Authors: Ya Zhao, Hongri Zhang, Guiyao Wang, Yanqi Yang
Categories: Research Article, Dry-wet cycle, Expansive soil, Fissures, Permeability characteristics, Soil-water characteristic curve
Source: Heliyon
Authors: Ya Zhao, Hongri Zhang, Guiyao Wang, Yanqi Yang
Expansive soils exhibit a relatively low permeability coefficient when structurally intact, allowing for their treatment as a homogeneous medium in calculations. However, the susceptibility of the slope's shallow area to numerous primary and secondary cracks under the influence of wetting and drying cycles challenges this approach. Failing to account for the impact of these surface cracks on the soil's permeability can result in a significant discrepancy between calculated and actual conditions. This study initially validated a predictive model for the soil-water characteristic curve that incorporates the effects of wetting and drying cycles. Subsequently, leveraging the fracture volume ratio parameter (pv) and the bimodal distribution characteristics of the dual-pore structure, we proposed a permeability coefficient model for expansive soils that considers fracture effects. This model was integrated with the validated soil-water characteristic curve model to facilitate the analysis of expansive soil's infiltration characteristics under cyclic wetting and drying conditions. The findings indicate that the predictive model accurately captures the hysteresis effect of expansive soil's soil-water characteristics. Moreover, the permeability coefficient model, which accounts for fractures, effectively reflects the infiltration properties of cracked expansive soil and enables the prediction and calculation of its permeability under multiple cycles of wetting and drying. This study introduces a predictive model for the soil-water characteristic curve, leveraging the hysteresis properties of expansive soil. Additionally, it presents a model for calculating the permeability coefficient of expansive soil, utilizing a dual-peak characteristic function. The development of these models establishes a theoretical basis for the computation and analysis of the soil's permeability attributes.
Rainfall infiltration, as a representative unsaturated flow process, distinguishes itself from saturated flow processes. Changes in matric suction significantly influence the water content and permeability coefficient of slope soil, resulting in a distinctive nonlinear fluctuating trend. To articulate the response process of soil water content more effectively, researchers suggest employing the soil-water characteristic curve to depict the water-holding and permeability capacities of unsaturated soil. Previous studies [[1], [2], [3]] have demonstrated a conspicuous hysteresis effect in the soil-water characteristic curve, with the desorption curve generally surpassing the absorption curve, forming a discernible hysteresis loop. The emergence of this hysteresis effect is intimately connected to the non-uniformity of the soil pore structure. For expansive soil, characterized by significant swelling-shrinkage behavior, alterations in soil structure induced by wet-dry cycles inevitably modify the soil's absorption and desorption capacities. This, consequently, leads to the intricate response of the internal seepage field in expansive soil slopes under the influence of wet-dry cycles. Current research predominantly concentrates on the progression of fissures within expansive soils. However, there is a scarcity of studies examining the evolution of these fissures under the influence of wet-dry cycles and their subsequent effects on soil permeability. Additionally, the development of theoretical models for this phenomenon remains largely unexplored. Therefore, it is of paramount importance to discuss the variation patterns of the soil-water characteristic curve, considering the impact of wet-dry cycles, for the comprehensive analysis of changes in the seepage field of expansive soil slopes under such conditions.
In addition to water-holding properties associated with soil structure, the permeability of the soil undergoes changes with variations in matric suction during the saturated-unsaturated flow process. Concerning the influence of crack structures on the permeability of expansive soil, some researchers, utilizing theoretical analysis methods, have proposed infiltration models considering crack effects. For example, Zheng et al. [4] suggested assuming a zero water depth (h = 0) when analyzing the influence of cracks on the seepage of expansive soil. Based on the differences in the impact of crack development on permeability, he proposed a theoretical analysis for the seepage of expansive soil slopes, considering crack effects. Yuan and Yin [5], based on the study of the evolution of cracks in expansive soil, established a mathematical analysis model for the unsaturated expansive soil slope, considering crack effects. He proposed characterizing the gradual healing of cracks due to soil expansion under the influence of rainfall infiltration through an expansion-time curve. Tan et al. [6] argued that the theory of unsaturated soil flow is analogous to heat conduction theory and proposed applying heat conduction theory to the analysis of unsaturated soil flow. With the rapid advancement of on-site monitoring technology and computer technology, researchers, through physical model experiments and numerical simulations, have intuitively delineated differences in the internal seepage field of expansive soil slopes with and without cracks. Zhou et al. [7], utilizing a self-made full-scale model test system combined with an FBG fiber grating deep flexible displacement system, investigated the spatiotemporal distribution patterns of slope water migration considering cracks under rainfall infiltration conditions. Yao et al. [8], based on the finite element method, comparatively analyzed the distribution characteristics of the slope seepage field with and without considering cracks. Wan et al. [9] established a finite element model for the seepage analysis of expansive soil slopes considering cracks under different rainfall conditions and employed Geo-Studio software to study the influence of different rainfall conditions on the seepage field of soil slopes with cracks. However, the studies previously mentioned have not thoroughly examined the patterns of seepage variation in expansive soils subjected to wetting and drying cycles. Distinct from other soil types, the development of a fracture network on the surface of expansive soils due to these cycles markedly augments their permeability. Despite this, current mathematical models for permeability coefficients have not sufficiently addressed the quantitative effects of the fracture network, which is induced by the wetting and drying cycles, on the permeability of expansive soils. Consequently, there is an absence of a seepage calculation model that incorporates the influence of these fractures.
