A discrete element approach to elastic properties of layered geomaterials

Discrete element methods (DEMs) are used for layered geomaterials to investigate the dependency of traditional engineering constants on material properties and loading conditions. Shear deformations and compression tests parallel and perpendicular to layering are conducted on samples of varying kerogen volume fractions, confining pressures, porosities, and layer geometries. The goal of this article is to develop a method to better characterize oil shale (a transversely isotropic layered geomaterial) while eliminating high experimental costs. The DEM simulations conducted in this study demonstrate strong dependencies of Young's modulus, Poisson's ratio, and shear modulus on kerogen volume fraction and porosity. Furthermore, a rule of thumb for layer thickness and particle resolution is proposed for simulation design. Results agree well with robust effective medium theories, solidify the ability of DEM to model the mechanical properties of layered heterogenous materials, and encourage the use of DEM to study more complicated layered media and material failure. Copyright © 2011 John Wiley & Sons, Ltd.     

Discrete element modeling of tool‐rock interaction I: rock cutting

Tool‐rock interaction processes can be classified as indentation or cutting depending on the direction of motion of the tool with respect to the rock surface. The modes of failure induced in the rock by an indenting or a cutting tool can be ductile and/or brittle. The ductile mode is associated with the development of a damage zone, whereas the brittle mode involves the growth of macrocracks. This is the first part of a series of two papers concerned with an analysis of the cutting and the indentation processes based on using the discrete element method. In this paper, numerical simulations of the cutting process are conducted to reproduce the transition from a ductile to a brittle failure mode with increasing depth of cut, which is observed in experiments. The numerical results provide evidence that the critical depth of cut d _* controlling the failure mode transition is related to the characteristic length ? = (K_Ic ∕ σ_c)² with K_Ic denoting the material toughness and σ_c its unconfined compressive strength. The nature of frictional contact between the cutter face and the rock in the ductile failure mode is also examined. It is shown that the inclination of the total cutting force is controlled by a multi‐directional flow mechanism ahead of the cutter that is related to the formation of a wedge of failed material, intermittently adhering to the cutter. As a result, the inclination of the total cutting force varies with the rake angle of the cutter and cannot be considered an intrinsic measure of the interfacial friction between the cutter and the rock. Copyright © 2012 John Wiley & Sons, Ltd.     

离散滑模控制在位置随动系统中的应用

根据改进的离散趋近律设计了位置随动系统的滑模变结构控制算法,仿真结果表明:该算法不仅实现了系统对位置信号的跟踪,还克服了常规离散趋近律参数选择不当出现的抖振现象,是一种具有应用价值的非线性控制方法。     

Stream flow forecasting using neuro‐wavelet technique

This paper proposes the application of a neuro‐wavelet technique for modelling monthly stream flows. The neuro‐wavelet model is improved by combining two methods, discrete wavelet transform and multi‐layer perceptron, for one‐month‐ahead stream flow forecasting and results are compared with those of the single multi‐layer perceptron (MLP), multi‐linear regression (MLR) and auto‐regressive (AR) models. Monthly flow data from two stations, Gerdelli Station on Canakdere River and Isakoy Station on Goksudere River, in the Eastern Black Sea region of Turkey are used in the study. The comparison results revealed that the suggested model could increase the forecast accuracy and perform better than the MLP, MLR and AR models. Copyright © 2008 John Wiley & Sons, Ltd.     

Analysis of soil‐structural interface behavior using three‐dimensional DEM simulations

The shear behavior at the interface between the soil and a structure is investigated at the macroscale and particle‐scale levels using a 3‐dimensional discrete element method (DEM). The macroscopic mechanical properties and microscopic quantities affected by the normalized interface roughness and the loading parameters are analyzed. The macro‐response shows that the shear strength of the interface increases as the normalized roughness of the interface increases, and stress softening and dilatancy of the soil material are observed in the tests that feature rough interfaces. The particle‐scale analysis illustrates that a localized band characterized by intense shear deformation emerges from the contact plane and gradually expands as shearing progresses before stabilizing at the residual stress state. The thickness of the localized band is affected by the normalized roughness of the interface and the normal stress, which ranges between 4 and 5 times that of the median grain diameter. A thicker localized band is formed when the soil has a rough shearing interface. After the localized band appears, the granular material structuralizes into 2 regions: the interface zone and the upper zone. The mechanical behavior in the interface zone is representative of the interface according to the local average stress analysis. Certain microscopic quantities in the interface zone are analyzed, including the coordination number and the material fabric. Shear at the interface creates an anisotropic material fabric and leads to the rotation of the major principal stress.     

An extended Greenwood‐Williamson modelbased normal interaction law for discrete element modelling of spherical particles with surface roughness

The current work aims to develop an improved random normal interaction law based on an extended Greenwood‐Williamson (GW) model for spherical particles with surface roughness in the discrete element modelling of particle systems. The extended GW model overcomes some theoretical defects of the classic GW model when incorporated into the discrete element framework. Based on 2 nondimensional forms in which only 2 surface roughness parameters are involved, an empirical formula of the improved interaction law is derived by the curve‐fitting technique. The resulting interaction law is incorporated into discrete element modelling to investigate the mechanical response of particle systems with different surface roughness. Numerical simulations are performed to model 1‐dimensional and 3‐dimensional compression tests to explore the macro and micro characteristics of granular particles with surface roughness. The results show that surface roughness makes the initial packing of a particle assembly looser and has a greater influence on looser packed samples as expected, but an assembly with moderate roughness may exhibit a higher strength. The limitations of the current development are also highlighted.     

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.     

基于离散元法对边坡二维极限平衡法的探讨

边坡稳定性分析的极限平衡法是要做一定假设的。本文考虑了离散元与极限平衡法基于刚体理论的相似性,用离散元法计算出极限平衡法中的各个计算分量值,然后代入到常用极限平衡法中分析计算,根据离散元法的计算结果讨论了各极限平衡法中各种假设的合理性,为极限平衡法的计算提供了一个新思路。结果表明Bishop法与离散元法的计算结果比较接近,是本文经过离散元法计算后所推荐使用的方法。     

基于平行黏结模型的水-岩作用下砂岩蠕变模拟及损伤机制研究

为探明库水位周期性升降作用下消落带岩体蠕变损伤机制,基于PFC中的平行黏结模型(parallel bond model, PBM),考虑水-岩作用对黏结的弱化和材料特性随时间的变化,提出水-岩作用下砂岩蠕变的离散元模拟方法,并在室内试验基础上开展水-岩作用下砂岩蠕变模拟。研究结果表明：在破坏应力水平下,试样微裂纹扩展与蠕变应变规律相似,可分为衰减扩展阶段、稳定扩展阶段、加速扩展阶段,且随水-岩作用周期增加,加速扩展阶段的耗时占总耗时的比例增大;试样蠕变破坏时,随水-岩作用周期增加,剪切裂纹占比逐渐增加,微裂纹倾角分布逐渐分散,倾角分布在65°和115°附近的微裂纹逐渐增加,试样的张性破坏减弱,剪性破坏增强;水-岩作用下,试样能储存的最大胶结能不断降低,且储存相同胶结能时对应的应变不断增大,与实际岸坡在水-岩作用下岩体整体承载能力降低、变形增大的规律一致。提出的水-岩作用下砂岩蠕变模拟方法具有较好的可行性,为库岸边坡岩石在库水位升降影响下的模型研究提供理论基础。