Determination of the anisotropy of an upper streambed layer in east-central Nebraska, USA

Information on the anisotropy of streambed hydraulic conductivity (K) is a necessity for analyses of water exchange and solute transport in the hyporheic zone. An approach is proposed for the determination of K, developed from existing in-situ permeameter test methods. The approach is based on determination of vertical and horizontal hydraulic conductivity of streambed sediments on-site and eliminates the effects of vertical flow in the hyporheic zone and stream-stage fluctuation, which normally influence in situ permeameter tests. The approach was applied to seven study sites on four tributaries of the Platte River in east-central Nebraska, USA. On-site permeameter tests conducted on about 172 streambed cores for the determination of vertical hydraulic conductivity (K _v) and horizontal hydraulic conductivity (K _h) at the study sites indicate that the study sites have relatively small anisotropic ratios, ranging from 0.74 to 2.40. The ratios of K _h to K _v from individual locations within a study site show greater variation than the anisotropic ratios from the mean or median K at each of the study sites.     

Heterogeneity of hydraulic conductivity and Darcian flux in the submerged streambed and adjacent exposed stream bank of the Beiluo River,northwest China

Recognizing the heterogeneity of hydraulic conductivity and hyporheic flow is critical for understanding contaminant transfer and biogeochemical and hydrological processes involving streams and aquifers. In this study, the heterogeneity of hydraulic conductivity and Darcian flux in a submerged streambed and its adjacent exposed stream banks were investigated in the Beiluo River, northwest China. In the submerged streambed, Darcian flux was estimated by measurement of vertical hydraulic conductivity (K _v) and vertical head gradient (VHG) using in-situ permeameter tests. On exposed stream banks, both horizontal hydraulic conductivity (K _h) and K _v were measured by on-site permeameter tests. In the submerged streambed, K _v values gradually decreased with depth and the higher values were concentrated in the center and close to the erosional bank. Compared to the exposed stream banks, the K _v values were higher in the streambed. From stream stage to the topmost layer of tested sediment, through increasing elevation, the K _h values increased on the erosional bank, while they decreased on the depositional bank. The values of VHG along the thalweg illustrate that downwelling flux occurred in the deepest area while upwelling flux appeared in the other areas, which might result from the change of streambed elevation. The higher value of the Darcian flux in the submerged streambed existed near the erosional bank.     

Statistical and geostatistical features of streambed hydraulic conductivities in the Platte River, Nebraska

This paper presents streambed hydraulic conductivities of the Platte River from south-central to eastern Nebraska. The hydraulic conductivities were determined from river channels using permeameter tests. The vertical hydraulic conductivities (K _v ) from seven test sites along this river in south-central Nebraska belong to one statistical population. Its mean value is 40.2 m/d. However, the vertical hydraulic conductivities along four transects of the Ashland test site in eastern Nebraska have lower mean values, are statistically different from the K _v values in south-central Nebraska, and belong to two different populations with mean values of 20.7 and 9.1 m/d, respectively. Finer sediments carried from the Loup River and Elkhorn River watersheds to the eastern reach of the Platte River lowers the vertical hydraulic conductivity of the streambed. Correlation coefficients between water depth and K _v values along a test transect indicates a positive correlation – a larger K _v usually occurs in the part of channel with deeper water. Experimental variograms derived from the vertical hydraulic conductivities for several transects across the channels of the Platte River show periodicity of spatial correlation, which likely result from periodic variation of water depth across the channels. The sandy to gravelly streambed contains very local silt and clay layers; spatially continuous low-permeability streambed was not observed in the river channels. The horizontal hydraulic conductivities were larger than the vertical hydraulic conductivities for the same test locations.     

High-resolution saturated hydraulic conductivity logging of borehole cores using air permeability measurements

Saturated hydraulic conductivity (K _s) is one of the most important parameters determining groundwater flow and contaminant transport in both unsaturated and saturated porous media. The hand-held air permeameter technique was investigated for high-resolution hydraulic conductivity determination on borehole cores using a spatial resolution of ～0.05 m. The suitability of such air permeameter measurements on friable to poorly indurated sediments was tested to improve the spatial prediction of classical laboratory-based K _s measurements obtained at a much lower spatial resolution (～2 m). In total, 368 K _s measurements were made on ～350 m of borehole cores originating from the Campine basin, northern Belgium, while ～5,230 air permeability measurements were performed on the same cores, resulting in a K _s range of seven orders of magnitude. Cross-validation demonstrated that, using air permeameter data as the secondary variable for laboratory based K _s measurements, the performance increased from R ²?=?0.35 for ordinary kriging (laboratory K _s only) to R ²?=?0.61 for co-kriging. The separate treatment of horizontal and vertical hydraulic conductivity revealed considerable anisotropy in certain lithostratigraphical units, while others were clearly isotropic at the sample scale. Air permeameter measurements on borehole cores provide a cost-effective way to improve spatial predictions of traditional laboratory based K _s.     

