Discrete numerical modeling of particle transport in granular filters

Granular filters are an essential component in earth dams to protect the dam core from seepage erosion. This paper uses the particle flow method (PFM) to study the mechanism of particle transport in a base soil–filter system. The distributions of the eroded base-soil particles in different filters are traced and analyzed. The eroded mass and intruding depth of the eroded particles into the filters are obtained under different times and hydraulic gradients. The simulation results show that the eroded mass and intruding depth of the base-soil particles into the filter are related to the representative particle size ratio of the base soil to the filter, hydraulic gradient and erosion time. The numerical predictions are also compared with the empirical filter design criterion. The results show that the particle flow model provides an effective approach for studying the filtration micro-property and the erosion mechanism in a base soil–filter system, which is useful for filter design.     

Fractal analysis of the roughness and size distribution of granular materials

The roughness, i.e. general shape and surface irregularity, of particulate soil is an important characteristic that affects the mass behavior of the soil. Characterization of roughness has typically been limited to visual comparison of particles to standard charts, although other more quantitative methods such as Fourier analysis have also been used. Particle size distribution is another important mass-behavioral characteristic of granular soils, and similar to roughness, is defined within limited boundaries. Fractal geometry can be applied to irregular or fragmented patterns such as roughness and grain size distribution to provide quantifying and unique numerical values. This paper presents an evaluation of the applicability of fractal dimensioning techniques to the quantification of both physical particle roughness and grain size distribution of granular soil. The divider and the area-perimeter fractal dimensioning techniques are used to quantify roughness of planar profiles of individual sand grains. The characterization of the size distribution of granular material using fractal geometry is evaluated through Korcak's fragmentation theory. As shown herein, both the divider and the area-perimeter fractal dimensioning techniques are useful in characterizing soil particle roughness, and the results confirm the importance of differentiating between textural and structural aspects of roughness. Fractal geometry can also be used to quantify the size distribution of granular soils with relatively well-graded size distributions.     

Numerical modelling of internal erosion during hydrate dissociation based on multiphase mixture theory

It has been reported that sand production, which is a simultaneous production of soil particles along with gas and water into a production well, forced to terminate the operation during the world's first offshore methane production test from hydrate-bearing sediments in the Eastern Nankai Tough. The sand production is induced by internal erosion, which is the detachment and migration of soil particles from soil skeleton due to seepage flow. The inflow of the eroded soil particles into the production well leads to damage of the production devices. In the present study, a numerical model to predict the chemo-thermo-mechanically coupled behavior including internal erosion during hydrate dissociation has been formulated based on the multiphase mixture theory. In the proposed model, the internal erosion is expressed as mass transition of soil particles from soil skeleton to the fluidized soil particles. Since the internal erosion is considered to depend on the soil particle size, mass of soil particles are divided into several groups that have different representative particle diameters, and the constitutive equations for the onset condition and the mass transition rate of the internal erosion are formulated for each group. Also, transportation of soil particles in the liquid phase is formulated for each particle size group in the proposed model. Finally, a simulation of the methane gas production from the hydrate-bearing sediment by depressurization method is presented, and the internal erosion and the dissociation behavior are discussed.     

A computational procedure to assess the distribution of constriction sizes for an assembly of spheres

The effectiveness of filters to counteract internal erosion in earth structures is particularly related to their ability to capture fine particles moving under seepage flow through the porous material. More precisely, fine particles are likely to be trapped by the narrowest paths between pores: the constrictions. This paper proposes a methodology to compute the constriction size distribution of model granular filters taking into account the relative density of the material. The approach is based upon probabilistic methods which adopt stated simple geometric packing arrangements to represent the solid structure in the extreme density states. Two new models are proposed for the design of the constriction size distribution according to the type of filter grading: continuously graded or gap-graded materials. The models require the usual material characteristics: the grading curve, and the minimum and maximum void ratios for this material. Calibrated on the basis of statistical analyses over numerical assemblies of spheres generated by a discrete element method, the proposed new models constitute a promising tool to significantly improve the modeling of filtration processes in granular materials.     

