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Warren Barrash - One of the best experts on this subject based on the ideXlab platform.
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semi analytical solution for flow in a leaky Unconfined Aquifer toward a partially penetrating pumping well
Journal of Hydrology, 2008Co-Authors: Bwalya Malama, Kristopher L. Kuhlman, Warren BarrashAbstract:Summary A semi-analytical solution is presented for the problem of flow in a system consisting of Unconfined and confined Aquifers, separated by an aquitard. The Unconfined Aquifer is pumped continuously at a constant rate from a well of infinitesimal radius that partially penetrates its saturated thickness. The solution is termed semi-analytical because the exact solution obtained in double Laplace‐Hankel transform space is inverted numerically. The solution presented here is more general than similar solutions obtained for confined Aquifer flow as we do not adopt the assumption of unidirectional flow in the confined Aquifer (typically assumed to be horizontal) and the aquitard (typically assumed to be vertical). Model predicted results show significant departure from the solution that does not take into account the effect of leakage even for cases where aquitard hydraulic conductivities are two orders of magnitude smaller than those of the Aquifers. The results show low sensitivity to changes in radial hydraulic conductivities for aquitards that are two or more orders of magnitude smaller than those of the Aquifers, in conformity to findings of earlier workers that radial flow in aquitards may be neglected under such conditions. Hence, for cases were aquitard hydraulic conductivities are two or more orders of magnitude smaller than Aquifer conductivities, the simpler models that restrict flow to the radial direction in Aquifers and to the vertical direction in aquitards may be sufficient. However, the model developed here can be used to model flow in Aquifer‐aquitard systems where radial flow is significant in aquitards. a 2008 Elsevier B.V. All rights reserved.
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semi analytical solution for flow in leaky Unconfined Aquifer aquitard systems
Journal of Hydrology, 2007Co-Authors: Bwalya Malama, Kristopher L. Kuhlman, Warren BarrashAbstract:This study presents a semi-analytical solution for the problem of leakage in an Unconfined Aquifer bounded below by an aquitard of finite or semi-infinite extent. The homogeneous anisotropic Unconfined Aquifer of infinite radial extent is pumped continuously at a constant rate from a well of infinitesimal radius. The aquitard is also homogeneous, anisotropic and of infinite radial extent. Flow in both the Aquifer and the aquitard is allowed to occur both vertically and horizontally. Exact solutions to the governing equations given in this work are developed in the double Laplace-Hankel transform space for drawdown response in the Unconfined Aquifer and the underlying aquitard. The inverse transforms of the solutions are obtained numerically. The theoretical results show that leakage can cause significant departure, at both early and late times, from the solution with no leakage. The solution presented here can be used in least-squares routines for estimation of hydraulic parameters for two-layered Unconfined Aquifer-aquitard systems.
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Semi-analytical solution for flow in leaky Unconfined Aquifer–aquitard systems
Journal of Hydrology, 2007Co-Authors: Bwalya Malama, Kristopher L. Kuhlman, Warren BarrashAbstract:This study presents a semi-analytical solution for the problem of leakage in an Unconfined Aquifer bounded below by an aquitard of finite or semi-infinite extent. The homogeneous anisotropic Unconfined Aquifer of infinite radial extent is pumped continuously at a constant rate from a well of infinitesimal radius. The aquitard is also homogeneous, anisotropic and of infinite radial extent. Flow in both the Aquifer and the aquitard is allowed to occur both vertically and horizontally. Exact solutions to the governing equations given in this work are developed in the double Laplace–Hankel transform space for drawdown response in the Unconfined Aquifer and the underlying aquitard. The inverse transforms of the solutions are obtained numerically. The theoretical results show that leakage can cause significant departure, at both early and late times, from the solution with no leakage. The solution presented here can be used in least-squares routines for estimation of hydraulic parameters for two-layered Unconfined Aquifer–aquitard systems
Kristopher L. Kuhlman - One of the best experts on this subject based on the ideXlab platform.
