Coupled bonded particle and lattice Boltzmann method for modelling fluid–solid interaction

This paper presents a two‐dimensional coupled bonded particle and lattice Boltzmann method (BPLBM) developed to simulate the fluid–solid interactions in geomechanics. In this new technique, the bonded particle model is employed to describe the inter‐particle movement and forces, and the bond between a pair of contacting particles is assumed to be broken when the tensile force or tangential force reaches a certain critical value. As a result the fracture process can be delineated based on the present model for the solid phase comprising particles, such as rocks and cohesive soils. In the meantime, the fluid phase is modelled by using the LBM, and the immersed moving boundary scheme is utilized to characterize the fluid–solid interactions. Based on the novel technique case studies have been conducted, which show that the coupled BPLBM enjoys substantially improved accuracy and enlarged range of applicability in characterizing the mechanics responses of the fluid–solid systems. Indeed such a new technique is promising for a wide range of application in soil erosion in Geotechnical Engineering, sand production phenomenon in Petroleum Engineering, fracture flow in Mining Engineering and fracture process in a variety of engineering disciplines. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

Numerical simulation of particle plugging in hydraulic fracture by element partition method

Hydraulic fracturing (HF) treatment often involves particle migration and is applied for propping or plugging fractures. Particle migration behaviors, e.g., bridging, packing, and plugging, significantly affect the HF process. Hence, it is crucial to effectively simulate particle migration. In this study, a new numerical approach is developed based on a coupled element partition method (EPM). The EPM is used to model natural and hydraulic fractures, in which a fracture is allowed to propagate across an element, thereby avoiding remeshing in fracture simulations. To characterize the water flow process in a fracture, a fully hydromechanical coupled equation is adopted in the EPM. To model particle transportation in fractures with water flow, each particle is treated as a discrete element. The particles move in the fracture as a result of being dragged by fluid. Their movement, contact, and packing behaviors are simulated using the discrete element method. To reflect the plugging effect, an equivalent aperture approach is proposed. Using this method, the particle migration and its effect on water flow are well simulated. The simulation results show that this method can effectively reproduce particle bridging, plugging, and unblocking in a hydraulic fracture. Furthermore, it is demonstrated that particle plugging significantly affects water flow in a fracture and hence the propagation of hydraulic fracture. This method provides a simple and feasible approach for the simulation of particle migration in a hydraulic fracture.     

Coupled three-dimensional discrete element–finite difference simulation of dynamic compaction

Discrete element method has been widely adopted to simulate processes that are challenging to continuum-based approaches. However, its computational efficiency can be greatly compromised when large number of particles are required to model regions of less interest to researchers. Due to this, the application of DEM to boundary value problems has been limited. This paper introduces a three-dimensional discrete element–finite difference coupling method, in which the discrete–continuum interactions are modeled in local coordinate systems where the force and displacement compatibilities between the coupled subdomains are considered. The method is validated using a model dynamic compaction test on sand. The comparison between the numerical and physical test results shows that the coupling method can effectively simulate the dynamic compaction process. The responses of the DEM model show that dynamic stress propagation (compaction mechanism) and tamper penetration (bearing capacity mechanism) play very different roles in soil deformations. Under impact loading, the soil undergoes a transient weakening process induced by dynamic stress propagation, which makes the soil easier to densify under bearing capacity mechanism. The distribution of tamping energy between the two mechanisms can influence the compaction efficiency, and allocating higher compaction energy to bearing capacity mechanism could improve the efficiency of dynamic compaction.

     

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.     

Quantitative analysis of piping erosion micro-mechanisms with coupled CFD and DEM method

