Micromechanical approach to effective viscoelastic properties of micro‐fractured geomaterials

The aim of this paper is to formulate a micromechanics‐based approach to non‐aging viscoelastic behavior of materials with randomly distributed micro‐fractures. Unlike cracks, fractures are discontinuities that are able to transfer stresses and can therefore be regarded from a mechanical viewpoint as interfaces endowed with a specific behavior under normal and shear loading. Making use of the elastic‐viscoelastic correspondence principle together with a Mori‐Tanka homogenization scheme, the effective viscoelastic behavior is assessed from properties of the material constituents and damage parameters related to density and size of fractures. It is notably shown that the homogenized behavior thus formulated can be described in most cases by means of a generalized Maxwell rheological model. For practical implementation in structural analyses, an approximate model for the isotropic homogenized fractured medium is formulated within the class of Burger models. Although the approximation is basically developed for short‐term and long‐term behaviors, numerical applications indicate that the approximate Burger model accurately reproduce the homogenized viscoelastic behavior also in the transient conditions.     

Numerical study of excavation induced fractures using an extended rigid block spring method

This paper presents a numerical study of fracturing process induced by excavation around a gallery using an extended rigid block spring method (RBSM). The surrounding rock mass is characterized by an assembly of rigid blocks based on a degraded Voronoi diagram. The macroscopic mechanical behavior of rock is related to that of interfaces between blocks. The mechanical behavior of each interface is described by its elastic stiffness and failure criterion. The failure process of interface is controlled by both normal stress and shear stress. Both tensile and shear failures are considered. The macroscopic fracturing process is described by the coalescence of cracked interfaces. The rock structural anisotropy is taken into account through a spatial variation of elastic stiffness and failure strength of interfaces. A series of sensitivity studies are performed to investigate effects of gallery orientation, failure strength of interfaces and rock structural anisotropy on gallery deformation and fracturing. Numerical results are compared with in-situ observations in terms of fracture patterns.     

On incremental non‐linearity in granular media: phenomenological and multi‐scale views (Part I)

On the basis of fundamental constitutive laws such as elasticity, perfect plasticity, and pure viscosity, many elasto‐viscoplastic constitutive relations have been developed since the 1970s through phenomenological approaches. In addition, a few more recent micro‐mechanical models based on multi‐scale approaches are now able to describe the main macroscopic features of the mechanical behaviour of granular media. The purpose of this paper is to compare a phenomenological constitutive relation and a micro‐mechanical model with respect to a basic issue regularly raised about granular assemblies: the incrementally non‐linear character of their behaviour. It is shown that both phenomenological and micro‐mechanical models exhibit an incremental non‐linearity. In addition, the multi‐scale approach reveals that the macroscopic incremental non‐linearity could stem from the change in the regime of local contacts between particles (from plastic regime to elastic regime) in terms of the incremental macroscopic loading direction. Copyright © 2005 John Wiley & Sons, Ltd.     

Particle simulation of thermally-induced rock damage with consideration of temperature-dependent elastic modulus and strength

Based on the particle simulation method, a thermo-mechanical coupling particle model is proposed for simulating thermally-induced rock damage. In this model, rock material is simulated as an assembly of particles, which are connected to each other through their bonds, in the case of simulating mechanical deformation, but connected to each other through thermal pipes in the case of simulating heat conduction. The main advantages of using this model are that: (1) microscopic parameters of this model can be directly determined from the related macroscopic ones; (2) the temperature-dependent elastic modulus and strength are considered in an explicit manner, so that thermally-induced rock damage can be realistically simulated in a thermo-mechanical coupling problem. The related simulation results from an application example have demonstrated that: (1) the proposed model can produce similar behaviors to those observed in experiments; (2) the final failure is initiated from the outer surface of the testing sample and propagates toward the borehole; (3) microscopic crack initiation and propagation processes can be reasonably simulated at the cooling stage.     

Meso‐scale particle modeling of concrete deterioration caused by alkali‐aggregate reaction

