An anisotropic elastoplastic model for soft clays based on logarithmic contractancy

A new constitutive model for soft structured clays is developed based on an existing model called S‐CLAY1S, which is a Cam clay type model that accounts for anisotropy and destructuration. The new model (E‐SCLAY1S) uses the framework of logarithmic contractancy to introduce a new parameter that controls the shape of the yield surface as well as the plastic potential (as an assumed associated flow rule is applied). This new parameter can be used to fit the coefficient of earth pressure at rest, the undrained shear strength or the stiffness under shearing stress paths predicted by the model. The improvement to previous constitutive models that account for soil fabric and bonding is formulated within the contractancy framework such that the model predicts the uniqueness of the critical state line and its slope is independent of the contractancy parameter. Good agreement has been found between the model predictions and published laboratory results for triaxial compression tests. An important finding is that the contractancy parameter, and consequently the shape of the yield surface, seems to change with the degree of anisotropy; however, further study is required to investigate this response. From published data, the yield surface for isotropically consolidated clays seems ‘bullet’ or ‘almond’ shaped, similar to that of the Cam clay model; while for anisotropically consolidated clays, the yield surface is more elliptical, like a rotated and distorted modified Cam clay yield surface. © 2015 The Authors. International Journal for Numerical and Analytical Methods in Geomechanics published by John Wiley & Sons Ltd.     

上海第4层黏土力学特性的弹塑性本构模拟

上海第4层黏土是典型的结构性海相软土,用一个本构模型统一地模拟不同应力路径下的力学特性对数值计算具有重要意义。对UNIFIED模型的结构性及超固结发展函数进行了改进,并提出了一种确定原状土材料参数和初始状态的方法。为了验证修正模型的正确性,用块状取土法取得上海第4层原状土样,进行了固结试验和三轴排水、不排水剪切试验。通过比较试验结果和本构模拟结果,明确了新的本构模型仅用一组材料参数就能统一地模拟上海第4层黏土在固结、排水及不排水三轴试验得到的应力-应变关系。模拟结果揭示了上海第4层黏土的结构比较稳定,即使在经历三轴剪切发生35%轴应变后仍能保持较高位的结构性。     

Constitutive approach for rate‐sensitive anisotropic structured clays

This paper describes a constitutive approach to model the behavior of rate‐dependent anisotropic structured clay. Rate‐sensitivity is modeled using overstress viscoplasticity. Clay structure is treated as a viscous phenomenon whereby the viscosity of the undisturbed structured clay is initially very high and the viscosity degrades or decreases with plastic straining until the intrinsic or residual viscosity is reached. A microstructure tensor approach is used to make the structured viscosity anisotropic; whereas, the intrinsic viscosity is assumed to be isotropic. The behavior of the constitutive model is compared with the measured response of two clays (Gloucester and St. Vallier clay) from Eastern Canada during triaxial compression tests on specimens trimmed at different orientations to the vertical. The comparisons show that the constitutive framework is able to describe the anisotropic and rate‐sensitive response of both clays. The response of the model is also examined for the more general case of anisotropic consolidated triaxial compression and extension. Copyright © 2010 John Wiley & Sons, Ltd.     

红粘土动本构关系与动模量衰减模型

针对高速交通循环荷载下红粘土路堑基床的动力稳定性问题,基于大量室内动三轴试验,研究了不同试验条件下原状结构红粘土动本构关系及动模量衰减规律。试验成果表明:原状结构红粘土动本构关系仍可用R.L.Kondner双曲线模型描述;动模量随动应变的增大非线性减小,具有明显的应变软化特征。围压、固结比、含水比对红粘土动本构特征及动模量衰减规律均有明显影响。不考虑其它因素,随围压或固结比的增大,动本构曲线逐渐偏向应力轴,随含水比的增大,动本构曲线逐渐偏离应力轴。同等条件下,动模量随围压、固结比的增大而增大,随含水比的增大而减小。基于回归分析,给出了不同试验条件下原状结构红粘土双曲线模型参数、动模量衰减经验公式及其拟合参数。     

基于次加载面理论改进的ALPHA模型及其数值实施

基于次加载面理论对ALPHA模型进行了改进,并在模型中考虑了土体初始各向异性;提出了与模型相适应的半隐式本构积分算法,据此在通用有限元软件ABAQUS平台上开发了相应的用户材料子程序;利用建立的计算程序,对不同排水条件的三轴试验进行了数值模拟。与已有研究成果对比表明,提出的半隐式本构积分算法,可较好地实现复杂本构模型的数值实施。改进的本构模型克服了修正剑桥模型预测的超固结土峰值强度过高、初始屈服面内假定为弹性变形等缺点,能够较好地描述土体初始屈服面内的的非线性和不可恢复性变形特征;通过变化模型参数,可模拟变形特性较为复杂的土体。     