Piping, as one of the critical patterns of internal erosion, has been reported as a major cause for failures of embankment dams and levees. The fundamental mechanism of piping was traditionally investigated through experimental trials and simplified theoretical methods in macroscale. Nevertheless, the initiation and progressive evolution of piping is a microscale phenomenon in its essence. The current understanding of the micro-mechanism of piping erosion is limited due to a lack of quantitative analysis and visualized evidence. And in fact, seepage flows can affect the soil fabrics and the development of contact forces between particles. But how these fabrics and contact forces evolve under a critical hydraulic gradient is still not fully understood. In this paper, the detailed process of piping erosion is investigated by using a coupled computational fluid dynamics and discrete element method (CFD–DEM) approach. The treatment of soil–flow interactions in CFD–DEM is explained by exchanging the momentum between the two phases. During the simulation, the piping erosion process is initiated by incrementally ascending differential water head across the soil samples. The three main stages of piping erosion (initial movement, continuation of erosion and total heave) can be identified from monitoring the particle velocity and positions. In addition, the evolution of contact force, hydraulic force, coordination number and void fraction is inspected to provide insight into the micro-mechanism of piping erosion. Two cases are simulated, one with a uniform particle size and a relatively uniform porosity distribution and the other with specific particle size and porosity distributions. An interesting finding from this study is that piping does not always initiate from the free surface and the evolution of piping depends heavily on the particle size and porosity distribution.     

三相耦合渗流侵蚀管涌机制研究及有限元模拟

管涌的发生、发展过程是土骨架相在渗流作用下侵蚀为可动细颗粒相,并随水相在孔隙通道中运移流失的过程。在该过程中,渗流与侵蚀相互耦合,相互促进,水相、土相、可动细颗粒相互作用,因此,管涌过程是一个多场、多相耦合的高度非线性的动态过程。现有的管涌试验结果表明,只有当水力梯度大于起始水力梯度时,细颗粒相才会随水相从土体中运移流失,土体才会发生管涌侵蚀,且管涌稳定后土体的孔隙率（稳定孔隙率）和水力梯度之间存在对应关系,根据该结果,提出管涌稳定孔隙率的概念,修正传统的渗流侵蚀本构方程,建立多孔介质中三相耦合的修正的渗流侵蚀管涌控制方程。最后,针对特定应力状态下的土体建立稳定孔隙率和水力梯度之间的对应关系。基于Galerkin有限元法编制有限元程序,在轴对称情况下对该土体的管涌过程进行数值模拟。结果表明,修正后的管涌控制方程能更全面地描述管涌发生、发展直至稳定状态的特性。     

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.     

黄土陡坡降雨冲刷试验及其三维颗粒流流-固耦合模拟

针对坡角为70°的黄土边坡,进行2.7 mm/min降雨强度下的室内坡面冲刷试验。根据边坡冲刷破坏的过程特征,将边坡侵蚀方式演变过程归纳为试验初期的片蚀、中期的细沟侵蚀、到后期的切沟侵蚀和坍塌。试验中坡顶处侵蚀强度大于其他部位,当坡面形成上下贯通的切沟之后,水流开始掏蚀沟槽底部土体,随着冲刷的持续,切沟两侧土体强度降低,坡顶土体发生坍塌。以此为基础利用三维颗粒流软件PFC3D对边坡降雨冲刷过程进行流-固耦合模拟,在模拟颗粒大变形的同时得到颗粒运动轨迹、孔隙率、流体单元内流速等重要参数,这些参数的定量变化过程反映了降雨过程中边坡遭受侵蚀程度及水流侵蚀能力的分布规律:坡顶处侵蚀最为强烈、水流侵蚀能力最强,且两者随高度降低呈减小趋势,与室内试验结果一致。     

Modeling of fluid–solid interaction in granular media with coupled lattice Boltzmann/discrete element methods: application to piping erosion

In this article, we present a numerical method to deal with fluid–solid interactions and simulate particle–fluid systems as encountered in soils. This method is based on a coupling between two methods, now widely used in mechanics of granular media and fluid dynamics respectively: the discrete element (DE) method and the lattice Boltzmann (LB) method. The DE method is employed to model interactions between particles, whereas the LB method is used to describe an interstitial Newtonian fluid flow. The coupling presented here is a full one in the sense that particle motions act on fluid flow and reciprocally. This article presents in details each of the two methods and the principle of the coupling scheme. Determination of hydrodynamic forces and torques is also detailed, and the treatment of boundaries is explained. The coupled method is finally illustrated on a simple example of piping erosion, which puts in evidence that the combined LB–DE scheme constitutes a promising tool to study coupled problems in geomechanics. Copyright © 2011 John Wiley & Sons, Ltd.     

