SPECTRAL RESPONSE FEATURES USED IN LAST IAEA STRESS TEST TO NPP CERNAVODA (ROMANIA) BY CONSIDERING STRONG NONLINEAR BEHAVIOUR OF SITE SOILS

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1 SPECTRAL RESPONSE FEATURES USED IN LAST IAEA STRESS TEST TO NPP CERNAODA (ROMANIA) BY CONSIDERING STRONG NONLINEAR BEHAIOUR OF SITE SOILS GHEORGHE MĂRMUREANU, ELENA-FLORINELA MANEA #, CARMEN ORTANZA CIOFLAN, ALEXANDRU MĂRMUREANU, DRAGOS TOMA-DANILĂ National Institute for Earth Physics, P. O. Box MG-2, RO Bucharest Magurele, Romania # Corresponding author: Received February 17, 2017 Abstract. Devastating and, in some sense, unforeseen earthquakes in Nepal, Japan, New Zealand, Haiti, Sumatra and elsewhere have triggered in last time a heated debate about the legitimacy and limitations of Probabilistic Seismic Hazard Assessment (PSHA). This method is a pure numerical creation, as it was developed from mathematical statistics and not based on earthquake physics. An important source of errors came from one of its key component: the Ground Motion Prediction Equation (GMPE), which describes a relationship between a ground motion parameter (PGA etc.), magnitude M, distance R., without taking into account the nonlinear behavior of site soils during strong earthquakes. In order to capture these effects, the spectral amplification factors (SAF) were computed for the last recorded rancea intermediate-depth events showing a decrease with the increase of earthquake magnitude of earthquakes and these values are far of those given by R.G.1.60 of the U. S. Atomic Energy Commission and IAEA ienna. These SAF were used by NIEP, as alternative analysis, for NPP Cernavoda (Romania) in last 2011 STRESS TEST asked by IAEA ienna after Japan strong earthquake (M w = 9.0). Key words: Seismic hazard analysis, strong rancea earthquakes, nonlinear soil behavior. 1. INTRODUCTION Estimating seismic ground shaking is an important step in anticipating earthquake effects on people and structures. Ground motion at a particular site can be influenced by three main elements: source, seismic wave s travel path, and local site conditions. If the first describes how the size and nature of the earthquake source controls the generation of earthquake waves, then the second describes the effect of the earth on these waves as they travel (at some depth) from source to a particular location (site), and the third describes the effect of the uppermost several hundred meters of rock and soil and the surface topography at that location on the resultant ground motion produced by the emerging or passing earthquake waves. Romanian Journal of Physics 62, 822 (2017)

2 Article no. 822 Gheorghe Mărmureanu et al. 2 In all extra-carpathian area (Fig. 1) the geophysical profile composition passes from clay to sandy clays or sands, from marl to sandy marl or sand lenses etc. The sedimentary cover, relatively thick (exceeding 5 km), is the result of four major cycles of sedimentation: Paleozoic, Permian-Triassic, Jurassic-Cretaceous and Upper Miocene Quaternary [1]. A soil is of basic type sand or gravel (termed coarse soils), silt or clay (termed fine soils) etc. For example, in south of Bucharest there are layers of 520 m of dense sand and in the north the thickness of all sedimentary layers is around 1,480 m [2, 3, 4]. Also, the sedimentary thickness reaches km [5] below Focsani Depression, located in front of Eastern Carpathian Curvature (Fig. 1) etc. Fig. 1 The RANCEA99 seismic refraction experiment: The crustal structure beneath the southeastern Carpathians and the Moesia Platform from a seismic refraction profile in Romania between the cities Bacau and Bucharest, traversing the rancea epicenter region in NNE SSW direction [5, 6]. 2. GROUND MOTION AND BASIC SEISMIC HAZARD Seismic wave attenuation can be thought of as consisting of two major elements, geometric spreading and absorption (sometimes called damping). The methodology used in most probabilistic seismic hazard analysis was first defined

