考虑损伤的平行黏结接触模型开发及其参数影响分析

为研究颗粒细观接触之间的损伤、断裂过程,基于离散元颗粒流程序(PFC^3D),在平行黏结模型的基础之上,引入拉伸损伤变量和剪切损伤变量表征颗粒黏结键的变形、强度及能量演化特征,根据最大应力准则确定黏结键损伤起始判据,通过C++语言编程对该接触模型进行二次开发。对单一黏结键进行拉伸、剪切、弯曲及扭转测试,对比理论计算结果,验证了考虑损伤的平行黏结接触模型的计算精度;建立三维细观离散元模型,模拟砂岩单轴压缩试验和花岗岩三轴试验,表明了该模型的适用性和准确性。在此研究基础之上,对考虑损伤的平行黏结模型进行参数影响分析,结果表明：损伤演化系数对应力-应变全曲线的弹性段范围、峰值应力以及达到峰值应力后的软化速率有显著影响;对比研究了应力-应变曲线在不同阶段黏结键损伤、裂隙萌发、扩展及贯通的演化过程;进一步研究了弹性应变能和耗散能的演化规律,引入了耗散能释放率参数,阐释了损伤演化系数越大应力-应变曲线达到峰值应力后下降速率越快的原因。     

脆性颗粒材料的动态多尺度模型研究

脆性颗粒材料的多尺度模型一般包含微观尺度的基本粒子、细观尺度的颗粒和宏观尺度的颗粒堆积体3个尺度。基于离散元方法（DEM）构建多尺度模型,并将该模型应用于动态加载。首先,对多尺度模型所涉及的两种接触模型和两种黏结模型的参数进行分析,详细讨论微细观模型参数与宏观材料常数之间的联系。然后,选用Hertz-Mindlin接触模型[1]和平行键黏结模型,建造石英砂的动态多尺度模型。通过选择合适的强度和局部阻尼参数发现,模型宏细观尺度上的动态压缩响应与对石英砂的相关试验结果吻合很好。利用多尺度模型和选定的参数,探讨与动态加载密切相关的局部阻尼机制对多尺度模型各个尺度上力学响应的影响。结果表明,阻尼越大则颗粒材料对波的衰减能力越强,但过高的阻尼会使团簇强度和模型的宏观压缩曲线都表现出异常的加载速度效应（后者实际是阻尼引起的微惯性效应）。另外,高阻尼会过度衰减颗粒破碎过程产生的应力波,从而阻碍颗粒破碎。最后,应用改进的动态多尺度模型,对脆性颗粒材料的动态破碎特性进行研究,发现该模型不但能给出与试验相吻合的颗粒级配曲线,还能揭示出颗粒破碎过程中微裂纹分布的空间不均匀性,即颗粒破碎过程中波的产生机制和衰减机制相互作用导致的微裂纹聚团分布的现象。     

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。     

岩石单轴压缩下能量与损伤演化规律研究

能量变化是材料各参数变化的本质特征。通过颗粒流模拟岩石单轴压缩试验,从细观力学角度分析能量转化、裂纹扩展及损伤演化规律。颗粒流利用细观颗粒的运动克服了宏观力学理论不易实现试件多裂纹破坏形态的缺点,以此研究能量变化更加合理。应力-应变各阶段能量与微裂纹及损伤存在着相互对应的发展关系。通过3种工况论证了宏-细观力学参数对应关系,采用最小二乘法拟合得出微裂纹与轴向应变呈幂次函数关系。采用割线模量定义损伤变量,取模量加速下降处（对应裂纹加速扩展）为损伤门槛,对应损伤阈值为0.158。3种工况下微裂纹数量与损伤呈线性发展关系,为损伤演化的深入研究提供参考。     

