Log Hydraulic Conductivity Research Articles

Numerical Investigation of Confining Pressure Effects on Microscopic Structure and Hydraulic Conductivity of Geosynthetic Clay Liners

A series of COMSOL numerical models were developed to explore how confining pressure impacts the microscopic structure and hydraulic conductivity of Geosynthetic Clay Liners (GCLs), taking into account the bentonite swelling ratio, mobile porosity, pore size, and tortuosity of the main flow path. The study reveals that the mobile porosity and pore size are critical factors affecting GCL hydraulic conductivity. As confining pressure increases, the transition of mobile water to immobile water occurs, resulting in a reduction in mobile water volume, the narrowing of pore channels, decreased flow velocity, and diminished hydraulic conductivity within the GCL. Mobile porosity undergoes a slight decrease from 0.273 to 0.104, while the ratio of mobile porosity to total porosity in the swelling process decreases significantly from 0.672 to 0.256 across the confining pressure range from 50 kPa to 500 kPa, which indicates a transition of mobile water toward immobile water. The tortuosity of the main flow path shows a slight increase, fluctuating within the range of 1.30 to 1.36, and maintains a value of around 1.34 as the confining pressure rises from 50 kPa to 500 kPa. At 50 kPa confining pressure, the minimum pore width measures 5.2 × 10−5 mm, with a corresponding hydraulic conductivity of 6.2 × 10−11 m/s. With an increase in confining pressure to 300 kPa, this compression leads to a narrower minimum pore width of 1.81 × 10−5 mm and a decrease in hydraulic conductivity to 5.11 × 10−12 m/s. The six-fold increase in confining pressure reduces hydraulic conductivity by one order of magnitude. A theoretical equation was derived to compute the hydraulic conductivity of GCLs under diverse confining pressure conditions, indicating a linear correlation between the logarithm of hydraulic conductivity and confining pressure, and exhibiting favorable agreement with experimental findings.

Modeling groundwater flow with random hydraulic conductivity using radial basis function partition of unity method

Simulating groundwater flows in heterogeneous aquifers is one of the most widely studied problems. The heterogeneity is modeled through random hydraulic conductivity fields log-normally distributed. In this paper, we aim to generate the realization of the log-normal hydraulic conductivity by summing up a finite number of random periodic modes with the Kraichnan algorithm. To address Neumann conditions, we propose a change of variables that results in Dirichlet boundary conditions along all boundaries of the computational domain. Then, we suggest using the radial basis function partition of unity method (RBFPUM) and RBFPUM with QR factorization (RBFPUM-QR) to analyze groundwater flow in the heterogeneous porous medium. We evaluate the performance of the proposed methods by increasing the number of random modes and the variance of the log-hydraulic conductivity fields using Gaussian and exponential correlation. In addition, we verify the effectiveness of the presented approaches in one and two dimensions using the method of manufactured solutions. Furthermore, we provide statistical inferences through Monte Carlo simulations. Numerical results demonstrate that RBFPUM-QR performs well in handling higher heterogeneity in both single realizations and Monte Carlo simulations.

Estimation of auto-covariance of log hydraulic conductivity from Generalized Sub-Gaussian porosity and particle size random fields

We derive analytical formulations relating the spatial covariance ( C Y ) of (log-transformed) hydraulic conductivities to auto- and cross-covariances of porosity ( ϕ ) and representative soil particle sizes within the framework of the classical Terzaghi model. The latter provides an empirical relationship which is widely used to obtain conductivity estimates. We frame the study within recent stochastic approaches and conceptualize appropriate transformations of ϕ and representative soil particle size as Generalized Sub-Gaussian (GSG) spatially cross-correlated random processes. Consistency of the theoretical framework against sample distributions of ϕ and particle size is assessed through the analysis of field data. A perturbation-based approach yields workable expressions of C Y upon truncating the otherwise exact analytical solution at given orders of approximations. Our analytical (truncated) log-conductivity covariance is in agreement with its Monte Carlo-based counterpart. A Global Sensitivity Analysis relying on classical Sobol indices quantifies the relative importance of all parameters embedded in the formulation of C Y . We show that parameters driving the GSG nature of the distribution of (transformed) porosity are key to the main features of C Y . We also document the relevance of properly capturing emergences of possible cross-correlations between ϕ and representative particle size to reconstruct conductivity fields.

