Measuring wave propagation characteristics in artificial sand-clay mixtures

Ultrasonic compressional (V _p ) and shear (V _s ) velocities have been measured on artificial sand-clay mixtures. The measurements were carried out in a drained triaxial load cell using a pulse transition method. The measuring device was equiped with a waveform storage facility. The investigated mixtures consisted mainly of kaolinite and quartz sand. Some mixtures also contained Na-montmorillonite, illites or quartz-flour. The acoustic behaviour was observed during a pressure increase up to 72 MPa vertical and 36 MPa horizontal pressure. At a given pressure,V _p andV _s in pure sand turned out to be similar to those in pure kaolinite. As predicted by the sand-clay model of Marion (1990), a velocity maximum corresponds to a minimum in total porosity. This porosity minimum marks the transition from a clayey sand to a sandy clay. It is not only reflected in bothV _p andV _s , but also in the quality of the received pulse. The effective tension of the received signal during 20µs after the first arrival, was used as an indication for P-wave pulse attenuation. This apparent attenuation decreases with increasing clay content and increases with increasing porosity. It is shown that clay mineralogy does not measurably affect wave velocities in clayey sands.     

Anisotropy and depth‐related heterogeneity of hydraulic conductivity in a bog peat. I: laboratory measurements

Anisotropy and heterogeneity of hydraulic conductivity (K) are suspected of greatly affecting rates and patterns of ground‐water seepage in peats. A new laboratory method, termed here the modified cube method, was used to measure horizontal and vertical hydraulic conductivity (K_h and K_v) of 400 samples of bog peat. The new method avoids many of the problems associated with existing field and laboratory methods, and is shown to give relatively precise measurements of K. In the majority of samples tested, K_h was much greater than K_v, indicating that the bog peat was strongly anisotropic. Log₁₀K_h, log₁₀K_v, and log₁₀ (K_h/K_v) were found to vary significantly with depth, although none of the relationships was simple. We comment on the scale dependency of our measurements. Copyright © 2002 John Wiley & Sons, Ltd.     

Changes over time in near-saturated hydraulic conductivity of peat soil following reclamation for agriculture

Reclamation of peat bogs for agriculture changes the physical and chemical characteristics of the peat matrix, for example, drainage and tillage accelerate decomposition, altering peat porosity, pore size distribution, and hydraulic properties. This study investigated changes in near-saturated hydraulic conductivity over time after drainage of peat soil for agricultural use by conducting tension infiltrometer measurements in a mire that has been gradually drained and reclaimed for agriculture during the past 80 years (with fields drained 2, 12, 40, and 80 years before the measurements). At pore water pressure closest to saturation (pressure head −1 cm), hydraulic conductivity in the newest field was approximately nine times larger than that in the oldest field, and a decreasing trend with field age was observed. A similar (but weaker) trend was observed with −3 cm pressure head (approximately four times larger in the newest field in comparison to the oldest), but at −6 cm head, there were no significant differences. These results indicate that peat degradation reduces the amount of millimetre-sized pores in particular. They also indicate that changes in peat macroporosity continue for several decades before a new steady state is reached.     

Practical issues in imaging hydraulic conductivity through hydraulic tomography

Hydraulic tomography has been developed as an alternative to traditional geostatistical methods to delineate heterogeneity patterns in parameters such as hydraulic conductivity (K) and specific storage (S(s)). During hydraulic tomography surveys, a large number of hydraulic head data are collected from a series of cross-hole tests in the subsurface. These head data are then used to interpret the spatial distribution of K and S(s) using inverse modeling. Here, we use the Sequential Successive Linear Estimator (SSLE) of Yeh and Liu (2000) to interpret synthetic pumping test data created through numerical simulations and real data generated in a laboratory sandbox aquifer to obtain the K tomograms. Here, we define "K tomogram" as an image of K distribution of the subsurface (or the inverse results) obtained via hydraulic tomography. We examine the influence of signal-to-noise ratio and biases on results using inverse modeling of synthetic and real cross-hole pumping test data. To accomplish this, we first show that the pumping rate, which affects the signal-to-noise ratio, and the order of data included into the SSLE algorithm both have large impacts on the quality of the K tomograms. We then examine the role of conditioning on the K tomogram and find that conditioning can improve the quality of the K tomogram, but can also impair it, if the data are of poor quality and conditioning data have a larger support volume than the numerical grid used to conduct the inversion. Overall, these results show that the quality of the K tomogram depends on the design of pumping tests, their conduct, the order in which they are included in the inverse code, and the quality as well as the support volume of additional data that are used in its computation.     

