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1.
Numerical solutions for problems in coupled poromechanics suffer from spurious pressure oscillations when small time increments are used. This has prompted many researchers to develop methods to overcome these oscillations. In this paper, we present an overview of the methods that in our view are most promising. In particular we investigate several stabilized procedures, namely the fluid pressure Laplacian stabilization (FPL), a stabilization that uses bubble functions to resolve the fine‐scale solution within elements, and a method derived by using finite increment calculus (FIC). On a simple one‐dimensional test problem, we investigate stability of the three methods and show that the approach using bubble functions does not remove oscillations for all time step sizes. On the other hand, the analysis reveals that FIC stabilizes the pressure for all time step sizes, and it leads to a definition of the stabilization parameter in the case of the FPL‐stabilization. Numerical tests in one and two dimensions on 4‐noded bilinear and linear triangular elements confirm the effectiveness of both the FPL‐ and the FIC‐stabilizations schemes for linear and nonlinear problems. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
2.
We presented a finite‐element‐based algorithm to simulate plane‐strain, straight hydraulic fractures in an impermeable elastic medium. The algorithm accounts for the nonlinear coupling between the fluid pressure and the crack opening and separately tracks the evolution of the crack tip and the fluid front. It therefore allows the existence of a fluid lag. The fluid front is advanced explicitly in time, but an implicit strategy is needed for the crack tip to guarantee the satisfaction of Griffith's criterion at each time step. We enforced the coupling between the fluid and the rock by simultaneously solving for the pressure field in the fluid and the crack opening at each time step. We provided verification of our algorithm by performing sample simulations and comparing them with two known similarity solutions. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
3.
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
4.
This paper extends the material point method to analyze coupled dynamic, two‐phase boundary‐valued problems via a velocity formulation, in which solid and fluid phase velocities are the variables. Key components of the proposed approach are the adoption of Verruijt's sequence of update steps when integrating over time and the enhancement of volumetric strains. The connection between fractional step method and the time‐stepping algorithm presented in this paper is addressed. Enhancement of volumetric strains allows lower order variations in pressure and mitigates spurious pressure fields and locking that plague low‐order finite‐element implementations. A stress averaging technique to smoothen stress variations is proposed, and the local damping procedure adopted by FLAC is extended to handle two‐phase problems. Special Kelvin‐Voigt boundaries are developed to suppress reflections at artificial boundaries. Idealized examples are presented to demonstrate the capability of the proposed framework to accurately capture the physics of wave propagation, consolidation and wave attack on a sea dike. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
5.
A new formulation of the element‐free Galerkin (EFG) method is developed for solving coupled hydro‐mechanical problems. The numerical approach is based on solving the two governing partial differential equations of equilibrium and continuity of pore water simultaneously. Spatial variables in the weak form, i.e. displacement increment and pore water pressure increment, are discretized using the same EFG shape functions. An incremental constrained Galerkin weak form is used to create the discrete system equations and a fully implicit scheme is used for discretization in the time domain. Implementation of essential boundary conditions is based on a penalty method. Numerical stability of the developed formulation is examined in order to achieve appropriate accuracy of the EFG solution for coupled hydro‐mechanical problems. Examples are studied and compared with closed‐form or finite element method solutions to demonstrate the validity of the developed model and its capabilities. The results indicate that the EFG method is capable of handling coupled problems in saturated porous media and can predict well both the soil deformation and variation of pore water pressure over time. Some guidelines are proposed to guarantee the accuracy of the EFG solution for coupled hydro‐mechanical problems. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
6.
