Comparing response of SDF systems to near‐fault and far‐fault earthquake motions in the context of spectral regions

In spite of important differences in structural response to near‐fault and far‐fault ground motions, this paper aims at extending well‐known concepts and results, based on elastic and inelastic response spectra for far‐fault motions, to near‐fault motions. Compared are certain aspects of the response of elastic and inelastic SDF systems to the two types of motions in the context of the acceleration‐, velocity‐, and displacement‐sensitive regions of the response spectrum, leading to the following conclusions. (1) The velocity‐sensitive region for near‐fault motions is much narrower, and the acceleration‐sensitive and displacement‐sensitive regions are much wider, compared to far‐fault motions; the narrower velocity‐sensitive region is shifted to longer periods. (2) Although, for the same ductility factor, near‐fault ground motions impose a larger strength demand than far‐fault motions—both demands expressed as a fraction of their respective elastic demands—the strength reduction factors R_y for the two types of motions are similar over corresponding spectral regions. (3) Similarly, the ratio u_m/u₀ of deformations of inelastic and elastic systems are similar for the two types of motions over corresponding spectral regions. (4) Design equations for R_y (and for u_m/u₀) should explicitly recognize spectral regions so that the same equations apply to various classes of ground motions as long as the appropriate values of T_a, T_b and T_c are used. (5) The Veletsos–Newmark design equations with T_a=0.04 s, T_b=0.35 s, and T_c=0.79 s are equally valid for the fault‐normal component of near‐fault ground motions. Copyright © 2001 John Wiley & Sons, Ltd.     

Evaluation of seismic energy demand

In this paper, a method is proposed in order to obtain a simplified representation of hysteretic and input energy spectra. The method is based on the evaluation of the equivalent number of cycles correlated to the earthquake characteristics by the proposed seismic index I_D. This procedure allows us to obtain peak values of the hysteretic and input energy that depend on the demanded ductility, on the seismic index I_D and on the peak pseudo‐velocity. The assessment of the input energy represents a first step towards the definition of a damage potential index capable of taking into account the effect of the duration of the ground motions. Copyright © 2001 John Wiley & Sons, Ltd.     

Consistent inelastic design spectra: Hysteretic and input energy

This is the second of two companion papers on inelastic design spectra (for strength, displacement, hysteretic and input energy) for systems with a prescribed ductility factor. All the spectra are consistent (interrelated and based on the same assumptions). This paper deals with two quantities related to cumulative damage: hysteretic and input energy. The input data for the procedure are the characteristics of the expected ground motion in terms of a smooth elastic pseudo-acceleration spectrum and the time integral of the square of the ground acceleration ∫a² dt. Simple, approximate expressions for two dimensionless parameters (the parameter γ and the hysteretic to input energy ratio E_HE_I) have been proposed. The parameter 7, which controls the reduction of the deformation capacity of structures due to low-cycle fatigue, depends on the natural period of the system, the prescribed ductility factor, the hysteretic behaviour and the ground motion characteristics. The ratio E_H/E_I is influenced by damping, the ductility factor and the hysteretic behaviour. Very good approximations to the inelastic spectra for hysteretic and input energy can be derived from the elastic spectrum using the spectra for the reduction factor R, proposed in the companion paper, and the proposed values for γ and E_H/E_I     

Newmark design spectra considering earthquake magnitudes and site categories

Newmark design spectra have been implemented in many building codes, especially in building codes for critical structures. Previous studies show that Newmark design spectra exhibit lower amplitudes at high frequencies and larger amplitudes at low frequencies in comparison with spectra developed by statistical methods. To resolve this problem, this study considers three suites of ground motions recorded at three types of sites. Using these ground motions, influences of the shear-wave velocity, earthquake magnitudes, source-to-site distances on the ratios of ground motion parameters are studied, and spectrum amplification factors are statistically calculated. Spectral bounds for combinations of three site categories and two cases of earthquake magnitudes are estimated. Site design spectrum coefficients for the three site categories considering earthquake magnitudes are established. The problems of Newmark design spectra could be resolved by using the site design spectrum coefficients to modify the spectral values of Newmark design spectra in the acceleration sensitive, velocity sensitive, and displacement sensitive regions.     

