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1.
A new artificial boundary approach for transient seepage problems in unbounded domain is presented. The artificial boundary condition at the truncated boundary is derived from the analytical solutions for transient seepage problems in one dimension, including solutions, respectively, for flow in one‐dimensional infinite space and for radial flow in an infinite layer, and then it is tentatively applied for some two dimensional problems in addition to the one‐dimensional problems mentioned above. The boundary conditions derived relate the time‐dependent boundary flux with the time derivative of the hydraulic head at the truncated boundary, which makes the implementation much easier compared with the infinite element method. The accuracy and efficiency of the artificial boundary are validated by several numerical examples, which shows that the proposed boundary can give very good results for one‐dimensional transient seepage problems, as expected, whereas reasonable results can be also obtained for two‐dimensional problems, such as two‐dimensional axisymmetric flow and flow in an infinite plane. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
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A Simple Approach to Account for Radial Flow and Boundary Conditions When Kriging Hydraulic Head Fields for Confined Aquifers 总被引：2，自引：0，他引：2
The estimation and mapping of realistic hydraulic head fields, hence of flow paths, is a major goal of many hydrogeological studies. The most widely used method to obtain reliable head fields is the inverse approach. This approach relies on the numerical approximation of the flow equation and requires specifying boundary conditions and the transmissivity of each grid element. Boundary conditions are often unknown or poorly known, yet they impose a strong signature on the head fields obtained by inverse analysis. A simpler alternative to the inverse approach is the direct kriging of the head field using the measurements obtained at observation wells. The kriging must be modified to incorporate the available information. Use of the dual kriging formalism enables simultaneously estimating the head field, the aquifer mean transmissivity, and the regional hydraulic gradient from head data in steady or transient state conditions. In transient state conditions, an estimate of the storage coefficient can be obtained. We test the approach on simple analytical cases, on synthetic cases with solutions obtained numerically using a finite element flow simulator, and on a real aquifer. For homogeneous aquifers, infinite or bounded, the kriging estimate retrieves the exact solution of the head field, the exact hydrogeological parameters and the flow net. With heterogeneous aquifers, kriging accurately estimates the head field with prediction errors of the same magnitude as typical head measurement errors. The transmissivities are also accurately estimated by kriging. Moreover, if inversion is required, the kriged head along boundaries can be used as realistic boundary conditions for flow simulation. 相似文献
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The formulation of an axi-symmetric infinite element for transient analysis of flow problems in unbounded domain is presented. The theoretical basis as well as the implementation of the element is discussed, and the element decay function is derived using the analytical solution of a one-dimensional axially symmetric configuration. The form of decay within the element is described as a function of both time and space, and thus the hydraulic head distribution in the far field is simulated rigorously. The accuracy and the efficiency of the proposed element are demonstrated through several numerical examples in infinite media. In general, it is shown that using the present infinite element transient flow problems in unbounded domains can be simulated effectively. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
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二维饱和多孔介质因点汇诱发比奥固结的解析解 总被引：1，自引：0，他引：1
给出了有限二维饱和多孔介质因点汇诱发的Biot固结的一个解析解。其中假设多孔介质为均匀各向同性和线弹性,假设孔隙压力场符合第1类边界条件,数学模型采用可压缩多孔介质模型。利用傅里叶和拉普拉斯变换及相应反演获得了双重无穷项级数和形式的精确解。然后特别探讨了定流量点汇诱发的稳态解析解,并用文献现有解析解进行了验证。所提出的解析解适合于验证数值解,并可用于深入分析有限二维多孔介质的流-固耦合行为。 相似文献
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本文通过对二维与三维问题的无界边界元的分析,指出二维问题中原有边界元上插值函数的缺点和不合理性,提出一种新型的无界边界元插值形式,对无界单元上的发散积分作了一些讨论。 相似文献
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In this paper, the infinite boundary elements developed previously in two and three dimensional problems are reviewed, and the shortcoming and irrationality of interpolation functions of those elements are pointed out. A new interpolation function of infinite boundary element is proposed. The divergent integration on infinite element is also discussed in this paper. 相似文献
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A boundary integral equation approach is presented for the two-dimensional plane strain analysis of horizontally layered elastic systems resting on a rough and rigid base. The validity of Somigliana identity for unbounded layers is discussed and an Infinite Boundary Element is proposed in order to take into account the lateral unboundedness of the physical problem in the discretized equations. This element is implemented in a computer code based on a successive stiffness solution procedure. A series of numerical tests concerning single- and multi-layered problems is illustrated, and the performance of the proposed solution method is compared with that of more traditional boundary element and finite element techniques. 相似文献
