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.     

A constitutive thermomechanical model for saturated clays

The structural deformation in clays results from microscopic phenomena involving the mechanical contact-stress change, the physico-chemical variation of repulsive forces in expansive clays, and thermal dilatancy of macropores. These textural strains are associated to three plastic mechanisms represented by respectively the yield surfacesf_Tm, f_R-A andf_T. Under a thermal cycle, the sizes of interlamellar spaces between clay platelets are not modified, hence the temperature cycle is expected to have no effect on repulsive forces and thus the second mechanism is not affected by temperature changes.

This paper suggests a formulation of a model of thermo-elasto-plastic behaviour of non-expansive saturated clays characterised by two plastic mechanisms. The mechanical yield surfacef_Tm of the contact-stress mechanism is based on a modified cam-clay model; the thermal softening yield surfacef_T is a plane separating two thermal domains. In normally consolidated conditions, the resulting response to an increase of temperature is compressive. However, in highly overconsolidated conditions, a small irreversible dilative volumetric strain is observed when the temperature is above a threshold value. In intermediate conditions, the material starts with an expansion and tends to a compression.

The constitutive model combines thermo-mechanical hardening, predominant in normally consolidated states (NCS) and absent in overconsolidated states (OCS) where the thermal softening occurs. The characterisation of the model requires information about rheological parameters obtained from oedometric and triaxial paths. Lastly, some numerical simulations of thermo-mechanical tests onremoulded Boom, ‘Bassin Parisien’ andPontida clays are presented, which show satisfactory agreement between experiments and model predictions.     

A note on thermomechanical anisotropy of clays

Deep clays exhibit a pronounced strain anisotropy both during mechanical loading as well as during heating and cooling at constant stress in drained isotropic conditions. During mechanical loading vertical strain is larger than the horizontal one. During heating the vertical strain is larger than the horizontal one within the elastic range; the opposite is observed in the elasto-plastic range. The above described response can be interpreted adopting a consistent rotational, kinematic hardening thermo-elasto-plastic constitutive law.     

Hypoplastic and viscohypoplastic models for soft clays with strength anisotropy

This paper presents a new viscohypoplastic model for soft clays accounting for their typical features—strength anisotropy and rate dependency. The model is based on the hypoplastic model for clays enhanced by the anisotropic shape of the asymptotic state boundary surface. It has been shown that if the surface is skewed, the model predicts different ultimate strength in compression and in extension. Additional enhancement makes the tensor L bilinear in the strain rate, which more realistically predicts the stress paths of K₀ consolidated samples. The new model has been evaluated by simulating laboratory experiments on soft marine clays (Singapore and Bangkok clays). The model can be easily calibrated using only undrained triaxial and odometer tests. The model is subsequently enhanced by the rate effects. The resulting viscohypoplastic model has been evaluated using experiments of remolded kaolin clay and St. Herblain clay. It is shown that the enhanced model can predict important features of soil viscous behavior, such as rate dependency of strength and preconsolidation pressure, relaxation, and creep.     

An effective combined framework for modelling the time-dependent behaviour of soft structured clays

A constitutive framework for the simulation of the time-dependent behaviour of soft structured clays has been developed from the combination of a number of existing modelling approaches. The formulation accounts, in a natural way, for time-dependent phenomena such as loading rate dependency, stress relaxation, ageing, and creep deformations under constant load. In addition, the effect of structure is accounted for. To demonstrate the potential of the proposed approach, a specific model based on this framework is described and applied to the simulation of a number of relevant laboratory tests from the literature.

     

A two‐surface thermomechanical model for saturated clays

This paper presents an advanced thermomechanical model – TEAM in the framework of two‐surface plasticity for saturated clays, with emphasis put on some important thermomechanical features of natural clays evidenced experimentally such as the limited thermomechanical elastic zone, the smooth transition from elastic to plastic behavior. Two plastic mechanisms are introduced in the model: one is to reproduce the thermoplasticity involving thermal expansion and contraction observed at high over‐consolidation ratios and the second one describes the temperature effect on the yield behavior. The model adopts additional yield surfaces, namely inner yield surfaces that are associated with the two proposed plastic mechanisms to account for the plastic behavior inside the existing conventional thermomechanical yield surface namely yield surfaces. The general expressions of the yield surfaces and plastic potentials in p′–q–T space are introduced. A progressive plastic hardening mechanism associated with the inner yield surface is defined, enabling the plastic modulus to vary smoothly during thermomechanical loadings inside the yield surfaces. Several tests on natural Boom clay along different thermomechanical loading paths have been simulated by TEAM, and results show its relevance in describing the thermomechanical behavior of saturated clays. Copyright © 2015 John Wiley & Sons, Ltd.     

