Modeling coupled erosion and filtration of fine particles in granular media

One of the major causes of instability in geotechnical structures such as dikes or earth dams is the phenomenon of suffusion including detachment, transport and filtration of fine particles by water flow. Current methods fail to capture all these aspects. This paper suggests a new modeling approach under the framework of the porous continuous medium theory. The detachment and transport of the fine particles are described by a mass exchange model between the solid and the fluid phases. The filtration is incorporated to simulate the filling of the inter-grain voids created by the migration of the fluidized fine particles with the seepage flow, and thus, the self-filtration is coupled with the erosion process. The model is solved numerically using a finite difference method restricted to one-dimensional (1-D) flows normal to the free surface. The applicability of the model to capture the main features of both erosion and filtration during the suffusion process has been validated by simulating 1-D internal erosion tests and by comparing the numerical with the experimental results. Furthermore, the influence of the coupling between erosion and filtration has been highlighted, including the development of material heterogeneity induced by the combination of erosion and filtration.

     

Mathematical and numerical filtration–advection–dispersion model of miscible grout propagation in saturated porous media

The development of a predictive model of behaviour of porous media during injection of miscible grout, taking into account convection, dilution and filtration of grout solution with interstitial water, as well as consolidation aspects, is presented. Model assumptions are reviewed and discussed first. During the establishment of the model, we insist on surface terms and their physical relevance in expressing adsorption effects. Constitutive laws such as Fick's law for diffusive mass transport, hydrodynamic dispersion tensor dealing with miscibility, are modified by taking into account filtration effects. A new surface term appears in mass balance equations as a consequence of filtration. According to the filtration laws used, an initial filtration rate is estimated on the basis of a one‐dimensional experimental campaign. The field equations are discretized by using Galerkin finite element and θ‐scheme standard method. For transport equation, Streamline Upwind Petrov Galerkin method is employed to prevent numerical oscillations. Lastly, confrontation of numerical results with laboratory experiments constitutes a first step to validate the model on a realistic basis. Copyright © 2001 John Wiley & Sons, Ltd.     

Application of the chlorine-36 method for the delineation of groundwater infiltration of large river systems: example of the Danube River in western Hungary (Szigetköz area)

The gravel aquifer within the Szigetköz Plain in northern Hungary is mainly fed by the infiltration of the Danube River. This infiltration process can be identified using the tritium/helium method to a distance of about 30 km away from the infiltration area of the Danube. In this study, chlorine-36 analyses are used as additional method. This natural radioisotope was also produced by nuclear bomb tests in the atmosphere. It is an ideal, stable constituent for this particular study due to its very long half-life (300,000 years), and consequently acts as an independent check of the established model of aquifer recharge. The chlorine-36 data of the analysed selected groundwater samples of this area clearly show the effect of the atmospheric nuclear bomb tests, with enhanced ³⁶Cl/Cl ratios of up to a factor 10 higher than the unaffected groundwater of the pre-bomb period within the study area. Finally, the observed ³⁶Cl values were introduced into a transport model with dispersion/advection-type flow of groundwater to deduce the transport parameters.     

Groutability of cement‐based grout with consideration of viscosity and filtration phenomenon

The groutability depends on the properties of the grout, its injection processes, and on the mechanical properties of the soil formation. During the process of pouring cement‐based grouting into a porous medium, a variation with time occurs in the viscosity of grout suspension. In addition, the particle filtration phenomenon will limit the expansion of the grouted zone because cement particles are progressively stagnant within the soil matrix. In this paper, a closed‐form solution was derived by implementing the mass balance equations and the generalized phenomenological filtration law, which can be used to evaluate the deposition of cement‐based grout in the soil matrix. The closed‐form solution relevant to a particular spherical flow was modified by a step‐wise numerical calculation, considering the variable viscosity caused by a chemical reaction, and the decrease in porosity resulting from grout particle deposition in the soil pores. A series of pilot‐scale chamber injection tests was performed to verify that the developed step‐wise numerical calculation is able to evaluate the injectable volume of grout and the deposition of grout particles. The results of the chamber injection tests concurred well with that of the step‐wise numerical calculation. Based on the filtration phenomenon, a viable approach for estimating the groutability of cement‐based grout in a porous medium was also suggested, which might facilitate a new insight in the design of the grouting process. Copyright © 2009 John Wiley & Sons, Ltd.     

