Seismic behavior of variable frequency pendulum isolator

Earthquake performance of a flexible one-story building isolated with a variable frequency pendulum isolator （VFPI） under near-fault and far-field ground motions is investigated. The frictional forces mobilized at the interface of the VFPI are assumed to be velocity dependent. The interaction between frictional forces of the VFPI in two horizontal directions is duly considered and coupled differential equations of motion of the isolated system in the incremental form are solved iteratively. The response of the system with bi-directional interaction is compared with those without interaction. In addition, the effects of velocity dependence on the response of the isolated system are also investigated. Moreover, a parametric study is carried out to critically examine the influence of important parameters on bi-directional interaction effects of the frictional forces of the VFPI. These parameters are： the superstructure time period, frequency variation factor （FVF） and friction coefficient of the VFPI. From the above investigations, it is observed that the dependence of the friction coefficient on relative velocity of the system does not have a noticeable effect on the peak response of the system isolated with VFPI, and that the bi-directional interaction of frictional forces of the VFPI is important and if neglected, isolator displacements will be underestimated and the superstructure acceleration and base shear will be overestimated.     

Seismic isolation of buildings with sliding concave foundation (SCF)

In this paper, a new base isolation system, namely the sliding concave foundation (SCF), is introduced and the behaviour of the buildings using such a system is theoretically investigated. A building supported on the new system behaves like a compound pendulum during seismic excitation. The pendulum behaviour accompanied by the large radius of foundation curvature shifts the fundamental period of the system to a high value (e.g. more than 8sec), in a frequency range where none of the previously recorded earthquakes had considerable energy. This results in a large decrease in the structural responses. Since small friction forces are essential on the contact surfaces, PTFE sheets can be used as sliding surfaces. Although the pure frictional sliding systems have the same efficiency as the SCF, in reducing the responses of the superstructure, the main advantage of the new system is a significant decrease in sliding displacement. The performance of the SCF subjected to a number of harmonic and non‐harmonic base excitations is studied and its ability to reduce the structural responses is examined. Some numerical examples are solved for a single‐degree‐of‐freedom (SDOF) structure and the responses are compared with the responses of the same SDOF structure on a fixed base or a pure frictional sliding support system. The comparisons confirm the effectiveness of the new system. Copyright © 2002 John Wiley & Sons, Ltd.     

Separation and sliding between soil and structure during strong ground motion

This paper presents an approach to the problem of separation and sliding between soil and structure in the finite element analysis of dynamic soil-structure interaction problems. Joint elements are arranged along the contact surface between soil and structure and they have a property such that tensile forces are not transmitted between the planes representing structure and soil in the finite element analysis. The dynamic properties governing the sliding are determined by the Mohr-Coulomb failure law determined from the cohesion and the friction angle between soil and structure. The proposed method is applied to (i) a model of a reactor building resting on the free surface of layered ground and (ii) a buried foundation structure. The numerical computations reveal the following results: that the translation is dominant in the motion of the structure when sliding is taking place between soil and structure, and that the rocking is dominant in the rest of the response. The amplitude of the response during sliding is increased on any one point of the structure and decreased on any one point of the ground compared with that of the fixed condition at the interface. In the case of the buried structure, it is observed in the computed results that the structure and soil move in the opposite direction along the vertical contact surface and are separated from each other in the near surface region during the strong phase of the excitation.     

Bidirectional shaking table tests of a low-cost friction sliding system with flat-inclined surfaces

