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.     

抛物线型屈服面人工冻土蠕变本构模型研究

利用自行研制的W3Z-200型冻土三轴压缩蠕变仪,对淮南地区深表土冻土进行了三轴蠕变试验。根据试验结果,提出以标准黏弹塑性模型为基础,并耦合温度自由度,应用抛物线型屈服准则对模型中的黏塑性项进行改进,建立了新的本构模型来描述高围压复杂应力状态下冻土的蠕变变形特征。基于ADINA有限元软件平台,开发了冻土本构子程序。对淮南某冻结井筒开挖过程进行了数值模拟,计算结果验证了冻土抛物线型黏弹塑本构模型的正确性和合理性。     

一种横观各向同性岩体蠕变模型

层状岩体由于层理面或者结构面的存在,在力学上具有横观各向同性的特点,现有的各向同性蠕变模型难以全面反映横观各向同性岩体的蠕变力学特性。为构建能够反映横观各向同性岩体的三维蠕变模型,以能反映瞬时应变、减速蠕变和稳态蠕变特征的黏弹性Burgers模型为基础,基于常泊松比假定,在三维各向同性蠕变本构方程的基础上,按照算子替换的方法,将横观各向同性柔度矩阵代替各向同性柔度矩阵,并考虑了平行和垂直层理方向岩体蠕变力学行为的差异性,推导了横观各向同性岩体的三维蠕变本构方程。根据本构方程的特点,提出了根据平行和垂直方向岩体蠕变试验结果进行三维蠕变本构模型中蠕变参数的辨识方法。将提出的模型应用于三轴蠕变试验参数辨识,从而获得了一套完整的三维蠕变参数,并与试验结果进行对比分析,从而验证了所提模型与方法的合理性和有效性。进一步,指出了传统蠕变试验设计方案的局限性,给出了横观各向同性材料蠕变试验设计建议。研究成果为研究岩体三维蠕变机制提供了新思路,可对岩体蠕变试验设计提供相应的科研支撑。     

An assessment of the creep behaviour of Brazilian salt rocks using the multi-mechanism deformation model

Salt rocks are geomaterials that exhibit several peculiarities, which require a particular approach in rock mechanics. In the field, those rocks are usually found in layered/bedded deposits and in domes or similar structures. Creep is one of the main deformation mechanisms associated with salt rocks, and this phenomenon is highly dependent on the stress state, temperature and mineralogy. Salt rock mechanics for engineering applications requires the definition of a powerful constitutive model and this is an ongoing challenge. Among the many available models, one of the most sophisticated physical constitutive models for salt rocks is the multi-mechanism deformation creep model (MD model). The main contribution of this work is to present a first effort in the use of the MD model for Brazilian salt rocks. Material-sensitive parameters have been calibrated for the Brazilian halite through two methodologies. Salt is modelled as an elasto-viscoplastic material. Numerical simulations using the finite element method have been carried out for triaxial creep tests, Pre-salt wellbore closure and mining gallery convergence in order to validate the parameter set and the methodologies. Excellent results have been observed in most of the applications for validation. Even so, validation efforts should continue to consolidate the parameters and identify possible limitations.     

一种基于应变能理论的黏弹塑性蠕变本构模型

从内能角度分析发生蠕变的机制,基于应变能理论,采用Perzyna黏塑性理论与西原正夫元件模型相结合,建立了一种能描述衰减蠕变、稳定蠕变和加速蠕变3个阶段全过程的蠕变统一本构模型。该模型考虑了应力状态对加速蠕变的影响,通过定义加速蠕变临界应变能密度值可以有效判断加速蠕变发生时刻,并在统一蠕变本构模型基础上进行简化,采用Drucker-Prager（D-P）屈服准则结合相关联流动法则,用过屈服应力比反映加速阶段蠕变应变速率变化,建立了一个实用的能预测加速蠕变并能反映蠕变3阶段全过程的简化蠕变本构模型,结果表明,数值模拟结果与试验数据基本吻合,研究成果为岩石蠕变断裂过程研究提供了一种新的思路。     