Stochastic analysis of the variability of groundwater flow fields in heterogeneous confined aquifers of variable thickness

The problem of flow through heterogeneous confined aquifers of variable thickness is analyzed from a stochastic point of view. The analysis is carried out on the basis of the integrated equations of the depth-averaged hydraulic head and integrated specific discharge, which are developed by integrating the continuity equation and equation for the specific discharge over the thickness, respectively. A spectrally based perturbation approach is used to arrive at the general results for the statistics of the flow fields in the Fourier domain, such as the variance of the depth-averaged head, and the mean and variance of integrated discharge. However, the closed-form expressions are obtained under the condition of steady unidirectional mean flow in the horizontal plane. In developing stochastic solutions, the input hydraulic conductivity parameter is viewed as a spatial random field characterized by the theoretical spatial covariance function. The evaluation of the closed-form solutions focuses on the influence of the controlling parameters, namely as a geometrical parameter defining the variation of the aquifer thickness and the correlation scale of log hydraulic conductivity, on the variability of the fluid fields. The application of the present stochastic theory to predict the total specific discharge under uncertainty using the field data is also provided.

Solute transport in bounded porous media characterized by generalized sub-Gaussian log-conductivity distributions

There are increasing evidences that probability distributions and associated statistical moments of a variety of hydrogeological and soil science variables and their spatial increments display distinctive scale-dependent features that are not captured by a typical Gaussian model. A Generalized Sub-Gaussian (GSG) model is able to capture key aspects of this pattern. We present the results of a suite of computational analyses set in a Monte Carlo framework and aimed at assessing the impact of a GSG structure of log hydraulic conductivity (Y) on transport of a conservative solute through a three-dimensional bounded porous medium under steady-state saturated Darcy flow. Our results indicate that the longitudinal spreading of a plume is on average significantly smaller for Sub-Gaussian than for Gaussian Y fields. Otherwise, the velocity field arising from a Sub-Gaussian Y field induces enhanced plume stretching with respect to what can be observed in a Gaussian Y setting, this aspect potentially influencing the strength of solute mixing within these two types of conductivity domains. We also find that, in some cases, it may be difficult to identify the nature of the underlying conductivity field relying solely on observations of solute concentrations migrating within the system. In this regard, we show that the action of local dispersion tends to mask the influence of Sub-Gaussianity on major transport metrics.

Inferring geostatistical properties of hydraulic conductivity fields from saline tracer tests and equivalent electrical conductivity time-series

We use Approximate Bayesian Computation and the Kullback–Leibler divergence measure to quantify to what extent horizontal and vertical equivalent electrical conductivity time-series observed during tracer tests constrain the 2-D geostatistical parameters of multivariate Gaussian log-hydraulic conductivity fields. Considering a perfect and known relationship between salinity and electrical conductivity at the point scale, we find that the horizontal equivalent electrical conductivity time-series best constrain the geostatistical properties. The variance, controlling the spreading rate of the solute, is the best constrained geostatistical parameter, followed by the integral scales in the vertical direction. We find that horizontally layered models with moderate to high variance have the best resolved parameters. Since the salinity field at the averaging scale (e.g., the model resolution in tomograms) is typically non-ergodic, our results serve as a starting point for quantifying uncertainty due to small-scale heterogeneity in laboratory-experiments, tomographic results and hydrogeophysical inversions involving DC data.

Tidal Effect on Groundwater Fluctuations and Saltwater Intrusion in Coastal Heterogeneous Aquifers. (Dept. C. ( Irrigation And Hydraulics ))

Groundwater table and saltwater wedge in coastal areas are commonly affected by tidal waves fluctuations. In this research, for the first time, a two-dimensional numerical model in plan is developed for simulating both the tidal fluctuation of the beach groundwater table and movement of interface between saltwater and freshwater in both coastal confined and unconfined heterogeneous aquifers. The sharp interface philosophy is adopted to simulate dynamics of freshwater flow. Tidal waves are simulated by simple harmonic motions in time. The solution is based on an approach of separating large and small time scales motions of groundwater fluctuations. The proposed model consists of two sub-models. The first one applied Finite Element Method (FEM) to simulate the hydraulic responses of the aquifer in large time scale and it is coupled with Finite Difference Method (FDM), in the second sub-model, to simulate the corresponding ones in small time scale. The model is verified against analytical solutions presented by other previous researchers in case of homogenous aquifer. To simulate the aquifer heterogeneity, unconditional random log-hydraulic conductivity fields are generated to present different hydraulic conductivity realizations for the aquifer under consideration. The application is carried out on both the hypothetical confined aquifer and the real Quaternary unconfined aquifer in El Arish-Rafah area, Egypt. Results show that both the groundwater fluctuation and saltwater intrusion due to tidal waves are affected by the aquifers heterogeneity and the tidal waves effects in confined aquifers are more significant than in unconfined aquifers.

