One-dimensional Infiltration Research Articles

Development and Application of a New Open-Source Integrated Surface–Subsurface Flow Model in Plain Farmland

Accurately characterizing rainfall runoff processes in plain farmland, especially at the plot scale with significant micro-topographic features, has presented challenges. Integrated surface–subsurface flow models with high-precision surface flow modules are appropriate tools, yet open-source versions are rare. To address this gap, we proposed an open-source integrated surface–subsurface flow model called the FullSWOF-Plain model, in which the one-dimensional subsurface module Hydrus-1D was integrated with a modified two-dimensional surface water flow module (FullSWOF-2D) using the sequential head method. Various experimental scenarios were simulated to validate the model’s performance, including two outflow cases (i.e., 1D and 2D) without infiltration, a classical one-dimensional infiltration case, and two typical rainfall events at the experimental field. The results demonstrate the accuracy of this proposed model, with the Nash–Sutcliffe efficiency (NSE) of the simulated discharge exceeding 0.90 in the experimental field case and the root mean squared error (RMSE) values for soil moisture at five depths consistently below 0.03 cm3/cm3. However, we observed a lag in the simulated response time of soil moisture due to the neglect of preferential flow. The micro-topography significantly influenced ponding time and ponding areas. Lower local terrain normally experienced earlier surface ponding. Scattered surface ponding water first occurred in the ditch and followed in the relatively low areas in the main field. The concentration process of surface runoff exhibited hierarchical characteristics, with the drainage ditch contributing the most discharge initially, followed by the connection of scattered puddles in the main field, draining excess surface water to the ditch through rills. This quantitative study sheds light on the impact of micro-topography on surface runoff in plain farmland areas.

One-dimensional infiltration in a layered soil measured in the laboratory with the mini-disk infiltrometer

Abstract Layered soils can consist of a thin little permeable upper layer over a more permeable subsoil. There are not many experimental data on the influence of this upper layer on infiltration. The mini-disk infiltrometer set at a pressure head of –3 cm was used to compare infiltration of nearly 40 mm of water in homogeneous loam and clay soil columns with that in columns made by a thin layer (1 and 3 cm) of clay soil over the loam soil. For each run, the Horton infiltration model was fitted to the data and the soil sorptivity was also estimated by considering the complete infiltration run. For the two layered soils, the estimates of initial infiltration rate and decay constant were similar but a thicker upper layer induced 2.4 times smaller final infiltration rates. Depending on the infiltration parameter and the thickness of the upper layer, the layered soils were characterized by 2.2–6.3 times smaller values than the loam soil and 2.2–6.6 higher values than the clay soil. Sorptivity did not differ between the homogeneous clay soil and the layered soil with a thick upper layer and a thin layer was enough to induce a decrease of this hydrodynamic parameter by 2.5 times as compared with that of the homogeneous loam soil. Even a thin upper layer influences appreciably infiltration and hydrodynamic parameters. Layering effects vary with the thickness of the upper layer and the considered parameter. The applied experimental methodology could be used with other soils and soil combinations.

A Dimension-Reduced Line-Element Method to Model Unsaturated Seepage Flow in Porous Media

Contrary to the continuum hypothesis, which averages water flow across the entire domain, including both grains and pores, the line-element model concentrates unsaturated flow in the pore space in the intermediate region of horizontal and vertical channels. The flux equivalent principle is used to deduce the equivalent unsaturated hydraulic conductivity, the flow velocity and the continuity equations. It is found that the relative hydraulic conductivities derived from the line-element model and the continuum model are identical. The continuity equations in the two models are also similar, except that the coefficient in the water content term is half that in the line-element model. Thus, the unsaturated flow problem in porous media is transformed into a one-dimensional problem. A dimension-reduced finite line-element method is proposed that includes a complementary algorithm for Signorini’s-type boundary conditions involving the seepage-face boundary and the infiltration boundary. The validity of the proposed model is then proved by good agreement with analytical, experimental and simulated results for one-dimensional infiltration in a vertical soil column, unsaturated flow in a sand flume with drainage tunnels, and transient unsaturated flow water-table recharge in a soil slab, respectively. In general, the proposed method has good computational efficiency, especially for smaller mesh sizes and short time intervals.