Predictive potential of Perzyna viscoplastic modelling for granular geomaterials

This paper reappraises Perzyna-type viscoplasticity for the constitutive modelling of granular geomaterials, with emphasis on the simulation of rate/time effects of different magnitude. An existing elasto-plastic model for sands is first recast into a Perzyna viscoplastic formulation and then calibrated/validated against laboratory test results on Hostun sand from the literature. Notable model features include (1) enhanced definition of the viscous nucleus function and (2) void ratio dependence of stiffness and viscous parameters, to model the pycnotropic behaviour of granular materials with a single set of parameters, uniquely identified against standard creep and triaxial test results. The comparison between experimental data and numerical simulations points out the predicative capability of the developed model and the complexity of defining a unique viscous nucleus function to capture sand behaviour under different loading/initial/boundary and drainage conditions. It is concluded that the unified viscoplastic simulation of both drained and undrained response is particularly challenging within Perzyna's framework and opens to future research in the area. The discussion presented is relevant, for instance, to the simulation of multiphase strain localisation phenomena, such as those associated to slope stability problems in variably saturated soils.     

AN INTERFACE MODEL TO DESCRIBE VISCOPLASTIC BEHAVIOR

A constitutive model to describe viscoplastic or time-dependent behaviour of interface materials is presented. Viscoplastic characteristics of the interface material are modeled based on Perzyna's theory of viscoplasticity and the Hierarchical Single Surface (HiSS) series of constitutive models. Experiments performed using a new interface test device to characterize the behaviour of cohesive soil–rock interfaces are described. Procedures to derive model parameters are presented together with validation of the model. Finite element implementation of the interface element is described along with verification of the model with respect to field behaviour of a creeping natural slope.     

饱和砂性土流变模型的试验研究

正确合理的土体本构模型确定是地面沉降模拟的关键之一。上海和江苏地区多年来野外分层标的实际观测资料表明该区含水层系统砂层变形具有流变特征,表现出变形滞后于含水层水位变化的现象。本文基于粘弹性理论,选取了常州含水层系统原状砂性土样进行单轴压缩试验,分析了砂性土流变荷载曲线,并选择现有的相关本构模型进行识别,从而确定能更好反映研究区土体变形规律的流变模型。结果表明,研究区砂性土可采用Burgers模型进行描述,反演获得的4个流变参数随荷载的增加表现出一定的规律性。     

Anisotropic viscoplastic modeling of rate‐dependent behavior of clay

The objective of this study is to derive an effective stress‐based constitutive law capable of predicting rate‐dependent stress–strain, stress path and undrained shear strength and creep behavior. The flow rule used in the MIT‐E3 model and viscoplasticity theory is employed in the derivation. The model adopts the yield surface capable of representing the yield behavior of the Taipei silty clay and assumes that it is initially symmetric about the K₀‐line. A method is then developed to compute the gyration and expansion of the loading surface to simulate the anisotropic behavior due to the principal stress rotation after shear. There are 11 parameters required for the model to describe the soil behavior and six of them are exactly the same as those used in the Modified Cam‐clay model. The five additional parameters can be obtained by parametric studies or conventional soil tests, such as consolidation tests, triaxial compression and extension tests. Finally, verification of the model for the anisotropic behavior, creep behavior and the rate‐dependent undrained stress–strain and shear strength of the Taipei silty clay is conducted. Copyright © 2010 John Wiley & Sons, Ltd.     

软弱破碎围岩隧道炭质页岩蠕变特性试验研究

采集贵广铁路天平山隧道典型软弱破碎围岩岩样,在室内开展三轴常规压缩和三轴压缩蠕变试验。基于岩石试验成果,分析炭质页岩的蠕变力学特性,低应力水平条件下岩石仅出现减速蠕变和等速蠕变阶段,在更高的应力水平条件下,岩石并未出现加速蠕变的现象,但围压在一定程度上提高岩石的屈服强度,弹性模量亦有随着围压增加而增大的趋势。据此,建立依托工程炭质页岩蠕变全过程的黏弹塑性应变软化蠕变力学模型,推导该蠕变力学模型在三维应力状态下的本构方程,并确定模型的参数,运用最小二乘法对模型的参数进行辨识。通过与试验曲线对比显示,所建蠕变模型能够描述依托工程炭质页岩的蠕变力学特征,可以用来研究该隧道软弱破碎围岩的蠕变性质和稳定性。     

Review of constitutive models for describing the time dependent behaviour of soft clays

Different classes of constitutive models have been proposed to capture the time-dependent behaviour of soft soil (creep, stress relaxation, rate dependency). This paper critically reviews many of the models developed based on understanding of the time dependent stress-strain-stress rate-strain rate behaviour of soils and viscoplasticity in terms of their strengths and weaknesses. Some discussion is also made on the numerical implementation aspects of these models. Typical findings from numerical analyses of geotechnical structures constructed on soft soils are also discussed. The general elastic viscoplastic (EVP) models can roughly be divided into two categories: models based on the concept of overstress and models based on non-stationary flow surface theory. Although general in structure, both categories have their own strengths and shortcomings. This review indicates that EVP analysis is yet to be vastly used by the geotechnical engineers, apparently due to the mathematical complication involved in the formulation of the constitutive models, unconvincing benefit in terms of the accuracy of performance prediction, requirement of additional soil parameter(s), difficulties in determining them, and the necessity of excessive computing resources and time.     

