A new friction law for sliding rigid blocks under cyclic loading

A rigid block sliding down an inclined plane under the action of gravity was monitored with accelerometers and an LVDT to investigate how the transition from static to kinetic friction develops. Once the transition patterns were identified, experiments were carried out to study the response of a dynamically excited rigid block sliding down the inclined plane of a shaking table. Harmonic time series were used as input motions. The laboratory results allowed the definition of a continuous friction law to model the continuous variation of the friction from its static to kinetic condition. This law was implemented into the commercial 3D distinct element code 3DEC to numerically reproduce the experiments carried out, thus validating the friction law. Afterwards, the friction law was used to evaluate the sliding due to the kinetics of the block. Three cases were analyzed: constant friction coefficient, Coulomb friction law and the proposed friction law. These computations were compared to laboratory measurements. It is found that permanent displacements computed by considering the new law are in better agreement with laboratory measurements.     

Response of multiply supported rigid plate to spatially correlated seismic excitations

The ground motions produced by an earthquake at the multiple support points of large structures can differ considerably. In this study, the quasi-static, the dynamic and the total structural responses of a multiply supported rigid plate to spatially varying multiple ground motion inputs are analysed. The results, together with those obtained by neglecting ground motion phase shifts and those by neglecting ground motion coherency losses, are compared with the corresponding structural responses to a single input. The comparisons show that the single input method overestimates translational responses and underestimates rotational responses. They also show that the responses are sometimes overestimated and sometimes underestimated by neglecting the coherency loss effects between the multiple ground motion excitations.     

L形连接件滑移摩擦柱脚节点抗震性能研究

柱脚节点是钢结构体系中的关键部位,其损伤将直接影响到结构体系的性能。基于损伤控制理念,提出了一种装配式L形连接件滑移摩擦柱脚节点。利用有限元软件ABAQUS建立了柱脚节点模型,考虑摩擦界面是否设置填充板和外连接件是否设置加劲肋,以及改变轴压比、连接件竖肢和水平肢厚度等因素,分析不同参数对节点受力模式、滞回曲线、耗能能力和损伤特征的影响。结果表明:柱脚节点主要承受摩擦力和轴压荷载的作用,柱端在受力过程中发生滑移,通过摩擦机制耗能,避免主体结构发生塑性损伤。填充板的设置增强了结构的摩擦性能,且在不同轴压荷载下均具有良好的延性和转动性能。在设置填充板的结构中,合理设置连接件竖肢厚度、水平肢厚度和加劲肋,在保证了节点摩擦耗能性能实现的同时,充分发挥了保护主体结构优势,达到了损伤控制的预期。     

考虑支座摩擦滑移的非规则曲线桥梁抗震性能研究

为研究支座摩擦滑移对非规则曲线桥梁抗震性能的影响,建立考虑支座摩擦滑移的非规则桥梁空间耦联模型,研究支座刚度及支座摩擦系数对其地震响应的影响。结果表明:支座摩擦滑移可以明显消耗地震能量,降低墩底弯矩,有效避免桥墩墩底塑性铰的形成;支座摩擦系数和初始刚度的选择对非规则曲线桥梁加速度减震率及梁体位移影响较大,应根据参数最优匹配的方法选取其最优组合。     

摩擦隔震结构中不同摩擦力模型在地震作用下结构响应分析

本文选用两种摩擦力模型来分析隔震结构的地震响应，运用newmark方法推导了隔震结构采用库仑摩擦力模型在地震作用下结构响应的计算公式。并编程计算了实例，进行了综合分析，得出质量比、摩擦系数对隔震效果的影响；并给出在其他结构参数相对稳定的条件下，滑移面摩擦系数的取值范围。     

