Predictive model of Arias intensity and Newmark displacement forregional scale evaluation of earthquake-induced landslide hazardin Greece

Konstantinos Chousianitis a,n, Vincenzo Del Gaudio b, Ioannis Kalogeras a,Athanassios Ganas a

a National Observatory of Athens, Institute of Geodynamics, Lofos Nymfon, 11810 Athens, Greeceb Dipartimento di Scienze della Terra e Geoambientali, Universita degli Studi di Bari, Campus, via E. Orabona 4, 70125 Bari, Italy

a r t i c l e i n f o

Article history:Received 8 November 2013Received in revised form18 May 2014Accepted 25 May 2014

Keywords:Newmark displacementArias intensityAttenuation relationEarthquake-induced landslidesGreece

a b s t r a c t

Defining the possible scenario of earthquake-induced landslides, Arias intensity is frequently used as ashaking parameter, being considered the most suitable for characterising earthquake impact, whileNewmark's sliding-block model is widely used to predict the performance of natural slopes duringearthquake shaking. In the present study we aim at providing tools for the assessment of the hazardrelated to earthquake-induced landslides at regional scale, by means of new empirical equations for theprediction of Arias intensity along with an empirical estimator of coseismic landslide displacementsbased on Newmark's model. The regression data, consisting of 205 strong motion recordings relative to98 earthquakes, were subdivided into a training dataset, used to calculate equation parameters, and avalidation dataset, used to compare the prediction performance among different possible functionalforms and with equations derived from previous studies carried out for other regions using global and/orregional datasets. Equations predicting Arias intensities expected in Greece at known distances fromseismic sources of defined magnitude proved to provide more accurate estimates if site condition andfocal mechanism influence can be taken into account. Concerning the empirical estimator of Newmarkdisplacements, we conducted rigorous Newmark analysis on 267 one-component records yielding adataset containing 507 Newmark displacements, with the aim of developing a regression equation thatis more suitable and effective for the seismotectonic environment of Greece and could be used forregional-scale seismic landslide hazard mapping. The regression analysis showed a noticeable highergoodness of fit of the proposed relations compared to formulas derived fromworldwide data, suggestinga significant improvement of the empirical relation effectiveness from the use of a regionally-specificstrong-motion dataset.

& 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Greece is characterised by high seismicity, which is attributedto its location, on top of the convergence boundary of twolithospheric plates, i.e. the European plate, which is being over-thrusted and moves to the southwest, and the African plate whichis being subducted and moves towards an approximately northdirection. Additionally, as effect of topographic and geologicalcharacteristics of its relief, the Greek area is subject to diffusephenomena of slope instability, which are exacerbated by the highseismic activity. These reasons have resulted in the fact thatearthquake-induced landslides have appeared almost everywhere

within the Greek territory, with the exception of the north Greekmainland [47]. This makes the estimation of where and in whatshaking conditions earthquakes are likely to trigger landslides akey element in hazard assessment. Such estimation comprisesan important information which can be used in conjunction withother commonly used factors (e.g. [59,5,6,48,60]) in order tooptimise land-use planning and decision-making procedure.

An earthquake can cause a slope to become unstable by theinertial loading it imposes or by causing a loss of strength in theslope materials. One of the shaking parameters that proved to bemore representative of the earthquake impact on slope stability isthe Arias intensity [4], which is proportional to the total energytransmitted by seismic waves to soil during an earthquake. Thusthe estimation of the Arias intensity expected on landslide proneslopes as effect of an earthquake of defined characteristics isuseful for a preliminary delimitation of area potentially subject

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Soil Dynamics and Earthquake Engineering

http://dx.doi.org/10.1016/j.soildyn.2014.05.0090267-7261/& 2014 Elsevier Ltd. All rights reserved.

n Corresponding author.E-mail address: chousianitis@noa.gr (K. Chousianitis).

Soil Dynamics and Earthquake Engineering 65 (2014) 11–29

to seismically induced mass movements, where a successive moreadvanced hazard analysis can be worthwhile to be carried out.

A possible successive level of hazard analysis refinement canbenefit from simplified models of slope stability analysis underdynamic conditions, which are applicable to regional scale evalua-tion. Among slope stability models, the permanent-displacementanalysis developed by Newmark [46] is often used to deriveestimates of coseismic landslide displacements for a givenrecorded or synthetic accelerogram. Newmark's analysis modelsthe part of the slope which is under stress as a uniform blocksliding over an inclined surface. For a known critical acceleration,it calculates the cumulative permanent displacement of the blockrelative to its base under a given shaking by means of a doubleintegration of its acceleration-time history. Thus, a conventionalNewmark analysis requires the selection of an appropriate earth-quake record and the determination of the critical acceleration ofthe investigated slope. This approach has been successfully appliedin many cases to evaluate, predict and map earthquake-inducedslope displacements (e.g. [70,69,23,49]). However, because strong-motion records at specific sites are not always available, severalrelations between seismic ground-motion parameters and com-puted landslide displacements have been developed, avoiding thecomputational complexity and the difficulties of selecting appro-priate earthquake time-histories associated with the conventionalNewmark analysis.

In view of providing, relatively to the Greece region, tools fordifferent level of evaluations of the landslide seismo-inductionhazard, in the present study we developed empirical relationshipsto predict expected values both of Arias intensity on landslide-prone

slopes and of coseismic landslide displacements according to New-mark's model, as effect of earthquakes of prefixed characteristics.We used a dataset of strong-motion records that incorporates themost recent information available spanning up to mid 2013. For thedevelopment of both equations, we separated a subset of recordsused to obtain the regression coefficients, from a second datasample that we used to compare the effectiveness of differentrelations in order to select the optimum model. We tried to makeboth samples as homogeneously distributed as possible over theindependent variables adopted in each regression model.

The most general functional form of the new predictiveequation for Arias intensity incorporates moment magnitude,epicentral distance, fault plane solution mechanism, and sitecategory. The coefficients of the explanatory variables werecalculated by employing a two-step procedure separating thedetermination of parameters representative of the energy releaseat source from those accounting for propagation effects. Withregard to the empirical estimator of Newmark displacementsuitable for the geological and seismotectonic setting of Greece,a rigorous Newmark analysis was conducted on a selected up-to-date dataset of strong ground-motion records. We tested formulasof different forms whose coefficients were computed throughmultivariate regression analyses. The derived properly calibratedregional relation is expected to considerably improve the effec-tiveness of the empirical estimator for the Greek area in compar-ison to equations that have been developed using global datasets.The derived formula allows the estimation of landslide dis-placement as a function of shaking intensity, quantified by Ariasintensity, and critical acceleration for regional earthquake-induced

Fig. 1. Epicentre distribution of the earthquakes used in the analyses along with spatial distribution of the Greek strong-motion stations used in the present study. Blacklines show the traces of the Hellenic Arc-Trench System (HAT), the Cephalonia Transform Fault (CTF), the Apulian Thrust (AT), the Volcanic Arc (VA) and the North AnatolianFault (NAF). Also shown the North Aegean Trough (NAT), the South Cretan Trough (SCT), the Pliny Trench (PT) and the Strabo Trench (StT).

K. Chousianitis et al. / Soil Dynamics and Earthquake Engineering 65 (2014) 11–2912

landslide hazard analysis and can be used to create scenarios ofearthquake-induced slope destabilisation.

2. Strong motion dataset

The strong-motion dataset that we used for all the analysescarried out in the present study is composed of 205 accelerogramsof the two horizontal components from 99 recording stations(Fig. 1). It is based on the HEAD v1.0 [67] strong-motion databasefor the period 1972–1999 and on selective strong-motion recordsof NOA-IG dataset for the period 2000–2013. The HEAD v1.0 isthe most comprehensive and homogenised database in Greecefor the aforementioned period, since although it consists mainlyof analogue records, their processing resulted after a relocationprocedure of the earthquakes [63] and a unified processingprocedure applied on a selective dataset of strong-motion recordsfrom NOA-IG and ITSAK accelerographic network. Since 2000 aunification of the Greek seismological networks occurred provid-ing in such a way more reliable earthquake parameter estimations,while the strong-motion analogue instruments were graduallyreplaced by digital ones and thus digitisation procedure errorseliminated. Especially since 2009, a serious instrumentationupgrade started in Greece with instruments of high resolutionand with a densification of the strong-motion network. The newgeneration instruments record continuously and provide the datain real time, enriching in such a way the strong-motion datasample with records of lower magnitudes in real near field and oflarger magnitudes in regional distances, as well.

Table 1 summarises the 98, mainly normal and strike-slipfaulting, Greek earthquakes from which the set of strong-motionrecords was obtained, while Fig. 1 presents their epicentraldistribution. It consists of all the major earthquakes occurred since1973, with epicentres covering the major part of Greece. Theirmagnitude ranges from Mw¼3.2 to Mw¼6.7, and the epicentraldistances cover a range from 1 km to 195 km. The data distributionwith respect to moment magnitude, epicentral distance, and siteclass is illustrated in Fig. 2. All of the records used are from strong-motion instruments that have been installed in the lower level ofbuildings of limited size (one-storey or at least low risen buildings)and at various surface geological conditions. The latter wereclassified into site typologies on the basis of the average shear-wave velocity of surface material in the top 30 m (Vs30), adoptingthe five Universal Building Code categories (A, B, C, D and E)proposed by NEHRP [45,68] (Table 1). Site class E (Vs30o180 m/s)were not included in the analyses since none of the accelerometricstations was installed in such geological conditions.

3. Predictive attenuation relation for Arias intensity

The most commonly used parameter to describe earthquakeground motion is peak ground acceleration, but since the work ofWilson and Keefer [71], the use of the Arias intensity, Ia, has beenproposed to quantify the effect of seismic shaking on groundfailure phenomena. This measure is defined as follows:

Iα ¼π2g

Z tf

0½αðtÞ�2d t ð1Þ

where g is the acceleration due to gravity, a(t) is the recordedacceleration time-history and tf is the duration of the groundmotion. This definition reveals the main advantage of Ariasintensity over PGA, in that it measures the total accelerationcontent of the record rather than just the peak value, providinga more complete characterisation of the shaking energy than PGA.It also has the advantage over other intensity measures, to be more

objective and comparable from one earthquake to the other,making it a reliable indicator of the capacity of the earthquakeshaking to trigger landslides [17]. Wilson [72] suggested Ariasintensity threshold values of 0.15 m/s for disrupted landslides and0.5 m/s for coherent slides, lateral spreads, and flows. Additionalanalyses by Keefer and Wilson [30] suggested minimum Ariasintensity of 0.11 m/s for the initiation of disrupted soil slides,0.32 m/s for the initiation of coherent slides, and 0.54 m/s forlateral spreads and flows, whereas successively Wilson [72] foundthe best-fit threshold for disrupted landslides to be 0.10 m/s.

The strong relation between Newmark displacement and Ariasintensity, as a parameter representing the energy of the seismicforces, and the current availability of a large dataset of strong-motion records led us to develop new Ground Motion PredictionEquations (GMPE) to estimate Arias intensity as a function ofmoment magnitude, epicentral distance, focal mechanism, and sitecategory. The high attenuation that characterises the Greek seis-motectonic environment is expected to have an impact on theground motion values at regional distances (4150 km), a fact thatcould cause considerable mismatch between values observed andcalculated through the ground motion predictive equations thathave been calibrated with data from epicentral distances shorterthan 150 km. So far, Danciu and Tselentis [12] have proposed anattenuation law for Arias intensity using data from 1972 to 1999.The dataset of the current study spans further than 1999 andincludes data until mid 2013. The importance of such a dataset inthe development of new attenuation relationships stems from theconsiderable densification of the strong-motion networks inGreece and the gradual replacement of analogue instrumentsexisting before 2000 with modern instruments providing datafrom small earthquakes at very short distances (o10 km) andfrom large events at regional distances. As a result, our strong-motion dataset gives the opportunity to improve predictive rela-tions for Arias intensity by extending their range of applicability tomagnitudes lower that 4.5 and epicentral distances larger than150 km.

3.1. Methodology

For the definition of a GMPE relative to Arias intensity webasically followed a two-step regression method described byHwang et al. [20], which, in turn, is based on an approachproposed by Joyner and Boore [28]. However some proceduralvariations were adopted with respect to the mentioned authors.

