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.     

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.     

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.     

Experimental investigation of microstructural changes in soils eroded by suffusion using X-ray tomography

Internal erosion is a complex phenomenon which represents one of the main risks to the safety of earthen hydraulic structures such as embankment dams, dikes or levees. Its occurrence may cause instability and failure of these structures with consequences that can be dramatic. The specific mode of erosion by suffusion is the one characterized by seepage flow-induced erosion, and the subsequent migration of the finest soil particles through the surrounding soil matrix mostly constituted of large grains. Such a phenomenon can lead to a modification of the initial microstructure and, hence, to a change in the physical, hydraulic and mechanical properties of the soil. A direct comparison of the mechanical behaviour of soil before and after erosion is often used to investigate the impact of internal erosion on soil strength (shear strength at peak and critical state) using triaxial tests. However, the obtained results are somehow contradictory, as for instance in Chang’s study (Chang and Zhang in Geotech Test J 34(6):579–589, 2011), where it is concluded that the drained strength of eroded soil decreases compared to non-eroded soil, while both Xiao and Shwiyhat (Geotech Test J 35(6):890–900, 2012) and Ke and Takahashi (Geotech Test J 37(2):347–364, 2014) have come to the opposite conclusion. A plausible explanation of these contradictions might be attributed to the rather heterogeneous nature of the suffusion process and to the way the coarse and fine grains are rearranged afterwards leading to a heterogeneous soil structure, a point that, for now, is not taken into account, nor even mentioned, in the existing analyses. In the present study, X-ray computed tomography (X-ray CT) is used to follow the microstructure evolution of a granular soil during a suffusion test, and, therefore, to capture the induced microstructural changes. The images obtained from X-ray CT reveal indeed that fine particles erosion is obviously not homogeneous, highlighting the existence of preferential flow paths that lead to a heterogeneous sample in terms of fine particles, void ratio and inter-granular void ratio distribution.

     

Modelling of internal erosion based on mixture theory: General framework and a case study of soil suffusion

A general thermo-hydro-mechanical framework for the modelling of internal erosion is proposed based on the theory of mixtures applied to two-phase porous media. The erodible soil is partitioned in two phases: one solid phase and one fluid phase. The solid phase is composed of nonerodible grains and erodible particles. The fluid phase is composed of water and fluidized particles. Within the fluid phase, species diffuse. Across phases, species transfer. The modelling of internal erosion is contributed directly by mass transfer from the solid phase towards the fluid phase. The constitutive relations governing the thermomechanical behaviour, generalised diffusion, and transfer are structured by the dissipation inequality. The particular case of soil suffusion is investigated with a focus on constitutive laws. A new constitutive law for suffusion is constructed based on thermodynamic conditions and experimental investigations. This erosion law is linearly related to the power of seepage flow and to the erosion resistance index. Owing to its simplicity, this law tackles the overall trend of the suffusion process and permits the formulation of an analytical solution. This new model is then applied to simulate laboratory experiments, by both analytical and numerical methods. The comparison shows that the newly developed model, which is theoretically consistent, can reproduce correctly the overall trend of the cumulated eroded mass when the permeability evolution is small. In addition, the results are provided for four different materials, two different specimen sizes, and various hydraulic loading paths to demonstrate the applicability of the new proposed law.     

Investigating the effect of flow direction on suffusion and its impacts on gap-graded granular soils

The flow direction is generally different from the gravity direction in geotechnical structures or slopes, the effect of which during suffusion remains unclear. This paper presents a coupled computational fluid dynamics and discrete element method approach to simulate the particle–fluid interaction relevant to this problem. The CFD-DEM approach is first benchmarked by a classic granular system problem, which is then used to investigate the characteristics of suffusion and its impact on the mechanical behavior. Five different angles between gravity and seepage directions for gap-graded soils with two fines contents are examined. Both the macroscopic and microscopic characteristics during suffusion and triaxial loading tests are analyzed. The direction angle is found to play a significant role affecting the erosion process and the mechanical consequence of soils. The results show that the greater the angle is, the harder it is for suffusion to occur and continue.

     

Understanding multiple thresholds of coupled social–ecological systems exposed to natural hazards as external shocks

External suffusion, as selective erosion of fine particles through the contact with a coarser layer and moving away, is an important phenomenon in dams which may lead to their failure. To study the initiation of external suffusion, caused by water level increase upstream the dam, a series of experimental investigations were conducted on laboratory-scale model, in the hydrodynamic laboratory of école polytechnique de Montreal. On the built model, clay/moraine formed the core, sand was used as a filter and gravel performed the role of the pervious layer. Several different models (in geometry and constituent materials) were built and subjected to the water level increase upstream, which resulted in changes in the hydraulic gradient. The results showed no evidence of considerable suffusion on the clay/moraine and sand interface, while the visual and quantitative data show the presence of suffusion on the sand and gravel interface. The results of the experiments show that, when focusing on the critical hydraulic gradient that initiates the movement of the clay/moraine particles, it can be concluded that despite the differences in test conditions, the critical hydraulic gradient has approximately the same value in all cases. It was also shown that increasing the length of the filter layer or applying stair-like slopes does not have great impacts on the initiation of suffusion, whereas the gravel-size distribution has a great impact on the erosion rate.     

