加载速率变化条件下砂土的黏塑特性及本构模型

 分析并研究饱和的、风干的砂土在平面应变压缩试验条件下的弹黏塑性特征,尤其是黏性特性。加载速率效应、蠕变以及应力松弛都是砂土材料本身黏性的反映,而与超孔隙水压力的消散无关。试验不仅实现了应变率逐步变化加载过程,同时也实现了蠕变加载和应力松弛过程。试验结果表明,在加载应变率发生突变时,对砂土应力–应变关系有明显的影响,呈现出刚性很高、近似于弹性的特性,而后随着应变的进一步增加,在明显屈服之后黏性应力逐渐衰减至基本惟一的应力–应变曲线。类似现象同样也发生在蠕变加载或应力松弛后以一恒定应变率突然重新加载的情况。基于非线性三要素模型框架,针对所观察到的砂土黏性特性,提出一种弹黏塑性本构模型。该模型可以描述砂土在任意加载历史下的黏性效应,包括加载应变率发生任意变化时的应力–应变响应、蠕变以及应力松弛。最后,利用该模型对上述砂土平面应变压缩试验结果进行模拟,所提案的三要素弹黏塑性本构模型能够很好地模拟砂土的黏性特性。     

Fem Simulation of the Viscous Effects on the Stress-Strain Behaviour of Sand in Plane Strain Compression

A stress-strain model called TESRA (Temporary Effects of Strain Rate and Acceleration), described in a non-linear three-component framework, has been proposed to simulate the effects of viscous property on the stress-strain behaviour observed in drained plane strain compression (PSC) tests on clean sands. According to the TESRA model, the current viscous stress component is obtained by integrating for a given history of irreversible strain increments of viscous stress component that developed by respective instantaneous irrecoverable strain increment and its rate and have decayed with an increase in the irreversible strain until the present. The TESRA model was implemented into a generalized elasto-plastic isotropic strain-hardening non-linear FE code. The integration scheme to obtain the viscous and inviscid stress components according to the TESRA model in FEM analysis needs some specific considerations including the relevant choice of the suitable rate parameter. The shear stress—shear (or axial) strain—time relations from five drained PSC tests on saturated Toyoura sand and air-dried Hostun sand were successfully simulated by the FE code embedded with the TESRA model. It is shown that the FE code can simulate the time-dependent stress-strain behaviour of sand accurately without spending any significant extra computational time or storage. The results of simulation using one element and multi-element are essentially the same.     

考虑应力路径和加载速率效应砂土的弹黏塑性本构模型

 利用室内多应力路径平面应变压缩试验结果,分析和研究密实砂土变形和强度特征的应力路径和加载速率效应。试验结果表明：一方面,不可恢复体积应变和剪切应变都具有明显的应力路径相关性,因而在传统塑性理论中将其作为硬化参量存在不合理性;另一方面,砂土的应力–应变特性与加载速率的变化存在着显著的关系。加载速率效应与蠕变和应力松弛一样均是砂土黏性的外在反映,其最重要的特征之一是加载速率发生突变时,应力也发生相应的突变,并呈现出刚性很大、近似弹性的特性。对试验结果的进一步分析发现,一种修正的不可恢复应变能W ir*及相关的函数与应力路径不相关。将W ir*作为硬化参量,并在非线性三要素模型的理论框架下,提出一种基于能量的砂土弹黏塑性本构模型。该模型可以考虑应力路径、压力水平、固有各向异性、孔隙比等因素对砂土变形和强度特征的影响,以及应变局部化和加载速率变化所产生的黏性特性。将上述模型嵌入到有限元程序中,并对平面应变压缩试验进行模拟计算,验证模型的精确性。研究结果表明,与现有的砂土本构模型相比,所提出的模型能更好地模拟应力路径及加载速率变化对砂土变形和强度特征的影响。     

Effects of Viscous Property and Wetting on 1-D Compression of Clay and Model Simulation

A series of one-dimensional (1D) compression tests on compacted kaolin powder were performed to evaluate the combined effects of the viscous property and wetting on the elasto-viscoplastic deformation of soil. In the tests, both creep deformation and collapse deformation due to wetting were allowed to take place at various fixed stress states during otherwise monotonic loading at a fixed strain rate. Combined effects of the viscous property and wetting on the stress-strain behaviour observed during 1-D compression were described by incorporating the wetting effects into a non-linear three-component elasto-viscoplastic model (a 3C model). Based on the experimental results, the effects of wetting on the inviscid stress and the irreversible strain relation of the plastic component of the 3C model and the property of the viscous component, having an Isotach property, are formulated as a function of the degree of saturation. Complicated rate- and time-dependent stress-strain behaviour observed during saturation at a fixed stress state and subsequent monotonic loading at a constant strain rate were successfully simulated.     