Building upon prior research, this study introduces a novel model for calculating the permeability coefficient of expansive soils, which incorporates the impact of fractures. This model utilizes the fundamental parameters of fracture geometry and the fracture volume ratio parameter (pv), in conjunction with the dual-pore structure's bimodal distribution traits. Additionally, by incorporating a predictive model for the soil-water characteristic curve that accounts for the cyclical effects of wetting and drying, this research establishes a theoretical framework for analyzing the seepage behavior of expansive soil slopes under variable moisture conditions.The specific research methodology is depicted in Fig. 1.Fig. 1Illustrates the technical research route.Fig. 1
Under wet-dry cycling conditions, the internal pore structure of expansive soil experiences notable alterations in size and distribution. At the microscopic level, these changes are characterized by an increased heterogeneity of the pore structure, which in turn induces macroscopic swelling and shrinkage, culminating in sample cracking. Studies have demonstrated that following the initial wet-dry cycle, the soil-water characteristic hysteresis of expansive soil is markedly pronounced. Specifically, the desorption curve consistently exceeds the adsorption curve, and the final saturation water content of the sample post-adsorption is significantly lower than its initial value [10]. With an increasing number of cycles, the area enclosed by the hysteresis loop notably diminishes, indicating that the adsorption and desorption curves converge. After approximately 3–4 cycles, the hysteresis loop area stabilizes. This suggests that wet-dry cycling effectively mitigates the disparity in water retention capacity during the adsorption and desorption phases of expansive soil, attributed to the pore structure's influence. However, the mitigating effect diminishes as the cycle count escalates (see Fig. 2).Fig. 2Schematic diagram of a typical soil-water characteristic curve.Fig. 2
Scholars including Charles and Pang [11], Miao et al. [12], and Ho et al. [13] conducted soil-water characteristic tests on samples of volcanic ash, Nanyang expansive soil, and fully weathered granite under various wet-dry cycling conditions. The results indicate that the area of the hysteresis loop in the SWCC model gradually decreases and eventually stabilizes with an increasing number of wet-dry cycles. By combining the preceding discussion, it can be inferred that an appropriate quantification method for the hysteresis loop establishes a strong relationship between soil wetting and drying curves. Thus, utilizing the quantification method of the hysteresis loop enables determining the patterns of variation and displacement in hysteresis loop size under varying wet-dry cycling conditions. By referring to the initial SWCC model curve, one can predict the behavior of the SWCC model for expansive soil under diverse wet-dry cycling conditions. This study employs the prediction model proposed by Zhang et al. [14] in predicting the soil-water characteristic curve across multiple wet-dry cycling conditions.
Zhang et al. put forward and developed a quantified representation formula that establishes a relationship between the number of wet-dry cycles (n) and the characteristic function of soil-water characteristic curves (f(n)) in his research [14]. This relationship is expressed as the following Equation (1):(1)f(n)=A+(1−A)e−Bn
The equation includes n, which signifies the number of wet-dry cycles; A represents a steady-state parameter that quantifies the ratio between the stable state and the initial state of the hysteresis loop, assuming values within the range of (0–1); B symbolizes a reduction parameter that illustrates the rate at which the hysteresis loop diminishes as the number of wet-dry cycles increases.
After introducing the function f(n) that characterizes the soil-water characteristic curve, using the initial adsorption and desorption curves as a basis, the formula to calculate the reduction coefficient β of the hysteresis loop following n cycles of wetting and drying can be expressed as Equation (2):(2)β=1−f(n)=1−[A+(1−A)e−Bn]
Based on the calculation expression, the coefficient β represents the extent to which the size of the hysteresis loop is reduced after the dry-wet cycle process compared to its initial state. Assuming an initial hysteresis loop area of S0 = 1, β effectively quantifies the reduction in the hysteresis loop after the nth dry-wet cycle (Equation (3)). The adsorption and desorption curves exhibit a significant downward shift trend after the dry-wet cycle, with a larger shift observed in the desorption curve [11,14]. The reduction in the hysteresis loop can be calculated by subtracting the shift in the adsorption curve, represented by W(n), from the shift in the desorption curve, represented by D(n) (Equation (4)).(3)β=[D(n)−W(n)]/S0
Equation (2) and Equation (3) can be used to deduce the (4)[D(n)−W(n)]/S0=1−f(n)=1−[A+(1−A)e−Bn]
To simplify the calculation of necessary parameters for the soil water characteristic curve (SWCC) model, this study assumes that the shape of wetting and drying curves remains constant regardless of the number of wetting and drying cycles. This implies that the curves maintain a constant parallel displacement during the cycling process, which is solely determined by the soil properties. This assumption forms the basis for introducing the parameter offset ratio C = W(n)/D(n), which establishes the relationship between the wetting curve offset W(n) and the drying curve offset D(n).
