Brittle crack growth in rocks

Fracture phenomena in rocks are associated with mainly mode I crack growth, sometimes superposed by shear or torsion. The present paper contributes to a fracture mechanics analysis of mode I and mixed mode crack propagation, by presenting reliable fracture toughness data for some rocks which include the effect of induced crack propagation rate, and the influence of effective pressure, and by numerical calculations on fracture propagation in layered rock formations. Empirical relations between fracture toughness,K _Ic' and induced crack opening displacement rate, as well as effective pressure, are given. The observedK _Ic pressure relation supports a theoretical model which takes into account the existence of microcracks in the crack tip region. Finite element calculations of fracture propagation in layered rock formations demonstrate the important effect of mixed mode crack growth. The numerical approach is particularly applied to single crack growth in hydraulic fracturing and in three point bending tests on layered single edge crack specimens.     

Hydraulic Conductivity Calibration of Logging NMR in a Granite Aquifer,Laramie Range,Wyoming

In granite aquifers, fractures can provide both storage volume and conduits for groundwater. Characterization of fracture hydraulic conductivity (K) in such aquifers is important for predicting flow rate and calibrating models. Nuclear magnetic resonance (NMR) well logging is a method to quickly obtain near-borehole hydraulic conductivity (i.e., K_NMR) at high-vertical resolution. On the other hand, FLUTe flexible liner technology can produce a K profile at comparable resolution but requires a fluid driving force between borehole and formation. For three boreholes completed in a fractured granite, we jointly interpreted logging NMR data and FLUTe K estimates to calibrate an empirical equation for translating borehole NMR data to K estimates. For over 90% of the depth intervals investigated from these boreholes, the estimated K_NMR are within one order of magnitude of K_FLUTe. The empirical parameters obtained from calibrating the NMR data suggest that “intermediate diffusion” and/or “slow diffusion” during the NMR relaxation time may occur in the flowing fractures when hydraulic aperture are sufficiently large. For each borehole, “intermediate diffusion” dominates the relaxation time, therefore assuming “fast diffusion” in the interpretation of NMR data from fractured rock may lead to inaccurate K_NMR estimates. We also compare calibrations using inexpensive slug tests that suggest reliable K_NMR estimates for fractured rock may be achieved using limited calibration against borehole hydraulic measurements.     

Fracture toughness and subcritical crack growth during high-temperature tensile deformation of Westerly granite and Black gabbro

The double torsion testing method has been used to determine catastrophic and subcritical crack propagation parameters for pre-cracked specimens of Westerly granite and Black gabbro under a number of environmental conditions.The critical stress intensity factor for catastrophic crack propagation (fracture toughness) of granite and gabbro has been measured at temperatures from 20 to 400°C, in a vacuum. At 20°C, the fracture toughness of Westerly granite was $\text{1.79 ± 0.02}\text{MPa}\text{·}\text{m}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, and for two blocks of Black gabbro it was $\text{3.03 ± 0.08}\text{MPa}\text{·}\text{m}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ and $\text{2.71 ± 0.15}\text{MPa}\text{·}\text{m}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, respectively. These values are very close to those reported by other investigators for tests conducted in air of ambient humidity at room temperature. For both rocks, fracture toughness at first increased slightly, and then decreased steadily on raising the temperature above ambient conditions. This behaviour is explained in terms of the density and distribution of thermally induced microcracks, as determined by quantitative optical microscopy.Subcritical crack growth behaviour has been studied at temperatures up to 300°C, and under water vapour at pressures of 0.6 to 15 kPa. Both the load relaxation and incremental constant displacement rate forms of the double torsion testing method were utilised to generate stress intensity factor/crack velocity diagrams. Crack growth was measured over the velocity range 5 × 10^?3 to 10^?7 m · s^?1. Increasing both temperature and water vapour pressure resulted in substantially higher crack growth rates. The overall effect of raising the temperature over the range studied here (20–300°C) was to increase the crack growth rate in granite and gabbro by ～5 and 7 orders of magnitude, respectively, at constant stress intensity factor and vapour pressure of water. For both rocks, the slopes of stress intensity factor/crack velocity curves were sensitive to changes in both temperature and water vapour pressure at low values of the latter parameter. Slopes fell substantially on raising the water vapour pressure, but were relatively insensitive to changes in temperature at these higher pressures. No subcritical crack growth limit was encountered.Estimates of the uncertainty in our experimental data are given. From the results of multiple load relaxation experiments on Westerly granite specimens, we estimate the uncertainty in position of stress intensity factor/crack velocity curves along the stress intensity axis to be c. 10% of the fracture toughness, and the uncertainty in slope of such curves to be c. 12%.Problems associated with the extrapolation of our experimental data to regions of higher effective confining pressure in the Earth's crust are discussed.     

