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 simple model for the prediction of the deflation threshold shear velocity of dry loose particles

A very important parameter in aeolian equations is the deflation threshold shear velocity, which quantifies the instant of particle motion. In this paper, a simple model is presented for the prediction of the threshold shear velocity of dry loose particles. It has the same functional form as the widely used models of Bagnold (1941) and Greeley & Iversen (1985), but differs in its treatment of the so‐called threshold parameter. As the new expression was based on the moment balance equation used by Greeley & Iversen, it includes a function for the aerodynamic forces, including the drag force, the lift force and the aerodynamic moment force, and a function for the interparticle forces. The effect of gravitation is incorporated in both functions. However, rather than using an implicit function for the effect of the aerodynamic forces as in the Greeley & Iversen model, a constant aerodynamic coefficient was introduced. From consideration of the van der Waals' force between two particles, it was also shown that the function for the interparticle cohesion force is inversely proportional to the particle diameter squared. The model was calibrated on data reported by Iversen & White (1982). The new expression compared, at least for terrestrial conditions, very well with the Greeley & Iversen model, although it is much simpler. It was finally validated with data from wind‐tunnel experiments on different fractions of dune sand and sandy loam soil aggregates. The soil aggregates were treated as individual particles with a density equal to their bulk density. The good agreement between observations and predictions means that, when predicting mass transport of particles above a given soil, minimally dispersed particle‐size distributions should be considered rather than the granulometric composition of the soil.     

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.     

3D finite element modeling of sand particle fracture based on in situ X‐Ray synchrotron imaging

Compressive loading of granular materials causes inter‐particle forces to develop and evolve into force chains that propagate through the granular body. At high‐applied compressive stresses, inter‐particle forces will be large enough to cause particle fracture, affecting the constitutive behavior of granular materials. The first step to modeling particle fracture within force chains in granular mass is to understand and model the fracture of a single particle using actual three‐dimensional (3D) particle shape. In this paper, the fracture mode of individual silica sand particles was captured using 3D x‐ray radiography and Synchrotron Micro‐computed Tomography (SMT) during in situ compression experiments. The SMT images were used to reconstruct particle surfaces through image processing techniques. Particle surface was then imported into Abaqus finite element (FE) software where the experimental loading setup was modeled using the extended finite element method (XFEM) where particle fracture was compared to experimental fracture mode viewed in radiograph images that were acquired during experimental loading. Load‐displacement relationships of the FE analysis were also compared with experimental measurements. 3D FE modeling of particle fracture offers an excellent tool to map stress distribution and monitors crack initiation and propagation within individual sand particles. Copyright © 2015 John Wiley & Sons, Ltd.     

Aerodynamic grain‐size distribution of blown sand

Aeolian sand entrainment, saltation and deposition are important and closely related near surface processes. Determining how grains are sorted by wind requires a detailed understanding of how aerodynamic sand transport processes vary within the saltating layer with height above the bed. Grain‐size distribution of sand throughout the saltation layer and, in particular, how the associated flux of different grain size changes with variation in wind velocity, remain unclear. In the present study, a blowdown wind tunnel with a 50 cm thick boundary layer was used to investigate saltating sand grains by analyzing the weight percentage and transport flux of different grain‐size fractions and the mean grain size at different wind velocities. It was found that mean grain size decreases with height above the sand bed before undergoing a reversal. The height of the reversal point ranges from 4 to 40 cm, and increases with wind velocity following a non‐linear relationship. The content of the finer fractions (very fine and fine sand) initially increases above the sand bed and then decreases slightly with height, whereas that of the coarser fractions (medium and coarse sand) exhibits the opposite trend. The content of coarser grains and the mean grain size of sand in the saltation layer increase with wind velocity, indicating erosional selectivity with respect to grains in multi‐sized sand beds; but this size selectivity decreases with increasing wind velocity. The vertical mass flux structure of fine sand and very fine sand does not obey a general exponential decay pattern under strong wind conditions; and the coarser the sand grain, the greater the decrease rate of their transport mass with height. The results of these experiments suggest that the grain‐size distribution of a saltating sand cloud is governed by both wind velocity and height within the near‐surface boundary layer.     

The effects of atmospheric stability intensity on the movement of windblown sand

Using a model that couples wind flow with the motion of sand particles under different atmospheric stability intensities, this paper studied the effects of atmospheric stability on the trajectory and velocity of sand particles in the saltation layer, and the duration before a steady state was achieved. The vertical velocity, horizontal distance, and the maximum height of saltating sand particles increased with increasingly negative stability intensity under unstable conditions. The wind–sand flow reached equilibrium more quickly with increasingly negative stability intensity under unstable conditions, but reached equilibrium more slowly with increasing stability intensity under stable conditions.     

