Porosity and Permeability in Ternary Sediment Mixtures

Permeability, k, and porosity, φ, were measured in mixtures of fine, medium, and coarse sand, where the volume fraction of each of the three components was systematically varied. The k was modeled well by the Kozeny‐Carman equation for three‐component mixtures by using a representative grain size parameter, d, computed by averaging the grain diameters of components recursively, with averaging methods based on whether finer components exist in sufficient volume to fill the pores within coarser components. The φ was modeled well by using linear interpolation with piecewise‐planar models. We explored the use of differing numbers of piecewise‐planar elements in the model, and illustrate the trade‐off between the increased accuracy and the increased data requirements that both come from adding more elements. The k model is a function of both d and φ, but more sensitive to d. The k model gave results consistent with measured values when computed using either measured φ values, or values from any of the φ models.     

A bed‐load transport model for rough turbulent open‐channel flows on plane beds

Data from flume studies are used to develop a model for predicting bed‐load transport rates in rough turbulent two‐dimensional open‐channel flows moving well sorted non‐cohesive sediments over plane mobile beds. The object is not to predict transport rates in natural channel flows but rather to provide a standard against which measured bed‐load transport rates influenced by factors such as bed forms, bed armouring, or limited sediment availability may be compared in order to assess the impact of these factors on bed‐load transport rates. The model is based on a revised version of Bagnold's basic energy equation i_bs_b = e_bω, where i_b is the immersed bed‐load transport rate, ω is flow power per unit area, e_b is the efficiency coefficient, and s_b is the stress coefficient defined as the ratio of the tangential bed shear stress caused by grain collisions and fluid drag to the immersed weight of the bed load. Expressions are developed for s_b and e_b in terms of G, a normalized measure of sediment transport stage, and these expressions are substituted into the revised energy equation to obtain the bed‐load transport equation i_b = ω G ^3·4. This equation applies regardless of the mode of bed‐load transport (i.e. saltation or sheet flow) and reduces to i_b = ω where G approaches 1 in the sheet‐flow regime. That i_b = ω does not mean that all the available power is dissipated in transporting the bed load. Rather, it reflects the fact that i_b is a transport rate that must be multiplied by s_b to become a work rate before it can be compared with ω. It follows that the proportion of ω that is dissipated in the transport of bed load is i_bs_b/ω, which is approximately 0·6 when i_b = ω. It is suggested that this remarkably high transport efficiency is achieved in sheet flow (1) because the ratio of grain‐to‐grain to grain‐to‐bed collisions increases with bed shear stress, and (2) because on average much more momentum is lost in a grain‐to‐bed collision than in a grain‐to‐grain one. Copyright © 2006 John Wiley & Sons, Ltd.     

The causes of bedload pulses in a gravel channel: the implications of bedload grain‐size distributions

Unsteady bedload transport was measured in two c. 5 m wide anabranches of a gravel‐bed braided stream draining the Haut Glacier d'Arolla, Switzerland, during the 1998 and 1999 melt seasons. Bedload was directly sampled using 152 mm square Helley–Smith type samplers deployed from a portable measuring bridge, and independent transport rate estimates for the coarser size fractions were obtained from the dispersion of magnetically tagged tracer pebbles. Bedload transport time series show pulsing behaviour under both marginal (1998) and partial (1999) transport regimes. There are generally weak correlations between transport rates and shear stresses determined from velocity data recorded at the measuring bridge. Characteristic parameters of the bedload grain‐size distributions (D₅₀, D₈₄) are weakly correlated with transport rates. Analysis of full bedload grain‐size distributions reveals greater structure, with a tendency for transport to become less size selective at higher transport rates. The bedload time series show autoregressive behaviour but are dif?cult to distinguish by this method. State–space plots, and associated measures of time‐series separation, reveal the structure of the time series more clearly. The measured pulses have distinctly different time‐series characteristics from those modelled using a one‐dimensional sediment routing model in which bed shear stress and grain size are varied randomly. These results suggest a mechanism of pulse generation based on irregular low‐amplitude bedforms, that may be generated in‐channel or may represent the advection of material supplied by bank erosion events. Copyright © 2003 John Wiley & Sons, Ltd.     

