Nonstationary flow surface theory for modeling the viscoplastic behaviors of soils

This paper presents a three-dimensional elastic viscoplastic model that can describe the time-dependent behaviors of soft clays. The constitutive model is formulated based on the nonstationary flow surface theory and incorporates new developments, including (i) an improved definition of the nonstationary flow surface that is capable of capturing the stress–strain behaviors under different loading paths, (ii) a unique stress–strain—viscoplastic-strain-rate equation that is able to explicitly describe the nonstationary flow surface, and (iii) a final stable state concept that identifies the final equilibrium state at the end of creep and stress relaxation, which is also used to simplify the loading criteria. The consistency condition is validated for the proposed model, and the viscoplastic multipliers are calculated by solving the consistency equations. The model performance is investigated and validated via simulation of both oedometer and triaxial tests. The numerical results demonstrate that the proposed model is able to reproduce the main viscoplastic behaviors of soils, including creep, undrained creep rupture, stress relaxation, rate effect and accumulated effect.     

Deformation properties of frozen soils

This paper gives a brief account of the results of a series of oedometer tests and triaxial creep tests on frozen soils.

The oedometer tests are performed on artificially frozen sand, silt and clay. The tests also include ice as a reference material. The results are given by parameters describing the tangent deformation modulus and the time resistance against creep.

The triaxial creep tests are carried out on the artificially frozen clay, and on a permafrost clay from Spitsbergen. The data are interpreted in accordance with Hult's theory. The artificially frozen clay shows much higher creep resistance than the permafrost clay.

In addition to deformation moduli and creep parameters the routine data of the materials tested are also included.     

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。     

New Viscoplastic Model for Design Analysis of Tunnels in Squeezing Conditions

Summary  This paper is intended to describe the SHELVIP (Stress Hardening ELastic VIscous Plastic) model, a new viscoplastic constitutive law which has been developed to incorporate the most important features of behaviour observed in tunnels excavated in severe to very severe squeezing conditions. This model couples the elastoplastic and time-dependent behaviour by using a plastic yield surface, as frequently adopted in tunnel design analysis, and the definition of a state of overstress referred to a viscoplastic yield surface. The model is formulated in all its detailed aspects. The related analytical closed-form solution for representing triaxial creep deformations is developed. Also developed is an incremental numerical solution for describing the triaxial stress–strain behaviour under constant strain rate conditions. The model is shown to fit very satisfactorily the results of creep tests on clay shales and relaxation tests on coal specimens, as recently performed for design analysis of tunnels in squeezing conditions. Correspondence: D. Debernardi, Department of Structural and Geotechnical Engineering, Politecnico di Torino, Torino, Italy     

结构性软黏土时效特性的一维弹黏塑性模拟

为了研究土体结构破坏对软黏土一维变形的时效特性的影响,在Bjerrum的等时间线体系基础上,提出了等黏塑性应变率线等黏塑性应变率线概念,建立了非结构性软黏土的一维弹黏塑性模型;为了描述土体结构渐进破坏特征,定义了结构性参数--结构应变,在非结构性模型的基础上推导了结构性软黏土一维弹黏塑性模型;讨论了通过试验法直接确定模型参数的方法,并利用新建模型对温州天然软黏土的一维常规压缩试验、天然Ariake 黏土的分级快速固结试验、结构性Berthierville黏土的一维等应变率压缩试验及长期蠕变试验进行模拟。模拟与试验结果的对比表明,该模型能较好地描述结构性软黏土一维压缩变形的时效特征。     

Numerical prediction of the creep behaviour of an unstabilised and a chemically stabilised soft soil

This paper examines the ability of volumetric and deviatoric creep laws associated with constitutive models to simulate the creep behaviour of a soft soil in its natural state or chemically stabilised state. Initially, the models/laws are validated by oedometer and triaxial creep tests, for the stabilised and unstabilised soils. Finally, the long-term behaviour of an embankment built on a soft soil reinforced with deep mixing columns is predicted based on the properties for a curing time of 28 days. The results show that the creep phenomenon should be considered in a long-term analysis of deep mixing columns.     

