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# Impact of initial water content on aggregate stability: a perspective based on soil internal forces

Yushan Zeng, Bin Wang, Ruifeng Yue, Fenli Zheng, Wangming Gu, Wengang

Wang, Frédéric Darboux

► To cite this version:

Yushan Zeng, Bin Wang, Ruifeng Yue, Fenli Zheng, Wangming Gu, et al. Impact of initial water content on aggregate stability: a perspective based on soil internal forces. Geoderma, 2025, 464, pp.117640. 10.1016/j.geoderma.2025.117640. hal-05397385

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# Impact of initial water content on aggregate stability: a perspective based on soil internal forces

Yushan Zeng<sup>a, ●</sup>, Bin Wang<sup>a,b,∗</sup>, Ruifeng Yue<sup>c</sup>, Fenli Zheng<sup>d</sup>, Wangming Gu<sup>a</sup>, Wengang Wang<sup>a</sup>, Frédéric Darboux<sup>e,●</sup>

## ARTICLE INFO

Handling editor: xxx

Keywords:

Soil water content

Aggregate stability

Water film

Soil internal forces

## ABSTRACT

The soil aggregate stability is closely linked soil moisture through its regulation of soil internal forces, such as the van der Waals attractive force, electrostatic repulsion, and surface hydration repulsion. However, the mechanism driving the stability at different initial water content remains unclear. This study conceptualizes a critical water content (CWC) threshold for the transition between stability enhancement and reduction, analyzing this phenomenon from the perspective of soil internal forces. Four initial water contents (ranging from 0.033 to 0.434 $g·g^{-1}$) were used to assess the effect of soil water content on soil internal force. The results reveal the presence of CWC in soil aggregate stability, which was more pronounced in the Yoder and the fast wetting treatment (Le Bissonnais method). Under Yoder's method, the mean weight diameter (MWD) first increased from 1.38 to 1.71 mm as the water content rose from 0.033 to 0.225 $g·g^{-1}$, and then decreased to 1.32 mm ($p < 0.05$). At the same time, the thickening of the water film from 1.1 to 2.8 nm caused the net soil internal force ($P_{net}$) to shift from repulsive (<1.15 nm) to attractive, reaching a peak of 13.9 atm before declining to zero. When water content exceeded 0.225 $g·g^{-1}$, $P_{net}$ showed a decreasing trend in attraction, indicating a reduction in aggregate cohesion and stability under high moisture content. Pearson correlation analysis revealed a highly significant correlation between soil internal forces ($P_{net}$) and aggregate stability (MWD) ($p < 0.01$). These findings suggest that initial soil water content influences aggregate stability by modulating soil internal forces, which partially explains the CWC phenomenon.

## 1. Introduction

Soil aggregate stability is essential for maintaining soil structure and function. More stable aggregates contribute to improved resistance to soil erosion (Amézketa, 1999; Hu et al., 2018; Ma et al., 2022). Several factors influence aggregate stability, including internal factors such as electrolyte composition (e.g., cation type, pH), clay minerals, and organic matter content, as well as external factors such as water content and temperature, which vary on short temporal scales, and biological activity, which acts over longer timescales (Amézketa, 1999; Bardelli et al., 2022). Among these, soil water exhibits considerable variability, influenced by factors such as soil type, topography, agricultural

management, and weather conditions (Wu et al., 2025). Soil moisture directly affects the processes of aggregation and disaggregation (Le Bissonnais and Singer, 1992; Le Bissonnais et al., 1995; Martinez-Mena et al., 2002; Pieri et al., 2009; Vermang et al., 2009; Wuddivira et al., 2009; Saedi et al., 2016; Fu et al., 2017). Therefore, soil water content is a critical factor in studying soil aggregate stability. While numerous studies have focused on the effects of dry-wet cycles, wetting rate, and other factors on aggregate stability, the mechanisms behind the impact of moisture variability on aggregate stability remain insufficiently understood.

The relationship between soil water content and aggregate stability is moisture-dependent rather than uniformly positive. Numerous studies have reported that, under relatively dry conditions, a moderate increase

<footnote><sup>a</sup> School of Soil and Water Conservation, Beijing Forestry University, Beijing 100083, China</footnote>

<footnote><sup>b</sup> Key Laboratory of Soil and Water Conservation, National Forestry and Grassland Administration, Beijing 100083, China</footnote>

<footnote><sup>c</sup> College of Science, Beijing Forestry University, Beijing 100083, China</footnote>

<footnote><sup>d</sup> State Key Laboratory of Soil and Water Conservation and Desertification Control, College of Soil and Water Conservation Science and Engineering, Northwest A&F University, Yangling, Shaanxi 712100, China</footnote>

<footnote><sup>e</sup> Univ. Grenoble Alpes, CNRS, INRAE, IRD, Grenoble INP, IGE, 38000 Grenoble, France</footnote>

<footnote>* Corresponding author at: School of Soil and Water Conservation, Beijing Forestry University, Beijing 100083, China.
E-mail addresses: wangbin1836@bjfu.edu.cn (B. Wang), flzh@ms.iswc.ac.cn (F. Zheng), Frederic.Darboux@inrae.fr (F. Darboux).</footnote>
Abbreviations

<table><tr><td>CWC</td><td>Critical water content</td></tr><tr><td>PL</td><td>Plastic limit</td></tr><tr><td>EDLs</td><td>Electrical double layers</td></tr><tr><td>P<sub>h</sub></td><td>Hydration repulsion</td></tr><tr><td>P<sub>e</sub></td><td>Electrostatic repulsion</td></tr><tr><td>P<sub>vdw</sub></td><td>Van der Waals forces</td></tr><tr><td>P<sub>net</sub></td><td>Soil internal force/Net force</td></tr><tr><td>AD</td><td>Air-dried water content</td></tr><tr><td>0.7FC</td><td>70 % of field capacity</td></tr><tr><td>FC</td><td>Field Capacity</td></tr><tr><td>SC</td><td>Saturated Water Content</td></tr><tr><td>SOM</td><td>Soil organic matter</td></tr><tr><td>SSA</td><td>Specific Surface Area</td></tr><tr><td>FW</td><td>Fast wetting</td></tr><tr><td>SW</td><td>Slow wetting</td></tr><tr><td>MWD</td><td>Mean weight diameter</td></tr><tr><td>VG</td><td>Van Genuchten model</td></tr><tr><td>DLVO theory</td><td>Derjaguin-Landau-Verwey-Overbeek theory</td></tr></table>

in moisture can reduce slaking susceptibility and improve soil aggregate coherence (Truman & Bradford, 1990; Shainberg et al., 1996; Nachtergaele & Poesen, 2002; Defersha et al., 2011; Wang et al. 2023). In contrast, under wetter conditions, excessive water can intensify disruptive processes such as slaking and differential swelling, resulting in reduced aggregate stability (Luk & Hamilton, 1986; Coote et al., 1988; Darvishan et al., 2015). Non-monotonic relationships have also been reported, where aggregate stability increases with rising moisture content up to a certain point and then decreases at higher moisture levels (Grissinger, 1966; Blake & Gilman, 1970; Ma et al., 2014; Larionov et al., 2014). This threshold, referred to as the Critical Water Content (CWC), marks the turning point at which the correlation between moisture content and aggregate stability shifts from positive to negative. This non-monotonic relationship is likely influenced by factors such as wetting rate and initial water content. Moragoda et al. (2022) suggest that the differences in study conclusions may come from varying initial moisture content. For example, Vermang et al. (2009) observed increase aggregate stability with moisture levels of 0.04, 0.12, and 0.19 $g·g^{-1}$ in Loess. However, for the same soil, Li et al. (2024) found that aggregate stability increased and then decreased with moisture levels of air-dry, 0.05, 0.10, 0.15, and 0.20 $g·g^{-1}$. Previous studies have reported similar patterns, with aggregate stability generally increasing under drier conditions and declining as soils become wetter. Despite differences in soil types and experimental methods, the CWC phenomenon emerges consistently (Grissinger, 1966; Larionov et al., 2014; Ma et al., 2014; Gong et al., 2015; Zhu et al., 2019; Liu et al., 2021; Li et al., 2024; Zhang et al., 2024). This consistency suggests the presence of a common underlying mechanism, while also underscoring the need for further verification under contrasting tillage systems and soil management conditions.

