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1.
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. 相似文献
2.
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. 相似文献
3.
Kousik Deb 《国际地质力学数值与分析法杂志》2008,32(10):1267-1288
The present study pertains to the development of a mechanical model for predicting the behavior of granular bed‐stone column‐reinforced soft ground. The granular layer that has been placed over the stone column‐reinforced soft soil has been idealized by the Pasternak shear layer. The saturated soft soil has been idealized by the Kelvin–Voigt model to represent its time‐dependent behavior and the stone columns are idealized by stiffer Winkler springs. The nonlinear behavior of the granular fill has been incorporated in this study by assuming a hyperbolic variation of shear stress with shear strain as in one reported literature. Similarly, for soft soil it has also been assumed that load‐settlement variation is hyperbolic in nature. The effect of consolidation of the soft soil due to inclusion of the stone columns has also been included in the model. Plane‐strain conditions are considered for the loading and foundation soil system. The numerical solutions are obtained by a finite difference scheme and the results are presented in a non‐dimensional form. Parametric studies for a uniformly loaded strip footing have been carried out to show the effects of various parameters on the total as well as differential settlement and stress concentration ratio. It has been observed that the presence of granular bed on the top of the stone columns helps to transfer stress from soil to stone columns and reduces maximum as well as differential settlement. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
4.
以结构性较强的天然饱和软黏土为研究对象,考虑了沉积作用对其自重应力的影响,以及压缩性和渗透性的非线性变化,推导了任意加载条件下结构性土一维大应变固结控制方程,并采用半解析的方法对方程进行求解计算。再将其退化为无结构性的饱和软黏土固结解,与已有的大应变固结解进行了对比,验证了该解的正确性。最后将该半解析解计算结果与小应变固结理论解、不考虑结构性的固结理论解计算结果进行对比分析。结果表明：大应变固结理论的沉降计算值大于小应变固结理论的计算值,且二者的差值随着荷载的增加而增加;当考虑土体的结构性时,地表沉降计算值小于不考虑土体结构性的沉降计算值。 相似文献
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A numerical model, called CCRS1, is presented for one‐dimensional large strain consolidation under constant rate of strain loading conditions. The algorithm accounts for vertical strain, general constitutive relationships, relative velocity of fluid and solid phases, changing compressibility and hydraulic conductivity during consolidation, and an externally applied hydraulic gradient acting across the specimen. Soil compressibility is rate independent, and as such, the current model is most appropriate for less‐structured clays. Verification checks show excellent agreement with analytical and numerical solutions for small and large strain conditions. A series of numeric examples indicates that compressibility and hydraulic conductivity constitutive relationships can have an important effect on constant rate of strain consolidation response. Results also indicate that analytical solutions obtained using small strain theory can be in significant error for large strain conditions with changing coefficient of consolidation. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
7.
Cheng‐Der Wang 《国际地质力学数值与分析法杂志》2007,31(13):1443-1475
This work presents analytical solutions for determining lateral force (force per unit length) and centroid location caused by horizontal and vertical surcharge surface loads acting on a cross‐anisotropic backfill. The surcharge loading types are point load, line load, uniform strip load, upward linear‐varying strip load, upward nonlinear‐varying strip load, downward linear‐varying strip load, and downward nonlinear‐varying strip load. The planes of cross‐anisotropy are assumed parallel to the backfill ground surface. The proposed solutions, derived by integrating the lateral stress solutions (Int. J. Numer. Anal. Meth. Geomech. 2005; 29 :1341–1361), do not exist in literature. Clearly, the type and degree of material anisotropy, loading distance from the retaining wall, and loading types markedly impact the proposed solutions. Two examples are utilized to illustrate the type and degree of soil anisotropy, and the loading types on the lateral force and centroid location in the isotropic/cross‐anisotropic backfills generated by the horizontal and vertical uniform, upward linear‐varying and upward nonlinear‐varying strip loads. The parametric study results demonstrate that the lateral force and centroid location accounting for soil anisotropy, loading distance from the retaining wall, dimension of the loading strip, and loading directions and types differ significantly from those estimated using existing isotropic solutions. The derived solutions can be added to other lateral pressures, such as earth pressure or water pressure, required for stability and structural analysis of a retaining wall. Additionally, they can simulate realistically actual surcharge loading problems in geotechnical engineering when backfill materials are cross‐anisotropic. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
8.
