Prediction of uniaxial compression PFC3D model micro‐properties using artificial neural networks

Artificial neural networks are used to predict the micro‐properties of particle flow code in three dimensions (PFC3D) models needed to reproduce macro‐properties of cylindrical rock samples in uniaxial compression tests. Data for the training and verification of the networks were obtained by running a large number of PFC3D models and observing the resulting macro‐properties. Four artificial networks based on two different architectures were used. The networks used different numbers of input parameters to predict the micro‐properties. Multi‐layer perceptron networks using Young's modulus, Poisson's ratio, uniaxial compressive strength, model particle resolution and the maximum‐to‐minimum particle ratio showed excellent performance in both training and verification. Adding one more variable—namely, minimum particle radius—showed degrading performance. Copyright © 2009 John Wiley & Sons, Ltd.     

Damage–viscoplastic consistency model with a parabolic cap for rocks with brittle and ductile behavior under low‐velocity impact loading

This paper presents a damage–viscoplastic cap model for rocks with brittle and ductile behavior under low‐velocity impact loading, which occurs, e.g. in percussive drilling. The model is based on a combination of the recent viscoplastic consistency model by Wang and the isotropic damage concept. This approach does not suffer from ill posedness—caused by strain softening—of the underlying boundary/initial‐value problem since viscoplasticity provides a regularization under dynamic loading by introducing an internal length scale. The model uses the Drucker–Prager (DP) yield function with the modified Rankine criterion as a tension cut‐off and a parabolic cap surface as a compression cut‐off. The parabolic cap is smoothly fitted to the DP cone. The strain softening law in compression is calibrated with the degradation index concept of Fang and Harrison. Thereby, the model is able to capture the brittle‐to‐ductile transition and hardening behavior of geomaterials under highly confined compression, which is the prevailing stress state under a bit‐button in percussive drilling. Rock strength heterogeneity is characterized statistically at the structural level using the Weibull distribution. An explicit time integrator is chosen for solving the FE‐discretized equations of motion. The contact constraints due to the impact of an indenter are imposed with the forward increment Lagrange multiplier method that is compatible with explicit time integrators. The model is tested at the material point level with various uniaxial and triaxial tests. At the structural level confined compression, uniaxial tension tests and a rock sample under low‐velocity impact are simulated. Copyright © 2009 John Wiley & Sons, Ltd.     

Influence of liquid bridges on the mechanical behaviour of polydisperse granular materials

We investigate a polydisperse granular material in which the particle interactions are governed by a capillary force law. The cohesion force for a grain‐pair with unequal diameters is expressed as an explicit function of the inter‐particle distance and the volume of the liquid bridge. This analytical relation is validated by experiments on a reference material. Then, it is completed by a rupture criterion and cast in the form of a force law that accounts for solid contact, capillary force and rupture characteristics of a grain‐pair. Finally, in order to evaluate the influence of capillary cohesion on the macroscopic behaviour, radial and axial compression tests on cylindrical assemblies of wet particles are simulated using a 3D distinct element method. Copyright © 2005 John Wiley & Sons, Ltd.     

Strength anisotropy of granular material consisting of perfectly round particles

The strength anisotropy of granular materials deposited under gravity has mostly been attributed to elongated particles' tendency to align long axes along the bedding plane direction. However, recent experiments on near‐spherical glass beads, for which preferred particle alignment is inapplicable, have exhibited surprisingly strong strength anisotropy. This study tests the hypothesis that certain amount of fabric anisotropy caused by the anisotropic stress during deposition under gravity can be locked in a circular‐particle deposit. Such locked‐in fabric anisotropy can withstand isotropic consolidation and leads to significant strength anisotropy. 2D discrete element method simulations of direct shear tests on circular‐particle deposits are conducted in this study, allowing for the monitoring of both stress and fabric. Simulations on both monodispersed and polydispersed circular‐particle samples generated under downward gravitational acceleration exhibit clear anisotropy in shear strength, thereby proving the hypothesis. When using contact normal‐based and void‐based fabric tensors to quantify fabric anisotropy in the material, we find that the intensity of anisotropy is discernible but low prior to shearing and is dependent on the consolidation process and the dispersity of the sample. The fact that samples with very low anisotropy intensity measurements still exhibit fairly strong strength anisotropy suggests that current typical contact normal‐based and void‐based second‐order fabric tensor formulations may not be very effective in reflecting the anisotropic peak shear strength of granular materials. Copyright © 2017 John Wiley & Sons, Ltd.     

