On the use of effective stress in three-dimensional hydro-mechanical coupled model

In the last decades, a number of hydro-mechanical elastoplastic constitutive models for unsaturated soils have been proposed. Those models couple the hydraulic and mechanical behaviour of unsaturated soils, and take into account the effects of the degree of saturation on the stress–strain behaviour and the effects of deformation on the soil–water characteristic response with a simple reversible part for the hysteresis. In addition, the influence of the suction on the stress–strain behaviour is considered. However, until now, few models predict the stress–strain and soil–water characteristic responses of unsaturated soils in a fully three-dimensional Finite Element code. This paper presents the predictions of an unsaturated soil model in a Three-dimensional Framework, and develops a study on the effect of partial saturation on the stability of shallow foundation resting on unsaturated silty soil. Qualitative predictions of the constitutive model show that incorporating a special formulation for the effective stress into an elastoplastic coupled hydro-mechanical model opens a full range of possibilities in modelling unsaturated soil behaviour.     

非饱和土水-力本构模型及其隐式积分算法

在已有工作基础上建立了水力-力学耦合的非饱和土本构模型,在硬化方程中考虑饱和度的影响,同时在土水特征曲线中考虑了塑性体变的影响,从而使模型可以反映非饱和土中的毛细现象与土中弹塑性变形现象的耦合行为。采用隐式积分方法,建立了非饱和土耦合模型的数值模型,并推导了得到了水力-力学耦合的非饱和土的一致切线模量。利用该算法编制了本构模型计算的子程序,使其能向外输出切线刚度矩阵,用于有限元计算。为了验证该算法和程序的正确性,用所编制程序对不同路径下的土体行为进行了预测。通过预测结果与试验结果相对比,表明程序预测结果与试验数据相吻合,模型可以较好地模拟土体的水力-力学耦合行为特性。     

Generalized plasticity state parameter‐based model for saturated and unsaturated soils. Part II: Unsaturated soil modeling

The aim of this paper is to extend the generalized plasticity state parameter‐based model presented in part 1 to reproduce the hydro‐mechanical behavior of unsaturated soils. The proposed model is based on two pairs of stress–strain variables and a suitable hardening law taking into account the bonding—debonding effect of suction and degree of saturation. A generalized state parameter for unsaturated state is proposed to reproduce soil behavior using a single set of material parameters. Generalized plasticity gives a suitable framework to reproduce not only monotonic stress path but also cyclic behavior. The hydraulic hysteresis during a drying—wetting cycle and the void ratio effect on the hydraulic behavior is introduced. Comparison between model simulations and a series of experimental data available, both cohesive and granular, are given to illustrate the accuracy of the enhanced generalized plasticity equation. Copyright © 2010 John Wiley & Sons, Ltd.     

考虑毛细滞回效应的非饱和多孔介质渗流与变形耦合本构模型

在Wheeler本构模型框架的基础上,提出了一个水力与力学耦合的本构模型。该模型中的土-水特征曲线采用毛细滞回内变量模型,能够更好地描述水力历史变化下毛细滞回现象对非饱和多孔介质变形的影响,同时也可描述非饱和多孔介质变形对渗流的影响。非饱和土的强度不仅与吸力有关,而且受到饱和度的影响。相同的吸力下,土样经过吸湿和脱湿路径的饱和度不同,因此,非饱和土的强度也不同。此模型以体积含水率的塑性变化和体变的塑性变化为硬化参数,不仅能描述基质吸力对非饱和土的强化作用,而且考虑了饱和度对强度及变形的影响。试验结果与模型预测基本吻合,证明该模型能够模拟非饱和土的主要特性。为了简化,此模型是在各向同性荷载下推得的,有待于推广到一般的应力状态     

A bounding surface model for unsaturated soils considering the microscopic pore structure and interparticle bonding effect due to water menisci

