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.     

A simple three‐dimensional distinct element modeling of the mechanical behavior of bonded sands

This paper presents a simple three‐dimensional (3D) Distinct Element Method (DEM) for numerical simulation of the mechanical behavior of bonded sands. First, a series of micro‐mechanical tests on a pair of aluminum rods glued together by cement with different bond sizes were performed to obtain the contact mechanical responses of ideally bonded granular material. Second, a 3D bond contact model, which takes into account the influences of bond sizes, was established by extending the obtained 2D experimental results to 3D case. Then, a DEM incorporating the new contact model was employed to perform a set of drained triaxial compression tests on the DEM bonded specimens with different cement contents under different confining pressures. Finally, the mechanical behavior of the bonded specimens was compared with the available experimental results. The results show that the DEM incorporating the simple 3D bond contact model is able to capture the main mechanical behavior of bonded sands. The bonded specimen with higher cement content under lower confining pressure exhibits more pronounced strain softening and shear dilatancy. The peak and residual strengths, the apparent cohesion and peak/residual friction angles, and the position and slope of the critical state line increase with increase in cement content. Microscopically, bond breakage starts when the system starts to dilate and the maximum rate of bond breakage coincides with the maximum rate of dilation. Bond breakage is primarily due to tension‐shear failure and the percentage of such failures is independent of both confining pressure and cement content. Copyright © 2015 John Wiley & Sons, Ltd.     

水泥胶结颗粒的微观力学模型试验

土体粒间胶结是建立天然结构性土本构模型的决定性因素之一,将胶结颗粒理想化为两铝棒,在指定位置处形成胶结。采用水泥作为胶结材料,对胶结颗粒进行了一系列简单加载试验（包括拉伸、压缩、压剪、压扭）和复杂应力路径试验,并与蒋明镜等所做的环氧树脂胶结试验进行对比。结果表明：胶结材料对胶结颗粒的力学性能存在一定影响,但基本规律符合蒋明镜等所提出的理想颗粒间胶结模型。水泥胶结抗拉强度低于环氧树脂胶结抗拉强度,但延性相对较好,抗压特性均呈塑性软化现象;二者的抗剪强度初始均随法向压力的增加而增大,当法向压力超过一定值时,又随法向压力的增加而减小（该压力称为界限法向压力）,但水泥胶结的界限法向压力明显高于环氧树脂胶结,扭转试验规律与剪切试验规律类似。在三维应力空间中（法向压力-扭矩-剪力）水泥胶结的强度包线呈橄榄球状,环氧树脂胶结强度包线呈水滴状。     

不同胶结厚度下粒间胶结力学特性的试验研究

为研究胶结物厚度对粒间胶结强度的影响,在蒋明镜等[1－4]已完成的0.6 mm厚度的环氧树脂和水泥微观胶结模型试验基础上,进一步选取1.0 mm和1.5 mm两种胶结厚度,通过一系列接触力学特性测试,并结合0.6 mm厚度的试验数据,分析了在不同胶结厚度和不同胶结物类型下,粒间胶结强度指标的变化规律。试验结果表明：随着胶结厚度的增加,峰值抗拉荷载增大,峰值抗压荷载减小;同一胶结厚度下,随着法向压力的增大,两种胶结物的峰值抗剪和抗扭荷载均先增大后减小,而同一法向压力下,随着胶结厚度的增加,二者的峰值抗剪和抗扭荷载均随之减小。在三维应力空间中（法向压力-扭矩-剪力）,两类胶结强度包线分别为水滴状、橄榄球状且随胶结厚度的增加而缩小,但形状不发生变化。     

Bond rolling resistance and its effect on yielding of bonded granulates by DEM analyses