CWC is often referred to as the optimal moisture content in previous studies (Moragoda et al., 2022). Watts et al. (1996) noted that the optimal moisture content for thixotropic hardening is around the plastic limit (PL). Many studies agree that the moisture content maximizing the soil erosion resistance corresponds to CWC (Blake & Gilman, 1970; Emerson, 1985; Kay & Dexter, 1990; Shainberg et al., 1996; Amézketa, 1999). However, the mechanisms behind CWC are still unclear. Some researchers have suggested that moisture increases aggregate stability by reducing slaking, owing to the reduction of the compression of trapped air (Poesen et al., 1999; Vermang et al., 2009). Others have pointed to the reduction of differential swelling (Moragoda et al., 2022). But these explanations do not fully explain why aggregate stability

decreases at higher moisture levels.

Several studies have explained the CWC phenomenon from the perspective of shear strength by examining how water content affects cohesion and internal friction (Grissinger 1966; Larionov et al. 2014). For example, Wang et al. (2019a) observed that both cohesion and friction angle first increased and then decreased with rising moisture, mirroring the CWC pattern. The reduction of aggregate stability at high moisture can be attributed to the decline in shear strength: when water content exceeds the plastic limit, clay particles disperse (Arnold & Allen, 1999), reducing interparticle cohesion and making aggregates more susceptible to breakdown (Kay & Dexter, 1990; Amézketa, 1999; Holz et al., 2015). This weakening is microscopically governed by changes in cohesion and the internal friction, which themselves are influenced by hydration effects (Reichert & Norton, 1994), cohesive bonding (Watts et al., 1996) and interparticle force (Grissinger, 1966; Shainberg et al., 1996; Larionov et al., 2014; Moragoda et al., 2022). Thus, while shear strength provides an important macroscopic indicator, it does not fully capture the underlying internal force dynamics that regulate aggregate stability.

Previous studies have emphasized the importance of physicochemical dispersion during the wetting process of soil aggregates, suggesting that changes in cohesion rather than shear strength offer a more convincing explanation for the CWC phenomenon (Li et al., 2024). During wetting, shifts in colloidal-scale attractive and repulsive forces promote particle separation and enhance dispersion (Le Bissonnais, 1996). Soil moisture also influences indirect processes during wetting: pre-wetting reduces trapped air and thereby weakens slaking forces, while partial clay swelling lowers differential stresses. These mechanisms operate independently from physicochemical dispersion. Because dispersion is difficult to measure directly, soil internal forces provide a useful proxy for assessing the balance between attraction and repulsion that governs particle cohesion and separation. In this study, we adopt soil internal forces as an explanatory framework to bridge colloidal-scale processes with the CWC phenomenon, consistent with recent evidence (Zhang et al. 2024). But there is limited theoretical support for the relationship between CWC and soil internal forces (Larionov et al., 2014).

The Derjaguin-Landau-Verwey-Overbeek (DLVO) theory provides the foundational framework for understanding how colloidal-scale interactions govern aggregate stability. Clay minerals, as their high surface charge promotes the formation of an extensive electrical double layers (EDLs), which makes them the primary media through which soil internal forces are expressed (Pashley, 1981; Hernández, 2023). This colloidal perspective explains how variations in water content regulate the balance between attractive (van der Waals) and repulsive (electrostatic or hydration) forces, thereby determining soil aggregate stability (Li et al., 2013; Leng 2012). Recent studies have advanced the calculation of soil internal forces (Hou et al., 2009; Hu et al., 2015, 2018; Li et al., 2009), examining the impact of electrostatic repulsion, van der Waals forces, and hydration repulsion on aggregate stability. These studies found that soil internal forces have significant impacts on aggregate stability (Hu et al., 2015; Liu et al., 2021; Ma et al., 2022; Ali et al., 2023). Soil internal forces provide a microscopic perspective for interpreting the CWC phenomenon. Variations in initial water content (e.g., air-dried versus pre-wetted conditions) alter physicochemical dispersion by modifying soil internal forces, thereby influencing aggregate stability. This emerging understanding lays a theoretical foundation for explaining soil aggregate stability and invites further investigation into the following questions: (1) How does soil water content regulate soil internal forces? and (2) What is the relationship between soil internal forces and aggregate stability?

Previous research suggests that soil internal forces vary with particle distance, typically calculated within the 0–5 nm range. Many studies focus on specific distance points (e.g., 1.5 nm, 1.6 nm, and 2 nm) to compare different soils (Hu et al., 2018; Liu et al., 2021; Ma et al., 2022; Ali et al., 2023). However, this approach often neglects the physical
context of these force variations, potentially limiting the reliability of comparisons. Soil internal forces are influenced by the EDL environment. In soil systems, water film thickness is commonly used as a practical and moisture-responsive approximation of the effective operating distance of the EDL (Tokunaga, 2011; Leão & Tuller, 2014), providing a physically meaningful basis for evaluating how moisture alters interparticle attractions and repulsions. Research has shown that water film thickness increases exponentially with soil water content (Dolinar & Škrabl, 2012; Dolinar & Macuh, 2016). A thicker water film corresponds to a greater distance for soil internal forces, thereby weakening particle interactions (Liu et al., 2020).

Among soil internal forces, hydration repulsion ($P_h$) and electrostatic repulsion ($P_e$) contribute to aggregate disintegration, while van der Waals forces ($P_{vdw}$) promote aggregation. $P_{vdw}$ depends on soil properties, such as organic matter content, while $P_h$ is independent of electrolyte type and concentration (Israelachvili, 1978). $P_e$ influenced by the electric field of the solution, is highly variable (Liu et al., 2020; Ali et al., 2023). Many studies calculate $P_e$ within the electrolyte range of $10^{-4}$ to 1.00 mol/L (Liu et al., 2021; Ma et al., 2022), often neglecting the fact that ionic concentration in the EDL differs significantly from that in the bulk solution. Soil particle surfaces carry substantial charge, creating a strong electric field (Wang et al., 2019b; Zhang and Pei, 2021), which can cause the ionic concentration at the particle surface to differ by thousands of times from that in the bulk solution (Peng et al., 2022). Li et al. (2011) showed that even when the bulk solution is diluted from $10^{-1}$ mol/L to $10^{-4}$ mol/L, the $Na^+$ concentration at the particle surface remains at 8.1 mol/L. Thus, to address the question (2), it is essential to optimize the calculation of $P_e$ in high-ion-concentration environments and analyze its relationship with aggregate stability.

In conclusion, while the CWC phenomenon is closely related to soil internal forces, existing theories are insufficient. This study investigates aggregate stability by examining the coupling effects of soil internal forces and initial water content, using black soil from Northeast China. As a typical agricultural soil with significant variability in water content, making it an ideal subject for our experimental investigation. Four different water content treatments ($0.033$ to $0.225 \text{ g} \cdot \text{g}^{-1}$) were designed to explore the CWC phenomenon across various aggregate breakdown mechanisms. The corresponding water film thickness was calculated to study soil internal force variations under different ion concentration environments ($10^{-3}$ to 8 mol/L) and their relationships with aggregate stability. The objectives of this study are: (i) to elucidate the mechanism of initial soil water content on soil internal forces, and (ii) to quantitatively characterize the relationship between mesoscale (1 nm – 1 µm) soil internal forces and macroscale (>1µm) aggregate stability. This research aims to provide new insights and methods for the understanding soil aggregate stability mechanism and contribute to advancing related theories.

