饱和粘土非线性渗流规律与径向固结

以多孔介质等效渗流概念得出粘土平均孔隙微尺度数量级范围在0.01 μm至0.1μm,与测试结果一致．实验结果表明饱和粘土微尺度孔隙渗流为非线性流．理论推导表明固液界面作用与渗透率平方根或孔隙半径成反比,固液界面相互作用是导致饱和粘土非线性渗流的重要原因．提出了精确描述饱和粘土微尺度孔隙非线性渗流基本规律的数学模型,其参数量纲明确,物理意义清楚．建立了饱和粘土非线性渗流新定律,统一描述了从较低到较高水力梯度全过程渗流曲线特征,达西定律是其特例．基于新定律,建立了饱和粘土非线性渗流定流量径向固结数学模型．以粘性边界层思想与稳态依序替换法及积分方程法,导出了粘土非线性渗流平均质量守恒方程及活动边界运动方程,给出了饱和粘土非线性渗流超孔隙水压力分布公式与平均固结度计算公式,获得了粘土层压力分布规律和平均固结度随时间变化规律．结果表明:饱和粘土非线性渗流使活动边界运动速度减小．研究结果为粘土地质工程与岩土工程应用提供了新的科学依据．达西渗流径向固结计算是新的非线性渗流固结计算的特例．     

各向异性介质中有衬砌的非圆形结构与SH波的相互作用

本文利用复变函数方法求解各向异性介质中有衬砌的非圆形结构与ＳＨ波的相互作用问题．各向异性介质可以用来模拟结构周围的地质条件．利用作者在文献［５，７］中的方法决定介质和衬砌结构中的散射波，结合Ｓａｖｉｎ在文献［６］中求解有衬砌结构所采用的对结构轮廓线进行近似处理的方法，并利用结构与介质的连续性条件与衬砌内边界上的边界条件，对问题进行求解．作为算例．本文讨论了在同一种各向异性介质中，两种不同材料组成的正方形有衬砌的结构与ＳＨ波的相互作用问题．给出了数值分析结果．     

各向异性介质中带衬砌的圆形结构与SH波相互作用

本文利用复变函数方法求解各向异性介质中带衬砌的圆形结构与ＳＨ波的相互作用问题。各向异性介质可以用来模拟地质条件。利用文献［５］中的方法则可决定介质中的散射波，再利用圆形结构上给出的边界条件，则可对问题进行求解，作为算例，本文给出了在一种各向异性介质中，二种不同材料组成的圆形带衬砌的结构与ＳＨ波相互作用问题的数值分析结果，并予以讨论。     

解Biot固结方程的有限元方法

饱和土固结的Biot理论[1]将固结过程作为一个弹性体应力和孔隙流流动的耦合问题,和Terzhigi理论[2]相比,它更能确切地反映固结机理.本文用经典变分原理导得固结问题一般的Biot有限元方程,具有明确的物理意义.这一结果已用来分析巴家咀土坝的固结过程,计算结果和工程实践一致.     

考虑应力沿深度变化的饱和软黏土一维固结半解析解

针对饱和软黏土,结合引入弹壶元件改进的分数阶Kelvin模型,同时考虑土体内应力沿深度变化的特点,利用Laplace变换推导获得其一维固结半解析解.首先,通过与文献中的试验结果及文献中的理论结果对比,说明了该模型的有效性;其次,详细地分析了不同分数阶阶数、不同总应力比以及不同分级线性加载等因素对饱和软黏土固结沉降以及孔隙水压力的影响,再现了饱和软黏土的固结沉降机理,以期为工程实践提供相关的理论基础.     

渗透各向异性土层的平面应变固结

提出了一种有效的可供选择的分析方法,来研究渗透各向异性多孔弹性土层的平面应变固结问题.从饱和多孔弹性土体的控制方程出发,建立了在Laplace-Fourier变换域内,土层中地基表面(z=0)和深度z处基本变量之间的关系.结合边界条件,得到了变换域内渗透各向异性有限土层的平面应变Biot固结问题的精确解.通过Laplace-Fourier逆变换,得到了物理域内的真实解.平面应变Biot固结土层的数值分析结果显示:渗透各向异性对土层的固结行为,有比较显著的影响.     

不确定Lur'e系统的鲁棒脉冲饱和镇定

对一类参数不确定的Lur'e系统,提出了具有饱和执行器的脉冲镇定问题.将饱和非线性项表示为有限个线性函数的凸组合,运用与脉冲时间序列关联的时变Lyapunov函数,建立了具有饱和脉冲输入的不确定Lur'e系统指数稳定性的判据,并获得了零解吸引域的估计.然后,基于线性矩阵不等式,给出了脉冲饱和控制器存在的条件,同时给出了求解最大吸引域估计的凸优化问题.最后,数值实例验证了所提出方法的有效性.     

