变荷载下考虑井阻随时空变化的竖井地基固结解

竖井排水固结法中井阻随时空演变（即由淤堵和弯折所引起的竖井排水能力下降）的现象已引起广泛关注,且变井阻对竖井地基固结速率的影响不容忽略。但目前能同时考虑变荷载及井阻随时间和空间变化的固结解析解还鲜有报道。考虑井阻随时空演变过程,引入实际中广泛采用的单级或多级加载模式,建立了竖井地基固结模型,并应用分离变量法获得固结模型的解析解答。通过与已有的解析解、有限差分解及工程实测值进行对比分析,充分验证了该模型的正确性。通过大量的计算,分析变井阻参数对竖井地基固结性状的影响。结果表明：竖井地基固结速率随竖井最终排水能力的增大而加快,随深度井阻参数及时间井阻参数的增大而减缓,且时间井阻参数的影响更为显著。     

Numerical Laplace-Fourier transform inversion technique for layered-soil consolidation problems: I. Fundamental solutions and validation

A numericl method for solving consolidation problems of layered soils is developed. Starting from the governing differential equations for the coupled poro-elastic medium, the governing partial differential equations are reduced to ordinary differential equations by means of the appropriate displacement functions and Laplace-Fourier transformation. Once the fundamental solution in the transformed domain has been found, the solution in the physical domain is obtained by numerically inverting the transformations. A series of soil consolidation problems have been solved and validated against existing solutions in order to compare the feasibility and the accuracy of the present technique.     

冻土的力学性质及研究现状

中国具有广大的季节冻土和多年冻土区,在冻土地区进行工程建设,就必须深入研究冻土的力学特性,以确保冻土地基上工程建筑物的稳定性。本文首先,简要介绍了我国冻土的分布状况和冻土区别于融土的基本特性,广义的冻土力学可分为冻融作用和已冻土力学性质两方面,冻胀、融沉和冻融循环引起的土力学性质的变化属于冻融作用的范畴。对于冻胀的研究较为深入,人们先后提出了多个理论来解释冻胀产生的机制,有的应用于计算分析中。对融沉的研究尽管具有较长的历史,但是多数停留在经验方法上,融化固结理论目前还有较大的局限性,因此提出一方面可以用人工神经网络法提高经验方法的精度和适用范围,另一方面应当发展融化固结大变形理论;冻融循环可以改变土的力学性质,介绍了作者的最近研究进展。针对已冻土的力学特性,从3方面进行了分析。冻土的强度主要沿用融土的强度理论,很难反映高应力下的压融现象;冻土动力学特性主要针对温度对动力学参数的影响,近年来冻土层对场地动力响应的影响越来越受到重视;冻土的本构关系多集中在蠕变研究,以经验公式法为主。最后,分析了多年冻土地区工程变形所涉及的物理力学过程。     

An Overview of Electrokinetic Consolidation of Soils

Electrokinetic stabilization is one of the techniques that improve the geotechnical properties of the soils. It was pioneered by Casagrande in late 1940s and has not seen much development since then, especially in large-scale field applications. Some bench scale studies have been carried out during the past two decades and there have been some small scale field studies and limited field applications, mostly on soft soils. Due to lack of understanding of the physiochemical and electrochemical changes in the soil during electrokinetic stabilization, uncertain energy costs, loss of efficiency with time and the corrosion of electrodes, this method is usually considered as a last resort for large-scale practical applications. The objective of this paper is to highlight the critical parameters affecting electrokinetic consolidation, and to discuss their effects on the efficiency of the process. A better understanding of these critical parameters and their effects will enable geotechnical engineers to design the electrokinetic consolidation operation more effectively and make it an economically viable process for many situations.     