First of all, the regression was carried out using the largestvalue Ia between the Arias intensities calculated along the twohorizontal components of the recording, instead of considering, asin Hwang et al. [20], the Ih value calculated on the componentresultant. This choice is motivated by the consideration that, forthe assessment of seismically induced landslide hazard, oneshould use a shaking parameter representative of ground motionalong a specific direction (i.e. the potential sliding direction) ratherthan the total shaking energy released in the horizontal plane. Ingeneral, the maximum between the Arias intensities of the tworecorded horizontal components does not necessarily coincideswith the maximum of the shaking energy among all the possiblehorizontal directions, but, on the other hand, neither the slidingdirection is necessarily parallel to such maximum, even thoughthis may often occurs (cf. [15]). Thus, the use of the largestbetween the horizontal components introduces uncertainties inthe shaking measures, which can be statistically treated in hazardassessment, whereas the use of Ih would tend to introduce asystematic overestimate.

Another procedural differentiation derives from the introduc-tion, within the two-step scheme, of variables representative ofsite effects and of the earthquake focal mechanism types. The use

K. Chousianitis et al. / Soil Dynamics and Earthquake Engineering 65 (2014) 11–29 13

Table 1Strong-motion records used in the analyses. Hypocentral parameters and moment magnitudes until 2009 are taken from the catalogue of Makropoulos et al. [38], while after2009 from the NOA seismicity catalogue (http://bbnet.gein.noa.gr).

Date (dd-mm-yy) Time Lat. Long. Mw Depth (km) Focal mec. No. of stations

04-11-1973 15:52:13 20.454 38.755 5.8 13 T 120-06-1978 20:03:24 23.242 40.732 6.2 3 N 124-02-1981 20:53:37 22.945 38.221 6.4 18 N 225-02-1981 02:35:52 23.103 38.126 6.1 30 N 110-03-1981 15:16:18 20.787 39.315 5.5 32 T 227-05-1981 15:04:00 21.004 38.805 5.1 39 T 117-01-1983 12:41:30 20.155 37.985 6.7 17 SS 117-01-1983 15:53:54 20.272 38.100 5.2 19 SS 117-01-1983 16:53:28 20.217 38.113 5.4 21 SS 131-01-1983 15:27:00 20.315 38.159 5.2 21 SS 123-03-1983 23:51:05 20.188 38.193 6.0 23 SS 124-03-1983 04:17:31 20.238 38.107 5.4 16 SS 106-08-1983 15:43:53 24.783 40.076 6.7 21 SS 126-08-1983 12:52:10 23.975 40.466 5.0 3 SS 325-10-1984 09:49:18 21.751 37.062 5.0 5 N 131-08-1985 06:03:45 20.554 39.009 4.7 33 T 309-11-1985 23:30:43 24.036 41.231 5.5 11 N 218-02-1986 14:34:03 22.108 40.756 5.2 20 N 113-09-1986 17:24:34 22.134 37.140 5.7 9 N 415-09-1986 11:41:30 22.130 37.040 5.1 15 N 414-12-1986 09:49:17 21.906 38.931 4.4 19 N 110-06-1987 14:50:11 21.369 37.145 5.3 48 N 105-10-1987 09:27:02 28.275 36.308 5.2 68 SS 224-04-1988 10:10:33 20.551 38.854 5.1 11 SS 218-05-1988 05:17:41 20.404 38.385 5.4 21 SS 216-10-1988 12:34:04 21.061 37.910 5.6 25 SS 220-10-1988 14:00:59 22.948 40.501 4.7 27 N 117-05-1990 08:44:03 22.277 38.370 4.7 39 N 121-12-1990 06:57:44 22.398 40.920 5.9 13 N 123-01-1992 04:24:16 20.480 38.413 5.2 25 T 130-05-1992 18:55:39 21.440 38.011 5.0 25 SS 318-11-1992 21:10:41 22.444 38.296 6.0 12 N 305-03-1993 06:55:06 21.448 37.084 5.4 39 N 126-03-1993 11:58:19 21.286 37.653 5.3 45 SS 213-06-1993 23:26:40 20.524 39.285 5.6 20 T 114-07-1993 12:31:49 21.810 38.180 5.4 12 SS 604-11-1993 05:18:36 22.044 38.401 5.2 9 N 125-02-1994 02:30:05 20.544 38.772 5.4 24 SS 123-05-1994 06:46:15 27.700 35.540 6.1 68 T 213-02-1995 13:16:36 22.758 40.695 4.7 10 SS 304-05-1995 00:34:11 23.652 40.540 5.1 14 N 113-05-1995 08:47:14 21.724 40.162 6.3 14 N 1015-05-1995 04:13:56 21.591 40.083 5.2 26 N 217-05-1995 04:14:26 21.626 40.074 5.2 21 N 319-05-1995 06:48:51 21.580 40.054 5.2 10 N 315-06-1995 00:15:50 22.235 38.401 6.3 3 N 715-06-1995 00:30:52 22.028 38.313 5.4 5 N 217-07-1995 23:18:15 21.584 40.108 5.4 22 N 205-08-1996 22:46:43 20.658 40.047 5.2 8 T 226-04-1997 22:18:34 21.364 37.194 4.4 45 SS 113-10-1997 13:39:37 22.038 36.303 6.6 13 T 421-10-1997 17:57:46 22.111 38.995 4.7 26 N 105-11-1997 21:10:28 22.361 38.364 5.6 13 N 318-11-1997 13:07:40 20.603 37.421 6.0 10 T 218-11-1997 13:13:51 20.636 37.584 5.4 46 SS 124-02-1998 15:11:44 27.993 36.442 4.4 31 N 508-03-1999 05:10:15 21.762 37.570 4.4 51 SS 111-06-1999 07:50:15 21.110 37.560 5.0 54 SS 529-06-1999 15:09:59 22.076 38.411 4.6 10 N 320-07-1999 19:15:20 21.877 38.374 4.1 21 N 103-09-1999 05:29:33 23.179 38.354 4.4 11 N 107-09-1999 11:56:51 23.571 38.059 5.8 9 N 1009-10-1999 10:31:13 22.228 38.342 4.1 4 SS 216-02-2000 13:45:55 20.210 38.190 4.0 5 SS 127-04-2000 19:03:46 22.080 38.310 4.7 13 N 126-07-2001 00:21:38 24.338 39.046 6.0 19 SS 310-09-2001 05:08:08 23.270 38.980 4.2 8 SS 114-08-2003 05:14:54 20.570 38.850 5.8 12 SS 314-08-2003 12:18:15 20.640 38.760 4.8 26 SS 214-08-2003 16:18:04 20.590 38.760 5.2 10 SS 123-01-2004 23:00:58 22.600 38.080 3.9 20 N 126-01-2004 09:14:13 22.600 38.070 3.2 6 N 117-02-2004 15:56:48 22.640 38.070 4.1 23 N 126-02-2004 23:12:11 22.610 38.060 3.3 21 N 1

K. Chousianitis et al. / Soil Dynamics and Earthquake Engineering 65 (2014) 11–2914

a two-step procedure is aimed at separating the calculation of thecoefficients for the terms pertaining the energy released by events(typically expressed as function of their magnitude) from thoseaccounting for the shaking energy attenuation with distance.Datasets used for regression generally show an artificial correla-tion between event energy and observation distance (longerdistance recordings being available only for more energetic events,whereas shorter distance recordings are prevailingly relative tosmaller events). This introduces a trade-off between magnitudeand distance dependence, potentially causing an underestimate ofattenuation with distance [28]. In the two-step procedure thisproblem is contrasted by independently determining the coeffi-cients for the two types of terms at two successive stages and, inparticular, those relative to propagation effects in the first step,and those relative to the energy released by source at the secondstage. In such a context, the coefficients for terms taking intoaccount site response have to be calculated in the first step,whereas those relative to focal mechanism influence in thesecond step.

A general equation for ground motion prediction can beexpressed according to the form

log Ia ¼ aþbM�c logffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiR2þh2

qþd

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiR2þh2

q

þ∑i ¼ 1;Neisiþ∑j ¼ 1;Mf jmjþεrþεe ð2Þ

where M is the magnitude event, R the source horizontal distance,si and mj are the N and M dummy binary variables used todistinguish site and focal mechanism types, respectively; theunknown regression parameters to be determined are a, b, c, d,ei, fj, h2, whereas εr and εe are the estimate errors due to thediscrepancies of the modelling of propagation and of source fromthe real cases, respectively.

It should be noticed that Eq. (2) is a quite general expressionincluding a logarithmic term of distance to represent geometricattenuation, a linear term of the same distance standing foranelastic attenuation and a coefficient h2 to introduce a limitationto ground motion as distance tends to zero. Simpler equationscould be adopted excluding one or both the last two elements,

Table 1 (continued )

Date (dd-mm-yy) Time Lat. Long. Mw Depth (km) Focal mec. No. of stations

14-02-2008 10:09:23 21.869 36.575 6.6 32 T 114-02-2008 12:08:55 21.750 36.220 6.1 35 T 120-02-2008 18:27:05 21.720 36.180 5.9 17 T 108-06-2008 12:25:30 21.483 37.968 6.3 16 SS 1914-10-2008 02:06:36 23.600 38.810 5.0 10 N 116-02-2009 23:16:40 20.900 37.240 5.7 13 SS 117-05-2009 11:59:03 22.690 38.120 4.8 18 N 117-05-2009 22:39:26 22.660 38.120 4.4 9 N 118-01-2010 15:56:09 21.950 38.410 5.1 20 N 122-01-2010 00:46:56 21.970 38.420 5.1 12 N 123-12-2010 08:02:30 20.590 38.300 3.9 19 SS 101-04-2011 13:29:10 26.564 35.643 6.0 63 SS 207-08-2011 14:35:34 21.831 38.392 4.7 20 N 110-06-2012 12:44:16 28.877 36.398 6.0 35 SS 112-09-2012 03:27:46 24.024 34.714 5.3 26 T 122-09-2012 03:52:25 22.738 38.086 4.9 25 N 223-10-2012 15:20:42 20.626 38.950 4.7 14 SS 108-01-2013 14:16:08 25.562 39.666 5.7 30 SS 306-04-2013 11:23:06 24.110 34.815 4.9 24 N 123-05-2013 14:09:05 20.583 38.647 4.7 10 SS 115-06-2013 16:10:56 25.063 34.336 6.1 31 T 115-06-2013 16:28:55 25.094 34.265 4.6 26 T 116-06-2013 21:39:05 25.128 34.276 5.8 28 N 107-08-2013 09:06:51 22.681 38.696 5.4 10 N 3

1

10

100

1000

3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0

Magnitude (Mw)

Dis

tanc

e (k

m)

Normal - A/B

Normal - B

Normal - C

Normal - D

Strike/Thrust - A/B

Strike/Thrust - B

Strike/Thrust - C

Strike/Thrust - D

Fig. 2. Distribution of moment magnitude and epicentral distance for the entire strong-motion dataset of the present study with respect to site conditions.

K. Chousianitis et al. / Soil Dynamics and Earthquake Engineering 65 (2014) 11–29 15

whereas site and mechanism effects may be disregarded or takeninto account using an optional number of dummy variables. Incase of GMPE relative to peak shaking parameters (e.g. PGA orPGV) the coefficient of the geometric attenuation is often fixed to apre-defined theoretical value equal to unit, but the same assump-tion cannot be adopted for Arias intensity. Even if some authors(e.g. [71]) adopted a pre-fixed value 2 on the basis of theoreticalconsiderations, we preferred to determine the coefficient c fromregression, in that it is possible that a value different from 2, incombination with the use of the saturation parameter h2, canaccount globally for attenuation without the need of adding anexplicit anelastic term.

At the first stage of the two step procedure the regression iscarried out on the following equation:

log Ia ¼ �c logffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiR2þh2

qþd

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiR2þh2

q

þ∑i ¼ 1;Neisiþ∑k ¼ 1;Lgknkþεr ð3Þ

where nk are the dummy variables and gk the correspondingcoefficients to be determined. Each couple (nk, gk) is associatedto only one of the L events included in the regression dataset: foran Ia value observed from a given event, the independent variablenk relative to this event is taken equal to 1 and all those relative toother events are set to 0. Assuming that the residual εr is a randomvariable having zero mean and variance sr

2, all the unknownparameters of Eq. (3) can be estimated by the ordinary least-squares method applied iteratively, starting from initial trialsolutions, to a system of equations obtained by linearising expres-sions like (3) (cf. [28]), i.e. a system

Y1 ¼X1B1þε1 ð4Þwhere Y1 is the vector of the log Ia values for each observation, X1

is the matrix of the partial derivatives of Eq. (3) with respect to allthe unknown parameters, B1 is the vector of such parameters andε1 is the vector of residuals.