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Unconfined Aquifer Flow Theory: From Dupuit to Present
Advances in Hydrogeology, 2013Co-Authors: Phoolendra K. Mishra, Kristopher L. KuhlmanAbstract:Analytic and semi-analytic solution are often used by researchers and practicioners to estimate Aquifer parameters from Unconfined Aquifer pumping tests. The non-linearities associated with Unconfined (i.e., water table) Aquifer tests makes their analysis more complex than confined tests. Although analytical solutions for Unconfined flow began in the mid-1800s with Dupuit, Thiem was possibly the first to use them to estimate Aquifer parameters from pumping tests in the early 1900s. In the 1950s, Boulton developed the first transient well test solution specialized to Unconfined flow. By the 1970s Neuman had developed solutions considering both primary transient storage mechanisms (confined storage and delayed yield) without non-physical fitting parameters. In the last decade, research into developing Unconfined Aquifer test solutions has mostly focused on explicitly coupling the Aquifer with the linearized vadose zone. Despite the many advanced solution methods available, there still exists a need for realism to accurately simulate real-world Aquifer tests
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Saturated–unsaturated flow in a compressible leaky-Unconfined Aquifer
Advances in Water Resources, 2012Co-Authors: Phoolendra K. Mishra, Velimir V. Vesselinov, Kristopher L. KuhlmanAbstract:An analytical solution is developed for three-dimensional flow towards a partially penetrating largediameter well in an Unconfined Aquifer bounded below by a leaky aquitard of finite or semi-infinite extent. The analytical solution is derived using Laplace and Hankel transforms, then inverted numerically. Existing solutions for flow in leaky Unconfined Aquifers neglect the unsaturated zone following an assumption of instantaneous drainage due to Neuman. We extend the theory of leakage in Unconfined Aquifers by (1) including water flow and storage in the unsaturated zone above the water table, and (2) allowing the finite-diameter pumping well to partially penetrate the Aquifer. The investigation of model-predicted results shows that aquitard leakage leads to significant departure from the Unconfined solution without leakage. The investigation of dimensionless time-drawdown relationships shows that the aquitard drawdown also depends on unsaturated zone properties and the pumping-well wellbore storage effects.
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semi analytical solution for flow in a leaky Unconfined Aquifer toward a partially penetrating pumping well
Journal of Hydrology, 2008Co-Authors: Bwalya Malama, Kristopher L. Kuhlman, Warren BarrashAbstract:Summary A semi-analytical solution is presented for the problem of flow in a system consisting of Unconfined and confined Aquifers, separated by an aquitard. The Unconfined Aquifer is pumped continuously at a constant rate from a well of infinitesimal radius that partially penetrates its saturated thickness. The solution is termed semi-analytical because the exact solution obtained in double Laplace‐Hankel transform space is inverted numerically. The solution presented here is more general than similar solutions obtained for confined Aquifer flow as we do not adopt the assumption of unidirectional flow in the confined Aquifer (typically assumed to be horizontal) and the aquitard (typically assumed to be vertical). Model predicted results show significant departure from the solution that does not take into account the effect of leakage even for cases where aquitard hydraulic conductivities are two orders of magnitude smaller than those of the Aquifers. The results show low sensitivity to changes in radial hydraulic conductivities for aquitards that are two or more orders of magnitude smaller than those of the Aquifers, in conformity to findings of earlier workers that radial flow in aquitards may be neglected under such conditions. Hence, for cases were aquitard hydraulic conductivities are two or more orders of magnitude smaller than Aquifer conductivities, the simpler models that restrict flow to the radial direction in Aquifers and to the vertical direction in aquitards may be sufficient. However, the model developed here can be used to model flow in Aquifer‐aquitard systems where radial flow is significant in aquitards. a 2008 Elsevier B.V. All rights reserved.
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semi analytical solution for flow in leaky Unconfined Aquifer aquitard systems
Journal of Hydrology, 2007Co-Authors: Bwalya Malama, Kristopher L. Kuhlman, Warren BarrashAbstract:This study presents a semi-analytical solution for the problem of leakage in an Unconfined Aquifer bounded below by an aquitard of finite or semi-infinite extent. The homogeneous anisotropic Unconfined Aquifer of infinite radial extent is pumped continuously at a constant rate from a well of infinitesimal radius. The aquitard is also homogeneous, anisotropic and of infinite radial extent. Flow in both the Aquifer and the aquitard is allowed to occur both vertically and horizontally. Exact solutions to the governing equations given in this work are developed in the double Laplace-Hankel transform space for drawdown response in the Unconfined Aquifer and the underlying aquitard. The inverse transforms of the solutions are obtained numerically. The theoretical results show that leakage can cause significant departure, at both early and late times, from the solution with no leakage. The solution presented here can be used in least-squares routines for estimation of hydraulic parameters for two-layered Unconfined Aquifer-aquitard systems.
