Experimental characterization and 3D DEM simulation of bond breakages in artificially cemented sands with different bond strengths when subjected to triaxial shearing

This paper describes the mechanical behavior of artificially cemented sands with strong, intermediate, and weak bond strengths, using experimentation and 3D discrete element method (DEM) simulation. The focus is on the features of bond breakage and the associated influences on the stress–strain responses. Under triaxial shearing, the acoustic emission rate captured in the experiment and the bond breakage rate recorded in the simulations show resemblance to the stress–strain response, especially for strongly and intermediately cemented samples, where a strain softening response is observed. The simulations further reveal the shear band formation coincides with the development of bond breakage locations due to the local weakness caused by the bond breakages. Strain softening and volumetric dilation are observed inside the shear band, while the region outside the shear band undergoes elastic unloading. The weakly cemented sample exhibits a strain hardening response instead; bond breakages and the associated local weaknesses are always randomly formed such that no persistent shear band is observed. Note that in the DEM simulation, the flexible membrane boundary is established by a network of bonded membrane particles; the membrane particle network is further partitioned into finite triangular elements. The associated algorithm can accurately distribute the applied confining pressure onto the membrane particles and determine the sample volume.     

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.     

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.     

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.     

Discrete element method simulations of bio-cemented sands

Microbially induced calcite precipitation (MICP) has emerged as a novel soil improvement method. In this paper, 3-D discrete element method (DEM) simulations are used to explore the behavior of MICP-cemented sands. Comparisons of the macro-scale response of numerical and physical specimens are made. Microstructure analyses indicate a shear band formed in the numerical specimens, consistent with physical experiments. The bond breakage pattern in numerical specimens is explored and compared to observed measurements from physical specimens. The relationship between dilatancy and stress-strain behavior is evaluated. The results indicate DEM is an effective technique to capture the mechanical behavior of MICP-cemented sand.     

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.     

Discrete element simulation of mine tailings stabilized with biopolymer

This paper presents a series of numerical simulations using discrete element method (DEM) to study the behavior of biopolymer-stabilized mine tailings (MT). Validation is conducted by comparing the DEM results with the experimental data. The macro-behavior comparison shows that the DEM simulations are in good agreement with experimental results. Analysis of the micro-parameters indicates more biopolymer induces larger tensile and shear strengths, confirming the experimental results which show that the strength of MT increases with higher biopolymer concentration. Analysis of the bond breakage pattern suggests that at the same strain level MT stabilized with higher biopolymer concentration show less bond breakage percentage. MT specimen under greater confining pressure develops larger shear band than that under lower confining pressure. Higher biopolymer concentration induces the increase in larger inter-particle bonding strength and thus larger cracking resistance and greater macro-strength.     

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。     

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。     

Study on the mechanical behavior of sands using 3D discrete element method with realistic particle models

Presented is a study on the geometrical characteristics of sand particles and the mechanical behavior of sand material under external loading. Based on computed tomography technique, a reconstruction method of granular particles was developed and used to build a database of 3D geometrical models for sand particles. The studied sand particles showed good regularities in morphological characteristics and thus were suitable to be used for the random generation of numerical samples. DEM tests using realistically shaped particles were proven to better simulate the mechanical behavior of the sample during elastoplastic loading stage, which was an issue for the simplified spherical particles. The generation, extension, and breakage of the force chains controlled the strain softening behavior of sands. Anisotropy analysis using the spherical harmonic series showed that the evolution of anisotropy directions and parameters corresponded well with the macroscopic mechanical behavior of the material. Pore volume computation based on Voronoi diagram was performed to illustrate the formation and evolution of localized shear zone. The mesoscopic analysis showed that particle shape significantly influences the mechanical behavior of sands and thus should be properly modeled in numerical simulations.