Numerical benchmark study for flow in highly heterogeneous aquifers

This article presents numerical investigations on accuracy and convergence properties of several numerical approaches for simulating steady state flows in heterogeneous aquifers. Finite difference, finite element, discontinuous Galerkin, spectral, and random walk methods are tested on two-dimensional benchmark flow problems. Realizations of log-normal hydraulic conductivity fields are generated by Kraichnan algorithms in closed form as finite sums of random periodic modes, which allow direct code verification by comparisons with manufactured reference solutions. The quality of the methods is assessed for increasing number of random modes and for increasing variance of the log-hydraulic conductivity fields with Gaussian and exponential correlation. Experimental orders of convergence are calculated from successive refinements of the grid. The numerical methods are further validated by comparisons between statistical inferences obtained from Monte Carlo ensembles of numerical solutions and theoretical first-order perturbation results. It is found that while for Gaussian correlation of the log-conductivity field all the methods perform well, in the exponential case their accuracy deteriorates and, for large variance and number of modes, the benchmark problems are practically not solvable with reasonably large computing resources, for all the methods considered in this study.

Towards Improving the Efficiency of Bayesian Model Averaging Analysis for Flow in Porous Media via the Probabilistic Collocation Method

The characterization of flow in subsurface porous media is associated with high uncertainty. To better quantify the uncertainty of groundwater systems, it is necessary to consider the model uncertainty. Multi-model uncertainty analysis can be performed in the Bayesian model averaging (BMA) framework. However, the BMA analysis via Monte Carlo method is time consuming because it requires many forward model evaluations. A computationally efficient BMA analysis framework is proposed by using the probabilistic collocation method to construct a response surface model, where the log hydraulic conductivity field and hydraulic head are expanded into polynomials through Karhunen–Loeve and polynomial chaos methods. A synthetic test is designed to validate the proposed response surface analysis method. The results show that the posterior model weight and the key statistics in BMA framework can be accurately estimated. The relative errors of mean and total variance in the BMA analysis results are just approximately 0.013% and 1.18%, but the proposed method can be 16 times more computationally efficient than the traditional BMA method.

Theoretical analysis of non‐Gaussian heterogeneity effects on subsurface flow and transport

AbstractMuch of the stochastic groundwater literature is devoted to the analysis of flow and transport in Gaussian or multi‐Gaussian log hydraulic conductivity (or transmissivity) fields, (x being a position vector), characterized by one or (less frequently) a multiplicity of spatial correlation scales. Yet Y and many other variables and their (spatial or temporal) increments, ΔY, are known to be generally non‐Gaussian. One common manifestation of non‐Gaussianity is that whereas frequency distributions of Y often exhibit mild peaks and light tails, those of increments are generally symmetric with peaks that grow sharper, and tails that become heavier, as separation scale or lag between pairs of Y values decreases. A statistical model that captures these disparate, scale‐dependent distributions of Y and in a unified and consistent manner has been recently proposed by us. This new “generalized sub‐Gaussian (GSG)” model has the form where is (generally, but not necessarily) a multiscale Gaussian random field and is a nonnegative subordinator independent of G. The purpose of this paper is to explore analytically, in an elementary manner, lead‐order effects that non‐Gaussian heterogeneity described by the GSG model have on the stochastic description of flow and transport. Recognizing that perturbation expansion of hydraulic conductivity diverges when Y is sub‐Gaussian, we render the expansion convergent by truncating Y's domain of definition. We then demonstrate theoretically and illustrate by way of numerical examples that, as the domain of truncation expands, (a) the variance of truncated Y (denoted by Yt) approaches that of Y and (b) the pdf (and thereby moments) of Yt increments approach those of Y increments and, as a consequence, the variogram of approaches that of . This in turn guarantees that perturbing to second order in (the standard deviation of Yt) yields results which approach those we obtain upon perturbing to second order in even as the corresponding series diverges. Our analysis is rendered mathematically tractable by considering mean‐uniform steady state flow in an unbounded, two‐dimensional domain of mildly heterogeneous Y with a single‐scale function G having an isotropic exponential covariance. Results consist of expressions for (a) lead‐order autocovariance and cross‐covariance functions of hydraulic head, velocity, and advective particle displacement and (b) analogues of preasymptotic as well as asymptotic Fickian dispersion coefficients. We compare these theoretically and graphically with corresponding expressions developed in the literature for Gaussian Y. We find the former to differ from the latter by a factor k = ( denoting ensemble expectation) and the GSG covariance of longitudinal velocity to contain an additional nugget term depending on this same factor. In the limit as Y becomes Gaussian, k reduces to one and the nugget term drops out.