Modelling and Simulation of Rate-Dependent Stress-Strain Behaviour of Granular Materials in Shear

A constitutive modelling of the elasto-viscoplastic stress-strain behaviour of geomaterials in shear that has been developed within a non-linear three-component model framework is validated by simulating a comprehensive series of drained triaxial compression (TC) and direct shear (DS) tests on a wide variety of granular materials. Illustrative simulations of rate-dependent stress-strain behaviour of geomaterial under typical laboratory test conditions were performed to analyse the structure of the model. The versatility of the proposed model and its applicability to a wide variety of shear loading histories is examined and demonstrated by these simulations. The following results are shown. Commonly with different basic viscosity types, Isotach, TESRA and P&N, the viscous stress component has a positive component that increases with an increase in the irreversible strain rate, which makes feasible stable and realistic simulations of rate-dependent stress-strain behaviour, including creep deformation, based on the proposed model. With different unbound granular material types having similar relative densities, the creep strain in TC tests and creep shear displacement in DS tests that develop by sustained loading at a given shear stress level for a given period tends to decrease with an increase in the particle roundness. This trend of behaviours is explained by a decrease in the viscosity type parameter, θ, associated with an increase in the particle roundness based on the simulations of these tests.     

A Simple Pneumatic Loading System Controlling Stress and Strain Rates for One-Dimensional Compression of Clay

A simple but automated pneumatic loading system that can control the stress and strain rates for one-dimensional (1D) compression of clay was developed. The rate-dependency of stress-strain behaviour due to the viscous property of clay was investigated by 1D compression tests on standard-size specimens by various loading methods: 1) Standard Consolidation Tests (SCTs), stepwise increasing the axial stress two times every one day; 2) ordinary Constant-Rate-of-Strain (CRS) tests at different strain rates; 3) special CRS tests including unloading and reloading cycles with different stress amplitudes at strain rates of which the absolute value was either kept constant throughout respective tests or changed at the start of reloading; and 4) special CRS tests including a number of sustained loading (SL) during otherwise primary loading or unloading or reloading at constant strain rate. Sufficiently low strain rates were employed to ensure essentially fully drained condition. The followings were found. Despite that the newly developed pneumatic loading system is rather simple, 1D compression tests following such various loading histories as above can be performed on four types of clay rather accurately. The stress-strain behaviour of clay is significantly rate-dependent, exhibiting significant creep strains at SL stages. The creep strain rate is significantly different whether SL starts during otherwise primary loading or unloading or reloading, controlled by the magnitude and sign of the initial strain rate at the start of SL. The whole observed trends of rate-dependent stress-strain behaviour can be qualitatively explained by the non-linear three-component elasto-viscoplastic model extended to cyclic loading conditions.     

Viscous Behaviour of Geogrids; Experiment and Simulation

The viscous properties of three types of geogrid polymer were evaluated by sustained loading tests lasting for 30 days at a load level about a half of its nominal rupture strength. The sustained loading tests were performed during otherwise monotonic loading (ML) at constant strain or load rate, unlike the conventional creep tests, in which the strain rate immediately before the start of sustained loading, which controls the creep strain rate, is not controlled or even not recorded. The following are presented in this study. The tensile rupture strength measured by ML that was started following a 30 day-long sustained loading was essentially the same as the one at the same strain rate at rupture obtained by continuous ML without any intermission of sustained loading. This fact indicates that creep is not a degrading phenomenon. Then, if free from chemical and mechanical degrading effects, the strength of a geosynthetic reinforcement (for a given strain rate at rupture) can be maintained until late in its service life. A non-linear three-component model is used to simulate the experimental results from the previous and present studies. The model can simulate very well not only the load-strain behaviour during ML with and without step changes in the strain rate and the one after sustained loading, but also the time histories of creep strain during sustained loading for short (one hour) and long (30 days) periods.     

