碎石桩复合地基非线性固结解析解

通过引入土体的e-lgσ和e-lgk对数模型,考虑了土体固结过程中压缩模量非线性增长和渗透系数非线性减小的特征,给出了一种碎石桩复合地基非线性固结解析解,并对复合地基的非线性固结性状进行了分析。结果表明,按应力和按变形定义的两种固结度不相等,按变形定义的固结度一般大于按应力定义的固结度;当压缩指数小于渗透指数时,不考虑土体的非线性特征会低估地基的固结度,而当压缩指数大于渗透指数时,不考虑土体的非线性则会高估地基的固结度;对于按应力定义的固结度来说,当压缩指数小于渗透指数时,随着附加应力的增大,地基固结速度加快,而当压缩指数大于渗透指数时,附加应力增大,地基固结减慢;对于按变形定义的固结度来说,不论压缩指数大于还是小于渗透指数,附加应力增大,地基固结速度总是加快。     

An analytical solution for the consolidation around a driven pile

Field studies have shown that the driving of a displacement pile into cohesive soil generates large excess pore pressures in the vicinity of the pile. These pore pressures are often larger than the effective overburden pressure and facilitate the installation of the pile. The subsequent increase in bearing capacity of the pile is largely controlled by the dissipation of the excess pore pressures and a consequent increase in the effective stresses acting on the pile. The paper presents a closed formanalytical solution for the radial consolidation of the soil around a driven pile, assuming that the soil skeleton deforms elastically. This assumption is examined in the light of the predicted effective stress changes in the soil and is shown to lead to, a realistic model for the decay of pore pressure near the pile with time after driving. Although the solution may be applied to any initial distribution of excess pore pressure, attention is focussed on that due to the expansion of a cylindrical cavity in an ideal elastic, perfectly plastic soil. The resulting logarithmic variation of excess pore pressure with radius is considered to be close to that generated around a pile as a result of driving. In addition to giving estimates of the time needed for a driven pile to achieve its maximum strength, the solution may also be used in the analysis of pressuremeter tests to provide in-situ measurements of the coefficient of consolidation of the soil.     

Consolidation around stone columns. Influence of column deformation

A solution is presented for the radial consolidation around stone columns under constant surcharge load. The solution considers the influence of vertical and radial deformation of the column, either in elastic and elastoplastic regimes. The solution is in terms of the average excess pore pressure in the soil. It is based on previous solutions, initially developed for rigid column, or including only vertical deformation. For elastic column, the solution gives the variation of strains and stresses between the undrained and final states, for which it coincides with the existing elastic solutions. All the results are given in closed form, and both the elastic and plastic deformations of the column lead to an equivalent coefficient of consolidation for the radial flow, which enables the application of the existing methods of integration of the consolidation equation. A parametric study is presented, showing the influence of the main problem features. A design example is used to illustrate the application to practical cases. Copyright © 2008 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。     

Viscosity effect on consolidation of poroelastic soil due to groundwater table depression

In this study, the viscosity effect on consolidation of poroelastic soil due to groundwater table depression is examined. A viscoelastic consolidation numerical model is developed to conduct this examination. By nondimensionalizing the governing equations the viscosity number that depends on hydraulic conductivity, viscous moduli, and thickness of soil is obtained to represent the viscosity effect on consolidation of poroelastic soil. The case of clay stratum sandwiched between sandy strata subjected to sudden and gradual groundwater table depressions is used to investigate the importance of viscosity effect to poroelastic consolidation. The results show that the displacement and pore water pressure of clay stratum are strongly related to the viscosity effect. The overestimation of soil displacement will occur if the viscosity effect is neglected. Hence, the viscosity effect needs to be considered in modeling consolidation of poroelastic soil under groundwater table depression.     