A coupled 3‐dimensional bonded discrete element and lattice Boltzmann method for fluid‐solid coupling in cohesive geomaterials

This paper presents a 3D bonded discrete element and lattice Boltzmann method for resolving the fluid‐solid interaction involving complicated fluid‐particle coupling in geomaterials. In the coupled technique, the solid material is treated as an assembly of bonded and/or granular particles. A bond model accounting for strain softening in normal contact is incorporated into the discrete element method to simulate the mechanical behaviour of geomaterials, whilst the fluid flow is solved by the lattice Boltzmann method based on kinetic theory and statistical mechanics. To provide a bridge between theory and application, a 3D algorithm of immersed moving boundary scheme was proposed for resolving fluid‐particle interaction. To demonstrate the applicability and accuracy of this coupled method, a benchmark called quicksand, in which particles become fluidised under the driving of upward fluid flow, is first carried out. The critical hydraulic gradient obtained from the numerical results matches the theoretical value. Then, numerical investigation of the performance of granular filters generated according to the well‐acknowledged design criteria is given. It is found that the proposed 3D technique is promising, and the instantaneous migration of the protected soils can be readily observed. Numerical results prove that the filters which comply with the design criteria can effectively alleviate or eliminate the appearance of particle erosion in dams.     

Determination of the constriction size distribution of granular filters by filtration tests

This paper presents the calibration of an experiment based on filtration tests, able to provide the cumulative constriction size distribution of granular materials. Here, simulations of these tests are performed using a discrete element method. Filters of same density but different thicknesses are created with a poly‐sized spherical material. Lateral periodic boundaries for the samples are used, and their size is calibrated so that a representative elementary volume is obtained. Fine particles are released on the created samples, and the particle size distribution of the collected material that successfully crossed the filters is computed. These particle size distributions are related to the underlying cumulative constriction size distribution (CSD) of the granular material involved in the samples. The CSD is derived using a probabilistic approach for the path length of individual particles through a granular material. We settle all the requisites related to the technique and to the fine particles that are released to allow reaching a correct CSD for the filter. The reference CSD used for the calibration of the experiment is obtained after a radical partition of the void space into Delaunay tetrahedra and a geometrical characterisation of constrictions on each tetrahedron face. Copyright © 2012 John Wiley & Sons, Ltd.     

Analysis of mechanical behaviour and internal stability of granular materials using discrete element method

Granular materials like sand are widely used in civil engineering. They are composed of different sizes of grains, which generate a complex behaviour, difficult to assess experimentally. Internal instability of a granular material is its inability to prevent the loss of its fine particles under flow effect. It is geometrically possible if the fine particles can migrate through the pores of the coarse soil matrix and results in a change in its mechanical properties. This paper uses the three‐dimensional Particle Flow Code (PFC3D/DEM) to study the stability/instability of granular materials and their mechanical behaviour after suffusion. Stability properties of widely graded materials are analysed by simulating the transport of smaller particles through the constrictions formed by the coarse particles under the effect of a downward flow with uniform pressure gradient. A sample made by an initially stable material according to the Kenney & Lau geometrical criterion was divided into five equal layers. The classification of these layers by this criterion before and after the test shows that even stable granular materials can lose fine particles and present local instability. The failure criterion of eroded samples, in which erosion is simulated by progressive removal of fine particles, evolves in an unexpected way. Internal friction angle increases with the initial porosity, the rate of lost fine particles and the average diameter D₅₀. Copyright © 2016 John Wiley & Sons, Ltd.     

Evaluation of Combined Base Soil Erodibility and Granular Filter Efficiency

Filters managed in zoned dams are designed according to criteria based on the grain size distribution of both filter and eroded soil. However, the constriction size distribution of the filter is the key parameter which governs the filter retention process of flowing eroded particles. To assess the filter efficiency regarding eroded particles, several filters and base soils are tested in a vertical cell with a configuration coupling erosion and filtration processes. For setting the boundary condition of eroded particles at the filter inlet, hole erosion test (HET) was performed on the base soil. The investigation of the evolution of filter behavior shows that the void ratio and the grain shape are of a great influence on filter efficiency. A new approach of filter clogging was proposed by evaluating a damage index which is affected by various parameters such as the ratio D₁₅/d₈₅ and the size of eroded particles. An approach linking the geometrical parameters (damage index) to the hydraulic conductivity leads to an estimation of the filter performance which provides a more quantifiable and realistic criterion. The results indicate that even existing criteria were not met; the tested filters remain efficient as regards to experimental data. An analytical approach based on constrictions size distribution was used and pore reduction was matched with experimental results.

