaxation mainly occurs at the contact surfaces of solids and liquids, i.e., at the surface of a solid, like the particle surfaces of rocks. By using Equation (2) and the T₂ spectral curve obtained from the NMR test, we are able to deduce the pore size distribution of the soil sample.

$${\displaystyle \frac{1}{T_{2S}}}={\rho }_2{\left({\displaystyle \frac{S}{V}}\right)}_{pore}$$

(2)

where $T_{2S}$ is the transverse relaxation time, ms; ${\rho }_2$ is the transverse surface relaxation rate, cm/ms; and ${(S/V)}_{pore}$ is the ratio of pore surface area to fluid volume, 1/cm. For simple-shaped pores, the value of S/V is related to the pore size. In this experiment, a cylindrical pore model was used. Assuming that the pore radius is r and the length of the pore tube is l, the value of S/V is 2/r.

2.4. Experimental Procedure

2.4.1. Test Block Preparation

This study used remolded expansive soils, prepared through the following procedure:

(1)

Pre-treatment of Soil Samples: Soil was initially air-dried naturally and then crushed with a crushing hammer, as depicted in Figure 3a.

(2)

Screening and Drying: In compliance with GBT 50123-2019 [32] (Chinese standard), the crushed soil was sifted using a 2 mm sieve and subsequently oven-dried at 100 °C for 24 h.

(3)

Adjustment of Water Content: The soil’s water content was adjusted to 14%. This step involved gradual water addition and frequent stirring to prevent clumping.

(4)

Sealing and Resting of Soil Samples: The adjusted soil samples were sealed with plastic film and left for 24 h, as shown in Figure 3b, to ensure uniform soil water integration.

(5)

Water Content: After resting, the water content was tested again to confirm that it remained within 14 ± 1%.

(6)

Preparation of the Specimen: To prevent interference with the NMR test’s magnetic field from steel and iron, petroleum jelly was applied between the specimen and the ring cutter for separation.

(7)

Compacting and Shaping: After the soil samples were smothered, some of the soil samples were placed into a ring knife mold coated with petroleum jelly. The soil samples were compacted 25 times with a percussive tester according to ASTM D698-12 [35], and then the specimens were removed and the ends were flattened with a paring knife, as shown in Figure 3c.

(8)

Separation and Weighing: The specimen block was detached from the ring cutter, and its mass was weighed, as shown in Figure 3d.

(9)

Repeat Preparation: This preparation process was repeated for multiple test blocks for subsequent experiments.

Figure 3. Test block preparation diagram.

Figure 3. Test block preparation diagram.

2.4.2. Rainfall Evaporation Cycle Experiment

In this experiment, we utilized soil samples prepared with a ϕ 61.8 × 20 mm ring cutter for rainfall evaporation cycle experiments to study the impact of rainfall evaporation on the microstructure of expansive soil. The key steps included the following:

(1)

Preparation for Simulated Rainfall Test: Considering the small area of soil samples affected by rainfall and the minimal flow rate required, the water level change in the storage tank was negligible. Initially, the tank was filled with water, and ring knife-prepared soil samples were placed in the soil-bearing container. Rainfall intensity was regulated using a controller, as detailed in Table 1, to execute the simulated rainfall test.

(2)

Rainfall Evaporation Cycle Treatment: The cycle comprised one day of rainfall followed by one day of drying using a 202-4A electric constant temperature drying oven (temperature range: 10–300 °C). Under simulated hot weather conditions, the oven was set to 40 °C with a relative humidity of 50 ± 2%.

(3)

Saturation Treatment: Kerosene, instead of water, was used to saturate the expansive soil test blocks due to the interactions between water and expansive soil, which could skew results. Kerosene’s inertness prevents such reactions, preserving the soil’s original state. The soil blocks were fully immersed in kerosene for 24 h to ensure complete saturation, as shown in Figure 4a.

(4)

NMR Observation: Post-saturation, the internal pore structure of the test blocks was observed using an NMR instrument to analyze the effects of the rainfall evaporation cycle on the soil’s microstructure.

Figure 4. Test block test chart.

Figure 4. Test block test chart.

