Abstract
An understanding of the mechanical properties and macroscopic behavior of unsaturated soil can be improved through an in-depth microscopic insight of the variables controlling the soil–water characteristic curve (SWCC). In this study, the effects of the initial conditions on the pore structure and SWCC of silty soil was examined. Their relationships to the soil behavior during water loss was addressed from both macroscopic and microscopic perspectives. In this study, patterns different from those of previous studies were revealed; this especially pertained to the effect of the initial water content on the SWCC. The SWCC was obtained using repeated centrifugation and filter paper tests. Mercury intrusion porosimetry (MIP) and scanning electron microscopy (SEM) were performed to collect the microstructure information. The results showed that soils compacted using the optimal dry side conditions had double S-shaped SWCC for their bimodal pore size distributions, and these pores were classified as intra-aggregate and inter-aggregate pores. Thus, these soils underwent two distinct stages of water loss during drying, and water loss occurred more easily in the first stage because of the presence of many large macropores or inter-aggregate pores. However, soils compacted at the optimum water content produced a single S-shaped SWCC for the multimodal pore structure. Water drained from these soils at a relatively constant rate from a more homogeneous and uniform pore system. This study has provided a comprehensive set of macroscopic and microscopic experimental data and well-established relationships among the PSD, SWCC and initial state of the silty soil.
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Introduction
The fundamental relationship between the soil suction and the volumetric water content is expressed as the soil‒water characteristic curve (SWCC) of soils1,2,3,4. Using the SWCC, the water availability5, the soil–water holding capacity6,7, the shear strength8,9, and the failure of slopes can be estimated10,11. Conventional drying SWCCs are commonly measured in the laboratory by subjecting saturated soil specimens to gradually increasing suction levels12,13,14. Soil suction management measures have been utilized and include the filter paper method15,16, vapor equilibrium technique17,18, and centrifugation method19,20,21. According to Rahardjo, the SWCC data obtained using a centrifuge closely matched those acquired using a pressure plate, salt solution, and temperature cell21. Moreover, Fu et al. enhanced the centrifugation method for analyzing the water retention characteristics of soils by conducting additional tests on the soil samples22. The SWCC data are needed to determine the parameters for hydraulic, thermal and mechanical models.
The behaviors of unsaturated collapsible soil, compacted soils, and expansive clay have been effectively interpreted by considering the impact of suction23,24,25,26. Other factors affecting the SWCCs of these soils have also been discussed and include the stress state27, temperature28,29, initial water content30,31,32, grain-size distribution33,34, wetting and drying30,35, and dry density33,34,36 characteristics. Specifically, Zeng et al. claimed that the initial water content can affect the SWCC by altering the pore structure of disintegrated carbonaceous mudstone30. Sun et al.37, Zhou et al.11, and Chen et al.34 reported that the density significantly affects the SWCC of compacted soils by the changes to the microaggregates, pore system and the contact mode of the soil particles. Soil microstructure is an important fundamental property that controls the soil behavior at the macroscale and can be classified into three categories: structure, texture, and soil mineralogy. A quantitative and qualitative understanding of the soil structure may enable an understanding of a SWCC in a relatively simple, fast and non-destructive manner as stated by Yudina38. Experimental results on the SWRC of the compacted sandy soils39, granite residual soils40, compacted loess41, silt loam soil36 and silty sand soil42 have recently been reported, and the emphasis has been on the influence of the soil structure. Their results show that observed structural and SWCC differences significantly influence the shear strength, the unsaturated property functions and the corresponding hydraulic characteristics or agricultural properties of the soil.
In general, the existing experimental studies on soils have not validated the reliability of the centrifugation method. Additionally, suction over a wide range (typically smaller than 10 kPa) using different methods was applied in this study. Also, the SWCC results for the soil prepared at different water content or density were validated based on a comparison to the results obtained from mercury intrusion porosimetry. In this study, structural data on silty soils with different initial conditions were collected using a combination of MIP and SEM. The SWCC for soil was conducted with the centrifugation and filter paper testing methods. The impacts of the initial density and initial water content on the particle size distribution (PSD) and SWCC were addressed in the discussion. And, their relationships were discussed in a macroscopic and microscopic perspective.