Measuring saturated hydraulic conductivity and anisotropy of peat by a modified split-container method

Long-term changes in the physical and hydraulic properties of peat result from the decomposition and consolidation processes. The saturated hydraulic conductivity (K _s) of peat is depth-dependent and could increase or decrease with depth; therefore, K _s determination on a large number of samples is required to more accurately assess field variability. The cube method is a popular laboratory procedure to determine K _s because it allows use of smaller sample dimensions, while minimizing edge effects. This article describes the design and use of an alternate split container to enclose undisturbed peat cubes during measurement of K _s and the application of this method to a field site in Northwest Territories, Canada. The method allows for simpler and more controlled K _s measurements while also permitting anisotropy measurements. Matched tests on identical samples (K _s range 21–314 m/d), using the split-container and wax methods, showed a good agreement for intermediate K _s values; however, significant deviations occurred for low and high K _s values. Hydraulic-conductivity measurements taken on field samples showed a decrease with depth and exhibited anisotropic hydraulic conductivity as expected based on previous studies.     

An analysis of methods for calculating constant terminal-settling velocities of spheres in liquids

Methods for calculating constant terminal-settling velocities (v_s)of spheres are examined for their validity and limitations of usefulness. A different approach is given which accurately predicts v_s for spheres over a wide range of hydraulic conditions based on past experimental work. The theory behind this approach is given along with the listing of a fortran program which directs the calculations of v_s.The practical limits of the author's method are stated, and tables of v_s may be generated from the program for common mineral densities over a range of sizes useful to sedimentologists.     

Hydraulic Conductivity and Coefficient of Consolidation of Two Sulphide Clays in Sweden

The variation and anisotropy in hydraulic conductivity and the coefficient of consolidation was investigated for two Swedish sulphide clays. A series of constant rate of strain oedometer tests was performed on samples trimmed in the vertical and horizontal direction. A methodology to evaluate the horizontal coefficients of consolidation c _h via the horizontal hydraulic conductivity k _h and the vertical compression modulus M _v is proposed. Laboratory evaluations of c _h are also compared with determinations of c _h from in situ piezometer measurements in vertically drained sulphide clay. Furthermore, the validity of the empirical correlation between hydraulic conductivity change index C _k and initial void ratio e ₀, C _k  = 0.5e ₀ (Tavenas et al. in Can Geotech J 20(4):645–660, 1983b), was investigated for the sulphide clays. The results from the investigation show large ranges in measured hydraulic conductivities and coefficients of consolidation. However, the results indicate that the correlation C _k  = 0.5e ₀ is valid. The anisotropy in hydraulic conductivity and the coefficient of consolidation of the sulphide clays tested seems to be small. For design purposes, multiple tests for assessment of hydraulic conductivity and the coefficient of consolidation should be made, and a partial factor of safety, depending on the requisite level of safety and the spatial variability of the parameters, should be introduced. For design purposes in this type of clay, k _h  = k _v and c _h  = c _v are suggested.     

Investigating spatial variability of vertical water fluxes through the streambed in distinctive stream morphologies using temperature and head data

Investigating the interaction of groundwater and surface water is key to understanding the hyporheic processes. The vertical water fluxes through a streambed were determined using Darcian flux calculations and vertical sediment temperature profiles to assess the pattern and magnitude of groundwater/surface-water interaction in Beiluo River, China. Field measurements were taken in January 2015 at three different stream morphologies including a meander bend, an anabranching channel and a straight stream channel. Despite the differences of flux direction and magnitude, flux directions based on vertical temperature profiles are in good agreement with results from Darcian flux calculations at the anabranching channel, and the Kruskal-Wallis tests show no significant differences between the estimated upward fluxes based on the two methods at each site. Also, the upward fluxes based on the two methods show similar spatial distributions on the streambed, indicating (1) that higher water fluxes at the meander bend occur from the center of the channel towards the erosional bank, (2) that water fluxes at the anabranching channel are higher near the erosional bank and in the center of the channel, and (3) that in the straight channel, higher water fluxes appear from the center of the channel towards the depositional bank. It is noted that higher fluxes generally occur at certain locations with higher streambed vertical hydraulic conductivity (K _v) or where a higher vertical hydraulic gradient is observed. Moreover, differences of grain size, induced by stream morphology and contrasting erosional and depositional conditions, have significant effects on streambed K _v and water fluxes.     

