Transient streambed hydraulic conductivity in channel and bar environments,Loup River,Nebraska

Streambed hydraulic conductivity (K) and vertical K (K _v) are key controls on groundwater and surface water exchange and biogeochemical fluxes through the hyporheic zone, but drivers of transient hydraulic properties in different fluvial environments are poorly understood. This study combines hydrogeology, geophysics, and sedimentology to reveal mechanisms of K and K _v transience in the upper 0.5 m of a sandy streambed during low discharge. Hydraulic tests (44 slug tests, 130 falling-head permeameter tests) and 130 grain-size analyses were repeated three times over 8 weeks on a 1,200 m² grid spanning: (a) a channel with continuously flowing water and mobile bed load; (b) an adjacent mid-channel bar that was stationary and infrequently submerged. Aerial photographs and ground-penetrating radar show scour and complete reworking of fluvial sediments in the channel. Bar sediments below the water table remained immobile, but infrequent flows of moderate discharge reworked the uppermost few centimetres of the bar top. Despite differences in sediment mobility and stream flow characteristics across environments, K and K _v exhibited order-of-magnitude differences in spatial heterogeneity and temporal variability in both the channel and bar. Mean K and K _v values in the channel were comparatively stable over time. In the immobile bar, mean K declined 20% and K _v declined 26% after increased discharge temporarily inundated the bar. Grain-size distributions were steady across both environments over time, but repeat geophysical surveys of the bar show a decrease in electrical conductivity, likely from porosity reduction. These findings suggest that sediment dynamics and stream flow characteristics in different streambed environments are important drivers of K transience during low discharge conditions. Specifically, pore clogging can be an important mechanism of transience over short durations (weeks to months) in immobile sediments subject to infrequent flows and minor reworking.     

The usefulness of outcrop analogue air permeameter measurements for analyzing aquifer heterogeneity: quantifying outcrop hydraulic conductivity and its spatial variability

Saturated hydraulic conductivity (K) is one of the most important parameters determining groundwater flow and contaminant transport in both unsaturated and saturated porous media. Although several well‐established laboratory methods exist for determining K, in situ measurements of this parameter remain very complex and scale dependent. Often, the limited accessibility of subsurface sediments for sampling means an additional impediment to our ability to quantify subsurface K heterogeneity. One potential solution is the use of outcrops as analogues for subsurface sediments. This paper investigates the use of air permeameter measurements on outcrops of unconsolidated sediments to quantify K and its spatial heterogeneity on a broad range of sediment types. The Neogene aquifer in northern Belgium is used as a case study for this purpose. To characterize the variability in K, 511 small‐scale air permeability measurements were performed on outcrop sediments representative over five of the aquifer's lithostratigraphic units. From these measurements, outcrop‐scale equivalent K tensors were calculated using numerical upscaling techniques. Validation of the air permeameter‐based K values by comparison with laboratory constant head K measurements reveals a correlation of 0.93. Overall, the results indicate that hand‐held air permeameters are very efficient and accurate tools to characterize saturated K, as well as its small‐scale variability and anisotropy on a broad range of unconsolidated sediments. The studied outcrops further provided a qualitative understanding of aquifer hydrostratigraphy and quantitative estimates about K variability at the centimetre‐scale to metre‐scale. Copyright © 2013 John Wiley & Sons, Ltd.     

Horizontal hydraulic conductivity of shallow streambed sediments and comparison with the grain‐size analysis results

