Pore‐scale modeling of fluid‐particles interaction and emerging poromechanical effects

A micro‐hydromechanical model for granular materials is presented. It combines the discrete element method for the modeling of the solid phase and a pore‐scale finite volume formulation for the flow of an incompressible pore fluid. The coupling equations are derived and contrasted against the equations of conventional poroelasticity. An analogy is found between the discrete element method pore‐scale finite volume coupling and Biot's theory in the limit case of incompressible phases. The simulation of an oedometer test validates the coupling scheme and demonstrates the ability of the model to capture strong poromechanical effects. A detailed analysis of microscale strain and stress confirms the analogy with poroelasticity. An immersed deposition problem is finally simulated and shows the potential of the method to handle phase transitions. Copyright © 2013 John Wiley & Sons, Ltd.     

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.     

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 the quicksand phenomenon by a 3D coupled Discrete Element ‐ Lattice Boltzmann hydromechanical model

This paper deals with the numerical simulation of the quicksand phenomenon using a coupled Discrete Elements – Lattice Boltzmann hydromechanical model. After the presentation of the developed numerical model, simulations of ascending fluid flow through granular deposits are performed. The simulations show that the quicksand actually triggers for a hydraulic gradient very close to the critical hydraulic gradient calculated from the global analysis of classical soil mechanics, that is, when the resultant of the applied external pressure balances submerged weight of the deposit. Moreover, they point out that the quicksand phenomenon does not occur only for hydraulic gradients above the critical hydraulic gradient, but also in some cases with slightly lower gradients. In such cases, a more permeable zone is first gradually built at the bottom of the deposit through a grain rearrangement, which increases the hydraulic gradient in the upper zones and triggers the phenomenon. Copyright © 2016 John Wiley & Sons, Ltd.     

Hydro-micromechanical modeling of wave propagation in saturated granular crystals

Biot theory predicts wave velocities in a saturated granular medium using the pore geometry, viscosity, densities, and elastic moduli of the solid skeleton and pore fluid, neglecting the interaction between constituent particles and local flow, which becomes essential as the wavelength decreases. Here, a hydro-micromechanical model, for direct numerical simulations of wave propagation in saturated granular media, is implemented by two-way coupling the lattice Boltzmann method (LBM) and the discrete element method (DEM), which resolve the pore-scale hydrodynamics and intergranular behavior, respectively. The coupling scheme is benchmarked with the terminal velocity of a single sphere settling in a fluid. In order to mimic a small amplitude pressure wave entering a saturated granular medium, an oscillating pressure boundary on the fluid is implemented and benchmarked with the one-dimensional wave equation. The effects of input waveforms and frequencies on the dispersion relations in 3D saturated poroelastic media are investigated with granular face-centered-cubic crystals. Finally, the pressure and shear wave velocities predicted by the numerical model at various effective confining pressures are found to be in excellent agreement with Biot analytical solutions, including his prediction for slow compressional waves.     

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.     

Pore scale study of permeability and tortuosity for flow through particulate media using Lattice Boltzmann method

In this paper, Lattice Boltzmann method (LBM) has been used to study the effects of permeability and tortuosity on flow through saturated particulate media and identify the relationships between permeability and tortuosity with other parameters such as particles diameter, grain specific surface, and porosity. LBM is a simple kinematic model that can incorporate the essential physics of microscopic and mesoscopic processes involved in flow through granular soils. The obtained results indicate that the 2D LB model, due to its inherent theoretical advantages, is capable of demonstrating that the porosity and specific surface are the most influential parameters in determining the intrinsic permeability of granular media. The obtained results show that particles' size diameter has a two‐fold effect on the coefficient of permeability: one is through specific surface and the other is by tortuosity factor. Numerical study also reveals that tortuosity of granular soils decreases almost linearly with increasing the porosity. Copyright © 2010 John Wiley & Sons, Ltd.     