河床水力传导度及其各向异性的测定

采用直接测定法观测了黑河中游段河床水力传导度及其各向异性,结果表明:河床水力传导度不仅存在较强的各向异性,而且存在空间尺度上的变异性.河床中心位置在垂直、水平和θ=30°方向的平均水力传导度分别为0.45、22.49和1.71 m/d,河床边分别为5.95、29.69、16.80 m/d.在同一测点,水力传导度随着与水平方向的夹角增大呈幂函数曲线下降.试验结果表明河床边是河水的主要渗漏区,并且以侧渗为主.     

Quantification of Aperture and Relations Between Aperture,Normal Stress and Fluid Flow for Natural Single Rock Fractures

Accurate quantification of rock fracture aperture is important in investigating hydro-mechanical properties of rock fractures. Liquefied wood’s metal was used successfully to determine the spatial distribution of aperture with normal stress for natural single rock fractures. A modified 3D box counting method is developed and applied to quantify the spatial variation of rock fracture aperture with normal stress. New functional relations are developed for the following list: (a) Aperture fractal dimension versus effective normal stress; (b) Aperture fractal dimension versus mean aperture; (c) Fluid flow rate per unit hydraulic gradient per unit width versus mean aperture; (d) Fluid flow rate per unit hydraulic gradient per unit width versus aperture fractal dimension. The aperture fractal dimension was found to be a better parameter than mean aperture to correlate to fluid flow rate of natural single rock fractures. A highly refined variogram technique is used to investigate possible existence of aperture anisotropy. It was observed that the scale dependent fractal parameter, K _v, plays a more prominent role than the fractal dimension, D _a1d, on determining the anisotropy pattern of aperture data. A combined factor that represents both D _a1d and K _v, D _a1d × K _v, is suggested to capture the aperture anisotropy.     

Influence of streambed hydraulic conductivity on solute exchange with the hyporheic zone

A conservative solute tracer experiment was conducted in Indian Creek, a small urban stream in Philadelphia, Pennsylvania to investigate the role of subsurface properties on the exchange between streamwater and the hyporheic zone (subsurface surrounding the stream). Sodium Bromide (NaBr) was used as a conservative tracer, and it was monitored in the surface water at two stations and in the upper bed sediments (shallow hyporheic zone extending from 7.5 to 10 cm below the streambed). The hydraulic conductivity (K) of the upper bed sediments and the lower bed sediments (10–12.5 cm below the streambed) was measured in situ. High tracer concentrations were observed in the upper layer at locations where the hydraulic conductivity of the upper layer was larger than that of the lower layer. Low concentrations in the upper layer were observed in the converse case. A statistically significant relationship between the mass retained in the upper layer and the difference of K values between layers was observed.     

Estimating regional-scale fractured bedrock hydraulic conductivity using discrete fracture network (DFN) modeling

Estimating bedrock hydraulic conductivity of regional fractured aquifers is challenging due to a lack of aquifer testing data and the presence of small and large-scale heterogeneity. This study provides a novel approach for estimating the bedrock hydraulic conductivity of a regional-scale fractured bedrock aquifer using discrete fracture network (DFN) modeling. The methodology is tested in the mountainous Okanagan Basin, British Columbia, Canada. Discrete fractures were mapped in outcrops, and larger-scale fracture zones (corresponding to lineaments) were mapped from orthophotos and LANDSAT imagery. Outcrop fracture data were used to generate DFN models for estimating hydraulic conductivity for the fractured matrix (K _m). The mountain block hydraulic conductivity (K _mb) was estimated using larger-scale DFN models. Lineament properties were estimated by best fit parameters for a simulated pumping test influenced by a fracture zone. Unknown dip angles and directions for lineaments were estimated from the small-scale fracture sets. Simulated K _m and K _mb values range from 10^–8 to 10^–7?m/s and are greatest in a N–S direction, coinciding with the main strike direction of Okanagan Valley Fault Zone. K _mb values also decrease away from the fault, consistent with the decrease in lineament density. Simulated hydraulic conductivity values compare well with those estimated from pumping tests.     

