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.     

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.

     

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.     

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。     

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.

     

A Thermodynamics-Based Model on the Internal Erosion of Earth Structures

The present paper describes a model of internal erosion of earth structures, based on rigorous thermodynamic principles and the theory of porous media. A particular focus of this paper is concerned with the initial stage of internal erosion, when the pore volume forms a continuous network, without the formation of macroscopic cavities or channels. The continuum approach is applicable in this case. The soil skeleton saturated by a pore fluid is treated as the superposition of three continua in interaction, with independent velocity fields. The pore fluid itself consists of a mixture of water and eroded particles. The erosion kinetics is based on the shear stress developed at the solid–fluid interface. The applicability of the model is illustrated by numerical simulations based on the finite element method. These simulations show how the phenomenon of piping can progressively arise, and preferentially in regions where hydraulic gradients are critical. Effects of mechanical degradations due to internal erosion are at the same time demonstrated.     

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.     

Numerical investigation of tunneling in saturated soil: the role of construction and operation periods

This paper numerically investigates the slurry shield tunneling in fully saturated soils with different hydraulic conductivities in short- and long-term scales. A fully coupled hydromechanical three-dimensional model that accounts for the main aspects of tunnel construction and the hydromechanical interactions due to tunneling process is developed. An elasto-plastic constitutive model obeying a double hardening rule, namely hardening soil model, is employed in the numerical simulations. The research mainly focuses on assessing the influence of soil hydraulic conductivity and the method to simulate backfill grouting in the tail void on the evolution of ground subsidence, excess pore water pressure and lining forces. Two different consolidation schemes have been taken into account to computationally address the tunnel construction in soil with low and high hydraulic conductivities. In addition, different methods are employed to simulate the tail void grouting as a hydromechanical boundary condition and to study its effects on the model responses. Finally, the influences of infiltration of the fluidized particles of grouting suspension into the surrounding soil and its corresponding time–space hydraulic conductivity evolution on the displacements and lining forces are studied.     

Implementation of a hydromechanical elastoplastic constitutive model for fully coupled dynamic analysis of unsaturated soils and its validation using centrifuge test results

Prediction of unsaturated soil behavior during earthquake loading has received increasing attention in geotechnical engineering research and practice in recent years. Development of a fully coupled analysis procedure incorporating a coupled hydromechanical elastoplastic constitutive model for dynamic analysis of unsaturated soils has, however, been limited. This paper presents the implementation of a coupled hydromechanical elastoplastic constitutive model into a fully coupled dynamic analysis procedure and its validation using a centrifuge test. First, the fully coupled finite element equations governing the dynamic behavior of unsaturated soils with the solid skeleton displacement, pore water pressure, and pore air pressure as nodal unknowns are briefly presented. The closest point projection method is then utilized to implement the coupled hydromechanical elastoplastic constitutive model into the finite element equations. The constitutive model includes hysteresis in soil–water characteristic curves, cyclic elastoplasticity of the solid skeleton, and the coupling mechanisms between the SWCCs and the solid skeleton. Finally, the analysis procedure is validated using the results from a dynamic centrifuge test on an embankment constructed of compacted unsaturated silt subjected to base shaking. Reasonable comparisons between the predicted and measured accelerations, settlements, and deformed shapes are obtained.

     

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.     

Investigation of slope instability induced by seepage and erosion by a particle method

A novel particle based Bluff Morphology Model (BMM) developed by the authors is extended in this paper to investigate the effect of two dimensional seepage on the stability and collapse of soil slopes and levees. To incorporate the seepage in the model, Darcy’s law is applied to the interactions among neighbouring soil particles and ghost particles are introduced along the enclosed soil boundary so that no fluid crosses the boundary. The contribution of partially saturated soils and matric suction, as well as the change in hydraulic conductivity due to seepage, are predicted well by the present model. The predicted time evolution of slope stability and seepage induced collapse are in reasonable agreement with the experimental results for homogeneous non-cohesive sand and multiple layered cohesive soils. Rapid drawdown over a sand soil is also investigated, and the location and time of the levee collapse occurrence are well captured. A toe erosion model is incorporated in the BMM model, and the location and quantity of erosion from lateral seepage flow is well predicted. The interplay of erosion, seepage and slope instability is examined.     

Numerical investigation of rainfall-induced fines migration and its influences on slope stability

Rainfall-infiltration-induced fines migration within soil slopes may alter the local porosity and hydraulic properties of soils, and is known to be a possible cause of the failure of slopes. To investigate the intrinsic mechanisms, a mathematical formulation capable of capturing the main features of the coupled unsaturated seepage and fines migration process has been presented. Within the formulation, an unsaturated erodible soil is treated as a three-phase multi-species porous medium based on mixture theory; mass conservation equations with mass exchange terms together with the rate equations controlling fines erosion and deposition processes are formulated as the governing equations and are solved by the FEM method. The influences of both the fines detachment and deposition on the stability of slopes under rainfall infiltration have been investigated numerically. The results show that depending on whether the fines move out or get captured at pore constrictions, both desired and undesired consequences may arise out of the fines migration phenomenon. It is suggested that more attention should be paid to those slopes susceptible to internal erosion whose safety analysis cannot be predicted by traditional methods.     