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Semi-analytical solution for flow in leaky Unconfined Aquifer–aquitard systems
Journal of Hydrology, 2007Co-Authors: Bwalya Malama, Kristopher L. Kuhlman, Warren BarrashAbstract:This study presents a semi-analytical solution for the problem of leakage in an Unconfined Aquifer bounded below by an aquitard of finite or semi-infinite extent. The homogeneous anisotropic Unconfined Aquifer of infinite radial extent is pumped continuously at a constant rate from a well of infinitesimal radius. The aquitard is also homogeneous, anisotropic and of infinite radial extent. Flow in both the Aquifer and the aquitard is allowed to occur both vertically and horizontally. Exact solutions to the governing equations given in this work are developed in the double Laplace–Hankel transform space for drawdown response in the Unconfined Aquifer and the underlying aquitard. The inverse transforms of the solutions are obtained numerically. The theoretical results show that leakage can cause significant departure, at both early and late times, from the solution with no leakage. The solution presented here can be used in least-squares routines for estimation of hydraulic parameters for two-layered Unconfined Aquifer–aquitard systems
Bwalya Malama - One of the best experts on this subject based on the ideXlab platform.
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semi analytical solution for flow in a leaky Unconfined Aquifer toward a partially penetrating pumping well
Journal of Hydrology, 2008Co-Authors: Bwalya Malama, Kristopher L. Kuhlman, Warren BarrashAbstract:Summary A semi-analytical solution is presented for the problem of flow in a system consisting of Unconfined and confined Aquifers, separated by an aquitard. The Unconfined Aquifer is pumped continuously at a constant rate from a well of infinitesimal radius that partially penetrates its saturated thickness. The solution is termed semi-analytical because the exact solution obtained in double Laplace‐Hankel transform space is inverted numerically. The solution presented here is more general than similar solutions obtained for confined Aquifer flow as we do not adopt the assumption of unidirectional flow in the confined Aquifer (typically assumed to be horizontal) and the aquitard (typically assumed to be vertical). Model predicted results show significant departure from the solution that does not take into account the effect of leakage even for cases where aquitard hydraulic conductivities are two orders of magnitude smaller than those of the Aquifers. The results show low sensitivity to changes in radial hydraulic conductivities for aquitards that are two or more orders of magnitude smaller than those of the Aquifers, in conformity to findings of earlier workers that radial flow in aquitards may be neglected under such conditions. Hence, for cases were aquitard hydraulic conductivities are two or more orders of magnitude smaller than Aquifer conductivities, the simpler models that restrict flow to the radial direction in Aquifers and to the vertical direction in aquitards may be sufficient. However, the model developed here can be used to model flow in Aquifer‐aquitard systems where radial flow is significant in aquitards. a 2008 Elsevier B.V. All rights reserved.
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semi analytical solution for flow in leaky Unconfined Aquifer aquitard systems
Journal of Hydrology, 2007Co-Authors: Bwalya Malama, Kristopher L. Kuhlman, Warren BarrashAbstract:This study presents a semi-analytical solution for the problem of leakage in an Unconfined Aquifer bounded below by an aquitard of finite or semi-infinite extent. The homogeneous anisotropic Unconfined Aquifer of infinite radial extent is pumped continuously at a constant rate from a well of infinitesimal radius. The aquitard is also homogeneous, anisotropic and of infinite radial extent. Flow in both the Aquifer and the aquitard is allowed to occur both vertically and horizontally. Exact solutions to the governing equations given in this work are developed in the double Laplace-Hankel transform space for drawdown response in the Unconfined Aquifer and the underlying aquitard. The inverse transforms of the solutions are obtained numerically. The theoretical results show that leakage can cause significant departure, at both early and late times, from the solution with no leakage. The solution presented here can be used in least-squares routines for estimation of hydraulic parameters for two-layered Unconfined Aquifer-aquitard systems.
