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SPECTRAL RESPONSE FEATURES USED IN LAST IAEA STRESS

TEST TO NPP CERNAVODA (ROMANIA) BY CONSIDERING

STRONG NONLINEAR BEHAVIOUR 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-077125 Bucharest – Magurele, Romania

E-mail: [email protected] #Corresponding author: [email protected]

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 Vrancea

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 Vienna. These SAF were used by NIEP,

as alternative analysis, for NPP Cernavoda (Romania) in last “2011 STRESS TEST”

asked by IAEA Vienna after Japan strong earthquake (Mw = 9.0).

Key words: Seismic hazard analysis, strong Vrancea 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)

mailto:[email protected]

mailto:[email protected]

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 15–20 km [5] below Focsani Depression, located in front of Eastern

Carpathian Curvature (Fig. 1) etc.

Fig. 1 – The VRANCEA99 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 Vrancea 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 Spectral response used in last IAEA stress test to NPP Cernavoda (Romania) Article no. 822

by Cornel [7] in 1968. At last ICTP Advanced Conference on Seismic Risk

Mitigation and Sustainable Development from Trieste (Italy) on 10–14 May, 2010,

Professor Z. Wang from University of Kentucky, USA [8] questioned: What is

Probabilistic Seismic Hazard Analysis (PSHA)?

where γ(y) is the annual probability of ground motion “y” being exceeded. In other

form:

where: S = the number of seismic areas; ν = the expected frequency, per time

period, per seismic area, – of earthquakes of magnitude at least mo; 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; fM(…) = probability density function (PDF) of

the magnitude distribution; fR(…) = 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) Variability 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

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methodology. More, in last strong Vrancea 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 ALTERNATIVE OF SEISMIC HAZARD EVALUATION FOR NPP CERNAVODA

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 (Sa), relative velocity (Sv), relative displacement (Sd) from response

spectra for a fraction of critical damping (ζ %) at fundamental period or any period

and peak values of acceleration (amax), velocity (vmax) and displacement (dmax),

respectively, from processed strong motion records , that is: (SAF)a= Smax

a /amax ;

(SAF)v = Smax

v /vmax ; (SAF)d = Smax

d /dmax; amax = y (t)max ; vmax = x (t)max; dmax =

= 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 Vrancea

earthquakes (Table 2). All data are obtained in the same conditions. The concept

was used for last Stress Test asked by IAEA Vienna for Romanian Cernavoda NPP

after strong 2011 Tohoku earthquake (MW = 9.0) on March 11, when NIEP, and

INCERC [10] recorded last three deep strong Vrancea earthquakes: August

30,1986 (MW = 7.1), May 30 (MW = 6.9) and May 31,1990 (MW = 6.4).

Fig. 2 – The absolute values of the variation of dynamic torsion modulus function (G, daN/cm2)

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].


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 Vrancea earthquakes:

August 30, 1986 (MW = 7.1 and h = 131.4 km); May 30,1990 (MW = 6.9 and

h = 90.9 km) and May 31,1990 (MW = 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 Gmax

= 7,000 daN/cm2, internal damping, Dmin = 3.7% and

density, ρ = 2,3 t/m3; next 7.00 m of fractured limestone with clay with G

max =

= 6,000 daN/cm2, Dmin = 3.6% and ρ = 2,1 t/m

3; next 34.00 m of marl with G

max =

= 4,470 daN/cm2, Dmin = 4.2% and density ρ = 2,1 t/m

3. The marl is going down

more than 270.00 m [11, 13]. In Tables 1 is given the data recorded at Cernavoda

NPP seismic station and spectral amplification factors (SAF) for last strong

Vrancea 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 Vrancea 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 Vrancea 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.


If we maintain the same amplification factor (SAF = 5.7851) as for relatively strong earthquake of May 31, 1990 with magnitude MW = 6.4 then at Cernavoda NPP Seismic Station for earthquake magnitude of May 30, 1990 (Mw=6.9) the peak acceleration has to be a*max = 0.1241(+21.6%), while the recorded values were only, amax = 0.102g. Similarly, for Vrancea earthquake of August 30,1986 (MW = 7.1), the peak acceleration has to be a*max = 0.0907g (+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 Vrancea magnitude and soil structure.

Table 1

Data recorded on Cernavoda NPP Seismic station and peak values of acceleration,

velocity and displacement

Nr. Vrancea earthquakes Component amax (cm/s2) vmax

(cm/s)

dmax

(cm)

1

August 30, 1986,

MW = 7.1; MGR = 7.0;

h =131.4 km

N-S

V

E-W

50.62

63.28

62.85

4.33

2.71

4.05

0.83

0.65

0.69

2

May 30,1990,

MW = 6.9; MGR = 6.7;

h = 90.9 km

N-S

V

E-W

107.11

53.10

100.43

9.83

7.28

9.80

3.37

4.26

2.71

3

May 31,1990,

MW = 6.4; MGR = 6.1;

h = 86.9 km

N-S

V

E-W

49.74

14.29

50.03

2.88

1.31

2.88

0.63

0.29

0.34

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 Vrancea earthquakes. The amplification factors are decreasing with increasing the magnitudes of deep strong Vrancea 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 Vrancea earthquake magnitude. The amplification factors decrease as the magnitude increases. If we will use for NPP Cernavoda site a relation of form: SAF = a MW

2 + b MW + c and if

we introduce data from Table 3 for MW =7.1; 6.9 and 6.4 we have: a = –1.7857; b = 21.6898 and c = –59.976 and

SAF = –1.7857 MW2 + 21.6898 MW – 59.876 (4)

and for MW = 7.2, SAF = 3.72; MW = 7.3, SAF = 3.29; MW = 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 Vienna are using, all time, a constant value, SAF= 3.13.


