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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 examines the axisymmetric torsional vibrations of an elastic pile and a hemispherical foundation embedded in a homogeneous elastic half-space. The embedded foundation–half-space system is decomposed into an extended half-space and a fictitious foundation. The deformations of the fictitious system are specified by an admissible function containing a set of generalized coordinates. The Lagrangian equations of motion are used to determine these coordinates associated with the assumed displacement function. Numerical results are presented for torsional impedance of an elastic pile and a hemisphere to illustrate the effects of relative flexibility and geometry. By employing certain simplifications on the pile–half-space system an approximate closed form solution is presented for the torsional impedance of an elastic pile.  相似文献   

3.
On the basis of some simplifying assumptions, a parametric analysis is made of the interaction effects on the effective period and damping of structures with embedded foundation in a soil layer. A simplified three-dimensional interaction model is used, in which the depth of a cylindrical foundation, the degree of contact between the ground and the footing walls and the depth of a homogeneous stratum over rigid rock are considered variable. The soil is replaced with impedance functions that are taken from a data base obtained with an appropriate numerical technique, so that suitable springs and -pots dependent on the excitation frequency are used. The system period and system damping are determined from the steady-state response of an equivalent single oscillator with flexible base subjected to a harmonic motion with constant amplitude, by equating its resonant response with that of a replacement oscillator with rigid base excited with the same motion. The influence of the foundation embedment and soil layer is investigated for several depths of both the footing and the stratum.It is confirmed that the system period decreases and the system damping increases with the foundation embedment only for sidewalls extending along the entire foundation depth. For embedded footings without sidewall or with sidewall in null contact with the surrounding soil, the effective system parameters behave opposite to those corresponding to the interface condition of total contact. Also, the system damping increases significantly with the layer depth, while the system period is practically insensitive to variations of this characteristic parameter. Finally, introducing additional permissible simplifications, an improved approximate solution for the effective period and damping of coupled systems is presented, which differs from previous analogous approximations in that damping factors of second order are not neglected and the foundation depth is explicitly considered.  相似文献   

4.
This paper is concerned with the dynamic response of rigid strip foundations of arbitrary geometry embedded in a homogeneous elastic half-space. The embedded rigid foundation is modelled by an equivalent domain in a uniform half-space which is subjected to an appropriate body force field. The components of the impedance matrix are determined through the solution of a linear simultaneous equation system which is established by invoking rigid body displacements of discrete locations within the equivalent domain and appropriate equilibrium consideration. It is found that high numerical efficiency and flexibility can be achieved using the body force model when compared to boundary integral formulations through the selection of appropriate displacement influence functions and a ‘parent domain’ in the analysis. Numerical results are presented to illustrate the influence of the embedment ratio, frequency of excitation, foundation geometry and Poisson's ratio on the vertical, horizontal, rocking and coupled impedances of a single embedded foundation. The effect on the impedance due to the presence of an adjacent embedment is investigated for various distances between foundations and embedment ratios.  相似文献   

5.
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   

6.
A linear theory is developed for the free, torsional vibrations of the single-span, boxgirder suspension bridge. Both symmetric and antisymmetric modes are considered. For the symmetric modes, which induce additional cable tension, it is shown that it is imperative to include the elasticity of the cables if correct solutions are to be obtained. Three examples of bridges with widely differing properties are presented to illustrate the applicability of the theory. Orthogonality of the torsional modes of vibration is proved in Appendix I and the modification to the analysis, required when rigid centre ties are present, is outlined in Appendix II. The theories presented herein can be readily extended to the three-span bridge.  相似文献   

7.
A modal analysis formulation of the equations of motion of horizontally excited embedded footings is presented. Numerical solutions obtained with these equations are compared with the results obtained from direct solutions. It is shown that the two methods of solution are in good agreement for frequencies near to the first resonance.  相似文献   

