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.     

不饱和土动弹塑性本构模型研究

以饱和度与有效应力为状态变量,通过引入描述不饱和与饱和土孔隙比差的状态变量,将Zhang等提出的饱和土体应力诱导各向异性动弹塑性本构模型推广到不饱和土体中,使其可描述不饱和土在动力循环荷载作用下的力学特性行为。通过对已有不饱和土体在完全不排水条件下的动三轴试验进行理论模拟,验证了所提出不饱和土本构模型的正确性。最后基于所提出本构模型,讨论了在不排水条件下初始饱和度对不饱和土动力特性研究。结果表明,不饱和土在动力荷载作用下,土体的孔隙比将减少,导致饱和度增加;当初始饱和度较高时,不饱和土会转化为饱和土,从而发生液化现象。该研究成果对研究不饱和土在地震等动力荷载作用下的力学特性行为具有重要意义。     

Coupled modelling of hydro‐mechanical behaviour of unsaturated compacted expansive soils

The Barcelona basic model cannot predict the mechanical behaviour of unsaturated expansive soils, whereas the Barcelona expansive model (BExM) can only predict the stress–strain behaviour of unsaturated expansive soils without the water‐retention behaviour being incorporated. Moreover, the micro‐parameters and the coupling function between micro‐structural and macro‐structural strains in the BExM are difficult to determine. Experimental data show that the compression curves for non‐expansive soils under constant suctions are shifted towards higher void ratios with increasing suction, whereas the opposite is true for expansive soils. According to the observed water‐retention behaviour of unsaturated expansive soils, the air‐entry value increases with density, and the relationship between the degree of saturation and void ratio is linear at constant suction. According to the above observation, an elastoplastic constitutive model is developed for predicting the hydraulic and mechanical behaviour of unsaturated expansive soils, based on the existing hydro‐mechanical model for non‐expansive unsaturated soil. The model takes into consideration the effect of degree of saturation on the mechanical behaviour and that of void ratio on the water‐retention behaviour. The concept of equivalent void ratio curve is introduced to distinguish the plastic potential curve from the yield curve. The model predictions are compared with the test results of an unsaturated expansive soil, including swelling tests under constant net stress, isotropic compression tests and triaxial shear tests under constant suction. The comparison indicates that the model offers great potential for quantitatively predicting the hydraulic and mechanical behaviour of unsaturated expansive soils. Copyright © 2011 John Wiley & Sons, Ltd.     

不同应力路径下饱和重塑黄土的力学特性

土体的力学特性往往因应力状态和应力路径而异。为了探讨垂直加载和等剪路径下饱和土的力学特性,制备饱和重塑黄土试样,通过固结不排水（CU）和常剪应力排水剪（CSD）三轴试验,分别测定并绘制其应力-应变曲线、孔隙水压力变化曲线和应力路径曲线。试验结果表明,饱和重塑黄土在2种路径下有明显不同的变形特点:CU路径下的应力-应变曲线皆呈弱软化型,孔隙水压力先快速上升后逐渐趋于稳定;CSD路径下维持偏应力为一常量,施加孔隙水压力后的很长时间内试样变形很小,当孔隙水压力增大至试验围压的60%~75%时,试样迅速破坏。CSD路径无偏应力峰值,文中根据轴应变随平均有效应力变化曲线定义了等效峰值破坏线。通过对比发现,2种路径下饱和重塑黄土的有效峰值强度指标差异明显,而有效残余强度指标相近,表明有效残余强度指标是重塑黄土内在属性,受应力路径的影响不大。该研究结果可为实际工程选取正确的应力路径试验提供参考。     

