饱和软土成层地基一维非线性固结解析解

假定土体在固结过程中压缩性和渗透性的变化成正比,基于 - 及 - 关系,推导出饱和软土成层地基一维非线性固结解析解,分别给出了按沉降定义和按有效应力定义的每层土平均固结度及整个土层总固结度的计算公式。采用Fortran语言编制了相应的计算程序,将计算得到的结果与已有双层地基一维非线性固结解析解计算结果进行比较,验证该解析解的正确性。利用该程序分析成层地基一维非线性固结性状,分别讨论了初始竖向渗透系数、初始体积压缩系数、荷载值及土层厚度对地基固结性状的影响。分析结果表明：在成层地基一维非线性固结过程中,初始竖向渗透系数对超静孔压的影响较为复杂,对上下层地基固结速率影响不同;初始体积压缩系数增大,超静孔压增大,固结速率变小;所加荷载值越大,超静孔压消散越慢,固结发展越慢;超静孔压消散速率不仅取决于土层厚度,同时取决于各层土渗透性的相对大小。     

任意荷载下欠固结地基的非线性一维固结

根据Gibson得到的固相坐标z下的非线性固结控制方程,运用Laplace变换求解了在任意荷载作用下的单层饱水欠固结地基一维非线性变形问题;通过Laplace逆变换,求得单层饱水欠固结地基在任意荷载作用下的一维非线性固结解。结合单层地基在几种常见荷载作用下固结变形的算例,对解进行了探讨,揭示了任意变荷载作用下单层饱和软粘土欠固结地基一维非线性固结的特性,得到了一些可用于指导工程实践的有益结论。     

循环荷载下黏弹性饱和土层的一维固结

针对单层黏弹性地基Merchant模型,运用Laplace变换,求得频域内单层黏弹性地基的一维固结解。通过Laplace逆变换,计算了单层黏弹性地基在任意循环荷载下的有效应力及平均固结度。此外,结合工程实例,研究了Merchant模型各参数对循环荷载下黏弹性地基固结的影响。结果表明,在黏弹性地基的固结过程中,有效应力和沉降的发展速率是不一致的,黏壶的存在使地基固结初期的有效应力增长加快,而使固结后期的有效应力增长减慢,同时使变形的发展滞后于有效应力的发展。研究结果亦表明,循环荷载下土体的固结对独立弹簧模量的变化要比Kelvin体中弹簧模量的变化敏感。     

变荷载下双层地基一维非线性固结近似解析解

目前考虑土体非线性压缩及渗透特性的双层地基非线性固结解均假定土体固结系数保持不变,能反映固结系数变化的双层地基非线性固结解还很鲜见。引入经典的e- 和e- 非线性关系描述土体的非线性压缩、渗透特性,在假定双层地基上、下土层压缩指数与渗透指数比值 相等且不等于1的基础上,得到变荷载下考虑土体固结系数变化的双层地基一维非线性固结近似解。该解答在 1条件下可退化为已有的 1时双层地基一维非线性固结解。基于此解探讨了双层地基上、下土层参数的相对比值对非线性固结性状的影响。结果表明：单面排水条件下 越小,下层土与上层土的相对压缩性越低、相对渗透性越高,则双层地基非线性固结速率越快;减小 值,增加双层地基中压缩性小、渗透性高的土层的厚度,会加快地基的固结速率。     

双层黏弹性地基一维固结分析

软土具有黏滞性,对其固结和变形会产生一定程度的影响。采用现有基于广义Voigt流变模型的单层黏弹性地基一维固结问题求解方法,获得各土层的孔压通解表达式。根据两层土体接触面处孔压和流量连续条件及边界条件,给出了系统的正交关系,进而确定通解中待定系数。广义Voigt模型反映了土体应力应变关系在不同时期的特征,因此该解有广泛的适用性。采用岩土工程中应用较广的Merchant流变模型对一工程算例进行了分析。分析结果表明,土体的黏滞性降低了土体的固结速度,且深度越深,影响幅度越大。     

双层广义Gibson地基轴对称问题求解

假定双层地基土体为弹性、不可压缩、剪切模量随深度线性变化的广义Gibson地基,在两层土体剪切模量表达式常数项与一次项系数之比相同条件下,采用Hankel变换,得到了表面分布轴对称荷载时地基土体应力、位移的积分形式解,讨论了下层深度、剪切模量等对位移的影响。获得的解可退化到半空间情况。     

