Fourier amplitude spectra of strong motion acceleration: Extension to high and low frequencies

It is shown how the empirical equations for scaling the Fourier amplitude spectra in the frequency band from ～0.1 to 25 Hz can be extended to describe the strong motion amplitudes in a much broader frequency range. At long periods, the proposed equations are in excellent agreement with (1) the seismological and field estimates of permanent ground displacement (near field) and (2) the independent estimates of seismic moment (far field). At high frequencies, f ≥ 25 Hz, the spectral amplitudes can be described by exp (? πkf), where k ranges from 0·02 (near source) to about 0·06 at an epicentral distance of about 200 km. It is also shown how amplification by local soil and geological site conditions can be defined to apply in the same broad frequency range.     

Numerical simulation of ground flow caused by seismic liquefaction

Flow failure of sandy subsoil induced by seismic liquefaction is known to cause significant damage to structures. It is induced not only by the dynamic forces exerted by seismic acceleration but also by the static gravity force in consequence of the topography of the ground. The ground flow may sometimes continue after the end of the seismic loading and finally the ground is significantly deformed to cause a failure.This paper numerically predicts the magnitude of flow that could occur when soil liquefaction continues for a sufficiently long period. It is considered that liquefied soil behaves like a viscous liquid, and hence, ground flow is governed by the principle of minimum potential energy. In the calculation, liquefied sand is assumed to be a viscous liquid that deforms in undrained conditions with its volume remaining constant. To consider the non-linearity due to large displacement, the updated Lagrangian method is used to solve the equation of motion. The Newmark β method is employed to calculate the time history of the ground motion. Finally, a simulation using this calculation method shows that the proposed method gives reasonable results for the conditions indicated.     

Sensitivity of the Sharpe and Worden gravity meters to vertical motion

Summary Using the least-squares method the constants of both gravity meters — seismometers — were derived from the amplitude responses, observed under vertical motion on a vibrating table in the 0.3–30 s range. The values of the seismogram amplitudes, above which seismic waves cause an observable displacement of the gravity meter reading beam, were determined for the SKD and Press-Ewing station seismographs.     

Seismic noise at the international gravity point in Prague-Ruzyně (Czechoslovakia)

Summary The vertical component of ground displacement was measured at the Prague - Ruzyn International Gravity Point in the frequency range of 1–300 Hz. The permanent noise, the vibrations caused by the observers during gravimetric observations and by the wind, as well as those due to normal operations at the airport, display maximum peak-to-peak amplitudes of 0.06 µm in the frequency range of 1–50 Hz; with a CG-2 gravimeter this is not detrimental to the accuracy of the observations. The taxiing of turbo-jet and jet aircraft and engine tests of aircraft generate vibrations in frequency ranges of 75–90 and 190–270 Hz. Their amplitudes, according to the results of laboratory tests published for various types of gravity meters (CG-2, GAK-PT, GVP-3, KVG), are of magnitudes which generate errors in tenths of mgl.     

Resonance capacity method for earthquake response analysis of hysteretic structures

The Resonance Capacity Method is proposed for the earthquake response analysis of hysteretic structures. Resonance Capacity is a physical quantity of structures which is related to the hysteretic energy absorbed by structures in one cycle and is equated to the acceleration, velocity and displacement amplitudes α₀, d₀ and d₀ of earthquake ground motions at resonance.¹ According to the idealized trapezoidal approximation of earthquake ground motions in the logarithmic period–velocity plane as proposed by Veletsos and Newmark,⁸ the Resonance Capacity property applies in each period range, short, medium and long, where α₀, v₀ and d₀ respectively are approximately constant. In the medium range of periods, the energy dissipated in hysteretic loops and the deformation amplitudes of a single-degree system with elasto–plastic force–deformation relationships are calculated for the case of El Centro 1940, 18 May earthquake, by this Resonance Capacity Method. The result is compared with results from conventional numerical response analyses obtained by Berg and Thomaides,¹⁴ Kato and Akiyama¹² and Veletsos and Newmark,⁸ and the general agreement is seen to be good. Therefore, it may be possible to apply this Resonance Capacity Method over the entire range of periods. By means of this method the earthquake response analysis of hysteretic systems can be performed easily, and the hysteretic energy and fatigue characteristics of structures may be taken into account directly, up to the point of fracture.     

