Accuracy of kinematic wave and diffusion wave for spatial‐varying rainfall excess over a plane

The kinematic‐wave and diffusive‐wave approximations were investigated for unsteady overland flow resulting from spatially varying rainfall excess. Three types of boundary conditions were adopted: zero flow at the upstream end, and critical flow and zero depth‐gradient at the downstream end. Errors were derived by comparing the dimensionless profiles of the flow depth over the plane with those computed from the dynamic‐wave solution. It was found that the mean errors for both the approximations were independent of the type of rainfall excess distribution for KF₀² > 5, where K is the kinematic‐wave number and F₀ is the Froude number. Therefore, the regions (KF₀², F₀) where the kinematic‐wave and diffusive‐wave solutions would be fairly accurate and for any distribution of spatially varying rainfall, were characterized. The kinematic‐wave approximation was reasonably accurate, with a mean error of less than 5% and for the critical depth at the downstream end, for KF₀² ≥ 20 with F₀ ≤ 1; if the rainfall excess was concentrated in a portion of the plane, the field where the kinematic‐wave solution was found accurate, it was more limited and characterized for KF₀² > 35 with F₀ ≤ 1. The diffusive‐wave solution was in good agreement with the dynamic‐wave solution with a mean error of less than 5%, in the flow depth, for KF₀² ≥ 15 with F₀ ≤ 1; for rainfall excess concentrated in a portion of the plane, the accuracy of the diffusion wave solution was in a region more restricted and defined for KF₀² ≥ 30 with F₀ ≤ 1. For zero‐depth gradient at the downstream end, the accuracy field of the kinematic‐wave was found to be greater and characterized for KF₀² > 10 with F₀ ≤ 1; for rainfall excess concentrated in a portion of the plane, the region was smaller and defined for KF₀² > 15 with F₀ ≤ 1. The diffusive‐wave solution was found accurate in the region defined for KF₀² > 7·5, whereas for rainfall excess concentrated in a portion of the plane, the field of accuracy was for KF₀² > 12·5 with F₀ ≤ 1. The lower limits of the regions, defined on KF₀², can be considered generally valid for both approximations, but for F₀ < 1 smaller lower limits were also characterized. Finally, the accuracy of these approximations was influenced significantly by the downstream boundary condition. Copyright © 2002 John Wiley & Sons, Ltd.     

Determination of the Geopotential Scale Factor from TOPEX/POSEIDON Satellite Altimetry

The geopotential scale factor R _o = GM/W _o (the GM geocentric gravitational constant adopted) and/or geoidal potential Wo have been determined on the basis of the first year's (Oct 92 – Dec 93) ERS-1/TOPEX/POSEIDON altimeter data and of the POCM 4B sea surface topography model: R _o °=(6 363 672.58°±0.05) m, W _o °=(62 636 855.8°±0.05)m ² s ^–2 . The 2°–°3 cm uncertainty in the altimeter calibration limits the actual accuracy of the solution. Monitoring dW _o /dt has been projected.     

Introductory notes on shock remanent magnetization and shock demagnetization of igneous rocks

Summary Effects of mechanical shocks of about 0.5 msec in duration on the remanent magnetization of igneous rocks are experimentally studied. The remanent magnetization acquired by applying a shock (S) in the presence of a magnetic field (H), which is symbolically expressed asJ _R (H₊S H_o), is very large compared with the ordinary isothermal remanent magnetization (IRM) acquired in the same magnetic field.J _R (H₊S H_o) is proportional to the piezo-remanent magnetization,J _R (H₊P₊P_o H_o).The effect of applyingS in advance of an acquisition of IRM is represented symbolically byJ _R (S H₊ H_o).J _R (S H₊ H_o) can become much larger than the ordinary IRM, and is proportional to the advance effect of pressure on IRM,J _R(P₊ P₀ H₊ H₀).The effect of shockS applied on IRM in non-magnetic space is represented by the shock-demagnetization effect,J _R(H₊ H₀ S), which also is proportional toJ _R(H₊ H₀ P₊ P₀).Because, the duration of a shock is very short, a single shock effect cannot achieve the final steady state. The effect ofn-time repeated shocks, is represented byJ ₀+J ^*(n), whereJ ₀ means the immediate effect and J ^*(n) represent the resultant effect of repeating, which is of mathematical expression proportional to [1–exp {–(n–1)}].