Substituting the offset ratio C = W(n)/D(n) into Equation (4) yields (Equation (5)):(5)[D(n)−D(n)C]/S0=1−f(n)=1−[A+(1−A)e−Bn]
Equation (4) yields the expression for D(n) as follows Equation (6):(6)D(n)=[1−f(n)]/(1−C)=[1−A+(1−A)e−Bn]/(1−C)
The expression for W(n) can be derived by substituting C = W(n)/D(n) into Equation (6) yields (Equation (7)):(7)W(n)=[1−f(n)]C/(1−C)=[1−A+(1−A)e−Bn]C/(1−C)
The predictive calculation formula for the volumetric moisture content corresponding to a certain matric suction on the drying and wetting curve after the nth cycle of wet and dry conditions is as follows Equations (8), (9):(8)θ(n)=θ(n−1)−Δθ(n−1)·D(n−1)(9)θ(n)=θ(n−1)−Δθ(n−1)·W(n−1)
The equation defines θ(n) as the volumetric moisture content at a specific matric suction on the drying curve of the soil following the nth cycle of wet and dry conditions. Δθ(n-1) denotes the discrepancy in volumetric moisture content at a certain matric suction between the wetting and drying curves of the soil after the *(n-1)*th cycle of wet and dry conditions. The definitions of the remaining parameters remain consistent with those given in the preceding equation.
In conclusion, by introducing the feature function f(n) of the soil characteristic curve and the offset ratio C = W(n)/D(n), while considering the impact of wet-dry cycles on the hysteresis loop, the prediction of the adsorption and desorption curves after each cycle can be made based on the initial moisture absorption and desorption curves of the soil.
When utilizing the SWCC model, proposed to assess the impacts of wet-dry cycles, the estimation of internal parameters can be predicted and adjusted based on the plasticity index of the soil. The specific formula for fitting the expression calculation is indicated below [14] Equation (10), (11).(10)A=a1+b1exp(c1IP)(11)C=a2+b2exp(c2IP)
The equation incorporates three fitting parameters, namely ai, bi, and ci, which are intricately associated with the inherent characteristics of the soil.
The fitting parameters ai, bi, and ci for the soil with IP = 0–32 are determined by collecting and summarizing experimental data from existing literature [11,15]. Equations (8), (9) can be calculated as shown below Equation (12), (13):(12)A=0.36078+0.02922exp(0.0727IP)(13)C=0.19561+0.00439exp(0.13812IP)
The study utilizes Guangxi expansive soil as a case study to forecast the soil-water characteristic curve post dry-wet cycles employing the proposed model. Fig. 3 illustrates the initial soil-water characteristic curve of the expansive soil, based on experimental measurements. Additionally, Table 1 displays the parameter values utilized in the soil-water characteristic curve prediction model.Fig. 3Initial cycle soil-water characteristic curve of expansive soil in Guangxi.Fig. 3Table 1Parameter values for highly expansive soil in Guangxi.Table 1Steady-state Parameter AReduction Parameter BOffset Ratio CPlasticity Index I~P~0.48720.26720.2
The values of the characteristic function f(n) of the water and soil characteristic curve, as well as the offset coefficients D(n) and W(n) corresponding to the absorption and desorption curves, are calculated by substituting the parameters into Equations (1), (5), (6) for different cycle times. The calculation results are shown in Table 2.Table 2Parameter calculation values at different cycling frequencies.Table 2n12345*f(n)0.5570.4970.4890.4880.488D(n)0.6040.6860.6970.6980.699W(n)*0.1620.1830.1860.1870.187
The parameters obtained from Table 2 can be substituted into Equations (7), (8) to predict the soil water characteristic curve after multiple wet-dry cycles, based on the initial curve. Fig. 4 displays the drying and wetting curves obtained from the SWCC prediction model that considers the influence of wet-dry cycles proposed in this study. The results indicate that, after the third wet-dry cycle, the drying and wetting curves of the soil mostly overlap, with a hysteresis loop size approaching zero. At this stage, the corresponding volumetric water contents at saturation are 0.456 (for the drying curve) and 0.453 (for the wetting curve). The volumetric water contents at saturation of the soil have decreased to 0.479 (for the drying curve) and 0.459 (for the wetting curve), respectively, compared to the first cycle. However, the drying curve exhibits a larger shift overall. This indicates that the theoretical calculations of the prediction model align with the observed variations from existing research, enabling the model to effectively predict changes in soil water characteristic curves influenced by wet-dry cycles.Fig. 4Prediction of soil-water characteristic curves for expansive soil in Guangxi under dry-wet cycling.Fig. 4
To validate the accuracy of the proposed SWCC model, this study fitted the absorption and desorption curves of the samples under different dry-wet cycling conditions, using the test results of the soil-water properties of expansive soil in Ganzhou City, Jiangxi Province [10]. The results of indoor physical property tests show that the expansive soil in this region exhibits significant water absorption, easy disintegration, and expansion characteristics with a plasticity index (Ip) of 14.1. Based on the mechanical properties of the soil samples and the fitting data, the reduced parameter B in the prediction model is set to 1, while the steady-state parameter A and the reduction ratio C can be derived from the plasticity index.