A discrete element modelling of bonded granulates and investigation on the bond effect on their behaviour are very important to geomechanics. This paper presents a two‐dimensional (2‐D) discrete element theory for bonded granulates with bond rolling resistance and provides a numerical investigation into the effect of bond rolling resistance on the yielding of bonded granulates. The model consists of mechanical contact models and equations governing the motion of bonded particles. The key point of the theory is that the assumption in the original bond contact model previously proposed by the authors (55th CSCE‐ASCE Conference, Hamilton, Ont., Canada, 2002; 313–320; J. Eng. Mech. (ASCE) 2005; 131 (11):1209–1213) that bonded particles are in contact at discrete points, is here replaced by a more reliable assumption that bonded particles are in contact over a width. By making the idealization that the bond contact width is continuously distributed with the normal/tangential basic elements (BE) (each BE is composed of spring, dashpot, bond, slider or divider), we establish a bond rolling contact model together with bond normal/tangential contact models, and also relate the governing equations to local equilibrium. Only one physical parameter β needs to be introduced in the theory in comparison to the original bond discrete element model. The model has been implemented into a 2‐D distinct element method code, NS2D. Using the NS2D, a total of 86 1‐D, constant stress ratio, and biaxial compressions tests have been carried out on the bonded granular samples of different densities, bonding strengths and rolling resistances. The numerical results show that: (i) the new theory predicts a larger internal friction angle, a larger yielding stress, more brittle behaviour and larger final broken contact ratio than the original bond model; (ii) the yielding stress increases nonlinearly with the increasing value of β, and (iii) the first‐yield curve (initiation of bond breakage), which define a zone of none bond breakage and which shape and size are affected by the material density, is amplified by the bond rolling resistance in analogous to that predicted by the original bond model. Copyright © 2006 John Wiley & Sons, Ltd.     

Modeling shear behavior and strain localization in cemented sands by two-dimensional distinct element method analyses

This paper presents a numerical investigation of shear behavior and strain localization in cemented sands using the distinct element method (DEM), employing two different failure criteria for grain bonding. The first criterion is characterized by a Mohr–Coulomb failure line with two distinctive contributions, cohesive and frictional, which sum to give the total bond resistance; the second features a constant, pressure-independent strength at low compressive forces and purely frictional resistance at high forces, which is the standard bond model implemented in the Particle Flow Code (PFC2D). Dilatancy, material friction angle and cohesion, strain and stress fields, the distribution of bond breakages, the void ratio and the averaged pure rotation rate (APR) were examined to elucidate the relations between micromechanical variables and macromechanical responses in DEM specimens subjected to biaxial compression tests.     

DEM analyses of one-dimensional compression and collapse behaviour of unsaturated structural loess

Natural loess is a kind of under-consolidated and unsaturated loose granulates (silts) with its microstructure characterized with large voids and inter-particle cementation. This paper presents a distinct element method (DEM) to investigate its macro- and micro-mechanical behaviour (compression and collapse behaviour) under one-dimensional (1D) compression condition. A relationship between bond strength in DEM model and initial water content is used to develop a bond contact model for loess. Then, DEM structural loess samples are prepared by the multi-layer under-compaction method, and cemented with the bond contact model. The effect of water content and void ratio on compression and collapse behaviour of loess is numerically investigated by simulating 1D compression and wetting tests on the DEM material. The DEM results agree qualitatively with available experimental observations in literatures. The wetting-induced deformation is independent of the sequence of wetting and loading under 1D compression condition. The macroscopic yielding and collapse behaviours are associated with bond breakage on microscopic scale. Moreover, bonds break in one of the two failure types in the simulations, i.e. tensile failure and shear failure (compression-shear failure and tension-shear failure), with bonds broken firstly mainly due to tension followed by shear when the samples are compressed, while mainly due to shear when the samples are wetted under a certain pressure. In addition, the contact orientations and deviator fabrics of contacts under 1D compression and wetting were also investigated.     

不同胶结宽度粒间胶结特性试验研究

胶结砂土中水泥含量、能源土中水合物的含量会导致其宏观力学特性的差异,从微观层面可以解释为颗粒之间胶结物含量的不同所导致的粒间力学性质的差异所致。为研究不同胶结物含量的胶结颗粒的力学特性,进行了不同胶结宽度的粒间胶结试验,试验结果表明：（1）峰值压缩荷载随胶结宽度的减小呈非线性变化,宽高比对峰值荷载有明显影响;（2）峰值拉伸荷载随胶结宽度减小而线性减小,宽高比对其影响不大;（3）峰值剪切荷载和峰值扭矩由两部分组成,即胶结部分和摩擦部分。且其变化趋势相似,随着法向荷载的增大,峰值荷载先随之增大,在达到临界应力比后,峰值荷载开始减小,当应力比达到1,即胶结破坏时,胶结部分不再发挥作用,此时粒间荷载由摩擦部分提供;（4）在压-剪-扭试验中,不同初始偏心距情况下得到的峰值荷载在剪力-扭矩平面内呈椭圆状。     

