Infiltration In Unsaturated Soils Research Articles

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.

Numerical solution of the Richards equation in unsaturated soil using the meshless Petrov–Galerkin method

Nowadays, infiltration tactics are widely used to manage storm water in urban areas. These techniques are used and recognized around the world due to their benefits, such as reducing the negative consequences of urbanization, reducing storm water flow in sewage systems and recharging groundwater. Richards equation is one of the most well-known equations for simulating water infiltration in soil in the unsaturated area. In the present study, a one-dimensional approach to the numerical solution of Richards equation is presented using meshless Petrov–Galerkin method and Kirchhoff transformation. The results of this modeling have been compared with analytical solution, laboratory data, and finite difference and meshless numerical methods. Given that the proposed model can provide an accurate representation of water level changes in unsaturated soil compared to analytical solution, laboratory data, finite difference method and MQ-RBF with the root mean square error equal to 0.09, 1.02, 0.7 and 0.1, it can be claimed that the model can model the flow of water infiltration in unsaturated soil.

Probabilistic Analysis of Highly Nonlinear Models by Adaptive Sparse Polynomial Chaos: Transient Infiltration in Unsaturated Soil

Polynomial chaos expansion (PCE) is widely adopted in geotechnical engineering as a surrogate model for probabilistic analysis. However, the traditional low-order PCE may be unfeasible for unsaturated transient-state models due to the high nonlinearity. In this study, a temporal-spatial surrogate model of adaptive sparse polynomial chaos expansions (AS-PCE) is established based on hyperbolic truncation with stepwise regression as surrogate models to improve computational efficiency. The uncertainty of pore water pressure of an unsaturated slope under transient-state rainfall infiltration considering hydraulic spatial variability is studied. The saturated coefficient of permeability [Formula: see text] is chosen to be spatial variability to account for the soil hydraulic uncertainty. The effects of location and time and the performances of AS-PCE are investigated. As rainfall goes on, the range of the pore pressure head becomes larger and the spatial variability of [Formula: see text] has little influence in the unsaturated zone with high matric suction. The pore pressure head under the water table suffers more uncertainty than it in the unsaturated zone. The [Formula: see text] in the high matric suction zone has a trend of rising first and then falling. Except for the high matric suction zone, the [Formula: see text] rise over time and they are almost 1 at the end of the time. It can be concluded that the AS-PCE performs better for low matric suction and positive pore pressure head and the fitting effect gradually increases as the rainfall progresses. The quartiles and at least up to second statistical moments can be characterized by the AS-PCE for transient infiltration in unsaturated soil slopes under rainfall.

Study of the water vertical infiltration path in unsaturated soil based on a variational method: application of power function distribution of D(θ)

ABSTRACT The classical Richards equation of water infiltration in unsaturated soil is a partial differential equation, which is non-linear and difficult to solve analytically. Taking time as the variable with the least action, the infiltration path as a function of time is established based on the Richards equation. The vertical infiltration problem of unsaturated soil under gravity is transformed into the functional extremum problem, and solved with the Euler-Lagrange equation. The results show that the diffusion coefficient D(θ) has a functional relationship with the depth of the wetting front. When the type of diffusion coefficient is known, the moisture content of the wetting front at a specified depth, the moisture content of the farthest wetting front and the maximum entropy distribution of soil moisture content can be obtained at the optimal path. Taking the optimal path as the standard, the accuracy of solving the Richards equation by Boltzmann transformation and linear transformation is tested.

A Simple Method for Predicting Rainfall-Induced Shallow Landslides

A method of practical interest is presented in this study for predicting shallow landslide triggering due to expected rainfall scenarios. The proposed approach is based on some closed-form expressions derived using physically-based models and requires a limited number of material parameters obtained from conventional tests. Two typical triggering mechanisms are considered: in the first case, a landslide is caused by a reduction in suction due to rain infiltration in unsaturated soils; in the second one, a slope failure occurs due to the formation of a water table with consequent generation of positive pore water pressures within the slope. A simple criterion is also provided to establish which triggering mechanism occurs. For each considered mechanism, a rainfall threshold curve is derived, which is formally similar to several empirical intensity-duration relationships proposed in the literature for predicting the occurrence of shallow landslides. However, unlike these empirical relationships, the present threshold curves explicitly depend on basic parameters such as slope geometry, soil properties, and pore water pressure existing at the depth of the potential slip surface before the rainfall. The proposed approach is also applied to well-documented case studies to assess its predictive capacity.

