New procedure for deriving multifrequential dynamic ... - Springer Link

Bull Earthquake Eng (2010) 8:813–846 DOI 10.1007/s10518-009-9169-7 ORIGINAL RESEARCH PAPER

New procedure for deriving multifrequential dynamic equivalent signals (LEMA_DES): a test-study based on Italian accelerometric records L. Lenti · S. Martino

Received: 25 April 2009 / Accepted: 10 December 2009 / Published online: 30 December 2009 © Springer Science+Business Media B.V. 2009

Abstract The here proposed LEMA_DES (Levelled-Energy Multifrequential Analysis for Dynamic Equivalent Signals) procedure is a new approach for defining multifrequential dynamic equivalent signals from real accelerograms, to be applied for physic-analogue and numerical geotechnical modelling of induced seismic effects. In this approach, the resulting equivalent signals satisfy criteria of spectral, energetic and kinematic equivalence to the related real prototypes. The approach was tested to analyse the accelerometric records of the November 23rd, 1980 Irpinia (Italy) earthquake. Based on 48 selected records, correlations were studied between the characteristic parameters of both real and equivalent signals. These correlations demonstrate that the proposed approach guarantees: i) the energy equivalence of the derived signals, except for a half order of magnitude, and ii) the equivalence of the peak ground acceleration (PGA) values with relative errors below 105%. The computed relative error on the cumulative energy of the LEMA_DES signals (Δr Veq %), which have spectral amplitudes at frequencies lower than 1 Hz, drops below 30%, while the same error increases above 2500%, in the same frequency range, for sinusoidal signals obtained according to traditional approaches. The PGAs of the LEMA_DES signals show a good fit with the PGA attenuation law proposed for the central-southern Apennines. Correlations between the Arias intensities and PGAs of the equivalent signals with respect to the actual ones demonstrate that their characteristic parameters: i) well represent the spatial variation in terms of energy and ground motion; ii) reproduce an analogue earthquake scenario with respect to the reference seismic event.

L. Lenti Laboratoire Central des Ponts et Chaussées, Paris East University, 58 Boulevard Lefebvre, 75732 Paris Cedex 15, France e-mail: [email protected] S. Martino Dipartimento di Scienze della Terra e Centro di Ricerca Previsione, Prevenzione e Controllo dei Rischi Geologici (CE.RI.), Università di Roma Sapienza, P.za U. Pilozzi 9, Rome, VA, Italy S. Martino (B) Dipartimento di Scienze della Terra, Università di Roma Sapienza, P.za A. Moro 5, 00185 Rome, Italy e-mail: [email protected]

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Bull Earthquake Eng (2010) 8:813–846

Keywords

Equivalent inputs · Accelerometric records · Analogue earthquake scenarios

1 Introduction An equivalent accelerometric signal can be regarded as an acceleration time history, inferred from a reference accelerometric record which can be defined in different ways on the basis of: a) equivalence criteria, b) type of reference accelerometric signal. In particular, equivalence criteria may concern: 1) the kinematic characteristics of the signal (e.g. peaks of acceleration, velocity and displacement, duration); 2) Fourier spectrum amplitude; 3) Fourier spectrum phase values; 4) response spectrum; 5) energy. Conversely, the types of reference accelerometric signal depend on different physical phenomena and are generally related to the propagation of waves. These waves fall under two categories, which depend on their emission sources: 1) natural sources (e.g. earthquakes, collapses, changes in the electromagnetic or gravitational potentials); 2) anthropogenic sources (e.g. oscillations of buildings, vibrations due to mechanic devices, electromagnetic emissions from telecommunication systems). As their definition suggests, equivalent signals are full-fledged analogue tools for modelling natural processes (real prototypes) as physical analogues (equivalent prototypes). In particular, the equivalent signals may be employed in technical-scientific applications (i.e. laboratory testing on soil samples, modelling at shaking table, dynamic modelling at centrifuge device) when common theoretical approaches or instrumental devices can hardly manage the whole complexity of the actual accelerometric signals. At this regard, the approach proposed in this paper optimises the existing ones, by obtaining accelerometric signals that can be regarded as more constrained to the real actions. Following this approach, a dynamic equivalent multifrequential accelerometric signal is derived by selecting a limited number of frequencies from the reference acceleration spectrum. The dynamic equivalent signal is sized on a reference prototype under criteria of energy, spectral and peak acceleration equivalence. The above mentioned equivalence criteria involve that the number of equivalent cycles, assigned to the selected frequencies, as well as the duration of the signal are variables depending on the generation process itself.

2 Equivalent signals from seismic accelerometric inputs: state of art A first definition of equivalent accelerometric signal to be used in geotechnical applications was proposed by Seed and Idriss (1969), Seed and Idriss (1971). Subsequently, this concept was used as part of a methodology to study the potential liquefaction of sandy soils under seismic shaking (Ishihara 1977; Seed 1979a,b; Seed et al. 1983). In particular, the Authors proposed the use of a monofrequential sinusoidal accelerogram, which was derived from a reference seismometric record under the following criteria: (1) (2)

use of an equivalent amplitude (amax ), equal to 65% of the peak ground acceleration (PGA) of the reference accelerogram; use of the maximum expected shear stress (τmax ), depending on ground motion amplitude and soil depth and corrected by a scaling factor (rd ) as a function of depth (Iwasaki 1986; and Cetin and Seed 2004);

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(3)

815

use of a number of equivalent (or characteristic) cycles (n c ) in the monofrequential sinusoidal signal, which is an empirical function of the reference earthquake moment magnitude.