## 2. Materials and methods

### 2.1. Soil sampling

Soil samples were collected from Keshan County (125°08′ — 125°37′E, 48°12′ — 48°23′N), Heilongjiang Province, China. It is

classified as Mollisols (USDA classification) or Chernozems (FAO classification), and has a clay loam texture. Keshan farm located in a region characterized by gentle, undulating terrain, with slope concentrated in 3° to 5° and an elevation between 240 and 340 m. The region primarily cultivates soybeans and corn. The soil erosion rate was $2,122 \text{ t} \cdot \text{km}^{-2} \cdot \text{a}^{-1}$, and deposition rate was $-1,185 \text{ t} \cdot \text{km}^{-2} \cdot \text{a}^{-1}$ (Zhou et al., 2025). The climate is temperate monsoon, with an average annual temperature of 1.1 °C and annual precipitation of approximately 500 mm (Chen et al., 2021). The frost-free period lasts for 122 days. Soil samples were taken from the top 0–20 cm layer. The basic physical and chemical properties of the soil are listed in Table 1.

### 2.2. Sample preparation

Soil samples were collected from the typical tillage layer of the study area, soil crumbs samples were collected in plastic boxes. Bulk density, saturated water content, and field capacity were measured using the cylindrical core method. Plant roots and other impurities were removed from the soil samples prior to aggregates stability analysis. The soil samples were first air-dried at room temperature, then separated into different aggregate sizes (<0.25 mm, 0.25–0.5 mm, 0.5–1 mm, 1–2 mm, 2–3 mm, 3–5 mm, and > 5 mm) by dry sieving. All aggregates were placed in an oven at 40 °C for 24 h to ensure the same samples’ moisture content. To investigate the effect of moisture content, initial soil moisture were set at four different levels: saturated condition (SC: 0.434 g·g⁻¹), field capacity (FC: 0.322 g·g⁻¹), 70 % of field capacity (0.7FC: 0.225 g·g⁻¹), and air-dried soil (AD: 0.033 g·g⁻¹). The PL is between FC and 0.7FC, enabling soil moisture gradient to capture the transitions in water film development and making the CWC behavior of aggregate stability more evident. The initial moisture content was controlled by adjusting the matric potential to −0.3 kPa to prevent slaking during the wetting process (Wang et al., 2012; Wang et al., 2014; Gu et al., 2020). After dry-sieving, aggregates of each size class were collected separately. For wet-sieving, a 5-g subsample was taken directly from the specific size fraction, while a 50-g mixed sample (<5 mm) was used for moisture conditioning. The samples were placed on saturated filter paper supported by a water-saturated sponge to ensure a controlled wetting rate. An iterative weighing-wetting-weighing procedure was employed to gradually adjust the samples to the target initial water content.

### 2.3. Determination of aggregate stability

Moisture-conditioned aggregates (1–2 mm, 2–3 mm, and 3–5 mm, <5 mm) obtained by dry-sieving were used as the initial material for the Yoder method and the fast wetting (FW) and slow wetting (SW) treatments based on the Le Bissonnais (LB) frameworks. Each size class (<0.25 mm, 0.25–0.5 mm, 0.5–1 mm, 1–2 mm, 2–5 mm, and > 5 mm) was analyzed in triplicate.

#### 2.3.1. Yoder wet-sieving method

The Yoder (1936) wet-sieving procedure was applied to <5-mm aggregates to evaluate aggregate stability under the combined action of all breakdown mechanisms. This method reflects field-relevant wetting conditions and enables the identification of CWC thresholds by

<table><caption>**Table 1**

Physical and chemical properties of the test soil.</caption><thead><tr><th>Clay (%)</th><th>Silt (%)</th><th>Sand (%)</th><th>Soil bulk density (g·cm<sup>-3</sup>)</th><th>SSA (g·m<sup>-2</sup>)</th><th>PL (g·g<sup>-1</sup>)</th><th>FC (g·g<sup>-1</sup>)</th><th>SC (g·g<sup>-1</sup>)</th></tr></thead><tbody><tr><td>33.6</td><td>39.1</td><td>27.3</td><td>1.28</td><td>66.5</td><td>0.257</td><td>0.322</td><td>0.434</td></tr><tr><td>SOM (%)</td><td>pH</td><td>&lt;0.25 mm</td><td>0.5–0.25 mm</td><td>Air-dried aggregate composition (%)</td><td>1–0.5 mm</td><td>2–1 mm</td><td>&gt;5 mm</td></tr><tr><td>6.21</td><td>6.36</td><td>6.0</td><td>7.7</td><td>11.1</td><td>17.4</td><td>43.5</td><td>14.3</td></tr></tbody></table>

SOM: Soil Organic Matter; Clay: <0.002 mm, Silt: 0.002–0.05 mm, Sand: 0.05–2 mm; SSA: Specific Surface Area; PL: Plastic Limit; FC: Field Capacity; SC: Saturated Water Content.
capturing the integrated response of aggregates to moisture variation.

### 2.3.2. LB wetting treatments

The LB method (Le Bissonnais, 1996) modifies only the initial matric potential by adjusting the moisture content, while all experimental steps remain unchanged. Aggregate stability was assessed using the Yoder-type apparatus with controlled immersion. Under FW treatment, ag-

(NaCl). However, the ion concentration in the EDL is significantly higher than that in the bulk solution (Li et al., 2011). Therefore, in this study, we set the $c_0$ in the range of $10^{-3}$ to 8 mol/L. Z is the cation valance; $\varphi(d/2)$ is the potential at the overlapping position of two EDLs for the adjacent particles, V, which is always negative, and can be calculated by the following equation (Li et al., 2013):

$$ \frac{\pi}{2} \left[ 1 + (1/2)^2 \exp\left(2ZF\varphi\left(\frac{d}{2}\right)/RT\right) + (3/8)^2 \exp\left(4ZF\varphi\left(\frac{d}{2}\right)/RT\right) \right] - \arcsin\exp(ZF\varphi_0 - ZF\varphi\left(\frac{d}{2}\right)/2RT) = (1/4)dk\exp\left(-ZF\varphi\left(\frac{d}{2}\right)/2RT\right) \quad (7) $$

gregates were immersed rapidly in water for 10 min. The resulting breakdown reflected the combined effects of physicochemical dispersion during initial wetting and the strong compressive forces generated by entrapped air during rapid hydration. Under SW treatment, aggregates were wetted gradually by capillary rise for 30 min, where breakdown was induced by physicochemical dispersion together with differential swelling of clay minerals under slow wetting conditions. Following wetting, remaining aggregates were sieved in ethanol to prevent additional breakdown, as its low surface tension minimizes slaking and dispersion (Le Bissonnais, 1996).

### 2.3.3. Calculation of stability indices

$$ R_{>1.0mm} = \sum w_{i>1mm} \quad (1) $$

$$ MWD = \sum w_i x_i \quad (2) $$

where: $w_i$ refers to the mass percentage of aggregate in each particle size, %; $w_{i>1mm}$ refers to the mass percentage of aggregates with particle sizes greater than or equal to 1.0 mm, %; and $x_i$ represents the average particle size for each adjacent particle size level, mm.

## 2.4. Determination of soil internal forces for different water contents

### 2.4.1. Calculation of soil internal forces

From the perspective of soil internal forces, it is proposed an approach to estimate the inter-particle forces under different moisture conditions. This estimation may serve as an indirect indicator of the intensity of physicochemical dispersion within aggregates across varying water contents.