Discrete simulations of a triaxial compression test for sand by DEM

A quasi‐static homogeneous drained triaxial compression test on cohesionless sand under constant lateral pressure was simulated using a three‐dimensional discrete element method. Grains were modelled by means of particle clusters composed of rigid spheres or spheres with contact moments imitating irregular particle shapes. Attention was paid to the effect of initial void ratio and grain shape mixture on the shear strength, volume changes, force chains, kinetic, elastic and dissipated energies. In addition, the effect of the mean grain size, grain size distribution, grain size range, specimen size and roughness and stiffness of boundaries was numerically analysed in initially dense sand. Some numerical results were compared with available experimental results. Copyright © 2014 John Wiley & Sons, Ltd.     

Granular contact dynamics with elastic bond model

This paper proposes an elastic bond model in the framework of contact dynamics based on mathematic programming. The bond model developed in this paper can be used to model cemented materials. The formulation can be reduced to model pure static problems without introducing any artificial damping. In addition, omitting the elastic terms in the objective function turns the formulation into rigid bond model, which can be used for the modeling of rigid or stiffly bonded materials. The developed bond model has the advantage over the explicit DEM that large time step or displacement increment can be used. The tensile and shear strength criteria of the bond model are formulated based on the modified Mohr–Coulomb failure criterion. The torque transmission of bonds is introduced based on rolling resistance model. The loss of shear or tensile strength, or torque transmission will lead to the breakage of bonds, and turn the bond into purely frictional contact. Three simple examples are first used to validate the bond model. Numerical examples of uniaxial and biaxial compression tests are used to show its potential in modeling cemented geomaterials. Numerical results show that elastic bonds are indeed necessary for the modeling of cemented granular material under static conditions.     

Microscopic contact model of lunar regolith for high efficiency discrete element analyses

The grains of lunar regolith are characterized with rough surfaces, angular shapes and mutual adhesions due to short-range interactions. These features control the macroscopic mechanical behavior of lunar regolith but have not been completely captured by contact models in previous Discrete Element Method (DEM) analyses. In this paper, a simplified two-dimensional microscopic contact model is proposed for high efficiency DEM analyses of lunar regolith. The model consists of three components in the normal, tangential and rolling directions respectively, plus two new parameters. A shape parameter is used to control the rolling resistance ability at the contact area between two particles to capture the features of grain shape and interlocking. The second parameter, micro-separation, which denotes the nominal minimum distance between the molecules of the two contacting particles, is introduced to account for van der Waals force as the major component of the short-range interactions that contribute to the adhesion of regolith grains in lunar environment conditions. The novel model has been implemented in a two-dimensional DEM code for numerical simulations of biaxial compression tests on lunar regolith. The effects of interparticle friction, grain shape, lunar environment conditions and void ratio on the strength of lunar regolith were numerically investigated. The results show that soils in the simulated lunar environment exhibit greater strength and more apparent strain-softening and shear dilatancy than on the Earth. The proposed model can capture the main features of the mechanical behavior of lunar regolith (apparent cohesion and high peak friction angle) and a wide range of strength indices can be obtained by the contact model.     

Study of mechanical behavior and strain localization of methane hydrate bearing sediments with different saturations by a new DEM model

