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1.
The effect of the rigid sidewall, which is usually combined with embedded footings, on the dynamic stiffness of the footings is considered. An efficient numerical technique is used to calculate the static and dynamic stiffness of circular footings embedded in a stratum. The results show that the increase in static stiffness with increasing height of the sidewall is most significant in the case of rocking. The dynamic stiffness coefficients change considerably, if the sidewall extends higher than about half the depth of embedment. The damping coefficients corresponding to vertical vibrations and rocking are likewise affected by the height of the sidewall. The damping coefficients corresponding to torsional and horizontal vibrations increase considerably with increasing height of the sidewall.  相似文献   

2.
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   

3.
A simplified discrete system in the form of a simple oscillator is developed to simulate the dynamic behavior of a structure founded through footings or piles on compliant ground, under harmonic excitation. Exact analytical expressions for the fundamental natural period and the corresponding damping coefficients of the above system are derived, as function of geometry and the frequency-dependent foundation impedances. In an effort to quantify the coupling between swaying and rocking oscillations in embedded foundations such as piles, the reference system is translated from the footing–soil interface to the depth where the resultant soil reaction is applied, to ensure a diagonal impedance matrix. The resulting eccentricity is a measure of the coupling effect between the two oscillation modes. The amounts of radiation damping generated from a single pile and a surface footing are evaluated. In order to compare the damping of a structure on a surface footing and a pile, the notion of static and geometric equivalence is introduced. It is shown that a pile may generate significantly higher radiation damping than an equivalent footing, thus acting as an elementary protective system against seismic action.  相似文献   

4.
An approximate analytical method is presented for the dynamic response of a rigid cylindrical foundation embedded in a poroelastic soil layer under the excitation of a time-harmonic rocking moment. The soil underlying the foundation base is represented by a single-layered poroelastic soil based on rigid bedrock while the soil along the side of the foundation is modeled as an independent poroelastic stratum composed of a series of infinitesimally thin layers. The accuracy of the present solution is verified by comparisons with existing solutions obtained from other researchers. Numerical results for the rocking dynamic impedance and dynamic response factor are presented to demonstrate the influence of nondimensional frequency of excitation, poroelastic soil layer thickness, depth ratio of the foundation and internal friction of the poroelastic soil.  相似文献   

5.
The system damping, the system frequency, the relative building response and the base rocking response peak amplitudes are studied, as those depend on the building mass and height, the flexibility of the soil, the structural damping, the type of incident waves and their angle of incidence. A linear two-dimensional model is used, which assumes the soil to be a homogeneous isotropic half-space, the foundation supporting the building to be a rigid embedded cylinder, and in which the building model is an equivalent single-degree-of-freedom oscillator. The system frequency and the system damping ratio are determined by measuring the width and the frequency of the peak in the transfer function of the oscillator relative response, using the analogy with the half-power method for a single-degree-of-freedom fixed-base oscillator. Previous similar studies are for dynamic soil-structure interaction only, and for simplified models in which the stiffness of the soil and the damping due to radiation are represented by springs and dashpots. The study in this paper differs from the previous studies in that the wave passage effects (or the kinematic interaction) are also included, and that no additional simplifications of the model are made. Results are shown for excitation by plane P- and SV-waves.  相似文献   

6.
A simplified damped oscillator model is proposed to simulate unbounded soil for the vertical vibration analysis of rigid embedded foundations. Based on the dynamic responses of a foundation–soil system, an optimal equivalent model is determined as the best simplified model. Magnification responses of a foundation–soil system simulated by the optimal equivalent model are well consistent with those obtained by the half-space theory and by a widely used computer program even as embedment depth or vibrating mass increases. The optimal equivalent model utilizing only three parameters can result in responses as accurate as the existing models, which use more parameters. This proposed method uses much simpler procedure than optimization techniques used by most existing discrete models. This proposed method may also be easily and accurately applied to practical soil–structure interaction analysis.  相似文献   

7.
A study of the dynamics of building-soil interaction is presented that includes embedding of the foundation and material damping. By considering buildings on rigid footings embedded into linear elastic soil with hysteretic damping, it is shown that the earthquake response of the building-foundation model may be found from the response to modified excitation of equivalent one-degree-of-freedom linear, viscously damped oscillators resting on rigid ground. For a single-storey building approximate formulas are developed for the modified natural frequency and damping ratio. Results show that the natural frequency and damping in the system increase with embedding. Effective damping also increases with internal friction in the soil. Ignoring these two factors may underestimate considerably the effective natural frequency and damping in the system. In spite of additional sources of energy dissipation provided by the soil, damping in the equivalent oscillator may be greater or smaller than that corresponding to the superstructure alone, depending upon the system parameters. For lightly damped superstructures, the peak amplitude of the steady-state overturning moment at the base of a building supported on flexible soil is significantly smaller than that corresponding to rigid ground. This result has practical implications for earthquake design.  相似文献   