     

结构性黄土一维湿陷特性的离散元数值模拟

针对结构性湿陷性黄土大孔隙和胶结特性,应用离散元生成了不同含水率结构性黄土试样,研究试样的一维湿陷特性。首先,根据已有的结构性黄土试验资料和胶结颗粒材料离散元数值试验成果,建立胶结强度和初始饱和度之间的关系。其次,采用蒋明镜等提出的分层欠压法[1]和胶结模型[2]制得不同含水率结构性黄土离散元试样,然后进行不同含水率双线法和同一含水率4个压力下单线法湿陷试验的离散元数值模拟。数值模拟结果表明,提出的离散元分析方法能模拟天然结构性湿陷性黄土的主要力学性质,随着含水率的减少,结构屈服应力和最大湿陷压力增加,湿陷系数随着压力先增加后减小,湿陷起始压力为饱和试样的结构屈服应力,单线法湿陷后压缩曲线与饱和试样的压缩曲线接近。此外,模拟结果还表明,不同含水率结构性黄土离散元试样的最大湿陷系数与天然结构性湿陷性黄土相差较远,但在最大湿陷系数与孔隙比的比值上相接近;结构屈服对应着胶结的逐步破坏,湿陷伴随着大量的胶结破坏。提出了基于胶结点数目的损伤变量,研究了其在加载和湿陷过程中的变化规律。研究成果为认识黄土复杂力学特性和建立其本构理论提供了基础。     

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。     

颗粒破碎及剪胀对钙质砂抗剪强度影响研究

钙质砂是海洋沉积物中的一种,富含碳酸钙或其他难溶碳酸盐类物质的特殊介质。由于其颗粒质脆,受力后易产生破碎,表现出与常规陆源砂不同的力学性质。通过对取自南沙群岛永暑礁附近海域的钙质砂进行三轴剪切试验,分析了钙质砂颗粒破碎与剪胀对其抗剪强度的影响。试验结果表明,颗粒破碎与剪胀对钙质砂强度有着重要影响,低围压下剪胀对其强度的影响远大于颗粒破碎,随着围压的增加,钙质砂颗粒破碎加剧,剪胀影响越来越小,而颗粒破碎的影响则越来越显著;颗粒破碎对强度的影响随着围压的增大而增大,当破碎达到一定程度后颗粒破碎渐趋减弱,其影响也渐趋于稳定。     

基于微观胶结厚度模型的深海能源土宏观力学特性离散元分析

首先,引入蒋明镜等提出的考虑水合物胶结厚度的深海能源土粒间微观胶结模型,用以反映能源土颗粒之间水合物微观胶结接触力学特性;其次,采用C++语言将模型程序化,并将其引入离散单元法中;然后,对选定的水合物饱和度经过实际二维离散元模拟调算,得出相应的水合物胶结尺寸,以修正水合物临界胶结厚度、最小胶结厚度及胶结宽度,进而确定水合物微观胶结参数;最后,根据所确定的胶结参数,针对不同水合物饱和度试样进行能源土宏观力学特性离散元双轴试验模拟,并从应力-应变、体变、剪胀角等方面与Masui等所进行的能源土室内三轴试验进行对比分析。结果表明：采用考虑粒间胶结厚度的水合物微观胶结模型,能够定性反映深海能源土的宏观力学特性,能源土试样的峰值强度、黏聚力和剪胀角均随水合物饱和度的增加而增加,但水合物饱和度对内摩擦角的影响规律不明朗;能源土试样的峰值强度、残余强度及体积剪缩量随着有效围压的增大而增大;剪胀角随有效围压的增大而减小。     

剪切作用下钙质砂颗粒破碎试验研究

钙质砂是一种海洋沉积物,与陆源砂比起来,钙质砂受力后易产生颗粒破碎,从而使其力学性质发生变化。对取自南沙群岛永暑礁附近海域的钙质砂进行了不同围压、不同应变下的三轴剪切试验,对试验前后的试样进行了颗粒大小分析试验。试验结果表明,钙质砂在三轴剪切作用下颗粒破碎十分严重,同时用Hardin模型对其破碎进行了度量,并就围压、剪切应变与破碎之间的关系进行了分析。     