单轴试验条件下粘土的粘塑性与模拟计算

利用饱和、湿润、风干以及烘干的藤森粘土的单轴排水固结试验进行了粘土粘塑性研究。试验过程中采用计算机应变控制的控制式三轴仪来实现加载速率，可在不同加载阶段实现不同的恒应变率加载试验。试验结果表明：各种不同饱和度藤森粘土的粘塑性都表现为等时特性；经过一定时间的蠕变后，粘土弹性模量会有较大的提高，且藤森粘土所表现出的粘塑性与粘土含水量的大小无关。研究结果表明，粘土的粘塑性应力-应变特性可以采用非线性三要素模型进行较好的描述。     

Viscous Properties of Granular Materials Having Different Particle Shapes in Direct Shear

The viscous properties of air-dried relatively poorly-graded granular materials having different particle shapes were evaluated by performing a series of direct shear (DS) tests. The applied loading histories include repeated step changes in the shear displacement rate (s) or repeated sustained loading stages during otherwise monotonic loading (ML) at a constant s under constant vertical stress. Test results of an angular gravelly soil (i.e., Chiba gravel-a) obtained from the present study and those of a wide variety of poorly-graded granular materials (i.e., glass beads and natural sands including Toyoura, Hostun, Silica No. 6a, Ticino, Silver Leighton Buzzard, Ottawa, Albany and Monterey sands) previously obtained by the authors are analysed. The viscous properties of granular materials can be adequately described by three basic parameters: i.e., the rate-sensitivity coefficient, the residual rate-sensitivity coefficient (or their ratio, i.e., the viscosity-type parameter) and the decay parameter. These parameters, as well as the viscosity type (i.e., Isotach, Combined, TESRA and P&N), are strongly affected by particle shape as quantified in terms of the degree of particle angularity while being rather independent of particle size. The creep deformation that takes place by sustained loading increases with an increase in the shear stress level, and it also increases with changes in the viscosity type associated with an increase in mainly the particle angularity and partly the coefficient of uniformity. The various viscous property types and transitions among them can be described by a single general equation incorporating these parameters. A non-linear three component model incorporating this general equation can simulate very well all of the various viscous responses observed in the DS tests referred to in the paper.     

Strain Energy-Based Elasto-Viscoplastic Constitutive Modelling of Sand for Numerical Simulation

It is shown that the use of visco-plastic shear or volumetric strain as the stress history-independent hardening parameter in an elasto-viscoplastic model for sand may result in inaccurate numerical simulations of geotechnical boundary value problems. A new elasto-viscoplastic constitutive model for sand is proposed, formulated based on a stress path-independent irreversible (or visco-plastic) strain energy-based hardening function. The function was derived based on results from drained plane strain compression (PSC) tests on saturated dense Toyoura sand along a wide variety of stress path. The model is coupled with an existing isotropically work-hardening and -softening, non-associated, elasto-plastic model for sand. The constitutive model takes into account the effects of loading rate due to viscous properties on the stress-strain behaviour as well as those of pressure level, inherent anisotropy and void ratio and work softening associated with strain localization into a shear band. It is shown that the proposed model can much better simulate the effects of stress history on the deformation characteristics of sand than many previous models. The FEM code incorporating the model is validated by simulating physical PSC tests and bearing capacity model tests of a strip footing on sand performed by previous studies.     

Time-Dependent Shear Deformation Characteristics of Geomaterials and their Simulation

The viscous aspects of the stress-strain behaviour of saturated and air-dried clean sands in drained plane strain compression (PSC) and saturated clean sand and soft clays in undrained triaxial compression (TC) are presented. Common as well as different viscous features among the different geomaterials are addressed. The general three-component model is used as the framework for constitutive modelling, in which the total strain rate ε is decomposed into elastic and irreversible components ε^e and ε^ir while the stress σ is decomposed into inviscid (non-viscous) and viscous components σ^f and σ^v. In the simplest model (called the new isotach model) among those described in the paper, σ^f is a nonlinear function of ε^ir, while σ^v is a non-linear function of ε^ir and always proportional to σ^f for primary loading. This model is relevant to kaolin for the full pre-peak range and a reconstituted low-plasticity clay (Fujinomori clay) at small strains, both in undrained TC. The model is modified to simulate the viscous effect that decays with ε^ir, as observed with clean sands and a natural soft clay. It is shown that the second type of model (called the viscous evanescent model and the TESRA model) simulates well the above-mentioned behaviour, not only during primary loading, but also at unloaded conditions. The model is further modified to simulate the behaviour of Fujinomori clay whereby the rate at which the viscous effect decays gradually increases with ε^ir (the general TESRA model). The viscous components σ^v of the three models can be represented by a set of common equations, and the other models are specifically simplified versions of the general TESRA model.     

