含裂隙非饱和土体的变形与渗流耦合的二维解析分析

含裂隙土体在降雨条件下的渗流规律相对比较复杂,为进一步讨论含裂隙土体渗流机制,在一维解析解的基础上,建立二维饱和-非饱和含裂隙土渗流解析模型,并通过Fourier积分变化推导出二维渗流控制方程的显式解析解。此解析解考虑了多裂隙情况下的孔隙水压力分布和流量边界条件。二维解析解能够准确地获得渗流和变形耦合非饱和土中水的入渗影响规律,并进一步讨论了降雨条件下,不同裂隙模式(裂隙深度、裂隙发育位置及裂隙密集程度)对坡体渗流的影响规律,探讨了含裂隙区域的孔隙水压力分布规律。     

不同初始孔隙比下非饱和黏土渗透性试验研究及模型预测

不同初始孔隙比下非饱和土渗透系数的试验测量及预测,是进行非饱和土渗流分析及水-力耦合研究的基础,相关工作具有重要的意义。以湖南邵阳红黏土为例,利用千斤顶制备5种不同初始孔隙密度塑土样;采用压力板仪测量其土-水特征曲线;选用变水头法测量其饱和渗透系数;自制有机玻璃桶试验装置,采用瞬态剖面法进行非饱和渗透试验,测量不同初始孔隙比土样的非饱和渗透系数。选用CCG(Childs和Collis-George)修正模型和陶-孔模型预测非饱和渗透系数,并与实测值进行比较,验证模型有效性。以上述试验及模型预测的成果为基础,研究初始孔隙比对非饱和(相对)渗透系数的影响规律。研究结果表明:湖南非饱和黏性土渗透系数随基质吸力增加而降低,在低基质吸力阶段(100 k Pa以内)变化较为剧烈,在高基质吸力阶段(100 kPa以上)变化较为缓慢;CCG模型预测误差较大,陶-孔模型预测值与实测值总体吻合较好;进气值之后,初始孔隙比对非饱和渗透系数的影响较小,对非饱和相对渗透系数的影响较大,相同基质吸力条件下初始孔隙比越小,相对渗透系数越大。     

考虑变形影响的黄土土-水特征及其滞后效应

为了研究变形对非饱和黄土土-水特征和滞后效应的影响,通过先构建恒定吸力条件下土体含水率与孔隙比的关系,再引入吸力的影响,建立了一个能够考虑变形的三维土-水特征曲面模型,模型能够很好地描述不同初始孔隙比黄土吸脱湿过程中含水率随孔隙比和吸力的变化规律。为了证实所提出模型的可靠性,对压实黄土进行一系列吸脱湿过程的土-水特征试验。试验结果表明,恒定吸力条件下土体含水率与孔隙比成线性关系,验证了模型的理论假设。另外由模型可以确定恒定孔隙比状态的土-水特征,将其与试验结果对比发现,脱湿路径由吸力引起的变形对土-水特征影响较大,会使特征参数减小,并抑制滞后效应。     

非饱和土二维固结简化计算的研究

针对较高饱和度的非饱和土二维固结问题展开研究。对于较高饱和度的非饱和土,如饱和度 时,将孔隙中气、水近似地看作可压缩的气、水混合流体后,非饱和土近似为土骨架和混合流体的二相土。考虑混合流体的压缩性,建立混合流体的连续方程。联立平衡方程和混合流体的连续方程,求出应力-应变和混合流体压力;再建立水连续方程求解水压力,继而求出气压力、吸力等。算例表明：加载和消散过程中,混合流体与水压力变化基本一致,气压的作用并不大;地基变形过程与高速公路填筑过程中地基变形发生规律一致。说明该简化方法是合理的,并促进了非饱和土固结变形计算走向实用化。     

