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1.
The paper examines the axisymmetric problem of the indentation of a poroelastic halfspace that is reinforced with an inextensible permeable/impermeable membrane located at a finite depth by a rigid indenter. The constitutive behavior of the poroelastic halfspace is described by the three-dimensional theory of poroelasticity proposed by M.A. Biot. The contact conditions between the indenter and the poroelastic halfspace are varied to accommodate both adhesive/frictionless contact and impermeable/permeable conditions. The formulation of the mixed boundary value problems uses the stress function approaches applicable to semi-infinite domains. Successive applications of Laplace and Hankel integral transforms are used to reduce the mixed boundary value problems to sets of coupled Fredholm integral equations of the second kind. These integral equations are solved using numerical approaches, applicable both for the solution of the systems of coupled equations and for Laplace transform inversion, to examine the time-dependent displacement of the rigid indenter. The analytical-numerical estimates for the time-dependent displacements of the rigid indenter are compared with results obtained using a finite element approach. 相似文献
2.
We present fully-discrete procedures for computing the impedance functions of rigid massless soil-structure interfaces that are embedded in arbitrarily heterogeneous half-spaces. The finite element method (FEM) is used for obtaining the wave responses of (visco-)elastic half-spaces truncated by Perfectly Matched Layers (PMLs), which provide the wave absorbing boundary conditions. The devised FEM-PML approach is verified in both time and frequency domains by using various benchmark solutions. Requirements on the prescribed input excitations for obtaining accurate impedances in the time domain as well as the relative computational cost of time- and frequency domain solutions are investigated. Accuracy of the implemented PMLs in extracting the impedance functions is also examined in comparison to Lysmer–Kuhlemeyer dashpots; and it was found that this simplified boundary treatment is generally inadequate. The utility of the proposed method is demonstrated by extracting the impedance matrix of rectangular and circular voids embedded in a linearly stiffening half-space. Impedance functions for such complex soil-structure systems are shown to be highly coupled and frequency-dependent due to wave reflections and interference caused by the soil heterogeneity and interface geometry. Fully discrete approaches, such as those proposed herein, are necessary to adequately capture these effects. 相似文献
3.
在地震波数值模拟中,为提高算法精度,需要使用高阶时间更新格式,而普通的非分裂完全匹配层（PML）吸收边界局限于低阶时间格式。辅助微分方程完全匹配层（ADE PML）是一种可以适应任意阶时间格式的非分裂完全匹配层技术,且可以直接应用复频移拉伸算子以提高PML在高角度入射时的效果。作者将ADE PML应用于声波方程四阶Runge Kutta时间格式的数值模拟中,对其吸收效能进行了检验。数值模拟表明,复频移ADE PML在高角度入射时表现优于非复频移ADE PML。另外,不同辅助变量更新格式的吸收效果存在微小差异,显格式下计算结果与解析解吻合较好。长时间能量衰减计算表明ADE PML可以稳定至2 × 105时间步。 相似文献
4.
A FIC‐based stabilized mixed finite element method with equal order interpolation for solid–pore fluid interaction problems 
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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
5.
Magnus Wangen 《Computational Geosciences》2013,17(4):647-659
A procedure based on the finite element method is suggested for modeling of 3D hydraulic fracturing in the subsurface. The proposed formulation partitions the stress field into the initial stress state and an additional stress state caused by pressure buildup. The additional stress is obtained as a solution of the Biot equations for coupled fluid flow and deformations in the rock. The fluid flow in the fracture is represented on a regular finite element grid by means of “fracture” porosity, which is the volume fraction of the fracture. The use of the fracture porosity allows for a uniform finite element formulation for the fracture and the rock, both with respect to fluid pressure and displacement. It is demonstrated how the fracture aperture is obtained from the displacement field. The model has a fracture criterion by means of a strain limit in each element. It is shown how this criterion scales with the element size. Fracturing becomes an intermittent process, and each event is followed by a pressure drop. A procedure is suggested for the computation of the pressure drop. Two examples of hydraulic fracturing are given, when the pressure buildup is from fluid injection by a well. One case is of a homogeneous rock, and the other case is an inhomogeneous rock. The fracture geometry, well pressure, new fracture area, and elastic energy released in each event are computed. The fracture geometry is three orthogonal fracture planes in the homogeneous case, and it is a branched fracture in the inhomogeneous case. 相似文献
6.