Lessons from the 2003 Tokachi-oki, Japan, earthquake for prediction of long-period strong ground motions and sloshing damage to oil storage tanks

The 2003 Tokachi-oki earthquake (M _w 8.0) in northern Japan generated large-amplitude long-period (4–8 s) ground motions in the Yufutsu sedimentary basin, causing severe damage to seven large oil storage tanks with floating roof structures because of severe sloshing of oil. The 30,000–40,000-m³ tanks having suffered the severe damage such as fires and sinking of floating roofs experienced the sloshing with large amplitudes exceeding 3 m in which the fundamental mode was predominant. The second mode of sloshing was also excited in the 110,000-m³ tanks in which their floating roofs sank into oil, indicating that the higher modes of sloshing as well as the fundamental mode should be considered in damage prediction. The strong ground motion recordings demonstrated the earthquake dependency of predominant periods and the substantial spatial variation of the long-period shaking observed within the Yufutsu basin, meaning the necessity of source- and site-specific prediction of long-period strong ground motions. The two-dimensional numerical modeling suggested the importance of detailed structures of soft near-surface sediments as well as deep basin structure for accurate prediction of long-period strong ground motions in deep sedimentary basins.     

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.     

Hysteretic energy spectrum and damage control

The inelastic response of single‐degree‐of‐freedom (SDOF) systems subjected to earthquake motions is studied and a method to derive hysteretic energy dissipation spectra is proposed. The amount of energy dissipated through inelastic deformation combined with other response parameters allow the estimation of the required deformation capacity to avoid collapse for a given design earthquake. In the first part of the study, a detailed analysis of correlation between energy and ground motion intensity indices is carried out to identify the indices to be used as scaling parameters and base line of the energy dissipation spectrum. The response of elastoplastic, bilinear, and stiffness degrading systems with 5 per cent damping, subjected to a world‐wide ensemble of 52 earthquake records is considered. The statistical analysis of the response data provides the factors for constructing the energy dissipation spectrum as well as the Newmark–Hall inelastic spectra. The combination of these spectra allows the estimation of the ultimate deformation capacity required to survive the design earthquake, capacity that can also be presented in spectral form as an example shows. Copyright © 2001 John Wiley & Sons, Ltd.     

Hazard mapping of normalized peak strain in soils during earthquakes: microzonation of a metropolitan area

Seismic hazard maps of the Los Angeles metropolitan area are illustrated for normalized peak strain and for 50 years of exposure. The strain estimates are based on scaling in terms of peak ground velocity. The proportionality factor is the phase velocity with which the wave energy is propagating. A simplified seismicity model is used in which all earthquakes occur on faults represented by buried lines and in one zone of diffused seismicity. Poissonian model of earthquake occurrence is assumed. The same model was used in the 1980's to illustrate a method for microzoning of the same area for response spectral amplitudes. Maps of logarithms of normalized peak strain, cε_max, are presented for probabilities of at least one exceedance p = 0·99, 0·9, 0·5, 0·1 and 0·01. These can be used to construct site specific probability distribution functions of the normalized peak strain, cε_max. Such maps are useful for design of new and for retrofit of existing structures, sensitive to strain and differential ground motions (bridges, tunnels, pipelines, etc.).     