Effect of peak ground acceleration to velocity ratio on ductility demand of inelastic systems

A statistical analysis is performed to investigate the significance of peak ground acceleration to velocity ratio (a/v) on the displacement ductility demand of simple bilinear hysteretic systems. Three groups of earthquake records representative of low, normal and high<a/v ranges are used as input ground motions. The design yield strength of the inelastic systems is specified from the base shear formula in the 1980 National Building Code of Canada (NBCC 1980) and that in NBCC 1985 respectively. The former case represents the common practice of specifying seismic design base shear based on a peak site acceleration, while in the latter case the base shear is specified based on peak ground velocity and a/v ratio. Mean displacement ductility demands are obtained for the three groups of ground motions; and the corresponding dispersion characteristics are examined. The results show that the ground motion<a/v range has a significant effect on the displacement ductility demand, and it should be accounted for in design strength specification.     

Sliding response of gravity dams including vertical seismic accelerations

Seismic safety assessment of gravity dams has become a major concern in many regions of the world while the effects of vertical seismic accelerations on the response of structures remain poorly understood. This paper first investigates the effect of including vertical accelerations in the sliding response analysis of gravity dams subjected to a range of historical ground motion records separated in two groups according to their source-to-site distance. Analyses showed that the incidence of vertical accelerations on the sliding response of gravity dams is significantly higher for near-source records than for farsource records. The pseudo-static 30% load combination rule, commonly used in practice to account for the non-simultaneous occurrence of the peak horizontal and vertical accelerations, yielded good approximations of the minimum safety factors against sliding computed from time-history analyses. A method for empirically estimating the vertical response spectra based on horizontal spectra, accounting for the difference in frequency content and amplitudes between the two components is investigated. Results from analyses using spectrum compatible horizontal and vertical synthetic records also approximated well the sliding response of a gravity dam subjected to series of simultaneous horizontal and vertical historical earthquake records.     

Pseudo relative velocity spectra of earthquake ground motion at high frequencies

The currently available empirical scaling laws for estimation of spectral amplitudes are limited to periods longer than 0–04 s. However, for design of equipment and stiff structures on multiple and distant supports, exposed to strong shaking near faults where peak accelerations can exceed 1g, specification of design ground motions at higher frequencies is required. This paper presents a method for extrapolation of pseudo-relative velocity spectral amplitudes of strong earthquake shaking to short periods (0–01 < T < 0–04 sec). The extrapolated spectra can be used as a physical basis for defining design spectral amplitudes in this higher-frequency range. The analysis in this paper implies that for typical strong motion accelerations, particularly on sedimentary sites in California, the peak ground accelerations are projected to be unaffected by frequencies higher than those recorded. Consequently, in California, the high-frequency pseudo-acceleration spectra can be approximated from the recorded absolute peak accelerations.     

Adaptation of the S-5-S pendulum seismometer for measurement of rotational ground motion

The Russian electrodynamic seismometer model S-5-S has been adapted for the measurement of rotational ground motion. The mechanical system of the original S-5-S seismometer consists of electrodynamic sensing and damping transducer coils mounted on an asymmetrical double-arm pendulum. This pendulum is suspended on a footing using two pairs of crossed flat springs, which operate as the axis of rotation. The pendulum is stabilised by an additional spring. The S-5-S can be used either as a vertical or as a horizontal sensor. The adaptation of the S-5-S seismometer described below involves removal of the additional spring and installation of an additional mass on the damping arm. Strain gauge angle sensors are installed on one pair of the crossed flat springs. The main dynamic parameters of the rotational seismometer created in this way, i.e. the natural period and damping, are controlled electronically by feedback currents proportional to the angular displacement and angular velocity, both fed to the damping transducer coil. This new seismometer, named the S-5-SR, enables measurement of the rotational component of ground motion around the horizontal or the vertical axes. The output signal from this S-5-SR seismometer can be proportional either to rotational displacement or rotational velocity.     

Magma convection and mixing dynamics as a source of Ultra-Long-Period oscillations

Many volcanic eruptions are shortly preceded by injection of new magma into a pre-existing, shallow (<10 km) magma chamber, causing convection and mixing between the incoming and resident magmas. These processes may trigger dyke propagation and further magma rise, inducing long-term (days to months) volcano deformation, seismic swarms, gravity anomalies, and changes in the composition of volcanic plumes and fumaroles, eventually culminating in an eruption. Although new magma injection into shallow magma chambers can lead to hazardous event, such injection is still not systematically detected and recognized. Here, we present the results of numerical simulations of magma convection and mixing in geometrically complex magmatic systems, and describe the multiparametric dynamics associated with buoyant magma injection. Our results reveal unexpected pressure trends and pressure oscillations in the Ultra-Long-Period (ULP) range of minutes, related to the generation of discrete plumes of rising magma. Very long pressure oscillation wavelengths translate into comparably ULP ground displacements with amplitudes of order 10⁻⁴–10⁻² m. Thus, new magma injection into magma chambers beneath volcanoes can be revealed by ULP ground displacement measured at the surface.     