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。     

基于离散元法的砂土破碎演化规律研究

颗粒破碎是影响砂土宏-微观力学性质的重要因素。采用改进型的可破碎颗粒生成方法,通过设置不同强度的平行黏结键模拟不同强度的可破碎颗粒,并借用基于离散元方法（DEM）的双轴压缩试验详细研究了可破碎性土在剪切过程中颗粒破碎率/平均破碎程度、微观尺度上的能量耗散分配机制、剪切破碎带形成以及断裂键各向异性的演化过程。结果表明,颗粒破碎强烈地影响砂土在宏观尺度上的力学响应、颗粒尺度上的能量分配机制以及剪切过程中的颗粒的组织结构演化。颗粒破碎主要影响小应变阶段各能量耗散元的分配机制,而在临界状态下剪切带内的颗粒摩擦以及破碎耗能是消耗外界功的主要因素。数值结果亦表明,颗粒的破碎伴随着整个剪切过程,但破碎率的增长速度却随着剪切应变的发展逐渐降低。另外,在剪切过程中,对于低破碎性土,在临界状态下剪切破碎带基本形成,带内的原有组织结构被打乱,断裂键的各向异性也随之弱化。     

岩石失稳破坏的键弹簧模型研究

岩石的失稳破坏是岩石力学的一个重要课题。本文根据微观原子键作用的特征,揭示了固体材料宏观破坏本质必然是微观键的拉破坏,发明了键弹簧,用以表征岩石宏观力学性质。在综合分析岩石破坏的宏细观特征及声发射特性的基础上,建立了岩石破坏的键弹簧模型,推导出用以判别系统失稳的虚余能判据。利用虚余能判据,对各种加载状态下岩石的失稳破坏进行了综合分析,讨论了岩石在单轴拉伸、压缩、剪切、真三轴单面卸载等条件下的失稳条件,及岩石系统失稳破坏的尺度效应和围压效应。进一步提出了岩石系统失稳的统一判据公式,指出系统加载失稳由加载条件、应力状态、几何参数共同决定,区别于传统系统失稳的刚度理论。最后介绍了岩石键弹簧模型失稳判据在工程上的应用。     

岩石裂纹损伤及围压对剪切破坏影响研究

岩石内部细观裂纹的存在,对压缩作用下岩石剪切断裂的宏观现象有着重要的影响。然而,能够通过解析解阐释细观裂纹几何特性、围压等影响因素对压缩作用下剪切断裂面角度变化趋势的研究很少。基于Ashby模型中提出的裂纹尖端应力强度因子,提出了一种改进的考虑裂纹角度影响的应力强度因子表达式。利用该改进的应力强度因子表达式,推出了一个可以预测岩石峰值强度的裂纹扩展、应变与应力之间的本构关系。结合本构关系的峰值强度与摩尔-库仑失效准则,得到了岩石损伤与内摩擦角、黏聚力、剪切强度及失效断裂面角度之间的理论关系;讨论了围压、裂纹尺寸、角度及摩擦系数对岩石宏观剪切断裂面角度的影响,通过试验结果验证了模型合理性。结果表明：随着损伤增大,内摩擦角、黏聚力及剪切强度不断减小;随着围压增大、摩擦系数增大和初始裂纹尺寸减小,剪切断裂面角度不断增大;随着裂纹角度增大,剪切断裂纹面角度先减小后增大。     

大理岩断裂能与细观结构几何特征相关性

岩石在细观尺度上是由矿物颗粒胶结而成,除细观结构的力学特性外,其几何特征（颗粒界面网络结构和颗粒粒度分布）也对宏观断裂能具有一定的影响。为了探索这种几何特征与大理岩断裂能之间的相关性,从而进一步揭示岩石细观断裂机制,首先通过三点弯曲试验测定大理岩的断裂能,然后在试验后的三点弯试件断口处取岩石切片,进行电镜（SEM）扫描以获取岩石细观结构图像。利用图像处理技术获取岩石细观颗粒的界面网络图。通过对颗粒界面网络图分析,发现颗粒界面网络拓扑结构与颗粒粒度分布具有较强的分形特征。将二者分形维数与试件宏观断裂能相对比,发现它们之间具有很强的相关性。界面网络分形维数与宏观断裂能具有很强的二次相关性,而粒度分布维数与宏观断裂能之间具有较强的线性相关性。宏观断裂能随着两种分形维数的增大而增大。该研究结果揭示了宏观断裂能与岩石细观结构几何特征的相关性,加深了对宏观断裂能细观机制的理解。     