Hybrid time integration and coupled solution methods for nonlinear finite element analysis of partially saturated deformable porous media at small strain 
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下载免费PDF全文 The goal of the paper is to determine the most efficient, yet accurate and stable, finite element nonlinear solution method for analysis of partially saturated deformable porous media at small strain. This involves a comparison between fully implicit, semi‐implicit, and explicit time integration schemes, with monolithically coupled and staggered‐coupled nonlinear solution methods and the hybrid combination thereof. The pore air pressure pa is assumed atmospheric, that is, pa=0 at reference pressure. The solid skeleton is assumed to be pressure‐sensitive nonlinear isotropic elastic. Coupled partially saturated ‘consolidation’ in the presence of surface infiltration and traction is simulated for a simple one‐dimensional uniaxial strain example and a more complicated plane strain slope example with gravity loading. Three mixed plane strain quadrilateral elements are considered: (i) Q4P4; (ii) stabilized Q4P4S; and (iii) Q9P4; “Q” refers to the number of solid skeleton displacement nodes, and “P” refers to the number of pore fluid pressure nodes. The verification of the implementation against an analytical solution for partially saturated pore water flow (no solid skeleton deformation) and comparison between the three time integration schemes (fully implicit, semi‐implicit, and explicit) are presented. It is observed that one of the staggered‐coupled semi‐implicit schemes (SIS(b)), combined with the fully implicit monolithically coupled scheme to resolve sharp transients, is the most efficient computationally. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
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Frictionless contact formulation for dynamic analysis of nonlinear saturated porous media based on the mortar method 下载免费PDF全文
下载免费PDF全文 A finite element algorithm for frictionless contact problems in a two‐phase saturated porous medium, considering finite deformation and inertia effects, has been formulated and implemented in a finite element programme. The mechanical behaviour of the saturated porous medium is predicted using mixture theory, which models the dynamic advection of fluids through a fully saturated porous solid matrix. The resulting mixed formulation predicts all field variables including the solid displacement, pore fluid pressure and Darcy velocity of the pore fluid. The contact constraints arising from the requirement for continuity of the contact traction, as well as the fluid flow across the contact interface, are enforced using a penalty approach that is regularised with an augmented Lagrangian method. The contact formulation is based on a mortar segment‐to‐segment scheme that allows the interpolation functions of the contact elements to be of order N. The main thrust of this paper is therefore how to deal with contact interfaces in problems that involve both dynamics and consolidation and possibly large deformations of porous media. The numerical algorithm is first verified using several illustrative examples. This algorithm is then employed to solve a pipe‐seabed interaction problem, involving large deformations and dynamic effects, and the results of the analysis are also compared with those obtained using a node‐to‐segment contact algorithm. The results of this study indicate that the proposed method is able to solve the highly nonlinear problem of dynamic soil–structure interaction when coupled with pore water pressures and Darcy velocity. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
9.
A FIC‐based stabilized mixed finite element method with equal order interpolation for solid–pore fluid interaction problems 下载免费PDF全文
下载免费PDF全文 A new mixed displacement‐pressure element for solving solid–pore fluid interaction problems is presented. In the resulting coupled system of equations, the balance of momentum equation remains unaltered, while the mass balance equation for the pore fluid is stabilized with the inclusion of higher‐order terms multiplied by arbitrary dimensions in space, following the finite calculus (FIC) procedure. The stabilized FIC‐FEM formulation can be applied to any kind of interpolation for the displacements and the pressure, but in this work, we have used linear elements of equal order interpolation for both set of unknowns. Examples in 2D and 3D are presented to illustrate the accuracy of the stabilized formulation for solid–pore fluid interaction problems. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
10.
This work presents the application of a Monte Carlo simulation method to perform an statistical analysis of transient variably saturated flow in an hypothetical random porous media. For each realization of the stochastic soil parameters entering as coefficients in Richards' flow equation, the pressure head and the flow field are computed using a mixed finite element procedure for the spatial discretization combined with a backward Euler and a modified Picard iteration in time. The hybridization of the mixed method provides a novel way for evaluating hydraulic conductivity on interelement boundaries. The proposed methodology can handle both large variability and fractal structure in the hydraulic parameters. The saturated conductivity K
s and the shape parameter vg in the van Genuchten model are treated as stochastic fractal functions known as fractional Brownian motion (fBm) or fractional Gaussian noise (fGn). The statistical moments of the pressure head, water content, and flow components are obtained by averaging realizations of the fractal parameters in Monte Carlo fashion. A numerical example showing the application of the proposed methodology to characterize groundwater flow in highly heterogeneous soils is presented. 相似文献
11.
采用现场液化试验,研究水平场地孔压增长模式,提出孔压增量计算模型。通过不同密实度砂土的液化试验,以加速度、埋深、砂土密实度等现场参数为指标构建孔压增量模型,发现现场和室内试验孔压增长模式的区别和联系,并验证该孔压模型的可靠性。研究结果表明：等幅循环荷载下,与现有动三轴等土单元试验的孔压增量随作用次数一直呈单调递减模式不同,现场试验孔压增量随作用次数呈现出先增大后减小的规律,中间存在阈值;通过参数分析和试验实例验证,构建的孔压增量计算模型,可更方便地用于随机荷载下水平场地的饱和砂土孔压计算。 相似文献
12.