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Zusammenfassung Die Effekte des mechanischen Stosses mit der Dauer von etwa 0.5 ms auf der remanenten Magnetisierung wurden experimentell nachgesucht. Das erworbene Remanenz der Magnetisierung nach dem Stoss (S) unter dem magnetischen Feld (H), das hier symbolisch alsJ _R(H₊ SH₀) bezechnet wird, ist sehr stark im Vergleich mit der normalen isothermischen remanenten Magnetisierung (IRM) unter demselben magnetischen Feld.J _R(H₊ S H₀) ist im Verhältnis zur piezoremanenten Magnetisierung,J _R(H₊ P₊ P₀ H₀).Der Effekt vom Stoss vor der Erwerbung von IRM wird symbolisch alsJ _R(S H₊ H₀) bezeichnet.J _R(S H₊ H₀) kann viel stärker als die normale IRM werden, im verhältnis zum Effekt des vorausgegebenen Drucks auf IRMJ _R(P₊ P₀ H₊ H₀).Der Effekt des Stosses auf IRM im Raum ohne magnetisches Feld wird mit dem Stossentmagnetisierungseffekt dargestellt,J _R(H₊ H₀ S), der auch proportional zuJ _R(H₊ H₀ P₊ P₀) ist.Da die Dauer einzelnen Stosses sehr kurz ist, kann der Effekt des einmaligen Stosses den endgültigen stabilen Zustand nicht erreichen. Der Effekt nachn-maligen wiederholten Stossen wird alsJ ₀+J ^*(n) bezeichnet, wobeiJ ₀ den unverzüglichen Effekt bedeutet, und J ^*(n) beschreibt den resultanten Effekt der Stosswiederholung, dessen mathematische Darstellung proporational zu [1–exp {–(n–1)}] ist.

     

The effects of alongshore variation in bottom topography on a boundary current—(topographically induced upwelling)

A theory which describes the constant f-plane flow of a steady inviscid baroclinic boundary current over a continental margin with a bathymetry that varies slowly in the alongshore but rapidly in the offshore directions is developed in the parameter regime (L_D/L)² ≤ Ro 1, where L_D is the internal deformation radius, L the horizontal length scale, and Ro the Rossby number. To lowest order in the Rossby number the flow is along isobaths with speed q_o = V_u(h,z)|Vh|/α, where V_u(h,z) is the upstream speed, α the upstream bottom slope at depth h, and Vh the bottom slope downstream at depth h. The lowest order flow produces a variation in the vertical component of relative vorticity along the isobath as the magnitude and direction of Vh vary in the downstream direction. The variation of vorticity requires a vertical as well as a cross-isobath flow at first order in the Rossby number. The first order vertical velocity is computed from the vorticity equation in terms of upstream conditions and downstream variations of the bathymetry. The density, pressure, and cross-isobath flow at first order in the Rossby number are then calculated. It is shown that in the cyclonic region of current (d/dh(V_u/α) > 0), if the isobaths diverge in the downstream direction ((∂/∂s)|Vh| < 0), then upwelling and onshore flow occur. The theory is applied to the northeastern Florida shelf to explain bottom temperature observations.     

Integrated assessment of lateral flow, density effects and dispersion in aquifer storage and recovery

Aquifer storage and recovery (ASR) involves the injection of freshwater into an aquifer for later recovery and use. This paper investigates three major factors leading to reduction in performance of ASR systems in brackish or saline aquifers: lateral flow, density-driven flow and dispersive mixing. Previous analyses of aquifer storage and recovery (ASR) have considered at most two of the above processes, but never all three together, and none have considered lateral flow and density effects together. In this analysis, four dimensionless parameters are defined to give an approximate characterisation of lateral flow, dispersive mixing, mixed convection (density effects during pumping) and free convection (density effects during storage). An extensive set of numerical models spanning a wide parameter range is then used to develop a predictive framework using the dimensionless numbers. If the sum of the four dimensionless numbers (denoted R_ASR) exceeds 10, the ASR operation is likely to fail with no recoverable freshwater, while if R_ASR < 0.1, the ASR operation is likely to provide at least some recovery of freshwater. The predictive framework is tested using limited data available from ASR field sites, broadly lending support to the framework. This study has several important implications. Firstly, the lack of completeness of field data sets in the literature must be rectified if we are to properly characterise mixed-convective flow processes in ASR operations. Once data are available, the dimensionless numbers can be used to identify suitable ASR sites and the desirable operational conditions that maximise recovery efficiencies.     