This paper presents a numerical investigation into mechanical behavior and strain localization in methane hydrate (MH) bearing sediments using the distinct element method (DEM). Based on the results of a series of laboratory tests on the bonded granules idealized by two glued aluminum rods and the available experimental data of methane hydrate samples, a pressure and temperature dependent bond contact model was proposed and implemented into a two-dimensional (2D) DEM code. This 2D DEM code was then used to numerically carry out a series of biaxial compression tests on the MH samples with different methane hydrate saturations, whose results were then compared with the experimental data obtained by Masui et al. [9]. In addition, stress, strain, void ratio and velocity fields, the distributions of bond breakage and averaged pure rotation rate (APR) as well as the evolution of strain localization were examined to investigate the relationships between micromechanical variables and macromechanical responses in the DEM MH samples. The numerical results show that: (1) the shear strength increases as methane hydrate saturation S_MH increases, which is in good agreement with the experimental observation; (2) the strain localization in all the DEM MH samples develops with onset of inhomogeneity of void ratio, velocity, strain, APR, and distortion of stress fields and contact force chains; and (3) the methane hydrate saturation affects the type of strain localization, with one shear band developed in the case of 40.9% and 67.8% methane saturation samples, and two shear bands formed for 50.1% methane saturation sample.     

DEM analyses of crack propagation in flawed rock mass under uniaxial compressionEI北大核心CSCD

A contact model for rock is established and imbedded into a DEM software by summarizing the bond granule tests. DEM simulation of uniaxial compression test on the pre-cracked Lac du Bonnet granite is performed, and then stress distributions are further analyzed and compared with the theoretical results. Different fracture criteria are employed to predict the crack initiation angles that are compared with theoretical ones. The results show that the failure modes obtained from DEM simulation are similar to experimental results, and stress distributions in DEM simulation are qualitatively similar to theoretical values. When the angle of pre-crack is small, the lateral stresses are compressive and tensile. The compressive strains concentrate at two edges, resulting in the tensile strains in the up-and downward cracks. When the angle of the pre-crack is large enough, the stress concentration is unobvious, leading to a discrepancy between the DEM and theoretical results. The crack extension angle resulting from uniaxial compression measured from DEM tests are in good agreement with those acquired from experimental tests. These angles are consistent with theoretical predictions by the maximum circumferential stress criterion and the maximum energy release rate criterion.     

粒间胶结接触力学特性的三维试验研究

为实现结构性砂土离散元接触模型合理性的三维试验验证,设计了一套可用于三维半球形理想胶结颗粒成型及实现不同加载条件下的接触力学特性测试装置,制备了一定胶结尺寸的环氧树脂半球形颗粒胶结试样,在一系列辅助加载装置中初步开展了不同加载条件（拉伸、压缩、剪切、弯转、扭转）下的力学性能测试。结果表明,该装置可用于实现三维情况下胶结颗粒接触力学特性测试;不同加载条件下的实测试验结果与二维试验成果基本一致;峰值剪切、弯矩、扭矩随着法向荷载的增大呈现先增大后减小的趋势,存在一个相同的临界法向荷载。     

含裂隙岩体单轴压缩裂纹扩展机制离散元分析

将由室内试验总结得到的岩石微观胶结模型嵌入离散元软件,对Lac du Bonnet花岗岩石进行预制单裂隙单轴压缩试验DEM数值模拟,分析了压缩过程中裂隙试样中应力的分布,并与理论计算结果进行对比分析,同时对各种断裂判据中裂纹起裂角的预测值进行了适用性的对比分析。结果表明,离散元模拟试样破坏形态与试验结果相近;离散元分析得到的应力分布与理论解在定性上相似;当预制角度较小时,侧向应力都处于拉压状态;由于裂隙左右两端压应变的集中造成了裂隙上下面拉应变的产生,造成了裂隙周围特殊的应力分布;当裂隙角度较大时,应力集中现象已不明显,因而,理论值与试验值有偏差;在断裂判据中最大周应力准则和最大能量释放率准则得到的裂纹扩展角与室内试验与DEM结果中的数值较为吻合。     

Size-dependent mechanical behavior of an intergranular bond revealed by an analytical model

The size of intergranular bonds significantly affects the macroscopic mechanical properties of geomaterials. A size-dependent bond contact model is desired in the distinct element method (DEM) for geomaterials formed by aggregates of bonded particles. This paper proposes an analytical solution of highly-precise stress fields of a biconcave bond between two identical disc-shaped particles under different loading paths based on Dvorkin’s solution. The Unified Strength theory is then introduced to obtain the initial failure domain in the bond. The proposed solution is consistent with results predicted by finite element simulations and experimental observations. The functions of bond stiffness with respect to all influencing parameters, i.e. bond width/thickness, particle radius and elastic parameters of bond material, are provided by the solution and empirically formulated by fitting a large number of analytical results. Additionally, the failure criterion or envelope under different combined loads is formulated for typical brittle bonds. The resulting failure criterion, approximated as an ellipsoid, depends on the size and material properties of the bonds. The proposed solution and equation can be implemented into a bond contact model used in DEM simulations of a geomaterial, where variation of bond sizes is significant and size-dependent contact model is important.     