将土骨架视为具有分数阶导数本构关系的黏弹性体,基于Biot两相饱和介质模型,建立具有球形空腔饱和分数导数黏弹性土体稳态振动的控制方程。通过引入势函数,得到球对称情形下具有球形空腔饱和分数导数黏弹性土体的位移、应力和孔隙流体压力等解析表达式。考察分数导数模型参数和饱和土参数等对土体振动特性的影响,结果表明,流体压缩性对饱和土体的动力特性有显著影响,而土骨架压缩性和流-固耦合系数的影响相对较小;分数导数阶数对土体动力特性的影响与材料参数比的取值有关。同时,边界不排水条件下饱和土体的动力响应大于排水条件下饱和土体的动力响应。 相似文献
13.
Philip Cardiff 《国际地质力学数值与分析法杂志》2015,39(13):1410-1430
Accurate prediction of the interactions between the nonlinear soil skeleton and the pore fluid under loading plays a vital role in many geotechnical applications. It is therefore important to develop a numerical method that can effectively capture this nonlinear soil‐pore fluid coupling effect. This paper presents the implementation of a new finite volume method code of poro‐elasto‐plasticity soil model. The model is formulated on the basis of Biot's consolidation theory and combined with a perfect plasticity Mohr‐Coulomb constitutive relation. The governing equation system is discretized in a segregated manner, namely, those conventional linear and uncoupled terms are treated implicitly, while those nonlinear and coupled terms are treated explicitly by using any available values from previous time or iteration step. The implicit–explicit discretization leads to a linearized and decoupled algebraic system, which is solved using the fixed‐point iteration method. Upon the convergence of the iterative method, fully nonlinear coupled solutions are obtained. Also explored in this paper is the special way of treating traction boundary in finite volume method compared with FEM. Finally, three numerical test cases are simulated to verify the implementation procedure. It is shown in the simulation results that the implemented solver is capable of and efficient at predicting reasonable soil responses with pore pressure coupling under different loading situations. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
14.
In recent years, a number of constitutive models have been proposed to describe mathematically the mechanical response of natural clays. Some of these models are characterized by complex formulations, often leading to non‐trivial problems in their numerical integration in finite elements codes. The paper describes a fully implicit stress‐point algorithm for the numerical integration of a single‐surface mixed isotropic–kinematic hardening plasticity model for structured clays. The formulation of the model stems from a compromise between its capability of reproducing the larger number of features characterizing the behaviour of structured clays and the possibility of developing a robust integration algorithm for its implementation in a finite elements code. The model is characterized by an ellipsoid‐shaped yield function, inside which a stress‐dependent reversible stiffness is accounted for by a non‐linear hyperelastic formulation. The isotropic part of the hardening law extends the standard Cam‐Clay one to include plastic strain‐driven softening due to bond degradation, while the kinematic hardening part controls the evolution of the position of the yield surface in the stress space. The proposed algorithm allows the consistent linearization of the constitutive equations guaranteeing the quadratic rate of asymptotic convergence in the global‐level Newton–Raphson iterative procedure. The accuracy and the convergence properties of the proposed algorithm are evaluated with reference to the numerical simulations of single element tests and the analysis of a typical geotechnical boundary value problem. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
15.
Soil models based on kinematic hardening together with elements of bounding surface plasticity, provide a means of introducing some memory of recent history and stiffness variation in the predicted response of soils. Such models provide an improvement on simple elasto‐plastic models in describing soil behaviour under non‐monotonic loading. Routine use of such models requires robust numerical integration schemes. Explicit integration of highly non‐linear models requires extremely small steps in order to guarantee convergence. Here, a fully implicit scheme is presented for a simple kinematic hardening extension of the Cam clay soil model. The algorithm is based on the operator split methodology and the implicit Euler backward integration scheme is proposed to integrate the rate form of the constitutive relations. This algorithm maintains a quadratic rate of asymptotic convergence when used with a Newton–Raphson iterative procedure. Various strain‐driven axisymmetric triaxial paths are simulated in order to demonstrate the efficiency and good performance of the proposed algorithm. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
16.