考虑温度影响的花岗岩蠕变全过程本构模型研究

以北山花岗岩为研究对象,采用MTS815岩石力学试验系统开展不同温度条件下的蠕变特性试验研究。考虑温度对花岗岩特征参数的影响,结合岩石蠕变破坏过程中的损伤演化规律,提出了一种新的高温损伤流变元件。通过将高温损伤流变元件代替经典西原模型中Newton元件的方法,构建了能够描述不同温度条件下花岗岩蠕变全过程的本构模型。分析了不同温度条件下花岗岩单轴蠕变试验结果,确定了模型参数,获得了温度对花岗岩蠕变关键参数的影响规律。通过对花岗岩高温蠕变模型进行参数敏感性分析,揭示了弹性模量、黏性系数等关键参数对花岗岩蠕变特性的影响规律,并验证模型在不考虑温度及损伤的影响条件下可退化为经典西原模型。研究表明,建立的花岗岩高温蠕变本构模型可以准确地描述花岗岩典型蠕变全过程的3个阶段,尤其是加速蠕变阶段。黏性系数受损伤的影响越大,花岗岩的稳定蠕变阶段越短,越容易发生加速蠕变。     

基于分数阶导数的非定常蠕变本构模型研究

针对锦屏二级水电站深埋长大隧洞围岩在开挖过程中呈现明显的流变劣化特征,基于分数阶微积分理论,用Abel黏壶替换西原模型中的牛顿黏壶,推导出基于分数阶导数的蠕变本构方程,同时考虑岩石在蠕变过程中,尤其是所受应力超过其长期强度时,蠕变参数是非定常的特征,把蠕变参数的非定常性引入本构方程中,建立了基于分数阶导数的非定常蠕变本构模型。结合锦屏二级水电站引水隧洞主要围岩之一的大理岩的室内剪切蠕变试验的结果,对模型中的参数进行反演,结果表明,基于分数阶导数的非定常蠕变本构模型能够在蠕变初期和拐点处与试验结果很好地吻合,并且可以克服西原模型不能反映蠕变第3阶段的不足。通过对模型中参数的敏感性进行分析,得出分数阶阶数、非定常参数对岩石蠕变的影响规律。研究结果表明,提出的基于分数阶导数的非定常蠕变模型能够很好地反映大理岩的蠕变全过程。     

Finite element modelling of pressuremeter tests and footings on frozen soils

A finite element code is developed to model the structure-frozen soil/ice interaction using a time incrementing, fully implicit, iterative algorithm, and a constitutive model based on the concept that total strain tensor consists of an elastic and a creep component. The code is used to investigate the applicability and limitations of the power law as the creep model for frozen soil by simulating two pressuremeter tests. Two extended phenomenological models based on the generalized power law are used in axisymmetric finite element analyses to simulate two, long-term, stage-loaded pressuremeter tests, and comparison of results with test data indicates that one model demonstrates a better ability to approximate the actual response to subsequent load steps, under certain restrictions. Stress analyses demonstrate the ability of the constitutive model to show transient as well as subsequent quasi-stationary stress stages in creep analysis. Additional simulations of short-term pressuremeter tests on ice are performed to further illustrate some limitations of the power-law model. Examples for prediction of creep settlements on frozen geomaterials are demonstrated by considering the interaction of fully flexible circular footings and concrete cylindrical footings (of different embedment depths) with frozen sands.     