Soil internal forces include the van der Waals attractive force ($P_{vdw}$), electrostatic repulsion ($P_e$), and surface hydration repulsion ($P_h$). The net force ($P_{net}$) for different water contents was calculated according to previous studies (Hou et al., 2009; Hu et al., 2018; Li et al., 2013):

$$ P_{net} = P_{vdw} + P_e + P_h \quad (3) $$

$$ P_h = 3.3 \times 10^4 e^{-5.76d} \quad (4) $$

$$ P_{vdw} = -A_{eff}/6\pi d^3 \times 10^{22} \quad (5) $$

$$ P_e = \frac{2}{101} RTc_0 \{\cosh[ZF\varphi(d/2)/RT] - 1\} \quad (6) $$

where: $P_{net}$ is the net force, atm; $P_h$ is the hydration repulsion, atm; $P_{vdw}$ is the van der Waals attractive force, atm; $P_e$ is the electrostatic repulsion, atm; $d$ is the water film thickness, nm (the calculation method is described in detail in Section 2.4.2); $A_{eff}(J)$ is the effective Hamaker constant in aqueous solution conditions ($1.25 \times 10^{-19}$ J) (Ma et al., 2022); $R = 8.314$ J mol$^{-1}$ K$^{-1}$; $T = 298$ K; $F = 96485.338$ C·mol$^{-1}$; $c_0$ is the electrolyte concentration of the solution, mol·L$^{-1}$. Previous studies (Liu et al., 2021; Ma et al., 2022) set $c_0$ in the range of $10^{-5}$ to 1.0 mol/L

where: $\varphi_0$ is the particle surface potential, V; $\kappa = \sqrt{8\pi F^2 Z^2 c_0 / \varepsilon RT}$, $\varepsilon=8.9 \times 10^{-10}$; $\varphi_0$ corresponds to each electrolyte concentration and is shown in Supplementary Table 1(Table S1). Previous studies (Liu et al., 2021; Ma et al., 2022) mainly focused on calculating $P_e$ under low-concentration conditions. However, formula (7) fails to describe $\varphi(d/2)$ accurately at high concentrations, hence being able to calculate $P_e$ in high-concentration environments is critical. As $d$ increases, $\varphi(d/2)>0$ occurs (Table S2), which is inconsistent with the assumption that $\varphi(d/2)$ is always less than 0. Consequently, $P_e(d)$ is not a monotonically decreasing function as stated by equation (6) (Fig. S1). In particular, the larger the concentration, the smaller $d$ at which $\varphi(d/2) > 0$ appears (Table S3). At a concentration of 1 mol/L, $\varphi(d/2) > 0$ appears at 2.5 nm, whereas at concentrations of $10^{-2}$ to $10^{-4}$ mol/L, $d$ increases to 26–270 nm. To be able to estimate $P_e$ for relevant conditions, this study uses an optimization algorithm to address the applicability issues of existing formulas in high-concentration environments (described in Section 3.2.1).

### 2.4.2. Determination of the distance d between soil particles

To investigate how water content regulates soil internal forces, this study quantitatively analyzes changes in soil internal forces by calculating water film thickness and matric suction at different moisture levels. Water film thickness is defined as the distance between particles, linking water content and soil internal forces. This approach allows for the determination of soil internal force environment at varying water contents.

The Van Genuchten (VG) model:

$$ \theta = \theta_r + (\theta_s - \theta_r) / [1 + (\alpha \cdot H)^N]^m \quad (8) $$

where: $\theta$ is the volumetric water content, cm·cm$^{-1}$; $\theta_r$ is the residual water content, cm·cm$^{-1}$; $\theta_s$ is the saturated water content, cm·cm$^{-1}$; $H$ is the matrix suction, cm; $\alpha$ inversely related to air entry value, cm$^{-1}$; $N$ reflects pore size heterogeneity; $m=1-1/n$ (where $n > 1$). The VG model was used to estimate matric suction based on soil moisture content. This attractive force explains why increased water content results in thicker water films: before saturation occurs, the matrix suction remains negative, continuously drawing in water and promoting film thickening, thereby providing a theoretical foundation for determining water film thickness.

To calculate the water film thickness, Dolinar & Macuh (2016) provided the formula:

$$ d = a \cdot \exp(b \cdot w) \quad (9) $$

where: $d$ is the water film thickness, m; $w$ is the mass water content, $g \cdot g^{-1}$; $a = 1.32 \cdot 10^{-10} \cdot A^{0.488}$ and $b = 36.42 \cdot A^{-0.655}$. with A the specific surface area of soil particles, $m^2 \cdot g^{-1}$. For conversion between mass water content and volumetric water content $= w \cdot \rho$, $\rho$ is the soil bulk density, $g \cdot cm^{-3}$, measured as $1.28 \cdot g \cdot cm^{-3}$ in this study using the standard core method.
## 2.5. Statistical analysis

Soil aggregate stability indices and water film thickness were calculated using EXCEL 2019, while the computation of soil internal forces was performed with Mathematica 14.0 and EXCEL 2019. All statistical analyses were carried out using SPSS 25. The aggregate stability indices were analyzed using One-way ANOVA with post-hoc Turkey tests (p < 0.05). The relationship between soil internal forces and aggregate stability was assessed using Pearson correlation (p < 0.05). The correction results for the P<sub>e</sub> calculation were evaluated using a non-parametric Mann-Whitney U Test (p < 0.05). Data from previous studies were extracted from published figures using the Get Data software, and compiled using Excel 2019. All figures were generated using Origin 2021.

# 3. Results

## 3.1. Effects of initial water content on aggregate stability under different breakdown mechanisms

### 3.1.1. Aggregate stability response to combined breakdown mechanisms

The size distribution of water-stable aggregates, as determined by the Yoder method, varied significantly between different initial soil water contents (Fig.S2). As the water content increases, both the content of aggregates > 1 mm (R<sub>>1mm</sub>) and the mean weight diameter (MWD) exhibited the CWC phenomenon (Fig. 1). The aggregate stability ranked as follows: 0.7FC > FC > AD > SC. R<sub>>1mm</sub> reached its maximum value of 51 % at 0.7FC, then decreased to 34 %. Meanwhile, MWD increased from 1.38 to 1.71 mm. Once water content exceeds 0.7FC, aggregate stability showed a negative correlation with moisture content (p < 0.01), decreasing to 1.32 mm and 34 %.

### 3.1.2. Aggregate stability response to individual breakdown mechanisms

We further analyze the impact of different breakdown mechanisms on the CWC phenomenon (Fig. 2). Statistical analysis revealed significant effects of breakdown mechanisms, aggregate size, and water content (p < 0.05), as well as significant two-way interactions among these factors (Table S4). The CWC phenomenon was evident in different initial size aggregates under the FW treatment, both for the R<sub>>1mm</sub> and the MWD indicators. The R<sub>>1mm</sub> was always maximum for the FC treatment, indicating a higher aggregate stability than at both lower (AD and 0.7FC) and higher (SC) water contents (Fig. 2a). For the MWD (Fig. 2b), as water content increased, the MWD of 1–2 mm aggregates (initial) increased from 0.55 (at AD) to 1.00 mm (at FC), then decreased to 0.53 mm (at SC); 2–3 mm aggregates (initial) increased from 0.56 (at AD) to 1.00 mm (at FC), then decreased to 0.53 mm (at SC); and 3–5 mm

aggregates (initial) increased from 0.81 (at AD) to 1.06 mm (at FC), then decreased to 0.66 mm (at SC). Under the SW treatment, the CWC phenomenon occurred only for 1–3 mm aggregates. The maximum stability occurred under the 0.7FC treatment according to both the R<sub>>1mm</sub> and MWD indicators.

## 3.2. Understanding the CWC phenomenon through soil internal forces

### 3.2.1. Refining the calculation framework for soil internal forces

To explain the CWC phenomenon from the perspective of soil internal forces, the calculation formula (6) for P<sub>e</sub> was optimized to better suit high-concentration environments, then calculate the distance d between particles (water film thickness). It is essential to verify whether soil water content can regulate these forces, and the relationship between the two. To further investigate the relationship between soil internal force and aggregate stability, it was established that φ(d/2) < 0, and that φ(d/2) is a monotonically increasing function of d. In equation (7), even if φ(d/2) > 0 occurs, d continues to increase, indicating continued water film thickening.

