Comparison of Dynamic 

Characteristics of 

Fukushima Nuclear Power Plant 

Containment Building Determined

From Tests and Earthquakes 

Office of Nuclear Regulatory Research 

NUREG/CR-4432

ANL-85-67
 

Comparison of Dynamic

Characteristics of

Fukushima Nuclear Power Plant

Containment Building Determined

From Tests and Earthquakes

Manuscript Completed: September 1985 

Date Published: October 1985 

Prepared by

M.G. Srinivasan, C.A. Kot, and B.J. Hsieh

Argonne National Laboratory

9700 South Cass Avenue 

Argonne, IL 60439

NRC Job Code A2217

Office of Nuclear Regulatory Research 

NUREG/CR-4432

ANL-85-67
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ARGONNE NATIONAL LABORATORY 

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COMPARISON OF DYNAMIC CHARACTERISTICS 

OF FUKUSHIMA NUCLEAR POWER PLANT 

CONTAINMENT BUILDING 

DETERMINED FROM TESTS AND EARTHQUAKES 

by 

M. G. Srinivasan, C. A. Kot, 

and B. J. Hsieh 

Components Technology Division 

Manuscript Completed: 

Date Published: 

September 1985 

October 1985 

Prepared for 

Division of Engineering Technology 

Office of Nuclear Regulatory Research 

U. S. Nuclear Regulatory Commission 

Washington, D. C. 20555 

under Interagency Agreement DOE 40-550-75 

NRC FIN No. A22l7 

NUREG/CR-4432 

ANL-85-67 

(Distribution Codes: 

RD and RM) 

ABSTRACT 

COMPARISON OF DYNAMIC CHARACTERISTICS OF FUKUSHIMA NUCLEAR POWER 

PLANT CONTAINMENT BUILDING DETERMINED FROM TESTS AND EARTHQUAKES 

by 

M. G. Srinivasan, C. A. Kot, B. J. Hsieh 

Modal parameters determined from response measured in dynamic tests and from 

analytical models for Simulating the tests and two subsequent earthquakes 

experienced by the containment building of Unit 1 of the Fukushima Power 

Station complex in Japan are compared for the purpose of evaluating the 

effectiveness of the dynamic tests in earthquake response prediction. The 

tests are found to have led to the correct identification of a fundamental 

frequency. The lack of agreement between test- and earthquake-determined 

modeshapes and damping is attributable more to the shortcomings of the 

simulation models than to differences in actual behavior. 

NRC 

FIN No. 

A2217 

Title 

Evaluation of Testing Methods for Safety Assessment of Nuclear Power 

Plant Structures 

iii 
PREFACE 

This report presents the results of an investigation conducted for the U.S. 

Nuclear Regulatory Commission (NRC), Office of Nuclear Regulatory Research 

(RES), Division of Engineering Technology (DET). The work was performed 

under a Standard Order for DOE work (FIN No. A2217). The project monitor 

was Dr. J. F. Costello, NRC/RES; his helpful suggestions and reviews are 

gratefully acknowledged. The authors also wish to thank Dr. H. Tanaka of 

the Tokyo Electric Power Co., Inc. for his help in clarifying many issues 

relating to this comparative study. 

C. A. Kot, Manager 

Structural and Fluid Mechanics Section 

Components Technology Division 

Argonne National Laboratory 

iv 
TABLE OF CONTENTS 

ABSTRACT. • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •• iii 

PREFACE. • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • i v 

EXECUTIVE SUMMA.RY...................................................... 1 

1. 

2. 

3. 

4. 

5. 

6. 

7. 

