Effect of air permeability at the bottom on rainfall infiltration

1 Introduction

The impact of rainfall infiltration presents a multifaceted scientific challenge, with significant applications observed in various fields, including landslide control, urban flood management, as well as soil and water conservation (Zhan and Ng, 2004; Tu et al., 2009; Muntohar and Liao, 2010; Feng et al., 2022). The fundamental essence of rainfall infiltration lies in the intricate material transport phenomena that involve the dynamic interplay between water and air phases. During the process of rainfall infiltration, water permeates through the interconnected air-filled pores within the soil matrix (Yazdani et al., 2024). The presence of pore air exerts pressure, creating resistance to the advancement of water infiltration (Tu et al., 2009; Muntohar and Liao, 2010; Feng et al., 2022; Feng et al., 2023).

The investigation of rainfall infiltration typically involves the use of experimental methods (Lee et al., 2011; Wu et al., 2017; Di Prima et al., 2018; Wang et al., 2020) and numerical methods (Chen et al., 2008, Liu et al. 2019a; Liu et al., 2019b). Experimental approaches are primarily used for qualitative exploration of infiltration regulation (Lu et al., 2024). However, in quantitative research, accurately analyzing the effect of a single-factor change on infiltration poses challenges due to the intricacy of simultaneously controlling multiple physical variables (Tai et al., 2024). In contrast, numerical methods provide a convenient way to control and manipulate multiple physical parameters, making them well-suited for investigating the relationship between a single variable and infiltration (Li et al., 2022). Based on mathematical models depicting unsaturated seepage phenomena in rainfall infiltration, unsaturated seepage theory can be classified into single-phase flow theory and multiphase flow theory (Tai et al., 2024). Traditional computational software and algorithms typically rely on the application of the Richards equation, which mainly describes single-phase water flow (Brooks, 1965). The two-phase flow theory accounts for the interaction between water and air (Tong et al., 2010; Chen and Wei, 2016; Cho, 2016; Hu et al., 2016), enabling a more accurate representation of the movement of water and air within the soil. Managing the entry and exit of material is crucial for establishing effective boundary control conditions in the two phase flow numerical simulation of material transport phenomena. It controls the intensity, overall quantity, distribution, and complexity of material transfer, enabling a better understanding and manipulation of system dynamics (Shi et al, 2024; Xiao et al., 2026). Consequently, in the simulation of the rainfall infiltration process, the boundary conditions governing the entry and exit of water and air phases play a critical role in regulating the seepage dynamics.

In analyzing rainfall-induced landslides, researchers have considered a range of boundary conditions to explore their impact and significance. One study focused on the condition of the no-flow boundary at the bottom edge of the calculation model, indicating that the hydraulic response to rainfall in a homogeneous infinite slope with an impermeable layer beneath can be categorized into two stages: the advancement of the wetting front and the elevation of the water table (Li et al., 2013). In Zhan et al. (2013), the lower boundary was defined with a zero pressure head at the phreatic water level, indicating that the water table was positioned at the lower boundary. Some researchers applied three distinct boundary conditions at the bottom of the soil layer (Ali et al., 2014): fully drained, partially drained, and impermeable. It revealed that the boundary conditions significantly affected either the occurrence or the depth of failure at a specific rainfall intensity. While it is commonly believed that air impedance in the flow zone during infiltration is insignificant, empirical studies have shown that restricting airflow within the unsaturated zone can significantly hinder the permeability rate (Jarrett et al., 1980; Siemens et al., 2013). Experimental projects investigating infiltration often used soil columns to manipulate and regulate the surface and depth boundary conditions (Yang et al., 2004; Bathurst, Ho et al., 2007). Another observation made by researchers was that in cases where a soil slope was situated above a relatively impermeable layer, the interaction between the soil and the less permeable layer created a pseudo-boundary. This pseudo-boundary led to the generation of positive pore water pressures within the soil, ultimately resulting in slope failure at the interface. A few studies (Tsai and Chiang, 2012; Zhan et al., 2013) have observed that when a less permeable layer underlies a soil slope, the interface between the soil and the less permeable layer behaves like a pseudo-boundary. This phenomenon generated positive pore water pressures, leading to slope failure at the interface. In research conducted by Anagnostopoulos et al. (2015), the bottom boundary condition of the soil column can be either a no-flow condition or a specified drainage condition. Meanwhile, the infiltration rate at the soil surface can be controlled either by the atmosphere or by Liu et al. (2011) considered two special conditions in his research: a shallow water table and an impermeable surface. Siemens also investigated the effect of different bottom conditions on infiltration (Siemens et al., 2014). The results showed that under closed conditions, the wetting front migrated significantly more slowly than under open conditions. The pore pressure response during the descent of the wetting front exhibited high similarity, except for a significantly prolonged time scale specifically observed under closed conditions. Accurately quantifying the permeability of a boundary and comprehensively analyzing the influence of boundary airflow on rainfall infiltration pose significant scientific challenges. Additionally, there is a scarcity of quantitative studies that specifically investigate the effect of bottom boundary permeability on rainfall infiltration.