A meso‐scale particle model is presented to simulate the expansion of concrete subjected to alkali‐aggregate reaction (AAR) and to analyze the AAR‐induced degradation of the mechanical properties. It is the first attempt to evaluate the deterioration mechanism due to AAR using the discrete‐element method. A three‐phase meso‐scale model for concrete composed of aggregates, mortar and the interface is established with the combination of a pre‐processing approach and the particle flow code, PFC2D. A homogeneous aggregate expansion approach is applied to model the AAR expansion. Uniaxial compression tests are conducted for the AAR‐affected concrete to examine the effects on the mechanical properties. Two specimens with different aggregate sizes are analyzed to consider the effects of aggregate size on AAR. The results show that the meso‐scale particle model is valid to predict the expansion and the internal micro‐cracking patterns caused by AAR. The two different specimens exhibit similar behavior. The Young's modulus and compressive strength are significantly reduced with the increase of AAR expansion. The shape of the stress–strain curves obtained from the compression tests clearly reflects the influence of internal micro‐cracks: an increased nonlinearity before the peak loading and a more gradual softening for more severely affected specimens. Similar macroscopic failure patterns of the specimens under compression are observed in terms of diagonal macroscopic cracks splitting the specimen into several triangular pieces, whereas localized micro‐cracks forming in slightly affected specimens are different from branching and diffusing cracks in severely affected ones, demonstrating different failure mechanisms. Copyright © 2012 John Wiley & Sons, Ltd.     

宏细观缺陷对岩体力学特性及边坡稳定影响研究

岩体是同时含有宏、细观缺陷的天然损伤地质体,如何更好地反映该两类缺陷对岩体力学特性的共同影响是亟待解决的一个重点和难点问题。采用FLAC3D中的弹脆性模型和Null模型分别描述完整岩石和上述两类缺陷的力学行为,用超细单元剖分计算模型的方法模拟岩体破坏,同时提出一个利用岩石孔隙率反映细观缺陷的新方法,研究细观缺陷即岩石孔隙率、裂隙倾角及长度等对裂隙岩体力学特性的影响。利用该方法研究了上述两类缺陷对岩质边坡临界滑面(CFS)及安全系数(FS)的影响。结果表明,宏观缺陷对岩体单轴压缩破坏模式、峰值强度和弹性模量起控制作用,同时控制岩质边坡的破坏模式和安全系数;尽管细观缺陷并不能改变宏观缺陷对岩体力学行为的控制作用,但其对这种控制作用将产生一定影响,宏细观缺陷以不同的作用机制对岩体力学特性产生影响。     

An extended Greenwood‐Williamson modelbased normal interaction law for discrete element modelling of spherical particles with surface roughness

The current work aims to develop an improved random normal interaction law based on an extended Greenwood‐Williamson (GW) model for spherical particles with surface roughness in the discrete element modelling of particle systems. The extended GW model overcomes some theoretical defects of the classic GW model when incorporated into the discrete element framework. Based on 2 nondimensional forms in which only 2 surface roughness parameters are involved, an empirical formula of the improved interaction law is derived by the curve‐fitting technique. The resulting interaction law is incorporated into discrete element modelling to investigate the mechanical response of particle systems with different surface roughness. Numerical simulations are performed to model 1‐dimensional and 3‐dimensional compression tests to explore the macro and micro characteristics of granular particles with surface roughness. The results show that surface roughness makes the initial packing of a particle assembly looser and has a greater influence on looser packed samples as expected, but an assembly with moderate roughness may exhibit a higher strength. The limitations of the current development are also highlighted.     

Characterization of clastic rock using a biconcave bond model of DEM

This paper presents a biconcave bond model to investigate the effect of the cementation between grains on the mechanical behavior of rock. The proposed model considers the shape of the bonds among particles that have a biconcave cement form, based on observations of microscopic rock images. The general equations of the proposed model are based on Dvorkin theory. The accuracy and efficiency of the bond model is improved in three ways. After the biconcave bond model is implemented in the discrete element method software Particle Flow Code in 2 Dimensions, a series of numerical uniaxial compression tests were performed to investigate the relationships between the micro‐ to macro‐parameters. The simulations revealed that the biconcave bond model reflects the effect of micro‐parameters, such as the elastic modulus and Poisson's ratio of the cement, on the macroscopic deformation of cemented granular material. Variations in the bond geometry caused extremely diverse macro‐mechanical behaviors. Experimental results concerning rock demonstrate that the biconcave bond model accurately captures the mechanical behavior of intact rock and supports an innovative method for investigating the relationships between the micro‐ and macro‐parameters of cemented granular material. Copyright © 2016 John Wiley & Sons, Ltd.     

A macroscopic damage‐plastic constitutive law for modeling quasi‐brittle fracture and ductile behavior of concrete

A new phenomenological macroscopic constitutive model for the numerical simulation of quasi‐brittle fracture and ductile concrete behavior, under general triaxial stress conditions, is presented. The model is particularly addressed to simulate a wide range of confinement stress states, as also, to capture the strong influence of the mean stress value in the concrete failure mechanisms. The model is based on a two‐surface damage‐plastic formulation. The mechanical behavior in different domains of the stress space is separately described by means of a quasi‐brittle or ductile material response:

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From micro scale to boundary value problem: using a micromechanically based model

Acta Geotechnica - A 3D multi-scale approach is presented to investigate the mechanical behavior of a macroscopic specimen consisting of a granular assembly, as a boundary value problem. The core...     