3 3 Spectral response used in last IAEA stress test to NPP Cernavoda (Romania) Article no. 822 by Cornel [7] in At last ICTP Advanced Conference on Seismic Risk Mitigation and Sustainable Development from Trieste (Italy) on May, 2010, Professor Z. Wang from University of Kentucky, USA [8] questioned: What is Probabilistic Seismic Hazard Analysis (PSHA)? 1 (ln y ln y ( y) vp( Y y) v {1 exp[ y 0 ln, y ln, y mr 2 ) ]d(ln y)} f M ( m) f R ( r)dmdr (1) where γ(y) is the annual probability of ground motion y being exceeded. In other form: S ln a g( m, r) P( A a) 1 exp( vi f i 1 ( r / m) f R i M i ( m)drdm 1 exp[ ( a)] (2) where: S = the number of seismic areas; ν = the expected frequency, per time period, per seismic area, of earthquakes of magnitude at least m o ; Φ'( ) = the standard normal complementary cumulative distribution function (CCDF) which is based on the usual assumption that the ground motion parameter is a lognormal aleatory variable. The ground motion distribution is possibly truncated. This function has a value less than unity; f M ( ) = probability density function (PDF) of the magnitude distribution; f R ( ) = probability density function (PDF) of distances, from the site, of the locations of earthquakes, given an earthquake occurs in the seismic area; λ(a) = annual rate of events with site ground motion level a or more. Under the additional assumption that the events in every source follow independent Poisson processes, the mean rate λ(a) can be used to compute the probability of exceeding, in any time interval of length t: P [A > a in time t] =1 e λ(a)t (3) in which P[.] is the probability of the event. Consequently, double integral Φ'( ) can t exceed value 1. PSHA was developed from mathematical statistics (e.g. Benjamin and Cornell, 1970 [9] under four fundamental assumptions [7]): (a) Constant in time average occurrence rate of earthquakes; (b) Equal likelihood of earthquake occurrence along a line or overall area source (single point); (c) ariability of ground motion at a site is independent; (d) Poisson (or memory lees) behavior of earthquake occurrence. In summary, the probabilistic seismic hazard analysis (PSHA model) is flaw: (1) it is not based on earthquake science (invalid physical models; point source; Poisson distribution); (2) invalid mathematics; (3) miss interpretation of annual probability of exceeding or return period. PSHA become a pure numerical creation [8]. A key component for seismic hazard assessment including all methods developed so far is the ground motion attenuation prediction equation (GMPE) which is a statistical tool in this

4 Article no. 822 Gheorghe Mărmureanu et al. 4 methodology. More, in last strong rancea earthquakes there are many peak ground accelerations larger than epicenter values [3]. Estimating seismic ground shaking is an important step in anticipating earthquake effects on people and structures. 3. NEW ALTERNATIE OF SEISMIC HAZARD EALUATION FOR NPP CERNAODA The authors, in order to make quantitative evidence of large nonlinear effects, used/ introduced and developed the concept of the nonlinear spectral amplification factor (SAF) as ratio between maximum spectral absolute acceleration (S a ), relative velocity (S v ), relative displacement (S d ) from response spectra for a fraction of critical damping (ζ %) at fundamental period or any period and peak values of acceleration (a max ), velocity (v max ) and displacement (d max ), respectively, from processed strong motion records, that is: (SAF) a = S max a /a max ; (SAF) v = S max v /v max ; (SAF) d = S max d /d max ; a max = y (t) max ; v max = x (t) max ; d max = = x(t) max. In Tables 1 are given the data recorded on Cernavoda NPP seismic station (Table 1) and spectral amplification factors (SAF) for last strong rancea earthquakes (Table 2). All data are obtained in the same conditions. The concept was used for last Stress Test asked by IAEA ienna for Romanian Cernavoda NPP after strong 2011 Tohoku earthquake (M W = 9.0) on March 11, when NIEP, and INCERC [10] recorded last three deep strong rancea earthquakes: August 30,1986 (M W = 7.1), May 30 (M W = 6.9) and May 31,1990 (M W = 6.4). Fig. 2 The absolute values of the variation of dynamic torsion modulus function (G, dan/cm 2 ) and torsion damping function (D%) of specific strain (γ%) for marl samples obtained in Hardin & Drnevich resonant columns (USA patent) from NIEP, Laboratory of Earthquake Engineering [11, 12, 13].