     

土体直剪力学特性颗粒尺度效应理论与试验研究

土体是一种颗粒物质,其强度与变形特性具有显著的颗粒尺度效应。根据土体颗粒间的连结性状和微重比,将土颗粒划分为基体颗粒与加强颗粒。构建了反映土体内部材料信息和颗粒特征信息的土体胞元,基于应变梯度理论建立可以描述土体颗粒尺度效应的土体胞元模型。设计一系列饱和重塑土的直接快剪试验以研究土体直剪力学特性的颗粒尺度效应,并定量计算了土体胞元模型的应变梯度和內禀尺度等微细观计算参数。试验结果表明,土体的剪切屈服应力随加强颗粒体积比和平均应变梯度的增加而增加,且与加强颗粒体积比呈近似线性关系,与平均应变梯度呈抛物线关系;加强颗粒粒径对土体的剪切屈服应力影响不明显。土体剪切屈服应力的试验结果与土体胞元模型的预测结果一致。     

On the evaluation of internal stability of gap-graded soil: a status quo review

Internal instability is a phenomenon of fine particle redistribution in granular materials under the seepage action and consequent change in the soil’s internal structure and hydraulic and mechanical properties. It is one of the primary causes of failures of sand-gravel foundations and embankment dams. The criteria establishment is considered the key to solving the erosion problems, so the existing internal stability criteria need a review and classification to study the recent development trends in soil seepage and erosion. Therefore, this paper aims at reviewing the internal stability factors of gap-graded soil with a focus on the internal erosion mechanism and internal stability evaluation based on geometric and hydraulic criteria. Firstly, the paper compared the effect of several commonly used geometric criteria for gap-graded soil evaluation, such as particle size, fine content, void ratio, and fractal dimension. Furthermore, it provided a hydraulic criteria overview and analyzed the effects of the hydraulic gradient, hydraulic shear stress, confining pressure, and pore velocity on internal erosion. The geometric–hydraulic coupling methods were introduced, with a detailed elaboration of the erosion resistance index method based on accumulated dissipated energy. The capabilities and limitations of these criteria were discussed throughout the paper. It was found that combined Kezdi’s criterion and Kenney and Lau’s criterion is more reliable to evaluate internal stability of soil. The gap-graded soil with fine particle content higher than 35% is not necessarily internally stable. Finally, the energy-based method (erosion resistance index method) can effectively reproduce the total amount of erosion mass and the final spatial distribution of fine particles and identifies erosion. The review's outcome can be used as a basis to evaluate the internal erosion risk for gap-graded soils. The evaluation methods discussed here can help identify the zones of relatively high erosion potential.

     

硅酸钾材料加固土遗址耐风蚀颗粒元模拟分析

西北干旱地区土遗址受风化、风蚀等破坏严重,大量土质文物亟待加固抢修。加固后土遗址的各耐环境因素及加固机制研究是土遗址加固的理论基础。首次引入颗粒元程序PFC,通过改变模型中颗粒间平行连接强度,对硅酸钾（简称PS）加固前后的土样进行数值模拟。在考虑实际土样颗粒粒径和密度的前提下,拟合了生土PS加固前后的抗压和抗拉强度,并将拟合后的颗粒元模型应用于风蚀模拟。通过随机生成挟沙风颗粒,以一定的速度撞向土体,模拟挟沙风的吹蚀作用。挟沙风颗粒数与循环步数成正比例,因此,可以用挟沙风颗粒数来代表吹蚀时间的长短。挟沙风颗粒的速度则代表挟沙风风速。模拟结果表明,在20 m/s的挟沙风吹蚀作用下,风蚀程度随吹蚀时间的增加而增大,未加固土样的风蚀程度增幅度远大于加固土样;同样吹蚀时间条件下,加固土样的抗风蚀强度明显高于未加固土样。这些模拟结论与风洞试验结果的统计规律一致。本研究拟合的颗粒流模型可进一步应用于PS加固机制研究及耐风蚀、雨蚀、冻融等诸环境影响分析研究。     

A coupled discrete element model for the simulation of soil and water flow through an orifice

Soil erosion around defective underground pipes can cause ground collapses and sinkholes in urban areas. Most of these soil erosion events are caused by fluidization of the surrounding soil with subsequent washing into defective sewer pipes. In this study, this soil erosion process is simplified as the gradual washout of sand particles mixed with water through an orifice. The discrete element method is used to simulate the large deformation behavior of the sand particles, and the Darcy fluid model is coupled with this approach to simulate fluid flow through porous sand media. A coupled 3D discrete element model is developed and implemented based on this scheme. To simulate previous experiments using this coupled model considering the current computing capacity, we incorporated a ‘supply layer’ to study the continuous erosion process. The coupled model can predict the erosion flow rates of sand and water and the shape of erosion void. Thus, the model can be used as an effective and efficient tool to investigate the soil erosion process around defective pipes. Copyright © 2017 John Wiley & Sons, Ltd.     