非连续子母块体理论模型研究(Ⅰ):基本理论

对节理岩体的非连续变形与破坏失稳的数值模拟分析是目前岩土力学与工程领域中的前沿课题之一,岩体由节理裂隙以及由其切割而成岩石块体组成,介于连续与非连续之间,由于其内部结构的不确定性造成了其宏观力学行为的复杂性。在讨论了岩体破坏失稳的研究尺度的基础上,从多尺度耦合的角度出发,同时考虑连续问题、非连续问题以及连续问题向非连续问题转化,提出了非连续子母块体理论模型。在非连续子母块体理论模型中,假定岩体与岩体内部被层理、节理等结构面所切割而成的岩石块体均属于宏观尺度,把宏观的岩石块体定义为母块体,用假想的人工节理将其继续分为若干更小的块体,更小的块体称为子块体,子块体为各向同性的均质体,并且在计算中不再发生破坏分解为更小的块体,作为计算分析的基本单元,子块体的研究尺度属于细观尺度。模型也重新定义了子块体间的接触,并将其划分为连续接触与非连续接触两种类型,连续接触在一定条件下发生破坏转化为非连续接触;采用增广拉格朗日乘子法对子块体间的接触进行处理,能够计算出准确的弹簧接触力。     

考虑颗粒棱角影响的直剪试验的离散元模拟

为了研究颗粒棱角对颗粒材料力学行为的影响,建立了具有不同棱角度的对称多面体颗粒,采用了一种简单并适合任意颗粒形状的接触本构模型,对三维离散元开源程序YADE进行了修改,研究了颗粒棱角度在模拟直剪试验中的影响以及接触力各向异性在剪切过程中的演化规律。研究结果表明,颗粒棱角度越小,颗粒间相互咬合自锁的作用越小,颗粒受剪更易转动,致使颗粒体系的剪切强度和剪胀性下降;竖向加载力越大,颗粒棱角度的影响越明显;法向接触力的各向异性在剪切过程中表现为先增后减最后趋向稳定的趋势;法向接触力的各向异性变化程度随颗粒棱角度的增大而增大。     

Stability analysis of tunnels driven in jointed rocks by means of a homogenized limit analysis approach

Conceived as a potential alternative to the classical design methods employed for analyzing the stability of underground structures driven in jointed rocks, the homogenization approach stems from the heuristic idea that, from a macroscopic point of view, a rock mass cut by a network of joints may be perceived as a homogenized continuum. The strength properties of the latter can be theoretically obtained from the failure conditions of its individual constituents: rock matrix and joint interfaces. At the material level, the limit analysis reasoning is used in the context of homogenization to formulate the homogenized strength criterion of a jointed rock mass in the particular situation of a single set of parallel joints. As it could be expected, the obtained closed‐form expressions show the strength anisotropy induced by joint preferential orientation. The support functions (π functions) associated with the homogenized strength criterion are also determined in both plane strain and three‐dimensional cases. This criterion is then applied to the investigation of stability analysis of a tunnel excavated in a jointed rock mass. Upper bounds estimated of the stability factor are derived from the implementation of the kinematic approach directly on the homogenized underground structure. Finally, the approach is applied to analyze and discuss the collapse of the Pinheiros subway station (São Paulo, Brazil). Copyright © 2014 John Wiley & Sons, Ltd.     

Multiscale modeling of a sensitive marine clay

This paper examines the mechanical behavior of a sensitive marine clay. Various laboratory tests on intact and reconstituted samples of Guinea Gulf marine clay were performed under isotropic compression and drained triaxial compression at constant confining stresses. Microstructure analysis on intact and reconstituted samples was also carried out under different loading conditions. The effect of inter‐aggregates bonding on mechanical properties is discussed. Based on experimental analysis, a new modeling method is proposed. In this approach, the clay is regarded as an assembly of aggregates of clay particles. An inter‐aggregate contact law is introduced relating contact forces to aggregates relative displacements. The deformation of the assembly can be obtained by integrating the movement of the inter‐aggregate contacts in all orientations. Thus, the effect of inter‐aggregates bonds and debonding is considered in a direct way. The model is evaluated through comparisons between the predicted and measured results on Guinea Gulf marine clay. The evolutions of local stresses, strains, and bonds in inter‐aggregates planes are discussed to explain the anisotropy induced by the applied loading. Copyright © 2010 John Wiley & Sons, Ltd.     