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.

Application of modified iterative method to simulate rainfall infiltration in unsaturated soils

A modified Gauss-Seidel iterative method (MP(m)-GS) with multistep preconditioner is developed to solve partial differential equations of rainfall infiltration. The finite difference method (FDM) is applied to numerical discretization. Furthermore, a system of linear equations is solved using an iterative scheme. For some unfavorable numerical conditions, such as large initial conditions, classical Picard iterative method usually has low accuracy and computational efficiency. Conventional linear iterative methods have a slower convergence rate, such as Gauss-Seidel (GS) and Jacobi iterative methods, particularly for small discrete space step size. Thus, MP(m)-GS is developed to simulate rainfall infiltration into unsaturated soils. The analytical solutions are employed to verify the proposed methods. The results indicate that the MP(m)-GS has higher computational efficiency and accuracy than the improved Picard methods. Compared with the conventional linear iterative methods GS and SOR, MP(m)-GS also demonstrates faster convergence rate and higher computation efficiency. The results show nice applications in modeling rainfall infiltration in unsaturated soils.

A generalized approximate analytical solution of horizontal infiltration in unsaturated soil

A generalized approximate analytical solution of horizontal infiltration in unsaturated soil

An improved Chebyshev semi-iterative method for simulating rainfall infiltration in unsaturated soils and its application to shallow landslides

A Chebyshev semi-iterative method (CSIM) with preconditioner (P-CSIM) is proposed to simulate numerically unsteady flow in unsaturated soils. An exponential function was used to linearize Richards’ equation, which was discretized using a finite difference method to obtain the linear equations. For layered soils, the numerical discretization takes into account the continuity of the pressure head at the interface. Conventional iterative approaches, including the Jacobi and the Gauss–Seidel iterative methods, require more iterations to obtain numerical solutions. The CSIM incurs more computational cost per iteration. The improved P-CSIM by comparison solves the linear equations in fewer iterations, with higher computational efficiency, and better robustness. The results indicate that the proposed P-CSIM provides good computational acceleration; specifically, at least 50% more than the CSIM and the Gauss–Seidel and Jacobi iterative methods. To simulate shallow landslides, the stability analysis of infinite slopes was developed to incorporate the time-varying pressure head and soil–water characteristic curves of unsaturated soils. The results of the examples indicate that the solver is able also to represent the increase of pressure head which may lead to a landslide. As a result, the proposed method with high computational efficiency can be developed to effectively analyze rainfall-induced shallow landslides in unsaturated soils.

Impact of fractal characteristics on evaporation and infiltration in unsaturated heterogeneous soils

ABSTRACT In this study, an approach is developed to investigate the impact of fractal characteristics of unsaturated soil between the water table and land surface on the steady-state evaporation and infiltration across a heterogeneous landscape. The soil domain is conceptualized as a collection of stream tubes of soils and the particle diameters in various stream tubes follow a fractal distribution. The saturated hydraulic conductivity of each stream tube is related to the representative particle diameter in the tube. The effective specific discharge is then integrated from the specific discharge for each stream tube and the fractal distribution. The effective evaporation and infiltration in unsaturated soils increase with the fractal dimension. The ratio of minimum over maximum diameters does not significantly affect the specific discharge in the fractal soil. The specific discharge in unsaturated fractal soils calculated by using the simple average particle diameter mostly over-predicts the actual effective specific discharge.

An approximate analytical solution of non linear partial differential equation for water infiltration in unsaturated soils by combined Elzaki Transform and Adomian Decomposition Method

The aim of the concerned paper is to describe the behaviour of the water infiltration problems in unsaturated soils. Governing equation of this phenomenon is known as Richards’ equation. The solution of the Richards’ equation has been found by Elzaki Adomian Decomposition Method. This method gives a solution in terms of convergent series. Comparison of the approximate solutions and exact solutions have been found here. MATLAB and MATHEMATICA are used to obtain numerical and graphical representation.