According to these criteria, the above mentioned method by Seed and Idriss does not impose specific constraints on the value of the equivalent sinusoidal frequency and, consequently, on the duration of the resulting cyclical signal. The original solution put forward by Seed and Idriss (1969), Seed and Idriss (1971) was validated by laboratory tests by use of cyclical triaxial equipment as well as cyclical direct shear (Seed et al. 1975; Seed 1976; Seed et al. 1981; Ishihara and Koga 1981). Various research teams (Malvick et al. 2002; Lin and Wang 2006; Rayhani and Naggar 2007; Stamatopoulos et al. 2007) have focused their experiments on the issues arising from seismically-induced effects (e.g. seismic amplification, landslides and liquefaction of loose soil) and developed analogue systems based on physical conditions of varying complexity. In these experiments, the seismic input is scaled from the reference accelerometric records (prototypal input), from which the dominant frequencies associated with the characteristic acceleration peaks are identified. Several experiments applied monofrequential cyclical signals to centrifuge devices, aiming at developing laboratory-scaled analogue models (Zelikson et al. 1981; Bourdin 1988; Balakrishnan et al. 1998; Semblat and Luong 1998; Balakrishnan and Kutter 1999; Kutter and Balakrishnan 1999) as well as at numerically simulating the mechanical behaviour of soils (Koseki et al. 1994; Peiris et al. 1998; Ghosh and Madabhushi 2004). These experiments demonstrated that the dynamic behaviour of soils depends on the frequency of the cyclic input. Therefore, these results evidenced the limits that are intrinsic in the application of monofrequential cyclical signals; the results of the same experiments suggested to control the energy content of equivalent cyclical signals in terms of Arias intensity value, based on reference earthquakes. Moreover, some numerical modelling was performed in dynamic conditions by applying cyclical equivalent inputs (Martino and Scarascia Mugnozza 2005; Martino et al. 2007; Bozzano et al. 2008b); the obtained results demonstrated that both landslide triggers and related displacements depend on the selected frequency. On the other hand, several numerical models of seismically-induced effects via finite element, finite difference and boundary element methods (FEM, FDM and BEM, respectively), have been performed by the use of dynamic accelerometric signals, obtained from recorded time histories (Chang et al. 2005; Dai et al. 2005; Wang et al. 2006; Costanzo et al. 2007). Nevertheless, for these applications, the original records need to be: i) filtered with respect to a given cut-off frequency (depending on the discretisation of the numerical model as well as to the geomechanical properties of the modelled materials); ii) processed in such a way as to obtain a null value of the accelerogram integral at the end of its duration (Semblat et al. 1999; Semblat and Brioist 2000). Additionally, in many of these applications, the PGA values of available records are scaled with respect to the ones of the expected earthquakes; however, roughly scaling real signals modifies their energy and spectral content and only the kinematic equivalence criteria results to be verified. Moreover, a unique selected record may not reflect the distinctive features of the local seismicity referred to the considered area. At this regard, the generation of synthetic accelerometric signals, consistent with local seismic ground motion response spectra, represents an alternative approach to the previously discussed ones (Boore 1983; Saragoni and Hart 1974; Gupta and Trifunac 1997; Boore 2000; Cascone and Rampello 2003). This approach generally requires a random phase spectrum function (Shinozuka 1970; Sabetta and Pugliese 1996) to be associated with the spectral

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amplitudes that characterise the artificial signal to be obtained; the spectral amplitudes are best fitted to the selected response spectrum. The signal resulting by combining the spectral amplitudes and the phase function is sized on the basis of the duration and the PGA of the reference earthquake. The so obtained synthetic signals can be regarded as comparable with real accelerometric time histories in terms of physical complexity (i.e. amplitude and phase spectra, duration, time-variable intensity of the signal); nevertheless, this complexity represents their limit for both numerical modelling and laboratory experiments. At this regard, could be considered that numerical modelling by FEM, FDM or BEM approaches are limited to an upper cut-off frequency strongly related to the mesh resolution (Zienkiewicz 2005), while many dynamic actuators for shaking tables, as well as for dynamic laboratory testing devices on soil samples, are limited to an upper threshold value of frequency, depending on the performance of hydraulic and electronic devices. This last condition is particularly relevant when lab-scaled analogue models are planned, i.e. by use of shaking tables or centrifuge devices, since in these models the scale factor strongly increases the values of frequencies to be actuated (Semblat and Pecker 2009). On the other hand, in analytical studies of seismically-induced effects, monochromatic equivalent cyclical signals have the advantage of simplifying the interpretation of numerical or experimental results. Their drawback lies in the fact that: i) they are not necessarily representative of the energy content of the reference signal, and ii) they may be unsuitable for modelling phenomena that are significantly dependent on a combination of frequencies. With refer to the above mentioned drawbacks for both synthetic inputs and monochromatic equivalent signals, the use of here proposed multifrequencial dynamic equivalent signals (best fitted to representative values of the reference earthquakes) may: i) check that the frequency content of the derived signals is defined within a representative/admissible range; ii) avoid upper-threshold frequency to be exceeded; iii) narrow the energy gap between real and simulated seismic actions; iv) control the maximum intensity of the adopted action and v) take into account seismically-induced effects arising from frequency combinations, i.e. from dynamic actions.

3 LEMA_DES procedure for deriving multifrequential dynamic equivalent signals The here proposed procedure for deriving multifrequential dynamic signals, equivalent to reference accelerograms, was implemented via the specially-designed LEMA_DES (Levelled-Energy Multifrequential Analysis for Dynamic Equivalent Signals) numerical program which executes the transactions in different steps (Fig. 1). The digital record of the 31st October, Molise earthquake (Ml = 5.4) at the CMM station (about 50 km far from the epicentre) of the Italian accelerometric network (Dipartimento della Protezione Civile 2004) has been selected to illustrate the LEMA_DES execution. The procedure consists in the generation of a sequence of functions and signals, summarised in the following, which correspond to the processing steps (Fig. 1) performed by the LEMA_DES program: Step 1 selection of the characteristic frequencies and deriving of the harmonic functions corresponding to monofrequential cyclical functions whose frequencies are equal to those selected from the smoothed Fourier spectrum of the reference accelerogram (F F Tri f ) (Figs. 2, 3); these functions have an amplitude proportional to the corresponding spectral densities of F F Tri f ;

123


817

Fig. 1 Sketch of the LEMA_DES procedure

Step 2 deriving of the sum signal S(t) by algebraically summing the adding functions (Figs. 4, 5a) which coincide with the corresponding harmonic functions (Fig. 4) until a duration Ti = n c /Fi (n c = number of equivalent cycles = 1 and Fi = frequency value of the corresponding harmonic function) while are zeroed in the time range Ti < t < Tend , where Tend is the highest among the duration of the considered sinusoids; Step 3 deriving of the shape signal T(t) (Fig. 5b) from the sum signal by a mathematical processing, in order to derive i) a null integral over its entire duration, ii) a Fourier spectrum whose spectral density at frequencies lower than the minimum frequency selected from F F Tri f is negligible, iii) amplitude values null for t > Tend ; Step 4 deriving of the preliminary equivalent signal E (t), consisting in a multifrequential dynamic signal which is energy-equivalent to the reference accelerogram, pass-band filtered in the range of the selected frequencies, but not yet best fitted in terms of PGA (Fig. 5c); Step 5 deriving of the resulting equivalent signal E(t) (Fig. 6) consisting in a multifrequential dynamic signal which is energy-equivalent to the reference accelerogram and best fitted in terms of PGA via an iterative procedure, this last one is performed by adding one integer to the previous n c value as to obtain a new sum signal S(t), with a longer Tend , and to re-process it from step 2 to step 5. A crucial step in the above-described procedure is the correct and objective choice of the characteristic frequencies of the F F Tri f (step 1) which are used to define the initial