Streambed horizontal hydraulic conductivity (K_h) has a substantial role in controlling exchanges between stream water and groundwater. We propose a new approach for determining K_h of the shallow streambed sediments. Undisturbed sediment samples were collected using tubes that were horizontally driven into streambeds. The sediment columns were analysed using a permeameter test (PT) on site. This new test approach minimizes uncertainties due to vertical flow in the vicinity of test tube and stream stage fluctuations in the computation of the K_h values. Ninety‐eight PTs using the new approach were conducted at eight sites in four tributaries of the Platte River, east‐central Nebraska, USA. The K_h values were compared with the nondirectional hydraulic conductivity values (K_g) determined from 12 empirical grain‐size analysis methods. The grain‐size analysis methods used the same sediment samples as K_h tests. Only two methods, the Terzaghi and Shepherd methods, yielded K_g values close to the K_h values. Although the Sauerbrei method produced a value relatively closer to K_h than other nine grain‐size analysis methods, the values from this method were not as reliable as the methods of Terzaghi and Shepherd due to the inconsistent fluctuation of the average estimates at each of the test sites. The Zunker, Zamarin, Hazen, Beyer, and Kozeny methods overestimated K_h, while the Slichter, US Bureau of Reclamation (USBR), Harleman, and Alyamani and Sen methods underestimated K_h. Any of these specific grain‐size methods might yield good estimates of streambed K_h at some sites, but give poor estimates at other sites, indicating that the relationship between K_g and K_h is significantly site dependent in our study. Copyright © 2011 John Wiley & Sons, Ltd.     

Evaluation of streambed hydraulic conductivity heterogeneity in an urban watershed

It has long been understood that streambed hydraulic conductivity plays an important role in surface-subsurface solute exchange. Using a portable falling head permeameter in situ, we estimated the horizontal hydraulic conductivity, K, of the near-surface streambed sediments at a total of 85 locations encompassing two depth intervals: 7.5–10 and 10–12.5 cm. The measurements were conducted in an 80 m reach of Indian Creek, a small urban stream in Philadelphia, PA, USA. We found that the ln K data within each sediment layer were Gaussian, but the combined data set was not. The results indicated that while the mean hydraulic conductivity decreased with depth, horizontal heterogeneity (e.g. the variance) increased with depth. This strong contrast between layers suggests that they should be treated as separated entities in modeling studies. Variogram analyses across the stream suggested symmetry with respect to the thalweg in the upper layer and fractality in the lower layer. The variograms along the streams suggested that the K data are random.     

Variability in the vertical hyporheic water exchange affected by hydraulic conductivity and river morphology at a natural confluent meander bend

River confluences and their associated tributaries are key morphodynamic nodes that play important roles in controlling hydraulic geometry and hyporheic water exchange in fluvial networks. However, the existing knowledge regarding hyporheic water exchange associated with river confluence morphology is relatively scarce. On January 14 and 15, 2016, the general hydraulic and morphological characteristics of the confluent meander bend (CMB) between the Juehe River and the Haohe River in the southern region of Xi'an City, Shaanxi Province, China, were investigated. The patterns and magnitudes of vertical hyporheic water exchange (VHWE) were estimated based on a one‐dimensional heat steady‐state model, whereas the sediment vertical hydraulic conductivity (K_v) was calculated via in situ permeameter tests. The results demonstrated that 6 hydrodynamic zones and their extensions were observed at the CMB during the test period. These zones were likely controlled by the obtuse junction angle and low momentum flux ratio, influencing the sediment grain size distribution of the CMB. The VHWE patterns at the test site during the test period mostly showed upwelling flow dominated by regional groundwater discharging into the river. The occurrence of longitudinal downwelling and upwelling patterns along the meander bend at the CMB was likely subjected to the comprehensive influences of the local sinuosity of the meander bend and regional groundwater discharge and finally formed regional and local flow paths. Additionally, in dominated upwelling areas, the change in VHWE magnitudes was nearly consistent with that in K_v values, and higher values of both variables generally occurred in erosional zones near the thalweg paths of the CMB, which were mostly made up of sand and gravel. This was potentially caused by the erosional and depositional processes subjected to confluence morphology. Furthermore, lower K_v values observed in downwelling areas at the CMB were attributed to sediment clogging caused by local downwelling flow. The confluence morphology and sediment K_v are thus likely the driving factors that cause local variations in the VHWE of fluvial systems.     

