考虑井阻及涂抹作用的非饱和土竖井地基固结解析解

以往的非饱和土竖井地基研究中未同时考虑竖井的井阻和涂抹作用,大部分按理想竖井进行研究,然而井阻和涂抹作用是影响非饱和土竖井地基固结的重要因素。针对这种情况,本文基于Fredlund非饱和土一维固结理论及等应变假设,引入变量将超孔隙压力耦合控制方程组转化为等价的线性偏微分方程组,考虑涂抹和井阻条件,并采用分离变量法和待定系数法,推导出了瞬时荷载下同时考虑井阻和涂抹作用的非饱和土竖井地基等应变固结解析解。将所得解析解进行退化,与既有的饱和土竖井地基等应变固结解析解对比,验证了本文解析解的正确性,并应用典型算例分析了井阻和涂抹作用对竖井地基固结的影响。结果表明,井阻因子G、井径比N、涂抹系数α及涂抹半径与竖井半径比S这四者任何一个值减小,非饱和土竖井地基的固结速度都将变快;井阻因子G小于0.1时,建议实际工程中不考虑井阻作用的影响;当涂抹半径与竖井半径比S大于5时,涂抹作用对竖井地基固结的影响与S=5时无明显差异。实际工程中建议提高非饱和土竖井地基的透水能力并减少施工扰动,以降低井阻和涂抹作用对非饱和土竖井地基固结影响。     

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。     

涂抹区重叠竖井地基固结特性研究

在软基处理工程中,经常出现竖井打设变密而地基固结效率降低的现象。鉴于此,建立了重叠涂抹区内土体水平向渗透系数的分布函数,给出了涂抹区重叠时竖井地基超静孔压和平均固结度的解析解。通过分析不同工况下竖井地基固结度随竖井间距的变化情况,探究了竖井间距减小而地基固结效率不增反减的成因。最后,探讨了涂抹作用和井阻作用对竖井最小临界间距的影响。结果表明：相邻竖井涂抹区重叠是竖井地基中出现竖井最小临界间距的根本原因。涂抹作用越大,则竖井最小临界间距越大;具体表现为当地基扰动程度增大时或涂抹区半径增大时,竖井最小临界间距随之增大。井阻作用越大,则竖井最小临界间距越小;具体表现为当竖井渗透系数减小时、竖井长度增大时或竖井半径减小时,竖井最小临界间距随之减小。     

砂墙地基二维固结自由应变解

将含竖向排水体地基的三维固结变形问题等效为平面应变问题进行数值分析时,砂墙地基二维固结解析解答是合理确定其等效固结计算参数的重要依据。为辨析现有砂墙地基等应变固结近似解答的适用性,针对微单元土体严格的二维固结微分方程,考虑对地基固结有重要影响的井阻作用,以及涵盖完全透水和不完全透水的更一般边界面排水条件,推求得到了其自由应变解答。并与现有解答进行对比分析,同时,分析了泊松比效应以及水平和竖向排水对地基固结的影响。结果表明,现有砂墙地基的等应变固结解答虽然近似,但已有足够精确;砂墙地基以水平向固结为主,竖向固结几乎可以忽略不计;地基固结速率随着泊松比的增大而增大,在将竖向排水体等效为砂墙时,应考虑其作用影响。     

Analytical solutions for consolidation aided by vertical drains

Soil disturbance caused during the installation of vertical drains reduces the in situ hydraulic conductivity of soft deposits in the immediate vicinity of the drains, resulting in a slower rate of consolidation than would be expected in the absence of disturbance. Experimental investigations have revealed the existence of two distinct zones, a smear zone and a transition zone, within the disturbed zone around the vertical drain. The degree of change in the hydraulic conductivity in the smear and transition zones is difficult to assess without performing of laboratory tests. Based on the available literature, four different profiles of hydraulic conductivity versus distance from the vertical drain were identified. Closed-form solutions for the rate of consolidation for each of these four hydraulic conductivity profiles were developed. It is found that different variations of the hydraulic conductivity profiles in the disturbed zone result in different rates of consolidation.     