On the physical essence of the b value for AE of rock tests and natural earthquakes in terms of fracture mechanics

The problem of physical essence of theb value forAE of rock tests and natural earthquakes has been a controversial topic during the past two decades. In the present paper the order and energy of each microfracturing of the microcrack system existing in a rock specimen is discussed from the viewpoint of fracture mechanics, then the whole series ofAE and subsequently the value ofb are determined. The order of microfracturing depends on the parametersKei/Kci whereKei is the effective stress intensity factor of thei-th microcrack andKci is the fracture toughness in the site of thei-th crack. The energy of eachAE can be expressed asηi ∫ loili Gids whereG is the energy release rate of microcarck,loi andli are the original and final crack lengths respectively andηi is the emanating efficiency for thei-th crack. If we assume that the distribution density function of microcrack lengthl isp(l)=Bl−v whereB andγ are constants, then the expressionb=3γ/2 can be deduced. Hence, we have come to the conclusion that the value ofb mirrors essentially the “crack-system-configuration” of the material, which means the distribution of the sizes, shapes and orientations of microcracks over space as well as the distribution of the other relevant physical parameters such as fracture toughness, friction coefficient, etc. Our conclusion is somewhat similar in character to Mogi’s. He concluded thet the heterogeneity of the material plays the most important role in determining the value ofb. The term heterogeneity of course covers the idea of “crack-system-configuration, but we think that our view has a little bit deeper insight to the problem than that of Mogi. This subject is supported by Chinese Joint Seismological Science Foundation.     

Hydraulic Tomography Offers Improved Imaging of Heterogeneity in Fractured Rocks

Fractured rocks have presented formidable challenges for accurately predicting groundwater flow and contaminant transport. This is mainly due to our difficulty in mapping the fracture‐rock matrix system, their hydraulic properties and connectivity at resolutions that are meaningful for groundwater modeling. Over the last several decades, considerable effort has gone into creating maps of subsurface heterogeneity in hydraulic conductivity (K) and specific storage (S_s) of fractured rocks. Developed methods include kriging, stochastic simulation, stochastic inverse modeling, and hydraulic tomography. In this article, I review the evolution of various heterogeneity mapping approaches and contend that hydraulic tomography, a recently developed aquifer characterization technique for unconsolidated deposits, is also a promising approach in yielding robust maps (or tomograms) of K and S_s heterogeneity for fractured rocks. While hydraulic tomography has recently been shown to be a robust technique, the resolution of the K and S_s tomograms mainly depends on the density of pumping and monitoring locations and the quality of data. The resolution will be improved through the development of new devices for higher density monitoring of pressure responses at discrete intervals in boreholes and potentially through the integration of other data from single‐hole tests, borehole flowmeter profiling, and tracer tests. Other data from temperature and geophysical surveys as well as geological investigations may improve the accuracy of the maps, but more research is needed. Technological advances will undoubtedly lead to more accurate maps. However, more effort should go into evaluating these maps so that one can gain more confidence in their reliability.     