Fig. 5 presents the experimental data of the soil-water characteristic curve (SWCC) under different cycles of wetting and drying, along with the distribution of the fitted curve. As the number of wetting and drying cycles increases, the decrease in water content corresponding to the matric suction during the desorption process is significantly higher than that during the adsorption process, with the most substantial decrease observed after the first cycle. The wetting and drying cycles effectively diminish the hysteresis effect of the soil-water characteristics of expansive soil, resulting in a decrease in the hysteresis loop area as the number of cycles increases. The plotted predicted SWCC curve in the graph demonstrates a good fit during the first cycle of wetting and drying, but there is some deviation afterwards. However, the fitted curve also exhibits the characteristic of a decrease in the hysteresis loop area and a fast decline in the desorption curve with an increasing number of wetting and drying cycles, aligning with the observed experimental results. The significant variations in the mechanical properties of expansive soil in different regions may be the primary reason for the fitting error, necessitating further discussion to determine the parameters relying only on the plasticity index.Fig. 5Fitted soil-water characteristic curves (SWCC) at different dry-wet cycling frequencies.Fig. 5
The results of the aforementioned discussion indicate that the wet-dry cycle significantly affects the water holding capacity of expansive soil. As the number of wet-dry cycles increases, the weakening effect on hysteresis gradually diminishes. However, the fundamental change in water holding capacity of expansive soil is primarily due to the occurrence and development of internal fissures influenced by the wet-dry cycle. These fissures cause alterations in the soil structure. Therefore, when examining how expansive soil's permeability performance responds to the wet-dry cycle, it is crucial to consider the characteristics of fissure evolution, integrate the inherent structure and external environmental effects of expansive soil, clarify the mechanism by which fissures influence the permeability performance during the wet-dry cycle, and develop a calculation model for the permeability coefficient that accounts for the impact of fissures.
Several engineering practices have provided substantial evidence that rainwater infiltration significantly affects slope stability [[16], [17], [18]]. Additionally, the presence of surface cracks plays a crucial role in the process of rainwater infiltration. Previous studies have demonstrated a significant disparity in seepage and stability analysis results when considering versus not considering cracks [19,20]. The current approach to addressing seepage problems involving cracks typically involves standardizing the cracks and simulating their impact by setting hydraulic boundary conditions. However, this approach fails to adequately capture the inherent permeability and unsaturated characteristics of cracks, as well as the irregularity of their development.
According to Burger and Shackelford [21], Zhang and Chen [22], and others, when soil contains two pore structures (large pores and small pores), the corresponding soil water characteristic curve exhibits a bimodal distribution, commonly referred to as a "double S″ shape. This phenomenon is frequently observed in fissured soil and discontinuous graded soil samples. Similarly, expansive soil affected by cracks can be viewed as a dual-pore structure composed of crack networks and intact natural soil structures. Therefore, when studying the soil water characteristics of expansive soil considering crack influence, a bimodal SWCC (Soil-Water Characteristic Curve) model can be used to describe the hydraulic characteristics of cracked soil. Subsequently, traditional seepage theories can be employed to analyze the seepage field.
To simplify the analysis and calculations, this paper proposes the following basic assumptions when determining the hydraulic parameters of soil considering (1)The permeability characteristics of the soil and crack networks are assumed to be isotropic.(2)Volume changes in the surrounding soil due to rainfall are disregarded, assuming that the volume of the crack networks remains constant.
Based on these assumptions, this paper conducts separate research on the soil water characteristics of the crack layer (i.e., the area corresponding to the crack network) and the natural soil layer (i.e., the area with intact original soil). For the crack layer, it is necessary to introduce a parameter that quantifies the degree of crack development. In this paper, the crack index δ [23] is employed as a quantitative evaluation metric for cracks. The specific calculation procedure is as follows Equation (14):(14)δ=∑i=1nliA
The formula incorporates the variable n, representing the total number of cracks. The symbol li is used to denote the length of the i-th crack. A denotes the total area of the specimen.
Although the development of fissures in expansive soils exhibits randomness and non-uniformity at a microscopic scale, their degree of evolution can be quantitatively expressed using macroscopic indicators, such as fissure density. Hence, simplifying the calculation and analysis of the model from a macroscopic perspective is essential. In this study, it is assumed that the width of fissures remains constant within the depth of their development, and the fissure network expands uniformly in the direction of its depth. With this assumption, the volumetric proportion parameter (pv) for the fissure network can be determined using the following expression (Equation (15)):(15)pv=VfV=b‾h‾∑i=1nliAh=b‾δ
The equation defines Vf as the volume of the fracture network. V represents the total volume of the soil. b‾ represents the average width of the fractures. h‾ represents the average depth of the fractures.
