Analytical solutions of one‐dimensional infiltration before and after ponding

Chen, Jiann-Mou; Tan, Yih–Chi; Chen, Chu–Hui

doi:10.1002/hyp.1202

Cited by 42 publications

(18 citation statements)

References 4 publications

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“…When = ≥0(saturated zone), changes in soil volume are mainly related to the compressibility of the soil skeleton; when = <0 (unsaturated zone), volume changes are primarily related to changes in moisture content. The Richards equation does not allow analytical solutions except in cases where simplifying hypotheses and/or particular boundary conditions are introduced (Basha 1999; Iverson 2000;Chen et al 2003). There are several two-or three-dimensional case studies of the infiltration phenomenon, performed using less restrictive hypotheses regarding the hydraulic and physical characteristics of the soils, for which numerical solutions are proposed (Hogart and Parlange 2000;Weeks et al 2004;Menziani et al 2007).…”

Section: General Descriptionmentioning

confidence: 99%

FLaIR and SUSHI: two mathematical models for early warning of landslides induced by rainfall

2010

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The development of Early Warning Systems in recent years has assumed an increasingly important role in landslide risk mitigation. In this context, the main topic is the relationship between rainfall and the incidence of landslides. In this paper, we focus our attention on the analysis of mathematical models capable of simulating triggering conditions. These fall into two broad categories: hydrological models and complete models. Generally, hydrological models comprise simple empirical relationships linking antecedent precipitation to the time that the landslide occurs; the latter consist of more complex expressions that take several components into account, including specific site conditions, mechanical, hydraulic and physical soil properties, local seepage conditions, and the contribution of these to soil strength. In a review of the most important models proposed in the technical and international literature, we have outlined their most meaningful and salient aspects. In particular, the Forecasting of Landslides Induced by Rainfall (FLaIR) and the Saturated Unsaturated Simulation for Hillslope Instability (SUSHI) models, developed by the authors, are discussed. FLaIR is a hydrological model based on the identification of a mobility function dependent on landslide characteristics and antecedent rainfall, correlated to the probability of a slide occurring. SUSHI is a complete model for describing hydraulic phenomena at slope scale, incorporating Darcian saturated flow, with particular emphasis on spatialtemporal changes in subsoil pore pressure. It comprises a hydraulic module for analysing the circulation of water from rainfall infiltration in saturated and nonsaturated layers in nonstationary conditions and a geotechnical slope stability module based on Limit Equilibrium Methods. The paper also includes some examples of these models' applications in the framework of early warning systems in Italy.

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Section: General Descriptionmentioning

confidence: 99%

FLaIR and SUSHI: two mathematical models for early warning of landslides induced by rainfall

2010

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“…Ku et al [35] developed a linearization process for the nonlinear Richards equation using the Gardner exponential model to analyze the transient flow in the unsaturated zone. Chen et al [36] derived transient solutions to linearized Richards equation for time-dependent surface fluxes using Fourier integral. However, there are still some restrictions for the direct usage of these idealized analytical solutions in realistic situations.…”

Section: Introductionmentioning

confidence: 99%

Numerical Investigation on Infiltration and Runoff in Unsaturated Soils with Unsteady Rainfall Intensity

Tan

Song

Zhang

et al. 2018

Water

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Abstract:Modeling infiltration into soil and runoff quantitative evaluations is very significant for hydrological applications. In this paper, a flow model of unsaturated soils was established. A computational process of soil water content and runoff prediction was presented that combines an analytical solution with numerical approaches. The solutions have good agreements with the experimental results and other infiltration solutions (Richards numerical solution and classical Green-Ampt solution). We analyzed the effects on cumulative infiltration and runoff under three conditions of rainfall intensity with same average magnitude. These rainfall conditions were (Case 1) decreasing rainfall, (Case 2) steady rainfall, and (Case 3) increasing rainfall, respectively. The results show that the cumulative infiltration in Case 1 is the highest among the three cases. The cumulative runoff under condition of Case 3 is smaller than that of decreasing rainfall at the initial stage, which then becomes larger at the later stage. The time of runoff under the conditions of Case 1 is earliest among the three rainfall conditions, which is about 50% earlier than Case 3. Therefore, project construction for urban flood control should pay more attention to urban flood defense in increasing rainfall weather than other rainfall intensities under the same average magnitude. The approaches presented can be utilized to easily and effectively evaluate infiltration and runoff as a theoretical foundation.

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“…Using Fourier integral transformation, Chen et al (2001aChen et al ( , 2001bChen et al ( , 2003Chen et al ( , 2005 derived solutions to the linearlized Richards equation with time-dependent surface fluxes. In this study, in a similar manner, the techniques of dimensionless transformation and Fourier integral transformation are applied to obtain analytical solutions of the water content profile in a partially penetrated pumping well whose location and length of screen with fluxes are specified.…”

Section: Introductionmentioning

confidence: 99%

Analysis of the water content in an unconfined aquifer with a partially penetrated pumping well

Chen¹

2008

Hydrological Processes

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Abstract:Most methods developed to represent water flow phenomena in an unconfined aquifer with a fully penetrated pumping well are either numerical, such as the well-known FEMWTER model, or experimental; analytical models of a partially penetrated pumping well are rare. This study employs the linearized Richards equation as the governing equation, with the aid of Fourier Integral Transformation, to obtain an analytical solution of the water content distribution in an unconfined aquifer with a partially penetrated pumping well. The results from this study could serve to substantiate in some sense results from numerical models. In addition, the theory developed herein can be modified to simulate a vacuum-pressured pumping well since it is derived by considering, among others, the location and length of a well screen with fluxes.

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Analytical solutions of one‐dimensional infiltration before and after ponding

Cited by 42 publications

References 4 publications

FLaIR and SUSHI: two mathematical models for early warning of landslides induced by rainfall

FLaIR and SUSHI: two mathematical models for early warning of landslides induced by rainfall

Numerical Investigation on Infiltration and Runoff in Unsaturated Soils with Unsteady Rainfall Intensity

Analysis of the water content in an unconfined aquifer with a partially penetrated pumping well

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