l. decanini^' f. mollaioli,^ g. f. panza,^ f. romanelli€¦ · synthetic signals, to be used...

The realistic definition of seismic input:

an application to the Catania area

L. Decanini ' F. Mollaioli, G. F. Panza, F. Romanelli

^ Dip di Ing. Strutturale e Geotecnica, Universita' di Roma "La

Sapienza", Rome, Italy

Email: decanini@hp 720. dsg. uniromal. it

Email: moll@scilla. ing. uniromal. it

^ SAND Group, ICTP, Miramar, Trieste, Italy

Email: panza@geosunO. univ. trieste. it

^ Dipartimento di Scienze delta Terra, Via Weiss 4, 34127 Trieste, Italy

Email: romanel@geosunO. univ. tries te. it

Abstract

The realistic definition of seismic input can be performed by means of advancedmodelling codes based on the modal summation technique. These codes andtheir extension to laterally heterogeneous structures allow us to accuratelycalculate synthetic signals, including body waves and of surface waves,corresponding to different source and anelastic structural models, taking intoaccount the effect of local geological conditions. For the estimation of thedestructive potential of the calculated signals, parameters obtained from their(a) direct analysis, (b) integration in the time or in the frequency domain, and(c) the structural (elastic and anelastic) response are investigated. As anexample of application of our analysis we consider the Catania (Sicily) areawhere a pilot project of GNDT (Gruppo Nazionale per la Difesa dai Terremoti)is in progress for the reduction of the seismic hazard at a sub-regional andurban scale. In such an urban area more than 500,000 people are living and theapplication of advanced seismological methods for the definition of earthquakes

Transactions on the Built Environment vol 38 © 1999 WIT Press, www.witpress.com, ISSN 1743-3509

426 Earthquake Resistant Engineering Structures

1 Introduction

The typical seismic hazard problem mainly consists in the study of the effectsassociated to earthquakes, both on regional and on local scale, for a successiveengineering analysis. The result of such an analysis, that has to be used for theseismic risk definition, can be expressed in various ways, e.g. with a descriptionof the groundshaking intensity due to an earthquake of a given magnitude("groundshaking scenario"), or with probabilistic maps of relevant parameters.

Historically, the most used parameter in the engineering analysis for thecharacterization of the seismic hazard is the PGA (Peak Ground Acceleration), asingle-value indicator relatively easy to determine but that leads often to wrongseismic risk estimates. Actually, the peak values alone can not describeadequately all the effects associated to the ground shaking, since the frequencycontent and the duration of a seismic wavetrain play a fundamental role. A morecomplete analysis includes the calculation of the response spectra: the responseof a given structure to the seismic ground motion can be studied analysing thebehaviour of a simple damped oscillator. While the Fourier spectra shows thefine tuning of the energy contained in a wavetrain, the response spectra gives themaximum response of a oscillator to the whole seismic motion.

Although it has been recognized that the characteristics of ground motionsuch as its intensity, frequency content and duration are relevant to estimate itsdamage potential, some of these characteristics are usually ignored for the sakeof simplicity.

On the other hand, the estimation of the damage potential of ground motion,by neglecting the mechanical characteristics of the earthquake-resistingstructures will usually lead to unreliable and inconsistent results. This is due tothe fact that the damage potential is not an absolute property of the groundmotion, but it also depends on its interaction with the earthquake-resistingstructure.

Thus, a rational methodology for the assessment of the earthquakedestructiveness potential, particularly in case of inelastic behavior, should takeinto account simultaneously the relevant characteristics of the ground motion andof the earthquake-resisting structure.

Linear Elastic Response Spectra (LERS) do not represent a completedescription of the ground motion damage potential in the case of inelasticbehavior, in which most of the energy transmitted to the structure is dissipatedthrough plastic deformations. The lessons learned from recent earthquakes andassociate research indicate that the elastic spectra ordinates are not directlyrelated to the structural damage. Extremely important factors such as the durationof the strong ground shaking and the sequence and duration of accelerationpulses are not taken into account adequately. The Inelastic Response Spectra(IRS), obtained directly from strong motion records, are necessary for the designat safety level, but they are not sufficient because they do not give a precisedescription of the quantity of the energy that will be dissipated through hystereticbehavior; they give only the value of the maximum ductility requirement. Inseveral cases the observed behavior is not consistent with the usual seismicstrength coefficients, but it can be explained by making use of energy concepts.


Earthquake Resistant Engineering Structures 427

A large number of parameters have been proposed in literature to measure thecapacity of an earthquake to damage built structures, but no one seems to becompletely satisfactory. The adoption of inadequate parameters can lead to thedefinition ofnon realistic design earthquake and, consequently, to the unreliableevaluation of the seismic risk.