8.
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   

9.
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   

10.
A numerical solution for evaluating the effects of foundation embedment on the effective period and damping and the response of soil–structure systems is presented. A simple system similar to that used in practice to account for inertial interaction effects is investigated, with the inclusion of kinematic interaction effects for the important special case of vertically incident shear waves. The effective period and damping are obtained by establishing an equivalence between the interacting system excited by the foundation input motion and a replacement oscillator excited by the free-field ground motion. In this way, the use of standard free-field response spectra applicable to the effective period and damping of the system is permitted. Also, an approximate solution for total soil–structure interaction is presented, which indicates that the system period is insensitive to kinematic interaction and the system damping may be expressed as that for inertial interaction but modified by a factor due to kinematic interaction. Results involving both kinematic and inertial effects are compared with those obtained for no soil–structure interaction and inertial interaction only. The more important parameters involved are identified and their influences are examined over practical ranges of interest. © 1998 John Wiley & Sons, Ltd.  相似文献   

11.
This study investigated the seismic performance and soil‐structure interaction of a scoured bridge models with pile foundation by shaking table tests using a biaxial laminar shear box. The bridge pier model with pile foundation comprised a lumped mass representing the superstructure, a steel pier, and a footing supported by a single aluminum pile within dry silica sand. End of the pile was fixed at the bottom of the shear box to simulate the scenario that the pile was embedded in a firm stratum of rock. The bridge pier model was subjected to one‐directional shakes, including white noise and earthquake records. The performance of the bridge pier model with pile foundation was discussed for different scoured conditions. It is found that the moment demand of pile increases with the increase of scoured depth whereas the moment demand of the bridge pier decreases, and this transition may induce the bridge failure mechanism transform from pier to pile. The seismic demand on scoured pile foundations may be underestimated and misinterpreted to a certain degree. When evaluating the system damping ratio with SSI, the system response may not be significantly changed even if the soil viscous damping contribution is varied. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

12.
In this research, a parametric study is carried out on the effect of soil–structure interaction on the ductility and strength demand of buildings with embedded foundation. Both kinematic interaction (KI) and inertial interaction effects are considered. The sub‐structure method is used in which the structure is modeled by a simplified single degree of freedom system with idealized bilinear behavior. Besides, the soil sub‐structure is considered as a homogeneous half‐space and is modeled by a discrete model based on the concept of cone models. The foundation is modeled as a rigid cylinder embedded in the soil with different embedment ratios. The soil–structure system is then analyzed subjected to a suit of 24 selected accelerograms recorded on alluvium deposits. An extensive parametric study is performed for a wide range of the introduced non‐dimensional key parameters, which control the problem. It is concluded that foundation embedment may increase the structural demands for slender buildings especially for the case of relatively soft soils. However, the increase in ductility demands may not be significant for shallow foundations with embedment depth to radius of foundation ratios up to one. Comparing the results with and without inclusion of KI reveals that the rocking input motion due to KI plays the main role in this phenomenon. Copyright © 2008 John Wiley & Sons, Ltd.  相似文献   

13.
Many free and forced vertical vibrations tests were conducted on surface and embedded models for footings on dry and moist poorly graded sand that has the following properties: D10 = 0·21 mm, D30 = 0·305 mm, D60 = 0·423 mm, Cu = 2, Cc = 1·05, Gs = 2·66, γmax = 1·74 cm−3 and γmin = 1·4 g cm−3. The tests were conducted at relative density Dr = 82%. The effect of mass, area, geometry, embedment, saturation, load amplitude and frequency were studied. For this purpose square, rectangular and circular models of concrete footings were chosen. Swieleh sand was chosen as the foundation soil. Results have been obtained for models having different mass, same base shape and area; models of different base area and equal base shape and mass; and models of different base shape geometry and about equal masses and base areas.Forced vertical vibration tests results showed an increase in natural frequency and a reduction in amplitude with the increase in embedment depth, degree of saturation and footing base area. Increasing the mass of model footing resulted in a decrease in the natural frequency while the dynamic response increased. Also, results showed that the circular model footing gives low values of dynamic response in comparison to other models.Free vertical vibration test results showed an increase in damping ratio with increase in the base area of the model footing, depth of embedment and saturation of sand. On the other hand, the results showed a decrease in damping ratio with increase in the footing mass. Circular footing gives the highest value of damping ratio among other footings.Results showed that the best method for evaluating the dynamic stiffness for vertical vibration is using Dobry and Gazetas1 (J. Geotech. Engng, ASCE, 1986, 112, 109–133) equations together with the formula proposed by Ronald and Bojan2 (J. Geotech. Engng, ASCE, 1995, 121, 274–286) for evaluating the equivalent shear modulus.  相似文献   

14.
In this paper, results of a detailed investigation on the dynamic response of rigid strip foundations in viscoelastic soils under vertical excitation are presented. An advanced boundary element algorithm developed by incorporating isoparametric quadratic elements and a sophisticated self-adapting numerical integration scheme has been used for this investigation. Foundations supported on three types of soil profiles, namely, homogeneous half-space, stratum-over-half-space and stratum-over-bedrock are considered. The influence of material properties like Poisson's ratio and material damping as well as the influence of geometrical properties such as depth of embedment and layer thickness are studied. The effect of the type of contact at the soil-foundation interface is also investigated.  相似文献   