Analytical solution to axisymmetric consolidation of unsaturated soil stratum under equal strain condition incorporating smear effects

This paper proposes closed‐form analytical solutions to the axisymmetric consolidation of an unsaturated soil stratum using the equal strain hypothesis. Following the 1‐dimensional (1D) consolidation theory for unsaturated soil mechanics, polar governing equations describing the air and water flows are first presented on the basis of Fick's law and Darcy's law, respectively. The current study takes into account the peripheral smear caused by an installation of vertical drain. Separation of variables and Laplace transformation are mainly adopted in the analytical derivation to obtain final solutions. Then, the hydraulic conductivity ratio, the radius of influence zone and smear parameters influencing time‐dependent excess pore pressures, and the average degree of consolidation are graphically interpreted. In this study, a comparison made between the proposed equal strain results and the existing free strain results suggests that both hypotheses would deliver similar predictions. Moreover, it is found that the smear zone resulting from vertical drain installations would hinder the consolidation rate considerably.     

基于非等温管道流竖井地基热排水固结模拟

针对新技术热排水固结法,采用非等温管道流模拟竖井中U型导热管的传热过程,考虑温度对竖井扰动区和未扰动区渗透性的影响,在COMSOL Multiphysics有限元软件中进行二次开发,建立了竖井地基热排水固结法的有限元模型。以热排水固结软基处理原型试验为例,重点分析了模型耦合、部分耦合和不耦合情况下软土地基的固结度。结果表明,相对于传统排水固结法的不耦合模型,部分耦合模型下因温度产生的孔压增量延缓了地基固结的发展,固结速率有所减慢;耦合模型下温度虽也产生一定的孔压增量,但温度有效地改善了竖井涂抹区土的渗透特性,地基的固结速率加快,固结周期缩短,与试验结果一致。     

A new analytical model for consolidation with multiple vertical drains

Various analytical theories of consolidation for soils with vertical drains have been proposed in the past. Most conventional theories are based on a cylindrical unit cell that contains only a single vertical drain. This paper described a new analytical model where a vertical drain located at the centre (the ‘inner vertical drain’) and is surrounded by two or three vertical drains (the ‘outer vertical drains’), the number of which depends on whether the configuration is triangular or rectangular. Both types of drains are combined into a cylindrical unit cell, and the water is assumed to flow both inwards to the inner vertical drain and outwards to the outer vertical drains distributed around the circumference. The outer radial boundary of the unit cell is regarded as a permeable boundary, with a drainage capacity of two or three separate vertical drains for triangular and rectangular configurations, respectively. The smear effects and the drainage resistances for both the inner and outer vertical drains are considered in the analysis as well. In this way, the equations governing the consolidation process with multiple vertical drains are derived, and the corresponding analytical solutions are obtained for instantaneously loading, ramp loading and multi‐stage of instantaneously loading and multi‐stage of ramp loading. The present solutions are finally compared with several conventional solutions for a single vertical drain in the literature. The results show that the present model predicts the same average degree of consolidation as conventional models do, which verifies the correctness of this new model. Finally, the settlement predicted by the present solution is compared with the measured settlement from a field test at the Port of Brisbane, Australia, which shows a good agreement between them. Copyright © 2016 John Wiley & Sons, Ltd.     

Analytical solutions for the consolidation of unsaturated foundation with prefabricated vertical drain

Based on the consolidation theory raised by Fredlund, the solutions for the equal-strain consolidation of unsaturated foundation with the prefabricated vertical drain considering smear effect and drain resistance are analytically formulated in this paper. Firstly, governing equations for excess pore pressures (i.e., excess pore-air and pore-water pressures) under the equal-strain hypothesis are derived with the introduction of radial boundary conditions. Afterwards, the obtained coupled equations are solved by applying general integration, decoupling process, and Fourier sine series expansion. The smear coefficients and factors of drain resistance corresponding to air and water phases are both captured explicitly in the final solutions. Furthermore, the degenerated solutions are employed to verify the reliability of the current solutions. Finally, a parametric study is conducted to study the consolidation characteristics of the proposed foundation model against modeling sizes (S and N), smear coefficients (α_a and α_w), and drain resistance factors (G_a and G_w).     