In this context, the damage potential of earthquake ground motion perhapsmay be adequately characterized by means of energy parameters. In fact, energy-based methods could provide more insight into the seismic performance andcould be considered as effective tools for a comprehensive interpretation of thebehavior observed during destructive events.

The main problem associated with the study of seismic hazard is to determinethe seismic ground motion at a given site, due to an earthquake, with a givenintensity and epicentral distance from the site. A solution for the study of seismichazard and associate seismic ground motion, at a given site and for a range of agiven distance from the fault, could be to use a complete set of recorded strongmotions and to group those accelerograms that have the same source, path andsite effects. In practice however, such a database is not available, being thenumber of available recorded signals still relatively low. An alternative way isbased on computer codes, developed from a detailed knowledge of the seismicsource process and of the propagation of seismic waves, that can simulate theground motion associated with the given earthquake scenario. In such a way,synthetic signals, to be used as seismic input in a subsequent engineeringanalysis, can be produced at a very low cost/benefit ratio. Anyway, the damagepotential of such signals need to be evaluated on the basis of the parameterscharacterizing the earthquake destructiveness power derived from the availablestrong motion records.

The realistic definition of seismic input can be performed by means ofadvanced modelling codes based on the modal summation technique (e.g.Florsch et al/). These codes and their extension to laterally heterogeneousstructures (e.g. Romanelli et al?) allow us to accurately calculate syntheticsignals, complete of body waves and of surface waves, corresponding todifferent models of the source and of the medium, taking into account the effectof local site conditions.

As an example of application of our analysis we consider the Catania (Sicily)area where a pilot project of GNDT (Gruppo Nazionale per la Difesa daiTerremoti) is in progress for the reduction of the seismic hazard at a sub-regionaland urban scale. In such an urban area more than 500,000 people are living andthe application of advanced seismological methods for the definition ofgroundshaking scenarios can play a crucial role in the analysis of the seismic riskand in the reduction of possible losses.

2 Examples of ground motion synthesis in the Catania area

For the definition of the seismic source model to be used in the computations wechoose to consider an earthquake similar to the destructive event that occurred onJanuary 11, 1693. The focal mechanism parameters of the seismic source,located approximately in the center (latitude: 37.44°; longitude: 15.23°) of the



Northern Segment of the Hyblean fault, are: strike equal to 352°, dip equal to80°, rake equal to 270°, focal depth equal to 10 km and seismic moment equal to3.2-10 Nm.

The calculation of synthetic signals for a potential large earthquake is a taskthat has to face with the difficult problem of the generation and propagation ofhigh frequency seismic waves, that are characterized by a big sensitivity to thesmall scale details of the rupture process and to the heterogenities present in thepropagation medium. Therefore, such a problem should be solved taking intoaccount the dynamics underlying the source physical process. However, in thiswork we want to focus mainly on the effects of the lateral heterogenities presentin the medium of propagation since one of the final goals is to estimate the siteeffects. To minimize the number of free parameters we decide to account forsource finiteness by properly weighting the source spectrum in the frequencydomain using the scaling laws of Gusev , as reported in Aki\ The propagation ofthe seismic waves in the Catania area is modelled using the geotechnicalinformations collected within GNDT (GNDT*), that supplies a simplifiedgeotechnical zonation map.

In Figure 1 the simplified geotechnical zonation map for the Catania area,together with the 13 simplified cross sections that were considered in theanalysis of Romanelli et al. , are shown. Romanelli et al.* decided to employ thesimplified map, in order to take into account the gross features of thegeotechnical zonation and to produce a sort of map of the ground motion. The 2-D models associated with each cross section are built up putting in weldedcontact (from 2 to 4) different 1-D models: the regional model is chosen asbedrock model and the geotechnical information related with the selectedboreholes are used for the local 1-D models. The map shown in Figure 1 is usedto define the borders between the local models, i.e. the distances between thevertical interfaces separating the different 1-D models. We decide here to studyin more detail, for the successive engineering analysis, the initial part of sectionS4 of Romanelli et al/, that the combination of the radiation pattern and of thepath effect makes one of the sections with the highest peak ground motionparameters. The model of section S4 that we consider in this work correspondsto the part between the coastline and the soft soils; the model is formed by three1-D models in welded contact, separated by vertical interfaces; the three laterallyhomogeneous models correspond to the bedrock model (MO) and to the two localmodels constructed using the data coming from the selected boreholes (seeFigure 2).