饱和地基上弹性基础的竖向振动特性研究

采用解析的方法研究了饱和地基上受一简谐竖向荷载作用下弹性基础的动力响应．在分析中,首先利用积分变换技术获得了饱和介质基本控制方程的变换解,然后基于基础-半空间完全放松接触、半空间表面完全透水或不透水的假设,建立了该动力混合边值问题的对偶积分方程,并把该对偶积分方程进一步化为易于数值求解的第二类Fredholm积分方程A·D2文末数值算例给出了动力柔度系数、位移和孔隙水压力随振动频域和土-基础体系物理力学参数特性的变化曲线．结果表明:饱和地基上弹性基础的动力响应完全不同于饱和地基上刚性圆板的动力响应．所用方法可用于研究波的传播、土-结构动力相互作用等许多问题．     

大应变固结理论的分区变分原理及其广义变分原理

土体材料本构特性的差异问题与大变形问题是分析岩土材料变形特性的基本问题．根据有限变形的描述方法构筑土体结构大变形固结方程,证明了大变形固结的变分原理A·D2应用分区子结构的连续条件,推导固结理论的分区变分原理．引用Lagrange乘子法构筑并证明了大变形固结问题在无约束状态下的广义分区变分原理．     

各向异性液体-多孔饱和介质在机械荷载作用下的弹性动力分析

将一个各向异性液体-多孔饱和介质的弹性动力分析,归结为一个横观各向同性液体-多孔饱和介质在机械荷载作用下的变形问题.自然界中有些物理问题,仅在一个方向发生变形,例如,与变形结构和变形柱有关的问题.土力学中,通常假设只有竖向沉降,从而归结为一维多孔弹性模型.采用各向异性液体-多孔饱和介质的一维变形模型,研究了在不同时间和距离下扰动的变化.给出了在不同类型荷载作用下,介质的各向异性对位移分布和应力分布的影响.     

Rate of consolidation of stone column-improved ground considering change in permeability and compressibility during consolidation

In the available mathematical formulations to determine the rate of radial consolidation of stone column-improved ground, the soil properties especially permeability and compressibility are assumed to be constant during consolidation process. However, permeability changes with void ratio (void ratio also changes with consolidation) and compressibility of soil varies along the consolidation curve (compressibility is a function of effective stress and void ratio). Thus, these properties are not constant during consolidation period. In the present paper, mathematical formulation is developed to determine the rate of consolidation of stone column-improved ground due to radial flow considering change in permeability and compressibility of soft soil during consolidation period. Equal strain approach has been considered in the analysis. The parabolic variation in permeability and compressibility within smear zone are incorporated in the formulation. It is observed that the variation of degree of consolidation due to change in stress concentration ratio and diameter ratio reduces when variable soil properties are considered. The difference between the degree of consolidation obtained considering variable and constant soil properties is almost constant due to variation of smear zone parameters. The time required to achieve 90% degree of consolidation increases or decreases (depending on the properties of soil) by around 50%–100% or up to 25%, respectively, when change in soil properties during consolidation is considered.     

非饱和土固结的混合物理论（Ⅰ）

非饱和土是由土粒、水、气组成的三相介质，本以混合物理论为基础研究了非饱和土的固结问题。中导出了各向异性多孔介质及非饱和土 的有效应力的理论公式，把有效应力原理和Curie对称原理作为非饱和土的两个重要的本构原理，建立了非饱和 土固结的数学模型：由25个方程求解25个未知量。在增量线性化的情况下，本模型简化为5个控制方程求解5个未知量：3个固相位移、孔隙水压力和孔隙气压力。模型中包含7个材料参数，都可由试验测定，便于工程应用，Biot理论是本模型的特例。     

Consolidation of a poroelastic sphere: Numerical investigations of Cryer's problem

In geomechanics the consolidation of a fluid-saturated soil is of great interest and many theories have been proposed in the recent years. A special case is the consolidation problem in a porous, fluid-saturated sphere under drainage and hydrostatic pressure. For this configuration Cryer [2] discussed the special effect of pore pressure response. We increase the complexity of the classical approach, taking into account a modified sphere with an undrained layer. This modification is an expansion of the original problem towards more realistic situations of a poroelastic rock which contains a heterogeneity (modified Cryer problem). It results in nearly effective drainage for the heterogeneity and significant differences in momentary stress state. The interaction between the skeleton and the pore fluid of the porous sphere is implemented numerically with Biot's theory of linear consolidation in an u _s-p-formulation. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A mathematical model to study the soil arching effect in stone column-supported embankment resting on soft foundation soil

