Effective Hydraulic Conductivity Research Articles

Scale‐dependency of effective hydraulic conductivity on fire‐affected hillslopes

AbstractEffective hydraulic conductivity (Ke) for Hortonian overland flow modeling has been defined as a function of rainfall intensity and runon infiltration assuming a distribution of saturated hydraulic conductivities (Ks). But surface boundary condition during infiltration and its interactions with the distribution of Ks are not well represented in models. As a result, the mean value of the Ks distribution ( ), which is the central parameter for Ke, varies between scales. Here we quantify this discrepancy with a large infiltration data set comprising four different methods and scales from fire‐affected hillslopes in SE Australia using a relatively simple yet widely used conceptual model of Ke. Ponded disk (0.002 m2) and ring infiltrometers (0.07 m2) were used at the small scales and rainfall simulations (3 m2) and small catchments (ca 3000 m2) at the larger scales. We compared between methods measured at the same time and place. Disk and ring infiltrometer measurements had on average 4.8 times higher values of than rainfall simulations and catchment‐scale estimates. Furthermore, the distribution of Ks was not clearly log‐normal and scale‐independent, as supposed in the conceptual model. In our interpretation, water repellency and preferential flow paths increase the variance of the measured distribution of Ks and bias ponding toward areas of very low Ks during rainfall simulations and small catchment runoff events while areas with high preferential flow capacity remain water supply‐limited more than the conceptual model of Ke predicts. The study highlights problems in the current theory of scaling runoff generation.

Determination of Watershed Infiltration and Erosion Parameters from Field Rainfall Simulation Analyses

Realistic modeling of infiltration, runoff and erosion processes from watersheds requires estimation of the effective hydraulic conductivity (Km) of the hillslope soils and how it varies with soil tilth, depth and cover conditions. Field rainfall simulation (RS) plot studies provide an opportunity to assess the surface soil hydraulic and erodibility conditions, but a standardized interpretation and comparison of results of this kind from a wide variety of test conditions has been difficult. Here, we develop solutions to the combined set of time-to-ponding/runoff and Green– Ampt infiltration equations to determine Km values from RS test plot results and compare them to the simpler calculation of steady rain minus runoff rates. Relating soil detachment rates to stream power, we also examine the determination of “erodibility” as the ratio thereof. Using data from over 400 RS plot studies across the Lake Tahoe Basin area that employ a wide range of rain rates across a range of soil slopes and conditions, we find that the Km values can be determined from the combined infiltration equation for ~80% of the plot data and that the laminar flow form of stream power best described a constant “erodibility” across a range of volcanic skirun soil conditions. Moreover, definition of stream power based on laminar flows obviates the need for assumption of an arbitrary Mannings “n” value and the restriction to mild slopes (<10%). The infiltration equation based Km values, though more variable, were on average equivalent to that determined from the simpler calculation of steady rain minus steady runoff rates from the RS plots. However, these Km values were much smaller than those determined from other field test methods. Finally, we compare RS plot results from use of different rainfall simulators in the basin and demonstrate that despite the varying configurations and rain intensities, similar erodibilities were determined across a range of infiltration and runoff rates using the laminar form of the stream power equation.

Long-term effects of an iron heater and Äspö groundwater on smectite clays: Chemical and hydromechanical results from the in situ alternative buffer material (ABM) test package 2

AbstractSmectite-rich clays are to be used in nuclear repositories for sealing in the radioactive waste. As the radioactive decay produces heat it may affect the chemical, physical and hydromechanical properties of the clay components in the repository. An ‘alternative buffer material’ (ABM) experiment is a Svensk Kärnbränslehantering AB (SKB)-led in situ heating test placed in boreholes in the Äspö tunnel (Sweden). The 2nd ABM package was dismantled in April 2013, after 6.5 y of equilibration with Äspö groundwater and 5 y of heating. The objective was to investigate the long-term effects of the iron heater and Äspö groundwater on four of 31 compacted blocks made of MX-80, Deponit CaN and Friedland clays.Compared to the starting materials, major changes in the exchangeable cation populations were observed. Within horizontal profiles, water-soluble sulfate, Ca, K and Mg increased; poorly crystalline Fe oxide contents decreased; total Mg, Ca and S increased; and a decrease in the amounts of total Na and K away from the host rock towards the heater was observed. At the boundary with the heater, an increase in the total Fe content, decreases in total Si and Al contents, precipitation of gypsum and anhydrite, dissolution of cristobalite and feldspars, and indications of the formation of trioctahedral clay minerals were observed. A decrease in swelling pressure for the Friedland clay (in drill-cored samples) was recorded which was recovered after grinding and recompaction. No effects of hydraulic conductivity were found, after 6.5 y of reaction time, in the subsurface of any of materials studied.