天然沉积粉质黏土的应力路径试验研究

天然沉积土在沉积过程中产生了结构性和各向异性,使其受力变形特性与重塑土存在明显的差异。实际工程中的天然土体往往在受荷过程中会经历不同的应力路径,因此,需要开展考虑结构性和各向异性影响的应力路径试验。通过研究不同应力路径下土体的力学特性,为建立复杂应力路径下的合理的本构模型提供试验依据。采用大直径PVC管取样器获取张家港地区地下2.5 m深的粉质黏土不扰动土样,通过GDS三轴仪对土样进行了K0固结不同排水应力路径试验。结果表明,应力路径对不扰动土样的体积变形和剪切变形均有显著影响,且球应力和偏应力对土的体应变和剪应变存在交叉影响。无论以体积变形为主还是剪切变形为主的应力路径下,应力-应变曲线都有明显的屈服性状。通过描绘试验所得各应力路径下的屈服点,获得张家港不扰动土样的屈服轨迹大致呈倾斜的椭圆形状,采用Wheeler模型的屈服面与试验屈服点的吻合程度要优于Nakano模型。     

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。     

Stress-strain behaviour of reconstituted illitic clay at different temperatures

Tests on specimens of reconstituted illitic clay have examined the influence of temperature on the mechanical behaviour of clay soils. The program involved consolidation to effective confining pressures up to 1.5 MPa, heating to 100°C, and tests on normally consolidated and overconsolidated specimens with OCR = 2. The tests included isotropic consolidation, undrained triaxial compression with pore water pressure measurement, drained tests along controlled stress paths to investigate yielding behaviour, and undrained tests which involved heating and measurement of the resulting induced pore water pressures. The large strain strength envelope is independent of temperature. However, peak undrained strengths increase with temperature because smaller pore water pressures are generated during shearing. An important contribution from the study is a series of results for the yielding of illitic clay at three different temperatures. For the first time, there is clear evidence of yield loci decreasing in size with increasing temperature. An associated flow rule can be assumed without serious error. The results contribute to the confirmation of a thermal elastic-plastic soil model developed by the authors from cam clay following the addition of a small number of extra assumptions. Depending on the initial stress state, heating under undrained conditions may produce shear failure.     

Material stability analysis of rock joints

For prediction of rockfalls, the failure of rock joints is studied. Considering these failures as constitutive instabilities, a second‐order work criterion is used because it explains all divergence instabilities (flutter instabilities are excluded). The bifurcation domain and the loading directions of instabilities, which fulfill the criterion, are determined for any piecewise linear constitutive relation. The instability of rock joints appears to be ruled by coupling features of the behavior (e.g., dilatancy). Depending on the loading parameters, instabilities can lead to failure, even before the plastic limit criterion. Results for two given constitutive relations illustrate the approach. Some given loading paths are especially considered. Constant volume (undrained) shear and τ‐constant paths are stable or not depending on the link between the deviatoric stress and strain along undrained paths, as found for soils. Some unstable loading paths are illustrated. Along these paths, failure before the plastic limit criterion is possible. The corresponding failure rules are determined. Copyright © 2012 John Wiley & Sons, Ltd.     

高边坡开挖应力路径下黄土变形和强度特性的试验研究

为了探究高边坡开挖路径下黄土的力学性质,首先采用线弹性有限元法模拟一高150m的人工边坡在开挖条件下,潜在破坏区黄土的应力路径。据此路径分别对天然和饱和试样做了三轴固结不排水试验,并做了相同固结应力的加载应力路径试验（CTC）。结果表明开挖应力路径下饱和试样的应力应变关系为应变软化,天然试样为应变硬化;CTC试验条件下,饱和试样应力应变也为应变软化,天然试样亦为应变硬化,但硬化比开挖应力路径明显。上述两种试验条件下,饱和试样的有效应力路径接近,强度包络线相同,有效强度参数相同;天然试样则不同,强度包络线近似平行,开挖应力路径下有效黏聚力c’高于CTC,有效内摩擦角φ’相差不大。实际工程中获取土体变形和强度性质时应考虑应力路径和含水率的影响。     

Review of fundamental principles in modelling unsaturated soil behaviour

An unsaturated soil is a state of the soil. All soils can be partially saturated with water. Therefore, constitutive models for soils should ideally represent the soil behaviour over entire ranges of possible pore pressure and stress values and allow arbitrary stress and hydraulic paths within these ranges. The last two decades or so have seen significant advances in modelling unsaturated soil behaviour. This paper presents a review of constitutive models for unsaturated soils. In particular, it focuses on the fundamental principles that govern the volume change, shear strength, yield stress, water retention and hydro-mechanical coupling. Alternative forms of these principles are critically examined in terms of their predictive capacity for experimental data, the consistency between these principles and the continuity between saturated and unsaturated states.     

