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...     

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。     

真空预压加固软土地基变形与固结计算研究

考虑真空度的衰减情况,对真空预压加固软基的变形和固结度计算方法进行了研究。先根据真空预压时砂井的真空压力状态建立了真空预压的空间轴对称变形模型,用位移法推导该模型在等应变条件下的变形及体积应变计算公式。在此基础之上结合Hansbo砂井地基固结理论和真空预压的边界条件,推导了忽略竖向渗流情况下的真空预压加固软土地基的固结解析解。比较文中计算方法与已有计算理论和现场试验实测资料结果表明,体积应变的计算对真空预压的孔压和固结度的计算有较大的影响,而直接引用传统堆载预压的体积应变计算公式计算会导致较大误差。在固结度计算中,采用Hansbo的近似方法能满足计算精度的要求,所得计算结果与实测结果吻合较好     

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     

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。     

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。     

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。     

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。     

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.     

A closed form analytical solution for two‐dimensional plane strain consolidation of unsaturated soil stratum

This paper discusses the excess pore‐air and pore‐water pressure dissipations and the average degree of consolidation in the 2D plane strain consolidation of an unsaturated soil stratum using eigenfunction expansion and Laplace transformation techniques. In this study, the application of a constant external loading on a soil surface is assumed to immediately generate uniformly or linearly distributed initial excess pore pressures. The general solutions consisting of eigenfunctions and eigenvalues are first proposed. The Laplace transform is then applied to convert the time variable t in partial differential equations into the Laplace complex argument s. Once the domain is obtained, a simplified set of equations with variable s can be achieved. The final analytical solutions can be computed by taking a Laplace inverse. The proposed equations predict the two‐dimensional consolidation behaviour of an unsaturated soil stratum capturing the uniformly and linearly distributed initial excess pore pressures. This study investigates the effects of isotropic and anisotropic permeability conditions on variations of excess pore pressures and the average degree of consolidation. Additionally, isochrones of excess pore pressures along vertical and horizontal directions are presented. It is found that the initial distribution of pore pressures, varying with depth, results in considerable effects on the pore‐water pressure dissipation rate whilst it has insignificant effects on the excess pore‐air pressure dissipation rate. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

碎石桩复合地基大变形非线性固结模型

基于分段线性差分法,建立了一种碎石桩复合地基大变形非线性固结模型SC1。该模型可以进行等应力和等应变条件下桩土复合地基固结分析,同时能够考虑涂抹区、井阻、桩土自重、变荷载,以及固结过程中桩土参数的非线性变化和大变形问题,并编制了 Fortran 计算程序。分别采用基于等应变假设的桩土复合地基解析解和室内试验数据验证了模型的正确性,小变形条件下,该模型数值解与有无井阻及涂抹区的桩土复合地基解析解均能较好吻合;大变形非线性条件下,模型计算结果与室内试验数据基本一致。采用该模型预测实际工程,随固结时间延长,模型等应力与等应变的沉降量计算值相差逐渐增大,现场实测值介于等应力和等应变条件下模型计算结果之间。     

A new simplified Hypothesis B method for calculating the consolidation settlement of ground improved by vertical drains

Vertical drains are widely used in soft ground improvements to accelerate the consolidation process. This paper develops a new simplified Hypothesis B method for calculating the consolidation settlement of a soil layer improved by vertical drains under the instant and ramp loadings. As a comparison, the traditional Hypothesis A method is also used to calculate the settlement. Then, a fully coupled finite element consolidation analysis is utilized to examine and verify this simplified method and Hypothesis A method. For the instant loading, Carrillo‐Barron method and Zhu‐Yin method are used to obtain the average degree of consolidation for vertical drain system. Typical parameters, such as over‐consolidation ratio (OCR), smear zone, and space ratio of vertical drains, are considered. It is found that the calculation results from the new simplified method in this study agree well with finite element simulations, and relative errors are in the range of 0.1% to 12.3%. Comparatively, there are obvious differences between the calculated results from Hypothesis A method and finite element results. Carrillo‐Olson method and Zhu‐Yin method are utilized to obtain the average degree of consolidation for the vertical drain system to consider the ramp loading. Equivalent time is determined from half of the construction period to calculate the creep compression under the ramp loading. The accuracy of this simplified Hypothesis B method using both Carrillo‐Olson method and Zhu‐Yin method is acceptable with the relative errors less than 9.4%.     

考虑土体非线性的CCSG桩复合地基固结解

混凝土芯砂石桩（CCSG）桩复合地基是一种新型多元复合地基。通过引入地基土体的e-lgσ和e-lgk对数模型,考虑地基土体固结过程中压缩模量和渗透系数非线性变化的特征,推导出基于等应变假设的CCSG桩复合地基非线性固结解析解,且现有的考虑土体非线性的砂井固结解和碎石桩复合地基固结解均是文中解的特例。根据该解析解得到桩土模量比、土体压缩指数与渗透指数比、荷载增量等无量纲参数变化时,CCSG桩复合地基的固结度曲线。分析结果表明,按应力和按变形定义的两种固结度不相等,通常按变形定义的固结速度较快;土体压缩模量和渗透系数的非线性变化对固结影响较大。最后通过和由实测数据获得的固结度曲线对比,验证了解析解的正确性。     

Consolidation of double‐layered ground with vertical drains

Vertical drains are usually installed in subsoil consisting of several layers. Due to the complex nature of the problem, over the past decades, the consolidation properties of multi‐layered ground with vertical drains have been analysed mainly by numerical methods. An analytical solution for consolidation of double‐layered ground with vertical drains under quasi‐equal strain condition is presented in this paper. The main steps for the computation procedure are listed. The convergence of the series solution is discussed. The comparisons between the results obtained by the present analytical method and the existing numerical solutions are described by figures. The orthogonal relation for the system of double‐layered ground with vertical drains is proven. Finally, some consolidation properties of double‐layered ground with vertical drains are analysed. Copyright © 2001 John Wiley & Sons, Ltd.     

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。     

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。     

非饱和土一维大变形固结模型

基于分段线性差分法,建立了一种非饱和土一维大变形固结模型。该模型可考虑土性参数非线性变化,可计算与分析大变形问题,并编制了Fortran计算程序。在现有解答和试验数据的基础上,对该模型进行了验证,瞬时加载情况下模型数值解与现有解答基本吻合,考虑加载过程下的数值解与试验数据吻合。进行了大变形算例分析,对比了加荷压密与消散固结阶段土层变形,探讨了孔隙气、水渗透系数比对土层沉降量、饱和度和不同应变情况下固结度的影响规律,分析了非饱和土大、小变形固结理论计算孔隙水（气）压和沉降量的差异。