Table 2

Spectral amplification factors (SAF). Cernavoda NPP site

Earthquake Damping

(ξ%) Comp. (g)

(g)/amax

Svmax Sv

max/vmax

August 30,1986;

MW = 7.1; h = 131.4

km

2% N-S V

E-W

0.277 0.295 0.366

5.36 4.57 5.71

35.443 34.442 34.221

8.18 12.70 8.44

5% N-S V

E-W

0.193 0.203 0.261

3.74 3.14 4.07

24.102 22.583 23.601

5.56 8.33 5.82

10% N-S V

E-W

0,131 0.149 0.191

2.53 2.31 2.98

17.482 15.031 15.440

4.03 5.54 3.81

20% N-S V

E-W

0.087 0,107 0.133

1.68 1.65 2.07

13.053 9.796

11.059

3.01 3.61 2.73

May 30,1990,

MW = 6.9; h = 90.9 km

2% N-S V

E-W

0.652 0.259 0.765

5.97 4.78 7.47

50.231 24.168 57.917

5.11 3.32 5.91

5% N-S V

E-W

0.398 0.153 0.485

3.65 2.83 4.75

31.722 20.112 38.166

3.23 2.76 3.89

10% N-S V

E-W

0.306 0.116 0.340

2.80 2.14 3.32

22.581 15.824 25.885

2.30 2.17 2.64

20% N-S V

E-W

0.222 0.090 0.217

2.03 1.66 2.12

15.624 12.042 16.114

1.59 1.65 1.64

May 31,1990,

MW = 6.4; h = 86.9 km

2% N-S V

E-W

0.259 0.068 0.430

5.11 4.67 6.53

17.825 15.646 32.644

3.09 11.94 11.33

5% N-S V

E-W

0.173 0.050 0.293

3.41 3.43 5.78

12.433 12.510 23.353

2.15 9.55 8.11

10% N-S V

E-W

0.115 0.035 0.217

2.27 2.40 3.30

8.639 8.984

15.784

1.50 6.86 5.48

20% N-S V

E-W

0.074 0.024 0.145

1.46 1.65 2.20

6.454 5.944

11.240

1.12 4.54 3.90


Table 3

Cernavoda NP Plant NIEP Seismic Station [11]; Φ = 44.340 N; λ = 28.030 E

Earthquake

MW

amax (g)

rec. (g)

SAF =

/ amax C Sa

*(g) a*(g) %

1986, 7.1 0.064 0.2610 4.0781 1.418 0.3702 0.090 41.8

1990, 6.9 0.102 0.4850 4.7549 1.216 0.5900 0.124 21.6

1990, 6.4* 0.050 0.2933 5.7851 1.000 0.2933 0.050 –

Table 4

Cernavoda NP Plant, INCERC Seismic Station [5, 11]; Φ = 44.341 N; λ = 28.033 E

Earthquake

MW

amax (g)

rec. (g)

SAF =

/ amax C Sa

*(g) a*(g) %

1986, 7.1 0.0695 0.2654 3.8201 1.4915 0.3958 0.1036 49.1

1990, 6.9 0.1028 0.4281 4.1643 1.3697 0.5863 0.1408 36.9

1990, 6.4* 0.0554 0.3160 5.7039 1.0000 0.3160 0.0554 –

*) This deep Vrancea earthquake with MW = 6.4 (MGR = 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 Vrancea earthquakes

Damping Aug. 30, 1986 (Mw = 7.1) May 30, 1990 (Mw = 6.9) May 31, 1990 (Mw = 6.4)

ξ% Samax/amax Sv

max/vmax Samax/amax Sv

max/vmax Samax/amax Sv

max/vmav

2% 4.74 3.61 5.58 3.72 6.22 4.84

5% 3.26(3.13) 2.69 3.63(3.13) 2,95 4.16(3.13) 3.48

10% 2.43 1.99 2.56 2,14 2.92 2.69

20% 1.78 1.50 1.82 1,58 2.13 1.86

max

aS

max

aS


Fig. 4 – Nonlinear dependence of spectral amplification factors (SAF)

of Vrancea 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

Vrancea 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.


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 Vrancea earthquakes. The spectral amplification factors are decreasing

when the magnitudes of Vrancea 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 Vienna, after Japan strong

earthquake (Mw = 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 Vrancea 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 72/2012-2016 and PN 16 35 02 02.

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