Damaging properties of ground motions and prediction of maximum response of structures based on momentary energy response

Dynamic damaging potential of ground motions must be evaluated by the response behaviour of structures, and it is necessary to indicate what properties of ground motions are most appropriate for evaluation. For that purpose, the behaviour of energy input process and hysteretic energy dissipation are investigated in this study. It is found that the momentary input energy that is an index for the intensity of input energy is related to the characteristics of earthquakes such as cyclic or impulsive, and to the response displacement of structures immediately. On the basis of these results, a procedure is proposed to predict inelastic response displacement of structures by corresponding earthquake input energy to structural dissipated damping and hysteretic energy. In this procedure the earthquake response of structures is recognized as an input and dissipation process of energy, and therefore structural properties and damaging properties of ground motions can be taken into account more generally. Lastly, the studies of the pseudodynamic loading test of reinforced concrete structure specimens subjected to ground motions with different time duration are shown. The purpose of this test is to estimate the damaging properties of ground motions and the accuracy of the proposed prediction procedure. Copyright © 2002 John Wiley & Sons, Ltd.     

The effects of repeated earthquake ground motions on the non‐linear response of SDOF systems

In many parts of the world, the repetition of medium–strong intensity earthquake ground motions at brief intervals of time has been observed. The new design philosophies for buildings in seismic areas are based on multi‐level design approaches, which take into account more than a single damageability limit state. According to these approaches, a sequence of seismic actions may produce important consequences on the structural safety. In this paper, the effects of repeated earthquake ground motions on the response of single‐degree‐of‐freedom systems (SDOF) with non‐linear behaviour are analysed. A comparison is performed with the effect of a single seismic event on the originally non‐damaged system for different hysteretic models in terms of pseudo‐acceleration response spectra, behaviour factor q and damage parameters. The elastic–perfect plastic system is the most vulnerable one under repeated earthquake ground motions and is characterized by a strong reduction of the q‐factor. A moment resisting steel frame is analysed as well, showing a reduction of the q‐factor under repeated earthquake ground motions even larger than that of an equivalent SDOF system. Copyright © 2002 John Wiley & Sons, Ltd.     

Response of base-isolated buildings to random excitations described by the Clough-Penzien spectral model

The stationary response of base-isolated buildings subjected to earthquake excitation is studied. The frequency content of earthquake input is described by the Clough-Penzien spectral model. The response parameters of interest are (1) the root-mean-square (RMS) displacement σ_x of the basement relative to the foundation (i.e. shear deformation of the isolation system) and (2) the ratio (σ_a/σ_a0) of the RMS value of the absolute acceleration at the roof of the isolated structure over the corresponding value when the isolation system is locked. The variation of these response parameters with the effective frequency f₀ of the base-isolated structure is investigated. As input, earthquakes with moment magnitudes M = 7-3 and M = 6-0 are considered. The acceleration spectra corresponding to these two earthquake sizes have pronouncedly different frequency content over the frequency range 0–1-1–0 Hz which is of primary importance for base-isolated structures. An important conclusion that comes from these analyses is that confidence in the effectiveness of a base-isolated system should be based primarily on its capacity to absorb/dissipate energy and less on its influence in shifting the fundamental period of the structure out of the range of dominant earthquake energy.     

Simulation of near source ground motion and its characteristics

It is fact that the severe ground motions of shear waves have a strong effect on the dynamic behavior of buildings and civil structures. We simulate near source strong motions of a pure shear wave and synthesize small motions, using the parameters based on the recorded accelerograms at the site that is regarded as a base rock in the Osaka basin, Japan. By making use of a stochastic technique, we can easily introduce higher frequency contents in the motions and apply the technique to the synthesis of small waves regarding as a green function. We also introduce to the analysis the useful relationships among the time duration T_d, the seismic moment M₀, the corner frequency f_c and the high cutoff frequency f_max which were regressed by a simple representation scheme. Considering two active faults that may affect severe damage on buildings and civil structures, we try to predict strong ground motions in Osaka basin and show the characteristics of them.     