Restoring forces on vertical circular cylinders forced by earthquakes

An eigenfunction solution is presented for the dynamic response of vertical circular cylinders to earthquake excitation in a compressible fluid of finite depth. This single eigenseries expansion eliminates the need for a double summation over both the eigenfunctions and the trial functions as required by Rayleigh-Ritz methods. Revised definitions for the added mass and hydrodynamic radiation damping coefficients per unit length are derived from the hydrodynamic fluid pressures. Based on comparisons between these newly defined coefficients, the compressibility of the fluid is found to be relatively more important at dimensionless frequencies greater than unity (ω > 1.0) when analysing both rigid and flexible cylinders having relatively large diameter to water depth ratios,r₀/h > 0.25 (squatty type). This conclusion regarding the relative importance of the fluid compressibility is derived from a comparison between the relative magnitudes and the vertical distributions over depth of both the added mass and radiation damping coefficients per unit length for both rigid and flexible squatty cylinders. From additional comparisons with Rayleigh-Ritz solutions that require trial functions, the results for totally immersed flexible slender cylinders (r₀/h< 0.10) are shown to be equivalent; but the results for totally immersed flexible squatty cylinders (r₀/h > 0.25) are not. The reason for this difference appears to be in the truncation of the trial function series in the Rayleigh-Ritz methods, which excludes the higher mode shapes, and in the definitions of the added mass coefficients. Comparisons with laboratory data for both rigid and flexible cylinders confirm the accuracy of the solutions obtained by the eigenseries in the limited frequency interval above the highest frequency for surface gravity waves (f > 1.0 Hz) and below the first dimensionless cut-off frequency for acoustic waves (ω< 1.0).     

Internal waves in a randomly stratified fluid

Abstract

We discuss the propagation of internal waves in a rotating stratified unbounded fluid with randomly varying stability frequency, N. The first order smoothing approximation is used to derive the dispersion relation for the mean wave field when N is of the form N ² = N _o ²(1 + ?μ), where μ is a centered stationary random function of either depth (z) or time (t), N _o = constant and O < ?² ≦ 1. Expressions are then derived for the change in phase speed and growth rate due to the random fluctuations μ; in particular, attention is focused on the behaviour of these expressions for short and long correlation lengths (case μ = μ(z)) and times (case μ = μ(t)). For the case μ = μ(z), which represents a model for the temperature and salinity fine-structure in the ocean, the appropriate statistics of the fluctuations observed at station P (50°N, 145°W) have been incorporated into the theory to estimate the actual importance of the effects due to these random fluctuations. It is found that the phase speed of the mean wave decreases significantly if (i) the wavelength is short compared to g/N_o ² or (ii) the wave number vector is essentially horizontal and the wave frequency is very close to N _o. Also, the random fluctuations cause a significant growth (decay) in the amplitude of a wave propagating upwards (downwards) through a depth of a few kilometers. However, in the direction of energy propagation, the kinetic energy is conserved. Finally, it is shown that the average effect of the depth dependent fluctuations at station P is to slightly decrease the stability frequency and the magnitude of the group velocity.     

Numerical simulations of transport of non-ergodic solute plumes in heterogeneous aquifers