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。     

黏性土失水开裂多场耦合离散元数值模拟

黏性土在失水过程中逐渐变形开裂,裂隙相互交错形成网络,这一过程涉及水热力等多场耦合的作用。本文基于南京大学自主研发的三维离散元软件MatDEM,采用紧密堆积离散元模型对土体开裂进行模拟。在此模型中,每个离散元单元代表一定体积的土颗粒、孔隙和孔隙水的集合体。单元具有含水量属性,并采用有限差分思想计算水分运移量,实现了水分场模拟。同时,考虑水分场对土体抗拉强度等力学性质的影响,建立水分场和应力场的耦合。在数值模拟中,假定土体表面水分以一定速率蒸发,根据试验数据由含水量计算单元直径和力学参数,从而实现黏土蒸发失水、收缩和开裂变形过程模拟。数值模拟与前人室内试验结果基本一致,能较好地再现开裂过程中的各个阶段。本文为研究多场作用下土体变形破坏模拟提供了一个新的思路。     

Pore‐scale modeling of surface erosion in a particle bed

A fully coupled transient two‐dimensional model was employed to study fundamentals of flood‐induced surface erosion in a particle bed. The interaction of the liquid and solid phases is the key mechanism related to surface erosion. The solid phase was idealized at a particle scale by using the discrete element method. The fluid phase was modeled at a mesoscale level and solved using the lattice Boltzmann method. The fluid forces applied on the particles were calculated on the basis of the momentum the fluid exchanges with the particle. The proposed approach was used to model both single particles and particle beds subjected to Couette flow conditions. The behavior of both the single particle and the particle bed depended on particle diameter and surface shear fluid velocity. The conducted simulations show that the fluid flow profile penetrates the bed for a small distance. This penetration initiates sheet‐flow and surface erosion as the fluid interacts with particles. The effect of suppressing particle rotation on the fluid‐induced forces on the particle was also examined. Suppressing particle spinning may lead to underestimated erosion rate. Results of fluid and particle velocities were compared against experimental results and appeared to agree with the observed trends.Copyright © 2013 John Wiley & Sons, Ltd.     

A continuum‐discrete hydromechanical analysis of granular deposit liquefaction

A coupled continuum‐discrete hydromechanical model was employed to analyse the liquefaction of a saturated loose deposit of cohesionless particles when subjected to a dynamic base excitation. The pore fluid flow was idealized using averaged Navier–Stokes equations and the discrete element method was employed to model the solid phase particles. A well established semi‐empirical relationship was utilized to quantify the fluid–particle interactions. The conducted simulations revealed a number of salient micro‐mechanical mechanisms and response patterns associated with the deposit liquefaction. Space and time variation of porosity was a major factor which affected the coupled response of the solid and fluid phases. Pore fluid flow was within Darcy's regime. The predicted response exhibited macroscopic patterns consistent with experimental results and case histories of the liquefaction of granular soil deposits. Copyright © 2004 John Wiley & Sons, Ltd.     

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.     

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.

     

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.

     

A Modified Mohr-Coulomb Model to Simulate the Behavior of Pipelines in Unsaturated Soils

At the present time, it is very common in practice to utilize Mohr-Coulomb model to simulate the soil behaviour in the application of soil-pipeline interaction problems. However, the traditional Mohr-Coulomb model is unable to predict the realistic loading that can apply on buried pipes during large ground deformation. Especially, the linear elastic-perfectly plastic Mohr-Coulomb model is not capable of simulating the unsaturated soil loading which can result larger than anticipated loading due to suction induced additional normal force between the soil particles. A user defined unsaturated modified Mohr-Coulomb model is developed within a generalized effective stress framework considering suction hardening effects to capture the realistic loading induced by unsaturated soil medium. Firstly, the model has been developed considering microscopic and macroscopic suction hardening mechanisms, and was implemented into a commercial finite element program associated with user subroutine written in FORTAN. Then the model was validated through a series of unsaturated triaxial compression tests conducted on the basis of different sand types having various initial conditions. Finally, the model has been applied to simulate the behaviour of pipelines subjected to lateral soil loading in unsaturated soils. The results revealed that the modified Mohr-Coulomb model has reasonable predictions when compared to the load-displacement response of pipes obtained from two large scale testing programs. The developed model can be used to predict the increased strength and stiffness associated with soil suction that increases lateral loads on pipelines, and thus has widespread relevance for simulating the pipeline response in unsaturated soils under externally imposed ground movement.     

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.