Hydraulic conductivity of shallow sandy aquifers: Effects of sedimentologic and diagenetic differences

The relationship between values of hydraulic conductivity determined from grain-size methods,K _gr, and those from pumping-test methods,K _pt, have been evaluated statistically using data from recent and older sandy materials. It is shown that both methods generally give the same values only in recent sediments that have not been subjected to significant diagenetic alteration and give variable results in older and diagenetically altered sediments. The ratioK _pt/K_gr appears to vary, probably in response to the degree of diagenetic alteration. It is further found that methods incorporating the effects of grain size (d1O or d50) and sorting could give betterK values than those incorporating the effect of grain-size only and, thus, suggest the joint inclusion of both parameters in the grain-size determination of permeability.     

Natural rock joint roughness quantification through fractal techniques

Accurate quantification of roughness is important in modeling hydro-mechanical behavior of rock joints. A highly refined variogram technique was used to investigate possible existence of anisotropy in natural rock joint roughness. Investigated natural rock joints showed randomly varying roughness anisotropy with the direction. A scale dependant fractal parameter, K _v, seems to play a prominent role than the fractal dimension, D _r1d, with respect to quantification of roughness of natural rock joints. Because the roughness varies randomly, it is impossible to predict the roughness variation of rock joint surfaces from measurements made in only two perpendicular directions on a particular sample. The parameter D _r1d × K _v seems to capture the overall roughness characteristics of natural rock joints well. The one-dimensional modified divider technique was extended to two dimensions to quantify the two-dimensional roughness of rock joints. The developed technique was validated by applying to a generated fractional Brownian surface with fractal dimension equal to 2.5. It was found that the calculated fractal parameters quantify the rock joint roughness well. A new technique is introduced to study the effect of scale on two-dimensional roughness variability and anisotropy. The roughness anisotropy and variability reduced with increasing scale.     

A proposed analysis of saturation-dependent anisotropy for US Department of Energy (DOE) Hanford site soils

Technetium (⁹⁹Tc) spreads predominantly laterally through US Department of Energy Hanford site sediments. Lateral transport implies that at higher tensions, h, in the unsaturated zone, the effective hydraulic conductivity, K, may be strongly anisotropic. A modeling procedure has been developed to predict characteristics of the Tc plumes. The procedure consists of: (1) Adapting existing numerical techniques based on critical path analysis to calculate K(h), (2) Statistically correlating predicted K at various h values with texture, (3) Seeking value of h, for which anisotropy and horizontal K values are both sufficiently large to accommodate multi-kilometer horizontal spreading, (4) Predicting the distribution of K values for vertical flow as a function of system support volume, (5) Comparing the largest likely K value in the vertical direction with the expected K in the horizontal direction, (6) Finding the length scale at which the two K values are roughly equal, and (7) Comparing that length scale with horizontal spreading of the plume. Predictions of the typical value of h at which spreading is occurring compares well with inference. However, the length scale at which Tc transport in the unsaturated zone changes from predominantly horizontal to more nearly vertical appears underestimated.     

Short Note: Effective Hydraulic Conductivity and Transmissivity for Heterogeneous Aquifers

Regional scale models of groundwater flow and transport often employ domain discretizations with grid blocks larger than typical scales of field data. For heterogeneous formations, this difference in scales is often handled by using effective (upscaled) parameters. We investigate the problem of upscaling hydraulic conductivity and transmissivity from a small scale of measurement to a larger scale of grid blocks. Transmissivity statistics is expressed in terms of statistics of hydraulic conductivity, and expressions for the effective (upscaled) hydraulic conductivity K _eff and transmissivity T _eff for steady state flow in confined heterogeneous aquifers are derived by means of stochastic averaging and perturbation analysis. These expressions reveal that the commonly used relation T _eff = BK _eff, where B is the confined aquifer thickness, is not generally valid.     

Numerical modeling of contaminant transport in a stratified heterogeneous aquifer with dipping anisotropy

The combined influence of dip angle and adsorption heterogeneity on solute transport mechanisms in heterogeneous media can be understood by performing simulations of steady-state flow and transient transport in a heterogeneous aquifer with dipping anisotropy. Reactive and non-reactive contaminant transport in various types of heterogeneous aquifer is studied by simulations. The hydraulic conductivity (K) of the heterogeneous aquifer is generated by HYDRO_GEN with a Gaussian correlation spectrum. By considering the heterogeneity of the adsorption distribution coefficient (K _d), a perfect negative correlation between lnK and lnK _d is obtained by using the spherical grains model. The generated K and K _d are used as input to groundwater flow and transport models to investigate the effects of dipping sedimentary heterogeneity on contaminant plume evolution. Simulation results showed that the magnitude of the dip angle strongly controls the plume evolution in the studied anisotropic and heterogeneous aquifer. The retarded average pore-water velocity (v/R) of the adsorption model significantly controls the horizontal spreading of the plume. The bottom plume is intensively retarded in the zones between the dipping lenses of lower hydraulic conductivity and the no-flow bottom boundary. The implications of these findings are very important for the management of contaminated heterogeneous aquifers.     

