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1.
A single uniform rectangular area, either homogeneous or heterogeneous, is considered in a soil medium (fundamental cell). Two governing ordinary differential equations in special form are developed for the fundamental cell. The ground supporting a partially embedded foundation is divided into a number of coarse rectangular areas (secondary cells). Each secondary cell is treated as either a single fundamental cell for homogeneous ground or a stack of fundamental cells for inhomogeneous ground. Differential equations for the assembly of secondary cells are formed with those for the fundamental cells. These equations lead to the soil responses in each cell expressed in simple closed form. They also lead to the convenient treatment of soil with appropriate Winkler-type models along the foundation faces and concentrated forces acting at the foundation corners. With them, the foundation responses are finally expressed in simple closed form. The approach is demonstrated for various cases and confirmed to produce the results reasonable enough for civil engineering use.  相似文献   

2.
A differential equation is formulated for the dynamic response of ground medium by using a simplified ground model. Applying Galerkin's procedure for weighted residual, this equation leads to a governing equation only at the ground surface. The equation indicates that the ground surface behavior can be computed even further by a simplified model. By solving the governing equation for the boundary conditions along the surface, expressions in simple closed forms are developed for the dynamic response analysis of a massless rigid foundation that rests on the ground surface. Despite their significant simplicity, the developed expressions compute the values very close to those computed by far more complex rigorous solutions. They are found to be capable of capturing the important characteristics of the dynamic ground behavior well.  相似文献   

3.
This study is concerned with the dynamic response of an arbitrary shaped rigid strip foundation embedded in an orthotropic elastic soil. The foundation is subjected to time-harmonic vertical, horizontal and moment loadings. The boundary-value problem related to an embedded foundation is analysed by using the indirect boundary integral equation method. The kernel functions of the integral equations are displacement and traction Green's functions of an anisotropic elastic half plane. Exact analytical solutions are used for the Green's functions. The boundary integral equation is solved by using numerical techniques. Selected numerical results are presented for the impedances of rectangular and semi-circular rigid strip foundations embedded in four types of anisotropic soils. A discussion on the influence of soil anisotropy and frequency of excitation on the impedances is presented. The versatility of the analysis is demonstrated by considering the through soil interaction between two semi-circular strip foundations.  相似文献   

4.
Presented is a systematic procedure for generating impedance (or compliance) matrices for foundations with arbitrary shapes, resting on an elastic half-space medium. A technique to decompose prescribed harmonic tractions on the half-space medium is employed to solve analytically the differential wave equations in cylindrical coordinates. However, the interaction stresses due to the vibration of a foundation with arbitrary shape are described in rectangular coordinates, and assumed to be piecewise constant in the region of the arbitrary shape. A coordinate transformation matrix is introduced for the piecewise constant tractions in order to use the solution of the differential wave equations in cylindrical coordinates. Finite element modelling is assumed in rectangular coordinates for the foundation itself. The impedance matrix is then obtained for the finite element model, using a variational principle and the reciprocal theorem. A simple example of a rigid square plate resting on a half-space medium and subjected to vertical excitation is used to demonstrate the efficiency and effectiveness of the procedure. Some numerical aspects are investigated and some possible extensions of the procedure are also discussed.  相似文献   

5.
Solutions for the displacements caused by dynamic loads in a viscoelastic transversely-isotropic medium are derived. The medium extends horizontally to infinity, but is bounded below by a rigid base. Stratification of the medium presents no difficulties. The medium is discretized in the vertical direction only; discretization in the horizontal direction is obviated by use of analytical solutions to the equations of motion. Application of the displacement solutions to soil-structure interaction is illustrated. A soil flexibility matrix (and hence, a stiffness matrix) for a surface foundation follows directly from the displacement solutions. A simple modification to obtain the soil stiffness for an embedded foundation of arbitrary geometry is described. Stiffnesses of rigid surface and embedded foundations are computed and compared with previously published results. In addition, the dynamic stiffness of a rigid surface foundation on a soil layer with linearly increasing shear modulus is compared to that for a homogeneous soil layer. A reduction in radiation damping is found to result from the inhomogeneity.  相似文献   

6.
Main purpose of this study is to evaluate the dynamic behavior of fluid–rectangular tank–soil/foundation system with a simple and fast seismic analysis procedure. In this procedure, interaction effects are presented by Housner's two mass approximations for fluid and the cone model for soil/foundation system. This approach can determine; displacement at the height of the impulsive mass, the sloshing displacement and base forces for the soil/foundation system conditions including embedment and incompressible soil cases. Models and equations for proposed method were briefly explained for different tank–soil/foundation system combinations. By means of changing soil/foundation conditions, some comparisons are made on base forces and sloshing responses for the cases of embedment and no embedment. The results showed that the displacements and base shear forces generally decreased, with decreasing soil stiffness. However, embedment, wall flexibility, and soil–structure interaction (SSI) did not considerably affect the sloshing displacement.  相似文献   