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818


Fig. 2 Data input for the CMM digital record (Dipartimento della Protezione Civile 2004): a time history of the reference accelerogram; b FFT of the original (left) and smoothed (right) reference accelerogram

harmonic functions (Fig. 4) and to generate all the other derived functions and signals. At this regard, an objective process was developed in order to infer from F F Tri f a discrete number of frequency bands and related spectral densities (Fig. 3). The reliability criterion for identifying the above bands is to test the spectral density exceedance of a threshold value, which is set as a percentage of the Maximum Spectral Acceleration Value (MSAV). In a first stage of the proposed procedure, this percentage is set to 30% of MSAV for selecting all the characteristic frequencies (Fig. 3a) while, in a second stage, the same percentage is set to the 40% for minimalising the number of the selected frequencies to a predefined value (Fig. 3b, c). To a first approximation, the choice of the 30% and the 40% of MSAV is reliable since it permits to detect the frequency values which mainly contribute to the energy of the reference signal and it is in strong analogy with the reliability percentages used in the literature for PGAs (Seed and Idriss 1969, 1971). However, as discussed in the follow, the percentage has been ex-post validated by directly comparing the results from signal processing with the initial data. The following criteria are assumed for identifying the total number of the bands and they rely on the assumption of aggregating multiple spectral peaks (relative maxima of F F Tri f ):

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819

Fig. 3 Example of procedure for selecting and minimalising the characteristic frequencies of the equivalent signal, referred to the accelerogram of Fig. 2: in a first stage the 30% of the MSAV is considered as exceedance threshold (a) while, in a second stage, the same threshold is set to 40% of the MSAV (b, c). In this example the procedure starts from 11 frequency bands and obtains 5 final characteristic frequencies

123

820


Fig. 4 a harmonic functions obtained by LEMA_DES after automatically selecting the characteristic frequencies from the FFT of the reference input (see Fig. 2b); b adding functions obtained by LEMA_DES from the harmonic functions

(1)

(2)

(3)

determining the amplitude difference (ale f t ) between the amplitude of the ith relative maximum (ai ) and the one of the neighbouring relative minimum at lower frequency, both considered to be net of the MSAV; determining the amplitude difference (aright ) between the amplitude of the ith relative maximum (ai ) and the one of the neighbouring relative minimum at higher frequency, both considered to be net of the MSAV; determining the frequency distance ( f ) between the ith relative maximum and the neighbouring relative maximum at a higher frequency.

Based on the above listed criteria the following conditions need to be checked in order to univocally define a frequency band: 1) ale f t > 1/3ai ; 2) aright > 1/3ai ; 3) f ≥ 0.5 Hz. As a consequence, each band remains associated with a discrete i-number of relative maxima (at the least equal to 1 in the extreme case of a peak-band). Each maximum belonging to

123


821

Fig. 5 Signals obtained by LEMA_DES during the processing: a sum signal S(t); b shape signal T(t); c preliminary equivalent signal E (t) with n c = 1

123

822


Fig. 6 a Resulting equivalent signal E(t) obtained by LEMA_DES; b related Fourier spectrum c related spectrogram showing the major spectral contribute of the lowest selected frequency on the LTAV and d final report, including: characteristic parameters of the reference input (average input PGA, percentage for valid PGA, valid input PGA), characteristic parameters of the equivalent signal (ending time, time step, PGA, Arias intensity), quality indexes for the equivalent signal (relative error on PGA, reliability)

a band is completely identified by a pair of spectral frequency (f) and a related amplitude (A) value (Fig. 3a). Nevertheless, in order to obtain an harmonic function, corresponding to each band, a single pair of f and A values has to be defined. Therefore, the frequency and the spectral amplitude values of the relative maxima, selected within each band, are used to compute weighted averages (with respect to their spectral amplitudes), for both frequency ( f ) and amplitude (A); as a consequence, each band is associated to a pair of characteristic values ( f , A). The maximum number of pairs of characteristic values, can be minimalise by lowering it to an integer that needs to be set in the proposed procedure; in any case, this integer should be related to the frequency range, resulting from the Fourier spectrum of the reference accelerometric record, i.e. typical of the natural or anthropogenic phenomenon. In particular, for the here considered analysis of seismic signals, the maximum number of characteristic frequencies is taken to be equal to 5 (Fig. 3c); i.e. proportionate to the 0–15 Hz frequency range of specific interest for the investigated phenomena. The minimalisation, if required, is carried out by the following step-sequence, until the remaining number of bands is equal to 5: (1) (2)

the bands associated to an A value strictly lower than 40% MSAV are discarded, starting from the lowest A value; the remaining bands, starting from the one associated to the lowest A value, are averaged with their closest ones.

123


823

According to the previously reported sequence of functions and signals (Fig. 5), the generated sum signal S(t) verifies only the spectral equivalence criterion. Starting from S(t), the shape signal T(t) is mathematically processed as to have a Fourier spectrum characterised by negligible amplitudes below the selected minimum frequency. In particular, the S(t) signal is high-pass filtered at the minimum selected frequency to obtain the shape signal T(t) with a null integral at the end of its duration. Nevertheless, the shape signal T(t) does not yet satisfy the energy equivalence criterion; the energy equivalence of T(t) with respect to the reference time history is imposed by deriving an energy scaling factor Fen from the integral of the square of the reference velocigram (Vri f ). This integral represents the cumulative kinetic energy for unit weight and can be regarded as a parameter widely reliable for different physical processes. Nevertheless, for the here discussed application (i.e., seismic accelerograms) the significance of the Vri f parameter has been ex-post validated by discussing the results obtained from a comparison with a more diffused seismic energy index (i.e. Arias intensity). In order to mathematically perform the above mentioned scaling, the reference velocigram was pass-band filtered within the range of the characteristic frequencies. The integral of the square of the filtered reference velocigram (V f ilt ) is computed by the form: Tri f V f ilt =

v 2f ilt (t)dt

(1)

0

where Tri f is the duration of the reference signal and ν f ilt (t) is the velocigram related to the filtered reference signal. The energy scaling factor Fen is computed by relating V f ilt to the integral of the square of the velocigram of the shape signal(VT ), by the form: Tri f 2 v f ilt (t)dt V f ilt 0 (2) = T Fen = end VT vT2 (t)dt 0 Consequently, a preliminary multifrequential dynamic equivalent signal E (t) is obtained as: E (t) = Fen T (t) (3) Although the signal E (t) satisfies the energy equivalence criterion, it has not yet been best fitted to the equivalent peak ground acceleration with respect to the PGA of the filtered reference time history (P G A f ilt ). The here proposed best-fitting process is an iterative one, which outputs the final value for the number of equivalent cycles (n c ) starting from the initial value n c = 1 of the signal E (t). and minimalises the deviation between the amplitude of the signal E (t) and the P G A f ilt . At this aim, it was observed that the terminal portion of E (t) (LTAV—Long Term Amplitude Value) has a sinusoidal shape, only due to the contribution of the lowest selected frequency. As a consequence, it has been assumed to be reliable to process this portion of the signal according to other Authors (Seed and Idriss 1971, 1979), i.e. by comparing the amplitude of the sinusoidal portion of E (t) with the 65% of the P G A f ilt . Nevertheless, the reliability of this assumption has been demonstrated by applying this processing to accelerometric records, as discussed in the follow. As a consequence, both the duration (i.e. number of equivalent cycles) and the PGA value of the resulting multifrequential equivalent signal E(t) are variables which depend on the iterative process. In this way, the resulting multifrequential dynamic equivalent signal E(t) satisfies all the considered convergence criteria, i.e. spectral, kinematic (in terms of PGA) and energy ones

