Flow Through Heterogeneous Geologic Media

Yeh, Tian Chyi Jim; Khaleel, Raziuddin; Carroll, Kenneth C.

doi:10.1017/cbo9781139879323

Cited by 60 publications

(98 citation statements)

References 153 publications

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“…In this paper, a variably saturated flow in a heterogeneous two‐dimensional (2‐D) vertical hillslope cross section is assumed described by the governing flow equation (Yeh et al, ):

\frac{\partial}{\partial x} ((),, K ((),, P) \frac{\partial P}{\partial x}) + \frac{\partial}{\partial z} ((),, K ((),, P) \frac{\partial ((),, P + z)}{\partial z}) = ([],, normalβ S_{s} + C ((),, P)) \frac{\partial P}{\partial t},

where P is the pressure head [L]; it is a positive value if the medium is fully saturated and is negative if the medium is unsaturated. z is the elevation head [L].…”

Section: Methodsmentioning

confidence: 99%

“…Following Yeh et al (), in order to describe K s heterogeneity in a hillslope as a random field, we will implicitly assume the random field has a joint lognormal distribution (although it is not necessary). This probability distribution is characterized by a mean (μ Ks ), a variance (

σ_{K_{s}}^{2}

), and a correlation structure described by a covariance function with some correlation scales (λ), which represent the average spatial fabric (i.e., average thickness, length, and width of heterogeneity of the hillslope).…”

Section: Methodsmentioning

confidence: 99%

“…It should be noted that acquiring spatial statistics of K s is not a trivial task in practice due to a limited amount of samples and the multi‐scale variability of K s in the field (Cao & Wang, , ; Wang, Cao, & Li, ). It is known that other parameters such as α, n , θ s , and θ r of the MVG model (Equations and ) do exhibit spatial variabilities (see summary by Yeh et al, ). Nevertheless, in this analysis, we will assume that their spatial variabilities have insignificant effects on slope stability issues, and they are assumed constant throughout the hillslope.…”

Section: Methodsmentioning

confidence: 99%

See 2 more Smart Citations

Sampling schemes for hillslope hydrologic processes and stability analysis based on cross-correlation analysis

Cai

Yeh

2017

Hydrol. Process.

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Cost‐effective sampling strategies to understand hydrologic processes in a hillslope are essential to the estimation of hillslope seepage and to the evaluation of slope stability. The objectives of this paper are (a) to introduce a stochastic cross‐correlation analysis to hillslope hydrologic processes and stability investigation and (b) to develop a cost‐effective sampling strategy to reduce the pore‐water pressure uncertainty at the region of our interest. The concept of stochastic representation of spatial variabilities of soil hydraulic properties is introduced first. We then develop a first‐order analysis method to determine spatiotemporal distribution of pore‐water pressure head (P) variance (unconditional variance or uncertainty) due to spatial variability of saturated hydraulic conductivity (Ks) in a variably saturated hillslope during rainfall. Subsequently, a cross‐correlation analysis is presented, which quantifies the spatial correlation between P at a given location and Ks at any part of a hillslope under a transient infiltration event. We afterward formulate a first‐order approximation of residual P variance (conditional variance or uncertainty) due to inclusions of Ks measurements. The developed methodology is applied to synthetic, heterogeneous, two‐dimensional hillslopes to investigate the effectiveness of several Ks sampling schemes. Results of this investigation show that boreholes and sampling locations should be placed at an interval of one correlation scale. They should be distributed over an area covering several correlation scales, rather than clustered together at the largest cross‐correlation region or at regions where prediction uncertainty is large (where our interest and concern are). Further, the results demonstrate that increasing the sampling density is useful but inefficient. Layering structures of hillslopes reduce the number of boreholes and samples required. At last, a cost‐effective sampling strategy for study of slope stability based on cross‐correlation is suggested, which minimizes the prediction uncertainty of P at critical locations.

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“…In this paper, a variably saturated flow in a heterogeneous two‐dimensional (2‐D) vertical hillslope cross section is assumed described by the governing flow equation (Yeh et al, ):

\frac{\partial}{\partial x} ((),, K ((),, P) \frac{\partial P}{\partial x}) + \frac{\partial}{\partial z} ((),, K ((),, P) \frac{\partial ((),, P + z)}{\partial z}) = ([],, normalβ S_{s} + C ((),, P)) \frac{\partial P}{\partial t},

where P is the pressure head [L]; it is a positive value if the medium is fully saturated and is negative if the medium is unsaturated. z is the elevation head [L].…”

Section: Methodsmentioning

confidence: 99%

σ_{K_{s}}^{2}

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Sampling schemes for hillslope hydrologic processes and stability analysis based on cross-correlation analysis

Cai

Yeh

2017

Hydrol. Process.

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“…Hence, the lithological structure of an aquifer is typically heterogeneous (Klingbeil et al ; Ritzi and Allen‐King ; Huysmans and Dassargues ). As a result, the hydraulic conductivity ( K ) in the aquifer, which has a dominant effect upon pollutant transport, may vary by several orders of magnitude within relatively short distances (Kitanidis ; Rubin ; Yeh et al ). Moreover, aquifers are poorly characterized: local measurements of the hydraulic parameters, such as core sampling during drilling operations can provide information on a very limited volume of the aquifer.…”

Section: Introductionmentioning

confidence: 99%

A Genetic Algorithm for Stochastic Inversion in Contaminant Subsurface Hydrology

Moreno¹,

Paster

2019

Groundwater

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Identifying the spatial distribution of hydrological properties of aquifers is a key problem in subsurface hydrology. The aquifer structure plays an important role in contaminant transport. Identifying the properties (primarily the hydraulic conductivity) is essentially an inversion problem that is ill‐posed, non‐unique and computationally intensive by definition. In this work, the non‐uniqueness of the inverse problem is tackled via a novel Genetic Algorithm approach combined with a geostatistical method (Sequential Indicator Simulations) for construction of realizations of properties spatial distributions, which are modeled as random. The Genetic Algorithm cross‐over operator is based on a novel concept of pilot‐planes: daughter realizations adopt pilot‐planes from one of their parents. In addition, each aquifer realization is conditioned on the geological hard data and is constructed by sampling the facies distribution, evaluated by indicator variograms. The approach is illustrated in two test cases: a synthetic two‐dimensional (2D) case and an actual three‐dimensional (3D) case. The results have shown the ability of the proposed approach to generate a set of realizations, where each individual exhibits minor deviations from the measurements. Further, a comparison between the proposed approach and direct (Monte Carlo) approach shows that the Genetic Algorithm was able to generate an ensemble of solutions with a better fitting of the measurements than the direct approach by a significantly reduced computational effort.

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“…Standard hydrogeology textbooks provide readers with the analytical tools to infer aquifer properties (i.e., storage and conductivity coefficients) based on field data, but few examine the impact of aquifer heterogeneities on these test results, or the associated issue of the scale effect, in detail. Flow Through Heterogeneous Geologic Media , by Yeh et al (), can be seen in large part as a revisitation of pumping‐test analyses for a new era, with a focus on giving modern hydrogeologists a better appreciation for the impact of heterogeneity.…”

mentioning

confidence: 99%