8.
In order to carry out parametric analysis of eccentric structure–soil interaction system, an analytical model based on branch mode decoupling method is presented in this paper. The solution of system equations is implemented in the frequency domain by assuming that the superstructure maintains classic normal modes. The transfer functions of translational and torsional response are derived later. The influence of eccentricity ratio, torsional to translational frequency ratio, height-to-base ratio and foundation flexibility on the curve and peak value of transfer functions and torsionally coupled degree are analyzed and discussed systematically. Results of analysis indicate that the flexibility of foundation soil can weaken the torsional response of superstructure substantially, and the natural frequencies of interaction system reduce as the flexibility of foundation soil increase. The influence of eccentricity ratio on the peak values of transfer functions varies with the torsional to translational frequency ratio, which can be summarized as the decrease of translational component and the increase of torsional component. The translational displacement of SSI system is larger than that of fixed-base condition, while the deformation amplitude is notably reduced. The torsional response decreases as well. As the height-to-base ratio increase, the varying tendency of response is further enhanced. The torsionally coupled degree of eccentric structure is remarkably affected by the torsional to translational frequency ratio, which is significantly reduced under soft soil condition.  相似文献   

9.
Due to the damage suffered by many skewed highway bridges during the San Fernando earthquake, 1971, a study is made on the dynamic response of this type of bridge. Using a beam model capable of flexural and torsional deformations, the mode shapes and frequency equations are presented. Due to the skewness of the intermediate supports, coupled flexural and torsional vibrations are shown to be excited by the vertical component of ground motion An analysis is carried out for the Foothill Boulevard Undercrossing, S.E. Bridge in the San Fernando Valley, California which suffered damage to the intermediate supports. The results of the analysis correlate well with the observed damage pattern of the bridge.  相似文献   

10.
The paper presents results of a study on the harmonic response of piles and pile groups embedded in a halfspace to various forms of seismic waves. These include the Rayleigh wave as well as obliquely incident P, SV and SH waves. The pertinent mixed boundary value problems of pile-soil-pile interaction are solved by a numerical model of the boundary integral nature. All modes of foundation vibrations, i.e. translational, rocking and torsional, are included in the model. The results presented are used to highlight the salient features of the seismic response of piles. In addition, the influence of certain pile-soil parameters, such as pile rigidity and pile spacing, on the seismic behaviour of pile foundations is investigated.  相似文献   

11.
An analytical approach is used to study the torsional vibrations of a rigid circular foundation resting on saturated soil to obliquely incident SH waves. Biot’s poroelastic dynamic theory is considered to characterize the saturated soil below the foundation, which is solved by Hankel transform later. In order to consider the scattering phenomena caused by the existence of the foundation, the total wave field in soil is classified into free-field, rigid-body scattering field and radiation scattering field. According to the classification of wave field and the mixed boundary-value conditions between the soil and the foundation, torsional vibrations of the foundation are formulated in two sets of dual integral equations. Then, the dual integral equations are reduced to Fredholm integral equation of the second kind to be solved. Combining with the dynamic equilibrium equations of the foundation, the expressions for the torsional vibrations of the foundation are obtained. Numerical results are presented to demonstrate the influence of excitation frequency, incident angle, the torsional inertia moment of the foundation and permeability of the saturated half-space on the torsional vibrations of the foundation.  相似文献   

12.
An approximate analytical approach is presented which makes it possible to consider soil properties and footing embedment in the analysis of the response of structures to external excitation such as wind and earthquake. The approach is based on modal analysis and the definition of stiffness and damping due to soil pertinent to each vibration mode. The approach also facilitates the analysis of coupled motions of a footing alone. The analysis of a tall chimney for the effects of gusting wind, vortex shedding and earthquake is used as an example.  相似文献   

13.
As the first part of a sequence focusing on the dynamic response of composite caisson-piles foundations (CCPFs1), this paper develops a simplified method for the lateral response of these foundations. A Winkler model for the lateral vibration of the CCPF is created by joining the two components, the caisson and the pile group, where the four-spring Winkler model is utilized for the caisson and axial–lateral coupled vibration equations are derived for the pile group. For determining the coefficients of the four-spring Winkler model for the caissons, embedded footing impedance is used and a modification on the rotational embedment factor is made for the sake of the geometrical difference between shallow footings and caissons. Comparisons against results from finite element simulations demonstrate the reliability of this modified four-spring Winkler model for caissons in both homogenous and layered soils. The proposed simplified method for the lateral vibration of CCPFs is verified also by 3D finite element modeling. Finally, through an example, the idea of adding piles beneath the caisson is proved to be of great significance to enhance the resistance of the foundation against lateral dynamic loads.  相似文献   