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824


Fig. 7 Comparison between cumulative curves for Vfilt (up) and Veq (down)

(Figs. 6, 7). Moreover, since the duration of the equivalent signal automatically derives from the PGA best-fitting process, a time compression index (Itc ), can be computed by the percentage ratio of the difference of the input and derived signals to the duration of the input signal. The final output of the LEMA_DES program (exemplified in Fig. 6d) consists in processing report with: 1) characteristic parameters of E(t) (final n c value, harmonic function frequencies and corresponding normalised spectral density amplitudes, duration, PGA, Arias intensity), 2) values resulting from the PGA best-fitting process (average PGA of input data, percentage validity of the average PGA used, percentage of the average PGA value used), 3) solution quality indicators (relative error on the PGA of the equivalent signal referred to the average PGA of input data, quality assessment of resulting equivalent signal, relative error between percentage value of the reference PGA and LTAV). The quality assessment may be: HIGH RELIABILITY (= high reliability of the result with relative convergence errors CRE ≤ 10%); MIDDLE RELIABILITY (= average reliability of the result with relative convergence errors 10% < CRE ≤ 50%); LOW RELIABILITY (= low reliability of the result with relative convergence errors CRE > 50%).

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825

4 Application to the November 23rd, 1980 Irpinia (Italy) earthquake An experimental analysis was carried out to test the reliability of the proposed procedure for deriving multifrequential dynamic equivalent signals, as well as its numerical implementation via the LEMA_DES program. The analysis relied on the accelerometric records of the Irpinia earthquake of November 23rd, 1980, which are originally stored in the database of ENEA-ENEL and presently available from the ITACA Archive (Working Group ITACA 2008). The choice of the database was driven by the following considerations: (a)

(b)

the earthquake was recorded by about 30 stations, equipped with three-component analogical accelerometers (Scarpa 1981; Rovelli et al. 1988; Cocco and Rovelli 1989; Capuano et al. 1992; Nostro et al. 1997); the stations, scattered within a radius of about 200 km, were run by various institutions; the earthquake triggered a large number of seismically-induced effects, widely reported in the literature (Carmignani et al. 1981; Hutchinson and Del Prete 1985; Genevois and Prestininzi 1982; D’Elia et al. 1985, 1986; Funiciello et al. 1988; Bozzano et al. 1996; Porfido et al. 2002), as well as in national earthquake catalogues (CPTI04 2004; DBMI04 2004; INGV and SGA 2007); these effects included ground cracking and surface faulting, landslides, variation of discharge in natural springs. In particular, many authors have already conducted back analyses on many of these seismically-induced landslides, using conventional approaches (Simonelli and Viggiani 1995; Crespellani et al. 1996; Romeo 2000; Martino et al. 2001; Martino and Scarascia Mugnozza 2005).

In addition to the above considerations, it should be pointed out that: 1) the accelerometric records of the November 23rd, 1980 Irpinia earthquake were all of analogical type; 2) some of the accelerometric stations which recorded the seismic event were not located on bedrock, but on thick debris or alluvia (responsible for amplification effects); 3) many of the stations which recorded the earthquake of November 23rd, 1980 were relocated in the years immediately following 1980; as a consequence, many of them did not provide additional strong motion records which might give insight into the characteristics of their original recording sites; 4) the earthquake was characterised by two main shocks which took place in a matter of about 40 s (Bernard and Zollo 1989) and almost half of the stations which detected the first main shock also recorded the second one. The November 23rd, 1980 Irpinia earthquake struck a wide area of the southern Apennines, making part of the Campania and Lucania regions (Cinque et al. 1991; Michetti et al. 2000). The epicentre of the main shock of the November 23rd, 1980 earthquake (Ms = 6.8) was located at 40.850◦ N and 15.280◦ E (CPTI04 2004; INGV and SGA 2007) with its hypocentre at a depth of 10 to 12 km (Westaway 1993; Westaway and Jackson 1984; Funiciello et al. 1988). The earthquake caused severe damage to over 800 villages and towns in Campania and Basilicata (some of which were completely evacuated after the earthquake) and about 3,000 casualties (Postpischl et al. 1985). In particular, the macroseismic field of the first main shock, occurred on 23 November 1980 (Bottari et al. 1981), shows isoseismic lines elongated in an approximately NW–SE direction (Fig. 8a). 4.1 Preliminary analysis of the accelerometric records All the stations which recorded the November 23rd, 1980 Irpinia earthquake were equipped with three-component analogical accelerometers, although of different model. In this study, use was made only of the accelerometric data recorded by the 21 ENEA-ENEL stations.

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Fig. 8 a Location of the ENEA–ENEL accelerometric stations which recorded the 23rd November 1980 Irpinia earthquake and macroseismic field, according to DBMI04 (2004); b location of the four zones derived for equal epicentral distances and used to obtained the earthquake analogue scenario for the Irpina earthquake by LEMA_DES

Table 1 summarises the characteristic parameters of the records obtained at these stations, while Fig. 8a shows their geographic position on a satellite image with details of the macroseismic field. The analysis of the considered accelerometric records was expected to test whether the proposed method was suitable to analyse a database of records concerning the same seismic event and to assess: (a)

(b)

whether the characteristic parameters of the obtained signals show some correlation with the properties of the recording sites, such as epicentral distance and geographic location; whether the resulting energy-equivalence signals were in agreement with the attenuation law proposed for the central-southern Apennines (Sabetta and Pugliese 1987) which was obtained by considering 95 recordings from 17 Italian earthquakes, among