2.5. Digital Image Processing

Image-Pro Plus 6.0 (IPP) is an advanced tool used for parsing and processing 2D and 3D images, offering extensive gauging capabilities and customization. This software was employed to determine the fissures on the surface of expansive soil specimens, following these following steps:

(1)

Image preparation: The image preparation stage is a crucial step in the experiment. When using a Canon EOS 1500D DSLR camera (Canon, Tokyo, Japan) to take pictures of the test surface, make sure that the camera is fixed on a stable tripod and adjust the height until the camera is able to cover an area of 61.8 mm × 61.8 mm. This ensures that the images captured are of high quality and accuracy, which facilitates subsequent image processing and analysis work.

(2)

Binarization: Binarization is a common image processing technique that highlights target features by converting a color or gray scale image into a binary image with only two colors (typically black and white). In MATLAB, code can be written to implement this process. First, the original color image needs to be converted to a greyscale image, and then the binarization threshold is determined automatically using an appropriate algorithm. For expansive soil test block images, the threshold is usually determined in the range of 0–1. By binarizing the image, the shape of the cracks in the image can be highlighted in black and white contrast, thus showing more clearly the intact part of the soil sample structure and the open part of the cracks.

(3)

Noise and error handling: The effects of noise and error must be considered when processing and analyzing image data. Image noise and the roughness of the soil sample surface may lead to stray dots in the binarized image, and these can cause errors in the black pixel statistics. In this case, the stray dots may form a fragmented distribution in the crack region, thus interfering with the accurate extraction of crack shape parameters. In order to effectively eliminate the effect of clutter, a professional image processing software, Adobe Photoshop, was used to morphologically process the binarized images for accurate distortion correction [36].

(4)

Parameter extraction: Fracture parameters were extracted using Image-Pro Plus 6.0 (IPP). First, import the binarized image and select the “Measurement” function in “Analysis”. This will present a measurement result window with various parameters that can be found in relation to the fissure. Using these parameters, information such as the number, total length, and average width of the cracks in the specimen section can be calculated.

3. Results and Analysis

3.1. Effect of Rainfall Evaporation Cycles on the Pore Structure of Expansive Soils

The distribution characteristics of the rainfall evaporation cycle, as determined by NMR tests under light and medium rainfall intensity levels, are depicted in Figure 5 and Figure 6. Following established pore classification criteria [37], the pores were categorized into three groups based on their radius sizes: micropores (r < 1.0 μm), small medium pores (1.0 μm ≤ r < 10 μm), and macropores (r ≥ 10 μm).

Figure 5 illustrates how the pore structure of expansive soils evolves with increasing cycles of rainfall and evaporation under light rainfall conditions. Micropores and small-to-medium pores dominate the soil, making up about 90% of the total porosity. Notably, the proportion of macropores generally increases with more cycles, rising from 4.9% to 14%, except during the fifth cycle. While the share of small-to-medium pores fluctuates slightly, it remains relatively stable overall, increasing from 45.23% to 54.35%. In contrast, the proportion of micropores shows a consistent downward trend, decreasing from 49.8% to 40.45%. These results suggest that under cyclic light rainfall, micropores are progressively replaced by macropores, leading to a coarser pore structure as the cycles progress.

Figure 6 highlights the changes in the pore structure of soil samples under medium rainfall conditions. In this scenario, micropores and small-to-medium pores remain the dominant components, though their average content slightly decreases compared to the light rainfall condition, making up about 85% of total porosity. The proportion of macropores shows a generally increasing trend with more rainfall evaporation cycles, rising from 3.32% to 19.41%. While the share of small-to-medium pores fluctuates, it generally trends downward, decreasing from 49.04% to 43.39%. Except for the first cycle, the proportion of micropores steadily declines from 47.64% to 37.20%. These observations suggest that under medium rainfall, the proportion of macropores increases while the micropores decrease, with small-to-medium pores following a more complex pattern of an initial decline before rising.