Stochastic response of rigid foundations

While the study of kinematic interaction (i.e. the dynamic response of massless foundations to seismic loads) calls, in general, for advanced analytical and numerical techniques, an excellent approximation was proposed recently by Iguchi.^1,2 This approximation was used by the authors to analyse embedded foundations subjected to spatially random SH-wave fields, i.e. motions that exhibit some degree of incoherence. The wave fields considered ranged from perfectly coherent motions (resulting from seismic waves arriving from a single direction) to chaotic motions, resulting from waves arriving simultaneously from all directions. Additional parameters considered were the shape of the foundation (cylindrical or rectangular) and the degree of embedment. It was found that kinematic interaction usually reduces the severity of the motions transmitted to the structure, and that incoherent motions do not exhibit the frequency selectivity (i.e. narrow valleys in the foundation response spectra) that coherent motions do.     

竖向地震动对滑动摩擦隔震桥梁结构地震反应的影响

利用接触摩擦单元建立了滑动摩擦隔震桥梁支座在竖向地震动作用下的有限元模型,通过算例讨论了竖向地震动对不同支座摩擦系数和不同刚度(墩径)滑动摩擦隔震桥梁地震反应的影响,初步探讨了竖向地震动的激励方向对分析结果的影响,分析结果表明,竖向地震动对滑动摩擦隔震桥梁结构的地震反应有较大的影响,在竖向地震动较为明显地区的滑动摩擦隔震桥梁结构设计时,应予以考虑。     

Effects of vertical excitation on the seismic performance of a seismically isolated bridge with sliding friction bearings

A finite element model is constructed for a sliding friction bearing in a seismically isolated bridge under vertical excitation with contact/friction elements. The effects of vertical excitation on the seismic performance of a seismically isolated bridge with sliding friction bearings and different bearing friction coefficients and different stiffness levels (pier diameter) are discussed using example calculations, and the effects of excitation direction for vertical excitation on the analysis results are explored. The analysis results shows that vertical excitation has a relatively large impact on seismic performance for a seismically isolated bridge with sliding friction bearings, which should be considered when designing a seismically isolated bridge with sliding friction bearings where vertical excitation dominates.     

Stochastic analysis of rigid foundation filtering

The effect of the space–time variation of earthquake ground motion on the translational response of structures supported on large rigid mat foundations is considered. A stochastic space–time ground motion model, based on the analysis of recordings from the SMART-1 seismograph array in Lotung, Taiwan, is used. Random vibration theory is utilized to obtain an expression for the reduction in the maximum structural response, for a specified probability level and strong motion duration. Numerical computations are performed to examine the sensitivity of the reduction in structural response to various ground motion and structural parameters. The results indicate that spatial correlation and travelling wave effects give rise to significant reductions in structural responses when the seismic waves have low apparent propagation velocities. Utilization of this result in the design of structures on large foundations should yield substantial cost savings.     

Equivalent series system to model a multiple friction pendulum system with numerous sliding interfaces for seismic analyses

Current structural analysis software programs offer few if any applicable device-specifi c hysteresis rules or nonlinear elements to simulate the precise mechanical behavior of a multiple friction pendulum system(MFPS) with numerous sliding interfaces.Based on the concept of subsystems,an equivalent series system that adopts existing nonlinear elements with parameters systematically calculated and mathematically proven through rigorous derivations is proposed.The aim is to simulate the characteristics of sliding motions for an MFPS isolation system with numerous concave sliding interfaces without prior knowledge of detailed information on the mobilized forces at various sliding stages.An MFPS with numerous concave sliding interfaces and one articulated or rigid slider located between these interfaces is divided into two subsystems: the fi rst represents the concave sliding interfaces above the slider,and the second represents those below the slider.The equivalent series system for the entire system is then obtained by connecting those for each subsystem in series.The equivalent series system is validated by comparing numerical results for an MFPS with four sliding interfaces obtained from the proposed method with those from a previous study by Fenz and Constantinou.Furthermore,these numerical results demonstrate that an MFPS isolator with numerous concave sliding interfaces,which may have any number of sliding interfaces,is a good isolation device to protect structures from earthquake damage through appropriate designs with controllable mechanisms.     

