Numerical study of inter‐particle bond failure by 3D discrete element method

The cohesive‐frictional nature of cementitious geomaterials raises great interest in the discrete element method (DEM) simulation of their mechanical behavior, where a proper bond failure criterion is usually required. In this paper, the failure of bond material between two spheres was investigated numerically using DEM that can easily reproduce the failure process of brittle material. In the DEM simulations, a bonded‐grain system (composed of two particles and bond material in between) was discretized as a cylindrical assembly of very fine particles connecting two large end spheres. Then, the bonded‐grain system was subjected to compression/tension, shear, rolling and torsion loadings and their combinations until overall failure (peak state) was reached. Bonded‐grain systems with various sizes were employed to investigate bond geometry effects. The numerical results show that the compression strength is highly affected by bond geometry, with the tensile strength being dependent to a lesser degree. The shear, rolling and torsion strengths are all normal force dependent; i.e., with an increase in the normal force, these strengths first increase at a declining rate and then start to decrease upon the normal force exceeding a critical value. The combined actions of shear force, rolling moment and torque lead to a spherical failure envelope in a normalized loading space. The fitted bond geometry factors and bond failure envelopes obtained numerically in this three‐dimensional study are qualitatively consistent with those in previous two‐dimensional experiments. The obtained bond failure criterion can be incorporated into a future bond contact model. Copyright © 2015 John Wiley & Sons, Ltd.     

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。     

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.     

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.     

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.     

A bond contact model for methane hydrate‐bearing sediments with interparticle cementation

While methane hydrates (MHs) can be present in various forms in deep seabeds or permafrost regions, this paper deals with MH‐bearing sediments (MHBS) where the MH has formed bonds between sand grains. A bond model based on experimentally validated contact laws for cemented granules is introduced to describe the mechanical behavior of the MH bonds. The model parameters were derived from measured values of temperature, water pressure and MH density. Bond width and thickness adopted for each bond of the MHBS were selected based on the degree of MH saturation. The model was implemented into a 2D distinct element method code. A series of numerical biaxial standard compression tests were carried out for various degrees of MH saturation. A comparison with available experimental data shows that the model can effectively capture the essential features of the mechanical behavior of MHBS for a wide range of levels of hydrate saturation under drained and undrained conditions. In addition, the analyses presented here shed light on the following: (1) the relationship between level of cementation and debonding mechanisms taking place at the microscopic level and the observed macro‐mechanical behavior of MHBS and (2) the relationship between spatial distribution of bond breakages and contact force chains with the observed strength, dilatancy and deformability of the samples. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

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。     

不同应力路径下土体的变形特性与破坏特性

在固结不排水加荷与卸荷两种情况下,基于土体常规的三轴压缩试验结果和真三轴平面应变试验结果,指出不同的应力路径下土体具有不同的变形特性和破坏特性,并且这些特性差异的根本原因在于不同的应力路径,有着其球应力p和广义剪应力q与球应力p的比值q/p的不同变化趋势。最后,依据Matsuoka-Nakai破坏准则和其相应的转化型式,进一步探讨了其破坏参数k2值的确定方法。试验检测的结果表明,Matsuoka-Nakai破坏准则能给出土体较为准确的破坏强度预测结果。     

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。     

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。     

基于颗粒离散元模型的不同加载速率下花岗岩数值试验研究

不同加载速率条件下岩石的力学特性,对于其动载下破裂内在机制的研究具有积极的意义。基于颗粒流理论,通过黏结颗粒模型（bonded particle model,简称BPM）虚拟实现不同加载速率0.001～0.500 m/s下花岗岩单轴压缩和巴西劈裂试验,定量分析加载速率对应力-应变、破裂形态、应变能率及声发射的影响。结果表明：单轴抗压强度和抗拉强度及其对应峰值应变随加载速率增加而非线性增长;单轴压缩作用下,随加载速率增加,试样由单一斜截面破坏向多斜截面破坏转变,且主控裂隙带宽度急剧增大,由裂纹数量及水平向高应变率区域变化规律可明显看出,试样破坏程度随着加载速率增加而逐渐加剧;巴西劈裂作用下试样从一条主控裂隙向多条主控裂隙转变,且裂纹向圆盘试样两侧边缘部分延伸,破坏程度加剧;单轴压缩和巴西劈裂作用下,声发射事件及应变能率均随加载速率增加而呈现出非线性增长趋势。     