At the second stage the estimated values gk provide theresponse variables of a set of L new equations

gk ¼ aþbMþ∑j ¼ 1;Mf jmjþεgþεe ð5Þ

where εg ¼ ðgk�gkÞ is the error affecting the estimate of gk. Theparameters a, b and fj can then be obtained by resolving thesystem

Y2 ¼X2B2þε2 ð6Þwhere Y2 is the vector of the values gk, X2 is the matrix of thevalues of the explanatory variables of (5), B2 is the vector of theunknown parameters of the second step and ε2 is the vector ofresiduals (εgþεe). Since εg and εe can be assumed independentand uncorrelated errors (cf. [28]), the variance s2 of the residualsof the system (6) can be assumed equal to the sum of variances ofthe two kinds of error. However, while a zero mean and a commonvariance s2

e can be attributed to errors εe, the same does not holdfor errors εg, which depend on the strength of constraints on gkdetermination (depending on the number of recordings availablefor each event). Such a situation requires the use of a weightedleast-squares approach, where the weighting matrix is the inverseof the square root of the covariance matrix given by the followingequation:

V2 ¼ varðεgÞþs2e I ð7Þ

with var(εg) consisting in the covariance matrix of errors εg(derived from the first step regression) and I being the identitymatrix. The estimates of the elements of the vector B2 can then beobtained from

B2 ¼ ðX2TV2

�1X2Þ�1X2TV2

�1Y2 ð8Þ

where the variance s2e is a priori unknown. However, s2

e can beestimated by attributing to it trial values, through an iterativeprocedure, until the standard deviation of residuals of theweighted equations becomes equal to 1 within a fixed approxima-tion (cf. [20]).

3.2. Data processing

From the Greek strong motion database, only recordings wereused for which two horizontal components were available, inorder to select the larger value Ia, expressed in m/s, between theArias intensities calculated for such components. Moment magni-tude, Mw, was adopted as parameter to quantify the source energy,whereas epicentral distances were used in the equation termsrepresenting the energy attenuation. The possible influence offocal mechanism was taken into account through a single dummyvariable which assumes the value 0 in case of sources of normalfault type and 1 for strike-slip or thrust mechanisms.

With regard to site effects, considering that a certain number ofrecording stations are classified as an A/B mix type, three differentalternative schemes were tested to represent local soil conditions.The most complete scheme makes use of 3 dummy variables s1, s2and s3: the first is set to 0 for the A/B site type and to 1 fordefinitely B type; the other two variables are set to 1 for C and Dtype, respectively, and 0 otherwise. A second adopted schemefollows the classification used by Ambraseys at al. [3] to char-acterise local soil condition in the definition of an European GMPE,i.e. a classification in rock sites (Vs304750 m/s, corresponding to Aand B types), stiff soils (360oVs30o750 m/s, corresponding to Ccategory) and soft soils (180oVs30o360 m/s, corresponding to Dcategory). Thus, according to the second scheme, two dummyvariables were used setting both of them to 0 for rock sites andtaking alternatively one or the other equal to 1 for stiff and softsoils, respectively. Finally we tested also a simplified scheme usinga single dummy variable set to 0 for rock sites and to 1 for all kindof soils.

Investigating the use of Eq. (2) to predict Arias intensity, onecould wonder if (i) all the terms present in the general formula areneeded and reliably determinable from the regression dataset and(ii) how many dummy variables are to be used, if any, for anefficient ground motion prediction accounting for site responseand focal mechanism influence. In order to test and compare theeffectiveness of the different GMPE forms one cannot simply relyon the goodness of fit of the equations to the regression dataset,since a fit improvement generally results from the increase ofparameters, regardless of additional parameter capacity of reallycapturing elements significant for prediction accuracy. Thereforeto evaluate the results of regressions obtained with differentformulae, an approach was followed based on the subdivision ofthe available dataset into two distinct groups: a larger one wasused as “training” dataset to calculate the equation parameters,whereas a smaller subset was used for a comparative validation ofthe regression results. The second subset additionally offers thepossibility to compare the effectiveness of the best equation foundfrom this analysis with the results obtained using GMPE's calcu-lated by other authors from different data, so to verify if the use ofregional equations gives a real advantage in terms of predictioncapacity.

Thus, considering that, with reference to the first step regres-sion (Eq. (3)) the quality of the estimates of the parameters gk isconditioned by the number of available recordings for each event,data of earthquakes recorded by a single station were excludedfrom the training dataset and were gathered to constitute adistinct dataset for the successive validation phase. The trainingdata group consists in 133 Arias intensities calculated for 37 eventsof magnitude between 4.1 and 6.6, recorded at distances between

K. Chousianitis et al. / Soil Dynamics and Earthquake Engineering 65 (2014) 11–2916

1 and 195 km; the validation dataset consists of 60 data distrib-uted in the magnitude range 3.2–6.7, and in the distance range1–118 km.

Both the groups were inspected to verify the data coverage overthe range of values of the regressor variables. Fig. 3 shows thedistribution of magnitude and distance for the two datasets: bothshow a good coverage for magnitude between 4.5 and 6.5 andfor distances between 10 and 100 km, but in the validationdatasets the higher magnitudes appear underrepresented and arelatively larger number of recordings at distances less than 10 kmcan be found.

Regression was carried out for 32 GMPE forms having incommon the presence of the first three terms of the Eq. (2) anddiffering for the combined inclusion or exclusion of the para-meters for anelastic attenuation (d), saturation with decreasingdistances (h2), focal mechanism influence (fj) and site effects (ei),the last being alternatively modelled through the use of 1, 2 or3 dummy variables. To synthesise the regression result represen-tation an identification code was assigned to each regression,consisting in a string where the optional parameters (in the orderd, h, f and e) are followed by 1 or 0, according to whether thatparameter is included or not in the equation, or, if a site effect term

is included, by the number of dummy variables employed for it(1, 2 or 3).

3.3. Results

The results of the 32 regressions are summarised in Table 2. Foreach regression, in addition to the values of the equation para-meters, the standard deviation s of the equation prediction wasestimated and reported together with the contribution sr and se

deriving to total standard deviation from record-to-record andevent-to-event variability, respectively: sr is basically related todiscrepancies of energy propagation modelling from reality,whereas se depends on errors in source energy modelling. Inorder to evaluate the quality of the regression results and thegoodness of fit, Table 3 reports some additional parameters, i.e. theStudent's test t values for each regression parameter, the numberof degrees of freedom relative to the first (dof1) and the second(dof2) step of regressions, the efficiency coefficients E [44] and themedians of the LH parameter introduced by Scherbaum et al. [62].

The t values, given by the ratios between parameter values andtheir estimated standard errors, allows to verify the significance ofeach parameter, in order to evaluate if the null hypothesis of a

1

10

100

1000

4.0 4.5 5.0 5.5 6.0 6.5 7.0

Magnitude (Mw)

Dis

tanc

e (k

m)

Normal - A/B

Normal - B

Normal - C

Normal - D

Strike/Thrust - A/B

Strike/Thrust - B

Strike/Thrust - C

Strike/Thrust - D

1

10

100

1000

3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0

Magnitude (Mw)

Dis

tanc

e (k

m)

Normal - A/B

Normal - B

Normal - C

Normal - D

Strike/Thrust - B

Strike/Thrust - C

Strike/Thrust - D

Fig. 3. Distribution of event magnitude–distance combinations for Greek accelerometer recordings used as training and validation dataset in GMPE parameterisation. Symbolsare differentiated according to recording site category (A/B, C, D) and event focal mechanism (normal or strike slip/thrust). (a) Training dataset and (b) validation dataset.

K. Chousianitis et al. / Soil Dynamics and Earthquake Engineering 65 (2014) 11–29 17

parameter value equal to zero can be rejected with high con-fidence. Taking into account that dof2 pertains to parameters a, b,f1 and dof1 to all the others, the null hypothesis can be alwaysrejected with a very high confidence level (at least 98%) forparameters a, b, c and for site coefficients when 1 or 2 dummyvariables are adopted. If 3 site variables are used, the confidence ofthe null hypothesis rejection is quite lower for the first coefficient(e1) (but still significant, being between 80% and 90%), which likelyreflects the weaker constraints provided by the dataset in distin-guishing the effects of the rarer A and B type sites. Also theparameter d relative to the anelastic attenuation term shows a lessstrong but still significant evidence of being different from zero(with confidence close or higher than 90%). Only the negligibilityof the saturation parameter h2 cannot be disproved (confidencelevel of rejection being at most of about 60%), especially if it isassociated to the presence of anelastic attenuation term (in suchcase the rejection confidence level resulting less than 50%). Thisappears a consequence of the scarcity of data relative to shortdistances (less than 10 km: see Fig. 3a), which prevents a reliableconstraining of h2 and suggests some caution in the use of GMPEfor very short distance predictions.

The equation goodness of fit to the regression dataset can beevaluated from the efficiency coefficient E, proposed, in thecontext of a hydrologic study, by Nash and Sutcliffe [44], butsuggested by Kaklamanos and Baise [29] as a better estimator thanthe commonly used determination coefficient R2 also for GMPEvalidation. This parameter is given by the following expression:

E¼ 1�∑ðyi�yn

i Þ2∑ðyi�yiÞ2

ð9Þ

where yi represents experimental observations, yi their meanvalues and yn

i the values correspondingly predicted by the model.Such a parameter quantifies how much the model equation worksbetter than the average as predictor of the response variable,giving negative results if the tested equation performs worse thanthe average, 0 if performs exactly like the average and 1 for perfectpredictions. It is possible to demonstrate that E coincides with R2 ifestimate errors are not correlated with the observed values, as onecan expect for a homogeneous distribution of the regressiondataset over the range of the observation values. However, if theregression data population is not well balanced between smalland large values, E results a more reliable estimator of the good-ness of fit.

Examining the efficiency coefficients for the results of theregressions carried out in this study, a clear trend to an improve-ment of goodness of fit can be observed as more parameters areincluded in the equation (see Table 3). However, as previouslydiscussed, this does not assures a corresponding improvement ofthe prediction capabilities of equations when applied to datadifferent from those of the regression dataset.

Another desirable property of a GMPE that has to be used forprobabilistic hazard estimates is a normal or log-normal distribu-tion of error estimates. The closeness of error distribution tonormality can be evaluated through the LH parameter introducedby Scherbaum et al. [62]. It measures the likelihood of findingresiduals with modulus equal to or larger than each of thoseobserved if observations are extracted from a normal distributionhaving mean and variance equal to those estimated for theobservations. Scherbaum et al. [62] showed that a normal dis-tribution of errors reflects on a homogeneous distribution of the

Table 2Results of regression for different equation forms. The regression parameters are named as in Eq. (2). The regression codes specify the parameter included in each regressionequation, in addition to those always present (i.e. a, b and c), through the parameter letter followed by 1 or 0, according to whether it is included or not in the equation, or, forthe case of site effect term, followed by the number of dummy variables (0, 1, 2 or 3) used to represent site types. The quantities s, sr, and se are the regression total standarddeviation, and those relative to the first and the second step, respectively; rms and rmsl are the root mean square of estimate errors resulting from the application ofequations to the validation dataset.

