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1.
An efficient finite–discrete element method applicable for the analysis of quasi‐static nonlinear soil–structure interaction problems involving large deformations in three‐dimensional space was presented in this paper. The present method differs from previous approaches in that the use of very fine mesh and small time steps was not needed to stabilize the calculation. The domain involving the large displacement was modeled using discrete elements, whereas the rest of the domain was modeled using finite elements. Forces acting on the discrete and finite elements were related by introducing interface elements at the boundary of the two domains. To improve the stability of the developed method, we used explicit time integration with different damping schemes applied to each domain to relax the system and to reach stability condition. With appropriate damping schemes, a relatively coarse finite element mesh can be used, resulting in significant savings in the computation time. The proposed algorithm was validated using three different benchmark problems, and the numerical results were compared with existing analytical and numerical solutions. The algorithm performance in solving practical soil–structure interaction problems was also investigated by simulating a large‐scale soft ground tunneling problem involving soil loss near an existing lining. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
2.
Previous analytic solutions to the problem of the consolidation of a deep clay stratum subjected to a surface loading, have been obtained for the assumed condition of a completely permeable upper surface. This may not be so in many applications, where the foundation causing the loading may be impermeable, and therefore only that part of the clay surface outside the loading is free to drain.In this paper a method is presented which may be used to obtain the time-settlement behaviour of a circular loading applied over an impermeable region of the surface of the clay. The solution technique involves representing the continuous values of fluid flow along the surface boundary as uniform blocks of flow. The solution is found in Laplace transform space and a numerical inversion technique is then used to obtain the time dependent solution.Two types of surface loading are examined; a completely uniform loading and a loading distribution which is approximately that of a rigid footing. For the uniform loading case, comparisons are made with previous solutions (permeable surface) and it is shown that the assumption of an impermeable loaded region leads to significant changes in the time-settlement behaviour of the loading. 相似文献
3.
A hybrid finite element method and differential quadrature method (DQM) is developed to estimate the dynamic response of two‐dimensional multilayered half‐spaces subjected to impulsive point loading. Nonreflecting absorbing boundary conditions consist of appropriate springs, and dampers are considered. The capabilities of the finite element method for solving boundary value problems with general domain, loading and systematic boundary treatment are combined with accurate and stable time marching capabilities of the DQM to develop an accurate and efficient numerical technique. The capability, efficiency, robustness and convergence of the DQM for solving the dynamic problem are demonstrated through numerical simulations of various half‐spaces with different time increments and layer arrangement. Also, comparison study when using Newmark's time integration scheme for the same problem is done. It can be concluded that the DQM as an unconditionally stable method is suitable for solving such a problem. Also, parametric study is performed to show the effect of the absorbing boundary conditions on the dynamic response. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
4.
竖向圆形荷载作用下弹性半空间问题的位移和应力解是桩基分析的基础。利用Hankel积分变换,首先导出了弹性地基半空间位移与应力的积分形式的通解。通过适当地引入边界条件和界面位移和应力的连续条件,求得了内部作用竖向圆形荷载时弹性地基半空间位移与应力的积分形式解。在此基础上,给出了不同深度处荷载作用投影范围内竖向位移和竖向正应力的平均值。数值结果验证了解析解的正确性。 相似文献
5.
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
6.
Two integration algorithms, namely the implicit return mapping and explicit sub-stepping schemes, are adopted in the anisotropic bounding surface plasticity model for cyclic behaviours of saturated clay and are implemented into finite element code. The model is a representative of a series of bounding surface models that have typical characteristics, including isotropic and kinematic hardening rules and a rotational bounding surface to capture complex but important cyclic behaviours of soils, such as cyclic shakedown and degradation. However, there is no explicit current yield surface in the model to which the conventional implicit algorithm returns the stress state back or the sub-stepping integration corrects the drift of the stress state. Hence, necessary modifications have been made for both of the integration schemes. First, the image stress point is mapped or corrected to the bounding surface instead of mapping back or correcting the stress state to the yield surface. Second, the unloading–loading criterion is checked to determine the image stress point rather than checking the yield criterion after giving the trial stress state in a conventional way. Comparative studies on the accuracy, stability and efficiency of the two integration schemes are conducted not only at the element level but also in solving boundary value problems of monotonic and cyclic bearing behaviours of rigid footings on saturated clay. For smaller strain increments, there is no significant difference in the accuracy between the two integration schemes, but the explicit integration shows a higher efficiency and accuracy. For relatively larger increments, the implicit return mapping algorithm presents good accuracy and more robustness, while the sub-stepping algorithm shows deteriorating accuracy and suffers the convergence problem. With the tolerance used in the present model, the bearing capacity of the rigid footing predicted by the return mapping algorithm is closer to the available analytical and numerical solutions, while the bearing capacity predicted by the sub-stepping algorithm shows a marginal increase. 相似文献
7.