NMR Logging to Estimate Hydraulic Conductivity in Unconsolidated Aquifers

Nuclear magnetic resonance (NMR) logging provides a new means of estimating the hydraulic conductivity (K) of unconsolidated aquifers. The estimation of K from the measured NMR parameters can be performed using the Schlumberger‐Doll Research (SDR) equation, which is based on the Kozeny–Carman equation and initially developed for obtaining permeability from NMR logging in petroleum reservoirs. The SDR equation includes empirically determined constants. Decades of research for petroleum applications have resulted in standard values for these constants that can provide accurate estimates of permeability in consolidated formations. The question we asked: Can standard values for the constants be defined for hydrogeologic applications that would yield accurate estimates of K in unconsolidated aquifers? Working at 10 locations at three field sites in Kansas and Washington, USA, we acquired NMR and K data using direct‐push methods over a 10‐ to 20‐m depth interval in the shallow subsurface. Analysis of pairs of NMR and K data revealed that we could dramatically improve K estimates by replacing the standard petroleum constants with new constants, optimal for estimating K in the unconsolidated materials at the field sites. Most significant was the finding that there was little change in the SDR constants between sites. This suggests that we can define a new set of constants that can be used to obtain high resolution, cost‐effective estimates of K from NMR logging in unconsolidated aquifers. This significant result has the potential to change dramatically the approach to determining K for hydrogeologic applications.     

Relationships between physical‐geochemical soil properties and erodibility of streambanks among different physiographic provinces of Tennessee,USA

Erosion of cohesive soils in fluvial environments is dependent on physical, geochemical and biological properties, which govern inter‐particle attraction forces and control detachment rates from stream beds and banks. Most erosion rate models are based on the excess shear stress equation where the soil erodibility coefficient (k_d) is multiplied by the difference between the boundary hydraulic shear stress (τ_b) and the soil critical shear stress (τ_c). Both k_d and τ_c are a function of soil properties and must be obtained through in situ field or laboratory testing. Many studies have generated predictive relationships for k_d and τ_c derived from various soil properties. These studies typically were conducted in watersheds within a single physiographic region with a common surficial geology and/or investigated a limited number of soil properties, particularly geochemical properties. With widely reported differences in relationships between τ_c and soil properties, this study investigated differences in predictive relationships for τ_c among different physiographic provinces in Tennessee, USA. Erodibility parameters were determined in the field using a mini‐jet test device. Among these provinces, statistically four unique clusters were identified from a dataset of 128 observations and these data clusters were used to develop predictive models for τ_c to identify dominant properties governing erosion. In these clusters, 16 significant physical and geochemical soil properties were identified for τ_c prediction. Among these soil properties, water content and passing #200 sieve (percentage soil less than 75 μm) were the dominant controlling parameters to predict τ_c in addition to clay percentage (< 2 μm), bulk density, and soil pore water chemistry. This study suggests that unique relationships exist for physiographic provinces that are likely due to soil physical‐geochemical processes associated with surficial geology that determine minerology of the cohesive soil. Copyright © 2017 John Wiley & Sons, Ltd.     

Salinograph trends as indicators of the recession characteristics of stream components

Compared to hydrograph recession analysis, which is widely applied in engineering hydrology, the quantitative assessment of stream salinity with time (i.e. the salinograph) has received significantly less attention. In particular, while in many previous hydrological studies an inverse relationship between hydrograph and salinograph responses is apparent, the concept of salinity accession (the inversely related salinity counterpart to hydrograph recession) has not been introduced nor quantitatively evaluated in previous literature. In this study, we conduct a mathematical analysis of salinograph accession, and determine new quantitative relationships between salinity accession and hydrograph recession parameters. An equation is formulated that reproduces the general trend in salinity accession. A salinity accession parameter k_c is then introduced and is shown to be the ratio of direct runoff to total stream flow recession parameters: k_r/k. The groundwater recession parameter k_g was estimated using a simple and rapid method that uses both salinograph and hydrograph data. Salinity accession type‐curves illustrate that under certain conditions, the relative steepness of individual salinographs is dependent upon the ratio of groundwater salinity to direct runoff salinity: C_g/C_r. The salinity accession algorithms are applied to two contrasting field settings: Scott Creek, South Australia and Sandy Creek, northern Queensland, Australia. It was found that k_g > k during periods of obvious stream flow recession, for the events analysed. Salinograph accession behaviour was fairly similar for both sites, despite contrasting environments. Using assumed end‐member salinities for groundwater and direct runoff based upon field observations, the behaviour of k_c from the Scott Creek site was approximately reproduced by varying the initial groundwater to runoff flow ratio: Q_g0/Q_r0, within reasonable parameter ranges. The use of salinograph information when used in addition to standard hydrograph analyses provided useful information on recession characteristics of stream components. Copyright © 2008 John Wiley & Sons, Ltd.     