Materials and methods
Soil characterization
The soil used in this experimental study was characterized as silty loam with low plasticity according to the United States Department of Agriculture (USDA) soil taxonomy system. The material was collected from Chanhe in the central region of Shanxi Province (34°27′N, 108°99′E), China. The particle size was characterized and presented in the form of a bimodal distribution (Fig. 1). Natural water content, natural density, specific surface area, specific gravity and other property indices were measured and are listed in Table 1. The values shown represent the averages from three independent tests. X-ray diffraction analysis was conducted on an air-dried powdered sample of a representative silt/clay size fraction using a Bruker ASX D8 advance X-ray diffractometer (Fig. 1). The X-ray diffraction results indicated that the material contained quartz (Qtz), calcite (Cal), chlorite (Chl), plagioclase (Pl), dolomite (Dol), illite (Il), potassium feldspar (Or), hornblende (Hbl), and muscovite (Ms), as previously determined in the laboratory43.
Particle size distributions and X-ray diffraction patterns of the tested soil.
Repeated centrifugation method assembly
The repeated centrifugation method used in this study was described by Fu et al.22. In this study, a high-speed refrigerated centrifuge (CR21G II, Japan) was utilized. In preparation for the centrifugation tests, three replicates (5 cm ×20 cm2) with a designed dry density of 1.30 g/cm3 and a target water content of approximately 13.00% were prepared. Subsequently, the soil samples underwent a 24-hour saturation process. Then, the samples were subjected to a specialized method of desaturation. Different values of suction were achieved by increasing the revolutions per minute (RPMs; rev/min). During each RPM increment, water was released from the sample until a state of equilibrium was achieved. The water loss amounts and heights of the soil samples were determined to calculate the gravimetric water content (GWC) and height shrinkage. The final RPMs for the three replications were 2800 rev/min, 5000 rev/ min and 9000 rev/min. According to the findings of Xing et al.20 and Fu et al.22, the soil density underwent significant changes throughout the centrifugation process. When the first run of the centrifugation test was finished, the densities of the three samples were 1.45 g/cm3, 1.52 g/cm3, and 1.60 g/cm3, and the final water contents were 18.16%, 13.96%, and 8.13%, respectively. After the first centrifugation test, the samples were resaturated and retested following the above steps at each RPM value. In the second centrifugation run, a slight increase in the bulk density was observed during the dehydration process. The maximum density change among the three soil samples was only 0.06 g/cm3; thus, this aspect was disregarded in this study.
Filter paper test
The contact filter paper method was initially introduced by Kim et al.44 and Likos and Lu16 and has undergone improvements by Li et al.45,46, Xie et al.47, and Hou et al.48; these researchers compared their proposed suction estimation procedures with the method outlined in American Society for Testing and Materials (ASTM) D5298-10. The enhanced test procedure had several advantages; these advantages included minimizing the exposure of the soil samples and filter papers to the pre-laboratory soil solvent, thereby changing the content caused due to moisture loss or absorption from the air. As a result, their findings were considered to be reliable.
According to Birle et al.31, the compaction property of the material exhibited a significant dependence on its preparation. Therefore, a specific procedure was developed in which samples were prepared from a basic material with a specific water content instead of wetting the dry soil powder directly to reach the desired value. By completing this process, the homogeneity of the aggregated soil particles were presumed to be preserved31. This procedure was applied to the material used in this study. First, a specific weight of water was added to the soil powder, and the resulting combination was mixed continuously and thoroughly and stored in an airtight container. After homogenization over two days, the water content was determined to be 6.13%. Then, the basic material was wetted to the target water content, and after two days, the rehomogenization phase was observed. Each soil sample was prepared in a standard mold by using sample preparation equipment, and they all had smooth surfaces. A secure contact surface between the filter paper and the bottom surface of the soil sample was ensured. The nominal height and diameter of the mold were 20 mm and 61.8 mm, respectively. At each density level, a total of approximately 50 samples were prepared from the basic material and divided into 25 groups. Samples compacted during drying and at the optimal water content were saturated (water-cured) prior to performing the filter paper suction measurements. Each sample took different durations to reach the various estimated water contents, and the drying curve was obtained from these data. Whatman ashless Grade 42 quantitative filter papers were placed in direct contact between the two soil samples for each group to prevent contamination49,50 (Fig. 2a,b). Waterproof tape was used to adhere the two soil specimens in each group together to prevent the evaporation of water44,48,50 (Fig. 2c). Specifically, to prevent evaporation during and after equilibration, the samples were sequentially wrapped in cling film and tinfoil, covered with wax, and placed in a sealed container (Fig. 2d,e,f). After all of the above steps were completed, the samples were stored at 20 °C in a humidity-controlled dark room (Fig. 2g). Following the recommendations of Chandler and Gutierrez51, a 2-week period was allocated to allow equalization. Subsequently, the filter paper was meticulously extracted from the soil samples (Fig. 2g) and weighed using a scale with an accuracy of 0.0001 g. The wet and dry soil samples were also weighed with a scale with an accuracy of 0.01 g to calculate the GWC. Estimations of matric suction were derived utilizing correlations that relied on the water content of the filter paper, as established by Crilly and Chandler52.