Considering the impact of fissures on the soil mass's pore structure, the expansive soil's pore architecture can be conceptualized as a dual-pore system, comprising large pores from the fissured soil layer and small pores from the natural soil layer. The pore size distribution displays a bimodal characteristic, illustrated in Fig. 6. Currently, three primary methods are employed to determine the parameters of the bimodal Soil-Water Characteristic Curve (SWCC) model. The first method involves segmented treatment, where the bimodal SWCC is divided into two combinations of single-pore SWCC, corresponding to the large and small pore structures. The main challenge lies in handling the connection point between these two curves. The second method is the total volume fraction approach. Under the assumption that volume moisture content equals porosity under saturated conditions, it divides the porosity represented by saturation moisture content into large and small pore components, ensuring the bimodal SWCC model's continuity. The third method is the unique parameter approach, which, by amalgamating curve shapes, elucidates the physical meaning of each parameter in the equation. In this study, we employed the total volume fraction method to construct the bimodal SWCC model for expansive soil. Based on the research conducted by Fredlund and Xing, Sun and Wang [24,25], the pore size distribution of the soil mass is assumed to follow a normal distribution. By overlaying the pore size distribution function of the fissured soil layer onto that of the natural soil layer, we can derive the comprehensive pore size function, taking into account the influence of fissures. This is calculated by the following Equation (16) [24]:(16)f(r)=fr(r)+fm(r)Fig. 6Schematic diagram of pore size distribution function for expansive soil.Fig. 6
The equation is expressed as where r denotes the pore radius, while fm(r) and fr(r) stand for the pore size distribution functions of the natural soil layer and the fissured soil layer, respectively.
Fredlund and Xing, Sun and Wang [24,25] introduced a methodology for computing the Soil-Water Characteristic Curve, utilizing the pore size distribution function of the soil medium. The expression for this method is articulated below Equation (17):(17)θs=∫RminRmaxf(r)drwithin the formula, θs signifies the overall soil saturation moisture content, whereas Rmax and Rmin denote the maximum and minimum pore radii of the soil, correspondingly.
During rainfall infiltration, water initially occupies the smaller pores (e.g., those with diameters less than R). Equation (17) can be reconfigured into the subsequent expression, representing the current soil moisture content (Equation (18)):(18)θw=∫RminRf(r)drIn accordance with the principles of capillary water management theory, the calculation of matric suction is applicable when the soil is in an unsaturated state, and it is expressed by the following formula (Equation (19)):(19)ψ=2Tcosαrwithin the formula, ψ denotes matric suction. T stands for the interfacial tension of the water phase, commonly set at 72.75 × 10^−3^ N/m. Additionally, α represents the contact angle at the water-soil interface, and when α equals 0, it signifies the air entry value of the soil.
Solving Equation (16) through (19) simultaneously yields (Equation (20)):(20)θ(ψ)=∫RminRfr(r)dr+∫RminRfm(r)dr=pvθsf∫ψ∞gf(ψ)dψ+(1−pv)θsm∫ψ∞gm(ψ)dψ=pvθf(ψ)+(1−pv)θm(ψ)
Within the formula, θsf and θsm denote the independent porosities of the fractured soil layer and the natural soil layer, respectively. Additionally, gf(ψ) and gm(ψ) represent the normalized porosity functions of the fractured soil layer and the natural soil layer, expressed as functions of matric suction (ψ). Furthermore, θf(ψ) and θm(ψ) stand for the moisture contents of the fractured soil layer and the natural soil layer, correspondingly.
In the absence of accounting for soil expansion and contraction caused by rainfall infiltration on soil fractures, θsf and θsm can be treated as the saturated moisture content for the fractured soil layer and the natural soil layer, respectively. Subsequently, when the soil reaches saturation (Equation (21)):(21)θs=pvθsf+(1−pv)θsm
Defined by the fracture volume ratio pv, when rainfall infiltration transpires and the fracture network saturates, we can infer that the fracture pores are water-filled. At this juncture, the saturation moisture content, denoted as θsf, approximates 1, while the residual moisture content equals 0.
In elucidating the connection between moisture content and matric suction within the fractured soil layer and the natural soil layer, the van Genuchten model (VG model) is employed in this study. Substituting the moisture content parameters for both soil layers yields the following (Equation (22)):(22)θ(ψ)=pv[11+(αfψ)nf]mf+(1−pv)[θrm+θsm−θrm1+(αmψ)nm]mmwithin the equation, α, m, and n serve as the fitting parameters for the van Genuchten model (VG model), while θr denotes the residual moisture content. Specifically, subscripts f and m correspond to the fractured soil and the natural soil, respectively, and the definitions of the other parameters remain consistent with those mentioned earlier.