This study uses the finite element method to establish a numerical calculation model of rainfall infiltration based on a water-air two-phase flow model. The objective is to analyze the influence of boundary conditions, including the ventilation condition and the air-sealing condition at the bottom of the soil column, on rainfall infiltration. Additionally, the study quantitatively assesses the permeability of the boundary and analyzes how varying levels of air permeability at the bottom boundary condition affect rainfall infiltration. To verify the simulation results, a laboratory rainfall infiltration test and Geostudio simulation were conducted to monitor pore air pressure and water contents under both ventilated and closed conditions. Finally, the variation in pore air pressure and water content obtained from the numerical simulation is compared with that obtained from a laboratory test.

2 Numerical simulation of rainfall infiltration

2.1 Governing equation of water-air two-phase flow

The governing differential equations for water-air two-phase flow include equations for the liquid phase (water) and the air phase. The conservation of mass in the water and air phase is considered, taking into account factors such as soil deformation, compressibility, viscosity, and saturation. The governing differential equations for water-air flow can be mathematically described as follows (Tong et al., 2013): where n represents the porosity, S r represents the degree of saturation, ρ β represents the density of the β phase k g / m 3 ( β = 1 is the water phase; g is the air phase), Q β represents the source of β phase (k g / m 3 · s, k represents the intrinsic permeability of soil that is determined by pore characteristics (m 2), μ β represents the viscosity coefficient of the β phase (P a · s), k r β represents the relative permeability coefficient of the β phase, p β represents the pressure of the water phase (P a), and g represents the gravitational acceleration (N / kg).

n S r ∂ ln ⁡ ρ l ∂ t + S ∂ n ∂ t + n ∂ S r ∂ t + ∇ · − k r l k μ l · ∇ p l + ρ l g − 1 ρ l Q l = 0 (1)

n 1 − S r ∂ ln ⁡ ρ g ∂ t + 1 − S r ∂ n ∂ t − n ∂ S r ∂ t + ∇ · − k r g k μ g · ∇ p g + ρ g g − 1 ρ g Q g = 0 (2)

Equations 1, 2 are nonlinear partial differential equations that describe the dynamics of a physical system in both the time and space domains. To obtain a numerical solution, these equations must be discretized in both time and space. This process involves approximating the continuous functions in the equations by a set of discrete values at specific points in the time and space domains.

A combination of the difference method for time discretization and the Galerkin finite element method for space discretization is used to incorporate boundary conditions into the numerical solution. This approach allows for accurate representation of the physical system and efficient computation of the solution.

The system of equations involves five unknowns: saturation, pore water pressure, pore air pressure, water phase relative permeability coefficient, and air phase relative permeability coefficient. The iterative solution is obtained by cyclically resolving Equations 1, 2, employing suitable numerical methods following established academic practices. This approach allows for determining the solution at discrete steps and updating it until convergence is reached. By combining the Galerkin finite element method for spatial discretization with a difference method for temporal discretization, this research aims to obtain accurate and efficient solutions for the water-air two-phase flow system.

2.2 Constitutive equations and parameters

The constitutive equations in the water-air two-phase flow model incorporate the soil water characteristic curve and the relative permeability of water and air. The soil water characteristic curve describes the relationship between the volumetric water content and soil suction. The relative permeability curves of water and air quantify the flow characteristics of each phase relative to the other, in order to accurately represent the dynamics of water and air movement in porous media.