Summary The edge function method is considered as an alternative to conventional numerical schemes for the solution of plane problems in rock mechanics. The essence of the approach is the approximation of the solution by a linear combination of solutions of the field equations. The unknowns in the linear combination are obtained from a system of equations which follows from the approximation of the boundary conditions by a boundary Galerkin energy method. No mesh generation is required over the domain or boundary of the problem. Previous edge function work in anisotropic elasticity is enhanced by the incorporation of a special solution for the effect of gravity. Examples are presented to illustrate the applicability of the method in determining stresses in various rock mechanics problems. A high level of accuracy is achieved with a relatively small number of degrees of freedom. Convergence is rapid because of the inclusion of special analytic solutions to model stress concentrations. The inclusion of the gravity force does, however, lead to a small increase in the number of degrees of freedom needed to achieve acceptable results. The optimum use of the edge function method, at present, may be as a special element within more general finite element or discrete element codes. 相似文献
8.
A Laplace transform is used to solve the problem of the steady state and transient response of a pinned head pile embedded into a viscoelastic Winkler soil medium. The pile is modeled as an Euler–Bernoulli beam while the soil medium is modeled using a Winkler subgrade approach. Two analytical solutions are developed to specifically address both steady state and transient loads encountered during dynamic pile testing. After choosing a proper contour integration in the complex plane, inverse integration is evaluated. The steady state solutions are associated to the residues of the integration around the poles while the transient solutions are associated to the integration paths along the contour integration. The derived solutions are applied to a case history for which results of dynamic pile tests are available. Dynamic pile flexion is generated by delivering eccentric impact using a dynamic loading test module. Validity of the proposed solution is discussed basing on geotechnical campaign and recorded pile head bending moment and rotation rate. 相似文献
9.
裂隙岩体因含有发育程度不同的裂隙、节理和断层等不连续面,致其渗透性具有各向异性、不连续性等特点,因此传统的有限元法对分布密集的裂隙岩体渗流场求解有一定的难度。本文提出了采用无单元Glaerkin法求解有自由面裂隙渗流问题,并推导了无单元法求解渗流场的基本方程和积分格式,给出了应用罚函数法处理渗流边界条件和自由面处理方法。采用IDL语言编制了二维无单元法计算软件LIDAREFM。文中以北京怀柔桥梓镇某裂隙岩体边坡渗流场计算为例,研究了复杂裂隙共同作用下渗流场特性和自由面分布,讨论了不同开度、不同连通程度的裂隙对渗流场的影响。研究结果表明:无单元法可以较好地解决有密集裂隙的岩体渗流场的求解问题,实现了裂隙处结点任意加密以及积分网格的独立布置,避免了对有自由面和裂隙穿越的子域的重新处理,简化了渗流问题的求解过程。 相似文献
10.
This paper presents a non‐linear coupled finite element–boundary element approach for the prediction of free field vibrations due to vibratory and impact pile driving. Both the non‐linear constitutive behavior of the soil in the vicinity of the pile and the dynamic interaction between the pile and the soil are accounted for. A subdomain approach is used, defining a generalized structure consisting of the pile and a bounded region of soil around the pile, and an unbounded exterior linear soil domain. The soil around the pile may exhibit non‐linear constitutive behavior and is modelled with a time‐domain finite element method. The dynamic stiffness matrix of the exterior unbounded soil domain is calculated using a boundary element formulation in the frequency domain based on a limited number of modes defined on the interface between the generalized structure and the unbounded soil. The soil–structure interaction forces are evaluated as a convolution of the displacement history and the soil flexibility matrices, which are obtained by an inverse Fourier transformation from the frequency to the time domain. This results in a hybrid frequency–time domain formulation of the non‐linear dynamic soil–structure interaction problem, which is solved in the time domain using Newmark's time integration method; the interaction force time history is evaluated using the θ‐scheme in order to obtain stable solutions. The proposed hybrid formulation is validated for linear problems of vibratory and impact pile driving, showing very good agreement with the results obtained with a frequency‐domain solution. Linear predictions, however, overestimate the free field peak particle velocities as observed in reported field experiments during vibratory and impact pile driving at comparable levels of the transferred energy. This is mainly due to energy dissipation related to plastic deformations in the soil around the pile. Ground vibrations due to vibratory and impact pile driving are, therefore, also computed with a non‐linear model where the soil is modelled as an isotropic elastic, perfectly plastic solid, which yields according to the Drucker–Prager failure criterion. This results in lower predicted free field vibrations with respect to linear predictions, which are also in much better agreement with experimental results recorded during vibratory and impact pile driving. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
11.
