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1.
Discrete models such as the lumped parameter model and the finite element model are widely used in the solution of soil amplification of earthquakes. However, neither of the models will accurately estimate the natural frequencies of soil deposit, nor simulate a damping of frequency independence. This research develops a new discrete model for one-dimensional viscoelastic response analysis of layered soil deposit based on the mode equivalence method. The new discrete model is a one-dimensional equivalent multi-degree-of-freedom (MDOF) system characterized by a series of concentrated masses, springs and dashpots with a special configuration. The dynamic response of the equivalent MDOF system is analytically derived and the physical parameters are formulated in terms of modal properties. The equivalent MDOF system is verified through a comparison of amplification functions with the available theoretical solutions. The appropriate number of degrees of freedom (DOFs) in the equivalent MDOF system is estimated. A comparative study of the equivalent MDOF system with the existing discrete models is performed. It is shown that the proposed equivalent MDOF system can exactly present the natural frequencies and the hysteretic damping of soil deposits and provide more accurate results with fewer DOFs. 相似文献
2.
A systematic procedure to construct a consistent global lumped-parameter model consisting of springs, dashpots and possibly masses with frequency-independent coefficients connecting the degrees of freedom of the nodes of any structure-medium interface for the unbounded medium is presented. The dynamic-stiffness matrix is first diagonalized which then permits each term to be modelled independently from the others. Physical insight is thus provided. Alternatively, the (symmetric) static-stiffness and damping matrices and possibly mass matrix of the unbounded medium can be established directly. 相似文献
3.
To calculate the hydrodynamic interaction forces of the reservoir directly in the time-domain, the dynamic stiffness of each mode of the semi-infinite uniform fluid channel is either represented by a lumped-parameter model with frequency-independent real coefficients of the springs, dashpots and masses and with only a few additional internal degrees of freedom, or the interaction forces are calculated recursively. For each mode characterized by its eigenvalue, the coefficients of the lumped-parameter model and the recursive coefficients are specified, which can be used directly in a practical application. The procedures exhibit many advantages: the only approximation (replacing the rigorous dynamic stiffness by a ratio of two polynomials) can be evaluated visibly. No unfamiliar discrete-time manipulations such as the z-transformation are used. The stiffness, damping and mass matrices corresponding to the lumped-parameter model are automatically symmetrical. Stability of the procedures is also guaranteed. Combining the lumped-parameter model of the semi-infinite uniform channel with the finite-element discretization of the irregular fluid region or calculating the interaction forces recursively allows a reservoir of arbitrary shape to be analysed directly in the time domain. Non-linearities in the dam can, thus, be taken into consideration in a seismic analysis. 相似文献
4.
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
5.
《Soil Dynamics and Earthquake Engineering》2012,33(1):42-55
Seismic analysis of soil–well–pier system was carried out using three different approaches to evaluate their comparative performance and associated complexities. These approaches were (a) two-dimensional nonlinear (2D-NL), (b) two-dimensional equivalent-linear (2D-EqL), and (c) one-dimensional spring–dashpot (1D). Soil was modeled as 2D plane-strain elements in the 2D-NL and 2D-EqL approaches, and as springs and dashpots in the 1D approach. Nonlinear behavior of soil was captured rigorously in the 2D-NL approach and approximately in the remaining two approaches. Results of the two approximate analyses (i.e., 2D-EqL and 1D) were compared with those of the 2D-NL analysis with the objective to assess suitability of approximate analysis for practical purposes. In the 1D approach, several combinations of Novak's and Veletsos' springs were used to come up with a simplified 1D model using three types of spring–dashpots. The proposed model estimates the displacement and force resultants relatively better than the other 1D models available in literature. 相似文献
6.
