Unsaturated hydro-mechanical-chemo coupled constitutive model with consideration of osmotic flow

Since low permeability rock has the potential to behave as an actual semi-permeable osmotic membrane, chemical osmosis may have an effect on water flow and needs to be accounted for in analysis. Hence, an advanced fully coupled formulation for modelling unsaturated hydro, chemical and mechanical effects is here presented based on modified mixture theory. Firstly, the classical Darcy’s law has been modified to include the chemical potential. Secondly, the mechanical deformation, which affects the permeability, has been coupled with the water and chemical flows by using Helmholtz free energy and the Gibbs–Duhem equation. Finally, an illustrative numerical example with relevance to radioactive waste disposal has been analysed to investigate the performance of the coupled formulation and the relative influence of parameters.     

A constitutive model for unsaturated soils with consideration of inter-particle bonding

The paper presents a physically-based constitutive model for unsaturated soils that considers the bonding effect of water menisci at inter-particle contacts. A bonding factor has been used to represent the magnitude of the equivalent bonding stress, defined as the bonding force per unit cross-sectional area. The average skeleton stress is employed to represent the effect of average fluid pressures within soil pores. Based on an empirical relationship between the bonding factor ζ and the ratio e/e_s (where e and e_s are void ratios at unsaturated and saturated states, respectively, at the same average skeleton stress), we propose an elasto-plastic constitutive model for isotropic stress states, and then extend this model to triaxial stress states within the framework of critical state soil mechanics. Because only one yield surface is needed in the proposed model, a relatively small number of parameters are required. Comparisons between experimental data and model results show that, in most cases, the proposed model can reasonably capture the important features of unsaturated soil behavior.     

A new Cosserat-like constitutive model for bedded salt rocks

Salt rocks are commonly used as geologic host rocks for storage of gas and crude oil, and are being considered for the disposal of radioactive waste. Different from the salt rock domes in many countries, the salt rock formations in China are usually laminar with many alternating layers, i.e. rock salt, anhydrite, and/or mudstone. Considering the unique stratigraphic characteristics of these salt rocks, a new Cosserat-like medium constitutive model is proposed in order to facilitate efficient modeling of the mechanical behavior of these formations. In this model, a new representative volume element, containing two different layers, is employed to simulate the compatibility of the meso-displacement between two different layers and also the bending effect. A new method for the deformation and failure analysis of bedded salt rocks is derived therefrom. Having the macro-average stresses, the conventional stresses in the different layers can be obtained in sequence. The conventional stresses can then be utilized in a routine way for the strength and failure analysis. For the initial numerical modeling, the new Cosserat-like medium is reduced to a transversely isotropic one. The simplified constitutive model for layered media is then implemented into FLAC3D codes. A test sample validates that the results by using the numerical model are in good agreement with that by using the built-in model, and the mesh size for the new model is reduced greatly. Finally, an application for the stability of oil storage caverns in deep thinly bedded salt rocks is carried out. The effects on convergence of storage caverns and on the failure of surrounding rock due to the presence of the mudstone interlayers (hard phase) are discussed in detail. Copyright © 2009 John Wiley & Sons, Ltd.     

An advanced hydro-mechanical constitutive model for unsaturated soils with different initial densities

This paper presents an advanced constitutive model for unsaturated soils, using Bishop’s effective stress (σ′) and the effective degree of saturation (S_e) as two fundamental constitutive variables in the proposed constitutive model. A sub-loading surface and a unified hardening parameter (H) are introduced into the σ′–S_e modelling framework to interpret the effects of initial density on coupled hydro-mechanical behaviour of compacted soils. Compared with existing models in the literature, the main advantage of the proposed model that it is capable of modelling hydro-mechanical behaviour of unsaturated soils compacted to different initial densities, such as the dependence of loading–collapse volume on initial void ratio and density effect on the shearing-induced saturation change. The proposed model requires 13 material parameters, all of which can be calibrated through conventional laboratory tests. Numerical studies are conducted to assess the performance of the model for a hypothetical soil under two typical hydro-mechanical loading scenarios. The proposed advanced unsaturated soil model is then validated against a number of experimental results for both isotropic and triaxial conditions reported in the literature.     