Hydrogeological assessment of non-linear underground enclosures

Excavations below the water table are usually undertaken by combining the protection of retaining walls with dewatering by pumping wells. Severe difficulties may arise if the retaining walls have defects. Therefore, their state must be determined and, if needed, the defects repaired or the dewatering system redesigned. The state of underground retaining walls can be evaluated using hydrogeological methods, but these methods are well-established only for linear excavations. The objective of this work is to propose a procedure to evaluate the state of non-linear underground enclosures by analysing the groundwater response to pumping inside the enclosure. The proposed method, which is based on diagnostic plots (derivative of drawdown with respect to the logarithm of time), allows (1) determining if an underground non-linear enclosure has isolated openings or numerous defects and (2) computing its effective conductance or effective hydraulic conductivity. The methodology is tested with data collected during the excavation of a shaft required for the construction of the high speed train (HST) tunnel in Barcelona, Spain. The procedure can be applied using the wells drilled for dewatering. Although a test before the excavation is recommended to evaluate the underground retaining walls (Watertightness Assessment Test), the method can be applied using data collected at the beginning of the dewatering stage.

Trajectory‐based modeling of fluid transport in a medium with smoothly varying heterogeneity

AbstractUsing an asymptotic methodology, valid in the presence of smoothly varying heterogeneity and prescribed boundaries, we derive a trajectory‐based solution for tracer transport. The analysis produces a Hamilton‐Jacobi partial differential equation for the phase of the propagating tracer front. The trajectories follow from the characteristic equations that are equivalent to the Hamilton‐Jacobi equation. The paths are determined by the fluid velocity field, the total porosity, and the dispersion tensor. Due to their dependence upon the local hydrodynamic dispersion, they differ from conventional streamlines. This difference is borne out in numerical calculations for both uniform and dipole flow fields. In an application to the computational X‐ray imaging of a saline tracer test, we illustrate that the trajectories may serve as the basis for a form of tracer tomography. In particular, we use the onset time of a change in attenuation for each volume element of the X‐ray image as a measure of the arrival time of the saline tracer. The arrival times are used to image the spatial variation of the effective hydraulic conductivity within the laboratory sample.

Models to Predict Compressibility and Permeability of Reconstituted Clays

In this paper, one-dimensional consolidation and permeability tests are conducted to investigate the compressibility and permeability of reconstituted marine clay that has been used as filling material for a land reclamation project in Tianjin, China. A curve-fitting method is used to best fit the measured consolidation and permeability data to determine the void ratio–effective stress relationship (compressibility) and hydraulic conductivity–void ratio relationship (permeability). Relatively good agreements are found when comparing the obtained relationships with model test data of reconstituted clays in literature. The proposed relationships could be used as preliminary tools for the calculation of the compressibility and permeability of the reconstituted clays in land reclamation projects.

Estimation of hydraulic conductivity function in unsaturated pyroclastic soils

A full understanding of slope failure conditions in unsaturated pyroclastic slope needs a fair analysis of groundwater flow and, therefore, a proper hydraulic soil characterization in terms of either soil water retention curves (SWRC) and hydraulic conductivity function (HCF). A practical method to detect the HCF by processing in situ data is provided, thus, the identification of the HCFs operating on site by applying the Soil Water Balance (SWB) to the pyroclastic soil cover is carried out. In this regard data monitoring (matrix suction and volumetric water content) collected at experimental field of Monteforte Irpino in Southern Italy over four years have been used. Moreover a comparison between the saturated hydraulic conductivity from lab test and from in situ measurements is carried out and the results confirm that the effective hydraulic conductivity operating at the site scale is higher than the hydraulic conductivity obtained in the laboratory for the whole range of suction measured at site.