双层饱和软土地基一维大应变固结研究

研究了双层软土地基一维非线性大应变固结问题,同时考虑了土体受沉积作用影响的自重分布以及渗透性在固结过程中的变化等因素。对此复杂问题,利用半解析法进行了求解。通过与已有的大应变固结解析解对比,检验了半解析法在大应变固结分析中的有效性。最后较为详细地分析了双层软土地基一维大应变固结性状,并与相应条件下的小应变固结作了比较。     

非均匀地基与均匀地基一维固结解答之间的转换关系

基于一维固结理论,研究了土层物理力学性质沿深度非均匀连续变化的固结问题。首先,利用分离变量法,获得了渗透系数和压缩系数随深度按指数函数变化的非均匀地基一维固结方程的解析表达式; 然后与Terzaghi固结理论的经典解答进行了比较,获得了两种解答之间的相似转换关系。这样,非均匀地基固结问题就可以用相同荷载以及边界条件下的均匀地基固结的经典解线性表示。因此,非均匀地基固结问题的求解转化为对相似转换系数的计算。该系数集中反映土层非均匀性对地基固结的影响,从而为解决非均匀地基一维固结问题提供了便捷途径。     

低频循环荷载下地基一维固结性状分析

给出了低频梯形循环荷载下单层地基一维固结解。对该循环荷载下地基固结特性、相应的影响因素以及平均固结度、有效应力随荷载的发展和变化规律进行了分析和讨论,并研究了有效应力最大和最小值随荷载的变化规律。在任一周期中,有效应力 的发展并不与荷载的变化同步,而是按一定规律滞后发展。     

Analytical theory for one‐dimensional consolidation of clayey soils exhibiting rheological characteristics under time‐dependent loading

This paper presents analytical solutions to the one‐dimensional consolidation problem taking into consideration the rheological properties of clayey soil under variable loadings. A four‐element rheological model is introduced, and different loading types are involved, i.e. constant loading, one‐step loading, triangular loading, rectangular loading, and isosceles–trapezoidal cyclic loading. The differential equations governing consolidation are solved by the Laplace transform. Based on the solutions obtained, the influences of the rheological parameters and loading conditions on the consolidation process are investigated. It has been shown that the consolidation behavior is mainly governed by four dimensionless parameters, a₁, a₂, b, and T_v0. Load shape has a great influence on the rate of consolidation. A decrease either in the modulus of the spring in the Kelvin body or in the viscosity coefficient of independent dashpot will slow down the rate of consolidation. An increase in the viscosity coefficient of the dashpot in the Kelvin body will make the rate of consolidation increase at an early stage but decrease at a later stage. For isosceles–trapezoidal cyclic loading, the consolidation rate in each cycle reaches a maximum at the end of the constant loading phase and the minimum at the end of this cycle. Copyright © 2008 John Wiley & Sons, Ltd.     

Non‐linear consolidation analysis of soil with variable compressibility and permeability under cyclic loadings

In this paper, a simple semi‐analytical method has been developed to solve the one‐dimensional non‐linear consolidation problems by considering the changes of compressibility and permeability of the soil layer, subjected to complicated time‐dependent cyclic loadings at the ground surface. The solution presented here takes into account e ～ lg k_v and e ～ lg σ′ linear responses. With c_k the slope of the e ～ lg k_v line and c_c as the slope of the e ～ lg σ′ line, the identified parameter c_c/c_k is found to control the rate of consolidation. Using the solutions obtained, some diagrams are prepared and the relevant behaviours of one‐dimensional non‐linear consolidation of saturated soft soil under cyclic loadings are discussed. The method in this paper does not require any special data; conventional oedometer data can be used. Therefore, the method is particularly efficient and convenient for engineering practice. Copyright © 2006 John Wiley & Sons, Ltd.     

Semi‐analytical solution to one‐dimensional consolidation for unsaturated soils with semi‐permeable drainage boundary under time‐dependent loading

This paper presents semi‐analytical solutions to Fredlund and Hasan's one‐dimensional consolidation of unsaturated soils with semi‐permeable drainage boundary under time‐dependent loadings. Two variables are introduced to transform two coupled governing equations of pore‐water and pore‐air pressures into an equivalent set of partial differential equations, which are easily solved by the Laplace transform. The pore‐water pressure, pore‐air pressure and settlement are obtained in the Laplace domain. Crump's method is adopted to perform the inverse Laplace transform in order to obtain semi‐analytical solutions in time domain. It is shown that the present solutions are more general and have a good agreement with the existing solutions from literatures. Furthermore, the current solutions can also be degenerated into conventional solutions to one‐dimensional consolidation of unsaturated soils with homogeneous boundaries. Finally, several numerical examples are provided to illustrate consolidation behavior of unsaturated soils under four types of time‐dependent loadings, including instantaneous loading, ramp loading, exponential loading and sinusoidal loading. Parametric studies are illustrated by variations of pore‐air pressure, pore‐water pressure and settlement at different values of the ratio of air–water permeability coefficient, depth and loading parameters. Copyright © 2017 John Wiley & Sons, Ltd.     