The cause of φ(d/2) > 0 arose from oversimplified truncation in the original formulation. Building on the work of Hou et al. (2009), we derived the relationship between φ(d/2) and d from the equation:

$$ \int_{0}^{\frac{\pi}{2}} \frac{d\beta}{\sqrt{1 - k^2 \sin^2 \beta}} - \int_{0}^{\frac{\arcsin\left(\frac{y_0 - y}{2}\right)}{2}} \frac{d\beta}{\sqrt{1 - k^2 \sin^2 \beta}} = \frac{1}{4} d\kappa e^{-\frac{y_0 - y}{2}} \quad (10) $$

where: y(d/2) = ZFφ(d/2)/RT, k = e<sup>y(d/2)</sup> = e<sup>ZFφ(d/2)/RT</sup>. We then performed a series expansion of both the complete and incomplete elliptic integrals:

Subtrahend:

$$ \int_{0}^{\frac{\pi}{2}} \frac{d\beta}{\sqrt{1 - k^2 \sin^2 \beta}} = \frac{\pi}{2} \left[ 1 + \left(\frac{1}{2}\right)^2 k^2 + \left(\frac{1 \cdot 3}{2 \cdot 4}\right)^2 k^4 + \dots + \frac{(2n - 1)!!}{(2n)!!} k^{2n} \right] \quad (11) $$

Minuend:

$$ \int_{0}^{\theta} \frac{d\beta}{\sqrt{1 - k^2 \sin^2 \beta}} = \theta + \left(\frac{1}{2}\right)^2 k^2 (\theta - \sin\theta\cos\theta) + \left(\frac{1 \cdot 3}{2 \cdot 4}\right)^2 k^4 (\theta - \sin\theta\cos\theta - \frac{2}{3}\sin^3\theta\cos\theta) + \dots \quad (12) $$

<figure><img src="image_3.png" /><figcaption>Fig. 1. Aggregate stability indicators for the Yoder (1936) method. (a) Content of water-stable aggregates > 1 mm (R<sub>>1mm</sub>) and (b) mean weight diameter (MWD) of aggregates under different water content.</figcaption></figure>
<figure><img src="image_4.png" /><figcaption>Fig. 2. Aggregate stability of the FW & SW treatments, for aggregates of 1–2 mm, 2–3 mm, and 3–5 mm size ranges at different water contents.</figcaption></figure>

In these equations, $\theta = \arcsin\left(\frac{y_0-y(d/2)}{2}\right)$, $n = 0, 1, \dots, $, Hou et al. (2009) provided the basis for selecting the remainder terms of the subtrahend (12) in the derivation, but did not verify whether retain only the first three terms of the minuend (11) was reasonable. The occurrence of $\varphi(d/2) > 0$ is most likely due to the conditions required for retaining just the first three terms of the minuend.

Precise calculation is carried out by adding remainder items. We analyzed data at 3.2 nm at 1 mol/L concentration, comparing the first 11 terms ($n = 0, 1, \dots, 10$) of the minuend with the first 3 terms ($t = 1, 2, 3$) of the subtrahend (Table 2). The rate of decrease for the remainder of the subtrahend is rapid: the first term (0.15) is 272 times larger than the second term and 27,540 times larger than the third term. Thus, retaining only the first term has a negligible effect on the result, consistent with Hou's judgment. In contrast, the remainder of the minuend decreases more gradually in the first few terms, with the difference becoming smaller in subsequent terms. From the first term (1.57) to the tenth term (0.048), the value only decreases by 31 times, while the reduction factor reaches 3,641 at the eleventh term. These findings indicate that retaining more terms of the minuend increases the distance $d$ of $\varphi(d/2) > 0$. At 1 mol/L condition, when the number of retained terms increases from three ($n = 2$) to eleven ($n = 10$), $d$ increases from 2.4 nm to 3.3 nm (Table S5).

This approach evaluates the relative contributions of $P_{vdw}$, $P_e$, and $P_h$ across different $d$ and remainder terms of the minuend ($n$) to determine the optimal truncation of the expansion remainder terms. From Table 3, the calculation results of the original formula ($n = 2$) show that at 1.1 nm, the ratio of $P_{vdw}/P_e$ ($n = 2$) is 2.34, and this ratio increases to 240 at 2.4 nm. The issue of $\varphi(d/2) > 0$ still persists up to $n = 5$ (Table S5), the vast difference still existed between $P_{vdw}$ and $P_e$, $P_{vdw}$ is 24 to 4063 times larger than $P_e$ ($n = 5$), and its contribution to $P_{net}$ is negligible. Therefore, adding $n$ to achieve a more precise calculation of $P_e$ is not a practical strategy, as its effect on the resulting net force is negligible, compared to the dominant forces.

A more effective approach for selecting the remainder terms. It is recommended optimizing the calculation of formula (7) for high-concentration environment. When the absolute value of a force at a

given $d$ is less than 1 % of $P_{net}$, it can be disregarded (set to 0). Using 1 mol/L data as an example (Table 3), the results of ignoring terms based on the original formula ($n = 2$) and the extended treatment ($n = 5$) are labeled as $P_{net1}$ and $P_{net2}$. The non-parametric Mann-Whitney U test indicates no significant difference between the two ($p > 0.05$), and neither differs significantly from $P_{net0}$ (origin) ($p > 0.05$). These results demonstrate that optimizing the original formula ($n = 2$) is the most convenient and effective approach. It efficiently handles cases where $\varphi(d/2) > 0$ as $d$ increases, while maintaining accuracy in the analysis. This confirms the method's feasibility and effectiveness for practical applications.

### 3.2.2. Response of water film thickness to moisture changes

To explain the CWC phenomenon from the perspective of soil internal forces, it is essential to verify whether soil water content can regulate these forces, with water film thickness being a key determinant in calculating soil internal forces. We calculated the water film thickness at different moisture levels to assess its functional variation (Dolinar & Macuh, 2016; Fig. 3). The van Genuchten (VG) model (SWCC, $\theta$) suggests that soil water potential changes significantly with varying water content, with matric suction being a critical factor influencing water film thickness. As soil moisture content transitions from AD to SC, the matric suction decreases from $10^6-10^7$ kPa to 0.01 kPa. Before SC occurs, the matrix suction remains positive, continuously drawing in water and promoting film thickening. It explains why increased water content results in thicker water films. During this, the water film thickness increases from 1.1 nm to 2.8 nm, with an average increase of 0.04 nm/% in mass water content ($w$, formula 9). In the Stern layer (i.e. below the plastic limit PL), the matric suction curve is steep, indicating a sharp change in water binding. During the transition from AD to 0.7FC, moisture content increases by 6 times, but water film thickness only increases by 0.5 times, yielding a growth rate of 0.03 nm/%. As moisture content increases further, the rate of water film thickening accelerates in the diffuse layer (above the PL), with a growth rate of 0.05 nm/% from 0.7FC to FC. Near saturation (FC – SC), the water film growth rate stabilizes at 0.05 nm/%, consistent with the 0.7FC–FC range.

The thickening of the water film exhibits distinct stages below PL, the

### Table 2

Expanded terms of minuend and subtrahend in the calculation formula for the potential at the middle of the overlap of the electrical double layers of two adjacent soil particles ($\varphi(d/2)$) at 1 mol/L (3.2 nm).

<table><thead><tr><th>d(nm)</th><th>φ(d/2)(mV)</th><th>n = 0</th><th>n = 1</th><th>n = 2</th><th>n = 3</th><th>n = 4</th><th>n = 5</th><th>n = 6</th></tr></thead><tbody><tr><td>3.2</td><td>-0.158</td><td>1.57<br>n = 7<br>6.32 E-2</td><td>3.88 E-1<br>n = 8<br>5.49 E-2</td><td>2.16 E-1<br>n = 9<br>4.84 E-2</td><td>1.48 E-1<br>n = 10<br>4.31 E-4</td><td>1.12 E-1<br>t = 1<br>1.50 E-1</td><td>8.95 E-2<br>t = 2<br>5.49 E-4</td><td>7.43 E-2<br>t = 3<br>5.43 E-6</td></tr></tbody></table>

Note: $n$ represents the factorial of the minuend; $t$ represents the $t$-th term of the subtrahend.
<caption>**Table 3**</caption>

Values of the soil internal force components (van der Waals attractive force $P_{vdw}$, electrostatic repulsion $P_e$, and surface hydration repulsion $P_h$) and the net action force $P_{net}$ at different distances $d$ under 1 mol/L concentration.