Analytical solution for the 1D consolidation of unsaturated multi-layered soil

The 1D consolidation of unsaturated multi-layered soil is studied based on the theory proposed by Fredlund and Hasan, and an analytical solution for a typical boundary condition is obtained by assuming all material parameters remain constant during consolidation. In the derivation of the analytical solution, the eigenfunction and eigenvalue for the multi-layered problem are first derived through the transfer matrix method. Then, by using the method of undetermined coefficients and the orthogonal relation of the eigenfunction, the analytical solution is obtained. The present method is applicable to various types of boundary conditions. Finally, numerical examples are provided to investigate the consolidation behavior of unsaturated multi-layered soil.     

Fully coupled elastoplastic hydro-mechanical analysis of unsaturated porous media using a meshfree method

This paper presents the first application of an advanced meshfree method, ie, the edge-based smoothed point interpolation method (ESPIM), in simulation of the coupled hydro-mechanical behaviour of unsaturated porous media. In the proposed technique, the problem domain is spatially discretised using a triangular background mesh, and the polynomial point interpolation method combined with a simple node selection scheme is adopted for creating nodal shape functions. Smoothing domains are formed on top of the background mesh, and a constant smoothed strain, created by applying the smoothing operation over the smoothing domains, is assigned to each smoothing domain. The deformation and flow models are developed based on the equilibrium equation of the mixture, and linear momentum and mass balance equations of the fluid phases, respectively. The effective stress approach is followed to account for the coupling between the flow and deformation models. Further coupling among the phases is captured through a hysteretic soil water retention model that evolves with changes in void ratio. An advanced elastoplastic constitutive model within the context of the bounding surface plasticity theory is employed for predicting the nonlinear behaviour of soil skeleton. Time discretisation is performed by adopting a three-point discretisation method with growing time steps to avoid temporal instabilities. A modified Newton-Raphson framework is designed for dealing with nonlinearities of the discretised system of equations. The performance of the numerical model is examined through a number of numerical examples. The state-of-the-art computational scheme developed is useful for simulation of geotechnical engineering problems involving unsaturated soils.     

土体三轴试验固结过程解析解

三轴试验是获取土体强度和应力变形特性的一个重要室内试验手段。三轴试验中,排水固结阶段试样的孔压消散及固结完成情况是非常重要的两个核心要素,它是进行后续剪切试验的基础和依据。基于等应变假设,推导了土体三轴剪切试验排水固结过程的解析解,以用于分析整个排水固结过程的孔压消散和固结完成程度。针对室内三轴固结排水(CD)试验,利用所推导的解析解对其排水固结过程的孔压和固结度进行了验算对比。结果表明,解析解计算得到的固结度和孔压消散曲线与室内三轴剪切试验的相应曲线吻合得较好,说明解析解可应用于三轴剪切试验排水固结过程分析。     

软土一维非线性固结近似解析解

软土非线性固结变形计算目前还主要依赖于数值方法,致使非线性固结理论的工程应用受到极大限制。引入经典的e-lg?' 和e-lgkv非线性关系,在自重应力均匀分布假定下通过变量代换并利用迭代法给出压缩指数Cc与渗透指数Ck比值不等于1时的非线性固结近似解析解。在Cc /Ck趋近1时本文解与其等于1时的差分解及精确解相差无几。但如果Cc /Ck值偏离1,该近似解会存在一定偏差,且偏差值会随Cc /Ck值偏离1的程度和外荷载增加而逐渐增大。在一般工程荷载作用下,如果Cc /Ck值介于0.9～1.1之间,本文解的平均固结度与差分解间最大偏差在2%左右。当Cc /Ck值在0.75～1.25之间时,本文解的平均固结度与差分解最大偏差在5%左右。如果Cc /Ck值在0.5～1.5之间,本文解的平均固结度与差分解间最大偏差在10%左右。当外荷载一定时,土层的非线性固结速率会随着Cc /Ck值的增大而减慢。如果Cc /Ck<1,土层的非线性固结速率会随外荷载的增大而加快;相反,如果Cc/Ck>1,土层的非线性固结速率会随外荷载增大而减慢。     

An analytical solution of one-dimensional consolidation for soft sensitive soil ground

