Significance of Directivity Effects During the 2011 Lorca

Bull Earthquake Eng https://doi.org/10.1007/s10518-017-0301-9

ORIGINAL RESEARCH PAPER

Signiﬁcance of directivity effects during the 2011 Lorca earthquake in Spain

1 2 Carlos Gordo-Monso´ • Eduardo Miranda

Received: 25 August 2017 / Accepted: 17 December 2017 Ó Springer Science+Business Media B.V., part of Springer Nature 2017

Abstract The May 11th 2011, Lorca earthquake in Southeastern Spain was a moderate magnitude event (Mw 5.1) yet it caused nine fatalities, more than 300 injuries and more than 462 million euros in economic loses. Peak ground accelerations as well as response spectral ordinates far exceed expected values from various ground motion prediction models. In particular, spectral ordinates computed from recorded ground motions significantly exceed those in current Spanish probabilistic seismic hazard models, as well as those in the Spanish and European building codes. The objective of this paper is to assess directivity effects on ground motions recorded during the 2011 Lorca earthquake, and to evaluate the significance of these effects in earthquake resistant design on moderate seismic regions. In the first part of this paper, we study the likelihood of the presence of a directivity pulse, by conducting a comparison of different parameters of recorded ground motions to analytical pulses. In the second part, we relate the recorded ground motion and its inelastic displacement spectra to some recent statistical models that try to capture the displacement demand features of earthquakes presenting directivity-pulse characteristics. It is shown that simple analytical pulses are capable of reproducing very well pulse-type near-fault ground motions recorded during the event. It is concluded that directivity effects played a major role in the large impact caused by this relatively small event. Furthermore, directivity effects which are typically ignored, both in probabilistic seismic hazard analysis and in most building codes, may lead to important underestimations of ground motions.

& Carlos Gordo-Monso´ [email protected] Eduardo Miranda [email protected]

1 E. T. S. de Ingenieros de Caminos C. y P., Universidad Polite´cnica de Madrid, 28040 Madrid, Spain 2 Civil and Environmental Engineering Department, Stanford University, Stanford, CA 94305, USA 123 Bull Earthquake Eng

Keywords Lorca earthquake Á Pulse Á Directivity Á Directionality Á Near-fault Á Inelastic spectra

1 Introduction

The Lorca, May 11th 2011, earthquake in South-Eastern Spain was a damaging event, especially considering its relatively low magnitude Mw 5.1 (Lopez-Comino et al. 2012; Cabanãs et al. 2013). The earthquake lead to a death-toll of 9 people, more than 300 people injured, and approximately 462 €M in direct economic losses (Alvarez-Cabal et al. 2013). The epicenter was located approximately 2 km east-northeast of the city of Lorca on the Alhama de Murcia fault in the southeastern seismic region of the Iberian Peninsula. The focal mechanism solution corresponds to a reverse and strike-strike slip faulting mechanism with a very shallow crustal depth of approximately 3 km (Cabanãs-Rodriguez et al. 2011), to 4 km (Martinez-Solares et al. 2012). Several source models have been proposed for this earthquake (Gonza´lez et al. 2012; Martıńez-Dıáz et al. 2012a, b; Rueda et al. 2014; Santoyo 2014), for which a good review and discussion is provided by Moratto et al. (2017). The maximum peak ground acceleration in the event, which was recorded at the Lorca station, was 0.37 g in the N30W component and is more than three times larger than the one specified in the Spanish code for this region (based on a 10% probability of exceedance in 50 years) and is also the largest peak ground acceleration ever recorded in Spain (Cabanãs et al. 2013; Moratto et al. 2017). The city of Lorca has a population of about 92,000 habitants. The earthquake produced the collapse of a 4-story modern reinforced concrete building (Fig. 1a) and the partial collapse of an eighteenth century church (Fig. 1b). However, most of the damage was caused by the fragility of some non-structural elements (Alvarez-Cabal et al. 2013), such as masonry parapets at roof level, masonry infills and unreinforced masonry claddings in buildings (Fig. 2). It is well known that rupture directivity effects can lead to strong pulse-like ground motions (Bertero et al. 1978; Anderson and Bertero 1987; Hall et al. 1995; Iwan 1997; Iwan et al. 1998; Alavi and Krawinkler 2001). Earthquakes produce a series of shear dislocation waves that propagate away from the rupture. The propagation of fault rupture toward a site, at a velocity close to the shear wave velocity, causes most of the seismic energy from the rupture to arrive in the form of a single large pulse of motion that occurs early in the seismic record (Somerville et al. 1997). Furthermore, the radiation pattern of

Fig. 1 a Collapsed modern reinforced concrete building. b Partial collapse of the Santiago Church, a masonry building dating from the eighteenth century (from Caban˜as-Rodriguez et al. 2011) 123 Bull Earthquake Eng