15.
Most offshore platforms are supported on long and large-diameter piles with variable wall-thickness along the length, and soil properties varying with depth. The design and analyses of these piles are made by modelling the soil-pile system with a beam-on-Winkler foundation. Therefore, evaluation of appropriate soil-pile springs for use in such analyses is a matter of concern. Fundamental characteristics of dynamic lateral load-deflection relationships for piles were studied analytically considering the soil-pile-structure interaction under seismic loading conditions. The soil layer was assumed homogeneous, linearly elastic with hysteretic type material damping, and overlying a rigid base. A superstructure with multi-degrees of freedom was supported by a single vertical pile hinged at the rigid base. Parametric studies were carried out to identify the influence of the system parameters on the behaviour of the dynamic lateral load-deflection relationships of piles. The lateral load-deflection relationships vary considerably with depth and are influenced not only by the dynamic properties of soil but also by the structural properties of a pile and loading conditions. These lateral load-deflection relationships can be used to define the soil-pile springs for the seismic response analysis of a soil-pile-structure system, and the results can be extended to problems with soil profiles with layering and non-linearity.  相似文献   

16.
The paper provides state-of-the-art information on the following aspects of seismic analysis and design of spread footings supporting bridge piers: (1) obtaining the dynamic stiffness (“springs” and “dashpots”) of the foundation; (2) computing the kinematic response; (3) determining the conditions under which foundation–soil compliance must be incorporated in dynamic structural analysis; (4) assessing the importance of properly modeling the effect of embedment; (5) elucidating the conditions under which the effect of radiation damping is significant; (6) comparing the relative importance between kinematic and inertial response. The paper compiles an extensive set of graphs and tables for stiffness and damping in all modes of vibration (swaying, rocking, torsion), for a variety of soil conditions and foundation geometries. Simplified expressions for computing kinematic response (both in translation and rotation) are provided. Special issues such as presence of rock at shallow depths, the contribution of foundation sidewalls, soil inhomogeneity and inelasticity, are also discussed. The paper concludes with parametric studies on the seismic response of bridge bents on embedded footings in layered soil. Results are presented (in frequency and time domains) for accelerations and displacements of bridge and footing, while potential errors from some frequently employed simplifications are illustrated.  相似文献   

17.
To represent a cylindrical rigid foundation vibrating in horizontal, vertical, rocking or torsional motions embedded in a soil layer resting on rigid rock, a lumped-parameter model is described. The coupling between the horizontal and rocking degrees of freedom is considered. For each degree of freedom eight frequency-independent real coefficients determine the springs, dashpots and the mass of the lumped-parameter model with two internal degrees of freedom. These coefficients are specified for various ratios of the radius of the foundation to the depth of the layer and lateral contact ratios. To derive the mechanical properties of the lumped-parameter model a systematic procedure of curvefitting of the dynamic-stiffness coefficient up to, in general, twice the fundamental frequency of the layer is applied, capturing the fact that below the (horizontal) fundamental frequency (cutoff frequency) no radiation of energy occurs. The lumped-parameter model can be used to represent the soil in a standard finite-element program for structural dynamics working in the time domain, whereby the structure can exhibit non-linear behaviour. Stability of the unbounded soil-layer model and of the total system is guaranteed. A hammer foundation with partial uplift of the anvil is analysed for illustration.  相似文献   

18.
The problem of the dynamic response of rigid embedded foundations subjected to the action of external forces and seismic excitation is analysed. It is shown that to calculate the response of rigid embedded foundations, or the response of flat rigid foundations subjected to non-vertically incident seismic waves, it is necessary to obtain not only the impedance matrix for the foundation, but also the forces induced by the incident seismic waves. Under these general conditions, rocking and torsional motion of the foundation is generated in addition to translation. The case of a two-dimensional rigid foundation of semi-elliptical cross-section is used as an example to illustrate the effects of the embedment depth and angle of incidence of the seismic waves on the response of the foundation.  相似文献   

19.
The performance of a well-designed layer of sand, and composites like layer of sand mixed with shredded rubber tire(RSM) as low cost base isolators, is studied in shake table tests in the laboratory. The building foundation is modeled by a 200 mm by 200 mm and 40 mm thick rigid plexi-glass block. The block is placed in the middle of a 1m by 1m tank filled with sand. The selected base isolator is placed between the block and the sand foundation. Accelerometers are placed on top of the footing and foundation sand layer. The displacement of the footing is also measured by LVDT. The whole setup is mounted on a shake table and subjected to sinusoidal motions with varying amplitude and frequency. Sand is found to be effective only at very high amplitude( 0.65 g) of motions. The performance of a composite consisting of sand and 50% shredded rubber tire placed under the footing is found to be most promising as a low-cost effective base isolator.  相似文献   

20.
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   

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