The reports after major earthquakes indicate that the earthquake-induced pounding between insufficiently separated buildings may lead to significant damage or even total collapse of structures. An intensive study has recently been carried out on mitigation of pounding hazards so as to minimize the structural damages or prevent collisions at all. The aim of this paper is to investigate the effectiveness of the method when two adjacent three-storey buildings with different (substantially different) dynamic properties are connected at each storey level by link elements (springs, dashpots or viscoelastic elements). The results of the study indicate that connecting the structures by additional link elements can be very beneficial for the lighter and more flexible building. The largest decrease in the response of the structure has been obtained for links with large stiffness or damping values, which stands for the case when two buildings are fully connected and vibrate in-phase. Moreover, by comparing the effectiveness of different types of link elements, it has been confirmed that the use of viscoelastic elements reduces the peak displacement of the structure at lower stiffness and damping values comparing to the case when spring and dashpot elements are applied alone. On the other hand, the results of the study demonstrate that applying the additional link elements does not really change the response of the heavier and stiffer building. The final conclusion of the study indicates that linking two buildings allows us to reduce the in-between gap size substantially while structural pounding can be still prevented. 相似文献
7.
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
8.
A simplified approximate method to analyze the rocking response of SDOF systems lying on compliant soil is introduced, accounting for soil inelasticity and foundation uplifting. The soil–foundation system is replaced by a nonlinear rotational spring, accompanied by a linear rotational dashpot, and linear horizontal and vertical springs and dashpots. Considering a square footing on clay under undrained conditions, the necessary moment–rotation (M–θ) relations are computed through monotonic pushover finite element (FE) analyses, employing a thoroughly-validated constitutive model. Cyclic pushover analyses are performed to compute the damping–rotation (CR–θ) relations, necessary to calibrate the rotational dashpot, and the settlement–rotation (Δw–θ) relations, required to estimate the dynamic settlement. The effectiveness of the simplified method is verified through dynamic time history analyses, comparing its predictions with the results of 3D FE analyses. The simplified method is shown to capture the entire rotation time history θ(t) with adequate accuracy. The latter is used to compute the time history of dynamic settlement w(t), employing a simplified approximate procedure. The proposed simplified method should, by no means, be considered a substitute for more sophisticated analysis methods. However, despite its limitations, it may be utilized for (at least preliminary) design purposes. 相似文献
9.
To simplify the analysis, three-dimensional soil–structure interaction problems are often modelled by considering a two-dimensional slice without changing the material properties of the soil. This procedure, although convenient, is of questionable validity because two-dimensional modelling inherently overestimates the radiation damping for translational and rocking motions. To make matters worse, two-dimensional modelling always entails an underestimation of the dynamic-spring coefficient for the translational motions. The damping ratio of the two-dimensional case, which is proportional to the ratio of the damping coefficient to the spring coefficient, will thus be even larger. Thus, reliance upon a two-dimensional analysis based on an equivalent slice of a strip foundation may result in a dangerously non-conservative design. Valuable insights into the essence of radiation damping and the difference between two-dimensional and three-dimensional models may be obtained via approximate strength-of-materials solutions based on cone–wedge models and travel-time considerations. By examining the decay of the waves along the axes of the cone–wedge models, the essence of radiation damping can be grasped. The heuristic concept of more spreading of waves in three dimensions than in two is misleading. Indeed, just the opposite is true: The less the amplitude spreads and diminishes with distance, the greater is the radiation damping. Because the damping ratio is grossly overestimated, two-dimensional modelling of a three-dimensional case cannot be recommended for actual engineering applications. It is more feasible to take the opposite approach and idealize slender soil–structure interaction problems with a radially symmetric model. As an alternative, when defining the equivalent slice of the two-dimensional strip foundation, the impedance of the soil can be changed to achieve a much better agreement of the high-frequency limits of the damping coefficients. In the low-frequency range this modified two-dimensional model also overestimates radiation damping, although to a lesser extent. As a by-product, the dimensions of the equivalent slice of a two-dimensional strip foundation are discussed; and equations for the aspect ratios determining the opening angles of the corresponding wedges are derived. Also addressed is the quite separate but related topic of the transition from square to slender rectangular foundations. 相似文献
10.