The interparticle bonding effect due to water menisci plays an important role in the hydromechanical coupling properties of unsaturated soils. This paper presents an unsaturated hydromechanical coupling model that considers the influence of matric suction, degree of saturation, and microscopic pore structure on the interparticle bonding effect. The enhanced effective stress and bonding variable are selected as constitutive variables. The bonding variable is correlated with the ratio between unsaturated void ratio and saturated void ratio. The deformation characteristics of unsaturated soils are described based on the bounding surface plasticity theory. A soil–water characteristic model that considers deformation and hydraulic hysteresis is integrated into the constitutive model to achieve hydromechanical coupling. The proposed model can effectively describe the hydromechanical coupling characteristics and the meniscus bonding force of unsaturated bimodal structure soils; the model parameters can be easily obtained through routine experiments. The experimental results of unsaturated isotropic compression, the wetting/drying cycle, and unsaturated triaxial shear tests are used to validate the capability of the proposed model.

     

非饱和土毛细滞回与变形耦合弹塑性本构模型

在修正剑桥模型的基础上,提出了一个非饱和土毛细滞回与骨架变形耦合的弹塑性本构模型。该模型考虑了基质吸力与饱和度对屈服应力的影响,可以同时描述非饱和土的弹塑性变形特性与毛细循环滞回效应。根据塑性体变的产生使非饱和土进气值增大的特点,建立了变形对土-水特征曲线影响的数学描述。该模型有效地考虑了饱和度对前期屈服应力的作用,准确地反映了土体在不同土-水状态条件下（脱湿和吸湿过程）强度特性的变化,而且还可以有效地描述水力循环历史对土体变形的影响。通过与试验数据对比,证明了该模型能够模拟非饱和土的主要力学特性。     

Influence of Unsaturated Soil Properties Uncertainty on Moisture Flow Modeling

The quality of a numerical modeling solution of moisture flow through unsaturated soil, in part, depends on properly described unsaturated soil properties. The variability of the Soil Water Characteristic Curve, SWCC, is attributed to hysteresis and reproducibility of measurement. Because the unsaturated conductivity function is rarely directly measured, the variability of the unsaturated soil hydraulic conductivity function is attributed to the uncertainty associated with the estimation of this parameter with currently available fitting functions, and hence a range of reasonable variation was considered. One-dimensional modeling of expansive soil under dry initial conditions (suction of 1,500 kPa) was performed; both potential evaporation and infiltration boundary conditions were considered. It was found that small variations in the unsaturated soil hydraulic conductivity function result in significantly different modeling outputs, as expected, while substential variation in SWCC alone (assuming the same unsaturated soil hydraulic conductivity for all SWCCs) produced almost identical soil response in terms of soil suction when the slope of the SWCC is similiar. Thus, proper characterization of the slope of the SWCC is important to proper suction profile determination.     

非饱和土毛细滞回内变量模型的修正

土-水特征关系是基质吸力和含水率之间关系。在反复干湿循环路径下土-水特征曲线呈现出毛细滞回特性。基于毛细滞回内变量理论和传统的土-水特征关系经验模型,提出了能模拟在任意干湿循环路径下土-水特征关系的修正模型。该模型比原模型增加了一个可逆参数,考虑了含水率的可逆变化,使扫描线在靠近边界线的时候斜率不会无限大,同时保留了原模型精度。通过与文献中的试验结果进行比较,修正模型可以更好地模拟非饱和土的土-水特征关系的循环滞回特性,并讨论了可逆参数的确定方法。     

吸力历史对非饱和土力学性质的影响

现在被广泛公认的由Fredlund提出的非饱和土力学的双参数理论,即净应力和吸力为非饱和土的应力状态变量,不能直接考虑吸力历史及其饱和度对非饱和土的应力-应变关系和强度的影响。非饱和土三轴试验结果表明,即使净应力和吸力相同的条件下,经过干-湿循环试样与未经过干-湿循环试样的应力比-应变关系和强度是不相同的。在其他条件相同时,经历过干-湿循环的试样比未经过干-湿循环试样的应力比-应变关系要高、强度大和体变小。经过干-湿循环试样的饱和度低而强度高,主要是由于经过先期较高的吸力,相当于受过较大的前期有效压力,使试样成为超固结土。更多不同吸力历史的对比试验有待于进一步研究,以便为非饱和土的水力-力学特性耦合弹塑性本构模型定量地表示上述非饱和土的性质提供基础性试验数据。     