混合型缓冲材料砌块渗透性及其各向异性研究

缓冲材料砌块具备良好的防渗性能,是保证高放废物处置库封闭性的关键。缓冲材料砌块经单轴加载挤压成型,块体尺寸大,测试与评价其渗透性能的均匀性和各向异性,对缓冲屏障设计具有重要价值。研究制备不同干密度的混合型缓冲材料砌块,定向切割获得砌块内部不同位置、不同方向的小试样,开展刚性壁和柔性壁渗透试验,综合评价了混合型缓冲砌块不同方向的水力传导系数。研究结果表明：砌块干密度越大,砌块的水力传导系数越低。所有砌块的水力传导系数均处于10?10 cm/s数量级,沿砌块z、?、r方向的水力传导系数基本相等,表明砌块渗透性具有良好的均匀性和各向同性,且满足高放缓冲材料防渗要求。两种试验方法获得的渗透结果差异较小,柔性壁渗透条件下砌块产生10%～20%的体积膨胀,导致其水力传导系数略大于刚性壁下的平行试样。引入CT试验,分析了渗透前后砌块的微观特性变化。试验证实,在饱和渗透之后,以CT值显示的砌块密度分布趋于均匀,砌块内部存在的微裂隙愈合消失。     

In Situ Stresses in Borehole Blanche-1/South Australia Derived from Breakouts,Core Discing and Hydraulic Fracturing to 2 km Depth

The development of Hot-Dry Rock (HDR) geothermal energy in Australia with drillings to some kilometres depth yields an impetus for deep stress logging. For the Olympic Dam HDR-project, borehole Blanche-1 was drilled to almost 2 km depth and provided the possibility to estimate the in situ stresses within the granitic borehole section by the analysis of borehole breakouts and core discing, as well as by hydraulic fracturing combined with acoustic borehole televiewer logging for fracture orientation determination. Although the stress magnitudes derived by the different methods deviate significantly, they clearly indicate for the depth range between 800 and 1,740 m a compressional stress regime of S _v ≤ S _h < S _H and a consistent East–West orientation of maximum horizontal compression in agreement with existing stress data for Australia. The minor horizontal stress S _h derived from the hydraulic fracturing closure pressure values is about equal to the overburden stress and may be regarded as most reliable.     

Crustal structure in the Changbaishan volcanic area, China, determined by modeling receiver functions

During 1998–1999, we installed a temporary broadband seismic network in the Changbaishan volcanic region, NE China. We estimated crustal structure using teleseismic seismograms collected at the network. We detected a near surface region of strong anisotropy directly under the main volcanic edifice of the volcanic area. We modeled 109 receiver functions from 19 broadband stations using three techniques. First we used a “slant-stacking” method to model the principal crustal P reverberation phases to estimate crustal thickness and the average crustal P to S speed ratio (v_p/v_s), assuming an average P-wave velocity in the crust. We then estimated crustal S-wave velocity (v_s) and v_p/v_s profiles by modeling stacked receiver functions using a direct search. Finally, we inverted several receiver functions recorded at stations closest to the main volcanic edifice using least squares to estimate v_s velocity profiles, assuming a v_p/v_s value. The results from the three estimation techniques were consistent, and generally we found that the receiver functions constrained estimates of changes in wave speeds better than absolute values. We resolved that the crust is 30–39 km thick under the volcanic region and 28–32 km thick away from the volcanic region, with a midcrust velocity transition at about 10–15 km depth. We estimated that the average crust P-wave velocity is about 6.0–6.2 km/s surrounding the main volcanic region, while it is slightly lower in the vicinity of the main volcanic edifice. The estimates of v_p/v_s were more ambiguous, but we inferred that the bulk crustal Poisson's ratio (which is related to v_p/v_s) ranges between 0.20 and 0.30, with a suggestion that the Poisson's ratio is lower under the central volcanic region compared to the surrounding areas. We resolved low S-wave velocities (down to about 3 km/s) in the middle crust in the region of the main volcanic edifice. The low velocity anomaly extends from about 5–10 to 15–25 km below the surface, probably indicating a region of elevated temperatures. We were unable to determine if partial melt is present with the data we considered in this paper.