Fig. 2 a, b Failure of unreinforced masonry cladding during the Lorca 2011 earthquake. c Failure of unreinforced masonry parapets on the roof level, the debris on the ground level are the remainings of the roof parapet completely torn apart. d Partial collapse of a reinforced concrete building (photo a from Cabanãs-Rodriguez et al. 2011, photos b–d from Alvarez-Cabal et al. 2013) the shear dislocation on the fault causes these large pulse-like ground motions that tend to be oriented in the direction perpendicular to the fault plane, leading to more intense ground motions in the normal component than in the parallel component. The potential of these near-fault pulse-like to cause large damage on structures was first recognized by Prof. Bertero and his collaborators as a result of ground motions recorded in the 1971 Mw 6.7 San Fernando Earthquake (Bertero et al. 1978). Not much attention was given to this type of ground motion until the 1994 Mw 6.9 Northridge earthquake occurred when a number of near-fault pulse-like ground motions were recorded and other investigators started working on this topic. For a literature review of work done after the 1994 Northridge earthquake the reader is referred to Alavi and Krawinkler (2001). However, as commented by Makris and Black (2004) most of the attention focused on the peak ground velocity of these pulse-like ground motions and not on the area under the acceleration pulses, referred to as the ‘‘incremental velocity’’ by Bertero et al. (1978), which provides a better characterization of what makes near-fault ground motion particularly destructive. Although near-fault pulse-like records have been included in the development of con- ventional ground motion prediction models (GMPE), formerly referred to as attenuation relationships, they do not properly account for directivity effects because most of them are aimed at predicting the geometric median of the intensity of the two horizontal components, therefore systematically underestimating the intensity of ground motions affected by directivity in the maximum direction, which is typically the fault-normal component. Furthermore, the standard deviation of most ground motion prediction models is averaged over all distances leading to underestimation of the dispersion, especially near the fault (Abrahamson 2000). The first ground motion prediction model to incorporate directivity effects was not developed until 1997, approximately 35 years after the first attenuation relations for instrumental intensity parameters were developed (Somerville et al. 1997). This first attenuation relation to incorporate directivity effects included two period-dependent modification factors: a first one to consider the position of the site relative to the geometry of the fault and its rupture direction, and a second one to amplify or deamplify in the fault-normal or fault-parallel directions, respectively. This first model only included directivity effects for earthquakes with magnitudes equal or larger than 6.5 Recently, such directivity effects have been observed in earthquakes with smaller magnitudes such as the 2004 Mw 6.0 Parkfield, earthquake (Shakal et al. 2005), the 2009 L’Aquila Mw 6.3 earthquake (Chioccarelli and Iervolino 2010) or the 2011 Mw 6.3

123 Bull Earthquake Eng

Christchurch earthquake (Bradley et al. 2014), pointing out that these damaging pulse-like ground motions can occur even in earthquakes with magnitudes between 6.0 and 6.5. This attenuation relationship with directivity effects by Somerville et al. (1997) was later modified by Abrahamson (2000) to make the directivity model distance dependent, in order to incorporate it in probabilistic seismic hazard analysis (PSHA). However, his model or more recent ones (e.g., Shahi and Baker 2013) only incorporate directivity effects for magnitudes larger or equal to 6.0. Several researchers (Lopez-Comino et al. 2012; Rueda-Nun˜ez et al. 2012; Rueda et al. 2014; Alguacil et al. 2014; Pro et al. 2014) have conjectured the presence of a directivity pulse in the 2011 Lorca 2011 earthquake. The objective of this paper is to evaluate directivity effects on ground motions recorded during the 2011 Lorca earthquake, and to evaluate the significance of these effects in earthquake resistant design on moderate seismic regions. In the first part of this paper, we study the likelihood of the presence of that pulse, by conducting a comparison of different parameters of recorded ground motions to analytical pulses. In the second part of the paper, we relate the recorded ground motion and its inelastic displacement spectra to some of the most recent statistical models that try to capture the displacement demand features of earthquakes presenting directivity-pulse characteristics.

2 Lorca 2011 earthquake ground motion data

There was an accelerograph station in the city of Lorca that recorded two horizontal ground motion signals in the N30W and N60E directions (Fig. 3a), which roughly match the fault- normal and fault-parallel directions of the causative Alhama de Murcia Fault (AMF). The corresponding elastic pseudo-acceleration spectra and their geometric mean are shown in Fig. 3b. In can be seen that spectral ordinates in the fault normal over a wide range of periods are more than twice than those in the fault parallel direction. This ﬁgure clearly illustrates how, if one were to design based on the geometric mean, one would signiﬁcantly underestimate the intensity of the motion in the fault-normal direction.

Lorca 2011 Recorded Ground Motions Lorca 2011 Pseudo-Acceleration Spectra 0.4 1.2 Fault-normal component (N30W) Fault-normal component (N30W) (b) (a) Fault-parallel component (N60E) 0.3 Fault-parallel component (N60E) 1.0 Geometric mean normal-parallel [g] a

[g] 0.2 g 0.8 0.1

0.0 0.6

-0.1 0.4

-0.2 0.2 Spectral Acceleration S

Ground Acceleration a -0.3

-0.4 0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 Time t [s] Period T [s]

Fig. 3 a Ground motion acceleration of the original signal recorded at the fault-normal and the fault- parallel directions. b Ground motion 5% damped spectra for both the as-recorded fault normal and fault- parallel ground motions, plotted along with the geometric mean spectrum 123 Bull Earthquake Eng

