未打穿竖向排水井地基固结理论

研究了单面排水条件下未打穿竖向排水井地基的固结问题,通过在排水井底面以下土层中设置虚拟排水井,得到了能考虑该土层三维渗流的解析解,这也是迄今与实际情况最接近的未打穿排水井地基固结解。根据所得解编制了计算程序,分析了未打穿竖向排水井地基的固结性状。并基于此解,对现有相关近似计算方法和解作了较完整的比较和讨论。     

真空联合堆载预压下竖井地基固结解析解

考虑真空度沿竖井的发展是一个深度的函数,同时堆载所引起的附加应力既随时间变化也随深度变化,还考虑了地基的径竖向渗流以及扰动区土体水平渗透系数的3种变化模式,推导了真空联合堆载预压下竖井地基固结度的一个较普遍的解析解,并分析了在真空度沿竖井线性下降,堆载线性施加和附加应力沿深度梯形分布等情况下的地基固结性状。结果表明,荷载线性施加时,真空度对地基固结度有较大影响,真空度越大,沿深度衰减越慢,固结越快;而在荷载瞬时施加时,真空度对固结度没有影响。在地基井径比和水平渗透系数与竖向渗透系数之比较小时,地基的竖向渗流对地基的固结度有较大的影响。     

An analytical solution for contaminant extraction from multilayered soil using PVD-enhanced system

Prefabricated vertical drains (PVDs) have been employed to enhance the in situ remediation of contaminated fine-grained soils. Subsurface heterogeneity can interfere with the distribution and extraction of contaminants during the remediation process. In the present study, an analytical solution for contaminant extraction from multilayered soil using a PVD-enhanced system is developed based on an equivalent planar two-dimensional model. The analytical solution is derived using a procedure that combines the Laplace transform, eigenfunction method and numerical Laplace inversion. The validity and accuracy of the solution are verified by comparison with an existing analytical solution and the results obtained using a numerical model. The effects of several key parameters on the performance of a PVD remediation system in a triple-layered contaminated soil are evaluated. The results indicate that the remediation efficiency for clay layers decreases with increasing hydraulic conductivity or thickness of the sand layer. The PVD remediation system may be unfeasible for contaminated sites with high subsurface heterogeneity caused by permeability contrast. The remediation process for clay layers can be accelerated by increasing the clay vertical dispersivity.     

循环荷载作用下饱和软粘土非线性一维固结

根据饱和软粘土地基非线性一维固结理论，针对单层饱水地基模型，运用Laplace变换求解了在循环荷载作用下的单层饱水地基一维非线性变形问题；通过Laplace逆变换，即可计算单层饱水地基在循环荷载作用下的非线性一维固结。结合单层地基在几种常见循环荷载作用下固结变形的算例，对解进行了探讨，揭示了循环荷载作用下单层饱和软粘土地基非线性一维固结的特性，得到了一些可用于指导工程实践的有意义的结论。     

任意荷载下分数阶导数黏弹性饱和土体一维固结

将分数阶导数理论引入Kelvin–Voigt模型,来描述黏弹性饱和土体的力学行为。对饱和土体一维固结方程和分数阶导数Kelvin–Voigt本构方程实施Laplace变换,联立求解得到变换域内有效应力和沉降的解析解。采用Crump方法实现Laplace数值反演,获得了任意荷载情况下物理空间内一维固结问题的半解析解。并将指数荷载情况下分数阶导数模型退化到黏弹性情形,结果与已有文献解析解相同,验证了本研究提出任意荷载情况下分数阶导数黏弹性解的可靠性。最后,分析了相关参数对固结沉降的影响。研究表明,任意荷载情形下分数阶导数黏弹性饱和土体一维固结发展过程与黏滞系数和分数阶次有关,分数阶次越大,固结沉降发展越快;黏滞系数越大,固结沉降变化越慢;荷载变化趋势与由荷载参数变化引起的沉降变化规律是一致的,且最终沉降量一致。本研究有助于深入认识分数阶黏弹性饱和土体的固结行为。     

