Green-Ampt Model Research Articles

Empirical formulas for dynamic effective suction head in the modified green-ampt model

The Green-Ampt model, which is a widely used infiltration model, assumes a constant effective suction head during infiltration; however, the capillary pressure is dynamic and related to the saturation rate. One factor affecting the dynamic suction head is the dynamic contact angle, which is parameterized using different formulas. Previous studies applied a power-law formula to parameterize the effective suction head, which substantially improved the ability to describe the velocity-dependent suction head. However, other dynamic contact angle formulas have not been tested. In this study, we performed a series of 1-D downward infiltration experiments with 60-cm sand columns and constructed modified Green-Ampt models (MGAMs) based on four formulas of dynamic contact angle (power-law, Jiang’s law, Hoffman’s law, and Cox-Voinov law) and a linear approximation. These modified Green-Ampt models were named MGAM-PW, MGAM-Jiang, MGAM-Hoff, MGAM-CV, and MGAM-LN. After parameter optimization, all modified Green-Ampt models resulted in similar root-mean-square errors, which were lower than those of the classical Green-Ampt model. The modified Green-Ampt models yielded similar values for the equilibrium suction head, which were larger than those of the classical Green-Ampt model. Among the modified Green-Ampt models, MGAM-CV has an intrinsic limitation in the range of parameter values. MGAM-Hoff typically requires more fitting parameters than do the other methods. MGAM-LN can be solved more efficiently than other modified Green-Ampt models because of its analytical solution and small number of fitting parameters. We demonstrated that the data length and slight time delay of the measurement affected optimization of the equilibrium suction head. Moreover, the relationship between the capillary pressure and saturation rate based on MGAM-PW was similar to the findings in the literature.

Modification of Green-Ampt model based on multi-stage characteristics of soil water infiltration

ABSTRACT Water infiltration in unsaturated soil is significantly affected by multi-stage characteristics that depend on the movement of the wetting front. We modified the Green-Ampt model to accurately capture these multi-stage characteristics during infiltration. The proposed model divides the water-infiltrated unsaturated soil into three zones, while the infiltration process itself is divided into three stages, with the quarter-elliptic wetting front curve being defined. The proposed model, together with other Green-Ampt based models, is analysed and compared with experimental investigations conducted in this study, as well as with published results from the literature. The results demonstrate the proposed modified model successfully describes the measured infiltration time for soil columns with different heights. Additionally, a parametric sensitivity analysis of the proposed model reveals the water infiltration process is mainly controlled by the hydraulic conductivity in the infiltrated zone and the suction head between the wetting front zone and the unpenetrated zone.

Infiltration, runoff, and slope stability behaviors of infinite slope with macropores based on an improved Green-Ampt model

Infiltration, runoff, and slope stability behaviors of infinite slope with macropores based on an improved Green-Ampt model

Influence of Long-Term Mulched Drip Irrigation on Upward Capillary Water Movement Characteristics in the Saline–Sodic Region of Northwest China

Capillary water, serving as a crucial intermediary between groundwater and crop root layer moisture, is important for both soil retention and crop utilization. To investigate the effect of mulched drip irrigation (MDI) on upward capillary water in cotton fields with different application years (0, 10, 14, 18, 20, and 24 years) in the saline–sodic region of Northwest China, an indoor soil column test (one-dimensional capillary water rise experiment) was conducted. The results showed that the wetting front transport law, capillary water recharge, and wetting front transport rate over time exhibited an increasing trend in the early stages of MDI application (10 and 14 years), peaking at 18 years of application, followed by a decreasing trend. The relationship between the capillary water recharge and rising height was fitted based on the Green–Ampt model, and their slopes reveal that 14 and 18 years of MDI application required the largest amount of water per unit distance, indicating an excellent water-holding capacity beneficial for plant growth. Conversely, 0 years required the smallest amount of water per unit distance. Based on the movement characteristics of upper capillary water, we confirmed that the MDI application years (0–18 years) improves soil infiltration capacity, while the long-term application years (18–24 years) reduces groundwater replenishment to the soil. Furthermore, the HYDRUS-1D model was employed to simulate the capillary water rise process and soil moisture distribution under different MDl application years. The results showed an excellent consistency with the soil column experiments, confirming the accuracy of HYDRUS-1D in simulating the capillary water dynamics in saline–sodic areas. The results would provide suggestions to achieve the sustainable development of long-term drip-irrigated cotton fields.