A field survey was carried soon after the May 11th event around the epicentral area, concluding that no signs of rupture on surface were present (Martıńez-Dıáz et al. 2012a). The AMF is a fault dipping 55°–75°NW with a reverse component that produced the surrounding sierras topography since the upper Miocene (Martıńez-Dıáz et al. 2012a, b). Tectonic interpretation of the seismological data has allowed several researchers (Martıńez-Dıáz et al. 2012a, b; Rueda et al. 2014) to determine the approximate fault area of rupture (Fig. 4a), and its slip distribution (Fig. 4b). From the latter, it is straightforward to observe how the rupture propagated from the hypocenter to an upward-southwest direction in a strike-reverse mechanism, toward the city of Lorca. The Joyner and Boore distance to the rupture surface projection is approximately Rjb = 1.26 km (Fig. 4a). No hanging-wall amplification effect is expected in the recorded ground motion, given that the recording site lies on the footwall side of the surface projection of the top edge of rupture. According to the NCSE-02 soil classification (Spanish Earthquake-Resistant Building Code, similar to NEHRP-2003 but with slightly different Vs,30 boundaries for each soil class), the recording site is located on a Class II soil (NCSE-02), (Blazquez-Martinez et al. 2014), corresponding to medium to soft rock, with shear wave velocity boundaries 400 m/ s B Vs,30 B 750 m/s, but relatively close to a large zone dominated by the deposits of the Guadalentıń river classified as Type III with 200 m/s B Vs,30 B 400 m/s. For the rest of the analysis, the underlying soil has been considered to have a Vs,30 = 575 m/s corresponding to the average of the upper and lower boundaries of class II. Figure 5a shows fault normal and fault-parallel 5% damped spectra, along with the Spanish Seismic Building Code (NCSE-02) and Eurocode 8 (EN-1998-1:2004) spectra for this soil classification.

3 Lorca 2011 earthquake pulse-like characteristics

Following the methodology proposed by Shahi and Baker (2013) to search for pulse-like patterns in earthquake ground motions and extract its prominent features (pulse period and pulse velocity and acceleration components) based on a wavelet decomposition of the

Fig. 4 a Rupture surface projection, plotted along with the Joyner and Boore distance to the ground motion recording station represented by a red segment, green yellow and orange circles represent epicenters of aftershocks, red circles represent the epicenter of the main shock and foreshock (adapted from Martı´nez- Dı´az et al. 2012a, b). b Local slip distribution along the fault plane of the Lorca 2011 earthquake, the white star shows hypocenter and the black triangle location of the recording station (adapted from Rueda-Nun˜ez et al. 2012) 123 Bull Earthquake Eng

Lorca 2011 Pseudo-Acceleration Spectra Lorca 2011 ground velocity time-histories 1.2 40 (a) Fault-normal component (N30W) (b) Fault-normal direction (N30W) Fault-parallel component (N60E) Fault-parallel direction (N60E) 1.0 Geometric mean normal-parallel 30 PGV maxima direction (N8W) Regional UHS 475yr - SISMUR [g]

a Spanish Code 475yr - NCSE02 Eurocode 475yr - Type 1 spectrum 0.8 [cm/s] 20 Eurocode 475yr - Type 2 spectrum g

0.6 10

0.4 0

0.2 Ground velocity v -10 Spectral Acceleration S

0.0 -20 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Period T [s] Time t [s]

Fig. 5 a 5% damped spectra for the fault-normal ad fault-parallel components, and their corresponding geometric mean, plotted along with the regional uniform hazard spectrum for TR = 475 years (Garcıá- Mayordomo et al. 2007; Gaspar-Escribano et al. 2008; Benito-Oterino et al. 2012), with the Spanish Seismic Building Code (NCSE-02) spectrum, and Eurocode 8 (EN-1998-1:2004) type 1 and 2 spectra for an equivalent soil classification (both of them anchored to the regionally predicted PGA as the single IM considered for their formulation). b Ground-velocity time-histories for the fault-normal direction (N30W), the fault-parallel direction (N60E), and the direction where PGV has been found 22° East of fault-normal direction (N8W) ground velocity time-history, it was found that a distinct pulse feature dominated the ground motion recordings. This method, similar in concept to that proposed by Baker (2007), enhances the recognition of pulse-like features looking for them not only in the recorded signal, but also in all possible orientations, making it orientation independent, and by enhancing the classification algorithm. The extracted pulse signal, shows a pulse period Tp = 0.48 s, a result identical to that obtained by Rueda et al. (2014) when applying the algorithm by Baker (2007). Additionally to the method proposed by Shahi and Baker, which is based on the use of the Daubechies 4 type wavelet (Db4), a similar pulse extraction was performed using the Mavroeidis and Papageorgiou (2003) wavelet (M&P). The M&P wavelet is a modification to the Gabor wavelet, except that instead of having a Gaussian time modulation it has a harmonic modulation facilitating closed-form solutions to oscillators subjected to this pulse. This wavelet, has the advantage of being defined by a small number of input parameters which have an unambiguous physical meaning. The parameter Tp controls the period of the pulse, A controls the amplitude of the harmonic, while c controls the width/duration of the modulating function which, together with Tp control the number of zero crossings in the wavelet, and finally the parameter m defines the phase of the amplitude-modulated harmonic. The results of this M&P wavelet pulse extraction show a pulse similar in shape and coincident in time with the previous one, although with a pulse period somewhat larger of Tp = 0.62 s. The other M&P wavelet parameters were found to be c= 2 and m = 0. The results of these analyses are shown in Fig. 6a for the case of the Db4 wavelet, and in Fig. 6b for the case of M&P wavelet. In both figures the record signal shown corresponds to the orientation where the strongest signal has been identified. Besides these two pulse-feature extraction methods based on the comparison between the ground motion record and the analytic pulse in the time domain, a different approach based on the comparison of the response spectra was used. In this complementary

