AN INTERFACE MODEL FOR ANALYSIS OF DEFORMATION BEHAVIOUR OF DISCONTINUITIES

An interface constitutive model is presented accounting for slip and sliding effects and also for dilatancy phenomena. The microslip effects are described by considering spherical asperity interaction with variation of contact area and generation of progressive or reverse slip zones. The incremental constitutive equations are derived with proper memory rules accounting for generation and annihilation of particular slip zones during the process of variable loading. It is further assumed that sliding of spherical contacts occurs along large asperities whose slope varies due to the wear process. The predicted shear and dilatancy curves are shown to provide close quantitative simulation of available experimental data. The strain ratchetting effect for non-symmetric cyclic loading was exhibited using the asperity wear model. The model presented could be applied to simulate rock joints, masonry, or concrete cracked interfaces, under monotonic and cyclic loading.     

A consistent formulation of a dilatant interface element

The paper considers a plane joint or interface element suitable for implementation into a standard non-linear finite element code. The element is intended to model discontinuities with rough contact surfaces, such as rock joints, where dilatant behaviour is present. Of particular concern is the formulation of a constitutive model which fully caters for all possible histories of opening, closing and sliding (accompained by dilation or contraction) in any direction. The non-linear incremental constitutive equations are formulated in a manner appropriate for a back-ward difference discretization in time along the path of loading. The advantage of such an approach is that no essential distinction need be drawn between opening, closing and sliding. Further, a convenient formulation of the constitutive equations is facilitated by representing the different contact conditions in relative displacement space. The state diagram in relative displacement space, however, changes from one time step to the next, and evolution equations for the updating must be formulated. These concepts are illustrated for two rock-joint models: a sawtooth asperity model and a limited dilation model. The models are based on a penalty formulation to enforce the contact constraints, and explicit equations for the tangent stiffness matrix and for the corrector step of the standard Newton–Raphson iterative algorithm are derived. These equations have been implemented as an user element into the finite element code ABAQUS⁷. Three examples are presented to illustrate the predictions of the formulation.     

Homogenized constitutive laws for rocks with elastoplastic fractures

This work deals with the development of a constitutive law for fractured rocks. Fractures are considered as penny‐shaped inclusions, whose constitutive law is deduced from an interface law and a regularization procedure. Such a method is applied to linear and non‐linear interface behaviours in order to reproduce effects such as an increase in stiffness during fracture closing, dilatancy or asperity surface degradation. Then, considering the fractured rock as a composite material, we use a Mori–Tanaka method to estimate the homogenized properties of the rock. Numerical experiments illustrate the interest of the proposed homogenization procedure. Copyright © 2007 John Wiley & Sons, Ltd.     

Determination of asperity damage parameters for constitutive models of rock discontinuities

Dilatancy and contact surface damage are important phenomena affecting the behaviour of rock joints and other geological discontinuities. Effective constitutive laws that incorporate these behaviours have recently been developed but require the specification of new material parameters that govern damage of asperity surfaces. Determination of the parameters that control damage is currently a difficulty that confronts practitioners. This brief will summarize the findings of Hutson and Dowding's investigation of joint surface asperity degradation and elaborate on the implications for application.     

A material model for inelastic rock deformation with spatial variation of pore pressure

This paper sets forth the theoretical background and basic numerical expressions for the incorporation of elastic-plastic constitutive equations for ductile rock into a finite element computer code. The derivation of an expression for the total strain rate is performed both for a total stress formulation and for a formulation that employs the concept of effective stress for inelastic behaviour. Specific expressions for the incremental strain rate are presented for the case of a porous material having a quadratic initial yield surface and observing the associated flow rule with a special hardening law for subsequent plastic deformation. A final section of the paper summarizes the expressions required to insert the quadratic yield surface model into a finite element code.     

循环剪切荷载作用下含二阶起伏体模拟岩石节理力学特性研究

利用人工材料浇注含二阶起伏体的模拟岩石节理试样,进行常法向荷载循环剪切试验,研究节理剪切力学特性在循环剪切过程中的劣化规律。试验结果表明：二阶起伏体对节理循环剪切力学特性有重要影响,剪切强度、剪切刚度、剪胀角随剪切循环次数增大而衰减,衰减趋势随着二阶起伏度的增大而加快;法向应力、二阶起伏度较大时,二阶起伏体对剪切力学特性的影响主要体现在第1轮剪切循环中,在随后的剪切循环中影响不明显;法向应力、二阶起伏度较小时,二阶起伏体的影响在前几轮循环剪切过程中均有较清晰的体现。基于Hertz接触力学理论,提出了节理面微凸体球面接触细观模型,揭示了节理循环剪切宏观试验现象的力学机制     

An anisotropic Model for Structured Soils: Part I: Theory

The paper presents an incremental plasticity constitutive Model for Structured Soils (MSS–2) to describe the effects of structure (stress history and bonding) on the mechanical behaviour of cohesive soils. Such effects are high initial stiffness, dilatancy and peak strength, their appreciable reduction upon strain-induced de-structuring and the evolution of material anisotropy. The proposed model advances present practice in incremental elasto-plasticity for structured soils by incorporating: (a) distorted ellipsoids, rotated with respect to the isotropic axis, for the Structure Strength Envelope (bounding surface) and the Plastic Yield Envelope (yield surface) to describe the evolution of structure and anisotropy, (b) an Intrinsic Compressibility Framework and a corresponding Intrinsic Strength Envelope which represents a lower bound of the Structure Strength Envelope and is used as reference locus for the structureless material, (c) an improved damage mechanism to model structure degradation by plastic strains and (d) a non-associated flow rule controlled by structure. The proposed model is modular, its features can be activated simultaneously or selectively, and the 3-D tensorial formulation facilitates direct implementation in finite elements codes.     

