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.     

三维离散元单轴试验模拟甲烷水合物宏观三轴强度特性

填充型水合物的砂性能源土试样可视为特殊的散粒体材料,即砂粒和水合物颗粒混合物,具有明显的非连续特征。为研究填充型水合物的能源土力学特性,初步探索了甲烷水合物在不同温度、反压条件下加荷模式的离散元模拟方法。离散元模拟中,将水合物块体视为由大量颗粒通过强胶结作用凝聚而成的整体,室内试验中的内部孔隙水压作用转化为水合物颗粒间的胶结力,故需要合理确定颗粒间胶结模型参数来实现反压的影响作用。通过参数反演建立了宏观强度、刚度参数与平行胶结模型的微观胶结参数间的宏、微观关系,基于已有室内甲烷水合物三轴试验资料,确定了给定温度和反压条件下的微观胶结参数取值,随后进行离散元单轴压缩试验。离散元单轴压缩试验模拟获得的水合物强度特性,与室内三轴试验结果符合较好;通过建立的宏、微观参数间的关系,实现了不同温度、反压下的水合物加荷模式的模拟。为进一步提出深海能源土离散元数值试验成样方法--孔隙填充水合物生成技术,形成含填充型水合物的能源土试样,研究其力学和变形特性奠定基础。     

Undrained Triaxial Behavior of Cement Treated Marine Clay

Clays treated with lower cement contents often exhibit behaviour similar to stiff clays with planar failure surface under triaxial compression. In the present work the behaviour of a marine clay treated with 5 % cement, subjected to undrained triaxial compression tests is studied. The pre-consolidation pressure of the cemented clay due to the cementation bonding is observed to be very high. It is attempted to model the behaviour of cement treated clay using a bounding surface plasticity formulation as the plastic behaviour of the cemented clays within the yield surface has to be considered. The effect of cementation is included in the model as the pre-consolidation pressure obtained from consolidation tests. The tensile strength due to cementation bonds is included in the equation of the bounding surface. Simulations of the undrained triaxial compression tests on cemented clays are carried out and the results are validated with the experimental results.     

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。     

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.     

Strength of two structured soils in triaxial compression

Oil sands are dense granular materials with interlocked structure and clay shales are heavily overconsolidated clays. They are classified as structured soil or weak rock, exhibiting high peak strength with severe softening and dilation, particularly at low confining stress. The triaxial compression test results indicate that both materials yield linear Mohr–Coulomb envelopes with an apparent cohesion for peak and residual strengths. However, the strength components mobilized from these two materials are very different. This paper investigates if these strength parameters are intrinsic properties or responses derived in triaxial compression conditions. Computer tomography scanning technique is used to aid in examining the micro‐structural features of the sheared specimens such as shear banding pattern, shear band thickness, spatial porosity distributions inside and outside shear bands. These micro‐structural features are used to explain the macro‐deformation response observed in the triaxial compression tests. Mobilization of strength components derived from interlocked structure, cementation, dilation, rolling and critical state are analysed for pre‐, post‐peak softening and residual stages. It is found that the empirical correlation such as Mohr–Coulomb failure criterion based on triaxial compression test results does not necessarily reflect the intrinsic properties of the test materials. Testing conditions are embedded in the empirical correlation. Copyright © 2001 John Wiley & Sons, Ltd.     

水泥土芯样强度变形特性及本构关系试验研究

为了研究现场施工工艺下水泥土的强度及变形特性,对水泥搅拌桩钻孔芯样进行了无侧限抗压强度试验与三轴试验,分析了水泥掺量与围压对水泥土芯样强度、变形特性的影响规律。结果表明：随着水泥掺量的提高,水泥土芯样的强度明显增强,变形模量显著增大,但其破坏应变变小,脆性增大;水泥掺量超过18%的水泥土芯样其应力-应变关系表现为软化型,随着围压的提高,其强度增强,破坏应变增大,脆性降低,且应力-应变关系曲线有可能发生转型;不同围压下的水泥土芯样三轴试验先为体缩,后变化为体胀,发生剪胀的应变较破坏应变略小,是由剪切面上颗粒错动引起的,在颗粒错动达到一定程度后抗剪强度才发挥到峰值;水泥土的结构屈服应力比较大,在围压的作用下其胶结结构未发生破损,强度包线满足摩尔-库仑线性强度规律;根据水泥土的强度变形特征,应力-应变全曲线分弹性、塑性、软化3个阶段,可采用Popovics模型对其进行模拟,与试验结果较为吻合。     

基于弹性张量离散化的脆延转变本构模型研究

外部荷载作用下的裂隙扩展在空间上一般是非均匀的,引起岩石材料的衍生各向异性。将材料离散成大量随机分布的由力键连结的物质点,基于力键的方向性,且将局部弹性张量离散成一定数量的方向张量,理论推导出力键模量与宏观弹性参数之间的关系。通过考虑力键断裂效应,建立了各向异性弹性损伤本构模型。为了模拟中等孔隙率岩石在常规三轴压缩试验中脆性向延性转变的力学行为,在力键断裂效应中引入损伤抑制函数。通过模拟Tennessee大理岩和Indiana石灰岩的常规三轴实验,并与试验数据对比,验证了模型的合理性和有效性。     

Discrete element analysis of uplift and lateral capacity of a single pile in methane hydrate bearing sediments