Particle transport within water-saturated porous media: Effect of pore size on retention kinetics and size selection

The transport and filtration behaviour of fine particles (silt) in columns packed with sand was investigated under saturated conditions by using step-input injections. Three samples of different particle size distributions (coarse medium, fine medium and a mixture of both) were used in order to highlight the influence of the pore size distribution on particle retention and size selection of recovered particles. The main parameters of particle transport and deposition were derived from the adjustment of the experimental breakthrough curves by an analytical model. The higher particle retention occurs in the mixture medium, owing to its large pore size distribution, and the filtration coefficient decreases with increasing flow velocity. Particle size distribution of recovered particles shows a thorough size selection: (i) the first recovered particles are the coarser ones; (ii) the size of the recovered particles increases with increasing flow velocity and enlarger pore distribution of the medium.     

The grain–fluid interaction as a self-stabilizing mechanism in fluvial bed load transport

A grain-scale model of fluvial bed load transport is described, with particular emphasis on the equilibrium between the saltating grains and the near bed flow, and its role in determining transport rate. The model calculates, explicitly, the modification of the velocity profile by the moving grains, together with the consequential reduction in surface fluid shear stress. As the surface fluid shear stress is reduced by the moving grains, so the entrainment rate decreases and the model reaches a steady state. The results provide insight into two important questions at a macroscopic level. First, they show that, in the absence of large static roughness, the dynamic roughness caused by the moving grains may be a significant contributor to flow resistance. Secondly, the model indicates the manner in which transport may be limited by a combination of the transport capacity of the flow and the availability of sediment for entrainment. Only in the case of high sediment availability does the fluid shear stress acting at the surface approach the critical entrainment value, reproducing the behaviour suggested by Bagnold (1956 ) and Owen (1964 ). This suggests that prediction formulae based on this assumption only describe the bed load transport system under particular conditions.     

Transport and retention of microparticles in packed sand columns at low and intermediate ionic strengths: experiments and mathematical modeling

Functional relationships correlating particle filtration coefficients and porewater ionic strength are herein proposed and validated, based on deposition experiments of micrometer-sized particles onto siliceous sand. Experiments were conducted using one-dimensional laboratory columns and stable monodisperse aqueous suspensions of negatively charged latex particles with a mean size of 1.90 μm. The role of ionic strength was systematically investigated and six different monovalent salt concentrations (1, 3, 10, 30, 100, 300 mM) were employed by addition of sodium chloride to the aqueous solution. A mathematical advection–dispersion-deposition transport model was adopted assuming that attachment and detachment of particles in the porous medium are concurrent mechanisms of particle filtration, and including a Langmuir-type blocking function to account for availability in deposition sites. The system of equations modeling colloid transport was solved numerically. Attachment rate and detachment rate coefficients were thereby determined for each employed ionic strength, as well as a blocking coefficient in the form of a maximum particle concentration in the solid phase. Therefore, functional relationships expressing the dependence of these coefficients on ionic strength were proposed, based on literature findings and present experimental observations. The existence of a critical salt deposition concentration (and release concentration) separating a favorable attachment (and detachment) regime from an unfavorable condition is assumed. In respect to the blocking coefficient, a power–law dependence on ionic strength is hypothesized. The proposed functional relationships proved adequate to reproduce the coefficient trends extrapolated from data fitting by the transport model. They may represent a powerful tool to describe and predict microparticle mobility in saturated porous media if embedded a priori in the related mathematical transport models.     