123 Bull Earthquake Eng

Velocity Record and Db4 Wavelet Velocity Record and M&P Wavelet 40 40 (a) Fault-normal component (N30W) (b) Fault-normal component (N30W) 30 Pulse Db4 wavelet 30 Pulse M&P wavelet

20 20

10 10

0 0

-10 -10 Velocity [cm/s] Velocity [cm/s]

-20 -20

-30 -30

-40 -40

Fig. 6 a Ground motion velocity time history of the record signal plotted along with the Db4 wavelet, and b plotted along with the M&P wavelet approach, the parameters are selected to minimize the differences between the pseudo- velocity response spectrum of the earthquake record and the pseudo-velocity response spectrum of an M&P analytic pulse as modiﬁed by Alonso-Rodrı´guez and Miranda (2015). The likely pulse parameters are found by performing a least-squares ﬁt between both spectra. With this approach, the most likely M&P pulse parameters were found to be Ap = 0.041 g, fp = 1.49 Hz, gp = 1.00, a = 0.18 (Fig. 7). The extracted pulse periods by the three methods have been compared to the period providing the maximum in the elastic pseudo-velocity response spectrum Tg = 0.53 s (Fig. 8b), showing values that except for the velocity spectrum match method, are

[g] M&P Pulse Fitted to Velocity Spectrum (A =0.041 g, f =1.49Hz, g =1.00, a=0.16) a p p p 1.2 1.0 (a) Fault Normal Component (N30W) 0.8 M&P Pulse 0.6 0.4 0.2 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0

Spect. Acceleration S Period T [s]

80 [cm/s]

v Fault Normal Component (N30W) 60 (b) M&P Pulse

0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 Period T [s] Spect. Velocity S

0.50 [g] g Fault Normal Component (N30W) 0.25 (c) M&P Pulse

0.00

-0.25

-0.50

Acceleration a 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Time t [s]

Fig. 7 a Pseudo-acceleration 5% damped spectra for the N30W component, and for the M&P wavelet with pulse parameters that match the pseudo-velocity spectrum. b Pseudo-velocity spectra for the fault-normal component, and for the M&P wavelet. c Acceleration record of the fault-normal component and of the velocity-spectrum ﬁtted pulse 123 Bull Earthquake Eng

Table 1 List of pulse periods obtained with each extraction method

Extraction method Pulse period Tp [s] Tg/Tp

Wavelet Db4 0.48 1.10 Wavelet M&P 0.62 0.85 Velocity spectrum match 0.67 0.79

Lorca 2011 Pseudo-Acceleration Spectra Lorca 2011 Pseudo-Velocity Spectra 1.2 80 (a) Fault-normal component (N30W) (b) Fault-normal component (N30W) Pulse Db4 wavelet 70 Pulse Db4 wavelet 1.0 Pulse M&P wavelet Pulse M&P wavelet

[g] 60 a

0.8 [cm/s] v 50

0.6 40

30 0.4

0.2

Spectral Velocity S 10 Spectral Acceleration S

0.0 0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 Period T [s] Period T [s]

Fig. 8 a Elastic pseudo-acceleration 5% damped spectra for the fault-normal component, and Db4 and M&P pulses. b Elastic pseudo-velocity spectra for the fault-normal component, and Db4 and M&P pulses somewhat larger than the correlation factor of q= 0.77 established by Ruiz-Garcıá(2011). Table 1 summarizes the period values obtained by each extraction methodology. The differences in period, which can be attributed to the uncertainty intrinsic to each methodology, become relevant when assessing the significance of the pulse in terms of the intended intensity measure: if this were a response spectrum, the spectrum match would provide a better fit. Once that the residual ground motion has been extracted, the cumulative squared velocity (CSV) was computed, in order to apply the criterion by Baker (2007) and to identify if the build-up of pulse energy arrived before than a large build-up of the original signal energy occurs. The limits proposed of obtaining a 10% of the CSV in the extracted pulse before obtaining a 20% of the CSV in the original ground motion are satisfied, as can be appreciated in Fig. 9b for the M&P pulse. The zero-crossings of the significant pulse are shown in intervals 1 and 2 of Fig. 9a, while Fig. 9b shows the contribution to the cumulative squared velocity (CSV) for this interval totaling a 79% of the CSV, along with the corresponding CSV for the extracted pulse. With the previous results at hand, one can observe that the relationship between the extracted pulse period and magnitude for the Lorca 2011 earthquake fits very well with the one proposed by Shahi and Baker (2013) for the ground motions showing pulse-like features in the NGA West2 database (Fig. 10a), even if the original research recommended not to use such a relationship for pulse periods shorter than Tp = 0.6 s. Similarly, the Mw- Tp relationship obtained by Mavroeidis and Papageorgiou (2003) for their ground motion catalogue fits with reasonable accuracy to the pulse period and magnitude for the Lorca event. 123 Bull Earthquake Eng