Feasibility of grain-size analysis methods for determination of vertical hydraulic conductivity of streambeds

Accurate estimation of streambed vertical hydraulic conductivity (K_v) is of great importance in the analysis of water quantity exchange and solute transfer between a stream and its sediments. The paper analyzed the inaccuracy of hydraulic conductivity values of sediments derived from grain-size distribution (K_g), which were determined from eight empirical grain-size methods to represent streambed K_v. In this study, the values of K_v for a streambed were derived using falling-head standpipe permeameter tests conducted at eight study sites in the Elkhorn River, Nebraska, and the tested streambed columns were then collected for grain-size analysis by sieving. These empirical methods were used to calculate the K_g values of the streambed from grain-size distribution data of sediments. Unlike many other studies, this study verifies K_g from grain-size distribution with K_v from permeameter tests on the basis of the same samples of streambed sediments. The K_g values derived from the eight empirical methods were larger than the K_v from permeameter tests; there are five methods that give K_g values of about 3–6 times larger than these K_v. The K_g values from the Kozeny formula followed by the Hazen formula give the largest overestimation error if they are used to represent the K_v of the streambed. The USBR and Shepherd formulas generated K_g values close to K_v, but these K_g values are still larger in general than the K_v values. Moreover, the new values of coefficient C for the empirical formulas were revised so that they can be used to calculate the approximate K_v of a streambed. Among the eight methods, the ratios of the original C values to the average new C range from 1.3 to 5.9. It can be hypothesized that smaller C values must be used in the estimation of K_v for general soil samples if these empirical formulas are used to calculate K_v.     

An Integrated Laboratory Method to Measure and Verify Directional Hydraulic Conductivity in Fine‐to‐Medium Sandy Sediments

The constant‐head permeameter test (CHPT) is widely used in sandy samples as a standard method in the laboratory to investigate hydraulic conductivity (K). However, it neither can be used to consistently determine directional hydraulic conductivity (DHC) nor guarantee the comparability of measured K values of samples with different sizes. Therefore, this paper proposes an integrated laboratory method, called modified CHPT (MCHPT), for the efficient determination and verification of consistent DHC values in fine‐to‐medium sandy sediments, based on a new methodological framework. A precise and standardized procedure for preparing the experimental setup of MCHPT was conducted, based on the integrated experimental setup of CHPT and tracer tests. Moreover, a formula was yielded for the time‐optimized sample saturation control. In comparison with grain size‐based methods, the validity of consistent K_h and K_v values determined by MCHPT was convincing.     

Depth‐dependent hydraulic conductivity distribution patterns of a streambed

Characterization of streambed hydraulic conductivity from the channel surface to a great depth below the channel surface can provide needed information for the determination of stream‐aquifer hydrologic connectedness, and it is also important to river restoration. However, knowledge on the streambed hydraulic conductivity for sediments 1 m below the channel surface is scarce. This study describes a method that was used to determine the distribution patterns of streambed hydraulic conductivity for sediments from channel surface to a depth of 15 m below. The method includes Geoprobe's direct‐push techniques and Permeameter tests. Direct‐push techniques were used to generate the electrical conductivity (EC) logs and to collect sequences of continuous sediment cores from river channels, as well as from the alluvial aquifer connected to the river. Permeameter tests on these sediment cores give the profiles of vertical hydraulic conductivity (K_v) of the channel sediments and the aquifer materials. This method was applied to produce K_v profiles for a streambed and an alluvial aquifer in the Platte River Valley of Nebraska, USA. Comparison and statistical analysis of the K_v profiles from the river channel and from the proximate alluvial aquifer indicates a special pattern of K_v in the channel sediments. This depth‐dependent pattern of K_v distribution for the channel sediments is considered to be produced by hyporheic processes. This K_v‐distribution pattern implied that the effect of hyporheic processes on streambed hydraulic conductivity can reach the sediments about 9 m below the channel surface. Copyright © 2010 John Wiley & Sons, Ltd.     