基于真空–堆载联合预压法的未打穿竖井地基固结分析

 在未打穿竖井情况下,用真空–堆载联合预压法来处理软土地基,既高效又经济。针对这种地基处理方法,应用Laplace 变换半解析法来进行分析。通过在竖井底面设置虚拟竖井来模拟竖井下三维渗流情况,并合理考虑真空度损失,得到真空度损失下竖井打入深度与沉降之间的关系。运用Laplace变换与逆变换,得到比较精确的解析解,并对影响竖井渗透作用的几个主要参数,如贯入度、井阻、真空度等进行对比分析,得到可供实际工程参考的竖井最优贯入度。     

Analytical solutions to the axisymmetric consolidation of a multi-layer soil system under surcharge combined with vacuum preloading

Surcharge combined with vacuum preloading is a common technique for accelerating the consolidation process in ground improvement. A unit cell model for the axisymmetric consolidation of a soft soil using a prefabricated vertical drain (PVD) under a surcharge, combined with vacuum preloading, is investigated in this study. Based on this model, analytical solutions for a multi-layer soil system are put forward and the explicit expressions for two-layer and one-layer systems are presented. The accuracy of the proposed solution is verified using an analytical solution available in the literature. In the parametric study, the influencing factors on the consolidation process, such as, the smear zone, the PVD spacing, the hydraulic conductivity in the radial direction, the coefficient of vacuum decrease, are taken into account. The water flow in the radial direction plays an important role in the consolidation process while the impact of the vertical flow mainly develops around the interfaces between two adjacent layers. In addition, the proposed analytical solution is applied in a case history with three different layers and the results are reasonable.     

考虑横向惯性效应时非均质土中大直径桩纵向振动特性及其应用

 基于Rayleigh-Love杆模型,研究考虑横向惯性效应时非均质土中大直径桩纵向振动特性。首先,采用虚土桩模型模拟桩底土对桩的支承作用,通过径向圈层间的剪切复刚度传递,考虑施工扰动造成的桩周土的径向非均质性;然后,将桩与虚土桩假设为Rayleigh-Love杆,建立其纵向振动控制方程,通过Laplace变换和阻抗函数递推方法,得到桩顶频域响应解析解,并通过Fourier逆变换得到桩顶时域响应半解析解;在此基础上,通过参数分析的方法,研究横向惯性效应对大直径桩纵向振动特性的影响以及与桩–土参数之间的关系;最后,将理论计算结果与现场实测曲线进行对比,验证了本文解的合理性。     

横观各向同性土中深埋圆形隧道的应力和位移分析

基于Biot固结理论,得到在横观各向同性饱和土体中开挖圆形隧道引起的应力、位移及孔隙水压力在时间的拉普拉斯变换域中的解。运用拉普拉斯数值逆变换,得到数值计算结果,分析了隧道边界条件和土体的横观各向同性性质对应力、位移场的变化及孔隙水压力消散的影响。     

应力变化的真空-堆载预压下竖井地基固结分析

考虑真空度沿竖井线性减小、堆载所引起的附加应力随深度变化以及地基涂抹区水平渗透系数呈线性变化,推导了附加应力变化的真空-堆载预压下竖井地基固度的一个解析解,并分析了地基固结性状。分析结果表明,在荷载瞬时施加时,真空预压的大小及沿竖井的衰减快慢对地基的固结速度没有影响;在单面排水条件下,竖井地基顶面的附加压力越大,固结越快;在地基井径比和水平渗透系数与竖向渗透系数之比较小时,地基的竖向渗流对地基的固结度有较大的影响。     

任意荷载下成层弹性地基的一维固结

针对成层弹性地基模型，运用Ｌａｐｌａｃｅ变换及矩阵传递法求解了任意荷载下成层弹性地基一维固结问题，得到了频域内的通解，通过Ｌａｐｌａｃｅ逆变换，即可计算成层弹性地基在任意荷载下的一维团结。经典的Ｔｅｒｚａｈｉ一维固结理论解是一个特例。此外，结合三层的地基算例，对解进行了探讨，揭示了成层弹性地基的固结特性。     

One-dimensional consolidation of unsaturated soils considering self-weight: Semi-analytical solutions