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Semi-analytical solution for flow in leaky Unconfined Aquifer–aquitard systems
Journal of Hydrology, 2007Co-Authors: Bwalya Malama, Kristopher L. Kuhlman, Warren BarrashAbstract:This study presents a semi-analytical solution for the problem of leakage in an Unconfined Aquifer bounded below by an aquitard of finite or semi-infinite extent. The homogeneous anisotropic Unconfined Aquifer of infinite radial extent is pumped continuously at a constant rate from a well of infinitesimal radius. The aquitard is also homogeneous, anisotropic and of infinite radial extent. Flow in both the Aquifer and the aquitard is allowed to occur both vertically and horizontally. Exact solutions to the governing equations given in this work are developed in the double Laplace–Hankel transform space for drawdown response in the Unconfined Aquifer and the underlying aquitard. The inverse transforms of the solutions are obtained numerically. The theoretical results show that leakage can cause significant departure, at both early and late times, from the solution with no leakage. The solution presented here can be used in least-squares routines for estimation of hydraulic parameters for two-layered Unconfined Aquifer–aquitard systems
You-kuan Zhang - One of the best experts on this subject based on the ideXlab platform.
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effect of heterogeneity on spatiotemporal variations of groundwater level in a bounded Unconfined Aquifer
Stochastic Environmental Research and Risk Assessment, 2016Co-Authors: Xiuyu Liang, You-kuan Zhang, Keith E SchillingAbstract:Spatiotemporal variations of groundwater level due to a white noise recharge time series and a random transmissivity field in a bounded Unconfined Aquifer was studied. The analytical solutions for the variance and covariance of groundwater level were derived with non-stationary spectral analyses and superposition principle. It was found that the fluctuations of groundwater level are spatially non-stationary due to a fixed head boundary condition and temporal non-stationary at early time but gradually became stationary as time progresses due to effect of the initial condition. The variation in groundwater level is mainly caused by the random source/sink in the case of temporally random recharge and spatially random transmissivity. The effect of heterogeneity is to increase the variation of groundwater level and the maximum effect occurs close to the constant head boundary because of the linear mean hydraulic gradient. The heterogeneity also enhances the correlation of groundwater level, especially at large time intervals and small spatial distances.
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temporal and spatial variation and scaling of groundwater levels in a bounded Unconfined Aquifer
Journal of Hydrology, 2013Co-Authors: Xiuyu Liang, You-kuan ZhangAbstract:Summary Temporal and spatial variation and scaling of groundwater level ( h ) due to a white noise source in an Unconfined Aquifer bounded by a no-flow boundary and a river were investigated with non-stationary spectral analyses. Analytical solutions for the variance ( σ h 2 ), covariance ( C hh ), and spectrum ( S hh ) of h described by a linearized Boussinesq equation were derived and verified by Monte Carlo simulations. It is found that in general the random process of h is temporally and spatially non-stationary and σ h 2 , C hh , and S hh are functions of space and time. The effect of a constant-head boundary is to reduce the variance and covariance at late times or the spectrum power at low frequencies near the boundary and thus to create a crossover or break point in temporal scaling of h ( x , t ). The simulation results support the common practice of estimating scaling parameters from the spectrum of observed groundwater levels. The results obtained in this study are consistent with published theoretical analyses and provide more general theoretical basis for field observations.
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Analytical solution for drainage and recession from an Unconfined Aquifer.
Ground water, 2011Co-Authors: Xiuyu Liang, You-kuan ZhangAbstract:One-dimensional transient groundwater flow from a divide to a river in an Unconfined Aquifer described by the Boussinesq equation was studied. We derived the analytical solution for the water table recession and drainage change process described with a linearized Boussinesq equation with a physically based initial condition. A method for determining the average water table in the solutions was proposed. It is shown that the solution derived in the form of infinite series can be well approximated with the simplified solution which contains only the leading term of the original solution. The solution and their simplification can be easily evaluated and used by others to study the groundwater flow problems, such as drainage and base flow estimation, in an Unconfined Aquifer.