Experimental verification of seismic vibration control using a semi‐active friction tuned mass damper

A tuned mass damper (TMD) system consists of an added mass with properly functioning spring and damping elements for providing frequency‐dependent damping in a primary structure. The advantage of a friction‐type TMD, that is, a nonlinear TMD, is its energy dissipation via a friction mechanism. In contrast, the disadvantages of a passive friction TMD (PF‐TMD) are its fixed and predetermined slip load and loss of tuning and energy dissipation capabilities when it is in a stick state. A semi‐active friction TMD (SAF‐TMD) is used to overcome these disadvantages. The SAF‐TMD can adjust its slip force in response to structure motion. To verify its feasibility, a prototype SAF‐TMD was fabricated and tested dynamically using a shaking table test. A nonsticking friction control law was used to keep the SAF‐TMD activated and in a slip state in earthquakes at varying intensities. The shaking table test results demonstrated that: (i) the experimental results are consistent with the theoretical results; (ii) the SAF‐TMD is more effective than the PF‐TMD given a similar peak TMD stroke; and (iii) the SAF‐TMD can also prevent a residual TMD stroke in a PF‐TMD system. Copyright © 2011 John Wiley & Sons, Ltd.     

Control of structures with friction controllable sliding isolation bearings

A friction controllable sliding isolation system was developed and experimentally and analytically investigated by Feng et al. (Feng, Q., Shinozuka, M. & Fujii, S. A. friction controllable sliding isolation system. J. Eng. Mech., ASCE, 1993, 119(6), in press), the control algorithm having been developed based on a key assumption that the structural motion is always in the sliding phase. However, this assumption may not be valid in cases where the sticking phase of the structural motion dominates. In this paper a new control algorithm is developed including the effects of stick—slip phases. Effect of time delay is included in the formulation. The developed algorithm is used to evaluate the accuracy and limitations of the algorithm with continuous sliding assumption. Response to various earthquake motions, simulated using the two control algorithms, is presented. Comparisons with experimental results are also presented. Effects of stick—slip phases on the response are evaluated.     

Influence of random heterogeneity of shear wave velocity on sliding mass response and seismic deformations of earth slopes

Soil shear wave velocity has been recognized as a governing parameter in the assessment of the seismic response of slopes. The spatial variability of soil shear wave velocity can influence the seismic response of sliding mass and seismic displacements. However, most analyses of sliding mass response have been carried out by deterministic models. This paper stochastically investigates the effect of random heterogeneity of shear wave velocity of soil on the dynamic response of sliding mass using the correlation matrix decomposition method and Monte Carlo simulation(MCS). The software FLAC 7.0 along with a Matlab code has been utilized for this purpose. The influence of statistical parameters on the seismic response of sliding mass and seismic displacements in earth slopes with different inclinations and stiffnesses subject to various earthquake shakings was investigated. The results indicated that, in general, the random heterogeneity of soil shear modulus can have a notable impact on the sliding mass response and that neglecting this phenomenon could lead to underestimation of sliding deformations.     

Stochastic deamplification of spatially varying seismic motions

The spatial and temporal characteristics exhibited by earthquake ground motions at points below the soil surface have important implications for both deeply embedded structures and for spatially extended constructed facilities. In most cases, the characteristics of the seismic motion are known only at the surface, since it is there where most (but not all) of the historical earthquake records have been obtained. While downhole arrays can provide valuable additional information on motion statistics below the surface, it is both possible and desirable to supplement the available database with predictive computational models. With this goal in mind, this paper presents an analytical model to estimate the statistical properties of seismic motions at any point in the ground on the basis of the statistical properties obtained from records on the surface. The emphasis is on the particular cases of stationary SH-waves propagating in a multi-layered soil, and of stationary P-waves propagating in a half-space. The stochastic deconvolution model considered here is based on a formulation with matrices of spectral density functions. Together with the existing formulation based on cross-correlation matrices proposed earlier by Kausel and Pais (J. Engng Mech. Div., ASCE 113 (2) (1998) 266–277), this stochastic deconvolution technique will be referred to as the Complete Stochastic Deamplification Approach (CSDA). The results obtained show that the reduction in the intensity of shaking with embedment is more pronounced when SH-waves propagate in a stratified soil than when they propagate in a homogeneous half-space. Also, it is found that incident P-waves exhibit greater coherency than incident SH-waves, an indication that it is important to distinguish between such wave types when developing coherence models from array data.     