Methane hydrate (MH) is extensively found in outer continental margins where offshore infrastructures with pile foundations are also common. The presence of MHs significantly alters the mechanical properties of the host marine sediments, and therefore affects the behavior of piles inside. This paper presents an attempt to investigate the performance of a single pile in methane hydrate bearing sands in seabed using the distinct element method. A novel bond contact model was employed for sandy grains cemented by MHs at contacts, and calibrated from the triaxial compression tests on synthetic specimens of methane hydrate bearing sands. The response of the pile subjected to axial pullout loads and lateral loads was simulated under different subsurface conditions characterized by different saturation levels of MHs. The results show that the presence of MHs increases the uplift capacity of the pile by changing the failure mode of the soils from the perimeter failure to the conical failure. The uplift capacity of the pile significantly deteriorates as a result of de-bonding, while the onset of the rapid de-bonding triggers the softening of the uplift load. In addition, the lateral capacity of the pile largely increases due to the presence of MHs. The pile in methane hydrate bearing sands is considered flexible rather than rigid as a result of the increased deformation modulus of soils due to MH cementation between particles. The lateral load–displacement diagram of the pile in methane hydrate bearing sands is not as smooth as that in clean sands with an abrupt drop associated with the onset of de-bonding.     

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.     

粉细砂的真三轴试验与强度特性

采用柔性真三轴仪对上海粉细砂进行了一系列不同中主应力系数条件下的真三轴试验,针对中主应力对粉细砂强度特性的影响进行了系统分析。基于真三轴试验结果对Mohr-Coulomb强度准则的形状函数进行了改进,并采用试验结果对强度准则进行验证。结果表明,建立在真三轴试验基础上的强度准则能更准确地反映砂土三维应力状态下的强度特性。     

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。     

固体材料应力-应变曲线趋势规律的普适性

本文通过砂岩及灰岩样本在单轴荷载下的试验发现,尽管其强度峰值及弹性模量值不同,但应力-应变曲线却极为相似。进一步的人工固体材料样本（包括石膏、混凝土、料礓石胶结石英材料等）的单轴抗压试验结果仍然给出了惊人相似的应力-应变曲线。这些曲线的综合概括形态是由三段相曲线顺序连接构成的S型曲线。中间依次出现两处相转化拐点。它表明各类固体材料在单轴荷载下应力-应变过程直至破坏的趋势性规律具有普适性。因此对各类地质工程的变形破坏过程的评价和预测有重要的参考价值。     

Laboratory determination of mechanical and hydraulic properties of chemically grouted sands

The purpose of this paper is to investigate mechanical and hydraulic properties of sands treated with mineral-based grouts through the results of a laboratory test programme consisting of unconfined compression tests (UCS), triaxial bender element tests (BeT) and constant flow permeability tests in triaxial apparatus. An improved apparatus was set up for obtaining high quality, multiple grouted specimens from a single column. Two selected natural sands having different grain sizes were grouted with two mineral-based silica grouts, resulting in different levels of improvement. The behaviour of the sands treated by mineral grouts, in terms of strength, initial stiffness and permeability, was compared with that exhibited by more traditional silicate grouts. The results of this study indicate that sands treated with mineral grouts result in higher strengths, higher initial shear modulus and lower permeability values than the sands treated with the silicate solution. The effect of grout type, effective confining pressure, and sand particle-size on small-strain shear modulus of grouted sand specimens was evaluated. Based on test results, the small strain shear modulus increment from treated to untreated specimens has been correlated with the unconfined compressive strength, obtaining a unique relationship regardless of grout type and grain-size of tested sands.     

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.     

Investigating the micro mechanics of cemented sand using DEM

The discrete element method has been used to investigate the micro mechanics of cemented sand. High‐pressure drained triaxial tests are modelled in 3D using a flexible membrane that allows the correct deformation to develop. Simulations with up to 12 MPa confining pressure are presented, which are compared with laboratory experiments on a sand with a range of cement contents. Cementation is modelled using ‘parallel bonds’, and various parameters and strength distributions are investigated. Varying levels of cementation are successfully modelled, with the correct qualitative behaviour observed and the separate effects of cementation and confining pressures demonstrated. The triaxial behaviour is found to be highly influenced by the distribution of bond strengths. Copyright © 2014 John Wiley & Sons, Ltd.     

Triaxial behaviour of a cemented gravely sand, Tehran alluvium

Cemented coarse-grained alluvium is present in a vast area of Tehran city, Iran including its suburbs. This deposit consists of gravely sand to sandy gravel with some cobbles and is dominantly cemented by carbonaceous materials. In order to understand the mechanical behaviour of this soil, a series of triaxial compression tests were performed on uncemented, artificially cemented and destructured samples. Hydrated lime was used as the cementation agent for sample preparation to model the Tehran deposit. The tests were performed on cemented samples after an appropriate time for curing. The tests on cemented samples show that a shear zone appears as the shear stress approaches the peak shear strength. During shearing these samples undergo dilation at confining stress lower than 1000kPa. However, the uncemented and destructured samples show contraction during shearing. Peak shear strength is followed by strain softening for all cemented samples. The shear strength increases with increasing cement content but the influence of the cementation decreases as the confining stress increases. With increasing cementation the stress-strain behaviour of samples tend towards the behaviour expected of high-density soils. Test results indicate that the failure envelope for cemented samples is curved and not linear.     

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。     

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.