Expansive soil specimens displaying conspicuous surface cracks exhibit a relatively intricate and loose structure. The direct determination of the permeability coefficient for the fractured soil layer through experimental methods poses considerable challenges, as illustrated in Fig. 7. When excluding the influence of fractured soil expansion caused by rainfall infiltration, the overall permeability coefficient for the soil with cracks and the permeability coefficient for the natural soil layer can be ascertained through constant head tests. Consequently, the permeability coefficient of the fractured soil layer can be computed using an equivalent medium model.Fig. 7Schematic diagram of soil mass with fissures.Fig. 7
Presuming the equivalent continuity of the porous media in both the fractured soil layer and the natural soil layer, the flow rate (q) through any cross-section containing fractured soil can be formulated as follows (Equation (23)):(23)q=pvqr+(1−pv)qmwithin the equation, qr and qm denote the flow rates through the pores of the fractured soil layer and the natural soil layer, respectively.
By substituting Equation (23) into Darcy's law, the result is (Equation (24)):(24)k(∂h∂Z−1)=pvkf(∂hf∂Z−1)+(1−pv)km(∂hm∂Z−1)within the equation, kf and km represent the permeability coefficients of the fractured and natural soil layers, and hf and hm denote the pressure heads in the fractured and natural soil layers, respectively.
Based on Peters and Klavetter' study [26], at a sufficiently large spatial and temporal scale, the pore water pressure in both the fractured soil layer and the natural soil layer reaches equilibrium, denoted as h = hf = hm. Consequently, Equation (24) can be formulated as Equation (25):(25)k=pvkf+(1−pv)kmIn accordance with the van Genuchten (VG) model, the functional relationship between the saturated permeability coefficient and matric suction is represented as follows (Equation (26)):(26)k=ksSe0.5[1−(1−Se1m)m]2In the equation, Se denotes effective saturation, calculated based on parameter Se=θ−θrθs−θr. The symbol ks signifies the saturated permeability coefficient, while m is an unspecified parameter associated with soil properties.
Substituting Equation (26) into Equation (25) yields the comprehensive permeability coefficient formula for expansive soil (Equation (27)), accounting for the influence of fractures.(27)k=pvksfSef0.5[1−(1−Sef1mf)mf]2+(1−pv)ksmSem0.5[1−(1−Sem1mm)mm]2
The calculation of the comprehensive permeability coefficient for expansive soil, accounting for crack effects, is accomplished through Equations (25), (22), (27). Utilizing the model for comprehensive permeability parameters and the predictive model for soil-water characteristic curves, considering the effects of dry-wet cycles as discussed in Section 2, predictions and calculations for the permeability characteristics of expansive soil under various dry-wet cycle conditions are performed. The specific steps for calculation are as (1)Conduct indoor physical property tests to measure the plasticity index (IP) of expansive soil samples. Substitute these values into Equations (8), (9) to determine the steady-state parameters A, reduction parameter B, and offset ratio C in the characteristic function f(n) of the soil-water characteristic curve.(2)Employ Equations (1), (6), (7) to solve the characteristic function f(n) of the soil-water characteristic curve for expansive soil under varying dry-wet cycle numbers. Determine the offset coefficients D(n) and W(n) corresponding to absorption and desorption curves.(3)Following the acquisition of offset coefficients for absorption and desorption curves during successive dry-wet cycles, employ Equations (8), (9) to compute the soil-water characteristic curve of expansive soil under various dry-wet cycle conditions, based on the initial sample's soil-water characteristic curve.(4)Employ digital image processing technology to acquire fundamental morphological parameters of surface cracks in expansive soil samples during successive dry-wet cycles. Develop a moisture content model, considering crack effects and based on the VG model.(5)Integrate the proposed layered model for expansive soil. Substitute the saturated permeability coefficient and effective saturation of natural soil and fractured soil into Equation (27). Obtain the comprehensive permeability coefficient calculation model, considering crack effects, for expansive soil.
In contrast to existing models for soil-water characteristic curves, the predictive model presented in this paper initiates from the response characteristics of hysteresis in expansive soil influenced by dry-wet cycle numbers. It innovatively establishes the characteristic function of the soil-water characteristic curve. Building on this foundation, the model quantitatively describes the offset phenomenon of absorption and desorption curves occurring in successive dry-wet cycles. This approach aligns it more closely with the moisture distribution characteristics within the slope of expansive soil influenced by dry-wet cycles. Taking into account the impact of dry-wet cycles on the saturation and moisture content of expansive soil, this paper introduces a layered model tailored to expansive soil. The model addresses the distinctive wetting and drying shrinkage, as well as crack characteristics of expansive soil. By quantitatively representing crack grids in the fractured soil layer, this paper establishes a comprehensive model for calculating permeability coefficients in expansive soil, considering the effects of cracks.