Analysis of pipeline leakage in unsaturated stratum: A new seepage-diffusion model

Accurate prediction of the spread of fluids leaking from underground pipelines is crucial for risk assessment. In this study, we developed a method for predicting the diffusion range of pipeline seepage fluids within an unsaturated stratum. First, we derived a seepage–diffusion equation based on the generalized Darcy’s law and subsequently analyzed the mechanism of fluid diffusion in the unsaturated stratum. We then constructed a model for the seepage–diffusion of a pipeline leakage fluid, incorporating variables such as the saturation, permeability coefficient, diffusion pressure, and diffusion distance of soil microelements across various time intervals, using a stepwise algorithm in tandem with the Green–Ampt model and VG–Mualen permeability coefficient function. We investigated the influence of fluid self-gravity, saturated permeability coefficient, initial saturation, and intra-pipe pressure on the diffusion distance of the pipeline leakage fluid in an unsaturated stratum, focusing on specific cases. The results indicate that an increase in the saturated permeability coefficient, initial saturation, and intra-pipe pressure leads to an increase in the fluid diffusion distance. A simulation test was conducted to validate the proposed seepage–diffusion model. The findings of this study can be employed to predict the diffusion range of pipeline leakage fluids in various formation types, providing a vital foundation for pipeline leakage accident management.

A simple, accurate, and explicit form of the Green–Ampt model to estimate infiltration, sorptivity, and hydraulic conductivity

AbstractFinding an explicit solution to the widely used Green–Ampt (G–A) one‐dimensional infiltration model has been subject of efforts for more than half a century. We derived an explicit semiempirical approach that combines accuracy with simplicity, a concept that has been generally neglected in previous studies. The equation is , with F (L), Ks (L/T), S (L/T0.5) and t (T) being cumulative infiltration, saturated hydraulic conductivity, sorptivity, and time, respectively. Relative errors (ɛ) by the application of this equation generally do not exceed ±0.3% in most applied infiltration problems faced by water resources engineering today. We show both numerically and mathematically that │ɛ│> 0.3% could only occur if Kst/F > 0.904, a criterion that could apply to sand and loamy sand soils (i.e., coarse texture) and if they experience infiltration rates for over 6 h and 19 h, respectively. Hence, we also derived a simple linear adjustment in the model as Fadj ≅ 0.9796 F + 0.335 S2/Ks to address these longer infiltration rates, and to assure that ɛ remains within the expected ±0.3% range of uncertainty. A linearized regression technique was also developed to accurately estimate S and Ks when the G–A model is used. We numerically demonstrated that our fitting method could be used even when the G–A approach is less valid (diffusive soils), provided that the actual value of the capillary length (λ) is initially known. An added benefit of our approach is that by setting λ equal to 1/3 and 2/3, it can significantly limit the range of initializing, unknown, a priori values of S and Ks, as these two parameters are estimated through the inverse solution of implicit infiltration models. Due to the model's simplicity and accuracy, our solution should find application among hydrologists, natural resource scientists, and engineers who wish to easily derive accurate estimations from the G–A infiltration approach and/or estimate sorptivity and hydraulic conductivity without encountering divergence problems.

Mechanical responses of shallowly buried pipelines to adjacent deep excavations considering heavy rainfall influence

Climate change has resulted in a high global incidence of heavy rainfall, severely damaging the urban infrastructure. The analytical method used to predict the mechanical response of pipelines under the influence of rainfall influence could serve as a valuable design basis in the preliminary stage. This study developed an analytical solution based on the stratified Green-Ampt model and displacement-controlled two-stage method. The first stage evaluates the greenfield soil displacement at pipeline elevation by employing the Mindlin solution and considering the superposed effects of excavation (unloading) and rainfall infiltration. The second stage predicts the mechanical responses of the pipeline by simplifying the pipeline–soil interaction into a continuous Euler–Bernoulli beam resting on a Winkler foundation model. The analytical solution was calculated using the finite difference method and verified against a published study. Finally, parametric studies were conducted to investigate the rainfall– excavation–pipeline interaction, including the rainfall intensity and duration, maximum lateral wall deflection, and pipeline location. The results showed that a 48-8-mm/h rainfall increased the maximum displacement and maximum bending moment of the pipeline by 6.54% and 7.93%, respectively. The prediction results provide practical guidance for designing deep excavations adjacent to pipelines buried under heavy rainfall conditions.