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The present study is aimed at working out the possible resistivity anomalies associated with hydrocarbon bearing structures. The anomaly due to a typical two-dimensional anticlinal structure filled with hydrocarbon, and overlying a basement of infinite resistivity was computed using the conformal mapping technique. A more realistic and elaborate model, which could not be simplified by conformal mapping, was studied using the finite element method. This model consisted of a two-dimensional anticlinal structure filled with oil or gas-embedded midway in a homogeneous layer which itself overlies a half-space of infinite resistivity, the electrical resistivity of the hydrocarbon bearing structure being simulated as infinite. 相似文献
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An extended version of the classical Generalized Backward Euler (GBE) algorithm is proposed for the numerical integration of a three‐invariant isotropic‐hardening elastoplastic model for cemented soils or weak rocks undergoing mechanical and non‐mechanical degradation processes. The restriction to isotropy allows to formulate the return mapping algorithm in the space of principal elastic strains. In this way, an efficient and robust integration scheme is developed which can be applied to relatively complex yield surface and plastic potential functions. Moreover, the proposed algorithm can be linearized in closed form, thus allowing for quadratic convergence in the global Newton iteration. A series of numerical experiments are performed to illustrate the accuracy and convergence properties of the algorithm. Selected results from a finite element analysis of a circular footing on a soft rock layer undergoing chemical weathering are then presented to illustrate the algorithm performance at the boundary value problem level. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
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We compare two methods of evaluating head covariance for two‐dimensional steady‐state flow in mildly heterogeneous bounded
rectangular aquifers. The quasi‐analytical approach, widely used in stochastic subsurface hydrology, is based on the Green's
function representation, and involves numerical four‐fold integration. We compare this approach with a numerical solution
of the two‐dimensional boundary‐value problem for head covariance. We show that the finite differences integration of this
problem is computationally less expensive than numerical four‐fold integration of slowly‐convergent infinite series.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
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An analysis method for transient groundwater flow during slug tests performed in vertical cutoff walls is presented. The analytical solution for evaluating hydraulic conductivity of vertical cutoff walls is derived by applying the method of images to the previously developed analytical solution that is exclusively applicable to an infinite aquifer. Two distinct boundary conditions are considered to account for the configuration of the vertical cutoff wall: the wall‐soil formation interfaces with or without the existence of filter cakes, that is, constant‐head boundary and no‐flux boundary conditions. A series of type curves is constructed from the analytical solution and compared with those of a partially penetrated well within an aquifer. The constant‐head boundary condition provides faster hydraulic head recovery than the aquifer case. On the other hand, the no‐flux boundary condition leads to a delayed hydraulic head recovery. The greater the shape factor and well offset from the center of the cutoff wall, and the smaller the width of the cutoff wall, the greater the effect of the boundary condition observed in the type curves. This result shows the significance of considering proper boundary conditions at the vertical cutoff wall in analyzing slug tests. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
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This paper investigates the two‐dimensional flow problem through an anisotropic porous medium containing several intersecting curved fractures. First, the governing equations of steady‐state fluid flow in a fractured porous body are summarized. The flow follows Darcy's law in matrix and Poiseuille's law in fractures. An infinite transversal permeability is considered for the fractures. A multi‐region boundary element method is used to derive a general pressure solution as a function of discharge through the fractures and the pressure and the normal flux on the domain boundary. The obtained solution fully accounts for the interaction and the intersection between fractures. A numerical procedure based on collocation method is presented to compute the unknowns on the boundaries and on the fractures. The numerical solution is validated by comparing with finite element solution or the results obtained for an infinite matrix. Pressure fields in the matrix are illustrated for domains containing several interconnected fractures, and mass balance at the intersection points is also checked. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
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We present a second-order analytic solution [in terms of a heterogeneous log-transmissivity Y(r) = ln T(r)] for the hydraulic head field in a finite 2D confined heterogeneous aquifer under steady radial flow conditions assuming fixed head boundary conditions at the well and at a circular exterior boundary. The solution may be used to obtain the gradient used in calculation of solute transport to a well in a heterogeneous transmissivity field. The solution, obtained using perturbation methods coupled with Green's function techniques, leads us to postulate a more general form of the head for arbitrarily large-variance fields and may be used to obtain moment relations between the log-transmissivity and head under convergent flow conditions when Y(r) is expressed as a random space function. We present expressions for the mean head field when the log-transmissivity is Gaussian and conditioned on the transmissivity value at the well for an arbitrary ln T covariance. Finally, we look at the effect of parameter variations on the mean head behavior and present numerical simulations verifying the second-order mean head expressions. 相似文献