Laboratory Characterization of Permeability and Its Anisotropy of Chelungpu Fault Rocks

In Taiwan an international project to drill into the Chelungpu fault (TCDP) was initiated after the M _w 7.6 Chi-Chi earthquake in 1999. At Takeng, two vertical holes (A and B) to depths of about 2 km have been drilled through the northern portion of the Chelungpu fault system. In this study, we conducted systematic hydromechanical tests on TCDP drillcores collected from Hole-A at various depths above and below the major slip zone of the Chelungpu fault. We focus on the measurements of permeability as function of pressure and the brittle failure behavior. Evolution of permeability as a function of pressure and porosity was measured using either steady-state flow or a pulse transient technique. When subjected to an effective pressure reaching 100 MPa, permeability values of shaly siltstone samples range from 10^?16 to 10^?19 m². In comparison, permeability values of porous sandstones are at least an order of magnitude higher, ranging from 10^?14 to 10^?18 m². To characterize permeability anisotropy associated with the bedding structure of the rocks of the Chelungpu fault, cylindrical samples were taken from the TCDP drillcores along three orthogonal directions, denoted X, Y and Z respectively. Direction Z is parallel to the TCDP core axis, and the other two directions are perpendicular to the core axis, with X (N105°E) perpendicular and Y (N15°E) parallel to the strike of the bedding. In shaly siltstones, permeability values of samples cored along the strike of bedding (direction Y) can be up to 1 order of magnitude higher than those cored perpendicular to the strike of bedding (direction X). These observations indicate that permeability anisotropy is controlled by the spatial distribution of bedding in Chelungpu fault host rocks. Permeability evolution of fault rocks plays an important role in dynamic weakening processes, which are particularly pertinent to large earthquakes such as the Chi-Chi earthquake. Our experimental data on permeability and its anisotropy of TCDP core samples provide necessary constraints on fault models and proposed weakening mechanisms.     

A Tube Seepage Meter for In Situ Measurement of Seepage Rate and Groundwater Sampling

We designed and evaluated a “tube seepage meter” for point measurements of vertical seepage rates (q), collecting groundwater samples, and estimating vertical hydraulic conductivity (K) in streambeds. Laboratory testing in artificial streambeds show that seepage rates from the tube seepage meter agreed well with expected values. Results of field testing of the tube seepage meter in a sandy‐bottom stream with a mean seepage rate of about 0.5 m/day agreed well with Darcian estimates (vertical hydraulic conductivity times head gradient) when averaged over multiple measurements. The uncertainties in q and K were evaluated with a Monte Carlo method and are typically 20% and 60%, respectively, for field data, and depend on the magnitude of the hydraulic gradient and the uncertainty in head measurements. The primary advantages of the tube seepage meter are its small footprint, concurrent and colocated assessments of q and K, and that it can also be configured as a self‐purging groundwater‐sampling device.     

Numerical study of circulation on the inner Amazon Shelf

We studied the circulation on the coastal domain of the Amazon Shelf by applying the hydrodynamic module of the estuarine and coastal ocean model and sediment transport. The first barotropic experiment aimed to explain the major bathymetric effects on tides and those generated by anisotropy in sediment distribution. We analyzed the continental shelf response of barotropic tides under realistic bottom stress parametrization (C _d ), considering sediment granulometry obtained from a faciologic map, where river mud deposits and reworked sediments areas are well distinguished, among others classes of sediments. Very low C _d values were set in the fluid mud regions off the Amapá coast (1.0 10^???4), in contrast to values around 3.5 10^???3 for coarser sediment regions off the Pará coast. Three-dimensional experiments represented the Amazon River discharge and trade winds, combined to barotropic tide influences and induced vertical mixing. The quasiresonant response of the Amazon Shelf to the M₂ tide acts on the local hydrodynamics by increasing tidal admittance, along with tidal forcing at the shelf break and extensive fluid mud regions. Harmonic analysis of modeled currents agreed well with the analysis of the AMASSEDS observational data set. Tidal-induced vertical shear provided strong homogenization of threshold waters, which are subject to a kind of hydraulic control due to the topographic steepness. Ahead of the hydraulic jump, the low-salinity plume is disconnected from the bottom and acquires negative vorticity, turning southeastward. Tides act as a generator mechanism and topography, via hydraulic control, acts as a maintainer mechanism for the low-salinity frontal zone positioning. Tidally induced southeastward plume fate is overwhelmed by northwestward trade winds so that they, along with background circulation, probably play the most important role on the plume fate and variability over the Amazon Shelf.     

