Nonlinear creep damage constitutive model for soft rocks

In some existing nonlinear creep damage models, it may be less rigorous to directly introduce a damage variable into the creep equation when the damage variable of the viscous component is a function of time or strain. In this paper, we adopt the Kachanov creep damage rate and introduce a damage variable into a rheological differential constitutive equation to derive an analytical integral solution for the creep damage equation of the Bingham model. We also propose a new nonlinear viscous component which reflects nonlinear properties related to the axial stress of soft rock in the steady-state creep stage. Furthermore, we build an improved Nishihara model by using this new component in series with the correctional Nishihara damage model that describes the accelerating creep, and deduce the rheological constitutive relation of the improved model. Based on superposition principle, we obtain the damage creep equation for conditions of both uniaxial and triaxial compression stress, and study the method for determining the model parameters. Finally, this paper presents the laboratory test results performed on mica-quartz schist in parallel with, or vertical to the schistosity direction, and applies the improved Nishihara model to the parameter identification of mica-quartz schist. Using a comparative analysis with test data, results show that the improved model has a superior ability to reflect the creep properties of soft rock in the decelerating creep stage, the steady-state creep stage, and particularly within the accelerating creep stage, in comparison with the traditional Nishihara model.     

粘弹塑性理论在混凝土变形中的应用

首先文章介绍了粘弹塑性统一本构模型的基本方程,根据混凝土的特点对统一本构模型进行了简化,简化后的模型对混凝土的无损伤段的变形模拟,取得了满意的结果。之后应用粘弹塑性统一本构模型对混凝土进行跳跃实验预测,同样获得了预期效果,证明粘弹塑性统一本构模型在混凝土的变形预测中的应用是成功的。     

Triaxial Small-Strain Viscoelastic-Viscoplastic Modeling of Asphalt Aggregate Mixes

A triaxial cross-anisotropic viscoelastic-viscoplastic constitutive model for asphalt aggregate mixtures is developed for the small-strain domain. The model follows the concept of strain decomposition by separately analyzing the viscoelastic and viscoplastic strain components. In order to calibrate the model, advanced triaxial testing was employed which included both hydrostatic and uniaxial creep and recovery cycles. The test-data is presented and analyzed along with the derivation of all model parameters. It is shown that the proposed model correlates extremely well with the entire test-data in both axial and radial directions.     

A constitutive model for the uplift behavior of anchors in cohesionless soils

Abstract

A series of triaxial tests has been performed to establish the stress‐strain curves for I‐Lan sand and Taipei silty sand. A constitutive model for the continuous strain hardening‐softening and volumetric dilatancy of these two soils is proposed, based on the results of triaxial tests. Using this model, a numerical program is then established, with FLAC software, to analyze the uplift behavior of model anchors in sand and field anchors in silty soil.

It was found from triaxial tests, that the peak friction angle increases with relative density of soil and decreases with confining pressure. A non‐associated flow rule between plastic strain increment and stress tensor was found. As accumulative plastic strain, relative density and confining pressure were changed, the mobilized friction angle and mobilized dilatancy angle also changed. All parameters needed for the proposed model can be expressed as functions of relative density and confining pressure. This model can calculate the stress‐ strain curves of cohesionless soils determined from triaxial tests accurately.

The load‐displacement behaviors determined from anchor tests are compared with those calculated from this numerical program, the numerical results are in good agreement with the test results not only for model anchors in sand but also for different types of field anchors in silty soil.     