The research used the Van Genuchten, (1980), proposed by van Genuchten in 1980, to describe the soil water characteristic curve. The van Genuchten model is a widely accepted empirical model that relates the soil–water retention curve and hydraulic conductivity to the effective saturation of the soil. It has been widely adopted in scientific literature to simulate the flow behavior of water and air in porous media.where p c is the matric suction, p o is the air-entry pressure, S r w is the residual degree of water saturation, and m is a model parameter that is related to the material. The parameter values were shown as follows: p o = 3.44, S r w = 0.1, m = 0.37.

p c = − p 0 S r − S r w 1 − S r w − 1 m − 1 1 − m (3)

The van Genuchten–Mualem model, developed by Mualem, (1976), was chosen to estimate the relative permeability coefficient of water (Figure 1). This empirical model is commonly used in scientific studies to characterize the relationship between water saturation in porous media and its relative permeability, representing the ability of water to flow through the porous medium compared to that of the air phase. The van Genuchten–Mualem model is widely used in the scientific community due to its ability to capture the nonlinear behavior of water flow in porous media under varying saturation conditions.where k r l is the relative permeability coefficient of water, and n is a model parameter related to the material.

k r l = S r − S r w 1 − S r w 0.5 * 1 − 1 − S r − S r w 1 − S r w 1 / n n 2 (4)

The Brooks, (1965), developed by Brooks and Corey, was chosen to estimate the relative permeability coefficient of air. This empirical model is widely used in scientific research to describe the relationship between air saturation in porous media and its relative permeability, quantifying the ability of air to flow through the porous medium relative to that of the liquid phase. The Brooks–Corey model is well-established in the scientific community and has been widely applied due to its ability to capture the complex flow behavior of air in porous media, including the effects of capillary pressure and pore size distribution. It has been employed in numerous studies to simulate airflow in various porous media systems and has been shown to provide accurate and reliable results in predicting air transport behavior.where k r g is the relative permeability coefficient of air, S r w is the residual degree of water saturation, and S r g is the residual degree of air saturation.

k r g = 1 − S r − S r w 1 − S r w − S r g 2 * 1 − S r − S r w 1 − S r w − S r g 2 (5)

3 Computational model

3.1 Geometric model and material properties

In this study, a one-dimensional numerical model was developed to simulate water-air flow in a homogeneous silica soil column. The soil column (Figure 2), with a height of 40 cm and a diameter of 12 cm, was discretized into 992 computational elements using a computational grid consisting of 1,071 nodes. The grid was designed to be denser near the top of the soil column and sparser toward the bottom. The minimum cell thickness in the computational grid was set to 0.1 cm to ensure accuracy in capturing the dynamics of water-air flow. This numerical model allowed for detailed simulations of the flow behavior in the silica soil column and provided insights into the complex interactions between water and air in porous media.

3.2 Boundary and initial conditions

This research adopted the specified saturation as the initial condition. This approach ensured that the simulations were initiated from a consistent and stable state, reducing potential biases resulting from uncertain initial conditions. Using a stable seepage field as the initial condition provided a robust starting point for investigating the dynamics of water-air flow in the soil column and facilitated a reliable analysis of the research findings.

Several assumptions were made to simplify the model and focus on the specific research objectives. First, it was assumed that rainfall intensity was significantly higher than infiltration intensity, which is a common assumption in studies of water-air flow in soil columns. Second, it was assumed that the surface of the soil column remained saturated throughout the simulation period. This assumption was based on the experimental setup and conditions of the research. In this calculation, the rainfall intensity is set at 50 mm/h, consistent with the subsequent experiments. Additionally, it was assumed that the influence of surface runoff on infiltration was negligible; therefore, surface runoff was not considered in the model. These assumptions were made in order to simplify the model and isolated the influence of other factors on the water-air flow mechanics studied. They were justified based on the specific research context and objectives, and their impact on the research findings was carefully considered and discussed in the analysis of the results.

Two different boundary conditions were applied in this research to investigate the water-air flow behavior in the soil column. The first case was the ventilation condition, where the surface and bottom of the column were set as atmospheric boundaries, and sides of the soil column were considered impermeable boundaries. The second case was the sealing air condition, where the surface of the column was treated as a permeable boundary, while the sides and bottom of the column were considered impermeable boundaries. These boundary conditions were selected to represent different scenarios and study the impacts of boundary conditions on the water-air flow dynamics in the soil column. The choice of these boundary conditions was thoroughly evaluated and justified, considering the research objectives and their direct applicability to real-world scenarios. The application of different boundary conditions provided valuable insights into the behavior of water and airflow in the soil column under different conditions and enhanced the understanding of the research findings.