Ageing Effects on the Yielding Characteristics of Cement-Mixed Granular Materials

Ageing effects on the elasto-viscoplastic property of compacted moist cement-mixed granular material (GM) were evaluated by performing a series of non-standard drained triaxial compression (TC) tests. Two types of GM, crushed gravelly soil from a quarry and crushed concrete aggregate (i.e., a recycled material), were used. The specimens were produced by moist-compaction and then cured at constant water content under unstressed conditions for seven days. They were re-cured basically for two days under different stress states during otherwise drained TC loading at a constant strain rate. Yielding characteristics upon the restart of drained monotonic loading (ML) at a constant strain rate toward ultimate failure at the same or increased or decreased confining pressure were evaluated. The stress-strain behaviour before the stress state reaches the current yield locus is very stiff and highly reversible. Unlike elasto-plastic materials exhibiting no ageing effects, the yield locus expands during sustained loading at a fixed effective stress state due to not only yielding associated with creep deformation, controlled basically by the viscous property, but also ageing, controlled basically by time-elapsing. The shape and location of current yield locus depends on the location of the current stress state relative to the current ultimate failure envelope. The observed yield characteristics were analyzed based on a newly introduced interactive double-yield concept while in the framework of the non-linear three-component elasto-viscoplastic model that takes into account ageing effects as well as an interaction between ageing and inviscid yielding (and its potential decay by irreversible straining). The trends of stress-strain-time behaviour observed with the two types of cement-mixed GMs are essentially the same.     

油砂的蠕变特性与本构模型研究

油砂是一种富含天然沥青的沉积砂。作为一种软化材料,油砂的蠕变性质较松砂和正常固结黏土等硬化材料更为复杂。通过开展油砂三轴蠕变试验,获得了不同应力和应变状态下油砂的蠕变特性;讨论了蠕变势与塑性势之间的关系,提出了等效变形过程的概念,分析等效变形过程的微观机制;讨论了蠕变速率与时间和不可恢复应变之间的关系,提出采用不可恢复应变作为内变量可以描述复杂条件下油砂的蠕变性质,并据此提出了油砂的内变量蠕变模型;应用临界状态理论,分析了硬化型和软化型土的蠕变性质;讨论了剪切带对密砂蠕变性质的影响。     

Viscous Property of Toyoura Sand Over a Wide Range of Shear Deformation Rate and its Model Simulation

As part of a long-term research program to evaluate the rate effects on the stress-strain behaviour of geomaterials, the viscous properties of a poorly-graded relatively angular quartz-rich sand, Toyoura sand, under air-dried conditions, were investigated by performing a comprehensive series of direct shear (DS) tests at a fixed normal stress equal to 50 kPa. The tests were performed on loose and dense specimens subjected to the following different loading histories: a) monotonic loading (ML) at constant shear displacement rate (s) differing by a factor up to 100,000; b) ML at constant s including otherwise a number of step changes in s by a factor of 100; and c) a number of sustained loading (SL) stages during otherwise ML at constant values of s differing by a factor up to 1,000. Tests a) revealed that, with dense specimens, the peak shear strength is remarkably independent of s while the residual shear strength noticeably decreases with an increase in s. That is, the viscous property is the so-called TESRA type at the peak stress state, while it is the so-called Positive & Negative (P&N) type at the residual state. With loose specimens, both peak and residual shear strengths decrease with an increase in s, indicating that the viscous property is already the P&N type at the peak stress state and definitely so at the residual state. These results are qualitatively and quantitatively consistent with those from tests b), by which the viscosity properties were quantified in terms of the rate-sensitivity coefficient. The results from tests c) showed that creep shear displacement, Δs, increases with a decrease in the tangent stiffness at the immediately preceding ML phase or with an increase in the shear stress level during the SL stage. The value of Δs for a given period steadily increases with an increase in s during the immediately preceding ML phase. These trends of viscous behaviour are simulated all very well by a non-linear three-component model incorporating a general expression of viscous stress.     

Aging Effects on Small Strain Shear Moduli and Liquefaction Properties of in-situ Frozen and Reconstituted Sandy Soils

In order to investigate the effects of different geological ages on liquefaction properties of sandy deposits, a series of undrained cyclic triaxial tests was performed on three kinds of in-situ frozen and their reconstituted samples which were retrieved from Holocene (Tone-river sand) and Pleistocene (Edo-river B and C sands) deposits. The specimens were subjected to isotropic consolidation at a specified confining stress which is equivalent to the in-situ overburden stress at the depth of sampling, and small strain shear moduli were measured before and during the undrained cyclic loading tests. The liquefaction properties and the small strain shear moduli were affected by not only the natural aging effect of the specimen but also the inter-locking effect that was enhanced by applying drained cyclic loading before the undrained cyclic loading tests. During liquefaction, different tendencies of degradation in the small strain shear moduli which would reflect the aging effects of the specimen were observed between Tone-river Holocene sand and Edo-river B and C Pleistocene sands. The applicability of reconstituted samples as substitutes for in-situ frozen samples was confirmed with Tone-river Holocene sand that has no cementation effect between soil particles, whereas it seems difficult to simulate fully the liquefaction behaviour of Edo-river B and C Pleistocene sands which have higher cementation effect.     