Fault Normal Component (N30W) Normalized Cumulative Squared Velocity 0.4 1.0 (b) 1 2 (a) 1 2 0.9 0.3 0.8 0.2

[g] 0.7

g 30.8% 0.1 0.6

0.0 0.5

0.4 -0.1 0.3 Acceleration a -0.2 48.4% 0.2 -0.3 0.1 Fault-normal component (N30W) Pulse M&P

-0.4 Ratio of Cumulative Squared Velocity 0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Time t [s] Time t [s]

Fig. 9 a Fault-Normal record component, where intervals 1 and 2 show signiﬁcant zero-crossings of the pulse. b Normalized cumulative squared velocity for the fault-normal component and the M&P pulse, where intervals 1 and 2 corresponding to zero-crossings amount 79% of the CSV

T - M Relationship Amplification factor A =S /S p w f a,pulse a,residual 5.5 Fault-normal / Residual Db4 (a) 5.0 (b) 101 Fault-normal / Residual M&P a,residual 4.5 Pulse Db4 / Residual Db4 /S Pulse M&P / Residual M&P 4.0 Shahi and Baker, 2011 [s] p

a,pulse 3.5 =S f 3.0

2.5 100 2.0

Pulse Period T NGA-West2 database 1.5 M&P 2003 database Shahi & Baker 2013 1.0 M&P 2003 with self-similarity Lorca 2011 Earthquake (Db4) 0.5 Lorca 2011 Earthquake (M&P) -1 10 0.0 5.0 5.5 6.0 6.5 7.0 7.5 8.0 0.00.20.40.60.81.01.21.41.61.82.0

Magnitude M Pulse amplification factor A w Period T [s]

Fig. 10 a Pulse period versus earthquake magnitude for the NGA-West2 database records containing a pulse, the M&P database and for the Lorca 2011 earthquake, plotted along with the (Shahi and Baker 2011) and (Mavroeidis and Papageorgiou 2003) expressions for pulse-period expectation. b Spectral acceleration ampliﬁcation factor Af due to directivity pulse (Shahi and Baker 2011), and pulse to residual ratios for each wavelet

Shahi and Baker proposed a local amplification factor Af = Sa,pulse/Sa,residual which amplifies spectral ordinates in the neighborhood of the pulse period. For this purpose, they adopted the functional form previously proposed by Ruiz-Garcıá and Miranda (2005). The amplification factor for the spectral acceleration due to the directivity pulse, that is, the ratio between the spectral acceleration of the extracted pulse to the spectral acceleration of the residual ground motion is plotted in Fig. 10b along with the expression proposed by Shahi and Baker (2011) for this parameter. This plot shows that the main characteristic of the pulse, the amplification around periods close to the pulse period is captured by the Shahi and Baker expression, although the amplification of the Lorca 2011 earthquake is somewhat larger than the one resulting from their statistical fit. The expression for the standard deviation of this amplification factor Af, as proposed by the authors, is related to the standard deviation used in a particular ground motion prediction equation (GMPE), and

123 Bull Earthquake Eng therefore its relevance will be analyzed later in this paper when the comparison to some GMPEs are performed.

4 Lorca 2011 earthquake directionality characteristics

Different authors (e.g., Baker and Cornell 2006; Boore et al. 2006; Boore 2010) have pointed out the difference in terms of spectral acceleration that can be present in a given pair of orthogonal ground motion records of the same event, and their relation to the spectral acceleration predicted by some GMPE model. The usual intensity measure of many attenuation models is the geometric mean of two spectral ordinates computed from as-recorded orthogonal records. This geometric mean value can depart significantly from the spectral acceleration in an orientation where a maximum would occur, especially in those cases where large polarization of the ground motion can be present. Boore (2010) developed direction-independent measures spectral ordinates. SaRotD50 corresponds to the median of spectral ordinates at all possible orientations, in other words, 50% of the orientations will provide larger spectral acceleration values, and the remaining 50% will provide smaller values. By contrast, SaRotD100 and SaRotD00 are intensity measures that provide information on what the maximum and minimum spectral acceleration in any possible direction, respectively. Figure 11 shows polarization plots of the Lorca 2011 earthquake for three chosen periods, one being the pulse period Tp = 0.48 s, where the red discontinuous line shows spectral acceleration amplitude at any given direction for that particular period. From this graph, one can observe a strong polarization of the ground motion, especially for orientations close to 25° East of the fault-normal direction. Fig- ure 5b shows the peak ground velocity (PGV) as a function of orientation, showing a clear maxima at approximately 22° East of the fault-normal direction. The orientation independent spectra corresponding to the minimum, median, and maximum accelerations are plotted in Fig. 12a, along with the as-recorded N30W and N60E components and their respective geometric mean. It can be seen that the fault-normal component practically corresponds to the maximum spectral ordinates in any direction SaRotD100. The degree of directionality or polarization of the ground motion can be analyzed by the ratio SaDRot100/SaDRot50, which is a measure of how large the strongest component is respect to the median value obtained for any arbitrary direction. This directionality pffiffiffi amplification factor can be shown to be, at maximum 2 = 1.41 for a perfectly polarized ground motion. Figure 12b shows the SaDRot100/SaDRot50 amplification factor computed for the recorded Lorca 2011 earthquake, along with the expression proposed by Shahi and Baker (2014) and ± one standard deviation (± r) ranges. From the plot we can observe how the Lorca 2011 earthquake presented strong directionality effects, larger than most of the ones derived empirically from the NGA-West2 database, and for many periods of engineering interest very close to a perfect polarization.