Connectivity metrics based on the path of smallest resistance

Connectivity is an intrinsic feature of heterogeneous hydraulic conductivity fields which governs the paths of smallest resistance, along which water and solute fluxes concentrate. It is often organized as a network of channels which shows the fastest Darcy velocities and provides pathways for particles contributing to early time solute breakthrough. In subsurface hydrology the topological or static connectivity metrics are poorly defined, thus connectivity is usually characterized by dynamic connectivity indicators, derived from effective flow and transport behavior. We obtain a connected channel network using information about hydraulic conductivity only and define static connectivity metrics based on resistance of the individual channels as well as the channel width. Then we compare the static connectivity metrics with connectivity indicators derived from flow and transport simulations to check whether these connectivity metrics are able to predict effective flow and transport. We find a good agreement for flow and an acceptable one for transport for a large range of 2-D hydraulic conductivity fields with different connectivity structures. We conclude that our method provides a good estimate of effective hydraulic conductivity and early time solute breakthrough using our connectivity metrics based on information of the resistance and geometry of the connected channel network.

Provenance of buried esker groundwater: the case of Vars-Winchester esker aquifer, Eastern Ontario, Canada

An innovative mode of groundwater recharge to a buried esker aquifer is considered. The current conceptual model affords a natural safeguard to underlying aquifers from the overlying muds. A hypothesis of groundwater recharge to a buried esker aquifer via preferential pathways across its overlying muds is tested here by heuristic numerical one-dimensional and two-dimensional modeling simulations. The hypothesis has been tested against two other conventionally accepted scenarios involving: (1) distal esker outcrop areas and (2) remote shallow-bedrock recharge areas. The main evidence comes from documented recharge pressure pulses in the overlying mud aquitard and in the underlying esker hydraulic-head time series for the Vars-Winchester esker aquifer in Eastern Ontario, Canada. These perturbations to the potentiometric surface are believed to be the aquifer response to recharge events. The migration rate of these pressure pulses is directly related to the hydraulic diffusivity of the formation. The measured response time and response amplitude between singular radar precipitation events and well hydrographs constituted the heuristic model calibration targets. The main evidence also includes mud-layering deformation (water escape features) which was observed in seismic surveys of the over-esker muds. These disturbed stratigraphic elements provide a realistic mechanism for migrating water to transit through the muds. The effective hydraulic conductivities of these preferential pathways in the muds were estimated to be between 2 × 10−6 and 7 × 10−6 m/s. The implications of these findings relate to the alleged natural safeguard of these overlying muds.

Influence of Alluvial Morphology on Upscaled Hydraulic Conductivity.

The hydraulic conductivity of aquifers is a key parameter controlling the interactions between resource exploitation activities, such as unconventional gas production and natural groundwater systems. Furthermore, this parameter is often poorly constrained by typical data used for regional groundwater modeling and calibration studies performed as part of impact assessments. In this study, a systematic investigation is performed to understand the correspondence between the lithological descriptions of channel-type formation and the bulk effective hydraulic conductivities at a larger scale (Kxeff , Kyeff , and Kzeff in the direction of channel cross section, along the channel and in the vertical directions, respectively). This will inform decisions on what additional data gathering and modeling of the geological system can be performed to allow the critical bulk properties to be more accurately predicted. The systems studied are conceptualized as stacked meandering channels formed in an alluvial plain, and are represented as two facies. Such systems are often studied using very detailed numerical models. The main factors that may influence Kxeff , Kyeff , and Kzeff are the proportion of the facies representing connected channels, the aspect ratio of the channels, and the difference in hydraulic conductivity between facies. Our results show that in most cases, Kzeff is only weakly dependent on the orientations of channelized structures, with the main effects coming from channel aspect ratio and facies proportion.