黄土三轴剪切蠕变特性研究

以陕西省杨凌示范区某黄土边坡黄土试样为研究对象,进行了一系列室内三轴剪切蠕变试验,对三轴应力条件下黄土的剪切蠕变特性进行了研究,分析了时间、偏应力水平对应变速率的影响。建立了适合杨凌地区黄土的经验蠕变模型,通过与Burgers模型的比较发现,该经验蠕变模型具有精度高、参数少且获取途径简便的优点,能够很好地描述杨凌地区黄土的应力–应变–时间关系。另外,由试验资料发现三轴应力条件下黏滞系数与偏应力、时间具有密切的关系,并推导出黏滞系数与偏应力、时间的经验公式,并对该经验关系进行了验证。     

Discrete element visco-elastic modelling of a realistic graded asphalt mixture

The Discrete Element Model has been used here to simulate constant strain rate uniaxial compression tests for a realistic asphalt mixture comprising graded aggregates. A numerical sample preparation procedure has been developed to represent the physical specimen. A parallel bond model has been used in the elastic modelling to give moment resistance at the contacts. Uniaxial constant strain rate loading and unloading tests have been simulated. The effects of the normal to shear contact stiffness ratio on the bulk properties, the parallel bond radius, the number of particles and their positions, and the loading speed have been investigated. A modified Burger's model has been used to introduce time-dependent contact stiffness with the ability to transmit moment and torsion. Two-ball clumps have been used to investigate the effect of particle shape. The effect of Burger's model parameters, the ratio of normal to shear Burger's model parameters, the bond radius multiplier, the friction coefficient and the bond strength distribution in the viscoelastic simulations have been investigated. Constant strain rate uniaxial compression tests have been undertaken in the laboratory where the axial stress–strain response has been measured for comparison with the numerical modelling results. The modified Burger's model has proved to be useful and ready for simulating uniaxial constant strain rate and creep tests in the laboratory.     

一个能够模拟软土时效特性的简单弹黏塑性模型(英文)

基于Perzyna超应力理论与修正剑桥模型,建立了一个能够模拟软土时效特性的简单的弹黏塑性本构模型,提出了参数的实验室确定方法。以室内试验为基础,模拟了不同试验条件下软土的时效特性:应变速率对先期固结压力和不排水抗剪强度的影响;一维固结与次固结特征及竖向应力对次固结系数的影响;不同应力水平下的不排水蠕变特征;不同应变水平下的应力松弛特征。通过实验数据与数值模拟的比较,对模型进行了验证,发现上述本构模型能够较好地描述不同加载路径下的正常固结与微超固结土的时效特征。同时,通过对同一试样的多阶段加卸载三轴实验、现场压力仪实验及实验室压力仪实验的模拟,发现此模型可以较好地拟合实验过程中复杂应力路径下软土的时效特征。     

循环荷载下土基的非线性剪切粘性（英文）

Experimental investigations of nonlinear shear viscosity of subgrade soils under periodic loading are conducted. Unsaturated subgrade soil samples are prepared to conduct triaxial shear tests under repeated loading that is used to simulate the cyclic stress induced by vehicles. Investigations included three aspects. First,a new nonlinear viscous model is introduced to describe the relation of shear stress and shear strain rate. This relation was reduced from the constitutive law of nonlinear poroviscosity suggested by the author before. Second,related constitutive parameters are investigated and calibrated with experimental results from triaxial shear tests. The nonlinear viscous parameters are assumed to be a function of deviatoric strain and loading repetitions. Third,both viscous and elastic behavior of soils associated with the deviatoric strain and the cyclic loading repetition is tudied. The correlation between shear viscosity and resilient modulus is discussed as well. This is the first attempt to find any correlation between soil viscosity and elasticity through laboratory investigations. In contrast,in traditional numerical computations (e.g.,the finite element method),the extra viscous term added to the governing equation is assumed to be related to system mass and rigidity.     

NONLINEAR VISCOSITY OF SUBGRADE SOILS UNDER CYCLIC LOADING

1 anODUCTIONBoth qualny and Haree of Pavment willlopIy depend on mechanical behavior of suWesoils, Wially the viscous mp of sUbgrade soilunder vehicle-induced dynaInic loading. However,little effort has bo mad in inveStigating soil viscousbehavior in both the laboratory and the field. In mostntnnerical and compute modeling inveStigations,poeters related to soil viscous behavior aretalitionally empintal. For example, cOmPLItr mode-ling wAn the finite elemen method (FEM) is one ofmoSt …