基于Cosserat理论的重力坝深层抗滑稳定分析

重力坝深层滑动主要表现为沿缓倾角的软弱结构面形成滑移通道,滑移通道内应变积聚且应变梯度急剧不连续,是典型的应变局部化现象,采用经典连续介质理论进行数值模拟时存在病态的有限元网格依赖性。引入Cosserat连续体理论作为正则化机制,提出了基于Cosserat理论的Mohr-Coulomb弹塑性模型,考虑非关联的流动法则,在经典塑性理论框架下采用向后Euler隐式积分算法进行应力更新。采用ABAQUS的自定义单元接口（UEL）进行二次开发,进行了平面应变条件下单轴受压的数值验证。数值模拟结果表明,该模型能保证应变局部化问题的正定性。基于Cosserat理论的重力坝深层抗滑稳定分析结果表明,采用超载法进行重力坝渐进破坏过程模拟时,基于经典连续体理论的模拟结果有较大的网格依赖性,而且结果偏于安全,而采用Cosserat连续体理论的结果对网格密度不敏感。     

Implicit integration of elastoplastic relations with reference to soils

The stress solution in plasticity with an associated or a non-associated flow rule is considered. Upon fully implicit integration of the relevant constitutive relations the stress is obtained as the projection of the (fictitious) elastic stress onto the yield surface for given values of the hardening softening variables. This projection is defined, for a general non-associated flow rule, in adjusted complementary elastic energy, which becomes exactly the complementary energy when the flow rule is associated. Isotropic elasticity and mean-stress dependent isotropic yield criteria (pertinent to soil) are considered and the implications of a certain class of non-associated flow rules are evaluated. This class relates to dilatant (or contractant) materials and involves non-associated plastic volume change. The corresponding stress solutions are shown to be strongly influenced by Poisson's ratio and by the dilation angle.     

非共轴本构模型在地基承载力数值计算中若干影响因素的探讨

土体在剪切变形过程中产生主应力方向的旋转时,主应变增量方向与主应力方向之间存在着非共轴现象,然而传统的弹塑性本构模型未能考虑该现象的影响。通过在屈服面的切线方向增加一项非共轴塑性应变增量,即可实现对非共轴现象的反映。采用显式积分算法和自动分步方法,将非共轴本构模型运用到桶形基础地基承载力问题的有限元计算中,并讨论了流动法则、内摩擦角、膨胀角等因素与非共轴模型的联系。计算结果表明：采用有限元程序默认容许误差时,该本构模型可达到理想的收敛精度,并且,该模型对关联、非关联流动法则均适用。采用共轴模型进行数值计算时,不同流动法则对计算结果的影响可以忽略;采用非共轴模型时,不同流动法则的计算结果之间存在差异。非共轴现象对地基承载力-位移曲线具有软化作用,并且,该软化作用在采用非关联流动法则时变得更加明显     

An analytical solution for axisymmetric tunnel problems in elasto-viscoplastic media

An analytical solution is presented for the time-dependent stresses and displacements in plane strain around a circular hole when it is loaded by an axisymmetric internal and far-field pressure. The material is assumed to be elasto-viscoplastic with dilatant plastic deformations according to a non-associated flow rule. Strain softening is considered by a modified St. Venant slider which is characterized by Mohr-Coulomb yield conditions for both the peak and the residual strengths.     

ELASTOPLASTIC RESPONSE OF PRESSURE SENSITIVE SOLIDS

Tensorially invariant constitutive relations are systematically derived for large strain elastoplastic response of geomaterials. The analysis centres on Mohr–Coulomb (MC) and Drucker–Prager (DP) models with arbitrary hardening and non-associated response. Both flow and deformation theories are constructed for each model with emphasis on linear incremental relations between the Eulerian strain rate tensor and the objective Jaumann stress rate tensor. Specifying the results for plane strain compression we find that deformation theory produces a much smaller tangent instantaneous shear modulus than flow theory. It follows that failure of ellipticity and onset of surface instabilities predicted by deformation theory for associated solids occur at much lower levels of strain than the corresponding flow theory results. On the other hand, flow theory predictions admit a considerable sensitivity to the level of non-associativity. In fact, at high levels of non-associativity flow theory predictions for loss of ellipticity can be at strains below those obtained from deformation theory. © 1997 John Wiley & Sons, Ltd.     

