Criteria for initiation of motion of rigid bodies to base excitation

It is known that when an unanchored rigid body is placed on a horizontal base which oscillates horizontally, it may undergo one of four modes of motion: rest, slide, slide–rock and rock. Initiation of a rigid body into these modes depends on the slenderness ratio of the body, the coefficient of friction between the body and the base and the acceleration of the base. In this study, the coefficient of friction and the base acceleration are considered random. For specific probability distributions of the coefficient of friction and the peak base acceleration, and for various values of the mean and standard deviation of the two random variables, the probabilities of occurrence of these modes of motion are obtained for a body of given slenderness ratio. It is shown that randomness of the coefficient of friction and base peak acceleration should not be ignored. Copyright © 2005 John Wiley & Sons, Ltd.     

Sliding fragility of block‐type non‐structural components. Part 2: Restrained components

This paper focuses on seismic vulnerability assessment of restrained block‐type non‐structural components under sliding response on the basis of seismic inputs specified by current seismic codes. The general representation of restrained equipment considered in this study consists of a rigid block restrained by four post‐tensioned, symmetrically arranged cables. Two sliding‐related failure modes are considered: restraint breakage and excessive absolute acceleration. Fragility analysis is proposed as an appropriate tool to evaluate these failure modes. Sample fragility curves developed through Monte‐Carlo simulations show that the restraint breakage limit state is sensitive to the parameters of the equation of motion. For instance, fragility estimates obtained without taking into account vertical base accelerations can be significantly unconservative for relatively large values of the coefficient of friction. In contrast, the excessive absolute acceleration limit state exhibits little sensitivity to the parameters of the equation of motion. Peak absolute acceleration response is almost always equal to or greater than the horizontal peak base acceleration. Representative results suggest that reasonable response estimates for blocks located at stories other than the ground in multistorey buildings can in general be obtained by simply scaling the ground acceleration to the peak acceleration at the corresponding storey. Copyright © 2002 John Wiley & Sons, Ltd.     

近断层地震动作用下风机塔地震反应分析

为了研究近断层地震动速度脉冲及强竖向地震动对风机塔地震响应的影响,以某陆上风电场1.5 MW风机塔为研究对象开展了结构在水平向脉冲型地震动、水平向非脉冲型地震动、水平与竖向地震动组合3种地震输入工况的时程分析。通过3种工况下塔顶位移时程、加速度时程、塔底剪力、弯矩及轴力的对比分析发现:近断层速度脉冲对结构塔顶水平位移、塔顶水平加速度、塔底剪力与弯矩均影响显著;竖向地震动会加大结构的塔顶竖向加速度响应及塔底轴力响应;随着竖向与水平加速度峰值比增大,塔顶竖向加速度响应增大,最大轴力随着峰值比增大而增大,最小轴力随着峰值比增大而减小。此外,增量动力分析表明,采用自接触的有限元模型可以更真实地预测风机塔的失稳破坏机制。     

Response of a double‐wedge base‐isolation device

A novel base‐isolation device is described and its performance is compared with that of a friction pendulum bearing. In its simplest form, the device consists of two wedges sliding on a horizontal plane in opposite directions and constrained from retreating by ratchets or bilinear dampers. The superstructure rests at the intersection of the two wedges. For a sufficiently large horizontal acceleration of the base, the structure starts to move up the inclined plane of one of the wedges, which remains fixed while the second wedge is slaved to follow the structure. As the direction of the base acceleration reverses, the process is reversed and the structure starts to climb on the second inclined plane while the first wedge follows. The overall result is that the horizontal acceleration of the structure is reduced with respect to that of the base and that kinetic energy associated with horizontal velocities is systematically transformed into potential energy. In the case of motion in a vertical plane, the device has the following advantages over a friction pendulum: (i) the sliding surface is linear instead of curved, (ii) kinetic energy is systematically transformed into potential energy during the strong ground motion, and (iii) the device is slowly self‐centering. Copyright © 2004 John Wiley & Sons, Ltd.     

