岩石流变损伤本构方程

根据岩石材料的微结构机理,基于简单机械模型,通过在不可逆应变和牛顿时间所构成的空间中合理的定义广义时间、引入四阶各向异性损伤张量,建立了岩石的流变损伤本构方程。该模型能够考虑复杂应力状态下材料的响应特性,各向异性损伤及其损伤的方向特征,静水压力的影响等。发展了相应的数值分析方法,并根据泥岩三轴蠕变试验结果进行了验证。     

Triaxial behaviour of transversely isotropic materials: application to sedimentary rocks

Failure and long‐term behaviour of oriented solids are studied. Transversely isotropic materials are considered and a mathematical formulation that respect the material symmetry is developed and applied to model the triaxial behaviour of sedimentary rocks. Two failure criteria and a viscoplastic constitutive model that describe, respectively, triaxial failure and triaxial creep tests are presented and discussed. The application of the developed models to describe the mechanical behaviour of Tournemire shale shows that theoretical predictions are in good agreement with the experimental data. In the present paper, the developed approach is applied to sedimentary rock materials, nevertheless, it can be generalized to any material that exhibits transverse isotropy. Copyright © 2007 John Wiley & Sons, Ltd.     

A New Elasto-Viscoplastic Damage Model Combined with the Generalized Hoek–Brown Failure Criterion for Bedded Rock Salt and its Application

According to the requirement of the West–East Gas Transmission Project in China, the solution-mined cavities located in the Jintan bedded salt formation of Jiangsu province will be utilized for natural gas storage. This task is more challenging than conventional salt dome cavern construction and operation due to the heterogeneous bedding layers of the bedded salt formation. A three-dimensional creep damage constitutive model combined with the generalized Hoek–Brown model is exclusively formulated and validated with a series of strength and creep tests for the bedded rock salt. The viscoplastic model, which takes the coupled creep damage and the failure behavior under various stress states into account, enables both the three creep phases and the deformation induced by vicious damage and plastic flow to be calculated. A further geomechanical analysis of the rapid gas withdrawal for the thin-bedded salt cavern was performed by implementing the proposed model in the finite difference software FLAC^3D. The volume convergence, the damage and failure propagation of the cavern, as well as the strain rate of the salt around the cavern, were evaluated and discussed in detail. Finally, based on the simulation study, a 7-MPa minimum internal pressure is suggested to ensure the structural stability of the Jintan bedded salt cavern. The results obtained from these investigations provide the necessary input for the design and construction of the cavern project.     

A constitutive model for crushed salt

A constitutive model for crushed salt is presented in this paper. A creep constitutive model is developed first and compared with test results. The constitutive model presented here concentrates on creep deformation because saline media behave basically in a ductile and time‐dependent way. An idealized geometry is used as a common framework to obtain stress–strain macroscopic laws based on two deformation mechanisms: fluid‐assisted diffusional transfer creep and dislocation creep. The model is able to predict strain rates that compare well with results from laboratory tests under isotropic and oedometric conditions. Macroscopic laws are written using a non‐linear viscous approach, which incorporates also a viscoplastic component, based on critical state theory. The viscoplastic term is intended for non‐creep deformation mechanisms such as grain reorganization and crushing. Copyright © 2002 John Wiley & Sons, Ltd.     

基于新型蠕变仪下的泥岩力学参数时效性研究

岩石在蠕变的过程中其基本力学参数变形模量E、内聚力c和内摩擦角是随时间和应力逐渐弱化的。本文对现行蠕变设备特点进行分析,研制了一套新型的五联单轴蠕变仪,此仪器能够在相同的应力条件下同时进行5个试件的蠕变试验。并且使用该仪器对宝鸡市秦源煤矿泥岩的力学参数E、c、在蠕变试验中的弱化规律进行了研究。提出了把粘塑性应变作为泥岩力学参数弱化的指标,得出了泥岩E、c、随粘塑性应变呈指数衰减的函数关系,并计算了该泥岩破坏时的E、c、。对该泥岩E、c、和粘塑性应变的函数关系式进行了分析,得到了岩石E、c、和应力(σ)以及时间(t)的耦合函数方程,为后续岩石非定常本构模型的研究奠定了基础。     

节理岩体等效流变损伤模型及其在卸载边坡中的应用

重大建设项目对施工过程中岩土体稳定性提出了更高的要求,常以一种动态设计施工模式来应对工程体的各类突发状况与病害。流变损伤模型既能反映岩土体在施工过程中变形的时效发展,又能反映其力学性质的时效劣化,继而能较准确地掌握工程体动态稳定性。基于以上考虑,为体现卸载边坡工程在卸载回弹阶段的瞬时塑性特征和时效演化阶段的黏塑性特征,因此,在流变模型中引入加载塑性元件和黏塑性元件,建立了复合黏弹塑（弹-黏-黏弹-黏塑-塑）模型,室内岩石压缩（卸载）蠕变试验证明了该流变模型的合理性,并对其参数进行辨识。在此基础上,从几何研究方法出发,引入反映节理分布的初始损伤张量及一种等效的依据黏塑性偏应变推导出的损伤演化方程,最终建立了一种新型的节理岩体等效流变损伤模型。将此模型用于川东红层某软硬岩互层型路堑边坡的卸载分析,结果表明：随不同的开挖阶段,易损部位（软岩集中段、软岩深埋段、软硬交接硬岩段）在瞬时卸载回弹阶段的塑性损伤和时效演化阶段的黏塑性损伤逐渐积累,边坡浅表部逐渐出现卸载损伤（松弛）带,在损伤累积中边坡各部位蠕变速率呈不同程度的增长。计算结果较好地反映了边坡变形、损伤发展与动态稳定性特征,其研究结果对于指导支护时机及相应的信息化施工具有一定的意义。     