冻融作用下岩石力-热-水耦合本构模型研究

在寒区隧道工程中,冻胀的水分迁移作用加剧了隧道围岩的冻融破坏。耦合水分迁移作用的岩石本构模型对防治冻融渗漏、崩塌等隧道围岩灾害有着重要意义。基于内状态变量理论,将冻胀过程中的水分迁移量作为本征变量引入Helmholtz自由能,在热力学框架下建立了一个岩石力-热-水耦合本构模型。模型描述了温度和水分迁移对冻融后岩石损伤阈值、等向强化饱和值、等向强化速率等力学参数的影响。模拟了岩石冻融后力学性质的劣化。区别于全量经验公式,本模型以增量形式给出,为复杂应力历史条件下的数值模拟提供了便利。通过将模型模拟曲线与冻融后岩石常规三轴压缩试验曲线进行对比,初步验证模型的可靠性,为实际寒区工程的冻胀破坏预测提供参考。     

基于Poulos弹性理论的被动桩改进算法

传统的Poulos弹性理论仅适合于均质土中土体侧向位移时桩的性状分析,无法考虑土的层状特性。通过引入层状地基中作用一水平集中力的广义Mindlin解和地面作用有竖向荷载时的应力和位移通解,对Poulos方法进行了改进,使之扩展到多层土中,还用于研究堆载条件下的被动桩变形和受力响应。算例分析表明,改进弹性理论要比Poulos方法更为严密、合理,提高了计算精度,应用范围也更广。     

非饱和裂隙岩体渗流的统计模型研究方法

常规方法研究非饱和裂隙介质往往采用宏观连续体的概念,然而现场试验证明,非饱和裂隙岩体中的渗流具有相当的非均质性。天然裂隙岩体的非饱和渗流是发生在三维裂隙网络中的多场非等温流,要在不完整的信息基础上刻画和表现介质的不均匀性,通常借助随机模拟的手段。将三维裂隙系统近似为概化的二维非均匀多孔介质的二维平面裂隙。采用模拟退火法将取自各种来源的信息资料通过建立适当的目标函数汇集至模型之中,以此模拟裂隙的空间特征。     

A constitutive model for unsaturated soil interfaces

A constitutive model based on the disturbed state concept is presented to describe the behavior of interfaces in unsaturated soil. The model is an extension of an existing model developed for a sand–steel interface. As opposed to the original model, the modified model incorporates two independent stress variables, which are the net normal stress and matric suction. The saturated and dry state of the interface can be modeled as a special case using the constitutive model presented in this paper. The modified model is capable of capturing the main features of unsaturated interfaces observed during laboratory testing, including increasing shear strength and strain softening with increasing suction and net normal stress and increasing dilatancy with increasing suction. Laboratory tests were carried out on unsaturated interfaces in a modified direct shear test apparatus. The observed behavior of interfaces between unsaturated soil and steel plates (rough and smooth) is presented in comparison with model predictions. Copyright © 2008 John Wiley & Sons, Ltd.     

一种盐岩流变损伤模型

在Carter流变模型基础上,引进损伤,提出了“损伤增速界限”的概念,从而,建立了一种盐岩流变损伤模型,并根据实验数据验证了模型的正确性。研究表明,这种盐岩流变损伤模型,不但能很好地反映高应力水平下盐岩的流变损伤特性,而且,也能真实地描述低应力水平下盐岩的初始蠕变损伤和稳态蠕变损伤。 损伤增速界限对损伤演化和蠕变发展影响很大,关系着加速蠕变的发生与否。研究还表明,不同产地、不同实验条件下表述盐岩损伤的参数离散性不大,该模型的应用范围较广。     

An adaptive time integration scheme for blast loading on a saturated soil mass

This paper presents a time integration scheme capable of simulating blast loading of relatively high frequency on porous media, using coarse meshes. The scheme is based on the partition of unity finite element method. The discontinuity is imposed on the velocity field, while the displacement field is kept continuous. The velocity discontinuity is postulated to occur in the time domain. The developed time integration scheme is unconditionally stable and has controllable numerical dissipation in the high frequency range. An important feature of the time scheme is that it allows for controlling the numerical damping in a consistent way. The time scheme has been implemented in combination with Biot’s theory of wave propagation in saturated porous media. Numerical examples have demonstrated that the proposed time scheme is, in addition to being accurate and stable, highly effective for coarse meshes. This makes the developed scheme suitable for large scale finite element analysis.     