Influence of different sites on seismic base shear of buildings

In this paper, a statistical study based on thirty-two strong rock motions is presented for the dynamic base shear of buildings on three different sites representing stiff soil, deep cohesionless soil and soft clay conditions. A short and squatty building and a tall and slender building are selected. For each building height, frame, wall and shearwall–frame systems are considered. It is found that short and squatty frame systems have the largest base shear. As for buildings on rock, the response of buildings on stiff and deep cohesionless soil conditions depends on the peak horizontal acceleration and peak horizontal velocity of the rock motion. Furthermore, the soil–structure interaction which affects only the stiff structures is found to reduce the dynamic base shear.     

A simple procedure to approximate slip displacement of freestanding rigid body subjected to earthquake motions

A simple calculation procedure for estimating absolute maximum slip displacement of a freestanding rigid body placed on the ground or floor of linear/nonlinear multi‐storey building during an earthquake is developed. The proposed procedure uses the displacement induced by the horizontal sinusoidal acceleration to approximate the absolute maximum slip displacement, i.e. the basic slip displacement. The amplitude of this horizontal sinusoidal acceleration is identical to either the peak horizontal ground acceleration or peak horizontal floor response acceleration. Its period meets the predominant period of the horizontal acceleration employed. The effects of vertical acceleration are considered to reduce the friction force monotonously. The root mean square value of the vertical acceleration at the peak horizontal acceleration is used. A mathematical solution of the basic slip displacement is presented. Employing over one hundred accelerograms, the absolute maximum slip displacements are computed and compared with the corresponding basic slip displacements. Their discrepancies are modelled by the logarithmic normal distribution regardless of the analytical conditions. The modification factor to the basic slip displacement is quantified based on the probability of the non‐exceedence of a certain threshold. Therefore, the product of the modification factor and the basic slip displacement gives the design slip displacement of the body as the maximum expected value. Since the place of the body and linear/nonlinear state of building make the modification factor slightly vary, ensuring it to suit the problem is essential to secure prediction accuracy. Copyright © 2006 John Wiley & Sons, Ltd.     

浮放设备地震滑移反应数值模拟研究

以前人研究建立的浮放设备滑移反应分析理论为基础,给出了浮放设备在水平和竖向地震输入下滑移反应运动微分方程,选取连续型的库仑摩擦力模型,采用Runge-Kutta法求解浮放设备地震滑移反应运动微分方程,可以得到浮放设备在地震作用下的绝对加速度、相对速度和相对位移反应时程。采用编制的计算程序,进行了浮放设备地震滑移反应参数影响研究,结果表明:浮放设备水平滑移反应随着水平地震地面输入或楼层反应输入的增大而增大,随着设备与支撑面之间摩擦系数的增大而减小;当水平向输入加速度峰值大于0.3g时,需要考虑竖向激励的影响。     

A study of response spectra for different geological conditions in Gujarat,India

In this study, the effect of ground geology on the acceleration response spectra is studied at 32 sites in Gujarat, India. The sites are grouped into Proterozoic, Mesozoic, Tertiary and Quaternary. The normalized acceleration response spectra at 5% damping of 407 strong ground motions (horizontal and vertical components) recorded at these sites varying in magnitude from 3.0 to 5.7 are determined. The study shows that the shape of the acceleration response spectra is influenced by the regional geology and local site conditions. The peak of maximum horizontal spectral amplification is between 0.03 and 0.05 s in Proterozoic formations, 0.06 and 0.10 s in Mesozoic formations, 0.06 and 0.08 s in Tertiary and 0.12 s in Quaternary formations. The maximum vertical spectral acceleration is at 0.025 s in Proterozoic, 0.07 s in Mesozoic, 0.05 s in Tertiary and 0.10 s in Quaternary formations. The average acceleration amplification factor in all the geological formations is between 2.5 and 3.0 both in horizontal and vertical components. It has been observed that acceleration response spectra at sites having same geological formations are also influenced by local site conditions. The study shows that the acceleration response spectrum in the current Indian code applicable for the entire country underestimates the seismic forces at hard-rock sites and overestimates at soft-soil sites. Using recorded strong motion data with Mw ranging from 3.5 to 5.7, an attenuation relationship is developed at six periods to predict geometric mean of horizontal spectral amplitudes for rock and soil sites. The spectral amplitudes predicted with the attenuation relationship match well with the observed one within statistical limits for hypocentral distances less than 200 km.     