Using the model of Figure 2 we calculate the synthetic signals, for thetransverse component of motion (SH problem), at a series of equally spacedsites. The distance between each site is 200 m and the total number of computedsignals is 20: 15 are calculated on the local model Ml (lavas) and 5 on M2(sands and clays). The synthetic signals are calculated with the modal summationtechnique for laterally heterogeneous models (Romanelli et al/), with a cut-offfrequency of 10 Hz. The angle between the fault strike and the direction of thesection (strike-section angle) is measured counterclockwise from the strikedirection; the strike-receiver anlgle for all of the sites is 50 degrees.



Legend10mm)

Figure 1: Simplified geotechnical zonation map of the Catania area and thelaterally heterogeneous cross-sections considered by Romanelli et alA

20 16 15

Figure 2: Model adopted for the initial part of section S4.

In Figure 3 the acceleration time series for the twenty sites along S4 areshown, together with the 1-D signals (left column) calculated with the modalsummation technique for laterally homogeneous structures (Florsch et al/) usingthe model MO and with a cut-off frequency of 10 Hz. From the comparison ofthe 1-D and the 2-D time series it can be seen that the shape of the main peak ofthe wavetrain is similar. However the 2-D time series show greater amplitudesalong all the section and the duration of the signal is highly increased. This canbe explained by the fact that the sharp horizontal gradient present at thebeginning of the local model represents a strong impedence contrast for theincoming wavefield. Such a contrast produces a strong scattered wavefield thatpropagates in the low-velocity layers at the surface of the local models.



time (s) 205 time (s) 20

Figure 3: Synthetic accelerograms (transverse component) computed along S4:bedrock model (left column) and laterally heterogeneous model (right column).

On each side the peak amplitudes (g) of the signals are shown

4.2 3.7 3.2 0.7 0.22.7 2.2 1.7distance (km)

Figure 4: 2D/1D response spectra ratios versus frequency and distance along S4.

Moreover, the PGA/PGV mean ratio, equal to 20.5, is quite well correlated tothe PGA/PGV mean ratio correspondent to accelerograms recorded on firm soil,at distances from the causative fault ranging from 12 to 30 Km, and formagnitude ranging from 6.5 to 7.1 (Decanini and Mollaioli ).

To estimate the site response we evaluate the ratio between the responsespectra (RSR) calculated, at a given site, for the 2-D and the 1-D signals in order



to reveal the resonant frequencies and the corresponding level of amplificationfor the twenty sites of S4. In Figure 4 the RSR ratios are plotted versusfrequency and versus the distance from the beginning of the local model (seealso Figure 2 for the reference system). The effect of the sharp lateralheterogeneities is to create a higly energetic component of scattered waves thatare dominant within the first 500 m after the vertical interfaces. The propagationin the last part of Ml seems to be responsible of the shifting of the resonantfrequencies in the RSR at sites 12-15. This fact indicates that the site effectdepends not only on the layering of the local geological structure, but that therelative position of the site with respect to the lateral heterogeneities is playingan important role for the local response.

3 Evaluation of the damage potential of the synthetic signals

Even though a number of parameters have been proposed in the literature formeasuring the capacity of earthquake ground motion to damage structures, mostof them are not consistent with building damage observed during earthquakes(Uang and Bertero*).

Among all the different parameters proposed for defining the damagepotential, perhaps one of the most promising is the Earthquake Input Energy (Ei)and associate parameters (the damping energy E% and the plastic hystereticenergy EH) that has been studied by Uang and Bertero . This parameter considersthe actual behavior of a structural system and depends on the dynamiccharacteristics of both the ground motion and the structure. The input energy is areliable parameter in selecting the most demanding earthquake and in theevaluation of the destructiveness of synthetic signals. Therefore, at a given sitethe input energy permits the selection of the possible critical motions for theresponse of the structure. However, in order to perform a reliable design, sizingand detailing when the damage can be tolerated, the input energy alone is notsufficient.

The fundamental concept in applying energy methods is the transformation ofthe equation of motion of a viscous damped single-degree-of freedom (SDOF)system into an energy balance equation in which the input energy to thestructure, due to the seismic shaking at the base is balanced by energy absorbedin the structure and by energy dissipated from the structure. Then, according tothe procedures described by Uang and Bertero*, the energy balance equation isgiven by,

Ei = Ek + E;: + Ea = Ek + E^ + Es + EH (1)

Where Ek represents the absolute kinetic energy, E% is the damping energy, andEa is the absorbed energy that is composed of the recoverable elastic strainenergy, Es, and of the irrecoverable plastic hysteretic energy EH.

