Response spectra for differential motion of columns, paper II: Out-of-plane response

It is shown that the common response spectrum method for synchronous ground motion can be extended to make it applicable for earthquake response analyses of extended structures experiencing differential out-of-plane ground motion. A relative displacementspectrum for design of first-story columns SDC (T, TT, z, zT, t, d) is defined. In addition to the natural period of the out-of-plane response, T, and the corresponding fraction of critical damping, z, this spectrum also depends on the fundamental period of torsional vibrations, TT, and the corresponding fraction of critical damping, zT, on the ‘‘travel time,’’ t (of the waves in the soil over a distance of about one-half the length of the structure), and on a dimensionless factor d, describing the relative response of the first floor. The new spectrum, SDC, can be estimated by using the empirical scaling equations for relative displacement spectra, SD, and for peak ground velocity, vmax. For recorded strong-motion acceleration, and for symmetric buildings, the new spectrum can be computed from Duhamel’s integrals of two uncoupled equations for dynamics equilibrium describing translation and rotation of a two-degree-offreedom system. This representation is accurate when the energy of the strong-motion is carried by waves in the ground the wavelengths of which are one order of magnitude or more longer than the characteristic length of the structure

Energy dissipation by nonlinear soil strains during soil-structure interaction excited by SH pulse

Three variants of a two-dimensional (2-D) model of a building supported by a rectangular, flexible foundation embedded in nonlinear soil are analyzed. The building, the foundation, and soil have different physical properties. The building is assumed to be linear, but the foundation and the soil can experience nonlinear deformations. It is shown that the work spent for the development of nonlinear strains in the soil can consume a significant part of the input wave energy, and thus less energy is available for excitation of the building. The results help explain why the damage, during the 1994 Northridge earthquake in California, to residential buildings in the areas that experienced large strains in the soil was absent or reduced

Zero baseline correction of strong-motion accelerograms

A new method is proposed for standard baseline correction of strong-motion accelerograms. It is based on high-pass filtering of the uncorrected digitized accelerogram data. Unlike the parabolic baseline correction, the new method has well-defined frequency transfer function properties which are largely independent of the record length

Preliminary analysis of the peaks of strong earthquake ground motion—dependence of peaks on earthquake magnitude, epicentral distance, and recording site conditions

Analyses of peak amplitudes of strong earthquake ground motion have been carried out with the emphasis on their dependence on earthquake magnitude, epicentral distance, and geological conditions at the recording site. Approximate empirical scaling functions have been developed which, for a selected confidence level, yield an estimate of an upper bound of peak accelerations, velocities, and displacements. The parameters in these scaling functions have been computed by least-squares fitting of the recorded data on peak amplitudes which are now available for a range of epicentral distances between about 20 and 200 km and are representative for the period from 1933 to 1971 in the Western United States. The possibility of extrapolating the derived scaling laws to small epicentral distances where no strong-motion data are currently available has been tested by comparing predicted peak amplitudes with related parameters at the earthquake source. These source parameters (average dislocation and stress drop) can be derived from other independent studies and do not contradict the inferences presented in this paper. It has been found that for an approximate 90 per cent confidence level the presently available data suggest that peak accelerations, velocities, and displacements at the fault and for the frequency band between 0.07 and 25 Hz probably do not exceed about 3 to 5 g, 400 to 700 cm/sec, and 200 to 400 cm, respectively. The logarithms of the peaks of strong ground motion seem to depend in a linear manner on earthquake magnitude only for small shocks. For large magnitudes this dependence disappears gradually and maximum amplitudes may be achieved for M ≈ 7.5. The influence of geological conditions at the recording site appears to be insignificant for peak accelerations but becomes progressively more important for peaks of strong-motion velocity and displacement

A three-dimensional dislocation model for the San Fernando, California, earthquake of February 9, 1971

The data from five strong-motion accelerograph stations centered above and surrounding the fault are used to develop an approximate three-dimensional dislocation model for the San Fernando earthquake. In the resulting model, the dislocation originates near the instrumentally determined epicenter at a depth of 9.2 km and then propagates southward and upward with a velocity of 2 km/sec. Calculated dislocation amplitudes of about 10 m in the hypocentral region have been found to decay to about 1 m toward the center of the fault and then build up again to about 6 m just before the fault intersects the ground surface in the San Fernando Valley. The assumed fault area of 130 km^2 and the assumed rigidity µ = 3 × 10^(11) dyne/cm^2 give a moment M_0 = 1.53 × 10^(26) dyne-cm. This study indicates that, with several strong-motion accelerographs suitably located in the epicentral region, it is possible to find a kinematic faulting process associated with the periods of ground motion which are longer than about 1 sec