3.2. Changing Law of Pore Characteristic Parameters of Expansive Soil

The data from the NMR experiments, including their corresponding T₂ spectral curves, enabled us to precisely calculate and collate the key parameters of the specimens subjected to varying numbers of cycles under light and medium rainfall intensity levels. These parameters encompass the total peak area, advantageous pore size, and porosity depicted in the T₂ spectral curves. The term ‘total peak area’ here signifies the cumulative area of all peaks in the NMR spectra. The collated results are presented in

Table 3. T₂ distribution curve characteristic parameters.

Rainfall Intensity	Characteristic Parameters	Number of Cycles
		0	1	2	3	4	5	6
light rainfall	Total peak area	3850.8	3874.9	3902.9	3925.9	4085.3	5974.0	6445.1
	advantageous pore size /μm	1.092	1.092	1.018	0.886	0.886	0.950	1.018
	Porosity/%	5.94	9.14	9.38	9.53	10.04	10.41	11.28
medium rainfall	Total peak area	4263.4	6502.2	7554.9	7838.1	7937.5	7447.5	—
	advantageous pore size /μm	1.092	0.886	1.254	1.092	1.345	1.254	—
	Porosity/%	6.58	8.28	9.54	11.92	12.35	11.65	—

.

Figure 7 illustrates the changes in the soil pore structure under varying rainfall conditions. Under light rainfall, the dominant pore size in the soil initially starts at 1.092 μm, decreases to 0.886 μm during the third and fourth rainfall evaporation cycles, and then rises again, showing some fluctuations. In contrast, under medium rainfall, the dominant pore size also starts at 1.092 μm, but undergoes more significant fluctuations, indicating that medium rainfall induces more drastic changes in the soil’s pore structure. This suggests that the dominant pore size in expansive soils fluctuates with increasing rainfall evaporation cycles, reflecting the ongoing changes in the soil’s internal structure. Notably, specimens are destroyed after the sixth cycle under medium rainfall, indicating that the internal structure of expansive soils continues to deteriorate until complete failure occurs. Additionally, under light rainfall, porosity gradually increases from 5.94% to 11.28%, indicating a steady increase in porosity with more cycles. Under medium rainfall, porosity begins at a higher initial value (6.58%) and rises to 12.35%, but slightly decreases to 11.65% in the final cycle, with the rate of increase slowing. Overall, porosity tends to increase with the number of rainfall evaporation cycles.

These observations suggest that rainfall evapotranspiration cycles have a significant effect on the soil porosity and dominant pore size, which vary under different rainfall conditions. During wet and dry cycles, soil porosity can be divided into inter-aggregate porosity and intra-aggregate porosity [38]. Inter-aggregate pores are larger in size than intra-aggregate pores, and these inter-aggregate microparticles are more likely to be carried by water during the rainfall evaporation cycle. Water gradually picks up tiny particles and water-soluble cement (water-soluble salts) from the soil as it flows into and out of the soil. Subsequently, the pores between the particles increase, the proportion of large pores increases, and the total expansion and deformation capacity of the soil sample decreases.

3.3. Characteristics and Quantitative Analysis of Cracks Development in Expansive Soil

3.3.1. Digital Image Processing and Analysis

Photographs of expansive soil specimens were taken and processed to capture images of the surface cracks following each rainfall and evaporation cycle. To facilitate the examination of fine-scale cracks within the soil, it is necessary to convert the images into a binary format. Refer to Figure 8 and Figure 9 for a detailed procedure on how to extract the fine-scale cracks.

Figure 8 demonstrates the impact of rainfall evaporation cycles on the soil cracks network under light rainfall conditions. After two cycles, an emerging crack network with increased crack width and quantity is visible, indicating further structural damage to the soil. However, following six cycles, the crack network appears less pronounced, with reduced crack width and numbers, suggesting a possible stabilization or significant adjustment in soil structure. Conversely, Figure 9 shows the effect of these cycles under medium rainfall conditions. Initially, after two cycles, cracks emerge on the soil surface, particularly concentrated in the center. By the fourth cycle, these cracks widen, signaling enhanced drying and cracking. After the fifth cycle, the cracks further proliferate in number and width, underscoring the considerable influence of the rainfall evaporation cycle on soil structure.