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A new finite element scheme is proposed, in this paper, for solving two-dimensional wave propagation problems in multilayered soils resting on a rigid base. The multilayered soils are treated as multiple horizontal layers of lateral infinite extension in geometry. Since these horizontal layers can be truncated by two artificially truncated vertical boundaries, two high-order artificial boundary conditions are applied for propagating the incoming waves from the interior domain into the far field of the system. Both the semi-analytical method and the truncated boundary migration procedure are used to derive the high-order artificial boundary conditions, which are comprised of a physically meaningful dashpot and a generalized energy absorber. The main advantage of using the proposed finite element scheme is that the derived artificial boundary condition can be straightforwardly implemented in the finite element analysis, without violating the band/sparse structure of the conventional finite element equation. The related numerical examples have demonstrated that the proposed finite element scheme is of high accuracy in dealing with wave propagation problems in multiple horizontal layers. 相似文献
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无限元是一种有效的人工边界,可用于处理弹性波的传播问题。在传统动力无限元的基础上,提出了一种采用分向插值技术的新型动力无限元,详细地推导了这种无限元的形函数,建立了完全解析形式的刚度矩阵,以提高计算效率,采用该无限元边界,计算了弹性介质中的线源Lamb问题,通过对比解析解答的地基表面位移,验证了该无限元的有效性。算例分析表明,采用此类无限元时,有限元单元边长建议取不超过1/8剪切波波长,网格边界到激励源点的距离宜取5倍剪切波波长。无限单元中的幅值衰减系数对计算结果影响甚微,建议取较小值。 相似文献
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极限分析有限元法讲座--Ⅱ有限元强度折减法中边坡失稳的判据探讨 总被引：141，自引：26，他引：141
边坡失稳,滑体滑出,滑体由稳定静止状态变为运动状态,同时产生很大的且无限发展的位移,这就是边坡破坏的特征。有限元中通过强度折减使边坡达到极限破坏状态,滑动面上的位移和塑性应变将产生突变,且此位移和塑性应变的大小不再是一个定值,有限元程序无法从有限元方程组中找到一个既能满足静力平衡又能满足应力-应变关系和强度准则的解,此时,不管是从力的收敛标准,还是从位移的收敛标准来判断有限元计算都不收敛。塑性区从坡脚到坡顶贯通并不一定意味着边坡破坏,塑性区贯通是破坏的必要条件,但不是充分条件,还要看是否产生很大的且无限发展的塑性变形和位移,有限元计算中表现为塑性应变和位移产生突变。在突变前计算收敛,突变之后计算不收敛,表征滑面上土体无限流动,因此可把有限元静力平衡方程组是否有解,有限元计算是否收敛作为边坡破坏的依据。- 相似文献
18.
ABAQUS动力无限元人工边界研究 总被引：2，自引：0，他引：2
针对动力场天然无限地基的数值模拟与地震波输入问题进行了一些有意义的研究,评述了现有动力计算常用无限元的优缺点,详细阐述了ABAQUS无限元理论体系框架,并加以改进,提出一种考虑外域地震动影响的ABAQUS动力无限元人工边界。采用等效边界力的叠加原理,对入射波和散射波分开处理,视入射波和散射波在边界上互不影响,将输入地震动转化为作用于有限元无限元交界面上的等效应力的方法来解决外源波的入射问题。算例验证结果表明：内源振动和固定边界会出现失真和扰动现象,同时该计算结果与黏弹性边界的计算结果对比可知,该方法对外行散射波的过滤作用优于黏弹性边界。因此,改进的ABAQUS动力无限元人工边界理论方法有效且具有一定的稳定性。 相似文献
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Hugo A. Loáiciga 《Mathematical Geosciences》2008,40(2):199-211
The equation of groundwater flow in marine island aquifers in which there is time-independent, spatially-variable recharge
and pumping is solved in closed form for rectangular, circular, and elliptical island geometries. The solution of the groundwater
flow equation is expressed in terms of the elevation of the phreatic surface within the flow domain. The depth of the seawater-freshwater
interface below mean sea level follows from the Dupuit–Ghyben–Herzberg relation. The method of solution presented in this
work relies on expanding the hydraulic head and forcing function (recharge and groundwater extraction) as Fourier series that
transforms the two-dimensional Poisson-type flow equations into second-order ordinary differential equations solvable using
classical theory. The important case of constant recharge (without groundwater extraction) leads to solutions in which the
hydraulic head is expressible as the product of a flow factor equal to the squared root of the ratio of recharge over hydraulic
conductivity times a geometric factor involving island shape parameters and flow boundary conditions. Estimability conditions
for the hydraulic conductivity are derived for the cases of constant recharge and spatially variable recharge with pumping. 相似文献
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A local artificial boundary for transient seepage problems with unsteady boundary conditions in unbounded domains 
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下载免费PDF全文 Numerical analysis of transient seepage in unbounded domains with unsteady boundary conditions requires a more sophisticated artificial boundary approach to deal with the infinite character of the domain. To that end, a local artificial boundary is established by simplifying a global artificial boundary. The global artificial boundary conditions (ABCs) at the truncated boundary are derived from analytical solutions for one‐dimensional axisymmetric diffusion problems. By applying Laplace transforms and introducing some specially defined auxiliary variables, the global ABCs are simplified to local ABCs to significantly enhance the computational efficiency. The proposed local ABCs are implemented in a finite element computer program so that the solutions to various seepage problems can be calculated. The proposed approach is first verified by the computation of a one‐dimensional radial flow problem and then tentatively applied to more general two‐dimensional cylindrical problems and planar problems. The solutions obtained using the local ABCs are compared with those obtained using a large element mesh and using a previously proposed local boundary. This comparison demonstrates the satisfactory performance and obvious superiority of the newly established boundary to the other local boundary. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献