Cavity expansion in unsaturated soils exhibiting hydraulic hysteresis considering three drainage conditions

Cavity expansion theory assists in the interpretation of in situ tests including the cone penetration test and pressuremeter test. In this paper, a cavity expansion analysis is presented for unsaturated silty sand exhibiting hydraulic hysteresis. The similarity technique is used in the analysis. The soil stress–strain behaviour is described by a bounding surface plasticity model. Results of oedometric compression tests, isotropic compression tests and triaxial shear tests for both saturated and unsaturated states are used to calibrate the model. The void ratio, suction, degree of saturation and effective stress are fully coupled in the analysis. The influence of where the initial hydraulic state is located on the soil–water characteristic curve on the cavity wall pressure is investigated and found to be significant. Also, the effects of three different drainage conditions (constant suction, constant moisture content and constant contribution of suction to the effective stress) on cavity wall pressure are studied. It is found that the drainage condition in which the contribution of suction to the effective stress is constant offers a good approximation to the other two. This may simplify interpretation of in situ tests. When testing occurs quickly, meaning a constant moisture content condition prevails, a constant contribution of suction condition can be assumed without loss of significant accuracy. The contribution of suction assumed in the interpretation can be taken as being equal to the in situ value, although this discovery may not be applicable to all soil types, constitutive models and soil–water characteristic curves. Copyright © 2015 John Wiley & Sons, Ltd.     

非饱和土的水力和力学特性及其弹塑性描述

简单回顾了非饱和土本构模型研究的发展历程,总结了近几年非饱和土弹塑性本构模型最新研究成果,重点介绍了能统一模拟非饱和土水力性状和力学性状耦合的弹塑性本构模型。通过对建立模型过程中的几个核心问题讨论,较详细地说明该类模型的结构、性能以及相关问题。非饱和土水力性状的滞回性用假定存在饱和度弹性区间的弹塑性过程来模拟;该类耦合模型不仅考虑了吸力对非饱和土水力性状和力学性状的影响,还考虑了饱和度对应力-应变关系和强度的影响以及土体变形对土-水特征曲线的影响。用同一套模型参数,耦合模型可统一预测在吸力控制或含水率控制下沿各种应力路径下非饱和土的水力-力学特性,并简单介绍了膨胀性非饱和土的弹塑性本构模型以及耦合模型在有限元数值计算中的应用。     

Application of Hysteretic Trends in the Preconsolidation Stress of Unsaturated Soils

This paper involves an evaluation of a relationship describing the evolution in yield stress of unsaturated soils during hydraulic hysteresis, and an application of this relationship in an elasto-plastic framework to predict the compression curves of unsaturated soils under drained (free outflow of air and water with constant suction) or undrained (constant water content with no outflow of water and varying suction) conditions. The yield stress was quantified as the apparent mean effective preconsolidation stress obtained from compression tests reported in the literature on specimens that had experienced different hydraulic paths. It was observed that the preconsolidation stress does not follow a hysteretic path when plotted as a function of matric suction, but does when plotted as a function of the degree of saturation. Accordingly, an existing logarithmic relationship between the preconsolidation stress and matric suction normalized by the air entry suction was found to match the experimental preconsolidation stress results. This same relationship was also able to satisfactorily predict the trends in preconsolidation stress with degree of saturation by substituting the hysteretic soil–water retention curve (SWRC) into the place of the matric suction. The relationship between preconsolidation stress and suction was combined with an elasto-plastic framework to predict the compression curves of soils during drained compression, while the wetting-path relationship between preconsolidation stress and degree of saturation was combined with the framework to predict the compression curves of soils during undrained (constant water content) compression. A good match was obtained with experimental data from the literature, indicating the relevance of considering the hysteretic SWRC and preconsolidation relationships when simulating the behavior of unsaturated soils following different hydro-mechanical paths.     

