变荷载作用下考虑半透水边界热传导性的一维饱和土热固结特性研究

为了研究温度变化对一维饱和土固结特性的影响,基于渗流方程和热传导方程,考虑了顶面边界的半透水性和热传导性,提出了变荷载作用下考虑半透水边界热传导性的一维饱和土热固结的半解析解,并分析了其固结特性。首先,引入Laplace变换分别求解了半透水边界条件下热力耦合模型和非热力耦合模型的一维饱和土热固结方程,推出了有效应力、温差和沉降的半解析解;其次,通过Crump方法进行Laplace数值反演,得到时间域内的解析解;然后,将所提解分别退化为单边排水条件下的一维饱和土热固结和Terzaghi一维固结的半解析解,结果与已有文献相同,验证了所推导解的可靠性;最后,通过算例分析了各外荷载作用下半透水边界参数、温度增量、热扩散系数和固结系数对热固结特性的影响。结果表明,半透水边界参数、热扩散系数、固结系数和温度增量对饱和土一维固结特性影响显著。     

半透水边界下分数阶黏弹性饱和土一维固结特性分析

为描述饱和土体的流变特性,引入分数阶导数Kelvin-Voigt黏弹性模型,采用解析方法对半透水边界下的分数阶黏弹性饱和土一维固结特性进行了研究。分别对骤加恒载下饱和土一维固结微分方程和分数阶Kelvin-Voigt黏弹性本构方程进行Laplace变换,并联立求解得到了双边半透水边界条件下分数阶黏弹性饱和土在Laplace变换域内的解析表达式。通过Crump方法实现Laplace数值反演,得到时间域内的半解析解。将所得到的解分别退化为分数阶黏弹性饱和土一维固结半解析解和双边半透水黏弹性饱和土一维固结半解析解,结果与已有文献半解析解相同,验证了提出的双边半透水边界条件下分数阶黏弹性饱和土一维固结解的可靠性。通过算例考察了半透水边界条件和分数阶黏弹性饱和土参数对一维固结特性的影响。研究表明,双边半透水边界下分数阶黏弹性饱和土一维固结发展过程与半透水边界条件、分数阶次和黏滞系数有关,且土体的压缩模量对饱和土一维固结最终沉降量有显著影响。     

变荷载作用下考虑半透水边界热传导性的一维饱和土热固结特性研究

为了研究温度变化对一维饱和土固结特性的影响,本文基于渗流方程和热传导方程,考虑了顶面边界的半透水性和热传导性,提出了变荷载作用下考虑半透水边界热传导性的一维饱和土热固结的半解析解,并分析了其固结特性。首先,引入Laplace变换分别求解了半透水边界条件下热力耦合模型和非热力耦合模型的一维饱和土热固结方程,推出了有效应力、温差和沉降的半解析解。其次,通过Crump方法进行Laplace数值反演,得到时间域内的解析解。然后,将本文已提出的解分别退化为单边排水条件下的一维饱和土热固结和Terzaghi一维固结的半解析解,结果与已有文献相同,验证了本文研究所推导出解的可靠性。最后通过算例分析了各外荷载作用下半透水边界参数、温度增量、热扩散系数和固结系数对热固结特性的影响。结果表明,半透水边界参数、热扩散系数、固结系数和温度增量对饱和土一维固结特性影响显著。     

任意荷载下双面半透水边界分数阶导数黏弹性饱和土层一维固结

基于Terzaghi一维固结理论,分析了考虑半透水边界条件的分数阶导数黏弹性饱和土层在随时间变化的任意荷载作用下一维固结问题。首先,应用Laplace变换联立求解饱和土层一维固结微分方程和分数阶Kelvin-Voigt黏弹性本构方程,推导出有效应力和沉降在Laplace变换域内的解析解,采用Crump方法进行Laplace逆变换,得到了时间域内的半解析解。然后将本文得到的半解析解分别退化为半透水边界条件下基于黏弹性假设的一维固结半解析解和双面透水边界条件下基于分数阶黏弹性假设的一维固结半解析解,结果与已有文献的半解析解相同,验证了本研究所提出解的可靠性。最后通过算例分别考察了半透水边界参数、分数阶黏弹性模型参数和荷载参数对饱和土层固结沉降的影响。研究表明,半透水边界条件参数、分数阶次与黏滞系数主要影响饱和土层固结的发展快慢,而饱和土层的最终沉降量主要受到土层压缩模量的影响;另外,饱和土层的固结规律与外荷载变化规律一致。     