5 Lorca 2011 earthquake as predicted by NGA-WEST2 GMPE

With the results obtained in previous sections regarding ground motion directionality and forward-directivity, we have compared the recorded ground motion N30W component to the results obtained from the 2008 Boore and Atkinson (B&A) GMPE (2008) adjusted to 123 Bull Earthquake Eng

Lorca 2011 Displacement Response Trace (T=0.2s) Lorca 2011 Displacement Response Trace (T=0.48s)

90 90 (a) 1 (b) 1 120 60 120 60 0.8 max

max 0.8 Δ Δ / / Y 0.6 Y 0.6 Δ 150 30 Δ 150 30 0.4 0.4

0.2 0.2

180 0 180 0

210 330 210 330

Sa/Sa Sa/Sa RotD100 RotD100 Displacement along fault-normal axis Δ / Δ 240 300 Displacement along fault-normal axis Δ / Δ resp max resp max 240 300 Fault trace Fault trace 270 270

Displacement along fault-parallel axis Δ /Δ Displacement along fault-parallel axis Δ /Δ X max X max

Lorca 2011 Displacement Response Trace (T=1s)

90 (c) 1 120 60

max 0.8 Δ / Y

Δ 0.6 150 30 0.4

0.2

180 0

210 330

Sa/Sa

Displacement along fault-normal axis RotD100 Δ / Δ resp max 240 300 Fault trace 270 Displacement along fault-parallel axis Δ /Δ X max

Fig. 11 Normalized displacement polarization plots, where Dresp is the elastic displacement response and Dmax is the maximum displacement in each direction for a single degree of freedom oscillator with vibration period of a T = 0.20 s, showing maximum polarization at an angle fairly close to the fault-normal direction (N30W recorded ground motion). b T = 0.48 s, the pulse period, showing maximum polarization at an angle 30° East of fault-normal direction. c T = 1.00 s, showing maximum polarization at an angle 25° East of fault-normal direction take into account the polarization and pulse-directivity effects as proposed by Shahi and Baker (2011, 2014). The results shown in Fig. 13 have been computed for an earthquake with reverse-slip fault mechanism, Mw 5.1, Joyner and Boore distance Rjb = 1.26 km, and aVs,30 = 575 m/s, which likely correspond to the characteristics of the recorded ground motion at the Lorca accelerometer. The graphs shown correspond to the bare B&A2008 GMPE (Fig. 13a), adjusted to take into account only the directionality effect (Fig. 13b), adjusted to take into account only the directivity pulse (Fig. 13c), and adjusted to take into account both the directionality and directivity effects (Fig. 13d). From Fig. 13 we can note that, although the value of PGA and spectral ordinates in the short period range (e.g. between 0 and 0.2 s) show differences from the expected median 123 Bull Earthquake Eng

Lorca 2011 Sa /Sa amplification factor (a) Lorca 2011 Pseudo-Acceleration Spectra (b) RotD100 RotD50 1.2 1.45 Fault-normal component (N30W) Fault-parallel component (N60E) 1.40 RotD50 1.0 Geometric mean

[g] Sa /Sa 1.35 a Drot00 Sa Drot50 0.8 Sa 1.30 Drot100

RotD100 1.25 0.6 1.20

0.4 1.15

1.10 ±σ Shahi & Baker 2014 0.2 Shahi & Baker 2014 median Spectral Acceleration S 1.05 Lorca 2011 earthquake Maximum completely polarized 0.0 1.00

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 Amplification factor Sa 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 Period T [s] Period T [s]

Fig. 12 a Acceleration 5% damped spectra for both the fault-normal and fault-parallel components, their geometric mean, and orientation independent spectra for the 0, 50, and 100% percentiles. b Spectral amplification factor SaDRot100/SaDRot50 due to polarization of the response for the Lorca 2011 earthquake, ploted along with the median and ± r of the Shahi and Baker (2014) model, and the theoretical maximum pffiffiffi value of SaDRot100/SaDRot50 = 2 corresponding to a completely polarized response value, these still fall within the uncertainty range of this particular GMPE. However, the results show how the recorded N30W ground motion departs significantly from the B&A 2008 GMPE, with many spectral ordinates (e.g., between 0.2 and 0.8 s) being more than two standard deviations above the median values, and how the adjustments proposed by Shahi and Baker present reasonably good agreement with the recorded ground motion if both directionality and directivity are taken into account.