Q and high-frequency strong motion spectra

Empirical scaling equations for Fourier amplitude spectra of strong ground motion are used to describe A₀ and τ in the assumed (high-frequency) shape of strong motion amplitudes: FS(_φ) = A₀e-^πτφ. The res of computed A₀ and τ with other related estimates of spectral amplitudes; (2) smooth decay of strong motion spectral amplitudes up to φ = 25 Hz, without an abrupt low-pass filtering of high frequecies; and (3) good agreement with other estimates of the regionally specific attenuation of high-frequncy seismic waves.As the recorded strong earthquake shaking in the western United States typically samples only the shallow (10 km) and local (100km) characteristics of wave attenuation, the processed strong motion accelerograms can be used as the most direct means of describing the nature of the high-frequency attenuation of the entire strong motion signal for use in earthquake engineering applications. Seismological body wave, Lg and coda wave estimates of Q sample different volumes of the crust surrounding the station, and involve different paths of the waves. These differences must be carefully documented and understood before the results can be used in earthquake engineering characterization of strong motion amplitudes.     

Duration of earthquake fault motion in California

Duration of high frequency (5–25 Hz) radiation of energy from earthquake sources in California is consistent with the estimates of fault length and with dislocation velocity estimates of 2–3 km/sec. This duration can be described by an exponential function of magnitude for 2·5 < M < 7·5. It is related to the times it takes the dislocation to spread over the fault width (1/f₂), and the fault length (～ 1/f₁), and to reach its ultimate amplitude (T₀). The results in this paper can be used to estimate the range of amplitudes and the duration of long period pulses of strong ground motion near faults, as these long period pulses can be related to the properties of high-frequency radiation from the source. Such pulses must be considered in the analyses of yielding structures, when the average peak acceleration of the pulse exceeds the yield resistance seismic coefficient of the structure.     

The source of the great Assam earthquake — an interplate wedge motion

The source of the Assam earthquake of Aug. 15, 1950 is revealed from amplitude observations of surface and body waves at Pasadena, Tokyo and Bergen. Seiches' amplitudes in Norway, initial P motions throughout the world, aftershocks and landslides distribution, PP/P ratio at Tokyo, R/L ratio and directivity at Pasadena, are also used. The ensuing fault geometry and kinematics is consistent with the phenomenology of the event and the known geology of the source area. It is found that a progressive strike-slip rupture with velocity 3 km/sec took place on a fault of length 250 km and width 80 km striking 330–337° east of north and dipping 55–60° to ENE. The use of exact surface-wave theory and asymptotic body-wave theory which takes into account finiteness and absorption, rendered an average shear dislocation of 35 m. A three-dimensional theory for the excitation of seiches in lakes by the horizontal acceleration of surface waves was developed. It is confirmed that Love waves near Bergen generated seiches with peak amplitude up to 70 cm depending strongly on the width of the channel.It is believed that the earthquake was caused by a motion of the Asian plate relative to the eastern flank of the Indian plate where the NE Assam block is imparted a tendency of rotation with fracture lines being developed along its periphery.Comparison with other well-studied earthquakes shows that although the magnitude of the Assam event superseded that of all earthquakes since 1950, its potency U₀dS (700,000 m × km²) was inferior to that of Alaska 1964 (1,560,000 m × km²) and Chile 1960 (1,020,000 m × km²).     

Determination of ductility factor considering different hysteretic models

In current seismic design procedures, base shear is calculated by the elastic strength demand divided by the strength reduction factor. This factor is well known as the response modification factor, R, which accounts for ductility, overstrength, redundancy, and damping of a structural system. In this study, the R factor accounting for ductility is called the ‘ductility factor’, R_μ. The R_μ factor is defined as the ratio of elastic strength demand imposed on the SDOF system to inelastic strength demand for a given ductility ratio. The R_μ factor allows a system to behave inelastically within the target ductility ratio during the design level earthquake ground motion. The objective of this study is to determine the ductility factor considering different hysteretic models. It usually requires large computational efforts to determine the R_μ factor. In order to reduce the computational efforts, the R_μ factor is prepared as a functional form in this study. For this purpose, statistical studies are carried out using forty different earthquake ground motions recorded at a stiff soil site. The R_μ factor is assumed to be a function of the characteristic parameters of each hysteretic model, target ductility ratio and structural period. The effects of each hysteretic model to the R_μ factor are also discussed. Copyright © 1999 John Wiley & Sons, Ltd.     