Statistical sample size for quality control programs of cement-based “solidification/stabilization”

Sampling requirements for the quality control (QC) of cement-based “solidification/stabilization” (S/S) construction cells do not currently specify the sample size considering the accuracy of the estimated effective hydraulic conductivity of the cells from the samples, nor considering the risk associated with drawing the wrong conclusions about the acceptability of the cells. In this paper, probabilistic simulations are performed to examine the influence of a soil–cement material’s mean, variance, and correlation length on sampling requirements for a QC program of cement-based S/S construction cells. The sampling requirements are determined by considering a hypothesis test, having nulled that the constructed material is unacceptable, and targeting acceptable probabilities of making an erroneous decision. Two types of errors can be made: (i) concluding that the material is acceptable when it actually is not, or (ii) failing to conclude that the material is acceptable when it actually is. The paper investigates how many samples are required to keep the probabilities of making these errors acceptably small. Plots are provided, which can be used to estimate the required number of samples. The paper concludes by discussing how the simulation-based results compare with current sampling requirements for the QC of an actual set of cement-based S/S construction cells.

The distributed-order fractional diffusion-wave equation of groundwater flow: Theory and application to pumping and slug tests

We present a distributed-order fractional diffusion-wave equation (dofDWE) to describe radial groundwater flow to or from a well, and three sets of solutions of the dofDWE for flow from a well for aquifer tests: one for pumping tests, and two for slug tests. The dofDWE is featured by two temporal orders of fractional derivatives, b1 and b2, which characterise small and large pores, respectively. By fitting the approximate solutions of the dofDWE to data from slug tests in the field, we determined the effective saturated hydraulic conductivity, Ke, transmissivity, Tf, and the order of fractional derivatives, b2 in one test and b2 and b1 in the second test. We found that the patterns of groundwater flow from a well during the slug tests at this site belong to the class of sub-diffusion with b2 < 1 and b1 < 1 using both the short-time and large-time solutions. We introduce the concept of the critical time to link Ke as a function of b2 and b1. The importance of the orders of fractional derivatives is obvious in the approximate solutions: for short time slug tests only the parameter b2 for flow in large pores is present while for long time slug tests the parameters b2 and b1 are present indicating both large and small pores are functioning.

Hybrid Finite-Discrete Element Simulation of the EDZ Formation and Mechanical Sealing Process Around a Microtunnel in Opalinus Clay

The analysis and prediction of the rock mass disturbance around underground excavations are critical components of the performance and safety assessment of deep geological repositories for nuclear waste. In the short term, an excavation damaged zone (EDZ) tends to develop due to the redistribution of stresses around the underground openings. The EDZ is associated with an increase in hydraulic conductivity of several orders of magnitude. In argillaceous rocks, sealing mechanisms ultimately lead to a partial reduction in the effective hydraulic conductivity of the EDZ with time. The goal of this study is to strengthen the understanding of the phenomena involved in the EDZ formation and sealing in Opalinus Clay, an indurated claystone currently being assessed as a host rock for a geological repository in Switzerland. To achieve this goal, hybrid finite-discrete element method (FDEM) simulations are performed. With its explicit consideration of fracturing processes, FDEM modeling is applied to the HG-A experiment, an in situ test carried out at the Mont Terri underground rock laboratory to investigate the hydro-mechanical response of a backfilled and sealed microtunnel. A quantitative simulation of the EDZ formation process around the microtunnel is first carried out, and the numerical results are compared with field observations. Then, the re-compression of the EDZ under the effect of a purely mechanical loading, capturing the increase of swelling pressure from the backfill onto the rock, is considered. The simulation results highlight distinctive rock failure kinematics due to the bedded structure of the rock mass. Also, fracture termination is simulated at the intersection with a pre-existing discontinuity, representing a fault plane oblique to the bedding orientation. Simulation of the EDZ re-compression indicates an overall reduction of the total fracture area as a function of the applied pressure, with locations of ineffective sealing associated with self-propping of fractures. These results are consistent with hydraulic testing data revealing a negative correlation between pressure values and an increase in the EDZ transmissivity.

Curve Number Estimation Accuracy on Disturbed and Undisturbed Soils

AbstractEstimates of the USDA-NRCS runoff curve number (CN) are generally based on a soil map and observed land cover. Because the CN method is increasingly applied to disturbed and urbanized land, the objective of this work was to collect effective saturated hydraulic conductivities, Ksat, and sorptivities, So, from a range of land use types, use the results to estimate a CN, and compare these CNs with CN estimates made from soil survey information and corresponding land cover. A total of 331 double ring infiltration tests were conducted over the 15 sites. Based on land use and site history, the test sites were classified into categories of engineered, urban altered, rural altered, rural unaltered, and prairie. Measured Ksat values were skewed so the medians of these data were a better predictor of central tendency. The prairie and rural unaltered median Ksat values were closer to soil map estimates than the other categories (between 0.0 and 91% different from soil survey). Two empirical methods develope...