摩擦摆基础隔震结构双向地震反应分析

采用双向耦合力学模型模拟摩擦摆支座的双向耦合效应,对摩擦摆基础隔震结构进行了单向和双向地震反应对比分忻,分析表明在双向地震作用下结构各层的加速度反应较小,隔震层的层间位移较大,而上部结构的层间位移较小,并且在双向地震作用下,支座的最大位移明显大于单向地震作用时的支座最大位移,因而应考虑双向地震作用对摩擦摆基础隔震结构地震反应和隔震支座性能的影响。     

Probability of actuating a seismic shutoff device

Automatic seismic shutoff devices are used to reduce the risk to gas and liquid distribution systems from earthquakes. In the USA, the gas shutoff devices are tested and certified according to the American Society of Civil Engineers' Standard ASCE 25. During tests, devices are shaken by simple harmonic (sinusoidal) motions of different frequencies and checked for actuation. Because earthquake motions are not sinusoidal, the amplitude of earthquake motions that will actuate these devices is not clearly understood. This paper determines the probability of actuating devices by earthquake motions of different amplitudes. The probability of actuation increases with increase in the resultant peak horizontal ground acceleration (PGA). The probability of actuation is 50% for PGA = 0.23g and 90% for PGA = 0.31g, where g = 9.81 m/s² = acceleration due to gravity. On a ‘stiff soil’ site in San Francisco, CA, the mean recurrence interval of actuation is 51 years. On a similar site in Boston, MA, the mean recurrence interval of actuation is 3000 years. ASCE 25 compliant devices are actuated by high frequencies in ground motions. There is greater uncertainty in the actuation of these devices by ground motions that are damaging to very flexible systems. Copyright © 2016 John Wiley & Sons, Ltd.     

长联大跨摩擦摆支座隔震连续梁桥多维地震反应分析

结合长联大跨连续梁桥的特点,以1座(65+123+156+123+10×90+55)m长联大跨摩擦摆支座隔震连续梁桥为背景,建立了全桥三维有限元模型,运用非线性时程分析法,分析了地震动输入模式、地震动强度、摩擦摆支座参数对该桥内力、位移和能量响应的影响。研究结果表明:(1)长联大跨连续梁桥布置摩擦摆支座,可有效延滞固定墩顶有效主梁质量效应,实现全桥协同抗震。大部分地震能量可通过支座滞回耗能散耗,大幅降低了该桥固定墩地震能量耗散需求。(2)长联大跨连续梁桥减隔震设计中,建议采用水平单向+竖向地震组合进行内力设计,采用三向地震组合进行位移设计。(3)强震作用下,支座摩擦因数取0.029~0.034时该桥隔震性能最优。     

Estimating the seismic displacement of friction pendulum isolators based on non‐linear response history analysis

A procedure for developing equations that estimate the isolator displacement due to strong ground motion is applied to buildings isolated with the friction pendulum system. The resulting design equations, based on rigorous non‐linear analysis, offer an alternative to the iterative equivalent‐linear methods used by current U.S. building codes. The governing equations of the system are reduced to a form such that the median normalized displacement of the system due to an ensemble of ground motions is found to depend on only the isolation period—a function of the curvature of the isolator—and the friction force at incipient slip normalized by peak ground velocity. The normalization is effective in minimizing the dispersion of the normalized displacement for an ensemble of ground motions, implying that the median normalized displacement is a reliable estimate of response. The design equations reflect the significant (20 to 38%) increase in displacement when the excitation includes two lateral components of ground motion instead of just one component. Equivalent‐linear methods are shown to underestimate by up to 30% the exact median displacement determined by non‐linear response history analysis for one component of ground motion, and building codes include at most a 4.4% increase for a second component. Copyright © 2003 John Wiley & Sons, Ltd.     