弹塑脆性岩土材料中柱形孔扩张大应变解

在应力跌落模型基础上引进软化阈值,建立弹塑脆性模型,模拟岩土材料的脆性软化特性,采用双剪统一强度理论和不相关联流动法则,考虑软化区的大应变,对柱形孔扩张问题进行求解,得出了扩张率-扩张压力的解析表达式。算例分析表明,软化阈值对扩张变形和塑性区范围影响显著,软化阈值越小,扩张变形和塑性区范围越大,且软化区占整个塑性区的比重越大;是否考虑中间主应力对屈服的影响,对解答也有明显的影响。     

Smeared crack approach: back to the original track

This paper briefly reviews the formulations used over the last 40 years for the solution of problems involving tensile cracking, with both the discrete and the smeared crack approaches. The paper focuses on the smeared approach, identifying as its main drawbacks the observed mesh‐size and mesh‐bias spurious dependence when the method is applied ‘straightly’. A simple isotropic local damage constitutive model is considered, and the (exponential) softening modulus is regularized according to the material fracture energy and the element size. The continuum and discrete mechanical problems corresponding to both the weak discontinuity (smeared cracks) and the strong discontinuity (discrete cracks) approaches are analysed and the question of propagation of the strain localization band (crack) is identified as the main difficulty to be overcome in the numerical procedure. A tracking technique is used to ensure stability of the solution, attaining the necessary convergence properties of the corresponding discrete finite element formulation. Numerical examples show that the formulation derived is stable and remarkably robust. As a consequence, the results obtained do not suffer from spurious mesh‐size or mesh‐bias dependence, comparing very favourably with those obtained with other fracture and continuum mechanics approaches. Copyright © 2006 John Wiley & Sons, Ltd.     

考虑颗粒破碎影响的粗粒土本构关系

粗粒土在较大的应力条件下容易产生颗粒破碎现象,而现有的大多数模型都没有考虑剪切过程中的颗粒破碎。模型将塑性功引入土体受力变形过程的能量方程中,推导得到土体流动法则。采用直线型屈服轨迹和非相关联流动法则,利用不排水应力路径计算得到硬化函数,建立了一个考虑颗粒破碎的粗粒土本构模型。对比分析表明：该模型对粗粒土在各种围压下的应力-应变和体应变计算结果与试验曲线吻合较好。     

An elastoviscoplastic constitutive model for geomaterials: Application to hydromechanical modelling of claystone response to drift excavation

An isotropic elastoviscoplastic constitutive model based on a generalized Hoek-Brown criterion is proposed. The plastic mechanism is characterized by a positive and a negative hardening, and a specific non-associated flow rule allows to take into account the evolution of the dilatancy. Several hydromechanical finite element simulations corresponding to realistic configurations of drift excavations in the underground research laboratory of Bure are presented. Regularization techniques are required to avoid localization phenomena due to softening. A second gradient formulation has been used as it is well suited for dilatant materials such as claystone. Numerical results are discussed and compared with experimental measurements.     

How fines content affects granular plasticity of under-filled binary mixtures

In recent years, binary mixtures have been the subject of numerous experimental and numerical studies. However, few attempts have been made on investigating the effect of fines content (fc) on the non-associated plasticity of binary mixtures, which is significant for constitutive modelling of such material. Thanks to 2D DEM simulations, this study aims to provide an understanding of how fc affects the non-associated character of the flow rule and the resulting material instability in binary mixtures. For under-filled materials (where coarse grains constitute most of the load-bearing skeleton), fine grains help to stabilize the granular assembly (1) by limiting macroscopic plastic deformations, which results in strain hardening, and (2) by reducing contractive microstructure reorganizations, which reduces the gap between the associated and non-associated flow rule directions. Fines content influences the plastic flow direction but has no influence on normal direction of yield surface. Eventually, perspectives on mesoscale mechanisms are given to highlight the role of fine grains in the geometrical and mechanical properties of granular materials.