Cavity expansion analyses of crushable granular materials with state‐dependent dilatancy

Crushability is one of the important behaviors of granular materials particularly under high stress states, and affects both the deformability and strength of the materials that are in essence associated with state‐dependent dilatancy. In this presentation, first, a new critical state model is proposed to take into account the three different modes of compressive deformation of crushable granular materials, i.e. particle rearrangement, particle crushing and pseudo‐elastic deformation. Second, the governing equations for cavity expansion in crushable granulates are introduced, in which the state‐dependent dilatancy as well as the bounding surface plasticity model are used. Then, the procedure to obtain semi‐analytical solutions to cavity expansion in the material is described in detail, in which a commercial differential equation solver is employed. Finally, cavity expansion analyses are carried out on Toyoura sand, a well‐documented granular material, to demonstrate the effects of crushability and state‐dependent dilatancy. The study shows that particle crushing does occur at both high stress and critical states and affects the stress fields and the deformation behavior of the material surrounding the cavity in association with state‐dependent dilatancy. This leads to conclusion that particle crushing and state‐dependent dilatancy have to be taken into account when cavity expansion theory is used to interpret cone penetration tests and pressuremeter tests. Copyright © 2011 John Wiley & Sons, Ltd.     

A bond failure criterion for DEM simulations of cemented geomaterials considering variable bond thickness

A series of micromechanical tests were conducted to investigate the bond failure criterion of bonded granules considering the effect of bond thickness, with the aim of enhancing the bond contact model used in the distinct element simulations of cemented geomaterials. The granules were idealized in a two‐dimensional context as one pair of aluminum rods bonded by resin epoxy or cement. The mechanical responses of nearly 500 rod pairs were tested under different loading paths to attain the yield loads of bonded granules at variable bond thickness. This study leads to a generic bond failure criterion incorporating the effect of the bond thickness. The results show that the bond compressive resistance largely decreases with increasing bond thickness owing to the presence of the confinement at the bond‐particle interface. The strength envelopes obtained from the combined shear compression tests and combined torsion compression tests have identical functional form, and they decrease in size with increasing bond thickness but remain unchanged in shape. Given the same cementation material, the generic bond strength envelope in a three‐dimensional contact force space under different loading paths remains the same in shape but shrinks with the increase of bond thickness. Copyright © 2014 John Wiley & Sons, Ltd.     

Thermodynamic‐based model for coupling temperature‐dependent viscoelastic,viscoplastic, and viscodamage constitutive behavior of asphalt mixtures

Based on the continuum damage mechanics, a general and comprehensive thermodynamic‐based framework for coupling the temperature‐dependent viscoelastic, viscoplastic, and viscodamage behaviors of bituminous materials is presented. This general framework derives systematically Schapery‐type nonlinear viscoelasticity, Perzyna‐type viscoplasticity, and a viscodamage model analogous to the Perzyna‐type viscoplasticity. The resulting constitutive equations are implemented in the well‐known finite element code Abaqus via the user material subroutine UMAT. A systematic procedure for identifying the model parameters is discussed. Finally, the model is validated by comparing the model predictions with a comprehensive set of experimental data on hot mix asphalt that include creep‐recovery, creep, uniaxial constant strain rate, and repeated creep‐recovery tests in both tension and compression over a range of temperatures, stress levels, and strain rates. Comparisons between model predictions and experimental measurements show that the presented constitutive model is capable of predicting the nonlinear behavior of asphaltic mixes under different loading conditions. Copyright © 2011 John Wiley & Sons, Ltd.     

Effects of Microparameters on Macroparameters of Flat-Jointed Bonded-Particle Materials and Suggestions on Trial-and-Error Method

The aims of this paper are to analyze the effects of microparameters on macroparameters of flat-jointed bonded-particle materials of particle flow code in two dimensions (PFC2D) and improve the efficiency of trial-and-error method in calibration of microparameters. The trial-and-error method is always used to calibrate the microparameters for a PFC2D model, but it is time-consuming and empirical. To improve the efficiency of the trial-and-error method, the effects of microparameters on macroparameters need to be analyzed. By using the trial-and-error method, a desirable set of microparameters for a uniaxial compression PFC2D model (with a flat-joint contact model as the contact model) of limestone were calibrated to match the macroscopic properties obtained from laboratory tests. Based on the calibration set of microparameters, effects of microparameters on macroparameters of the PFC2D model were studied by the orthogonal design method. On this basis, a flowchart of calibrating microparameters via trial-and-error method was proposed. This flowchart was used to calibrate the microparameters of granite. The macroparameters and failure characteristics determined from numerical simulation were very similar to those of laboratory tests, confirming the effectiveness of the proposed flowchart.     