For the newly deposited soil, the consolidation will occur under the self-weight and external load jointly if the soil is treated by the stack pre-pressure method. The soil stress caused by self-weight has a significant influence on its consolidation process no matter the soil is either saturated or unsaturated. However, the soil’s self-weight is ignored in the one-dimensional (1D) consolidation theory for unsaturated soils (Fredlund and Hasan, 1979). In this paper, we derived the semi-analytical solutions for excess pressures and normalized settlement in 1D dimensional consolidation of unsaturated soils considering self-weight. The analytical solutions were obtained by Crump’s method (Crump, 1976), through a computing program coupling the calculation of initial excess pore pressures with the inverse Laplace transform of the obtained solutions. Then, the proposed solutions are verified through a degradation case. Several 2D charts are presented to visualize the solutions, and various examples are employed to discuss the key factors that affect one-dimensional consolidation behavior of unsaturated soils when self-weight is considered. It can be found that the relative excess pore pressure will be restrained for the one-dimensional consolidation when considering self-weight.     

泥炭质土层盾构施工扰动引起隧道长期沉降的研究

为了研究泥炭质土层盾构施工扰动引起隧道的长期沉降问题,将隧道周围土体视为连续、均质、各向同性的饱和黏弹性介质,采用五元件模型描述泥炭质土的流变特性,耦合Terzaghi-Rendulic二维固结理论,建立了隧道衬砌在完全不透水的情况下,盾构施工扰动引起周围土体超孔隙水压力消散的控制方程。采用分离变量法、保角映射、Laplace变换及逆变换等数学方法对该控制方程进行求解,得到了隧道周围土体超孔隙水压力消散的解析解,最后对土体的竖向应变进行积分获得了隧道长期沉降的计算公式。结合一工程算例分析了昆明泥炭质土层超孔隙水压力消散及隧道长期沉降的变化规律,研究结果表明:与上海软黏土相比,在初始阶段泥炭质土层中超孔隙水压力的消散速度较快,然后迅速变缓并趋于稳定。泥炭质土层中隧道的长期沉降持续时间更长且沉降量更大,在900 d的时间内隧道沉降趋于稳定,其累积沉降量约高达150 mm。此外,昆明泥炭质土的流变特性显著,如将土体中超孔隙水压力消散90%作为主固结沉降的完成时刻,则土体次固结沉降约占隧道总沉降量的36%,是隧道长期沉降中不可忽视的一个重要组成部分。     

Solutions for a completely saturated porous elastic solid with impeded boundaries

Analytical solutions are presented for the consolidation of a semi-infinite stratum and a finite soil layer with an impeding layer located on the surface subjected to a vertical point loading. The Laplace transform and the Hankel transform are used with respect to time and the radial coordinate, respectively. Solutions of other distributed loadings, including the circular loading, can be easily obtained by integrating those of the point loading. The consolidation degree, excess pore water pressure, vertical total stress, and the shear stress of the consolidating layer are analyzed in this study. The consolidation rate decreases with the increase in the thickness of the impeding layer. Stresses of the consolidating layer vary during the consolidation due to the coupling of the excess pore water dissipation and the soil skeleton deformation. Further, the Mandel-Cryer effect is also analyzed in this study.     

Numerical Analyses on Consolidation of Clayey Ground Improved by Vertical Drain System Based on 3-D Elasto-Viscous Model

This paper addresses a proposal on the three-dimensional elasto-viscous consolidation theory and discusses on its applicability. In order to predict the three-dimensional consolidation behavior of clayey ground improved by vertical drain system, one-dimensional consolidation theory based on an elasto-viscous liquid model proposed by Yoshikuni et al. (1994), which can express secondary consolidation without considering any distinction between normally consolidated and overconsolidated regions, is extended to three-dimensional condition. This theory is applied to the consolidation of a hollow cylindrical body that models a clayey ground improved by a vertical drain system. Then, a rigorous solution of elastic consolidation theory, a FEM solution based on elasto-plastic theory and a FDM solution using three-dimensional elasto-viscous theory are compared with the test results obtained using the three-dimensional consolidation test apparatus developed by the authors (Baek and Moriwaki, 2004). Based on the results of analyses, it is evident that the three-dimensional consolidation theory proposed by authors could simulate the consolidation behavior of clayey ground improved by vertical drains, such as the secondary consolidation and the radial displacement during the three-dimensional consolidation process.     