Transport of non-ergodic solute plumes by steady-state groundwater flow with a uniform mean velocity, μ, were simulated with Monte Carlo approach in a two-dimensional heterogeneous and statistically isotropic aquifer whose transmissivity, T, is log-normally distributed with an exponential covariance. The ensemble averages of the second spatial moments of the plume about its center of mass, <S _{i i} (t)>, and the plume centroid covariance, R _{i i} (t) (i=1,2), were simulated for the variance of Y=log T, σ _Y ²=0.1, 0.5 and 1.0 and line sources normal or parallel to μ of three dimensionless lengths, 1, 5, and 10. For σ _Y ²=0.1, all simulated <S _{i i} (t)>−S _{i i} (0) and R _{i i} (t) agree well with the first-order theoretical values, where S _{i i} (0) are the initial values of S _{i i} (t). For σ _Y ²=0.5 and 1.0 and the line sources normal to μ, the simulated longitudinal moments, <S ₁₁(t)>−S ₁₁(0) and R ₁₁(t), agree well with the first-order theoretical results but the simulated transverse moments <S ₂₂(t)>−S ₂₂(0) and R ₂₂(t) are significantly larger than the first-order values. For the same two larger values of σ _Y ² but the line sources parallel to μ, the simulated <S ₁₁(t)>−S ₁₁(0) are larger than but the simulated R ₁₁ are smaller than the first-order values, and both simulated <S ₂₂(t)>−S ₂₂(0) and R ₂₂(t) stay larger than the first-order values. For a fixed value of σ _Y ², the summations of <S _{i i} (t)>−S _{i i} (0) and R _{i i} , i.e., X _{i i} (i=1,2), remain almost the same no matter what kind of source simulated. The simulated X ₁₁ are in good agreement with the first-order theory but the simulated X ₂₂ are significantly larger than the first-order values. The simulated X ₂₂, however, are in excellent agreement with a previous modeling result and both of them are very close to the values derived using Corrsin's conjecture. It is found that the transverse moments may be significantly underestimated if less accurate hydraulic head solutions are used and that the decreasing of <S ₂₂(t)>−S ₂₂(0) with time or a negative effective dispersivity, defined as , may happen in the case of a line source parallel to μ where σ _Y ² is small.     

Numerical simulations of transport of non-ergodic solute plumes in heterogeneous aquifers

Transport of non-ergodic solute plumes by steady-state groundwater flow with a uniform mean velocity, μ, were simulated with Monte Carlo approach in a two-dimensional heterogeneous and statistically isotropic aquifer whose transmissivity, T, is log-normally distributed with an exponential covariance. The ensemble averages of the second spatial moments of the plume about its center of mass, <S _{i i} (t)>, and the plume centroid covariance, R _{i i} (t) (i=1,2), were simulated for the variance of Y=log T, σ _Y ²=0.1, 0.5 and 1.0 and line sources normal or parallel to μ of three dimensionless lengths, 1, 5, and 10. For σ _Y ²=0.1, all simulated <S _{i i} (t)>−S _{i i} (0) and R _{i i} (t) agree well with the first-order theoretical values, where S _{i i} (0) are the initial values of S _{i i} (t). For σ _Y ²=0.5 and 1.0 and the line sources normal to μ, the simulated longitudinal moments, <S ₁₁(t)>−S ₁₁(0) and R ₁₁(t), agree well with the first-order theoretical results but the simulated transverse moments <S ₂₂(t)>−S ₂₂(0) and R ₂₂(t) are significantly larger than the first-order values. For the same two larger values of σ _Y ² but the line sources parallel to μ, the simulated <S ₁₁(t)>−S ₁₁(0) are larger than but the simulated R ₁₁ are smaller than the first-order values, and both simulated <S ₂₂(t)>−S ₂₂(0) and R ₂₂(t) stay larger than the first-order values. For a fixed value of σ _Y ², the summations of <S _{i i} (t)>−S _{i i} (0) and R _{i i} , i.e., X _{i i} (i=1,2), remain almost the same no matter what kind of source simulated. The simulated X ₁₁ are in good agreement with the first-order theory but the simulated X ₂₂ are significantly larger than the first-order values. The simulated X ₂₂, however, are in excellent agreement with a previous modeling result and both of them are very close to the values derived using Corrsin's conjecture. It is found that the transverse moments may be significantly underestimated if less accurate hydraulic head solutions are used and that the decreasing of <S ₂₂(t)>−S ₂₂(0) with time or a negative effective dispersivity, defined as , may happen in the case of a line source parallel to μ where σ _Y ² is small.     

A new drain spacing formula

Abstract

A drain spacing formula is derived considering the variation in radial flux and the area above the drain level in the radial flow zone. The extent of the radial flow zone is ascertained by applying a mass balance and differentiability criterion of the water surface profile at the interface of radial and Dupuit-Forchheimer flow zones. The radial flow zone extends from the centre of the tile drain a distance of 2/π times the depth to impervious layer below the drain. For a normal ratio of recharge rate to hydraulic conductivity (R/K ≤ 0.0025), the water surface profile in the radial flow zone computed using Hooghoudt's formula is very different from the profile obtained by the new drain spacing formula; however, Hooghoudt's formula computes the maximum water table height which marginally differs from that found by the present method. For a ratio of high recharge rate to hydraulic conductivity (R/K = 0.1) and close drain spacing (L/D = 2), the difference in the maximum heights is 21%. Hooghoudt's formula overestimates the maximum water table position for L/D < 40. Unlike Hooghoudt's equivalent depth, the equivalent depth obtained using the present method is a function of the ratio of recharge rate to hydraulic conductivity.     