A new development of the scaled boundary finite element method for wave motion in layered half-space
The scaled boundary finite element method (SBFEM) developed by Wolf and Song has shown certain parallels to the finite element method (FEM) and boundary element method (BEM). Because of its semi-analytical nature, SBFEM is particularly suitable for the analysis of wave propagation in unbounded domains. This paper makes a certain modification of the standard SBFEM. A new idea of scaling surface instead of a scaling center is introduced to formulate the governing SBFE equations for the analysis of wave propagation in multilayered half-space, which leads to simplifying the modeling and saving considerably the computational effort. In addition, by employing the proposed approach, some problems encountered in engineering practice, which are difficult to deal with by the conventional SBFEM, for example, 3D foundation impedance on half-space with irregular geographical features, can be effectively solved. The proposed approach also helps to simplify the solution of shell structures. Numerical examples are provided to validate the accuracy and efficiency of the proposed approach. 相似文献
7.
We develop a finite element discretization and multigrid solver for a Darcy–Stokes system of three-dimensional vuggy porous media, i.e., porous media with cavities. The finite element method uses low-order mixed finite elements in the Darcy
and Stokes domains and special transition elements near the Darcy–Stokes interface to allow for tangential discontinuities
implied by the Beavers–Joseph boundary condition. We design a multigrid method to solve the resulting saddle point linear
system. The intertwining of the Darcy and Stokes subdomains makes the resulting matrix highly ill-conditioned. The velocity
field is very irregular, and its discontinuous tangential component at the Darcy–Stokes interface makes it difficult to define
intergrid transfer operators. Our definition is based on mass conservation and the analysis of the orders of magnitude of
the solution. The coarser grid equations are defined using the Galerkin method. A new smoother of Uzawa type is developed
based on taking an optimal step in a good search direction. Our algorithm has a measured convergence factor independent of
the size of the system, at least when there are no disconnected vugs. We study the macroscopic effective permeability of a
vuggy medium, showing that the influence of vug orientation; shape; and, most importantly, interconnectivity determine the
macroscopic flow properties of the medium.
This work was supported by the U.S. National Science Foundation under grants DMS-0074310 and DMS-0417431. 相似文献
8.
Mahantesh S. Hiremath Ranbir S. Sandhu Leslie W. Morland William E. Wolfe 《国际地质力学数值与分析法杂志》1988,12(2):121-139
Biot's dynamic equations of motion for one-dimensional wave propagation in a fluid-saturated linear elastic isotropic soil are solved using Laplace transformation followed by numerical inversion and the results compared with a direct finite element formulation. A soil column of finite dimension subjected to velocity boundary conditions is analysed, allowing for reflection of waves from boundaries. Comparison of time histories at given points along the column shows that the finite element solution gives good agreement with the Laplace transform solution for low as well as high drag. 相似文献
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A number of phenomena and processes in geosciences can be summarized by second order partial differential equations. The major numerical methods for their solution include the classical finite difference method and the finite element method newly developed in the last two or three decades. Since 1977 the author has proved that for the Laplace and Poisson equations, these two methods are identical and are different only in the process of formulation. For transient problems, such as heat conduction in the earth and the groundwater and oil-gas unsteady flow in porous media, there are some differences in resulting linear algebraic euqations. In general, two methods give similar results, but when the time step is decreased to some extent, the resulting algebraic equation will be consistent with the anti-heat conduction equation rather than the original heat conduction equation. This is the reason why unrealistic potentials are produced by the finite element method. Such a problem can be overcome by using the 相似文献
11.