An analytical solution of one-dimensional consolidation for soft sensitive soil ground is presented. The moving boundary is introduced to indicate the notable change of consolidation behaviour of sensitive soil with the increase of stress level. It is assumed that the soil structure of the upper subsoil gradually destroys downwards with the dissipation of pore pressure, and the coefficient of consolidation as well as the coefficient of permeability of the upper subsoil become small, which hinders the dissipation of pore pressure of the lower subsoil. The consolidation degree curve obtained from the present solution is found to lie between the two curves obtained from Terzaghi one-dimensional consolidation solution with the parameters of the undisturbed soil and the remolded soil. The calculated results provide a new explanation for a general phenomenon in the consolidation of soft sensitive soil ground, as that for high loadings the consolidation is longer than for small ones. It should be pointed out from this study that both the deep mixing method and the long vertical drains methods are effective techniques for improving deep sensitive soil ground. Copyright © 2004 John Wiley & Sons, Ltd.     

Dual-porosity elastoplastic analyses of non-isothermal one-dimensional consolidation

A numerical solution, using the finite difference method, and based on a porothermo-elasto-plastic formulation for dual-porosity one-dimensional consolidation has been presented. The model is fully coupled to ensure the interactive behavior of fluid flow, heat flow and solid deformations in the conservation of momentum, mass and energy equations. A bi-linear stress-strain relationship is used to accommodate elastoplastic deformation behavior. A double effective stress law, proposed by Elsworth and Bai (1992), is applied to describe constitutive relationships among the stresses, pressures and temperatures. In order to examine the dual-porosity and thermal effects on the soil consolidation individually, isothermal and non-isothermal consolidations for a dual-porosity column are analyzed. In comparison to the single porosity approach, the present study shows that the pore pressure dissipation is faster and Mandel's effect (Mandel, 1953) is more pronounced at early times of the source disturbance for dual-porosity consolidation. One of the significant parameters affecting the dual-porosity consolidation is the fracture spacing (fracture density); the smaller the fracture spacing, the faster the column drainage.     

深层搅拌桩周围土体劈裂的研究与分析

现场测试结果表明：深层搅拌桩施工可以在周围土体中产生很高的超静孔隙水压力,其量值可能超过土体的静水劈裂压力。搅拌桩施工时和周围土体的相互作用可以用受剪的孔穴扩张过程来模拟。针对搅拌桩施工引起的周围土体的劈裂现象,提出了一种基于拉伸破坏原理的劈裂分析方法。分析结果表明：搅拌叶片的旋转对桩周围土体的劈裂起着很重要的作用。通过室内模型桩打设试验可以观测到搅拌桩周围土体的劈裂现象。分析现场搅拌桩施工时桩周土体中的孔隙水压力测试结果,表明现场施工可以引起劈裂。劈裂裂缝对于搅拌桩的性状有如下两方面的正面作用：其一,水泥浆体可以流入劈裂裂缝;其二,超静孔隙水压可以通过劈裂裂缝快速消散。这两者的作用加快了受扰动的周围土体的强度恢复。     

Axisymmetric consolidation of a poroelastic soil layer with a compressible fluid constituent due to groundwater drawdown

Axisymmetric consolidation of a poroelastic soil layer with a compressible fluid constituent induced by groundwater drawdown was studied based on Biot’s axisymmetric consolidation theory. Laplace and Hankel transforms were employed to solve the governing equation. Explicit analytical solutions are obtained in the Laplace–Hankel transform domain when groundwater drawdown is induced by a constant pumping well. Based on the solutions, numerical computations were performed to study the influences of the compressibility of the fluid constituent on the consolidation behavior of the soil layer.     

An explicit one-dimensional consolidation solution with semi-permeable drainage boundary for unsaturated soil

Existing solutions for analyzing one-dimensional (1-D) consolidation of unsaturated soil are only derived to cater to two extreme drainage conditions (fully drained and undrained). This study presents a new explicit solution for 1-D consolidation of unsaturated soil with semi-permeable drainage boundary. Based on the assumptions of two independent stress variables and the governing equations proposed by Fredlund, the eigenfunction expansion method is adopted to develop an explicit analytical solution to calculate excess pore-water and pore-air pressures in an unsaturated soil when it is subjected to external loads. The developed general solutions are expressed in terms of depth, z, and time, t. For the semi-permeable drainage boundary, eigenvalues and eigenfunctions in the space domain are developed. The technique of Laplace transform is used to solve the coupled ordinary differential equations in the time domain. The newly derived explicit solution is verified with the existing semi-analytical method in the literature, and an excellent agreement is obtained. Compared with the semi-analytical solution, the newly derived analytical solution is more straightforward and explicit so that this solution is relatively easier to be implemented into a computer program to carry out a preliminary assessment of 1-D consolidation of unsaturated soil.     