Roadbed Subsidence Mechanisms under the Driven of Penetration-Soak Coupling

Roadbed subsidence is one of the main types of highway flood damage, the periodic fluctuation of the river water level and the softening of the subgrade soils by the river water immersion for a long time are the main inducement factors of the subgrade subsidence. Based on the theory of absorbing water infiltration in unsaturated soil, calculation formula of dynamic stability coefficient of subgrade is established by using the Swedish arc method. Example analysis shows that, soil roadbed suffers the water permeability-soak, road-bed’s stability reduce with the time, and leads to roadbed subsidence. Research results for improving roadbed subsidence water logging mechanism understanding level have a positive meaning.

Modeling runoff and microbial overland transport with KINEROS2/STWIR model: Accuracy and uncertainty as affected by source of infiltration parameters

Summary Infiltration is important to modeling the overland transport of microorganisms in environmental waters. In watershed- and hillslope scale-models, infiltration is commonly described by simple equations relating infiltration rate to soil saturated conductivity and by empirical parameters defining changes in infiltration rate with soil water content. For the microbial transport model KINEROS2/STWIR used in this study, infiltration in unsaturated soil is accounted for by a net capillary drive parameter, G , in the Parlange equation. Scarce experimental data and multiple approaches for estimating parameter G introduce uncertainty, reducing reliability of overland water flow and microbial transport models. Our objectives were to evaluate reliability and robustness of three methods to estimate parameter G and associated accuracy and uncertainty in predicting runoff and fecal coliform (FC) transport. These methods include (i) KINEROS2 fitting to the experimental cumulative runoff data; (ii) estimating solely on soil texture; and (iii) estimating by individual pedotransfer functions (PTFs) and an ensemble of PTFs from basic soil properties. Results show that the most accurate prediction was obtained when the G parameter was fitted to the cumulative runoff. The KINEROS2-recommended parameter slightly overestimated the calibrated value of parameter G and yielded less accurate predictions of runoff, FC concentrations and total FC. The PTFs-estimated parameters systematically deviated from calibrated G values that caused high uncertainty in the KINEROS2/STWIR predictions. Averaging PTF estimates considerably improved model accuracy, reducing the uncertainty of runoff and FC concentration predictions. Overall, ensemble-based PTF estimation of the capillary drive can be efficient for simulations of runoff and bacteria overland transport when a single effective value is used across the study area.

An Extension of the Talbot–Ogden Hydrology Model to an Affine Multi-Dimensional Moisture Content Domain

The Talbot–Ogden hydrology model provides a fast mass conservative method to compute infiltration in unsaturated soils. As a replacement for a model based on Richards equation, it separates the groundwater movement into infiltration and redistribution for every time step. The typical feature making this method fast is the discretization of the moisture content domain rather than the spatial one. The Talbot-Ogden model rapidly determines how well ground water and aquifers are recharged only. Hence, it differs from models based on advanced reservoir modeling that are uniformly far more expensive computationally since they determine where the water moves in space instead, a completely different and more complex problem. According to the pore-size distribution curve for many soils, this paper extends the one dimensional moisture content domain into a two dimensional one by keeping the vertical spatial axis. The proposed extension can describe any pore-size or porosity distribution as an important soil feature. Based on this extension, infiltration and redistribution are restudied. The unconditional conservation of mass in the Talbot–Ogden model is inherited in this extended model. A numerical example is given for the extended model.

토석류 발생 사면의 불포화토 사면안정해석

This paper is research results of slope stability analysis associated with seepage infiltration for unsaturated soil in debris-flow occurrence slopes. Site investigations were carried out in two slopes, located at Inje in Kangwon province where debris flow occurred in 2006 and at Yangpyung in Kyeunggi province where it occurred in 2010. For unsaturated soil sampled at the zone of debris-flow initiation, soil water characteristic curves with tempe pressure cells and shear strength parameters with newly designed shear strength apparatus were obtained respectively. The commertially available software SEEP/W was used to analyze seepage infiltration in unsaturated soil, based on their properties obtained from test results and the actual rainfall data at the moment of debris flow occurrence, and slope stability analysis with the program of SLOPE/W, associated with results of seepage analysis, was performed to simulate slope failure. As results of this research, seepage infiltration to unsaturated soil due to intensive rainfall was found to cause increase of ground water table as well as degree of saturation. Through this research slope stability analysis for unsaturated soil, considering the actual rainfall characteristic, might be a reasonable method of investigating characteristics of debris flow behavior, in particular, the moment of debris flow occurrence.

