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1.
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   

2.
《岩土力学》2017,(7):2071-2079
移动单元法在处理移动荷载下结构动力行为分析方面具有求解高效的优势,但目前针对饱和多孔介质动力响应的移动单元法的研究成果甚少。根据饱和多孔介质u-p格式动力控制方程,利用移动坐标系建立了饱和多孔介质瞬态及稳态动力控制方程的移动单元列式,通过编制相应的计算程序将计算结果与已有文献结果对比验证了算法的正确和有效性。基于移动单元法建立了移动荷载下饱和沥青路面-弹性基层系统计算模型,分析了移动荷载下该模型的瞬态动力响应规律,并与其稳态动力响应进行了对比分析,分析表明,其水动力特性较稳态响应呈现出明显的瞬态效应。基于稳态动力响应结果分析了荷载速度、排水边界、渗透系数对饱和沥青路面动力响应的影响规律,算例研究结果可以为分析水动力作用下沥青路面水稳定性功能损伤机制提供参考。  相似文献   

3.
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   

4.
A fully coupled meshfree algorithm is proposed for numerical analysis of Biot’s formulation. Spatial discretization of the governing equations is presented using the Radial Point Interpolation Method (RPIM). Temporal discretization is achieved based on a novel three-point approximation technique with a variable time step, which has second order accuracy and avoids spurious ripple effects observed in the conventional two-point Crank Nicolson technique. Application of the model is demonstrated using several numerical examples with analytical or semi-analytical solutions. It is shown that the model proposed is effective in simulating the coupled flow deformation behaviour in fluid saturated porous media with good accuracy and stability irrespective of the magnitude of the time step adopted.  相似文献   

5.
This paper outlines the development as well as implementation of a numerical procedure for coupled finite element analysis of dynamic problems in geomechanics, particularly those involving large deformations and soil-structure interaction. The procedure is based on Biot’s theory for the dynamic behaviour of saturated porous media. The nonlinear behaviour of the solid phase of the soil is represented by either the Mohr Coulomb or Modified Cam Clay material model. The interface between soil and structure is modelled by the so-called node-to-segment contact method. The contact algorithm uses a penalty approach to enforce constraints and to prevent rigid body interpenetration. Moreover, the contact algorithm utilises a smooth discretisation of the contact surfaces to decrease numerical oscillations. An Arbitrary Lagrangian–Eulerian (ALE) scheme preserves the quality and topology of the finite element mesh throughout the numerical simulation. The generalised-α method is used to integrate the governing equations of motion in the time domain. Some aspects of the numerical procedure are validated by solving two benchmark problems. Subsequently, dynamic soil behaviour including the development of excess pore-water pressure due to the fast installation of a single pile and the penetration of a free falling torpedo anchor are studied. The numerical results indicate the robustness and applicability of the proposed method. Typical distributions of the predicted excess pore-water pressures generated due to the dynamic penetration of an object into a saturated soil are presented, revealing higher magnitudes of pore pressure at the face of the penetrometer and lower values along the shaft. A smooth discretisation of the contact interface between soil and structure is found to be a crucial factor to avoid severe oscillations in the predicted dynamic response of the soil.  相似文献   

6.
饱和多孔介质动力应变局部化分析中的内尺度律   总被引:4,自引:2,他引:4  
张洪武 《岩土力学》2001,22(3):249-253
对饱和多孔介质动力应变局部化分析中的材料内尺度律问题进行研究,讨论了当软化发生时饱和多孔介质分析的动力学稳定性问题,研究工作表明,由于液体相的作用,饱和多孔材料的动力学特性与单相固体材料有着明显的不同,特别是当应变局部化发生时,在特定情况下将仍存在可通过材料软化区域的动力波,也就是波动问题仍具有弥散特性,在此基础上,给出多孔材料的内尺度律的判定公式,讨论了内尺度律存在的条件。  相似文献   

7.
在非饱和多孔介质渗流分析中,近饱和条件下物理模型与数值模型之间的差异会导致数值不稳定问题。为解决这一问题,并保证模拟结果的可靠性,提出了3种方法,并在有限元分析程序U-DYSAC2中分别进行了程序代码的实施。通过数值试验与试验数据的比较,证实了在近饱和条件下土-水特征曲线和水力传导函数的高非线性可引起数值收敛性、稳定性和精度问题,而且在不同条件下含水率和基质吸力的预测结果差异明显。在3种方法中,修正的Van Genuchten模型(MVGM)方法对含水率的预测较为准确,而Line方法对基质吸力的预测较为合理。因此,解决在分析近饱和条件下非饱和多孔介质渗流问题时,为获得接近真实的模拟结果,采用合适的数值方法进行预测是非常关键的。  相似文献   