Sample preparation for the filter paper test.
Samples with dry densities of 1.45 g/cm3, 1.52 g/cm3, and 1.60 g/cm3 were carefully prepared (Fig. 3), and their drying curves were determined using the filter paper test to assess the accuracy and reliability of the data acquired through the repeated centrifugation method. Additionally, seven samples with predefined initial conditions were selected to explore the influence of these variables on SWCC (Fig. 3). The average initial water contents of Samples 5, 6, 7, 8, 9 and 10 were all 9.16%, at the dry side of optimum moisture content. For Samples 1, 2, 3 and 4, the water content was 17.50%, near the optimum (Fig. 3).
Compaction curve and the initial information for samples tested in the experiment.
Microstructural observation
To investigate the microstructural variations in the designed soil, SEM and MIP tests were performed. Samples with initial densities of 1.39, 1.45, 1.52, and 1.60 g/cm3 were prepared at initial water contents of 9.16 and 17.50% and were analyzed using an AutoPore IV 9500 instrument for MIP analysis manufactured by American Mack Instruments. The tests were performed with mercury pressures between 0.45 psia to 44997.46 psia; these pressures corresponded to pore radii of 397751.3 nm to 4 nm. To reduce the influence of the sample size on the microstructure, samples with same size (1 cm diameter and 2 cm height) were examined. To preserve the microstructure of the soil, the soil specimens were rapidly frozen using liquid nitrogen before conducting the MIP tests. The cumulative porosity and pore size distribution were obtained. The Quanta FEG SEM system was used to reveal the microstructural differences induced from different initial conditions. Figure 5 shows the collected SEM micrographs with 800× magnification and a resolution of 3.68 μm.
SWCC prediction model and its relationship with PSD
Researchers have proposed many prediction methods of SWCC. Leong and Rahardjo53 and Ridley and Wray54 conducted detailed discussion on the Brooks–Corey (BC) model2, van Genuchten (VG) model4 and Fredlund and Xing (FX) model55. The BC model was suitable for coarse granular soils which pore water could be drained when the suction was low56,57. The BC model had several disadvantages; for example, it lost applicability and had no inflection point in the high suction range. Considering the inflection point, the VG model was suitable for various soil types and had great flexibility in the full suction range. The FX model was suitable for a variety of soils, and the SWCC of the full suction range could be obtained. In this study, the VG model and FX model were mainly predominantly used to predict the test data to obtain SWCC in the full suction range.
Mercury and air are nonwetting fluids. For pores of the same diameter, the process of mercury intrusion into porous media would be similar to that of air intrusion into soil in the drying path of the SWCC58,59,60,61,62. Therefore, the PSD obtained from MIP could be related to the SWCC. The Young–Laplace equation assumed that the soil did not deform63,64, and the volume of pores with no mercury intrusion could be used to express the water content or saturation of soil after the corresponding matric suction was applied during the SWCC test56. The Young–Laplace equation for the relationship between the matric suction (ψ) and the diameter of the cylindrical pore was as follows:
where ua is the pore air pressure; uw is the pore water pressure; θw is the contact angle between the air‒water–pore wall; σw is the surface tension at the solid–liquid interface (at 20 ℃, σw = 0.07275 N/m) and D is the equivalent pore diameter at a specific matric suction.