Application of a simplified Green-Ampt model to the Maga earthfill dam under rainfall conditions: A sensitivity analysis case of an infiltration model

The present paper applies a simplified Green-Ampt (GA) infiltration model for the numerical modelling of seepage processes within the body of the Maga earth dam, located in the Far-North Cameroon, under rainfall conditions. The parametrization approach makes possible the predictions of infiltrations parameters for various textures that constitute the body of earth dam and its vicinities. The effects of soil texture, permeability coefficient, rain intensity and initial moisture on infiltration rate and cumulative depth are investigated using numerical simulations carried out by running an Excel VBA code. A proposed optimization procedure of the literature is then used to improve the GA model parameters and accuracy of predictions. A case sensitivity analysis of the infiltration model parameters has also been made. Initial and saturated water contents, rain intensity and permeability coefficient at saturation have been identified as the most influents parameters for the model predictions, with obvious interactions between inputs. The contribution of main effects and interactions of above inputs ranges between 68.8 % and 90.03 % of the total variance. Comparisons of numerical results with the experimental ones obtained from the literature on real cases of simulated rainfall on main sub-Saharan soils have been done. The results show that numerical simulations underestimated 60 % and 56.25 % of the hydrodynamics parameters respectively for one and four simulated rain-sequence with relative errors (RE) ranging between −76.22 % and 300.25 %. The most representative results were obtained for 53.13 % of the predicted hydrodynamics parameters with RE value ranging between −23.90 % and 12.75 %. The obtained results proved that, the simplified GA model exhibited an acceptable accuracy in predicting seepage processes for ferruginous and degraded vertic soils. Therefore, the present study contributes to understand the role of numerical simulations tools in modelling and predicting subsurface phenomenon as seepage, for areas with high floods risks in a context of significant climate changes.

Stability analysis of rainfall-induced landslide considering air resistance delay effect and lateral seepage

Accumulation landslides are prone to occur during the continuous infiltration of heavy rainfall, which seriously threatens the lives and property safety of local residents. In this paper, based on the Green-Ampt (GA) infiltration model, a new slope rainfall infiltration function is derived by combining the effect of air resistance and lateral seepage of saturated zone. Considering that when the soil layer continues to infiltrate after the saturation zone is formed, the air involvement cannot be discharged in time, which delays the infiltration process. Therefore, the influence of air resistance factor in soil pores is added. According to the infiltration characteristics of finite long slope, the lateral seepage of saturated zone is introduced, which makes up for the deficiency that GA model is only applicable to infinite long slope. Finally, based on the seepage characteristics of the previous analysis, the overall shear strength criterion is used to evaluate the stability of the slope. The results show that the safety factor decreases slowly with the increase of size and is inversely correlated with the slope angle and initial moisture content. The time of infiltration at the same depth increases with the increase of size and slope angle, and is inversely correlated with the initial moisture content, but is less affected by rainfall intensity. By comparing with the results of experimental data and other methods, the results of the proposed method are more consistent with the experimental results than other methods.

Soil macropores induced by plant root as a driver for vertical hydrological connectivity in Yellow River Delta

Abstract The protection and management of the wetland should consider the changes in hydrological connectivity (HC) caused by the structural modifications of the soil macropores. The main purpose of our work is to clarify and quantify the influence of the soil macropores volume on the vertical soil hydrodynamic process mechanically and statistically by taking the form of a case study in Yellow River Delta (YRD), and further reveal the vertical hydrological connectivity in this area. Based on X-ray computed tomography and constant head permeability test, the results showed a highly spatial heterogeneity of the soil structure in the YRD, hydraulic parameter (Ks) was negatively correlated with bulk density and positively with soil macropore volume, soil aeration and maximum water capacity. Using Hydrus 1-D software and the Green–Ampt model, we estimated the characteristics of the hydrodynamic process in the soil without macropores, then evaluated the effect of the soil macropore on soil hydrodynamic process by comparing the experimental results with the simulation results. We found that increasing soil microporosity improved the convenience of water movement, which would enhance the HC of the region. The results will further help to reveal the eco-hydrological process at a vertical scale in soil and provide a theoretical guide for wetland conservation and restoration.

Comparison of infiltration model performance based on basic infiltration rate for small watersheds in Papua region, Indonesia

Research on soil water infiltration in equatorial climates like Indonesia is limited. Despite Papua accounting for 29% of Indonesia’s surface water, there’s a shortage of hydrological data. This study aimed to identify the best infiltration model tailored to the characteristics of basic infiltration rates in Papua’s small watersheds. Observations were made at 95 points across 11 small watersheds in Papua. Based on equatorial basic infiltration rate theories, analysis classified infiltration values against observation time. The performance of four infiltration models — Horton, Philip, Kostiakov, and Green Ampt — were compared. The results indicated the Philip model as superior, with average scores of 0.901 (R), 0.814 (NSE), and 0.424 (RSR), followed by the Horton and Green Ampt models. These three models showed excellent performance. However, the Kostiakov model was found lacking and needs modification. Further research on rapid and very rapid classifications is vital for enhancing infiltration rate predictions in small equatorial watersheds.