Variability quantification of excess pressure head in heterogeneous deformable aquifers

The direct effect of changes in applied total stresses on fluid-saturated geologic materials is reflected in fluctuations in pore pressure. The quantification of these pressure changes has traditionally been based on the classical poroelasticity theory, developed ignoring the natural variability in aquifer properties (parameters). Uncertainty of excess pore pressure prediction is therefore expected to be large when applying the classical model to field aquifer systems which generally have high degree of heterogeneity. Very limited attention to this issue has been paid. The motivation for this work is to quantify the uncertainty associated with the classical model, the spatial variability of the predicted excess pressure head in the field, where the groundwater flow is produced by the changes in total stress. The stochastic methodology used to develop the results of this study is based on the nonstationary spectral approach. It is found that the heterogeneity and correlation length scale of the log hydraulic conductivity process, and the pore compressibility parameter play essential roles in enhancing the variability in excess pressure head. In addition, the pore pressure head distribution predicted using the classical poroelasticity theory is subject to large uncertainty at a large depth in heterogeneous aquifers.

Characterizing the impact of roughness and connectivity features of aquifer conductivity using Bayesian inversion

Summary The conductivity of an aquifer is usually difficult to represent in a precise manner due to having both a high degree of spatial variability combined with a scarcity of information. As a result, the conductivity is commonly modeled as a spatial random field, defined by its expected value and a covariance function. This covariance is usually parameterized by fitting a model function to experimental data derived from point measurements of the conductivity. In this study, we investigated the two features that are often difficult to discern when using such classic characterization schemes: roughness and connectivity. These two features both share the fact that, based on point measurements of the conductivity alone, they are difficult to discern. It therefore stands to reason that the use of additional data could alleviate this problem. To that end, we used the Method of Anchored Distributions (MAD), which is a novel Bayesian tool for the inverse characterization of spatial random fields. MAD is versatile with respect to the used data, it has a modular structure and it does not assume any formal relationship between the target variable, i.e. the log hydraulic conductivity, and the data used for the inversion process, e.g. head measurements, draw-down from pumping tests or breakthrough curves. With respect to the characterization of the aforementioned features, we investigated the impact of several factors, such as different data types on the characterization process. Our findings suggest that both roughness and connectivity have only a limited impact on flow predictions, suggesting that the choice of such features is of lesser relevance if one is mainly interested in flow simulations. In case of roughness, this limited sensitivity was also seen for transport predictions if the solute had already travelled some distance. Connectivity however, can be a decisive factor for such simulations.

On the validity of travel-time based nonlinear bioreactive transport models in steady-state flow