Regr. code a b c h2 d e1 e2 e3 f1 r rr re rms rmsl

d0h0f0e0 �3.727 0.886 1.965 0.545 0.449 0.308 0.278 0.657d0h0f0e1 �4.247 0.904 1.893 0.378 0.528 0.432 0.305 0.266 0.672d0h0f0e2 �4.229 0.910 1.935 0.332 0.551 0.516 0.426 0.291 0.262 0.679d0h0f0e3 �4.582 0.913 1.900 0.376 0.611 0.843 0.528 0.424 0.315 0.249 0.675d0h0f1e0 �3.856 0.892 1.965 0.263 0.538 0.449 0.296 0.246 0.625d0h0f1e1 �4.354 0.910 1.893 0.378 0.237 0.524 0.432 0.296 0.241 0.647d0h0f1e2 �4.319 0.915 1.935 0.332 0.551 0.195 0.514 0.426 0.288 0.238 0.655d0h0f1e3 �4.671 0.917 1.900 0.376 0.611 0.843 0.194 0.526 0.424 0.312 0.228 0.652d0h1f0e0 �3.649 0.901 2.090 27.8 0.572 0.449 0.354 0.207 0.658d0h1f0e1 �4.108 0.927 2.088 47.5 0.391 0.561 0.430 0.360 0.203 0.693d0h1f0e2 �4.132 0.927 2.059 30.6 0.343 0.548 0.537 0.426 0.327 0.193 0.652d0h1f0e3 �4.484 0.932 2.027 29.9 0.369 0.617 0.835 0.548 0.423 0.348 0.193 0.651d0h1f1e0 �3.750 0.912 2.090 27.8 0.284 0.562 0.449 0.338 0.195 0.602d0h1f1e1 �4.189 0.936 2.088 47.5 0.391 0.266 0.552 0.430 0.346 0.191 0.645d0h1f1e2 �4.202 0.936 2.059 30.6 0.343 0.548 0.216 0.533 0.426 0.321 0.180 0.613d0h1f1e3 �4.554 0.941 2.027 29.9 0.369 0.617 0.835 0.216 0.544 0.423 0.342 0.179 0.614d1h0f0e0 �4.273 0.894 1.393 �0.0057 0.577 0.442 0.370 0.213 0.584d1h0f0e1 �5.072 0.921 1.153 �0.0073 0.432 0.557 0.418 0.368 0.199 0.612d1h0f0e2 �4.881 0.919 1.284 �0.0062 0.397 0.530 0.553 0.418 0.363 0.196 0.600d1h0f0e3 �5.291 0.925 1.225 �0.0065 0.396 0.694 0.838 0.564 0.414 0.383 0.192 0.598d1h0f1e0 �4.470 0.904 1.393 �0.0057 0.291 0.565 0.442 0.352 0.198 0.578d1h0f1e1 �5.248 0.929 1.153 �0.0073 0.432 0.274 0.547 0.418 0.353 0.190 0.620d1h0f1e2 �5.056 0.927 1.284 �0.0062 0.397 0.530 0.237 0.547 0.418 0.354 0.185 0.604d1h0f1e3 �5.469 0.933 1.225 �0.0065 0.396 0.694 0.838 0.239 0.557 0.414 0.372 0.182 0.607d1h1f0e0 �4.234 0.892 1.421 7.3 �0.0055 0.626 0.445 0.441 0.199 0.581d1h1f0e1 �5.063 0.918 1.154 5.0 �0.0073 0.432 0.595 0.420 0.421 0.194 0.616d1h1f0e2 �4.822 0.919 1.284 6.3 �0.0062 0.397 0.530 0.597 0.420 0.425 0.181 0.577d1h1f0e3 �5.231 0.925 1.226 5.5 �0.0065 0.396 0.694 0.838 0.606 0.416 0.440 0.179 0.577d1h1f1e0 �4.386 0.905 1.421 7.3 �0.0055 0.290 0.612 0.445 0.421 0.186 0.560d1h1f1e1 �5.201 0.930 1.154 5.0 �0.0073 0.432 0.272 0.584 0.420 0.405 0.182 0.609d1h1f1e2 �4.968 0.930 1.284 6.3 �0.0062 0.397 0.530 0.235 0.591 0.420 0.415 0.169 0.578d1h1f1e3 �5.380 0.936 1.226 5.5 �0.0065 0.396 0.694 0.838 0.237 0.598 0.416 0.430 0.167 0.582

K. Chousianitis et al. / Soil Dynamics and Earthquake Engineering 65 (2014) 11–2918

observation LH values among probability equispaced intervals. Asingle synthetic parameter well representing the agreement ofresidual distribution with a normal one is the median of LH valuesthat should be close to 50%. Table 2 reports the LH mediansobtained for each regression: one can notice that the regressionsshowing LH median closer to 50% appears those obtained forequations including the anelastic attenuation term, but withoutthe saturation term h2.

However, a more objective evaluation of the effectiveness ofdifferent equations in predicting ground motion can be obtainedonly applying such equations to data different from those used todetermine equation parameters. Thus the previously mentionedvalidation dataset was used to compare the predictive capabilitiesof different formulae. The linear and logarithmic errors of Iaestimates provided by different equations for this dataset werecalculated. Table 2 reports the root mean square both of errors(rms) and of logarithmic error (rmsl), the latter being directlycomparable with the regression standard deviations s. The valuesof rms, rmsl and s for each equation form are also comparativelyrepresented in Fig. 4.

One can notice that the inclusion of more parameters in theregression equation seems actually to improve the predictioncapability by reducing the errors. The logarithmic errors show aslightly more irregular variation, but the overall trend appears thesame. Thus, the equation providing the lowest value of rms is thatincluding all the considered parameters (code d1h1f1e3), whereasthe minimisation of logarithmic errors is obtained for the equationexcluding only the site effect term (code d1h1f1e0). The latter isalso the equation showing the best fit according to the efficiencycoefficients calculated for the validation dataset (Eval in Table 3). Asit can be expected, these efficiency coefficients are always quitelower that those obtained for the training dataset. Additionally, for

the equations including both the anelastic attenuation term (d)and the saturation factor (h2) the values of rmsl appears better inagreement with the regression standard deviations s, indicatingthat these reflect more reliably the variability of observationdiscrepancies from the equation predictions on data different fromthose used in regressions. On the contrary, for simpler formulaesuch variability appears rather underestimated by s. This canhave important consequences on the reliability of probabilistichazard estimates that make use of standard deviation in GMPEapplication.

On the whole the improvement of GMPE prediction capabilityseems to justify the adoption of all the terms appearing in thegeneral form of Eq. (2). With regard to the site effect term,however, one can observe that, although estimate error tends todecrease as the number of dummy variables increase from 0 to 3,the improvement derived increasing from 2 to 3 the number ofsite variables appears negligible. Thus, also considering the uncer-tain determination of the coefficient e1 when it is employed todistinguish A and B type sites, the use of 2 site variables only,according to the Ambraseys et al. [3] site classification, appearspreferable.

In conclusion, for Arias intensity estimates, expressed in m/s,we propose the use of the following 4 equations, according to theavailability of information on the different explanatory variables:

a) if focal mechanism and site typology are known,

log Ia ¼ �4:968ð70:919Þþ0:930ð70:149ÞM

�1:284ð70:442Þ logffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiR2þ6:282ð719:433Þ

q

�0:006ð70:003ÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiR2þ6:282ð719:433Þ

q

þ0:397ð70:129Þs1þ0:530ð70:155Þs2

Table 3Student's test t values for regression parameters obtained using different equations. The regression code are like in Table 2. The numbers dof1 and dof2 are the degrees offreedom for the first and the second step of regression; E and Eval are the efficiency coefficients calculated from the training and the validation datasets, respectively; LHmed isthe median of the observation likelihood distribution according to Scherbaum et al. [62].

Regr. code t(a) t(b) t(c) t(h2) t(d) t(e1) t(e2) t(e3) t(f1) dof1 dof2 E LHmed Eval

d0h0f0e0 �4.479 5.595 11.102 95 35 0.286 39.50 0.244d0h0f0e1 �5.146 5.857 11.064 3.011 94 35 0.343 41.55 0.211d0h0f0e2 �5.265 6.049 11.343 2.625 3.501 93 35 0.353 40.87 0.194d0h0f0e3 �5.521 6.090 11.175 1.502 2.722 3.377 92 35 0.366 43.37 0.203d0h0f1e0 �4.707 5.743 11.102 1.549 95 34 0.360 43.58 0.317d0h0f1e1 �5.331 5.974 11.064 3.011 1.422 94 34 0.409 47.53 0.267d0h0f1e2 �5.381 6.109 11.343 2.625 3.501 1.179 93 34 0.406 45.41 0.250d0h0f1e3 �5.634 6.151 11.175 1.502 2.722 3.377 1.179 92 34 0.416 48.51 0.255d0h1f0e0 �4.317 5.636 8.706 0.7 94 35 0.214 37.03 0.244d0h1f0e1 �4.861 5.943 8.308 0.9 3.104 93 35 0.262 41.46 0.161d0h1f0e2 �5.093 6.130 8.900 0.8 2.685 3.486 92 35 0.336 42.40 0.257d0h1f0e3 �5.356 6.188 8.817 0.8 1.476 2.743 3.347 91 35 0.350 44.15 0.258d0h1f1e0 �4.540 5.837 8.706 0.7 1.670 94 34 0.367 45.87 0.365d0h1f1e1 �5.061 6.132 8.308 0.9 3.104 1.604 93 34 0.408 46.88 0.273d0h1f1e2 �5.220 6.241 8.900 0.8 2.685 3.486 1.311 92 34 0.440 47.76 0.343d0h1f1e3 �5.482 6.303 8.817 0.8 1.476 2.743 3.347 1.319 91 34 0.452 47.89 0.341d1h0f0e0 �4.767 5.607 4.180 �2.0110 94 35 0.444 50.21 0.402d1h0f0e1 �5.674 5.926 3.600 �2.7000 3.511 93 35 0.492 53.47 0.344d1h0f0e2 �5.554 6.074 3.754 �2.1855 3.113 3.429 92 35 0.513 54.33 0.371d1h0f0e3 �5.852 6.130 3.632 �2.3023 1.620 3.120 3.431 91 35 0.525 51.86 0.374d1h0f1e0 �5.070 5.818 4.180 �2.0110 1.707 94 34 0.476 52.22 0.416d1h0f1e1 �5.950 6.121 3.600 �2.7000 3.511 1.642 93 34 0.517 52.16 0.327d1h0f1e2 �5.770 6.218 3.754 �2.1855 3.113 3.429 1.426 92 34 0.527 54.90 0.361d1h0f1e3 �6.070 6.279 3.632 �2.3023 1.620 3.120 3.431 1.447 91 34 0.537 51.89 0.355d1h1f0e0 �4.519 5.597 3.204 0.3 �1.6540 93 35 0.440 52.67 0.410d1h1f0e1 �5.462 5.915 2.836 0.3 �2.3417 3.482 92 35 0.490 56.34 0.337d1h1f0e2 �5.225 6.076 2.905 0.3 �1.8697 3.081 3.409 91 35 0.520 55.87 0.418d1h1f0e3 �5.524 6.141 2.835 0.3 �1.9751 1.609 3.086 3.411 90 35 0.532 55.76 0.418d1h1f1e0 �4.766 5.823 3.203 0.3 �1.6541 1.703 93 34 0.488 55.05 0.451d1h1f1e1 �5.692 6.117 2.836 0.3 �2.3417 3.482 1.627 92 34 0.524 56.61 0.352d1h1f1e2 �5.407 6.224 2.905 0.3 �1.8697 3.081 3.409 1.415 91 34 0.532 57.38 0.415d1h1f1e3 �5.709 6.295 2.835 0.3 �1.9751 1.609 3.086 3.411 1.438 90 34 0.542 57.20 0.408

K. Chousianitis et al. / Soil Dynamics and Earthquake Engineering 65 (2014) 11–29 19

þ0:235ð70:166Þm1 ð10Þ

(standard deviation¼0.591);b) if focal mechanism is unknown,

log Ia ¼ �4:822ð70:923Þþ0:919ð70:151ÞM�1:284ð70:442Þ log

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiR2þ6:282ð719:433Þ

q

�0:006ð70:003ÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiR2þ6:282ð719:433Þ

q

þ0:397ð70:129Þs1þ0:530ð70:155Þs2 ð11Þ

(standard deviation¼0.597);c) if site category is unknown,

log Ia ¼ �4:386ð70:920Þþ0:905ð70:155ÞM�1:421ð70:444Þ log

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiR2þ7:312ð721:0783Þ

q

�0:006ð70:003ÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiR2þ7:312ð721:0783Þ

q

þ0:290ð70:170Þm1 ð12Þ

(standard deviation¼0.612);d) if both mechanism and site category are unknown,

log Ia ¼ �4:234ð70:937Þþ0:892ð70:159ÞM�1:421ð70:444Þ log

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiR2þ7:323ð721:051Þ

q

�0:005ð70:003ÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiR2þ7:312ð721:0783Þ

qð13Þ

(standard deviation¼0.626).

For Eq. (10), Fig. 5 also shows the values predicted for thevalidation dataset against the correspondingly observed ones. Thegeneral agreement between predictions and observations, appre-ciable from the point distance from the “perfect agreement” line(black diagonal line) is acceptable, even though the equationshows a slight tendency to overestimate small Ia values and tounderestimate the larger ones.