Common Evolution of Mechanical and Transport Properties in Thermally Cracked Westerly Granite at Elevated Hydrostatic Pressure

Increasing the damage and crack porosity in crustal rocks can result in significant changes to various key physical properties, including mechanical strength, elastic and mechanical anisotropy, and the enhancement of transport properties. Using a Non-Interactive Crack Effective Medium (NIC) theory as a fundamental tool, we show that elastic wave dispersion can be inverted to evaluate crack density as a function of temperature and is compared with optically determined crack density. Further, we show how the existence of embedded microcrack fabrics in rocks also significantly influences the fracture toughness (K_IC) of rocks as measured via a suite of tensile failure experiments (chevron cracked notch Brazilian disk). Finally, we include fluid flow in our analysis via the Guéguen and Dienes crack porosity-permeability model. Using the crack density and aspect ratio recovered from the elastic-wave velocity inversion, we successfully compare permeability evolution with pressure with the laboratory measurements of permeability.     

Fracture Toughness and Fracture Roughness Interrelationship in Thermally treated Westerly Granite

This paper presents an experimental work aimed at assessing the correlation between fracture toughness (K _IC ) and fracture roughness for a series of Westerly granite specimens thermally treated up to 850°C. Mode I fracture toughness as a function of thermal treatment is determined using Cracked Chevron Notched Brazilian Disc specimens. The degree of roughness of the resultant fracture surfaces is analyzed with the aid of a high accuracy, high precision stereo-topometric measurement system. Roughness and toughness values display a negative correlation as a function of temperature. Fracture toughness decreases with increasing temperature due to the gradual opening of grain-grain boundaries in response to thermal stresses. Mode I fractures preferentially follow these weakened grain-grain boundaries, which in addition to the thermal expansion of individual grains, result in rougher failure profiles with increasing temperature. At low temperature, a distinct anisotropy in roughness was observed in all fracture surfaces with higher roughness values perpendicular to the direction of fracture propagation. However, higher treatment temperatures resulted in the homogenization of fracture roughness in all directions. These results confirm the important link among petrofabric analysis, fracture toughness, and fracture roughness in response to thermal treatment.     

Fracture Toughness Measurements and Acoustic Emission Activity in Brittle Rocks

Fracture toughness measurements under static loading conditions have been carried out in Barre and Lac du Bonnet granites. An advanced AE technique has been adopted to monitor real-time crack initiation and propagation around the principal crack in these tests to understand the processes of brittle failure under tension and related characteristics of the resulting fracture process zone. The anisotropy of Mode I fracture toughness has been investigated along specific directions. Microcrack density and orientation analysis from thin section studies have shown these characteristics to be the primary cause of the observed variation in fracture toughness, which is seen to vary between 1.14 MPa.(m)^1/2 and 1.89 MPa.(m)^1/2 in Barre granite. The latter value represents the case in which the crack is propagated at right angles to the main set of microcracks. The creation of a significant fracture process zone surrounding the propagating main crack has been confirmed. Real-time imaging of the fracture process and formation of fracture process zone by AE techniques yielded results in very good agreement with those obtained by direct optical analysis.     

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.     

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.     

Effect of Injected Water on Hydraulic Fracturing Deduced from Acoustic Emission Monitoring

—In order to investigate the effects of injected water in hydraulic fracturing, experiments were conducted on cubic granite specimens, comparing fracturings induced by conventional water injection with those induced by pressurization of a urethane sleeve, thereby realizing "hydraulic fracturing" without the use of fracturing fluid. In both experiments, a shear type mechanism was found to be dominant in fault plane solutions of AE events. However, in the case of water injection, cracks extended rapidly with large drops in hole water pressure and bursts of AE, whereas in pressurization by the urethane sleeve, cracks extended stepwise with no such large drops in hole pressure and no bursts of AE. The difference in crack extension in the two experiments can be analyzed by comparing relations between crack length and stress intensity factor of mode I at a crack tip. The observation and analysis indicate that existence of fracturing fluid like water helps initiated cracks to extend rapidly and widely in hydraulic fracturing in actual HDR fields. Received September 12, 1996, accepted January 24, 1997     

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.     