This paper presents a numerical scheme for fluid‐particle coupled discrete element method (DEM), which is based on poro‐elasticity. The motion of the particles is resolved by means of DEM. While within the proposition of Darcian regime, the fluid is assumed as a continuum phase on a Eulerian mesh, and the continuity equation on the fluid mesh for a compressible fluid is solved using the FEM. Analytical solutions of traditional soil mechanics examples, such as the isotropic compression and one‐dimensional upward seepage flow, were used to validate the proposed algorithm quantitatively. The numerical results showed very good agreement with the analytical solutions, which show the correctness of this algorithm. Sensitivity studies on the effect of some influential factors of the coupling scheme such as pore fluid bulk modulus, volumetric strain calculation, and fluid mesh size were performed to display the accuracy, efficiency, and robustness of the numerical algorithm. It is revealed that the pore fluid bulk modulus is a critical parameter that can affect the accuracy of the results. Because of the iterative coupling scheme of these algorithms, high value of fluid bulk modulus can result in instability and consequently reduction in the maximum possible time‐step. Furthermore, the increase of the fluid mesh size reduces the accuracy of the calculated pore pressure. This study enhances our current understanding of the capacity of fluid‐particle coupled DEM to simulate the mechanical behavior of saturated granular materials. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
17.
This paper presents a u‐p (displacement‐pressure) semi‐Lagrangian reproducing kernel (RK) formulation to effectively analyze landslide processes. The semi‐Lagrangian RK approximation is constructed based on Lagrangian discretization points with fixed kernel supports in the current configuration. As a result, it tracks state variables at discretization points while allowing extreme deformation and material separation that is beyond the capability of Lagrangian formulations. The u‐p formulation following Biot theory is incorporated into the formulation to describe poromechanics of saturated geomaterials. In addition, a stabilized nodal integration method to ensure stability of the domain integration and kernel contact algorithms to model contact between bodies are introduced in the u‐p semi‐Lagrangian RK formulation. The proposed method is verified with several numerical examples and validated with an experimental result and the field data of an actual landslide. 相似文献
18.
库水位下降时的岸坡非稳定渗流问题研究 总被引：5，自引：1，他引：4
水位下降时岸坡的渗流是涉及土体由饱和向非饱和状态过渡的水-气二相流过程,目前相关研究成果大都假设孔隙气压力为0,忽略孔隙气的影响。根据水、空气的质量守恒定律和达西定律,结合多相流理论建立水-气二相流模型,采用高效的积分有限差分法求解,通过变换主要变量,实现饱和（单相）与非饱和（二相）的相互转变,并给出各种边界条件下合理的数学处理方法。通过Muskat渗流问题,验证了上述模型的正确性;并对某土质岸坡水位下降时的非稳定渗流问题进行分析,结果表明,岸坡的基质吸力小于浸润线以上的负孔隙水压力,在浸润线以上的很大区域为毛细管水饱和带,其土体饱和且基质吸力为0,这对边坡稳定十分不利,精确分析水位下降的边坡稳定问题时,孔隙气压力变化的影响值得研究。 相似文献
19.
In this paper, the application of an efficient, transparent and accurate kinematic-cyclic constitutive model based on the fuzzy-set concepts and incremental plasticity theory is presented to show its capability in modeling cyclic mobility of saturated granular soil. The nature and kinematic mechanism of the membership functions in the fuzzy-set constitutive model are illustrated. The model’s capability of modeling soil dilatancy is investigated. Important features of volume change and pore water pressure build-up related to soil cyclic mobility are captured. The formulation of the proposed model is relatively simple and it can be readily implemented in finite element codes. The enhanced fuzzy-set model is capable of simulating ground motion problems particularly related to cyclic mobility, soil liquefaction, and spreading behavior. 相似文献
20.
非饱和土化学-塑性耦合本构行为的数值模拟 总被引：2，自引：0，他引：2
基于Hueckel提出的饱和黏土化学-塑性本构模型和Gallipoli提出的非饱和土弹塑性本构模型,提出了一个新的非饱和多孔介质的化学-塑性本构模型,并建立了该模型的隐式积分算法,算法中考虑了化学软化和非饱和吸力的影响。在已有的非饱和多孔介质有限元分析程序平台上进行了程序研发,对孔隙水中化学污染物浓度变化对非饱和土力学行为的影响进行数值模拟,使所研制的程序能够进行岩土工程问题的化学-力学耦合非线性分析。 相似文献