土工膜与土界面剪切特性细观研究

填埋场衬垫系统中,土与土工膜界面剪切强度较低,易造成失稳破坏。目前国内外学者主要采用室内试验对土与土工膜界面的宏观剪切特性进行研究,而对界面剪切特性的细观研究较少。为了从细观角度研究土与土工膜界面的剪切特性,本文采用EsyS-particle程序对土工膜与土界面直剪试验进行了离散元数值模拟分析。采用摩擦接触模型模拟砂土;采用黏结模型颗粒模拟土工膜,通过紧密排列土工膜颗粒以模拟土工膜的光滑表面。通过室内拟合试验,选取和校准材料的细观参数。分析结果表明,离散元模型能较好的模拟界面应力-应变关系;剪切带的厚度约为两倍平均土颗粒直径;剪切带中的土颗粒发生较大位移,孔隙比增大,而剪切带之外的土颗粒位移和孔隙比变化较小;随着剪切位移的增加,颗粒间接触力逐渐向左端集中,力链方向由垂直逐渐倾斜。     

平行黏结模型宏细观力学参数相关性研究

采用变量控制法较全面地分析了各细观参数与宏观参数的定量关系,表明：弹性模量E随颗粒模量Ec、黏结模量 、平行黏结半径乘子 呈线性增长,随颗粒刚度比kn /ks、黏结刚度比 呈对数减小;泊松比则主要受kn /ks和 的影响,两者之间呈对数关系;颗粒键的黏结强度决定了材料的强度,室内材料黏聚力c和抗拉强度 主要受法向平行黏结强度 、平行黏结强度比 的影响,随 线性增长,随 对数减小;摩擦角 主要受颗粒摩擦系数u影响,两者呈对数关系。分析裂隙扩展特征,表明材料法向黏结强度 和切向黏结强度 的相对大小决定裂纹分布规律,随 增大,岩样的拉破坏区域减少,而压剪破坏区域增加,破坏面由剪切破坏向共轭破坏发展;材料的强度离散性越小,岩样破坏趋于集中,破坏面明显,强度均值标准差比值 >3.5为宜; 增加,宏观破坏形式向共轭破坏发展。细观参数的选取除了匹配强度参数,同时还需要考虑破坏形式的一致,考虑多参数相互影响,建立了宏细观参数之间的经验公式,对细观参数进行优化选择,并做了实例验证。室内试验和数值模拟获得的峰值荷载、变形参数、剪切强度等数值接近,应力-应变演化规律相同,破坏形态一致,表明细观参数结果是可靠的。     

Micromechanical analysis of the failure process of brittle rock

The failure process of brittle rock submitted to a compression state of stress with different confining pressures is investigated in this paper based on discrete element method (DEM) simulations. In the DEM model, the rock sample is represented by bonding rigid particles at their contact points. The numerical model is first calibrated by comparing the macroscopic response with the macroscopic response of Beishan granite obtained from laboratory tests. After the validation of numerical model in terms of macroscopic responses, the failure process of the DEM model under unconfined and confined compression is studied in micro‐scale in detail. The contact force network and its relation to the development of micro‐cracks and evolution of major fractures are studied. Confining pressure will prohibit the development of tensile cracks and hence alter the failure patterns. An in‐depth analysis of micro‐scale response is carried out, including the orientation distribution and probability density of stress acting on parallel bonds, the effect of particle size heterogeneity on bond breakage and the evolution of fabric tensor and coordination number of parallel bond. The proposed micromechanical analysis will allow us to extract innovative features emerged from the stresses and crack evolution in brittle rock failure process. Copyright © 2014 John Wiley & Sons, Ltd.