RESISTED EXERCISES

The Arias intensity (Eq.8) defined without the π/(2g) factor, was also considered as a damage threshold indicator in [39] and it was considered as an alternative to CAV.

𝐼 = ∫ 𝑎 (t) ² dt (8)

A plot of the integral in Eq. 8 as a function of time (upper limit of the integral varying from 0 to Td), normalized by the Arias intensity, is referred to as a Husid plot. Such plots allow the strong motion portion (effective strong motion duration) of the earthquake time-history to be identified.

The equations defining both the CAV and the Arias intensity identify their DIP category as an integral parameter and, in general, the CAV and Arias intensity cumulative integral are simply alternative representations of the same information about the strength and duration of an earthquake time-history. The un-normalized Husid plot can be used to determine the effective duration of the strong motion portion of the earthquake time-history.

In the working group, the relation between the damage mode of SSCs due to earthquake motion and the CAV value was also discussed. Damage experiences, especially with earthquakes with a long strong motion duration, suggest that an integral parameter like CAV can be an important DIP. Regarding the physical meaning of CAV, focused on damage of structures subjected to seismic motions, Ref. [45] concludes as follows:

 CAV is proportional to the product of the strong motion duration and the average energy of the strong motion acceleration.

 CAV needs to be an adequate damage indicator since it is correlated with the main parameters controlling damage phenomena, that is, with the number of load cycles and its median frequency, and with the amplitude of the alternating load, which is proportional to the ground motion acceleration amplitude.

This conclusion suggests that CAV is a parameter that is deeply linked to cumulative fatigue damage.

CAV is normally calculated for each of the three directions of recorded earthquake motion with the reported value being the maximum of the three. On the other hand, the JMA instrumental seismic intensity takes all three directions into consideration. Thus, for the purpose of comparison of these parameters, this publication evaluates the resultant CAV value with the SRSS combination method for the three directional calculated CAV values.

damaging motion to SSCs. Since both the spectral criteria and the CAV value are based on the observed damage threshold of commercial and industrial SSCs, the use of such criteria for nuclear power plant SSCs is judged to be sufficiently conservative.

The criteria of US NRC Regulatory Guide 1.166 [46] are intended to prevent the premature shutdown of a plant due to nearby, small magnitude, seismic events. Based on the review of the lack of damage to fossil plants and industrial facilities when subjected to significant earthquakes, a reference spectrum (see Fig. 19) was developed [47], which represents the seismic input level (in terms of a 5 % damped response spectrum) that equipment has sustained without loss of post-earthquake function. This reference spectrum is common to eight (later revised to 20) equipment classes. It represents the input level to which at least 30 equipment items of a given class were subjected to in several earthquakes at several facilities in different earthquakes without loss of post-earthquake function. The equipment considered in the study is similar to equipment in nuclear power plants.

Associated with each equipment class is a set of caveats, or restrictions [47] associated with the construction and installation of the components which need to be verified. The maximum spectral acceleration between 2.5 and 7.5 Hz in the reference spectrum is 1.2 g (Fig. 24). This level is not a damage threshold, but a lower bound of it, since a significant number of items did not fail at this level. A statistical evaluation can demonstrate that the reference spectrum is a high-confidence-of-a-low probability-of-failure capacity level for the given equipment class.

In the frequency range above 10 Hz, the EPRI NP-5930 report [39] concluded that earthquake damage to civil-mechanical SCCs was not likely, due to the low response levels and resultant material strains. However, for electrical components and devices, malfunction due to shaking at frequencies greater than 10 Hz requires consideration. In recent years, for hard rock sites in intra-plate regions such as Scandinavia, central and eastern North America, much of the Indian subcontinent, and eastern South America, earthquake motions are expected to have spectral content in the 10-20 Hz or 20-30 Hz range. For these sites, the concern associated with electrical component or device malfunction in the greater than 10 Hz range is valid.

The seismic qualification of electrical and instrumentation and controls equipment has been typically carried out by shake table testing. In many instances, fragility testing, up to malfunction or failure, has been conducted in order to determine the margin above required qualification testing levels. Generic equipment ruggedness spectra (GERS) have been prepared [48] for several equipment classes, which document the results of these tests and the attained level of shaking up to failure (Fig. 25).

The averaging method of the response spectra used in this publication follows that of EPRI NP-5930, after a sensitivity study carried out by the working group. EPRI NP-5930 defines the method as follows [39]:

“The averaging is performed using spectral values at frequencies evenly spaced in the logarithmic domain. This leads to a lower density of points as the frequency increases;

therefore, the computed averaged spectral acceleration has a higher contribution from the low frequency range spectral values, which are more damaging.”

FIG. 24. Seismic Motion Reference Spectrum for lack of damage in power utility and industrial equipment given certain caveats are met for the particular class of equipment [47].

FIG. 25. Example of generic equipment ruggedness spectra (GERS) for low voltage switchgear based on shake table test data [48]. (Courtesy of EPRI)

4.2. SEISMIC INTENSITY SCALES AND DAMAGE INDICATING PARAMETERS