Unsaturated soils are three‐phase porous media consisting of a solid skeleton, pore liquid, and pore gas. The coupled mathematical equations representing the dynamics of unsaturated soils can be derived based on the theory of mixtures. Solution of these fully coupled governing equations for unsaturated soils requires tremendous computational resources because three individual phases and interactions between them have to be taken into account. The fully coupled equations governing the dynamics of unsaturated soils are first presented and then two finite element formulations of the governing equations are presented and implemented within a finite element framework. The finite element implementation of all the terms in the governing equations results in the complete formulation and is solved for the first time in this paper. A computationally efficient reduced formulation is obtained by neglecting the relative accelerations and velocities of liquid and gas in the governing equations to investigate the effects of fluid flow in the overall behavior. These two formulations are used to simulate the behavior of an unsaturated silty soil embankment subjected to base shaking and compared with the results from another commonly used partially reduced formulation that neglects the relative accelerations, but takes into account the relative velocities. The stress–strain response of the solid skeleton is modeled as both elastic and elastoplastic in all three analyses. In the elastic analyses no permanent deformations are predicted and the displacements of the partially reduced formulation are in between those of the reduced and complete formulations. The frequency of vibration of the complete formulation in the elastic analysis is closer to the predominant frequency of the base motion and smaller than the frequencies of vibration of the other two analyses. Proper consideration of damping due to fluid flows in the complete formulation is the likely reason for this difference. Permanent deformations are predicted by all three formulations for the elastoplastic analyses. The complete formulation, however, predicts reductions in pore fluid pressures following strong shaking resulting in somewhat smaller displacements than the reduced formulation. The results from complete and reduced formulations are otherwise comparable for elastoplastic analyses. For the elastoplastic analysis, the partially reduced formulation leads to stiffer response than the other two formulations. The likely reason for this stiffer response in the elastoplastic analysis is the interpolation scheme (linear displacement and linear pore fluid pressures) used in the finite element implementation of the partially reduced formulation. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
12.
In this paper, we are interested in the modeling of wave propagation in viscoelastic media. We present a family of models which generalize the Zeners model. We achieve its mathematical analysis: existence and uniqueness of solutions, energy decay and propagation with finite speed. For the numerical resolution, we extend a mixed finite element method proposed in [8]. This method combines mass lumping with a centered explicit scheme for time discretization. For the resulting scheme, we prove a discrete energy decay result and provide a sufficient stability condition. For the numerical simulation in open domains we adapt the perfectly matched layers techniques to viscoelastic waves [23]. Various numerical results are presented. 相似文献
13.
We study and compare five different combinations of finite element spaces for approximating the coupled flow and solid deformation system, so-called Biot’s equations. The permeability and porosity fields are heterogeneous and depend on solid displacement and fluid pressure. We provide detailed comparisons among the continuous Galerkin, discontinuous Galerkin, enriched Galerkin, and two types of mixed finite element methods. Several advantages and disadvantages for each of the above techniques are investigated by comparing local mass conservation properties, the accuracy of the flux approximation, number of degrees of freedom (DOF), and wall and CPU times. Three-field formulation methods with fluid velocity as an additional primary variable generally require a larger number of DOF, longer wall and CPU times, and a greater number of iterations in the linear solver in order to converge. The two-field formulation, a combination of continuous and enriched Galerkin function space, requires the fewest DOF among the methods that conserve local mass. Moreover, our results illustrate that three out of the five methods conserve local mass and produce similar flux approximations when conductivity alteration is included. These comparisons of the key performance indicators of different combinations of finite element methods can be utilized to choose the preferred method based on the required accuracy and the available computational resources.
相似文献14.