成层竖向排水井地基固结分析

实际工程中竖井地基具有成层性,有时竖井也并未完全打穿软土层。在竖井打设区满足竖井等应变固结理论、下卧层满足一维太沙基固结理论假设的基础上,将现有竖井地基固结理论推广到成层未打穿竖井地基情况。利用边界条件和竖直向连续条件,确定该系统的正交关系,并给出了其固结解答,该解具有广泛的适用性。通过对竖井打设区和下卧层层数的变化,即可获得现有关于简单未打穿竖井地基的固结解答。将该解答编制成应用程序,对一算例进行了分析。结果表明,平均固结度按孔压定义和按变形定义是不相同的,硬表层的存在会加快其下土层的固结。     

Consolidation of sensitive clay with vertical drain

The coefficient of consolidation is one of the most important parameters that control the rate of consolidation. Conventional consolidation theories assume that the coefficient of consolidation is constant during the whole consolidation process. In the case of sensitive clay, the coefficient of consolidation is strongly dependent on the level of effective stress of clay. With the dissipation of pore water pressure and the increase of effective stress, the soil structure of the upper subsoil is gradually destroyed downwards and its coefficient of consolidation becomes smaller. At the same time, the coefficient of permeability of the vertical drains drops down because of the kinking or bending effect. The destructured upper subsoil and the kinking of the vertical drain hinder the dissipation of the pore pressure in the lower subsoil. This paper presents a model to describe the above important phenomena during the consolidation of sensitive clay with vertical drain. The solution for proposed model can be obtained by extending the closed‐form solution of the consolidation of double‐layered ground with vertical drain by the interactive method introducing the concept of the moving boundary and the reduction of discharge capacity of vertical drain. The numerical results obtained from the finite element method package PLAXIS (Ver. 7.2) are adopted to compare those obtained from the present algorithm. Moreover, the rationality of the moving boundary is explained by the distributions of the excess pore water pressure in natural soil zone along the radial direction. Wenzhou airport project is taken as a case study in this paper. The results for the sensitive soil with decaying sand drain agree very well with the in situ measured data. The calculated results can properly explain two general phenomena observed in the consolidation of soft sensitive soil ground with vertical drains: one is that the time to achieve the same consolidation degree is much longer under heavy loading than that under light loading; the other is that the consolidation speed is much slower in the lower subsoil than in the upper subsoil. Finally, it is indicated that the vertical drains can decrease the hindrance effect of the destructured subsoil. Copyright © 2007 John Wiley & Sons, Ltd.     

粘性土-砂井地基单井固结模型的改进

单井固结模型的计算中通常将砂井周围土体简单划分为涂抹区和非涂抹区,不符合实际砂井周围土体的渗透系数分布复杂的事实。本文在Terzaghi固结理论的基础上提出了改进的单井固结模型,以一个待定参数流量系数Cq取代涂抹区和非涂抹区渗透系数来刻画砂井周围土体的横向渗透性特征,使单井固结问题得到高度简化又不失严密性。本文将改进模型用于非完整砂井单井固结的最终沉降量的数值计算,并将计算结果与谢康和改进法以及Hart法的解析解进行了比较,证明了改进模型数值解的可靠性。     

考虑涂抹区压缩及渗透系数变化的堆载预压固结解

为评估涂抹区土体压缩和渗透系数变化对含竖向排水体地基固结的影响,采用等体积应变假设,考虑涂抹区土体的压缩变形及其水平向渗透系数沿径向分别呈线性和抛物线分布,并考虑井阻作用以及地基附加球应力沿深度任意分布,推导了随时间线性堆载预压条件下固结微分方程的显式解析解答,分析了涂抹区半径、水平向渗透系数的分布模式、以及体积压缩系数对地基整体平均固结度的影响。结果表明,涂抹区土体采用均匀折减的水平向渗透系数明显低估了地基的固结速率,而当涂抹区半径较大时,不考虑涂抹区土体的压缩变形将会高估地基的固结速率。在含竖向排水体地基固结问题的分析中,这些影响不可忽视。     