变荷载下连续排水边界黏弹性地基一维固结性状分析

在考虑软黏土流变特性的基础上,结合工程实际,引入连续排水边界条件,建立了变荷载下连续排水边界黏弹性地基一维固结模型。通过分离变量法与常数变易法,求得了变荷载作用及连续排水边界条件下的饱和软黏土一维固结模型的解析解,进一步研究了透水边界条件和土体参数对超孔隙水压力、有效应力的影响。研究结果表明:上下边界透水性的不同会直接影响超孔隙水压力的变化;越靠近透水性大的边界处的土体固结速度越快,且随着其离排水边界的距离减小,对固结速度的影响逐渐增大;另外,软土层的渗透系数、Kelvin体弹簧的弹性模量和黏滞系数等对土颗粒间的有效应力影响较大。     

变荷载下连续排水边界粘弹性地基一维固结性状分析

本文在考虑软黏土流变特性的基础上,结合工程实际,引入连续排水边界条件,建立了变荷载下连续排水边界粘弹性地基一维固结模型。通过分离变量法与常数变易法,求得了变荷载作用及连续排水边界条件下的饱和软黏土一维固结模型的解析解,进一步研究了透水边界条件和土体参数对超孔隙水压力、有效应力的影响。研究结果表明:上下边界透水性的不同会直接影响超孔隙水压力的变化;越靠近透水性大的边界处的土体固结速度越快,且随着其离排水边界的距离减小,对固结速度的影响逐渐增大;另外,软土层的渗透系数、Kelvin体弹簧的弹性模量和黏滞系数等对土颗粒间的有效应力影响较大。     

变荷载下连续排水边界粘弹性地基一维固结性状分析

本文在考虑软黏土流变特性的基础上,结合工程实际,引入连续排水边界条件,建立了变荷载下连续排水边界粘弹性地基一维固结模型。通过分离变量法与常数变易法,求得了变荷载作用及连续排水边界条件下的饱和软黏土一维固结模型的解析解,进一步研究了透水边界条件和土体参数对超孔隙水压力、有效应力的影响。研究结果表明:上下边界透水性的不同会直接影响超孔隙水压力的变化;越靠近透水性大的边界处的土体固结速度越快,且随着其离排水边界的距离减小,对固结速度的影响逐渐增大;另外,软土层的渗透系数、Kelvin体弹簧的弹性模量和黏滞系数等对土颗粒间的有效应力影响较大。     

连续排水边界下分数阶黏弹性饱和土体一维固结分析

采用分数阶Kelvin模型来描述饱和土体的流变特性,在连续排水边界条件下,利用Laplace变换推导出变换域内的饱和土体一维固结解析解,再通过Crump法对有效应力和固结沉降进行数值反演,得到了分数阶导数黏弹性饱和土体的一维固结半解析解。将连续排水边界退化到Terzaghi排水边界,退化后的结果与已有文献一致,验证了所得半解析解的可靠性。最后,基于所得解,分析了相关参数对土体固结的影响。结果表明,界面参数反映排水边界的透水性,从而影响土体中超孔隙水压力的消散速率;黏滞系数在固结后期对沉降发展影响较大,其值越大,沉降发展越慢;当阶次a不为零时,分数阶次越小,土体表现出的黏滞性越强,整体固结沉降发展越缓慢,次固结沉降发展也越缓慢。     

循环荷载下半透水边界土层一维固结解析解

研究了在循环荷载作用下具有双面半透水边界的饱和粘土层的一维固结问题。根据瞬时加载条件下的解答,采用积分方法得到了循环荷载条件下的解析解。根据解析解的结果,通过计算分析了边界条件和加载条件对土体固结过程的影响,可知：砂垫层和下卧层的渗透性减小会明显减缓固结过程;在循环荷载的一个周期内,孔压和固结度都会达到最大值和最小值各一次。     