含细粒砂土反常剪切行为的数值模拟研究

针对含细颗粒砂土的反常剪切行为,开展了双轴剪切试验的数值模拟,从宏细观角度分析了其反常剪切行为发生的内在机制。数值模拟结果表明,增加围压能提高含细颗粒砂土的抗剪切液化能力,该反常行为的根本原因在于围压上升使得粗细颗粒更有效地参与了力链传递,增加了颗粒间的接触,增强了土体的密实度。细颗粒在土骨架中的移动对砂土的液化起着至关重要的作用,而粗颗粒仅起次要作用。研究表明,细颗粒在剪切过程中会持续从有效土骨架中移出成为无效颗粒,而部分粗颗粒也因失去细颗粒的支撑作用会脱离土骨架,直至试样最终液化。细颗粒一般参与土骨架中的弱力链,而粗颗粒则一般参与强力链,导致细颗粒较粗颗粒更容易在土骨架中移动。     

Influence of relative density of the granular base soil on filter performance

Perpendicular contact erosion due to poorly designed filters is a frequent hazard for water-retaining structures serving as lifeblood to the community. This phenomenon occurs when the fine particles of a base soil at the contact interface with a coarser material are detached and transported through pores formed by the coarse particles. Therefore, most filter design criteria focus on the gradation of coarse particles or the gradation of pore constrictions. Meanwhile, the parameters of the base soil, such as relative density, are often overlooked. On the one hand, some experts neglect the impact of relative density because perpendicular contact erosion occurs at the interface, where fine particles expose themselves to larger pores. On the other hand, it is a general belief that the more compacted a base soil is, the less susceptible it will be to erosion as the seepage is reduced. This paper discusses this dilemma from a mutual perspective which assesses the influence of relative density from experimental, numerical, and analytical standpoints. The experimental study reveals that there is an optimal relative density which will release the least eroded mass. The influence is crucial as it can change the status of stability to unstable. The physical essence of the phenomenon is expressed by a numerical study at the micro-scale, which investigates the redistribution of flow lines and stress resulting from a particle detachment. The discovery at the micro-scale is confirmed by an analytical evaluation at the macro-scale, which assesses the redistribution of pore constrictions.

     

Three-dimensional hydromechanical modeling of internal erosion in dike-on-foundation

Currently, numerical studies at the real scale of an entire engineering structure considering internal erosion are still rare. This paper presents a three-dimensional (3D) numerical simulation of the effects of internal erosion within a linear dike located on a foundation. A two-dimensional (2D) finite element code has been extended to 3D in order to analyze the impact of internal erosion under more realistic hydromechanical conditions. The saturated soil has been considered as a mixture of four interacting constituents: soil skeleton, erodible fines, fluidized fine particles, and fluid. The detachment and transport of the fine particles have been modeled with a mass exchange model between the solid and the fluid phases. An elastoplastic constitutive model for sand-silt mixtures has been developed to monitor the effect of the evolution of both the porosity and the fines content induced by internal erosion upon the behavior of the soil skeleton. An unsaturated flow condition has been implemented into this coupled hydromechanical model to describe more accurately the seepage within the dike and the foundation. A stabilized finite element method was used to eliminate spurious numerical oscillations in solving the convection-dominated transport of fluidized particles. This numerical tool was then applied to a specific dike-on-foundation case subjected to internal erosion induced by a leakage located at the bottom of the foundation. Different failure modes were observed and analyzed for different boundary conditions, including the significant influence of the leakage cavity size and the elevation of the water level at the upstream and downstream sides of the dike.     

基于颗粒组构特性的散体材料本构模型研究

通过散体介质材料单元颗粒排列组构表达的细观结构力学关系,建立了用颗粒密集度、颗粒排列组构关系和颗粒间摩擦特性等非连续介质材料特性参数描述的散体介质材料本构模型,从而实现散体介质材料宏观连续介质描述的等效应力表达.通过该模型可采用数值方法进行散体介质材料准静态情况下的力学特性分析.文中最后基于有限元软件ABAQUS,进行了该本构模型的二次开发.数值算例结果验证了所建立散体介质材料本构模型的适用性.     