     

An elastoplastic constitutive model for frozen saline coarse sandy soil undergoing particle breakage

The mechanical property of frozen saline sandy soil is complicated due to its complex components and sensitivity to salt content and confining pressure. Thus, a series of triaxial compression tests were carried out on sandy samples with different Na₂SO₄ contents under different confining pressures to explore the effects of particle breakage, pressure melting, shear dilation and strain softening or hardening. The test results indicate that the stress–strain curves exhibit strain softening/hardening phenomena when the confining pressures are below or above 6 MPa, respectively. A shear dilation phenomenon was observed in the loading process. With increasing confining pressure, the strength firstly increases and then decreases. By taking into consideration the changes between the grain size distributions before and after triaxial compression tests, a failure strength line incorporating the influences of both particle breakage and pressure melting is proposed. In order to describe the deformation characteristics of frozen saline sandy soil, an elastoplastic incremental constitutive model is established based on the test results. The proposed model considers the plastic compressive, plastic shear and breakage mechanisms by adopting the non-associated flow rule. The breakage mechanism can be reflected by an index related to the initial, current and ultimate grain size distributions. The hardening parameters corresponding to compressive and shear mechanisms consider the influence of particle breakage. Then the effect of particle breakage on both the stress–strain and volumetric strain curves is analyzed. The calculated results fit well with the test results, indicating that the developed constitutive model can well describe the mechanical and deformation features of frozen saline sandy soil under various stress levels and stress paths. In addition, the strain softening/hardening, contraction, high dilation and particle breakage can be well captured.

     

Symmetric tangential stiffness formulation for non-associated plasticity

A numerical scheme is proposed in which the response of a material with non-associated flow rule is made equivalent to that of a material with associated flow rule and a modified stress/strain direction dependent hardening/softening rule. The scheme has obvious computational advantage since finite element programs with tangential stiffness formulations can be used without resort to non-symmetric equation solution routines.     

Gradient plasticity modelling of strain localization in granular materials

The flow stress in the yield surface of plastic constitutive equation is modified with a higher order gradient term of the effective plastic strain to model the effect of inhomogeneous deformation in granular materials. The gradient constitutive model has been incorporated into the finite element code ABAQUS and used to simulate biaxial shear tests on dry sand. It is shown that the shape of the post-peak segment of the load displacement curve predicted by the numerical analysis is dependent on the mesh size when gradient term is not used. Use of an appropriate gradient coefficient is shown to correct this and predict a unique shape of the load displacement curve regardless of the mesh size. The gradient coefficient required turns out to be approximately inversely proportional to the mesh elemental area. Use of the strain gradient term is found to diffuse the concentration of plastic strains within shear band resulting in its consistent width. The coefficient of the higher gradient term appears as a function of the grain size, the mean confining stress, and the plastic softening modulus. Copyright © 2004 John Wiley & Sons, Ltd.     

基于Hoek-Brown准则的隧洞围岩变形研究

由于在许多实际条件下,比如节理岩体中,线性的M-C准则不太适用,非线性的Hoek-Brown比较适用,因此,可以尝试使用这一非线性屈服准则对洞室变形进行研究。研究隧洞变形时,将围岩分为弹性区、应变软化区、塑性流动区。采用Hoek-Brown准则和非关联流动法则对洞室变形进行了理论推导;软化区域围岩参数随着塑性变形增加而变化,解析法难以求得应力,采用龙格－库塔方法进行数值计算,求解得到塑性软化区和流动区半径,并最终求得洞室变形。通过算例计算表明,在不考虑软化区和流动区时,方法和Carranza-Torres计算结果相差甚小;随着原岩应力的增加,膨胀角对洞室变形的影响增大。     

一种考虑黏聚强度的改良土弹塑性本构模型

改良土中土颗粒和水化物形成具有一定结构的聚合体而表现出较强的结构性。与重塑正常固结土相比,改良土的结构性更强且具有一定的超固结比。在变形发展过程中,由于聚合体结构逐渐破坏,黏聚强度逐渐损失,土体表现出应变软化的力学特性。基于适用于超固结重塑黏土的统一硬化模型,引入改良土黏聚强度及其随塑性变形的演化规律,对统一硬化参数进行了修正,并采用更适用于改良土的非关联的流动法则,建立了一个可以较好地描述改良土力学特性的弹塑性本构模型。通过与水泥改良土和石灰改良土的三轴剪切排水试验的结果进行对比,该模型能够较为合理地描述改良土加载过程中黏聚强度损失对其力学特性的影响。黏聚强度的存在导致土体表现出超固结土的特性,当黏聚强度损失时会加剧土体的软化速度。     