A method for the analysis of soil slips triggered by rainfall

A method of practical interest is presented for the analysis of shallow landslides triggered by rain infiltration in unsaturated soils, such as soil slips or slab slides. The method combines an analytical solution to evaluate the change in pore water pressure due to rain infiltration whose rate is described by a general time-dependent function, and the infinite slope model to assess the occurrence of landslide due to a prescribed rainfall.

Influence of evaporation on transient suction distribution in unsaturated soil

This paper presents the results of numerical analysis on influence of evaporation process on the transient suction distribution induced by rainfall infiltration in unsaturated soil. Transient seepage and slope stability analyses were carried out using commercial software SEEP/W and SLOPE/W (Geo-Slope International, 2007a, b) on 1-year data representing a site at Johor Bahru, Malaysia. Soil samples were collected and relevant data, that is, soil water characteristics curve (SWCC), hydraulic conductivity curve, and shear strength parameters were gained through interpretation of laboratory test results. The study was performed for two typical periods: dry period and wet period, that is, March and June, and two conditions: Rainfall alone and combination of rainfall and evaporation. Residual water content was assigned at the beginning of all analyses. The results show that evaporation gives a positive effect on slope stability by reducing the effect of rainfall on suction distribution. Consideration of evaporation in transient seepage analysis gives a better prediction of suction distribution in soil and slope stability. Key words: Infiltration, evaporation, unsaturated soil, suction, transient seepage analyses.

Analytical solutions to 1-D horizontal and vertical water infiltration in saturated/unsaturated soils considering time-varying rainfall

Analytical solutions to 1-D horizontal and vertical water infiltration in saturated/unsaturated soils are developed that can consider the variation of rainfall with time. In this model, water content and the permeability coefficient are assumed to be exponential functions of the pressure head, and diffusivity is constant. By means of Fourier integral transformation, the analytical solutions are expressed as infinite series. The steady-state solutions for horizontal and vertical infiltration in unsaturated soils are then derived. The solutions can consider both flux and pressure head boundaries. The solutions are easy to implement compared with numerical solutions, although the restricted assumptions may limit their applicability in some ways. The analytical solutions provide a reliable tool for checking the accuracy of various numerical methods under the condition of constant diffusivity. Finally, the analysis carried out in a case study indicates that the pressure head differences caused by the transient infiltration in both the horizontal and vertical directions can be estimated using the steady-state solutions, and the effect of gravity on water infiltration mainly depends on the boundary conditions.

Infiltration in unsaturated soils – An analytical approach

An approximate analytical solution has been established for the well known Richards’ equation for unsaturated flow of transports in soils. Despite the importance of Richards’ equation in geotechnical and geoenvironmental applications, most solutions to the problem are generally based on numerical methods often having limitations in application. It is therefore advantageous to explore analytical solutions to the problem. The proposed solution is based on homotopy analysis method (HAM). The method is superior over traditional perturbation techniques in a sense that it is not dependent on the assumption of a small parameter as the initial step. Several simple cases have been explored to describe the application of HAM to Richards’ equation. The results obtained by HAM are also compared with existing solutions to demonstrate the accuracy of the proposed method.

Entropy theory for derivation of infiltration equations

An entropy theory is formulated for modeling the potential rate of infiltration in unsaturated soils. The theory is composed of six parts: (1) Shannon entropy, (2) principle of maximum entropy (POME), (3) specification of information on infiltration in terms of constraints, (4) maximization of entropy in accordance with POME, (5) derivation of the probability distribution of infiltration, and (6) derivation of infiltration equations. The theory is illustrated with the derivation of six infiltration equations commonly used in hydrology, watershed management, and agricultural irrigation, including Horton, Kostiakov, Philip two‐term, Green‐Ampt, Overton, and Holtan equations, and the determination of the least biased probability distributions of these infiltration equations and their entropies. The theory leads to the expression of parameters of the derived infiltration equations in terms of measurable quantities (or information), called constraints, and in this sense these equations are rendered nonparametric. Furthermore, parameters of these infiltration equations can be expressed in terms of three measurable quantities: initial infiltration, steady infiltration, and soil moisture retention capacity. Using parameters so obtained, infiltration rates are computed using these six infiltration equations and are compared with field experimental observations reported in the hydrologic literature as well as the rates computed using parameters of these equations obtained by calibration. It is found that infiltration parameter values yielded by the entropy theory are good approximations.