6 Lorca 2011 earthquake inelastic spectra

Baez and Miranda (2000) showed that modifying the elastic spectral ordinates to take into account directivity effects in near-fault pulse-like ground motions was not enough because most structures are not designed to remain elastic and because the ratio of inelastic to elastic spectral ordinates of these types of ground motions can differ from those recorded away from the rupture. Various authors (e.g., Baez and Miranda 2000; Akkar et al. 2004; Ruiz-Garcıá and Miranda 2005; Ruiz-Garcıá 2011; Iervolino et al. 2012) have proposed expressions for describing inelastic to elastic displacement ratios for near-fault pulse-like ground motions. The displacement and force time-histories corresponding to systems with periods ranging from 0.01 to 2.00 s, force reduction factors (R = 1, 2, 4, 5, 6), and a post-yield stiffness ratio of 3% for the Lorca 2011 N30W component have been computed. In Fig. 14 three displacement time-histories are shown for different period ratios T/Tp (short period range, pulse period range, and long period range) for the stated range of force reduction factors. In all cases, the displacement time-histories seem dominated by a large abrupt inelastic displacement increment soon after the 6 s mark, rather than a steady increase in inelastic displacement produced by consecutive pulses. Ruiz-Garcıá and Miranda (2003) proposed estimating the ratio of inelastic to elastic spectral ordinates with an expression, which formed the basis of the simplified expression (1) included in ASCE 41-06.

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Boore & Atkinson 2008 GMPE - No Pulse, Shahi & Baker 2014 Correction - No Pulse, No Directionality Yes Directionality 1.8 1.8 ±σ Boore & Atkinson 2008 (b) ±σ Shahi & Baker 2014 1.6 (a) Median Boore & Atkinson 2008 1.6 Median Shahi & Baker 2014 Lorca 2011 earthquake Lorca 2011 earthquake [g] 1.4 [g] 1.4 a a

1.2 1.2

1.0 1.0

0.8 0.8

0.6 0.6

0.4 0.4 Spectral Acceleration S 0.2 Spectral Acceleration S 0.2

0.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 Period T [s] Period T [s]

Shahi & Baker 2011 Correction - Yes Pulse, Shahi & Baker 2011 and 2014 Corrections - Yes Pulse, No Directionality Yes Directionality 1.8 1.8 ±σ (c) ±σ Shahi & Baker 2011 (d) Shahi & Baker 2011, 2014 1.6 Median Shahi & Baker 2011 1.6 Median Shahi & Baker 2011, 2014 Lorca 2011 earthquake

Lorca 2011 earthquake [g] a [g] 1.4 1.4 a

1.2 1.2

1.0 1.0

0.8 0.8

0.6 0.6

0.4 0.4 Spectral Acceleration S

Spectral Acceleration S 0.2 0.2

0.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 Period T [s] Period T [s]

Fig. 13 a Boore and Atkinson (2008) 5% damped spectral acceleration median prediction and ± r intervals. Response spectra for the Lorca 2011 N30W component, b The Shahi and Baker (2014) modified model of spectral acceleration to the B&A (2008) model, considering the amplification due to directionality of the strongest component. c The Shahi and Baker (2011) modified model, considering the amplification due to the near-fault forward directivity pulse. d The Shahi and Baker (2011, 2014) modified model due to both directionality and directivity pulse 1 C ¼ 1 þ ðÞÁR À 1 ð1Þ R a Á T2 where R is the ratio of lateral strength required to maintain the system elastic to the lateral strength of the structure, T is the fundamental period of vibration of the structure, and a is a parameter that depends on site conditions. Ruiz-Garcıá and Miranda (2005), Ruiz-Garcıá (2011) proposed modifications to the previous equations to estimate inelastic displacements of structures near major faults as follows: 2 3 6 1 7 2 C 1 R 1 4 5 h Tp exp h Ln T 0:08 ; R ¼ þ ðÞÁÀ 2 þ 2 Á T Á 3 Á Tp À h T 1 Á Tp ð2Þ

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Displacement history T/T =0.4 Displacement history T/T =1.0 p p 30 80 R=1.0 (b) R=1.0 (a) R=2.0 R=2.0 60 20 R=4.0 R=4.0 R=5.0 R=5.0 R=6.0 R=6.0 40 [mm]

[mm] 10 Δ Δ 20 0 0

-10 -20 Displacement Displacement -20 -40

-30 -60 0 2 4 6 8 10 12 14 16 0246810121416 Time t [s] Time t [s]

Displacement history T/T =2.1 p 60 (c) R=1.0 R=2.0 40 R=4.0 R=5.0 R=6.0 20 [mm] Δ 0

-20

-40 Displacement

-60

-80 0 2 4 6 8 10 12 14 16 Time t [s]

Fig. 14 (a–c) Displacement time-histories for increasing force reduction factors for systems with natural period T = 0.20 s (T/Tp = 0.40), T = 0.48 s (T/Tp = 1.0), and T = 1.00 s (T/Tp = 2.10)