饱和土体圆柱形热源热固结问题的一个近似解

在考虑土骨架和孔隙水热膨胀特性差异的基础上,根据力平衡条件、有效应力原理、能量守衡定理及线弹性应力–应变关系,建立了考虑耦合效应的饱和土体热固结问题控制方程。利用 Fourier 变换、Laplace 变换及其逆变换,给出了热固结问题的求解方法。对一无限长圆柱形热源向外传导和扩散问题进行研究,给出了非等温条件下周围饱和土体的温度、孔隙水压力和位移的解析解,并对其变化规律进行研究,分析了热固结系数等参数的影响。     

Fully coupled solution for the consolidation of poroelastic soil around geosynthetic encased stone columns

The paper presents an extension of a recently developed fully coupled elastoplastic method (Pulko and Logar, 2016) for the analysis of a poroelastic thick-walled soil cylinder around an elastoplastic end-bearing stone column to account for the influence of an elastic geosynthetic encasement. The method was developed in the framework of Biot's consolidation theory (Biot, 1941) and is based on a unit cell concept, wherein the column encasement is modeled as a thin elastic membrane, which can only sustain tension and acts in the radial direction. Analytical closed-form expressions for excess pore pressures, stresses, strains, displacements and encasement forces were derived in the Laplace domain. The final elastoplastic solution in time domain was obtained numerically by using efficient numerical scheme for the inverse Laplace transform. The validity of the solution was checked against finite element analyses and compared with previously developed analytical methods. The results showing the influence of column encasement on transient state of settlements, strains, excess pore pressures and encasement forces under instantaneous or time dependent load are presented and discussed.     

成层未打穿砂井地基固结Lagrange插值解法

考虑井阻和涂抹区的影响,建立成层未打穿砂井地基固结的数值模型和算法。将未打穿砂井底面下的软土层视为虚拟排水井,同时将未打穿砂井转化为打穿的多段砂井,使得土层边界条件和数值计算过程简单化。对超孔隙水压力用Lagrange插值多项式等结点插值近似,把砂井打设区固结方程转化为结点的超孔隙水压力的简单微分方程组,砂井固结方程转化为一线性代数方程组,以4层土为例,导出详细的计算公式。如增加土层数,仅需改变边界结点系数公式。最后,把该解法与相关近似方法的计算结果进行分析比较,并给出一个多层软土路基预压加固工程案例。结果表明,将下卧层简化为一维固结与考虑其三维固结对计算结果影响很小。     

多层地基Terzaghi一维固结解

分析了传统Terzaghi一维固结方程的求解方法的缺点及局限性,提出了结合传递矩阵的分析技术来求解多层地基Terzaghi一维固结问题的方法。运用Laplace变换法求解Terzaghi一维固结方程,得到了单层地基的初参数解及传递矩阵,然后用传递矩阵法推导出多层地基Terzaghi一维固结问题理论解答,并就单层固结与多层固结分析进行了相应的数值计算,得到了简明的解析解。结果表明:提出的计算方法计算工作量小,精度高,适于工程应用。     

双层非饱和土地基一维固结半解析解

基于Fredlund和Hasan的非饱和土一维固结理论,将非饱和地基假定为双层,引入层间渗流连续条件,得到双层非饱和土地基一维固结控制方程。采用Laplace变换将偏微分方程组转化为常微分方程组,求解得到双层非饱和土地基在单面、双面渗透边界条件下超孔隙压力和沉降在Laplace域内的解;并利用Crump数值方法实现Laplace逆变换,最终得到时间域内双层非饱和土地基一维固结的半解析解。通过与已有文献和有限差分解的结果比较,验证了所得半解析解的有效性。基于得到的解答,结合算例考察了不同层间渗透系数比下,双层非饱和土地基中超孔隙压力的分布规律;并通过参数分析讨论了土层厚度比和层间渗透系数比对双层非饱和土地基沉降的影响。