The significance of channel recharge rates for estimating debris‐flow magnitude and frequency

The quantification of debris‐flow hazard requires estimates of debris‐flow frequency and magnitude. Several methods have been proposed to determine the probable volume of future debris flows from a given basin, but most have neglected to account for debris recharge rates over time, which may lead to underestimation of debris‐flow volumes in basins with rare debris flows. This paper deals with the determination of debris recharge rates in debris‐flow channels based on knowledge of debris storage and the elapsed time since the last debris flow. Data are obtained from coastal British Columbia and a relation is obtained across a sample of basins with similar terrain and climatic conditions. For Rennell Sound on the west coast of the Queen Charlotte Islands, the power‐law relation for area‐normalized recharge rate, R_t, versus elapsed time, t_e was R_t = 0·23t_e^?0·58 with an explained variance of 75 per cent. A difference in recharge rates may exist between creeks in logged and unlogged forested terrain. The power function for undisturbed terrain was R_t = 0·20t_e^?0·49, while the function for logged areas was R_t = 0·30t_e^?0·77. This result suggests that for the same elapsed time since the last debris flow, clearcut gullies tend to recharge at a slower rate than creeks in old growth forest. This finding requires verification, particularly for longer elapsed times since debris flow, but would have important implications for forest resource management in steep coastal terrain. This study demonstrates that commonly used encounter probability equations are inappropriate for recharge‐limited debris flow channels. Copyright © 2005 John Wiley & Sons, Ltd.     

Errors of kinematic wave and diffusion wave approximations for time‐independent flows with infiltration and momentum exchange included

Error equations for kinematic wave and diffusion wave approximations were derived for time‐independent flows on infiltrating planes and channels under one upstream boundary and two downstream boundary conditions: zero flow at the upstream boundary, and critical flow depth and zero depth gradient at the downstream boundary. These equations specify error in the flow hydrograph as a function of space. The diffusion wave approximation was found to be in excellent agreement with the dynamic wave approximation, with errors below 2% for values of KF (e.g. KF ≥ 7·5), where K is the kinematic wave number and F is the Froude number. Even for small values of KF (e.g. KF = 2·5), the errors were typically less than 3%. The accuracy of the diffusive approximation was greatly influenced by the downstream boundary condition. For critical flow depth downstream boundary condition, the error of the kinematic wave approximation was found to be less than 10% for KF ≥ 7·5 and greater than 20% for smaller values of KF. This error increased with strong downstream boundary control. The analytical solution of the diffusion wave approximation is adequate only for small values of K. Copyright © 2005 John Wiley & Sons, Ltd.     

Accuracy of the kinematic wave and diffusion wave approximations for time-independent flows with infiltration included

Errors in the kinematic wave and diffusion wave approximation for time-independent (or steady-state) cases of channel flow with infiltration were derived for three types of boundary conditions: zero flow at the upstream end, and critical flow depth and zero depth gradient at the downstream end. The diffusion wave approximation was found to be in excellent agreement with the dynamic wave approximation, with errors of less than 1·4% for KF²₀≥7·5, and up to 14% for KF²₀≤0·75 for the upstream boundary condition of zero discharge and finite depth, where K is the kinematic wave number and F₀ is the Froude number. The kinematic wave approximation was reasonably accurate except at the channel boundaries and for small values of KF²₀ (≤1). The accuracy of these approximations was significantly influenced by the downstream boundary, both in terms of the magnitude of the error and the segment of the channel reach for which these approximations would be applicable. © 1998 John Wiley & Sons, Ltd.     

