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Daniel T. C. Yao Waldyr Lopes de Oliveira‐Filho Xiao‐Chuan Cai Dobroslav Znidarcic 《国际地质力学数值与分析法杂志》2002,26(2):139-161
The consolidation and desiccation behaviour of soft soils can be described by two time‐dependent non‐linear partial differential equations using the finite strain theory. Analytical solutions do not exist for these governing equations. In this paper, we develop efficient numerical methods and software for finding the numerical solutions. We introduce a semi‐implicit time integration scheme, and show numerically that our method converges. In addition, the numerical solution matches well with the experimental result. A boundary refinement method is also developed to improve the convergence and stability for the case of Neumann type boundary conditions. Interface governing equations are derived to maintain the continuity of consolidation and desiccation processes. This is useful because the soil column can undergo desiccation on top and consolidation on the bottom simultaneously. The numerical algorithms has been implemented into a computer program and the results have been verified with centrifuge test results conducted in our laboratory. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
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The governing equations for the coupled processes of consolidation and creep of two-layered soft soils are established. The Nishihara rheological model is adopted to simulate the elasto-viscoplastic characteristics of soft soils, disregarding the effects of the soil self-gravity. A semi-analytical theory combined with numerical and analytical methods is introduced to solve the governing equations of the one-dimensional rheological model. The computational procedure and the approximate solutions for two-layered soft soils subjected to surface loading are obtained for two drainage conditions. The solutions and the computational procedure are used to study the effects of the two layers and constitutive parameters on rheological consolidation behavior of soft soils. It can be concluded that two layers affect the rate of excess pore water pressure dissipation and settlement development. The parametric studies show that when the parameters of the upper layer remain constant, increases in the permeability and elastic modulus in the lower layer accelerate the dissipation of the excess pore water pressure, and meanwhile increases in the viscosity coefficient and viscoplastic limit slows down the dissipation of the excess water pressure. 相似文献
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假定土体在固结过程中压缩性和渗透性的变化成正比,基于 - 及 - 关系,推导出饱和软土成层地基一维非线性固结解析解,分别给出了按沉降定义和按有效应力定义的每层土平均固结度及整个土层总固结度的计算公式。采用Fortran语言编制了相应的计算程序,将计算得到的结果与已有双层地基一维非线性固结解析解计算结果进行比较,验证该解析解的正确性。利用该程序分析成层地基一维非线性固结性状,分别讨论了初始竖向渗透系数、初始体积压缩系数、荷载值及土层厚度对地基固结性状的影响。分析结果表明：在成层地基一维非线性固结过程中,初始竖向渗透系数对超静孔压的影响较为复杂,对上下层地基固结速率影响不同;初始体积压缩系数增大,超静孔压增大,固结速率变小;所加荷载值越大,超静孔压消散越慢,固结发展越慢;超静孔压消散速率不仅取决于土层厚度,同时取决于各层土渗透性的相对大小。 相似文献
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Based on the Fredlund consolidation theory of unsaturated soil, exact solutions of the governing equations for one‐dimensional consolidation of single‐layer unsaturated soil are presented, in which the water permeability and air transmission are assumed to be constants. The general solution of two coupled homogeneous governing equations is first obtained. This general solution is expressed in terms of two functions psi1 and ψ2, where ψ1 and ψ2, respectively, satisfy two second‐order partial differential equations, which are in the same form. Using the method of separation of variables, the two partial differential equations are solved and exact solutions for three typical homogeneous boundary conditions are obtained. To obtain exact solutions of nonhomogeneous governing equations with three typical nonhomogeneous boundary conditions, the nonhomogeneous boundary conditions are first transformed into homogeneous boundary conditions. Then according to the method of undetermined coefficients and exact solutions of homogenous governing equations, the series form exact solutions are put forward. The validity of the proposed exact solutions is verified against other analytical solutions in the literature. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