14.
An approximate solution of the classical eigenvalue problem governing the vibrations of a structure on an elastic soil is derived through the application of a perturbation analysis. For stiff soils, the full solution is obtained as the sum of the solution for a rigid-soil and small perturbing terms related to the inverse of the soil shear modulus. The procedure leads to approximate analytical expressions for the system frequencies, modal damping ratios and participation factors for all system modes that generalize those presented by other authors for the fundamental mode. The resulting approximate expressions for the system modal properties are validated by comparison with the corresponding quantities obtained by numerical solution of the eigenvalue problem for a nine-story building. The accuracy of the proposed approach and of the classical normal mode approach is assessed through comparison with the exact frequency response of the test structure.  相似文献   

15.
An approximate solution of the classical eigenvalue problem governing the vibrations of a relatively stiff structure on a soft elastic soil is derived through the application of a perturbation analysis. The full solution is obtained as the sum of the solution for an unconstrained elastic structure and small perturbing terms related to the ratio of the stiffness of the soil to that of the superstructure. The procedure leads to approximate analytical expressions for the system frequencies, modal damping ratios and participation factors for all system modes that generalize those presented earlier for the case of stiff soils. The resulting approximate expressions for the system modal properties are validated by comparison with the corresponding quantities obtained by numerical solution of the eigenvalue problem for a nine-story building. The accuracy of the proposed approach and of the classical normal mode approach is assessed through comparison with the exact frequency response of the test structure.  相似文献   

16.
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   

17.
A simple and fast evaluation method of soil–structure interaction (SSI) effects of embedded structures is presented via a cone model. The impedances and the effective input motions at the bottom of an embedded foundation are evaluated by means of the cone model. Those quantities are transformed exactly to the corresponding values at the top of the foundation. The evaluated quantities are combined with the super-structure at the top of the foundation. The transfer function amplitude of the interstory drift of a single-degree-of-freedom super-structure is computed for various cases, i.e. no SSI, SSI without embedment, SSI with shallow embedment, SSI with deep embedment. Soil properties are also varied to investigate in more detail the SSI effects of embedded structures. It is found that, while the transfer function amplitude is reduced by the increase of embedment in general, the characteristics of the transfer function amplitude for a very small ground shear wave velocity and large embedment are irregular and complicated.  相似文献   

18.
The recently streamlined strength-of-materials approach using cones to calculate vibrations of foundations embedded in layered half-spaces and full-spaces is applied to incompressible and nearly-incompressible soil and to axi-symmetric embedments of arbitrary shape. For incompressible soil the axial-wave velocity in the cones is limited to twice the shear-wave velocity and a trapped mass for the vertical motion and a trapped mass moment of inertia for the rocking motion moving as a rigid body with the under-most disk of an embedded foundation are introduced. In the case of a fully embedded foundation, a mass and a mass moment of inertia are also assigned to the upper-most disk. For an axi-symmetric embedment of arbitrary shape, the disks have varying radii. No modifications to the formulation are, however, required. For these two extensions the strength-of-materials approach using cones leads to the same sufficient engineering accuracy as is achieved in other more conventional cases. This is demonstrated in a vast study. Thus the same other advantages also apply: physical insight with conceptual clarity, simplicity and sufficient generality.  相似文献   

19.
A study on the dynamic response of a railway track is presented via a 3-D formulation based on the frequency domain Boundary Element Method (BEM) and the Finite Element Method (FEM). The railway track consists of a group of surface, massive, rigid footings resting on a viscoelastic half-space and connected by an overlaying rail structure. The BEM, employing the full-space fundamental solutions and quadrilateral elements, is used for the simulation of the elastic half-space while the FEM is used to model the rigid footings and the rail superstructure. The loading function consists of a set of externally applied, harmonic or transient loads. Frequency as well as transient, by way of FFT, results are presented for various modes of vibration. Various numerical studies assess the through-the-soil interaction of the adjacent footings, the influence of soil damping, the effect of the overlaying structure on the frequency content of the system, and the effective simulation of an infinitely long railway track by a truncated one.  相似文献   

20.
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   

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