Similarly, Iervolino et al. (2012) proposed a similar functional form as a function of the period normalized to the pulse period T/Tp but added an extra term to capture that local maximum in displacement demand. All the four expressions (ASCE/SEI 2007; Ruiz- Garcıá and Miranda 2003; Ruiz-Garcıá 2011; Iervolino 2012) have been evaluated (with values Tg = 0.56, and Tp = 0.48) for force reduction factors of R = [4, 6], and then compared to the inelastic to elastic displacement ratios CR obtained for the Lorca 2011 earthquake. Figure 15a, b shows the computed CR ratios without period normalization, and Fig. 15c, d with the period normalized to T/Tp. The apparent trends show that the Lorca 2011 earthquake presented larger inelastic displacements than what could be expected at all range of periods and force reduction factors for the Iervolino et al. (2012) expression (in the order of ?r), while the Ruiz-Garcıá and Miranda (2005) expression shows a better fit in predicting the inelastic displacements. The Ruiz-Garcıá and Miranda (2005), Ruiz- Garcıá(2011) expression shows a more conservative trend, predicting larger displacements than observed for T C 0.25 s. However none of the aforementioned expressions is able to capture the large local maxima occurring at T = 0.20 s, or conversely T/Tp = 0.40. On the other hand, the expressions by ASCE/SEI (2007) and by Ruiz-Garcıá and Miranda (2003), clearly underestimate the inelastic displacement caused by the Lorca 2011 earthquake at

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Inelastic to elastic displacement ratio C for R=4 Inelastic to elastic displacement ratio C for R=6 R R (a) 4.5 (b) 4.5 Lorca 2011 earthquake Lorca 2011 earthquake 4.0 Median ASCE 41-06 4.0 Median ASCE 41-06 Median Ruiz-Garcia & Miranda, 2003 Median Ruiz-Garcia & Miranda, 2003 3.5 Median Ruiz-Garcia, 2011 3.5 Median Ruiz-Garcia, 2011 Median Iervolino et al. 2012 Median Iervolino et al. 2012 elast elast +σ Iervolino et al. 2012 +σ Iervolino et al. 2012 Δ Δ 3.0 3.0 / / 2.5 2.5

2.0 2.0 inelast,R inelast,R Δ Δ 1.5 1.5 = = R R 1.0 1.0 C C

0.5 0.5

0.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 Period T [s] Period T [s]

Inelastic to elastic displacement ratio C for R=4 Inelastic to elastic displacement ratio C for R=6 R R (c) 4.5 (d) 4.5 Lorca 2011 earthquake Lorca 2011 earthquake 4.0 Median ASCE 41-06 4.0 Median ASCE 41-06 Median Ruiz-Garcia & Miranda, 2003 Median Ruiz-Garcia & Miranda, 2003 3.5 Median Ruiz-Garcia, 2011 3.5 Median Ruiz-Garcia, 2011 Median Iervolino et al. 2012 Median Iervolino et al. 2012 elast

+σ Iervolino et al. 2012 elast +σ Iervolino et al. 2012 Δ 3.0 3.0 Δ / / 2.5 2.5

2.0 2.0 inelast,R inelast,R Δ

1.5 Δ 1.5 = = R

1.0 R 1.0 C C

0.5 0.5

0.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 Normalized Period T/T Normalized Period T/T p p

Fig. 15 Inelastic displacement ratio CR of inelastic-to-elastic displacements for different force reduction factors for the Lorca earthquake, plotted along with the median prediction by Ruiz-Garcı´a & Miranda (2003), ASCE/SEI (2007), Ruiz-Garcı´a(2011), and with the median and ? r prediction by Iervolino et al. (2012) a for R = 4, b for R = 6, c for R = 4 with normalized abscissa T/Tp, d for R = 6 with normalized abscissa T/Tp periods shorter than T/Tp = 0.8, not surprisingly because they do not intend to represent the increased displacement demands caused by directivity.

7 Conclusions

An analysis of ground motions recorded during the Lorca, May 11th 2011, earthquake has been carried out in terms of spectral accelerations and in terms of inelastic displacement spectra, both aimed at comparing them with recent developments in ground motion prediction models and in inelastic response models for near-fault zones. Peak ground accelerations and response spectra ordinates at the Lorca recording station were significantly larger than those expected using probabilistic seismic hazard analyses and those specified in the Spanish and European building codes. We conclude that these unexpectedly large accelerations were caused by a strong forward-directivity pulse with a period close to Tp = 0.6 s. This finding has important consequences for earthquake resistant design because directivity effects are currently not explicitly addressed in most seismic codes.

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Furthermore, this earthquake illustrates that important directivity effects can occur even in Mw 5.1 events. It is shown that two relatively simple wavelets are capable of reproducing the main features of the time series of the fault-normal component of the recorded ground motions as well as the main characteristics of response spectral ordinates. Furthermore, modiﬁca- tions recently proposed for considering directionality and directivity effects based on NGA2 ground motions, despite currently being recommended only for seismic events with Mw [ 6.0, together with expressions of inelastic displacements ratios speciﬁc for near- fault pulse-like ground motions, if they are applied to these smaller magnitude events, are capable of capturing the main features of both elastic and inelastic spectra of the motion recorded in the fault-normal direction.

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