Effective hydraulic conductivity of nonstationary aquifers

Assuming that the ln hydraulic conductivity in an aquifer is mathematically approximated by a spatial deterministic surface, or trend, plus a stationary random noise, we treat the problem of finding what the effective hydraulic conductivity of that aquifer is. This problem is tackled by spectral methods applied to a type of diffusion equation of groundwater flow, together with suitable coordinate transformations. Analytical (exact) solutions in terms of elementary functions are presented for one- and three-dimensional finite and infinite domains. Stability criteria are obtained for the solutions, in terms of a critical parameter, that turns out to involve the product of correlation scale and trend gradient. For the case of finite and symmetrical domains, additional provisions to insure the stability of numerical calculations of effective hydraulic conductivity are provided. Effective hydraulic conductivity is an important property, with potential applications in the calibrations of groundwater and transport numerical models.     

Effective hydraulic conductivity of nonstationary aquifers

Assuming that the ln hydraulic conductivity in an aquifer is mathematically approximated by a spatial deterministic surface, or trend, plus a stationary random noise, we treat the problem of finding what the effective hydraulic conductivity of that aquifer is. This problem is tackled by spectral methods applied to a type of diffusion equation of groundwater flow, together with suitable coordinate transformations. Analytical (exact) solutions in terms of elementary functions are presented for one- and three-dimensional finite and infinite domains. Stability criteria are obtained for the solutions, in terms of a critical parameter, that turns out to involve the product of correlation scale and trend gradient. For the case of finite and symmetrical domains, additional provisions to insure the stability of numerical calculations of effective hydraulic conductivity are provided. Effective hydraulic conductivity is an important property, with potential applications in the calibrations of groundwater and transport numerical models.     

Diagrammatic theory of effective hydraulic conductivity

This work presents a stochastic diagrammatic theory for the calculation of the effective hydraulic conductivity of heterogeneous media. The theory is based on the mean-flux series expansion of a log-normal hydraulic conductivity medium in terms of diagrammatic representations and leads to certain general results for the effective hydraulic conductivity of three-dimensional media. A selective summation technique is used to improve low-order perturbation analysis by evaluating an infinite set of diagrammatic terms with a specific topological structure that dominates the perturbation series. For stochastically isotropic media the selective summation yeilds the anticipated exponential expression for the effective hydraulic conductivity. This expression is extended to stochastically anisotropic media. It is also shown that in the case of non homogeneous media the uniform effective hydraulic conductivity is replaced by a non-local tensor kernel, for which general diagrammatic expressions are obtained. The non-local kernel leads to the standard exponential behavior for the effective hydraulic conductivity at the homogeneous limit.     

Diagrammatic theory of effective hydraulic conductivity

This work presents a stochastic diagrammatic theory for the calculation of the effective hydraulic conductivity of heterogeneous media. The theory is based on the mean-flux series expansion of a log-normal hydraulic conductivity medium in terms of diagrammatic representations and leads to certain general results for the effective hydraulic conductivity of three-dimensional media. A selective summation technique is used to improve low-order perturbation analysis by evaluating an infinite set of diagrammatic terms with a specific topological structure that dominates the perturbation series. For stochastically isotropic media the selective summation yeilds the anticipated exponential expression for the effective hydraulic conductivity. This expression is extended to stochastically anisotropic media. It is also shown that in the case of non homogeneous media the uniform effective hydraulic conductivity is replaced by a non-local tensor kernel, for which general diagrammatic expressions are obtained. The non-local kernel leads to the standard exponential behavior for the effective hydraulic conductivity at the homogeneous limit.     

Usefulness of flux measurements during hydraulic tomographic survey for mapping hydraulic conductivity distribution in a fractured medium

Using the first-order analysis, we investigate the spatial cross-correlation between hydraulic conductivity variation and specific discharge (flux) as well as its components measured in a borehole under steady-state flow conditions during cross-hole pumping tests in heterogeneous aquifers. These spatial correlation patterns are found to be quite different from that between the hydraulic conductivity variation and the hydraulic head measurement in the same borehole. This finding suggests that a specific discharge measurement carries non-redundant information about the spatial distribution of heterogeneity, even this measurement is collected from the same location where the head measurement is taken. As such, specific discharge observations should be included in the analysis of hydraulic tomography to increase the resolution of estimated aquifer heterogeneity. Using numerical experiments, we demonstrate the effectiveness of the joint interpretation of both hydraulic heads and fluxes for mapping fracture distributions in a hypothetic geologic medium.     