An empirical probabilistic approach for constraining the uncertainty of long-term solute transport predictions in fractured rock using in situ tracer experiments

Although radionuclide tracer tests have been carried out for over 30  years, the role of tracer tests in radioactive waste repository performance assessment (PA) has been questioned due to the differences between the time scales for tracer tests and PA. The possibility of using in situ tracer tests to constrain PA time scale (over 10,000  years) solute transport has been demonstrated using a systematic “microstructural model” approach to define advective and retentive materials. A series of simulations were conducted of the “TRUE-1” sorbing solute transport experiments in a well-characterized block of fractured granite. These experiments were then used to constrain the uncertainty of long-term transport on the same pathways, using a gradient several orders of magnitude smaller. The comparison of uncertainty of this long-term transport, with and without this conditioning step, provided a measure of the ability of tracer tests to reduce PA time-scale uncertainty. Although this approach for quantifying uncertainty reduction is somewhat empirical, it does indicate the potential usefulness of tracer experiments in reducing the uncertainty of the key PA time-scale transport parameters such as the flow wetted surface, provided that immobile zone properties such as sorption (Kd), porosity and diffusivity are available.     

Modelling the performance of industrial ball mills using single particle breakage data

Ball milling is an energy-intensive unit operation and usually consumes a major proportion of the power drawn by a typical mineral processing plant. Hence, substantial economic benefits can be achieved by optimal design and by operating ball milling circuits under optimum process conditions. This requires an accurate ball mill modelling technique.In the multi-segment ball mill model, the size-dependent material transport within the mill varies systematically with the amount of coarse particles present in each segment. The ore-specific breakage distribution function can be determined from single particle breakage tests conducted using a computer-monitored twin pendulum apparatus. When the ore-specific breakage distribution function is used in the multi-segment, a constant relationship between the breakage rate parameters and mill diameter is observed. Thus, the performance of an industrial ball mill can be adequately described using the ore-specific breakage distribution function together with the systematic variation of the material transport and the breakage rate functions with process conditions and mill diameter, respectively.This ball mill modelling technique is illustrated using a case study on the design of a ball milling circuit for a particular grinding requirement and another case study on modelling the performance of an industrial ball milling circuit.     

Deposition of heterogeneous radiocolloid from groundwater on enclosing rocks

A model of precipitation of radiocolloid particles on enclosing rocks at colloid-facilitated transport of radionuclides by groundwater is considered. The model proposed is based on probabilistic analysis of deposition of heterogeneous colloidal particles on fixed sites of groundwater filtration channels, which are formed by connected systems of pore_ and fracture voids in enclosing rocks. The model takes into account heterogeneity of the system of colloidal particles and competition of different particles for the same potential deposition sites. Theoretical analysis is based on the solution of the system of Kolmogorov-Feller equations. The limit values of the obtained solutions correspond to the equilibrium distribution of radiocolloid particles of different sizes between the groundwater and the enclosing rocks. In the case of a homogeneous system of particles, the obtained distribution is reduced to the Langmuir isotherm.     

Modelling coupled heat and contaminant transport in groundwater

This paper presents the results of a research programme conducted on the geotechnical centrifuge at The University of Western Australia to investigate coupled heat and contaminant transport in the soil surrounding a buried waste source. The phenomena which govern heat and contaminant transport through porous media are discussed, the principles of geotechnical centrifuge modelling are outlined, and relevant scaling laws that govern the relationship between a centrifuge model and the prototype, with respect to the problem of coupled waste transport, are presented. A model test, simulating two-dimensional migration from a buried heat and contaminant source, is described, and the results from four model tests are presented. The experimental data show that hydraulic instability is responsible for the transport of contaminant in the soil around the source and that the mode of instability is determined by the magnitude of the effective Rayleigh number.     

Changes in fine sediment size distributions due to interactions with streambed sediments

In the classical view of fine sediment transport and deposition in streams, particles are expected to be removed from flowing water simply by direct sedimentation onto the streambed. However, recent research has demonstrated that fine sediments can propagate into pore spaces in the streambed due to hyporheic exchange and be removed by a combination of physical and chemical processes. This behaviour can significantly alter fine sediment size distributions during in-stream sediment transport because the physical transport of fine particles and their attachment to bed sediment grains are both a function of the particle size. Herein, we present model simulations for deposition of suspended sediments with a bimodal size distribution. We also applied this approach to analyse the results of laboratory flume observations of suspended sediment deposition. Results from model simulations and flume experiments clearly show that the rate of particle deposition increases with increasing particle size. Thus, the larger particles are preferentially removed from mixtures and there is a fining of the mixed suspensions over time. Both particle deposition mechanisms, i.e. particle sedimentation and filtration, contribute to the fining of the mixed fine particle suspensions over time, and their effects are clearly demonstrated using the fundamental process-based model. These results clearly demonstrate the effects of stream-subsurface exchange on the temporal evolution of the suspended fine sediment size distribution in downstream transport.     