Experimental investigation on the train-induced subsidence prediction model of Beiluhe permafrost subgrade along the Qinghai-Tibet Railway in China

Based on dynamic triaxial test at low temperature of the frozen clay from the Beiluhe permafrost subgrade along the Qinghai-Tibet Railway (QTR), residual deformation laws and dynamic subsidence prediction model of permafrost subgrade under train traffic were studied. First, time history curves of residual strain of frozen soil are obtained and analyzed under different temperatures, frequency, confining pressure and moisture content. And conclusions can be drawn that the axial strain rate is greatly affected by the amplitude of dynamic stress, as well as increases with dynamic to static stress ratio and temperature rising, while it decreases with the raise of frequency and moisture content. Hereby, the power functions were adopted to fit the relationships of axial dynamic strain rate vs. stress ratio, temperature, frequency, and moisture content, respectively. Simultaneously, the permafrost dynamic subsidence mechanism was interpreted rationally and the variation of fitting parameters was discussed. Furthermore, the long-term traffic loading subsidence model was established through observing the axis residual strain time histories of frozen specimens under the longtime cyclic loading and adopting the amendment of vibratory number of times. The model can comprehensively consider the effects of stress state, temperature, moisture content, and confining pressure of frozen soil, as well as the vibratory frequency and vibration number of longtime cyclic loading. Consequently, the model can be applied to the train-induced subsidence forecast investigation of permafrost subgrade. The paper has an important significance for rational safety evaluation on long-term operation of permafrost regions railway such as QTR. Meanwhile, the investigation provides basic data for the further research on dynamic damage constitutive model of frozen soil under train traffic and the gradual improvement of railroading criterion in cold regions.     

PVC涂层膜材料不同应力下非线性蠕变特性的预测

对方平组织为基布的PVC (polyvinylchloride)涂层膜材料进行了经、纬两方向五种应力条件下的拉伸蠕变试验.利用七参数(四个蠕变柔量与三个推迟时间)广义Kelvin-Voigt线性粘弹性蠕变模型对试验数据进行了分析,从中发现:对于单个应力,线性粘弹性蠕变模型具有很好的拟合效果,而对于多个应力,三个推迟时间参数保持不变,并以此为基础,将七参数广义Kelvin-Voigt线性粘弹性蠕变模型修改为适合膜材料的七参数(四个蠕变柔量与三个推迟时间)非线性粘弹性和十四参数(八个蠕变柔量与六个推迟时间)非线性粘弹塑蠕变模型,并把十四参数非线性粘弹塑蠕变模型合并为四个蠕变柔量与三个推迟时间的七参数非线性模型,再将这两种非线性模型中的三个推迟时间设定为与线性粘弹性蠕变模型相同,同时还设定非线性部分均来自于四个蠕变柔量,最后借助四阶多项式对不同应力与对应的蠕变柔量进行了拟合,结果发现:该方法可以很好预测其他应力的蠕变特性.     

Linear elastic constitutive relation for multiphase porous media using microstructure superposition: Freeze-thaw soils

The constitutive relation derived in our previous work based on the microstructure superposition technique is implemented here for three-phase microstructure configuration to study the mechanical behavior of freeze-thaw soils. Three scenarios were considered for the frozen soils: frozen soil consisting of only two solids, soil skeleton and ice; frozen soil with soil skeleton, ice, and void; and frozen soil consisting soil skeleton, ice and pores saturated with fluid. The frozen soil studied is Alaska frozen soil mainly consisting of clay and silt particles at temperature about −10 °C. The effective elastic constants were calculated for the media under each scenario using two sets of elastic constants of soil skeleton (clay mineral). The modeled results were compared with Hashin-Shtrikman's upper bound solution and the experimentally measured data. In addition to be able to model the mechanical behavior of freeze-thaw soils, the derived constitutive relation, as indicated in the results of this study, could also be used as a tool in determining the microstructure of freeze-thaw soils by measuring the elastic constants of soil skeleton, the elastic properties and unfrozen water content of the media.     

Study on long-term stability of Qinghai–Tibet Railway embankment

In order to predict long-term stability of Qinghai–Tibet Railway (QTR) embankment, a moisture, heat and creep couple model is deduced on the basis of principal theories of numerical heat transfer, physics of frozen soil, frozen soil mechanics and rheology of frozen soil. And in this model, the moisture and temperature field are interacted with each other, the parameters of frozen soil change with soil temperature variation and an in-situ creep equation of frozen soil is also included. Meanwhile, a finite element program is written. Then, the long-term stability of the embankment is studied in detail. Through comparing with observation data, it is found that the proposed analytical model is correct and reasonable, thus it can well describe and predict the long-term stability problem of the QTR embankment. Additionally, it is a reference to analyze the deformation problems of other buildings in permafrost regions.     