The underlying mechanism for these changes is the soil’s physical response to wetting and drying cycles. During wetting, water movement can cause soil particle migration, particularly near crack edges, exacerbating crack formation and expansion. In the drying phase, the thinning water film between soil particles strengthens particle attraction, leading to shrinkage and, consequently, the development of surface and internal cracks.

The process of soil expansion crack development during the rainfall cycle under evapotranspiration can be classified into four stages [39]. The initial stage is characterized by the generation of cracks, which are initially formed and may be concealed or nearly imperceptible. Only a few minor cracks are observed during the first evaporation cycle subsequent to rainfall. The subsequent stage is characterized by crack expansion, as major cracks emerge along with numerous secondary cracks, which experience full development during the second evaporation cycle following rainfall. The subsequent stage involves the growth of cracks, with primary cracks continuing to progress while secondary cracks undergo gradual healing and disappearance. This phenomenon takes place during the third and fourth cycles of rainfall evaporation. The final stage is characterized by stable cracking, during which primary cracks display steady growth while secondary cracks experience substantial healing. This stage occurs in the fifth and sixth cycles of evaporation following rainfall.

3.3.2. Cracking Quantification Results and Analysis

In order to further investigate the crack development patterns in expansive soil under rainfall evaporation cycles, a quantitative analysis of the cracks is required. Firstly, the Image-Pro Plus 6.0 (IPP) software is used to calibrate the spatial scale and extract surface cracks from the binary crack images obtained in the previous step. The morphology and structural characteristics of the cracks are then examined in the crack images. Several crack indicators are proposed and quantitatively analyzed, including (1) the number of cracks, representing the quantity of crack development based on the frames of adjacent nodes; (2) the total crack length, calculated by summing the lengths of all cracks from their skeleton; (3) the average crack width, measuring the degree of crack expansion using the ratio of the total crack area to the total crack length; and (4) the surface crack rate, reflecting the extent of soil sample cracking by comparing the total surface crack area to the total surface area of the sample.

The quantitative analysis of the images can yield specific parameters, effectively enhancing the speed and accuracy of image processing.

Table 4. Quantitative analysis results of surface cracks.

Rainfall Intensity	Rift Indicator	Number of Evaporative Cycles of Rainfall
		0	1	2	3	4	5	6
Light rainfall	Number of crack bars	0	23	111	86	67	39	27
	Total crack length/mm	0	53.34	166.96	127.28	84.07	70.00	31.73
	Average crack width/mm	0	0.29	0.5	0.57	0.53	0.48	0.52
	Surface cracking rate/%	0	0.41	2.28	1.89	1.36	1.05	0.49
medium rainfall	Number of crack bars	0	14	64	44	46	32	—
	Total crack length/mm	0	6.77	100.18	88.89	78.10	84.15	—
	Average crack width/mm	0	0.17	0.45	0.62	0.65	0.85	—
	Surface cracking rate/%	0	0.04	1.11	1.99	2.34	2.31	—

presents the specific values of each quantitative crack index for expansive soil specimens subjected to rainfall evaporation cycles with light and medium rainfall intensities. Based on these values, the measurement index curves were plotted for different cycle times under light and medium rainfall intensities, as depicted in Figure 10.

Based on Figure 10a, the number of crack strips in the expansive soil specimen exhibited a continuous increase during the initial two rainfall evaporation cycles, particularly following the second cycle. This rise in the number of crack strips can be associated with the second stage of expansive soil crack formation, characterized by the generation of primary cracks accompanied by the creation of numerous secondary cracks. At this stage, the cracks become fully manifested on the surface of the expansive soil specimen, marking the peak in the development of the number of cracks. Subsequently, the number of cracks gradually declined as the number of rainfall and evaporation cycles increased, indicating that the progressive healing and disappearance of secondary cracks during the later stages of expansive soil development contributed to the reduction in the crack count within the sample.