Wave velocities and attenuation of shaley sandstones as a function of pore pressure and partial saturation

We obtain the wave velocities and quality factors of clay‐bearing sandstones as a function of pore pressure, frequency and partial saturation. The model is based on a Biot‐type three‐phase theory that considers the coexistence of two solids (sand grains and clay particles) and a fluid mixture. Additional attenuation is described with the constant‐Q model and viscodynamic functions to model the high‐frequency behaviour. We apply a uniform gas/fluid mixing law that satisfies the Wood and Voigt averages at low and high frequencies, respectively. Pressure effects are accounted for by using an effective stress law. By fitting a permeability model of the Kozeny– Carman type to core data, the model is able to predict wave velocity and attenuation from seismic to ultrasonic frequencies, including the effects of partial saturation. Testing of the model with laboratory data shows good agreement between predictions and measurements.     

Melt segregation inside a partially molten zone: Theory,numerical models and implications

For the problem of matrix compaction and melt segregation a general mush continuity equation is derived, which explicitly expresses the coupling between the melt percolation and the inelastic matrix deformation and closes the governing equation set. Besides, a general equation is obtained, which describes the change in the volume of pore space due to all the possible reasons (inelastic matrix deformation, the phase transitions, and the advection of porosity by the matrix flow). The features of the isothermal melt segregation inside a partially molten zone are demonstrated using one-dimensional (1D) numerical solutions. It follows from the solutions that the pattern and the characteristic time of the melt segregation inside a partially molten zone of thickness L are controlled by the segregation parameter γ _c = (L/δ _c )², where the compaction length δ _c = k(φ₀)η/(φ₀μ) depends on the permeability, k, the value of characteristic porosity, φ₀, and the viscosities of the matrix, η, and melt, μ. The solutions demonstrate that at any value of γ _c , layers that are highly enriched in melt compared to the maximum initial porosity are formed in the upper part of the zone. At the same time, the evolution of the system and the segregation time differ considerably in the limits of γ _c ≪ γ* and γ _c ≫ γ*, where γ* depends on the boundary and initial conditions of the problem, and γ* is about 80 for the problem of melt segregation inside a partially molten zone with the maximum in the initial melt distribution located in the middle of the zone. At γ _c ≪ γ*, which corresponds to the segregation of low-viscosity ultrabasic melts (kimberlites, carbonatites), all the melt accumulates to the roof of the zone, and the segregation time does not depend on the matrix permeability and melt viscosity and decreases with an increase in the thickness of the zone as L ⁻¹. The latter can be the reason for the formation of clusters of the same age and same composition eruptions characteristic of the kimberlite provinces. In the opposite limiting case, γ _c ≫ γ*, the segregation time does not depend on the matrix viscosity and scales as L with a wave sequence forming in the upper part of the zone, which, probably, elucidates the origin of the rhythmical layering of the large tholeiitic basalt plutons.     

Erodibility of cohesive streambeds in the loess area of the midwestern USA

Excess stress parameters, critical shear stress (τ_c) and erodibility coefficient (k_d), for degrading channels in the loess areas of the midwestern USA are presented based on in situ jet‐testing measurements. Critical shear stress and k_d are used to define the erosion resistance of the streambed. The jet‐testing apparatus applies hydraulic stresses to the bed and the resulting scour due to the impinging jet is related to the excess stress parameters. Streams tested were primarily silt‐bedded in texture with low densities, which is typical of loess soils. Results indicate that there is a wide variation in the erosion resistance of streambeds, spanning six orders of magnitude for τ_c and four orders of magnitude for k_d. Erosion resistance was observed to vary within a streambed, from streambed to streambed, and from region to region. An example of the diversity of materials within a river system is the Yalobusha River Basin in Mississippi. The median value of τ_c for the two primary bed materials, Naheola and Porters Creek Clay Formations, was 1·31 and 256 Pa, respectively. Streambeds composed of the Naheola Formation are readily eroded over the entire range of shear stresses, whereas only the deepest flows generate boundary stresses great enough to erode streambeds composed of the Porters Creek Clay Formation. Therefore, assessing material resistance and location is essential in classifying and modelling streambed erosion processes of these streams.     

