土体强度与变形尺度特性的理论与试验分析

土体是一种颗粒介质,其强度与变形特性具有显著的颗粒尺度效应。采用胞元土体模型和三轴抗剪试验分析了土体强度和变形的尺度效应特性。根据土体中不同尺度颗粒间相互作用表现出的聚集和摩擦效应,提出了“基体-增强颗粒”土体胞元模型,胞元体由基体和增强颗粒组成,其中基体由微小土颗粒集成,而增强颗粒为砂粒,宏观土体则简化为由许多胞元体构成的介质。引入广义球应变和广义等效应变,基于应变能导出了考虑颗粒尺度效应的应力-应变关系以及屈服应力计算公式;同时,针对增强颗粒不同粒径和体分比的土体进行一系列三轴不排水抗剪试验,给出了应力-应变和屈服应力尺度效应的测试结果。试验和理论计算结果均表明,土体强度和变形的尺度效应随增强颗粒的体分比增加以及粒径的减小而增强,由此反映出土体强度和变形显著的尺度效应;土体强度和变形尺度效应的理论预测结果与试验具有较好的一致性。     

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。     

应力路径对砂土变形特性影响的细观机制研究

在对已有试验结果进行分析基础上,从细观角度研究了砂土变形机制。通过对简化的颗粒单元体的受力及变形分析,推导了主应力比与θ的关系以及孔隙比与θ的关系。结果表明,颗粒单元体变形过程中主应力比与孔隙比有着对应的关系,这与"应力路径对塑性体应变的影响主要是由应力比引起的"的试验结论是一致的。从细观角度分析了应力路径(主要是主应力比)影响砂土变形的过程。研究表明,砂土体中存在着大孔隙以及两种基本状态的颗粒单元体结构孔隙,它们是控制砂土变形特性的关键因素,大孔隙受应力路径影响不大,而颗粒单元体结构孔隙则与应力路径密切相关,主要表现为主应力比对塑性体应变的影响;从细观角度分析了峰值应力比与相变应力比的关系,即初始孔隙比越小,相变应力比越低,峰值应力比越高,这与宏观试验结果是一致的。     

一种适用于孔隙体积应变的有效应力方程

土力学奠基石Terzaghi有效应力原理被广泛应用于油藏孔隙和渗透率应力敏感研究中,然而其对于岩石孔隙体积应变的适用性存在争议。对颗粒不可压缩和颗粒可压缩的多孔介质分别进行了受力分析,推导了总体积、颗粒骨架、孔隙体积的有效应力表达式,与Biot、Skepmton有效应力方程对比,建立了适用于孔隙体积应变的新型有效应力方程,并进行了试验论证和应用举例。研究表明:在颗粒不可压缩多孔介质中,有效应力为超出平衡孔隙流压之外的颗粒间宏观等效应力;在颗粒可压缩变形多孔介质中,有效应力为其相同应变下的等效应力,有3种有效应力分别适用于总体积应变、颗粒体积应变、孔隙体积应变;新提出的孔隙体积有效应力方程与孔隙度、岩石总体积压缩系数、颗粒压缩系数、总应力和流压相关,4个理论计算式计算结果在3种多孔介质试验测试结果中的偏差均在5%以内;孔隙体积有效应力系数解决了如何定量增总应力来等效模拟储层降流压生产过程这一关键问题,3个压缩系数关系式理论计算准确方便。     

基于颗粒组构特性的散体材料本构模型研究

通过散体介质材料单元颗粒排列组构表达的细观结构力学关系,建立了用颗粒密集度、颗粒排列组构关系和颗粒间摩擦特性等非连续介质材料特性参数描述的散体介质材料本构模型,从而实现散体介质材料宏观连续介质描述的等效应力表达.通过该模型可采用数值方法进行散体介质材料准静态情况下的力学特性分析.文中最后基于有限元软件ABAQUS,进行了该本构模型的二次开发.数值算例结果验证了所建立散体介质材料本构模型的适用性.     

颗粒材料剪胀性的微观力学分析

剪胀性是颗粒材料在加载过程中表现出来的重要变形特性。以孔隙胞元描述颗粒材料内部结构的最小单元,通过对单个孔隙胞元进行剪切受力分析,探讨了剪切过程中颗粒材料体积的改变对应力比和单个孔隙胞元形状的依赖关系,解释了排列密实的颗粒材料在剪切过程中先压缩后剪胀的微观机制。用离散元数值模拟得到了在双轴剪切过程中单个孔隙胞元形状以及孔隙胞元体积变形的演化过程。离散元数值结果表明,加载过程中孔隙胞元形状由初始各向同性到沿大主应力方向变大变长、体积变形先压缩后膨胀,并且体积变形在加载过程中存在局部化现象,体积变化大的孔隙胞元在较大变形时,排列成倾斜的窄带。综合孔隙胞元的受力分析和离散元数值结果表明,致密排列颗粒材料的剪胀性与微观尺度上孔隙胞元的几何结构及其内部的力链传递方式密切相关。     