In the MIP test, a nonwetting fluid (mercury) was forced through porous media. The pore size was determined by the Washburn equation63, which assumed that the pores in the soil were cylindrical channels. The mercury intrusion curve was converted to a pore size distribution curve by the Young–Laplace Equation64:
where P is the mercury intrusion pressure, Pa; uHg and uVHg are the pressures of liquid mercury (nonwetting fluid) and mercury vapor (wetting fluid), respectively; σnw is the surface tension of mercury (at 20 ℃, σnw = 0.484 N/m); and θnw is the contact angle of the mercury–pore wall–gas phase and usually varies between 130° and 140°. For loess, θnw is generally 130°, and for clay minerals, the contact angle is usually 140°65. D is the pore diameter when the mercury intrusion pressure is P.
When mercury and air intruded the cylindrical pores with same diameter, the relationship between the matric suction (ua-uw) and mercury intrusion pressure (uHg-uVHg) could be expressed as Eq. (3). In this manner, the pore size distribution obtained from MIP could be converted to the relationship between the pore size and matric suction and was thus related to the SWCC.
Results and discussion
Effect of the initial water content on the PSD
The cumulative pore volumes of samples with identical initial densities prepared at initial water contents of 9.16 and 17.50% are nearly the same, whereas their pore sizes show bimodal and multimodal distributions, respectively (Fig. 4). At low values, the water capillary content effect tends to bind silt particles and clay together and generally promotes the flocculation of the colloids during sample preparation, resulting in grain–clay aggregates66. In this case, water is mainly stored in the aggregates, and the large voids between aggregates and silt grains are mainly occupied by air. Additionally, a soil prepared under dry conditions has more aggregates than a soil prepared under wet conditions67,68,69. This phenomenon can be observed in the SEM image in Fig. 5a. The SEM images indicate that the microstructure of the soil is non-homogeneous, primarily due to the irregular positioning of the clay aggregates70. These soils exhibit a double-pore structure, with two distinct classes of pores varying in size and corresponding to intra-aggregate pores (< 1 μm) and inter-aggregate pores (> 1 μm) (Figs. 4, 5)67,71,72,73,74. When the water content is optimal, water pushes the grains apart during sample preparation and produces a dispersed soil fabric structure75. In Fig. 5c,d, the clay fraction has a relatively homogeneous distribution. Clay particles are clearly visible among the grains and are bound together to fill the intergrain pores. The degree of flocculation decreases, and the pores are more uniform. In this case, the differentiation between the micropore and macropore systems is often no longer significant67. Consequently, the volumes and sizes of inter-aggregate pores decrease. A multimodal pore size distribution with a low peak inter-aggregate porosity is normally observed.
Pore structures for the samples with different initial water contents.
SEM images of soils.
Influence of the soil shrinkage on the SWCC during centrifugation
The soil shrinkage curve (SSC) is a plot of the void ratio (e) versus the moisture ratio (v)76,77,78,79,80,81,82,83. Both the void ratio and moisture ratio are standardized by the volume of the solids, as stated by Lu and Dong84. Subsequently, the SSC employed represents the variation in the soil volume corresponding to the changes in the water volume.
The dry density changes and the relationship of e versus v for one specific soil are shown in Fig. 6. The shrinkage rate is calculated by ∂e/∂v. During the first dehydration process, the soil samples are consolidated, The dry density increases as the void ratio decreases because of the increasing suction level. The void ratio decreases from 1.08 to 0.69, the density increases from 1.30 to 1.60 g/cm3, and the final water content is 8.13%. The final bulk density is 23% greater than the initial value. As the applied matric suction increases, the slopes of the curve in Fig. 6a decrease. Notably, the initial substantial height shrinkage is primarily influenced by the porous and loose soil structure. According to the test, a significant volume is occupied by the macropores that leads to compression. Subsequently, the diminishing pore space, low compressibility of the small pores, and absence of macropores in the later stages contribute to the reduction in the rate of the height shrinkage under high matric suction. The absence of the zero-shrinkage phases in the SSC at low matric suction can be attributed to the incomplete degradation of the samples (Fig. 6a). Apparently, zero shrinkage can be achieved when the samples are subjected to high matric suction, as noted by Fu et al.22. However, clear indications of the structural and normal shrinkage can be observed(Fig. 6b). During the drying process from a saturated condition along the diagonal line, the reduction in the water volume exceeds the reduction in the number of voids. This difference causes a deviation of the shrinkage curve from the diagonal line due to a low shrinkage rate (Fig. 6b). As the soil continues to dry, the reductions in the water volume and bulk soil volume become nearly equal. At this stage, the shrinkage curve becomes approximately parallel to the diagonal line.