A viscoplastic model including anisotropic damage for the time dependent behaviour of rock

This paper presents a new constitutive model for the time dependent mechanical behaviour of rock which takes into account both viscoplastic behaviour and evolution of damage with respect to time. This model is built by associating a viscoplastic constitutive law to the damage theory. The main characteristics of this model are the account of a viscoplastic volumetric strain (i.e. contractancy and dilatancy) as well as the anisotropy of damage. The latter is described by a second rank tensor. Using this model, it is possible to predict delayed rupture by determining time to failure, in creep tests for example. The identification of the model parameters is based on experiments such as creep tests, relaxation tests and quasi‐static tests. The physical meaning of these parameters is discussed and comparisons with lab tests are presented. The ability of the model to reproduce the delayed failure observed in tertiary creep is demonstrated as well as the sensitivity of the mechanical response to the rate of loading. The model could be used to simulate the evolution of the excavated damage zone around underground openings. Copyright © 2005 John Wiley & Sons, Ltd.     

A constitutive law for rock salt based on creep and relaxation tests

Summary The paper deals with uniaxial relaxation tests on rock salt which are the basis for a constitutive equation. Since so far no regard was paid to relaxation behaviour, corresponding test results are not available and hence a special device for performing of uniaxial relaxation tests had to be constructed. Some interesting test results are discussed in the paper. These results are useful for the verification of constitutive equations. A critical analysis of conventional constitutive laws and their fundamentals shows that these material laws have considerable imperfections and are rested on substantial restrictions. Particularly, they are not able to describe relaxation behaviour sufficiently. Consequently, a constitutive law is proposed consisting of a strain hardening approach with separate creep and relaxation functions. By post-calculation of different laboratory tests it could be shown that in comparison to conventional steady-state creep equations this material law describes the viscous behaviour of rock salt more realistically.     

A Generalized Plasticity-Based Model for Sandstone Considering Time-Dependent Behavior and Wetting Deterioration

Based on the concept of generalized plasticity, this study proposes a constitutive model to describe the time-dependent behavior and wetting deterioration of sandstone. The proposed model (1) exhibits nonlinear elasticity under hydrostatic and shear loading, (2) follows the associated flow rule for viscoplastic deformation, (3) adopts a creep modulus that varies with the stress ratio, (4) considers the primary and secondary creep behaviors of rock, and (5) considers the effect of wetting deterioration. This model requires 13 material parameters, comprising 3 for elasticity, 7 for plasticity, and 3 for creep. All parameters can be determined easily by following the suggested procedures. The proposed model is first validated by comparison with triaxial tests of sandstone under different hydrostatic stress and cyclic loading conditions. In addition, the model is versatile in simulating time-dependent behavior through a series of multistage creep tests. Finally, to consider the effects of wetting deterioration, triaxial and creep tests under dry and water-saturated conditions are simulated. Comparison of the simulated and experimental data shows that the proposed model can predict the behavior of sandstone in dry and saturated conditions.     

泥质砂岩蠕变特性与锚固控制效应试验研究

通过泥质砂岩单轴压缩蠕变试验,揭示岩石蠕变变形与破坏的特点,反映了不同应力路径下的岩石蠕变速率与发展过程,建立了泥质砂岩的非线性蠕变模型,并通过对试件施加侧向刚性约束和锚固约束,以反映地下工程围岩在平面应变状态和支护状态下的蠕变特性。研究结果表明,锚固约束可以显著提高岩石发生稳定蠕变的应力阀值,减缓蠕变速率。根据改进的蠕变方程进行试验数据的拟合,确定了改进的西原模型蠕变方程中的各物理量。与单轴蠕变试验结果对比表明,该模型的计算结果与试验数据吻合较好,说明改进的西原模型可较好地反映岩石加锚后的蠕变特征。研究结果对深部地下工程围岩的变形与稳定控制研究具有重要的指导意义。     

Investigation into MOGA for identifying parameters of a critical-state-based sand model and parameters correlation by factor analysis

Adding refinement and accuracy to constitutive models of soil results in the introduction of complexities along with more model parameters. These parameters (such as hardening-/softening-, dilatancy-/contractancy-related parameters and critical state parameters) are usually not easily obtained in a straightforward way. How to identify these key parameters and estimate their correlations of advanced soil models is a particular issue for geotechnical engineering. This paper was aimed to investigate multi-objective genetic algorithms for identifying parameters of advanced sand models based on standard laboratory tests, followed by the correlation analysis of parameters. A critical-state-based sand model has been developed to simulate three triaxial compression tests performed on loose and dense Hostun sand. Two widely used genetic algorithms with two initialisation methods are examined. The performance of the two genetic algorithms is assessed by comparing their simulation performance using optimal parameters, the convergence speed and the distribution of solutions on the Pareto front. The optimal parameters can then be classified into two factors by their correlation relationship.