考虑围压对粗粒土蠕变特性影响的Burgers模型参数修正方法研究

传统的Burgers模型假设只有偏应力引起蠕变,而没有考虑围压对蠕变特性的影响,因此其主要用于描述岩石的蠕变特性。但不同于岩石,堆石料等粗粒土是由颗粒集合而成的摩擦型材料,其蠕变特性与围压密切相关。为了考虑围压对粗粒土蠕变特性的影响,该文首先推导了Burgers模型的三轴蠕变理论解,并根据各参数物理意义,提出一套简便实用的参数反演方法,用于获取同一围压不同偏应力下粗粒土的Burgers模型参数;进而总结并分析不同粗粒土的三轴蠕变实验结果,发现幂函数能较好地描述Burgers模型各参数随围压变化的规律;在此基础上,提出考虑围压对粗粒土蠕变特性影响的Burgers模型参数修正方法,并通过三组粗粒土的蠕变实验结果验证了所提方法的有效性。     

混凝土三轴蠕变统计损伤模型研究

为探讨混凝土三轴蠕变特性,采用SAM-2000微机控制电液伺服材料三轴试验机并配备压力自平衡式三轴压力室对混凝土进行了三轴压缩试验和三轴蠕变试验,结果表明:围压的存在可以显著提高混凝土的承载能力,围压越大,混凝土的轴向承载能力越高,蠕变变形量和变形速率越小。假设混凝土破坏为其内部微元破坏累积所致,微元破坏概率与混凝土应变存在一定关系P[#x003b5;],且服从Weibull分布,结合三轴压缩试验结果,计算得到了描述混凝土损伤特性的统计损伤变量;基于Burgers流变模型,通过引入损伤变量建立了混凝土三轴蠕变统计损伤模型,利用MATLAB软件进行了模型参数拟合,经对比分析,模型曲线与试验曲线拟合结果较理想,主偏应力越大,拟合结果越精确。此模型可供今后研究参考。     

Anisotropic viscoplasticity constitutive model for directionally solidified superalloy

Abstract

The macroscopic deformation behaviour of a Ni-based directionally solidified (DS) superalloy was experimentally investigated, and an anisotropic constitutive model of the material was developed. Monotonic and creep tests were performed on uniaxial test specimens machined from DS plates so that the angle between the loading direction and the solidified grain direction varied between 0 and 90°. Tension-torsion creep tests were also conducted to examine the anisotropic behaviour under multiaxial stress conditions. The material exhibited marked anisotropy under elastic and viscous deformation conditions, whereas it showed isotropy under plastic deformation conditions of high strain rates. Then crystal plasticity analyses were carried out to identify slip systems under creep loading conditions, assuming the anisotropic creep behaviour of the DS material. A viscoplastic constitutive model for expressing both the anisotropic elasticity-viscosity and the isotropic plasticity was proposed. The elastic constants were determined using a self-consistent approach, and viscous parameters were modelled by crystal plasticity analyses. The calculation results obtained using the constitutive model were compared with the experimental data to evaluate the validity of the model. It was demonstrated that the constitutive model could satisfactorily describe the anisotropic behaviour under uniaxial and multiaxial stress conditions with a given set of material parameters.     