多重耗散函数率无关塑性力学在粘土模型中的应用

由于经典的塑性力学无法根据Drucker塑性公设从理论上证明非相关联流动准则,因而从连续介质热力学基本原理出发研究土的弹塑性模型。根据率无关塑性力学理论,通过Gibbs自由能和多个独立耗散函数,建立土的多重屈服准则及其流动准则,证明了屈服准则重数和独立耗散函数个数相等,分析了耗散函数形式对屈服准则和塑性流动准则的影响。分析了一簇新的能够同时考虑相关联流动准则和非相关联流动准则的粘土的Gibbs自由能和耗散函数的表达式,殷宗泽双屈服面模型是其特例,但新模型具有更为明确的物理含义,能考虑非相关联流动准则的情况。根据粘土室内实验选取了模型参数,并与实测应力-应变曲线进行对比,说明新模型可以模拟粘土的多重屈服面本构关系。     

The analysis of finite elasto-plastic consolidation

A theoretical formulation and a numerical solution method are proposed for the problem of the time dependent consolidation of an elasto-plastic soil subject to finite deformations. The soil is assumed to be a two-phase material with a skeleton which may yield according to a general yield criterion with plastic flow governed by a general flow law, and whose pore fluid flows according to Darcy's Law. Governing equations are cast in a rate form and constitutive laws are expressed in a frame indifferent manner. The method of analysis is illustrated by several examples of practical interest for both a soil with an elastic skeleton and a soil with an elasto-plastic skeleton which obeys a Morh–Coulomb yield criterion and a non-associated flow law.     

On viscoplastic regularisation of strain-softening rocks and soils

Constitutive models for rocks and soils typically incorporate some form of strain softening. Moreover, many plasticity models for frictional materials use a nonassociated flow rule. Strain softening and nonassociated flow rules can cause loss of well-posedness of the initial-value problem, which can lead to a severe mesh dependence in simulations and poor convergence of the iterative solution procedure. The inclusion of viscosity, which is a common property of materials, seems a natural way to restore well-posedness, but the mathematical properties of a rate-dependent model, and therefore the effectiveness with respect to the removal of mesh dependence, can depend strongly on how the viscous element is incorporated. Herein, we show that rate-dependent models, which are commonly applied to problems in the Earth's lithosphere, such as plate tectonics, are very different from the approach typically adopted for more shallow geotechnical engineering problems. We analyse the properties of these models under dynamic loadings, using dispersion analyses and one-dimensional finite difference analyses, and complement them with two-dimensional simulations of a typical strain localisation problem under quasi-static loading conditions. Finally, we point out that a combined model, which features two viscous elements, may be the best way forward for modelling time-dependent failure processes in the deeper layers of the Earth, since it not only enables modelling of the creep characteristics typical of long-term behaviour but also regularises the initial/boundary-value problem.     

Localization in rate-dependent shearing deformation, with application to torsion testing

The localization of plastic deformation in rock is of particular interest in geology in connection with the formation of “ductile” shear zones. It is commonly conjectured that strain softening, as evidenced by a falling stress–strain curve at constant strain rate, is likely to lead to strain localization. Yet observations in torsion tests at constant twist rate fail to show such an effect. However, a more sophisticated analysis using the theory of Fressengeas and Molinari (J. Mech. Phys. Solids 1987, 35, 185–211) for material showing strain-rate dependence of the flow stress does show that, when the boundary conditions are specified in terms of displacements, no localization is predicted in case of strain softening. In contrast, if the boundary conditions are set in terms of forces, localization can be expected for a strain softening material. This prediction needs experimental testing.     

基于统一强度理论深埋圆形隧道围岩的剪胀分析

基于连续介质理论中岩体的剪胀角与围压和塑性剪切应变密切相关,隧洞周边岩体的应力状态因开挖卸荷而发生应力重分布,迫使其围压由原地应力逐渐衰减,塑性剪切应变不断增加,引起剪胀效应呈非线性变化。首先,基于统一强度理论和非关联流动法则,将潜在塑性区围岩按等围压释放划分为若干同心圆,提出了考虑中间主应力和非线性剪胀性的有限差分法,计算应变软化围岩的力学问题,并以实例验证其正确性。其次,通过参数分析,研究塑性区内岩体的剪胀角受中间主应力、临界软化系数和支护力的影响规律。研究结果表明,中间主应力主要影响剪胀角的峰值,随着中间主应力效应增加,剪胀峰值增加;临界软化系数主要影响剪胀角的变化率,随着临界软化系数的增加,剪胀角变化缓慢;中间主应力和临界软化系数共同影响塑性区剪胀角的变化;随着支护力的增加,洞壁处的剪胀角增加;双剪强度理论计算的位移值较小,应谨慎采用,同时采用Mohr-Coulomb强度准则时可以适当考虑围岩的承载潜力。