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It is well known that the Babuska–Brezzi stability criterion or the Zienkiewicz–Taylor patch test precludes the use of the finite elements with the same low order of interpolation for displacement and pore pressure in the nearly incompressible and undrained cases, unless some stabilization techniques are introduced for dynamic analysis of saturated porous medium where coupling occurs between the displacement of solid skeleton and pore pressure. The numerical manifold method (NMM), where the interpolation of displacement and pressure can be determined independently in an element for the solution of u–p formulation, is derived based on triangular mesh for the requirement of high accurate calculations from practical applications in the dynamic analysis of saturated porous materials. The matrices of equilibrium equations for the second‐order displacement and the first‐order pressure manifold method are given in detail for program coding. By close comparison with widely used finite element method, the NMM presents good stability for the coupling problems, particularly in the nearly incompressible and undrained cases. Numerical examples are given to illustrate the validity and stability of the manifold element developed. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
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Stabilized single-point 4-node quadrilateral element for dynamic analysis of fluid saturated porous media 总被引：2，自引：0，他引：2
An accurate and efficient low-order quadrilateral mixed u?Cp element suitable for dynamic analysis of fluid saturated porous media is presented. The element uses physical hourglass stabilization to facilitate single-point integration for the solid phase, and non-residual stabilization of the fluid phase to circumvent instability in the incompressible-impermeable limit due to the use of equal-order interpolation for the displacement and pressure fields. Element behavior is verified and demonstrated through several numerical examples. 相似文献
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The development of stability problems related to classical mixed methods has recently been observed. In this study, a soil-water coupled boundary-value problem, one type of stability problem, is presented using the element-free Galerkin method (EFG method). In this soil-water coupled problem, anomalous behavior appears in the pressure field unless a stabilization technique is used. The remedy to such numerical instability has generally been to adopt a higher interpolation order for the displacements than for the pore pressure. As an alternative, however, an added stabilization term is incorporated into the equilibrium equation. The advantages of this stabilization procedure are as follows: (1) The interpolation order for the pore pressure is the same as that for the displacements. Therefore, the interpolation functions in the pore pressure field do not reduce the accuracy of the numerical results. (2) The stabilization term consists of first derivatives. The first derivatives of the interpolation functions for the EFG Method are smooth, and therefore, the solutions for pore pressure are accurate. In order to validate the above stabilization technique, some numerical results are given. It can be seen from the results that a good convergence is obtained with this stabilization term. 相似文献
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Frictionless contact formulation for dynamic analysis of nonlinear saturated porous media based on the mortar method 
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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
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Modelling of coupled fluid‐mechanical problems in fractured geological media using enriched finite elements 下载免费PDF全文
下载免费PDF全文 Jose Roberto Silvestre Euripedes do Amaral Vargas Jr. Luiz Eloy Vaz Antonio Claudio Soares 《国际地质力学数值与分析法杂志》2015,39(10):1104-1140
Geological environments, such as petroleum reservoirs, normally exhibit physical discontinuities, for example, fractures and faults. Because of the reduced thickness of these discontinuities, finite element formulations with strong discontinuity have been applied to the numerical modelling of geological environments. Until now, two relevant characteristics of petroleum reservoirs have not been addressed by these formulations. The first is the pore pressure jump in the direction normal to a discontinuity in a fluid‐mechanical coupling condition, which is present primarily in sealing faults owing to the contrast of permeability with the porous medium. The absence of this jump can affect the prediction of the deformability of a physical discontinuity. Furthermore, reservoir models frequently use coarse meshes. Thus, the method used to evaluate the pore pressure in the discontinuity may exhibit a strong dependence relative to the mesh refinement. Based on these characteristics, in this study, a formulation of an enriched finite element for application to coupled fluid‐mechanical problems with pre‐existing physical discontinuities saturated by a single fluid is presented. The formulation employs discontinuous interpolation functions and enables the reproduction of jumps of displacement and pore pressure associated with a discontinuity inside the element without the need to discretise it. An approximation to estimate the pore pressure in the discontinuity was developed, one which seeks to minimise the influence of refinement. The element's response is verified by comparison with a one‐dimensional analytical solution and simple examples that are simulated using commercial software. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