Simulation of scree‐slope dynamics: investigating the distribution of debris avalanche events in an idealized two‐dimensional model

We present a two‐dimensional model of the development of scree slopes using the discrete‐element method. We concentrate on the dynamics of the accumulating debris at the cliff foot rather than on the failure modes of the cliff‐face or shape of the underlying rock surface. The evolution of this unconsolidated material is intermittent and systematically changing over time, with an early high disturbance regime, dominated by a characteristic event size (where 65% of particles in the debris are in motion to some extent), replaced at later times by many shallow slides interspersed with infrequent large events that involve motion through almost the full scree depth. These large slides lead to a stratigraphy in which the layers of material are stretched almost horizontal near the base of the slope. The scree surface thus shows a gradient in age with most recent rock‐fall close to the cliff and the oldest rock‐fall debris outcropping at the foot. The final surface slope tends to show little curvature, and the final mean slope is well correlated with the angle of internal friction of the particles, although the change is very small over a wide range of friction angles [final slope (in degrees relative to horizontal) ~ 0.043 × internal friction angle + 17.49, with a correlation coefficient of 0.89, p‐value 0.0001]. Some weak size‐segregation of the debris is found, but this seems to have little to do with individual particles bounding down the slope. The shape of the rock core agrees largely with the analytic forms given by Fisher–Lehmann and Bakker–Le Heux expressions, but the original simple Fisher quadratic can give the best fit. Overall the evolution shows a remarkable insensitivity to the model parameters, suggesting that the controls on dry scree‐slope evolution are primarily geometric in character. Copyright © 2014 John Wiley & Sons, Ltd.     

Sliding fragility of block‐type non‐structural components. Part 1: Unrestrained components

Motivated by the development of performance‐based design guidelines with emphasis on both structural and non‐structural systems, this paper focuses on seismic vulnerability assessment of block‐type unrestrained non‐structural components under sliding response on the basis of seismic inputs specified by current seismic codes. Two sliding‐related failure modes are considered: excessive relative displacement and excessive absolute acceleration. It is shown that an upper bound for the absolute acceleration response can be assessed deterministically, for which a simple yet completely general equation is proposed. In contrast, fragility curves are proposed as an appropriate tool to evaluate the excessive relative displacement failure mode. Sample fragility curves developed through Monte‐Carlo simulations show that fragility estimates obtained without taking into account vertical base accelerations can be significantly unconservative, especially for relatively large values of the coefficient of friction. It is also found that reasonable estimates of relative displacement response at stories other than the ground in multistorey buildings cannot in general be obtained by simply scaling the ground acceleration to the peak acceleration at the corresponding storey. Failure modes considered in this study are found to be essentially independent of each other, a property that greatly simplifies assessment of conditional limit states. Copyright © 2002 John Wiley & Sons, Ltd.     

场地地震安全性评价中确定设计地震动参数方面若干问题的研究

研究了确定设计地震动参数中涉及的若干问题,其中包括基岩水平加速度反应谱衰减关系的选择、震源深度对基岩水平加速度峰值及基岩反应谱曲线的影响、强度包络线函数及输入随机相位的选择、土体非线性特性参数和土层剪切波速值的选择、设计地震动反应谱的标定等问题。在有关方面的研究中基于一个典型场地计算剖面,采用一维等效线性化模型并通过逐项变换某些研究参数的方法,研究了有关方面对设计地震动参数可能产生的影响及存在的误差和相应的规律,有关研究结果对合理确定设计地震动参数具有一定的实用价值。     

Response of a nuclear power plant on aseismic bearings to horizontally propagating waves

The nuclear island of Koeberg with a large basemat, a non-linear base isolation effective in the horizontal direction only, founded on rock, is analysed for inclined body waves and for a combination of surface and body waves associated with prescribed horizontal and vertical components of the control motion. When compared to vertical incidence, an additional rocking component arises, generated by the horizontally propagating vertical component. As the aseismic bearings do not isolate against this rocking component, the corresponding horizontal response bears comparison with that of a conventional structure. The ratio of the response for horizontally propagating waves and that for vertically incident waves is thus considerably larger for the base-isolated structure than for a conventional one. However, the actual design incorporating other loading cases is affected much less.     