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。     

Analytical models for consolidation of combined composite ground improved by impervious columns and vertical drains

In recent years, a new technique of ground improvement, which involves the combined use of impervious column and vertical drains, has been proposed and utilized in many field projects to accelerate consolidation and increase bearing capacity of soft soil ground. To cover the possible distribution patterns of impervious columns and vertical drains, 2 analytical models, including Model A with outward flow and Model B with inward flow within the soils, are proposed to predict the consolidation of combined composite ground by considering the following factors: (1) disturbance effects of both impervious columns and vertical drains, (2) the well resistance of vertical drains, and (3) time‐variant loadings. The average degrees of consolidation predicted by the proposed analytical models are compared with several existing solutions and then against the measured data in the literature. The consolidation behavior of a combined composite ground is investigated by the proposed analytical solutions. The results show that the combined use of impervious columns and vertical drains can remarkably accelerate the consolidation rate of soft soils compared with the single use of either of them. The average degrees of consolidation predicted by both analytical models agree well with the measured data. Compared with Model B, Model A usually predicts a faster consolidation rate because of a shorter drainage path. Many factors can influence consolidation behavior of combined composite ground, such as loading scheme, distribution patterns and the disturbance effects of impervious columns and vertical drains, and compression modulus ratio of impervious column to soil.     

多层地基非轴对称Biot固结的理论解

提出了一种新方法来推导多层地基非轴对称Biot固结问题的传递矩阵,相应的理论推导工作量较少。基于柱坐标系下非轴对称Biot固结的基本方程,通过引入中间变量,并对坐标 进行Fourier级数展开,对时间 和坐标 进行Laplace-Hankel变换,得到了6×6阶和2×2阶的两组常微分方程;然后,两组常微分方程进行关于 的Laplace变换和逆变换,得到了单层地基非轴对称Biot固结问题的传递矩阵;结合边界条件和连续条件,运用传递矩阵法得到多层地基非轴对称Biot固结问题在Laplace-Hankel变换域内的解,通过Laplace-Hankel逆变换得到了该问题物理域的真实解答。编制了计算程序,并进行了数值计算与分析。该方法具有计算速度较快的特点,方便工程应用。     

吹填超软土固结特性试验分析

为探讨吹填超软土的固结特性以及含水率与加荷比对次固结系数的影响规律,利用改装后的低压固结仪和常规的高压固结仪进行了分级加载固结试验。试验结果表明,正常沉积重塑土的固结系数随着固结压力的变化整体上呈现出逐渐增加的趋势,而超软土则表现为S型,即在低应力水平作用下,超软土的固结系数呈现下凹型增长; 之后随着固结压力的增加,固结系数近线性增长,但增量比逐渐减小。与正常沉积重塑土不同,超软土的次固结系数随着固结荷载的变化存在峰值; 加荷比对超软土次固结系数影响较大,较小的荷载增量可降低次固结系数; 超软土及正常沉积重塑土的次固结系数均表现为随含水率的增加而增加。     

Modelling non-darcian flow in one-dimensional consolidation

A numerical investigation has been worked in order to better understand the mechanism of consolidation of fine-grained solis with very low permeability.

By using a simple one-dimensional finite difference scheme it has been possible to assess the effects of laws different from Darcy's law upon the consolidation phenomenon of such materials, all other hypotheses worked out by Terzaghi being unchanged.

The deviation from the classical theory of the hydraulic behaviour of soils increases the more the gradient dependent flow rate deviates from Darcy's law and the more the initial pore water pressure dissipates.

First comparisons with experimental data have also been made, in order to verify the reliability of the numerical results.     

考虑井阻时空变化的竖井地基非线性固结解析解

软土固结过程中展现出明显的非线性压缩和渗透特性,同时竖井的淤堵效应常导致井阻在固结过程中随深度和时间不断演化,但目前能考虑井阻随时空演化的竖井地基非线性固结解析解还很鲜见。通过引入孔隙比与有效应力及孔隙比与渗透系数间的半对数模型描述了土体的非线性固结特性,建立了能同时考虑井阻随时空变化和涂抹影响的竖井地基非线性固结模型,并采用分离变量法获得了固结模型的解析解。将特定参数下固结解的计算结果与实测数据、已有的竖井地基固结解答进行了对比分析以验证其可靠性。最后,对竖井地基的非线性固结性状开展了大量计算分析。结果表明：竖井渗透系数随深度线性衰减越明显则地基固结速率越慢;外荷载一定时,随着软土压缩指数c_c与渗透率指数c_k之比的增大,竖井地基固结速度减慢;在c_c /c_k值不变的情况下,外荷载增加,地基固结速率加快。在涂抹区的3种径向渗透系数变化模式中,抛物线变化模式下的地基固结速度最快,线性变化模式下的地基固结速度次之,恒定模式下的地基固结速度最慢,且这种性状并不因为考虑井阻变化或土体非线性固结特性而发生改变。     