A modified permeameter for determination of unsaturated coefficient of permeability

The design details of a modified permeameter used for determining the unsaturated coefficient of permeability of tailings are presented in this Paper. This permeameter can accommodate a large tailings specimen, 200 × 200 × 400 mm high, and uses the Instantaneous Profile Method (IPM) to determine the variation of unsaturated coefficient of permeability with respect to soil suction using a single specimen. The soil-water characteristic curve data can also be simultaneously determined from the modified permeameter. The key design features in comparison to a conventional permeameter include the provision of adjustable sensors that move along with the tailings as it settles due to desaturation during the testing period. The advantages of using a modified permeameter in the determination of the coefficient of permeability of unsaturated tailings are also discussed in this paper. Tests were carried out by providing suction using hanging column technique in the suction range of 0–10 kPa. Such an apparatus can easily be modified to accommodate higher suction values.     

基于广义位势理论的接触面本构模型一般表述

基于广义位势理论建立的岩土体材料本构模型以及岩土体材料与结构接触面本构模型原理相通,只是前者是在三轴剪切试验条件下的三维应力空间建模,后者是在单剪试验条件下的二维应力空间建模。单剪试验条件下土与结构的接触面问题可以看作是法向与切向应力空间上的二维问题,其试验结果可以表达成由应力、应变组成的二维矢量。结合接触面力学特性,确定应力空间中的势函数以及塑性状态方程,可以推导出双重势面接触面弹塑性本构方程的一般表达式。进一步取两个势函数分别为法向应力和切向应力,建立简化双重势面接触面弹塑性模型的本构方程,该方程可直接应用于有限元等数值分析。结合试验实例对建模方法的合理性进行验证,模型拟合效果良好。研究结果表明,基于广义塑性位势理论建立接触面本构模型无需推求塑性势函数和屈服函数,可以直接得到弹塑性刚度矩阵,且建模方便。     

一种基于修正西原模型的冻土蠕变本构关系

冻土在高应力水平下通常会表现出加速蠕变特性。经典西原（Nishihara）模型可以反映衰减蠕变和稳态蠕变,但不适用于描述加速蠕变。通过对Nishihara模型中黏性元件进行修正,将黏弹性元件中的定常的黏滞系数修正为时间的函数,并在黏塑性元件中采用非定常、非牛顿黏性元件,得到的蠕变柔量可以考虑应力水平和时间的影响,使其能够反映其加速蠕变的过程。用提出的模型分别对一维和三维应力、不同应力水平下的冻土蠕变试验数据进行了拟合,拟合结果能够反映冻土从衰减蠕变和稳定蠕变状态进入加速蠕变的过程,说明了该模型对于描述冻土在不同应力下不同蠕变状态的适用性。     

一种横观各向同性岩体蠕变模型

层状岩体由于层理面或者结构面的存在,在力学上具有横观各向同性的特点,现有的各向同性蠕变模型难以全面反映横观各向同性岩体的蠕变力学特性。为构建能够反映横观各向同性岩体的三维蠕变模型,以能反映瞬时应变、减速蠕变和稳态蠕变特征的黏弹性Burgers模型为基础,基于常泊松比假定,在三维各向同性蠕变本构方程的基础上,按照算子替换的方法,将横观各向同性柔度矩阵代替各向同性柔度矩阵,并考虑了平行和垂直层理方向岩体蠕变力学行为的差异性,推导了横观各向同性岩体的三维蠕变本构方程。根据本构方程的特点,提出了根据平行和垂直方向岩体蠕变试验结果进行三维蠕变本构模型中蠕变参数的辨识方法。将提出的模型应用于三轴蠕变试验参数辨识,从而获得了一套完整的三维蠕变参数,并与试验结果进行对比分析,从而验证了所提模型与方法的合理性和有效性。进一步,指出了传统蠕变试验设计方案的局限性,给出了横观各向同性材料蠕变试验设计建议。研究成果为研究岩体三维蠕变机制提供了新思路,可对岩体蠕变试验设计提供相应的科研支撑。     

