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sono state effettuate con Tromino e analizzate con software Grilla, mentre le misure in array sono
state fatte usando array di Tromino ad apertura sintetica sincronizzati attraverso il canale GPS.
Questi array, che hanno utilizzato sino a nove elementi, hanno permesso la misura simultanea
HVSR in tutti i nodi. Ciò ha permesso altresì di verificare l’effetto di eventuali modi superiori sia
negli array che negli HVSR e di effettuare considerazioni sulla natura 1D o meno del sottosuolo
(Mulargia e Castellaro, 2007). Gli array sono stati disegnati per una resilienza ottimale agli alias,
utilizzando distanze di spaziatura prime tra loro. La tecnica a stazione singola proposta si è dimostrata capace di fornire curve teoriche di dispersione delle onde di Rayleigh e stime di Vs30 coerenti con quelle misurate dagli array ESAC and ReMi (Fig. 3), nonché un buon accordo con la geologia di superficie. La tecnica proposta appare pertanto come una alternativa veloce e a basso costo
per la stima di Vs30 e la classificazione sismica dei suoli secondo la normativa vigente.
Ovviamente, come ogni tecnica, anche quella proposta ha dei limiti. Essi sono:
1. la tecnica proposta si basa su un modello predeterminato del rumore sismico;
2. si fonda sull’assunto 1D del sottosuolo, mentre molto spesso i il sottosuolo non è 1D (Mulargia
e Castellaro, 2007a). Il grande vantaggio della tecnica HVSR è che essa permette di riconoscere
la presenza di eterogeneità laterali mentre le tecniche ad array non lo permettono affatto;
3. poiché l’ampiezza del rapporto H/V a basse frequenze (indicativamente sotto 0.5 Hz) dipende
dalle condizioni meteorologiche (Mulargia and Castellaro, 2007b), la tecnica è applicabile solo
sopra questa frequenza;
4. poiché l’ampiezza dei picchi H/V dipende in certa misura anche dal lisciamento adottato, il profilo di Vs è approssimato;
5. nei casi in cui sia presente un’inversione di velocità, l’inversione della curva HVSR diventa più
complicata, in quanto le discontinuità stratigrafiche minori vengono mascherate. In questi casi
peraltro, la comparsa dei modi superiori nelle corrispondenti registrazioni in array, porta anche
queste ultime a soffrire, sia per la scarsa affidabilità del picking che per l’inversione, che diventa instabile.
Bibliografia
Castellaro S., e Mulargia F.; 2007: Vs30, parametro obbligatorio ma inefficace per la stima dell’amplificazione sismica, Roma,
GNGTS.
Mulargia F. e Castellaro S.; 2007a: The large inaccuracy of measured Vs profiles: non 1-D subsoil? Roma, GNGTS.
Mulargia F. e Castellaro S.; 2007b: Single station passive seismic stratigraphy to almost 2 km depth, Roma, GNGTS.
Ben-Menahem A. e Singh S.J.; 1981: Seismic waves and sources, Springer-Verlag, New York, 1108 pp.
Mucciarelli M. e Gallipoli M.R.; 2006: Comparison between Vs30 and other estimates of site amplification in Italy, Conf. Earthq.
Eng. and Seismol., Geneva, 3-8 Sept., no. 270.
SEISMIC SITE EFFECT: SV WAVES PHASE SHIFT IN VISCO-ELASTIC
NON LINEAR MEDIA
V. Di Fiore(1) and P.P. Bruno(2)
(1) Consiglio Nazionale delle Ricerche, IAMC, Naples
(2) Istituto Nazionale di Geofisica e vulcanologia, Osservatorio Vesuviano, Naples
Local seismic amplification function (SAF) depends on elastic and geometric parameters of the
soil. In fact, many authors have carried out research in this particular field obtaining very important
results (e.g. Seed et al., 1986; Aki et al., 1988; Bravo et al., 1988; Cao and Lee, 1989; Lee et al.,
1990, 1992; Bruno et al.,1999; Rapolla et al., 2002). In most bibliography record, the seismic amplification function (SAF) was studied taking into account only the amplitude variation with respect
to frequency. Because the overburden can also generate constructive or destructive interference, in
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this paper we attempted to understand the influence of those parameters (i.e. layers thickness and its
shear wave velocity) on the ground motion phase shift. In our study, we assumed a visco-elastic and
non-linear behavior of the overburden. In fact, nonlinear effects, such as an increase in damping and
reduction in shear wave velocity as excitation strength increases, are commonly recognized in the
dynamic loading of soil especially at shear strains larger than 10-5 – 10-4 percent (Seed et al., 1986;
Beresnev and Wen, 1995a; Kramer, 1996). We studied 25 synthetic models characterized by different mechanical properties and variable thickness. In order to model the soil behavior in one-dimensional analysis we needed experimental values of mechanical parameters that were taken from idriss
et al., 1990.