3.3 Boundary permeability

The air-sealing state of the soil boundary is influenced by several factors, including the geometric size, water content, and pore characteristics of the soil in the boundary region. The soil’s flow rate under a unit of air pressure is used as an indicator to establish a standardized measure of air permeability. Relative permeability, a dimensionless variable, is the ratio of the air flow rate at the bottom boundary to the air saturation flow rate at the top boundary.where η is the relative permeability (dimensionless unit), v d is the airflow rate at the bottom boundary of the column (cm / ⁡ min), and v u is the airflow rate at the surface boundary of the column (cm / ⁡ min).where k r g is the air permeability coefficient at the boundary region, k is the intrinsic permeability coefficient, μ g is the air viscosity coefficient at the boundary region, and i is the pressure gradient under unit pressure at the boundary region.where μ g is the saturated air velocity for unit gradient.

η = v d v u (6)

v d = k r g k μ g · i (7)

v u = 1 · k μ g · 1 (8)

During the research process, the influence of different boundary permeability conditions on infiltration was calculated using examples with initial saturations of 15% and 60%. A permeability of 0 indicates a completely airtight boundary at the bottom, while a permeability of 1 indicates a completely permeable boundary.

4 The influence of boundary condition on rainfall infiltration

4.1 The influence of ventilation and sealing air condition on rainfall infiltration

4.1.1 Effect of initial saturation on saturation distribution under ventilation and sealing air conditions

The distribution of saturation in the soil column was analyzed under both ventilation and sealed air conditions, with initial saturation levels of 60% and 15%, as presented in Figures 3, 4. The distribution of saturation along the depth was influenced by matric suction and the relative permeability of the water phase. In cases of lower initial saturation, matric suction in the soil was higher, resulting in a more intense inflow of water into the soil element. However, at this point, the relative permeability coefficient of the water phase was lower, resulting in a decrease in the outflow intensity of water. This difference between inflow and outflow intensity contributed to a steeper wetting front in the column. In contrast, scenarios with higher initial saturation levels resulted in water infiltration predominantly occurring through narrower pathways. As a result, the difference between the inflow and outflow intensities was minimal, leading to a relatively moderate advancement of the wetting front. Additionally, under the closure condition, the pressure of pore air was much higher than in ventilated condition, impeding the infiltration of water. Consequently, when considering the same initial saturation condition and depth, the soil column exhibited significantly higher saturation levels when exposed to ventilation compared to being sealed.

4.1.2 Effect of ventilation and closure conditions on air pressure

At the closure condition, when the surface was saturated, a significant and rapid increase in pore air pressure was observed. This phenomenon was profoundly influenced by variations in surface ventilation conditions and the processes of water infiltration and squeezing within the soil matrix. During the initial stages of saturation, a high degree of water infiltration led to extrusion, generating pore air. However, due to the limited time for pore air diffusion in the soil, there is an upper limit on the maximum attainable pore air pressure, as shown in Figure 5. As the rate of infiltration gradually decreased, there was a consequential enhancement in pore air mobility within the soil. Consequently, the pore air pressure underwent a slow decline, eventually stabilizing. This stabilization marked the point where the extent of water penetration tends to reach a state of equilibrium.

In the initial stage of ventilation, as the surface of the soil column became saturated, there was a noticeable increase in pore air pressure. This increase resulted from a significant amount of water infiltrating and squeezing, leading to the formation of pore air. Once the soil column reached saturation, the release of pore air became concentrated at the bottom. When the bottom boundary remained open, more air entered from below, impeding water infiltration and restricting the release of pore air from the top. Due to a slightly faster release of pore air pressure compared to its generation rate, the pore air pressure gradually exhibited a downward fluctuation trend.