非饱和土应力场与渗流场耦合一维解析求解与参数分析

由于基质吸力的存在,非饱和土应力场与渗流场耦合问题的解析求解变得非常困难。为有效分析该耦合场的耦合基本规律,本文采用Reynolds输运定律、Darcy定律,并结合多孔介质流体运动规律,推导了非饱和土应力场与渗流场耦合场的控制方程。在该耦合场控制方程中,非饱和土的渗透系数是基质吸力的函数,使得非饱和土耦合场控制方程具有强非线性的特征,而同伦分析法在求解强非线性微分方程时在选择线性算子以及辅助参数上具有明显的优势。因此,通过选取适当的初始猜测解与辅助参数,应用同伦分析法将非线性方程转换为线性的微分方程组,最后求解微分方程组得到耦合问题的解析解。在非饱和土应力场与渗流场耦合问题3阶变形近似解析解中,重点分析了辅助参数h、去饱和系数a、拟重对基质吸力分布的影响。研究结果表明:辅助参数h影响着解析解的收敛性,且随着h的增大,基质吸力总体上呈现减少趋势;基质吸力随着去饱和系数a的增大而减少,且基质吸力随着拟重的增大而呈现减少趋势。     

非饱和土土-水特征曲线预估方法研究

在Wei等[1]基于多相孔隙介质非平衡渗流理论提出的多孔介质热动力学混合物理论模型的基础上,建立了一个能描述不考虑土骨架变形的非饱和土土-水特征曲线动态模型。依据非饱和土土-水特征曲线动态模型,推导出不考虑土骨架变形的气-水两相非饱和土的饱和度演化方程。利用饱和度演化方程并结合多步流动瞬态试验的成果,通过数值反演,提出了一种能利用多步流动瞬态试验数据快速确定非饱和土土-水特征曲线的方法。通过对低液限粉土及低液限黏土的多步流动瞬态试验研究发现,饱和度演化方程能较好地模拟非饱和土在小基质吸力步长变化下饱和度的变化规律。此外,通过对多步流动瞬态试验试样饱和度的模拟确定的非饱和土土-水特征曲线与联合测试系统测得的土-水特征曲线的结果较为一致。     

非饱和土的一种分类方法

根据理想模型中土颗粒和孔隙水之间的几何关系、热力学原理和土力学基本理论,研究了土的非饱和性在非饱和土中引起的力系。给出了张力吸力和吸力比的定义,并在考虑基质吸力作用面积的基础上定义了等效吸力的概念。按照孔隙水弯液面是否与土颗粒表面搭接,将非饱和土分为搭接非饱和土和不搭接非饱和土两类。进而根据搭接状态将搭接非饱和土细分为水封闭非饱和土和搭接双开敞非饱和土,根据孔隙气状态将不搭接非饱和土细分为不搭接双开敞非饱和土和气封闭非饱和土。在搭接非饱和土中,出现张力吸力并对土体的强度产生增强作用;在不搭接非饱和土中,表面张力只是沿着液面传播,不对土的强度产生效应。另外,张力吸力只对强度问题有贡献,它不是渗流问题的驱动力。     

非饱和堤岸的渗流特征及其稳定性研究

通过试验确定了非饱和黏土层的土-水特征曲线和强度参数,通过理论分析建立了非饱和堤岸渗流-应力耦合模型。在此基础上,利用耦合计算程序分析了非饱和土堤岸在河水位变动时的非稳定渗流场特征,结合强度折减有限元法分析了河水位反复升降后非饱和堤岸稳定性的变化。结果表明：水位快速上升时,堤脚渗透流速下降后又逐步上升并趋向稳定,河水位快速上升使堤岸边坡的稳定性降低,随着渗流场中孔隙水压力的调整,堤岸边坡的安全系数又有所回升;河水位骤降时,黏性土层饱和度变化相对滞后,水位骤降加大了堤岸的渗透流速,边坡的稳定性迅速降低,水位下降约120 h后堤岸边坡进入较危险时段;非饱和土的基质吸力提高了堤岸边坡整体稳定性,河水位反复升降降低了堤岸边坡整体稳定性,且河水位越低,水位反复升降对堤岸稳定性产生的影响越大     

