Reducing the anisotropy of a Brazilian disc generated in a bonded-particle model

The Brazilian test is a widely used method for determining the tensile strength of rocks and for calibrating parameters in bondedparticle models（BPMs）. In previous studies, the Brazilian disc has typically been trimmed from a compacted rectangular specimen. The present study shows that different tensile strength values are obtained depending on the compressive loading direction. Several measures are proposed to reduce the anisotropy of the disc. The results reveal that the anisotropy of the disc is significantly influenced by the compactibility of the specimen from which it is trimmed. A new method is proposed in which the Brazilian disc is directly generated with a particle boundary, effectively reducing the anisotropy. The stiffness（particle and bond） and strength（bond） of the boundary are set at less than and greater than those of the disc assembly, respectively,which significantly decreases the stress concentration at the boundary contacts and prevents breakage of the boundary particle bonds. This leads to a significant reduction in the anisotropy of the disc and the discreteness of the tensile strength. This method is more suitable for carrying out a realistic Brazilian test for homogeneous rock-like material in the BPM.

A coarse-grained bonded particle model for large-scale rock simulation

For solving the computationally intensive problem encountered by the discrete element method(DEM)in simulating large-scale engineering problems,it is essential to establish a numerical model that can effectively simulate large-scale rocks.In this study,the coarse-graining effect of a linear-Mindlin with bonding model was studied in the unconfined compression strength(UCS)and Brazilian tensile strength(BTS)tests.We found that the main reason for the coarse-graining effect of the BTS tests is that the type I fracture toughness is positively correlated with the size of the particles.Based on the results analysis and fracture mechanics,the coarse-grained(CG)modeling theory was combined with a bonded particle model(BPM)for the first time and a coarse-grained bonded particle model(CG-BPM)was developed,which can be effectively used to model the tensile strength of large-scale rocks with different particle sizes.The excavation damage zone(EDZ)in an underground research laboratory(URL)was selected as an application case,which shows that the coarse-grained bonding model presented in this paper is more accurate and reliable than the traditional one in large-scale rock simulation,at least in the scenario where tensile failure is dominant.

Coupled hydro-thermo-mechanical modeling of hydraulic fracturing in quasi-brittle rocks using BPM-DEM

This paper presents an improved understanding of coupled hydro-thermo-mechanical(HTM) hydraulic fracturing of quasi-brittle rock using the bonded particle model(BPM) within the discrete element method(DEM). BPM has been recently extended by the authors to account for coupled convective econductive heat flow and transport, and to enable full hydro-thermal fluidesolid coupled modeling.The application of the work is on enhanced geothermal systems(EGSs), and hydraulic fracturing of hot dry rock(HDR) is studied in terms of the impact of temperature difference between rock and a flowing fracturing fluid. Micro-mechanical investigation of temperature and fracturing fluid effects on hydraulic fracturing damage in rocks is presented. It was found that fracture is shorter with pronounced secondary microcracking along the main fracture for the case when the convectiveeconductive thermal heat exchange is considered. First, the convection heat exchange during low-viscosity fluid infiltration in permeable rock around the wellbore causes significant rock cooling, where a finger-like fluid infiltration was observed. Second, fluid infiltration inhibits pressure rise during pumping and delays fracture initiation and propagation. Additionally, thermal damage occurs in the whole area around the wellbore due to rock cooling and cold fluid infiltration. The size of a damaged area around the wellbore increases with decreasing fluid dynamic viscosity. Fluid and rock compressibility ratio was found to have significant effect on the fracture propagation velocity.

正交-响应面法在PBM细观参数标定中的应用

数值模拟作为研究岩石力学特性、再现细观裂纹演化的主要途径,已受到大量关注。现有的数值模拟参数标定方法主要为试错法及正交试验法,但二者都未能充分考虑细观参数交互作用的影响,模拟精度欠佳且宏观破坏形态与室内试验存在较大差异。因此,采用正交-响应面法相结合的数值分析方法,首先通过正交试验筛选出具有显著影响的平行黏结模型(PBM)细观参数,其次应用响应面法(RSM)研究其交互作用对模型试样宏观参量的影响规律,最后结合岩石宏观破坏形态提出一套PBM参数标定流程。结果表明:有效模量E*与刚度比k n/k s对弹性模量E影响显著;k n/k s、接触摩擦系数μ、最小颗粒半径R_(min)对泊松比ν影响显著;黏聚力c与法向黏结强度σc及其交互作用对单轴抗压强度UCS影响显著,应用响应面法计算分析得出的细观参数的模拟值与试验值误差绝对值小于7%,且二者应力应变曲线力学特征相似,宏观破坏形态相同,证明所提出的PBM细观参数标定流程具备科学性和可靠性。