SSC and bulk density changes during the first dehydration process with centrifugation.
The corrected and uncorrected SWCCs with and without soil shrinkage considered are calculated20 (Fig. 7). The corrected SWCCs consistently exhibit higher values than the uncorrected SWCCs, and the differences become more pronounced as suction increase. During the SWCC measurement process, the soil volume is assumed to be constant. However, with the centrifugation approach, a considerable volume change can be observed (Fig. 6) and results in potential errors. Thus, the SWCC for rigid soil (uncorrected SWCC) does not reflect the actual retention behaviors of the samples.
Corrected and uncorrected SWCCs for the three samples measured during the first dehydration process.
Data from the filter paper test and centrifugation method
To validate the feasibility of utilizing fast and simple methods for generating SWCCs, a comparison is conducted between the suction data obtained using the centrifugation and filter paper techniques (Fig. 8). The SWCCs for the three soil samples indicate that the repeated centrifugation method provides comparable results to the filter paper method. The entire boundary effect zone can be evaluated. However, only some of the S-shaped SWCCs within the measurement range from 0 to 2000 kPa can be characterized. As reported in a previous paper45 and the discussion in Sect. 3.6, the inter-aggregate pores are weak and collapsible for the contact modes of the particles around the large pores are sensitive to the soil shrinkage produced in the centrifugation test. Thus, macropores became progressively disconnected and its area, size are clearly lowered during hydration45. Thus, the pore size of the samples become more uniform. The data obtained using the centrifugation method are in good agreement with the drying curves of the soil prepared at the optimal water content. However, the double S-shaped SWCCs for the soil prepared at low initial water contents in this study cannot be measured using a centrifuge, as discussed later.
Drying curves of the soil compacted at different initial water contents measured with the filter paper and centrifugation tests.
The SWCCs of the soil appear to vary in the middle suction range. However, the SWCCs begin merging at high suction levels. At an initial density of 1.39 g/cm3, the two curves for Sample 1 and Sample 6 initially deviate from each other and then approach each other during the drying process until the suction exceeds 600 kPa and the water content reaches 13.50% (Fig. 8). At an initial density of 1.45 g/cm3, the curves approach each other at a suction of 800 kPa and a corresponding water content of 17.00%. At an initial density of 1.52 g/cm3, for Sample 3 and Sample 8, the curves approach each other at a suction of 4000 kPa and a corresponding water content of 12.50% (Fig. 8). At an initial density of 1.60, the drying curves of Sample 4 and Sample 9 approach each other at a high suction of 2.2 × 104 and a low water content of 10.00%. The drying curves are assumed to be independent of the compaction water content when the suction and/or the water content exceed a certain value. At a given density, although the increase in water content has an effect on both the intra-aggregate and inter-aggregate pores, a small difference in the intra-aggregate pore structure system is shown in Fig. 4. Moreover, this difference become much less pronounced as the pore diameter decreases. When the diameter is less than a certain value, such as 0.04 μm for soil at a density of 1.39 g/cm3, the samples show a near identical micropore system; this system contributes to the indistinct rate of the water loss among the soils at high suction range. Thus, the convergence of the drying curves can be observed. Therefore, the initial conditions affect the retention behavior of the examined soil in the middle suction range, and no significant influence is observed in the high suction range. These results are similar to those reported by Birle et al.31. Soils compacted at the optimal water content exhibit higher levels of water retention. This difference can be attributed to the relatively small pore system, as discussed previously.
SWCC and PSD for samples prepared at a water content of 9.16%
According to Eq. (3), the mercury intrusion pressure can be converted to matric suction; this is plotted in the same coordinate system with the SWCC. The measured data can be apparently divided into two groups. Thus, segmental fitting method was used based on the the VG model and the FX model by using Origin user-defined function. The correlation coefficients of the VG model are significantly greater than those of the FX model; these results indicate a better fit for the VG model. Table 2 lists the fitting parameters of the VG model which can be precisely output from the Origin based on the measured data; here, α, n and m are the fitting parameters related to the air enter value, pore size distribution and overall symmetry of the curve.