Nick Cartwright - One of the best experts on this subject based on the ideXlab platform.
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Modelling the effects of porous media deformation on the propagation of water-table waves in a sandy Unconfined Aquifer
Hydrogeology Journal, 2017Co-Authors: Seyed Mohammad Hossein Jazayeri Shoushtari, Nick CartwrightAbstract:Cet article examine l’influence de la déformation du milieu poreux sur la dispersion des ondes de la surface piézométrique dans un aquifère sableux libre en utilisant un modèle numérique qui couple l’équation de Richard avec un modèle poro-élastique. Cette étude était motivée par les résultats de Shoushtari et al. (2016) qui n’étaient pas capables de reproduire la dispersion des ondes observées dans des données issues d’un réservoir à sable, tant avec des modèles numériques de l’équation de Richard (faisant l’hypothèse d’un milieu poreux rigide) qu’avec des solutions analytiques existantes. La dispersion des ondes de la surface piézométrique est quantifiée par un nombre d’onde complexe extrait de profils d’amplitude et de phase prédits. Une analyse de sensibilité a été réalisée afin d’évaluer l’influence des principaux paramètres dans le modèle poro-élastique, à savoir le module de Young ( E ) et le coefficient de Poisson ( ν ). Pour une courte période d’oscillation ( T = 16.4 s), le taux d’accroissement du retard de phase ( k _i) est sensible aux valeurs retenues pour E et ν , ce qui démontre une relation inverse avec les deux paramètres. Les modifications de l’amplitude du taux de décroissance ( k _r) sont cependant négligeables. Pour une période d’oscillation plus longue ( T = 908.6 s), des variations des valeurs de E et ν ont seulement induit de faibles changements tant de k _r que de k _i. Dans les deux cas de courte et de longue périodes, le modèle poro-élastique est incapable de reproduire la dispersion des ondes observée dans les données existantes en laboratoire. Par conséquent, la déformation du milieu poreux ne peut pas expliquer la dissipation d’énergie additionnelle dans les données obtenues au laboratoire. Shoushtari SMH, Cartwright N, Perrochet P, Nielsen P (2016) The effects of oscillation period on groundwater wave dispersion in a sandy Unconfined Aquifer: sand flume experiments and modelling. J Hydrol 533:412–440. This paper examines the influence of porous media deformation on water-table wave dispersion in an Unconfined Aquifer using a numerical model which couples Richards’ equation to the poro-elastic model. The study was motivated by the findings of Shoushtari et al. (J Hydrol 533:412–440, 2016) who were unable to reproduce the observed wave dispersion in their sand flume data with either numerical Richards’ equation models (assuming rigid porous media) or existing analytic solutions. The water-table wave dispersion is quantified via the complex wave number extracted from the predicted amplitude and phase profiles. A sensitivity analysis was performed to establish the influence of the main parameters in the poro-elastic model, namely Young’s modulus ( E ) and Poisson’s ratio ( ν ). For a short oscillation period ( T = 16.4 s), the phase lag increase rate ( k _i) is sensitive to the chosen values of E and ν , demonstrating an inverse relationship with both parameters. Changes in the amplitude decay rate ( k _r), however, were negligible. For a longer oscillation period ( T = 908.6 s), variations in the values of E and ν resulted in only small changes in both k _r and k _i. In both the short and long period cases, the poro-elastic model is unable to reproduce the observed wave dispersion in the existing laboratory data. Hence porous media deformation cannot explain the additional energy dissipation in the laboratory data. Shoushtari SMH, Cartwright N, Perrochet P, Nielsen P (2016) The effects of oscillation period on groundwater wave dispersion in a sandy Unconfined Aquifer: sand flume experiments and modelling. J Hydrol 533:412–440. En este trabajo se analiza la influencia de la deformación de medios porosos en la dispersión de ondas de la capa freática en un acuífero no confinado mediante un modelo numérico que acopla la ecuación de Richards con el modelo poro-elástico. El estudio fue motivado