Slope Stability Analysis under Heavy Rainfall Conditions Based on a Modified Green-Ampt Model

Slope Stability Analysis under Heavy Rainfall Conditions Based on a Modified Green-Ampt Model

Rainfall Infiltration through Stratified Colluvial Deposits: Analytical Approach vs. Numerical Modelling

This work investigates the rainfall infiltration process within homogeneous and stratified colluvial deposits caused by short (1–3 h) and intense (40–90 mm/h) rainfall, using both analytical and numerical infiltration modelling. The findings of the investigation demonstrate that the classic Green–Ampt model can be employed effectively to study homogeneous colluvial covers with permeability equal to or lower than kw = 10−5 m/s and that are subject to a 1 h rainfall with intensity I ≥ 45–50 mm/h. In these circumstances, a top-down saturation front forms within the colluvial deposit, leading to the saturation of a 70–100 cm-thick layer. This critical condition occurs every 5–10 years in the mountain area of the Friuli Venezia Giulia Region (NE Italy), which corresponds to a lower return period of critical hydrologic events when compared with other mountain basins in the Alps due to the higher initial degree of saturation characterising colluvial covers in this area (70–95%). When analysing stratified colluvial covers, the Dagan–Bresler approximate model, as well as the numerical modelling, emphasised the strong influence that abrupt variations in the permeability of the various soil layers have on the infiltration process at depth. In particular, the presence of a top organic soil horizon that is rich in macro-pores and is characterised by a higher permeability (k = 10−4 m/s) actually reduces the possibility of surficial ponding, which is the basic condition of the “piston” models. The highly permeable top soil allows for a rapid downward infiltration up to contact with the underlying colluvial material, which is less permeable (k = 10−5 m/s). Therefore, a perched water table forms starting from the organic soil–colluvium interface, originating pore–water overpressures within the colluvial deposit, with maximum values in the order of 5–10 kPa.

Stability Analysis for Three-Dimensional Earth-Retaining Structures Subjected to Rainfall Based on a Modified Green–Ampt Model

Stability Analysis for Three-Dimensional Earth-Retaining Structures Subjected to Rainfall Based on a Modified Green–Ampt Model

Stability analysis of heterogeneous infinite slopes under rainfall-infiltration by means of an improved Green–Ampt model

Rainfall infiltration analysis has a great significance to the mitigation and risk assessment of rainfall-induced landslides. The original Green–Ampt (GA) model ignored the fact that a transitional layer exists in infiltration regions of soils under the rainfall permeation; moreover, it cannot effectively analyze the rainfall-infiltrated heterogeneous slope considering the spatial variability of saturated hydraulic conductivity ( ks ). In this study, an improved GA model is proposed for the rainfall-infiltration analysis of heterogeneous slopes. Four common slope cases are investigated to validate the effectiveness of the proposed model. An infinite slope model is taken as an illustrative example to investigate the distributions of volumetric water content and slope stability under the rainfall infiltration. The results show that the distributions of volumetric water content and factor of safety ( Fs) obtained from the proposed model are in very good agreement with the numerical results of the Richards' equation. In contrast, the modified GA model obtains biased distributions of volumetric water content and smaller Fs for the same cases. The results show that the proposed GA model can accurately identify the location of critical slip surface of the slope, and as such it provides an efficient method for risk analysis and control of slopes susceptible to landslide.

Stochastic Analysis of the Drawdown Time of Infiltration Basins in the Presence of Heterogeneous Soils

AbstractThe drawdown time is important for the design and assessment of infiltration basins. This paper investigates its dependence on soil heterogeneity, and simple analytical solutions for the mean and the variance are given. The solutions are tested through Monte Carlo simulations in various realistic scenarios, using a modified Green Ampt model for layered soils and a model based on the integration of the 1‐D Richards equation. The impact of the employed approximations is assessed, and the leading role of the spatial distribution of the saturated hydraulic conductivity is emphasized. The effects of other relevant design and natural factors, including the initial water level and water content distribution, are also investigated.