Structural features and mechanical behaviour of a pyroclastic weak rock

The results of an extensive programme of laboratory testing on intact and reconstituted samples of a pyroclastic weak rock from the volcanic complex of the Colli Albani (Central Italy) are presented. The deposit is known as Pozzolana Nera and may be assimilated to a bonded coarse grained material. The nature of bonds and the micro‐structural features were examined by means of diffractometry, optical and electron microscopy. As bonds are made of the same constituents of grains and aggregates of grains, bond deterioration and particles breakage upon loading are indistinguishable features of the mechanical behaviour. The testing programme consisted mainly of one‐dimensional and drained and undrained triaxial compression tests in a wide range of confining pressures up to 58 MPa. As confining stress increases, the mechanical behaviour of the material changes from brittle and dilatant to ductile and contractant; for both brittle and ductile behaviour failure is associated with the formation of shear surfaces separating the sample in several parts at the end of test. The experimental stress–dilatancy relationships are compared with the classical stress–dilatancy theories for a purely frictional material and for a material with friction and cohesion between particles. The analysis of the data indicates that peak strength results from the interplay between degradation of inter‐particle bonds, increasing friction between particles and increasing rate of dilation. Copyright © 2001 John Wiley & Son, Ltd.     

胶结颗粒接触力学特性测试装置研制

为验证天然结构性砂土离散元模拟中接触模型及其参数的合理性,设计了一套用于理想胶结颗粒成型及实现不同加载条件下接触力学特性测试装置。通过胶结颗粒成型装置在两大小相同的铝棒间形成具有特定几何尺寸的胶结物,随后,采用一系列辅助加载装置实现简单及复杂加载条件下胶结颗粒接触力学特性的测试。试验结果表明：该装置可用于胶结颗粒在不同加载条件下接触力学特性的测试,实测胶结颗粒接触力学响应与天然砂土离散元中接触模型基本相符,且其抗剪和抗扭强度均随着法向压力的增大而增大,在三维应力空间中胶结颗粒强度包线呈椭圆抛物面状。     

在不同加载速率条件下花岗岩的破坏准则

本文应用岩石快速加载设备,系统地研究加载速率在10-1～105公斤/厘米2/秒范围内,花岗岩的抗压、抗拉和抗剪破坏特征,得出强度随加载速率变化的规律,并提出了花岗岩的动力破坏准则.     

Failure Criterion of Granite at Different Loading Rates

A study of failure properties of granite specimens under compression, tension, shear conditions at different loading rates has been conducted. The tests, having loading rates from 10-1 to 108 kg/cm2/sec, were carried out on a fast loading equipment for rock mechanics teat. It has been found that the strength of the granite specimens increases with the increasing of loading rates. Based on this study and some results from field tests, a criterion of dynamic failure of granite is presented.     

Three‐dimensional elasto‐plastic model for unsaturated compacted soils with different initial densities

This paper presents an elasto‐plastic model for unsaturated compacted soils and experimental results obtained from a series of suction‐controlled triaxial tests on unsaturated compacted clay with different initial densities. The initial density dependency of the compacted soil behaviour is modelled by establishing experimental relationships between the initial density and the corresponding yield stress and thereby between the initial density and the location and slope of normal compression line. The model is generalized to three‐dimensional stress states by assuming that the shapes of the failure surface and the yield surface in the deviatoric plane are given by the extended SMP criterion. A considerable number of the isotropic compression, triaxial compression and extension tests on unsaturated compacted clay with different initial densities were performed using a suction‐controllable triaxial apparatus, to measure the stress–strain–volume change in different stress paths and wetting paths. The model has well‐predicting capabilities to reproduce the mechanical behaviour of specimens compacted under different conditions not only in isotropic compression but also in triaxial compression and triaxial extension. Copyright © 2003 John Wiley & Sons, Ltd.     

考虑水合物胶结厚度的深海能源土粒间胶结模型研究

天然气水合物被公认是解决当前能源危机的潜在新型能源而备受关注。含水合物的海底土体称为深海能源土。水合物在能源土中有不同的赋存形式（如填充型水合物和胶结型水合物等）,由于胶结型水合物对整体强度的贡献比其他存在形式更大,尤其是饱和度较低的情况。针对于胶结型水合物的赋存形式进行研究,水合物作为胶结物质存在于土颗粒之间,胶结厚度会在一定范围内变化。为真实地反映此现象,通过对能源土试样的电镜扫描图片整理分析,获得水合物饱和度与粒间胶结厚度的函数关系。基于前期已经完成的不同粒间胶结厚度下胶结力学特性的试验研究成果,为探究胶结厚度变化对能源土体宏观力学特性的影响,建立了考虑水合物胶结厚度的能源土粒间胶结模型,并介绍此模型中相关胶结参数及其确定方法。     

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.