4.2 The influence of air permeability boundary on rainfall infiltration

4.2.1 Effect of initial saturation on saturation distribution under ventilation and sealing air conditions

The capability of infiltration, a crucial parameter in rainfall infiltration, is influenced by the saturated permeability coefficient of soil and the hydraulic gradient, following Darcy’s law. For the purpose of analysis and comparison, the relative infiltration capability is adopted to measure the effectiveness of rainfall infiltration. This dimensionless variable is defined as the ratio of the rainfall infiltration rate to the saturated permeability coefficient of the soil. The saturated permeability coefficient is solely related to the soil itself, so the infiltration rate is essentially determined by the hydraulic gradient. During the initial phase of rainfall infiltration, the surface soil had low saturation, and the liquid pathways within the pores were relatively narrow; as a result, a higher hydraulic gradient was needed to enable the flow. Furthermore, in this stage, capillary suction was also significant, requiring water to overcome this force to facilitate movement, necessitating a larger hydraulic gradient. Consequently, the infiltration rate was high during the early infiltration period. As the duration of rainfall increased, soil saturation levels rose, matric suction decreased rapidly, followed by a decline in the hydraulic gradient. Therefore, the infiltration rate showed a relatively large decline at the beginning and then remained stable. When the soil surface became saturated, pore air became trapped in the pores. As shown in Figure 6, with continuous infiltration, pore air was squeezed by water, causing a rapid increase in pore air pressure and a potential blocking effect on water infiltration. The pore air pressure produced by the effect of pore air being squeezed by water infiltration varied under different boundary air permeability conditions. A smaller boundary air permeability led to a faster increase in pore air pressure, which then remained at a relatively higher level. Moreover, the smaller the boundary air permeability, the greater the resistance to water phase infiltration, resulting in a smaller infiltration rate. This observation suggested that water infiltration ability was influenced by air permeability conditions, leading to a reduced infiltration rate under low air permeability (Figure 7).

The influence of boundary air permeability on the saturation distribution was particularly pronounced in the shallow soil layer. The rate of decrease of the wetting front was slower when the boundary air permeability was low. The impact of boundary air permeability on soil saturation was closely associated with the duration of rainfall infiltration. Specifically, as the duration of rainfall increased, the influence of boundary air permeability on infiltration became more prominent. This observation can be attributed to the decrease in the magnitude of infiltration, resulting in a larger impact of air permeability on the accumulated infiltration amount during a longer rainfall duration, leading to a slower decline of the wetting front.

4.2.2 Effect of air permeability on infiltration capability

This study simulated the influence of the relative capability of infiltration under different air permeability boundary conditions, with an initial saturation set at 15%. As depicted in Figure 8, the findings indicated a direct relationship between soil boundary air permeability and the stable capability of infiltration. With an increase in the air permeability of the soil boundary, the stable infiltration capability also exhibited a corresponding rise. Notably, the sensitivity of the infiltration capability to variations in boundary permeability was much more pronounced when the soil permeability was low, gradually diminishing as the air boundary permeability increased. These results suggest that the impact of air boundary permeability on the infiltration capability was much more significant in soils characterized by lower permeability levels.

To further investigate the relationship between boundary permeability and stable infiltration strength, a logarithmic function was fitted to the data: y = 0.0987 ln(x) + 1.7329, where y represents the capability of infiltration, and x represents the boundary permeability. The fitting determination coefficient (R ²) was 0.9938, indicating a good fit of the logarithmic function to the data. The fitting relationship in Figure 8 is based solely on numerical simulation results and has not yet been experimentally validated.

Additionally, the process of rainfall infiltration involves the alternating flow of water and air in the soil pores. The movement of the air phase inevitably influences the infiltration of the water phase. When the boundary permeability is poor, and the air phase is trapped in the soil pores, the blocking effect of air on capability of infiltration becomes apparent.

4.3 Comparison with GeoStudio

4.3.1 Numerical model in GeoStudio

The soil column (Figure 9), 40 cm in height and 12 cm in diameter, was discretized into 992 computational elements using a grid of 1,071 nodes in the GeoStudio software for simulation and result validation. The boundary and initial conditions for the calculation process align with those outlined in Section 2.3.2.

4.3.2 Comparison of pore air pressure with the two-phase model

‘Relative error’ denotes the measure of accuracy in an approximation compared to the true or exact value. It is typically expressed as the absolute difference between the estimated value and the true value, divided by the absolute value of the true value. In this research, ‘relative error’ specifically pertains to the comparison between the simulation results from GeoStudio and the modelled results.

In this research, the relative error is calculated using the following formula:

R e l a t i v e e r r o r = M o d e l l e d v a l u e − G e o s t u d i o v a l u e M o d e l l e d v a l u e * 100 % (9)

In the ventilation condition, a comparison was conducted between the calculated pore air pressure using GeoStudio software and the results obtained from simulating a two-phase flow model (Figure 10). The accompanying graph visually illustrated this comparison. Both simulations indicated the challenge of achieving stable air pressure within the slope under identical temporal conditions, revealing noticeable fluctuations. A more detailed examination of the error between the two simulations showed that the deviation falls within a 30% range, aligning with expectations (Figure 11). This level of difference is considered acceptable within the predetermined margin of error, suggesting reasonable agreement between the two simulation methods.