INTRODUCTION ••••••••••••••••••••••••••••••••• e- ••••••••••••••••••• 

DESCRIPTION OF THE STRUCTURE ••••••••••••••••••••••••••••••••••••• 

FORCED VIBRATION TESTS OF 1969 ••••••••••••••••••••••••••••••••••• 

EARTHQUAKE OF 1970 ••••••••••••••••••••••••••••••••••••••••••••••• 

MIYAGIKEN-OKI EARTHQUAKE OF 1978 ••••••••••••••••••••••••••••••••• 

COMP ARI SONS •••••••••••••••••••••••••••••••••••••••••••••••••••••• 

CONCLUSIONS •••••••••••••••••••••••••••••••••••••••••••••••••••••• 

2 

2 

4 

6 

8 

12 

16 

REFERENCES. • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 17 

v 
LIST OF FIGURES 

Figure Title Page 

1 Fukushima Unit 1 Containment Building ••••••••••••••••••••••.••••• 18 

LIST OF TABLES 

Table Title Page 

1 Comparisons of Model Parameters •••••••••••••••••••••••••••••••••• 19 

vi 
EXECUTIVE SUMMARY 

The objective of the study reported is the evaluation of the effectiveness 

of dynamic tests for characterizing the dynamic properties of a containment 

building that determine its earthquake response. The containment building 

in this case is that of the Unit 1 of Fukushima Nuclear Power Station 

Complex in Japan. It was subjected to forced vibration tests in 1969 and to 

two earthquakes subsequently: a small earthquake in 1970 and the larger 

Miyagiken-Oki earthquake in 1978. The containment response to all the three 

events was recorded and used in studies to characterize the system dynamics. 

Natural periods and modeshapes were estimated directly from the dynamic 

tests. Modal parameters were not directly obtained in the same manner 

(i.e., by a parameter estimation method) from earthquake response. Instead 

analytical models were devised by different investigators to simulate 

earthquake response. A lumped parameter model was used to simulate both the 

tests and the 1970 earthquake. The physical parameters of this model were 

adjusted until computed response agreed with the measured response. The 

modal parameters of the model were also determined. 

Two independent analyses were performed to simulate the 1978 earthquake. 

Though both the analyses used almost the same physical properties of 

materials, the models employed were very different. In one case the 

building was idealized as two vertical beams while the site (i.e., soil) 

extending in all directions up to a relatively large distance was modeled in 

great detail. In the other case, the superstructure was modeled with a 

greater number of vertical and horizontal beams while the soil was 

represented by springs and dampers. Measured ground motion was used as 

input excitation, either directly or through a convolution analysis. Modal 

properties for the two models were also determined. 

It was difficult to compare even the modal parameters as it was not possible 

to reconcile the various modes computed for the different models. Only two 

modes could be determined to be common among the different analyses. It is 

seen that the dynamic tests correctly identified the fundamental period. 

Damping determination both from the tests and the earthquakes is so 

dependent on the modeling assumptions that no conclusion can be drawn about 

it. As the simulation approach introduces significant uncertainties, this 

approach should be replaced by direct parameter estimation techniques for 

obtaining reliable estimates of modal parameters from measured response. 

1 
2 

1. INTRODUCTION 

The study described in this report was part of a program sponsored by the 

U.S. Nuclear Regulatory Commission (NRC) to evaluate the utility and 

limitations of dynamic testing of nuclear power plant buildings for safety 

assessment. The basis of the evaluation was the actual testing experience 

relating to large, as-built civil engineering structures, including nuclear 

plant buildings. In the coarse of a survey of reported testing experience, 

the results of which were published elsewhere [1,2], it was found that the 

reactor building of Unit 1 of the Fukushima Nuclear Power Station Complex in 

Japan was one of the very few nuclear power plant structures for which 

response was recorded during both dynamic tests and natural earthquakes. If 

the recorded data were available to the present authors, this would have 

presented a very good opportunity to determine how reliable the test results 

would have been for predicting earthquake response. As recorded data was 

not available to us, the objective of this study was limitedd to an 

evaluation of the effectiveness of dynamic tests for obtaining the dynamic 

characteristics of the system that influence earthquake response. The 

dynamic characteristics are the modal parameters, and the source of 

information on these was published literature on the test and earthquake 

response of the building. 