por los hallazgos de Shoushtari et al. (2016) que fueron incapaces de reproducir la dispersión de las ondas observadas en los datos de un canal de arena, tanto con modelos numéricos de la ecuación de Richards (suponiendo un medio poroso rígido) como con las soluciones analíticas existentes. La dispersión de las ondas de la capa freática se cuantifica a través del número de onda complejo extraído de los perfiles de fase y amplitud predichos. Se realizó un análisis de sensibilidad para establecer la influencia de los parámetros principales en el modelo de poro-elástico, a saber, el módulo de Young ( E ) y el coeficiente de Poisson ( ν ). Durante un periodo de oscilación corto ( T = 16.4 s), el ritmo de incremento del retardo de fase ( k _i) es sensible a los valores elegidos para E y ν , demostrándose una relación inversa con ambos parámetros. Sin embargo, los cambios en el ritmo de decaimiento de la amplitud ( k _r), fueron despreciables. Para un período más largo de oscilación ( T = 908.6 s), las variaciones en los valores de E y ν resultaron en sólo en pequeños cambios tanto en k _r como en k _i. En los dos casos período corto y largo, el modelo de poro-elástico es incapaz de reproducir la dispersión observada de la onda en los datos de laboratorio existentes. Por lo tanto la deformación de un medio poroso no puede explicar la disipación de energía adicional en los datos de laboratorio. Shoushtari SMH, Cartwright N, Perrochet P, Nielsen P (2016) The effects of oscillation period on groundwater wave dispersion in a sandy Unconfined Aquifer: sand flume experiments and modelling. J Hydrol 533:412–440. 本文利用把Richards方程式与多孔--弹性模型耦合的数值模型检查了非承压含水层多孔介质变形对水位波弥散的影响。受到Shoushtari等人(2016)的研究结果激发而进行了这项研究,Shoushtari等人采用数值Richards方程式模型(假设为严格的多孔介质)或现有的解析方法在砂槽数据中并不能再现观测到波弥散。通过从预测的幅相剖面提取的复合的波数量化了水位波弥散。进行了灵敏度分析,建立了多孔—弹性模型中主要参数的影响,即杨氏模量( E )和泊松比( v )。对于很短的振荡周期( T = 16.4 s),相位滞后增长率( k _i)对所选的 E 值和 ν 的值非常敏感,显示出了与两个参数的逆相关。然而,振幅衰退率( k _r)变化可以忽略不计。对于较长的振荡周期( T = 908.6 s), E 值和 ν 值的变化只造成了 k _r and k _i.很小的变化。在短期和长期情况下,多孔—弹性模型不能在现有的实验数据中再现 观测到的波弥散。因此,多孔介质变形不能解释实验数据中的额额外的能量耗散。Shoushtari SMH, Cartwright N, Perrochet P, Nielsen P (2016) The effects of oscillation period on groundwater wave dispersion in a sandy Unconfined Aquifer: sand flume experiments and modelling [(振荡周期对砂质飞承压含水层地下水波弥散的影响:砂槽实验和模拟]. J Hydrol 533:412–440. Este artigo examina a influência da deformação do meio poroso na dispersão da oscilação do nível freático em um aquífero livre utilizando um modelo numérico que acoplou a equação de Richard ao modelo poro-elástico. O estudo foi motivado pelas descobertas de Shoushtari et al. (2016) que foram incapazes de reproduzir a dispersão da oscilação de dispersão observada na informação da calha de areia tanto com modelos numéricos de Richard (assumindo meio poroso rígido) quanto soluções analíticas existentes. A dispersão da oscilação do nível freático é quantificada pelo complexo número de oscilações extraídas da amplitude predita e fase do perfil. Uma análise da sensibilidade foi realizada para estabelecer a influência dos parâmetros principais no modelo poro-elástico, designado modulo de Young ( E ) e razão de Poisson ( v ). Para um curto período de oscilação ( T = 16.4 s), o aumento da taxa atraso de atraso da fase ( k _i) é sensível a valores escolhidos de E e v , demonstrando uma relação inversa com ambos os parâmetros. Mudanças na taxa de decaimento da amplitude ( k _r), no entanto, foram insignificantes. Para um longo período de oscilação ( T = 908.6 s), variações nos valores de E e v resultaram apenas em pequenas mudanças em ambos k _r e k _i.Em ambos os casos, curtos ou longos períodos, o modelo poro-elástico foi incapaz de reproduzir a dispersão da oscilação observada em dados existentes de laboratório. Consequentemente a deformação no meio poroso não pode explicar a energia de dissipação adicional nos dados laboratoriais. Shoushtari SMH, Cartwright N, Perrochet P, Nielsen P (2016) The effects of oscillation period on groundwater wave dispersion in a sandy Unconfined Aquifer: sand flume experiments and modelling [Os efeitos do período de oscilação na dispersão da oscilação das águas subterrâneas em um aquífero livre arenoso: experimentos e modelagem em calha de areia]. J Hydrol 533:412–440.