一种改进的粘土亚塑性本构模型

简要地介绍了Herle和Kolymbas针对黏土建立的亚塑性本构模型的方法。结合黏土的特性以及对响应包络线的分析,详细地列出了HK模型几个尚未解决的问题,并对该模型3个参数分别进行了改进,建立了改进后的HK亚塑性公式以及参数的确定方法。改进后的模型继承了HK模型参数少、易确定以及公式简洁等特点,使HK模型不仅具有严密的数学和力学基础,而且具有较好的实际意义。     

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。     

A new and simple stress-dependent water retention model for unsaturated soil

The water retention curve (WRC) is an important hydraulic property of unsaturated soil needed for seepage analysis. Experimental evidence shows that the WRC is affected by various factors such as net stress and soil type. Many attempts have been made to describe the effects of net stress by including the void ratio in a water retention model. But the void ratio (i.e., soil density) is not the only parameter altered by the application of net stress. The pore structure, including the pore size distribution, pore shape and pore orientation, is also changed. Thus the influence of net stress on the WRC should not be treated as equivalent to density effects. In this study, it is verified that the inclusion of the void ratio cannot adequately capture the effects of net stress on the water retention behaviour. A new and simple water retention model is thus developed by considering the stress effects on the void ratio as well as the pore structure. The model is then applied to simulate the WRCs of three different soils tested over a wide range of stress conditions, including isotropic and anisotropic stress conditions. The results show that better predictions of experimental data can be made by incorporating the effects of net stress on both the void ratio and the pore structure.     

基于统计强度理论的破裂岩体本构模型研究

借助损伤力学思想,基于统计强度理论,提出一种适用于深部工程破裂区破裂岩体的本构模型建立方法,并通过室内试验和数值试验进行了验证。将破裂岩体划分为无数微元立方体,微元立方体的强度与岩石破裂程度有关,且各立方体强度随机分布,故可用强度反映破裂岩体的破裂程度,据此提出一种破裂岩体本构模型建立方法。其中,根据岩石破裂面间的摩擦力做功等于材料破裂后释放的应变能,得到从力学角度定义的岩石破裂程度变量;另外,假定微元立方体强度分布服从Weibull分布,应力水平满足Hoek-Brown准则。利用泥质砂岩破裂岩体典型三轴试验结果,建立泥质砂岩破裂岩体本构模型,并进行了验证,结果表明模型计算曲线与试验曲线吻合度较好。利用离散元软件PFC进行了补充数值试验验证研究,证明了泥质砂岩破裂岩体理论模型的良好计算效果,进而证明提出的本构模型建立方法的可行性。     

A linear constitutive model for unsaturated poroelasticity by micromechanical analysis

This paper extends the Biot theory of poroelasticity from the saturated to unsaturated case. The Biot phenomenological model uses parameters that are easily observable, such as the deformation of porous frame, total stress, pore pressure, and fluid specific discharge. Such model is preferred for engineering applications. At this macroscopic level, the extension of Biot theory from saturated to unsaturated is straightforward. The constitutive constants, however, are combined properties of solid, pore space, and fluids. In the unsaturated case, the constants are functions of the degree of saturation. Their measurements and tabulation over a range of saturation is generally not feasible for practical applications. In this work, a Biot-Willis type analysis is performed for the unsaturated case to provide a theory that the bulk material constants can be evaluated using laboratory measurable micromechanical constants under saturated condition, plus a capillary pressure curve (saturation versus suction pressure) typically available for unsaturated porous medium, without the need of measurement at each state of saturation. In particular, it is demonstrated that the surface energy contained in the meniscus interface manifests as a “capillary modulus,” given by the negative inverse slope of the capillary pressure curve. A rigorous analysis based on the thermodynamic variational energy approach is also conducted to lend theoretical support to the phenomenological approach. The presented model can bring a closure to the practical engineering modeling of the deformation of partially saturated porous medium that lacks the information of material constants over the range of saturation.