Effect of the Mid-Layer on the Diversion Length and Drainage Performance of a Three-Layer Cover with Capillary Barrier

The capillary barrier is a type of soil cover system commonly used in various geotechnical applications, such as limiting infiltration for slopes or landfills or providing cover for solid waste. It serves to prevent the movement of water through the soil layers by utilizing contrasting particle sizes. This paper focuses on investigating the effect of the granular layer on the performance of a three-layer cover with a capillary barrier, integrating the granular layer within clayey sand. The investigation involved one-dimensional infiltration tests utilizing four uniform granular soils with varying grain sizes. These tests were instrumental in calibrating soil water characteristic curves and hydraulic conductivity curves via back analysis. Subsequently, numerical analyses were conducted using a 15 m long model for each of the four distinct cover types. The results indicated that the fine gravel significantly improved the barrier performance beyond one-dimensional tests, owing to its high permeability and the influence of the slope. After the capillary barrier failure, the intermediate layers transitioned into efficient drainage layers, particularly in the gravel layer with the highest lateral drainage capacity. Clayey sand at the bottom delayed percolation, thereby supporting the conversion of the intermediate layer into an effective drainage component. Overall, the multi-layer system showed superior percolation performance compared to the clayey sand cover lacking a granular layer.

Analysis of Water Volume Required to Reach Steady Flow in the Constant Head Well Permeameter Method

The most common method for in situ measurement of saturated hydraulic conductivity (Ksat) of the vadose zone is the constant head well permeameter method. Our general objective is to provide an empirical method for determining volume of water required for measuring Ksat using this procedure. For one-dimensional infiltration, steady state reaches as time (t) → ∞. For three-dimensional water flow from a cylindrical hole under a constant depth of water, however, steady state reaches rather quickly when a saturated bulb forms around the hole. To reach a quasi-steady state for measuring Ksat, we assume an adequate volume of water is needed to form the saturated bulb around the hole and increase the water content outside of the saturated bulb within a bulb-shaped volume of soil, hereafter, referred to as wetted soil volume. We determined the dimensions of the saturated bulb using the Glover model that is used for calculating Ksat. We then used the values to determine the volume of the saturated and wetted bulbs around the hole. The volume of water needed to reach a quasi-steady state depends on the difference between the soil saturated and antecedent water content (Δθ). Based on our analysis, between 2 and 5 L of water is needed to measure Ksat when Δθ varies between 0.1 and 0.4 m3 m−3, respectively.

Influence of Interlayer Soil on the Water Infiltration Characteristics of Heavy Saline–Alkali Soil in Southern Xinjiang

Interlayer soil is common in southern Xinjiang, because interlayer can reduce the infiltration rate of soil water. To simulate the interlayer soil in heavy saline–alkali cotton fields, this paper adopted a vertical one-dimensional infiltration test. T1 (315 mm), T2 (270 mm), and T3 (225 mm) and different interlayer positions (T5, 315 mm) and thicknesses of the interlayer (T6, 315 mm) with the same irrigation volume, as well as one perforation and sand filling treatment (T4, 315 mm), were set. The influence of different irrigation amounts, locations, and thicknesses of the interlayer and sand injection on water infiltration was analyzed. The analysis results showed that with the increase in irrigation amount, the water infiltration rate and the migration distance of the wet front increased, but did not penetrate to the bottom soil (90 cm). Under the same irrigation volume, the increase in interlayer thickness (T6) compared with the increase in interlayer position (T5), the change in soil moisture content in the upper and lower layers of the interlayer was greater, and the advance time of wetting front migration and cumulative infiltration were slightly higher. After tunneling and sand filling (T4), the infiltration rate of water was increased, the migration time of the wet front was reduced, and the profile water content of each soil layer was improved. The Kostiakov model could better simulate the water infiltration characteristics of interlayer soil with different profile configurations in heavily saline–alkali land. The results showed that in all of the treatments, only the wet front of the soil moisture reached 100 cm in the T4 treatment, and the maximum was only 87.8 cm in the other treatments, indicating that too little irrigation water or the upward movement and thickening of the interlayer were not conducive to water infiltration. For the interlayer soil area in the heavy saline–alkali land in southern Xinjiang, the appropriate irrigation water should be more than 315 mm. The treatment of drilling first and then filling sand can be used as a simple but effective measure to increase the water infiltration rate of the interlayer soil, and can thus be applied to the layered soil structure in the interlayer position of 60–80 cm.