Associated and non-associated constitutive relations for undrained behaviour of isotropic soft clays

Incremental theory of plasticity has been used to derive associated and non-associated stress–strain relations for analysing the undrained stress-strain response of isotropic normally and lightly overconsolidated clays. A series of comparisons between the theoretical stress-strain-pore pressure response and laboratory test results for 3 in. × 6 in. samples of very high degree of repeatability and reproduceability have been described. From these comparisons it can be seen that both the associated and, non-associated Cam clay models appear to give consistently the best correlations between the theoretical results and the experimental observations.     

Benchmarking the thermomechanical behaviour of clays — a progress report — the CEC interclay project

In 1989 a small-scale exercise conducted by the CEC as part of its research programme into the underground storage of radioactive waste highlighted the difficulty of making accurate predictions a priori, of the geomechanical behaviour of clay. Given source data about the Boom clay from the underground research facility at Mol, three organisations independently performed f.e. analyses of two somewhat hypothetical problems. While the results were very broadly in agreement, they were shown to be sensitive to both the type of constitutive model used and the way data was fitted to the model.

Subsequently, the CEC sponsored a more comprehensive benchmark exercise called INTERCLAY II. This involves eleven organisations from various member states of the EC in a project encompassing the three aspects of software development for predictive modelling: verification, validation on the laboratory scale and the treatment of in-situ tests. The paper briefly describes the exercise currently in progress and presents the main results achieved to date concentrating on validation aspects.     

Microstructure and volume change behaviour of soft clays: a boundary element simulation

The relationship between the microstructure and the volume change behaviour of fine-grained soft soils is analysed by using a model derived from the experimental observation of the microstructure of soft clays, and the Boundary Element Method (BEM). The soil is modelled as a bidimensional porous matrix containing circular pores. The matrix is linear elastic and obeys a Tresca failure criterion, and the pore size distribution follows a Gaussian normal law. The pores are randomly located, with a minimum distance between them. Volume decrease during compression is due to the collapse of the pores. The collapse of a pore is activated once the stress state at the pore boundary calculated by the BEM is reaching the Tresca failure criterion, thus leading to a non-linear analysis process. An isotropic incremental loading test as well as a loading–unloading test are presented and discussed, showing that the model is able to reproduce properly the experimental volume change behaviour of soft clays and other porous geomaterials like chalk. Numerical results show that a macroscopic hardening elastoplastic behaviour could be obtained from a model elaborated from microstructure observation. © 1997 by John Wiley & Sons, Ltd.     

一个描述软黏土时效特性的一维弹黏塑性模型

为了描述软黏土一维应力-应变关系的时效特性,基于Bjerrum的等时间线体系,提出等黏塑性应变率线概念,推导了黏塑性应变率与黏塑性应变增量的关系,建立了软黏土的一维弹黏塑性模型;从理论上分析了新建模型与3种典型的一维弹黏塑性时效本构模型的内在联系,表明新建模型与其他3种模型在本质上是等效的,且形式更简洁,物理意义更明确;利用新建模型对软黏土的固结-蠕变耦合效应、应变率效应、应力松弛效应等时效特性进行了理论分析,并得到了相应的解析解;结合宁波软黏土的一维固结试验,阐述了模型参数的确定方法,并用新建模型对宁波软黏土的固结-蠕变试验、温州软黏土的一维多级等应变率试验、香港海相软黏土的一维应力松弛试验进行模拟,验证了新建模型的有效性。研究结果表明,新建模型能很好地模拟软黏土的一维时效特性。     

软黏土的各向异性临界状态模型

剑桥模型只适用于正常固结软黏土,不能描述不等向固结土的应力-应变行为的各向异性特性。基于剑桥模型,在其椭圆屈服面中引入各向异性张量和一个形状参数,建立了一个各向异性屈服面,提出了一个适用于等向和不等向固结软黏土的本构模型。各向异性张量的初始值由初始固结应力状态确定,其演化过程由一个与塑性剪应变和塑性体应变都有关的硬化法则描述。形状参数的引入保证了各向异性屈服面的灵活性和适应性。通过对Boston Blue黏土、高岭土和Otaniemi黏土的三轴试验结果的模拟,验证了模型的模拟能力。     

Time-dependent behaviour of deep clays

The time-dependent behaviour of deep saturated clays is related both to the effects of hydraulic diffusion and of viscosity. In this paper, we present first, by means of an experimental approach, the main features of the mechanical properties of deep clays. Then, we study the effects of these specific behaviours on the time-dependent behaviour of underground structures. We present theoretical and numerical investigations of the effects of pore pressure diffusion resulting from a tunnel excavation in a poroplastic or poroviscoplastic medium. Finite-element calculations show that the time-dependent convergence of the tunnel wall is non negligible. Then, we focus on the behaviour of a cylindrical thermal source buried in a deep clay.