岩石材料冲击压缩特性细观模拟方法研究

岩石材料的细观特性对宏观力学性能有着重要影响。为了分析岩石材料颗粒形态、孔隙和含水等细观特性对宏观冲击响应行为的影响规律,从岩石材料的细观特性入手,结合材料细观结构照片,经制图软件矢量化和轮廓处理,建立了能够反映材料细观分布特性的岩石材料有限元模型。基于AUTODYN有限元计算软件,对岩石材料冲击压缩细观行为进行数值模拟,获取材料颗粒形态、孔隙和含水等细观特性对材料宏观冲击压缩特性的影响规律。确定岩石材料冲击Hugoniot参数,应用于冲击开坑仿真中,并与已有的试验结果进行了对比。结果表明:数值仿真结果与已有试验数据吻合较好;孔隙率和含水率对岩石材料冲击波衰减规律有十分显著的影响;细观模拟确定的Hugoniot参数运用到岩石材料宏观动力学行为数值模拟中,可有效反映岩石材料中颗粒、孔隙和含水等细观特性对冲击开坑行为的影响规律。     

抗转动特性对颗粒材料分散性失稳的影响研究

对于岩土类的颗粒材料,在特定的应变加载路径下会发生非局部化的失稳现象,此时应力状态处于Mohr-Coulomb屈服面内,试样整体急剧失稳。采用颗粒离散元方法,研究抗转动特性对颗粒材料在等比例应变加载路径下宏、细观力学特性的影响。模拟发现,较为松散的试样更易发生分散性失稳,此时颗粒集合体的应力-应变状态满足Hill材料失稳准则。采用考虑颗粒转动的接触模型进行离散元模拟,通过改变颗粒间接触的转动摩擦系数,从宏观和细观层面分析等比例应变加载路径中颗粒材料的稳定性。颗粒抗转动能力的增强可以降低材料发生分散性失稳的可能性,随着转动摩擦系数的增加,应力路径由应变软化逐渐转为应变硬化,原本会发生分散性失稳的松散颗粒集合体表现出与密实颗粒集合体相似的宏观力学特性;颗粒集合体的内部结构表现出相应的细观作用机制,转动摩擦系数的增加有效地抑制了颗粒转动,虽然降低了颗粒体系的配位数,但增加了颗粒之间的接触力,增强了颗粒体系力链结构的稳定性和各向异性,形成稳定的结构持续抵抗外荷载的施加,从而试样整体不会形成松散的接触状态而失去稳定性。     

颗粒材料的微观临界状态理论模型

存在临界状态是颗粒材料的一个重要特性。基于孔隙胞元的颗粒离散元方法对二维颗粒体进行双轴加载数值试验,在详细分析数值模拟结果的基础上,从微观几何组构的角度揭示了临界状态的存在机制。基于剪胀性原理,提出了以接触价键表征的微观临界状态理论模型,得到了接触价键与塑性剪切应变的关系表达式,理论模型的结果和二维离散元数值模拟得到的结果吻合较好。通过比较不同情况下数值结果和理论模型中的参数,得到以下结论：表征微观临界状态的参数（临界接触价键和达到临界状态所需要的塑性剪切应变）依赖于颗粒体的微观特性,如颗粒形状、表面摩擦性质、颗粒体的围压和初始孔隙比。     

基于黏弹性接触的颗粒材料蠕变特性研究EI北大核心CSCD

强黏结土体或胶凝砂砾石料等颗粒材料的颗粒间存在较大黏结力,在低应力情况下主要由颗粒接触特性决定颗粒材料的宏观蠕变特性。基于颗粒细观力学方法,研究了二维各向同性颗粒材料的蠕变特性。首先引入速率相关的力与位移关系描述颗粒材料细观颗粒间特性。其次,运用Laplace变换,将时间域内的线黏弹性颗粒材料细观均匀化问题转化为拉氏空间内线弹性颗粒材料细观均匀化问题,随后基于颗粒材料线弹性问题在Reuss、Voigt和一般位移场三种假设下的解,通过Laplace逆变换得到颗粒材料相应的宏观蠕变特性解析模型,并建立了材料蠕变特性的上下限。最后,通过理论模型的解析解与商业软件(PFC2D)的数值结果的对比,验证了理论模型的合理性。     

A generalised D matrix for anisotropic elastic granular media

A matrix relating stress and elastic strain tensors for anisotropic particulate materials has been derived. The magnitude of the matrix depends on the state of the material anisotropy. Anisotropy in granular materials depends on strain because normal and tangential particle contact forces, as well as the spatial distribution of the contacts, vary with stress and strain. However, the rotation tensor and the strain tensor cannot be independent; they must satisfy certain constraints to meet the requirement for macroscopic stress tensor symmetry. These conditions and constraints lead to the derivation of the matrix presented in this article. The principal directions of the stress tensor and strain tensor are generally not coincident, and the values of deformation parameters, Young's modulus and Poisson's ratio, are direction dependent; these two aspects are also discussed in this paper. Whereas this matrix can be used in static numerical analyses for elastic problems, we note that this relationship can also be used as a basis upon which to derive a fully incremental stress–strain relationship for anisotropic granular materials in the plastic state, where the anisotropy is evolving with strain.     