By examining Figure 10b, we can observe a similarity between the trends in both the total length and the number of cracks in expansive soil specimens. During the initial two cycles of rainfall and evaporation, the total length of cracks steadily increased. After the second cycle, a significant increase was observed, which corresponds to the second stage of crack development in expansive soils. At this stage, there was a peak in the growth of the total length of cracks. Subsequently, as the number of rainfall and evaporation cycles increased, the total length of cracks gradually decreased. This indicates that the gradual healing of secondary cracks, following the second stage of expansive soil development, contributed to the reduction in the total length of cracks in the specimens.

Based on Figure 10c, the average width of cracks in expansive soil specimens shows a tendency to increase as the number of rainfall and evaporation cycles increases, particularly under medium rainfall intensities. This implies that the extent of crack opening in expansive soils augments as the number of rainfall and evaporation cycles increases. With an increasing number of rainfall and evapotranspiration cycles, expansive soils undergo the formation of primary cracks followed by a significant generation of secondary cracks. Over time, the primary cracks progress and expand, whereas the secondary cracks gradually heal. Consequently, this leads to an enlargement in crack width accompanied by a reduction in the overall number of cracks. Therefore, the average width of cracks increases as the number of rainfall and evaporation cycles rises.

Based on Figure 10d, the surface cracking rate of expansive soil specimens under light rainfall intensity reached its maximum after the second cycle of rainfall and evaporation, followed by a gradual decline. This suggests that following the second cycle of rainfall and evaporation, the formation of primary cracks in expansive soils consistently lags behind the healing process of secondary cracks, leading to a decrease in the surface cracking rate and an overall reduction in the extent of cracking observed in the soil samples. When subjected to medium rainfall intensity, expansive soils exhibited a peak surface cracking rate after the fourth cycle of rainfall and evaporation, followed by a subsequent decrease. This suggests that prior to the fourth cycle of rainfall and evaporation, the overall extent of cracking in expansive soils kept escalating, which implies that the growth of primary cracks outpaced the healing of secondary cracks. However, once the development of primary cracks in the soil samples reached a steady state, the surface cracking rate commenced its decline.

3.3.3. Developmental Pattern of Main Cracks in Expansive Soils

Considering that the damage to expansive soil takes place during the development and stabilization stage of the main crack, and that the secondary crack is mostly healed by this point, it is hypothesized that the deformation and damage of expansive soil, under the influence of rainfall and evaporation cycles, are associated with the development of its main crack. Therefore, this section aims to thoroughly analyze and study the developmental pattern of the main crack in expansive soil. The surface crack images of the expansive soil were processed using Image-Pro Plus 6.0. The main crack was then extracted individually, and various quantitative indices related to the main crack were calculated, as presented in

Table 5. Quantitative analysis results of surface main cracks.

Rainfall Intensity	Main Crack Indicator	Number of Evaporative Cycles of Rainfall
		2	3	4	5	6
Light rainfall	Crack length/mm	16.752	18.939	21.436	27.909	11.796
	Average crack width/mm	0.833	0.838	0.823	0.835	0.635
	Crack area/mm2	13.947	15.869	17.635	23.316	7.488
Medium rainfall	Crack length/mm	12.199	30.991	22.685	33.486	—
	Average crack width/mm	0.660	1.248	1.717	1.329	—
	Crack area/mm2	8.053	38.672	38.947	44.507	—

. Since the data for the second main crack, which began to develop on the expansive soil specimen’s surface after the fourth cycle of medium rainfall intensity, is limited, the corresponding indices are not individually listed in the table. Utilizing the data from Table 5 and the indices of the second main crack after four cycles of medium rainfall intensity, a curve illustrating the variations in main crack measurements throughout the rainfall evaporation cycle was constructed. This curve is depicted in Figure 11.

Based on Figure 11a, the length of the main crack in the expansive soil test showed a gradual increase as the number of rainfall evaporation cycles increased, except for the sixth cycle. This trend was observed under light rainfall intensity. At medium rainfall intensity, the length of the first main crack exhibited a fluctuating increase as the number of cycles increased, while the length of the second main crack remained relatively constant. Overall, as the number of rainfall evaporation cycles increased, the length of the main crack also increased. As can be seen from Figure 8, the number of fissures on the surface of the expanded soil began to decrease after three cycles of rainfall evaporation, and the total length of the fissures also decreased, but the length of the main fissures still increased, indicating that the secondary fissures were gradually healing and the main fissures were still developing. By the sixth cycle, the secondary fissures had basically healed and the main fissures had began to heal, resulting in a decrease in the length of the main fissures and a decrease in the curve of the sixth cycle.