Stochastic energy analysis of seismic isolated bridges

In this paper, a parametric stochastic analysis of isolated bridge is proposed with the aim to assess isolation performance and to investigate effects of energetic influence on protection efficiency. The analysis has been carried out in terms of two stochastic parameters of pear-deck maximum displacement and hysteretic energy response, of which a qualitative trend has been observed.Isolated bridge is described by a simple two degree of freedom (TDoF) Bouc–Wen hysteretic model, which has been introduced for its intrinsic ability in reproducing a wide range of real devices behavior. With the aim of taking into consideration intrinsic stochastic nature of seismic events, the ground motion and the structural response have been described by random vibration approach. Results obtained show that protection achieved by shifting structural natural period and reducing input energy by devices dissipation have counteracting effects if related to deck lateral displacement.     

Stochastic considerations in seismic analysis of structures

A method is presented for stochastic modelling of a design earthquake by a power spectral density function for seismic analysis of structures. The method can be adopted with information currently available in the form of design response spectra for earthquake motion. Accurate seismic responses of structures can be easily obtained using such stochastic models. The methods for accurate response analysis of structures with closely spaced modes and for generation of floor response spectra of a building using a prescribed ground response spectrum directly are also presented. The hypothesis that a design earthquake can be modelled by a power spectral density function is used only implicitly in developing these methods.     

Impact of the equivalent center of mass separating from the sliding surface on the isolation performance of friction pendulum bearings

A new equivalent center of mass model of FPBs(friction pendulum bearings) is introduced, and based on this model, coefficient j of the equivalent center of mass separating from the sliding surface is defined. It is thought in theory that j has a significant impact on the isolation parameter of FPBs, since the equivalent post-yielding stiffness and friction coefficients are not simply determined by sliding radius and sliding friction pairs. The results of numerical simulation analysis using ABAQUS conducted on two groups of FPBs support this viewpoint. For FPBs with the same sliding radius and sliding friction pairs, the FPB modules of structural analysis software such as ETABS could only distinguish the equivalent transformation using j one by one. The seismic response data obtained in a base isolation calculation example of FPBs are very different, which reveals that j's impact on the isolation effectiveness of FPBs cannot be ignored. The introduction of j will help improve the classical structural theory of FPBs and the weak points of structural analysis software based on this theory, which is important in achieving more accurate analyses in structural design.     

Seismic isolation of rigid cylindrical tanks using friction pendulum bearings

Storage tanks are vulnerable to earthquakes, as numerous major earthquakes have demonstrated. The trend of recent revisions to make seismic design criteria for large‐scale industrial storage tanks increasingly stringent has made development of cost‐effective earthquake‐resistant design and retrofit techniques for industrial tanks imperative. This study assesses the feasibility of seismic base isolation for making liquid‐filled storage tanks earthquake resistant. The sliding‐type friction pendulum seismic (FPS) bearings are considered rather than the elastomeric bearings because the dynamic characteristics of an FPS‐isolated tank remain unchanged regardless of the storage level. This work has devised a hybrid structural‐hydrodynamic model and solution algorithm, which would permit simple, accurate and efficient assessment of the seismic response of rigid cylindrical storage tanks in the context of seismic isolation. Extensive numerical simulations confirm the effectiveness of seismic base isolation of rigid cylindrical tanks using FPS bearings. Copyright © 2001 John Wiley & Sons, Ltd.