Variability quantification of excess pressure head in heterogeneous deformable aquifers

Chang, C. M.; Yeh, Hund‐Der

doi:10.1016/j.apm.2016.05.026

Cited by 3 publications

(4 citation statements)

References 44 publications

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“…A vertical gradient in excess pressure is therefore created, and the flow occurs in response to that. This groundwater flow problem is described in detail by Chang and Yeh (). It is further assumed that the vertical log hydraulic conductivity (ln K ) field can be treated as a spatially random process (a stochastic process).…”

Section: Statement Of the Problemmentioning

confidence: 99%

“…Chang and Yeh () developed relationships between the stochastic structures of ln K and those of induced excess pressure head based on the assumption that a load decreasing linearly with time is applied vertically on the upper part of a finite‐thickness aquifer. Their results governing the groundwater flow field will be applied to investigate the behaviour of variability of solute travel time, which are given by (Eqs 17 and 31 of Chang & Yeh, )

Φ ((),, Z, t) = - \frac{16}{π^{3}} \frac{β_{p} Λ L^{2}}{K_{G}} T_{1} ((), η) sin ((), \frac{π}{2} ξ),

Φ ((),, Z, t) = \int_{- \infty}^{\infty} Α_{Φ} ((),;, Z, t, R) e^{iRZ} {dZ}_{f} ((), R),

where Φ represents the mean of excess pressure head, and ϕ represents small pressure head fluctuations about the mean.…”

Section: Development Of Lagrangian Velocity Statisticsmentioning

confidence: 99%

Φ ((),, Z, t) = - \frac{16}{π^{3}} \frac{β_{p} Λ L^{2}}{K_{G}} T_{1} ((), η) sin ((), \frac{π}{2} ξ),

Φ ((),, Z, t) = \int_{- \infty}^{\infty} Α_{Φ} ((),;, Z, t, R) e^{iRZ} {dZ}_{f} ((), R),

where Φ represents the mean of excess pressure head, and ϕ represents small pressure head fluctuations about the mean. In addition, Λ denotes the uniform decreasing rate of vertical loading, η = K G t /( SL 2 ), S is the storage coefficient defined as S = ρ f g ( β p + nβ f ), ρ f is the density of fluid, β p and β f are the coefficients of soil compressibility and fluid compressibility, respectively, K G = exp[ F ], F is the mean of log hydraulic conductivity, n is the porosity, L is the vertical length of the flow domain, ξ = Z / L , and

A_{Φ} ((),;, Z, t, R) = \frac{4}{π^{2}} \frac{β_{p} Λ}{K_{G}} sin ((), \frac{π}{2} ξ) e^{- italiciRZ} ([], T_{1} ((), η) ω_{1} ((), R) + T_{2} ((), η) ω_{2} ((), R)),

T_{1} ((), η) = 1 - exp ((), - \frac{π^{2}}{4} η),

T_{2} ((), η) = \frac{π^{2}}{4}

…”

Section: Development Of Lagrangian Velocity Statisticsmentioning

confidence: 99%

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Quantification of Lagrangian travel time statistics under nonstationary random groundwater flow conditions

Chang

Yeh

2018

Hydrological Processes

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This study presents a Lagrangian description of advection dominated field-scale transport of inert solutes, namely, the statistics of advective solute travel time and trajectory, in nonstationary random groundwater flow fields. The vertical flow field is generated by the effects of changes in total stress applied in fluid-saturated heterogeneous deformable porous media. The Lagrangian statistics are developed directly from the velocity statistics based on the application of stochastic methodology such as the representation theorem and Fourier-Stieltjes integral representation. The focus of our numerical evaluation is placed on the influence of the soil compressibility on the Lagrangian statistics. The prediction on the statistics of solute travel time and trajectory may serve as the basic input to the environmental risk assessment. KEYWORDS heterogeneous deformable porous media, nonstationary groundwater flow fields, soil compressibility, statistics of the solute travel time

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Section: Statement Of the Problemmentioning

confidence: 99%

Φ ((),, Z, t) = - \frac{16}{π^{3}} \frac{β_{p} Λ L^{2}}{K_{G}} T_{1} ((), η) sin ((), \frac{π}{2} ξ),