Travel-time based models simplify the description of reactive transport by replacing the spatial coordinates with the groundwater travel time, posing a quasi one-dimensional (1-D) problem and potentially rendering the determination of multidimensional parameter fields unnecessary. While the approach is exact for strictly advective transport in steady-state flow if the reactive properties of the porous medium are uniform, its validity is unclear when local-scale mixing affects the reactive behavior. We compare a two-dimensional (2-D), spatially explicit, bioreactive, advective–dispersive transport model, considered as “virtual truth”, with three 1-D travel-time based models which differ in the conceptualization of longitudinal dispersion: (i) neglecting dispersive mixing altogether, (ii) introducing a local-scale longitudinal dispersivity constant in time and space, and (iii) using an effective longitudinal dispersivity that increases linearly with distance. The reactive system considers biodegradation of dissolved organic carbon, which is introduced into a hydraulically heterogeneous domain together with oxygen and nitrate. Aerobic and denitrifying bacteria use the energy of the microbial transformations for growth. We analyze six scenarios differing in the variance of log-hydraulic conductivity and in the inflow boundary conditions (constant versus time-varying concentration). The concentrations of the 1-D models are mapped to the 2-D domain by means of the kinematic (for case i), and mean groundwater age (for cases ii & iii), respectively. The comparison between concentrations of the “virtual truth” and the 1-D approaches indicates extremely good agreement when using an effective, linearly increasing longitudinal dispersivity in the majority of the scenarios, while the other two 1-D approaches reproduce at least the concentration tendencies well. At late times, all 1-D models give valid approximations of two-dimensional transport. We conclude that the conceptualization of nonlinear bioreactive transport in complex multidimensional domains by quasi 1-D travel-time models is valid for steady-state flow fields if the reactants are introduced over a wide cross-section, flow is at quasi steady state, and dispersive mixing is adequately parametrized.

Transverse mixing in three-dimensional nonstationary anisotropic heterogeneous porous media

Groundwater plumes originating from continuously emitting sources are typically controlled by transverse mixing between the plume and reactants in the ambient solution. In two-dimensional domains, heterogeneity causes only weak enhancement of transverse mixing in steady-state flows. In three-dimensional domains, more complex flow patterns are possible because streamlines can twist. In particular, spatially varying orientation of anisotropy can cause steady-state groundwater whirls. We analyze steady-state solute transport in three-dimensional locally isotropic heterogeneous porous media with blockwise anisotropic correlation structure, in which the principal directions of anisotropy differ from block to block. For this purpose, we propose a transport scheme that relies on advective transport along streamlines and transverse-dispersive mass exchange between them based on Voronoi tessellation. We compare flow and transport results obtained for a nonstationary anisotropic log-hydraulic conductivity field to an equivalent stationary field with identical mean, variance, and two-point correlation function disregarding the nonstationarity. The nonstationary anisotropic field is affected by mean secondary motion and causes neighboring streamlines to strongly diverge, which can be quantified by the two-particle semivariogram of lateral advective displacements. An equivalent kinematic descriptor of the flow field is the advective folding of plumes, which is more relevant as precursor of mixing than stretching. The separation of neighboring streamlines enhances transverse mixing when considering local dispersion. We quantify mixing by the flux-related dilution index, which is substantially larger for the nonstationary anisotropic conductivity field than for the stationary one. We conclude that nonstationary anisotropy in the correlation structure has a significant impact on transverse plume deformation and mixing. In natural sediments, contaminant plumes most likely mix more effectively in the transverse directions than predicted by models that neglect the nonstationarity of anisotropy.

Uncertainty in applying the linear poroelasticity model to field situations as a result of periodic loading in heterogeneous aquifers

The solid Earth's surface frequently experience changes in total stresses as a result of periodic loading. When the fluid-saturated porous media deform in response to changes in stress, the induced variations in pore volume affect the pore water pressure. The fluid flow therefore occurs in response to the gradient in the induced excess pore water pressure. This work aims at quantifying the spatial variability in excess pressure head produced by the periodic loading accounting for the variation of log hydraulic conductivity (lnK). It is important for the rational management of groundwater resources. A closed-form expression is developed by the nonstationary spectral approach to analyse the influence of the statistical properties of lnK process, the hydraulic parameters, and the spatial position. The general stochastic framework outlined in this work provides a basis for assessing the impact of statistical properties of input aquifer parameters on the output variability (or uncertainty). Copyright © 2014 John Wiley & Sons, Ltd.

Multimodel Bayesian analysis of groundwater data worth

AbstractWe explore the way in which uncertain descriptions of aquifer heterogeneity and groundwater flow impact one's ability to assess the worth of collecting additional data. We do so on the basis of Maximum Likelihood Bayesian Model Averaging (MLBMA) by accounting jointly for uncertainties in geostatistical and flow model structures and parameter (hydraulic conductivity) as well as system state (hydraulic head) estimates, given uncertain measurements of one or both variables. Previous description of our approach was limited to geostatistical models based solely on hydraulic conductivity data. Here we implement the approach on a synthetic example of steady state flow in a two‐dimensional random log hydraulic conductivity field with and without recharge by embedding an inverse stochastic moment solution of groundwater flow in MLBMA. A moment‐equations‐based geostatistical inversion method is utilized to circumvent the need for computationally expensive numerical Monte Carlo simulations. The approach is compatible with either deterministic or stochastic flow models and consistent with modern statistical methods of parameter estimation, admitting but not requiring prior information about the parameters. It allows but does not require approximating lead predictive statistical moments of system states by linearization while updating model posterior probabilities and parameter estimates on the basis of potential new data both before and after such data are actually collected.