水平及竖向地震共同作用下双线隧道的响应分析

基于有效的土-结相互作用有限元数值模拟方法,利用有限元软件ABAQUS对水平及竖向地震共同作用下双线盾构隧道的地震响应进行分析研究。地震动输入选取近场地震Loma、ChiChi、Mammoth和WoLong的基岩水平及竖向加速度时程记录。结果表明,不同近场地震记录对隧道结构的作用不同,隧道的地震反应与场地性质及地震动的频谱特性密切相关。对比隧道在水平及竖向地震动共同作用下的响应与单向水平地震动作用下的响应,发现隧道的最大地震附加内力及其分布均发生较大的变化,在隧道结构抗震设计中需引起重视。另外,分析中还考虑了在双向地震动共同作用下,隧道间距、土-结接触面的摩擦系数、土-结相对刚度、输入的地震记录和竖向地震动相对强度对隧道地震响应的影响等,研究结果对隧道工程的抗震设计具有一定的参考价值。     

Motions of rigid bodies and criteria for overturning by earthquake excitations

This investigation deals with motions of rigid bodies on a rigid floor subjected to earthquake excitations, and criteria for overturning of the bodies. In order to study any motions of a body in a plane, the motions are classified into six types, i.e. (1) rest, (2) slide, (3) rotation, (4) slide rotation, (5) translation jump and (6) rotation jump. Then, the following are studied: the equations of motion, transitions of motion, and motions after impact between the body and the floor. One of the features of this investigation is the introduction of the tangent restitution coefficient which enables us to estimate the magnitude of the tangent impulse at the instant of impact. A computer program was developed to simulate the motions of bodies subjected to horizontal and vertical ground motions, numerically solving the non-linear equations of motion. Several types of simulation were carried out and the following conclusions were found. The coefficient of friction must be greater than the breadth—height-ratio in order for the body to rock. The motions after impact from translation jump are greatly influenced by the normal and tangent restitution coefficients. As criteria for overturning of bodies, at least two factors must be taken into account: the horizontal acceleration and the velocity of the floor. Then it is possible to estimate the motions of the floor from the overturning of bodies in a more reliable manner than before.     

A parametric study of seismic behavior of roller seismic isolation bearings for highway bridges

A roller seismic isolation bearing is proposed for use in highway bridges. The bearing utilizes a rolling mechanism to achieve seismic isolation and has a zero post‐elastic stiffness under horizontal ground motions, a self‐centering capability, and unique friction devices for supplemental energy dissipation. The objectives of this research are to investigate the seismic behavior of the proposed bearing using parametric studies (1) with nonlinear response history analysis and (2) with equivalent linear analysis according to the AASHTO guide specifications, and by comparing the results from both analysis methods (3) to evaluate the accuracy of the AASHTO equivalent linear method for predicting the peak displacement of the proposed bearing during an earthquake. Twenty‐eight ground motions are used in the studies. The parameters examined are the sloping angle of the intermediate plate of the bearing, the amount of friction force for supplemental energy dissipation, and the peak ground acceleration levels of the ground motions. The peak displacement and base shear of the bearing are calculated. Results of the studies show that a larger sloping angle does not reduce the peak displacement for most of the parametric combinations without friction devices. However, for parametric combinations with friction devices, it allows for the use of a higher friction force, which effectively reduces the peak displacement, while keeping a self‐centering capability. The AASHTO equivalent linear method may underestimate the peak displacement by as much as 40%. Vertical ground motions have little effect on the peak displacement, but significantly increase the peak base shear. Copyright © 2009 John Wiley & Sons, Ltd.     