Stress Recovery Procedure for the Bonded Particle Model

In the simulation of discontinuous block systems,the discrete element method(DEM)has better computational efficiency and convergence than the finite element method(FEM).When several DEM particles are bonded together with parallel bonds(the bonded particle model,BPM),various shapes and block fractures can be simulated.The main aim of the BPM is to simulate a continuous material in which the stress distribution is continuous.Since the existing stress result for a single particle is an average value over the particle’s area,stress results do not exist in the area between particles.In this paper,the stress value for a single two-dimensional DEM particle is deduced.A stress recovery procedure with a linear stress function for a triangular element generated by the centroids of three bonded particles is proposed.In this way,the recovered stress field for the whole mesh composed of all triangular elements is continuous.A stress gradient exists in the whole mesh.This can also provide more accurate stress values for judging a fracture inside a block.Symmetrical and asymmetrical models are simulated by the BPM and FEM.Similar to the FEM results,the recovered stress results for the BPM can describe the stress distribution in the simulated continuous blocks.For the model with the theoretical stress solution,the recovered result and the theoretical solution coincide well.

基于离散元和全析因实验设计的BPM力学参数

为研究岩石微观力学参数与宏观力学性能之间关系并提高岩石破碎离散元仿真效率,从破碎原理出发,基于EDEM进行单轴压缩数值分析,研究摩擦系数、材料剪切模量、微观颗粒个数、平行键强度和刚度对岩石抗压强度和宏观刚度的影响.再通过全析因实验设计得到影响岩石力学性能关键的主效应和交互效应,并以此为变量运用回归方法对黏结颗粒模型(bonded particle model,简称BPM)的宏观力学参数进行预测并进行方差、拟合优度和残差分析.仿真及物理实验结果证明该预测模型可行,误差率小于10%.

矿石破碎颗粒黏结模型黏结键特征及表征

目的针对矿石颗粒黏结模型与实际矿石破碎特性存在差异造成的仿真不准确问题,重点对不同粒级矿石颗粒黏结模型中的黏结键特征进行研究。方法依据矿石强度尺寸效应理论,设计铜矿石颗粒黏结模型中基础颗粒间的黏结键参数,应用离散元方法对30,40,60 mm三种粒级铜矿石矿样进行落重试验和破碎仿真。本文给出黏结键等效临界变形的概念,讨论了矿石落重试验t10和冲击能量的关系,探讨黏结键参数变化规律。结果结果表明,三种粒级铜矿石颗粒黏结模型破碎仿真与落重试验粒级质量分数的平均误差分别为1.75%,1.66%,1.84%,试验和仿真得到的破碎粒度质量分数具有很好的一致性;法向和切向等效临界变形可以表征黏结键强度,单位冲击能量下落重试验的tn10可以表征矿石强度。结论利用黏结键等效临界变形和tn10的对应关系确定黏结键参数,提高了矿石颗粒黏结模型的建模效率和仿真精度。

离散元法在矿石破碎中的应用研究进展

离散元法(Discrete Element Method,DEM)是一种非连续介质力学数值计算方法,已被广泛应用于矿物加工破碎过程的研究,用于分析和求解离散系统中颗粒的运动规律、碰撞和破碎特性,为研究矿物的破碎机理、优化破碎设备的工作参数和机械结构提供了重要的理论研究手段。介绍了离散元法数值模拟技术中两种用于模拟矿物颗粒破碎的仿真模型:键合粒子模型(Bonded Particle Model,BPM)和颗粒替换模型(Particle Replacement Model,PRM),并对两种模型的基本原理、模型缺陷、优化进展及应用进行了概述,综述了利用DEM研究圆锥破碎机、颚式破碎机、冲击式破碎机、反击式破碎机等各类破碎设备在不同矿物特性、设备结构以及工作参数影响下的破碎性能表现的研究进展,讨论了DEM在碎矿研究领域存在的优势及局限性,并提出了基于DEM研究矿物破碎问题的发展方向。