Determination of critical shear stress of non‐cohesive soils using submerged jet test and turbulent kinetic energy

Laboratory tests using Jet Erosion Testing (JET) apparatus, impinging normally on a horizontal boundary, were conducted to determine the critical shear stress (τ_c) of non‐cohesive soil samples. A three‐dimensional (3D) SonTek/YSI 16 MHz Micro‐Acoustic Doppler Velocimeter (MicroADV) was used to measure turbulent kinetic energy (TKE) at a radial limit of entrainment in the wall jet zone and the measurements were used to calculate τ_c of the samples. The results showed that TKE increases exponentially with increasing particle size. The τ_c from this study were comparable (R² = 0.8) to the theoretical τ_c from Shields diagram after bed roughness scale ratio (D/k_s), due to the non‐uniform bed conditions, was accounted for. This study demonstrated that JET and TKE can be used to determine τ_c of non‐cohesive soils. The use of JET and TKE was found to be faster and easier when compared to the conventional approach of using flumes. A relationship of TKE at the onset of incipient motion (TKE_c) and samples’ D₅₀ developed in this study can be used to predict τ_c of non‐cohesive soils under similar non‐uniform conditions. Copyright © 2015 John Wiley & Sons, Ltd.     

Sediment transferring function of the lower reaches of the Yellow River influenced by drainage basin factors and human activities

Since 1986, with a sharp decrease in water dis-charges, the Yellow River has entered a period charac-terized by low discharges and seasonally occurring dry-ups[1,2]. Since 1999, more strict management of water diversion has been imposed, and therefore the dry-ups have been well under control. However, the lower reaches of the Yellow River is still predominated by low-discharges, and has become a man-induced shrinking river. In the past 40 years, significant effect of soil and water conservat…     

The Frequency Dependence of Harmonic Fluid Flow Through Networks of Cracks and Pores

—The "dynamic" permeability k(ω) of heterogeneous networks of cracks, tubes and spheres, was determined by numerically simulating the harmonic flow of an interstitial fluid for a wide range of frequencies. For comparison with previous works, this procedure was applied to the 100 network realizations used in Bernabé (1995). In most cases, the calculated frequency dependence of the real and imaginary parts of k(ω) was consistent with the JKD model (Johnson et al., 1987), showing a transition from "viscous", macroscopic flow at low frequencies to "inertial" flow at high frequencies. The viscous skin depth δ _c at the transition was found to be proportional to the critical capillary radius r _c from a capillary invasion (Katz and Thompson, 1986). A simple explanation is that these two length scales arise from the same percolation problem. On the other hand, δ _c was not well correlated with the JKD parameter Λ. The conclusion is that Λ and δ _c (or r _c ?) are two independent parameters, derived from two unrelated approaches (i.e., weighted averaging and percolation theory). Finally, an attempt was made to relax the initial assumptions of a rigid solid matrix and an incompressible fluid. It was observed that the effect of the fluid compressibility could occasionally be very large, especially when networks with large amounts of storage pore space were considered.     

Effect of consolidation ratios on maximum dynamic shear modulus of sands

The dynamic shear modulus (DSM) is the most basic soil parameter in earthquake or other dynamic loading conditions and can be obtained through testing in the field or in the laboratory. The effect of consolidation ratios on the maximum DSM for two types of sand is investigated by using resonant column tests. And, an increment formula to obtain the maximum DSM for cases of consolidation ratio κc>1 is presented. The results indicate that the maximum DSM rises rapidly when κc is near 1 and then slows down, which means that the power function of the consolidation ratio increment κc-1 can be used to describe the variation of the maximum DSM due to κc>1. The results also indicate that the increase in the maximum DSM due to κc>1 is significantly larger than that predicted by Hardin and Black's formula.     