One−Dimensional Seepage of Unsaturated Soil Based on Soil−Water Characteristic Curve

The uneven pore water distribution in unsaturated soil will cause water movement, change the hydraulic and mechanical characteristics of soil, and then cause soil damage. Therefore, it is important to study the hydraulic characteristics of unsaturated soil. In this paper, the law of conservation of mass and Darcy’s law were used to analyze the unit soil after seepage to obtain a continuous equation. Combined with the soil-water characteristic curve (SWCC), the effect of matric suction and permeability coefficient of unsaturated soil on infiltration rate is substituted into the equation. Through the analysis of pore water stress of the unit soil, the function of the unsaturated permeability coefficient with the effective saturation degree is obtained, and the theoretical formula of the one-dimensional infiltration rate of unsaturated soil is derived. Compared with other models, this formula has fewer parameters and is easy to use.

Quantifying and assessing the infiltration potential of green infrastructure in urban areas using a layered hydrological model

Spatial heterogeneity in hydrological responses is an important element in urbanized watersheds. One of the main challenges in simulating urban hydrology is the lack of layered information and knowledge of the true infiltration potential of stormwater infrastructure systems. In this study, changes in the infiltration characteristics of three green infrastructures (GIs), with and without underground barriers, were simulated during a designed rain event in Xiamen, China, using a layered, one-dimensional infiltration model. The variations in the maximum infiltration rate (MIR) and cumulative infiltration (CI) for permeable pavements, vegetative swales, and rain gardens were found to differ in response to 204 scenarios of pervious material thickness, even though they were linearly correlated. Comparisons between the GIs, with and without barriers, revealed that the MIR was almost unchanged, while CI varied considerably with the depth to the impervious layer. To explore the impacts of barriers on infiltration potential, simulations with depths to the impervious layer from 700 to 1000 mm were compared. We statistically evaluated the infiltration potential with all possible scenarios for the GIs. Identifying the potential impacts of infiltration processes beneath GI can be beneficial in urban stormwater management.

Pathways and Estimate of Aquifer Recharge in a Flood Basalt Terrain; A Review from the South Fork Palouse River Basin (Columbia River Plateau, USA)

Aquifer recharge is one of the most important hydrologic parameters for understanding available groundwater volumes and making sustainable the use of natural water by minimizing groundwater mining. In this framework, we reviewed and evaluated the efficacy of multiple methods to determine recharge in a flood basalt terrain that is restrictive to infiltration and percolation. In the South Fork of the Columbia River Plateau, recent research involving hydrologic tracers and groundwater modeling has revealed a snowmelt-dominated system. Here, recharge is occurring along the intersection of mountain-front alluvial systems and the extensive Miocene flood basalt layers that form a fractured basalt and interbedded sediment aquifer system. The most recent groundwater flow model of the basin was based on a large physio-chemical dataset acquired in laterally and vertically distinctive locations that refined the understanding of the intersection of the margin alluvium and the spatially variable basalt flows that filled the basin. Modelled effective recharge of 25 and 105 mm/year appears appropriate for the basin’s plain and the mountain front, respectively. These values refine previous efforts on quantifying aquifer recharge based on Darcy’s law, one-dimensional infiltration, zero-flux plane, chloride, storage, and mass-balance methods. Overall, the combination of isotopic hydrochemical data acquired in three dimensions and flow modelling efforts were needed to simultaneously determine groundwater dynamics, recharge pathways, and appropriate model parameter values in a primarily basalt terrain. This holistic approach to understanding recharge has assisted in conceptualizing the aquifer for resource managers that have struggled to understand aquifer dynamics and sustainable withdrawals.