Generation of probabilistic displacement response spectra for displacement-based design

Displacement response spectrum (DRS), as the input, is of great significance to the displacement-based design just like the acceleration response spectrum to the traditional force-based design. Although the procedure of performance-based, in particular the displacement-based design has achieved considerable development, there is not a general DRS covering an enough long period range for common seismic design yet. This paper develops a systematic ground motion data processing procedure for the purpose of correcting the noise in the earthquake records and generating consistent DRS for seismic design. An adaptive algorithm is proposed to determine the cutoff frequency of the high-pass digital filter. The DRS of more than 500 recorded earthquake ground motions are generated and they are classified into three groups according to the ratio of the peak ground acceleration to the peak ground velocity (A/V) and/or the ratio of the peak ground velocity to the peak ground displacement (V/D). In each group, all the ground motions are normalized with respect to a selected scaling factor. Their corresponding DRS are obtained and then averaged to get the mean and standard deviation DRS, which can be used for both deterministic and probabilistic displacement-based design.     

Tilt measurements in western Canada

Pairs of short baselength mercury-level tiltmeters mounted on shallow piers coupled to sedimentary rocks have been used to monitor ground tilting at three inland locations in western Canada. Noise levels have been estimated over large Nyquist intervals to evaluate site conditions and for comparison with results observed in crystalline rocks at other locations. The results show that tilt noise patterns are similar for different locations, and that noise levels are higher for unconsolidated sediments. Tidal estimates for the principal lunar semidiurnal constituentM ₂ were obtained from the least noisy sections of the tilt series. Uncertainties in the estimated amplitudes for the record lengths considered range from 4 to 20% depending on location and azimuth. Comparison of the observedM ₂ tide with those predicted for an elastic Earth loaded by two different ocean configurations (Schwiderski or Parke) shows better agreement with the Schwiderski marine tidal model. Differences between observaton and theory suggest a strain-induced perturbation source.     

断层活动的重力效应ht

本文对介质变形造成的重力变化作了定量分析, 通过质点位移法(拉格朗日法)导出了介质位移场和由它产生的附加重力场之间的积分关系式.应用已有的弹性和粘弹性半空间任意倾角断层位错的位移表达式, 本文通过三维空间数值积分, 计算了弹性介质和广义开尔文介质中断层不同的运动方式所产生的地表附加重力场, 以及介质流变性导致的重力随时间的变化趋势.参考唐山地震前沧东断裂的活动和震时断层错动, 计算了震前震后相应的重力变化, 其结果与实测重力资料有一定程度的符合.      

Correlations of peak acceleration,velocity and displacement with earthquake magnitude,distance and site conditions

A brief review of proposed correlations between peak accelerations and earthquake magnitude and distance has been presented. It has been found that most investigators agree favourably on what should be the amplitude of peak accelerations for the distance range between about 20 and 200 km. For distances less than 20 km, there is significant disagreement in the predicted peak amplitudes, reflecting the lack of data there and the uncertainties associated with the extrapolation. Correlations of peak accelerations, peak velocities and peak displacements with earthquake magnitude, epicentral distance and the geologic conditions of the recording sites have been presented for 187 accelerograms recorded during 57 earthquakes. This data set describes strong earthquake ground motion in the Western United States during the period from 1933 to 1971. For large earthquakes, dependence of peak acceleration, velocity and displacement amplitudes on earthquake magnitude seems to be lost. This suggests that the amplitudes of strong ground motion close to a fault are scaled primarily by the maximum dislocation amplitudes and the stress drop, rather than the overall ‘size’ of an earthquake as measured by magnitude. The influence of geologic conditions at the recording station seems to be of minor importance for scaling peak accelerations, but it becomes noticeable for the peaks of velocity and even more apparent for the peaks of displacement.     

Modelling of raked pile foundations in liquefiable ground

Raked piles are believed to behave better than vertical piles in a laterally flowing liquefied ground. This paper aims at numerically simulating the response of raked pile foundations in liquefying ground through nonlinear finite element analysis. For this purpose, the OpenSees computer package was used. A range of sources have been adopted in the definition of model components whose validity is assessed against case studies presented in literature. Experimental and analytical data confirmed that the backbone force density–displacement (p–y) curve simulating lateral pile response is of acceptable credibility for both vertical and raked piles. A parametric investigation on fixed-head piles subject to lateral spreading concluded that piles exhibiting positive inclination impart lower moment demands at the head while those inclined negatively perform better at liquefaction boundaries (relative to vertical piles). Further studies reveal substantial axial demand imposed upon negatively inclined members due to the transfer of gravity and ground-induced lateral forces axially down the pile. Extra care must be taken in the design of such members in soils susceptible to lateral spreading such that compressive failure (i.e. pile buckling) is avoided.