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The details of the Element Free Galerkin (EFG) method are presented with the method being applied to a study on hydraulic fracturing initiation and propagation process in a saturated porous medium using coupled hydro-mechanical numerical modelling. In this EFG method, interpolation (approximation) is based on nodes without using elements and hence an arbitrary discrete fracture path can be modelled.The numerical approach is based upon solving two governing partial differential equations of equilibrium and continuity of pore water simultaneously. 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 of equations and a fully implicit scheme is used for discretization in the time domain. Implementation of essential boundary conditions is based on the penalty method. In order to model discrete fractures, the so-called diffraction method is used.Examples are presented and the results are compared to some closed-form solutions and FEM approximations in order to demonstrate the validity of the developed model and its capabilities. The model is able to take the anisotropy and inhomogeneity of the material into account. The applicability of the model is examined by simulating hydraulic fracture initiation and propagation process from a borehole by injection of fluid. The maximum tensile strength criterion and Mohr–Coulomb shear criterion are used for modelling tensile and shear fracture, respectively. The model successfully simulates the leak-off of fluid from the fracture into the surrounding material. The results indicate the importance of pore fluid pressure in the initiation and propagation pattern of fracture in saturated soils. 相似文献
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The development of a numerical procedure for the finite element analysis of anchors dynamically penetrating into saturated soils is outlined, highlighting its unique features and capabilities. The mechanical behaviour of saturated porous media is predicted using mixture theory. An algorithm is developed for frictional contact in terms of effective normal stress. The contact formulation is based on a mortar segment-to-segment scheme, which considers the interpolation functions of the contact elements to be of order N, thus overcoming a numerical deficiency of the so-called node-to-segment (NTS) contact algorithm. The nonlinear behaviour of the solid constituent is captured by the Modified Cam Clay soil model. The soil constitutive model is also adapted so as to incorporate the dependence of clay strength on strain rate. An appropriate energy-absorbing boundary is used to eliminate possible wave reflections from the artificial mesh boundaries. To illustrate the use of the proposed computational scheme, simulations of dynamically penetrating anchors are conducted. Results are presented and discussed for the installation phase followed by ‘setup’, i.e., pore pressure dissipation and soil consolidation. The results, in particular, reveal the effects of strain rate on the generation of excess pore pressure, bearing resistance and frictional forces. The setup analyses also illustrate the pattern in which pore pressures are dissipated within the soil domain after installation. Hole closure behind a dynamic projectile is also illustrated by an example. 相似文献
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地震作用下自由场中饱和砂土的应力-应变推导 总被引：2，自引：1，他引：1
水平自由场地震响应分析是岩土地震工程实践的重要内容之一。利用香港科技大学土工离心机上的双向振动台,进行了饱和砂土自由场在水平双向地震作用下的动力模型试验。根据应力和应变的定义以及达朗贝尔原理,由试验观测的土体加速度、位移和孔隙水压力数据直接推导得到不同深度处砂土的应力和应变,揭示了振动过程中饱和砂土的应力路径和应力-应变关系演化过程,以及与超静孔隙水压力发展的联系。 相似文献
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This paper presents an iterative, incremental pressure‐stabilized fractional step algorithm for coupled hydro‐mechanical problems with mixed formulations of the displacement–pressure ( u –p) model in saturated soil dynamics that allows the use of finite elements with equal low order of interpolation approximation of u and p. In comparison with the original fractional step algorithm, the distinct features of the proposed algorithm lie in its enhanced stability owing to the introduction of both an iteration procedure and a finite increment calculus (FIC) process into the algorithm. The introduction of the iterative procedure makes the velocity term satisfy the momentum conservation equation in an implicit sense and allows much larger time step sizes to be used than those limited in existing explicit and semi‐implicit versions of the algorithm. The introduction of the FIC process removes the dependence of the stability of the proposed algorithm on the time step size, as a result it allows to using the incremental version of the algorithm and evades the minimum time step size requirement presented in the existing versions of the fractional step algorithm that restricts the application of the algorithm to saturated soil dynamics problems with high frequencies. Numerical experiments demonstrate the effectiveness and improved performance of the proposed iterative pressure‐stabilized fractional step algorithm. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