Spatial variability in streambed hydraulic conductivity of contrasting stream morphologies: channel bend and straight channel

Streambed hydraulic conductivity is one of the main factors controlling variability in surface water‐groundwater interactions, but only few studies aim at quantifying its spatial and temporal variability in different stream morphologies. Streambed horizontal hydraulic conductivities (K_h) were therefore determined from in‐stream slug tests, vertical hydraulic conductivities (K_v) were calculated with in‐stream permeameter tests and hydraulic heads were measured to obtain vertical head gradients at eight transects, each comprising five test locations, in a groundwater‐dominated stream. Seasonal small‐scale measurements were taken in December 2011 and August 2012, both in a straight stream channel with homogeneous elevation and downstream of a channel meander with heterogeneous elevation. All streambed attributes showed large spatial variability. K_h values were the highest at the depositional inner bend of the stream, whereas high K_v values were observed at the erosional outer bend and near the middle of the channel. Calculated K_v values were related to the thickness of the organic streambed sediment layer and also showed higher temporal variability than K_h because of sedimentation and scouring processes affecting the upper layers of the streambed. Test locations at the channel bend showed a more heterogeneous distribution of streambed properties than test locations in the straight channel, whereas within the channel bend, higher spatial variability in streambed attributes was observed across the stream than along the stream channel. Copyright © 2014 John Wiley & Sons, Ltd.     

Impacts of Streambed Heterogeneity and Anisotropy on Residence Time of Hyporheic Zone

The hyporheic zone (HZ), which is the region beneath or alongside a streambed, plays an important role in the stream's ecology. The duration that a water molecule or a solute remains within the HZ, or residence time (RT), is one of the most common metrics used to evaluate the function of the HZ. The RT is greatly influenced by the streambed's hydraulic conductivity (K), which is intrinsically difficult to characterize due to its heterogeneity and anisotropy. Many laboratory and numerical studies of the HZ have simplified the streambed K to a constant, thus producing RT values that may differ from those gathered from the field. Some studies have considered the heterogeneity of the HZ, but very few have accounted for anisotropy or the natural K distributions typically found in real streambeds. This study developed numerical models in MODFLOW to examine the influence of heterogeneity and anisotropy, and that of the natural K distribution in a streambed, on the RT of the HZ. Heterogeneity and anisotropy were both found to shorten the mean and median RTs while increasing the range of the RTs. Moreover, heterogeneous K fields arranged in a more orderly pattern had longer RTs than those with random K distributions. These results could facilitate the design of streambed K values and distributions to achieve the desired RT during river restoration. They could also assist the translation of results from the more commonly considered homogeneous and/or isotropic conditions into heterogeneous and anisotropic field situations.     

Bootstrap Calibration and Uncertainty Estimation of Downhole NMR Hydraulic Conductivity Estimates in an Unconsolidated Aquifer