Comparing the Gradual Deformation with the Probability Perturbation Method for Solving Inverse Problems 总被引：1，自引：0，他引：1
Jef Caers 《Mathematical Geology》2007,39(1):27-52
Inverse problems are ubiquitous in the Earth Sciences. Many such problems are ill-posed in the sense that multiple solutions
can be found that match the data to be inverted. To impose restrictions on these solutions, a prior distribution of the model
parameters is required. In a spatial context this prior model can be as simple as a Multi-Gaussian law with prior covariance
matrix, or could come in the form of a complex training image describing the prior statistics of the model parameters. In
this paper, two methods for generating inverse solutions constrained to such prior model are compared. The gradual deformation
method treats the problem of finding inverse solution as an optimization problem. Using a perturbation mechanism, the gradual
deformation method searches (optimizes) in the prior model space for those solutions that match the data to be inverted. The
perturbation mechanism guarantees that the prior model statistics are honored. However, it is shown with a simple example
that this perturbation method does not necessarily draw accurately samples from a given posterior distribution when the inverse
problem is framed within a Bayesian context. On the other hand, the probability perturbation method approaches the inverse
problem as a data integration problem. This method explicitly deals with the problem of combining prior probabilities with
pre-posterior probabilities derived from the data. It is shown that the sampling properties of the probability perturbation
method approach the accuracy of well-known Markov chain Monte Carlo samplers such as the rejection sampler. The paper uses
simple examples to illustrate the clear differences between these two methods 相似文献
12.
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
13.
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
14.
Sylvain Weill Raphael di Chiara-Roupert Philippe Ackerer 《Computational Geosciences》2014,18(5):697-709
The diffusive wave approximation of the Saint-Venant equations is commonly used in hydrological models to describe surface flow processes. Numerous numerical approaches can be used to solve this highly nonlinear equation. Nonlinear time integration schemes—also called methods of lines (MOL)—were proven very efficient to solve other nonlinear problems in geosciences but were never considered to deal with surface flow modeling with the diffusive wave equation. In this paper, we study the relative performance of different time and space integration schemes by comparing the results obtained with classical approaches and with nonlinear time integration approaches. The results show that (i) the integration method with a higher order in space shows high accuracy regarding an integrated indicator such as the global mass balance error but is less accurate regarding local indicators, and (ii) nonlinear time integration techniques perform better than classical ones. Overall, it seems that integration techniques combining nonlinear time integration and a low spatial order need to be considered when developing hydrological modeling tools owing to their simplicity of implementation and very good performance. 相似文献
15.
Laboratory consolidation of structured clayey soils is analysed in this paper. The research is carried out by two different methods. The first one treats the soil as an isotropic homogeneous equivalent Double Porosity (DP) medium. The second method rests on the extensive application of the Finite Element Method (FEM) to combinations of different soils, composing 2D or fully 3D ordered structured media that schematically discretize the complex material. Two reference problems, representing typical situations of 1D laboratory consolidation of structured soils, are considered. For each problem, solution is obtained through integration of the equations governing the consolidation of the DP medium as well as via FEM applied to the ordered schemes composed of different materials. The presence of conventional experimental devices to ensure the drainage of the sample is taken into account through appropriate boundary conditions. Comparison of FEM results with theoretical results clearly points out the ability of the DP model to represent consolidation processes of structurally complex soils. Limits of applicability of the DP model may arise when the rate of fluid exchange between the two porous systems is represented through oversimplified relations. Results of computations, obtained having assigned reasonable values to the meso‐structural and to the experimental apparatus parameters, point out that a partially efficient drainage apparatus strongly influences the distribution along the sample and the time evolution of the interstitial water pressure acting in both systems of pores. Data of consolidation tests in a Rowe's cell on samples of artificially fissured clays reported in the literature are compared with the analytical and numerical results showing a significant agreement. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
16.