冻土旁压试验与单轴试验对比

为了认识冻土旁压试验结果与常规试验结果之间的关系,在室内分别开展了冻结重塑黏土的旁压试验和单轴压缩试验,并对试验结果进行了对比分析。结果表明,在各级荷载作用下旁压曲线一般都呈现应变速率衰减的趋势,而单轴曲线在冻土破坏时会出现渐进流动阶段。旁压试验的应力-应变曲线呈现应变硬化型,而且出现初始拟弹性阶段;而单轴试验的应力-应变曲线则属于应变软化型,并在轴向应变大约为10%时达到剪应力峰值。温度相同时,旁压试验的剪切强度以及初始弹性模量都要大于单轴试验,且温度越低差值越大。     

Homogenization of anisotropic elastoplastic behaviors of a porous polycrystal with interface effects

This paper is devoted to develop a theoretical framework to predict the macroscopic transversely isotropic elastoplastic behavior of clay‐like material, which is viewed as a porous polycrystal. We consider evolutions of two local plastic mechanisms of grains and interface simultaneously, for which a Schmid criterion is used for the strength of sheet‐like grains and a Tresca criterion for the strength of interfaces between particles. By adapting the standard incremental method, we propose firstly a classic self‐consistent model, which does not consider the effect of interface, then a generalized self‐consistent model in which the solid phase is represented by laminated (or isotropic) spherical grains surrounded by interfaces. Comparisons of numerical predictions between these two methods are performed and have demonstrated the validity of the generalized self‐consistent model taking account of interface effects. Numerical simulations of uniaxial compression tests have shown that the macroscopic elastoplastic behavior of polycrystalline (clay‐like) material can be successfully predicted by the way of considering the two local plastic mechanisms at microscopic scale. Copyright © 2013 John Wiley & Sons, Ltd.     

Characterization of clastic rock using a biconcave bond model of DEM

This paper presents a biconcave bond model to investigate the effect of the cementation between grains on the mechanical behavior of rock. The proposed model considers the shape of the bonds among particles that have a biconcave cement form, based on observations of microscopic rock images. The general equations of the proposed model are based on Dvorkin theory. The accuracy and efficiency of the bond model is improved in three ways. After the biconcave bond model is implemented in the discrete element method software Particle Flow Code in 2 Dimensions, a series of numerical uniaxial compression tests were performed to investigate the relationships between the micro‐ to macro‐parameters. The simulations revealed that the biconcave bond model reflects the effect of micro‐parameters, such as the elastic modulus and Poisson's ratio of the cement, on the macroscopic deformation of cemented granular material. Variations in the bond geometry caused extremely diverse macro‐mechanical behaviors. Experimental results concerning rock demonstrate that the biconcave bond model accurately captures the mechanical behavior of intact rock and supports an innovative method for investigating the relationships between the micro‐ and macro‐parameters of cemented granular material. Copyright © 2016 John Wiley & Sons, Ltd.     

Experimental study and constitutive modelling of elasto‐plastic damage in heat‐treated mortar

This study investigates the effect of a heat‐treatment upon the thermo‐mechanical behaviour of a model cement‐based material, i.e. a normalized mortar, with a (w/c) ratio of 0.5. First, a whole set of varied experimental results is provided, in order to either identify or validate a thermo‐mechanical constitutive model, presented in the second paper part. Experimental responses of both hydraulic and mechanical behaviour are given after different heating/cooling cycling levels (105, 200, 300, 400^°C). The reference state, used for comparison purposes, is taken after mass stabilization at 60^°C. Typical uniaxial compression tests are provided, and original triaxial deviatoric compressive test responses are also given. Hydraulic behaviour is identified simultaneously to triaxial deviatoric compressive loading through gas permeability K_gas assessment. K_gas is well correlated with volumetric strain evolution: gas permeability increases hugely when ε_v testifies of a dilatant material behaviour, instead of contractile from the test start. Finally, the thermo‐mechanical model, based on a thermodynamics approach, is identified using the experimental results on uniaxial and triaxial deviatoric compression. It is also positively validated at residual state for triaxial deviatoric compression, but also by using a different stress path in lateral extension, which is at the origin of noticeable plasticity. Copyright © 2009 John Wiley & Sons, Ltd.     