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This paper presents the analytical layer‐element method to analyze the consolidation of saturated multi‐layered soils caused by a point sink by considering the anisotropy of permeability. Starting from the governing equations of the problem, the solutions of displacements and stresses for a single soil layer are obtained in the Laplace–Hankel transformed domain. Then, the analytical layer‐element method is utilized to further derive the solutions for the saturated multi‐layered soils in the transformed domain by combining with the boundary conditions of the soil system and continuity conditions between adjacent layers. The actual solutions in the physical domain can be acquired by the inversion of Laplace–Hankel transform. Numerical results are carried out to show the accuracy and stability of the proposed method and evaluate the influence of sink depth and anisotropic permeability on excess pore pressure and surface settlement. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
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Axisymmetric consolidation of multi-layered soils induced by groundwater extraction from a dewatering well is studied with consideration of the anisotropic permeability and the well length. Laplace-Hankel transforms are utilized to solve the governing equations. The analytical layer-element method is used to build relationships between displacements, stresses, excess pore pressure and seepage velocity in the transformed domain. The real solutions can be obtained by the inversion of Laplace-Hankel transforms. A series of parametric studies, especially the length of a dewatering well and the combined effect of pumping and recharging, are conducted to analyze the consolidation behaviors of layered soils. 相似文献
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In this paper, a coupling method between finite element and analytical layer‐elements is utilized to analyze the time‐dependent behavior of a plate of any shape and finite rigidity resting on layered saturated soils. Based on the integral transform techniques together with the aid of an order reduction method, an analytical layer‐element solution is derived from the governing equations for three‐dimensional Biot consolidation with respect to a Cartesian coordinate system and then extended to be the fundamental solution for the layered saturated soil under a point load. The Mindlin plate is modeled by eight‐noded isoparametric elements. The governing equations of the interaction between soil and plate in the Laplace‐Fourier transformed domain are deduced by referring to the coupling theory of FEM/BEM, and the final solution is obtained by applying numerical inversion. Numerical examples concerned with the time‐dependent response of a plate are performed to demonstrate the influence of soil and plate properties on the interaction process. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
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非饱和土是地球表层土体一种常见的存在形式。与经典的饱和土Biot固结理论相比,非饱和土固结理论还亟待发展。基于Fredlund非饱和土双应力变量固结理论,放弃传统理论固结过程中骨架总应力不变的假设,推导出变荷载作用下非饱和土全耦合轴对称固结理论的控制方程组。通过Laplace-Hankel变换处理变量t和r,所得的控制方程被处理为常微分方程组;扩展的精细积分法将被进一步运用求解方程组以得到层状非饱和土地基在变换域内的固结解答,而最终的解答将通过Laplace-Hankel逆变换技术求得。将非饱和土地基退化为饱和土地基,与现有文献结果进行对比,验证所提方法结果的可靠性;最后,提供3个数值算例,以讨论加载时间T0、孔隙水关于净应力的体积变化系数m1w以及土体分层性对非饱和土固结特性的影响。 相似文献
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运用对偶积分方程来求解层状横观各向同性地基与墙下条形基础的共同作用问题。从直角坐标平面应变问题控制方程出发,通过傅里叶（Fourier）变换和层间连续性条件,可以得到层状横观各向同性地基的传递矩阵解。基于该传递矩阵解,并利用条形基础与地基接触的混合边值条件,推导出一组关于基础挠度和地基反力的对偶积分方程。考虑墙下条形基础受到竖向集中荷载的情况,利用弹性薄板理论先求解出条形基础挠度;随后应用雅可比（Jacobi）正交多项式和级数展开的方法,将对偶积分方程转化为线性代数方程组进行求解。编制了相应的计算程序,其计算结果与有限元软件ABAQUS的结果基本吻合,从而验证了所提理论的正确性。算例分析表明,板土相对刚度与地基成层性对地基反力、地表沉降和沿z轴竖向正应力有很大的影响。 相似文献
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A numerically efficient and stable method is developed to analyze Biot's consolidation of multilayered soils subjected to non‐axisymmetric loading in arbitrary depth. By the application of a Laplace–Hankel transform and a Fourier expansion, the governing equations are solved analytically. Then, the analytical layer‐element (i.e. a symmetric stiffness matrix) describing the relationship between generalized displacements and stresses of a layer is exactly derived in the transformed domain. Considering the continuity conditions between adjacent layers, the global stiffness matrix of multilayered soils is obtained by assembling the inter‐related layer‐elements. Once the solution in the Laplace–Hankel transformed domain that satisfies the boundary conditions has been obtained, the actual solution can be derived by the inversion of the Laplace–Hankel transform. Finally, numerical examples are presented to verify the theory and to study the influence of the layered soil properties and time history on the consolidation behavior. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