混合非齐次边界下非饱和土一维固结解析解

非饱和土的固结研究对道路工程、软土地基处理工程等具有十分重要的意义。基于Fredlund和Hasan提出的非饱和土一维固结理论,给出了土体内孔隙水压力和孔隙气压力变化的控制方程,并给出了单层非饱和土的初始条件与一类随时间变化的混合非齐次边界条件,构成了非饱和土一维固结的定解问题。通过非齐次边界条件齐次化和特征函数展开法,得到了土体内孔隙水压力和孔隙气压力消散的精确时域解析解。最后,通过对比验证了解析方法的正确性,并分析了边界条件指数变化对非饱和土体内孔隙水压力和孔隙气压力的消散以及土体沉降的影响。结果表明,边界处孔压或孔压梯度随时间的指数变化对非饱和土固结过程有明显影响。     

非饱和土的蒸发效应与影响因素分析

采用非饱和土等温流和考虑热湿耦合的非等温流方程,结合不同的蒸发计算模型,分析了大气蒸发效应对非饱和土吸力变化的影响,并对控制蒸发量计算的多个参数进行了影响程度分析。结果表明,考虑实际蒸发量和非饱和土热湿耦合的水分运动公式能较好地模拟大气影响下非饱和土吸力变化状态,通常所采用的等温流方程加以潜在蒸发量计算非饱和土吸力变化会高估表层蒸发和吸力的下降程度。控制地面蒸发的主导因素是外部气象条件,尤其以太阳净辐射量和风速为最,土体自身特性参数影响程度有限。     

Analytical solution to 1D coupled water infiltration and deformation in unsaturated soils

An analytical solution to 1D coupled water infiltration and deformation is derived using a Fourier integral transform. Exponential functional forms are used to represent the hydraulic conductivity–pore‐water pressure relationship and the soil‐water characteristic curve. Fredlund's incremental‐linear constitutive model for unsaturated soils is adopted. The analytical solution considers arbitrary initial pore‐water pressure distributions and flux and pressure boundary conditions. The corresponding analytical solutions to coupled steady‐state problems are also obtained. The analytical solutions demonstrate that the coupling of seepage and deformation plays an important role in water infiltration in unsaturated soils. In the early stages of infiltration, the difference between uncoupled and coupled conditions becomes marked over time, and in late stages, the difference caused by the coupling effects diminishes toward the steady state. The difference between the uncoupled and coupled conditions increases with decreasing desaturation coefficient (α). Pore‐water pressure or deformation changes caused by the coupling effects are mainly controlled by the degree of soil volume change due to a change in soil suction (H). The smaller the absolute value of H, the greater the effect of coupling on the infiltration and deformation. The ratio of rainfall intensity to saturated permeability (q/k_s) also has a strong influence on the coupled seepage and deformation. Copyright © 2008 John Wiley & Sons, Ltd.     

Analytical solution to 1D coupled water infiltration and deformation in two‐layer unsaturated soils

An analytical solution to 1D coupled water infiltration and deformation in layered soils is derived using a Laplace transformation. Coupling between seepage and deformation, and initial conditions defined by arbitrary continuous pore‐water pressure distributions are considered. The analytical solutions describe the transient pore‐water pressure distributions during 1D, vertical infiltration toward the water table through two‐layer unsaturated soils. The nonlinear coupled formulations are first linearized and transformed into a form that is solvable using a Laplace transformation. The solutions provide a reliable means of comparing the accuracy of various numerical methods. Parameters considered in the coupled analysis include the saturated permeability (k_s), desaturation coefficient (α), and saturated volumetric water content (θ_s) of each soil layer, and antecedent and subsequent rainfall infiltration rates. The analytical solution demonstrates that the coupling of seepage and deformation plays an important role in water infiltration in layered unsaturated soils. A smaller value of α or a smaller absolute value of the elastic modulus of the soil with respect to a change in soil suction (H) for layered unsaturated soils means more marked coupling effect. A smaller absolute value of H of the upper layer soil also tends to cause more marked coupling effect. A large difference between the saturated coefficients of permeability for the top and bottom soil layers leads to reduced rainfall infiltration into the deep soil layer. The initial conditions also play a significant role in the pore‐water pressure redistribution and coupling effect. Copyright © 2011 John Wiley & Sons, Ltd.     

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。     

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.     