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The method of smoothed particle hydrodynamics (SPH) has recently been applied to computational geomechanics and has been shown to be a powerful alternative to the standard numerical method, that is, the finite element method, for handling large deformation and post‐failure of geomaterials. However, very few studies apply the SPH method to model saturated or submerged soil problems. Our recent studies of this matter revealed that significant errors may be made if the gradient of the pore‐water pressure is handled using the standard SPH formulation. To overcome this problem and to enhance the SPH applications to computational geomechanics, this article proposes a general SPH formulation, which can be applied straightforwardly to dry and saturated soils. For simplicity, the current work assumes hydrostatic pore‐water pressure. It is shown that the proposed formulation can remove the numerical error mentioned earlier. Moreover, this formulation automatically satisfies the dynamic boundary conditions at a submerged ground surface, thereby saving computational cost. Discussions on the applications of the standard and new SPH formulations are also given through some numerical tests. Furthermore, techniques to obtain the correct SPH solution are also proposed and discussed throughout. As an application of the proposed method, the effect of the dilatancy angle on the failure mechanism of a two‐sided embankment subjected to a high groundwater table is presented and compared with that of other solutions. Finally, the proposed formulation can be considered a basic formulation for further developments of SPH for saturated soils. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
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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
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Two formulations for calculating dynamic response of a cylindrical cavity in cross‐anisotropic porous media based on complex functions theory are presented. The basis of the method is the solution of Biot's consolidation equations in the complex plane. Employing two groups of potential functions for solid skeleton and pore fluid (each group includes three functions), the u–w formulation of Biot's equations are solved. Difference of these two solutions refers to use of two various potential functions. Equations for calculating stress, displacement and pore pressure fields of the medium are mentioned based on each two formulations. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
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饱和土变形过程模拟的统计损伤方法研究 总被引：1，自引：0，他引：1
针对传统损伤理论的不足与局限性,从研究岩土材料损伤的合理定义入手,并通过深入探讨饱和土损伤的微观力学机制,建立了适合于饱和土的新型损伤模型。在此基础上,引进统计损伤理论,建立了模拟特定围压下饱和土变形全过程的统计损伤本构模型及其参数确定方法。通过探讨饱和土损伤统计本构模型参数与围压的关系,建立了该模型的合理修正方法,从而建立了反映不同围压条件的统一饱和土损伤统计本构模型。理论与试验结果分析表明了该模型的合理性,该模型不仅能反映饱和土的变形全过程,而且能反映孔隙水压力对饱和土变形的影响。 相似文献
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饱和可液化土中地下结构在强震作用下会由于土层液化而上浮,从而对地下结构造成破坏。可液化土在地震结束之后,将由于超静孔隙水压力的消散而产生固结变形,而地下结构在土层震后固结过程中的响应是一个值得研究的问题。以地下结构在土层震后固结过程中的垂直位移为重点,应用非线性动力两相体有限元方法研究饱和可液化土和地下结构相互作用体系在地震后土层固结过程中的响应。研究结果表明,地下结构的上浮趋势不会在地震结束时立即结束,而是在土层超静孔隙水压力经过一段时间的重分布及消散以后停止,之后地下结构有一定的沉降位移,但沉降位移远小于上浮位移,因此地下结构在震后会残留向上的垂直位移。文中还讨论了土层的应力路径响应、水压消散过程及截断墙与土层渗透系数对地下结构在震后固结过程中响应的影响,试图讨论饱和可液化土中地下结构在震后固结中响应的机理。 相似文献
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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
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粘弹性准饱和土中球空腔的动力响应 总被引：2，自引：0，他引：2
从工程实际出发,采用粘弹性两相介质模型,考虑土骨架的粘性以及流体与固体之间的耦合作用,利用Laplace变换求解了粘弹性准饱和土中球空腔的动力响应问题,得到了变换域内的解析解。借助数值Laplace反变换,数值分析了粘弹性准饱和土中球空腔动力响应的位移、应力及孔压的变化规律。为分析地下结构动力响应提供了一种有效的方法,模型符合工程实际,有一定的工程应用价值。 相似文献
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A coupled elastic–plastic finite element analysis based on simplified consolidation theory for unsaturated soils is used to investigate the coupling processes of water infiltration and deformation. By introducing a reduced suction and an elastic–plastic constitutive equation for the soil skeleton, the simplified consolidation theory for unsaturated soils is incorporated into an in-house finite element code. Using the proposed numerical method, the generation of pore water pressure and development of deformation can be simulated under evaporation or rainfall infiltration conditions. Through a parametric study and comparison with the test results, the proposed method is found to describe well the characteristics during water evaporation/infiltration into unsaturated soils. Finally, an unsaturated soil slope with water infiltration is analyzed in detail to investigate the development of the displacement and generation of pore water pressure. 相似文献