Using the coupled model of finite and infinite elements, the compliance of a rigid raft (plate) on a viscoelastic medium is calculated in this paper. Further, the effects of different proportions of radiation damping and material damping in the total damping and the distribution of wave motion in the near field are also investigated. From the numerical results, it can be concluded that: (1) the radiation damping plays an important role in the total damping, compared to the material damping; (2) the material damping has some effect on the compliance of the raft; (3) under the action of harmonic concentrated loads, the displacement amplitudes in the near field gradually decrease with the increase in the distance from the raft and the material damping; (4) the strata characteristics of the soil medium have considerable influence on the compliance of the raft and the distribution of wave motion in the near field. 相似文献
11.
John P. Wolf 《地震工程与结构动力学》1991,20(1):33-41
A systematic procedure to develop consistent (symmetric) stiffness, damping and mass matrices with real coefficients to represent any unbounded soil is developed. These property matrices are based on the lumped-parameter models of Reference 1. Either stiffness and damping matrices corresponding to first-order differential equations involving the internal degrees of freedom and those on the structure-soil interface result or, alternatively, in addition mass matrices are introduced, corresponding to second-order differential equations, which reduce the number of internal degrees of freedom by a factor 2. The stiffness, damping and mass matrices can easily be incorporated in a general-purpose structural dynamics program working in the time domain, whereby the structure can even be non-linear. 相似文献
12.
An efficient discrete model for predicting the dynamic through-the-soil interaction between adjacent rigid, surface foundations supported by a homogeneous, isotropic and linear elastic half-space is presented. The model utilizes frequency-independent springs and dashpots, and the foundation mass, for the consideration of soil–foundation interaction. The through-the-soil coupling of the foundations is attained by frequency-independent stiffness and damping functions, developed in this work, that interconnect the degrees of freedom of the entire system of foundations. The dynamic analysis of the resulting coupled system is performed in the time domain and includes the time lagging effects of coupled dynamic input due to wave propagation using an appropriate modification of the Wilson-θ method. The basic foundation interaction model is also extended to the evaluation of coupled building-foundation systems. © 1998 John Wiley & Sons, Ltd. 相似文献
13.
For a class of civil engineering structures, that can be accurately represented by ‘coupled shear walls’ (CSWs), a discrete model for the analysis of the dynamic interaction with the underlying soil is proposed. The CSWs, with one or more rows of openings, rest on a rigid foundation embedded in the elastic or viscoelastic half-space. A hierarchical finite element model based on an equivalent continuum approach is adopted for the structure. A frequency-domain boundary element method is used to represent the half-space. Finally, the set of equations governing the response of the coupled soil-structure system to harmonic lateral loads acting on the structure is also given. The frequency deviation effect with respect to the fixed-base structure and the effects of radiation and material damping in the soil are presented for different characteristics of the structure and different soil properties. 相似文献
14.
John P. Wolf 《地震工程与结构动力学》1991,20(1):11-32
A systematic procedure to develop a consistent lumped-parameter model with real frequency-independent coefficients to represent the unbounded soil is developed. Each (modelled) dynamic-stiffness coefficient in the frequency domain is approximated as a ratio of two polynomials, which is then formulated as a partial-fraction expansion. Each of these terms is represented by a discrete model, which is the building block of the lumped-parameter model. A second-order term, for example, leads to a discrete model with springs and dampers with two internal degrees of freedom, corresponding to two first-order differential equations, or, alternatively, results in a discrete model with springs, dampers and a mass with one internal degree of freedom, corresponding to one second-order differential equation. The lumped-parameter model can easily be incorporated in a general-purpose structural dynamics program working in the time domain, whereby the structure can even be non-linear. A thorough evaluation shows that highly accurate results are achieved, even for dynamic systems with a cutoff frequency. 相似文献
15.
16.
This study aims to investigate experimentally the vibration properties of rigid body placed on sand ground surface. The rigid body models with circular or rectangular base with variable mass, inertial moment and base sizes, were prepared, and the vibration behavior was observed in some series of free vibration tests and forced vibration tests. The observed behavior was analyzed and the vibration mode, vibration period and damping ratio were examined. It was found that the natural vibration period depends not only on the mechanical properties of rigid body and ground, but also on the magnitude of vibration amplitude. This suggested the notable effect of nonlinear strain dependent stiffness of ground material. A physical model with distributed spring–dashpot element was used to model the interactive mechanical behavior between rigid body and ground. The stiffness of the spring–dashpot element was evaluated through the modal analysis of the observed vibration behaviors. The effects of base shape, base size and base pressure on the stiffness of spring–dashpot element are discussed. The spring–dashpot model was verified with the behavior observed in forced vibration tests. 相似文献
17.