DEM simulations of methane hydrate exploitation by thermal recovery and depressurization methods

Methane hydrate (MH, also called fiery ice) exists in forms of pore filling, cementing and load-bearing skeleton in the methane hydrate bearing sediment (MHBS) and affects its mechanical behavior greatly. To study the changes of macro-scale and micro-scale mechanical behaviors of MHBS during exploitation by thermal recovery and depressurization methods, a novel 2D thermo-hydro-mechanical bonded contact model was proposed and implemented into a platform of distinct element method (DEM), PFC2D. MHBS samples were first biaxially compressed to different deviator stress levels to model different in-situ stress conditions. With the deviator stress maintained at constant, the temperature was then raised to simulate the thermal recovery process or the pore water pressure (i.e. confining pressure for MH bond) was decreased to simulate the depressurization process. DEM simulation results showed that: during exploitation, the axial strain increased with the increase of temperature (in the thermal recovery method) or decrease of pore water pressure (in the depressurization method); sample collapsed during MH dissociation if the deviator stress applied was larger than the compression strength of a pure host sand sample; sample experienced volume contraction but its void ratio was slightly larger than the pure host sand sample at the same axial strain throughout the test. By comparison with the laboratory test results, the new model was validated to be capable of reproducing the exploitation process by thermal recovery and depressurization methods. In addition, some micro-scale parameters, such as contact distribution, bond distribution, and averaged pure rotation rate, were also analyzed to investigate their relationships with the macroscopic responses.     

结构性土二元介质本构模型及破损率影响因素的研究

岩土类材料是非均质的具有微缺陷的天然材料,岩土破损力学将岩土材料抽象成由结构块和结构带组成的非均质二元结构体。破损率演化方程反映了岩土材料在外部荷载作用下,结构块向结构带动态变化程度的过程。从细观尺度上分析结构性土体变形、破坏过程发展机制,揭示土体在荷载作用下结构块向结构带转化的过程。最后,针对杨陵黄土,通过三轴剪切试验,研究围压、含水率对破损率演化规律的影响。研究结果表明,单参数模型的破损率与围压和含水率没有关系,使从实验上证明参数模型的破损率是大主应变的函数。     

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.     

3D analysis of kinematic behavior of granular materials in triaxial testing using DEM with flexible membrane boundary

This paper describes the constitutive behavior and particle-scale kinematics of granular materials in three-dimensional (3D) axisymmetric triaxial testing using discrete element method (DEM). PFC3D code was used to run the DEM simulations using a flexible membrane boundary model consisting of spherical particles linked through flexible contact bonds. The overall deformation behavior of the specimen was then compared with the specimen with rigid boundary and experimental measurements. Computed tomography was used to track the evolution of particle translation and rotation within a laboratory triaxial specimen in 3D. The DEM model of the flexible membrane specimen successfully predicted the stress–strain behavior when compared with laboratory experiment results at different confining pressures. The DEM results showed that the rigid specimen applies a uniform deformation and leads to non-uniformities in the confining stress along the particle-boundary interface in the lateral direction. In contrast, the flexible specimen better replicates the uniformly applied confining stress of a laboratory triaxial experiment. The 3D DEM simulations of the specimen with flexible membrane overpredicted particle translation and rotation in all directions when compared to a laboratory triaxial specimen. The difference between the particle translation and rotation distributions of DEM specimens with rigid and flexible membrane is almost negligible. The DEM specimen with flexible membrane produces a better prediction of the macroscopic stress–strain behavior and deformation characteristics of granular materials in 3D DEM simulations when compared to a specimen with rigid membrane. Comparing macroscale response and particle-scale kinematics between triaxial simulation results of rigid versus flexible membrane demonstrated the significant influence of boundary effects on the constitutive behavior of granular materials.