分数阶导数黏弹性饱和土体一维固结半解析解

将分数阶微积分理论引入Kelvin-Voigt本构模型,以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上述分数阶导数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,从而获得了物理空间一维固结问题的半解析解,并将其退化到弹性和黏弹性两种经典情形,分析表明,它与经典解析解完全相同,这证明了经典弹性和黏弹性解析解可视为本研究提出分数阶导数黏弹性解的特例。开展了参数研究,即分析了相关各种参数对固结沉降的影响。研究表明,瞬时荷载情形下分数阶导数黏弹性饱和土体一维固结最终沉降量与黏滞系数和分数阶次无关,而不同黏滞系数和分数阶次对固结时间有较大影响。其研究结果有助于深入认识黏弹性饱和土体的固结力学行为。     

Equal strain consolidation for stone columns reinforced foundation

Column consolidation and deformation are considered by assuming that the quantity of water flowing through the disturbed soil zone into the column is not equal to that flowing out from the column and the difference between them is equal to the volume change of the column. In addition, three patterns of distribution of the horizontal permeability of soil in the disturbed zone are also considered to account for the disturbance effect of columns construction on the surrounding soil. These three patterns include the constant distribution pattern (Pattern I), the linear distribution pattern (Pattern II) and the parabolic distribution pattern (Pattern III). By incorporating the aforementioned characteristics into the analyses, the governing equations containing two variables (i.e. the average excess pore-water pressures within the column and within the entire foundation at any depth) for the consolidation of a composite foundation are derived. The solutions of the governing equations are then obtained using a new initial condition derived from the assumption of equal strain and the equilibrium condition. On the basis of the solutions for excess pore-water pressures, the average degree of consolidation of a composite foundation is obtained and discussed. Finally, a comparison is made of some available solutions. Copyright © 2009 John Wiley & Sons, Ltd.     

群桩桩间横观各向同性土体固结问题级数解

通过分析群桩成桩后桩间土体固结的边界条件和初始条件,建立了饱和黏土中群桩桩间横观各向同性土体的空间轴对称固结问题的定解条件,应用数学物理方法求得该问题的级数解。通过土体固结与桩承载力的时效性之间的关系,利用承载力的实测资料换算得到的等效固结度,验证了解的合理性和适用性。同样,应用级数解求得的桩间土体的固结度可用于群桩基础的承载力的时效分析。     

饱和黏土中单桩桩周土空间轴对称固结解

通过分析单桩成桩后桩周土体固结的边界条件和初始条件,建立了饱和黏土中单桩桩周横观各向同性土体的空间轴对称固结问题的定解条件,应用数学物理方法求得该问题的级数解答。通过土体固结与桩承载力的时效性之间的关系,利用承载力的实测资料换算得到的等效固结度,验证了解答的合理性和适用性。同样,应用级数解答求得的桩周土体的固结度可用于桩的承载力的时效分析。     

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。     

基于数值建模方法的弹塑性固结问题解耦研究

研究了弹塑性固结问题的解耦方法。首先,在数值建模方法下得出土的弹塑性本构关系,推导了两类问题下的应力-应变关系统一矩阵式,并将数值建模方法与Biot固结理论相结合,建立了基于此本构关系的固结问题控制方程的增量形式。考虑应力路径的影响,讨论了此类液-固耦合问题的解耦条件,导出了在该条件下的扩散方程和非耦合控制方程,并编制有限元程序计算了两个典型算例,通过对比分析表明,该方法简单合理,能考虑剪胀性对固结规律的影响。