SEISMIC CLASSIFICATION OF ROCK MASS QUALITIES*

Correlations between longitudinal velocities and rock mechanic parameters such as fracture frequencies and “Rock Quality Designation” (RQD) values have been studied, based upon velocity data from various rock types and different geographical locations. The dispersion of values at different sites studied is on average ± 0.8 cracks per meter and for the RQD values ± 3.5%. Within sites the dispersion of individual values relative to the average for the site is ± 1.0 – 2.0 cracks per meter and ± 2 – 6% for the RQD values. The deviations are rather moderate, especially when considering the variation of rock type involved in the studies: amphibolite, granite, gneiss, meta-anorthosite, pegmatite, porphyry, quartzite, and mylonite. The studies thus confirmed earlier assumptions that there is a strong correlation between longitudinal velocity and fracturing and that the velocities can be used to give rather accurate predictions of the quality of rock masses for construction purposes. The accuracy of the predictions increases if the velocity level of the more competent rock is taken into account. The correlation between velocity and fracturing is related to jointed but unweathered igneous and metamorphic rock and cannot be applied without introducing serious errors to a site where the rocks present a higher degree of alteration and weathering. Comparisons between rock permeability and longitudinal velocity proved that a more reliable general correlation is not likely to be found. By comparing the elastic moduli E_dyn, μ, and k with ø, V_p/V₈, and k/μ, indications have been obtained where the optimum rock conditions for a certain site are to be encountered. This has been verified by a similar comparison where the elastic moduli have been replaced by fracturing values. The value of the longitudinal velocity as a means to evaluate rock quality increases if the position of the velocity in the range of the Poisson's ratio has been established. The average relationships between longitudinal velocities and the corresponding elastic moduli proved to be: The values from each site differ from the average values with about ± 2 GPa for E_dyn and about ± 1 GPa for μ and k. It was confirmed that in igneous and metamorphic rocks longitudinal velocities ≤ 4000 m/s generally indicate rock masses where heavier tunnel support will be needed. This velocity limit corresponds to an average fracture frequency of about 10 cracks per meter and a RQD value of about 65 %. The prediction of the tunnel reinforcements needed at a particular site will, however, be improved if the general velocity level of the more competent rock is considered.     

Comparison of Hydraulic Tomography with Traditional Methods at a Highly Heterogeneous Site

Over the past several decades, different groundwater modeling approaches of various complexities and data use have been developed. A recently developed approach for mapping hydraulic conductivity (K) and specific storage (S_s) heterogeneity is hydraulic tomography, the performance of which has not been compared to other more “traditional” methods that have been utilized over the past several decades. In this study, we compare seven methods of modeling heterogeneity which are (1) kriging, (2) effective parameter models, (3) transition probability/Markov Chain geostatistics models, (4) geological models, (5) stochastic inverse models conditioned to local K data, (6) hydraulic tomography, and (7) hydraulic tomography conditioned to local K data using data collected in five boreholes at a field site on the University of Waterloo (UW) campus, in Waterloo, Ontario, Canada. The performance of each heterogeneity model is first assessed during model calibration. In particular, the correspondence between simulated and observed drawdowns is assessed using the mean absolute error norm, (L₁), mean square error norm (L₂), and correlation coefficient (R) as well as through scatterplots. We also assess the various models on their ability to predict drawdown data not used in the calibration effort from nine pumping tests. Results reveal that hydraulic tomography is best able to reproduce these tests in terms of the smallest discrepancy and highest correlation between simulated and observed drawdowns. However, conditioning of hydraulic tomography results with permeameter K data caused a slight deterioration in accuracy of drawdown predictions which suggests that data integration may need to be conducted carefully.     

Performance of Gradient and Gradient-Free Optimizers in Transient Hydraulic Tomography