冻结黏土三轴试验微观变形机理的离散元分析

基于三维颗粒离散单元法,赋予颗粒相应的细观参数,并采用黏结发生在接触颗粒间有限范围内的模型来考虑冻土颗粒中冰的胶结作用,建立了冻结黏土三维离散元数值模型.在相同围压、不同温度和相同温度、不同围压下对冻结黏土的室内三轴试验进行数值模拟,对比了数值试验与室内测试的应力-应变曲线,两者吻合较好.数值模拟结果表明:围压增大会使得接触黏结逐渐失效,在剪切带中胶结冰的破坏区域将增大,而温度的降低则会产生相反结果,这些微观变化都将对冻结黏土的宏观力学变形产生较大影响,同时,细观参数对温度的依赖性也很明显.冻结黏土三轴试验微观变形离散元模拟思路及方法可为今后运用离散单元法研究冻土力学行为提供一定的参考.     

含石量和颗粒破碎对土石混合料强度的影响研究

The characteristics of particle breakage and shear strength of soil-rock aggregate with six rock contents under six normal pressures were studied from macro and mecro perspectives by large-scale direct shear test, particle observation test and particle sieving test. The relationship between macroscopic shear strength properties and mecroscopic particle breakage characteristics was established, thus further revealing the influence mechanism of rock content and particle breakage on the shear strength characteristics of soil-rock aggregate. The results showed that particle breakage mainly occurred near the shear plane. The breakage morphology can be divided into surface grinding, local fracture, complete fracture and complete breakage, resulting from the stress concentration caused by uneven contact forces between particles. Due to particle breakage, the content of fine particles increased, coarse grains decreased, and intermediate grains fluctuated. The relative particle breakage Br increased with the increase of normal pressure ?n or rock content P5, which accorded with the function of two variables. With the increase of normal pressure ?n, the shear strength τ increased nonlinearly and met the modified M-C strength criterion. When the rock content P5 increased, the cohesive force c0 of soil-rock aggregate decreased, the internal friction angle ?0 of soil-rock aggregate increased, and the non-linear parameter Δ? increased. Particle breakage was the direct cause of non-linear strength characteristics of soil-rock aggregate.     

黏性材料细观与宏观力学参数相关性研究

岩土工程数值模拟技术中参数选取的正确性是反应材料真实力学特性的基本前提。借助于颗粒离散元分析软件PFC2D,对黏性土类材料样本开展了大量的平面双轴压缩试验。通过记录不同围压下样本的轴向应力峰值,并依据摩尔-库仑强度准则对数值试样的剪切强度参数（内摩擦角、黏聚力）进行标定。着重探讨了黏性材料细观参数中颗粒刚度比kn /ks（0.5～10共12组）、颗粒粘结强度SBS（0～50 kPa共12组）、颗粒摩擦系数?（0～6共16组）以及颗粒粘结强度比K（0.1～10共15组）和材料宏观剪切强度参数以及材料剪切特性之间的相关性。研究结果表明：颗粒粘结（法向、切向）强度同对材料黏聚力呈线性相关;颗粒摩擦系数与材料内摩擦角呈近似对数相关;颗粒刚度比大小对材料剪切强度参数变化亦有微弱的影响;此外,K值（切向粘结强度/法向粘结强度）是影响材料的剪切破坏形态的重要因素。最后,采用了两个多元非线性拟合公式,定量地描述了以上各细观参数和材料宏观剪切强度参数的联合关系,并给出了K值的建议取值,为后续的研究提供重要的理论基础。     