砂性土细颗粒起动临界水力坡降计算方法

地下水渗流作用下内部不稳定砂性土将发生潜蚀现象,潜蚀作用引起的土体渗透破坏会对土工建筑物或地基造成不良影响。考虑土体有效应力和细颗粒应力折减,建立渗流场中细颗粒受力模型,根据极限受力平衡状态得到潜蚀过程中砂性土细颗粒起动临界水力坡降计算公式,并通过DEM-CFD耦合方法以及现有试验数据进行验证。结果表明：砂性土中细颗粒以滚动方式起动,起动临界水力坡降受渗流水流、土体特性以及颗粒自身特性共同影响;砂性土表层细颗粒起动临界水力坡降受埋深影响较大,埋深1 cm的细颗粒最高、最低起动临界水力坡降相差10.169%,埋深10 cm时差异减少至1.061%。该计算方法与数值模拟和渗流试验结果的最大标准误差分别为6.038%、11.211%,可以较为准确地预测砂性土细颗粒起动临界水力坡降。     

径流驱动土壤分离过程的影响因素及机制研究进展

土壤侵蚀包括土壤分离、泥沙输移和泥沙沉积3个子过程,研究这些过程发生、发展的水力、地形、土壤及地表特性等临界条件及各过程间相互影响、相互制约的机制,是建立土壤侵蚀过程模型继而准确预报土壤侵蚀的基础。为加强对径流驱动土壤分离过程的认识,推动土壤侵蚀过程与机理的研究,从径流水动力学特性、土壤特性、近地表特性、土壤分离过程的时空变异特性等方面对径流驱动的土壤分离过程影响因素及机制进行了总结和梳理,在此基础上,从土壤分离过程研究的时空尺度、土壤分离过程的动力学机制、细沟发育及其形态特征、网络结构对土壤分离过程的影响机制、土壤分离与泥沙输移的耦合机制、土壤分离测定方法与标准、土壤侵蚀阻力参数获取与预报等方面,展望了该领域有待深化的问题及今后的发展方向。     

Three-dimensional DEM modeling of the stress–strain behavior for the gap-graded soils subjected to internal erosion

In this work, 3D discrete element method modeling of drained shearing tests with gap-graded soils after internal erosion is carried out based on published experimental results. The erosion in the model is achieved by randomly deleting fine particles, mimicking the salt dissolving process in the experiments. The present model successfully simulates the stress–strain behavior of the physical test by employing the roll resistance and lateral membrane. The case without erosion shows a strain-softening and dilative response, while strain-hardening and contractive response starts to occur as the degree of erosion increases. The dilative to contractive transition is mainly caused by the increase in void ratio due to the loss of fine particles. The change from dilative behavior to contractive behavior is more abrupt for the specimen with larger fine particle percentage because the soil skeleton is mainly controlled by the fine particles instead of by the coarse soil particles. The transition from “fines in sand” to “sand in fines” might be associated with the rapid increasing in the contacts associated with fine particles in the specimen as the percentage of fine content increases. The erosion scenario based on the hydraulic gradient is also modeled by deleting the fine particles based on the ranking of the contact force. Compared with the scenario based on random deletion, the remaining fine particles for the erosion scenario based on the ranking of contact force are more dispersedly distributed, which might benefit the small strain stiffness but result in a smaller strength. This work provides some insights for better understanding the mechanism behind the internal erosion and the associated stress–strain behavior of soil. The gradient of the critical state line increases with more loss of fine particles denoting that the fine particles are helpful for holding the structure of the soils from larger deformation.

     

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.     

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.

     

A coupled CFD-DEM investigation of suffusion of gap graded soil: Coupling effect of confining pressure and fines content

Suffusion involves fine particles migration within the matrix of coarse fraction under seepage flow, which usually occurs in the gap-graded material of dams and levees. Key factors controlling the soil erodibility include confining pressure (p′) and fines content (F_c), of which the coupling effect on suffusion still remains contradictory, as concluded from different studies considering narrow scope of these factors. For this reason, a systematical numerical simulation that considers a relative wide range of p′ and F_c was performed with the coupled discrete element method and computational fluid dynamics approach. Two distinct macroresponses of soil suffusion to p′ were revealed, ie, for a given hydraulic gradient i = 2, an increase in p′ intensifies the suffusion of soil with fines overfilling the voids (eg, F_c = 35%), but have negligible effects on the suffusion of gap-graded soil containing fines underfilling the voids (eg, F_c = 20%). The micromechanical analyses, including force chain buckling and strain energy release, reveal that when the fines overfilled the voids between coarse particles (eg, F_c = 35%) and participated heavily in load-bearing, the erosion of fines under high i could cause the collapse of the original force transmission structure. The release of higher strain energy within samples under higher p′ accelerated particle movement and intensified suffusion. Conversely, in the case where the fines underfilled the voids between coarse particles (eg, F_c = 20%), the selective erosion of fines had little influence on the force network. High p′ in this case prevented suffusion.     