Numerical modelling of fluid-induced soil erosion in granular filters using a coupled bonded particle lattice Boltzmann method

This paper presents a three-dimensional coupled bonded particle and lattice Boltzmann method (BPLBM) with an immersed moving boundary scheme for the fluid-solid interaction. It is then applied to investigate the erosion process of soil particles in granular filters placed within earth dams. The microscopic migration of soil particles can be clearly visualised as the movement of particles can be directly recorded. Three granular filters with different representative size ratios are simulated and the numerical results are seen to match the empirical criteria. In addition, the effect of the representative size ratio of granular filters, hydraulic loading and erosion time are discussed.     

A numerical study of particle motion and two‐phase interaction in aeolian sand transport using a coupled large eddy simulation – discrete element method

Wind‐blown sand movement, considered as a particle‐laden two‐phase flow, was simulated by a new numerical code developed in the present study. The discrete element method was employed to model the contact force between sand particles. Large eddy simulation was used to solve the turbulent atmospheric boundary layer. Motions of sand particles were traced in the Lagrangian frame. Within the near‐surface region of the atmospheric boundary layer, interparticle collisions will significantly alter the velocity of sand. The sand phase is quite dense in this region, and its feedback force on fluid motion cannot be ignored. By considering the interparticle collision and two‐phase interaction, four‐way coupling was achieved in the numerical code. Profiles of sand velocity from the simulations were in good agreement with experimental measurements. The mass flux shows an exponential decay and is comparable to reported experimental and field measurements. The turbulence intensities and shear stress of sand particles were estimated from particle root‐mean‐square velocities. Distributions of slip velocity and feedback force were analysed to reveal the interactions between sand particles and the continuous fluid phase.     

Meso‐scale particle modeling of concrete deterioration caused by alkali‐aggregate reaction

A meso‐scale particle model is presented to simulate the expansion of concrete subjected to alkali‐aggregate reaction (AAR) and to analyze the AAR‐induced degradation of the mechanical properties. It is the first attempt to evaluate the deterioration mechanism due to AAR using the discrete‐element method. A three‐phase meso‐scale model for concrete composed of aggregates, mortar and the interface is established with the combination of a pre‐processing approach and the particle flow code, PFC2D. A homogeneous aggregate expansion approach is applied to model the AAR expansion. Uniaxial compression tests are conducted for the AAR‐affected concrete to examine the effects on the mechanical properties. Two specimens with different aggregate sizes are analyzed to consider the effects of aggregate size on AAR. The results show that the meso‐scale particle model is valid to predict the expansion and the internal micro‐cracking patterns caused by AAR. The two different specimens exhibit similar behavior. The Young's modulus and compressive strength are significantly reduced with the increase of AAR expansion. The shape of the stress–strain curves obtained from the compression tests clearly reflects the influence of internal micro‐cracks: an increased nonlinearity before the peak loading and a more gradual softening for more severely affected specimens. Similar macroscopic failure patterns of the specimens under compression are observed in terms of diagonal macroscopic cracks splitting the specimen into several triangular pieces, whereas localized micro‐cracks forming in slightly affected specimens are different from branching and diffusing cracks in severely affected ones, demonstrating different failure mechanisms. Copyright © 2012 John Wiley & Sons, Ltd.     