Study on the particle breakage of ballast based on a GPU accelerated discrete element method

Breakage of particles will have greatly influence on mechanical behavior of granular material(GM)under external loads,such as ballast,rockfill and sand.The discrete element method(DEM)is one of the most popular methods for simulating GM as each particle is represented on its own.To study breakage mechanism of particle breakage,a cohesive contact mode is developed based on the GPU accelerated DEM code-Blaze-DEM.A database of the 3D geometry model of rock blocks is established based on the 3D scanning method.And an agglomerate describing the rock block with a series of non-overlapping spherical particles is used to build the DEM numerical model of a railway ballast sample,which is used to the DEM oedometric test to study the particles’breakage characteristics of the sample under external load.Furthermore,to obtain the meso-mechanical parameters used in DEM,a black-analysis method is used based on the laboratory tests of the rock sample.Based on the DEM numerical tests,the particle breakage process and mechanisms of the railway ballast are studied.All results show that the developed code can better used for large scale simulation of the particle breakage analysis of granular material.     

Simulation of hydraulic fracture propagation near a natural fracture using virtual multidimensional internal bonds

A virtual multidimensional internal bond (VMIB) model developed to simulate the propagation of hydraulic fractures using the finite‐element method is formulated within the framework of the virtual internal bond theory (VIB) that considers a solid as randomized material particles in the micro scale, and derives the macro constitutive relation from the cohesive law between the material particles with an implicit fracture criterion. Hydraulic pressure is applied using a new scheme that enables simulation of hydraulically driven cracks. When the model is applied to study hydraulic fracture propagation in the presence of a natural fracture, the results show the method to be very effective. It shows that although the in situ stress ratio is the dominant factor governing the propagation direction, a natural fault can also strongly influence the hydraulic fracture behavior. This influence is conditioned by the shear stiffness of the fault and the distance to the original hydraulic fracture. The model results show that when the fault is strong in shear, its impact on hydraulic fracture trajectory is weak and the hydraulic fracture will likely penetrate the fault. For a weak fault, however, the fracture tends to be arrested at the natural fault. The distance between the fault and the hydraulic fracture is also important; the fault influence increases with decreasing distance. The VMIB does not require selection of a fracture criterion and remeshing when the fracture propagates. Therefore, it is advantageous for modeling fracture initiation and propagation in naturally fractured rock. Copyright © 2010 John Wiley & Sons, Ltd.     

基于粘结和摩擦特性的岩石变形与破坏的研究

就微观结构而言,矿物颗粒之间或相互粘结或相互分离,Coulomb准则的粘结力和内摩擦力在局部不能同时存在.粘结力是在变形作用下丧失的,材料丧失粘结力之后通过摩擦承载.若承载能力降低,屈服破坏仅在局部断面发生,具有脆性特征;反之将发生分布的屈服破坏,具有延性特征.围压增加可以使裂隙能够承载的摩擦力超过岩石材料的粘结力,那么当轴向应力增加到粘结力时,材料发生剪切屈服产生塑性变形,而摩擦力不会增加到其最大值,裂隙也不发生滑移.利用摩擦的概念可以理解不同岩石的变形、承载和破坏随围压变化的特征.      