Migration mechanism of fine particles in aquifer during water injection

Water injection in aquifers to stabilize water level is a novel method to prevent shaft failure. However, with the progression of water injection, the flow rate of water injection decreases gradually. Through analysis, it is considered that the fine particles in sand migrate to form a dense structure, which hinders the increase of water flow. In order to investigate the migration mechanism of fine particles in the aquifer during water injection, experimental tests and numerical simulations were conducted in the present study. First, the physical experiment was designed, and it was shown that the water pressure difference between the two pressure gauges gradually decreased, while the water flow rate per hour slowly decreased. Furthermore, the permeability coefficient of sand near the outlet became smaller and smaller with the migration of fine particles, which indicated that the fine particles among sand grains migrated gradually from the water injection inlet to the outlet. Additionally, the water flow channels formed slowly. Then, the microscopic mechanism of fine particle migration was studied using particle flow code numerical simulation. During water injection, water pressure and porosity of sand decreased from the water injection inlet to the outlet, while the coordination number of particles increased on the whole. Contact force chain gradually strengthened near the outlet side during water injection. The trends of force chain distribution, the coordination number distributions and the evolution of porosity were consistent, which highlighted the process of fine particles migrating from the injection inlet to the outlet in the aquifer.

     

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.     

基于三维流-固耦合模型的油井出砂细观机制研究

油井出砂机制的研究是提高油藏产能和石油开采成本减小的关键课题,而常规的宏观力学理论和方法不能全面反映油藏开采过程中油井出砂的发生和发展。鉴于砂岩储层的物理性质和射孔试验特征,从岩土力学的角度建立基于柱坐标系的三维颗粒流数值模型,与理论分析成果进行比较,以说明该细观数值模型可行性,有效地模拟出砂过程中的渗流及流-固耦合效应。在该基础上,综合考虑流体压力梯度力和拖曳力,基于PFC3D模型模拟流体不同运动时的砂岩性态。数值分析得到的模型宏观应力图形说明流体运动对砂岩力学特性的影响不可忽略,且在相同条件下,流量越大,砂岩的塑性区越大,形成砂岩破坏出砂的几率也越大。同时,不同工况的砂岩黏结分布和颗粒转动图形表明,相同条件下流量越大,颗粒间平行黏结破坏越多,颗粒转动越大,失去黏结约束的颗粒也越多,出砂量就越大,可见两种细观特征图形与宏观应力图形变化规律一致,该模型可用于油井出砂机制的研究,可为出砂量预测及出砂控制提供新的研究思路。     

Effects of weak layers on particle velocity measurements

Summary Results are presented from a testing program to study the effect weak layers embedded in a strong rock strata have on particle velocity when subjected to explosive loading. A similar computational study had been conducted earlier with WONDY — a finite difference Langrangian code developed at Sandia National Laboratory. The experiments were conducted using models fabricated from Hydrocal containing a single dry sand layer or clay layer through which the stress wave traveled. Particle velocity was measured in front of and past the weak layer to determine attenuation, pulse shape changes, and displacement loss. The results from the model testing indicated that particle velocity amplitude decreased significantly when the stress wave passed through the weak layer. The velocity pulse width on the other hand was found to remain relatively constant when passing through the weak layer. The computational results from WONDY predicted similar behavior and hence were in good agreement with the tests. In the experiments, the velocity loss across a sand layer was found to be much larger than the loss across a clay layer. The stress wave velocity in the sand layer was found to be significantly smaller than in the Hydrocal while the experimentally determined wave velocity in the clay was nearly equal to the wave velocity in the Hydrocal.     

流体黏性对油井砂岩力学响应的影响

随着黏度较大的油藏陆续投入开发,油藏黏性对储层砂岩力学特性的影响研究意义重大。基于柱坐标系建立射孔试验的三维颗粒流数值模型,考虑不同黏性的流体运动对砂岩力学响应的影响,反映油井的出砂过程。砂岩的宏观应力曲线说明流速相同时,随着黏滞系数的增大,切向应力和偏应力均增大,使得砂岩剪切破坏的几率增大,砂岩更容易屈服破坏而出砂。另外,砂岩黏结应力图说明油井附近的应力较大,且随着黏滞系数增大,黏结张拉应力的增大是局部的,而剪应力的增大是全局的,且变化趋势更明显;颗粒的旋转也说明随着流体黏性的增大,颗粒旋转增大,砂岩形成离散颗粒而出砂的几率增大。上述结果与实际开采中的砂岩力学响应吻合,说明了在相同的外界条件下,黏性越大的流体运动对砂岩受力的影响越大,出砂越明显,该成果对不同黏性的油藏开采采用有效的防砂方法提供了重要的科学依据。     

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.     