Revisiting the existence of an effective stress for wet granular soils with micromechanics

A possible effective stress variable for wet granular materials is numerically investigated based on an adapted discrete element method (DEM) model for an ideal three‐phase system. The DEM simulations consider granular materials made of nearly monodisperse spherical particles, in the pendular regime with the pore fluid mixture consisting of distinct water menisci bridging particle pairs. The contact force‐related stress contribution to the total stresses is isolated and tested as the effective stress candidate for dense or loose systems. It is first recalled that this contact stress tensor is indeed an adequate effective stress that describes stress limit states of wet samples with the same Mohr‐Coulomb criterion associated with their dry counterparts. As for constitutive relationships, it is demonstrated that the contact stress tensor used in conjunction with dry constitutive relations does describe the strains of wet samples during an initial strain regime but not beyond. Outside this so‐called quasi‐static strain regime, whose extent is much greater for dense than loose materials, dramatic changes in the contact network prevent macroscale contact stress‐strain relationships to apply in the same manner to dry and unsaturated conditions. The presented numerical results also reveal unexpected constitutive bifurcations for the loose material, related to stick‐slip macrobehavior.     

Constitutive modelling of granular materials using a contact normal-based fabric tensor

This paper presents a fabric tensor-based bounding surface model accounting for anisotropic behaviour (e.g. the dependency of peak strength on loading direction and non-coaxial deformation) of granular materials. This model is developed based on a well-calibrated isotropic bounding surface model. The yield surface is modified by incorporating the back stress which is proportional to a contact normal-based fabric tensor for characterising fabric anisotropy. The evolution law of the fabric tensor, which is dependent on both rates of the stress ratio and the plastic strain, rules that the material fabric tends to align with the loading direction and evolves towards a unique critical state fabric tensor under monotonic shearing. The incorporation of the evolution law leads to a rotational hardening of the yield surface. The anisotropic critical state is assumed to be independent of the initial values of void ratio and fabric tensor. The critical state fabric tensor has the same intermediate stress ratio (i.e. b value) and principal directions as the critical state stress tensor. A non-associated flow rule in the deviatoric plane is adopted, which is able to predict the non-coaxial flow naturally. The stress–strain relation and fabric evolution of model predictions show a satisfactory agreement with DEM simulation results under monotonic shearing with different loading directions. The model is also validated by comparing with laboratory test results of Leighton Buzzard sand and Toyoura sand under various loading paths. The comparison results demonstrate encouraging applicability of the model for predicting the anisotropic behaviour of granular materials.

     

A critical state sand plasticity model accounting for fabric evolution

Fabric and its evolution need to be fully considered for effective modeling of the anisotropic behavior of cohesionless granular sand. In this study, a three‐dimensional anisotropic model for granular material is proposed based on the anisotropic critical state theory recently proposed by Li & Dafalias [2012], in which the role of fabric evolution is highlighted. An explicit expression for the yield function is proposed in terms of the invariants and joint invariants of the normalized deviatoric stress ratio tensor and the deviatoric fabric tensor. A void‐based fabric tensor that characterizes the average void size and its orientation of a granular assembly is employed in the model. Upon plastic loading, the material fabric is assumed to evolve continuously with its principal direction tending steadily towards the loading direction. A fabric evolution law is proposed to describe this behavior. With these considerations, a non‐coaxial flow rule is naturally obtained. The model is shown to be capable of characterizing the complex anisotropic behavior of granular materials under monotonic loading conditions and meanwhile retains a relatively simple formulation for numerical implementation. The model predictions of typical behavior of both Toyoura sand and Fraser River sand compare well with experimental data. Copyright © 2013 John Wiley & Sons, Ltd.     