Phenomenological fractional stress–dilatancy model for granular soil and soil-structure interface under monotonic and cyclic loads

The stress–dilatancy relation is of critical importance for constitutive modelling of geomaterial. A novel fractional-order stress–dilatancy equation had been developed for granular soil, where a nonlinear stress–dilatancy response was always predicted. However, it was experimentally observed that after a certain extent of shearing, an almost linear response between the stress ratio and the dilatancy ratio, rather than the nonlinear response, usually existed. To capture such stress–dilatancy behaviour, a new fractional stress–dilatancy model is developed in this study, where an apparent linear response of the stress–dilatancy behaviour of soil after sufficient shearing is obtained via analytical solution. As the fractional order varies, the derived stress–dilatancy curve and the associated phase transformation state stress ratio keep changing. But, unlike existing researches, no other specific parameters, except the parameter related to fractional order, concerning such shift are required. Then, the developed stress–dilatancy model is applied to constitutive modelling of granular soil and soil–structure interface, for further validation. A series of test results of different granular soils and soil–structure interfaces under different loading conditions are simulated and compared, where a good model performance is observed.

     

Resilient characterization of pavement materials

The paper presents an approach for characterizing pavement materials using the modified linear elastic behaviour. The secant modulus of elasticity is expressed in terms of the stress invariants and an expression for the secant Poisson's ratio is derived using path independence of the total work along a closed loading cycle. Triaxial test results of granular base–subbase materials which exhibit strong non-linear behaviour and dilatancy are analysed and presented. The constitutive law is included in a finite element program and results of pavement analyses are discussed. It is found that the secant Poisson's ratio of granular base materials reaches values between 0·6 and 0·7, indicating a volume increase under high stress ratios. The pavement response predicted using the above material characterization is compatible with non-destructive test results.     

Incrementalization of a single hardening constitutive model for frictional materials

The governing equations for an elasto‐plastic constitutive model for frictional materials such as soil, rock, and concrete are presented, and the incremental form is indicated in preparation for implementation of the model in a user‐defined module for finite element calculations. This isotropic, work‐hardening and ‐softening model employs a single yield surface, it incorporates non‐associated plastic flow, and its capability of capturing the behaviour of different types of frictional materials under various three‐dimensional conditions has been demonstrated by comparison with measured behaviour, as presented in the literature. The incrementalization procedure is indicated and the resulting equations for the single hardening model are presented together with parameters for a dense sand. Following the implementation of the model, these parameters are used for evaluation of different integration schemes as presented in a companion paper by Jakobsen and Lade (Int. J. Numer. Anal. Meth. Geomech. 2002; 26 :661). Copyright © 2002 John Wiley & Sons, Ltd.     

Decoupling Conditions for Elasto-plastic Consolidation Question Based on Numerical Modeling Method

INTRODUCTION Theconsolidationofsaturatedsoilisanimpor tantsubjectingeomechanics.Biot(1941)proposed thethree dimensionalconsolidationtheory,whichis basedontheprincipleofeffectivestress,continuity conditionsandequilibriumequations.Theremarka blesuccessofthistheoryistheanalysisofthetime dependenteffectandcouplingeffectofsoilandpore water.Thus,thetheoryisaclassictheoryinsatu ratedsoilstatistics.Itwasalmostunfeasibletoperformanalysesof thistheorywithoutthedevelopmentofhigh speed computersandnu…     

A constitutive model for a laboratory rock joint with multi-scale asperity degradation

This paper presents a joint constitutive model that considers separately the mechanical contribution of waviness and unevenness of a joint to shear behaviour. The critical asperities for waviness and unevenness are determined from geometric properties in a lab-scale joint. The wear process is employed to model the degradation in dilation and strength during shear. From dimensional analysis, asperity degradation constants are developed using geometric parameters including asperity angle, wavelength, and amplitude as well as rock strength and stress. The applicability of the proposed model was assessed by performing direct shear tests on three joint roughness coefficient (JRC) profiles and providing its correlation with experimental results. Additionally, experimental data taken from literature were used to validate the model’s performance.     