123

D

D

D

SNN

RCC

GRG

D

D

SSV

VSS

D

C

SGR

LRG

B

BNV

D

B

BVN

C

B

MRT

TDG

B

BRN

GSN

B

RNR

C

B

STR

C

A

ARN

A

ALT

BSC

TRR

1.310

A

−0.114

−0.264

−0.234

0.346

−0.197

0.159

−0.488

−0.260

−0.591

−0.272

0.170

−0.196

−0.217

−0.137

0.150

−0.242

−0.382

−0.342

−0.168

0.167

−0.303

−0.412

−0.242

0.599

−0.285

0.092

1.398

−0.531

1.043

−0.485

0.160

−1.835

−1.909

−2.244

3.338

−0.304

−0.326

−0.318

na

na

na

na na

−0.248

na

−0.151 −0.360

1

1

na

2

na

1

2

na

na

2

na

2

2

1

2

Recorded main shock

0.164

−0.421

−0.335

0.348

−0.455

0.992

2.606

−0.701

−1.018

−0.860

0.588

1.880

−1.698

PGA_WE (g/10)

−2.250

0.348

−0.539

0.558

1.063

1.671

PGA_UP (g/10)

−0.959

−1.519

A

CLT

BGI

PGA_NS (g/10)

Zone

Label

na

na

na

na

na

na

nr

nr

na

32

na

nr

36

na

na

39

na

38

35

nr

38.5

Cut (s)

time

Table 1 Characteristic parameters of the November 23rd, 1980 accelerometric records at the ENEA-ENEL stations

na

na

na

na

na

na

0.010

0.099

na

0.038

na

0.064

0.042

na

na

0.366

na

0.189

0.056

0.327

0.601

Arias_NS m/s (1)

na

na

na

na

na

na

0.007

0.003

na

0.013

na

0.031

0.018

na

na

0.166

na

0.118

0.023

0.168

0.443

Arias_UP m/s (1)

na

na

na

na

na

na

0.007

0.051

na

0.040

na

0.069

0.048

na

na

0.321

na

0.150

0.065

0.429

0.843

Arias_WE m/s (1)

Bull Earthquake Eng (2010) 8:813–846 827

123

123

D

D

D

D

D

SSV

SNN

RCC

GRG

VSS

na

na

na

na

na

na

nr

nr

na

0.010

na

nr

0.016

na

na

0.260

na

0.103

0.007

nr

0.469

Arias_NS m/s (2)

na

na

na

na

na

na

nr

nr

na

0.005

na

nr

0.018

na

na

0.095

na

0.042

0.005

nr

0.383

Arias_UP m/s (2)

na

na

na

na

na

na

nr

nr

na

0.014

na

nr

0.048

na

na

0.163

na

0.090

0.010

nr

0.383

Arias_WE m/s (2)

na

na

na

na

na

na

0.0030

0.0202

na

0.0080

na

0.0380

0.0021

na

na

0.0205

na

0.1232

0.0058

0.0534

0.1116

Vrif _NS m2 /s (1)

na

na

na

na

na

na

0.0014

0.0115

na

0.0030

na

0.0543

0.0008

na

na

0.0078

na

0.0980

0.0031

0.0217

0.0748

Vrif _UP m2 /s (1)

na

na

na

na

na

na

0.0011

0.0260

na

0.0115

na

0.0375

0.0062

na

na

0.0164

na

0.0627

0.0058

0.1234

0.1272

Vrif _WE m2 /s (1)

na is for not available data (due to observed amplification effects from the H/V ratios), nr is for not recorded data

D

D

C

TDG

LRG

C

ARN

GSN

C

TRR

BVN

B

B

MRT

C

B

BRN

SGR

B

RNR

BNV

B

B

STR

A

A

A

BGI

BSC

A

CLT

ALT

Zone

Label

Table 1 continued

na

na

na

na

na

na

nr

nr

na

0.0093

na

nr

0.0016

na

na

0.0778

na

0.0458

0.0020

nr

0.2522

Vrif _NS m2 /s (2)

na

na

na

na

na

na

nr

nr

na

0.0037

na

nr

0.0008

na

na

0.0204

na

0.0391

0.0010

nr

0.2452

Vrif _UP m2 /s (2)

na

na

na

na

na

na

nr

nr

na

0.0112

na

nr

0.0037

na

na

0.0173

na

0.0755

0.0019

nr

0.2673

Vrif _WE m2 /s (2)

828 Bull Earthquake Eng (2010) 8:813–846


829

which 17 recordings were selected from the 21 available for the November 23rd, 1980 earthquake (these last ones stored in the ENEA-ENEL accelerometric database). For the here applied procedure, all the 21 corrected accelerometric records of the November 23rd, 1980 earthquake, were considered. Moreover, these records underwent prior processing with a view to discard the records associated to stations with local amplification effects, since the derived equivalent inputs could not be compared with the attenuation law, obtained for real records on outcropping bedrock (Sabetta and Pugliese 1987). At this aim, H/V ratios were analysed for each measuring site and, clearing the case of evident amplification effects, the geographic positions of the stations were also considered. Since 19 of the 21 analysed stations recorded both the two main shocks of November 23rd, 1980 earthquake on a single accelerometric trace, a cut time was used to split the two events (Table 1). Nevertheless, it is worth stressing that the proposed LEMA_DES procedure can be applied also for deriving equivalent signals from records referred to amplifying sites, i.e. to be regarded as actions for structural dynamic analysis. Based on the radial distance from the epicentre of the first main shock, the stations were grouped in 4 zones of epicentral distance: zone A (0–30 km); zone B (30–60 km), zone C (60–90 km), zone D (>90 km) (Fig. 7b; Table 1). Based on the results of the preliminary analysis on seismic amplification effects, the accelerometric records at Sturno (STR), Brienza (BRN), Arienzo (ARN), Mercato San Severino (MRT), Roccamonfina (RCC), Garigliano (GRG), San Giorgio La Molara (SGR), San Severo (SSV), Sannicandro Garganico (SNN), Lauria-Galdo (LRG) and Vieste (VSS) stations were excluded from the processing of the equivalent signals by LEMA_DES, since their H/V ratios pointed out significant amplification effects which can generally be referred to thick alluvia or debris. Table 1 provides the characteristic parameters of the accelerometric records that LEMA_DES used for processing the dynamic equivalent signals. 4.2 Derived dynamic equivalent inputs A total of 30 accelerometric records obtained from 10 stations of the ENEA-ENEL network and from each recorded component of the seismic motion (i.e. NS, UP and WE) were analysed. Where available, two distinct accelerograms were obtained for the two main shocks. Hence, a total of 48 records were considered for processing via LEMA_DES program. The findings (Table 2) evidence that: (1) (2) (3) (4) (5) (6)

the minimum number of frequencies automatically selected by the LEMA_DES is 2; the minimum frequency automatically selected by LEMA_DES lies in the 0.28–1.74 Hz range; the maximum frequency automatically selected by LEMA_DES lies in the 1.72– 10.15 Hz range; the number of equivalent cycles obtained at convergence by LEMA_DES varies in the range 1–10; the duration of the resulting signals varies in the range 1.61–19.43 s; all the equivalent signals obtained by LEMA_DES have a medium to high reliability level, corresponding to CRE% values that always lie below 50%.