冰湖溃决洪水的二维水动力学数值模拟

为分析冰湖溃决洪水过程,建立了一个二维非恒定流数值模型,可以定量的开展冰湖溃决洪水预测.数值模型的基本控制方程采用二维浅水水流方程,数值方法采用可以捕捉激波的WAF TVD二阶精度格式,并用非界面追踪的方法处理干湿边界.通过理想情况下一维解析解的验证和二维复杂地形情况的数值试验,证明数值模型具有较好的精度和可靠性,并且可以适应复杂地形.将数值模型应用于一个典型的冰湖溃决事件,定量地预估了该冰湖溃决洪水过程,结果表明:水流流速很高,床面剪切应力很大,可能诱发活跃的泥沙运动,形成泥石流灾害.     

筑堤土防渗性状试验研究

结合淮河入海水道河道工程,通过渗透变形试验确定了筑堤土料的渗透变形型式、临界水力坡降和允许坡降,同时指出了采用泓道开挖土筑堤的施工控制措施、质量要求和防渗措施。     

Depth–transport functions and erosion–deposition diagrams as indicators of slope inclination and time-averaged traction forces: applications in tropical reef environments

The trigonometric relationship between slope inclination, the horizontally acting time‐averaged traction force and the vertical depth of transport allows the estimation of one factor, when both others are known. Depth–transport functions can be deduced by comparing the depth distributions of living organisms and their skeletal remains, and this paper simplifies this comparison using foraminifera in which a single test represents an individual. Differences in distribution parameters between living individuals and empty tests allow depth–transport functions to be determined; these functions differ between species at a single transect according to the varying buoyancies of the tests. Within a single species, differences in depth–transport functions between locations are based on either slope inclination or traction intensities. After establishing a mean depth–transport function by averaging species‐characteristic functions, the time‐averaged traction force acting on the studied transect can be calculated. Transport intensities are also estimated using an erosion–deposition diagram that combines the relative frequency distributions of living individuals and empty tests. The proportion of ‘eroded’, ‘parautochthonous’ and ‘allochthonous’ tests mirrors the influence of both slope inclination and traction force for the deposition of empty tests. To test the model, six species of symbiont‐bearing benthic foraminifers were investigated at two transects in front of a NW Pacific coral reef. One transect is distinguished by a strong slope flattening below the steep reef slope (30 m), whereas further steepening characterizes the equivalent part in the other transect. These differences are mirrored in the depth–transport functions as well as in the erosion–deposition diagrams of all species. The time‐averaged traction forces differ in intensities between transects, because of the position of the reef front with respect to the predominant wind direction. However, the form of the functions is identical and distinguished by an increase from the surface to 35 m depth, followed by a decrease down to 105 m. This can be explained by successive onshore and offshore forces acting on the shallow slope, such as the tropical cyclones that cross the region every summer.     

波浪作用下沙坝剖面形成过程的数值模拟

建立了波浪、底部离岸流、泥沙运动和沙滩剖面演变耦合数学模型,模拟了实验室中波浪作用下沙坝剖面的形成过程,讨论了各个物理参数对剖面上的水动力和地形变化的影响。通过参数率定,较好地复演了不规则波作用下沙滩地形由均匀斜坡向沙坝剖面的演变,波高、底部离岸流、输沙率和剖面演变的计算结果与实测数据吻合良好。采用数值实验和误差分析方法,讨论了破碎波水滚倾角、泥沙扩散系数和床面休止角等物理参数对计算结果的影响。研究表明,所建立的模型能较好地描述波浪作用下沙坝剖面形成过程中的重要物理机制。     