Generation of a realistic 3D sand assembly using X‐ray micro‐computed tomography and spherical harmonic‐based principal component analysis

Three‐dimensional particle morphology is a significant problem in the discrete element modeling of granular sand. The major technical challenge is generating a realistic 3D sand assembly that is composed of a large number of random‐shaped particles containing essential morphological features of natural sands. Based on X‐ray micro‐computed tomography data collected from a series of image processing techniques, we used the spherical harmonics (SH) analysis to represent and reconstruct the multi‐scale features of real 3D particle morphologies. The SH analysis was extended to some highly complex particles with sharp corners and surface cavities. We then proposed a statistical approach for the generation of realistic particle assembly of a given type of sand based on the principle component analysis (PCA). The PCA aims to identify the major pattern of the coefficient matrix, which is made up of the SH coefficients of all the particles involved in the analysis. This approach takes into account the particle size effect on the variation of particle morphology, which is observed from the available results of micro‐computed tomography and QICPIC analyses of sand particle morphology. Using the aforementioned approach, two virtual sand samples were generated, whose statistics of morphological parameters were compared with those measured from real sand particles. The comparison shows that the proposed approach is capable of generating a realistic sand assembly that retains the major morphological features of the mother sand. Copyright © 2016 John Wiley & Sons, Ltd.     

考虑钙质砂细观颗粒形状影响的液体拖曳力系数试验

钙质砂作为南海岛礁填筑常用的岩土材料,其渗透性很大程度上决定着填筑后土体的固结和沉降。拖曳力系数是表达流体对土体颗粒表面力的参数,也是表征颗粒状土体渗透能力的一个重要参数,目前国内外对钙质砂拖曳力系数的研究十分有限。首先引入一个修正的三维参数 对钙质砂这种天然非规则颗粒材料的形状进行定量描述,然后开展一系列单个钙质砂颗粒在液体中沉降试验,利用高速相机记录颗粒沉降过程,结合图像处理技术获得颗粒沉降平衡速度Ut,进而计算出拖曳力系数CD和雷诺数Re,最后拟合出包含CD、Re及 三个参数的钙质砂拖曳力系数半经验模型。结果发现,在相同雷诺数条件下钙质砂的形状系数 越大,拖曳力系数越小。通过与其他研究结果对比发现,其表面微孔隙越发育,拖曳力系数越小的规律。该模型能够考虑不规则颗粒形状对拖曳力系数的影响,从而提高对土体渗透性预测的精度,对南海岛礁填筑工程中钙质砂固结和沉降的计算也具有重要意义。     

Development of Unsteady Windblown Sand Transport

The threshold condition and mass flux of aeolian sediment transport are the essential quantities for wind erosion prediction, dust storm modeling and geomorphological evolution, as well as the sand control engineering design. As a consequence, they have long been the key issues of windblown sand physics. Early researches on aeolian sediment transport focus mainly on steady transport process. While recently, synchronous, high frequency measurements show that wind field in atmospheric boundary layer is always unsteady, showing up as intense fluctuation of wind speed, which thus results in the intense spatial-temporal variability of aeolian sand transport. It has been proven that unsteady sand/dust transport is closely related with boundary layer turbulence and affects significantly the determination of threshold condition and the prediction of aeolian transport rate. The researches of experiment, theory analysis and numerical simulation on unsteady sand/dust transport in recent two decades are reviewed. Finally, open questions and future developments are suggested.     

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.     

An upscaling method and a numerical analysis of swelling/shrinking processes in a compacted bentonite/sand mixture