Semi-analytical solution to one-dimensional consolidation for viscoelastic unsaturated soils

This paper presents a semi-analytical solution to one-dimensional consolidation of viscoelastic unsaturated soils with a finite thickness under oedometric conditions and subjected to a sudden loading. The solution is obtained by using Lee’s correspondence principle based on the semi-analytical solution to one-dimensional consolidation of elastic unsaturated soils. The boundary contains the top surface permeable to water and air and the bottom impermeable to water and air. A typical example is given to show the evolution of excess pore-air and pore-water pressures as well as the total degree of consolidation of the soil layer with time for different ratios of air–water permeability coefficient, elastic modulus and viscoelastic coefficient. The one-dimensional consolidation behavior of viscoelastic unsaturated soil is discussed according to the semi-analytical solution. These results contribute to a better understanding of the consolidation behavior of viscoelastic unsaturated soils.     

Numerical solution for consolidation and desiccation of soft soils

The consolidation and desiccation behaviour of soft soils can be described by two time‐dependent non‐linear partial differential equations using the finite strain theory. Analytical solutions do not exist for these governing equations. In this paper, we develop efficient numerical methods and software for finding the numerical solutions. We introduce a semi‐implicit time integration scheme, and show numerically that our method converges. In addition, the numerical solution matches well with the experimental result. A boundary refinement method is also developed to improve the convergence and stability for the case of Neumann type boundary conditions. Interface governing equations are derived to maintain the continuity of consolidation and desiccation processes. This is useful because the soil column can undergo desiccation on top and consolidation on the bottom simultaneously. The numerical algorithms has been implemented into a computer program and the results have been verified with centrifuge test results conducted in our laboratory. Copyright © 2001 John Wiley & Sons, Ltd.     

基于有效固结应力法确定结构性黏性土不排水抗剪强度

由于结构性的存在使得很多天然黏性土的强度和变形特性不同于重塑土和非结构性土。首先回顾了适用于确定重塑土和非结构性土不排水抗剪强度的有效固结应力法,并推导了相应的方程。在此基础上,对于结构性黏性土,采用两段不同斜率（内摩擦角正切）和截距（黏聚力）的直线模拟其抗剪强度包络线,建立了确定其不排水抗剪强度的有效固结应力法方程;当有效应力小于结构屈服应力时,有效固结应力方程中有效应力部分需乘以0.8的修正系数;只要已知剪切前的有效应力,利用相应的有效固结应力法公式,可确定结构性土体的不排水抗剪强度。利用连云港结构性软黏土的等压固结三轴试验数据,验证了有效固结应力法的适用性。分析表明：对于连云港软黏土的不排水抗剪强度,有效固结应力法的计算结果与试验结果吻合较好;对于结构屈服应力,有效固结应力法的预测结果与试验数据点的拟合结果有一定偏差,但并不明显。     

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。     

考虑起始坡降双层地基的大应变非线性固结

天然软土成层分布特性及土中渗流存在起始水力坡降的现象已被人们熟知。但变荷载下能同时考虑黏土中起始水力坡降、软土非线性压缩渗透特性及大应变特性的双层地基固结理论还鲜见报道。在拉格朗日坐标系中建立以超静孔压为变量的双层软土地基大应变非线性固结模型并给出其有限差分解。通过与考虑起始水力坡降的单层地基大应变非线性固结数值计算结果对比,验证了差分解的可靠性。着重分析了上、下土层起始坡降无量纲参数R1、R2对双层地基固结性状的影响,分析在大应变与小应变假定下双层地基超静孔压消散及固结沉降变形的异同。结果表明：上层土无量纲参数R1对双层地基固结性状的影响程度较下层土无量纲参数R2显著;大应变假定下双层地基渗流前锋的下移速度要快于小应变假定下的移动速度;大应变假定下考虑起始水力坡降的双层软土地基超静孔压消散速率要比小应变假定下快,且大应变假定下考虑起始水力坡降的双层地基最终沉降量要比小应变假定下大。     