5 5 Spectral response used in last IAEA stress test to NPP Cernavoda (Romania) Article no. 822 The Spectral Amplification Factors (SAF) were finally computed for absolute accelerations at 5% fraction of critical damping (ζ = 5%) in two seismic stations on NPP Cernavoda site for last strong and deep rancea earthquakes: August 30, 1986 (M W = 7.1 and h = km); May 30,1990 (M W = 6.9 and h = 90.9 km) and May 31,1990 (M W = 6.4 and h = 86.9 km). The geophysical profile for NPP Cernavoda site is as follows: first 5.00 m of fractured limestone with shear modulus G max = 7,000 dan/cm 2, internal damping, D min = 3.7% and density, ρ = 2,3 t/m 3 ; next 7.00 m of fractured limestone with clay with G max = = 6,000 dan/cm 2, D min = 3.6% and ρ = 2,1 t/m 3 ; next m of marl with G max = = 4,470 dan/cm 2, D min = 4.2% and density ρ = 2,1 t/m 3. The marl is going down more than m [11, 13]. In Tables 1 is given the data recorded at Cernavoda NPP seismic station and spectral amplification factors (SAF) for last strong rancea earthquakes (Table 2). All data are obtained in the same conditions. Fig. 3 Dependence of dynamic torsion modulus function (G, dan/cm²) and of torsion damping function (D%) and with shear strains (γ%) and frequency (ω) for clay samples obtained in Hardin & Drnevich resonant columns (USA patent) from NIEP, Laboratory of Earthquake Engineering from NIEP. Between 1 and 10 Hertz, shear modulus G and damping D are constant, domain used in design of civil engineering structures [11, 12]. In Tables 3, 4 and Fig. 4, spectral amplification factors are given where the effect of the nonlinearity in Cernavoda NPP site is characterized by the coefficient c. The coefficient c is the ratio of SAF for May 31,1990 rancea earthquake to SAF for each stronger earthquake. Sa*(g) and a*(g) are the maximum spectral acceleration and, respectively, maximum acceleration if the system would have a linear response (behavior) to the fundamental period. For rancea earthquake of May 31, 1990 (MGR = 6.1) the response can be assumed to be in elastic range and we have the possibility to compare the nonlinear effects with those predicted by a linear model.