Numerical modelling of the effect of curing time on the creep behaviour of a chemically stabilised soft soil

This work studies the effect of the curing time on the creep behaviour of a stabilised soft soil, using volumetric and deviatoric creep laws associated with constitutive models. Results of unconfined compressive strength tests for several curing times are used to define the time evolution of the mechanical and creep properties. The models/creep laws are validated by oedometer and triaxial creep tests, for 28 and 90 days of curing. The long-term behaviour of an embankment built on a soft soil reinforced with deep mixing columns shows that the effect of curing time decreases the settlement and increases the improvement factor.     

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.     

Creep behavior of soft clay subjected to artificial freeze–thaw from multiple-scale perspectives

Relying on the application of the artificial freezing method on subway tunnel construction, a series of triaxial creep tests were carried out to study the creep behavior changes of Shanghai soft clay subjected to artificial freeze–thaw action. On this basis, MIP tests were conducted with the soil samples before and after creep for comparison to investigate the microstructure changes. The results indicate that freeze–thawed soil produces smaller creep deformation and instantaneous deformation than the unfrozen soil. On a micro-level, during the creep process, the soil skeleton reaches a new structure balance with smaller pore volume and pore area. But the diameter of the maximum pore increases. The change rate of total intrusion volume is a pivotal micro-parameter to evaluate creep strain as there is a good linear relationship between them.

     

An efficient optimization method for identifying parameters of soft structured clay by an enhanced genetic algorithm and elastic–viscoplastic model

Soft structured clays usually exhibit complex behaviors, which can lead to difficulties in the determination of parameters and high testing costs. This paper aims to propose an efficient optimization method for identifying the parameters of advanced constitutive model for soft structured clays from only limited conventional triaxial tests. First, a new real-coded genetic algorithm (RCGA) is proposed by combining two new crossover and mutation operators for improving the performance of optimization. A newly developed elastic–viscoplastic model accounting for anisotropy, destructuration and creep features is enhanced with the cross-anisotropy of elasticity and is adopted for test simulations during optimization. Laboratory tests on soft Wenzhou marine clay are selected, with three of them being used as objectives for optimization and others for validation. The optimization process, using the new RCGA with a uniform sampling initialization method, is carried out to obtain the soil parameters. A classic genetic algorithm (NSGA-II)-based optimization is also conducted and compared to the RCGA for estimating the performance of the new RCGA. Finally, the optimal parameters are validated by comparing with other measurements and test simulations on the same clay. All comparisons demonstrate that a reliable solution can be obtained by the new RCGA optimization combined with the appropriate soil model, which is practically useful with a reduction in testing costs.     

A frozen soil creep model with strength attenuation

A frozen soil creep model with shear strength attenuation was proposed based on a soft soil creep model. K ₀ compression and triaxial shear tests were conducted to obtain the model parameters. With triaxial creep tests, the performance of soft soil creep model was verified at first. It was shown that different creep stages can only be described separately, which was due to a constant failure line used in the model. After incorporating strength attenuation into the original model, relative position between stress point and failure line is time dependent, and the progressive development of creep strain from primary to tertiary stage can be captured reasonably.     

A viscoplastic subloading soil model for rate‐dependent cyclic anisotropic structured behaviour

This paper presents a new purely viscoplastic soil model based on the subloading surface concept with a mobile centre of homothety, enabling the occurrence of viscoplastic strains inside the yield surface and avoiding the abrupt change in stiffness of the traditional overstress viscoplastic models. This is required for overconsolidated soils. The model is formulated to reproduce the soil rate‐dependent behaviour under cyclic loading (changes in loading direction) and incorporates both initial and induced anisotropy, as well as destructuring. The model shows good qualitative response to some imposed three‐dimensional stress paths under quasi‐inviscid (elastoplastic) behaviour. Some of the main time‐dependent aspects of soil behaviour that the model is capable of reproducing were also illustrated. The capability of the model to adequately reproduce the results from an undrained triaxial test performed on stiff overconsolidated clays from the Lisbon region (Formação de Benfica), with an unloading–reloading deviatoric stress cycle at constant mean stress, that incorporates a series of staggered fast loading and creep stages, was evaluated. The model was able to reproduce well the main observed aspects of the time‐dependent stress–strain response and pore pressure evolution of a stiff overconsolidated clay under complex loading. The revised and generalised viscoplastic subloading surface concept is viable and can be applied to a consistent extension to viscoplasticity, including in the interior of the yield surface, of existing elastoplastic models formulated for soils and other materials. Copyright © 2016 John Wiley & Sons, Ltd.     