Liquefaction and cyclic mobility model for saturated granular media

A new constitutive law for the behaviour of undrained sand subjected to dynamic loading is presented. The proposed model works for small and large strain ranges and incorporates contractive and dilative properties of the sand into the unified numerical scheme. These features allow to correctly predict liquefaction and cyclic mobility phenomena for different initial relative densities of the soil. The model has been calibrated as an element test, by using cyclic simple shear data reported in the literature. For the contractive sand behaviour a well‐known endochronic densification model has been used, whereas a plastic model with a new non‐associative flow rule is applied when the sand tends to dilate. Both dilatancy and flow rule are based on a new state parameter, associated to the stiffness degradation of the material as the shaking goes on. Also, the function that represents the rearrangement memory of the soil takes a zero value when the material dilates, in order to easily model the change in the internal structure. Proceeding along this kind of approach, liquefaction and cyclic mobility are modelled with the same constitutive law, within the framework of a bi‐dimensional FEM coupled algorithm developed in the paper. For calibration purposes, the behaviour of the soil in a cyclic simple shear test has been simulated, in order to estimate the influence of permeability, frequency of loading, and homogeneity of the shear stress field on the laboratory data. Copyright © 2006 John Wiley & Sons, Ltd.     

Three-dimensional DEM investigation of critical state and dilatancy behaviors of granular materials

The critical state is significant to the mechanical behaviors of granular materials and the foundation of the constitutive relations. Using the discrete element method (DEM), the mechanical behaviors of granular materials can be investigated on both the macroscopic and microscopic levels. A series of DEM simulations under true triaxial conditions have been performed to explore the critical state and dilatancy behavior of granular materials, which show the qualitatively similar macroscopic responses as the experimental results. The critical void ratio and stress ratio under different stress paths are presented. A unique critical state line (CSL) is shown to indicate that the intermediate principal stress ratio does not influence the CSL. Within the framework of the unique critical state, the stress–dilatancy relation of DEM simulations is found to fulfill the state-dependent dilatancy equations. As a microscopic parameter to evaluate the static determinacy of the granular system, the redundancy ratio is defined and investigated. The results show that the critical state is very close to the statically determinate state. Other particle-level indexes, including the distribution of the contact forces and the anisotropies, are carefully investigated to analyze the microstructural evolution and the underlying mechanism. The microscopic analysis shows that both the contact orientations and contact forces influence the mechanical behaviors of granular materials.     

Numerical modelling of shear socketed piers

When a socketed pier embedded in a rock mass is pushed down, the concrete asperities slide over the matching rock asperities. Consequently, the normal stress across the rock–concrete interface increases due to the dilation of the rough contact. The objective of this paper is to model the behaviour of such rough interfaces analytically. A plasticity‐based interface model is developed and implemented in a finite element program. Various features of the model such as failure criterion, plastic potential, bond degradation and dilatancy are presented. Interface parameters obtained from laboratory tests are used to simulate the interaction between concrete and rock numerically. A comparison between laboratory observations and numerical predictions is presented. Copyright © 2000 John Wiley & Sons, Ltd.     

基于统一硬化参数的深海能源土本构模型

深海能源土是指含天然气水合物（俗称"可燃冰"）的深海沉积物,其本构特性的模拟对可燃冰的安全开采至关重要。首先分析了水合物对能源土强度、剪胀和软化等力学特性的影响机理,水合物饱和度越大,对能源土力学特性影响越显著。然后在修正剑桥模型的基础上,通过引入水合物的饱和度和统一硬化参数来修正屈服函数,以反映水合物对能源土强度、剪胀、软化等特性的影响,建立了能考虑天然气水合物胶结作用形成及退化影响的深海能源土弹塑性本构模型,推导了相应的弹塑性矩阵。最后,通过模拟结果与已有能源土三轴试验数据对比分析,表明模型能很好地预测能源土强度、剪胀和软化等特性,验证了模型的合理性和有效性。     

Developing a 3D elastoplastic constitutive model for soils: A new approach based on characteristic stress

This paper presents a new approach for the development of an elastoplastic constitutive model to predict the strength and deformation behaviour of soils under general stress conditions. The proposed approach was based on characteristic stress, which considers the effect of the intermediate principal stress on the material strength. Referring to the Cam-clay model, the shear dilatancy equation, plastic potential function and hardening parameter for the developed model were all derived using the characteristic stress. The model predictions indicated that the established model could quantitatively reproduce the negative dilatancy behaviour, positive dilatancy behaviour, and three-dimensional strength properties of soils.     

不同加载方向条件下堆石料剪胀特性试验研究

剪胀方程描述的是塑性应变增量比例大小的变化规律,是构建弹塑性模型的重要组成部分。然而目前堆石料的剪胀方程大都是根据等围压 路径得到的,这些剪胀方程是否能反映不同应力路径条件下堆石料的剪胀规律还尚不明了。开展了等围压 、等轴向力 、等平均主应力p、等主应力比 共4种应力路径下的堆石料大型三轴试验,研究了应力路径对堆石料剪胀规律的影响。试验表明：不同路径的剪胀比 和应力比 均呈近似线性关系,但剪胀比与应力比不存在一致的关系,表现出明显的应力路径相关性;在 - 空间中,剪胀线随着应力增量方向的变化会发生平移和转动,其斜率 和截距参数 均随 ( )的增大而增大;目前的剪胀理论不能较好地描述剪胀的应力路径相关性,提出了一个考虑应力增量方向影响的修正剪胀方程并对其进行了试验验证。