Φ ((),, Z, t) = \int_{- \infty}^{\infty} Α_{Φ} ((),;, Z, t, R) e^{iRZ} {dZ}_{f} ((), R),

where Φ represents the mean of excess pressure head, and ϕ represents small pressure head fluctuations about the mean.…”

Section: Development Of Lagrangian Velocity Statisticsmentioning

confidence: 99%

Φ ((),, Z, t) = - \frac{16}{π^{3}} \frac{β_{p} Λ L^{2}}{K_{G}} T_{1} ((), η) sin ((), \frac{π}{2} ξ),

Φ ((),, Z, t) = \int_{- \infty}^{\infty} Α_{Φ} ((),;, Z, t, R) e^{iRZ} {dZ}_{f} ((), R),

A_{Φ} ((),;, Z, t, R) = \frac{4}{π^{2}} \frac{β_{p} Λ}{K_{G}} sin ((), \frac{π}{2} ξ) e^{- italiciRZ} ([], T_{1} ((), η) ω_{1} ((), R) + T_{2} ((), η) ω_{2} ((), R)),

T_{1} ((), η) = 1 - exp ((), - \frac{π^{2}}{4} η),

T_{2} ((), η) = \frac{π^{2}}{4}

…”

Section: Development Of Lagrangian Velocity Statisticsmentioning

confidence: 99%

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Quantification of Lagrangian travel time statistics under nonstationary random groundwater flow conditions

Chang

Yeh

2018

Hydrological Processes

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“…Fourier spectral method has been applied in many studies [13,14]. The three-dimensional discretization is defined analogously.…”

Section: Algorithmmentioning

confidence: 99%

Curve and Surface Smoothing Using a Modified Cahn‐Hilliard Equation

Choi

Jeong

Kim

2017

Mathematical Problems in Engineering

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We present a new method using the modified Cahn-Hilliard (CH) equation for smoothing piecewise linear shapes of two-and three-dimensional objects. The CH equation has good smoothing dynamics and it is coupled with a fidelity term which keeps the original given data; that is, it does not produce significant shrinkage. The modified CH equation is discretized using a linearly stable splitting scheme in time and the resulting scheme is solved by using a Fourier spectral method. We present computational results for both curve and surface smoothing problems. The computational results demonstrate that the proposed algorithm is fast and efficient.

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Stochastic analysis of the interaction between excess fluid flow and soil deformation in heterogeneous deformable porous media

Chang,

Ni,

Lin

et al. 2024

Physics of Fluids

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Since aquifers deform under applied stresses, it is important to understand the interaction between fluid flow and soil deformation, as the deformation of the solid matrix affects the storage of water in the void space and may reach an extent that causes land subsidence under certain conditions. Geological heterogeneity has a major influence on groundwater movement and can therefore affect the amount of compaction. The aim of this work is, therefore, to perform a stochastic analysis of the influence of the variability of hydraulic conductivity fields on the interaction between excess fluid flow and soil deformation in heterogeneous, deformable porous media. The stress equilibrium equation and the storage equation together form a pair of coupled constitutive equations to describe the interaction of deformation (volume strain) and excess pore fluid pressure head. Using the Fourier–Stieltjes representation approach and a perturbation approximation, the coupled equations are solved analytically in the Fourier space domain for the case of unidirectional excess mean flow. Based on these solutions and the representation theorem, results are obtained for the variances of excess pore fluid pressure head and volume strain. They serve as an index of variability quantification for the evaluation of the variability of the log conductivity field and the compressibility coefficient of the soil on the variability of pressure head and volume strain fields. An illustration of the application of the proposed stochastic theory to predict the excess pore pressure and volume strain under uncertainty is also given.

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Variability quantification of excess pressure head in heterogeneous deformable aquifers

Cited by 3 publications

References 44 publications

Quantification of Lagrangian travel time statistics under nonstationary random groundwater flow conditions

Quantification of Lagrangian travel time statistics under nonstationary random groundwater flow conditions

Curve and Surface Smoothing Using a Modified Cahn‐Hilliard Equation

Stochastic analysis of the interaction between excess fluid flow and soil deformation in heterogeneous deformable porous media

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