In particular, the distribution of the convergence process error (CRE%) and of the PGAeq error vs. the PGA of the filtered reference signal (Δr PGAeq %) shows that, for over 60% of the records, almost one of the two errors lies below 20% (Table 2; Fig. 9). This proves the validity of the assumption adopted for the PGA best-fitting process, consisting in the comparison between the LTAV and the 65% of the PGA f ilt .

123

123

9

10

5

2

5

3

4

2

5

5

3

5

5

ALT_UP_1

BGI_UP_1

BNV_UP_1

BSC_UP_1

BVN_UP_1

CLT_UP_1

GSN_UP_1

RNR_UP_1

TDG_UP_1

2

2

2

3

2

2

4

1

5

4

CLT_NS_2

2

3

4

4

BVN_NS_2

RNR_NS_2

5

BSC_NS_2

2

2

2

4

2

9

5

8

7

2

2

nc

TRR_NS_2

5

5

TRR_NS_1

ALT_NS_2

5

2

RNR_NS_1

4

GSN_NS_1

TDG_NS_1

4

4

BVN_NS_1

CLT_NS_1

3

4

4

BNV_NS_1

4

ALT_NS_1

BGI_NS_1

BSC_NS_1

nf

Label

0.38

1.23

0.72

0.85

1.57

0.65

0.46

0.95

0.6

0.51

0.94

0.39

0.88

0.56

0.55

0.42

0.69

1.29

0.68

1.16

1.49

0.57

0.77

0.75

0.93

f min (Hz)

5.06

6.91

1.86

8.66

5.05

1.92

2.29

3.45

4.89

2.45

4.92

2.49

4.66

3.73

8.94

5.47

2.00

7.28

2.97

2.79

6.50

2.84

4.47

5.72

10.15

f max (Hz)

5.25

1.61

2.76

2.35

3.18

15.35

19.43

3.13

3.33

3.88

4.24

2.55

2.25

5.34

3.62

4.75

2.88

3.09

2.93

7.74

3.34

14.02

9.10

2.65

2.12

ttot (s)

0.20

1.33

0.17

1.10

0.35

0.28

0.20

0.80

0.25

0.16

0.86

1.72

0.23

0.52

0.09

0.24

0.40

1.66

0.19

0.95

0.41

0.42

0.30

1.05

0.34

PGAeq (m/s2 )

0.008

0.037

0.002

0.081

0.007

0.060

0.024

0.057

0.004

0.003

0.090

0.206

0.003

0.048

0.002

0.008

0.262

0.120

0.003

0.258

0.014

0.109

0.030

0.094

0.010

Ariaseq (m/s)

0.010

0.003

0.001

0.012

0.000

0.021

0.001

0.010

0.001

0.002

0.010

0.113

0.001

0.025

0.001

0.005

0.006

0.008

0.001

0.022

0.000

0.045

0.008

0.019

0.001

Veq (m2 /s)

Table 2 Characteristic parameters of the equivalent signals obtained by LEMA_DES for the available records of Table 1

23.8

6.4

11.9

16.1

6.5

1.2

1.2

0.0

28.5

17.7

3.5

4.0

24.8

10.2

8.2

15.6

11.3

2.5

3.2

3.0

10.8

1.8

0.8

5.3

34.3

CRE (%)

22.1

104.6

12.0

29.3

39.1

45.3

22.8

20.3

27.1

13.0

22.7

20.4

23.4

31.1

30.5

30.7

36.0

88.4

22.0

19.1

10.2

44.9

18.3

15.5

26.5

r PGAeq (%)

M

H

M

M

H

H

H

H

M

M

H

H

M

M

H

M

M

H

H

H

M

H

H

H

M

rlb

830 Bull Earthquake Eng (2010) 8:813–846

4

5

4

4

5

5

3

ALT_WE_2

BSC_WE_2

BVN_WE_2

CLT_WE_2

RNR_WE_2

TRR_WE_2

5

3

2

5

2

2

4

2

7

2

0.88

1.08

0.7

1.08

0.37

1.08

0.55

0.28

1.74

1.31

0.75

0.37

0.55

0.53

0.85

0.65

0.42

0.65

0.28

1.05

0.55

0.62

0.81

f min (Hz)

3.78

7.67

4.07

4.58

2.69

5.35

4.13

2.11

5.35

5.21

3.85

4.50

1.72

4.41

2.73

5.77

3.43

5.46

7.36

7.22

2.42

5.98

8.92

f max (Hz)

5.64

2.77

2.84

4.60

5.39

1.84

7.26

7.13

4.02

6.09

2.65

5.39

5.44

5.65

4.69

3.06

11.89

3.04

3.56

1.89

5.42

3.21

3.69

ttot (s)

0.20

0.74

1.45

0.29

0.43

0.23

0.23

0.32

1.43

0.14

2.04

0.32

0.75

0.44

1.08

0.37

0.08

0.46

1.48

0.12

0.30

0.08

0.14

PGAeq (m/s2 )

0.008

0.052

0.144

0.006

0.036

0.002

0.015

0.011

0.110

0.003

0.236

0.005

0.082

0.034

0.203

0.009

0.002

0.017

0.216

0.001

0.022

0.001

0.004

Ariaseq (m/s)

0.001

0.004

0.067

0.001

0.044

0.000

0.007

0.026

0.004

0.000

0.040

0.005

0.032

0.020

0.036

0.002

0.002

0.005

0.142

0.000

0.012

0.001

0.001

Veq (m2 /s)

5.8

9.5

11.5

4.6

19.9

20.4

5.7

39.7

2.2

6.6

4.0

48.0

5.3

9.0

0.9

25.6

2.5

28.8

18.3

10.2

6.7

10.8

6.2

CRE (%)

12.0

4.2

35.9

60.0

22.4

0.4

22.1

18.0

59.4

12.6

65.8

13.0

51.3

23.3

34.2

41.0

23.6

35.6

4.0

24.0

33.9

43.3

40.9

r PGAeq (%)

H

H

M

H

M

M

H

M

H

H

H

M

H

H

H

M

H

M

M

M

H

M

H

rlb

Symbols in the table: nf is the number of the automatically selected frequencies, nc is the number of characteristic cycles, Ttot is the total duration of the equivalent input, PGAeq is the equivalent PGA, Ariaseq is the equivalent Arias intensity, Vri f is the integral value of the square of the velocigram for the reference signal, CRE% is the percentage convergence error, Δr P G A% is the percentage relative error on PGA, referred to the reference value (PGAri f ), rlb is the reliability of the obtained signal ( L low, M middle, H high)