The model implemented to study the input motion phase shift at the free surface, consist of an
overburden layer overlaying a horizontal seismic basement (half-space). The overburden is constituted by a single layer whose thickness was varied from 6 to 30 m with 1 m step. For each step on
thickness the shear wave velocity ranged from 200 to 600 m/s with 100 m/s step. For all models the
overburden’s density was 1.40 g/cm3, the bedrock shear wave velocity (SV) was set to 750 m/s while
the mass density was 1.8 g/cm3. Fig. 1 reports the non linear strains over damping and strain over
shear modulus curves that we used in our study (idriss et al., 1990). The models used for simulating the soil stress-strain response during a cyclic loading is the viscoelastic Kelvin-Voigt model
(Bardet et al., 2000).The differential equation that describes the viscoelastic Kelvin-Voigt behaviour
is:
(1)
where:
u is the horizontal displacement; G is the shear modulus; δ is the mass density; η is a mass-proportional damping coefficient; t is the time; z is the depth.
We also utilized a linear equivalent analyses procedure (Idriss and Sun, 1992; Sugito, 1995) to
solve for the nonlinear behavior of visco-elastic medium.
Our study we assumed a shear wave (SV) propagating vertically upward in a one-dimensional
Fig. 1 – Material behaviour obtained by experimental curves: a) shear modulus and b) damping ratio of the
overburden SV shear strain amplitude. c) and d) are the curves referred at the bedrock (Idriss, 1990).
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Fig. 2 – Scheme of the synthetic models utilized in
our study. H is variable from 6 to 30 m; shear wave
velocity variable from 200 to 600 m/s; mass
density overburden is 1.40 g/cm3; The bedrock
have a mass density of 1.80 g/cm3 and a shear
wave velocity of 750 m/s.
layered system, in which the soil layers are: (1) horizontally homogenous, (2) of infinite horizontal
extent, and (3) subjected only to horizontal (SV) motion from bedrock (Fig. 2).
To solve equation (1), we used the “continuous strata” approximation. In this approximation the
soil deposit is divided into m-1 layers having various thickness hi and unit mass for i = 1 to m-1.
In such generic subsurface, if we indicate with Aj and Bj the upward and downward waves, at
any time and in a continuous subsoil, the solutions of equation (1) are:
where K* the complex wavenumber, is:
where G* is the complex shear modulus:
The results obtained, are relative to 25 models, are summarized in the Figs. 3 and 4.
Results show that the energy focusing/defocusing effects may potentially arise by constructive
or destructive interference due to phase shift.
We have seen by numerical analysis that:
1. generally, the zero phase shifts are presents greater at lower frequency, lower thickness layers and
higher seismic waves velocity;
2. phase shift is not linear, is strong for Vs<400 m/s and for high frequency (>2.5 Hz);
Phase shifts may introduce additional amplification in seismic signal by constructive/destructive
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Fig. 3 – Phase shift (degrees) versus the overburden thickness (meters) and frequency for several SV wave velocity
of the overburden (200-400 m/s).
interference. The combination of both effects is to be then considered for a correct estimate of the
seismic site response. In the engineering practice point 2 is often underestimated. In this paper we
attempted do analyze the effect of velocity and thickness variation in the overburden on phase shifts.
It’s clear that in all models an univocal and linear behavior of the phase shift with respect to velocity and thickness do not exist. Therefore, not being possible found a physics low between the phase
shift and the elastic or geometrics parameters, every single case must be studied.
Applying these techniques, we will be able in future to forecast the effects on the wavefield at
free surface in terms of phase shift and then, modifying the thickness or the mechanical characteristics of soil, the interference constructive could be eliminated or however be attenuated.
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Fig. 4 – Phase shift (degrees) versus the overburden thickness (meters) and frequency for several SV wave velocity
of the overburden (500-600 m/s).
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References
Aki, K., 1988. Local site effects on ground motion. In Earthquake Engineering and Soil Dynamics II - Recent Advances in Ground
Motion Evaluation. ed. J. L. Von. Thun, Geotechnical Special Pubblication N. 20, ASCE, New York, 103-155.
Bardet, J. P. And Tobita T.(2001) “NERA, A computer program for Nonlinear Earthquake site Response Analysis of layered soils
deposits,” University of Southern California, Los Angeles.
Bravo, M.A., Sanchez-Sesma, F.J. and Chavez-Garcia, F.J., 1988. Ground motion on stratified alluvial deposits for incident Sh
waves. Bull. Seismol. Soc. America, 78, 436-450.
Bruno P.P.G., Di Fiore V., Rapolla A. and Roberti N. (1999) Influence of geometrical and geophysical parameters on the seismic
site amplification factor. EJEEG, 4, 51-70.