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This paper presents analytical solutions to the one‐dimensional consolidation problem taking into consideration the rheological properties of clayey soil under variable loadings. A four‐element rheological model is introduced, and different loading types are involved, i.e. constant loading, one‐step loading, triangular loading, rectangular loading, and isosceles–trapezoidal cyclic loading. The differential equations governing consolidation are solved by the Laplace transform. Based on the solutions obtained, the influences of the rheological parameters and loading conditions on the consolidation process are investigated. It has been shown that the consolidation behavior is mainly governed by four dimensionless parameters, a1, a2, b, and Tv0. Load shape has a great influence on the rate of consolidation. A decrease either in the modulus of the spring in the Kelvin body or in the viscosity coefficient of independent dashpot will slow down the rate of consolidation. An increase in the viscosity coefficient of the dashpot in the Kelvin body will make the rate of consolidation increase at an early stage but decrease at a later stage. For isosceles–trapezoidal cyclic loading, the consolidation rate in each cycle reaches a maximum at the end of the constant loading phase and the minimum at the end of this cycle. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
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Embankments on Soft Soil Reinforced with Stone Columns: Numerical Analysis and Proposal of a New Design Method 总被引：5，自引：1，他引：4
José Leitão Borges Tiago Sabino Domingues António Silva Cardoso 《Geotechnical and Geological Engineering》2009,27(6):667-679
A parametric study of an embankment on soft soils reinforced with stone columns is performed using a computer program based
on the finite element method. The cylindrical unit cell formulation is used by modeling one column and its surrounding soft
soil with confined axisymmetric behaviour. The computer program incorporates the Biot consolidation theory (coupled formulation
of the flow and equilibrium equations) with constitutive relations simulated by the p–q–θ critical state model. The following parameters are analysed: the replacement area ratio, the deformability of the column
material, the thickness of the soft soil, the deformability of the fill and the friction angle of the column material. Based
on the results of this study, a new design method is proposed, relating the settlement improvement factor to the two factors
that revealed major influence: the replacement area ratio and the ratio between the deformability of the soft soil and the
deformability of the column material. 相似文献
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A numericl method for solving consolidation problems of layered soils is developed. Starting from the governing differential equations for the coupled poro-elastic medium, the governing partial differential equations are reduced to ordinary differential equations by means of the appropriate displacement functions and Laplace-Fourier transformation. Once the fundamental solution in the transformed domain has been found, the solution in the physical domain is obtained by numerically inverting the transformations. A series of soil consolidation problems have been solved and validated against existing solutions in order to compare the feasibility and the accuracy of the present technique. 相似文献
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A general analytical solution, which is more explicit than the one given by Schiffman and Stein,1 for the problem of one-dimensional consolidation of layered soils is presented. A relevant computer program is developed and the computed results on some examples are included. From these results, an in-depth study on the one-dimensional consolidation behaviour of layered systems is then made. It is demonstrated through these examples that both the solution technique and the computer program developed are very efficient. It is found that the effects of coefficients of permeability and volume compressibility of soil on the consolidation of layered systems are different and cannot be embodied into the coefficient of consolidation of soil. The stiffness of soil layer also plays an important role on the rate of consolidation. 相似文献
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采用简化的k-σ′和mv-σ′分段模型,通过把结构性土一维固结问题转化为上、下层土体厚度不断变化的双层地基一维固结问题,得出了变荷载下结构性土一维固结近似解,并与数值解对比验证了解的合理性。分析结构破坏后渗透系数和体积压缩系数的变化分别对结构性土固结特性的影响表明,在固结系数减小程度相同的情况下,渗透系数减小程度增加则按孔压定义的固结度减小程度加大,而体积压缩系数不断增加则按变形定义的固结度减小程度加大;固结过程中按孔压定义的固结度大于按变形定义的固结度,且随着体积压缩系数增加程度加大,二者的差距加大。 相似文献