A novel low-cost friction sliding system for bidirectional excitation is developed to improve the seismic performance of reinforced concrete (RC) bridge piers. The sliding system is a spherical prototype developed by combining a central flat surface with an inclined spherical segment, characterized by stable oscillation and a large reduction in response accelerations on the flat surface. The inclined part provides a restoring force that limits the residual displacements of the system. Conventional steel and concrete are employed to construct a flat-inclined spherical surface atop an RC pier. The seismic forces are dissipated through the frictions generated during the sliding movements; hence, the seismic resilience of bridges can be ensured with a low-cost design solution. The proposed system is fabricated utilizing a mold created by a three-dimensional printer, which facilitates the use of conventional concrete to construct spherical shapes. The concrete surface is lubricated with a resin material to prevent abrasion from multiple input ground motions. To demonstrate the effectiveness of the system, bidirectional shaking table tests are conducted in the longitudinal and transverse directions of a scaled bridge model. The effect of the inclination angle and the flat surface size is investigated. The results demonstrate a large decrease in response acceleration when the system exhibits circular sliding displacement. Furthermore, the inclination angle that generates the smallest residual displacement is identified experimentally.     

Response of sliding structures to harmonic support motion

The problem of response of a single degree of freedom structure supported on a sliding foundation and subjected to harmonic support motions is considered. The non-linear governing equations of motion are derived. It turns out that these equations are linear in each sliding and non-sliding phase and can be solved in closed forms in each phase. The equations for evaluation of the beginning and ending times of different phases are also formulated and solved numerically. The response for different coefficients of friction and various levels of excitation is evaluated and presented graphically. It is concluded that sliding supports can be quite effective in isolating structures from support excitations.     

Assessment of concrete bridges subjected to ground motion with an arbitrary angle of incidence: static and dynamic approach

A nonlinear static analysis methodology for the derivation of a set of pushover curves for any angle of incidence of the seismic action (multidirectional pushover curves) for bridges is developed, wherein the interaction between axial force and biaxial moments at critical pier sections or biaxial shear forces at the bearings is taken into account. Dynamic pushover curves (base shear vs. peak deck displacement) for arbitrary angle of incidence of the excitation, are derived for both unidirectional (single-component) and bidirectional (dual-component) ground motion. It is found that neglecting the minor horizontal component leads to underestimation of bridge response, especially along the bridge principal directions and that the angle of incidence of bidirectional excitation affects bridge response, but to a lesser extent than in the case of unidirectional excitation. The proposed procedure is then applied to a straight symmetric bridge, its results are checked against those from response-history analysis, and is found to be sufficiently accurate for practical application. Using the derived results it is also found that the design of the selected bridge is safe since for the design bidirectional earthquake the bridge starts to behave inelastically (the first plastic hinge forms), while its failure occurs for about four times the design seismic action.     

A simplified multisupport response spectrum method

A simplified multisupport response spectrum method is presented.The structural response is a sum of two components of a structure with a first natural period less than 2 s.The first component is the pseudostatic response caused by the inconsistent motions of the structural supports,and the second is the structural dynamic response to ground motion accelerations.This method is formally consistent with the classical response spectrum method,and the effects of multisupport excitation are considered for any modal response spectrum or modal superposition.If the seismic inputs at each support are the same,the support displacements caused by the pseudostatic response become rigid body displacements.The response spectrum in the case of multisupport excitations then reduces to that for uniform excitations.In other words,this multisupport response spectrum method is a modification and extension of the existing response spectrum method under uniform excitation.Moreover,most of the coherency coefficients in this formulation are simplified by approximating the ground motion excitation as white noise.The results indicate that this simplification can reduce the calculation time while maintaining accuracy.Furthermore,the internal forces obtained by the multisupport response spectrum method are compared with those produced by the traditional response spectrum method in two case studies of existing long-span structures.Because the effects of inconsistent support displacements are not considered in the traditional response spectrum method,the values of internal forces near the supports are underestimated.These regions are important potential failure points and deserve special attention in the seismic design of reticulated structures.     

Periodic response of a sliding oscillator system to harmonic excitation

This paper deals with the periodic response of an oscillating system which is supported on a frictional interface. The base excitation is assumed harmonic and the frictional force is assumed to be of the Coulomb type. Though each segment of the motion of such a system is described by linear equations, its complete response is highly non-linear and varied. The most fundamental periodic solutions are derived analytically and numerically. The results indicate that such a system has several subharmonic resonant frequencies and that while the friction reduces the peak response of the system when it is excited at its ‘fixed-base’ natural frequency, ω_n, the sliding can induce considerably higher levels of response, when compared with those of a non-sliding, fixed-base system, for frequencies less than ω_n. The results obtained herein may find application in the area of vibration isolation.     