Cao, H., & Lee, V.W., Scattering of plane SH-wave by circular cylindrical canyons with variable depth-to-width ratio. European J.
Of Earthquake Eng., III(3), 29-37.
Davis, P.M., Kohler M., and Husker A. 2001, Earthquake Hazard from Focusing of Seismic Waves by Basin Structures, Annual
Project Summary Report, USGS/NEHRP External Research Earthquake Hazards Program Grant # 00HQGR0076
Fishman, K.L. and Ahmad, S., 1995. Seismic response for alluvial valleys subjected to SH, P and SV waves. Soil Dynamics and
Earthquake Engineering, 14, 249-258.
Hardin B.O., 1978, The nature of stress-strain behaviour for soil – State of the Art. Proc. “Geotechnical Engineering and Soil
Dynamics”, ASCE, Pasadena (California).
Idriss, I. M. (1990) “Response of Soft Soil Sites during Earthquakes”, Proceedings, Memorial Symposium to honor Professor Harry
Bolton Seed, Berkeley, California, Vol. II, May.
Idriss, I. M. and Sun, J. I. (1992) “User’s Manual for SHAKE91,” Center for Geotechnical Modeling, Department of Civil
Engineering, University of California, Davis.
Kramer, S. L. (1996). Geotechnical Earthquake Engineering, Prentice Hall, Upper Saddle River, New Jersey, pp. 254-280.
Lanzo G. & F. Silvestri (1999) Risposta sismica locale: teoria ed esperienze. 160 pp., Hevelius Edizioni, Benevento.
Lee, V.W., 1990. On the scattering of plane SH waves by a semi-parabolic cylindrical canyons in an elastic half-space. Geophy.
Journ., 100, 79-86.
Lee V.W., Karl J. ,1990, Diffraction of SV waves by underground, circular, cylindrical cavities. Soil Dynamics and Earthquake
Engineering 11, 445–456.
Rapolla, A., Bais, G. Bruno, P. P. G. Di Fiore, V. (2002), Earth modeling and estimation of the local seismic ground motion due to
site geology in complex volcanoclastic areas. Annals of Geophysics, 45-6, 779-790.
Rassem, M., Heidebrecht, A.C. and Ghobarah, 1995. A Simple engineering model for the seismic site response of alluvial valleys.
Soil Dynamics and Earthquake Engineering, 14, 199-210.
Seed, H. B., Wong, R. T., Idriss, I. M. and Tokimatsu, K. (1986) “Moduli and Damping factors for Dynamic Analyses of
Cohesionless Soils,” Journal of the Geotechnical Engineering Division, ASCE, Vol. 11 2, No. GTI 1, November, pp.1016-1032.
Sheriff R.E. and Geldart L.P.,1995. Exploration Seismology. Cambridge University Press II Ed., 183-184.
Sugito, M. (1995) “Frequency-dependent equivalent strain for equi-linearized technique,” Proceedings of the First International
Conference on Earthquake Geotechnical Engineering, Vol. 1, A. A. Balkena, Rotterdam, the Netherlands, pp. 655-660.
Sun, J. I., Golesorkhi, R. and Seed, H. B. (1988) “Dynamic Moduli and Damping Ratios for Cohesive Soils,” Report No.
UCB/EERC-88/15, Earthquake Engineering Research Center, University of California, Berkeley, 42p.
Vucetic, M. and Dobry, R. (1991) “Effect of Soil Plasticity on Cyclic Response,” Journal of the Geotechnical Engineering Division,
ASCE, Vol. 111, No. 1, January, pp. 89-107.
VALUTAZIONE COMPARATIVA E DI ATTENDIBILITÀ DELLE STIME DI
PERICOLOSITÀ SISMICA IN RAPPORTO AGLI OSSERVABILI DISPONIBILI:
APPLICAZIONE ALL’AREA ITALIANA
D. Albarello(1) e V. D’Amico(2)
(1) Dipartimento di Scienze della Terra, Università di Siena
(2) Istituto Nazionale di Geofisica e Vulcanologia, Sezione di Milano-Pavia
E’ esperienza comune il fatto che le procedure numeriche disponibili migliorano assai più velocemente dei dati di base necessari alla loro applicazione. Ne consegue anche che, pur condividendo le stesse informazioni di partenza, diverse procedure producono risultati spesso assai differenti.
Le stime di pericolosità sismica rappresentano un buon esempio di questa situazione. Negli ultimi
anni sono molte le mappe di pericolosità a scala nazionale che si sono succedute come effetto sia
delle variazioni apportate alle basi di dati che di differenti scelte metodologiche implementate nelle
procedure di calcolo adottate. In questo contesto si pone il problema di una valutazione comparati-
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