The equations obtained in this study were compared withGMPE published by different authors and obtained from differentdata. In particular we considered the following formulae:

1) The equation proposed by Wilson and Keefer [72]

log Ia ¼ �4:1þM�2 log r70:44 ð14Þwhere r is the source distance measured from the slip surface,the coefficients for magnitude and distance terms were derivedfrom theoretical considerations and the constant (correspond-ing to the parameter a of Eq. (2)) was calculated from aregression using a dataset including about 30 recordings of8 Californian events, 1 from Hawaii and 1 from Japan; 0.44 isthe regression standard deviation;

2) the equation published by Jibson [21]

log Ia ¼ �4:9þ0:98 M�1:35 log r ð15Þ

Residual rms

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

d0h0

f0e0

d0h0

f0e1

d0h0

f0e2

d0h0

f0e3

d0h0

f1e0

d0h0

f1e1

d0h0

f1e2

d0h0

f1e3

d0h1

f0e0

d0h1

f0e1

d0h1

f0e2

d0h1

f0e3

d0h1

f1e0

d0h1

f1e1

d0h1

f1e2

d0h1

f1e3

d1h0

f0e0

d1h0

f0e1

d1h0

f0e2

d1h0

f0e3

d1h0

f1e0

d1h0

f1e1

d1h0

f1e2

d1h0

f1e3

d1h1

f0e0

d1h1

f0e1

d1h1

f0e2

d1h1

f0e3

d1h1

f1e0

d1h1

f1e1

d1h1

f1e2

d1h1

f1e3

regression code

rms

rmsrmslσ

Fig. 4. Comparison among the root mean square of errors (rms) and of logarithmic errors (rmsl) in the Arias estimates obtained by applying the considered equations to thevalidation dataset. The regression codes are the same as in Table 2. The regression equation standard deviations (s) are also shown.

d1h1m1s2

0.0001

0.001

0.01

0.1

1

10

0.001 0.01 0.1 1 10

Observed Ia

Pre

dict

ed Ia

Fig. 5. Diagram of Arias intensity values predicted by the equation including all theconsidered explanatory variables against the values observed for the validationdataset. The diagonal black line marks combination of predicted/observed valuescorresponding to a perfect agreement.

K. Chousianitis et al. / Soil Dynamics and Earthquake Engineering 65 (2014) 11–2920

where all the parameters were calculated from the samedataset used by Wilson and Keefer [72], integrated by record-ings of the 1978 earthquake of Tabas (Iran);

3) the equation obtained by Sabetta and Pugliese [75], which,modified to provide Ia in the same units of the others, assumesthe form

log Ia ¼ �4:066þ0:911M�1:818 logffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiR2þ28:09

qþ0:139S1þ0:244S270:397 ð16Þ

where R is the epicentral distance, the parameters wereobtained from a dataset of Italian accelerometer recordingsand the site variables S1 and S2 are both set to 0 for rock site (S-wave velocity higher than 800 m/s) and are alternatively set to1 in case of soils (S-wave velocityo800 m/s) having thicknesslarger or smaller than 20 m, respectively;

4) the equation obtained by Mahdavifar et al. [36] for Northernand Central Iran

log Ia ¼ �3:88þ0:810M� logffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiR2þH2

q�0:002

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiR2þH2

qð17Þ

where H is the focal depth;5) the preferred equation, among those derived by Stafford et al.

[65] for New Zealand, providing the largest between the Iavalues calculated from the two horizontal component, i.e.

ln Ia ¼ �6:5032þ2:6495M�3:3137 ln ½Rþexpð0:5045MÞ�þ0:0439Hþ0:5461SCþð0:4014�0:1480 ln Ia;rockÞSDþ0:2241FR71:1300 ð18Þ

where R is the Joyner–Boore distance (calculated from the faultrupture vertical projection on the surface), H is the focal depth,SC and SD are site dummy variables assuming values 1 for C andD site, respectively, and 0 otherwise, Ia,rock is the Arias intensitycalculated for a rock site (introduced to take into accountnonlinear site effects depending on shaking amplitude), FR isa focal mechanism dummy variable assuming value 1 forreverse mechanism and 0 otherwise;

6) the equation published by Rajabi et al. [50]

log Ia ¼ �2:659þ0:601M� log R�0:011R70:430 ð19Þobtained for Zagros Mountains (Western Iran);

7) the equation published by Lee et al. [31] for Arias intensitycalculated from a Taiwan strong motion dataset as averagebetween the values obtained for the two horizontal compo-nents of ground motion, i.e.

ln Ia ¼ 3:757�1:043ðM�6Þþ18:077 lnðM=6Þ�2:251 ln

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiR2þ9:562

q�1:042 lnðVS30=1130Þ

�0:214 FNþ0:220 FR70:994 ð20Þ

where R is the closest distance to the rupture plane for largeearthquakes and the hypocentral distance for others, VS30 is theaverage shear-wave velocity in the soil upper 30 m, assuming areference value of 1130 m/s for rocks, FR and FN are the focalmechanism dummy variables assuming alternatively value 1 fornormal and reverse mechanisms, respectively, and 0 for strike-slipmechanisms.

Fig. 6 shows comparatively Arias intensity attenuation withdistance for three magnitude values (6.5, 5.0 and 3.5) according toGMPE's published by different authors. To make curves compar-able, they were calculated for basic typologies of site and event, i.e.for rock sites and normal fault events, also assuming a standardvalue of 10 km for hypocentral depth when this parameter isrequired (Eqs. (17) and (18)).

It can be observed that curves are considerably different interms of shape (which reflects the differences of the adoptedfunctional forms) and absolute values: for curves obtained in thisstudy absolute values are generally lower than for others exceptfor Taiwan and, in some magnitude–distance range, for NewZealand curves. Differences are also observed with regard to therates of Ia attenuation with distance and of Ia increase withmagnitude. These differences clearly reflect diversities in stressregime and structural geology among the regions for which curveswere derived. The GMPE's obtained in this study for Greece show abetter resemblance with that obtained for Italy (Sabetta andPugliese [75]), which possibly reflect a geological similaritybetween the two regions, and for New Zealand at magnitudesequal or larger than 5.0, which is the lower magnitude boundaryin the New Zealand dataset [65]. In general regression standarddeviations obtained for the Greek data appear larger than those ofother equations, but this is an aspect difficult to be interpreted:indeed, the data scattering depends not only on the equationcapacity of more efficiently capturing the influence of differentexplanatory factors, but also on the size and heterogeneity of theregression datasets, which in the considered studies appear ratherdifferent.

An additional comparative test consisted in examining theperformances of some of these equations as Arias intensitypredictors for the validation Greek dataset. Such performanceswere evaluated on the basis of the root mean square ofestimate errors (rms) and logarithmic errors (rmsl) and alsoconsidering the efficiency coefficient (Eval). Table 4 summarisesthe results obtained, compared to the performances of thepreferred equation resulting from this study (i.e. Eq. (10)) andof equations, among those analysed in this study, whoseformulation are more similar to those adopted by previousstudies. Thus the formulae by Wilson and Keefer [72] andJibson [21] are comparable to the equation including only thebasic parameters a, b and c (code d0h0f0e0), that by Sabettaand Pugliese [75] is assimilable to the equation characterisedby a two variable site term and lacking in anelastic attenuationand focal mechanism terms (code d0h1f0e2), the Mahdavifaret al. [36] formula is similar to the equation lacking in site andfocal mechanism terms (code d1h1f0e0) and that by Rajabiet al. [50] excludes also the saturation parameter (coded1h0f0e0).

It is apparent that, not only the Eq. (10) provides much moreaccurate Ia estimates than previously published formulae, butalso equations of this study having a formulation similar tothose proposed by other studies performs better, at least interms of estimate errors (even though equations excludingparameter d do not appear better than their preceding homo-logues in terms of logarithmic errors and efficiency coeffi-cient). Examining the diagram of predicted versus observed Iavalues (Fig. 6d) one can observe that the performance of theWilson and Keefer [72] equation appears mainly penalised bythe presence of some cases of very large estimate errors andthat by Jibson [21] by an unbalanced distribution of positiveand negative errors for lower and higher Ia values (both aspossible effect of the model oversimplification). On the otherhand, the estimates of formulae based on regional data showmore systematic deviations, with a prevalence of underesti-mates for the Italian equation and of overestimates for theIranian ones. This likely reflects differences in stress regimeand in seismic energy propagation efficiency related to struc-tural geology characteristics. Thus, the adoption of regionallydifferentiated equations appears fully justified in order toimprove ground motion predictions.

K. Chousianitis et al. / Soil Dynamics and Earthquake Engineering 65 (2014) 11–29 21

4. Regression model for predicting Newmark displacement

A large number of empirical relationships that predict the slopedisplacement of rigid sliding masses are available. These expressNewmark displacement as a function of critical acceleration,which represents the dynamic shear resistance of the sliding mass,together with one or more parameters that quantify the energy ofthe seismic forces (e.g. PGA, Arias intensity, event magnitude or

combination of them). As an example, Ambraseys and Menu [1]proposed an empirical model which makes use of regressionequations for estimating Newmark displacement as a function ofthe critical acceleration ratio K, i.e. the ratio between criticalacceleration ac and PGA. Equations of different forms, includingvarious parameters, have been successively proposed by severalauthors [73,7,22,2,35,24,58,11,21,61,55,19,51]. These regressionmodels allowed the use of a simplified Newmark analysis forvarious applications, like seismic landslide microzonation, model-ling of earthquake-induced landslide scenarios and exceedanceprobability prediction of fixed values of landslide displacements[39,34,35,40–43,13,14,16,54,56]. Predictive models for the estima-tion of the sliding displacement of flexible sliding masses also exist(e.g. [9,10,57]).

In the present study, in order to obtain empirical estimators ofNewmark displacement, we adopted regression models whichmake use of Arias intensity alone to describe the earthquakeshaking. This is justified by the consideration that Arias intensity,deriving from the integration of the square of the entire accelera-tion time history, is a measure that, differently from otherparameters, includes the characteristics of amplitude, frequencycontent, and duration of ground motion. Thus, it incorporate moreinformation content in a single parameter and this is why the useof Arias intensity was suggested by Jibson [22] for a simplifiedapproach to hazard estimates. Actually, it has been found to be aneffective predictor of earthquake damage potential in relation to

1.E-03

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

1 10 100 1000

Distance (km)

Ia (m

/s)

This studyW&K85J87S&P96M07S09R10L12

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

1.E+01

1 10 100 1000

Distance (km)

Ia (m

/s)

This study

W&K85

J87

S&P96

M07S09

R10

L12

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

1.E+01

1 10 100 1000

Distance (km)

Ia (m

/s)

This studyW&K85J87S&P96M07S09R10L12

0.0001

0.001

0.01

0.1

1

10

0.001 0.01 0.1 1 10

Observed Ia

Pre

dict

ed Ia

Wilson & Keefer, 1985Jibson, 1987Sabetta & Pugliese, 1996Mahdavifar et al., 2007Rajabi et al., 2010

Fig. 6. Comparison among GMPE obtained in this and previous studies (W&K85¼Wilson and Keefer, 1985; J87¼ Jibson, 1987; S&P96¼Sabetta and Pugliese, 1996;M07¼Mahdavifar et al., 2007; S09¼Stafford et al., 2009; R10¼Rajabi et al., 2010; L12¼Lee et al., 2012). Attenuation with distance of Arias intensity predicted on a rock sitefor normal fault events of magnitude 6.5 (a), 5.0 (b) and 3.5 (c). (d) Diagram of Arias intensity values predicted by different equations against the values observed for thevalidation dataset. The diagonal black line marks combination values corresponding to a perfect agreement.

Table 4Performances in terms of root mean square of errors (rms) and logarithmic errors(rmsl) and of efficiency coefficient (Eval) for equations published by differentauthors, tested on the validation dataset. As comparison the performances of thisstudy preferred equation (d1h1f1e2) and of those having a similar formulation as inprevious published studies are also reported.

Equation rms rmsl Eval

d1h1f1e2 0.169 0.578 0.415[71] 0.491 0.617 0.334[21] 0.385 0.605 0.359d0h0f0e0 0.278 0.657 0.244Sabetta and Pugliese 1996 0.386 0.581 0.409d0h1f0e2 0.193 0.652 0.257[36] 0.310 0.687 0.174d1h1f0e0 0.199 0.581 0.410[50] 0.310 0.828 �0.198d1h0f0e0 0.213 0.584 0.402

K. Chousianitis et al. / Soil Dynamics and Earthquake Engineering 65 (2014) 11–2922

seismic slope stability [72,17] and correlates well with earthquake-induced landslide distribution [74].

With regard to the parameter representing slope strength, wepreferred the use of critical acceleration ac alone rather thancritical acceleration ratio K. In principle the use of K offers thepossibility of providing a better approximation of Newmarkdisplacement for limit conditions (e.g. one can correctly obtain azero displacement value when critical acceleration ac is exactlyequal to PGA). However, this does not represent a significantadvantage in the practical use of empirical estimators, if oneconsider that, while formulations including K require the deter-mination of PGA as additional parameter, they suffer, as any otherformulation, from prediction errors (cf. [25]), especially for regres-sor values external to the range covered by the dataset used inregression. This is not a severe problem considering that empiricalestimators are not generally used to obtain realistic estimates ofslope movement under particular conditions in the study of asingle slope, where a more advanced numerical modelling wouldbe more appropriate, but to obtain hazard estimates in regionalscale studies, through the calculation of an index of slope perfor-mance that can be related to the slope failure probability (cf. [24]).From this point of view, estimate errors at limit conditions, withsmall probability of occurrence, do not significantly influence theresults of hazard assessment. On the other hand the use of K hasthe disadvantage of requiring the simultaneous definition of AriasIntensity and PGA, which may not be easy to determine: indeed, inprobabilistic estimates of Newmark displacement at a site, oneshould consider, for each possible value of Arias intensity expectedat that site, not only its occurrence probability, but also theassociated probability of different values of PGA.