基于上下负荷面的弹黏塑性本构模型及应力积分算法实现

为了描述天然软土的时间相依以及结构性特征,提出了一种能考虑土体超固结和结构性的实用弹黏塑性本构模型。它以Asaoka和Hashiguchi的上下负荷面作为某一应变速率下的参考屈服面,按照相对过应力的基本思路,新引入了两个能通过不同应变速率三轴压缩试验测定的率敏性参数 和 ,建立了以当前应力、黏塑性应变以及黏塑性应变速率为状态变量的动屈服准则函数,并给出了基于Newton-Raphson迭代的应力积分算法,且成功地将其嵌入到大型有限元软件ABAQUS中。最终通过数值算例来验证模型的正确性以及应力积分算法的可靠性。结果表明：该模型能同时描述土体的率敏性、蠕变以及结构性特征,模型参数物理意义明确、易懂可测,预测结果与试验数据吻合良好,可用于复杂边值问题的有限元计算。     

Comparison of two creep degradation modeling approaches for soft structured soils

The creep degradation is a common phenomenon for soft structured clays. In this paper, the creep degradation behavior for soft structured clays is first studied by combining intrinsic creep behavior and the structure indicator. A creep-implicit model and a creep-explicit model corresponding to a stress-based and a creep-based structure indicators are developed, respectively, under one-dimensional condition. Parameters determination for both models is straightforward from oedometer tests. Coupled with consolidation theory, both models are used to simulate oedometer tests with different structural levels and load durations on three clays. The predictive ability of the two models on creep behavior, creep degradation behavior and evolution of structure indicator is analyzed. The relationship between the two structure indicators is discussed based on experimental results. The comparison between experimental and numerical results demonstrates that both models can accurately describe the creep degradation behavior of soft structured clay under one-dimensional loading.     

重塑上海软土的压缩和剪切变形特性试验研究

根据典型上海软土重塑土样的等向压缩试验,测K0与不测K0的单向压缩试验结果,得到不同试验条件下的压缩指数Cc和膨胀指数Cs,并分析了它们之间的关系。进行三轴排水剪切试验,得到了重塑上海软土在不同超固结比和围压下的变形和强度特性,并计算出重塑上海软土的内摩擦角。最后,根据一组不同荷载下的长期单向压缩试验结果,得到重塑上海软土的次压缩系数C?与荷载之间的关系。上述研究得到的初步结论及相关参数可为工程实践、超固结上海软土本构模型的建立提供参考数据。     

德州松软土蠕变特性及其模型研究

利用TSS10型三轴流变试验机对德州松软土开展不同围压下的三轴固结不排水蠕变试验,获得变形、应变率与应力和时间的变化关系,分析蠕变性状和特征,建立其分数阶类Maxwell蠕变模型。结果表明:德州松软土具有明显非线性蠕变特性,高应力水平的蠕变变形大于低应力下的蠕变变形;介绍分数阶蠕变模型原理,引用了分数阶类Maxwell蠕变模型,并求取德州松软土的类Maxwell蠕变模型参数和验证其描述德州松软土蠕变变形的适宜性。     

基于应变软化指标的岩石非线性蠕变模型

研究并提出一种以应变软化指标为基础的岩石非线性蠕变模型。首先,基于岩石三轴压缩试验结果,分析提出一种峰后应变软化指标R1来描述岩石峰后力学参数软化与塑性变形间的关系。接着,通过分析加速蠕变阶段与峰后段的联系,建立加速蠕变应变软化指标R2,并以此为基础构建非线性黏塑性体。然后,将其与Hook体和Kelvin元件串联,组建非线性蠕变模型,并将模型嵌入ABAQUS有限元程序。最后,针对砂岩和泥岩三轴蠕变试验建立数值模型,模拟曲线与试验曲线吻合良好,说明所建模型适用于硬岩/软岩加速蠕变现象的模拟。其中,参数 对加速蠕变曲线形态起调节作用,显示模型模拟脆性?延性流变破坏的特点。另外,模型参数均可由常规压缩破坏试验以及蠕变试验确定,易于获取。     

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。     

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。