Response of multi-degree-of-freedom structures with sliding supports

The response of multi-degree-of-freedom (MDOF) structures with sliding supports is studied. The problem of sliding structures is a discontinuous one in that different numbers of equations of motion with varying forcing functions are required for the sliding and non-sliding phases. The numerical difficulties involved in this regard in an incremental finite element analysis can be circumvented through the introduction of a fictitious spring for the sliding support. Such a treatment enables one to study the higher mode effects on MDOF sliding structures under the excitation of harmonic or earthquake motions. The dynamic characteristics of MDOF sliding structures will be highlighted in the analysis of a four-storey shear building with sliding support.     

滑移摩擦隔震系统在多向地面运动作用下的试验研究

基础隔震通常只考虑隔离水平地面运动，而对竖向地面运动的影响注意不够，本文进行了滑移摩擦隔震系统的振动台房屋模型试验，研究多向地面运动输入时上部结构反应和隔震系统的性能，试验中分别对模型输入了不同方向的地震动，其中包括水平单向、水平双向、水平和竖向及三向地震动输入，对试验结果进行了分析比较，结果表明竖向地震动输入对上部结构的水平地震反应有显著影响，同时在橡胶隔震支座中产生了竖向拉力。     

On the effective seismic input for non-linear soil-structure interaction systems

Two equivalent semi-discrete formulations are presented for the problem of the transient response of soil-structure interaction systems to seismic excitation, considering linear behaviour of the soil material and arbitrary non-linear structural properties. One formulation results in a direct method of analysis in which the motion in the structure and the entire soil medium, rendered finite by an artificial absorbing boundary, is determined simultaneously. The other represents a substructuring technique in which the structure and the soil are analysed separately. The forces induced in the discretized system by the incident seismic motion are obtained as part of the general formulation by using the free-field motion of the unaltered soil as the earthquake input. It is shown that these forces act within the soil region in the direct method, but only on the soil-structure interface in the substructure formulation. Both sets of forces, however, involve only the displacements and tractions acting on the fictitious surface in the unaltered (linear) soil which coincides with the soil-structure interface of the complete system. It is shown, further, that the free-field displacements alone define a minimal set of data for evaluating the seismic response of the structure, since the tractions and displacements on that surface are interrelated. In practice, the minimal set must be obtained by extrapolating the available information, as the free-field ground motion at a site is usually specified at a single reference point.     

Modelling aspects of structures isolated with the frictional pendulum system

Different modelling aspects of structures isolated using the frictional pendulum system and subjected to earthquake ground motions are studied herein. Although the vertical dynamics of these structures is given special emphasis, other effects such as large isolator deformations and bidirectional input motion are also considered. Different structural models of the FPS are developed and tested for single-storey structures and a real four-storey building frame; among them, an ‘exact’ formulation of the FPS force–deformation constitutive relationship is presented. Results show that global building responses can be computed within 20 per cent error in the mean using a simplified model that ignores the vertical motion of the building; however, structural member deformations and forces need to be computed using a model that considers such motion. This is of particular importance when there exist correlation between the horizontal and vertical components of ground motion. Further, a physical model of the FPS is introduced and used to determine the response of a real four-storey frame, including uplift and downward impact. Results from this analysis show that local column responses may vary substantially depending on the stiffness of the isolation storey and the presence of a mass at the isolation level. Such mass is capable of filtering the large increase in column shear that results from the impact of the structure after uplift. Uplift occurs at several instants of the response of the structure considered, leading to an increase in column base shear as large as 3 times the shear obtained by ignoring the vertical dynamics of the building. © 1998 John Wiley & Sons, Ltd.     

