Mihailo D. Trifunac

A note on the useable dynamic range of accelerographs recording translation

Since the late 1970s, the dynamic range and resolution of strong motion digital recorders have leaped from 65 to 135 dB, opening new possibilities for advanced data processing and interpretation. One of these new possibilities is the calculation of permanent displacement of the ground or of structures, associated with faulting or with non-linear response. Proposals on how permanent displacements could be recovered from recorded strong motion have been published since 1976. The analysis in this paper concludes that permanent displacements of the ground and of structures in the near-field can be calculated provided all six components of strong motion (three translations and three rotations) have been recorded, and the records are corrected for transducer rotation, misalignment and cross-axis sensitivity.

Rocking strong earthquake accelerations

In this paper, the method presented by Lee and Trifunac (1985) for generating synthetic torsional accelerograms has been extended to the estimation of synthetic rocking accelerograms and of their response spectra. Results from our previous regression analyses for the characterization of strong shaking in terms of (1) earthquake magnitude and epicentral distance, or (2) Modified Mercalli Intensity at the site are utilized here again. The effects of geologic environment, in terms of site parameters or the representative depth of sediments, which influence amplification, and the dispersive properties of ground motion are also included. The synthetic rocking accelerogram is then constructed from the horizontal and vertical acceleration components.

A note on rotational components of earthquake motions on ground surface for incident body waves

Abstract This paper shows that the Fourier amplitude spectra of rocking and torsional components of strong shaking on ground surface can be derived exactly in terms of (1) wavelength of incident waves, (2) Fourier amplitude spectra of vertical (for incident P and SV waves) or horizontal (for incident SH waves) ground motion, and (3) the angle of incidence of plane body waves, θ 0 . Application of these results in earthquake engineering is discussed.

Nonlinear soil response as a natural passive isolation mechanism—the 1994 Northridge, California, earthquake

Abstract The spatial relationship between areas with severely damaged (red-tagged) buildings and areas with large strains in the soil (indicated by reported breaks in the water distribution system), observed during the 1994 Northridge earthquake, is analysed. It is shown that these areas can be separated almost everywhere. Minimal overlapping is observed only in the regions with very large amplitudes of shaking (peak ground velocity exceeding about 150 cm s −1 ). One explanation for this remarkable separation is that the buildings on ‘soft’ soils, which experienced nonlinear strain levels, were damaged to a lesser degree, possibly because the soil absorbed a significant portion of the incident seismic wave energy. As a result, the total number of severely damaged (red-tagged) buildings in San Fernando Valley, Los Angeles and Santa Monica may have been reduced by a factor of two or more. This interpretation is consistent with the recorded peak accelerations of strong motion in the same area. It is concluded that significant reduction in the potential damage to wood frame single family dwellings may be expected in areas where the soil experiences ‘large’ strains (beyond the linear range) during strong earthquake shaking, but not significant differential motions, settlement or lateral spreading, near the surface.

Empirical criteria for liquefaction in sands via standard penetration tests and seismic wave energy

Five empirical equations are presented, describing initiation of liquefaction in fully saturated sands, in terms of standard penetration values and initial overburden stress on level ground. These equations are based on 90 case histories of liquefaction, and relate empirically the pore pressure increase to earthquake magnitude, epicentral distance, energy of strong motion at the site, peak ground velocity, Fourier amplitude of velocity and duration of strong motion. The results are given in terms of raw standard penetration values corrected for overburden pressure. For all the models presented, the standard deviation of the residuals, representing the differences between the observed and predicted penetration values is less than six blow counts.

Frequency dependent attenuation of strong earthquake ground motion

New shape for the frequency dependent attenuation function of Fourier amplitude spectra of recorded strong earthquake ground acceleration has been developed. It has been found that for distances less than about 100 km there is clear frequency dependent variation of the attenuation functions, with high frequency amplitudes attenuating faster with distance.

RESPONSE SPECTRA FOR DIFFERENTIAL MOTION OF COLUMNS

The validity of the response spectrum concept for determining loads in structures excited by differential earthquake ground motion is examined. It is shown that the common definition of response spectrum for synchronous ground motion can be reconciled to remain valid in cases when the columns of extended structures experience different motions. Then, a relative displacement response spectrum for design of first-storey columns, SDC(T, δ, ζ, τ), is defined. In addition to natural period, T, and fraction of critical damping, ζ, this spectrum depends also on the ‘travel time’, τ (of the waves in the soil over distances about one half width, or length of the structure), and on a factor, δ, specifying the relative displacement of the first floor. It is shown how this spectrum can be determined using existing empirical scaling equations for relative displacement spectra SD(T, ζ) and for peak velocity and peak acceleration of strong ground motion. These new spectra are illustrated for a horizontal component of a record in the near field of the 1994 Northridge earthquake. The results show that differential motions are more important for short period (stiff) than for longer period (flexible) structures, and for structures founded on softer ground (small shear wave velocity).

Peak velocities and peak surface strains during Northridge, California, earthquake of 17 January 1994

We present contours of the largest horizontal and vertical recorded peak velocities of strong ground motion during the Northridge, California, earthquake. Above the fault, the horizontal peak velocities exceeded 100 cm/s. The vertical velocities were larger than 20 cm/s. We also present contours of peak horizontal and vertical strain factors. Through most of the San Fernando Valley and the Santa Susana Mountains, the horizontal surface strain factor was larger than 10−3. The largest horizontal strain factor computed was for the Rinaldi Receiving Station ∼10−2·2. The corresponding vertical strains were >10−3·25 and 10−13, respectively. Through most of the Los Angeles Basin the horizontal peak surface strain factors were between 10−3·75 and 10−3.

Northridge, California, earthquake of 1994: density of pipe breaks and surface strains

Abstract Empirical scaling equations are presented which relate the average number of water pipe breaks per km2, n , with the peak strain in the soil or intensity of shaking at the site. These equations are based on contour maps of peak surface strain evaluated from strong motion recordings, and observations of intensity of ground shaking and damage following the Northridge, California, earthquake of 17 January 1994. Histograms for the number of pipe breaks per km2, n, are presented for several ranges of values of the horizontal peak strain and for several values of the site intensity. The observed distribution of pipe breaks is also used to speculate on possible more detailed geographical distribution of near surface strains in the San Fernando Valley and in central Los Angeles. The results can be used to predict number of pipe breaks in the San Fernando Valley and in Los Angeles, for a scenario earthquake or in probabilistic seismic hazard calculations, considering all possible scenarios that contribute to the hazard and the likelihood of their occurrence during specified exposure. Such predictions will be useful for emergency response planning (as the functioning of the water supply is critical for sanitation and in fighting fires caused by earthquakes), to estimate strains during future and past earthquakes in areas where no strong motion was recorded and in defining design guidelines for pipelines and other structures and structural systems sensitive to strains in the ground.

Empirical models for scaling pseudo relative velocity spectra of strong earthquake accelerations in terms of magnitude, distance, site intensity and recording site conditions

Our previous empirical scaling model for Pseudo Relative Velocity (PSV) spectrum amplitudes has been refined here by introducing the frequency dependent attenuation of amplitudes with distance 9 . The new model also considers the depth of earthquake focus and the approximate characterization of the source size to compute the ‘representative’ source to station distances in addition to all other scaling parameters used previously 4 . The form of the probability distribution function of spectral amplitudes proposed by Trifunac and Anderson 4 to describe the distribution of the residuals about the chosen regression model has been confirmed by this analysis.