Analysis of unsaturated seepage in infinite slopes by means of horizontal ground infiltration models

This paper describes a simple methodology to calculate the two-dimensional seepage across an infinite unsaturated slope using models of one-dimensional infiltration through horizontal ground. The methodology decomposes the seepage across the infinite slope into antisymmetric and symmetric parts, whose respective solutions are combined to calculate the actual flow regime. The antisymmetric solution is trivial and does not even require integration of the governing continuity equation, while the symmetric solution, albeit non-trivial, reduces to the case of one-dimensional flow through horizontal ground, for which solutions already exist. The methodology is generally applicable to the calculation of distinct seepage regimes across unsaturated slopes with different hydraulic properties under both stationary and transient conditions. The paper also defines the gradient of the piezometric head parallel to the slope, which is the Neumann boundary condition to be imposed on slope sections perpendicular to the ground surface. The rigorous definition of this gradient overcomes the need of imposing arbitrary boundary conditions in finite-element models. Finally, the paper demonstrates that all infiltrated water crosses the slope along the shortest path – namely, the path normal to the surface – while the flow parallel to the slope is entirely fed by an upstream source at infinite distance.

Analytical solution for coupled hydro-mechanical modeling of infiltration in unsaturated soils

Simulating water infiltration in unsaturated soils is an important step in analyzing a wide range of engineering and geosciences applications. The infiltration problem inherently possesses a coupled hydro-mechanical problem in which the unsaturated flow and the soil deformation interact and affect each other. This hydro-mechanical coupling, however, has been ignored in the majority of existing analytical solutions, mainly due to the complexity associated with the mathematical derivation. This paper presents a novel analytical solution for coupled hydro-mechanical modeling of one-dimensional (vertical) infiltration in unsaturated soils. We present an analytical solution for two problems where infiltration is applied at the top boundary as a constant pressure head (first problem) or as a constant flow rate (second problem). A parametric study was performed to examine the effects of hydro-mechanical coupling and various soil parameters on pressure head and strain profiles versus depth. Results reveal that the coupling effect can be pronounced for various values of saturated hydraulic conductivity, Gardner’s α parameter, and Young’s Modulus. The solution can be readily incorporated into site-specific (e.g., groundwater modeling, slope stability) or regional-scale (e.g., landslide mapping) analyses of unsaturated natural and man-made slopes and earthen structures subject to infiltration. Further, the presented analytical framework offers a benchmark for the validation of numerical methods.

Experimental Investigation of the Different Polyacrylamide Dosages on Soil Water Movement under Brackish Water Infiltration.

The use of soil conditioners in conjunction with brackish water irrigation is critical for the efficient development and use of brackish water as well as the enhancement of the structure of saline soil and stimulating crop growth. This study investigated the effects of different polyacrylamide (PAM) dosages (0, 0.02%, 0.04%, and 0.06%) on the water flow properties of sandy loam during brackish water infiltration using one-dimensional vertical and horizontal soil column infiltration experiments. The results showed that: (1) PAM could lower the soil infiltration rate and increase soil water retention performance under brackish water infiltration conditions. (2) PAM had a significant effect on the parameters of the Philip and Kostiakov infiltration models. The soil sorption rate S and the empirical coefficient λ were the smallest, and the empirical index β was the largest when the PAM dosage was 0.04%. (3) PAM dosage displayed a quadratic polynomial connection with the soil saturated water content and the saturated hydraulic conductivity. The soil saturated water content was highest when the PAM dosage was 0.04%, the intake suction hd of the Brooks-Corey model increased by 15.30%, and the soil water holding capacity was greatly improved. (4) Soil treated with PAM could absorb more water under the same soil water suction, whereas the soil unsaturated hydraulic conductivity and its growth rate decreased. The soil saturated diffusion rate Ds, as well as the soil water diffusion threshold, rose. Finally, the 0.04% PAM dosage could improve soil hydrodynamic characteristics under brackish water infiltration, which is beneficial for the efficient utilization of brackish water.