Sub-surface characterization in fractured aquifers is challenging due to the co-existence of contrasting materials namely matrix and fractures. Transient hydraulic tomography (THT) is proved to be an efficient and robust technique to estimate hydraulic (K_m, K_f) and storage (S_m, S_f) properties in such complex hydrogeologic settings. However, performance of THT is governed by data quality and optimization technique used in inversion. We assessed the performance of gradient and gradient-free optimizers with THT inversion. Laboratory experiments were performed on a two-dimensional, granite rock (80 cm × 45 cm × 5 cm) with known fracture pattern. Cross-hole pumping experiments were conducted at 10 ports (located on fractures), and time-drawdown responses were monitored at 25 ports (located on matrix and fractures). Pumping ports were ranked based on weighted signal-to-noise ratio (SNR) computed at each observation port. Noise-free, good quality (SNR > 100) datasets were inverted using Levenberg–Marquardt: LM (gradient) and Nelder–Mead: NM (gradient-free) methods. All simulations were performed using a coupled simulation-optimization model. Performance of the two optimizers is evaluated by comparing model predictions with observations made at two validation ports that were not used in simulation. Both LM and NM algorithms have broadly captured the preferential flow paths (fracture network) via K and S tomograms, however LM has outperformed NM during validation ( $$). Our results conclude that, while method of optimization has a trivial effect on model predictions, exclusion of low quality (SNR ≤ 100) datasets can significantly improve the model performance.     

Shear and tension hydraulic fractures in low permeability rocks

Laboratory hydrofracture experiments were performed on triaxially stressed specimens of oil shale and low-permeability granite. The results show that either shear or tension fractures could develop depending on the level of differentials stress, even in specimens containing preexisting fractures. With 1 kb of confining pressure and differential stress greater than 2kb, hydraulic fluid diffusion into the specimens reduced the effective confining pressure until failure occurred by shear fracture. Below 2kb of differential stress, tension fractures occurred. These results suggest that hydraulic fracturing in regions of significant tectonic stress may produce shear rather than tension fractures. In this casein situ stress determinations based on presumed tension fractures would lead to erroneous results.     

A Type-Curve Method for the Analysis of Pumping Tests with Piecewise-Linear Pumping Rates

Aquifer hydraulic parameters are commonly inferred from constant-rate pumping tests, while variable pumping rates are frequently encountered in actual field conditions. In this study, we propose a generally applicable dimensionless form of the analytical solution for variable-rate pumping tests in confined aquifers. In particular, we adopt a piecewise-linear fitting of variable pumping rates and propose a new type-curve method for estimating the hydraulic conductivity (K ) and specific storage (S_s ) of the investigated confined aquifer. For each test, a series of type curves, which depend on the variable pumping rates, the location of observation wells and the introduced first dimensionless inflection time, need to be provided for matching the observed drawdown data on a log-log graph. We first demonstrate the applicability and robustness of this method through a synthetic pumping test. Subsequently, we apply this method to analyze drawdown data from four pumping tests conducted within a multilayered aquifer/aquitard system in Wuxi city, Jiangsu Province, China. The parameter estimates are then compared with those reported by PEST. The K and S_s values estimated by the new type-curve method are found to be quite close to PEST-based estimates. Parameter estimation results demonstrate the difference in K and S_s values between observation wells. The difference could be attributed to the spatial heterogeneity in K and S_s . A future research topic may focus on the characterization of K and S_s heterogeneity with the currently available drawdown data from variable-rate pumping tests.     

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.     

Factors affecting the measurement of the vertical hydraulic conductivity of a streambed sediment using standpipe tests

The vertical hydraulic conductivity (K_v) of a stream or lake sediment is often determined in the field using standpipe tests. Calculation of K_v is based on the assumption that the hydraulic head in the pipe is equal to that of the stream or lake stage. In this work, a modified equation for K_v is developed for the standpipe test which is applicable when this assumption is not valid. The equation involves not only the hydraulic head at different times but also the difference in the hydraulic head (a) between the groundwater level and river stage. The effects of certain factors on K_v, such as the ratio of the hydraulic head at different times (h₁/h₂), the difference a, and the initial water table height (h₀), are also discussed. The results show that when h₁/h₂ is constant, the relative error (E_r) in K_v increases with the ratio a/h₂. Furthermore, if a/h₂ < 0.05, then for any value of h₁/h₂, E_r is less than 5% using the modified equation. Also, if a/h₂ is large, hydraulic head readings with larger h₁/h₂ ratios must be used to avoid large E_r values. The results of a field test also indicate that the error in K_v decreases as the value of h₀ increases. Copyright © 2013 John Wiley & Sons, Ltd.     

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.