4.1. Methodology

To produce well-constrained regression equations for predict-ing Newmark displacements, we analysed both of the horizontalcomponents of acceleration from our strong-motion dataset. Foreach record, we determined the Arias intensity, by integrating thecorresponding squared acceleration values, according to Eq. (1).Then, we conducted a rigorous Newmark analysis, as implementedby Jibson et al. [27], for several values of critical acceleration,ranging from 0.02 to 0.4 g, i.e. the range of practical interest forseismic slope-stability problems. We processed a total of 267 one-component records, since acceleration-time histories of somerecords did not exceed the critical acceleration and consequentlyNewmark displacement was not computed for them. This yieldeda dataset containing 507 Newmark displacements, calculated asthe average of the displacements resulting from the positive andnegative accelerations. In our dataset Arias intensity values werederived in a range between a minimum of 0.4 cm/s and amaximum of 120.3 cm/s.

The Greek seismotectonic environment is characterised by highattenuation. This has been pointed out in various studies since thelate 80 s, especially for the Aegean Sea area and for the upper20 km of the lithosphere, using different approaches (e.g.[18,32,66]). This feature was expected to have an impact onparameters related to landslide susceptibility to failure (e.g. criticalacceleration) and to seismic shaking (e.g. Arias intensity), asproved by the Newmark displacements that were calculated forthe Greek dataset. For critical acceleration equal to 0.4 g, nodisplacements were calculated, while for 0.3 g, only seven valueswere derived, even though we incorporated all major Greek eventswith magnitudes up to Mw¼6.7. The above observations giveevidence that empirical equations which have been developedusing global data might not prove effective to reliably predictearthquake-induced landslide displacements in Greece due to thecharacteristics of its seismotectonic regime and the strong

attenuation of some parts of the Greek area. The suitability ofequations derived from global data was tested by applying to theGreek data the empirical relation developed by Jibson [25] relatingNewmark displacement as a function of Arias Intensity and criticalacceleration. We adopted Jibson's model because it has proved tobe considerably effective and has been used by many authors toassess and map regional seismic landslide hazards. In Fig. 7 theentire Greek dataset fitting with the Jibson [25] (Eq. (9) of hispaper) is shown. The results show that mainly for critical accel-eration 0.05 g, 0.1 g and 0.2 g, Newmark displacements are sig-nificantly underestimated across the entire range of Arias intensitybelow 1 m/s. It is evident that the best-fit lines through each acsubset deviate from the model and that the Greek dataset ischaracterised by much more narrow distances between each acbest-fit line. This diversity is likely due to differences in duration,spectral properties and peak acceleration of the Greek datasetwith respect to the global dataset that was used by Jibson [25] togenerate the regression models. It is also highlighted from Fig. 7that the range of Arias intensity below 1.5 m/s is of practicalinterest for Greece and thus empirical estimators for the calcula-tion of Newmark displacements within the Greek area requireimproved effectiveness for ground shakings characterised by Iαvalues at the aforementioned range. In contrast, regression equa-tions that have been calibrated using global data consider mainlyArias Intensity values between 0.1 and 10 m/s and exclude valuesbelow 0.1 m/s, which in the case of Greece are crucial for correctlyestimating the slope of the best-fit lines of the model. The aboveremarks demonstrate the need of developing a distinct regionalempirical equation intended for proper assessment of seismiclandslide hazard within the area of Greece. Towards the goal of aproperly calibrated relation, it is very important to account for theprevailing geological and seismotectonic characteristics that areincorporated in the Greek strong-motion recordings.

The analysis for the selection of the optimal empirical modelrelating Newmark displacement with critical acceleration andArias intensity was carried out through multivariate regressionanalyses. We tested equations of different functional formsreported in literature and, in particular, after Jibson et al. [24],Jibson [25] and Hsieh and Lee [19], the following formulations:

log Dn ¼ C1 log IaþC2acþC7s ð21Þ

log Dn ¼ C1 log IaþC2 log acþC7s ð22Þ

log Dn ¼ C1ac log IaþC2acþC7s ð23Þ

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10

Arias Intensity (m/s)

Dis

plac

emen

t (cm

)

0.02g0.05g0.1g0.2g0.02g0.05g0.1g0.2g

Fig. 7. Dataset fitting with the equation of Jibson [25] without changing itscoefficients, for critical accelerations equal to 0.02 g, 0.05 g, 0.1 g and 0.2 g.

K. Chousianitis et al. / Soil Dynamics and Earthquake Engineering 65 (2014) 11–29 23

log Dn ¼ C1 log IaþC2acþC3ac log IaþC7s ð24Þ

In the above formulas the scaling coefficients C1, C2, C3, C are to bedetermined from the regression analysis and s is the standarddeviation of the model. The Dn is in cm, Ia is in cm/s, and ac is interms of g.

Due to the fact that, adding more parameters, the predictiveequation is expected to be capable of fitting better the observeddata even only because it can fit better a random “noise” due toobservation errors, the smaller standard deviations and highercorrelation coefficient are not sufficient to verify that a model witha larger number of parameters works better (i.e. Eq. (24) incomparison to the rest). In order to optimise the choice of theempirical estimator of the expected landslide displacements andto correctly assess whether or not the additional parametersimprove the predictive capability of a model, we conducted theregressions on the basis of two different sample datasets. Startingfrom the above described entire dataset, we separated a “trainingdataset” which we used to obtain the regression coefficients, froma “validation dataset” which we used to verify the predictivecapacities of the different estimators. The subset of records thatformed the “training dataset” were selected with an optimisationcriterion aimed at obtaining a smaller data sample which we triedto make as homogeneously distributed as possible over theindependent variables adopted in the regression model, i.e. Ariasintensity and critical acceleration. In such a way we mainly tried toavoid having a regression dataset with an excessive concentrationof data in a limited range of variables, which could have anexcessive influence on regression results producing an equationscarcely representative of what can be observed for differentvalues of the independent variables. Subsequently we used therest of the data to form the “validation dataset” in order tocompare the fit of the different functional forms to experimentalobservations.

In Fig. 8, the Newmark displacements versus Arias intensity areplotted for critical accelerations between 0.02 g and 0.2 g. Thedataset shown in the plot is the “training dataset”. The determina-tion coefficients range between 0.89 and 0.96 and all fits aresignificant above the 95% confidence level. The best fits of theGreek dataset show a slightly steeper slope as the critical accel-eration gets larger, thus indicating that Arias intensity and criticalacceleration interact in determining Newmark displacement. Thisinteraction can be modelled by taking as basis Eqs. (21) and (22)

and introducing a mixed term which is respectively the productac log Ia or log ac log Ia. The first case already corresponds to Eq.(24), while the second is reported in Eq. (25). For analysiscompleteness we carried out two other regressions using asindependent variables ac log Ia and log ac log Ia, replacing the acand log ac terms of Eqs. (21) and (22). Using as variable log Iatogether with its product by ac or its logarithm implies that thepredictive equation includes a term (aþbac) � log Ia[or (aþb logac) � log Ia], i.e. a linear dependence of log Ia coefficient on ac(or its logarithm) which is coherent with the variation of the bestfit line slope found for different ac's observed in Fig. 8. The abovementioned forms correspond to the following formulations:

log Dn ¼ C1 log IaþC2 log acþC3 log Ia log acþC7s ð25Þ

log Dn ¼ C1 log IaþC2ac log IaþC7s ð26Þ

log Dn ¼ C1 log IaþC2 log ac log IaþC7s ð27ÞIn the regression analyses we considered critical acceleration

values of 0.02, 0.05, 0.1 and 0.2 g, because above this threshold thevery few Newmark displacements yielded by our strong-motiondataset, did not allowed the extraction of robust results. The use ofa hybrid model with global data in order to account for criticalacceleration 0.3 g and 0.4 g in developing the prediction modelcould have been considered, but at the price of altering theregional nature of the expected regression model. It should bealso noticed that it is not really important to extend regression tothe case of very small values of critical acceleration (i.e. close tozero). Wilson and Keefer [72] suggested to fix a minimum criticalacceleration (they proposed 0.05 g) when slope susceptibility toseismically induced failures is to be examined, because for verylow ac values the slope is very unstable and consequently has ahigh probability to fail under various and more frequent non-seismic causes before suffering a seismic shaking.

4.2. Results and discussion

The coefficients of the equations derived from the multivariateregression analyses are summarised in Table 5. We show theadjusted squared multiple determination coefficient (R2) and thestandard deviation of the logarithm of Newmark displacement(s log D), along with the standard error of the regression coeffi-cients, since it is a measure that can be used to evaluate if thecoefficients are significant.

By inspecting the Table 5 we conclude that Eqs. (23), (26) and(27) may not adequately predict Newmark displacement values.Eq. (23) presents the smallest R2 and the largest s log D, while Eqs.(26) and (27) also gave small values of R2 and large values ofs log D, with coefficient C1 in the latter case appearing insignificant.For the rest of the functional forms the regression results are ofgood quality. Coefficient standard errors are always much smallerthan coefficients themselves so to pass the Student's t significancetest with a confidence level larger than 99%. Since the comparisonof the regression results is more significant between equationsusing the same number of variables, it is evident that Eq. (22)appears better than (21) and Eq. (25) appears better than (24).However, any statement on the best predictive equation can bemade only after having applied the equations to the validationdataset.

With regard to the validation dataset, we used the ensemble ofall the data that we did not used in obtaining the regressioncoefficients, verifying that they are not unbalanced over theindependent variables. To select the optimum model among thefour formulas that displayed the best performance during theprevious step (i.e. Eqs. (21), (22), (24) and (25)) we first graphicallycompare the four regression models with the best-fit lines

R = 0.8915

R = 0.9212

R = 0.9591

R = 0.9804

0.001

0.01

0.1

1

10

100

1000

0.1 1 10 100 1000

Arias Intensity (cm/s)

Dis

plac

emen

t (cm

)

0.02g0.05g0.1g0.2g0.2g0.1g0.05g0.02g

Fig. 8. Newmark displacements versus Arias intensity for critical accelerationsranging from 0.02 to 0.2 g. Solid colour lines represent best-fit lines through each acdata subset.

K. Chousianitis et al. / Soil Dynamics and Earthquake Engineering 65 (2014) 11–2924

obtained for each of the four critical acceleration values (Fig. 9).The fitting is better when using Eqs. (22) and (25) especially forlarger values of critical acceleration. This implies that the bestestimator of the coseismic displacements for our dataset is a log-linear function of the critical acceleration and a log-linear functionof the Arias intensity. Additionally, when we incorporated inter-action between them, the results are slightly improved, especiallyfor ac¼0.2 g, and more reliable predictions across the range of thepotential input values for Greece are achieved. Then, in order toassess the effectiveness of the regression models to fit the data, a

plot of residuals (i.e. the difference between observed and pre-dicted Arias intensities) is very helpful in detecting whether or nota correlation between the residuals and each independent variableused in the model exists. The examination of their distributionversus Arias intensity and critical acceleration for the test datasetdid not revealed any systematic variation as a function of eachindependent variable, as it is illustrated in Fig. 10. Residual valuesfor both models (22) and (25) present low scattering and do notappear correlated to the values of the independent variables. Theonly difference between their distributions appears for critical

Table 5Coefficients (C1, C2, C3, C), corresponding standard errors, adjusted squared multiple determination coefficient (R2) and standard deviation of the logarithm of displacement(s log D) of each equation tested in the multivariate regression analysis.