7.
The total system studied in this paper is a layered soil stratum with a rigid bedrock and a cylindrical cavity on the surface. Analytic solutions for the layered medium with prescribed harmonic displacement time history on the surface of the cylindrical cavity are presented. The whole soil domain is divided into interior and exterior domains. The interior domain is the projection of the cylindrical cavity down to the rigid bedrock, whereas the exterior domain is then the soil medium complement to the interior domain. The displacement and stress fields in both domains are expanded as an infinite series of Fourier components with respect to the azimuth. For each Fourier component in the infinite series, the solutions for both domains are found independently by solving the general differential equations of wave propagation satisfying the boundary conditions of the top surface and the lower rigid boundary. Displacement and stress continuity conditions are then imposed on the vertical interface between the two domains using the formulation of a weighted residual. For the soil-structure interaction problem, the impedance matrix at the interface between the structure and the soil medium can be easily generated using the analytic solutions, which can then be combined with the finite element model of the structure. A simple example is presented to demonstrate the effectiveness of the procedure presented.  相似文献   

8.
To calculate the dynamic-stiffness matrix in the time domain (unit-impulse response functions) of the unbounded medium, the infinitesimal finite element cell method based solely on the finite element formulation and working exclusively in the time domain is developed. As in the cloning algorithm, the approach is based on similarity of the unbounded media corresponding to the interior and exterior boundaries of the infinitesimal finite element cell. The derivation can be performed exclusively in the time domain, or alternatively in the frequency domain. At each time station a linear system of equations is solved. The consistent-boundary method to analyse a layered medium in the frequency domain and the viscous-dashpot boundary method are special cases of the infinitesimal finite element cell method. The error is governed by the finite element discretization in the circumferential direction, as the width of the finite-element cell in the radial direction is infinitesimal. The infinitesimal finite element cell method is thus ‘exact in the finite-element sense’. This method leads to highly accurate results for a vast class of problems, ranging from a one-dimensional spherical cavity to a rectangular foundation embedded in a half-plane.  相似文献   

9.
Local transmitting boundaries for transient elastic analysis   总被引：1，自引：0，他引：1  
The aim of this paper is to investigate and develop alternative methods of analyzing problems in dynamic soil–structure-interaction (SSI). The interaction means that the amplitude of structural response is effected by additional energy dissipation through radiation and material damping in the soil. The surrounding soft soil behaves as a natural damper for a massive and stiff structure supported or embedded in it. The main focus is the major difficulty posed by such an analysis — the phenomena of waves that radiate outward from the excited structures towards infinity. In numerical calculations only a finite region of the foundation medium is analyzed and something is done to prevent the outgoing radiation waves from reflecting at the boundary region.Development of a simple and efficient finite element (FE) procedure for the solution directly in the time domain of transient SSI problems is the main concern. The central feature of the procedure is local absorbing boundaries used to render the computational domain finite. These boundaries are local in both time and space and are completely defined by a pair of symmetric stiffness and damping matrices. As the effort for implementing them is the same as for the impedance boundary condition (BC) considering the angle of incidence, standard assembly procedure can be used. Due to the local nature they also preserve the overall structure of the global equations of motion. Even though the focus is in the time domain the same equations of motions can be used to determine the solution under time-harmonic excitation directly in the frequency domain. Explicit formulae for the element matrices are included in the paper and numerical examples for transient radiation model problems to illustrate the validity and accuracy of the new procedures, are given.  相似文献   

10.
This paper deals with the effect of the foundation mass on the filtering action exerted by embedded foundations. The system under examination comprises a rigid rectangular foundation embedded in a homogeneous isotropic viscoelastic half‐space under harmonic shear waves propagating vertically. The problem is addressed both theoretically and numerically by means of a hybrid approach, where the foundation mass is explicitly included in the kinematic interaction between the foundation and the surrounding soil, thus referring to a “quasi‐kinematic” interaction problem. Based on the results of an extensive parametric study, it is shown that the filtering problem depends essentially on three dimensionless parameters, i.e.: the dimensionless frequency of the input motion, the foundation width‐to‐embedment depth ratio, and the foundation‐to‐soil mass density ratio. In complements to the translational and rotational kinematic interaction factors that are commonly adopted to quantify the filtering effect of rigid massless foundations on the free‐field motion, an additional kinematic interaction factor is introduced, referring to the horizontal motion at the top of a rigid massive foundation. New analytical expressions for the above kinematic interaction factors are proposed and compared with foundation‐to‐free‐field transfer functions computed from available earthquake recordings on two instrumented buildings in LA (California) and Thessaloniki (Greece). Results indicate that the foundation mass can have a strong beneficial effect on the filtering action with increasing foundation‐to‐soil mass density and foundation width‐to‐embedment depth ratios.  相似文献   