In previous work (Decanini and Mollaion ^) the absolute energy equation isused, since this criterion has the advantage that the physical input energy isreflected, in that EI represents the work done by the total base shear at thefoundation displacement, and it is suitable for the estimation of the energy terms


432 Earthquake Resistant Engineering Structures •

in the range of periods of interest for the majority of the structures. EI can beexpressed by:

dVET fd= —m J dt

(2)

where m is the mass, Ut = u + Ug is the absolute displacement of the mass, and u§is the earthquake ground displacement. In the following the input energy per unitmass, i.e. Ei/m, will be denoted as EI.

Figure 5 shows a comparison between the elastic input energy of threesynthetic signals (synth_l, synth_3 and synth_5), evaluated for a damping ratioequal to 5%, and two accelerograms (Santa Cruz UCSC/Lick Obs. Elect. Lab.,UcscO; and Gilroy # 1, Gavilan College, Water Tower, Gav. Tower 90) recordedduring the Loma Prieta earthquake (1989; M=7.1) on firm soil (SI) and atdistances from the surface projection of the causative fault (Df) equal to 15 and16 km, respectively. It can be observed that the frequency content is almost thesame in both cases, and the maximum values of EI are concentrated within therange of periods 0.3 < T < 0.5 s. Therefore, distances from the causative faultbeing equal, the synthetic signals provide an elastic energy comparable to thatobtained from records taken on firm soil for a magnitude approximately equal to7.1. In confirmation of the previous assertion, Figure 6 illustrates a comparisonbetween the synthetic signals, represented by the first signal, the mean and themean plus one standard deviation (SD) of all the signals, and the design inputenergy spectrum proposed by Decanini and Mollaiolf for a soil SI, for adistance 12 < Df< 30 km, and a magnitude 6.5 < M < 7.1.It should be recalledthat lavas with Vs=350 m/s lie at the boundary of the distinction between firm(SI) and intermediate (S2) soil. Both the spectral shapes and the maximumvalues of the input energy of the synthetic signals are consistent with the designspectrum, even though the spectra of the synthetic signals appear to be moreconcentrated around their maximum values.

= 5%

-Gav. Tower 90 |-Ucsc 0-synth_l-synth_3synth 5

Figure 5: Elastic EI (cm /s ) spectra. Comparison between synthetic signals andstrong motion records of Loma Prieta earthquake (1989), Soil SI.



Figure 6: Elastic E% (cms) spectra. Comparison between synthetic signals anddesign input energy spectrum (firm soil SI, 12 < Df < 30 km, 6.5 < M < 7.1)

4 Conclusions

As a result of the study performed, it is possible to draw the followingconsiderations:

a) The parameters PGA, PGV, to and PGA/PGV fall within the range ofvalues normally found on firm soil, magnitude and distance to the causative faultbeing equal.

b) The synthetic signals provide an energy response which is typical ofaccelerograms recorded on firm soil; at a distance to the causative fault between12 and 30 km, and a magnitude between 6.5 and 7.1.

c) The energy-based parameters is a powerful tool to evaluate thedestructiveness of both synthetic signals and strong motion records.

Acknowledgements

We acknowledge financial support from GNDT, MURST (40% and 60% funds),EEC Contract ENV-CT94-0491, ENV-CT94-0513, ENV4-CT96-0491.

References

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2. Romanelli, F., Bing, Z., Vaccari, F. & Panza, G.F., AnalyticalComputation of Reflection and Transmission Coupling Coefficients forLove Waves, Geophys. J. Int., 125 , pp. 132-138, 1996.



3. Gusev, A. A., Descriptive statistical model of earthquake source radiationand its application to an estimation of short period strong motion,Geophys. J. R. Astron. Soc., 74, pp. 787-800, 1983.

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6. Romanelli, F., Vaccari, F. & Panza, G.F., Site response estimation andground motions scenario in the Catania area. Submitted to Journal ofseismology.

1. Decanini, L.D. & Mollaioli, F., Formulation of Elastic Earthquake InputEnergy Spectra, Earthquake Engineering and Structural Dynamics; 27,pp. 1503-1522, 1998.

8. Uang, C.M. & Bertero, V.V., Implications of Recorded EarthquakeGround Motions on Seismic Design of Buildings Structures. Report No.UCB/EERC-88/13, Earthquake Engineering Research Center, Universityof California at Berkeley, 1988.

9. Uang, C.M & Bertero, V.V., Evaluation of seismic energy in structures.Earthquake Engineering and Structural Dynamics, 19, pp. 77-90, 1990.

10. Decanini, L. & Mollaioli, F., Toward the definition of the relationbetween hysteretic and input energy, 6th U.S. National Conference onEarthquake Engineering, Seattle, May 31-June 4, 1998.


l. decanini^' f. mollaioli,^ g. f. panza,^ f. romanelli€¦ · synthetic signals, to be used...

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