Interpretation of hydraulic conductivity in a fractured-rock aquifer over increasingly larger length dimensions

A comparison of the hydraulic conductivity over increasingly larger volumes of crystalline rock was conducted in the Piedmont physiographic region near Bethesda, Maryland, USA. Fluid-injection tests were conducted on intervals of boreholes isolating closely spaced fractures. Single-hole tests were conducted by pumping in open boreholes for approximately 30 min, and an interference test was conducted by pumping a single borehole over 3 days while monitoring nearby boreholes. An estimate of the hydraulic conductivity of the rock over hundreds of meters was inferred from simulating groundwater inflow into a kilometer-long section of a Washington Metropolitan Area Transit Authority tunnel in the study area, and a groundwater modeling investigation over the Rock Creek watershed provided an estimate of the hydraulic conductivity over kilometers. The majority of groundwater flow is confined to relatively few fractures at a given location. Boreholes installed to depths of approximately 50 m have one or two highly transmissive fractures; the transmissivity of the remaining fractures ranges over five orders of magnitude. Estimates of hydraulic conductivity over increasingly larger rock volumes varied by less than half an order of magnitude. While many investigations point to increasing hydraulic conductivity as a function of the measurement scale, a comparison with selected investigations shows that the effective hydraulic conductivity estimated over larger volumes of rock can either increase, decrease, or remain stable as a function of the measurement scale. Caution needs to be exhibited in characterizing effective hydraulic properties in fractured rock for the purposes of groundwater management.

Effective Saturated Hydraulic Conductivity of an Infiltration-Based Stormwater Control Measure

AbstractInfiltration rates into field soils have a large variability, and a statistical value that represents the overall infiltration in a site is needed. The Green-Ampt equation was used to develop a one-dimensional, multisoil model to predict the water surface drawdown in an infiltration-based stormwater control measure (SCM) as a function of time. Results were used to compare the accuracy of assuming the SCM was comprised of a single soil with an overall effective saturated hydraulic conductivity set equal to (1) the geometric mean of the spatially distributed hydraulic conductivity values of the multisoil SCM, (2) the arithmetic mean of the hydraulic conductivity values, and (3) a best-fit hydraulic conductivity value. Results indicated that the use of the geometric mean consistently underestimated infiltration and use of the arithmetic mean consistently overestimated infiltration. A relationship to more consistently and accurately predict the best-fit value of saturated hydraulic conductivity used a...

Effective Hydraulic Conductivity for a Soil of Variable Pore Size with Depth

Two models were derived for the estimation of effective hydraulic conductivity (K e ) of a soil layer based on exponential and inverse square variation of hydraulic conductivity with soil depth. Darcy’s law was applied to a vertical soil stratum subdivided into a finite number of layers. The relationship between K e and layer thickness is of quadratic form with R 2 ≈ 1.As the layer thickness increases, the values of K e for the exponential model increases drastically, exceeding the K e estimate of the power model. The percentage difference between the two models assumes an asymptotic form to the y-axis at a percentage difference of 5%, as the size of layer approaches zero. power model gives lower estimates of K e than the exponential model within soil depth range of 1.5m ≤ D ≤ 3.2m for n = 2; 0.8m ≤ D ≤ 1.9m for n = 50; and 0.7m ≤ D ≤ 1.9m for n = 100 and above. For very shallow soil stratum (D ≤ 2), the exponential model gives better and more realistic estimates of K e than the power model; while for medium to deep soil stratum (D ≥ 2), the power model gives better estimates of K e . http://dx.doi.org/10.4314/njt.v34i3.30

Heterogeneity of Infiltration Rates in Alluvial Floodplains as Measured with a Berm Infiltration Technique