结构性土一维非线性大应变固结半解析解

以结构性较强的天然饱和软黏土为研究对象,考虑了沉积作用对其自重应力的影响,以及压缩性和渗透性的非线性变化,推导了任意加载条件下结构性土一维大应变固结控制方程,并采用半解析的方法对方程进行求解计算。再将其退化为无结构性的饱和软黏土固结解,与已有的大应变固结解进行了对比,验证了该解的正确性。最后将该半解析解计算结果与小应变固结理论解、不考虑结构性的固结理论解计算结果进行对比分析。结果表明：大应变固结理论的沉降计算值大于小应变固结理论的计算值,且二者的差值随着荷载的增加而增加;当考虑土体的结构性时,地表沉降计算值小于不考虑土体结构性的沉降计算值。     

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。     

变荷载下基于指数渗流双层地基一维固结分析

在土中渗流服从指数形式的前提下,建立了变荷载作用下双层地基的一维固结控制微分方程。利用有限差分法求得孔隙水压力的数值解,并通过与解析解对比对其可靠性进行了验证。对双层地基在指数形式渗流时不同参数下的固结性状进行分析,结果表明：单面排水条件下,双层地基中上层土渗流指数的大小对固结速率起决定性作用,而下层土渗流指数大小对固结速率的影响很小;如果上、下两层土体的压缩性不同,则地基按变形定义的平均固结度和按孔压定义的平均固结度不再相等;地基中下层土与上层土的相对压缩性越低、相对渗透性越高,则地基的固结速率越快;增大压缩性小、渗透性高的土层相对厚度,会加快双层地基的固结速率。     

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.     

非饱和土拟二维平面应变固结问题的解析计算方法

基于Fredlund非饱和土一维固结理论,建立了二维平面应变条件下的固结方程组,并得到了单层非饱和土平面应变条件下的解析解。基于相关理论,假设体变系数和渗透系数都为常量,同时考虑到瞬时加载条件下,沿着土体深度方向上产生均匀或者线性分布的初始超孔隙压力,建立了二阶二元偏微分方程组。求解时,引入函数方法来降低方程的阶数,然后通过分离变量法获得方程的通解。在此基础上,结合一个针对单面排水条件下二维平面应变问题案例,通过与数值解对比,验证了所提方法的正确性。并采用所提方法计算获得了二维平面下超孔隙水压力、气压力沿垂直和水平方向消散的等时线,通过计算对比,分析了不同线性分布情况下,初始超孔隙压力对固结消散过程的影响。研究结果表明：初始超孔隙压力的不同分布对超孔隙气压力消散的影响几乎可以忽略,而对超孔隙水压力消散的影响更大。     

One-dimensional consolidation of soil under multistage load based on continuous drainage boundary

In engineering practice, a rapid loading rate can result in ground failure when the strength of soft soils is relatively low, and a multistage loading scheme is always utilized to deal with this situation. Firstly, under a multistage load and the continuous drainage boundary, an analytical solution of excess pore-water pressure and consolidation degree is obtained by virtue of the superposition formula of excess pore-water pressure, and a more general continuous drainage boundary under arbitrary time-dependent load is developed. Then, a comparison with existing analytical solutions is conducted to verify the present solution. A preliminary attempt on applying the continuous drainage boundary into the finite element model is made, and the feasibility of the numerical model for the one-dimensional consolidation under the continuous drainage boundary is verified by comparing the results calculated by FEM with that from present analytical solution. Finally, the consolidation behavior of soil is investigated in detail for different int erface parameters or loading scheme. The results show that, in land reclamation projects, a horizontal drain should be placed close to the boundary with a smaller interface parameter to improve the consolidation efficiency. The degree of consolidation is also related to the applied time-dependent load and interface parameters.     