Finite element consolidation analysis of soils with vertical drain

This paper presents a finite element procedure for the analysis of consolidation of layered soils with vertical drain using general one‐dimensional (1‐D) constitutive models. In formulating the finite element procedure, a Newton–Cotes‐type integration formula is used to avoid the unsymmetry of the stiffness matrix for a Newton (Modified Newton) iteration scheme. The proposed procedure is then applied for the consolidation analysis of a number of typical problems using both linear and non‐linear soil models. Results from this simplified method are compared with those from a fully coupled consolidation analysis using a well‐known finite element package. The average degree of consolidation, excess porewater pressure and average vertical effective stress are almost the same as those from the fully coupled analysis for both the linear and non‐linear cases studied. The differences in vertical effective stresses are tolerable except for the values near the vertical drain boundaries. The consolidation behaviour of soils below a certain depth of the bottom of vertical drain is actually one‐dimensional for the partially penetrating case. Therefore, there are not much differences in whether one uses a one‐dimensional model or a three‐dimensional model in this region. The average degree of consolidation has good normalized feature with respect to the ratio of well radius to external drainage boundary for the cases of fully penetrating vertical drain using a normalized time even in the non‐linear case. Numerical results clearly demonstrate that the proposed simplified finite element procedure is efficient for the consolidation analysis of soils with vertical drain and it has better numerical stability characteristics. This simplified method can easily account for layered systems, time‐dependent loading, well‐resistance, smear effects and inelastic stress–strain behaviour. This method is also very suitable for the design of vertical drain, since it greatly reduces the unknown variables in the calculation and the 1‐D soil model parameters can be more easily determined. Copyright © 2000 John Wiley & Sons, Ltd.     

任意附加应力下竖井径竖向耦合固结等应变解

竖向排水体包括砂井和塑料排水板已广泛应用于加速软黏土地基的固结。不同形式的轴对称条件下含竖向排水体均质各向同性地基的固结解析解答也相继被提出,而各种解答均假定地基中附加应力在竖向排水体的深度范围内是均匀分布的。显然,当竖向排水体深度与地面堆载区宽度的比值相对较高,或竖向排水体的影响区域靠近地面堆载区的边缘时,这个假定并不适用。为此,在现有径竖向耦合固结等应变解的基础上,提出任意分布的地基附加应力条件下的解答,并分析附加应力分布形式和线性加载速率对地基固结的影响。结果表明,均匀分布的附加应力条件下的解答低估了地基的固结速率,而瞬时加载条件下的解答则高估了地基的固结速率。     

复杂荷载作用下考虑下卧层三维渗流的未打穿竖井地基固结分析

针对任意复杂变荷载作用下未打穿的竖井地基,通过在竖井底面以下土层中设置虚拟竖井,使其能够合理考虑下卧层土体三维渗流问题,运用Laplace变换,求得频域内竖井地基的固结解。通过Laplace逆变换,得到了任意荷载作用下竖井地基的平均固结度、孔压消散曲线、沉降曲线。结合具体算例,对影响竖井地基固结的主要影响因素进行了详细分析,并将现有未打穿竖井地基平均固结度近似计算方法的精度和适用的范围进行了对比,得到了一些有益于工程实践的结论。     