Conditional Simulation of Flow in Heterogeneous Porous Media with the Probabilistic Collocation Method

AbstractA stochastic approach to conditional simulation of flow in randomly heterogeneous media is proposed with the combination of the Karhunen-Loeve expansion and the probabilistic collocation method (PCM). The conditional log hydraulic conductivity field is represented with the Karhunen-Loeve expansion, in terms of some deterministic functions and a set of independent Gaussian random variables. The propagation of uncertainty in the flow simulations is carried out through the PCM, which relies on the efficient polynomial chaos expansion used to represent the flow responses such as the hydraulic head. With the PCM, existing flow simulators can be employed for uncertainty quantification of flow in heterogeneous porous media when direct measurements of hydraulic conductivity are taken into consideration. With illustration of several numerical examples of groundwater flow, this study reveals that the proposed approach is able to accurately quantify uncertainty of the flow responses conditioning on hydraulic conductivity data, while the computational efforts are significantly reduced in comparison to the Monte Carlo simulations.

Induced groundwater flux by increases in the aquifer's total stress.

Fluid-filled granular soils experience changes in total stress because of earth and oceanic tides, earthquakes, erosion, sedimentation, and changes in atmospheric pressure. The pore volume may deform in response to the changes in stress and this may lead to changes in pore fluid pressure. The transient fluid flow can therefore be induced by the gradient in excess pressure in a fluid-saturated porous medium. This work demonstrates the use of stochastic methodology in prediction of induced one-dimensional field-scale groundwater flow through a heterogeneous aquifer. A closed-form of mean groundwater flux is developed to quantify the induced field-scale mean behavior of groundwater flow and analyze the impacts of the spatial correlation length scale of log hydraulic conductivity and the pore compressibility. The findings provided here could be useful for the rational planning and management of groundwater resources in aquifers that contain lenses with large vertical aquifer matrix compressibility values.

Markov Chain Monte Carlo Approach for Parameter Uncertainty Quantification and Its Impact on Groundwater Mass Transport Modeling: Influence of Prior Distribution

Abstract Markov Chain Monte Carlo (MCMC) theory and stochastic simulation techniques were incorporated to analyze the effect of different prior knowledge on quantifying parameter uncertainty and its impact on mass transport in heterogeneous aquifer. The MCMC algorithm employing the Metropolis-Hastings rule (MH-MCMC) was used to obtain the posterior distribution of log-hydraulic conductivity. Random simulation technology, Sequential Gaussian Simulation, was used to generate a spatial stochastic hydraulic conductivity field. We investigated two different assumptive prior knowledge scenarios, a uniform prior distribution and a Gaussian prior distribution. Results showed that the prior knowledge could affect the posterior distributions of parameters. When the Gaussian prior distribution was adopted, there was a better convergence of parametric posterior distribution and a decrease in the zone of uncertainty influence and the area of confidence interval on groundwater mass transport modeling. However, it was d...

Estimation of spatial covariance of log conductivity from particle size data

AbstractWe derive analytical relationships between the spatial covariance of the (natural) logarithm of hydraulic conductivity (K) and that of representative soil particle sizes and porosity. The latter quantities can be directly measured during routine sedimentological analyses of soil samples and provide a way of incorporating K estimates into groundwater flow models at a relatively modest experimental cost. Here we rely on widely used empirical formulations requiring measurements of representative particle diameters and, in some cases, of medium porosity. We derive exact formulations relating the spatial covariance of these quantities and K and present workable approximations on the basis of perturbation methods. Our formulations provide a direct link between key geostatistical descriptors of sedimentological and hydraulic parameters of heterogeneous aquifers which can be employed in classical estimation and simulation procedures. The approach and theoretical results are tested on an extensive data set comprising 411 particle size curves collected at 12 boreholes in a small‐scale alluvial aquifer.