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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 (αa and αw), and drain resistance factors (Ga and Gw). 相似文献
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Pedro Alves Costa José Leitão Borges Manuel Matos Fernandes 《Geotechnical and Geological Engineering》2007,25(6):617-629
The studies of excavations in soft clayey soils are normally based on undrained total stress analyses. A better approach consists
of taking into account the effects of consolidation during the excavation-bracing process and after the completion of the
construction by means of coupled finite element analyses in effective stresses. In this paper, the geotechnical behaviour
of a braced excavation in the soft soils of San Francisco (USA) is analysed, both during and after the construction period.
Numerical analyses are performed with a finite element program, which incorporates the Biot consolidation theory (coupled
formulation of the water flow and equilibrium equations) and soil constitutive relations simulated by the p-q-θ critical state model. Numerical results are compared with field results. 相似文献
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Semi‐analytical solution to one‐dimensional consolidation for unsaturated soils with semi‐permeable drainage boundary under time‐dependent loading 
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下载免费PDF全文 This paper presents semi‐analytical solutions to Fredlund and Hasan's one‐dimensional consolidation of unsaturated soils with semi‐permeable drainage boundary under time‐dependent loadings. Two variables are introduced to transform two coupled governing equations of pore‐water and pore‐air pressures into an equivalent set of partial differential equations, which are easily solved by the Laplace transform. The pore‐water pressure, pore‐air pressure and settlement are obtained in the Laplace domain. Crump's method is adopted to perform the inverse Laplace transform in order to obtain semi‐analytical solutions in time domain. It is shown that the present solutions are more general and have a good agreement with the existing solutions from literatures. Furthermore, the current solutions can also be degenerated into conventional solutions to one‐dimensional consolidation of unsaturated soils with homogeneous boundaries. Finally, several numerical examples are provided to illustrate consolidation behavior of unsaturated soils under four types of time‐dependent loadings, including instantaneous loading, ramp loading, exponential loading and sinusoidal loading. Parametric studies are illustrated by variations of pore‐air pressure, pore‐water pressure and settlement at different values of the ratio of air–water permeability coefficient, depth and loading parameters. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
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Stress history plays an important role in controlling the consolidation behavior of soft clays, but few models exist that can provide quantitative estimate of its influence. In this paper, the Gibson–Lo rheological model is used to simulate the coupled processes of drainage and creep of soft soils that takes stress history into account. A hybrid combination of analytical and numerical methods is adopted to solve the governing equations of consolidation with the nonlinear rheological model. The methodology is applied to a saturated soft soil subjected to surface loading. The soil profile is separated into normally consolidated and overconsolidated layers by a boundary that is allowed to move. Comparisons of the model predictions and its simulations are used to evaluate the effects of stress history, model parameters, and loading pattern on consolidation behavior. It is shown that stress history influences the location of the moving boundary, variations of the profiles of excess pore water pressure dissipation, stress and deformation‐based average degrees of consolidation. Parametric studies conducted show that when soil is stiffer, the excess pore water pressure dissipates much more quickly, and thus the soil consolidates much faster especially at the early stages. The results also show that soil viscosity influences the deformation‐based average degree of consolidation at the latter stages. The consolidation process of soil layer under linear loading is shown to lag behind those under instantaneous loading: the longer the loading period is, the smaller the average degrees of consolidation are no matter how they are defined. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献