Dynamics of seasonal recharge beneath a semiarid vegetation on the gnangara mound,Western Australia

To estimate seasonal changes in recharge to the underlying sandy aquifer, the soil water dynamics of the unsaturated zone was monitored down to a depth of 20 m over a period of three years (1985 to 1987). The measurements were made by a neutron probe at eight locations beneath a native vegetation in a semiarid region, Western Australia, receiving precipitation of 775 mm yr^?1. A relatively simple method, based on the analyses of sequentially measured soil water profiles involving utilization of zero flux plane in the unsaturated zone, is presented and used to compute seasonal recharge rates. Drainage fluxes (recharge rates) below two specified depths were estimated. These were: R₁ (water flux at a depth of 10 m, just below the maximum rooting depth) and R₂ (water flux at a depth of 18 m, just above the water table). These two estimates were significantly different both on a seasonal and annual basis, but their cumulative values for the three year period were very similar. While the annual precipitation varied from 525 to 850 mm yr^?1, the corresponding spatially averaged R₁ varied from 34 to 149 mm yr^?1, and R₂ varied from 65 to 80 mm yr^?1. A significant difference in recharge between the upslope and downslope positions on a hillslope was ascribed to differences in vegetation density of the understorey and differences in hydraulic properties of subsoils. For the three year period, the average R₁ and R₂ were 13 per cent and 10 per cent of the precipitation respectively. These values compare favourably with a long-term estimate based on an environmental tracer technique.     

Analysis of the nonlinear storage–discharge relation for hillslopes through 2D numerical modelling

Storage–discharge curves are widely used in several hydrological applications concerning flow and solute transport in small catchments. This article analyzes the relation Q(S) (where Q is the discharge and S is the saturated storage in the hillslope), as a function of some simple structural parameters. The relation Q(S) is evaluated through two‐dimensional numerical simulations and makes use of dimensionless quantities. The method lies in between simple analytical approaches, like those based on the Boussinesq formulation, and more complex distributed models. After the numerical solution of the dimensionless Richards equation, simple analytical relations for Q(S) are determined in dimensionless form, as a function of a few relevant physical parameters. It was found that the storage–discharge curve can be well approximated by a power law function Q/(LK_s) = a(S/(L²(? ? θ_r)))^b, where L is the length of the hillslope, K_s the saturated conductivity, ? ? θ_r the effective porosity, and a, b two coefficients which mainly depend on the slope. The results confirm the validity of the widely used power law assumption for Q(S). Similar relations can be obtained by performing a standard recession curve analysis. Although simplified, the results obtained in the present work may serve as a preliminary tool for assessing the storage–discharge relation in hillslopes. Copyright © 2012 John Wiley & Sons, Ltd.     

Estimating agricultural deep drainage lag times to groundwater: application to Antelope Valley,California, USA

Estimates of groundwater volumes available in semiarid regions that rely on water balance calculations require the determination of both surface to groundwater lag times and volumes from irrigation or rainfall initiated recharge. Subsurface geologic material hydraulic properties (e.g. hydraulic conductivities, water retention functions) necessary for unsaturated flow modelling are rarely available as are the instrumented field tests that might determine such lag times. Here we develop a simple two‐parameter (specific yield, S_y, and pore‐size distribution index, λ), one‐dimensional unsaturated flow model from simplifications of the Richards equation (using the Brooks‐Corey relationships) to determine lag times from agricultural deep drainage associated with the irrigation of alfalfa hay and various row crops in the Antelope Valley of California, USA. Model‐predicted lag times to depths of 85 m bgs (below ground surface) were similar to that measured in a 2‐year ponded recharge field trial, slightly overestimating that measured by approximately 15% (0.51 vs 0.44 years). Lag time estimates were most sensitive to estimated deep percolation rates and roughly equally sensitive to the model hydraulic parameters. Generally, as subsurface material textures coarsen towards larger S_y and λ values for all S_y >10%, lag times progressively increase; however, at S_y <10%, lag times decrease substantially suggesting that particular combinations of S_y and λ values that may be associated with similarly textured materials can result in the prediction of different lag times for S_y approximately 10%. Overall, lag times of 1–3 years to a depth of 69 m bgs were estimated from deep drainage of agricultural irrigation across a variety of irrigation schedules and subsurface materials. Copyright © 2012 John Wiley & Sons, Ltd.     