<table><thead><tr><th rowspan="2">d(nm)</th><th colspan="2">P<sub>e</sub></th><th rowspan="2">P<sub>vdw</sub></th><th rowspan="2">P<sub>h</sub></th><th rowspan="2">P<sub>net0</sub> (origin)</th><th rowspan="2">P<sub>net1</sub></th><th rowspan="2">P<sub>net2</sub></th></tr><tr><th>n = 2 (origin)</th><th>n = 5</th></tr></thead><tbody><tr><td>1.1(AD)</td><td>21.33</td><td>21.37</td><td>-49.82</td><td>58.99</td><td>30.50</td><td>30.49</td><td>30.53</td></tr><tr><td>1.2</td><td>15.63</td><td>15.70</td><td>-38.38</td><td>33.16</td><td>10.41</td><td>10.41</td><td>10.48</td></tr><tr><td>1.3</td><td>11.41</td><td>11.52</td><td>-30.18</td><td>18.64</td><td>-0.13</td><td>-0.13</td><td>-0.03</td></tr><tr><td>1.4</td><td>8.29</td><td>8.43</td><td>-24.17</td><td>10.48</td><td>-5.40</td><td>-5.40</td><td>-5.26</td></tr><tr><td>1.5</td><td>5.96</td><td>6.16</td><td>-19.65</td><td>5.89</td><td>-7.80</td><td>-7.80</td><td>-7.60</td></tr><tr><td>1.6</td><td>4.24</td><td>4.48</td><td>-16.19</td><td>3.31</td><td>-8.64</td><td>-8.64</td><td>-8.40</td></tr><tr><td>1.7(0.7FC)</td><td>2.96</td><td>3.24</td><td>-13.50</td><td>1.86</td><td>-8.68</td><td>-8.68</td><td>-8.40</td></tr><tr><td>1.8</td><td>2.01</td><td>2.32</td><td>-11.37</td><td>1.05</td><td>-8.31</td><td>-8.31</td><td>-8.00</td></tr><tr><td>1.9</td><td>1.32</td><td>1.65</td><td>-9.67</td><td>0.59</td><td>-7.76</td><td>-7.76</td><td>-7.43</td></tr><tr><td>2.0</td><td>0.83</td><td>1.15</td><td>-8.29</td><td>0.33</td><td>-7.13</td><td>-7.13</td><td>-6.81</td></tr><tr><td>2.1</td><td>0.48</td><td>0.79</td><td>-7.16</td><td>0.19</td><td>-6.49</td><td>-6.49</td><td>-6.19</td></tr><tr><td>2.2</td><td>0.25</td><td>0.52</td><td>-6.23</td><td>0.10</td><td>-5.88</td><td>-5.88</td><td>-5.60</td></tr><tr><td>2.3</td><td>0.10</td><td>0.33</td><td>-5.45</td><td>0.06</td><td>-5.29</td><td>-5.29</td><td>-5.06</td></tr><tr><td>2.4(FC)</td><td>0.02</td><td>0.20</td><td>-4.80</td><td>0.03</td><td>-4.75</td><td>-4.80</td><td>-4.60</td></tr><tr><td>2.5</td><td>-</td><td>0.11</td><td>-4.24</td><td>0.02</td><td>-</td><td>-4.24</td><td>-4.14</td></tr><tr><td>2.6</td><td>-</td><td>0.05</td><td>-3.77</td><td>0.01</td><td>-</td><td>-3.77</td><td>-3.77</td></tr><tr><td>2.7</td><td>-</td><td>0.01</td><td>-3.37</td><td>0.01</td><td>-</td><td>-3.37</td><td>-3.37</td></tr><tr><td>2.8(SC)</td><td>-</td><td>0.00</td><td>-3.02</td><td>0.00</td><td>-</td><td>-3.02</td><td>-3.02</td></tr></tbody></table>

Note: – Indicate that when $\varphi(d/2) > 0$, no calculations are performed; $P_{net0} = P_e$ (n = 2) + $P_{vdw} + P_h$; $P_{net1} = P_e$ (n = 2) + $P_{vdw} + P_h$, for $d > 2.3$ nm, where $P_e$ & $P_h = 0$; $P_{net2} = P_e$ (n = 5) + $P_{vdw} + P_h$, for $d > 2.6$ nm, where $P_e = 0$ and for $d > 2.3$ nm, $P_h = 0$.

<figure><img src="image_5.png" /><figcaption>**Fig. 3.** Dual effects of soil moisture on water film thickness and matric suction. Moisture (%, v/v) as a function of water film thickness (nm) and matric suction (SWCC).</figcaption></figure>

high soil water potential leads to strong binding of water molecules to soil particle, forming a uniform water film at specific moisture levels (Yu et al., 2019), resulting in slower thickening. Conversely, above PL, the water film thickness increases at a faster rate.

### 3.2.3. Response of aggregate stability to soil internal forces

Building on the optimized calculation of soil internal forces, this section investigates the relationship between soil internal forces and aggregate stability. As the water film thickness increases, both $P_h$ and $|P_{vdw}|$ showed a decreasing trend (Fig. 4a). Specifically, $P_h$ reached 0 atm at 1.9 nm, and $|P_{vdw}|$ reached 0 atm after 4 nm (Fig. 4a). Since matric suction reaches zero at SC, no further thickening of water films occurs, and subsequent analysis of soil internal forces is therefore meaningful only under unsaturated conditions. From AD to SC, both $P_h$ and $|P_{vdw}|$ decreased, with the most significant reductions occurring between the AD and 0.7FC, where $|P_{vdw}|$ and $P_h$ decreased sharply at rates of 61 atm/

nm and 53 atm/nm, respectively. The changes in $P_e$ varied with the electrolyte concentration (Fig. 4b). As electrolyte concentration increased, $P_e$ decreased. In high-concentration electrolyte environments (1–8 mol/L), $P_e$ dropped to 0 atm before SC (2.8 nm). While $P_h$ and $P_e$ promote the breakup of aggregates, $|P_{vdw}|$ acted as an attractive force, promoting aggregation. This relationship allows us to deduce the influence of changes in soil internal forces under varying moisture conditions on aggregate stability. As water film thickness increased, all the three forces changed monotonically, while $P_{net}$ exhibited more complex variations with increasing inter-particle distance $d$ (Fig. 4c). In low-concentration environments ($10^{-1}$ to $10^{-3}$ mol/L), $P_{net}$ remained repulsive (i.e. $> 0$). However, in concentrations larger than $10^{-1}$ mol/L, $P_{net}$ transitioned from repulsion (i.e. $> 0$) to attraction (i.e. $< 0$), go through a minimum, and ultimately approached zero.

As shown by Li et al. (2011), when the bulk solution was diluted from 0.1 mol/L to $10^{-4}$ mol/L, the $Na^+$ concentration on the soil particle surface remained around 8.1 mol/L. Therefore, a $Na^+$ concentration of 8 mol/L was used for subsequent analysis. At this concentration, $P_{net}$ exhibited repulsion at short distances, but shifted to attraction after 1.15 nm, reached a maximum attraction of 13.9 atm at 1.45 nm as attraction decayed more slowly than repulsion. For the four moisture levels considered in this study, $P_{net}$ was initially repulsive (7.9 atm) at AD, was attractive (12 atm) at 0.7FC, became less attractive (4.5 atm) at FC, and then 3 atm (attractive) at SC.