An Analytical Solution of the One-Dimensional Steady-State Van Genuchten-Based Infiltration Equation for a Heterogeneous Soil with a Root-Water Extraction Function

An Analytical Solution of the One-Dimensional Steady-State Van Genuchten-Based Infiltration Equation for a Heterogeneous Soil with a Root-Water Extraction Function

Capillary Barriers during Rainfall Events in Pyroclastic Deposits of the Vesuvian Area

In the present paper, the capillary barrier formation at the interface between soil layers, which is characterized by textural discontinuities, has been analyzed. This mechanism has been investigated by means of a finite element model of a two-layer soil stratification. The two considered formations, belonging to the pyroclastic succession of the “Pomici di Base” Plinian eruption (22 ka, Santacroce et al., 2008) of the Somma–Vesuvius volcano, are affected by shallow instability phenomena likely caused by progressive saturation during the rainfall events. This mechanism could be compatible with the formation of capillary barriers at the interface between layers of different grain size distributions during infiltration. One-dimensional infiltration into the stratified soil was parametrically simulated considering rainfall events of increasing intensity and duration. The variations in the suction and degree of saturation over time allowed for the evaluation of stability variations in the layers, which were assumed as part of stratified unsaturated infinite slopes.

An improved genetic algorithm for determining modified water-retention model for biochar-amended soil

Biochar has been globally recognized as a soil amendment to ameliorate the degraded soil structures. We investigated the different biochar percentages contributed to the changes in soil water retention, soil infiltration, and water-holding capacity of one dimensional scale. Besides, infiltration models were compared, and an improved genetic algorithm (GA) combined with multi-objective optimization and elitist strategy was proposed to upgrade the modified van-Genuchten (VG) model. Results indicated that observed cumulative infiltration displayed reductions by 14.06%, 46.62%, and 71.78% for the soil mixed with 5%, 10%, and 15% biochar, respectively, relative to the pure soil. The Kostiakov model was more effective than the Philip model in predicting cumulative infiltration. Furthermore, the constructed modified VG model based on the inversed hydraulic parameters was capable of predicting soil moisture at suction less than 2070 kPa (i.e., 1.38 times wilting point) but caused an underestimation beyond it. This research has the potential to replace the soil water retention curve (SWRC) measurement by one-dimensional infiltration experiment with parameters inversed from the improved GA combined with a modified VG model. It is time-saving and efficient during the SWRC study.

Critical Continuous Rainfall Map for Forecasting Shallow Landslide Initiations in Busan, Korea

In recent years, precipitation patterns in Korea have shifted to be characterized as short and intense rainfalls. In consideration of shallow landslide initiations primarily governed by heavy rainfalls at short-time scales that diminish drainage effects, the concept of critical continuous rainfall is proposed as a single-rainfall-variable threshold for shallow landslide forecasting. To generate a critical continuous rainfall map for hillslope areas in a city of Korea (Busan), this study designed and applied a systematic modeling process. As a preparatory stage, input datasets of geo-hydraulic properties and geotechnical properties were assembled using estimation techniques based on experiment data of field samples. The inherent and fixed critical continuous rainfall values for hillslope areas in Busan were derived through one-dimensional infiltration analysis coupled with infinite slope stability calculations. As a result of a detailed analysis of historical rainfall records in a case study area over a period of 11 years, three false forecasting cases were recorded, whereas all landslide-triggering rainfall events were correctly captured with no missed forecasting cases. The results of the case study indicate that the proposed critical continuous rainfall may be useful as an effective and straightforward indicator for forecasting the initiation of shallow landslides.

Comparison of Two-Parameter Vertical Ponded Infiltration Equations

Five two-parameter (sorptivity, S, and saturated hydraulic conductivity, Ks) vertical one-dimensional infiltration equations are compared quantitatively over the whole time range from zero to very long times. These equations are Green-Ampt (GA), Talsma-Parlange (TP), Brutsaert (B), Swartzendruber (SW), and Valiantzas (V). The results showed that the cumulative infiltration i (t) predictions of equations B, SW, and V are between the two limit soils characterized by GA and TP equations. Compared with the TP equation, the equations of B, SW, and V showed a maximum discrepancy of 3.8%, 5.6%, and 9.88%, respectively, while compared with the GA equation showed a maximum discrepancy of 14.8%, 11.4%, and 7.8%, respectively. However, the differences among SW, B, and V are lower. The study of cumulative infiltration data of four porous media showed that the S/Ks ratio may be a criterion for the appropriate infiltration equation selection. The S/Ks values for the porous media studied ranged from 2.6 to 136 min0.5. The V equation showed very good prediction of the results in the case of low S/Ks values (coarse-textured soils), while the SW equation in the case of high values (fine-textured soils). Also, the linear form of the V equation was applied for direct estimation of the two parameters, S and Ks, using vertical infiltration data of four porous media with relatively good results (0.980 < R2 < 0.999).