球模仪测试冻土松弛模量的非线性Kelvin解答及其试验研究

冻土的松弛模量是进行蠕变力学分析的关键参数。但在理论方面, 尚未基于球模仪试验建立较完善的松弛模量表征公式。基于半空间黏弹性理论和分数阶微积分理论, 获得了松弛模量公式的非线性Kelvin模型解答并进行了材料参数影响分析。在给出恒载条件下, 可以用单轴蠕变试验的分析结果评估基于球形压痕试验的冻土松弛模量来预测准确性。随后分别以冻结细砂的球模仪试验曲线、 冻结砂和冻结砂质黏土的单轴蠕变曲线为例, 预测了各条试验曲线和冻土的松弛模量, 并通过其他试验实测数据进行了检验。结果表明： 该松弛模量表征公式的材料参数最少, 随各材料参数变化具有较佳单调性; 基于球形模板试验, 非线性Kelvin解答能对冻结细砂的松弛模量和位移曲线做出合理可靠的预测。非线性Kelvin模型能很好地吻合单轴蠕变试验曲线, 基于单轴蠕变试验的冻结砂松弛模量随时间变化规律和数值范围与球模仪试验分析结果较一致, 冻结砂质黏土的松弛模量随应力和温度的变化规律再现了已有研究结论。     

一种有限元转化为颗粒离散元的方法及其应用研究

为了充分发挥有限元与颗粒离散元各自的优势,提出了一种由有限元转化为颗粒流的方法。数值模型首先用较粗的有限元网格进行离散,并在单元上引入连续介质本构模型。力学计算开始后,实时跟踪各单元的应力状态。一旦某单元的应力满足Mohr-Coulomb准则或最大拉应力准则,删除该单元,同时创建具有一定数目、随机分布且微嵌入的颗粒簇。其后,该单元所在区域的非连续变形及失稳断裂由颗粒簇演化获得。各颗粒的质量、材料参数、速度、位移、接触力等信息根据插值从有限元单元中继承。为了实现有限元与颗粒流接触面的耦合计算,引入了点-棱（二维）及点-面（三维）接触模型,通过法向及切向弹簧实现接触力的计算。颗粒球与有限元板的碰撞分析、单轴压缩、岩石切割等案例展示了上述方法的精确性及合理性。     

Granite rock fragmentation at percussive drilling – experimental and numerical investigation

The aim of this study is to numerically model the fracture system at percussive drilling. Because of the complex behavior of rock materials, a continuum approach is employed relying upon a plasticity model with yield surface locus as a quadratic function of the mean pressure in the principal stress space coupled with an anisotropic damage model. In particular, Bohus granite rock is investigated, and the material parameters are defined based on previous experiments. This includes different tests such as direct tension and compression, three‐point bending, and quasi‐oedometric tests to investigate the material behavior at both tension and confined compression stress states. The equation of motion is discretized using a finite element approach, and the explicit time integration method is employed. Edge‐on impact tests are performed, and the results are used to validate the numerical model. The percussive drilling problem is then modeled in 3D, and the bit‐rock interaction is considered using contact mechanics. The fracture mechanism in the rock and the bit penetration‐ resisting force response are realistically captured by the numerical model. Copyright © 2013 John Wiley & Sons, Ltd.     

弱化节理剪切力学特征的颗粒流模拟研究

在黏结颗粒模型中引入强度弱化因子生成弱化介质材料,进行弱化模型试件的单轴抗压强度试验。结果表明,弱化作用在降低试件单轴抗压强度的同时,还将导致试件弹性模量逐步下降。这一结果符合相关室内试验的研究成果。为进一步对岩石强度弱化模拟方法进行效果检验,利用颗粒流程序内置的FISH语言建立弱化岩石节理直剪试验模型,进行不同法向应力条件下弱化岩石节理的直剪试验。结果表明：弱化节理模型试件表现出类似于真实节理的一系列宏观剪切力学特征;不同壁面弱化程度条件下,节理模型试件的抗剪强度及剪切峰值膨胀角的试验结果与法向应力的依存关系均符合经典的JRC-JCS模型。由此表明,所采用的岩石强度弱化模拟方法可以较好地再现岩石介质的强度弱化效应。通过模型试件内微裂纹发展演化特征的研究表明,壁面弱化作用可导致试件内裂纹发育数目的快速增长、微裂纹分布范围的迅速扩大,以及剪切裂纹发育比例的迅速提高,由此从细观角度揭示了弱化节理面更易于产生宏观剪切破坏的原因。研究成果可以为弱化岩石节理的抗剪强度及大型岩质边坡的稳定性研究提供参考。     