各向异性弹黏塑性模型在ABAQUS中的研发

通过将Perzyna过应力理论与临界状态理论相结合,并引入Wheeler旋转硬化法则,提出一个能描述土体初始各向异性及应力诱发各向异性的三维弹黏塑性本构模型。模型考虑流变发生的下限,在三维应力空间,模型存在形状相似的静屈服面及动态加载面。采用缩放形式的幂函数。本构模型数值算法采用回映算法,借助ABAQUS软件UMAT子程序接口实现。并通过对三轴不排水蠕变试验的模拟,确定合适的积分步长。此后,分别对三轴不排水蠕变试验及常应变率三轴不排水剪切试验进行了模拟。模拟中通过设置不同参数值,可将模型退化为各向同性模型,并对这两种模拟结果进行了比较。模拟结果表明：(1) 对于三轴不排水蠕变,在低剪应力水平下,各向同性模型和各向异性模型模拟的结果相差不大,而在高剪应力水平下,各向异性模型模拟结果更接近试验结果;(2) 对于常应变率加载试验的模拟,模型合理反映了土体不排水强度随着加载速率的增大而增大现象。     

New Viscoplastic Model for Design Analysis of Tunnels in Squeezing Conditions

Summary  This paper is intended to describe the SHELVIP (Stress Hardening ELastic VIscous Plastic) model, a new viscoplastic constitutive law which has been developed to incorporate the most important features of behaviour observed in tunnels excavated in severe to very severe squeezing conditions. This model couples the elastoplastic and time-dependent behaviour by using a plastic yield surface, as frequently adopted in tunnel design analysis, and the definition of a state of overstress referred to a viscoplastic yield surface. The model is formulated in all its detailed aspects. The related analytical closed-form solution for representing triaxial creep deformations is developed. Also developed is an incremental numerical solution for describing the triaxial stress–strain behaviour under constant strain rate conditions. The model is shown to fit very satisfactorily the results of creep tests on clay shales and relaxation tests on coal specimens, as recently performed for design analysis of tunnels in squeezing conditions. Correspondence: D. Debernardi, Department of Structural and Geotechnical Engineering, Politecnico di Torino, Torino, Italy     

Thermodynamic‐based model for coupling temperature‐dependent viscoelastic,viscoplastic, and viscodamage constitutive behavior of asphalt mixtures

Based on the continuum damage mechanics, a general and comprehensive thermodynamic‐based framework for coupling the temperature‐dependent viscoelastic, viscoplastic, and viscodamage behaviors of bituminous materials is presented. This general framework derives systematically Schapery‐type nonlinear viscoelasticity, Perzyna‐type viscoplasticity, and a viscodamage model analogous to the Perzyna‐type viscoplasticity. The resulting constitutive equations are implemented in the well‐known finite element code Abaqus via the user material subroutine UMAT. A systematic procedure for identifying the model parameters is discussed. Finally, the model is validated by comparing the model predictions with a comprehensive set of experimental data on hot mix asphalt that include creep‐recovery, creep, uniaxial constant strain rate, and repeated creep‐recovery tests in both tension and compression over a range of temperatures, stress levels, and strain rates. Comparisons between model predictions and experimental measurements show that the presented constitutive model is capable of predicting the nonlinear behavior of asphaltic mixes under different loading conditions. Copyright © 2011 John Wiley & Sons, Ltd.     

南宁膨胀土非线性流变模型研究

对南宁非饱和膨胀土进行一系列的加载-卸载固结蠕变试验,得到了不同含水率的膨胀土在不同应力水平下应变-时间曲线和不同时刻的应力-应变等时曲线簇。通过对膨胀土各阶段蠕变变形的分析,得到了膨胀土的固结蠕变是包含有黏弹性变形和黏塑性变形成分的非线性蠕变。采用模型流变与经验流变理论相结合的方法,将膨胀土的蠕变变形分成线性和非线性两部分进行分析,蠕变柔量和线性黏弹性模量随时间减小,而线性黏塑性模量随时间增大。结合膨胀土的线性黏塑性模型和非线性黏塑性经验模型,建立能够描述膨胀土非线性流变的黏塑性本构方程。根据试验所得数据,通过非线性拟合方法得到各模型参数,用该模型进行数值分析得到的理论与蠕变试验结果对比非常吻合。研究成果为实际工程提供了流变变形计算分析的可靠依据。     

A parametric analysis for the Dafalias-Kaliakin bounding surface viscoplastic model based on the Diflupress L.D. test

In order to predict delayed settlements of heavy structures, the authors decided to use the elasto-viscoplastic model of Dafalias-Kaliakin. To identify the parameters of the constitutive equations, they use above all the data of a new in-situ test, the Diflupress L.D. designed to approach the creep behavior of soil. In a first section, the principle of the model is presented. Then, the important parameters of the model are identified, mostly from in-situ test data since the laboratory tests data are not numerous and reliable. Finally, a study of sensitivity on the parameters which influence the viscoplastic response of the model is made.     