8.
In this paper, a mathematical model is presented for the analysis of dynamic fracture propagation in the saturated porous media. The solid behavior incorporates a discrete cohesive fracture model, coupled with the flow in porous media through the fracture network. The double‐nodded zero‐thickness cohesive interface element is employed for the mixed mode fracture behavior in tension and contact behavior in compression. The crack is automatically detected and propagated perpendicular to the maximum effective stress. The spatial discretization is continuously updated during the crack propagation. Numerical examples from the hydraulic fracturing test and the concrete gravity dam show the capability of the model to simulate dynamic fracture propagation. The comparison is performed between the quasi‐static and fully dynamic solutions, and the performance of two analyses is investigated on the values of crack length and crack mouth opening. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

9.
杨多兴  李琦  王舒 《岩土力学》2014,35(7):2047-2056
首次将高精度时空守恒元/解元方法推广到可压缩流体饱和孔隙介质中孔隙压力波传播的数值计算中。将孔隙度梯度从源(汇)项中分离,直接引入流通量,改进了理论模型。通过对孔隙介质激波问题的数值模拟,验证了方法的精度和有效性。在此基础上,提出了孔隙介质中二维黎曼问题,并揭示了孔隙压力波存在接触间断、激波、膨胀波、压缩波等复杂的结构特征。该成果对二氧化碳地质封存、二氧化碳提高石油采收率、页岩气压裂开采以及地震破裂过程的研究具有重要的理论与应用意义。  相似文献   

10.
含液各向异性多孔介质应变局部化分析   总被引:4,自引:0,他引:4  
张洪武  周雷  黄辉 《岩土力学》2004,25(5):675-680
工程中的含液多孔介质如饱和或非饱和岩土材料往往具有各向异性特性。采用Rudnicki建立的针对岩土材料的各向异性本构模型,对轴对称压缩试验中的含液多孔介质骨架的各向异性力学行为进行了分析;基于不连续分叉理论,导出了静态非渗流条件下处于轴对称应力状态的含液多孔介质应变局部化发生的临界模量、剪切带方向以及不连续速度矢量的显式表达式,在此基础上计算并讨论了材料参数变化和孔隙液体存在对各向异性多孔介质应变局部化的影响。  相似文献   

11.
In this paper a new methodology to simulate saturated soils subjected to dynamic loadings under large deformation regime (locally up to 40% in equivalent plastic strain) is presented. The coupling between solid and fluid phases is solved through the complete formulation of the Biot’s equations. The additional novelty lies in the employment of an explicit time integration scheme of the \(u-w\) (solid displacement–relative fluid displacement) formulation which enables us to take advantage of such explicit schemes. Shape functions based on the principle of maximum entropy implemented in the framework of Optimal Transportation Meshfree schemes are utilized to solve both elastic and plastic problems.  相似文献   

12.
Application of yield design to porous media usually requires a preliminary calculation of the fluid flow net. The stability analysis is then carried out with seepage forces associated with the flow. We assume here that the flow is steady and that the yield criterion is defined by a function of the effective stress tensor. The formulation that we propose here allows taking into account seepage force in the expression of the kinematic stability conditions by means of hydraulic boundary conditions without calculation of the fluid flow. One obtains a formulation of the kinematic condition similar to the case of classic, non-porous media. The method is illustrated by two examples: a cylinder subjected to fluid flow and a vertical cut. It can be adapted to various boundary conditions and to the case of a criterion defined by a function of a generalized effective stress tensor. We also give a method to derive rigorous lower bounds using approximate fluid pressure field. Copyright © 2004 John Wiley & Sons, Ltd.  相似文献   

13.
An edge-based smoothed point interpolation method is adopted for coupled hydro-mechanical analysis of saturated porous media with elasto-plastic behaviour. A novel approach for the evaluation of the coupling matrix of the porous media is adopted. Stress integration is performed using the substepping method, and the modified Newton-Raphson approach is utilised to address the nonlinearities arising from the elasto-plastic constitutive model used in the formulation. Numerical examples are studied and the results are compared with analytical solutions and those obtained from the conventional finite element method (FEM) to evaluate the performance of the proposed model.  相似文献   

14.
A meshless method based on the local Petrov–Galerkin approach is proposed to analyze 3-d axisymmetric problems in porous functionally graded materials. Constitutive equations for porous materials possess a coupling between mechanical displacements for solid and fluid phases. The work is based on the u–u formulation and the incognita fields of the coupled analysis in focus are the solid skeleton displacements and the fluid displacements. Independent spatial discretization is considered for each phase of the model, rendering a more flexible and efficient methodology. Both displacements are approximated by the moving least-squares (MLS) scheme. The paper presents in the first time a general meshless method for the numerical analysis of axisymmetric problems in continuously nonhomogeneous saturated porous media. Numerical results are given for boreholes in continuously nonhomogeneous porous medium with prescribed misfit and exponential variation of material parameters in the excavation zone.  相似文献   