Micromechanical assessment of an internal stability criterion

The internal stability of a soil is a measure of its susceptibility to suffusion and suffosion, two forms of internal erosion. The internal stability of granular filters must be carefully considered when designing new embankment dams and assessing the risk associated with existing embankment dams. Current guidelines for assessing the internal stability of such filters were empirically derived from macroscale observations and consider the shape of the particle-size distribution curve. These guidelines lack a fundamental, scientific micromechanical basis. The initiation and propagation of internal erosion is clearly a particle-scale phenomenon, and this paper applies particulate mechanics to provide a micromechanical justification for one currently used stability criterion. The study used discrete element simulations of idealised virtual soil samples that had various degrees of internal stability when assessed using the criterion proposed by Kézdi [10]. The internal topologies of stable and unstable samples were analysed by considering the distributions of inter-particle contact forces, the number of particle–particle contacts and the average particle stresses. Clear correlations are observed between the filter stability criterion and the average number of contacts per particle and the probability that a given particle participates in stress transmission. The phenomenon of a critical fines content, at which the existing guidelines are no longer considered to be valid, is also considered.     

Decoupled Erosion of Authigenic and Detrital Components in Soil

In the study of surface processes, it is generally assumed that erosion occurs equally throughout the soil profile so that chemical depletion of the topsoil can represent the intensity of chemical weathering and the duration of surface exposure to cosmogenic radiation can reflects the soil residence time, and then the rate of erosion can be calculated. In comparison with fresh bedrock, the depletion of soluble elements in soil mainly comes from fine-grained secondary clay components, while the depletion degree of detrital minerals is weak. The preferential erosion of fine-grained secondary clay will lead to the underestimation of weathering intensity, and the retention time of detrital mineral will be longer than the total retention time of soil， and thus the soil erosion rate will be underestimated. Based on the uranium isotope comminution ages of soil in the Lesotho Highlands, we found that erosion operates differentially between the detrital and authigenic components of the soil. Uranium isotope comminution ages show a soil residence time of (543±32) ka for the detrital particles. In contrast, soil residence time of the authigenic phases is constrained to be (22±11) ka according to the accumulation of recoiled ²³⁴U from the absorbed ²³⁸U to river water. The residence time of secondary clay matches with the regional erosion rate 24-33 t/(km²·a) calculated from weathering flux, indicating that secondary clay is the main component of soil erosion. The results indicate that the decoupled erosion of different components in soil may be common. This finding implies that the intensity of weathering based on bulk soil erosion and the rate of soil erosion determined by exposure dating of coarse soil grains may be invalidated due to the preferential erosion of authigenic particles. As a result, a lower estimate of weathering flux may be made, and therefore the role of chemical weathering in the global carbon cycle could be underestimated.     

土体力学特性颗粒尺度效应的理论与试验研究

土体是一种复杂的颗粒体系,其强度与变形具有显著的颗粒尺度效应。为考虑土体不同尺度土颗粒对其宏观力学特性的影响,根据土颗粒间相互作用产生的黏聚和摩擦物理效应而非纯粹几何尺寸,划分土颗粒尺度层次以构造反映土体内部材料信息和颗粒特征信息的土体胞元。基于土体不同尺度结构层次上力学响应的特征,引入微重比的概念,建立具有多尺度分层次理论框架的胞元土体理论,解释土体力学特性颗粒尺度效应的物理机制,把微细观土力学理论从定性分析推进到定量计算的水平。设计一系列饱和重塑土的三轴不固结不排水剪切试验对土体的颗粒尺度效应进行测试,并定量计算胞元土体理论的应变梯度和內禀尺度等微细观计算参数。试验和理论计算结果均表明,土体强度和变形的颗粒尺度效应随加强颗粒的体分比增加以及粒径减小而增强,反映出土体强度和变形显著的颗粒尺度效应;土体强度和变形尺度效应的理论预测与试验结果具有较好的一致性。     

Internal erosion in dike-on-foundation modeled by a coupled hydromechanical approach

One of the major causes of instability in geotechnical structures such as dikes or earth dams is internal erosion, an insidious process that occurs over a long period of time. Research on this topic is still fairly new and much more needs to be understood in order to solve the problems posed by this phenomenon. This paper proposes a hydromechanical model based on porous continuous medium theory to assess how internal erosion impacts the safety of earthen structures. The saturated soil is considered as a mixture of four interacting constituents: soil skeleton, erodible fines, fluidized fine particles, and fluid. The detachment and transport of the fine particles are described by a mass exchange model between the solid and the fluid phases. An elastoplastic constitutive model for sand-silt mixtures has been developed to monitor the effect of the evolution of both porosity and fines content induced by internal erosion upon the behavior of the soil skeleton. The model has been numerically solved with the finite element method. It has then been applied to the specific case study of a dike foundation subjected to internal erosion induced by the presence of a karstic cavity beneath the alluvium layer. The numerical results show the onset of erosion, the time-space evolution of the eroded zone, and the hydromechanical response of the soil constituting the dike, all of which highlights the effects of the cavity location, the erosion rate, and the fines content.