Model for analysis of fiber-reinforced clayey soil

Fiber-reinforced soils have many applications in improving the response of clayey soils. In this paper, an analytical model for the analysis of fiber-reinforced soil in the framework of modified cam clay model is presented. The analytical model is verified using experimental results from the standard undrained triaxial tests with pore water pressure measurements. Tests have been conducted on clayey soil specimens reinforced with randomly oriented discrete coir fibers with different percentages of fiber contents. Numerical simulations of triaxial compression tests on fiber-reinforced clay specimens were also performed. Results are presented in the form of stress vs. strain curves for plain soil as well as fiber-reinforced soil for various fiber contents based on the model developed. The results demonstrate the applicability of proposed analytical model in predicting the stress strain response of fiber-reinforced soils.     

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。     

Kinematic hardening predictions of large stress-reversals in 3-D test on loose sand

A rotational kinematic hardening constitutive model with the capability of predicting the behavior of soil during 3-D stress-reversals has been developed. An existing elasto-plastic constitutive model, the Single Hardening Model, utilizing isotropic hardening serves as the basic framework in these formulations. To this framework is added the capability of handling cross-anisotropic behavior as well as the kinematic hardening mechanism to capture inherent anisotropy of the sand in addition to the large stress-reversals. The model involves thirteen parameters, which can be determined from simple laboratory experiments, such as isotropic compression, drained triaxial compression and triaxial extension tests. The results from a series of true triaxial tests with large stress-reversals performed on loose cross-anisotropic Santa Monica Beach sand are employed for comparison with predictions.     

一个考虑循环荷载作用的简化模型

基于塑性硬化模量场理论和多重屈服面模型,结合各向同性硬化准则和移动硬化准则,在新的应力空间建立了一个新型不排水循环荷载作用下的多屈服面模型,并推导了一个适合三轴试验的简化的多屈服面模型。在此基础上,结合一个循环荷载作用下的动孔压模型,进行了饱和软黏土的动三轴模拟试验。结果表明,文中建立的多屈服面模型能够较好地模拟循环三轴试验、直剪试验和平面应变条件下的试验。     

A class of incrementally non-linear constitutive relations and applications to clays

A general framework to develop incrementally non-linear constitutive relations is given. In this constitutive theory it is needless to define plastic potential surfaces and yield functions which are very difficult to exhibit experimentally in a consistent manner. An incrementally non-linear of second order model which belongs to that class of constitutive relations is presented and applied to the simulation of triaxial tests carried out on a normally consolidated kaolin. Drained tests were utilized to calibrate the constitutive relations whereas axisymmetrical and threedimensional undrained tests permitted to study the validity of the model. Some comments in relation with the International Workshop on Constitutive Relations for Soils (Grenoble, 1982) are given and a constitutive instability is discussed.     

A simple hypoplastic model for normally consolidated clay

The paper presents a simple constitutive model for normally consolidated clay. A mathematical formulation, using a single tensor-valued function to define the incrementally nonlinear stress–strain relation, is proposed based on the basic concept of hypoplasticity. The structure of the tensor-valued function is determined in the light of the response envelope. Particular attention is paid towards incorporating the critical state and to the capability for capturing undrained behaviour of clayey soils. With five material parameters that can be determined easily from isotropic consolidation and triaxial compression tests, the model is shown to provide good predictions for the response of normally consolidated clay along various stress paths, including drained true triaxial tests and undrained shear tests.     

重塑超固结上海软土力学特性及弹塑性模拟

对典型上海软土重塑样进行了围压不变和平均主应力不变的三轴排水剪切试验,得到重塑上海软土在不同初始超固结比和围压条件下的应力-应变关系,弄清了超固结比、围压以及应力路径对重塑上海软土的变形和强度特性的影响;根据土体的应力-应变曲线得到重塑上海软土的临界状态应力比及内摩擦角。采用姚仰平等建议的基于伏斯列夫面的超固结土本构模型,并根据等向压缩及三轴排水剪切试验确定其模型参数,对保持围压和平均主应力不变的三轴压缩试验进行了模型预测。预测结果表明,此超固结土本构模型能较好地反映重塑超固结上海软土的变形和强度特性。     

Evaluation of an anisotropic elastoplastic–viscoplastic bounding surface model for clays

An anisotropic time-dependent bounding surface model for clays is developed by generalizing a previous time-independent model that adopts a flexible bounding surface. It is based on the framework for coupled elastoplasticity–viscoplasticity for clays and Perzyna’s overstress theory. Three viscoplastic parameters were introduced and explained in detail. The model was validated against undrained creep tests for both isotropically and anisotropically consolidated clays, undrained and drained stress relaxation tests on some undisturbed clays, and undrained triaxial tests with varying strain rates on natural Hong Kong marine deposit clay. The general agreement between the model simulations and test results was satisfactory. The varying effects of lower-level parameters were discussed on the undrained multistage stress relaxation response for normally consolidated soils which had been ignored in literature. The flexibility of the model in capturing the shear strengths, which is the unique feature of the current model, was shown in the simulations of time-dependent triaxial tests on Taipei silty clay. All the simulations show that the proposed model is a relatively practical model considering both anisotropy and time dependency of clays.     