In the closure condition, a comparison was conducted between the calculated pore air pressure using GeoStudio software and the results obtained from simulating a two-phase flow model (Figure 12). Both simulation results indicated that under the closure condition, the pore air pressure exhibited an initial increase followed by a gradual trend toward stabilization. Analyzing errors in both simulation scenarios revealed a clear pattern in error changes over the course of the infiltration duration (Figure 13). Initially, the error decreased, followed by an upward trend. Particularly noteworthy was the divergent pattern observed during the start and end phases of infiltration. However, throughout the entire analysis, the error consistently remained below 30%. Consequently, the simulation results can be considered reliable.

Figures 14, 15 showed the contour plots of the GeoStudio and two-phase flow simulation results at the same time instant under fully ventilated and fully closed conditions. Under the ventilation condition (Figure 14), a significant observation was the notable increase in pore pressure at the base of the soil column, contrasting with the minimal pressure observed at the top, approaching zero. This consistent trend was replicated in both GeoStudio and the two-phase flow model, perfectly conforming to the anticipated behavior in closure conditions. Meanwhile, under the closure condition (Figure 15), a distinct scenario unfolded. Pore pressure at the top and bottom of the soil column, corresponding to the ventilated regions, converged toward zero. Notably, the point of maximum pore pressure shifted to the midsection of the soil column, gradually decreasing with prolonged rainfall. This observed pattern closely aligned with theoretical expectations, offering valuable insights into the nuanced interplay of ventilation and rainfall duration on the dynamic pore pressure distribution within the soil column.

5 Experiment validation

5.1 Experimental apparatus

Water infiltration may amplify soil moisture and elevate pore water pressure, reducing soil strength and jeopardizing slope stability. A more profound scientific understanding of these phenomena can help forecast and mitigate landslides triggered by rainfall events. The process of water infiltration in a soil slope can be effectively modeled using a one-dimensional vertical model (Figure 16) of the slope soil column. To investigate the intricate process of water infiltration along the soil profile, an experimental apparatus was designed and developed to monitor soil moisture and pore air pressure at distinct depths.

The experimental model of this study comprises a test sample, a rainfall simulation system, and an automatic data acquisition system. Precision placement of pressure and soil moisture sensors at multiple predetermined positions along the soil column was implemented to ensure accurate measurements. Figure 17 illustrates a schematic diagram of this experimental setup, outlining the key components and their interconnection.

The experimental setup consisted of a cylindrical container made of plexiglass, measuring 40 cm in height and 12 cm in diameter. The plexiglass cylinder was equipped with pressure sensors at heights of 11 cm, 22 cm, and 33 cm, and moisture sensors at heights of 10 cm, 20 cm, and 30 cm to collect data during the experiment. The materials and their arrangement in the cylinder were chosen to mimic a real-world soil profile, and the setup was designed to measure and monitor variations in pressure and soil moisture at different depths during the test.

Rainfall simulation system. The proposed rainfall simulation system is capable of simulating a range of rainfall intensities while maintaining a nearly uniform spatial distribution of rain rate. The system utilized a pump as the water supply source to generate rainfall over the soil surface, with the intensity of the rainfall regulated through the precise combination of a sprinkler and water pressure settings. This enabled controlled manipulation of the rainfall intensity, making it replicable in experimental conditions. The resulting rainfall was uniformly distributed across the soil surface, mimicking natural rainfall patterns. According to the Royal Meteorological Institute of Belgium, rainfall-induced landslides easily occur when the rainfall intensity exceeds 50 mm/h; the maximum rainfall intensity recorded in Belgium is about 142 mm/h. Therefore, for this study, the model tests were conducted at the minimum value of 50 mm/h.

Data acquisition system. In the experimental setup, data collection involved measurements of air pressure, soil moisture, and rainfall infiltration during the rainfall process. Pressure transducers used for this purpose were Honeywell 24 P C/26 P C Series Low Pressure Sensors. These sensors are available in gauge or differential configurations and are constructed using a four-active-element piezoresistive bridge design. The gauge sensors reference atmospheric pressure, while the differential sensors allow for the simultaneous measurement of two independent pressure sources. EVTSCAN soil moisture sensors were employed to measure soil moisture in the experiment. Known for their high precision, fast response time, and stable output, these sensors are suitable for accurate soil moisture measurement. A 50 L bucket served as the water supply source, with slope surface runoff collected into the bucket after being filtered. The mass of the bucket was monitored in real time to measure the rainfall infiltration during the experiment.