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 Model Study of the Estuarine Turbidity Maximum along the Main Channel of the Upper Chesapeake Bay

A three-dimensional, intratidal sediment transport model is developed for the estuarine turbidity maximum (ETM) in the upper Chesapeake Bay. The model considers three particle size classes, including the fine class mostly in suspension in the water column, the medium class alternately suspended and deposited by tidal currents, and the coarse size suspended only during the times of relatively high energy events. Based on the results of a box model, depth-limited erosion with continuous deposition is employed for the medium and coarse classes by varying the critical shear stress for erosion as a function of eroded mass. For the fine class, mutually exclusive erosion and deposition is employed with a small constant value for the critical shear stresses for erosion and deposition to assure quick erosion of recently deposited fine particles but without allowing further erosion of consolidated bed sediments. The model is run to simulate the annual condition in 1996, and the model generally gives a reasonable reproduction of the observed characteristics of the ETM relative to the salt limit and tidal phase. The model results for 1996 are analyzed to study the characteristics of the ETM along the main channel of the upper bay in intertidal and intratidal time scales. Under a low flow condition, local erosion/deposition and bottom horizontal flux convergence are the main processes responsible for the formation of the ETM, with the settling flux confining the ETM to the bottom water. Under a high flow condition, a distinctive ETM is formed by strong convergence of the downstream flux of sediments eroded from the upstream of the null zone and the upstream flux of sediments settled at the downstream of the null zone. Intratidal variation of the ETM is mainly controlled by erosion and the tidal transport of eroded sediments for a low flow condition. Under the direct influence of a high flow event, the ETM is mainly formed by erosion during ebbing tidal current strengthened by large freshwater discharge and by convergence of ebbing freshwater discharge and flooding tidal current. During the rebounding stage of a high flow event, intratidal variations are mainly controlled by tidal asymmetry caused by the interaction between tidal currents, gravitational circulation, and stratification.     

The influence of the void fraction on the particle migration: A coupled computational fluid dynamics–discrete element method study about drag force correlations

Granular soils subjected to flow through their soil skeleton can show a behaviour in which fine particles migrate through the pore space between coarser particles. This process is called internal instability or suffusion. This contribution deals with the numerical analysis of the migration of fine particles in a soil column subjected to fluid flow with unresolved coupled computational fluid dynamics–discrete element method (CFD–DEM) with special regards to the used drag force correlation. The contribution investigates the influence of the Schiller–Naumann model and its extension with a voidage term on the migration behaviour of fine particles. The voidage term is further varied with a parameter, which controls the impact of the change of the void fraction on the drag force. It could be observed that the Schiller–Naumann model does not yield in a suffusive behaviour while the extended models show significant particle migration. Thereby, increasing the impact of the void fraction on the drag force results in stronger particle migration. These results reveal the need for good validation techniques. They indicate how the drag force correlation can be adapted to depict the correct particle migration behaviour.     

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.     

Physical model study on the clay–sand interface without and with geotextile separator

In most marine reclamation projects, sand fill is placed directly on soft marine seabed soils. The sand particles can easily penetrate into the soft marine soils, and the soft soil can also move into the pore spaces inside the sand at the initial contact interface between the sand and the soft marine soil. In this case, the permeability and the volume of the sand above the initial surface are reduced. To avoid this problem, a geotextile separator is often placed on the surface of the soft marine soils before placing the sand. In this study, a two-dimensional physical model is utilized to study the geotextile separator effects. The initial conditions of a clayey soil, sand fill, and surcharge loading were kept the same in the physical model test with the only difference being that a geotextile separator was either placed on the clay surface or omitted. The settlements of the initial interface were recorded and compared for the two cases without or with the geotextile separator. The particle size distribution of the soils taken across the interface zone for different time durations was then measured, analyzed, and compared. Based on an analysis of the results, the sand percolation depth was 40 mm and fine particle suffusion was apparent when the sand was placed directly on the marine slurry surface without a geotextile separator. However, when a geotextile separator was used sand percolation was avoided, and the fine particle suffusion was effectively diminished. A relative fine particle fraction is defined to illustrate the migration of fine particles from the clay to the sand soils. The fine particle percentages of the Hong Kong Marine Deposits–sand mixtures were calculated for the cases with and without a geotextile separator using an empirical formula and micromechanical modeling to obtain a better understanding of the effects of geotextile separators in practice.