Coupling effects between thermal, hydraulic and mechanical behaviours are very important in soft and low permeable deep clays (saturated compressible clays with high porosity). We show in particular that the displacements and the stresses are very sensitive to the constitutive model. Irreversible behaviour may be traduced by appearance of residual stresses within the rockmass.     

Fractal models for predicting soil hydraulic properties: a review

Modern hydrological models require information on hydraulic conductivity and soil-water retention characteristics. The high cost and large spatial variability of measurements makes the prediction of these properties a viable alternative. Fractal models describe hierarchical systems and are suitable to model soil structure and soil hydraulic properties. Deterministic fractals are often used to model porous media in which scaling of mass, pore space, pore surface and the size-distribution of fragments are all characterized by a single fractal dimension. Experimental evidence shows fractal scaling of these properties between upper and lower limits of scale, but typically there is no coincidence in the values of the fractal dimensions characterizing different properties. This poses a problem in the evaluation of the contrasting approaches used to model soil-water retention and hydraulic conductivity. Fractal models of the soil-water retention curve that use a single fractal dimension often deviate from measurements at saturation and at dryness. More accurate models should consider scaling domains each characterized by a fractal dimension with different morphological interpretations. Models of unsaturated hydraulic conductivity incorporate fractal dimensions characterizing scaling of different properties including parameters representing connectivity. Further research is needed to clarify the morphological properties influencing the different scaling domains in the soil-water retention curve and unsaturated hydraulic conductivity. Methods to functionally characterize a porous medium using fractal approaches are likely to improve the predictability of soil hydraulic properties.     

天然沉积结构性土的次固结变形预测方法

结构性土存在着其特有的变形和强度特性,次固结特性也表现出明显区别于与重塑土。通过对连云港天然沉积原状土和重塑土进行一维压缩次固结试验,研究了典型结构性土的次固结特性。试验结果表明,土体由于受结构性影响,结构破坏前后其次固结特性发生明显变化;结构屈服前（固结压力小于固结屈服压力）不发生次固结变形或次固结变形甚微;当土体处于屈服状态时,土体次固结变形突然增大,次固结系数Cα出现峰值;结构屈服后（固结压力大于固结屈服压力）,Cα随固结压力的增大而减小,表现为与当前的应力水平和时间密切相关的特性,应力水平对Cα的影响会随着次固结时间的增长而削弱。基于以上机制,建立了考虑结构性影响的次固结变形计算模型,该模型中Cα不仅与压缩指数Cc有关,且也与时间有关,基于该模型计算得到的Cα值和次固结变形均与试验值吻合较好。     

A generalized model for geosynthetic reinforced railway tracks resting on soft clays

The present study pertains to the development of a foundation model for predicting the behavior of geosynthetic reinforcement railway track system rested on soft clay subgrade. The ballast and sub‐ballast layers have been idealized by Pasternak shear layer. The geosynthetic layer is represented by a stretched rough elastic membrane. Burger model has been used to characterize the soft clay subgrade. Numerical solutions have been obtained by adopting the finite difference scheme combined with non‐dimensioning the governing equations of the proposed model. The results confirm that the present model is quite capable of predicting the time‐dependent settlement response of geosynthetic reinforcement railway track system placed on soft clay subgrade. The surface settlement profile and mobilized tensile load of geosynthetics has been evaluated by considering variation in the wheel load, sleeper width, thickness of ballast and sub‐ballast layers and shear modulus of ballast and sub‐ballast layers. It has been observed that an increase in the sleeper width by 24% results in the reduction in central settlement and mobilized tensile load by 6.5% and 20.1%, respectively. It was found that with a 50% increase in the thickness of the ballast layer, the central settlement has decreased by 7.3% and the mobilized tension at the zone of maximum curvature has increased by 24.6%. However, with an increase in the thickness of the sub‐ballast layer, a considerable reduction in both central settlement and the mobilization of tension on geosynthetic has been noticed. The pattern of variation of settlement and mobilized tension for an increase in the shear modulus of ballast and sub‐ballast material was found to be almost similar. Copyright © 2014 John Wiley & Sons, Ltd.     