5.2 Soil materials used in the tests

Sandy soil landslides are prevalent in numerous countries, particularly in mountainous regions characterized by abundant rainfall (Maurizio Polemio, 1999; Uchimura et al., 2009; von Ruette et al., 2013). Silica sands are extensively employed in laboratory experiments to investigate the failure mechanisms associated with rain-induced landslides triggered by Wang and Sassa, (2003). Silica sands were used to examine the water infiltration process under a single rainfall intensity. Table 1 presents the fundamental physical properties of the silica sands, including specific gravity, dry density, void ratio, and permeability coefficient. Furthermore, Figure 18 illustrates the grain-size distributions of the silica sands.

TABLE 1. Physical properties of soils used in this study.

5.3 Experimental process

5.3.1 Experiment preparation

The air tightness of this setup was assessed before the experiment. An exhaust hole and a reliable valve were positioned at the bottom of the soil column, enabling limited air discharge through the specimen’s upper surface when the valve was closed. The soil sample was then sealed with a glass cover, and a predetermined pressure was applied through the bottom valve to assess air tightness. Satisfactory air tightness was determined by observing air pressure dissipation rates below 1% per hour. A rainfall infiltration test was conducted after a 3-day stabilization period to minimize the impact of initial conditions and air tightness monitoring. Monitoring of indicators continued until stability was achieved. Additionally, the water tank was covered to mitigate evaporation, and a thin glass plate carefully covered the top of the soil sample to prevent moisture loss.

5.3.2 Model experiment under ventilation condition

The experiment was initiated by opening the exhaust vent at the base of the soil column to simulate and observe the water infiltration process under rainfall conditions. Real-time data from multiple sensors were diligently recorded throughout the experiment. As soon as water accumulation was observed in the gravel layer at the bottom of the soil sample, the rainfall was promptly halted. Subsequently, continuous monitoring of the sensor data ensued until all measurements stabilized, indicating the completion of the experiment.

5.3.3 Model experiment under sealed air condition

Considering that the test sample was permeated under ventilated conditions, resulting in water-filled pores in the soil, it was deemed unsuitable to continue the model experiment under air-sealed conditions. Hence, a new sample was prepared, following the same filling standards and using the same material as the previous sample, to conduct the model test under air-sealed conditions. The experimental conditions were meticulously maintained to ensure consistency with the ventilation condition test. Long-term monitoring was conducted, and the model test was concluded only when all relevant parameters had stabilized, signifying the completion of the experiment.

5.3.4 Model experiments under different boundary permeability conditions

In order to establish controlled boundary permeability conditions, the bottom of the soil column was filled with soil samples that were saturated to varying levels. The soil used for the model test under air-sealing conditions was prepared to meet the same filling standard and was composed of the same material as in the previous experiments. Prolonged monitoring was conducted to observe the behavior of various parameters, and the model test was concluded when all parameters achieved a stable state.

5.4 Experimental results

Comprehensive data were collected and meticulously monitored during the entire duration of this experiment. The analysis in this study encompassed the examination of the rainfall infiltration rate, variations in water content, and air pressure. These variables were thoroughly investigated and assessed to derive meaningful insights and draw valid conclusions within the scope of this research.

5.4.1 The monitoring result of infiltration rate

The determination of the rainfall infiltration rate was accomplished by recording the weight of the bucket during infiltration experiments conducted under two distinct conditions: ventilation and closure (air sealing). The experiments were conducted for 40 min, and the obtained results were compared. Figure 19 presents the findings, illustrating the gradual decline of the rainfall infiltration rate until reaching a stable state under both conditions, albeit with varying convergence values. Initially, a minimal disparity was observed in the infiltration rate between ventilation and air-sealing conditions, measuring 0.81 cm/s and 0.82 cm/s, respectively. However, as the rainfall continued infiltrating the soil column, a rapid decrease in the infiltration rate was observed, with a steeper decline evident under the air-sealing condition. This phenomenon can be attributed to the inhibitory effect of enclosed air on rainwater infiltration, resulting in reduced permeability. Furthermore, the time required to achieve a stable state was significantly prolonged under the air-sealing condition, likely due to the obstructive impact of enclosed air on the infiltration process. Ultimately, the infiltration rate stabilized at approximately 0.0035 cm/s and 0.002 cm/s under ventilation and air-sealing conditions, respectively. These findings highlight the substantial reduction in rainfall infiltration rate caused by air sealing, leading to decreased permeability and an extended duration to attain a stable state.