An explicit one-dimensional consolidation solution with semi-permeable drainage boundary for unsaturated soil

Existing solutions for analyzing one-dimensional (1-D) consolidation of unsaturated soil are only derived to cater to two extreme drainage conditions (fully drained and undrained). This study presents a new explicit solution for 1-D consolidation of unsaturated soil with semi-permeable drainage boundary. Based on the assumptions of two independent stress variables and the governing equations proposed by Fredlund, the eigenfunction expansion method is adopted to develop an explicit analytical solution to calculate excess pore-water and pore-air pressures in an unsaturated soil when it is subjected to external loads. The developed general solutions are expressed in terms of depth, z, and time, t. For the semi-permeable drainage boundary, eigenvalues and eigenfunctions in the space domain are developed. The technique of Laplace transform is used to solve the coupled ordinary differential equations in the time domain. The newly derived explicit solution is verified with the existing semi-analytical method in the literature, and an excellent agreement is obtained. Compared with the semi-analytical solution, the newly derived analytical solution is more straightforward and explicit so that this solution is relatively easier to be implemented into a computer program to carry out a preliminary assessment of 1-D consolidation of unsaturated soil.     

Stress history effects on 1‐D consolidation of soft soils: a rheological model

Stress history plays an important role in controlling the consolidation behavior of soft clays, but few models exist that can provide quantitative estimate of its influence. In this paper, the Gibson–Lo rheological model is used to simulate the coupled processes of drainage and creep of soft soils that takes stress history into account. A hybrid combination of analytical and numerical methods is adopted to solve the governing equations of consolidation with the nonlinear rheological model. The methodology is applied to a saturated soft soil subjected to surface loading. The soil profile is separated into normally consolidated and overconsolidated layers by a boundary that is allowed to move. Comparisons of the model predictions and its simulations are used to evaluate the effects of stress history, model parameters, and loading pattern on consolidation behavior. It is shown that stress history influences the location of the moving boundary, variations of the profiles of excess pore water pressure dissipation, stress and deformation‐based average degrees of consolidation. Parametric studies conducted show that when soil is stiffer, the excess pore water pressure dissipates much more quickly, and thus the soil consolidates much faster especially at the early stages. The results also show that soil viscosity influences the deformation‐based average degree of consolidation at the latter stages. The consolidation process of soil layer under linear loading is shown to lag behind those under instantaneous loading: the longer the loading period is, the smaller the average degrees of consolidation are no matter how they are defined. Copyright © 2012 John Wiley & Sons, Ltd.     

不同温度应力路径下饱和黏土剪切特性

在精准温控动三轴试验系统上开展了不同温度及不同升温路径饱和黏土剪切试验研究,探讨了不同温度对饱和软黏土不排水剪切特性的影响,分析不同升温固结方式对饱和软黏土孔压发展、体变、强度以及模量的影响规律。试验结果显示：在4～76 ℃试验研究范围内,环境温度升高导致饱和软黏土的不排水剪切强度有所减少,但温度升高对土体模量增加影响明显,温度T和模量ET关系可用ET = 2.69T 0.3表达;升温变化时正常固结黏土产生超孔隙水压力并随着温度增大而增大,升温热固结后土的剪切强度将明显提高,且排水状态下升温固结对土剪切强度增长小于升温完成后再固结情况;土体从26 ℃分别升高20、40 ℃时,升温引起的超孔压比分别为0.41、0.61,剪切峰值强度分别增加8.23%、22.37%。研究表明：升温幅值增大会使土体热固结程度越大,升温分级越多,热固结也越充分,其对应的体变、强度增长率则越大;同时最终温度及热固结路径对其剪切相转换特征存在影响,升温越高、热固结路径越多其剪胀性越明显,但温度变化范围、固结分级、热固结路径总体上对孔隙水压力的发展基本不产生影响。     

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.     

Large deformation elastic electro-osmosis consolidation of clays

This paper presents the theoretical background of an elastic electro-osmosis consolidation model for saturated soils experiencing large strains, which considers volumetric strains induced by changes in both the hydraulic and electric driven pore water flows. Three fully coupled governing equations, considering the soil mechanical behaviour, pore water transport and electrical field, and their numerical implementation within an updated Lagrangian finite element formulation, are presented. The proposed model is first verified against a classical one-dimensional analytical solution for electro-osmosis consolidation to demonstrate its accuracy and efficiency. Then, various numerical examples are investigated to study the deformation characteristics and time dependent evolution of excess pore pressure. Finally, the importance of considering large strains in a consistent and proper way is demonstrated, and differences compared to models based on small strain theory are highlighted.