Estimating field‐saturated soil hydraulic conductivity by a simplified Beerkan infiltration experiment

Field‐saturated soil hydraulic conductivity, K_fs, is highly variable. Therefore, interpreting and simulating hydrological processes, such as rainfall excess generation, need a large number of K_fs data even at the plot scale. Simple and reasonably rapid experiments should be carried out in the field. In this investigation, a simple infiltration experiment with a ring inserted shortly into the soil and the estimation of the so‐called α* parameter allowed to obtain an approximate measurement of K_fs. The theoretical approach was tested with reference to 149 sampling points established on Burundian soils. The estimated K_fs with the value of first approximation of α* for most agricultural field soils (α* = 0.012 mm^?1) differed by a practically negligible maximum factor of two from the saturated conductivity obtained by the complete Beerkan Estimation of Soil Transfer parameters (BEST) procedure for soil hydraulic characterization. The measured infiltration curve contained the necessary information to obtain a site‐specific prediction of α*. The empirically derived α* relationship gave similar results for K_fs (mean = 0.085 mm s^?1; coefficient of variation (CV) = 71%) to those obtained with BEST (mean = 0.086 mm s^?1; CV = 67%), and it was also successfully tested with reference to a few Sicilian sampling points, since it yielded a mean and a CV of K_fs (0.0094 mm s^?1 and 102%, respectively) close to the values obtained with BEST (mean = 0.0092 mm s^?1; CV = 113%). The developed method appears attractive due to the extreme simplicity of the experiment. Copyright © 2012 John Wiley & Sons, Ltd.     

Evaluating the effect of using artificial pore water on the quality of laboratory hydraulic conductivity measurements of peat

Pore dilation, the compaction of humic acids on peat fibres due to the process of flocculation, causes the hydraulic conductivity of peat to increase with increasing pore water electrical conductivity. This is a reversible process and a reduction in the pore water conductivity produces a decrease in the hydraulic conductivity due to the constriction of pores. We verify how this dilation and constriction of pores, resulting from the application of artificial pore water (primarily deionized water), affects laboratory measurements of the hydraulic conductivity of peat. Repeat measurements of the hydraulic conductivity were performed on samples of Sphagnum peat. It is shown that the application of deionized water during constant head permeameter tests causes a significant decrease in the hydraulic conductivity. Between tests, the hydraulic conductivity of the peat continues to decline without an associate decrease in the pore water electrical conductivity because of a lagged pore constriction effect. We suggest that the use of artificially high or low pore water electrical conductivities, during laboratory hydraulic conductivity measurements, is likely to lead to significant errors. Experimental protocols must, therefore, be revised to take better account of the pore water chemistry. The ionic concentrations of the natural pore fluid should be replicated during hydraulic conductivity tests, either by using pore fluid extracted from the study site or by artificially replicating the major ionic composition of the natural pore fluid. In addition, prior to the hydraulic conductivity measurements, peat samples should be flushed with this solution until the hydraulic conductivity stabilizes and the samples subsequently allowed to equilibrate. Copyright © 2010 John Wiley & Sons, Ltd.     

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.     

Evaluation of vertical variations in hydraulic conductivity in unconsolidated sediments

Detailed information on vertical variations in hydraulic conductivity (K) is essential to describe the dynamics of groundwater movement at contaminated sites or as input data used for modeling. K values in high vertical resolution should be determined because K tends to be more continuous in the horizontal than in the vertical direction. To determine K in shallow unconsolidated sediments and in the vertical direction, the recently developed direct-push injection logger can be used. The information obtained by this method serves as a proxy for K and has to be calibrated to obtain quantitative K values of measured vertical profiles. In this study, we performed direct-push soil sampling, sieve analyses and direct-push slug tests to obtain K values in vertical high resolution. Using the results of direct-push slug tests, quantitative K values obtained by the direct-push injection logger could be determined successfully. The results of sieve analyses provided lower accordance with the logs due to the inherent limitations of the sieving method.     

Effect of spatial variation in hydraulic conductivity on groundwater flow by alternate solution techniques

The behaviour of an aquifer in which there is spatial variation in hydraulic conductivity is simulated by means of a Monte Carlo procedure. The lognormal function is used to model the distribution of conductivities. Thus variations in hydraulic head and specific discharge are studied. As an alternate technique a finite-difference technique is adopted for comparative purposes. The standard deviation of two-dimensional flows is related to the standard deviation of conductivity. Hence, an empirical probability distribution of flows is obtained by specific values of the variance in conductivities.     