These results demonstrated that as soil water content increases, the water film thickens, causing soil internal forces to transition from repulsion to attraction between AD and 0.7 FC. This suggests an increase in aggregation force. Beyond 0.7FC, internal forces showed a decreasing trend in attraction, indicating a reduction in aggregation force. The variation pattern of $P_{net}$ in these two stages (AD – 0.7FC, 0.7FC – SC) closely resembles the CWC phenomenon. The maximum attraction at 0.7FC matches the highest aggregate stability as measured by both $R_{>1mm}$ and MWD indicators for the Yoder and the FW treatments. It is noteworthy that certain deviations from the hypothesized relationship were observed. Specifically, while aggregate stability is lowest at SC, the strongest repulsion at the AD condition. These differences suggest that additional mechanisms may influence aggregate stability under high moisture conditions.

In conclusion, Pearson correlation analysis gives a highly significant correlation between $P_{net}$ and MWD ($p < 0.01$, Table S6), supporting the hypothesis that soil internal forces can partially explain the observed CWC phenomenon.
<figure><img src="image_6.png" /><figcaption>**Fig. 4.** Interparticle distance ($d$, refers to water film thickness) and ionic strength govern the magnitude and direction of soil internal forces. (a) The van der Waals force ($|P_{vdw}|$) & hydration repulsion ($P_h$), (b) electrostatic repulsion ($P_e$), and (c) net force ($P_{net}$).</figcaption></figure>

# 4. Discussion

## 4.1. Conditions governing the occurrence of the CWC phenomenon

These findings align with previous studies showing that aggregate stability increases to an optimal moisture level and subsequently declines under conditions of excessive wetting (Grissinger, 1966; Lehrsch & Jolley, 1992; Kværnø & Øygarden, 2006; Zhou et al., 2012; Ma et al., 2014; Li et al., 2024; Zhang et al., 2024). Both the Yoder and FW tests showed a clear CWC phenomenon. It must be underlined that both Yoder and FW tests start with the direct immersion of aggregates into water. Direct immersion is known to promote the mechanism of aggregate slaking. Hence, if both tests showed the CWC phenomena, it could be because they both activate the slaking mechanism. This implies that the higher wetting rates may increase the possibility of the occurrence of the CWC phenomenon (Lado et al., 2004). Wuddivira et al. (2009) observed that at a wetting rate of 7.5 mm/h, only soils with high organic matter and clay content showed the CWC phenomenon. However, at a higher wetting rate (75 mm/h), the phenomenon was observed across a broader range of soils.

We hypothesize this is primarily due to the lack of uniform water film coverage, which prevents these forces from acting effectively across particle surfaces. Because soil internal forces depend on the development of EDL-associated water layers, a minimum level of moisture is required for these films to become continuous (Yu et al., 2019). Previous studies indicate that disruptive pressures generated by other breakdown mechanisms, including differential swelling, slaking, raindrop impact, and osmotic stress, generally remains below 3 atm (Liu et al., 2021). Building on this benchmark, we propose that internal forces must exceed this disruptive threshold, plus provide additional stabilizing capacity, in order to govern aggregate behavior. Therefore, we adopt a conservative mechanistic threshold in which $P_{net} < -6$ atm indicates internal forces likely dominate aggregate stability, while values between -6 atm and -3 atm represent a transitional region where both mechanisms may contribute. In our results, $|P_{net}|$ was repulsive (7.9 atm) at AD, strongly attractive (12 atm) at 0.7FC, moderately attractive (4.5 atm) at FC, and approximately 3 atm (attractive) at SC. Although a repulsive $|P_{net}|$ of 7.9 atm is calculated at AD moisture, the discontinuous nature of water films at this stage (Tokunaga, 2011) prevents this repulsion from being transmitted uniformly throughout the aggregate fabric. As a result, its effective impact is substantially weaker than that of concurrent disruptive processes such as slaking and differential swelling.

As moisture content increases, slaking pressures diminish due to

reduced entrapment, allowing soil internal forces to exert progressively greater control over aggregate stability. When $|P_{net}|$ exceeds the 3 atm disruptive threshold, internal forces have the potential to dominate breakdown dynamics. This mechanistic trend aligns with the observations of Li et al. (2024), who reported that slaking was the primary driver of changes in $MWD_{FW}$ at 3 %-15 % moisture, whereas physicochemical dispersion became dominant at 15 %-20 % moisture, once water films became sufficiently continuous for internal forces to act. These findings suggest that the CWC phenomenon is not solely governed by soil internal forces but is influenced by the combined effects of breakdown mechanisms like slaking. In this study, the SW treatment also resulted in CWC phenomenon in smaller aggregate size classes. Slaking and differential swelling act at low water content stages. Due to small aggregate size and pore size, slaking does not necessarily dominate during this phase. Therefore, even in the absence of slaking mechanisms the CWC phenomenon can still be observed (SW treatment).

Slaking is deemed to be less efficient in breaking down wet aggregates because pores are filled with water and so entrapped air cannot be compressed as much. So, it would be expected that aggregates are more stable when they are more humid (Le Bissonnais, 1996). Across the full moisture range from AD to SC, aggregate stability showed a clear non-monotonic pattern: it increased from AD to 0.7FC and then declined sharply from 0.7FC to SC, consistent with the CWC phenomenon. This transition suggests that different mechanisms dominate under lower and higher moisture conditions, highlighting the need for further studies to clarify how slaking processes interact with the CWC response. This pattern indicates a shift in the dominant breakdown mechanism across moisture conditions. Under drier states, rapid wetting entrains air and generates pressures that disrupt aggregates before interparticle forces can act effectively. As moisture increases, water films develop into a thicker and more uniform layer. Under these conditions, soil internal forces begin to exert a stronger influence on aggregate stability. This progression reflects a gradual transition from slaking-dominated to internal-force-dominated behavior. This suggests that slaking may dominate in drier states, soil internal forces may dominate in wetter one. Hence, further studies are required to elucidate the link between slaking mechanism and CWC phenomena.

The CWC phenomenon is also impacted by various soil properties, including soil organic matter content, Hamaker constant, clay charge, and electrolyte concentration (Yu et al., 2017; Xu et al., 2020; Liu et al., 2021; Liu et al., 2023). For instance, soils with low organic matter content tend to exhibit CWC phenomenon, while soils with high organic matter content show consistently decreasing erosion amounts without
exhibiting such a transitional threshold (Wuddivira et al., 2009; Li et al., 2024). This variability indicates that soil properties can either enhance or diminish the expression of the CWC phenomenon (Wang et al., 2023; Li et al., 2024). Notably, the CWC phenomenon does not always correlate directly with erosion process. Studies have shown that even when aggregate stability follows a CWC pattern, the erosion amounts do not display a clear inflection point (Li et al., 2024). This suggests that while the CWC phenomenon exists, its direct influence on erosion process may not always be evident.

Thus, the occurrence of the CWC phenomenon is influenced by water film coverage, slaking, and soil properties, which contribute to the uncertainty and complexity of CWC phenomenon. This uncertainty underscores the complex interactions occurring across the particle-scale, aggregate-scale, and erosion processes. Our findings reveal the existence of the CWC phenomenon, with evidence suggesting that the dynamics of soil internal forces may play a critical role in its emergence. Although the experimental results identified the CWC in Mollisols at approximately 22 % gravimetric moisture content (0.7FC), its precise determination requires further investigation.

## 4.2. Limitations of soil internal forces in explaining the CWC phenomenon

This study coupled soil internal force with initial moisture content to analyze aggregate stability. Experimental and statistical analyses reveal that water content significantly affected the soil internal force by altering water film thickness. A highly significant correlation (p < 0.01) between soil internal force and aggregate stability was observed. The mesoscopic scale (1 nm – 1 µm) of soil internal forces provides a more direct explanation for the CWC phenomenon. Earlier studies have attempted to elucidate CWC phenomenon by examining water content's effect on soil erodibility, cohesion or shear strength. We further argue that the effect of water content on soil erodibility and shear strength reflects the CWC phenomenon. Previous studies have shown that after the PL, clays begin to disperse, reducing soil shear strength and increasing susceptibility to disintegration (Kay & Dexter, 1990; Amézketa, 1999; Arnold & Allen, 1999; Holz et al., 2015.) Our findings suggest that water film thickening significantly accelerates after the PL, with the growth rate increasing from 0.03 to 0.05 nm/% between 0.7 FC to FC. This phenomenon supports the idea that increased water film thickness lubricates the inter-particle contact surface, altering the tension of water film and promoting the dispersion of clay particles after PL.