By observing Figure 11b, we can deduce that the average width of the main crack in the expansive soil specimen remained relatively stable as the number of cycles increased under light rainfall conditions. The average width of main crack 1 generally exhibited an upward trend with increasing rainfall evaporation cycles under medium rainfall conditions. Furthermore, the change was more pronounced, and there was also a notable increase in the average width of main crack 2. Overall, the average width of the main crack in expansive soils exhibited minor changes under the influence of light rainfall cycles but underwent a substantial increase under the influence of medium rainfall cycles.

As shown in Figure 11c, the area of the main crack in the expansive soil specimen gradually increased with the number of cycles under light rainfall conditions. After the third rainfall evaporation cycle, the area of main crack 1 in the expansive soil significantly increased, followed by a decrease in the growth rate. Meanwhile, there was a slight increase in the area of main crack 2. The combined index curves of the length, average width, and area of the main crack indicate that under the medium rainfall evaporation cycle, the development rate of the main crack in the expansive soil is higher. Therefore, it can be hypothesized that the development rate of the main crack in the expansive soil is influenced by rainfall intensity, given the same number of rainfall evaporation cycles. Moreover, a higher intensity level corresponds to a faster development rate of the main crack.

3.4. Modeling of Cracking Development in Expansive Soils

In assessing the structural deterioration of expansive soil, the average crack width is a crucial metric. Figure 12a illustrates the correlation between the number of rainfall evaporation cycles and the average crack width. Under light rainfall conditions, an increase in average crack width correlates with the number of cycles, following a modified logistic curve function (Equation (3)), with a high correlation coefficient (R² = 0.98). This aligns with previous research [29] and suggests that the average crack width will eventually stabilize. In contrast, under medium rainfall conditions, the relationship is modeled by a linear regression (Equation (4)), with a correlation coefficient of R² = 0.96, indicating a linear increase in the average crack width with more cycles. Figure 12b compares experimental and fitted values, showing close alignment in most cases, with differences ranging from 0 to 0.05 mm. However, for certain groups (K, L, and M) under medium rainfall conditions, the discrepancies are more pronounced, with absolute errors of 0.072 mm, 0.072 mm, and 0.068 mm, respectively. This variance suggests increased uncertainty factors under medium rainfall conditions. Further analysis reveals the average absolute error of the fit to be 0.036 mm, and the average relative error to be 8.1%, indicating a high overall accuracy of the fitting model.

$$y=c_y+{\displaystyle \frac{y_m}{1+a_y\times e^{-b_{y}x}}}$$

(3)

$$y=0.038+0.17x$$

(4)

where y is the average crack width, mm; x is the number of rainfall cycles; and the correction factor c_y, set at −0.15, is used to correct for forecast deviations. The parameter y_m represents the maximum possible value of the average crack width predicted b_y the model, and its determined value is 0.68 mm. The parameter a_y is closely related to the second inflection point of the curve (value 3.62), while the parameter is b_y a value of 1.97.

Comparing the two models highlights significant variances in the crack width growth patterns under different rainfall conditions. Under light rainfall, the crack width growth appears to approach a saturation state, indicating that after a certain number of evaporation cycles, the impact of light rainfall on crack development reaches a threshold. Essentially, following an initial rapid phase, crack growth progressively slows and eventually stabilizes. In contrast, under medium rainfall conditions, the crack width exhibits a continuous linear growth, implying that the effects of medium rainfall persistently widen the cracks, leading to structural damage. This disparity likely stems from the differences in the water infiltration and evaporation rates between the two rainfall intensities. Under medium rainfall conditions, the continuous infiltration of moisture led to the continuous expansion of the cracks, the expanded soil was divided by the cracks, and the healing cracks could not produce the occlusion and bonding between the soil blocks until they were destroyed. In contrast, under light rain conditions, the width of the cracks became relatively stable after reaching a certain level. This is because the formation of cracks results in the formation of new evaporation surfaces on the inner walls of the cracks, increasing the evaporation area. Water no longer needs to rise from the bottom to the soil surface as it can evaporate directly from the soil on the inner wall of the crack. This shortens the distance over which water evaporates, accelerating the change in water content. Consequently, this reduces the hydraulic gradient between the upper and lower layers of the soil, leading to a more even distribution of water content within the soil. For these reasons, the rate of change in soil moisture content increases. When the water content in the soil is reduced to a certain value, the tensile force of shrinkage deformation created by the water content gradient no longer exceeds the tensile strength of the soil. As a result, cracks no longer expand [40]. These findings provide an important perspective for understanding the effects of different rainfall conditions on soil structural stability.