Wetting front migration model of ion-adsorption rare earth during the multi-hole unsaturated liquid injection

In the process of ion-adsorption rare earth ore leaching, the migration characteristics of the wetting front in multi-hole injection holes and the influence of wetting front intersection effect on the migration distance of wetting fronts are still unclear. Besides, wetting front migration distance and leaching time are usually required to optimize the leaching process. In this study, wetting front migration tests of ion-adsorption rare earth ores during the multi-hole fluid injection (the spacing between injection holes was 10 cm, 12 cm and 14 cm) and single-hole fluid injection were completed under the constant water head height. At the pre-intersection stage, the wetting front migration laws of ion-adsorption rare earth ores during the multi-hole fluid injection and single-hole fluid injection were identical. At the post-intersection stage, the intersection accelerated the wetting front migration. By using the Darcy's law, the intersection effect of wetting fronts during the multi-hole liquid injection was transformed into the water head height directly above the intersection. Finally, based on the Green-Ampt model, a wetting front migration model of ion-adsorption rare earth ores during the multi-hole unsaturated liquid injection was established. Error analysis results showed that the proposed model can accurately simulate the infiltration process under experimental conditions. The research results enrich the infiltration law and theory of ion-adsorption rare earth ores during the multi-hole liquid injection, and this study provides a scientific basis for optimizing the liquid injection well pattern parameters of ion-adsorption rare earth in situ leaching in the future.

A novel approximate solution to slope rainfall infiltration

Slope rainfall infiltration is a critical component of the Earth's hydrologic processes. Although various infiltration models have been proposed to simulate rainfall infiltration, simple and accurate ones are still scarce. This work developed a non-integral infiltration model for sloping surfaces, called modified approximate solutions under constant pressure conditions (MASCP). New expressions were proposed to improve slope infiltration simulation by introducing a developing saturated zone in soil water content (SWC) profile to quantify the role of ponding water during infiltration. The MASCP was then extended to simulate the infiltration with uniform and non-uniform initial SWC distributions under complex rainfall patterns. The model performance was evaluated by comparing with Hydrus-1D and the sloping Green-Ampt model for four distinct textured soils. The results demonstrated that the ponding time and infiltration rate simulated by the MASCP agreed well with those by Hydrus-1D at all given conditions. Besides, the MASCP yielded higher simulation accuracy than the sloping Green-Ampt model, especially for coarse-textured soils, low rainfall intensity, and long rainfall hiatus. In conclusion, the MASCP is a simple and accurate computation tool for slope rainfall infiltration modeling.

Applicability of the Modified Green-Ampt Model Based on Suction Head Calculation in Water-Repellent Soil

Water repellency has a great influence on water infiltration into soil. Currently, there is no modified correlation model that is applicable to the water infiltration of water-repellent soils (WRS). In order to better construct a model suitable for water infiltration in water-repellent soil, our objectives are to validate the effect of a modified Green-Ampt model. We modified the model by assuming that the saturated and unsaturated zones had the same thickness and by combining three formulas of the suction head (Sf VG, Sf BC, Sf GP) and the average saturated hydraulic conductivity. Therefore, we obtained three modified models: the Green-Ampt-VG, Green-Ampt-BC, and Green-Ampt-GP models. Indoor one-dimensional water infiltration experiments were conducted to simulate the cumulative infiltration (CI), the distance of the wetting front (Zf), and the infiltration rate of a hydrophilic treatment and repellent treatments. The results showed that as the degree of repellency increased, the soil suction head decreased, and the relationship between the value of the soil suction head and the degree of WRS was exponential. In addition, the simulated values of the modified CI formula highly fit the measured values of all treatments in the three models (RMSE: 1.696, 1.812, and 0.694). The modified Green-Ampt-VG model had the best simulation effect on the infiltration rate (RMSE: 0.036) and Zf (RMSE: 3.976). The results indicated that the suction head values obtained from the parameters of the VG model were closest to the actual values compared the other models. These results can provide a reference for the solution of problems involving the suction head and water infiltration into WRS in the future.

Assessment of the infiltration of water-in-oil emulsion into soil after spill incidents

The issue of inland oil spills exerts an adverse impact on environmental and ecological health. Many cases are concerned with water-in-oil emulsions, especially in the oil production and transport system. To understand the contamination and take an efficient response work after spill, this study investigated the infiltration behavior of water-in-oil emulsions and the influencing factors by measuring the characteristics of different emulsions. The results showed that an increase of water and fine particle content and decrease in temperature would improve the viscosity of emulsions and reduce the infiltration rate, whereas salinity levels had a negligible impact on infiltration if the pour point of emulsion systems was far higher than the freezing point of water droplets. It is worth mentioning that excessive water content at a high temperature may cause demulsification during the infiltration process. The oil concentration in different soil layers was related to the viscosity of emulsion and infiltration depth, and the adopted Green-Ampt model simulated well under low temperature. This study reveals the new features of emulsion infiltration behavior and distribution patterns under different conditions and is helpful for the response work after spill accidents.