Flood routing based on diffusion wave equation using mixing cell method

A one-dimensional non-linear diffusion wave equation is derived from the Saint Venant equations with neglect of the inertia terms. This non-linear equation has no general analytical solution. Numerical schemes are therefore employed to discretize the space and time axes and convert the differential equation to difference form. In this study, the mixing cell method is used to convert the diffusion wave equation to difference form, in which the difference term can be eliminated by selecting an optimal space step size Δx when time step size Δt is given. When the time step size Δt→0, the space step size Δx=Q/(2S₀BC]_k) where Q is discharge, S₀ is bed slope, B is channel width and C_k is kinematic wave celerity, which is the same as the characteristic length proposed by Kalinin and Milyukov. The results of application to two cases show that the mixing cell and linear channel flow routing methods produce hydrographs that are in agreement with the observed flood hydrographs. © 1997 John Wiley & Sons, Ltd.     

Control strategy for variable damping element considering near‐future excitation influence

A control strategy is proposed for variable damping elements (VDEs) used together with auxiliary stiffness elements (ASEs) that compose a time‐varying non‐linear Maxwell (NMW) element, considering near‐future excitation influence. The strategy first composes a state equation for the structural dynamics and the mechanical balance in the NMW elements. Next, it establishes a cost function for estimating future responses by the weighted quadratic norms of the state vector, the controlled force and the VDEs' damping coefficients. Then, the Euler equations for the optimum values are introduced, and also approximated by the first‐order terms under the autoregressive (AR) model of excitation information. Thus, at each moment t_k, the strategy conducts the following steps: (1) identify the obtained seismic excitation information to an AR model, and convert it to a state equation; and (2) determine VDEs' damping coefficients under the initial conditions at t_k and the final state at t_k+L, using the first‐order approximation of the Euler equations. The control effects are examined by numerical experiments. Copyright © 2000 John Wiley & Sons, Ltd.     

Using Grain‐Size Distribution Methods for Estimation of Air Permeability

Knowledge of air permeability (k_a) at dry conditions is critical for the use of air flow models in porous media; however, it is usually difficult and time consuming to measure k_a at dry conditions. It is thus desirable to estimate k_a at dry conditions from other readily obtainable properties. In this study, the feasibility of using information derived from grain‐size distributions (GSDs) for estimating k_a at dry conditions was examined. Fourteen GSD‐based equations originally developed for estimating saturated hydraulic conductivity were tested using k_a measured at dry conditions in both undisturbed and disturbed river sediment samples. On average, the estimated k_a from all the equations, except for the method of Slichter, differed by less than ± 4 times from the measured k_a for both undisturbed and disturbed groups. In particular, for the two sediment groups, the results given by the methods of Terzaghi and Hazen‐modified were comparable to the measured k_a. In addition, two methods (e.g., Barr and Beyer) for the undisturbed samples and one method (e.g., Hazen‐original) for the undisturbed samples were also able to produce comparable k_a estimates. Moreover, after adjusting the values of the coefficient C in the GSD‐based equations, the estimation of k_a was significantly improved with the differences between the measured and estimated k_a less than ±4% on average (except for the method of Barr). As demonstrated by this study, GSD‐based equations may provide a promising and efficient way to estimate k_a at dry conditions.     

Field observations of the vertical distribution of sand transport characteristics over fine,medium and coarse sand surfaces

The vertical distribution of sand transport characteristics is an important issue in aeolian research. Surface characteristics affect sand transport processes, but their effects are not yet fully understood. To provide more data on this subject, we observed sand transport in 16 field experiments above surfaces covered by fine, medium and coarse sand. The sand transport rate over relatively coarser‐grained medium and coarse surfaces could be expressed as a Gaussian peak function: q _z = a + b exp (?0.5[(|z – C _h|)/d ]^e), where q _z is the measured sediment transport at height z above the bed and a , b , C _h, d , and e are regression coefficients. The measured sand transport flux peak values (H _h) were linearly related to C _h, and both values were significantly related to the mean surface grain size. However, for the relatively finer‐grained medium and fine sand surfaces, the sediment transport could be expressed as an exponential function. The cumulative sand transport below 0.1 m was directly related to the mean surface grain size, and the relationship could be expressed as the following exponential function: C _z = f + g exp –M _z/i , where C _z is the cumulative sand transport at height z above the bed, M _z is the mean grain size and f , g , and i are regression coefficients. Above 0.1 m, there were no significant relationships between the cumulative sand transport and the mean surface grain size. The mean grain size decreased with increasing height below the peak height and then increased with increasing height. The surface grain size distribution and proportions of the particles in different grain size categories controlled the mean grain size as a function of height. The observed changes in the sand transport rate and grain size with height will provide support for sand disaster mitigation, numerical modelling and studies of dune formation. Copyright © 2016 John Wiley & Sons, Ltd.     