Figure 13 displays the relationship between the average crack width and the porosity of expansive soils. A linear regression model was applied to analyze the data, yielding a correlation coefficient (R²) of 0.84, as depicted in Equation (5). This model demonstrates a significant positive correlation, suggesting that the average crack width in expansive soil increases in tandem with porosity. Observing the graph, it is evident that all data points align within the model’s predicted confidence interval, indicating a strong congruence between the actual observed values and the model’s predictions. This correlation is pivotal for understanding and forecasting the mean crack width in expansive soils. On a microscopic level, these results elucidate the crack development pattern in expansive soils and furnish experimental data and a theoretical foundation for future research in this domain.

$$y=-0.72+0.12n$$

(5)

where y is the average crack width, mm, and n is the porosity, %.

4. Conclusions

In this study, we observed the unfolding of cracks in expansive soil under rainfall evaporation cycle conditions. The observations were made from two perspectives: internal (using NMR test) and surface (using image analysis). Two sets of tests were conducted to analyze the detailed mechanism of expansive soil structure deterioration in the context of rainfall evaporation cycles. The following are the main conclusions drawn from our research:

(1)

In the presence of light and medium rainfall cycles, the pore space within a soil sample is predominantly composed of micropores, small pores, and medium-sized pores, which together typically account for over 85% of the total pore volume. As the number of rainfall evaporation cycles increases, the micropores and small- and medium-sized pores in expansive soils gradually transform macropores. The extent of this transformation is directly proportional to the level of rainfall intensity.

(2)

Expansive soils exhibit enhanced porosity resulting from the significant accumulation of free water during hygroscopicity, but partially contract during dehumidification, which restores a portion of the internal pores and leads to a gradual reduction in porosity. Once dehumidification reaches a steady state, the soil sample undergoes a process of expansion and contraction, resulting in the formation of irreversible pores. As the number of cycles increases, the irreversible pores also multiply, leading to a gradual rise in effective porosity, ultimately culminating in the disintegration of the soil sample due to dispersion.

(3)

Based on the grayscale processing and binarization of cracking images on the surface of expansive soil, the development of cracking under rainfall evaporation cycles can be categorized into four stages. By extracting cracking from expansive soil samples and conducting quantitative analysis, including the main cracking length, average width, and area measurements, it was observed that the development of primary cracking in expansive soil was more rapid during evaporation cycles accompanied by middle-intensity rainfall events.

(4)

When assessing the structural deterioration of expansive soil, the average width of cracks serves as a crucial indicator, with larger widths indicating a higher risk of sample failure. Under varying rainfall conditions, the relationship between the number of rainfall cycles and the mean crack width was modeled using both a linear regression model and a modified logistic function. These models demonstrated high accuracy, with correlation coefficients (R²) of 0.98 and 0.96, respectively. Moreover, a significant positive correlation exists between the porosity and average crack width, evidenced by a correlation coefficient (R²) of 0.84. This suggests that as porosity increases, so does the average width of cracks in expansive soil, further emphasizing the importance of porosity as a predictive factor in soil structural integrity.

(5)

Further studies will need to investigate the whole process of evaporation. The cycles modify the fine structure of expansive soil, changing the whole process of the rainfall evaporation cycle, meaning it will be necessary to investigate the evaporation (dehumidification) of expansive soil.