A kinematic hardening based model for unsaturated soils considering different hydraulic conditions

At present, several of the existing elastoplastic constitutive models are adapted for describing the stress–strain behavior of unsaturated soils. However, most of them present certain limitations in this field. These limitations can be related to the basic model and/or added unsaturated state variables and formulations. In this regard, inability to model the hydro‐mechanical behavior in constant water (CW) conditions is an example of these limitations. In this paper, an advanced version of CJS model is selected for adaptation to the unsaturated states. Adaptation to unsaturated states is achieved in the framework of effective stress approach. Effective stress equation and unsaturated state variables are selected based on the recent research existing in the literature. The developed model is capable of describing the complex behavior of unsaturated soil in the CW condition in addition to predicting the behavior at failure and post–failure, nonlinear elastoplastic behavior at low levels of stress and strain (by selecting a very small elastic domain), as well as wetting and collapse behaviors. In order to validate the model, results of triaxial tests in CD and CW conditions are used. The validation results indicate the good capability of the proposed model. Behavior of the unsaturated soils during wetting is an important issue. For this reason, the model is also evaluated based on the results of wetting and collapse triaxial tests. A comparison between the tests and simulation results shows that the model is able to predict the soil behavior under the wetting path. Copyright © 2016 John Wiley & Sons, Ltd.     

A hierarchical thermo‐hydro‐plastic constitutive model for unsaturated soils and its numerical implementation

Unsaturated soils are highly heterogeneous 3‐phase porous media. Variations of temperature, the degree of saturation, and density have dramatic impacts on the hydro‐mechanical behavior of unsaturated soils. To model all these features, we present a thermo‐hydro‐plastic model in which the hydro‐mechanical hardening and thermal softening are incorporated in a hierarchical fashion for unsaturated soils. This novel constitutive model can capture heterogeneities in density, suction, the degree of saturation, and temperature. Specifically, this constitutive model has 2 ingredients: (1) it has a “mesoscale” mechanical state variable—porosity and 3 environmental state variables—suction, the degree of saturation, and temperature; (2) both temperature and mechanical effects on water retention properties are taken into account. The return mapping algorithm is applied to implement this model at Gauss point assuming an infinitesimal strain. At each time step, the return mapping is conducted only in principal elastic strain space, assuming no return mapping in suction and temperature. The numerical results obtained by this constitutive model are compared with the experimental results. It shows that the proposed model can simulate the thermo‐hydro‐mechanical behavior of unsaturated soils with satisfaction. We also conduct shear band analysis of an unsaturated soil specimen under plane strain condition to demonstrate the impact of temperature variation on shear banding triggered by initial material heterogeneities.     

常剪应力路径下含气砂土的三轴试验

天然气水合物完全分解时,产生的气体使得能源土孔隙压力急速增加,有效应力减小,进而引起土体液化破坏。此时深海能源土斜坡的应力状态与静力液化失稳过程可简化为含气土在常剪应力排水(或不排水)应力路径下的破坏问题。以此为背景,提出了制备含气砂土试样的改进充气管法,并开展了含气砂土的常剪应力路径三轴试验。22组试验结果表明:同一孔隙比的含气密砂在不同围压与常剪应力下具有相同的失稳线;含气砂土试样失稳时的应力比和体变均随初始相对密实度的增大而增大;含气密砂在常剪应力路径下饱和度对失稳特征影响的规律性在排水与不排水条件下均不明显,但在不排水条件下含气砂土的孔压(或体变)对变形的敏感性降低;含气密砂在常剪应力路径到达失稳点之后,排水条件下是瞬变的液化鼓胀破坏,不排水条件下是渐变的剪切破坏。     

