Finite layer analysis of consolidation. II

The theory developed in Part I of this paper is extended to apply to the consolidation of horizontally layered soils under both axially symmetric and general surface loading. The method again leads to a considerable reduction in the amount of core storage necessary for computer solution and can be implimented on a mini-computer.     

Finite element consolidation analysis of embankments

The construction of earth embankments may lead to the development of excess pore pressures in foundation and embankment soils. The ability to predict the development and dissipation of these pore pressures is important in assessing the performance of such structures. This paper describes a finite element analysis method that allows the prediction of the behaviour of embankments including stress-deformation and consolidation behaviour. The application of the method is demonstrated through application to a reinforced embankment on peat and clay and to a high rockfill dam.     

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.     

Finite layer analysis of viscoelastic layered materials

A method is presented for obtaining the creep settlement of strip or circular loadings applied to horizontally layered soil profiles. The solution method involves applying a fourier (strip loading) or Hankel (circular loading) transform to the governing equations, which reduces the two of three dimensional problem to one involving a single spatial demension. This leads to great savings in computer storage and data preparation time, and since an exact solution may be found for each layer of material, the method has advantages over conventional finite layer techniques where field quantities must be approximated at a number of positions within each layer. The type of formulation presented hearein makies it possible to work in terms of the creep functions of the soil rather than the relaxation functions. This has distinct advantages, as it is often easier to measure the creep behaviour of a soil in the laboratory. Numerical techniques are used to invert the laplace and Hankel transforms and this means that any type of creep function (which is invertible) may be used to describe the material properties of the soil.     

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。     

横观各向同性土体有限层分析

首先概括介绍了三维横观各向同性比奥固结有限层分析方法,并采用已经发表的4个算例结果来考证所编制的计算程序,然后详细地讨论了横观各向同性对瞬时沉降、最终沉降和固结性状的影响,发现横观各向同性对计算结果的影响分别高达33 %,24 % 和40 %,最后给出了一些对工程实践有一定参考价值的计算图表。     

地下水向水平井三维流动的有限层分析

基于地下水向水平井三维流动数学模型,利用半解析数值分析原理推导了层状各向异性承压含水层有限层方程,给出了水平井源汇项计算公式,编制了相应的计算程序,实现了有限层方程的求解。通过算例的解析解和有限差分解验证了有限层法及程序的正确性,对比分析了有限层法与有限差法的计算效率。结果表明,有限层法适于层状各向异性承压含水层中地下水向水平井三维流动问题的模拟分析,且具有较高的计算效率。     

考虑流变性状的软土地基固结有限元分析

对具有流变性状的软土地基固结特性进行了研究,编制了相应的有限元程序。利用该程序对某高速公路软土地基固结问题进行了计算和分析。通过计算结果与实测结果的对比可得到以下结论：在软土地基的固结变形计算中,考虑流变性状的影响是必要的,其计算值与实测值比较吻合。     

Finite layer analysis of laterally loaded piles in cross-anisotropic soils

This paper presents a finite layer method for the analysis of laterally loaded piles in isotropic and cross-anisotropic layered soils. Excellent agreement is found between the isotropic solutions computed by the finite layer method and the more rigorous finite element method. Some theoretical solutions are presented to demonstrate the effect of soil anisotropy. Two full scale field case histories have been analysed by the method using isotropic and cross-anisotropic soil models.     

Finite element analysis of consolidation of layered clay soils using an elastic visco-plastic model

This paper presents a general one-dimensional (1-D) finite element (FE) procedure for a highly non-linear 1-D elastic visco-plastic (1-D EVP) model proposed by Yin and Graham for consolidation analysis of layered clay soils. In formulating the 1-D FE procedure, a trapezoidal formula is used to avoid the unsymmetry of the stiffness matrix for a Newton (modified Newton) iteration scheme. Unlike many other 1-D FE approaches in which the initial in situ stresses (or stress/strain states) are considered indirectly or even not considered, the initial in situ stress/strain states are taken into account directly in this paper. The proposed FE procedure is used for analysis of 1-D consolidation of a clay with published test results in the literature. The FE modelling results are in good agreement with the measured results. The FE model and procedure is then used to analyse the consolidation of a multi-layered clay soils with a parametric study on the effects of the variations of creep parameters in Yin and Graham's 1-D EVP model. It is found that the creep parameters ψ/V and t₀ have significant influence on the compression and porewater pressure dissipation. For some boundary conditions, changes of parameters in one layer will have some effects on the consolidation behaviour of another layer due to the different consolidation rates. Finally, the importance of initial stress/strain states is illustrated and discussed. Copyright © 1999 John Wiley & Sons, Ltd.     

Finite volume approach for finite strain consolidation

The paper presents the finite volume formulation and numerical solution of finite strain one‐dimensional consolidation equation. The equation used in this study utilises a nonlinear continuum representation of consolidation with varying compressibility and hydraulic conductivity and thus inherits the material and geometric nonlinearity. Time‐marching explicit scheme has been used to achieve transient solutions. The nonlinear terms have been evaluated with the known previous time step value of the independent variable, that is, void ratio. Three‐point quadratic interpolation function of Lagrangian family has been used to evaluate the face values at discrete control volumes. It has been shown that the numerical solution is stable and convergent for the general practical cases of consolidation. Performance of the numerical scheme has been evaluated by comparing the results with an analytical solution and with the piecewise piecewise‐linear finite difference numerical model. The approach seems to work well and offers excellent potential for simulating finite strain consolidation. Further, the parametric study has been performed on soft organic clays, and the influence of various parameters on the time ate consolidation characteristics of the soil is shown. Copyright © 2015 John Wiley & Sons, Ltd.     