Analysis of slug tests in formations of high hydraulic conductivity

A new procedure is presented for the analysis of slug tests performed in partially penetrating wells in formations of high hydraulic conductivity. This approach is a simple, spreadsheet-based implementation of existing models that can be used for analysis of tests from confined or unconfined aquifers. Field examples of tests exhibiting oscillatory and nonoscillatory behavior are used to illustrate the procedure and to compare results with estimates obtained using alternative approaches. The procedure is considerably simpler than recently proposed methods for this hydrogeologic setting. Although the simplifications required by the approach can introduce error into hydraulic-conductivity estimates, this additional error becomes negligible when appropriate measures are taken in the field. These measures are summarized in a set of practical field guidelines for slug tests in highly permeable aquifers.     

Upscaling of hydraulic conductivity and telescopic mesh refinement

Performance assessments of repositories for the underground disposal of nuclear fuel and waste include models of ground water flow and transport in the host rocks. Estimates of hydraulic conductivity, K, based on field measurements may require adjustment (upscaling) for use in numerical models, but the choice of upscaling approach can be complicated by the use of nested modeling, large-scale fracture zones, and a high degree of heterogeneity. Four approaches to upscaling K are examined using a reference case based on exhaustive site data and an application of nested modeling to evaluate performance assessment of a waste repository. The upscaling approaches are evaluated for their effects on the flow balance between nested modeling domains and on simple measures of repository performance. Of the upscaling approaches examined in this study, the greatest consistency of boundary flows was achieved using the observed scale dependence for the rock domains, measured values from the large-scale interference test for the conductor domain, and a semivariogram regularization based on the Moye model for packer test interpretation. Making the assumption that large fracture zones are two-dimensional media results in the greatest changes to the median of travel time and improves the flow balance between the nested models. The uncertainty of upscaling methods apparently has a small impact on median performance measures, but a significant impact on the variances and earliest arrival times.     

Comparison of upscaling methods to estimate hydraulic conductivity

A hydraulic field test program was performed at a hard rock laboratory (Asp? HRL) on the Swedish east coast to test upscaling theories. The test program investigated the rock volume around a borehole located at a depth of approximately 340 m below sea level. Hydraulic packer tests were performed at various scales, from 2 m to the entire borehole length of 296 m. From this set of data the predictive ability of different upscaling methods could be evaluated. The comparison of the evaluated "true" field scale hydraulic conductivity with the upscaled hydraulic conductivity yielded that the majority of the upscaling methods tested in this paper predict the large scale values with significant accuracy. However, the ability to predict rapidly decreases when the variance of the natural logarithm of hydraulic conductivity of the subsamples is larger than one. Such a variance is consistently found in the crystalline rocks at the tested site at the 2 m scale. However, at scales of 10 m and larger, a variance larger than one is uncommon. Therefore, it is concluded that there exists a smallest possible scale for use of hydraulic pumping test results for estimating the effective hydraulic conductivity at scales typical for regional flow.     

Measuring the hydraulic conductivity of shallow submerged sediments

The hydraulic conductivity of submerged sediments influences the interaction between ground water and surface water, but few techniques for measuring K have been described with the conditions of the submerged setting in mind. Two simple, physical methods for measuring the hydraulic conductivity of submerged sediments have been developed, and one of them uses a well and piezometers similar to well tests performed in terrestrial aquifers. This test is based on a theoretical analysis that uses a constant-head boundary condition for the upper surface of the aquifer to represent the effects of the overlying water body. Existing analyses of tests used to measure the hydraulic conductivity of submerged sediments may contain errors from using the same upper boundary conditions applied to simulate terrestrial aquifers. Field implementation of the technique requires detecting minute drawdowns in the vicinity of the pumping well. Low-density oil was used in an inverted U-tube manometer to amplify the head differential so that it could be resolved in the field. Another technique was developed to measure the vertical hydraulic conductivity of sediments at the interface with overlying surface water. This technique uses the pan from a seepage meter with a piezometer fixed along its axis (a piezo-seep meter). Water is pumped from the pan and the head gradient is measured using the axial piezometer. Results from a sandy streambed indicate that both methods provide consistent and reasonable estimates of K. The pumping test allows skin effects to be considered, and the field data show that omitting the skin effect (e.g., by using a single well test) can produce results that underestimate the hydraulic conductivity of streambeds.