Analytical solution for one‐dimensional consolidation of unsaturated soils using eigenfunction expansion method

This paper introduces an exact analytical solution for governing flow equations for one‐dimensional consolidation in unsaturated soil stratum using the techniques of eigenfunction expansion and Laplace transformation. The homogeneous boundary conditions adopted in this study are as follows: (i) a one‐way drainage system of homogenous soils, in which the top surface is considered as permeable to air and water, whereas the base is an impervious bedrock; and (ii) a two‐way drainage system where both soil ends allow free dissipation of pore‐air and pore‐water pressures. In addition, the analytical development adopts initial conditions capturing both uniform and linear distributions of the initial excess pore pressures within the soil stratum. Eigenfunctions and eigenvalues are parts of the general solution and can be obtained based on the proposed boundary conditions. Besides, the Laplace transform method is adopted to solve the first‐order differential equations. Once equations with transformed domain are all obtained, the final solutions, which are proposed to be functions of time and depth, can be achieved by taking an inverse Laplace transform. To verify the proposed solution, two worked examples are provided to present the consolidation characteristics of unsaturated soils based on the proposed method. The validation of the recent results against other existing analytical solutions is graphically demonstrated. Copyright © 2013 John Wiley & Sons, Ltd.     

A simple analytical solution to one‐dimensional consolidation for unsaturated soils

This paper presents a simple analytical solution to Fredlund and Hasan's one‐dimensional (1‐D) consolidation theory for unsaturated soils. The coefficients of permeability and volume change for unsaturated soils are assumed to remain constant throughout the consolidation process. The mathematical expression of the present solution is much simpler compared with the previous available solutions in the literature. Two new variables are introduced to transform the two coupled governing equations of pore‐water and pore‐air pressures into an equivalent set of partial differential equations, which are easily solved with standard mathematical formulas. It is shown that the present analytical solution can be degenerated into that of Terzaghi consolidation for fully saturated condition. The analytical solutions to 1‐D consolidation of an unsaturated soil subjected to instantaneous loading, ramp loading, and exponential loading, for different drainage conditions and initial pore pressure conditions, are summarized in tables for ease of use by practical engineers. In the case studies, the analytical results show good agreement with the available analytical solution in the literature. The consolidation behaviors of unsaturated soils are investigated. The average degree of consolidation at different loading patterns and drainage conditions is presented. The pore‐water pressure isochrones for two different drainage conditions and three initial pore pressure distributions are presented and discussed. Copyright © 2013 John Wiley & Sons, Ltd.     

非饱和土固结理论新进展

总结了国内外多年来在非饱和土固结理论领域研究的主要理论成果,内容包括国内外非饱和土固结理论研究的概况,涉及线性、非线性、弹塑性和结构性等方面,非饱和土固结理论的研究具有非常好的应用前景。但非饱和土固结理论还很不成熟,有待广大科研工作者的进一步研究。     

Finite element analysis of consolidation of layered clay soils using an elastic visco-plastic model

This paper presents a general one-dimensional (1-D) finite element (FE) procedure for a highly non-linear 1-D elastic visco-plastic (1-D EVP) model proposed by Yin and Graham for consolidation analysis of layered clay soils. In formulating the 1-D FE procedure, a trapezoidal formula is used to avoid the unsymmetry of the stiffness matrix for a Newton (modified Newton) iteration scheme. Unlike many other 1-D FE approaches in which the initial in situ stresses (or stress/strain states) are considered indirectly or even not considered, the initial in situ stress/strain states are taken into account directly in this paper. The proposed FE procedure is used for analysis of 1-D consolidation of a clay with published test results in the literature. The FE modelling results are in good agreement with the measured results. The FE model and procedure is then used to analyse the consolidation of a multi-layered clay soils with a parametric study on the effects of the variations of creep parameters in Yin and Graham's 1-D EVP model. It is found that the creep parameters ψ/V and t₀ have significant influence on the compression and porewater pressure dissipation. For some boundary conditions, changes of parameters in one layer will have some effects on the consolidation behaviour of another layer due to the different consolidation rates. Finally, the importance of initial stress/strain states is illustrated and discussed. Copyright © 1999 John Wiley & Sons, Ltd.