Hydrodynamic behaviour of coarse bioclastic sand from shelly cheniers

Cheniers from Mont‐Saint‐Michel bay (France) are coarse shelly sand ridges migrating on the mudflat up to the salt marshes where they accumulate and merge in a littoral barrier. In this macrotidal setting and low wave forcing, the cheniers are rarely submerged. However, they are found to move up to several metres during coincidence of spring tide and wave activity. Their processes of migration, morphology and internal structure (composition of the beddings, grain size, sorting and grain arrangement) are thought to be closely related to the hydrodynamic behaviour of the coarse and shelly sediment. This paper focuses on the hydrodynamic behaviour of bioclastic sand sampled from the cheniers: settling velocities of the shell fragments were measured using a 2 m long sedimentation tube. Thresholds of motion under unidirectional current, velocity and turbulence vertical profiles were characterized in a small recirculating flume using Laser Doppler Anemometry (LDA). The flat‐shaped bioclastic particles feature low settling velocities and reveal a good resistance to the re‐suspension effect of the flow when imbricated in a sediment bed. The shear stress in the bottom boundary layer has been measured in the viscous and log sub‐layers. Nikuradse roughness heights (k_s) for shell debris beds of different sizes have been quantified. It is found that k_s ≈ 2·56d₅₀. This value is close to the ones used for classic rounded sand grains despite their major differences of shape. The dual behaviour of the shell fragments (low settling velocity, good resistance to unidirectional flow) should be considered as a key to understanding how this coarse material is transported across the tidal flat, and finally accumulated as cheniers. Further flume experiments including wave activity and tidal fluctuations are necessary to better quantify these complex processes. Copyright © 2010 John Wiley & Sons, Ltd.     

Experimental investigation of the elastic modulus of a fractal system—A model of fractured rocks

The elastic properties of a physical model representing a damaged rock matrix were studied using a square lattice deformed under tensile stress. The elastic modulusM of such a system varies in agreement with percolation theory as|x–x _c | ^f , wherex is the damage parameter andx _c the threshold value of the damage parameter,f3.6. Atxx _c the scale dependence ofM can be expressed asML ^–f/v , whereL is the size of the sample andv the correlation exponent in percolation theory.The experimental results are of interest in assessing elastic properties in earthquake focal zones and fault zones in general.     

A simple method using climatic variables to estimate canopy temperature,sensible and latent heat fluxes in a winter wheat field on the North China Plain

Estimation of evapotranspiration from a crop field is of great importance for detecting crop water status and proper irrigation scheduling. The Penman–Monteith equation is widely viewed as the best method to estimate evapotranspiration but it requires canopy resistance, which is very difficult to determine in practice. This paper presents a simple method simplified from the Penman–Monteith equation for estimating canopy temperature (T_c). The proposed method is a biophysically‐sound extended version of that proposed by Todorovic. The estimated canopy temperature is used to calculate sensible heat flux, and then latent heat flux is calculated as the residual of the surface energy balance. An eddy covariance (EC) system and an infrared thermometer (IRT) were installed in an irrigated winter wheat field on the North China Plain in 2004 and 2005, to measure T_c, and sensible and latent heat fluxes were used to test the modified Todorovic model (MTD). The results indicate that the original Todorovic model (TD) severely underestimates T_c and sensible heat flux, and hence severely overestimates the latent heat flux. However, the MTD model has good capability for estimating T_c, and gives acceptable results for latent heat flux at both half‐hourly and daily scales. The MTD model results also agreed well with the evapotranspiration calculated from the measured T_c. Copyright © 2008 John Wiley & Sons, Ltd.