Relationship Between Peak Ground Acceleration,
Effective Peak Acceleration and Effective Peak Velocity

What is the relationship between peak ground acceleration PGA and "effective peak acceleration," Aa, or between peak ground velocity and "effective peak velocity," Av, as these parameters appear on building code maps?

Aa and Av have no clear physical definition, as such. Rather, they are building code constructs, adopted by the staff that produced the Applied Technology Council (1978) (ATC-3) seismic provisions. Maps for Aa and Av were derived by ATC project staff from a draft of the Algermissen and Perkins (1976) probabilistic peak acceleration map (and other maps) in order to provide for design ground motions for use in model building codes. Many aspects of that ATC-3 report have been adopted by the current (in use in 1997) national model building codes, except for the new NEHRP provisions.

This process is explained in the ATC-3 document referenced below, (p 297-302). Here are some excerpts from that document:

p. 297. "At the present time, the best workable tool for describing the design ground shaking is a smoothed elastic response spectrum for single degree-of-freedom systems . . .

p. 298. "In developing the design provisions, two parameters were used to characterize the intensity of design ground shaking. These parameters are called the Effective Peak Acceleration (EPA), Aa, and the Effective Peak Velocity (EPV), Av. These parameters do not at present have precise definitions in physical terms but their significance may be understood from the following paragraphs.

"To best understand the meaning of EPA and EPV, they should be considered as normalizing factors for construction of smoothed elastic response spectra for ground motions of normal duration. The EPA is proportional to spectral ordinates for periods in the range of 0.1 to 0.5 seconds, while the EPV is proportional to spectral ordinates at a period of about 1 second . . . The constant of proportionality (for a 5 percent damping spectrum) is set at a standard value of 2.5 in both cases.

". . . The EPA and EPV thus obtained are related to peak ground acceleration and peak ground velocity but are not necessarily the same as or even proportional to peak acceleration and velocity. When very high frequencies are present in the ground motion, the EPA may be significantly less than the peak acceleration. This is consistent with the observation that chopping off the spectrum computed from that motion, except at periods much shorter than those of interest in ordinary building practice has very little effect upon the response spectrum computed from that motion, except at periods much shorter than those of interest in ordinary building practice. . . On the other hand, the EPV will generally be greater than the peak velocity at large distances from a major earthquake . . .

p. 299. "Thus the EPA and EPV for a motion may be either greater or smaller than the peak acceleration and velocity, although generally the EPA will be smaller than peak acceleration while the EPV will be larger than the peak velocity.

". . . For purposes of computing the lateral force coefficient in Sec. 4.2, EPA and EPV are replaced by dimensionless coefficients Aa and Av respectively. Aa is numerically equal to EPA when EPA is expressed as a decimal fraction of the acceleration of gravity . . ."

Now, examination of the tripartite diagram of the response spectrum for the 1940 El Centro earthquake (p. 274, Newmark and Rosenblueth, Fundamentals of Earthquake Engineering) verifies that taking response acceleration at .05 percent damping, at periods between 0.1 and 0.5 sec, and dividing by a number between 2 and 3 would approximate peak acceleration for that earthquake. Thus, in this case, effective peak acceleration in this period range is nearly numerically equal to actual peak acceleration.

However, since the response acceleration spectrum is asymptotic to peak acceleration for very short periods, some people have assumed that effective peak acceleration is 2.5 times less than true peak acceleration. This would only be true if one continued to divide response accelerations by 2.5 for periods much shorter than 0.1 sec. But EPA is only defined for periods longer than 0.1 sec.

Effective peak acceleration could be some factor lower than peak acceleration for those earthquakes for which the peak accelerations occur as short-period spikes. This is precisely what effective peak acceleration is designed to do.

On the other hand, the ATC-3 report map limits EPA to 0.4 g even where probabilistic peak accelerations may go to 1.0 g, or larger. THUS EPA IN THE ATC-3 REPORT MAP may be a factor of 2.5 less than than probabilistic peak acceleration for locations where the probabilistic peak acceleration is around 1.0 g.

The following paragraphs describe how the Aa, and Av maps in the ATC code were constructed.

The USGS 1976 probabilistic ground motion map was considered. Thirteen seismologists were invited to smooth the probabilistic peak acceleration map, taking into account other regional maps and their own regional knowledge. A final map was drawn based upon those smoothing's. Ground motions were truncated at 40 % g in areas where probabilistic values could run from 40 to greater than 80 % g. This resulted in an Aa map, representing a design basis for buildings having short natural periods. Aa was called "Effective Peak Acceleration."

An attenuation function for peak velocity was "draped" over the Aa map in order to produce a spatial broadening of the lower values of Aa. The broadened areas were denominated Av for "Effective Peak Velocity-Related Acceleration" for design for longer-period buildings, and a separate map drawn for this parameter.

Note that, in practice, the Aa and Av maps were obtained from a PGA map and NOT by applying the 2.5 factors to response spectra.

Note also, that if one examines the ratio of the SA(0.2) value to the PGA value at individual locations in the new USGS national probabilistic hazard maps, the value of the ratio is generally less than 2.5.

References

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