5.4.2 The monitoring result of moisture content

Figures 20–22 depict the temporal evolution of water content at various depths within the soil column. The results illustrate a similar distribution pattern of water content in the soil column under both ventilation and air-sealing conditions during the initial 30-min period. However, as the surface soil approached saturation, a distinct difference in the rate of wetting front advancement became evident between the two conditions.

Specifically, under air-sealing conditions, the wetting front exhibited a significantly slower progression compared to situations with ventilation. Consequently, considerable differences arose in the water content distribution throughout the soil column. The observed temporal dynamics highlight the critical influence of ventilation on the infiltration process and subsequent water content distribution within the soil column as it approaches saturation.

5.4.3 The monitoring result of pore air pressure

The findings presented in Figures 23, 24 exhibit substantial variations in air pressure measurements within a soil column at different depths, depending on air sealing or ventilation conditions. Specifically, under the air-sealing condition, the mean air pressure within the soil column was noticeably higher than in situations with ventilation. Conversely, establishing stable air pressure within the soil column proved challenging under the ventilation condition, as significant fluctuations were observed. Conversely, infiltration rapidly increased the air pressure along the slope when the air-sealing condition was maintained. While minor fluctuations were present after reaching a certain threshold, the overall range of fluctuation remained minimal. These observations emphasized the pronounced impact of air sealing or ventilation on the dynamic behavior of air pressure within soil columns, thus emphasizing the necessity for controlled experimental conditions to measure and interpret air pressure data in soil systems accurately.

In this study, only fully ventilated and fully sealed conditions were tested. No different soil densities were used, and no adjustable air valve was installed. Therefore, boundary air permeability was simulated only through numerical modeling, and boundary air permeability was not considered in the experimental process.

6 Conclusion

Soil can be considered a material with relatively low air permeability, situated between air-permeable and air-impermeable conditions. This study proposes a measurement index for the relative air permeability of soil and investigates its impact on infiltration. The paper explores the influence of boundary air permeability on various aspects of the rainfall infiltration process, including the magnitude of infiltration, pore pressure, wetting front advancement, and saturation distribution. The analysis is based on water-air two-phase flow theory and the finite element method. The following conclusions were drawn from the study:

• Two comparisons were conducted between the calculated pore air pressure under ventilation and closure conditions using GeoStudio software and the results obtained from simulating the two-phase flow model. Both comparisons showed that the error consistently remained below 30%, indicating that the simulation results can be considered reliable.
• The results of the calculations revealed a logarithmic relationship between the capability of infiltration and the boundary air permeability. Specifically, a decrease in air permeability corresponded to a decline in the extent of infiltration. Moreover, as the air permeability further decreased, the influence of pore air on the rate of change in the extent of infiltration became increasingly pronounced.
• The results obtained from the rainfall infiltration test conducted under impermeable conditions at the base of the soil mass revealed the significant impact of boundary air permeability on the dynamics of pore air pressure. This influence was linked to the effectiveness of water vapor extrusion, closely associated with the boundary air permeability condition. When air fluidity was restricted, pore air pressure increased, supporting the saturated surface region. Consequently, water infiltration was obstructed, leading to a reduction in the rate of water permeation. Pore air pressure during the water-air extrusion process was significantly affected by the soil’s pore structure, moisture content, and the maximum pore air pressure gradient that can develop within the soil. Excessive pore air pressure gradients within the soil resulted in continuous air breakthroughs within the pore channels, eventually leading to air overflow from the soil surface. This phenomenon induced fluctuations in pore air pressure, albeit centered around a relatively stable value.
• The air generated during rainfall infiltration significantly hindered the percolation of rainwater, leading to an overall reduction in the infiltration rate. Furthermore, the intricate interplay between the infiltration rate, water content, and porosity during rainfall resulted in coordinated variations in air pressure. This observation underscored the coupled effect of water and air during infiltration, laying the groundwork for subsequent in situ testing endeavors.
• The results indicate that air sealing significantly reduces the infiltration rate and alters the distribution of the saturated zone, which may increase the risk of shallow slope instability during rainfall. These findings provide a basis for optimizing ventilation measures and air permeability boundaries in slope engineering, and have reference significance for landslide prevention.

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Footnotes

Edited by: Luchuan Ding, Tongji University, China

Reviewed by: Yiping Gan, Putian University, China

Jinquan Shi, The Hong Kong University of Science and Technology, Hong Kong SAR, China