Experimental study on the creep behavior of frozen clay with thermal gradient

Thermal gradient is one of the main features in frozen engineering, especially in artificial frozen wall (AFW) in deep alluvium. This paper investigated the creep behaviors of frozen soil with thermal gradient. A series of uniaxial creep tests were carried out on frozen saturated clay under various thermal gradients and creep stresses by GFC (freezing with non-uniform temperature without experiencing K₀ consolidation) method. Two stages were observed during the whole creep process, i.e., instantaneous elastic deformation and decaying creep deformation. Radial creep deformation of ε₃ almost increases linearly with an increase in axial creep deformation of ε₁, and the slope of ε₃–ε₁ curve increases as the thermal gradient (or creep stress) increased. Long-term strength decreases as the thermal gradient (or the creep time) increased. Considering the correction equation on thermal gradient, the generalized Kelvin model consisting of one Hooke element and two Kelvin elements has been developed to describe the axial creep deformation. The validity of the model is verified by comparing its calculated results with the results of creep tests under both low and high thermal gradient. It is found that the axial creep deformation behavior of frozen saturated clay can be represented by generalized Kelvin model, and the proposed model reflects thermal gradient effects to the creep deformation well.     

土与结构接触面土体软/硬化本构模型及数值实现

基于土与结构接触面变形特性分析,将接触面土体的剪切滑动面与单元体三维应力状态下的八面体面相对应,通过土的三维弹塑性本构模型在八面体面上的剪切应力-应变关系,建立了接触面土体剪切应力-应变关系;将接触面土体法向压缩变形与侧限压缩条件相对应,通过侧限压缩条件下的荷载变形关系,建立了接触面土体法向应力-应变关系;进一步将接触面土体切向与法向耦合,建立了接触面土体本构模型,模型只有4个材料参数,参数物理意义明确,可由等向压缩试验和常规三轴压缩试验确定。与接触面土体试验结果的对比分析表明,所建立的本构模型可较好地描述接触面土体切向软/硬化特性与法向变形规律。结合有限元软件ABAQUS,编制了FRIC模型子程序,通过模拟土与结构界面剪切滑移过程表明,编制的FRIC子程序可较好地模拟土与结构界面接触的非线性力学行为。     

基坑开挖数值模拟中土体本构模型的选取

基坑开挖数值分析中的一个关键问题是选取一个合适的土体本构模型。该文通过对基坑开挖过程中土体的主要应力变化路径进行分析, 指出开挖条件下的土体本构模型应能合理考虑土体变形特性的应力路径相关性和压硬性。在介绍与分析几种常用土体本构模型特点的基础之上, 通过模拟应力路径三轴试验、基坑工程算例与工程实例的对比分析, 探讨了常见土体本构模型的适用性。分析表明, Hardening Soil Model采用了不同的加荷与卸荷模量, 能够反映土体应力路径的影响, 且考虑了土体模量的应力水平相关性, 能预测得到较合理的坑壁侧移、地表沉降以及支护结构的内力, 因而建议采用Hardening Soil Model进行基坑开挖数值模拟分析。     

动力荷载下聚氨酯泡沫材料本构关系研究进展

聚氨酯泡沫材料是一种应用广泛、应变率敏感、静水压力相关的多孔介质材料。文中综述了近年来国内外聚氨酯泡沫材料本构关系的研究进展。通过对几种应变率相关的本构模型,如粘弹、粘弹塑性等类型本构进展的介绍,分析了这些本构的特点和适用范围。根据已有的实验和本构关系,指出建立聚氨酯泡沫材料动态本构关系过程中需要考虑的主要问题,最后展望了聚氨酯泡沫材料的本构关系发展趋势。     

The influence of cryostructure on the creep behavior of ice-rich permafrost

Unconfined constant stress creep (CSC) tests were performed in order to look at the influence of cryostructure on the creep behavior of ice-rich undisturbed permafrost soils and remolded frozen soils within the temperature range from − 1 °C to − 2 °C. Undisturbed ice-rich permafrost soils were sampled from a Pleistocene age yedoma or “ice-complex” permafrost deposit in Interior Alaska. Cryostructure or the pattern of ice inclusions within a frozen soil is a direct indicator of the geologic and cryogenic genesis of permafrost soils. The data indicate that cryostructure influences the creep behavior of permafrost soils. Undisturbed soils with massive cryostructure showed higher induced creep strains and minimum strain rates than the more ice-rich undisturbed soils. Remolded soils with massive cryostructure experienced significantly lower creep strains and lower strain rates than the undisturbed soils. Deformation rates increase rapidly above a threshold stress value for remolded soils. From an engineering viewpoint, use of creep rates from remolded soils is non conservative and under predicts the creep rates of undisturbed soils. The orientation of ice lenses can facilitate motion along the ice lens–soil contact. Similarly, folding of ice lenses may occur, thus inducing anisotropic lateral strains. The ice facies tested indicate that for the temperature and stress range tested, ice creeps at a slower rate than frozen soils.     