Numerical modelling of railway ballast at the particle scale

The paper describes the development of a technique to simulate triaxial tests on specimens of railway ballast numerically at the particle scale and its validation with reference to physical test data. The ballast particles were modelled using potential particles and the well‐known discrete element method. The shapes of these elemental particles, the particle size distribution and the number of particles (N = 2800) in each numerical triaxial specimen all matched closely to the real ballast material being modelled. Confining pressures were applied to the specimen via a dynamic triangulation of the outer particle centroids. A parametric study was carried out to investigate the effects on the simulation of timestep, strain rate, damping, contact stiffness and inter‐particle friction. Finally, a set of parameters was selected that provided the best fit to experimental triaxial data, with very close agreement of mobilized friction and volumetric strain behaviour. Copyright © 2015 John Wiley & Sons, Ltd.     

Characterisation of confinement effect on jointed rock pillars using a Synthetic Rock Mass approach

Confinement effect on jointed rock pillars is numerically characterised in this research using a Synthetic Rock Mass (SRM) approach. The SRM is an integrated model incorporating a discrete fracture network within a Particle Flow Code 3D particle assembly. In this paper, the confinement effect on a 3D jointed pillar SRM model is investigated in a series of simulations, including biaxial compression tests and true and conventional triaxial compression tests. The numerical results suggest that the applied confining stresses generally result in higher pillar strengths and ductile post‐peak responses. More brittle post‐peak behaviour is simulated in the biaxial and true triaxial tests when the pillar is confined by a high stress in one lateral direction and by a zero/low stress in the other lateral direction. This phenomenon is attributed to significant lateral pillar dilation in the less confined direction. Detailed pillar failure modes are monitored in the uniaxial and triaxial tests. Axial splitting fractures and long shear zones cutting through the pillar are simulated when the pillar is able to dilate in the direction of least confinement. Localised shearing along joints and failed rock blocks is the dominant failure mode when the pillar dilation is resisted by the applied confining stresses. The pillar remains relatively intact with limited cracking in the pillar core in the highly confined triaxial tests. Copyright © 2016 John Wiley & Sons, Ltd.     

Critical contact stiffness concept and simulation of crack generation in particle models of large length-scales

When the particle simulation method is used to simulate large length-scale problems, such as crustal length-scale problems in the field of geology, it is necessary to include gravity effect into the particle model. To consider gravity effect appropriately, there is a minimum value requirement for the contact stiffness of a particle so that unexpected particle overlap can be avoided. This minimum value is called the critical contact stiffness of a particle due to gravity effect. Using the vertical force equilibrium condition of a particle at the bottom of a two-dimensional particle model, a theoretical formula has been successfully derived for determining the critical contact stiffness of the particle in this paper. For the two-dimensional particle model consisting of circular particles of unit thickness, there is a relationship between the critical contact stiffness of a particle and the critical elastic modulus of the particle material when a linear-elastic-contact model between any two particles is used. Since the elastic moduli of most crustal rocks are greater than the corresponding critical elastic modulus of the particle material, it has been theoretically demonstrated that the particle simulation method, which is based on the linear-elastic-contact model between any two particles, is suitable for simulating gravity effect within the particle model of a large length-scale. The related simulation results have demonstrated the usefulness of the particle simulation method for simulating spontaneous crack generation patterns within brittle crustal rocks.     

A constitutive model for rock accounting for viscosity and yield stress degradation

A viscoplastic constitutive model of rock is proposed for which both yield stress and viscosity undergo variation during the deformation process. The model is initially formulated for a uniaxial stress state; its extension for a general stress state is also provided. Model parameters are determined from compression tests at different values of strain rate, and its application to simulate results of such tests is given. The examples of stress redistribution in a coal seam due to progressing longwall exploitation are presented by applying the developed degradation model. The model provides good simulation of material response in both stable and post-critical stages.