Eq. C1 Std. err. C2 Std. err. C3 Std. err. C Std. err. R2 r log D

(21) 1.654 0.051 �10.750 0.489 – – �1.371 0.064 0.894 0.328(22) 1.706 0.040 �2.001 0.068 – – �4.770 0.117 0.934 0.259(23) 19.924 1.373 �38.324 2.496 – – 0.592 0.090 0.634 0.611(24) 1.354 0.078 �20.572 1.403 6.348 0.893 �0.944 0.078 0.930 0.270(25) 2.228 0.158 �2.498 0.156 0.373 0.107 �5.495 0.237 0.949 0.231(26) 1.857 0.078 �5.870 0.417 – – �1.812 0.086 0.804 0.446(27) �0.059 0.097 �1.168 0.073 – – �1.796 0.079 0.833 0.411

0.001

0.01

0.1

1

10

100

1000

0.1 1 10 100 1000

Arias Intensity (cm/s)

Dis

plac

emen

t (cm

)

0.02g0.05g0.1g0.2g0.05g0.2g0.1g0.02g

0.001

0.01

0.1

1

10

100

1000

0.1 1 10 100 1000

Arias Intensity (cm/s)

Dis

plac

emen

t (cm

)

0.02g0.05g0.1g0.2g0.2g0.1g0.05g0.02g

0.001

0.01

0.1

1

10

100

1000

0.1 1 10 100 1000

Arias Intensity (cm/s)

Dis

plac

emen

t (cm

)

0.02g0.05g0.1g0.2g0.2g0.1g0.05g0.02g

0.001

0.01

0.1

1

10

100

1000

0.1 1 10 100 1000

Arias Intensity (cm/s)

Dis

plac

emen

t (cm

)

0.05g0.1g0.2g0.02g0.05g0.1g0.2g0.02g

Fig. 9. Validation dataset fitting with the empirical relations of (a) Eq. (21), (b) Eq. (22), (c) Eq. (24) and (d) Eq. (25). In each plot, dashed lines represent the correspondingequation, while for comparison the best-fit lines obtained for each ac data subset are illustrated as coloured lines (colours as in the previous figure through each ac datasubset).

K. Chousianitis et al. / Soil Dynamics and Earthquake Engineering 65 (2014) 11–29 25

acceleration of 0.2 g where model (25) illustrates a better beha-viour. Also, we computed the root mean square (RMS) of residualsof the experimental data from the values predicted by the twomodels. We found approximately similar values of RMS, equal to0.268 and 0.264 for Eqs. (22) and (25) respectively.

Finally, for Eq. (25), which appears the model providing thebest predictive performance for our dataset, a qualitative assess-ment of normality of residual distribution was carried out. Fig. 11presents the Probability Density Function (PDF) graph along withthe Cumulative Distribution Function (CDF) graph of the residuals.The former displays the theoretical PDF of the normal distributionin comparison with the residuals from the analysis. The height of

each bar of the histogram represents the proportion of the data ineach class. The latter graph displays the theoretical CDF of thenormal distribution along with the empirical CDF based on ourresiduals. Thus, the PDF graph illustrates the shape of the dis-tribution of our dataset residuals, while the CDF graph shows howwell a normal distribution can be assumed as representative ofexceedance probability estimates. Given the slight superiority ofmodel (25) to predict Newmark displacements for critical accel-eration equal to 0.2 g, we select it as the most suitable empiricalpredictive relation for Newmark displacements in Greece. Itshould be noted that the obtained Newmark displacement empiri-cal estimator should be used for a range of ac values covered by thedata set used for the regression (i.e. from 0.02 to 0.2 g).

The regression model presented in Eq. (25) is able to providegood predictions of coseismic displacements that a rigorous New-mark analysis would yield. Newmark analysis is a valuable tool topredict the performance of natural slopes under seismic shaking,especially for the relatively shallow, brittle failures, which com-prise the majority of the earthquake-induced landslides andgenerally consist the basis for seismic landslide microzonation(e.g. [41,13,54,55]; Rajabi et al., [76]). However, it is important tomention the highly simplistic nature of Newmark's model andrecall that it contains many limitations which in some cases makethe rigorously calculated Newmark displacements to be indices ofdynamic slope performance rather than precise predictions ofactual slope displacement. These limitations include the approx-imation of the landslide as a rigid-plastic body, the lack ofpermanent displacements for accelerations below the criticalacceleration, the assumption that the sliding surface deformplastically only when the critical acceleration is exceeded, the lack

-2

-1

0

1

2

0.1 1 10 100 1000

Arias Intensity (cm/s)

Res

idua

ls (c

m)

-2

-1

0

1

2

0 0.05 0.1 0.15 0.2 0.25

Critical acceleration (g)

Res

idua

ls (c

m)

-2

-1

0

1

2

0.1 1 10 100 1000

Arias Intensity (cm/s)

Res

idua

ls (c

m)

-2

-1

0

1

2

0 0.05 0.1 0.15 0.2 0.25

Critical acceleration (g)

Res

idua

ls (c

m)

Fig. 10. Distribution of the logarithmic residuals of Newmark displacement interms of Arias intensity and critical acceleration for (a) Eq. (22) and (b) Eq. (25).

Residuals (cm)

0.60.40.20-0.2-0.4-0.6

Rel

ativ

e Fr

eque

ncy

0.16

0.14

0.12

0.1

0.08

0.06

0.04

0.02

0

Residuals (cm)

0.60.40.20-0.2-0.4-0.6

10.90.80.70.60.50.40.30.20.1

0

Fig. 11. (a) Relative histogram of the logarithmic residuals of Newmark displace-ment for Eq. (25). The red curve denotes the theoretical Probability DensityFunction of the normal distribution. (b) Theoretical cumulative distribution func-tion of the normal distribution (red line) versus empirical cumulative distributionfunction based on the logarithmic residuals of Newmark displacement for Eq. (25)(blue line). (For interpretation of the references to colour in this figure legend, thereader is referred to the web version of this article.)

K. Chousianitis et al. / Soil Dynamics and Earthquake Engineering 65 (2014) 11–2926

of consideration of a dependence of the critical acceleration onstrain, the hypothesis that static and dynamic strengths are thesame and constant and the disregard of the effects of dynamicpore pressure. The above assumptions make Newmark's methodto be well-matched to model landslides in relatively stiff and drymaterial which move as a coherent mass along a well-defined slipsurface, i.e. shallow slides and falls in rock and in soil. However inmany other cases, such as for deeper and larger failures in softermaterials, these assumptions can represent limitations too restric-tive for reliable results, and other types of permanent displace-ment analysis are recommended. The latter comprise methodsthat have improved Newmark's model to account for the deform-ability of the system as well as the dynamic displacement andinclude decoupled models [37,33] and fully coupled models[9,53,52]. The main difference between them is that in thedecoupled analysis the sliding displacement is computed afterestimating the dynamic response of the sliding mass withoutconsidering a failure surface, while in the coupled analysis thedynamic and sliding responses are estimated simultaneously.Coupled analysis is considered the most rigorous form of sliding-block analysis and yields the most accurate estimates of displace-ment for deeper landslides in softer material. The reader isreferred to Jibson [26] for a comprehensive discussion on thedifferent types of permanent-displacement methods. Apart fromthe effect of flexible slopes discussed above, Stamatopoulos [64]took into consideration the increase in critical acceleration asdisplacement occurs due to the fact that the downward movementof the sliding mass tries to stabilise the block. Recently, Baziar et al.[8] implemented the Stamatopoulos [64] model within adecoupled analysis and demonstrated how the rotational effectchanges the permanent displacements obtained by the originaldecoupled analysis.

5. Conclusions

Within the framework of the present study we provide tools forthe assessment of hazards related to earthquake-induced slopefailures. All of our analyses were based only on a dataset ofearthquakes located in the Greek area and therefore taking intoconsideration the prevailing seismotectonic characteristics that areincorporated in the strong-motion recordings. We developed fournew GMPEs for Arias intensity, to be used alternatively accordingto the availability of information on different explanatory vari-ables, and an empirical estimator of coseismic displacementsbased on Newmark's model. So far the only empirical attenuationrelationship for the prediction of Arias intensity for the area ofGreece is that of Danciu and Tselentis [12]. However, our newGMPEs were derived using the most recent information availableand were estimated considering the largest Ia value between theArias intensities calculated along the two horizontal componentsof the recording. On the contrary, up to now no empiricalestimators of Newmark displacement were available and this isthe first time that a tool to estimate the expected permanentdisplacement induced by seismic shaking of defined energy hasbeen incorporated in a regression model for Greece.

All of the regression analyses were performed on the basis of alarge strong-motion dataset, referring to events of magnitude3.2rMwr6.7, which were recorded from 1973 to 2013. Weillustrated the need of developing a specific Newmark displace-ment regression equation for Greece, since empirical equationsthat have been developed using global data did not provedeffective to reliably predict earthquake-induced landslide displa-cements within the Greek area. The geologic and seismotectonicfeatures of Greece, such as the high attenuation of the Aegean Seaarea, which are incorporated in the strong-motion recordings,

generate differences in the properties of the acceleration timehistories relative to shaking, in comparison to other areas of theworld. This fact can lead regression equations calibrated on globaldata to not accurately predict Newmark displacement within theGreek area and underline the need of regional equations for abetter predictive capability.

The new predictive equations to estimate Arias intensity weredeveloped using a two-step procedure separating the determina-tion of equation parameters accounting for the amount of energyrelease by the source from those relative to propagation effects.Four optimal equations were obtained according to formulationsoptionally including, in addition to the dependence on momentmagnitude and epicentral distance, the inclusion of termsaccounting for focal mechanism and site local conditions. Theresults of test conducted on a validation dataset different from thatused for regression, showed that the equation prediction capabil-ities actually benefit from the inclusion of additional independentvariables relative to site effect and focal mechanism types. Thus,information on these aspects of seismic energy transmitted toslope should be considered whenever available. Furthermore,since the employed dataset incorporates data that were notavailable at the time of the development of the previouslyproposed attenuation relation [12], the new equations derived inthe present study extend the range of applicability relative tomagnitudes and regional distances.

A regional regression equation to estimate Newmark displace-ment Dn, based only on a Greek strong-motion dataset was notavailable in literature before this study, thus we tested a variety offunctional forms. We adopted regression models using Ariasintensity Ia as the descriptor of ground motion, because it bettercharacterises the damaging effects of the seismic shaking, andrelate it with critical acceleration ac as parameter representing theslope strength to seismically induced failures. The best constrainedregression equation is expressed as function of the logarithms of Iaand ac and their product, which accounts for the apparent increaseof the rate of log Dn variation with Ia as ac increases. The analysis ofthe residuals resulting from the regression did not show systema-tic trends as a function of the independent variables used in thismodel. The intended use of this equation is for regional-scaleassessment and mapping of seismic landslide hazards in the Greekarea, since it was calibrated using a homogeneous strong-motiondatabase that reflects the seismotectonic environment of Greece.

Acknowledgements

The authors would like to thank three anonymous reviewersfor insightful comments and useful suggestions that helped toimprove the manuscript.

References

[1] Ambraseys NN, Menu JM. Earthquake-induced ground displacements. EarthqEng Struct Dyn 1988;16:985–1006.

[2] Ambraseys NN, Srbulov M. Earthquake induced displacements of slopes. SoilDyn Earthq Eng 1995;14:59–71.

[3] Ambraseys NN, Simpson KA, Bommer JJ. Prediction of horizontal responsespectra in Europe. Earthq Eng Struct Dyn 1996;25(4):371–400.

[4] Arias A. A measure of earthquake intensity. In: Hansen RJ, editor. Seismicdesign for nuclear power plants. Cambridge, MA: Massachusetts Institute ofTechnology Press; 1990. p. 438–83.

[5] Bathrellos GD, Gaki-Papanastassiou K, Skilodimou HD, Papanastassiou D,Chousianitis KG. Potential suitability for urban planning and industry devel-opment using natural hazard maps and geological-geomorphological para-meters. Environ Earth Sci 2012;66(2):537–48.

[6] Bathrellos GD, Gaki-Papanastassiou K, Skilodimou HD, Skianis GA, Chousiani-tis KG. Assessment of rural community and agricultural development usinggeomorphological–geological factors and GIS in the Trikala prefecture (CentralGreece). Stoch Environ Res Risk Assess 2013;27(2):573–88.

K. Chousianitis et al. / Soil Dynamics and Earthquake Engineering 65 (2014) 11–29 27

[7] Baziar MH, Dobry R, Elgamal AWM. Engineering evaluation of permanentground deformation due to seismically-induced liquefaction. Technical reportNCEER-92-0007, National Center for Earthquake Engineering Research, StateUniversity of New York, Buffalo; 1992.

[8] Baziar MH, Rezaeipour H, Jafarian Y. Decoupled solution for seismic perma-nent displacement of earth slopes using deformation-dependent yield accel-eration. J Earthq Eng 2012;16(1):917–36.

[9] Bray JD, Rathje EM. Earthquake-induced displacements of solid-waste land-fills. J Geotech Geoenviron Eng 1998;124:242–53.

[10] Bray JD, Travasarou T. Simplified procedure for estimating earthquake-induceddeviatoric slope displacements. J Geotech Geoenviron Eng 2007;133(4):381–92.

[11] Carro M, De Amicis M, Luzi L, Marzorati S. The application of predictivemodelling techniques to landslides induced by earthquakes: the case study ofthe 26 September 1997 Umbria–Marche earthquake (Italy). Eng Geol2003;69:139–59.