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。     

A density‐dependent elastoplastic hydro‐mechanical model for unsaturated compacted soils

This paper presents a three‐dimensional elastoplastic constitutive model for predicting the hydraulic and mechanical behaviour of unsaturated soils. It is based on experimental results obtained from a series of controlled‐suction triaxial tests on unsaturated compacted clay with different initial densities. Hydraulic hysteresis in the water‐retention behaviour is modelled as an elastoplastic process, with the elastic part modelled by a series of scanning curves and the elastoplastic part modelled by the main drying and wetting curves. The effect of void ratio on the water‐retention behaviour is studied using data obtained from controlled‐suction wetting–drying cyclic tests on unsaturated compacted clay with different initial densities. The effect of the degree of saturation on the stress–strain‐strength behaviour and the effect of void ratio on the water‐retention behaviour are considered in the model, as is the effect of suction on the hydraulic and mechanical behaviour. The initial density dependency of the compacted soil behaviour is modelled by experimental relationships between the initial density and the corresponding yield stress and, thereby, between the initial density and the normal compression line. The model is generalized to three‐dimensional stress states by assuming that the shapes of the failure and yield surfaces in the deviatoric stress plane are given by the Matsuoka–Nakai criterion. Model predictions of the stress–strain and water‐retention behaviour are compared with those obtained from triaxial tests with different initial densities under isotropic compression, triaxial compression and triaxial extension, with or without variation in suction. The comparisons indicate that the model accurately predicts the hydraulic and mechanical behaviour of unsaturated compacted soils with different initial densities using the same material constant. Copyright © 2006 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。     

非饱和土的新非线性模型及其应用

为描述非饱和土的应力-应变特性,基于非饱和土三轴剪切试验,提出泊松比变化率（即切线泊松比随轴向应变的变化速率）的概念,发现非饱和土的切线模量和泊松比变化率均随轴向应变的增加呈指数衰减规律,基于此提出了一种描述非饱和土应力-应变关系的新非线性模型。该模型不仅能描述应变硬化,而且能描述应变软化;能对非饱和土三轴不固结不排水剪、固结排水剪、固结不排水剪试验的应力-应变关系进行描述;模型共包含6个参数,物理意义明确,确定方法简便。利用提出的模型对国内外文献中的三轴试验进行了模拟,结果表明,模拟结果与试验数据有很好的吻合度,从而验证了模型对试验数据的合理性和适用性。     

软土在不同应力路径下的力学特性分析

通过固结不排水剪应力路径试验对广州南沙典型软土在不同固结条件的力学特性进行了系统研究。分析了初始固结状态对软黏土应力路径依赖性的影响,比较了不同应力路径下土的应力-应变关系特征和孔隙水压力变化规律,探讨了孔压分布与土体变形特征的关系,认为侧向卸荷会造成剪应力增加、体应力减小,从而使土体产生剪胀趋势。研究结果还表明,不排水条件下的有效应力路径主要与土样初始固结状态有关,因而同一固结状态下的有效应力路径具有唯一性。另外,试验中的剪切控制方式对有效应力路径有明显影响,但对土体抗剪强度的影响可以忽略。     

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。     

基于状态曲面的非饱和土强度准则及其验证

考虑体变对非饱和土土-水状态的影响,将状态曲面函数引入传统的Vanapalli强度公式得到与孔隙比相关的抗剪强度准则,新准则使用饱和土的强度参数和两条不同孔隙比对应的土-水特征曲线。选择一种尾矿砂和高岭土的混合土料为研究对象,进行一系列的土-水特征曲线试验、吸力控制的等向压缩和三轴剪切试验。试验结果表明,新准则能更准确地预测非饱和土的强度,证明了传统强度预测的误差主要来源于忽略了体变导致的土-水状态变化,并提出在不同应力空间内精确地获得抗剪强度包线的方法,合理地解释了强度包线斜率在净应力-强度平面内随吸力增大、强度包线形状在吸力-强度平面内随净应力发生变化的特性。