Soil arching is a common phenomena in pile or columnar (vibroconcrete columns, soil–cement columns by mixing or grouting, stone columns) supported geosynthetic-reinforced or unreinforced embankments resting on soft soil. Due to soil arching, stress acting on soft soil or geosynthetic reinforcement decreases and stress on piles or columns increases. In this paper, using mechanical elements (such as spring, dashpot), a generalized mathematical model has been developed to study the soil arching effect in stone column-supported geosynthetic-reinforced and unreinforced embankments resting on soft soil. Pasternak model concept has been used to model the embankment soil. The soft soil has been idealized by spring-dashpot system to include the time-dependent behavior. The stone columns and geosynthetic reinforcement are idealized by stiffer nonlinear springs and rough elastic membrane, respectively. The consolidation effect of soft soil due to inclusions of stone columns has also been included in the model to study its effect on soil arching. Plane strain condition has been considered in the analysis. A finite difference scheme has been used to solve the governing differential equations and results are presented in non-dimensional form. It has been observed that the height of embankment, degree of consolidation of soft soil, stiffness of the stone column material, spacing between the stone columns, use of geosynthetic reinforcement and properties of soft and embankment soils (such as ultimate bearing capacity of soft soil, shear modulus and ultimate shearing resistance of embankment soil) significantly influence the degree of soil arching.     

Ben's consolidation of knowledge structures about infinite sets

According to a recently proposed model for processes of abstraction in context, the construction of a new structure is to be followed by a consolidation phase. In this paper, we develop an empirically based, theoretical analysis of consolidation that emerges from a sequence of interviews about the comparison of infinite sets with a talented student. We take for granted that construction has occurred in the first interview and analyze the second one. Our analysis shows that consolidation can be identified by means of the psychological and cognitive characteristics of self-evidence, confidence, immediacy, flexibility and awareness. We also found three modes of thinking conducive to consolidation, one related to problem solving, one to reflective activity and an intermediate one.     

Influence of the saturation–suction relationship in the formulation of non-saturated soil consolidation models

The main scope of this paper is to present a fully coupled numerical model for isothermal soil consolidation analysis based on a combination of different stress states. Being originally a non-symmetric problem, it may be straightforward reduced to a symmetric one, and general guidelines for the conditions in which this reduction may be carried out, are addressed. Non-linear saturation–suction and permeability-suction functions were incorporated into a Galerkin approach of the non-saturated soil consolidation problem, which was solved using the finite element method.In order to validate the model, various examples, for which previous solutions are known, were solved. The use of either a strongly non-linear and non-symmetric formulation or a simple symmetric formulation with accurate prediction in deformation and pore-pressures is extremely dependent on the soil characteristic curves and their derivatives and this aspect is taken into account in the present mathematical approach. The emergent coupling effects may be easily uncoupled in the computer model by merely recasting some coefficients of the discrete equation system.     

圆柱土样Biot固结模型的Green函数及其土体体积应变规律

通过建立横观各向同性圆柱土样轴对称Biot固结问题的Green·函数,得到了用Green函数表示的径向位移分布表达式和相应的空隙水压力的精确解析解.该方法不仅避免了将问题的解分解为弹性静力学解和渗流拟动态解的叠加的过程和复杂的积分变换,而且问题的级数解形式简洁,收敛速度较快,便于数值计算和圆柱土样的全场渗流固结规律的分析.最后以此结果具体分析了Mandel-Cryer效应在圆柱土样不同位置的强弱程度和土的泊松比对Mandel-Cryer效应的影响,表明本文方法的正确性.     

非饱和土的非线性固结模型和弹塑性固结模型及其应用

把作者最近提出的非饱和土的增量非线性本构模型及由作者改进的Alonso等人提出的非饱和土弹塑性模型引入陈正汉建立的非饱和土的固结理论,得到非饱和土的非线性固结模型和弹塑性固结模型,设计了有关程序,求解了地基在分级加载条件下的固结过程和塑性区的动态扩展,从而把非饱和土固结问题的研究推到了一个新水平。     

定荷载和双面排水条件下非饱和土一维固结的解析解

基于多孔介质弹性理论,结合粒间吸应力表示的有效应力原理,建立了非饱和土固结的耦合偏微分控制方程.考虑一维问题,采用Laplace积分变换,得到了定荷载和双面排水条件下非饱和土固结的解析解答.通过数值算例,分析了土体饱和度对超孔隙水压力、有效应力以及土层沉降的影响规律.结果表明,土体的初始饱和度越高,则孔隙水压力消散得越快,有效应力增加越快.