土坡稳定分析的颗粒流模拟

边坡的失稳破坏运动是一个存在岩土体的滑动、平移、转动的复杂过程,具有宏观上的不连续性和单个块体运动的随机性。采用颗粒流模拟土坡的变形破坏全过程,不需要假定滑移面的位置和形状,颗粒根据所受到的接触力调整其位置,最终从抗剪强度最弱的面发生剪切破坏,因此离散元法是模拟边坡变形破坏力学行为的比较理想的途径。运用PFC（颗粒流）程序对砂性土坡和黏性土坡分别进行数值模拟,分析细观参数对土坡破坏型式的影响。结果显示,土性对边坡的破坏型式有很大的影响,随着颗粒黏性的增大,边坡破坏类型从塑性破坏向脆性破坏过渡。     

Physical and numerical investigation of a cemented granular assembly of steel spheres

In this paper, steel spheres embedded in a cement matrix were studied using numerical and physical ISRM testing procedures. A challenge in discrete element simulations is to select appropriate micro‐mechanical models and parameters, to recover the observed macro‐mechanical behavior. An ideal experiment on cohesive granular assemblies constructed identical to numerical ones would validate these micro models for a set of measured micro‐parameters. The first part of the paper summarizes the previous studies in this area, outlines such experimental methodology and depicts the steps followed for the preparation and the testing of cemented granular assemblies together with the derivation of micro‐parameters. The second part discusses the results of numerical and physical ISRM standard tests including uniaxial and triaxial compression, Brazilian tensile and shear box tests. Physical samples were prepared using steel balls bonded with Portland cement, cured under controlled laboratory conditions and tested in compression, tension and shearing. Acoustic emissions were monitored in uniaxial tests to characterize the damage thresholds relative to volumetric strains. Numerical simulations were conducted with PFC 3D using micro‐mechanical parameters derived from physical testing. Parametric sensitivity studies were carried out to look into the dependency of macroscopic responses on the parameters. The results from both numerical and physical tests showed good correspondence in macroscopic behavior i.e. peak strength, stages of damage, mode of failures. However, the numerical simulations reflected a stiffer mechanical response than physical assemblies. Copyright © 2010 John Wiley & Sons, Ltd.     

A Strain Rate Dependent Constitutive Model for the Lower Silurian Longmaxi Formation Shale in the Fuling Gas Field of the Sichuan Basin,China

Shale, as a kind of brittle rock, often exhibits different nonlinear stress-strain behavior, failure and time-dependent behavior under different strain rates. To capture these features, this work conducted triaxial compression tests under axial strain rates ranging from 5×10?6 s?1 to 1×10?3 s?1. The results show that both elastic modulus and peak strength have a positive correlation relationship with strain rates. These strain rate-dependent mechanical behaviors of shale are originated from damage growth, which is described by a damage parameter. When axial strain is the same, the damage parameter is positively correlated with strain rate. When strain rate is the same, with an increase of axial strain, the damage parameter decreases firstly from an initial value (about 0.1 to 0.2), soon reaches its minimum (about 0.1), and then increases to an asymptotic value of 0.8. Based on the experimental results, taking yield stress as the cut-off point and considering damage variable evolution, a new measure of micro-mechanical strength is proposed. Based on the Lemaitre’s equivalent strain assumption and the new measure of micro-mechanical strength, a statistical strain-rate dependent damage constitutive model for shale that couples physically meaningful model parameters was established. Numerical back-calculations of these triaxial compression tests results demonstrate the ability of the model to reproduce the primary features of the strain rate dependent mechanical behavior of shale.     

边坡稳定分析条块力-位移法及其应用

在现行条分法的基础上,建立了一种全新的边坡条块力-位移分析方法。现行条分法中条块底边的力学参数采用极限平衡状态力学参数,即每个条块底边均处于极限平衡状态,这种极限平衡状态对于残余应力是较为适宜的。采用理想弹塑性模型和一种全新的本构模型描述土条块底边力学特性,并以不平衡推力法为例,提出了临界状态条块的确定方法,针对可能的破坏模式进行了分析,并提出了边坡整体破坏各条块的应力和位移的确定方法,计算出相应的稳定系数,如传统强度折减法、综合下滑力-抗滑力法、主推力法、综合位移法和富余位移法稳定系数。通过计算分析论证了理想弹塑性模型在不改变力学参数的情况下是难以描述边坡渐近破坏过程的,而一种全新的本构模型可以描述渐近破坏各条块的力学行为。提出的条块力-位移法可以确定边坡在不同荷载和位移条件下的稳定性,也可以获得边坡的推力变化和滑面移动特征,进而实施边坡的应力、位移和稳定性的初步预测预报。