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influence of hysteresis on groundwater wave dynamics in an Unconfined Aquifer with a sloping boundary
Journal of Hydrology, 2015Co-Authors: Seyed Mohammad Hossein Jazayeri Shoushtari, Pierre Perrochet, Nick Cartwright, Peter NielsenAbstract:In this paper, the influence of hysteresis on water table dynamics in an Unconfined Aquifer was examined using a numerical model to solve Richards’ unsaturated flow equation. The model was subject to simple harmonic forcing across a sloping boundary with a seepage face boundary condition. Time series from both hysteretic and non-hysteretic models were subject to harmonic analysis to extract the amplitude and phase profiles for comparison with existing sand flume data (Cartwright et al., 2004). The results from both model types show good agreement with the data indicating no influence of hysteresis at the oscillation period examined (T = 348 s). The models were then used to perform a parametric study to examine the relationship between oscillation period and hysteresis effects with periods ranging from 3 min to 180 min. At short oscillation periods, (T ≈ 180 s) the effects of hysteresis were negligible with both models providing similar results. As the oscillation period increased, the hysteretic model showed less amplitude damping than the non-hysteretic model. For periods greater than T = 60 min, the phase lag in the non-hysteretic model is greater than for the hysteretic one. For periods less than T = 60 min this trend is reversed and the hysteretic model produced a greater phase lag than the non-hysteretic model. These findings suggest that consideration of hysteresis dynamics in Richards’ equation models has no influence on water table wave dispersion for short period forcing such as waves (T ≈ 10 s) whereas for long period forcing such as tides (T ≈ 12.25 h) or storm surges (T ≈ days) hysteresis dynamics should be taken into account.
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water table waves in an Unconfined Aquifer experiments and modeling
Water Resources Research, 2003Co-Authors: Nick Cartwright, Peter Nielsen, Scott L DunnAbstract:[1] Comprehensive measurements are presented of the piezometric head in an Unconfined Aquifer during steady, simple harmonic oscillations driven by a hydrostatic clear water reservoir through a vertical interface. The results are analyzed and used to test existing hydrostatic and nonhydrostatic, small-amplitude theories along with capillary fringe effects. As expected, the amplitude of the water table wave decays exponentially. However, the decay rates and phase lags indicate the influence of both vertical flow and capillary effects. The capillary effects are reconciled with observations of water table oscillations in a sand column with the same sand. The effects of vertical flows and the corresponding nonhydrostatic pressure are reasonably well described by small-amplitude theory for water table waves in finite depth Aquifers. That includes the oscillation amplitudes being greater at the bottom than at the top and the phase lead of the bottom compared with the top. The main problems with respect to interpreting the measurements through existing theory relate to the complicated boundary condition at the interface between the driving head reservoir and the Aquifer. That is, the small-amplitude, finite depth expansion solution, which matches a hydrostatic boundary condition between the bottom and the mean driving head level, is unrealistic with respect to the pressure variation above this level. Hence it cannot describe the finer details of the multiple mode behavior close to the driving head boundary. The mean water table height initially increases with distance from the forcing boundary but then decreases again, and its asymptotic value is considerably smaller than that previously predicted for finite depth Aquifers without capillary effects. Just as the mean water table over-height is smaller than predicted by capillarity-free shallow Aquifer models, so is the amplitude of the second harmonic. In fact, there is no indication of extra second harmonics ( in addition to that contained in the driving head) being generated at the interface or in the interior.