Numerical modeling of multiphase fluid flow in deforming porous media: A comparison between two- and three-phase models for seismic analysis of earth and rockfill dams

In this paper, a fully coupled numerical model is presented for the finite element analysis of the deforming porous medium interacting with the flow of two immiscible compressible wetting and non-wetting pore fluids. The governing equations involving coupled fluid flow and deformation processes in unsaturated soils are derived within the framework of the generalized Biot theory. The displacements of the solid phase, the pressure of the wetting phase and the capillary pressure are taken as the primary unknowns of the present formulation. The other variables are incorporated into the model using the experimentally determined functions that define the relationship between the hydraulic properties of the porous medium, i.e. saturation, relative permeability and capillary pressure. It is worth mentioning that the imposition of various boundary conditions is feasible notwithstanding the choice of the primary variables. The modified Pastor–Zienkiewicz generalized constitutive model is introduced into the mathematical formulation to simulate the mechanical behavior of the unsaturated soil. The accuracy of the proposed mathematical model for analyzing coupled fluid flows in porous media is verified by the resolution of several numerical examples for which previous solutions are known. Finally, the performance of the computational algorithm in modeling of large-scale porous media problems including the large elasto-plastic deformations is demonstrated through the fully coupled analysis of the failure of two earth and rockfill dams. Furthermore, the three-phase model is compared to its simplified one which simulates the unsaturated porous medium as a two-phase one with static air phase. The paper illustrates the shortcomings of the commonly used simplified approach in the context of seismic analysis of two earth and rockfill dams. It is shown that accounting the pore air as an independent phase significantly influences the unsaturated soil behavior.     

Explicit approximate analytical solutions of seepage‐deformation in unsaturated soils

An approximate analytical solution is presented for the coupled seepage and deformation problem of unsaturated soils. Because of the matric suction dependence of both saturation and permeability coefficient, the coupled governing equations are strongly nonlinear. To obtain an analytical solution, these coupled governing equations are linearized and analytically solved for a specified saturation using the eigenfunction method. Then, the obtained analytical solutions are extended to the entire saturation range. Comparison between the current solution and the previous theoretical solution indicates that the proposed solution yields excellent results. Due to its analytical nature, the proposed procedure can be effectively used to obtain the solution of the coupled seepage and deformation of unsaturated soils.     

非饱和土广义有效应力原理

综述了非饱和土有效应力的沿革,并就非饱和土有效应力的研究和发展中存在的问题进行了讨论。基于多相孔隙介质理论推导得到的变形功的表达式,提出了非饱和土广义有效应力原理。该原理认为,由非饱和土中的单应力变量的有效应力或双应力变量理论很难唯一地确定非饱和土的变形和强度。广义有效应力原理实质上就是要综合考虑影响非饱和土变形和强度的三种广义应力以及与其对偶的广义变形,给出考虑因素更为全面、理论基础更为坚实的广义有效应力原理。它为非饱和土基本性质的研究和本构方程的建立奠定了坚实而科学的理论基础。     

降雨入渗条件下非饱和土边坡稳定分析

针对降雨入渗土坡的稳定问题,建立一个考虑水力渗透系数特征曲线、土-水特征曲线以及修正的Mohr-Coulomb破坏准则的非饱和土流固耦合有限元计算模型,进行雨水入渗下非饱和土边坡渗流场和应力场耦合的数值模拟,得到非饱和土边坡变形与应力的若干重要规律。研究成果为降雨入渗条件下非饱和土边坡的稳定分析提供了基础。     

非饱和上海软土水力和力学特性耦合弹塑性模拟

目前大多数非饱和土的弹塑性本构模型用非饱和击实土的试验结果进行验证,但现场其他类型的土,如沉积土经常有在非饱和状态下外部环境变化的情况。现有的非饱和土弹塑性模型是否适用于沉积土一类的现场土是需要研究的课题。进行非饱和上海第③层土的吸力控制排水排气三轴剪切试验,使用文中提出的能统一考虑非饱和土水力性状和力学性状的弹塑性本构模型,预测上述三轴试验结果,并与试验数据进行比较。比较结果显示,建立的本构模型能够很好地预测非饱和上海软土的水力和力学性质,说明该模型不仅可以适用击实土的预测,还能够很好地适用于其他类型非饱和土的水力和力学性质的模拟。     

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。