海相结构软土的次固结研究

现有次固结计算方法没有考虑土结构性的影响,但自然沉积土大都具有结构性。海相软土一维次固结试验研究表明,对于结构性土,次固结不仅在超固结状态时与荷载有关,且在土体结构破坏的过程中也与荷载有关。当固结压力小于先期固结压力时,次固结系数随压力增长较快;当固结压力大于先期固结压力且小于结构完全屈服压力时,次固结系数随固结压力增长缓慢;当固结压力大于结构完全屈服压力时,次固结系数不随固结压力变化。次固结系数变化与否的荷载分界点不是先期固结压力,而是结构完全屈服压力。对于海相结构软土,其次固结系数变化在超固结、结构破坏、正常固结3个阶段随荷载变化的规律不同。最后,提出了考虑土结构性的一维次压缩计算方法。     

Theoretical investigation of the effects of consolidation on contaminant transport through clay barriers

Consolidation of clayey contaminant barriers such as landfill liners has been postulated as a cause of early breakthrough of contaminants. In this paper we theoretically investigate this proposition. For this purpose a sophisticated one‐dimensional, large‐deformation model of coupled mechanical consolidation and solute transport is employed. This new model is a generalization of existing coupled consolidation and solute transport models described in the literature. It takes into account both non‐linearities in geometry as well as constitutive relations. The latter relate the compressibility, hydraulic conductivity and coefficient of effective diffusivity to the deformation of the soil. The model is applied to a case study of a clay liner and geomembrane system. Results obtained from numerical solution of the model equations are compared with those from various simplified models, including a ‘diffusion only’ (i.e. a rigid soil) model traditionally used in contaminant barrier design. For barriers incorporating low compressibility soils (as for many well compacted clays), there is little difference between contaminant transit (i.e. breakthrough) times predicted by the two models. However, for contaminant barriers incorporating more compressible soils, consolidation is shown to significantly accelerate transport. These results indicate the potential importance of accounting for the effects of soil consolidation and highlight the limitations of existing models when modelling solute transport through composite barriers utilizing soft soils. Based on these limited results, we suggest a possible way of taking into account soil consolidation using simplified models. Copyright © 2008 John Wiley & Sons, Ltd.     

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。     

Analytical modeling on consolidation of stiffened deep mixed column-reinforced soft soil under embankment

Stiffened deep mixed (SDM) column is a new ground improvement technique to improve soft soil, which can be used to increase bearing capacity, reduce deformation, and enhance stability of soft soil. This technique has been successfully adopted to support the highway and railway embankments over soft soils in China and other countries. However, there have been limited investigations on its consolidation under embankment loading. This paper developed an analytical solution for the consolidation of embankment over soft soil with SDM column in which core pile is equal to or shorter than outer DM column. The consolidation problem was simplified as a consolidation of composite soil considering the load shear effect of core pile. The developed solution was verified by a comparison with the results computed by three-dimensional (3-D) finite element analysis. A parametric study based on the derived solution was conducted to investigate influence factors—length of core pile, diameter of core pile, diameter of SDM column, modulus of DM column, and permeability coefficient of DM column—on the consolidation behavior of SDM column-supported embankment over soft soil. The developed solution was applied to a case history of SDM column-supported embankment, and a good agreement was found between the predictions and the field measurements.     

Semi-analytical solution for one-dimensional consolidation of fractional derivative viscoelastic saturated soils

This paper presents a semi-analytical solution to one-dimensional consolidation equation of fractional derivative Kelvin-Voigt viscoelastic saturated soils subjected to different time-dependent loadings. The theory of fractional calculus is first introduced to Kelvin-Voigt constitutive model to describe consolidation behavior of viscoelastic saturated soils. By applying Laplace transform upon the one-dimensional consolidation equation of saturated soils, the analytical solutions of effective stress and settlement in the Laplace transform domain are obtained. The present solutions are more general and have good agreements with available solutions from the literature, and are degenerated into ones for one-dimensional consolidation of elastic and viscoelastic saturated soils.