Predicting physical equations of soil detachment by simulated concentrated flow in Ultisols (subtropical China)

Soil detachment in concentrated flow is due to the dislodging of soil particles from the soil matrix by surface runoff. Both aggregate stability and shear strength of the topsoil reflect the erosion resistance of soil to concentrated runoff, and are important input parameters in predicting soil detachment models. This study was conducted to develop a formula to predict soil detachment rate in concentrated flow by using the aggregate stability index (As), root density (R_d) and saturated soil strength (σ_s) in the subtropical Ultisols region of China. The detachment rates of undisturbed topsoil samples collected from eight cultivated soil plots were measured in a 3.8 m long, 0.2 m wide hydraulic flume under five different flow shear stresses (τ = 4.54, 9.38, 15.01, 17.49 and 22.54 Pa). The results indicated that the stability index (As) was well related with soil detachment rate, particularly for results obtained with high flow shear stress (22.54 Pa), and the stability index (As) has a good linear relationship with concentrated flow erodibility factors (K_c). There was a positive linear relationship between saturated soil strength (σ_s) and critical flow shear stress (τ_c) for different soils. A significant negative exponential relationship between erodibility factors (K_c) and root density (R_d) was detected. This study yielded two prediction equations that allowed comparison of their efficiency in assessing soil detachment rate in concentrated flow. The equation including the root density (R_d) may have a better correlation coefficient (R² = 0.95). It was concluded that the formula based on the stability index (As), saturated soil strength (σ_s) and root density (R_d) has the potential to improve methodology for assessing soil detachment rate in concentrated flow for the subtropical Chinese Ultisols. Copyright © 2012 John Wiley & Sons, Ltd.     

Numerical simulation of groundwater flow patterns using flux as upper boundary

Since the 1960s, most of the studies on groundwater flow systems by analytical and numerical modelling have been based on given‐head upper boundaries. The disadvantage of the given‐head approach is that the recharge into and discharge from a basin vary with changes in hydraulic conductivity and/or basin geometry. Consequently, flow patterns simulated with given‐head boundaries but with different hydraulic conductivities and/or basin geometry may not reflect the effects of these variables. We conducted, therefore, numerical simulations of groundwater flow in theoretical drainage basins using flux as the upper boundary and realistically positioned fluid‐potential sinks while changing the infiltration intensity, hydraulic conductivities, and geometric configuration of the basin. The simulated results demonstrate that these variables are dominant factors controlling the flow pattern in a laterally closed drainage basin. The ratio of infiltration intensity to hydraulic conductivity (R_ic) has been shown to be an integrated pattern‐parameter in a basin with a given geometric configuration and possible fluid‐potential‐sink distribution. Successively, the changes in flow patterns induced by stepwise reductions in R_ic are identical, regardless of whether the reductions are due to a decrease in infiltration intensity or an increase in hydraulic conductivity. The calculated examples show five sequential flow patterns containing (i) only local, (ii) local–intermediate, (iii) local–intermediate–regional, (iv) local–regional, and (v) just regional flow systems. The R_ic was found to determine also whether a particular sink is active or not as a site of discharge. Flux upper boundary is preferable for numerical simulation when discussing the flow patterns affected by a change of infiltration, the hydraulic conductivity, or the geometry of a basin. Copyright © 2012 John Wiley & Sons, Ltd.     

A numerical study on response modification,overstrength, and displacement amplification factors for steel plate shear wall systems

Design recommendations for steel plate shear wall (SPSW) systems have recently been introduced into seismic provisions for steel buildings. Response modification (R), overstrength (Ω_o), and displacement amplification (C_d) factors for SPSW systems presented in design codes were based on professional experience and judgment. A numerical study has been undertaken to evaluate these factors for SPSW systems. Forty‐four unstiffened SPSW possessing different geometrical characteristics were designed based on the recommendations given in the AISC Seismic Provisions. Bay width, number of stories, story mass, and steel plate thickness were considered as the prime variables that influence the response. Twenty records were selected to include the variability in ground motion characteristics. In order to provide a detailed analysis of the post‐buckling response, three‐dimensional finite element analyses were conducted for the 44 structures subjected to the selected suite of earthquake records. For each structure and earthquake record, two analyses were conducted in which the first includes geometrical nonlinearities and the other includes both geometrical and material nonlinearities, resulting in a total of 1760 time history analyses. In this paper, the details of the design and analysis methodology are given. Based on the analysis results, response modification (R), overstrength (Ω_o), and displacement amplification (C_d) factors for SPSW systems are evaluated. Copyright © 2008 John Wiley & Sons, Ltd.