4

TDG_WE_1

TRR_WE_1

8

5

5

GSN_WE_1

5

CLT_WE_1

RNR_WE_1

2

5

BVN_WE_1

3

3

3

4

2

3

4

BNV_WE_1

5

ALT_WE_1

BGI_WE_1

5

2

BSC_WE_1

4

TRR_UP_2

1

5

5

CLT_UP_2

RNR_UP_2

3

2

4

5

BSC_UP_2

BVN_UP_2

3

2

5

3

TRR_UP_1

ALT_UP_2

nc

nf

Label

Table 2 continued

Bull Earthquake Eng (2010) 8:813–846 831

123

832


Fig. 9 Relative error on PGA vs. Convergence Relative Error (CRE%)

The comparison among Vri f and Arias intensity values of the original records with the respective values of the derived dynamic signals (Veq and Ariaseq , respectively) shows a linear correlation on a bilogaritmic scale (Fig. 10a, b). The resulting correlation lines can be considered coincident, according to the statistical test on coincidence of the regressions (null hypothesis: the two datasets have the same regression line— F = 0.597 and α-type error = 0.553, Kleinbaum and Kupper 1978). Nevertheless, the relative error of the regression lines’ angle, related to 45◦ , is of about 50%; this error derives from the use of the pass-band filter applied on the original accelerograms according to the LEMA_DES procedure, which causes Veq and Ariaseq to be lower than the respective reference values of about an half order of magnitude. At this regard, it is worth considering that the obtained linear correlations demonstrate that the filtering processing has an effect which is proportional to the energy level. The comparison between the PGA values of the original records with the respective values of the derived dynamic signals (PGAeq ) shows a linear correlation on a bilogaritmic scale (Fig. 10c). The very low (90 km). The previously defined analogue scenario was derived by associating equivalent signals (eventually distinguished for components of the ground motion) for each zone of epicentral distance (Fig. 8b). At this aim all the records referred to the same zone are processed by the LEMA_DES as to compute average FFTs and PGAs (see steps from 2 to 12 in paragraph 3.2). This permits to reduce the natural variability within a sample of records and to obtain equivalent signals, which can be regarded as characteristic for the considered zone. For processing by LEMA_DES the differentiation by the horizontal seismic motion components was also preserved, so as to derive 2 multifrequential dynamic equivalent signals (NS and WE, respectively) for each distance class. In total, 8 dynamic equivalent signals were derived (Figs. 13, 14, 15) in order to obtain the analogue scenario referred to the Irpinia earthquake.

123

836


Fig. 13 Acceleration time histories (m/s2 vs. s) of the resulting equivalent signals (only horizontal components NS and WE) obtained by LEMA_DES and referred to the four zones (A–D), equidistant from the November 23rd, 1980 earthquake epicentre

123


837

Fig. 14 Reference acceleration Fourier spectra (m/s vs. Hz) of the resulting equivalent signals (only horizontal components NS and WE) obtained by LEMA_DES and referred to the four zones ( A–D), equidistant from the November 23rd, 1980 earthquake epicentre

123

838


Fig. 15 Final report of the resulting equivalent signals (only horizontal components NS and WE) obtained by LEMA_DES and referred to the four zones (A–D), equidistant from the November 23rd, 1980 earthquake epicentre

123


839

Fig. 16 Validity of the attenuation law by Sabetta and Pugliese (1987), with related standard errors (dashed line), for the real accelerometric records of the November 23rd, 1980 Irpinia main shock (a) and for the equivalent signals obtained by LEMA_DES for each recording station (b) and for each distance class (c)

With refer to the selected records, the related PGAs were calculated for the first main shock and their values proved to fit the attenuation law proposed by Sabetta and Pugliese (1987). This law relates PGA to epicentral distance only for the horizontal components of seismic motion and is considered to be applicable to the entire sector of the central-southern Apennines. The validity of the Sabetta and Pugliese (1987) attenuation law for the considered accelerometric records, of the 23rd November 1980 Irpinia earthquake, is shown in Fig. 16a. The Sabetta and Pugliese (1987) attenuation law was also compared with: i) the dynamic equivalent signals obtained for the horizontal components of the accelerometric records (Fig. 16b) and ii) the dynamic equivalent signals obtained for each distance class (Fig. 16c); these comparisons point out that the derived equivalent signals fit the attenuation law. Also the variations of Arias intensities with distance, considering the horizontal components of the seismic motion, were assessed for both the original records and the equivalent signals for each distance class. The resulting plots (Fig. 17a) show that Arias intensities have a linear

123

840


Fig. 17 a Attenuation of Arias values for the real records of the November 23rd, 1980 Irpinia main shock and the respective equivalent signals (eq) by LEMA_DES—b Ariaseq vs PGAeq for the equivalent signals by LEMA_DES, referred to the November 23rd, 1980 Irpinia main shock (the different zones A–D are also shown)

correlations on a bilogaritmic scale; these results, also taking into account the correlation showed in Figs. 11b, 16b, c, are coherent with the Italian attenuation laws of strong ground parameter for epicentral distances between 10 and 100 km (Sabetta and Pugliese 1987, 1996). The regression lines for the original records and the equivalent signals for each distance class are not coincident; nevertheless, the Common B-Coefficient test by Potthoff (1966) demonstrates their parallelism (null hypothesis: the lines are parallel—F = 1.298 and α-type error = 0.265). This result is justified by the lowering of the energy values of the equivalent signals due to the filtering processing. Also the Arias intensities vs PGA values for the horizontal components of the equivalent signals obtained for each distance class are linearly correlated on a bilogaritmic scale (Fig. 17b). This linear regression is coincident with the corresponding linear regression obtained for all the equivalent signals (Fig. 11) as proved by the statistical test on coincidence of the regressions (null hypothesis: the two datasets have the same regression line—F = 0.232 and α-type error = 0.794, Kleinbaum and Kupper 1978). The 8 derived dynamic signals were tested for reliability in terms of relative errors on convergence (CRE%) and on PGA (Δr PGAeq ). Based on these tests, the signals resulting from the LEMA_DES processing run are fully admissible, as the values of CRE% are always below 48% and the values of Δr PGAeq are always below 60%. Moreover, no particular relation has been identified between relative errors and epicentral distance. Hence, the characteristic parameters of the multifrequential dynamic equivalent signals obtained by LEMA_DES show a spatial variation consisting in both energy and ground motion lowering with increasing epicentral distance.

123


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In view of a natural risk mitigation, the resulting analogue scenario can be more generally referred to local recurrent earthquakes, since it is derived from real accelerometric records in terms of characteristic, and therefore representative, physical properties.