15.
A numerical model based on the theory of mixtures is proposed for the nonlinear dynamic analysis of flow and deformation in unsaturated porous media. Starting from the conservation laws, the governing differential equations and the finite element incremental approximations suitable for nonlinear large deformation static and dynamic analyses are derived within the updated Lagrangian framework. The coupling between solid and fluid phases is enforced according to the effective stress principle taking suction dependency of the effective stress parameter into account. The effect of hydraulic hysteresis on the effective stress parameter and soil water characteristic curve is also taken into account. The application of the approach is demonstrated through numerical analyses of several fundamental nonlinear problems and the results are compared to the relevant analytical solutions. The effects of suction, large deformations and hydraulic hysteresis on static and dynamic response of unsaturated soils are particularly emphasized.  相似文献   

16.
马强  周凤玺  刘云帅 《冰川冻土》2016,38(4):898-903
基于Biot理论,假定固体颗粒和孔隙内流体均不可压缩,建立了以固体骨架位移表示的的控制方程.考虑单层饱和多孔介质在竖向简谐荷载作用下一维动力响应,通过理论推导获得了骨架位移、应力以及孔隙流体压力等物理量的解析表达式.基于饱和土的简谐动力模型试验数据,与所得到的理论解答相结合,将饱和多孔介质材料参数反演问题归结为非线性多峰函数的最优化问题.全局最优解的求解采用了遗传算法和模拟退火算法,并通过试验和数值算例验证了所得材料参数的正确性.  相似文献   

17.
武文华  李锡夔 《岩土力学》2009,30(5):1477-1482
对饱和多孔介质提出了一个含溶混污染物输运(传质)过程的混合元方法,其中污染物输运过程数学模型包含了对流、机械逸散、分子弥散和吸附等机制。固相位移、应变和有效应力,孔隙水压力、压力空间梯度和Darcy速度,污染物浓度、浓度空间梯度和浓度流量在单元内均为独立变量分别插值。基于胡海昌-Washizu三变量广义变分原理,结合可以滤掉虚假振荡的特征线方法,推导出饱和土中水力-力学-传质耦合问题控制方程的单元弱形式,并导出了混合元计算公式。数值模拟证明了所提出的方法可以提供与传统4点积分方案同样精度,同时能够提高计算效率。  相似文献   

18.
Crack nucleation has been the subject of important contributions in the last two last decades. However, it seems that few attention has been granted to the case of saturated porous media. This is the question addressed in the present paper which is devoted to nucleation in traction mode. From a physical point of view, nucleation is a sudden phenomenon, so that the material response is both adiabatic and undrained. In the spirit of the variational approach, the nucleated crack is viewed as the final state of a region of space in which the material undergoes a full damage process. In traction mode, the opening of a saturated crack in undrained condition induces a drop of fluid pressure. In case of low fluid compressibility, the presence of the fluid delays the brittle failure usually associated with nucleation, as long as the fluid pressure remains above the saturation vapor pressure. Nucleation is therefore possible only if a partial vaporization of the fluid takes place.  相似文献   

19.
An alternative coupled large deformation formulation combined with a meshfree approach is proposed for flow–deformation analysis of saturated porous media. The formulation proposed is based on the Updated Lagrangian (UL) approach, except that the spatial derivatives are defined with respect to the configuration of the medium at the last time step rather than the configuration at the last iteration. In this way, the Cauchy stresses are calculated directly, rendering the second Piola–Kirchhoff stress tensor not necessary for the numerical solution of the equilibrium equations. Moreover, in contrast with the UL approach, the nodal shape function derivatives are calculated once in each time step and stored for use in subsequent iterations, which reduces the computational cost of the algorithm. Stress objectivity is satisfied using the Jaumann stress rate, and the spatial discretisation of the governing equations is achieved using the standard Galerkin method. The equations of equilibrium are satisfied directly, and the nonlinear parts of the system matrix are derived independent of the stresses of the medium resulting in a stable numerical algorithm. Temporal discretisation is effected based on a three‐point approximation technique that avoids spurious ripple effects and has second‐order accuracy. The radial point interpolation method is used to construct the shape functions. The application of the formulation and the significance of large deformation effects on the numerical results are demonstrated through several numerical examples. Copyright © 2015 John Wiley & Sons, Ltd.  相似文献   

20.
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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