For typical Loess, Ultisols, Vertisols, and Mollisols, etc., aggregate stability initially increases and then decreases (Fig. 5) (Ma et al., 2014; Li et al., 2024; Zhang et al., 2024). Together, these previous studies highlighted the generality and repeatability of the CWC phenomenon. This study further examines the applicability and limitations of soil internal forces in explaining the CWC phenomenon by calculating these forces for Ultisols, Mollisols, and Loess soils. To ensure comparability across datasets, we applied systematic selection criteria that included clay content, organic matter content, CEC, and vegetation type, as these properties govern specific surface area and surface charge, thereby directly influencing the calculations of soil internal forces.

For Ultisols, data from Ma et al. (2014) and Ali et al. (2023) were compared, with parameters selected from perennial vegetation systems to enhance comparability. The results demonstrated that aggregate stability increased with rising moisture before declining at higher contents (Fig. 6a), while splash erosion decreased initially and then increased (Fig. 6b). Importantly, the $P_{net}$ (calculated using equations 3–5) shifted from repulsion to attraction at around 5 % moisture and reached its maximum attractive force near 15 %, which aligns closely with the observed CWC (Fig. 6c). A marginal correlation (p = 0.057) was detected between splash erosion and $P_{net}$, suggesting that the relationship between internal forces and aggregate breakdown, though not strongly significant in this dataset, follows the mechanistic patterns consistent with the CWC phenomenon. In Mollisols (Fig. 7), a significant correlation (p < 0.05) was identified between soil internal force and splash erosion, clearly exhibiting a CWC trend (Table S6). Although the calculated $P_{net}$ at 15 % and 20 % moisture were very similar (13.7 atm and 13.0 atm, respectively), the observed CWC peak for splash erosion occurred at 20 % moisture content. This discrepancy suggests that under drier conditions, slaking processes may exert greater influence on aggregate breakdown than soil internal forces. Based on the aggregate stability data from this study, the CWC is approximately 22 % moisture content (0.7FC), confirming that the inflection point of soil internal forces should not be interpreted as a direct predictor of CWC. Instead, it provides mechanistic insight into the processes underlying aggregate stability. The differing CWC values observed in Mollisols (20 %) and Ultisols (15 %) are consistent with their contrasting soil properties. Mollisols contain higher levels of organic matter, which promote the formation of larger inter-aggregate pores and enhance slaking forces during wetting. To counterbalance these stronger disruptive forces and reach the turning point of stability, Mollisols require a correspondingly

<figure><img src="image_7.png" /><figcaption>Fig. 5. The critical moisture content (CWC) phenomenon observed in different soils using various methods for assessing aggregate stability.</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>**Fig. 6.** Response of aggregate stability, splash erosion, and net force ($P_{net}$) to increasing distance ($d$, refers to water film thickness) in Ultisols. (a) aggregate stability (MWD); (b) splash erosion; (c) $P_{net}$ (8 mol/L).</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>**Fig. 7.** Response of splash erosion, and net force ($P_{net}$) to increasing distance ($d$, refers to water film thickness) in Mollisols. (a) splash erosion; (b) $P_{net}$ (8 mol/L).</figcaption></figure>

greater level of interparticle attraction, resulting in a higher CWC. This comparison highlights how soil physicochemical properties can modulate the moisture threshold at which the CWC response occurs (Wuddivira et al., 2009; Ma et al., 2014). For the Loess, direct comparison was hampered by significant differences in key properties between studies. A closer correspondence is anticipated when all parameters originate from the same soil. Taken together, these findings indicate a broadly consistent pattern across soil types, supporting the general applicability of interpretations derived from soil internal forces.

Although soil internal forces and initial moisture content offer a direct explanation for the CWC phenomenon, important limitations remain. The interactions among soil physicochemical properties, moisture dynamics, and aggregate breakdown mechanisms are highly complex, and the present analysis cannot fully resolve how these factors jointly shape the CWC response. Further work is therefore needed to clarify these multi-scale linkages. Li et al. (2011) found that when the

bulk solution is diluted from 0.1 mol/L to $0.1 \times 10^{-3}$ mol/L, the $Na^+$ concentration on the surface of soil particles remains at 8.1 mol/L. For the calculation, we simplified the ion types and concentrations in the EDL by assuming a $Na^+$ concentration of 8 mol/L. However, we acknowledge that the actual types and concentrations in the EDL ions are far more complex. These ions can dynamically change with slight variations in inter-particle distance (Kang et al., 2022; Peng et al., 2022). Scaling soil internal forces from particle interactions to aggregates-level behavior remains a major challenge. Thus, the soil internal force values here represent theoretical particle-scale estimates under specific moisture conditions, rather than size-specific aggregate responses. This limitation underscores the need for further work to examine how these forces propagate across scales and influence aggregate stability.

Soil moisture modifies soil internal forces through changes in water film thickness, and these forces subsequently influence aggregate stability via multiple, interacting pathways. Because these processes are
strongly coupled and non-monotonic, establishing a single deterministic
functional relationship is challenging. To address this complexity,
Pearson correlation analysis was used as an exploratory tool to test
whether systematic associations exist between soil internal forces and
aggregate stability. Although correlation analysis does not establish
causality, the consistent and significant associations observed in both
Ultisols and Mollisols indicate that these relationships are systematic
rather than coincidental. In this context, the present study does not
attempt to fully quantify all causal pathways from colloidal forces to
aggregate stability. Instead, it aims to identify consistent trends in the
variation of internal forces with water content and to demonstrate how
these patterns parallel the observed CWC phenomenon.

5. Conclusions

This study investigates the CWC phenomenon by examining how
initial moisture content simultaneously affects soil internal forces and
aggregate stability, and how these interactions together shape the
observed response. Results indicate that as soil moisture increases, the
relationship between aggregate stability and moisture content shifts
from a positive to a negative correlation beyond a critical water content
threshold. This shift is particularly pronounced under fast wetting
treatment. As moisture content rises, the water film thickness between
soil particles increases from 1.1 to 2.8 nm, triggering a shift in soil in-
ternal forces from repulsion to attraction. This change is strongly
correlated with the CWC phenomenon (p < 0.01). This study demon-
strates that the relationship between soil internal forces and the CWC
phenomenon is consistent across major soil types such as Ultisols and
Mollisols, highlighting the broader applicability of the proposed mech-
anism. From a practical perspective, identifying the CWC threshold and
its drivers can improve soil erosion prediction and inform management
strategies, including irrigation scheduling and organic amendments, to
enhance aggregate stability under variable moisture regimes. The CWC
phenomenon is not governed by moisture content alone. Its expression is
also influenced by moisture-driven processes such as slaking, as well as
intrinsic soil properties and the dynamics of the wetting process. These
interacting factors introduce complexity and uncertainty into the
macroscopic expression of CWC. Future research should therefore inte-
grate multi-factorial experiments with mechanistic modeling to more
fully disentangle the coupled effects of soil moisture and internal forces.

Funding sources

National Natural Science Foundation of China (No. 42477338,
42177326).

CRediT authorship contribution statement

**Yushan Zeng:** Writing - review & editing, Writing - original draft, Visualization, Validation, Methodology, Investigation, Data curation, Conceptualization. **Bin Wang:** Supervision, Conceptualization, **Ruifeng Yue:** Validation, **Fenli Zheng:** Supervision. **Wangming Gu:** Investigation. **Wengang Wang:** Supervision. **Frédéric Darboux:** Validation, Supervision, Methodology.

Declaration of competing interest

The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influence
the work reported in this paper.

**Appendix A. Supplementary data**

Supplementary data to this article can be found online at https://doi.
org/10.1016/j.geoderma.2025.117640.

Data availability

Data will be made available on request.

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