土柱变密度溶质运移试验推求水平及垂直方向弥散度研究

基于溶质运移对流弥散理论的变密度海水入侵模型广泛用于海水入侵研究,而水动力弥散系数是影响模型模拟效果的关键性参量之一。利用传统土柱溶质运移试验结合旁侧抽水,采用数值反演法成功获取了水平及垂直两方向弥散度。相对于传统方法,在不增加试验复杂度的前提下,同时推求了不同方向的弥散度,提高了试验效率,节约了试验成本,可广泛用于测定水动力弥散系数等参数。     

A comparison of estimated and calculated effective porosity

 Effective porosity in solute-transport analyses is usually estimated rather than calculated from tracer tests in the field or laboratory. Calculated values of effective porosity in the laboratory on three different textured samples were compared to estimates derived from particle-size distributions and soil–water characteristic curves. The agreement was poor and it seems that no clear relationships exist between effective porosity calculated from laboratory tracer tests and effective porosity estimated from particle-size distributions and soil–water characteristic curves. A field tracer test in a sand-and-gravel aquifer produced a calculated effective porosity of approximately 0.17. By comparison, estimates of effective porosity from textural data, moisture retention, and published values were approximately 50–90% greater than the field calibrated value. Thus, estimation of effective porosity for chemical transport is highly dependent on the chosen transport model and is best obtained by laboratory or field tracer tests. Received, March 1997 · Revised, August 1997 · Accepted, August 1997     

Connectivity and single/dual domain transport models: tests on a point-bar/channel aquifer analogue

In porous aquifers, groundwater flow and solute transport strongly depend on the sedimentary facies distribution at fine scale, which determines the heterogeneity of the conductivity field; in particular, connected permeable sediments could form preferential flow paths. Therefore, properly defined statistics, e.g. total and intrinsic facies connectivity, should be correlated with transport features. In order to improve the assessment of the relevance of this relationship, some tests are conducted on two ensembles of equiprobable realizations, obtained with two different geostatistical simulation methods—sequential indicator simulation and multiple point simulation (MPS)—from the same dataset, which refers to an aquifer analogue of sediments deposited in a fluvial point-bar/channel association. The ensembles show different features; simulations with MPS are more structured and characterised by preferential flow paths. This is confirmed by the analysis of transport connectivities and by the interpretation of data from numerical experiments of conservative solute transport with single and dual domain models. The use of two ensembles permits (1) previous results obtained for single realizations to be consolidated on a more firm statistical basis and (2) the application of principal component analysis to assess which quantities are statistically the most relevant for the relationship between connectivity indicators and flow and transport properties.     

多孔介质中磷负载纳米铁运动特性的模型试验

纳米零价铁在多孔介质中的运动能力影响其作为污染地下水修复材料的应用潜力。已有研究多采用一维柱试验研究纳米零价铁的运动行为,对于其二维运动行为的报道有限。自主研发了模拟多孔介质中纳米颗粒运动的模型试验系统,采用细、中、粗3种不同粒径的玻璃珠模拟土体,通过取样测量和图像分析等方法获得了磷负载纳米铁在多孔介质中的运动行为。一维柱试验结果表明磷负载纳米铁在中玻璃珠和粗玻璃珠中均有一定的运动能力,其液相回收率分别为50.3%和41.0%,而在细玻璃珠中运动能力较差;二维模型试验表明磷负载纳米铁在中玻璃珠中的滞留量随距离逐渐降低,而在粗玻璃珠中则呈现出滞留量随距离先升高后降低的趋势。由模型试验结果分析可知,磷负载纳米铁的运动和滞留过程与多孔介质孔隙结构和流速密切相关,颗粒阻塞与表面沉积等不同物理过程的共同作用导致了其在不同粒径多孔介质中运动特性的差异。研究成果可用于评估磷负载纳米铁的运动能力及分析其在多孔介质中的运移和滞留机制,为纳米零价铁技术的工程应用和环境风险评价提供参考依据。