As shown in Fig. 9, the SWCCs for the soils compacted at 9.16% exhibit double S-shaped SWCCs. According to Cai et al.85, the SWCCs tend to stabilize in the intermediate suction range, regardless of the initial densities. The two pore systems in the pore size distribution density correspond to the two stages of the bimodal SWCC. The water loss process of the pores among the saturated aggregates corresponds to the first stage of the SWCC curve, whereas that of the pores within the saturated aggregates corresponds to the second stage. Consequently, the compacted soils likely undergo two distinct stages of water loss during the drying process. Water is lost more easily in the first stage than in the second stage because of the presence of many large macropores or inter-aggregate pores; these results are similar to the observations by Burton et al.86, Liu et al.87 and Sun et al.88.
SWCCs and PSDs of the soils compacted at water contents lower than the optimal value.
In this study, the bimodal SWCC curve is divided into three zones based on the typical S-shaped SWCC curve. The first zone is the saturation zone (ψ < ψa). In the drying path, the saturation zone represents the saturation stage controlled by the total porosity of the soil sample. In this zone, the soil sample is completely saturated until the matric suction reaches the air enter value. At this stage, the saturated water content of the soil sample is controlled by the total porosity of the soil sample. When the matric suction exponentially increases, the volumetric water content slightly changes. The second zone is the transition zone (ψa≤ ψ < ψi). When the matric suction is on the positive side of the air enter value, the water in the saturated intergranular pores or the inter-aggregate macropores is preferentially drained from the soil sample as the matric suction increases. Due to the large size and volume of the inter-aggregate pores, when the suction exponentially increases, the water in the macropores decreases relatively fast, and the slope of the SWCC curve is relatively large. The third zone is the residual zone (ψ≥ ψi). When the suction exceeds the inflection point of the SWCC curve, the small pores in the aggregates are in a saturated state. As the suction continues to increase, the water in the aggregates slowly drains, and the water loss rate is much lower.
SWCC and PSD for samples prepared at the optimal water content
Figure 10 shows the relationship curve of the matric suction and volumetric water content of the soil sample compacted at the optimal water content; here, the curve shows a typical “S” shape. In this section, SVsoils in SVOFFICE 5 is used to fit the measured data to a continuous SWCC curve, and the prediction functions applied are the VG function and the FX function. When the FX fitting function is used, the correlation coefficients are significantly greater than those of the VG fitting function; these results indicated a better fit for the FX fitting function. Table 3 lists the prediction parameters for the soil samples with different densities.
SWCCs and PSDs for soil compacted at the optimal water content.
When the initial water content of the compacted soil sample is high or close to the optimal value, the PSD of the compacted soil sample exhibits a multipeak pore structure, and the peak value is much lower as Figs. 4, 10 present. For these reasons, these soil is reflected by a uniformly descending drying curve. Water drains from the soil at a relatively constant rate during drying. Therefore, a single S-shaped drying curve within the measured suction range is produced (Fig. 10). The three peaks of the pore size distribution density curve of the compacted soil sample with the optimal water content from large to small correspond to the large inter-aggregate pores, the small inter-aggregate pores and the intra-aggregate pores (Fig. 10). In the transition zone, the water in the large inter-aggregate pores in the soil sample is gradually replaced by air, followed by the small inter-aggregate pores. At this time, the volumetric water content rapidly decreases, and water and air coexist in the soil sample. The slope of the SWCC curve is relatively small in the residual zone, and the water in the soil sample is basically present inside the aggregates or adhered to the particles. When the matric suction exponentially increases, the volumetric water content decreases very slowly (Fig. 10).
Effects of the dry density on the PSD and SWCC for the samples prepared at a water content of 9.16%
Figure 11 shows the cumulative pore volume and pore size distribution of the samples with different initial dry densities that were prepared at water contents below the optimal value. Due to the low dry density, the total pore volume is high, as expected. As the density increases, the proportions of the pores smaller than 1 μm (inter-aggregate pores) are 0.0715, 0.0743, 0.0907, 0.0992, 0.0799, and 0.0793 for soils with initial densities of 1.30, 1.39, 1.45, 1.52 1.60 and 1.67 g/m3, respectively (Fig. 11); the corresponding total pore volumes are 0.3134, 0.3007, 0.2892, 0.2602, 0.2224, and 0.1899, respectively, and the pores with sizes between 1 μm and 30 μm account for 0.2246, 0.2246, 0.2246, 0.2246, 60.3, 0.1379, and 0.1060, respectively (Fig. 11). Therefore, the decrease in the total pore volume when the soil density increases mainly results in a reduction in pores with sizes of 1–30 μm (Fig. 11) Thus, the drying curves are notably different in the first stage of drying because large pores reduce suction and influence the SWCC (Fig. 12).