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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Wei Dong Guo 《国际地质力学数值与分析法杂志》2000,24(2):135-163
Viscoelastic or creep behaviour can have a significant influence on the load transfer (t–z) response at the pile–soil interface, and thus on the pile load settlement relationship. Many experimental and theoretical models for pile load transfer behaviour have been presented. However, none of these has led to a closed‐form expression which captures both non‐linearity and viscoelastic behaviour of the soil. In this paper, non‐linear viscoelastic shaft and base load transfer (t–z) models are presented, based on integration of a generalized viscoelastic stress–strain model for the soil. The resulting shaft model is verified through published field and laboratory test data. With these models, the previous closed‐form solutions evolved for a pile in a non‐homogeneous media have been readily extended to account for visco‐elastic response. For 1‐step loading case, the closed‐form predictions have been verified extensively with previous more rigorous numerical analysis, and with the new GASPILE program analysis. Parametric studies on two kinds of commonly encountered loading: step loading, ramp (linear increase followed by sustained) loading have been performed. Two examples of the prediction of the effects of creep on the load settlement relationship by the solutions and the program GASPILE, have been presented. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
11.
This paper presents an exact analytical solution to fully coupled axisymmetric consolidation of a semi‐infinite, transversely isotropic saturated soil subjected to a uniform circular loading at the ground surface. The analysis is under the framework of Biot's general theory of consolidation. First, the governing equations of consolidation are transformed into a set of equivalent partial differential equations with the introduction of two auxiliary variables. These partial differential equations are then solved using Hankel–Laplace integral transforms. Once solutions in the transformed domain have been obtained, the actual solutions in the physical domain for displacements and stress components of the solid matrix, pore‐water pressure and fluid discharge can be finally obtained by direct numerical inversion. The accuracy of the numerical solutions developed is confirmed by comparison with an existing exact solution for an isotropic and saturated soil that is a special case of the more general problem addressed. Numerical analyses are also presented to investigate the influence of the degree of material anisotropy on the consolidation settlement. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
12.
Cheng‐Der Wang 《国际地质力学数值与分析法杂志》2005,29(14):1341-1361
This study derives analytical solutions for estimating the lateral stress caused by horizontal and vertical surcharge strip loads resting on a cross‐anisotropic backfill. The following loading types are employed in this work: point load, line load, uniform strip load, upward linear‐varying strip load, upward nonlinear‐varying strip load, downward linear‐varying strip load and downward nonlinear‐varying strip load. The cross‐anisotropic planes are assumed to be parallel to the horizontal surface of the backfill. The solutions proposed herein have never been mentioned in previous literature, but can be derived by integrating the point load solution in a Cartesian co‐ordinate system for a cross‐anisotropic medium. The calculations by the presented solutions are quick and accurate since they are concise and systematized. Additionally, the proposed calculations demonstrate that the type and degree of material anisotropy and the horizontal/vertical loading types decisively influence the lateral stress. This investigation presents examples of the proposed horizontal and vertical strip loads acting on the surface of the isotropic and cross‐anisotropic backfills to elucidate their effects on the stress. The analytical results reveal that the stress distributions accounting for soil anisotropy and loading types are quite different from those computed from the available isotropic solutions. Restated, the derived solutions, as well as realistically simulating the actual surcharge loading circumstances, provide a good reference for the design of retaining structures for the backfill materials are cross‐anisotropic. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
13.