In order to implement the seepage calculation model proposed, which accounts for fracture effects in practical scenarios, this study centers on experimental research utilizing expansive soil sourced from Guangxi. Permeability tests were carried out on expansive soil samples, subjecting them to varying wet-dry cycle conditions. The thickness of the chosen expansive soil sample was 4 cm, as illustrated in Fig. 8. Following the preparation of the expansive soil samples, they were initially positioned in a vacuum saturation apparatus and saturated for a period of 24 h. After concluding the saturation process, the saturation permeability coefficient for the expansive soil samples was determined through the use of the TST-55 variable water head permeameter.Fig. 8Layered diagram of fissures in expansive soil test blocks.Fig. 8
Given the substantial integrity of expansive soil samples in the preliminary wet-dry cycle, the saturated permeability coefficient derived after the initial wet-dry cycle serves as the permeability coefficient for the underlying natural soil layer. Post the wet-dry cycle treatment and guided by the distribution of fractures at varying depths, it can be roughly categorized into three the fracture surface layer, the fracture development layer, and the underlying natural soil layer. Notably, no conspicuous fracture development was observed in the lowermost natural soil layer, suggesting that, at this juncture, the soil's permeability closely approximates that of the natural soil. The measured saturated permeability coefficient for the samples is regarded as the comprehensive permeability coefficient, accounting for the impact of fractures. Table 3 displays the comprehensive saturated permeability coefficients for moderately and highly expansive soil samples.Table 3Comprehensive Permeability Coefficient (k) of Expansive Soil at Different Cycling Frequencies (Unit: cm·s^−1^).Table 3ExpansivenessFirst cycleSecond cycleThird cycleFourth cycleFifth cycleMedium expansive soil1.22 × 10^−9^2.70 × 10^−9^1.28 × 10^−8^1.88 × 10^−8^2.33 × 10^−8^Highly expansive soil4.05 × 10^−9^7.25 × 10^−9^3.50 × 10^−8^4.79 × 10^−8^5.13 × 10^−8^
The essential morphological parameters of cracks in expansive soil samples following consecutive wet-dry cycles were acquired through laboratory experiments. Following this, Table 4 illustrates the crack density and average crack width of moderately and highly expansive soil samples across varying wet-dry cycle numbers.Table 4Degree of fissure development at different cycling frequencies.Table 4ExpansivenessFirst cycleSecond cycleThird cycleFourth cycleFifth cycleMedium expansive soilFracture ratio δ0.0130.0450.0460.0490.050Average width b‾1.11.11.21.51.78Highly expansive soilFracture ratio δ0.0140.0490.0560.0600.063Average width b‾1.21.43.33.53.7
The values for the crack volume ratio (pv) and air entry value (ψ) under various wet-dry cycle numbers are derived by incorporating the data from Table 4 into Equations (15), (19). These results are presented in Table 5.Table 5Values of pv and ψ at Different Cycling Frequencies.Table 5ExpansivenessFirst cycleSecond cycleThird cycleFourth cycleFifth cycleMedium expansive soilp~v0.0140.0490.0550.0740.089ψ/cm2.722.652.431.941.64Highly expansive soilpv~0.0170.0680.1840.210.23*ψ/*cm2.432.080.880.840.79
The discourse regarding the soil-water characteristics of expansive soil samples highlights that the saturation moisture content in expansive soil is subject to the influence of wet-dry cycles, manifesting a gradual decline. Consequently, when computing the permeability coefficient of expansive soil under distinct wet-dry cycle conditions, it is imperative to assess the fluctuation of saturation moisture content concerning the number of wet-dry cycles. The detailed outcomes of saturation moisture content calculations are presented in Table 6.Table 6Saturation volumetric water content at different cycling frequencies.Table 6Saturation volumetric water content.First cycleSecond cycleThird cycleFourth cycleFifth cycleθs0.4680.460.4560.4540.453
Utilizing the experimental outcomes, the parameters of the VG model were calibrated, yielding the following values for the VG model parameters in both the natural soil layer and the fractured soil layer.