Pore structures of the samples with different initial dry densities prepared at water contents below the optimal value.
Drying curves for the samples with different initial dry densities.
Based on the pore size distributions, the samples prepared at water contents below the optimal value exhibit typical bimodal shapes. The small pores, which are the pores inside aggregations, are not influenced by the density increase; this behavior differs from that of the macropores (Fig. 11). This phenomenon potentially occurs because the soil aggregates exhibit a comparatively high stiffness at a low water content. This flocculation of the colloids is relatively stable and insensitive to the forces that occur during the static compression or dynamic compaction89; this trend is the same for samples that are prepared at varying densities for comparable micropore systems31. The large pores, which correspond to the pores between aggregates or grains are affected noticeably by initial density. The peak decreases from 0.55 to 0.24 ml/g, and the dominant macropore diameter decreases from 20.19 to 3.17 mm as density increases from 1.30 to 1.67 g/m3. The inter-aggregate pores are weak and collapsible (Fig. 11) since the contact modes of the particles around the large pores are not stable and are thus sensitive to dynamic compaction or static compression. This effect is observed during compression and gradually weakens as the pore sizes the progressively decrease75. This phenomenon can be observed from the SEM images; notably, with increasing density, pore deformation occurs in the zones where grains are clean and have large pores surrounding them70. Furthermore, the areas with clay aggregates in the pore space are highly resistant and not very sensitive to local collapse. Therefore, as the density evolves during compression, the effect is related to the largest class of pores, as determined by Delage and Lefebvre90 and Kochmanova and Tanaka91, who studied clay soil during consolidation.
The drying paths of the samples, which were compacted at nearly the same initial water content, exhibit distinct variations, as shown in Fig. 12. According to the figure, the initial dry density noticeably affects the SWCCs. Soils with different initial densities compacted at a drier-than-optimal water content show an identical trend for bimodal SWCCs, resulting from the double-pore structure. A flat SWCC in the moderate suction range is clearly observed. The corresponding suction is the residual suction and is higher for high-density soils than for other soils (Fig. 12). This trend arises because it is necessary to increase the suction to move the water stored in small and low-volume macropores. In the first stage (transition zone), the rate of reduction in the volumetric water content of the low-density soils is high because of the increasingly predominant macropore system. The slope of the SWCC in this stage is related to the dominant pore structure. In the second stage, when the suction exceeds the residual matric suction, water is slowly lost, and the difference in the rate of water loss among the soils appears indistinct. Regardless of the dry density, the slopes of the curves appear to align; these results are in agreement with those from Romero and Vaunat92. The effect of the initial dry density on the drying curves for compacted soil samples can be effectively reduced when the suction exceeds 10 MPa (Fig. 12). At an initial water content of 9.16%, the increase in density has no effective influence on the micropore system (Fig. 11). All samples show a common dominant micropore diameter of approximately 0.04 μm. This characteristic contributes to the convergence of the drying curves at suction levels exceeding 10 MPa. The pore structure primarily governs suction above 10 MPa for the samples analyzed in this study. Therefore, the capillary forces resulting from the micropores are largely independent of the initial dry density; these results are similar to those reported by Romero et al.58 for clayey silt.
Effects of the dry density on the PSD and SWCC for the samples prepared at the optimum
Figure 13 shows the effects of the density on the cumulative pore volume and pore size distribution when soil is prepared at the optimal water content. Pores can be classified into four different zones. Zone 1 and zone 4 include the related pores that are only slightly influenced by density. Zone 2 corresponds to the micropores and is unaffected by the density. The pores in zone 3 have a pore diameter between 0.3 and 100 μm, the volume fraction of the pores decreases considerably as the density increases. The change in pore volume with increasing density results from the reduction in the pore sizes ranging from 1 to 30 μm for soil compacted at a water content of 9.16%. Therefore, the wide diameter range of the pores is affected by the density, and the effect is more pronounced than that under compression at a water content of 9.16%. This phenomenon results from the dependence of the soil structure on the water content. When the initial water content is high or near the optimal value, the capillary effect decreases, and the compressibility of a soft aggregate is high; these particles and the soil structure are vulnerable to external forces. Thus, small and some large inter-aggregate pores can be affected.