考虑土中指数形式渗流定律以及土体的非线性固结特性,以超静孔隙水压力为变量在拉格朗日坐标系内建立了软土一维大变形固结问题的控制方程及其求解条件,并运用有限差分法获取其数值解答。在指数形式渗流定律退化为达西定律下,通过将差分解与已有的半解析解进行对比,验证了数值计算的可靠性。最后对指数形式渗流定律下软土一维非线性大变形固结性状进行计算分析,结果表明： 1时,软土的非线性大变形固结速率会随外载增大而减慢; 1时,软土的非线性大变形固结速率会随着外荷载的增加而加快;软土非线性大变形固结速率要比非线性小变形固结速率快,且差别会随荷载增大而加剧;此外,大变形固结理论的最终沉降值要小于小变形固结理论,且差别会随着荷载的增大而加剧。 相似文献
14.
A closed form analytical solution for two‐dimensional plane strain consolidation of unsaturated soil stratum 下载免费PDF全文
下载免费PDF全文 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. 相似文献
15.
Si-jie Liu Xue-yu Geng Hong-lei Sun Yuan-qiang Cai Xiao-dong Pan Li Shi 《国际地质力学数值与分析法杂志》2019,43(4):767-780
The system of vacuum pressure combined with vertical drains to accelerate soil consolidation is one of the most effective ground improvement methods. The consolidation theories of soft soil improved by vertical drains including void ratio–dependent compressibility and permeability have been widely applied in practice to predict the consolidation behavior. In this paper, analytical solutions of the consolidation of vertical drains are derived incorporating the loss and propagating stage of vacuum pressure. In addition, special solutions are obtained for the cases of instantaneous surcharge loading and staged surcharge loading, based on the general solution. The solution is verified by ignoring the propagating stage of vacuum pressure formation and comparing it with an existing solution. The effects of vacuum pressure loss and propagating stage combined with other parameters are investigated through the ratio between excess pore water pressure and surcharge loading. 相似文献
16.
简单介绍了真空-堆载联合预压下饱和软土竖井地基大变形固结沉降模型（VRCS1模型）,该模型能考虑大应变、材料非线性、非达西流、真空折损和竖井未打穿等因素。使用该模型对澳大利亚巴利纳支路某现场沉降进行预测,结果与现场实测数据吻合良好。基于该工程案例,讨论了分级堆载、循环荷载、真空联合堆载、上边界为等应力/等应变条件以及排水板打入深度等因素对竖井地基固结过程的影响规律。计算结果表明：分级堆载可降低土体超静孔压峰值进而改善土体稳定性;循环荷载使土体固结过程发生震荡,且土体沉降峰值迟于超静孔压峰值和荷载峰值出现;真空荷载和堆载作用机制有本质区别,真空荷载不可简单以堆载替代;上边界等应变条件下的固结速率一般快于等应力条件,工程真实条件一般介于两者之间;排水板打入深度超过0.9倍土层厚度时,再加大打入深度加速固结效果不明显。 相似文献
17.
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. 相似文献
18.
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. 相似文献
19.
Analysis of large deformation of geomaterials subjected to time‐varying load poses a very difficult problem for the geotechnical profession. Conventional finite element schemes using the updated Lagrangian formulation may suffer from serious numerical difficulties when the deformation of geomaterials is significantly large such that the discretized elements are severely distorted. In this paper, an operator‐split arbitrary Lagrangian–Eulerian (ALE) finite element model is proposed for large deformation analysis of a soil mass subjected to either static or dynamic loading, where the soil is modelled as a saturated porous material with solid–fluid coupling and strong material non‐linearity. Each time step of the operator‐split ALE algorithm consists of a Lagrangian step and an Eulerian step. In the Lagrangian step, the equilibrium equation and continuity equation of the saturated soil are solved by the updated Lagrangian method. In the Eulerian step, mesh smoothing is performed for the deformed body and the state variables obtained in the updated Lagrangian step are then transferred to the new mesh system. The accuracy and efficiency of the proposed ALE method are verified by comparison of its results with the results produced by an analytical solution for one‐dimensional finite elastic consolidation of a soil column and with the results from the small strain finite element analysis and the updated Lagrangian analysis. Its performance is further illustrated by simulation of a complex problem involving the transient response of an embankment subjected to earthquake loading. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
20.
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