三层堤基中细砂层厚度对管涌影响的试验研究

对由弱透水黏土层、细砂层和强透水砂砾层组成的三层堤基进行了管涌发展的砂槽模型试验,为了便于观察分析,细砂层由各种颜色的细彩砂依次排列在砂砾石层上表面,通过改变彩砂层的厚度分析研究了不同细砂层厚度对管涌发生、发展机制及过程的影响。试验结果表明,三层堤基细砂层厚度的不同使管涌发生的临界水力梯度、涌砂量和通道发展的速度不同,与双层堤基有很大区别。临界水力梯度是由多种元素决定的,包括破坏土体的性质及其整体性等;细砂层的存在使流量在渗透变形初期对涌砂不敏感;在试验中发生的相同水位下多次间歇性涌砂,其原因一方面是颗粒在运动过程中发生堵塞,另一方面是通道边界的土体失去支撑发生应力释放,抵抗力随着时间逐渐减小。     

Hydro-mechanical coupled analysis of near-wellbore fines migration from unconsolidated reservoirs

Oil or gas production from unconsolidated reservoirs could be hampered by sand migration near the wellbore. This paper presents a numerical investigation of production-induced migration of fine sands towards a wellbore drilled in a gap-graded sediment. The solid–fluid interaction is simulated by coupling the discrete element method and the dynamic fluid mesh. With the merit of DEM and a dynamic mesh, the model is capable of naturally capturing particle movements and spatiotemporal variations of hydraulic properties of the sediment at the pore scale. The results show that fine particles are mobilized by radial flow under an imposed hydraulic gradient, and the increase in the hydraulic gradient causes an increase in the fines production. The microscopic pattern of sand migration is clearly visualized through the simulation. The presence of fine particles affects the process of fines migration through two competing mechanisms. Under a low fine content, fine sands mainly serve as the fines production source, and thus, fines production is enhanced as the fine content increases up to a critical value, beyond which fines production is weakened with a further increase in the fine content since the blocking effect gradually dominates. A barrier layer is likely formed during sand migration due to settling and jamming of fine sands at the throats of pores, as fine sands migrate with the radial flow towards the wellbore. This layer is helpful to slow down sand migration, while it could impede production due to reduced permeability in the affected reservoir.

     

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.     

间断级配砂砾石土的渗透变形试验研究

渗透变形是颗粒材料中细颗粒在渗流作用下发生重分布且导致土体的内部结构、水力及力学特性发生变化的现象,是导致砂砾石土地基及堤防结构破坏的主要原因之一。利用自主研发的刚性壁渗透仪对不同级配及细颗粒含量的间断级配砂砾石土在恒定水头渗流作用下进行渗透变形全过程试验,监测了渗流过程中的局部水力梯度空间分布以及竖向位移变化,分析了渗透试验结束后土体的颗粒级配空间分布变化。研究结果表明：土粒中细颗粒所处的欠填、满填及过填3种堆积状态决定了粗、细颗粒间不同的接触方式,影响其渗透性。渗透试验结束后细颗粒流失量沿试样高度的空间分布可以划分为3个区域,即顶部流失区、中部均匀区及底部流失区。局部水力梯度的快速下降伴随着竖向位移的突变,意味着渗透变形的开始;渗透变形启动时的局部水力梯度大于全局水力梯度,证实了采用大尺寸试验执行渗透试验的必要性。细颗粒处于过填状态的试样依然会发生渗透变形且导致强烈的沉降变形,值得进一步的研究。     

土体渗透稳定性判定准则

土体的渗透稳定性是指在渗流条件下宽级配土体内粗颗粒阻止细颗粒流失的能力,土体的渗透稳定性受几何条件、水力条件和物理条件的影响。从几何条件出发,通过对收集的167种土的室内渗透侵蚀试验结果的分析,基于对土体渗透稳定性控制变量地研究,将土分成良好级配土和间断级配土两大类;基于细粒（小于0.063 mm）含量的不同,将每类土又细分为3类,针对不同细类土提出了不同的渗透稳定性几何判定准则。从水力条件出发,研究了应力状态对土体渗透侵蚀起动及破坏水力梯度的影响。试验结果表明,起动水力梯度和破坏水力梯度都随着围压的增大而增大,是由于增大围压使得颗粒间的摩擦力增大的结果。     

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.

     

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.