6 Article no. 822 Gheorghe Mărmureanu et al. 6 If we maintain the same amplification factor (SAF = ) as for relatively strong earthquake of May 31, 1990 with magnitude M W = 6.4 then at Cernavoda NPP Seismic Station for earthquake magnitude of May 30, 1990 (M w =6.9) the peak acceleration has to be a* max = (+21.6%), while the recorded values were only, a max = 0.102g. Similarly, for rancea earthquake of August 30,1986 (M W = 7.1), the peak acceleration has to be a* max = g (+41.8%), instead of actual acceleration value of 0.064g recorded at Cernavoda NPP Seismic Station (Table 3). The present analysis indicates that the effect of nonlinearity could be very important and from Table 3 is 41.87%; from Table 4 is 49.1% and for stronger earthquakes it will be larger. In addition, these spectral amplification factors are function of the earthquake rancea magnitude and soil structure. Table 1 Data recorded on Cernavoda NPP Seismic station and peak values of acceleration, velocity and displacement Nr. rancea earthquakes Component a max (cm/s 2 ) 1 August 30, 1986, M W = 7.1; M GR = 7.0; h =131.4 km v max (cm/s) d max (cm) May 30,1990, M W = 6.9; M GR = 6.7; h = 90.9 km May 31,1990, M W = 6.4; M GR = 6.1; h = 86.9 km From Tables 3 and 4 we can see that there is a strong nonlinear dependence of the spectral amplification factors (SAF) on earthquake magnitude [7] for all records made on NPP Cernavoda Site for last strong rancea earthquakes. The amplification factors are decreasing with increasing the magnitudes of deep strong rancea earthquakes and these values are far of that given by Regulatory Guide 1.60 of the U. S. Atomic Energy Commission [13]. The spectral amplification factors (SAF) and, in fact, the nonlinearity, is functions of rancea earthquake magnitude. The amplification factors decrease as the magnitude increases. If we will use for NPP Cernavoda site a relation of form: SAF = a M W 2 + b M W + c and if we introduce data from Table 3 for M W =7.1; 6.9 and 6.4 we have: a = ; b = and c = and SAF = M W M W (4) and for M W = 7.2, SAF = 3.72; M W = 7.3, SAF = 3.29; M W = 7.4, SAF = 2.87; M = 7.5, SAF = 2,35 etc. Regulatory Guide 1.60 of the U. S. Atomic Energy Commission and IA.EA ienna are using, all time, a constant value, SAF= 3.13.

7 7 Spectral response used in last IAEA stress test to NPP Cernavoda (Romania) Article no. 822 Table 2 Spectral amplification factors (SAF). Cernavoda NPP site Earthquake Damping (ξ%) Comp. (g) (g)/a max Sv max S v max /v max 2% August 30,1986; M W = 7.1; h = km 5% 10% , % , May 30,1990, M W = 6.9; h = 90.9 km 2% 5% 10% 20% % May 31,1990, M W = 6.4; h = 86.9 km 5% 10% 20%

8 Article no. 822 Gheorghe Mărmureanu et al. 8 Earthquake M W Table 3 Cernavoda NP Plant NIEP Seismic Station [11]; Φ = N; λ = E a max (g) rec. (g) max S a SAF = / a C S * a (g) a * (g) % max 1986, , , 6.4* Earthquake M W Table 4 Cernavoda NP Plant, INCERC Seismic Station [5, 11]; Φ = N; λ = E a max (g) rec. (g) max S a SAF = / a C S * a (g) a * (g) % max 1986, , , 6.4* *) This deep rancea earthquake with M W = 6.4 (M GR = 6.1) thought that it is still generating elastic strains in soils. On the other hand, from Table 5 we can see that there is a strong nonlinear dependence of the spectral amplification factors on earthquake magnitude [8 11, 17] for all seismic stations on Romanian territory on extra-carpathian area (Iaşi, Bacău, Focşani, Bucharest-NIEP, Bucharest-INCERC etc.). Table 5 Median values of (SAF) on extra-carpathian area to strong rancea earthquakes Damping Aug. 30, 1986 (M w = 7.1) May 30, 1990 (M w = 6.9) May 31, 1990 (M w = 6.4) ξ% S max a /a max S max v /v max S max a /a max S max v /v max S max a /a max S max v /v mav 2% % 3.26(3.13) (3.13) 2, (3.13) % , % ,