Consolidation behaviour of finely laminated clays

Thin highly permeable laminations have a significant influence on the rate of consolidation of many natural clays. Horne [1] presented analytical solutions for a particular type of problem. The range of solutions has been extended by the authors, who have used the more general finite element technique to solve consolidation problems of finely laminated clays under various geometry, load, and boundary conditions. Solutions are presented in graphical form to enable engineers to predict the rate of settlement for strip loads imposed on the surface of laminated clays. The effect of the laminations on the pore water pressure distribution, and the significant difference between a laminated (composite) material and an anisotropic material, are examined.     

海相沉积软黏土的弹塑性本构模型研究

在深入探讨海相沉积原状软黏土压缩、变形等力学特性和详细分析加载屈服面随荷载情况变化的基础上,确认了海相沉积原状软黏土的强度、变形特性与结构屈服应力密切相关。即当固结压力小于结构屈服应力时,其力学特性与超固结重塑土的力学特性类似;当固结压力大于结构屈服应力时,其力学特性与正常固结重塑土的力学特性类似。为描述海相沉积原状软黏土的上述力学特性,将姚仰平等提出的超固结重塑土本构模型引入到海相沉积软黏土弹塑性本构模型的构建中。在本构模型构建过程中,考虑了海相沉积原状软黏土具有的抗拉强度及其演化规律,软黏土强度包线的特点及其进一步修正的表达式,使模型更符合海相原状软黏土的强度、变形特性。最后,将3种不同海相沉积软黏土固结排水剪切试验得到的应力-应变-体变曲线与模型预测结果进行对比。比较结果显示,本文提出的弹塑性本构模型能很好地描述海相沉积原状软黏土的剪缩硬化、剪胀软化以及变形的应力水平依存性等力学特性。     

循环荷载作用下竖向排水板加固软黏土的孔隙水压力累积特性研究

采用大型动三轴试验仪进行重塑高岭土试样的循环三轴试验,试样直径为300 mm,高度为600 mm。圆柱体试样中心放置了一块竖向排水板,在循环加载试验进行时和结束后都可进行径向排水。试验结果验证了径向排水可以有效地消散循环荷载引起的孔隙水压力。通过结合径向固结理论与不排水循环加载土体模型,提出了一个循环荷载作用下径向固结模型,用来描述在允许径向排水的情况下软黏土在循环荷载作用下的孔压累积特性。模型中考虑了应力历史和孔隙水压力消散对孔隙水压力生成的影响,并用大型循环三轴试验结果进行验证。研究发现,当施加较大循环荷载时,径向排水减缓了孔隙水压力累积到临界值的速率,因而土体在破坏前可以经历更多次的循环荷载;当施加中等循环荷载时,径向排水可有效阻止孔隙水压力增长至临界值。除此之外,还研究了加载间歇期对孔压累积特性的影响,结果显示3组循环加载结束后,累积孔隙水压力开始减小,表明之后更多的循环加载并不会引起孔隙水压力的累积增长。     

Numerical predictions of the behaviour of soft clay with two anisotropic elastoplastic models

The numerical predictions obtained with the Melanie and MIT-E3 models are compared. Firstly, the performance of the constitutive models is checked against undrained triaxial tests. The models are then used to replicate the behaviour of an embankment built on soft clay. The numerical results are compared with the field data in terms of settlements, lateral displacements and excess pore pressures. Additionally, the numerical predictions are also analysed in terms of yield area, contours of vertical effective stresses, horizontal effective stresses and shear stresses and in terms of effective stress paths.     

Modelling the behaviour of an embankment on soft clay with different constitutive models

The paper investigates the effect of constitutive models on the predicted response of a simplified benchmark problem, an embankment on soft soil. The soft soil is assumed to have the properties of POKO clay from Finland and five different constitutive models are used to model the deposit. Two of the models are isotropic models, i.e. the Modified Cam Clay model and the Soft‐Soil model. The other models are recently proposed constitutive models that account for plastic anisotropy. The S‐CLAY1 and S‐CLAY1S models are embedded in a standard elasto‐plastic framework and account for anisotropy via a rotational hardening law. In addition, the S‐CLAY1S model accounts for bonding and destructuration. In contrast, the Multilaminate Model for Clay (MMC) accounts for plastic anisotropy by utilizing so‐called multilaminate framework. The results of numerical simulations show that accounting for anisotropy results in notable differences in the predicted settlements and horizontal movements compared to the predictions using the isotropic models. There are also significant differences in the K₀ predictions by the different constitutive models and this has a significant impact on the results. Copyright © 2006 John Wiley & Sons, Ltd.