Physical Model of Vertical Water Movement Inside a Soil-Column Apparatus for Infiltration Study with A Two-Way Orientation Approach

To improve the theory of Richard's equation, studying infiltration under free-draining conditions at the ground surface is necessary. Verification is required to clarify the physical model of water movement. The aim of this study was to describe multistage measurements of both the wetting and the drying front scheme of one-dimensional infiltration at laboratory scale. A soil-column infiltration apparatus was built consisting of a double acrylic wall, a sensor set and a light bulb. Acrylic was chosen as the material for the wall to minimize possible heat conduction on the wall side, which was wrapped in double insulation to achieve adiabatic condition. The following three main sensors were used and controlled by a microcontroller: water-content, pressure and temperature sensors. Meanwhile, the light bulb at the top of the apparatus was set to non-isothermal condition. The instrument was successfully built to describe vertical water movement. Slight modifications were carried out to ensure more precise observation. This resulted in the initiating of new shape interpretation based on the water-ponding measurement to refine the simplified pattern that was introduced by the conventional Green-Ampt theory.

Laboratory evaluation of falling-head infiltration for saturated soil hydraulic conductivity determination

Falling-head one-dimensional infiltration procedures, such as the simplified falling-head (SFH) technique, yield estimates of saturated soil hydraulic conductivity, Ks, with parsimonious and rapid experiments. Factors that can influence determination of Ks by the SFH technique were tested in the laboratory on three repacked soils differing by particle diameter ranges (0-2000, 0- 105 and 105-2000 mm, respectively). Using the theoretically calculated depth of ponding on the infiltration surface, D, instead of the measured one had a small impact on the Ks calculations (means differing by a factor of 1.1-1.2, depending on the soil). For the finest soil, Ks decreased by 3.1 times as D increased from 40 to 135 mm but D did not affect Ks for the coarsest soil, yielding in general the highest Ks values. The abrupt increase of the infiltration rate close to the end of the run did not influence appreciably Ks calculations since it determined an increase in Ks by a mean factor never exceeding 1.1. The most frequent result of the developed procedure for estimating the α* parameter was failure of the experiment although the valid α* calculations were plausible, being higher for the coarse textured soil (17 m–1) than the finer soils (9.2-9.3 m–1). The depth of the wetting front at the end of the run was 1.1-1.2 times deeper than that calculated theoretically before the run, depending on the soil. In conclusion, the method used to determine D should not affect very much Ks determination but larger D values can yield smaller Ks values in fine-textured soils. Air escapes from the sampled soil volume when almost all water had infiltrated but this circumstance does not have a great impact on calculation of Ks. A falling-head one-dimensional ponded infiltration process is not recommended to estimate α*. The theoretical depth of the wetting front can approximately be predicted before the run. The SFH technique appears a rather robust method to simply and rapidly determine Ks.

A modified physical-based water-retention model for continuous soil moisture estimation during infiltration: experiments on saline and non-saline soils

ABSTRACT Water infiltration is an issue of vital concern to farmland irrigation. Besides, a soil-water evaluation during infiltration benefits irrigation determination and salt leaching, which has still not been well revealed through a physical-based model regarding continuous soil-water estimation. We conducted one-dimensional infiltration on non-saline loam soil and saline sandy loam soil to propose a modified water-retention model which was expected to estimate continuous soil-water changes during infiltration. Results indicated that for the non-saline soil and the saline soil with different salinities, the modified water-retention model can be established based on the vertical one-dimensional algebraic model and the Kostiakov model. But different from the traditional vertical one-dimensional algebraic model, the new established model can be adopted for calculating and predicting continuous water content during infiltration at any duration, with higher accuracy than using HYDRUS, due to direct parameter acquisition from the observed infiltration data rather than indirect acquisition from soil water characteristic curve. The established potential relationship between soil moisture and cumulative infiltration promotes the development of precise agriculture.