The numerical integration of the stress–strain relationship is an important part of many finite element code used in geotechnical engineering. The integration of elasto-plastic models for unsaturated soils poses additional challenges associated to the presence of suction as an extra constitutive variable with respect to traditional saturated soil models. In this contribution, a range of explicit stress integration schemes are derived with specific reference to the Barcelona Basic Model (BBM), which is one of the best known elasto-plastic constitutive models for unsaturated soils. These schemes, however, do not address possible non-convexity of the loading collapse (LC) curve and neglect yielding on the suction increase (SI) line. The paper describes eight Runge–Kutta methods of various orders with adaptive substepping as well as a novel integration scheme based on Richardson extrapolation. The algorithms presented also incorporate two alternative error control methods to ensure accuracy of the numerical integration. Extensive validation and comparison of different schemes are presented in a companion paper. Although the algorithms presented were coded for the Barcelona Basic Model, they can be easily adapted to other unsaturated elasto-plastic models formulated in terms of two independent stress variables such as net stress and suction. 相似文献
17.
A boundary element approach for time harmonic axisymmetric problems using the complete space point load fundamental solution is presented. The fundamental solution is integrated numerically along the azimuthal co-ordinate of each axisymmetric element. To increase the accuracy of the numerical integration a simple co-ordinate transformation is proposed. The approach is applied to the computation of the dynamic stiffness functions of rigid circular foundations on layered viscoelastic soils. Three different sites are considered: a uniform half-space, a soil layer on a half-space, and a soil consisting of four horizontal layers and a compliant half-space. The numerical results obtained by the proposed approach for surface circular foundations are very close to corresponding published results obtained by different procedures. 相似文献
18.
将任意挡墙水平变位模式分解为抛物线柔性模式和梯形刚性模式,并通过求解平面应变方程,得到挡墙在抛物线柔性变位模式下的理论解,给出地表土体的沉降曲线,分析土体沉降规律,同时将理论解应用于工程案例分析,通过与4个基坑开挖实例沉降归一化曲线的对比,分析解的适用性。结果显示,当挡墙发生抛物线变位模式时,地表沉降整体规律为向下凹槽型,最大沉降发生在距离墙背一定距离处,与实际情况相符。理论解形式表明,最终的表达式与弹性参量无关;归一化的沉降曲线显示,理论预测的最大沉降位置与实测值接近,且土体沉降模式与实测结果一致,说明理论解是合理的。 相似文献
19.
Luz Angélica Caudillo-Mata Eldad Haber Christoph Schwarzbach 《Computational Geosciences》2017,21(5-6):963-980
In order to reduce the computational cost of the simulation of electromagnetic responses in geophysical settings that involve highly heterogeneous media, we develop a multiscale finite volume method with oversampling for the quasi-static Maxwell’s equations in the frequency domain. We assume a coarse mesh nested within a fine mesh that accurately discretizes the problem. For each coarse cell, we independently solve a local version of the original Maxwell’s system subject to linear boundary conditions on an extended domain, which includes the coarse cell and a neighborhood of fine cells around it. The local Maxwell’s system is solved using the fine mesh contained in the extended domain and the mimetic finite volume method. Next, these local solutions (basis functions) together with a weak-continuity condition are used to construct a coarse-mesh version of the global problem. The basis functions can be used to obtain the fine-mesh details from the solution of the coarse-mesh problem. Our approach leads to a significant reduction in the size of the final system of equations and the computational time, while accurately approximating the behavior of the fine-mesh solutions. We demonstrate the performance of our method using two 3D synthetic models: one with a mineral deposit in a geologically complex medium and one with random isotropic heterogeneous media. Both models are discretized using an adaptive mesh refinement technique. 相似文献
20.
基于一维固结理论,研究了土层物理力学性质沿深度非均匀连续变化的固结问题。首先,利用分离变量法,获得了渗透系数和压缩系数随深度按指数函数变化的非均匀地基一维固结方程的解析表达式; 然后与Terzaghi固结理论的经典解答进行了比较,获得了两种解答之间的相似转换关系。这样,非均匀地基固结问题就可以用相同荷载以及边界条件下的均匀地基固结的经典解线性表示。因此,非均匀地基固结问题的求解转化为对相似转换系数的计算。该系数集中反映土层非均匀性对地基固结的影响,从而为解决非均匀地基一维固结问题提供了便捷途径。 相似文献