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。     

考虑径向渗透系数变化的真空预压竖井地基固结解析解

针对真空预压条件下竖井地基固结问题,考虑竖井地基扰动区土体径向渗透系数变化的3种模式(扰动区渗透系数为常数、线性变化、抛物线变化)和竖井井阻随时间变化等因素影响;建立数学计算模型,采用解析解法,推导了考虑径向渗透系数因施工扰动而变化的真空预压竖井地基固结问题的解析解。基于此解,编制了计算程序,绘制出了考虑扰动区土体径向渗透系数变化和竖井井阻随时间变化影响的真空预压竖井地基固结曲线图。研究表明:井阻变化率对固结速率有较大影响;在土体扰动区径向渗透系数变化的3种模式中,渗透系数为抛物线变化时固结速率最快,渗透系数为线性时次之,渗透系数为常数时固结速率最慢。     

线性加载下塑料排水板地基固结理论探讨

针对目前国内外塑料排水地基固结计算均近似采用砂井等效模型的不足,本文将塑料排水板等效为形状极为接近的扁椭圆柱体,根据同焦椭圆柱理论及等应变假设,推导了线性加载下塑料排水板地基的固结解析解;根据ADINA有限元计算及现有学者数值计算成果对比验证了本文理论的正确性。通过与目前不同砂井等效模型对比分析,认为在理想竖井的二维平面固结理论下,本文理论与Long & Covo等效法“d_w=0.5b+0.7δ”较为接近,说明扁矩形截面的排水“形状效应”比等面积圆形截面更优;对于考虑井阻影响时,我国《海堤工程设计规范》（GB/T 51015-2014）以及《真空预压加固软土地基技术规程》（JTS147-2-2009）中建议的等效法均具有一定误差,建议采用本文理论计算。此外,地基荷载线性加载时间越长,地基前期固结速率越慢,与骤加恒载情况差异越显著。     

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。     

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。     

考虑漏气及井阻非线性的真空预压地基固结解析解

基于径向固结理论和等应变假设,考虑真空预压过程中真空泵故障、漏气等不利影响以及排水体井阻时空非线性影响,推导了以排水体中超静孔隙水压uw为函数的3阶拟线性偏微分方程,并将膜下真空度随时间的变化曲线作为边界条件,考虑吹填土的自重固结影响,分别给出了真空预压地基考虑漏气影响且排水体渗透系数随深度线性衰减及时间指数衰减时的固结解析解。最后通过与现有多个固结解的对比分析,认为它们一般为新解的特例,并通过算例计算比较分析,认为井阻随时间影响参数A_2对固结度的影响比随深度影响参数A_1更敏感。当参数A_2足够大时,则认为排水体很快就淤堵以至于不具备排水能力,参数A1则可等效反映真空度随深度的衰减影响,且真空预压过程中漏气对地基固结度具有直接影响,漏气越严重则固结排水越慢,需延长真空预压时间,以保证真空预压效果。     

考虑加载过程及桩体固结变形的碎石桩复合地基固结解析解

为了完善碎石桩复合地基固结理论,通过假设从桩体排出的水量等于流入桩体的水量与桩体体积变化之和以及地基扰动区土体水平渗透系数呈线性变化,并考虑上部荷载逐渐施加,推导了考虑桩体体积变化的碎石桩复合地基超静孔压及固结度解析解。当加载时间趋于零时,本文解可退化为瞬时加载情况下的解;当加载时间及桩径同时趋于零时,本文解可进一步退化为Terzaghi一维固结解,这证明了本文解的正确性。通过与已有解的比较,对地基固结性状进行了分析。结果表明,加载过程对地基固结度影响显著,加载历时越长,固结越慢;在各种条件下,不考虑桩体固结变形时地基固结始终比考虑桩体变形时快,并且其影响随着加载历时变小、桩径比变小、桩土模量比变小、桩土渗透系数变小而逐渐增大,这说明在实际工程固结计算中不考虑桩体固结变形是偏于不安全的。     

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。     

变荷载下考虑三维渗流的未打穿砂井地基固结分析

为探讨未打穿砂井地基的固结特性,基于三维固结理论和叠加原理,考虑变荷载条件,将砂井打设区和下卧层土体的固结均视为三维问题,分别导出了单级线性加载条件下砂井打设区和下卧层土体的固结度解析解,由此给出了地基整体的平均固结度计算式,并引入fzero函数基于Matlab编制了相应的计算程序。算例对比分析结果表明,受加载历时影响,砂井打设区和下卧层土体的固结度都较瞬时加载有所减小,且减幅随加载历时延长而增大。同时,将下卧层土体的固结视为三维要比一维更能合理考虑径向渗流,使得地基固结度计算值与模型试验推算值吻合较好     

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。     

Consolidation of vertical drain with depth-varying stress induced by multi-stage loading

An explicit analytical solution is developed for the consolidation of vertical drain with both radial and vertical drainage by adopting a depth-varying stress induced by multi-stage loading. The well resistance and smear effect are also considered. The smear effect is described by three decay patterns of horizontal permeability towards drains within the smeared zone, including a reduced constant pattern, a linear decay pattern and a parabolic decay pattern. A parameter analysis is performed to investigate the consolidation behavior of the vertical drain. The convergence of the proposed series solution is discussed.     

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。     

一种竖井地基竖墙化等效计算方法

考虑井阻作用,推导了等应变条件下竖墙地基水平向固结解析解,并与等应变条件下的竖井地基径向固结解析解进行比较,得到竖墙地基平面应变问题和竖井地基轴对称问题之间的等效方法。该方法转换公式简单,且能保证两种情形下同一深度处平均孔压在任一时刻相等,确保了转换为平面应变有限元分析的准确性。     

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.     

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.