General
In order to test the capabilities of the newly developed system, an application to a well documented case study is presented. In particular the area of Fabriano, in Central Italy, was selected. Fabriano was hit by a strong motion earthquake in September-November 1997, and subsequently a microzonation study was prepared for the Fabriano area by the GNDT (i.e., Italian National Group for Earthquake Protection [13]). The geology of Fabriano is characterized by the presence of marls and marly limestones of marine origins overlain by alluvial deposits, debris derived from landslides and water runoff related processes, and anthropic landfills.
In our study two different analyses were performed on this area. The first analysis was carried out for a relatively small area (about 1.5x1.5km) where both geotechnical and geophysical data are available (Fig. 3). The second analysis was carried out for a larger area (about 35x50km) where the only available information is provided by the national geological map (scale 1:100,000). Each of the two analyses is composed of two steps. The first step includes the computation of the hazard in rock using the seismic hazard module, whereas the second step includes the computation of the hazard at the ground surface. As mentioned earlier, the latter is achieved by convolving the bedrock hazard with the amplification functions derived via the site amplification module. The computations are carried out over a grid of pre-defined locations.



Seismic Hazard at the bedrock
The seismic hazard at the bedrock for the Fabriano area was computed using the seismic hazard module. In order to make possible a comparison with the reference study cited above [13] we used the same zonation system ZS4 proposed by the GNDT that is currently adopted for seismic mapping at national scale [14]. The attenuation law for rock developed specifically for Italy by Sabetta and Pugliese [15] was adopted. The same attenuation law was used also in the reference microzonation study [13], and therefore it is suitable for a direct comparison. We also carried out an independent complete analysis of the available seismic catalogs. Note that the software allows multiple choices of microzonations and attenuation relationships, if needed.
The seismic zonation and the seismic catalog information used as input for the analyses are summarized in Fig. 4.


Site Amplification
Many site amplification analyses were run throughout the Fabriano area at the nodes of a pre-defined grid. The amplification functions at each grid location were estimated using the response surface developed according



to the methodology described in the previous section. Given that the seismic hazard at the bedrock does not vary substantially in small areas, for the central part of Fabriano we carried out the computations only for the centroid. In this area, however, a grid composed of 169 (12 x 13) nodes was adopted for the site amplification analysis, with a distance of 125m between adjacent nodes (see the computation grid in Fig. 3). The soil deposit at each node of the grid is characterized, in general, by a different fundamental period (see values shown in Fig. 3), which is estimated based on microtremors [13]. The fundamental period at each location was used as input to the polynomial response surface to compute the amplification functions for each level of bedrock ground motion.

Similarly, in the large area, a grid composed of 25 (5 x 5) nodes was adopted for the hazard in rock, with a distance between nodes of 11km. As before, a finer grid composed of 100 (i.e., 10 x 10) nodes was adopted for site amplification analysis, with a distance between contiguous nodes of 5.5km (see Fig. 6). In contrast with the central Fabriano area, the fundamental periods established for each geological unit here were estimated based only on the description provided by the geological maps. No microtremors-based results were available. To check the accuracy of the adopted response surface, for comparison purposes two detailed finite element analyses were performed at two specific locations, 2MS and 12MS, within the small area. These are two locations (see Fig. 3) where the results of both geotechnical and geophysical investigations were available [16 and 17]. The two soil columns, which are close to two nodes of the aforementioned computation grid, were analyzed using the program SUMDES [7]. As we did for the development of the response surface, the soil amplification analyses at 2MS and 12MS were performed by applying to the soil column 78 different real acceleration time histories recorded on rock outcrops. For simplicity, rock outcrop ground motions were applied at



the base of the soil column, without any deconvolution. These analyses allowed to compute, at the two selected locations, the elastic fundamental period of oscillation of the soil deposit and the amplification functions AF(f) to be used, in conjunction with the hazard curves computed in rock, as input data for the convolution process.

The computed fundamental period was 0,18s at location 12MS and 0,27s at location 2MS, which are consistent with the periods shown in Fig. 3, estimated based on microtremors.

In the finite element analyses the amplification functions AF(f) were computed, for each soil column and for each oscillation frequency, by a non-linear regression of the 78 result sets. These directly computed AF(f) are considered here as the benchmark for the results from the response surface technique. Note, again, that AF(f) depends on both the oscillation frequency and the spectral acceleration at the rock outcrop. In particular the following regression function was adopted:




where:

z: Amplification function AF(f);

x: Spectral acceleration at the rock outcrop.

The regression constants (b1 to b3) and the standard errors (obtained at the two selected locations (2MS and 12MS) are shown in Table II.


Seismic Hazard Maps

Once that the analyses are performed, the system can display interactively the following results both at the bedrock and at the ground surface:

   1.  Maps of PGA/spectral accelerations for a given return period, or, alternatively, of return periods for a fixed level PGA/spectral acceleration.
   2.   Uniform hazard response spectra for each single location of the map and for a given return period.