11.
The paper presents a numerical model for the analysis of the soil–structure kinematic interaction of single piles and pile groups embedded in layered soil deposits during seismic actions. A finite element model is considered for the pile group and the soil is assumed to be a Winkler‐type medium. The pile–soil–pile interaction and the radiation problem are accounted for by means of elastodynamic Green's functions. Condensation of the problem permits a consistent and straightforward derivation of both the impedance functions and the foundation input motion, which are necessary to perform the inertial soil–structure interaction analyses. The model proposed allows calculating the internal forces induced by soil–pile and pile‐to‐pile interactions. Comparisons with data available in literature are made to study the convergence and validate the model. An application to a realistic pile foundation is given to demonstrate the potential of the model to catch the dynamic behaviour of the soil–foundation system and the stress resultants in each pile. Copyright © 2009 John Wiley & Sons, Ltd.  相似文献   

12.
The vertical and rocking response of rigid rectangular foundations resting on a linear-elastic, compressible, non-homogeneous half-space soil model is studied. The non-homogeneity is described by a continuous yet bounded increase of shear modulus with depth. The mixed boundary value problem is solved by means of the semi-analytical method of the subdivision of the foundation/soil contact area whereby the influence functions for the sub-regions are determined by integration of the corresponding surface-to-surface Green's functions for the particular soil model. Impedance functions are given for representative values of the non-homogeneity parameters, the Poisson's ratio and the foundation geometry over a wide range of frequencies. Significant features associated with the soil non-homogeneity are pointed out. Copyright © 1999 John Wiley & Sons Ltd.  相似文献   

13.
This paper presents a formulation for estimation of the frequency and damping of a soil‐structure interaction system based on the classical modal analysis and solving the system eigenvalue problem. Without loss of generality, the structure is represented by a single degree of freedom oscillator, while the soil effects are included through impedance functions for in‐plane motion of a 2D rigid foundation. For the results presented in this paper, the impedance functions were computed by the indirect boundary element method for a rectangular foundation embedded in a soil layer over elastic bedrock. The study shows that the classical modal‐analysis approach works well, with the exception of squat, stiff structures, even though the impedance functions are frequency‐dependent and the soil‐structure interaction system does not possess normal modes. The study also shows that system frequency and damping are independent of the wave passage effects, contrary to findings of some previous studies, and that the site conditions, represented by the soil‐layer thickness and stiffness contrast between bedrock and soil layer, have significant influences on both system frequency and system damping. Finally, the paper examines the accuracy of some of the simple methods for estimation of these two system parameters and comments on some conflicting conclusions of previous studies about the effects of foundation embedment.  相似文献   

14.
Embedded foundation in layered soil under dynamic excitations   总被引：1，自引：0，他引：1  
The critical step in the substructure approach for the soil–structure interaction (SSI) problem is to determine the impedance functions (dynamic-stiffness coefficients) of the foundations. In the present study, a computational tool is developed to determine the impedance functions of foundation in layered soil medium. Cone frustums are used to model the foundation soil system. Cone frustums are developed based on wave propagation principles and force-equilibrium approach. The model is validated for its ability to represent the embedded foundation in layered medium by comparing the results with the rigorous analysis results. Various degrees of freedom, such as, horizontal, vertical and rocking are considered for this study.  相似文献   

15.
An impedance matrix is derived for the relationship between displacements and external excitations of a rigid or flexible foundation embedded in a layered soil medium. The unknown contact distributed force between the foundation and soil is expanded in the frequency domain as a twofold series of azimuthal and radial components; each term represents a basic or fundamental distribution. As a result, the total response of the soil, either of displacements or stresses, has the same type of series expression except for the fundamental distributions replaced by influence functions. The coefficients of the series expansion, appearing in both equilibrium conditions of the foundation and compatibility conditions on the contact surface, relate the foundation displacements and excitations, and, therefore, result in the impedance matrix. Avoidance of integral equations in the soil-structure interaction analysis is the merit of the present approach.  相似文献   