6 Discussion The here proposed LEMA_DES procedure, based on equivalence criteria for energy, spectral content and peak acceleration, generates multifrequential dynamic equivalent signals which may be used as inputs to various experimental applications. These applications usually involve the construction of models which should be in physical analogy with the real dynamically-acting forces taken as reference; these models may in turn rely on both physical analogue approaches (including laboratory tests on specimens) and numerical stressstrain simulations via FEM, FDM or BEM codes. The acting forces applied to these models should not only be in physical analogy with the real prototypes, but also: i) manageable by mechanical or electro-hydraulic systems used by laboratory devices (Ketcham et al. 1991; Kutter et al. 1994; Sato 1994), or ii) suitable for numerical models, in relation with the accuracy levels due to the discretisation of the considered domains as well as the physical-mechanical parameter values of the simulated materials. Experimental laboratory tests, consisting in physical analogue models, have been performed for some decades. These tests make use of shaking tables to replicate the effects that seismic motion have on models of buildings and/or infrastructures. The latest-generation tests use centrifuge devices, which may be equipped with dynamic actuators to simulate seismically-induced effects even on natural systems, such as layered soils (monodimensional basins) or inclined planes (slopes). In spite of these developments, the scaling of prototypal accelerations and the repeatability of non-cyclical signals are a still open experimental field at worldwide level. In the various analogue and numerical modelling techniques, the management of dynamic equivalent signals and the control of their spectral content, kinematic parameters and energy represent some of the most significant applications of the here proposed methodology. Indeed, their specific characteristics make an effective trade-off between complexity of the real prototype and extreme simplification of monofrequential cyclical signals. The effectiveness of this trade-off is mainly owed to: i) duration of the dynamic equivalent signal with respect to the one of the real prototypal signal; ii) the smoothed configuration of the resulting signal, which is achieved after selecting a finite number of dominant frequencies from the spectrum of the real prototype within a specific frequency band, and iii) the null value of the integral of the resulting accelerometric signal at the end of its duration. A further development of the proposed methodology may be the use of multifrequential dynamic equivalent signals to typify the corresponding real dynamic ones in terms of spectral, energy and kinematic properties, and to make their identification repeatable and objective. Based on these distinctive properties, multiple accelerometric records might be associated with different categories of sources. The related applications might be the management of records of precursor events in complex natural systems by establishing causal links between dynamically-acting forces and emitted vibrations. Such an approach might help to monitor natural phenomena (i.e. earthquakes, collapses, failures) and thus mitigate the related geological risk.

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7 Conclusions The new LEMA_DES (Levelled-Energy Multifrequential Analysis for Dynamic Equivalent Signals) approach to define multifrequential dynamic equivalent signals from accelerometric records is here proposed; in this approach, the resulting equivalent signals satisfy criteria of spectral, energy and kinematic (in terms of PGA) equivalence with respect to the real prototypes. A specially developed computational program supported the implementation of the above methodology. The LEMA_DES procedure was applied to analyse the accelerometric records for the first two main shocks of the November 23rd, 1980 Irpinia earthquake (Italy), available from the ITACA Archive (Working Group ITACA 2008). Previous analysis of the records permitted to select those representing sites with minimum local amplification effects. The 48 selected records were analysed: i) individually, to test the reliability of the proposed methodology on a high number of records, and ii) collectively, by considering concentric zones with respect to their epicentral position, to test the reliability of the resulting signals in reproducing the reference seismic scenario. In the sample consisting of the 48 selected records, correlations were analysed between the characteristic parameters of both the real and the equivalent signals. These correlations demonstrate that, in the considered test study, the proposed approach guarantees: i) the energy equivalence of the obtained signals, regardless of the energy level considered, except for a half order of magnitude, and ii) the equivalence of the PGA values with relative errors below 105%. Moreover, the relative error on the integral of the square of the velocigram of the resulting dynamic equivalent signal (Δr Veq %), obtained for multifrequential signals derived by LEMA_DES, results of an order of magnitude lower than the one obtained for the sinusoidal signals, according to the Seed and Idriss (1969), Seed and Idriss (1971) approach. This finding demonstrate that the lack of energy control in the Seed and Idriss approach causes the diverge of the obtained energy parameters from the real ones, if low frequencies are used for the construction of the sinusoidal signals. On the other hand, the proposed multifrequential approach guarantees Δr Veq % lower than about 100%, over the full range of frequencies of the investigated test study and these errors decrease with lowering of the minimum frequency which characterise the FFT of the equivalent signals. The dynamic equivalent signals obtained for the horizontal components of the records were compared with the PGA attenuation law proposed by Sabetta and Pugliese (1987). The comparison evidences that the equivalent signals are in good agreement with the attenuation law and demonstrates that the characteristic parameters of the multifrequential dynamic equivalent signals obtained by LEMA_DES approach for the November 23rd,1980 Irpinia earthquake generally reproduce its spatial variation in terms of energy as well as ground motion lowering, with increasing epicentral distance. Based on the obtained results, the LEMA_DES approach for generating multifrequential dynamic equivalent signals proves to be highly reliable for experimental applications. These applications include analogue laboratory modelling with shaking table or centrifuge devices, as well as numerical simulations based on FDM, FEM or BEM codes, focused on seismically induced effects (e.g. local seismic response, gravitational instability and loose soil liquefaction). Other applications of the here proposed approach may be performed after the following implementations: i) vary the criteria of frequency selection for different frequency ranges, ii) set a frequency-dependent weight for the energy contribution to the equivalent signal, and iii) take into account possible not null initial phases in the harmonic function.

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In conclusion, the proposed approach represents a reliable alternative to the methodologies for generating dynamic equivalent signals that are currently adopted in the field of geotechnical engineering and engineering geology. In its current configuration, the proposed methodology is mainly devoted to seismic signals; however, it may be fine-tuned and tailored to managing dynamic signals of a different nature, possibly associated with different sources, which may be of interest to a larger number of disciplines. Acknowledgments The Authors wish to thank A. Prestininzi and G. Scarascia Mugnozza for their scientific suggestions and oral communications; A. Paciello and D. Rinaldis for providing the corrected accelerometric records from the original ENEA-ENEL database; A. Pugliese for the critical review of the paper; A. Zini for the revision of the statistics. This research study was funded as part of the PRIN2005 national project “Induced seismic hazard: analysis, modelling and predictive scenarios of earthquake triggered landslides” (project leader: G. Scarascia Mugnozza) and was developed as a frame of the Co-operation Agreement between the Research Centre on Geological Risks CE.RI., of the University or Rome (Italy) “Sapienza”, and the “Laboratoire Central des Ponts et Chaussées” (Paris, France) on processing and analysis of seismic ground motions and analysis of possible relation between seismic records and local geological conditions (scientific supervisors: A. Prestininzi and J. Roudier).

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