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.     

Inelastic spectra to predict period elongation of structures under earthquake loading

Period lengthening, exhibited by structures when subjected to strong ground motions, constitutes an implicit proxy of structural inelasticity and associated damage. However, the reliable prediction of the inelastic period is tedious and a multi‐parametric task, which is related to both epistemic and aleatory uncertainty. Along these lines, the objective of this paper is to investigate and quantify the elongated fundamental period of reinforced concrete structures using inelastic response spectra defined on the basis of the period shift ratio (T_in/T_el). Nonlinear oscillators of varying yield strength (expressed by the force reduction factor, R_y), post‐yield stiffness (a_y) and hysteretic laws are examined for a large number of strong motions. Constant‐strength, inelastic spectra in terms of T_in/T_el are calculated to assess the extent of period elongation for various levels of structural inelasticity. Moreover, the influence that structural characteristics (R_y, a_y and degrading level) and strong‐motion parameters (epicentral distance, frequency content and duration) exert on period lengthening are studied. Determined by regression analyses of the data obtained, simplified equations are proposed for period lengthening as a function of R_y and T_el. These equations may be used in the framework of the earthquake record selection and scaling. Copyright © 2015 John Wiley & Sons, Ltd.     

THE INDUCTIVE RESPONSE OF A HORIZONTAL CONDUCTING CYLINDER BURIED IN A UNIFORM EARTH FOR A UNIFORM INDUCING FIELD*

The inductive response of a conducting horizontal cylinder embedded in a uniform earth is studied using numerical results obtained for an analytical solution for the problem of a conducting cylinder buried in a homogeneous earth for the case of a uniform inducing field. A check of the validity of the numerical results is made by a comparison with analogue model measurements for a number of cases. Numerical results for a range of cylinder radii (a = 1–10 km), depths of burial (d= 0–4 km), conductivity contrasts (σ₂= 10^?2-10 Sm^?1), and source frequencies (f= 10^?1-10^?4 Hz) of interest in the interpretation of magnetotelluric field measurements are presented. The results indicate that for a uniform inducing field the conductivity and depth of burial of a horizontal cylindrical inhomogeneity are best determined through a measurement of the amplitudes H_y, H_z and E_x and the phases φ_y and Ψ_x.     

Visual characterization technique for gravel‐cobble river bed surface sediments; validation and environmental applications Contribution to the programme of CIRSA (Centre Interuniversitaire de Recherche sur le Saumon Atlantique)

This paper presents an evaluation of the feasibility and the reliability of a visual characterization technique for gravel–cobble river bed surface substrate. Based on principal axis regressions, using phi scale (ϕ), comparisons of visual estimation and grid sampling techniques show that useful predictive relations (R² = 0·78–0·88) exist between visual estimates of the surface d₁₆, d₅₀ and d₈₄ and estimates obtained for the same percentiles with the grid sampling technique. Comparisons of visual estimation and the surface‐bulk sampling technique also indicate a predictive relation (R² = 0·70) between the d₅₀ of the two methods. Trained operators can visually estimate gravel–cobble bed surface d₁₆ to uncertainties of 41 per cent, d₅₀ to 15 per cent and d₈₄ to 11 per cent (for example, there is a 5·5 mm error on a d₈₄ size of 50 mm). Furthermore, evidence shows that if operators are properly trained, a calibration relation for each percentile can be applied independently of operators. This visual characterization allows effective detailed mapping of spatial patterns in substrate size distribution along extensive reaches of gravel‐bed rivers. The technique can be very useful in creating terrain models for various geomorphological, hydrological and biological applications such as the determination of entrainment thresholds, hydraulic roughness and substrate suitability for benthic insects or salmonid habitat. Copyright © 2001 John Wiley & Sons, Ltd.