A micromorphic elastoplastic model and finite element simulation on failure behaviors of granular materials

One of the purposes in this study is to develop a modified micromorphic continuum model for granular materials on the basis of a micromechanics approach. A symmetric curvature tensor is proposed in this model, and a symmetric couple stress tensor is derived conjugating the symmetric curvature tensor. In addition, a correct derivation is presented to obtain the symmetric stress tensor conjugated with the symmetric strain tensor. The modified model provides a complete deformation mode for granular materials by considering the decomposition for motions (displacement and rotation) of particles. Consequently, the macroscopic constitutive relationships and constitutive moduli are derived in expressions of the microstructural information. Furthermore, the balance equations and boundary conditions are obtained for the modified micromorphic model. By considering the extended Drucker-Prager yield criterion, the micromorphic elastoplastic model is developed. Another purpose of this study is to derive the finite element formulation for the developed micromorphic elastoplastic model. Based on the ABAQUS user element (UEL) interface, numerical simulations investigated the load-displacement relationship and the strain localization behavior of granular materials and investigated the influence of microscopic parameters in the micromorphic model on these macroscopic mechanical responses. Numerical results illustrate the presented model's capability of simulating the strain-softening and strain localization behaviors, and the capability of considering the influence of microstructural information on the macroscopic mechanical behaviors of granular materials.     

Strength anisotropy of granular material consisting of perfectly round particles

The strength anisotropy of granular materials deposited under gravity has mostly been attributed to elongated particles' tendency to align long axes along the bedding plane direction. However, recent experiments on near‐spherical glass beads, for which preferred particle alignment is inapplicable, have exhibited surprisingly strong strength anisotropy. This study tests the hypothesis that certain amount of fabric anisotropy caused by the anisotropic stress during deposition under gravity can be locked in a circular‐particle deposit. Such locked‐in fabric anisotropy can withstand isotropic consolidation and leads to significant strength anisotropy. 2D discrete element method simulations of direct shear tests on circular‐particle deposits are conducted in this study, allowing for the monitoring of both stress and fabric. Simulations on both monodispersed and polydispersed circular‐particle samples generated under downward gravitational acceleration exhibit clear anisotropy in shear strength, thereby proving the hypothesis. When using contact normal‐based and void‐based fabric tensors to quantify fabric anisotropy in the material, we find that the intensity of anisotropy is discernible but low prior to shearing and is dependent on the consolidation process and the dispersity of the sample. The fact that samples with very low anisotropy intensity measurements still exhibit fairly strong strength anisotropy suggests that current typical contact normal‐based and void‐based second‐order fabric tensor formulations may not be very effective in reflecting the anisotropic peak shear strength of granular materials. Copyright © 2017 John Wiley & Sons, Ltd.     

On the stress-force-fabric equation in triaxial compressions: Some insights into the triaxial strength

The strength of granular materials during triaxial compression is investigated via a grain scale analysis in this paper. A 3D Discrete Element Method (DEM) program provides the triaxial strength data and helps to validate the micromechanical analysis. Some standard methods in statistics are employed first to quantitatively examine the assumptions made when deriving the stress-force-fabric (SFF) equation. After careful validation, a more concise format for the SFF equation is proposed for triaxial compressions. With this SFF equation, the strength is found to be jointly contributed by the magnitudes of the contact force anisotropy and fabric anisotropy. The influence of the initial void ratio, confining pressure and loading direction on the development of contact force anisotropy and fabric anisotropy is examined and presented. With similar techniques, the “force” term in the SFF equation is further decoupled, and an equation is obtained such that it explicitly links the contact force term with the friction coefficient between grains, a tensor defined as a statistic of the normal contact forces and a tensor defined as a statistic of the mobilisation status of contacts. Based on this equation, another equation regarding the stress ratio of granular assembly is obtained, and it clearly indicates two sources that contribute to the phenomenological friction nature of granular assembly. These two sources are caused by the contact force at the grain scale. The first is the anisotropy of the average normal contact forces, and the second is the mobilisation of contacts.     

A generalized constitutive relation for a randomly packed particle assembly

A generalized stress-strain relationship is derived for a randomly packed particle assembly taking into account the effect of particle rotation. A second-order polynomial function is assumed for the field of particle displacement. From the principle of virtual work, stress measures for a granular solid are expressed in terms of contact forces, contact moments, and geometric measures for the particle structure. An explicit stress-strain relationship is derived for isotropic packing with equal-sized particles. Examples of a representative element under torsion and bending are given to demonstrate the applicability of the presently derived higher-order stress-strain relationship.     

Numerical investigations of shear localization in a micro‐polar hypoplastic material

In this paper a micro‐polar continuum approach is proposed to model the essential properties of cohesionless granular materials like sand. The model takes into account the influence of particle rotations, the mean grain size, the void ratio, the stresses and couple stresses. The constitutive equations for the stresses and couple stresses are incrementally non‐linear and based on the concept of hypoplasticity. For plane strain problems the implementation of the model in a finite element program is described. Numerical studies of the evolution of micro‐polar effects within a granular strip under plane shearing are presented. It is shown that the location and evolution of shear localization is strongly influenced by the initial state and the micro‐polar boundary conditions. For large shearing the state quantities tend towards a stationary state for which a certain coupling between the norm of the stress deviator and the norm of the couple stress tensor can be derived. Copyright © 2003 John Wiley & Sons, Ltd.