This paper presents an upscaling concept of swelling/shrinking processes of a compacted bentonite/sand mixture, which also applies to swelling of porous media in general. A constitutive approach for highly compacted bentonite/sand mixture is developed accordingly. The concept is based on the diffuse double layer theory and connects microstructural properties of the bentonite as well as chemical properties of the pore fluid with swelling potential. Main factors influencing the swelling potential of bentonite, i.e. variation of water content, dry density, chemical composition of pore fluid, as well as the microstructures and the amount of swelling minerals are taken into account. According to the proposed model, porosity is divided into interparticle and interlayer porosity. Swelling is the potential of interlayer porosity increase, which reveals itself as volume change in the case of free expansion, or turns to be swelling pressure in the case of constrained swelling. The constitutive equations for swelling/shrinking are implemented in the software GeoSys/RockFlow as a new chemo‐hydro‐mechanical model, which is able to simulate isothermal multiphase flow in bentonite. Details of the mathematical and numerical multiphase flow formulations, as well as the code implementation are described. The proposed model is verified using experimental data of tests on a highly compacted bentonite/sand mixture. Comparison of the 1D modelling results with the experimental data evidences the capability of the proposed model to satisfactorily predict free swelling of the material under investigation. Copyright © 2004 John Wiley & Sons, Ltd.     

用转换函数研究珠峰站地壳结构

[STBZ][ZW（*][HT6H]〓收稿日期：；修回日期：. *基金项目：[HT6SS][ZK（]国家重点基础研究发展计划项目“青藏高原形成对全球变化的响应与适应对策”（编号：2005CB422001）；中国科学院知识创新工程重要方向项目“青藏高原内陆俯冲与造山作用”（编号：KZCX3 SW 143）资助.[ZK）] [HT6H]〓作者简介：[HT6SS]（1983 ），男，海南儋州人，硕士研究生，主要从事地震波传播理论研究.[WT6HZ]E mail:[WT6BZ]youliangsu@yahoo.com.cn[ZW）] [HT4F][HT5K]（）[JZ）] [HT5H][GK2] 摘〓要：[HT5K]为开展高喜马拉雅地区地质构造—气候反馈作用的研究，中国科学院青藏高原研究所于2004年开始在珠峰地区建立了综合观测研究站，并于2004年下半年开始相继开展了大气边界层（含辐射和土壤观测）、大气湍流和辐射系统、风温廓线、无线电探空系统、沙尘暴观测、冰川变化等大气科学观测研究、地表过程的环境研究和地球动力学研究。为了解珠峰站下方的地质构造，于2005年8月在综合观测研究站布设了宽频带地震仪（记录器为Reftek130，摆为STS2），并于2006年5月取得首批数据。利用宽频带地震仪提供的三分量地震波形记录，应用转换函数及快速模拟退火算法对珠峰站下的地壳横波速度结构进行了反演。反演结果表明，珠峰站的莫霍（Moho）面深度在70 km，地壳结构复杂，尤其在中上地壳，明显呈高低速互层结构，反映了板块边界处构造活动、物质交换活跃，表明这些地区还未达到均衡。为高喜马拉雅地区地质构造—气候反馈作用的研究提供地球物理依据。     

Field measurements of the flux and speed of wind-blown sand

A field experiment was conducted to measure the flux and speed of wind-blown sand under known conditions in a natural setting. The experiment, run at Pismo Beach, California, involved a tract 100 m long (parallel with the wind) by 20 m wide. The site was instrumented with four arrays of anemometers to obtain wind velocity profiles through the lower atmospheric boundary-layer, temperature probes to determine atmospheric stability and wind vanes to determine wind direction. From these measurements, wind friction speeds were derived for each experimental run. In order to measure sand saltation flux, a trench 3 m long by 10 m wide (transverse to the wind direction) by 0·5 m deep was placed at the downwind end of the tract and lined with 168 collector bins, forming an ‘egg-box’ pattern. The mass of particles collected in each bin was determined for four experimental runs. In order to assess various sand-trap systems used in previous experiments, 12 Leatherman traps, one Fryberger trap and one array of Ames traps were deployed to collect particles concurrently with the trench collection. Particle velocities were determined from analysis of high-speed (3000 and 5000 frames per second) motion pictures and from a particle velocimeter. Sand samples were collected from the trench bins and the various sand traps and grain size distributions were determined. Fluxes for each run were calculated using various previously published expressions, and then compared with the flux derived from the trench collection. Results show that Bagnold's (1941) model and White's (1979) equation most closely agree with values derived from the trench. Comparison of the various collector systems shows that the Leatherman and Ames traps most closely agree with the flux derived from the trench, although these systems tended to under-collect particles. Particle speeds were measured from analysis of motion pictures for saltating particles in ascending and descending parts of their trajectories. Results show that particle velocities from the velocimeter are in the range 0·5–7·0 m s^?1, compared to a wind friction velocity of 0·32–0·43 m s^?1 and a wind velocity of 2·7–3·9 m s^?1 at the height of the particle measurements. Descending particles tended to exceed the speeds of ascending particles by ～ 0·5 m s^?1.