Pore size distributions of the samples with different initial dry densities prepared at the optimal water content.
At the same initial water content, the SWCCs of samples with high initial dry densities are higher than those of samples with low initial dry densities; this especially applies to those in the moderate suction range (Fig. 14). A higher dry density correlates to a smaller pore volume, a greater water holding capacity, a lower dehydration rate and a more gradually sloped drying curve. The effects of the initial water content and dry density are significant in the middle portions of the SWCC, where capillary forces are generally predominant93,94. During the desaturation process, the influences of adsorptive and osmotic forces intensify at high suction ranges and exhibit comparable magnitudes despite variations in their initial water contents93,94. The independent effects of the environmental factors on the drying curves indicate that the micropore region shows an intrinsic property of the material95. Furthermore, the similarities of the drying curves in the high suction range may be related to the mineralogical composition56. The joining of the SWCCs presented in Figs. 12, 14 at high suction levels indicates that the relative insensitivity of the SWCC in the micropore range is independent of the initial conditions.
Drying curves for the samples with different initial dry densities.
Conclusions
In this study, the sensitive dependence of the initial conditions on the PSD and SWCC results were examined, and their relationships were determined in relation to the macroscopic and microscopic behaviors.
Soil samples could be significantly compacted during centrifugation. Thus, when the soil shrinkage for rigid soil was disregarded, the measured SWCC could not be used to reflect the actual retention behavior. The data obtained using centrifugation were in good agreement with the data from filter paper tests for soils prepared at the optimal moisture content within the measured suction range. For the limitation of the centrifuge speed, only suction ranges from 0 to 2000 kPa could be captured. The entire S-shaped soil-water characteristic curve was likely extended if the applied rotation speed was higher.
Pore size distributions of samples prepared at initial water contents of 9.16% and 17.50% exhibited bimodal and multimodal distributions, respectively. Samples compacted at low water contents exhibited double-pore structures with two classes of predominant pores consisting of intra-aggregate and inter-aggregate pores. Thus, the drying process responded to double S-shaped SWCCs. The soil samples subsequently lost water in two clear stages during drying; moreover, the water loss more easily occurred in the first stage because of the presence of many large macropores and inter-aggregate pores. When the soil was compacted at a higher water content, multimodal pore size distributions with low peak values were observed. Thus, a single S-shaped SWCC curve was obtained. Water drained from these soils at a relatively constant rate from a more homogeneous and uniform pore system. At the identical initial water content, the SWCCs of samples with high initial dry densities were higher than those of samples with low initial dry densities. The inter-aggregate pores were significantly influenced as the density increased. However, small pores were not influenced by changes in the density. Thus, the drying curves at suction levels greater than 10 MPa converged.
The distribution of the pore structure systems can be used as input data for the constitutive models and conservation equations that are based on the double structure concept of soils. The SWCC from this study can be used to numerically model the water movement in the unsaturated soil, and the soil-water storage, field capacity and soil aggregate stability in agricultural engineering can be estimated. Moreover, in geotechnical engineering, SWCC is also widely used to evaluate and predict the failure of foundations and slopes during rainfall.
Data availability
Te datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.
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Te authors would like to sincerely thank the editors and reviewers of this paper, who provided useful comments that improved the manuscript substantially.
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This research was financially supported by the National Natural Science Foundation of China (Grant No. 42201011, 41877225, 42230712) and the Young Talent Fund of Association for Science and Technology in Shanxi (Grant No. CLGC20225).
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Funding acquisition, Lincui Li and Xi-an Li; Methodology, Cheng Li and Yonghong Li; Data collection, Lincui Li; Project administration, Xi-An Li; Writing-Original draft, Lincui Li; Writing-Review and editing, Yong Li, Yiping He and Chaowei Yao; Sampling and experimentation, Lincui Li and Wang Li.
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Li, L., Li, XA., Li, Y. et al. Assessing the relationships among the initial conditions, PSD and SWCC of compacted soil. Sci Rep 15, 10327 (2025). https://doi.org/10.1038/s41598-025-94325-2
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DOI: https://doi.org/10.1038/s41598-025-94325-2