Non‐linear response analyses of rectangular rigid bodies subjected to horizontal and vertical ground motion

This investigation deals with non‐linear seismic responses of free‐standing rectangular rigid bodies on horizontally and vertically accelerating rigid foundations. The responses are classified into two initial responses and four subsequent responses, accordingly the equations of motion governing the liftoff, slip and liftoff–slip interaction motions and boundary conditions corresponding to commencement and termination of the motions are defined. The time histories of responses presented herein show that the body is sensitive to small changes in the friction coefficient and slenderness, and to the wave properties and intensity of ground motions. Systematic trends are observed: the bodies on the low‐grip foundation avoid overturning while they are allowed to slip regardless of details of ground motions; the long period earthquakes tend to make the body overturn and slip largely. In contrast, the timing when liftoff and slip commences and terminates and their directions do not directly correspond with intensity of ground motions. Moreover, the vertical ground motion adds irregularities on the responses, since it excites or damps the responses. It is concluded that governing equations of motion and boundary conditions in view of discontinuous non‐linear systems are necessary to analyse actual motions of the rectangular rigid bodies subjected to horizontal and vertical ground motion. Copyright © 2002 John Wiley & Sons, Ltd.     

Hydrodynamic pressures and response of gravity dams to vertical earthquake component

Hydrodynamic pressures and structural response of concrete gravity dams, including dam-reservoir interaction, due to the vertical component of earthquake ground motions are investigated. The response of the dam is approximated by the deformations in the fundamental mode of vibration, and the effects of deformability of bed rock on hydrodynamic pressures are recognized in the analysis. Expressions for the complex frequency response functions for the dam displacement, dam acceleration and lateral hydrodynamic force are derived. These results along with the Fast Fourier Transform algorithm are utilized to compute the time-history of responses of dams of 100, 300 and 600 ft height, with full reservoir, for different values of elastic modulus of mass concrete: 3.0, 3.5, 4.0, 4.5 and 5.0 million psi, to the vertical component of El Centro, 1940, and Taft, 1952, ground motions. It is concluded that the hydrodynamic forces caused by vertical ground motion are affected substantially by damreservoir interaction and depend strongly on the modulus of elasticity of the dam. The dam response to the vertical component of ground motion is compared with that due to the horizontal component. It is concluded that because the vertical component of ground motion causes significant hydrodynamic forces in the horizontal direction on a vertical upstream face, responses to the vertical component of ground motion are of special importance in analysis of concrete gravity dams subjected to earthquakes.     

Static and seismic limit equilibrium analysis of sliding retaining walls under different surcharge conditions

The static and seismic sliding limit equilibrium condition of retaining walls is investigated, and analytical solutions for the angle of the active slip surface, the critical acceleration coefficient and the coefficient of active earth pressure are provided for different surcharge conditions. In particular, walls retaining a horizontal backfill without surcharge, walls supporting an extended uniform surcharge applied at different distances from the wall and walls supporting a limited uniform surcharge or linear uniform surcharge parallel to the wall are considered in the analysis.The solutions have been derived in the framework of the limit equilibrium approach, considering the effect of the wall through its weight, and accounting for the shear resistance at the base of the wall and the inertia force arising in the wall under seismic conditions.For the wall without surcharge the effect of the vertical component of the seismic acceleration as well as the effects of the inclination of the wall internal face and of the soil–wall friction were also investigated.The angle of the slip plane, the critical seismic acceleration coefficient and the coefficient of active earth pressure are given as functions of dimensionless parameters and the boundary conditions for the applicability of each solution are specified. The influence of soil weight, surcharge conditions and inertia forces on the active earth pressure coefficient is analysed.     

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.     

垂直向地震作用对节理岩体失稳破坏的影响

基于线弹性断裂力学理论分析了垂直向地震作用对节理岩体地震动力破坏的影响。在仅考虑峰值时,最不利的单向地震动加速度方向是水平倾向坡外,双向则依据破裂机制是拉剪或压剪,加速度分别是水平倾向坡外与向下或向上的组合。地震动的幅值、作用方向及双向地震动的组合都可使岩体的破坏机制发生转化,并且是突变的、不可逆的。较低峰值的双向地震动产生的应力强度因子可能大于较高峰值的单向地震动所产生的应力强度应子。在岩体节理分布特征和静态应力场一定的初始条件下,第一个导致岩体中产生破裂的地震动加速度幅值及其方向的组合唯一地决定了岩体不可逆破坏发展的方向、机制及最终的破坏特征,其复杂性远大于静力作用时的情况。对岩体地震动力破坏问题的认识应充分考虑垂直向地震动的重要影响。