16.
An alternate formulation of the ‘substructure deletion method’ suggested by Dasgupta in 19791 has been successfully implemented. The idea is to utilize simple Green's functions developed for a surface problem to replace the more complicated Green's functions required for embedded problems while still being able to generate an accurate solution. Since the exterior medium is usually represented by a continuum model, the interior medium in the present approach will also be represented by a continuum model rather than a finite element model as suggested originally, thereby eliminating the incompatibility between the solutions of the interior and exterior media. Detailed studies of the method's accuracy and limitations were performed using two-dimensional examples in wave scattering of canyons and alluvial valleys, problems which are more suitable for this method than the embedded foundation problem. The results obtained indicate that the alternate formulation gives accurate results only when the vertical dimension of the scattering object is not too large; if the aspect ratio (vertical over lateral) exceeds a certain limit, the results will not approach the known results given by boundary integral equation solutions or indirect boundary integral equations no matter what the refinement of the model may be. The greatest advantage of the present method is that the task of calculating Green's functions is reduced significantly; computational time using this new formulation is approximately five times less than for conventional boundary integral equation methods.  相似文献   

17.
The dynamic soil–structure interaction of a rigid rectangular foundation with the subsoil represents a mixed-boundary value problem. This problem is formulated in terms of a system of coupled Fredholm integral equations of the first kind. The subsoil is modelled by a homogeneous, linear-elastic and isotropic half-space which is perfectly bonded to the rigid, rectangular foundation. An approximate solution for the resultant loads between the foundation and the half-space due to a unit forced displacement or rotation is obtained using the Bubnov–Galerkin method. Using this method the displacement boundary value conditions are exactly satisfied and the contact stress distributions between the foundation and the half-space are approximated by series expansions of Chebyshev polynomials. This method provides a simple means of studying the soil-structure interaction of rectangular foundations with different inertia properties.  相似文献   

18.
A numerical scheme is developed in the paper for calculating torsional, vertical, horizontal, coupling and rocking impedances in frequency domain for axial-symmetric foundations embedded in layered media. In the scheme, the whole soil domain is divided into interior and exterior domains. For the exterior domain, the analytic solutions with unknown coefficients are obtained by solving three-dimensional (3D) wave equations in cylindrical coordinates satisfying homogeneous boundary conditions. For the interior domain, the analytical solutions are also obtained by solving the same 3D wave equations satisfying the homogeneous boundary conditions and the prescribed boundary conditions. The prescribed conditions are the interaction tractions at the interfaces between embedded foundation and surrounding soil. The interaction tractions are assumed to be piecewise linear. The piecewise linear tractions at the bottom surface of foundation will be decomposed into a series of Bessel functions which can be easily fitted into the general solutions of wave equations in cylindrical coordinates. After all the analytic solutions with unknown coefficients for both interior and exterior domains are found, the variational principle is employed using the continuity conditions (both displacements and stresses) at the interfaces between interior and exterior domains, interior domain and foundation, and exterior domain and foundation to find impedance functions.  相似文献   

19.
To explore the seismic performance of a high-rise pile cap foundation with riverbed scour, a finite element model for foundations is introduced in the OpenSees finite element framework. In the model, a fiber element is used to simulate the pile shaft, a nonlinear p-y element is used to simulate the soil-pile interaction, and the p-factor method is used to reflect the group effects. A global and local scour model is proposed, in which two parameters, the scour depth of the same row of piles and the difference in the scour depth of the upstream pile and the downstream pile, are included to study the influence of scour on the foundation. Several elasto-plastic static pushover analyses are performed on this finite element model. The analysis results indicate that the seismic capacity (or supply) of the foundation is in the worst condition when the predicted deepest global scout depth is reached, and the capacity becomes larger when the local scour depth is below the predicted deepest global scout depth. Therefore, to evaluate the seismic capacity of a foundation, only the predicted deepest global scout depth should be considered. The method used in this paper can be also applied to foundations with other soil types.  相似文献   

20.
大地电磁二维对称各向异性介质的有限元数值模拟   总被引：5，自引：0，他引：5       下载免费PDF全文
假定垂直轴为二维对称各向异性介质主轴之一，构造走向与另一主轴方向成任一夹角，用伽勒金（Ｇａｌｅｒｋｉｎ）有限元法和矩形网格，优化地合成总体刚度矩阵，使二维各向异性介质的基本方程形成有限元代数方程组，求出各节点场值，并利用ＭＯＭ法求出辅助场，进而求出张量阻抗等响应函数．同时还对有关文献的计算模型进行了数值模拟检验  相似文献   

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