Characterization of hydraulic conductivity (K) in aquifers is critical for evaluation, management, and remediation of groundwater resources. While estimates of K have been traditionally obtained using hydraulic tests over discrete intervals in wells, geophysical measurements are emerging as an alternative way to estimate this parameter. Nuclear magnetic resonance (NMR) logging, a technology once largely applied to characterization of deep consolidated rock petroleum reservoirs, is beginning to see use in near‐surface unconsolidated aquifers. Using a well‐known rock physics relationship—the Schlumberger Doll Research (SDR) equation—K and porosity can be estimated from NMR water content and relaxation time. Calibration of SDR parameters is necessary for this transformation because NMR relaxation properties are, in part, a function of magnetic mineralization and pore space geometry, which are locally variable quantities. Here, we present a statistically based method for calibrating SDR parameters that establishes a range for the estimated parameters and simultaneously estimates the uncertainty of the resulting K values. We used co‐located logging NMR and direct K measurements in an unconsolidated fluvial aquifer in Lawrence, Kansas, USA to demonstrate that K can be estimated using logging NMR to a similar level of uncertainty as with traditional direct hydraulic measurements in unconsolidated sediments under field conditions. Results of this study provide a benchmark for future calibrations of NMR to obtain K in unconsolidated sediments and suggest a method for evaluating uncertainty in both K and SDR parameter values.     

Modeling Transient Streaming Potentials in Falling‐Head Permeameter Tests

We present transient streaming potential data collected during falling‐head permeameter tests performed on samples of two sands with different physical and chemical properties. The objective of the work is to estimate hydraulic conductivity (K) and the electrokinetic coupling coefficient (C_l) of the sand samples. A semi‐empirical model based on the falling‐head permeameter flow model and electrokinetic coupling is used to analyze the streaming potential data and to estimate K and C_l. The values of K estimated from head data are used to validate the streaming potential method. Estimates of K from streaming potential data closely match those obtained from the associated head data, with less than 10% deviation. The electrokinetic coupling coefficient was estimated from streaming potential vs. (1) time and (2) head data for both sands. The results indicate that, within limits of experimental error, the values of C_l estimated by the two methods are essentially the same. The results of this work demonstrate that a temporal record of the streaming potential response in falling‐head permeameter tests can be used to estimate both K and C_l. They further indicate the potential for using transient streaming potential data as a proxy for hydraulic head in hydrogeology applications.     

Constraints on hydraulic parameters and implications for groundwater flux across the upland–estuary interface

Analyses of independent laboratory- and field-scale measurements from two sites on Sapelo Island, Georgia reveal heterogeneity in hydraulic parameters across the upland–estuary interface. Regardless of the method used (short-duration pumping tests, amplitude attenuation of tidal pumping data, sediment grain size distributions, and falling head permeameter tests), we obtain hydraulic conductivity of 10⁻⁴ m s⁻¹ for the fine-grained, well-sorted, clean sands that make up the upland areas. Proximal to the upland–estuary boundary, the tidal pumping analyses and permeameter tests suggest that hydraulic conductivities decrease by more than two orders of magnitude, a result consistent with the presence of a clogging layer. Such a clogging layer may arise due to a variety of physical, chemical, or biological processes. The extent and orientation of the layers of reduced hydraulic conductivity near the upland–estuary boundary influence the nature of the aquifer's response to tidal forcing. Where the lower conductivity layer forms a relatively flat creek bank, tidal pumping produces a primarily mechanical response in the adjacent aquifer. Where the creek bank is nearly vertical, there is a more direct hydraulic connection between the tidal creek and the adjacent aquifer. The clogging layer likely contributes to the development of complicated flow pathways across the upland–estuary boundary. Effective flow paths calculated from tidal pumping data terminate within the marsh, beyond the boundary of the upland aquifer, suggesting a diffuse regime of groundwater discharge in the marsh. We postulate that, in many settings, submarsh flow may be as important as seepage faces for groundwater discharge into the marsh–estuary complex.     