Sliding-uplifting response of rigid blocks to base excitation

In the present paper a two-degree-of-freedom system is considered which allows the simulation of rigid blocks uplifting and sliding on frictional foundations; the monolateral constraint between block and base is schematized by means of a joint model, which allows the contact problem to be discretized. The joint model is governed by normal and shear constitutive laws, which have been derived by the phenomenological behaviour of stone blocks and rock joints, as given by rock mechanics. Furthermore, a numerical procedure has been developed in order to solve the non-linear equations governing the motion of the block-base system, and to analyse the dynamic response of this system under seismic excitation; particular attention has been paid to the influence of the vertical displacement on the slip response.     

覆水场地地震反应分析

随着各种海洋结构物的兴建,覆水场地的地震反应逐渐成为研究热点。基于任意拉格朗日-欧拉描述,推导时变区域上的流体运动方程,给出流场、结构的接触条件和流场网格运动控制方法。对于平坦覆水场地,水平向地震动作用下,根据Couette流理论证明该类场地流体作用可以忽略;竖向地震动激励下,横向均匀场地可以通过动水压力公式准确考虑流体作用,横向非均匀场地则需要通过流固耦合方法考虑流体作用,以海底隧道为例加以说明。对于起伏场地,天然起伏场地在地震动激励下的动力反应具有明显的流固耦合特征,以三角形起伏场地为算例;结构物的兴建造成的人工起伏场地同样需要考虑流固耦合效应,以某沉管隧道在水平向地震动激励下的动力反应为算例,并根据结果初步提出该类结构物流固耦合分析的简化计算方法。     

大跨度空间网格结构多维多点随机地震反应分析

本文建立了三维正交地震动多点激励下大跨度空间网格结构的随机地震反应分析方法,依据现行抗震设计规范的有关规定,确定了平稳随机地震动功率谱密度的模型参数。数值仿真分析了一柱距80m的正方形平板网架分别在一维地震动或三维地震动的一致激励、行波激励和考虑部分相干效应的随机激励下的地震反应。结果表明:考虑地震动的空间效应会很大程度地改变结构杆件的内力,其中控制杆件的内力增幅达到30%;地震动的行波效应对结构杆件内力的影响比随机地震动的部分相干效应的影响更大;三维地震作用比一维地震作用下结构杆件的内力大。由此得出结论,对于大跨度空间网格结构,必须进行多维多点地震激励下的随机地震反应分析。     

双向地震波作用下巨子型有控结构建筑的隔震设计

为了增强巨子型有控结构建筑的动力特性,提升其稳定性,设计双向地震波作用下建筑有控结构。采用3种磁流变阻尼器(MRD)与滑移隔震混合控制结构构成单体建筑有控结构,其包括巨结构和子结构,并建立该有控结构的动力分析模型。在动力分析模型中输入水平和竖向地震,得到模型的竖向和水平滑动状态运动微分方程,依据这两个方程采用自适应模糊神经网络优化动力分析模型,构建优化模型。从优化模型出发,通过实例实验分析得出,优化设计双向地震波作用下建筑有控结构时,在其上部结构层间和隔离层各安装一个MRD,可确保优化设计后的有控结构在不同双向地震工况下的地震反应控制效果最佳,且有控结构在双向地震工况2下,结构第一层、中间三层以及顶层的加速度和位移的时程曲线走向一致,且差距微小;同时有控结构的巨结构顶层侧移响应随着子结构刚度增加而提高,动力特性没有明显的变化,子结构随着其自身刚度增加顶层侧移响应表现稳定,子结构动力特性增强。     

Seismic response of multi‐span simply supported bridges to a spatially varying earthquake ground motion