考虑复杂荷载及井阻非线性时竖井地基固结解析解研究

根据浙江沿海地区滩涂围垦中的淤泥基础海堤工程设计经验,认为软土工程中竖井地基固结计算需考虑井阻随时间的影响,基于竖井渗透系数随时间指数衰减关系假定,利用竖井地基径向固结理论和等应变假设,并考虑多级线性加载及循环荷载等复杂荷载作用,重新推导了考虑井阻非线性影响下竖井地基固结解析解,通过与TANG X W等(2000)、Zhu G等（2004）恒定井阻地基固结理论的对比,验证了本文理论的正确性。根据本文理论,通过对比分析,认为线性加载时间越长,竖井地基前期固结速率越慢,与骤加恒载工况差异越显著。在循环荷载作用下,地基固结速率一般介于荷载最大值和荷载最小值的恒载情况之间;且固结度随外荷载的波动而相应地滞后性震荡,竖井渗透系数衰减越快,其震荡越明显,最终趋向于稳定震荡。     

考虑温度耦合效应的竖井地基固结有限元分析

针对塑料排水板(PVD)安装热源能提升PVD性能、加速竖井地基固结这一工程现象,基于热-水-应力 (T-H-M) 三场全耦合的有限元方法来模拟利用热源进行地基处理新技术(PVTD)。首先,以微分形式与等效弱形式分别给出T-H-M耦合控制方程,并推导出其有限元方程组。然后在多场耦合有限元软件中建立饱和土的T-H-M全耦合模型,并通过与已有解析解比较,验证了模型正确性。最后,对一个经典有涂抹区的竖井地基算例,分不耦合温度(UT)、耦合温度但不考虑其对饱和土物性影响(CT)、耦合温度考虑温度对饱和土渗透性影响(CTP) 3种情况进行固结计算分析。研究结果表明,相对于无热源竖井地基,CT情况下由于热源产生的附加孔隙水压力,固结速度略有下降;CTP情况下,由于热源有效改善涂抹区的渗透性能,竖井地基固结速率明显加快。上述研究结论从理论上较好地阐明了PVTD的作用机制。     

考虑涂抹区渗透系数变化的非饱和土砂井地基固结特性分析

在以往对非饱和土砂井地基固结理论研究中,均将涂抹区与非涂抹区土体渗透系数视为相等,这与实际工程并不相符。本文将考虑涂抹区土体渗透系数的变化,分析其对超孔隙气、水压力消散规律的影响。基于Fredlund一维固结理论以及Darcy定律和Fick定律,对有限厚度线弹性非饱和土砂井地基,在大面积均布瞬时荷载作用下,考虑涂抹区土体渗透系数的变化,利用Laplace变换并引入Bessel函数推导出Laplace变换下的解,再通过Crump方法编程实现Laplace逆变换得到超孔隙气压力、超孔隙水压力的半解析解。利用典型算例进行计算,分别得到在不同半径、不同涂抹区半径和不同涂抹程度的情况下,超孔隙气压力、超孔隙水压力随时间的变化规律。得出考虑涂抹作用时,超孔隙气、水压力的消散速度降低;涂抹区半径越大、涂抹程度越高速度越慢,反之消散越快。本研究丰富了非饱和土砂井固结理论,对非饱和土砂井固结特性的研究具有一定的工程参考价值。     

考虑影响区真实形状的竖向排水井地基固结解

针对现有竖向排水井地基固结解析理论对影响区一律采用圆形等效假定的缺陷,研究了影响区真实形状为正六边形的按梅花形布置的竖向排水井地基的固结问题。通过建立新固结方程和引入新的边界条件,并考虑土体水平渗透系数变化,得到了相应的解析解。对于土体水平渗透系数的3种变化模式,分别给出了各种模式下的特殊解。在此基础上,分析了3种模式下3个主要的无量纲参数对地基固结性状的影响,并比较了计算结果和现有理论结果。分析结果表明,影响区和涂抹扰动区范围越大,固结越慢;土体的最大与最小水平渗透系数之比越小,固结越快;在相同条件下,考虑扰动区渗透系数线性变化的模式2固结最快,而假定扰动区渗透系数不变的模式1的解与现有理论解相当接近,验证了现有竖向排水井地基固结解析理论中对影响区采用圆形等效假定的合理性