LBM–DEM modeling of fluid–solid interaction in porous media

Three porous media flow problems, in which the fluid mechanical interactions are critical, are studied in a mesoscopic–microscopic coupling system. In this system, fluid flow in the pore space is explicitly modeled at mesoscopic level by the lattice Boltzmann method, the geometrical representation and the mechanical behavior of the solid skeleton are modeled at microscopic level by the particulate distinct element method (DEM), and the interfacial interaction between the fluid and the solids is resolved by an immersed boundary scheme. In the first benchmark problem, the well‐known and frequently utilized Ergun equation is validated in periodic particle and periodic pore models. In the second problem, the upward seepage problem is simulated over three stages: The settlement of the column of sphere under gravity loading is measured to illustrate the accuracy of the DEM scheme; the system is solved to hydrostatic state with pore space filled with fluid, showing that the buoyancy effect is captured correctly in the mesoscopic–microscopic coupling system; then, the flow with constant rate is supplied at the bottom of the column; the swelling of the ground surface and pore pressure development from the numerical simulation are compared with the predictions of the macroscopic consolidation theory. In the third problem, the fluid‐flow‐induced collapse of a sand arch inside a perforation cavity is tested to illustrate a more practical application of the developed system. Through comparing simulation results with analytical solutions, empirical law and physical laboratory observations, it is demonstrated that the developed lattice Boltzmann–distinct element coupling system is a powerful fundamental research tool for investigating hydromechanical physics in porous media flow. Copyright © 2012 John Wiley & Sons, Ltd.     

Extended CFD–DEM for free‐surface flow with multi‐size granules

Computational fluid dynamics and discrete element method (CFD–DEM) is extended with the volume of fluid (VOF) method to model free‐surface flows. The fluid is described on coarse CFD grids by solving locally averaged Navier–Stokes equations, and particles are modelled individually in DEM. Fluid–particle interactions are achieved by exchanging information between DEM and CFD. An advection equation is applied to solve the phase fraction of liquid, in the spirit of VOF, to capture the dynamics of free fluid surface. It also allows inter‐phase volume replacements between the fluid and solid particles. Further, as the size ratio (SR) of fluid cell to particle diameter is limited (i.e. no less than 4) in coarse‐grid CFD–DEM, a porous sphere method is adopted to permit a wider range of particle size without sacrificing the resolution of fluid grids. It makes use of more fluid cells to calculate local porosities. The developed solver (cfdemSolverVOF) is validated in different cases. A dam break case validates the CFD‐component and VOF‐component. Particle sedimentation tests validate the CFD–DEM interaction at various Reynolds numbers. Water‐level rising tests validate the volume exchange among phases. The porous sphere model is validated in both static and dynamic situations. Sensitivity analyses show that the SR can be reduced to 1 using the porous sphere approach, with the accuracy of analyses maintained. This allows more details of the fluid phase to be revealed in the analyses and enhances the applicability of the proposed model to geotechnical problems, where a highly dynamic fluid velocity and a wide range of particle sizes are encountered. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

Numerical study of two‐phase fluid distributions in fractured porous media

Two‐phase fluid distributions in fractured porous media were studied using a single‐component multiphase (SCMP) lattice Boltzmann method (LBM), which was selected among three commonly used numerical approaches through a comparison against the available results of micro X‐ray computed tomography. The influence of the initial configuration and the periodic boundary conditions in the SCMP LBM for the fluid distribution analysis were investigated as well. It was revealed that regular porous media are sensitive to the initial distribution, whereas irregular porous media are insensitive. Moreover, to eliminate the influence of boundaries, the model's buffer size of an SCMP LBM simulation was suggested to be taken as approximately 12.5 times the average particle size. Then, the two‐phase fluid distribution of a porous medium was numerically studied using the SCMP LBM. Both detailed distribution patterns and macroscopic morphology parameters were reasonably well captured. Finally, the two‐phase fluid distributions in a fractured porous media were investigated. The influence of the degree of saturation, fracture length, and fracture width on the fluid distributions and migration was explored. Copyright © 2015 John Wiley & Sons, Ltd.     