E. Bruce Pitman 《国际地质力学数值与分析法杂志》1993,17(6):385-400
The equations governing the elastic-plastic deformation of granular materials are typically hyperbolic, or contain small-magnitude damping or rate effects. A finite element algorithm is the standard method for the numerical integration of these systems. In particular, finite elements allow great flexibility in the design of grid geometry. However, modern finite difference methods for hyperbolic systems have been successful in aerodynamics computations, resolving wave structures more sharply than finite element schemes. In this paper we develop a finite difference scheme for granular flow problems. We report on a second-order Godunov-type scheme for the integration of hyperbolic equations for the elastoplastic deformation of a simple model of granular flow. The Godunov method includes a characteristic tracing step in the integration, providing minimal wave dispersion, and a slope limiting step, preventing unphysical oscillations. The granular flow model we consider is hyperbolic, but hyperbolicity is lost at a large value of accumulated plastic strain. This loss of hyperbolicity is a tell-tale signal for the formation of a shear band within the sample. Typically, when systems lose hyperbolicity a regularization mechanism is added to the model equations in order to maintain the well posedness of the system. These regularizations include viscosity, viscoplasticity, higher-order gradient effects or stress coupling. Here we appeal to a very different kind of regularization. When the system loses hyperbolicity and a shear band forms, we treat the band as an internal boundary, and impose jump conditions at this boundary. Away from the band, the system remains hyperbolic and the integration step proceeds as usual. 相似文献
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Displacement and mixed finite element formulations of shear localization in materials are presented. The formulations are based on hypoplastic constitutive laws for soils and the mixed enhanced treatment involving displacement, strain and stress rates as independently varied fields. Included in these formulations are the standard displacement method, the three‐field mixed formulation, the enhanced assumed strain method and the mixed enhanced strain method. Several numerical examples demonstrating the capability and performance of the different finite element formulations are presented. The numerical results are compared with available experimental data for Hostun RF sand and numerical results for Karlsruhe sand on biaxial tests. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
17.
In this paper, we present a numerical model for simulating two-phase (oil–water and air–water) incompressible and immiscible flow in porous media. The mathematical model which is based on a fractional flow formulation is formed of two nonlinear partial differential equations: a mean pressure equation and a water saturation equation. These two equations can be solved in a sequential manner. Two numerical methods are used to discretize the equations of the two-phase flow model: mixed hybrid finite elements are used to treat the pressure equation, h-based Richards' equation and the diffusion term in the saturation equation, the advection term in the saturation equation is treated with the discontinuous finite elements. We propose a better way to calculate the nonlinear coefficients contained in our equations on each element of the discretized domain. In heterogeneous porous media, the saturation becomes discontinuous at the interface between two porous media. We show in this paper how to use the capillary pressure–saturation relationship in order to handle the saturation jump in the mixed hybrid finite element method. The two-phase flow simulator is verified against analytical solutions for some flow problems treated by other authors. 相似文献
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In modeling of many geomechanics problems such as underground openings, soil-foundation structure interaction problems, and in wave propagation problems through semi-infinite soil medium the soil is represented as a region of either infinite or semi-infinite extent. Numerical modeling of such problems using conventional finite elements involves a truncation of the far field in which the infinite boundary is terminated at a finite distance. In these problems, appropriate boundary conditions are introduced to approximate the solution of the infinite or semi-infinite boundaries as closely as possible. However, the task of positioning the finite boundary in conventional finite element discretization and the definition of the boundary and its conditions is very delicate and depends on the modeller's skill and intuition. Moreover, such a choice is influenced by the size of the domain to be discretized. Consequently, the dimensions of the global matrices and the time required for solution of the problem will increase considerably and also selection of the arbitrary location of truncated boundary may lead to erroneous result. In order to over come these problems, mapped infinite elements have been developed by earlier researchers (Simoni and Schrefier, 1987). In the present work the applicability of infinite element technique is examined for different geomechanics problems. A computer program INFEMEP is developed based on the conventional finite element and mapped infinite element technique. It is then validated using selected problems such as strip footing and circular footing. CPU time taken to obtain solutions using finite element approach and infinite element approach was estimated and presented to show the capability of coupled modeling in improving the computational efficiency. Mesh configurations of different sizes were used to explore the enhancement of both computational economy and solution accuracy achieved by incorporation of infinite elements to solve elastic and elasto-plastic problems in semi-infinite/finite domain as applied to geotechnical engineering. © Rapid Science Ltd. 1998 相似文献
20.
从双程声波方程出发,在交错网格空间中推导了地震波逆时延拓的高阶有限差分算子,依据最佳匹配层(PML)的方程分裂思路,得到了一阶声波方程的PML边界条件及其高阶差分格式,采用零时间成像条件和上行、下行波场互相关成像条件,实现了声波方程的叠后与叠前逆时深度偏移。逆时偏移对sigsbee_2b模型理论数据的偏移成像得到了满意效果。 相似文献