9 9 Spectral response used in last IAEA stress test to NPP Cernavoda (Romania) Article no. 822 Fig. 4 Nonlinear dependence of spectral amplification factors (SAF) of rancea earthquake magnitude from records in extra-carpathian area. 4. CONCLUDING REMARKS Regions far from the edges of tectonic plates present some of the most difficult conditions for Probabilistic Seismic Hazard Assessment (PSHA). The values of the maximum earthquake magnitudes that will ever happen on faults are some of the least defensible elements of PSHA (7). It is important to note that the basic equation (1) for PSHA was derived from mathematical statistics, therefore it should be applied to very large databases. The rancea strong motion records are limited to the 3 events used in this study and attempts to enlarge the input by acquiring seismic records from different tectonic regions is quite questionable. An important source of errors came from a key component of PSHA: the ground motion prediction equation (GMPE) which describes a relationship between a ground motion parameter (PGA etc.), magnitude M, distance R and uncertainty (ε) which after Klügel [14] is just the main error in disaster of Fukushima Daichii (Japan) Nuclear Power Plant [16]. Strong ground accelerations from large earthquakes can produce a non-linear response in shallow soils (Tables 3 5 and Figs. 2, 3, 4). On the other hand, when a non-linear site response is present, then the shaking from large earthquakes cannot be predicted by simple scaling of records from small earthquakes.

10 Article no. 822 Gheorghe Mărmureanu et al. 10 A strong nonlinear dependence of the spectral amplification factors (SAF) with earthquake magnitude was observed at all records at NPP Cernavoda Site for last strong rancea earthquakes. The spectral amplification factors are decreasing when the magnitudes of rancea intermediate-depth earthquakes increase and these values are far of that given by Regulatory Guide 1.60 of the U. S. Atomic Energy Commission [15]. These results show that the spectral amplification factors (SAF) and, in fact, the nonlinearity, are functions of earthquake magnitude. These SAF values were used by NIEP, as alternative analysis, for NPP Cernavoda (Romania) in last 2011 STRESS TEST asked by IAEA ienna, after Japan strong earthquake (M w = 9.0) for all Nuclear Power Plants from Europe. In last part of paper, the authors are coming with a new methodology to construct site design response spectra by using spectral amplification factors for last three strong rancea earthquake recorded on site and by taking into consideration the strong nonlinear behavior of soils between rock base and free field. Acknowledgements. This work was performed in the frame of the Projects BIGSEES contract 72/ and PN REFERENCES 1. M. Sandulescu, Overview on Romanian geology. In: Berza, T. (Ed.), Alcapa II Field Guidebook: Geological Evolution of the Alpine Carpathian Pannonian System., Rom. J. Tecton. Reg. Geol. 74, pp (1994). 2. G. Mărmureanu, C.O. Cioflan, A. Mărmureanu, Researches on local seismic hazard (microzonation) of the metropolitan area Bucharest, TECHNOPRES (2010). 3. G. Mărmureanu, Certainties / uncertainties in hazard and seismic risk assessment of strong rancea earthquakes, Romanian Academy Publishing House, 350 p. (2016). 4. E. F. Manea, C. Michel,. Poggi, D. Fäh, M. Radulian, F. S. Balan, Improving the shear wave velocity structure beneath Bucharest (Romania) using ambient vibrations. Geophysical Journal International 207 (2), 1 November 2016, Pages , gji/ggw306 (2016). 5.. Raileanu, A. Bala, F. Hauser, C. Prodehl, W. Fielitz, Crustal properties from S-wave and gravity data along a seismic refraction profile in Romania. Tectonophysics 410.1: (2005). 6. F. Hauser,. Raileanu, W. Fieltz, A.Bala, C. Prodehl, G. Polonic, A.Schulze, RANCEA 99 The crustal structure beneath the southeastern Carpathians and the Moesia Platform from seismic refraction profile in Romania, Tectonophysics 340, (2002). 7. A. C. Cornell, Eng. seismic risk analysis, BSSA 58 (5), (1968). 8. Z. Wang, Seismic hazard and risk assessment and mitigation policy in USA. ICTP Advanced Conference on Seismic Risk Mitigation and Sustainable Development; geologichazards (2010). 9. J. R. Benjamin, C. A. Cornell, Probability, statistics, and decision for civil engineers. Courier Corporation (2014). 10. S. Borcia, Data processing of strong motion records obtained during rancea Earthquakes (1977, 1986, ; ). Academic Soc. Ed. M.T. Botez (2010).

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