不同应力路径下剪切带的数值模拟

采用回映应力更新算法,编写了基于伏斯列夫面的超固结黏土本构关系模型子程序,嵌入非线性有限元软件ABAQUS。通过对单元试验进行三轴压缩、三轴伸长及平面应变等问题的模型预测,再现了超固结黏土在不同初始超固结比和应力路径时的变形和强度特性,从而验证了子程序的正确性。借助该本构模型,对三轴压缩、三轴伸长及平面应变应力路径下超固结黏土体变形局部化问题,进行了三维数值模拟。分析结果表明：超固结黏土在三轴压缩及伸长状态时,土体变形局部化在应力-应变关系软化时出现,而平面应变状态时,在应力-应变关系硬化阶段出现,其超固结黏土的剪胀特性在剪切带的形成过程中起重要作用。     

Identification of constitutive parameters of soil using an optimization strategy and statistical analysis

The paper at hand investigates a strategy to calibrate different constitutive models for soils via back analysis. The efficiency and reliability of the parameter identification for soil models is worked out. In order to demonstrate of how to utilise identification procedures, results from optimisation against conventional oedometer and drained triaxial compression tests on natural Pappadai clay are presented and discussed. The aim of geotechnical optimisation problems is to obtain a set of model parameter values that provide the best match between soil model simulations and appropriate measurements. For the parameter identification process, a constrained population-based algorithm is chosen, namely the Particle Swarm Optimiser. The identification is carried out in an initial step separately on each test and then simultaneously on oedometer and triaxial tests. The evaluation is performed employing three different constitutive models of varying complexity and number of constitutive parameters.A subsequent residual analysis and the computation of confidence intervals for the parameters provide valuable results to assess the quality of the identified parameters in correlation with the evaluated data. Therefore, criteria of the utility and reliability of the mathematical models for further prognosis computations can be estimated.     

泥岩弹塑性损伤本构模型及其参数辨识

以连续介质力学和不可逆热力学为基础,将损伤引入到修正的Mohr-Coulomb准则中,建立了泥岩弹塑性损伤本构模型反映泥岩软硬化行为,通过构建损伤势函数导出了泥岩的损伤演化方程,编制了泥岩弹塑性损伤本构模型及其参数反演程序。并根据非排水条件下泥岩三轴试验结果,采用多目标函数优化反分析法获得了泥岩本构模型参数。研究成果表明,所提出的弹塑性损伤本构模型能有效地描述泥岩在不同应力状态下的力学特性。     

考虑各向异性的软黏土扰动状态本构模型

以大量试验结果为依据,运用物理意义明确、获取简便快捷、经济实用的土电阻率结构指标进行软黏土扰动变量的表征和测定。以三轴试验与电阻率测试结果为基础,进行了扰动函数的构建。在软黏土扰动状态描述中,引入旋转硬化因子,用以考虑应力诱发各向异性,进而构建了考虑各向异性的软黏土扰动状态概念本构模型。模型从一定程度上克服了传统扰动变量获取方法的弊端,克服了传统借用数学演绎手段建立扰动函数的不足,提高了模型应用的适用性。在模型构建中,融入初始应力各向异性的影响,从而使模型能更好地反映软土实际工程情况。三轴排水剪切试验验证结果表明,该模型可较好反映软黏土受荷下的结构变化情况和受力特性。     

A simple critical-state-based double-yield-surface model for clay behavior under complex loading

The critical state concept has been widely used in soil mechanics. The purpose of this study is to apply this concept in the framework of multi-mechanism elastoplasticity. The developed model has two yield surfaces: one for shear sliding and one for compression. In this model, the location of the critical state line is explicitly considered and related to the actual material density to control the peak strength and the phase transformation characteristics. The stress reversal technique is incorporated into the model for describing clay behavior under complex loading including changes of stress direction. The determination of the model parameters is discussed; it requires only one drained or undrained triaxial test up to failure with an initial isotropic consolidation stage. The model is used to simulate drained and undrained tests under monotonic loading with different over-consolidation ratios on various remolded and natural clays, including true triaxial tests with different Lode’s angles. Drained and undrained tests under cyclic loadings are also simulated by using the set of parameters determined from monotonic tests. The comparison between experimental results and numerical simulations demonstrate a good predictive ability of this new simple model.