Plastic limit load of Grade 91 steel pipe containing local wall thinning defect at high temperature

This paper aims to predict the plastic limit load of Grade 91 pipe at high temperature by experimental and numerical analysis methods. The elastic–plastic constitutive relation of P91 considering creep damage at high temperature is proposed and the effectiveness is verified by high-temperature instantaneous tensile test after creep of P91 sample. Then, using the elastic–plastic constitutive relation considering creep damage, the plastic limit loads of P91 pipe containing local wall thinning (LWT) defect at high temperature have been calculated by finite element (FE) method and the accuracy is checked by high-temperature burst experiment after creep of T91 pipe containing LWT. Finally, the fracture analysis and metallographic analysis of Grade 91 sample and pipe containing LWT defect are performed. The results show that the elastic–plastic constitutive relation of P91 considering creep damage proposed by this paper can well describe the elastic–plastic behavior of P91 under creep condition and is useful to calculate the plastic limit load of P91 pipe containing LWT. The failures of P91 tensile samples and T91 pipes containing LWT defect are both plastic fracture. This research would provide an optional method for structure integrity analysis of the pipe containing LWT defect at high temperature.     

沥青砂粘弹塑蠕变损伤本构模型实验研究

针对沥青砂的非线性材料特性,结合连续损伤力学理论,对传统Burgers模型进行改造,提出了粘弹塑蠕变损伤本构模型,通过对不同实验条件下沥青砂单轴蠕变试验结果的非线性拟合,获得模型参数,然后利用模型进行预测分析,得到了不同应力水平与环境温度下的蠕变曲线和损伤演化曲线,通过比较发现该文模型能够更合理地反映沥青砂加速蠕变的非线性特征,而且蠕变过程中损伤演化的速度受蠕变时间、应力水平与环境温度的影响很大。     

A micromechanics model of creep deformation in dispersion-strengthened metals

A micromechanics model, in which work-hardening caused by second-phase particles and a recovery process by diffusion of atoms were taken into account, has been proposed for explaining the creep deformation of dispersion-strengthened metals in high-temperature creep. A constitutive equation of the projection was employed to describe the whole creep curves from the onset of loading to rupture. The results of the calculations based on the present model have been compared with those of experiments on the carbon steels containing spherical cementite particles. There was a correlation between the experimental creep curves and the calculated ones. The changes in the calculated creep strain and creep rate with time have also been compared with the experimental results on carbon steels. The micromechanics model was found to be applicable to any kind of two-phase material, if the constitutive equation was appropriately chosen.     

Constitutive modeling of creep-fatigue interaction for normal strength concrete under compression

Conventional approaches to model fatigue failure are based on a characterization of the lifetime as a function of the loading amplitude. The Wöhler diagram in combination with a linear damage accumulation assumption predicts the lifetime for different loading regimes. Using this phenomenological approach, the evolution of damage and inelastic strains and a redistribution of stresses cannot be modeled. The gradual degration of the material is assumed to not alter the stress state. Using the Palmgren–Miner rule for damage accumulation, order effects resulting from the non-linear response are generally neglected.In this work, a constitutive model for concrete using continuum damage mechanics is developed. The model includes rate-dependent effects and realistically reproduces gradual performance degradation of normal strength concrete under compressive static, creep and cyclic loading in a unified framework. The damage evolution is driven by inelastic deformations and captures strain rate effects observed experimentally. Implementation details are discussed. Finally, the model is validated by comparing simulation and experimental data for creep, fatigue and triaxial compression.