Numerical study of inter‐particle bond failure by 3D discrete element method

The cohesive‐frictional nature of cementitious geomaterials raises great interest in the discrete element method (DEM) simulation of their mechanical behavior, where a proper bond failure criterion is usually required. In this paper, the failure of bond material between two spheres was investigated numerically using DEM that can easily reproduce the failure process of brittle material. In the DEM simulations, a bonded‐grain system (composed of two particles and bond material in between) was discretized as a cylindrical assembly of very fine particles connecting two large end spheres. Then, the bonded‐grain system was subjected to compression/tension, shear, rolling and torsion loadings and their combinations until overall failure (peak state) was reached. Bonded‐grain systems with various sizes were employed to investigate bond geometry effects. The numerical results show that the compression strength is highly affected by bond geometry, with the tensile strength being dependent to a lesser degree. The shear, rolling and torsion strengths are all normal force dependent; i.e., with an increase in the normal force, these strengths first increase at a declining rate and then start to decrease upon the normal force exceeding a critical value. The combined actions of shear force, rolling moment and torque lead to a spherical failure envelope in a normalized loading space. The fitted bond geometry factors and bond failure envelopes obtained numerically in this three‐dimensional study are qualitatively consistent with those in previous two‐dimensional experiments. The obtained bond failure criterion can be incorporated into a future bond contact model. Copyright © 2015 John Wiley & Sons, Ltd.     

On the implicit immersed boundary method in coupled discrete element and lattice Boltzmann method

The coupled discrete element method and lattice Boltzmann method (DEMLBM) has increasingly drawn attention of researchers in geomechanics due to its mesoscopic nature since 2000. Immersed boundary method (IBM) and immersed moving boundary (IMB) are two popular schemes for coupling fluid particle in DEMLBM. This work aims at coupling DEM and LBM using the latest IBM algorithm and investigating its accuracy, computational efficiency, and applicability. Two benchmark tests, interstitial fluid flow in an ideal packing and single particle sedimentation in viscous fluid, are carried out to demonstrate the accuracy of IBM through semi-empirical Ergun equation, finite element method (FEM), and IMB. Then, simulations of particle migration with relatively large velocity in Poiseuille flow are utilized to address limitations of IBM in DEMLBM modeling. In addition, advantages and deficiencies of IBM are discussed and compared with IMB. It is found that the accuracy of IBM can be only guaranteed when sufficient boundary points are used and it is not suitable for geomechanical problems involving large fluid or particle velocity.     

Discrete element method analysis of non‐coaxial flow under rotational shear

This study focuses on non‐coaxial flow behavior of cohesionless soil undergoing cyclic rotational shear, with a special interest in the effects of particle‐scale characteristics. To this end, we perform a series of 2D discrete element simulations with various particle shapes, inter‐particle coefficient of friction, initial density, and stress ratios. The validity and efficacy of the numerical model is established by systematically comparing numerical simulation results with existing laboratory testing results. Such comparison shows that the numerical simulations are capable of capturing mechanical behavior observed in laboratory testing under rotational shear. We further demonstrate and quantify a strong yet simple relationship between the deviatoric part of the normalized strain increment and the non‐coaxial angle, denoted by and ψ, respectively. This quantitative correlation between ψ and is independent of applied stress ratio, initial and current void ratio, and the number of cycles applied, but dependent on the principal stress orientation and particle‐scale characteristics. At the same , specimens with higher inter‐particle friction angle or smaller particle aspect ratio show greater non‐coaxial angles. A simple model is able to fit this ψ‐ relationship well, which provides a useful relationship that can be exploited in developing constitutive models for rotational shearing. Copyright © 2014 John Wiley & Sons, Ltd.     

颗粒沉降的格子Boltzmann模拟与PIV实验验证

在格子Boltzmann方法中引入大涡模拟,对球形颗粒在静水中沉降引起的紊动流场进行了数值模拟。数值模拟沉速与理论值以及粒子图像测速系统(PIV)实验结果吻合,验证了模型的合理性。同时分析比较了颗粒沉降过程中尾部紊动流场分布以及尾流流速值,发现数值模拟结果与实测结果趋势、数值基本一致,进一步说明了利用格子Boltzmann方法与大涡模拟技术相结合可以合理模拟泥沙颗粒在紊流区的沉降。