Cost Comparisons of Aquifer Heterogeneity Characterization Methods

The characterization of heterogeneity in hydraulic conductivity (K) is a major challenge for subsurface remediation projects. There are a number of field studies that compare the K estimates obtained using various techniques, but to our knowledge, no field‐based studies exists that compare the performance of estimated K heterogeneity fields or the associated characterization costs. In this paper, we compare the costs of characterizing the three‐dimensional K heterogeneity and its uncertainty estimates of a glaciofluvial aquifer‐aquitard sequence at a 15 m × 15 m × 18 m field site situated on the University of Waterloo campus. We compare geostatistical analysis of high resolution permeameter K data obtained from repacked core samples in five boreholes and hydraulic tomography analysis of four pumping tests consisting of up to 41 monitoring points per test. Aside from the comparison of costs, we also assess the performance of each method by predicting several pumping tests. Our analysis reveals that hydraulic tomography is somewhat more costly than the geostatistical analysis of high resolution permeameter K data due to the higher capital costs associated with the method. However, the equipment may be reused at other sites; hence these costs may be recovered over the life of the equipment. More significantly, hydraulic tomography is able to capture the most important features of the aquifer‐aquitard sequence leading to more accurate predictions of independent pumping tests. This suggests that more robust remediation systems may be designed if site characterization is performed with hydraulic tomography.     

Seepage mechanisms and permeability differences between loess and paleosols in the critical zone of the Loess Plateau

The soil in the Loess Plateau has special permeability characteristics due to the alternating distribution of loess and paleosol layers. Using an analysis of the physical properties, microstructure and thermogravimetric analysis of loess and paleosol, this paper examines strata seepage mechanisms in the loess tableland area and considers the applicability of a hydraulic conductivity empirical formula. The analysis shows that hydraulic conductivity attenuation with depth can be represented by a negative exponential model, while hydraulic conductivity values are not normally distributed. The best-fitting models of hydraulic conductivity in the horizontal (K_H) and vertical (K_V) directions are Gaussian models, and both have strong spatial correlations. This study of the difference in permeability between loess and paleosol found that the depositional environment was the dominant causal factor, making the average hydraulic conductivity of most loess layers greater than that of the underlying paleosol layers. Different microstructures between loess and paleosol also confirmed the microscopic explanation in permeability anisotropy and their permeability difference. Thermogravimetric analysis determined temperature ranges for different types of water lost by heat, and then calculated ratios of bound water mass to liquid limit, with an average of 0.768. A modified formula suitable for loess was obtained by integrating the consistency index method and effective porosity ratio model into the hydraulic conductivity empirical formula. Compared with the results of laboratory tests and uncorrected formulas, the modified formula provides a good estimate of strata hydraulic conductivity. Accurate understandings of seepage mechanisms and permeability differences in the loess area are important, promoting ecological restoration and providing scientific guidance for the sustainable development of the Loess Plateau.     

Numerical investigation of the anisotropic hydraulic conductivity behavior in heterogeneous porous media

The behavior of the mean equivalent hydraulic conductivity normal and parallel to stratification (K₁, and K₂, respectively) is studied here through Monte Carlo simulations of three-dimensional, steady-state flow in statistically anisotropic, bounded, and heterogeneous media. For water flow normal to stratification in strongly heterogeneous porous media (²_Y=3) the value of K₁ is not unique; it ranges from an arithmetic to a geometric, and finally, to a harmonic mean behavior depending on field dimensions, and medium anisotropy. For a fixed anisotropy ratio and variance of Y = ln K, the larger the distance, in the direction perpendicular to stratification, over which water flow takes place, the faster the rate at which, K_H, behavior is approached. However, even for large anisotropy ratios, harmonic mean behavior appears to be a good approximation only for aquifer thickness L₁ that is large enough to allow stratified flow to occur. For small aquifer thickness (L₁/₁<8, where ₁ is the integral scale normal to stratification) the limiting behavior, for large anisotropy ratios, appears to be, instead, that of two-dimensional flow, i.e., water flows primarily parallel to the planes of stratification. When the aquifer thickness is very small compared to the horizontal dimensions (and with relative similar integral scales in the three directions) a behavior resembling arithmetic mean conditions is exhibited, i.e., water flow takes place through heterogeneous, vertical, soil volumes. The geostatistical expressions of Desbarats (1992a) for upscaling hydraulic conductivity values were utilized and closed form empirical relations were developed for the main components of the upscaled hydraulic conductivity tensor.