Preliminary empirical model for scaling Fourier Amplitude Spectra of strong ground acceleration in terms of earthquake magnitude, source-to-station distance, and recording site conditions

An empirical model for scaling Fourier Amplitude Spectra of strong earthquake ground acceleration in terms of magnitude, M, epicentral distance, R, and recording site conditions has been presented. The analysis based on this model implies that: 1.(a) the Fourier amplitude spectra of strong-motion accelerations are characterized by greater energy content and relatively larger amplitudes for long-period waves corresponding to larger magnitudes M, 2.(b) the shape of Fourier amplitude spectra does not vary appreciably for the distance range between about 10 and 100 km, and 3.(c) long-period spectral amplitudes (T > 1 sec) recorded on alluvium are on the average 2.5 times greater than amplitudes recorded on basement rocks, whereas short-period (T < 0.2 sec) spectral amplitudes tend to be larger on basement rocks. It has been shown that the uncertainties which are associated with the forecasting of Fourier amplitude spectra in terms of magnitude, epicentral distance, site conditions, and component direction are considerable and lead to the range of spectral amplitudes which for an 80 per cent confidence interval exceed one order of magnitude. A model has been presented which empirically approximates the distribution of Fourier spectrum amplitudes and enables one to estimate the spectral shapes which are not exceeded by the presently available data more than 100 (1 - p) per cent of time where p represents the desired confidence level (0 < p <1)

Napetosti i središnji interval frekvencija pri akceleraciji tla za jakih potresa

The peak of smooth Fourier amplitude spectra, ((FS(T))max, of strong motion acceleration recorded in California is modelled via dimensional analysis. In this model, the spectrum amplitudes are proportional to (1) sigma - the root-mean-square (r.m.s.) amplitude of the peak stresses on the fault surface in the areas of high stress concentration (asperities), and (2) (log10N)1/2, where N is the number of contributing (sampled) asperities. The results imply simple, one asperity, earthquake events for M ≤ 5, and multiple asperity events for M ≥ 5 (N ~ 10 near M = 7and N ~ 100 near M ~ 8). The r.m.s. value of the peak stress drop on the fault, sigma, appears to increase with magnitude for M ≤ 6, and then it levels off near 100 bars, for M ≥ 6. For M > 6, ((FS(T))max continues to grow with magnitude, because of the larger number of asperities from which the sample is taken (N ~ 100 for M = 8), not because of increasing sigma.Ekstremi izgla|enih Fourierovih spektara, (FS(T))max, akcelerograma jakih potresa u Kaliforniji modelirani su dimenzionalnom analizom. U tom modelu spektri amplitude proporcionalni su sa: (1) sigma– r.m.s. iznosu amplitude vršnih napetosti u područjima visoke napetosti na rasjednoj plohi i (2) (log10N)1/2 – gdje je N broj takvih područja. Jednostavni modeli rasjeda s jednim područjem visoke koncentracije napetosti prikladni su za opis potresa s magnitudom M ≥ 5, dok za veće magnitude u obzir treba uzeti više takvih područja (N ~ 10 oko M = 7 i N ~ 100 za M ~ 8). r.m.s. iznos parametra sigma čini se da raste s magnitudom za M ≥ 6, dok je za veće magnitude približno konstantan i iznosi oko 100 bara. Za M > 6, (FS(T))max raste s magnitudom zbog velikog broja područja visoke napetosti koja doprinose spektru (N ~ 100 za M = 8), a ne zbog povećanja sigma

Scaling Earthquake Motions in Geotechnical Design

The traditional approach to scaling earthquake ground motion for geotechnical design applications is based on peak ground acceleration. This approach is useful when the physics of the problem depends linearly only on the nature of the high frequency (short wavelength) inertial part of strong motion. For nonlinear response analyses, the representative strain (~ velocity) and the number of stress reversals (~ duration of shaking) must also be considered. For long (large) structures (bridges and dams), the relative displacement of multiple foundations and the quasi-static deformation of the complete structure may contribute to the largest design levels. Thus, the modern design criteria must consider all the relevant scaling parameters and not just the high frequency inertial part of strong earthquake shaking. In this paper, the above points are illustrated via several examples