By substituting values from Table 5, Table 6, Table 7 into Equations (22), (27), the saturated permeability coefficients for the fractured soil layer can be derived, as presented in Table 8. Upon juxtaposing Table 8 with Fig. 9, it becomes evident that the saturated permeability coefficients for the fractured soil layer of expansive soil, calculated using the proposed seepage model, essentially stabilize after the third wet-dry cycle. The trends in variation of saturated permeability coefficients in the fractured soil layer of highly expansive soil and moderately expansive soil are essentially parallel, with the former being roughly 2.5 times that of the latter.Table 7VG model parameters for expansive soil in Guangxi.Table 7Natural soilFissure soilPerformance indicatorsVG model parameters α/(cm^−1^)VG model parametersNVG model parametersMVG model parametersΑ/(cm^−1^)VG model parametersNVG model parametersMMedium expansive soil0.021.20.1670.0181.80.444Highly expansive soil0.021.20.1670.0181.30.230Table 8Permeability Coefficient (k) of Fissure Soil Layer in Expansive Soil at Different Cycling Frequencies (Unit: cm·s^−1^).Table 8ExpansivenessFirst cycleSecond cycleThird cycleFourth cycleFifth cycleMedium expansive soil1.22 × 10^−9^6.03 × 10^−8^2.70 × 10^−7^2.89 × 10^−7^2.93 × 10^−7^Highly expansive soil4.05 × 10^−9^1.75 × 10^−7^6.67 × 10^−7^7.94 × 10^−7^7.51 × 10^−7^Fig. 9Comparative diagram of fissure soil layer and comprehensive permeability coefficient in medium and highly expansive soils under different dry-wet cycling conditions.Fig. 9
The analysis above demonstrates that the computational model proposed in this study is capable of predicting and calculating the permeability performance of expansive soil, taking into account cracks, by utilizing known soil parameters and the frequency of dry-wet cycles. This computational model enables the assessment of permeability under varying conditions. In contrast to the comprehensive permeability coefficient, the saturated permeability coefficient of expansive soil with crack layers exhibits an order of magnitude increase. This significant difference underscores the importance of considering crack presence in permeability assessments. Furthermore, these findings offer explanations for the substantial variations in permeability performance observed between expansible soil with intact surfaces and soil with surface cracks. This insight contributes to a deeper understanding of the factors influencing soil permeability. In practical expansive soil slopes, the repetitive occurrence of dry-wet cycles creates a conducive environment for the formation of surface cracks in the ground, significantly improving the infiltration performance of the slope. This phenomenon enhances the understanding of the environmental factors influencing crack development in slopes. This process establishes advantageous pathways for rainwater infiltration, thereby accelerating the development and extension of expansive soil cracks deep within the slope. This observation contributes to a more comprehensive understanding of the mechanisms underlying crack propagation in slopes.
This study addresses the water retention and permeability behavior of expansive soils under wetting and drying cycles, focusing on the dual-peak Soil-Water Characteristic Curve (SWCC) resulting from both intact and fractured soil structures. A fracture volume ratio parameter for expansive soils has been introduced to delineate fracture development characteristics, and a permeability coefficient calculation model that accounts for fracture effects has been formulated. Key findings (1)A quantitative link between the number of wetting and drying cycles and the hysteresis loop area has been established to address the observed decline in soil-water characteristic hysteresis. By incorporating a characteristic function of the SWCC and a shift ratio, a predictive model for the SWCC that considers cycle counts has been developed. The reduction parameter B quantifies the extent to which wetting and drying cycles affect the water retention capacity of expansive soils.(2)The proposed models were validated against experimental data from the literature, demonstrating their efficacy in analyzing the influence of wetting and drying cycles on SWCC hysteresis and in accurately forecasting the SWCC under multiple cycles. Wetting and drying cycles notably reduce the hysteresis effect of expansive soil's water retention, with the hysteresis loop area diminishing as cycle counts increase. However, relying solely on the plasticity index for fitting may lead to errors due to variations in the mechanical properties of expansive soils across different regions.(3)Considering the fracture grid distribution in expansive soil samples under wetting and drying cycles, the soil has been categorized into natural and fractured layers. A dual-peak SWCC model for expansive soils, informed by the pore size distribution of both layers, has been developed. Utilizing Darcy's law and the theory of equivalent media, a permeability coefficient calculation model that incorporates fracture impacts has been established.(4)A comparative analysis of the saturated and comprehensive permeability coefficients of the fractured soil layer in expansive soils revealed significant differences in permeability performance between intact and surface-cracked soils. The saturated permeability coefficient is significantly higher than the comprehensive one, indicating that fracture development substantially enhances the seepage capacity of expansive soils.(5)The models introduced in this study are capable of calculating the permeability coefficient of expansive soil with a degree of accuracy, especially under conditions of repeated wetting and drying cycles and when accounting for fractures. Nonetheless, these models are not without scope for refinement. Subsequent research is encouraged to scrutinize the determination of parameters for the soil-water characteristic curve and to evaluate the influence of the soil's expansive properties on permeability. Such endeavors will be pivotal in augmenting the models' applicability and precision.
The work described in this paper was fully supported by a grant from the Title of the Excellent Young Scientist Project for Scientific Research from the 10.13039/100009377Education Department of Hunan Province in 2023 (Project Number: 23B1040), 10.13039/501100012166National Key Research and Development Program Project (Project Number: 2019YFC1509800), List of Key Technological Projects in the Transportation Industry, Ministry of Transportation, Year 2022 (Reference Number: 2022-MS5-125), and the 10.13039/501100017691Guangxi Key Research and Development Plan (Reference Number: AB23075184).
The datasets generated or analyzed during this study are available from the corresponding author on reasonable request.
Ya Zhao: Writing – original draft, Conceptualization. Hongri Zhang: Methodology, Formal analysis, Conceptualization. Guiyao Wang: Data curation. Yanqi Yang: Writing – review & editing.
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.