Images provided by the software are shown, as examples, in Figs. 5 and 6. All data are shown for a return





period of 475 years (i.e., 10% probability of exceedance in 50 years). Fig. 5 shows the PGA for the small zone at the ground surface. The values are presented as contour lines, and are referred to a geographical coordinate system. Fig.6 shows the PGA for the large zone at the ground surface. The different ranges of PGA values are shown with different colors. Fig. 7, still referred to the small zone, shows a seismic disaggregation plot in Distance and Magnitude for a given oscillator frequency.

Examples of uniform response spectra both at the bedrock and at the ground surface are discussed in the following section.


In Fig. 8, the response spectrum at the bedrock for a mean return period of 475 years computed by means of the developed software and the one provided in the reference microzonation study [18] are shown for comparison purposes. The two spectra were obtained applying the same attenuation law for rock [15] . The same seismic zonation was adopted in both studies in order to make possible a direct comparison of the results. It is observed that although different computer programs and computation procedures were adopted, and although completely independent analyses of the seismic catalogs were carried out, the two spectra are very close to each







other, and can be considered identical for practical purposes.

As an aside, an additional analysis was carried out where the epistemic uncertainty in the input parameters of the seismicity model (e.g., parameters of the Gutenberg-Richter relation for earthquake occurrence) was considered via a logic tree procedure. Accounting for epistemic uncertainty provides information on the level of confidence on the seismic hazard estimates. As an example, the response spectra obtained at the bedrock for two different confidence levels (i.e., 50% and 84%) are shown in Fig. 9. Note that, although not done for this illustratory example, the software can handle epistemic uncertainty in attenuation laws and/or seismic zonations. Fig. 9 also shows the response  spectrum obtained at the same location without considering epistemic uncertainties for comparison purposes. It is observed that the median spectral acceleration values fall relatively close to (but do not coincide with) the values obtained in the simplified analysis.

 




Hazard at the Ground Surface
The benchmark response spectra obtained at the ground surface at Locations 2MS e 12MS using the finite element code SUMDES are compared with those obtained at the same locations by means of the response surfaces implemented in the computer program. In Figs. 10a and 10b both sets of surface spectra are obtained by neglecting the dispersion (i.e., by setting the standard error to zero) in the AF(f) during the convolution. Of course, the dispersion in the estimate obtained by response surface is considerably larger than that provided by the finite element analyses on the soil columns. The spectra are similar for a large range of frequencies. This in turn means that the median AF(f) values estimated by the two methods are virtually the same (namely, the estimate from the response surface is unbiased in this case). When, however, the dispersion is correctly accounted for in the convolution then the spectra estimated using both methods depart from each other. In particular, for frequencies below 5Hz the spectra estimated using the response surface approach are considerably larger (by up to 80% for some frequencies) than the benchmark ones (Figs. 11a and 11b). The larger uncertainty in the response-surface AF(f) estimate (see Fig. 12) translates into a higher surface hazard. It derives from considering a large number of possible different







stratigraphies having in common only the fundamental period of the soil deposit. On the other hand, the estimate of AF(f) via direct amplification analysis is performed on a specific soil column.

Similarly to what done for the hazard in rock, an additional analysis that accounts for the epistemic uncertainty in the input seismic parameters was also carried out for the estimation of the surface hazard. The surface response spectra obtained at location MS12 for two different confidence levels (i.e., 50% and 84%) are shown in Fig. 13. Also shown in the same figure, for comparison purposes, is the spectrum obtained without keeping into account the epistemic uncertainty on the parameters mentioned above. Even in this case it is observed that the median spectral acceleration values fall relatively close to (but do not coincide with) the values obtained in the simplified analysis.





Conclusions
An automated seismic hazard software was developed to define probabilistic seismic hazard maps that account for site amplification effects. This software relies on advanced probabilistic procedures and analytical tools for soil amplification analyses. Despite this level of sophistication, it is suitable for mapping large areas where little information on local soil characteristics is available.

Most emphasis is placed on the site amplification module which relies upon a pre-computed response surface for obtaining amplification functions of soil deposits without running nonlinear dynamic analyses of the soil column. The response surface presented in this paper, which was derived from a large number of non-linear finite element analyses, uses only the elastic fundamental frequency of the soil column as a predictor for the amplification function. This approach is quite simple, in that it does not distinguish among soils with similar stiffness at very small strain levels but with different stress-strain behavior in the non-linear range, and/or with different susceptibility to cyclic mobility effects. However it is appropriate in the majority of the cases where little geotechnical information is available and identification of the predominant soil type is not possible. In such cases, very common when mapping large areas, the relatively large scatter affecting the regression process simply reflects the limited knowledge of the local soil stratigraphy. The generation, currently in progress, of more specific response surfaces for different soil deposits with same fundamental frequency of vibration, will be beneficial for cases where a better knowledge of the soil column characteristics is available. However, the case study presented in this paper shows that the response surface approach used in in this study can provide sufficiently accurate results, at least in the cases considered so far.


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