Oblique impact breakage unification of nonspherical particles using discrete element method

Particle breakage commonly occurs during processing of particulate materials,but a mechanistic model of particle impact breakage is not fully established.This article presents oblique impact breakage characteristics of nonspherical particles using discrete element method(DEM)simulations.Three different particle shapes,i.e.spherical,cuboidal and cylindrical,are investigated.Constituent spheres are agglomerated with bridging bonds to model the breakage characteristics under impact conditions.The effect of agglomerate shapes on the breakage pattern,damage ratio,and fragment size distribution is fully investigated.By using a newly proposed oblique impact model,unified breakage master surfaces are theoretically constructed for all the particle shapes under oblique impact conditions.The developed approach can be applied to modelling particulate processes where nonspherical particles and oblique impact breakage are prevailing.

Heterogeneities of grain boundary contact for simulation of laboratoryscale mechanical behavior of granitic rocks

From a practical point of view,grain structure heterogeneities are key parameters that control the rock response and still remains a challenge to incorporate in a quantitative manner.One of the less discussed topics in the context of the grain-based model(GBM)in the particle flow code(PFC)is the contact heterogeneities and the appropriate contact model to mimic the grain boundary behavior.Generally,the smooth joint(SJ)model and linear parallel bond(LPB)model are used to simulate the grain boundary behavior.However,the literature does not document the suitability of different models for specific problems.Another challenge in implementing GBM in PFC is that only a single bonding parameter is used at the grain boundaries.The aim of this study is to investigate the responses of a laboratory-scale specimen with SJ and LPB models,considering grain boundary heterogeneous and homogeneous contact parameters.Uniaxial and biaxial compression tests are performed to calibrate the response of Creighton granite.The stressestrain curves,volumetric dilation,inter-crack(crack in the grain boundary),and intra-crack(crack within the grain)development,and failure patterns associated with different contact models are examined.It was found that both the SJ and LPB models can reproduce the pre-peak behavior observed for a granitic rock type.However,the LPB model is unable to reproduce the post-peak behavior.Due to the large interlocking effect originating from the balls in contact and the ball size in the LPB model,local dilation is induced at the grain boundaries.This overestimates the volumetric dilation and residual shear strength.The LPB model tends to result in discontinuous inter-cracks and stress localization in the rock specimen,resulting in fine fragments at the rock surface during failure.

基于EDEM的辊式破碎机的破碎性能分析

考虑到大型矿山机械设备的研发与优化需要建立在大量实验数据的基础上,但是实体研发不仅需要耗费大量人力物力,而且时效性低,利用EDEM仿真软件对辊式破碎机工作性能进行分析。首先使用三维建模软件建立齿辊式破碎机三维模型,导入EDEM软件中,在软件中设置运动部件运动参数;然后设置颗粒工厂,生成模拟物料,利用颗粒粘结模型(BPM)模拟破碎物料;最后运行仿真程序,进行物料破碎模拟,得到不同工况下的运行参数。仿真结果表明,齿辊转速度增加,产量和功率会随之增加,但是产量的增长趋势会随之减缓。随着齿辊间距的增加,产量会随之增加,但是产量的增长并不是线性的,增速会出现先减慢再增快的趋势,为辊式破碎机的参数优化和选型提供了参考。

构造煤的常规三轴试验仿真参数敏感度分析研究

目前,煤与瓦斯突出、冒顶等动力事故不间断发生,严重威胁煤矿安全生产,揭示动力灾害背后煤岩体力学损伤演化机制至关重要。利用离散元软件PFC^(3D),构建了以构造煤体为原型的颗粒流模型,通过改变模型的接触模量、刚度比、黏结强度比、内摩擦角、摩擦因数参数,对模型进行了常规三轴试验仿真参数敏感度分析。结果表明,接触模量对构造煤模型力学性能的影响主要体现在模型变形性能;刚度比对构造煤模型的强度和变形特性存在影响;黏结强度比对构造煤模型的最大抗压强度与峰值应变均有影响;内摩擦角对模型的损伤破坏形式存在影响;摩擦因数对构造煤模型影响体现在模型的强度与峰值应变。而后指导了参数标定过程,得出模拟结果与实验结果具有较好的一致性。研究结果为后续煤岩动力灾害机理的研究奠定了基础。