This paper carries out a parametrical study of the pounding phenomenon associated with the seismic response of multi‐span simply supported bridges with base isolation devices. In particular, the analyses focus on the causal relationship between pounding and the properties of a spatially varying earthquake ground motion. In order to include the effect of the torsional component of pounding forces on the seismic response of the whole structure, a three‐dimensional (3D) finite element model has been defined and 3D non‐linear time‐history analyses have been performed. A parametrical study on the size of the gaps between adjacent bridge decks has highlighted that the pounding effects are amplified when the spatially varying ground motion time histories at each support are considered. Because of a spatially varying input, the pounding forces can assume values 3–4 times larger than those derived by a conventional seismic analysis with uniform input or with spatial input but considering ground motion wave passage effect only. The numerical results show that in order to achieve an acceptably safe structural performance during seismic events, a correct design of the isolation devices should take into account the relative displacements calculated by means of a non‐linear time‐history analysis with multi‐support excitation. Copyright © 2002 John Wiley & Sons, Ltd.     

The masonry arch as a four-link mechanism under base motion

The dynamic response of an unreinforced masonry arch is examined, modelling the rigid body motions of arch segments under the influence of gravitational and inertial forces. This extends earlier studies of single rocking blocks, stacked blocks, and portal mechanisms of blocks; the masonry arch is analysed as another kinematic form of such a system. In this first effort a part-circular planar arch ring is studied and excitation is restricted to horizontal ground acceleration of the base. The mechanism kinematics are presented and the governing equation of motion is derived in non-linear form. The instantaneous form is determined for small rotations about the initial geometry and is used to study the conditions for the onset of mechanism motion. Possible failure conditions are posed and bounding principles are stated. One possible failure condition, direct overturning as a four-link mechanism, is studied for one simplified base motion. The results show that an arch geometry establishes good resistance to earthquake excitation in that ground acceleration must exceed a rather high threshold before any mechanism motion would develop; however, once that threshold has been passed the arch has relatively modest resistance before failure. Other possible failure conditions are discussed; one emerges from pounding effects between segments at impact, and another develops from sliding of blocks over one another as the internal forces (normal and tangential to the masonry joint) vary with the inertial forces.     

Interaction of foundation−structure systems with seismically precarious slopes: Numerical analysis with strain softening constitutive model

This paper studies the combined effects of earthquake-triggered landslides and ground shaking on foundation−structure systems founded near slope crests. Plane-strain nonlinear finite element dynamic analyses are performed. The soil constitutive model is calibrated against published data to simulate the (post-peak) softening behavior of soil during a seismic event and under the action of gravitational forces. The plastic shear zones and the yield accelerations obtained from our dynamic analyses are shown to be consistent with the slip surfaces and the seismic coefficients obtained by classical pseudostatic limiting equilibrium and limit analysis methods. The foundation and frame columns and beams are modeled as flexural beam elements, while the possibility of sliding and detachment (separation) between the foundation and the underlying soil is considered through the use of special frictional gap elements. The effects of foundation type (isolated footings versus a rigid raft) on the position of the sliding surface, on the foundation total and differential displacements, and on the distress of the foundation slab and superstructure columns, are explored parametrically. It is shown that a frame structure founded on a properly designed raft could survive the combined effects of slope failure and ground shaking, even if the latter is the result of a strong base excitation amplified by the soil layer and slope topography.     

Dynamic analysis of stacked rigid blocks

The dynamic behavior of a structural model of two stacked rigid blocks subjected to ground excitation is examined. Assuming no sliding, the rocking response of the system standing free on a rigid foundation is investigated. The derivation of the equations of motion accounts for the consecutive transition from one pattern of motion to another, each being governed by a set of highly nonlinear differential equations. The system behavior is described in terms of four possible patterns of response and impact between either the two blocks or the base block and the ground. The equations governing the rocking response of the system to horizontal and vertical ground accelerations are derived for each pattern, and an impact model is developed by conservation of angular momentum considerations. Numerical results are obtained by developing an ad hoc computational scheme that is capable of determining the response of the system under an arbitrary base excitation. This feature is demonstrated by using accelerograms from the Northridge, CA, 1994, earthquake. It is hoped that the two-blocks model used herein can facilitate the development of more sophisticated multi-block structural models.