<abstract> <b><sc>Abstract.</sc></b> Hydrologic heterogeneities (e.g., macropores and gravel outcrops) in floodplains are hypothesized to play an integral role in impacting flow and leaching between the soil surface and shallow alluvial aquifers, which are intricately connected to streams. Infiltration is often assumed to be uniform, but this neglects the spatial variability common in anisotropic, heterogeneous alluvial floodplain soils. The objective of this research was to quantify infiltration and hydraulic conductivity across a range of scales (point to 100 m²) using a berm infiltration technique. Plot-scale leaching experiments were performed across a range of soil types at each of three floodplain sites in northeastern Oklahoma and northwestern Arkansas. Plots maintained a constant head of 2 to 9 cm for up to 52 h. Effective saturated hydraulic conductivity (K_eff), based on plot-scale infiltration rates and a one-dimensional Darcy flow equation, ranged between 0.6 and 68 cm h^-1 and varied considerably even within a single floodplain. The K_eff was also calculated at the point scale using particle size distributions and Retention Curve (RETC). Point-scale estimates were significantly lower than plot-scale K_eff and also failed to capture the variability of K_eff. The estimated permeability of the limiting layer reported in soil surveys was consistent with point-scale estimates of K_eff but was lower than plot-scale K_eff at most sites. Tension infiltrometers showed that macropores accounted for approximately 84% to 99% of the total saturated hydraulic conductivity. The plot scale (1 to 100 m²) generally appears to be within the representative elementary volume (REV), but drift in K_eff occurs beyond the REV due to changing geomorphic formations. Plot-scale infiltration tests are recommended over point-scale estimates, although only small plots (1 m × 1 m) are necessary.

Derivation of the Relationships between Green-Ampt Model Parameters and Soil Hydraulic Properties

The Green–Ampt model (GAM) is a widely used water infiltration model. However, it lacks a reliable theoretical basis to independently and simultaneously determine the GAM parameters of effective hydraulic conductivity (Kₑ) and the average matric pressure head at the wetting front (Hf) from those commonly measured soil hydraulic properties. In this paper, we derived an approximate analytical solution similar to GAM for one-dimensional vertical infiltration into soils with initially uniform soil moisture distribution, with Kₑ and Hf being simultaneously related to the Brooks–Corey (BC) model parameters. The new relationships are not restricted to the piston-type moisture profile or delta-type water diffusivity like in the traditional GAM (TGAM). Infiltration experiments on three soils of various textures were conducted to validate the new approximate analytical solution and the corresponding GAM parameters. It was demonstrated that the predicted cumulative infiltrations and soil moisture profiles by the GAM with Kₑ and Hf calculated by the new expressions (new GAM, NGAM) generally agreed well with the numerical solutions, especially for initially dry soils. In contrast, cumulative infiltrations were considerably over-predicted by the TGAM using Kₑ = Kₛ and Hf calculated by Neuman’s equation. Our theoretical analysis further indicated that even without air entrapped during infiltration, the effective hydraulic conductivity can still be less than the saturated hydraulic conductivity Kₛ. The relative effective hydraulic conductivity ζ (Kₑ/Kₛ) and the relative average matric pressure head at the wetting front η (-Hf/hd where hd is absolute value of the air-entry suction) show a dependency only on soil pore structure index (n) and effective initial soil-water saturation (Sᵢ). The values of ζ increased but η decreased with Sᵢ and n. The theoretical ranges of ζ and η were from 0.5 and 2 for dry heavy-texture soils to 1 and 0 for saturated soils, respectively, which are consistent with the experimental values reported in literatures.

Stochastic analysis of the hydraulic conductivity estimated for a heterogeneous aquifer via numerical modelling

Abstract. The paper aims to evaluate the impacts of the average hydraulic conductivity of the heterogeneous aquifer on the estimated hydraulic conductivity using the observations from pumping tests. The results of aquifer tests conducted at a karst aquifer are first introduced. A MODFLOW groundwater flow model was developed to perform numerical pumping tests, and the heterogeneous hydraulic conductivity (K) field was generated using the Monte Carlo method. The K was estimated by the Theis solution for an unconfined aquifer. The effective hydraulic conductivity (Ke) was calculated to represent the hydraulic conductivity of a heterogeneous aquifer. The results of numerical simulations demonstrate that Ke increase with the mean of hydraulic conductivity (EK), and decrease with the coefficient of variation of the hydraulic conductivity (Cv). The impact of spatial variability of K on the estimated Ke at two observation wells with smaller EK is less significant compared to the cases with larger EK.