对辊破碎机对钨矿石的层压破碎特性研究

针对岩石破碎过程的复杂性以及传统仿真模型的局限性——反映替换颗粒群信息少且无法定位替换颗粒群中某一颗粒,使得所模拟的颗粒无法被连续破碎,导致仿真精度较低等问题,提出了通过离散元应用编程接口开发的改进破碎模型——多次替换的颗粒黏结模型(bonded particle model,BPM)。该方法能实现颗粒在破碎过程中的多次连续替换,更加贴近实际破碎过程,可提升仿真精度。基于对辊破碎机的三维模型与参数标定后的钨矿石颗粒群,对破碎机内的钨矿石颗粒群进行层压破碎可视化仿真分析,并结合室内试验研究了对辊破碎机的层压破碎特性,以验证数值仿真的有效性。结果表明:通过仿真得到的钨矿石颗粒受力与破碎速率的关系说明对辊破碎机可实现层压破碎;钨矿石碎后粒径分布误差为0.889~1.940 mm,且碎后粒径分布满足正态分布,说明仿真分析准确且有效。不同粒径配比下的钨矿石层压破碎试验结果表明,颗粒间相互作用力对破碎效率的影响程度大于颗粒低孔隙率。研究结果为进一步提高对辊破碎机的生产效率提供了依据,且所提出的改进破碎模型为物料的破碎研究提供了一种新方法。

考虑各向异性影响的冻土修正线性黏结接触模型开发及应用

针对冻土的各向异性特性,基于线性黏结接触模型,建立了能够反映冻土各向异性特性的修正线性黏结接触模型,并通过C++语言生成供颗粒流程序PFC^(3D)调用的离散元本构子程序DLL。首先对单一接触进行了拉伸、直接剪切测试,通过对比数值与理论结果,验证了考虑各向异性影响的冻土修正线性黏结接触模型的正确性。此外,模拟了不同温度条件下的冻土三轴压缩试验,并与试验得到的应力-应变曲线进行对比,结果表明,所提出的修正线性黏结接触模型对冻土具有较好的适用性。基于标定后的模型细观参数,开展了一系列的三轴压缩离散元数值模拟,利用模拟结果探讨了虚拟弱面法向倾角对冻土的应力-应变曲线特征、强度及抗剪强度指标的影响,并分析了有效配位数、细观组构量的演化规律。研究结果可为冻土各向异性宏-细观力学特性提供数值基础。

Microdamage study of granite under thermomechanical coupling based on the particle flow code

The thermomechanical coupling of rocks refers to the interaction between the mechanical and thermodynamic behaviors of rocks induced by temperature changes.The study of this coupling interaction is essential for understanding the mechanical and thermodynamic properties of the surrounding rocks in underground engineering.In this study,an improved temperature-dependent linear parallel bond model is introduced under the framework of a particle flow simulation.A series of numerical thermomechanical coupling tests are then conducted to calibrate the micro-parameters of the proposed model by considering the mechanical behavior of the rock under different thermomechanical loadings.Good agreement between the numerical results and experimental data are obtained,particularly in terms of the compression,tension,and elastic responses of granite.With this improved model,the thermodynamic response and underlying cracking behavior of a deep-buried tunnel under different thermal loading conditions are investigated and discussed in detail.

Study on disc cutter chipping of TBM based on field data and particle flow code simulation

Using tunnel boring machines to excavate high-strength intact rock masses is becoming more common.Due to the interactions between disc cutters and rocks,abnormal wear of disc cutters,especially cutter chipping,has become a common phenomenon.Existing research has mainly focused on normal wear of disc cutters without addressing abnormal wear cases.This study used the disc cutter consumption data of a tunnel project in China to investigate the abovementioned problem based on field research.According to the fail-ure patterns and fracture surface characteristics,the cutter chipping patterns were mainly categorized into four types:granule chipping,patch chipping,primary collapse,and secondary collapse.To further simulate the evolution of disc cutter chipping,based on the linear plastic bond model,a new contact model called the modified plastic bond(MPB)model was proposed to solve the metal simulation prob-lem in Particle Flow Code software.To this end,a set of uniaxial tensile and compressive tests were initially conducted to verify the applicability of the MPB model.Then,a series of three-dimensional rock-cutting simulation tests were conducted to reflect the evolu-tionary processes involved in each type of cutter chipping.The cutter chipping mechanism and morphological characteristics were clas-sified and summarized in detail.The results revealed that the cutting speed and penetration growth led to a rising trend in the probability and intensity of the cutter chipping.The presence of initial defects also induced an adverse effect on the service life of the cutter.The results indicated suitable working conditions for the cutter and suggested ways to control tunneling parameters and avoid frequent cutter chipping cases.