干湿路径影响粉土小应变剪切模量的试验研究

天然土尤其是地表浅层土常处于非饱和状态,其小应变剪切模量是预测地基变形及土工结构物动力反应的一个重要参数。通过对非饱和压实粉土三轴样进行弯曲元试验,研究了吸力和干湿路径对其小应变剪切模量的影响。试验结果表明,非饱和压实粉土样的小应变剪切模量各向异性忽略不计;小应变剪切模量G0(vh)、G0(hh)和G0(hv)均随吸力增大而非线性增大;同一吸力下不同干湿路径上的土样,饱和度不同,其小应变剪切模量随饱和度升高而减小,主要原因是土的平均骨架应力和土中毛细水的作用。根据试验结果对非饱和土小应变剪切模量的半经验公式进行了改进,同时考虑了吸力与饱和度的作用。     

A novel approach for modelling soil–water characteristic curves with hysteresis

Soil–water characteristic curves can be defined as the relationship between the degree of saturation and suction of an unsaturated soil. Geomaterials, such as clays, sands, and geotextiles, usually exhibit hysteresis between drying and wetting curves. In addition, each drying and wetting curve is nonlinear in shape, which may be approximated by sigmoid curves. In geotechnical engineering, it is common to adopt analytical expressions for these curves that must be calibrated iteratively by trying different values for the constitutive parameters. In this paper, a novel approach for modelling the nonlinear saturation–suction response with hysteresis is presented, where a simple differential equation is introduced to describe the shapes of the curves. The great advantage of this new technique is the ease with which the parameters can be determined. In addition, the implementation of the resulting equations into fully hydro-mechanical models for numerical analyses is straightforward. Some features of the behaviour predicted with the new representation are studied and validations against real laboratory curves for soils are presented. The technique is simple, yet versatile due to the rational basis used in the deduction of the equations, which allows for future extensions to soils displaying more complex unsaturated behaviour.     

Predicting the dependency of a degree of saturation on void ratio and suction using effective stress principle for unsaturated soils

The paper presents an approach to predicting variation of a degree of saturation in unsaturated soils with void ratio and suction. The approach is based on the effective stress principle for unsaturated soils and several underlying assumptions. It focuses on the main drying and wetting processes and does not incorporate the effects of hydraulic hysteresis. It leads to the dependency of water retention curve (WRC) on void ratio, which does not require any material parameters apart from the parameters specifying WRC for the reference void ratio. Its validity is demonstrated by comparing predictions with the experimental data on four different soils taken over from the literature. Good correlation between the measured and predicted behaviour indirectly supports applicability of the effective stress principle for unsaturated soils. Copyright © 2009 John Wiley & Sons, Ltd.     

循环荷载下非饱和结构性黏土的弹塑性双面模型

非饱和黏土的结构性能够显著影响其力学特性。基于非饱和土经典模型BBM（Barcelona basic model）和一种可描述循环塑性的硬化法则,引入体积破损率的作为标准土体结构破损的参数,建立了一个描述常吸力下非饱和结构性黏土静态及动态力学特性的弹塑性双面模型。模型在应力空间中包含与重塑非饱和土屈服面几何相似的结构性边界面和加载面,采用径向映射法则和可移动的记忆中心原理,通过结构性边界面和加载面在应力空间中的演化来反映循环加载过程中非饱和结构性黏土的循环塑性特征和结构损伤过程。通过与相关非饱和黏土控制吸力试验数据的比较,表明该模型能够较好地反映静态加载下非饱和结构性黏土的力学特性,而模型预测的循环荷载下的应力?应变特征也具有一定的合理性。     

Monitoring the Performance of Unsaturated Soil Slopes

Field monitoring is necessary for the geotechnical engineer to verify design assumptions. More importantly, the field data may also be assembled into a comprehensive case record that is available for use when checking validity of any analytical and numerical models. The ongoing process of back-analysis in unsaturated soil engineering can help to refine and improve our understanding, providing guidance for future designs, where the effects of soil suction and hydraulic hysteresis are still being explored. A range of recent field studies of the mechanisms of rainfall infiltration into slopes is presented. In addition, some physical simulations of unsaturated soil slopes subjected to rainfall, rising ground water table and changes of moisture in centrifuge model tests are reported.