We present and evaluate the formulation of a reduced‐dimension (one‐dimensional) finite element for the nonlinear analysis of a vibrating disk in a two‐dimensional unbounded domain. As this problem is relevant in studies of the dynamic response of laterally loaded piles, numerous spring‐and‐dashpot representations of the disk undergoing displacement in an unbounded material domain have been developed to date: static and dynamic, linear and nonlinear. With the focus on material nonlinearity, the present simplified formulation circumvents the complications associated with nonlinear springs and dashpots. Indeed, the continuum‐based treatment described herein accounts for the interaction between the two modes of energy dissipation, due to wave propagation in the unbounded domain and loss associated with inelastic behavior. The formulation is a good compromise between the competing desires for realistic representation and efficient computation. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
18.
This paper presents a systematic procedure for the seismic response analysis of highway overcrossings. The study employs an elementary stick model and a more sophisticated finite element formulation to compute response quantities. All dynamic stiffnesses of approach embankments and pile groups are approximated with frequency‐independent springs and dashpots that have been established elsewhere. A real eigenvalue analysis confirms the one‐to‐one correspondence between modal characteristics obtained with the three‐dimensional finite element solutions and the result of the simpler stick‐model idealization. A complex eigenvalue analysis yields modal damping values in the first six modes of interest and shows that modal damping ratios assume values much higher than those used by Caltrans. The validity of the proposed method is examined by comparing the computed time response quantities with records from the Meloland Road and Painter Street overcrossings located in southern and northern California, respectively. The proposed procedure allows for inexpensive parametric analysis that examines the importance of considering soil–structure interaction at the end abutments and centre bent. Results and recommendations presented by past investigations are revisited and integrated in comprehensive tables that improve our understanding of the dynamic characteristics and behaviour of freeway overcrossings. The study concludes with a step‐by‐step methodology that allows for a simple, yet dependable dynamic analysis of freeway overcrossings, that involves a stick model and frequency‐independent springs and dashpots. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
19.
The overall damping of linear arch dam-water-foundation rock systems depends on the material damping of dam concrete, the material and radiation damping of semi-unbounded foundation rock, and the dam-water interaction. In this paper, the effective damping ratio of these factors is separately evaluated for Mauvoisin arch dam in Switzerland to quantitatively discuss their contributions, and to guide the damping selection in the numerical analysis. This paper also aims to investigate if the material and radiation damping of the foundation rock can be replaced by increasing the material damping of the dam to simplify numerical analysis models. The seismic responses of Mauvoisin arch dam are analyzed using the semi-unbounded and massless foundation models, respectively. The results show that the overall effective damping ratio of the system can be approximately expressed as the summation of the individual effective damping and thus the increased material damping of the dam can approximate the material and radiation damping of the semi-unbounded foundation rock. 相似文献
20.
Konstantinos Mykoniou Christoph Butenweg Britta Holtschoppen Sven Klinkel 《地震工程与结构动力学》2016,45(11):1779-1796
A refined substructure technique in the frequency domain is developed, which permits consideration of the interaction effects among adjacent containers through the supporting deformable soil medium. The tank‐liquid systems are represented by means of mechanical models, whereas discrete springs and dashpots stand for the soil beneath the foundations. The proposed model is employed to assess the responses of adjacent circular, cylindrical tanks for harmonic and seismic excitations over wide range of tank proportions and soil conditions. The influence of the number, spatial arrangement of the containers and their distance on the overall system's behavior is addressed. The results indicate that the cross‐interaction effects can substantially alter the impulsive components of response of each individual element in a tank farm. The degree of this impact is primarily controlled by the tank proportions and the proximity of the predominant natural frequencies of the shell‐liquid‐soil systems and the input seismic motion. The group effects should be not a priori disregarded, unless the tanks are founded on shallow soil deposit overlying very stiff material or bedrock. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献