Effects of model size and particle size on the response of sea-ice samples created with a hexagonal-close-packing pattern in discrete-element method simulations

We investigated the effects of model size and particle size on the simulated macroscopic mechanical properties, uniaxial compressive strength, Young＇s modulus, and flexural strength of sea-ice samples, using the discrete-element method （DEM） with a bonded-particle model. Many different samples with a hexagonal-close-packing pattern and a unique particle size were considered, and several ratios of particle size to sample dimension （D/L） were studied for each sample. The macroscopic mechanical properties simulated by the DEM decrease monotonously with an increase in D/L. For different samples with different particle sizes, the macroscopic mechanical properties will be identical when D/L is constant. The quanti- tative relationships between macroscopic mechanical properties and ratio of particle size to sample size are important aspects in engineering applications of the DEM method. The results provide guidance on the choice of a particle size in the DEM simulation for numerical samples with a hexagonal-close-packing pattern.

基于颗粒离散元模型的花岗岩压缩试验模拟研究

基于颗粒流理论,以黄岛国家石油储备库地下洞库的花岗岩室内试验测试为背景,借助PFC2D(particle flow code)的黏结颗粒模型(bonded particle model,BPM)建立双轴压缩模型。以花岗岩室内试验的宏观力学参数和破坏形态为参照,通过"试错法"得出黏结颗粒模型相对应的细观物理力学性质参数。模拟试验的弹性模量、泊松比与室内试验值吻合较好,BPM模型由于选用圆形颗粒导致黏聚力和内摩擦角与室内试验值相比有一定偏差。模拟试验与室内试验的试件破坏形态均以单斜面剪切破坏为主。采用校准的细观物理力学性质参数,应用BPM模型再现花岗岩压缩试验全过程,深入分析微裂纹萌生演化及能量变化规律。研究表明,压缩过程中岩石试件内裂纹扩展主要经历平稳发展-急剧增加-平稳发展3个阶段;变形过程中,花岗岩试件边界能、应变能、黏结能、摩擦能及动能在各个阶段的变化很好地解释花岗岩受力破坏的细观力学机制。

大理岩脆-延-塑转换特性的细观模拟研究

针对锦屏深埋大理岩峰后变形破坏的脆-延-塑转换特性,采用颗粒流程序(PFC)中的簇单元模型(CPM)对其进行细观模拟研究。经过对室内试验结果的反复模拟校准,获得描述锦屏深埋大理岩力学性质的一组细观物理力学性质参数。模型试验结果表明:试样的一系列宏观力学表现,包括弹性模量、泊松比、单轴与启裂抗压强度、应力-应变曲线、峰值与残余强度包络线、拉压强度比以及破坏形态等均与锦屏深埋大理岩的试验结果具有良好的一致性。对不同围压下裂纹发育规律的研究表明:不同应力状态下细观裂纹发育特征的显著差异是导致大理岩的变形破坏出现脆-延-塑转换特性的主要原因;张性裂纹的大量发育决定介质的脆性破坏模式,而剪切裂纹数目的快速增长则促使介质由脆性破坏模式逐渐向延-塑性破坏模式转换。

等效岩体技术在岩体工程中的应用

以某露天矿边坡为工程背景,结合岩石力学参数室内和现场原位试验,基于颗粒流理论和PFC3D程序,运用等效岩体技术,建立充分反映节理分布特征并考虑细观破裂效应的等效岩体模型,采用Fish语言编制加卸载命令流,研究岩体的强度和力学效应。研究结果表明:(1)等效岩体在单轴压缩时,轴向应力–应变曲线分为弹性变形阶段、非稳定破裂塑性阶段和破裂后阶段,抗压强度和弹性模量与标准岩块试样相比,有较大幅度降低;(2)随围压增大,等效岩体抗压强度和残余强度明显提高,延性特征增强,逐渐向理想塑性过渡;(3)等效岩体技术能有效地描述岩体受节理分布影响而表现的各向异性特征;(4)等效岩体内部微裂纹主要沿节理走向分布并扩展,破坏形式受主导节理面产状及性质控制。