[12] Danciu L, Tselentis G-A. Engineering ground-motion parameters attenuationrelationships for Greece. Bull Seismol Soc Am 2007;97(1B):162–83.

[13] Del Gaudio V, Pierri P, Wasowski J. An approach to time-probabilisticevaluation of seismically induced landslide hazard. Bull Seismol Soc Am2003;93:557–69.

[14] Del Gaudio V, Wasowski J. Time probabilistic evaluation of seismically inducedlandslide hazard in Irpinia (Southern Italy). Soil Dyn Earthq Eng2004;24:915–28.

[15] Del Gaudio V, Wasowski J. Advances and problems in understanding theseismic response of potentially unstable slopes. Eng Geol 2011;122:73–83.

[16] Haneberg WC. Effects of digital elevation model errors on spatially distributedseismic slope stability calculations: an example from Seattle, Washington.Environ Eng Geosci 2006;12:247–60.

[17] Harp EL, Wilson RC. Shaking intensity thresholds for rock falls and slides:evidence from 1987 whittier narrows and superstition hills earthquakestrong-motion records. Bull Seismol Soc Am 1995;85:1739–57.

[18] Hashida T, Stavrakakis G, Shimazaki K. Three-dimensional seismic attenuationstructure beneath the Aegean region and its tectonic implication. Tectono-physics 1988;145:43–54.

[19] Hsieh SY, Lee CT. Empirical estimation of the Newmark displacement from theArias intensity and critical acceleration. Eng Geol 2011;122:34–42.

[20] Hwang H, Lin CK, Yeh YT, Cheng SN, Chen KC. Attenuation relations of Ariasintensity based on the Chi-Chi Taiwan earthquake data. Soil Dyn Earthq Eng2004;24:509–17.

[21] Jibson RW. Summary of research on the effects of topographic amplification ofearthquakes shaking on slope stability. Open File Report 87-268, US GeologicalSurvey, Menlo Park, California; 1987.

[22] Jibson RW. Predicting earthquake-induced landslide displacements usingNewmark's sliding block analysis. Transportation Research Record 1411.Washington, D.C.: Transportation Research Board, National Research Council;1993: p. 9–17.

[23] Jibson RW, Keefer DK. Analysis of the seismic origin of landslides: examplesfrom the New Madrid seismic zone. Bull Geol Soc Am 1993;105:521–36.

[24] Jibson RW, Harp EL, Michael J. A method for producing digital probabilisticseismic landslide hazard maps. Eng Geol 2000;58:271–89.

[25] Jibson RW. Regression models for estimating coseismic landslide displace-ment. Eng Geol 2007;91:209–18.

[26] Jibson RW. Methods for assessing the stability of slopes during earthquakes –a retrospective. Eng Geol 2011;122:43–50.

[27] Jibson RW, Rathje EM, Jibson MW, Lee YW. SLAMMER – Seismic LandslideMovement Modeled using Earthquake Records: U.S. Geological Survey Tech-niques and Methods, book 12, chapter B1; 2013.

[28] Joyner WB, Boore DM. Methods for regression analysis of strong-motion data.Bull Seismol Soc Am 1993;83:469–87.

[29] Kaklamanos J, Baise LG. Model validations and comparisons of the nextgeneration attenuation of ground motions (NGA–West) project. Bull SeismolSoc Am 2011;101:160–75.

[30] Keefer DK, Wilson RC. Predicting earthquake-induced landslides, with empha-sis on arid and semi-arid environments. In: Sadler PM, Morton DM, editors.Landslides in a semiarid environment, 2. Riverside, CA: Inland GeologicalSociety of Southern California Publications; 1989. p. 118–49.

[31] Lee CT, Hsieh BS, Sung CS, Lin PS. Regional Arias intensity attenuationrelationship for Taiwan considering VS30. Bull Seismol Soc Am2012;102:129–42.

[32] Ligdas CN, Main IG, Adams RD. 3-D structure of the lithosphere in the Aegeanregion. Geophys J Int 1990;102:219–29.

[33] Lin JS, Whitman RV. Earthquake induced displacements of sliding blocks. JGeotech Eng 1983;112:44–59.

[34] Luzi L, Pergalani F. Applications of statistical and GIS techniques to slopeinstability zonation (1:50.000 Fabriano geologic map sheet). Soil Dyn EarthqEng 1996;15:83–94.

[35] Luzi L, Pergalani F. Slope instability in static and dynamic conditions for urbanplanning: the “Oltre Po Pavese” case history (Regione Lombardia – Italy). NatHazards 1999;20:57–82.

[36] Mahdavifar MR, Jafari MK, Zolfaghari MR. The attenuation of Arias intensity inAlborz and Central Iran. In: Proceedings of the Fifth International Conferenceon Seismology and Earthquake Engineering, Tehran, Iran; 2007.

[37] Makdisi FI, Seed HB. Simplified procedure for estimating dam and embank-ment earthquake-induced deformations. ASCE J Geotech Eng Division1978;104:849–67.

[38] Makropoulos K, Kaviris G, Kouskouna V. An updated and extended earthquakecatalogue for Greece and adjacent areas since 1900. Nat Hazards Earth Syst Sci2012;12:1425–30.

[39] Mankelow JM, Murphy W. Using GIS in the probabilistic assessment ofearthquake triggered landslide hazards. J Earthq Eng 1998;2(4):593–623.

[40] Miles SB, Ho CL. Rigorous landslide hazard zonation using Newmark's methodand stochastic ground motion simulation. Soil Dyn Earthq Eng 1999;18(4):305–23.

[41] Miles SB, Keefer DK. Evaluation of seismic slope performance models using aregional case study. Environ Eng Geosci 2000;6:25–39.

[42] Miles SB, Keefer DK. Seismic Landslide Hazard for the City of Berkeley,California. US Geological Survey Miscellaneous Field Studies Map MF-2378;2001.

[43] Murphy W, Mankelow J. Obtaining probabilistic estimates of displacement ona landslide during future earthquakes. J Earthq Eng 2004;8:133–57.

[44] Nash JE, Sutcliffe JV. River flow forecasting through conceptual models: Part I,a discussion of principles. J Hydrol 1970;10:282–90.

[45] NEHRP. Recommended provisions for seismic regulations for new buildingsand other structures, Part 1: Provisions, FEMA 222A Building Seismic SafetyCouncil, Washington D.C.; 1994: 290 pp.

[46] Newmark NM. Effects of earthquakes on dams and embankments. Geotech-nique 1965;15:139–59.

[47] Papadopoulos GA, Plessa A. Magnitude–distance relations for earthquake-induced landslides in Greece. Eng Geol 2000;58:377–86.

[48] Papadopoulou-Vrynioti K, Bathrellos GD, Skilodimou HD, Kaviris G, Makro-poulos K. Karst collapse susceptibility mapping considering peak groundacceleration in a rapidly growing urban area. Eng Geol 2013;158:77–88.

[49] Pradel D, Smith PM, Stewart JP, Raad G. Case history of landslide movementduring the Northridge earthquake. J Geotech Geoenviron Eng ASCE2005;131:1360–9.

[50] Rajabi AM, Khamehchiyan M, Mahdavifar MR, Del Gaudio V. Attenuationrelation of Arias intensity for Zagros Mountains region (Iran). Soil Dyn EarthqEng 2010;30:110–8.

[51] Rajabi AM, Mahdavifar MR, Khamehchiyan M, Del Gaudio V. A new empiricalestimator of coseismic landslide displacement for Zagros Mountains Region(Iran). Nat Hazards 2011;59:1189–203.

[52] Rathje EM, Bray JD. Nonlinear coupled seismic sliding analysis of earthstructures. J Geotech Geoenviron Eng ASCE 2000;126:1002–14.

[53] Rathje EM, Bray JD. An examination of simplified earthquake-induceddisplacement procedures for earth structures. Can Geotech J 1999;36:72–87.

[54] Rathje EM, Saygili G. Probabilistic seismic hazard analysis for the slidingdisplacement of slopes-Scalar and vector approaches. J Geotech GeoenvironEng ASCE 2008;134:804–14.

[55] Rathje EM, Saygili G. Probabilistic assessment of earthquake-induced slidingdisplacements of natural slopes. Bull N Z Soc Earthq Eng 2009;41:18–27.

[56] Rathje EM, Saygili G. Pseudo-probabilistic versus fully probabilistic estimatesof sliding displacements of slopes. J Geotech Geoenviron Eng ASCE2011;137:208–17.

[57] Rathje EM, Antonakos G. A unified model for predicting earthquake-inducedsliding displacements of rigid and flexible slopes. Eng Geol 2011;122:51–60.

[58] Romeo R. Seismically induced landslide displacements: a predictive model.Eng Geol 2000;58:337–51.

[59] Rozos D, Bathrellos GD, Skilodimou HD. Comparison of the implementation ofrock engineering System (RES) and analytic hierarchy process (AHP) methods,based on landslide susceptibility maps, compiled in GIS environment. A casestudy from the Eastern Achaia County of Peloponnesus, Greece. Environ EarthSci 2011;63(1):49–63.

[60] Sabatakakis N, Koukis G, Vassiliades E, Lainas S. Landslide susceptibilityzonation in Greece. Nat Hazards 2013;65(1):523–43.

[61] Saygili G, Rathje EM. Empirical predictive models for earthquake-inducedsliding displacements of slopes. J Geotech Geoenviron Eng ASCE 2008;134(6):790–803.

[62] Scherbaum F, Cotton F, Smit P. On the use of response spectral-reference datafor the selection and ranking of ground motion models for seismic-hazardanalysis in regions of moderate seismicity: the case of rock motion. BullSeismol Soc Am 2004;94:2164–85.

[63] Skarlatoudis AA, Papazachos BC, Margaris BN, Theodulidis N, Papaioannou C,Kalogeras I, et al. Empirical peak ground-motion predictive relations forshallow earthquakes in Greece. Bull Seismol Soc Am 2003;93:2591–603.

[64] Stamatopoulos CA. Sliding system predicting large permanent co-seismicmovements of slopes. Earthq Eng Struct Dyn 1996;25(10):1075–93.

[65] Stafford PJ, Berril JB, Pettinga JR. New predictive equations for Arias intensityfrom crustal earthquakes in New Zealand. J Seismol 2009;13:31–52.

[66] Stavrakakis GN, Drakatos G, Karantonis G, Papanastassiou D. A tomographyimage of the Aegean region (Greece) derived from inversion of macroseismicintensity data. Annali Geofisica 1997;40(1):99–110.

[67] Theodulidis N, Kalogeras I, Papazachos C, Karastathis V, Margaris B, ChPapaioannou, et al. HEAD 1.0: a unified Hellenic accelerogram database.Seismol Res Lett 2004;75:36–45.

[68] Uniform Building Code. In: International Conference of Building Officials, USA,1997; vol. 2: 489 pp.

[69] Wieczorek GF, Wilson RC, Harp EL. Map showing slope stability duringearthquakes in San Mateo County California: US Geological Survey Miscella-neous Investigations Map I-1257-E; 1985.

K. Chousianitis et al. / Soil Dynamics and Earthquake Engineering 65 (2014) 11–2928

[70] Wilson RC, Keefer DK. Dynamic analysis of a slope failure from the 6 August1979 Coyote Lake, California, earthquake. Bull Seismol Soc Am1983;73:863–77.

[71] Wilson RC, Keefer D. Predicting areal limits of earthquake-induced landsliding.In: Ziony JI, editor. Earthquake Hazards in the Los Angeles Region – An Earth-science Perspective, U.S. Geological Survey Professional Paper 1360; 1985: p.317–45.

[72] Wilson RC. Relation of Arias intensity to magnitude and distance in California.Open-File report 93-556, US Geological Survey, Reston, Virginia, 1993; 42 pp.

[73] Yegian MK, Marciano EA, Ghahraman VG. Earthquake induced permanentdeformations: probabilistic approach. J Geotech Eng 1991;117:35–50.

[74] Lee CT, Huang CC, Lee JF, Pan KL, Lin ML, Dong JJ. Statistical approachto earthquake-induced landslide susceptibility. Eng. Geo. 2008;100:43–58.

[75] Sabetta F, Pugliese A. Estimation of response spectra and simulation ofnonstationary earthquake ground motion. Bull. Seismo. Soc. Am. 1996;86(2):337–52.

[76] Rajabi AM, Khamehchiyan M, Mahdavifar MR, DelGaudio V, Capolongo D. Atime probabilistic approach to seismic landslide hazard estimates in Iran. SoilDyn. and Earthq. Eng. 2013;48:25–34.

K. Chousianitis et al. / Soil Dynamics and Earthquake Engineering 65 (2014) 11–29 29