循环荷载下黏弹性饱和土层的一维固结

针对单层黏弹性地基Merchant模型,运用Laplace变换,求得频域内单层黏弹性地基的一维固结解。通过Laplace逆变换,计算了单层黏弹性地基在任意循环荷载下的有效应力及平均固结度。此外,结合工程实例,研究了Merchant模型各参数对循环荷载下黏弹性地基固结的影响。结果表明,在黏弹性地基的固结过程中,有效应力和沉降的发展速率是不一致的,黏壶的存在使地基固结初期的有效应力增长加快,而使固结后期的有效应力增长减慢,同时使变形的发展滞后于有效应力的发展。研究结果亦表明,循环荷载下土体的固结对独立弹簧模量的变化要比Kelvin体中弹簧模量的变化敏感。     

双层软土非线性固结理论研究

对固结系数的非线性变化进行了理论分析,推导了固结系数的非线性控制方程,指出了γ因子对固结系数非线性变化的影响。考虑到固结系数、渗透系数、压缩系数整体变化以及双层软土一维非线性固结方程求解困难,建立了差分格式的双层软土一维非线性固结差分方程,利用差分法对该方程进行了求解,为工程中复杂方程的计算提供了一种新的方法。研究表明:固结系数并不是决定双层软土非线性固结性状的唯一指标,须综合考虑各种因素的影响。     

Finite layer analysis of the behaviour of a raft on a consolidating soil

A numerical method is developed in this paper for the analysis of the behaviour of a raft resting on a consolidating soil. The response of the raft under an applied loading is determined using the finite layer method for the soil and the finite element method for the raft. By considering deflection compatibility on the contact surface, the distribution of contact pressure is computed at various time steps. The settlement and bending moment in the raft is then evaluated by applying the calculated contact pressure back to the raft. It is shown that, in some cases, the maximum moment in the raft occurs during consolidation and that checking the final moment in the raft by use of elastic theory may not be sufficient.     

Numerical simulation of secondary consolidation of soil: Finite element application

A rheological model has been developed for simulating the secondary consolidation of soils. Numerical procedures have been incorporated into a coupled consolidation program using results from a representative oedometer test. A solution of a two-dimensional problem has also been performed. The technique is numerically stable and has provided satisfactory predictions for the consolidation settlements and the dissipation of pore water pressure within soils.     

考虑固结的透水管桩沉桩全过程有限元模拟

运用透水管桩技术加快沉桩后桩周土体内超静孔隙水释放,进而消除沉桩施工中超静孔压的不利影响。基于有限元数值计算法,利用ABAQUS有限元软件建立透水管桩模型,实现透水管桩贯入过程以及桩周土体固结过程模拟。对比CEM圆柱孔扩张理论验证数值计算结果;阐述透水管桩贯入过程中位移场以及超静孔压场变化规律;对比分析静压桩和透水管桩桩周土体固结性状,结果表明透水管桩能加速超静孔压消散,短期内实现桩基承载力的快速提升。     

交通荷载下横观各向同性土的Biot固结分析

在竖向荷载和切向荷载共同作用下,求解了具有下卧基岩的横观各向同性土的Biot固结问题。首先,基于Biot固结理论得到控制方程,同时引入3个状态变量;然后,对时间t进行Laplace变换和对半径r进行Hankel变换。利用Laplace-Hankel联合积分变换求解状态方程,得到交通荷载作用下横观各向同性土骨架位移、孔隙水压力等的一般积分形式解。结合算例验证了该方法的正确性,并分析了切向荷载和竖向荷载共同作用下对横观各向同性土层沉降和孔压的影响,可以发现切向荷载和竖向荷载共同作用所产生的前期沉降明显小于竖向荷载单独作用的情况。为了更好地模拟实际情况,竖向荷载还采用正弦循环荷载。在循环荷载作用下,沉降变化周期滞后于荷载周期。     

The analysis of finite elasto-plastic consolidation

A theoretical formulation and a numerical solution method are proposed for the problem of the time dependent consolidation of an elasto-plastic soil subject to finite deformations. The soil is assumed to be a two-phase material with a skeleton which may yield according to a general yield criterion with plastic flow governed by a general flow law, and whose pore fluid flows according to Darcy's Law. Governing equations are cast in a rate form and constitutive laws are expressed in a frame indifferent manner. The method of analysis is illustrated by several examples of practical interest for both a soil with an elastic skeleton and a soil with an elasto-plastic skeleton which obeys a Morh–Coulomb yield criterion and a non-associated flow law.     

Finite element modeling of the consolidation behavior of multi-column supported road embankment

A multi-column composite foundation is a new concept utilizing different column types with varying lengths and diameters to support the embankment fill and to mobilize the strength and stiffness of the soil at shallow depths. This study presents the results of finite element analyses using the finite element software PLAXIS to investigate the consolidation behavior of a road embankment constructed on a multi-column composite foundation. The finite element results are calibrated for a period of 200 days. The settlement, horizontal displacement, differential settlement, column axial force, and the development and dissipation of excess pore pressure are presented and discussed in detail. It is concluded that a multi-column composite foundation allows a fast rate of consolidation and significantly increases the embankment stability. A multi-column composite foundation formed by CFG–lime columns is more effective than one formed by SC–lime columns. The CFG–lime columns improve the long-term stability of the embankment because the compression modulus of CFG columns is significantly greater than that of SC columns.