Numerical modelling of the effect of curing time on the creep behaviour of a chemically stabilised soft soil

This work studies the effect of the curing time on the creep behaviour of a stabilised soft soil, using volumetric and deviatoric creep laws associated with constitutive models. Results of unconfined compressive strength tests for several curing times are used to define the time evolution of the mechanical and creep properties. The models/creep laws are validated by oedometer and triaxial creep tests, for 28 and 90 days of curing. The long-term behaviour of an embankment built on a soft soil reinforced with deep mixing columns shows that the effect of curing time decreases the settlement and increases the improvement factor.     

白垩系饱和冻结砂岩蠕变试验及本构模型研究

冻结法作为穿越富水软岩地层的重要施工方法,冻结壁的长期稳定性对于工程安全有着至关重要的作用。蠕变破坏是诱发冻结壁变形的显著特点之一,对研究冻结岩石蠕变的特性有重要的理论和工程意义。以白垩系饱和冻结砂岩为研究对象,开展–10 ℃低温冻结条件下,不同围压（0、2、4、6 MPa）的三轴蠕变力学试验。分析了饱和冻结砂岩蠕变变形,根据现有黏弹塑性模型开展了参数辨识并探究蠕变参数的变化规律,基于此提出考虑温度及损伤效应的蠕变本构模型。研究结果表明：低温冻结削弱蠕变过程中颗粒间的相互胶结力,使其蠕变特征明显;而围压却在一定程度上抑制饱和冻结砂岩内部损伤的发展,导致稳态蠕变速率随围压的升高出现明显的下降趋势。随围压的增加饱和冻结砂岩的蠕变破坏形态呈现出从剪切破坏到张拉破坏再到局部塑形硬化破坏的变化过程。在黏弹塑性模型的基础上,总结蠕变参数 、 和 随荷载的增加呈现先增后减的趋势,拐点为屈服应力;而参数 在大于屈服应力后出现并呈现先增后减的趋势。结合冻结岩石蠕变数据对定义的应力-低温耦合蠕变本构模型进行了参数辨识,并将该模型的计算结果与蠕变试验数据对比,验证所建立非线性模型的正确性与合理性。     

考虑初始损伤和蠕变损伤的岩石蠕变全过程本构模型

考虑到天然岩石存在不同程度初始损伤以及蠕变过程中岩石受载后裂隙扩展而导致的新损伤,对具有初始损伤的岩石蠕变特性进行全面描述。根据不闭合结构面应力与法向变形之间的关系,提出裂隙岩石塑性变形体元件,描述岩石蠕变过程中的瞬时塑性变形。引入初始损伤影响因子,建立具有初始损伤的岩石损伤变量演化方程,构建模拟岩石加速蠕变的蠕变损伤体元件。将裂隙岩石塑性变形体和蠕变损伤体与描述瞬时弹性变形和黏弹性变形的广义开尔文模型进行串联组合,形成能够反映具有初始损伤的岩石瞬时弹-塑性变形、稳定蠕变和加速蠕变的蠕变全过程本构模型,提出了进行少量蠕变试验既能解析模型参数的方法,在不同应力水平下模型理论曲线与蠕变试验曲线吻合。     

2D viscoplastic finite element modelling of slow landslides: the Portalet case study (Spain)

This paper proposes a hydro-geomechanical finite element model to reproduce the kinematic behaviour of large slow landslides. The interaction between solid skeleton and pore fluids is modelled with a time dependent u–p _w formulation and a groundwater model that takes into account recorded daily rainfall intensity. A viscoplastic constitutive model based on Perzyna’s theory is applied to reproduce soil viscous behaviour and the delayed creep deformation. The proposed model is applied to Portalet landslide (Central Spanish Pyrenees). This is an active paleo-landslide that has been reactivated by the construction of a parking area at the toe of the slope. The stability analysis reveals that, after the constructive solutions were undertaken, the slope is in a limit equilibrium situation. Nevertheless, time-dependent analysis reproduces the nearly constant strain rate (secondary creep) and the acceleration/deceleration of the moving mass due to hydrological changes. Overall, the model reproduces a 2-m displacement in the past 8  years that coincides with in situ monitoring data. The proposed model is useful for short- and mid-term predictions of secondary creep. However, long-time predictions remain uncertain, stability depends strongly on the position of the water table depth and new failures during tertiary creep due to soil temporal microstructural degradation are difficult to calibrate.