岩石颗粒破碎的尺寸效应

固体颗粒破碎强度的尺寸效应是一种普遍存在的现象,冰块、岩石颗粒、陶瓷和混凝土块等的破碎强度都表现出随颗粒直径增加而减小的现象,分形模型为解释固体颗粒破碎强度的尺寸效应提供了可行的方法。本文采用Steacy和Sammis分形模型模拟了岩石颗粒压碎特征,分析岩石颗粒破碎后的颗粒分布规律,给出颗粒破碎分维的确定方法,建立颗粒压碎强度与粒径的理论关系,颗粒破碎强度与颗粒粒径的关系用分维D表示为fdD-3。已有的颗粒破碎分布的数据表明,岩石颗粒破碎的分维大约为2.50～2.60,颗粒破碎强度符合用分维表示的尺寸效应。     

基于PFC2D岩石颗粒破碎强度和能量的分形模型

颗粒的破碎强度随着粒径的增大而减小,即颗粒破碎的尺寸效应,分形模型为解释固体颗粒破碎的尺寸效应提供了可行的方法。根据岩石颗粒破碎时的分形特征,采用Sammis破碎准则,通过模拟分析得出岩石颗粒破碎能量和强度的分形模型,建立和验证用分维D来表示岩石颗粒破碎的能量和强度准则,得出并验证了岩石颗粒破碎分维的确定方法。利用离散元软件PFC2D的黏结颗粒模型BPM（Bonded Particle Model）模拟了小孔隙率n=0.12和大孔隙率n=0.3,即密实和松散两种情况。其中小孔隙率采用在模型上添加小颗粒的新方法,分别做了400组粒径不等的数值模拟试验,从粒径与破碎强度、破碎能量之间的关系和应力-应变曲线3个方面进行了统计,验证了岩石颗粒破碎强度与分维D的理论关系为σ_f∝dD-3,并得出颗粒破碎时的能量和与分维D之间的关系为E_f∝dD-1。验证了分形理论在分析颗粒破碎的尺寸效应中的较好应用,为确定岩石颗粒的破碎强度和岩石堆砌体剪切强度提供新的方法和参考意见。     

Simulation of mixed-mode fracture using SPH particles with an embedded fracture process zone

This paper focuses on the modelling of mixed-mode fracture using the conventional smoothed particle hydrodynamics (SPH) method and a mixed-mode cohesive fracture law embedded in the particles. The combination of conventional SPH and a mixed-mode cohesive model allows capturing fracture and separation under various loading conditions efficiently. The key advantage of this framework is its capability to represent complex fracture geometries by a set of cracked SPH particles, each of which can possess its own mixed-mode cohesive fracture with arbitrary orientations. Therefore, this can naturally capture complex fracture patterns without any predefined fracture topologies. Because a characteristic length scale related to the size of the fracture process zone is incorporated in the constitutive formulation, the proposed approach is independent from the spatial discretisation of the computational domain (or mesh independent). Furthermore, the anisotropic fracture responses of materials can be naturally captured thanks to the orientation of the fracture process zone embedded at the particle level. The performance of the proposed approach demonstrates its potentials in modelling mixed-mode fracture of rocks and similar quasi-brittle materials.     

Parameters controlling pressure and fracture behaviors in field injectivity tests: A numerical investigation using coupled flow and geomechanics model

Field injectivity tests are widely used in the oil and gas industry to obtain key formation characteristics. The prevailing approaches for injectivity test interpretation rely on traditional analytical models. A number of parameters may affect the test results and lead to interpretation difficulties. Understanding their impacts on pressure response and fracture geometry of the test is essential for accurate test interpretation. In this work, a coupled flow and geomechanics model is developed for numerical simulation of field injectivity tests. The coupled model combines a cohesive zone model for simulating fluid-driven fracture and a poro-elastic/plastic model for simulating formation behavior. The model can capture fracture propagation, fluid flow within the fracture and formation, deformation of the formation, and evolution of pore pressure and stress around the wellbore and fracture during the tests. Numerical simulations are carried out to investigate the impacts of a multitude of parameters on test behaviors. The parameters include rock permeability, the leak-off coefficient of the fracture, rock stiffness, rock toughness, rock strength, plasticity deformation, and injection rate. The sensitivity of pressure response and fracture geometry on each parameter is reported and discussed. The coupled flow and geomechanics model provides additional advantages in the understanding of the fundamental mechanisms of field injectivity tests.     

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.