2. DESCRIPTION OF THE STRUCTURE 

Tokyo Electric Power Company's Fukushima Nuclear Power Station Complex is 

located on the Pacific Coast in Northern Japan's Fukushima prefecture. The 

complex has six Soiling-Water-Reactor power plant units. The units were 

completed at different times during the seventies. The 460-MWe Unit 1 was 

completed in 1970 and commenced operation in 1971. Units 1 through 5 have a 

Mark 1 (light-bulb/torus) type of containment and Unit 6 has a Mark 2 type 

of containment. The plant is founded on a competent soft-mudstone formation 

with a thickness of more than 300 m. The grade level of the site, at 10 m 

above sea level, was prepared by excavating a hill of original height of 

about 35 m above sea level. 
3 

The reactor building of Unit 1, which was subjected both to forced vibration 

tests and natural earthquakes is about 58 m in height from the base of the 

foundation mat, the depth of embedment of which is about 14 m below ground 

level (Fig. 1). The building consists of a reinforced concrete structure up 

to a height of about 43 m from the base, and a steel structure and truss 

roof above this level. The reinforced concrete structure consists of six 

floors, including the basement floor. The plan dimensions of the building 

are 42 m x 42 m at lower sections, and 42 m x 31 m at upper sections. The 

building is structurally isolated from the adjacent turbine building and 

radwaste building. The reactor pressure vessel is at the center of the 

building, surrounded successively by a concrete gamma shield wall, a bulbshaped steel containment vessel, and a reinforced concrete shield wall. The 

reactor pressure vessel is connected to the gamma shield wall with 

horizontal supports and the steel containment vessel is connected to the 

gamma shield wall by a stabilizer. The containment v~ssel is also connected 

to the other reinforced concrete shield wall with shear lugs. 

According to some of the earlier references, [3,4], the soft- or sandymudstone soil has a plane wave speed of 1700 mIs, shear wave speed of 610 

mIs, and a Young's modulus of 18 t/cm2• It is not clear what was the basis 

for determining these values. The analytical models used in various 

investigations, however, had to use values for shear wave speed, and Young's 

modulus different from the above to correctly simulate dynamic response. If 

tests for determining the soil properties were used as the basis for 

selecting the values of the mechanical parameters, these tests have not been 

identified or referred to by most investigators. 

The buildings were designed by both static and dynamic methods of aseismic 

design procedure. In the static method, a seismic coefficient of 0.48 was 

used. The dynamic design was based on a seismic analysis of response to a 

peak horizontal ground acceleration of about 0.18 g [3]. 
4 

3. FORCED VIBRATION TESTS OF 1969 

A set of forced vibration tests was performed on the reactor building of 

Unit 1 in November 1969, immediately after the completion of the building 

[3,4]. A sinusoidal shaker was installed on the 5th floor, the uppermost 

floor of the reinforced concrete structure. Steady-state excitation in two 

mutually-perpendicular directions (parallel to the outer walls of the square 

building referred to as N-S and E-W directions) was provided by the 

shaker. The shaker was capable of operating in a frequency range of 0.2 to 

20 Hz, and of producing a peak force of 3 tonnes. The horizontal 

displacements at the basement, 2nd floor, 5th floor, roof, reactor pressure 

vessel, . gamma shield wall and the containment vessel were measured. The 

rotational motion of the foundation mat was also measured. The measurements 

included the phase lags of all the responses. 

tests were of the order of 30-40 x 10-6 m. 

The peak amplitudes in the 

The response data was acquired and analyzed with the "MIK System" [5] in 

real time, to give frequency response curves. The MIK system obtains the 

response amplitude and phase through a cross correlation of the response 

signal and the force signal. The periods of vibrations were obtained from 

the· peaks of the resonance curves, the first three periods being 0.25 s, 

0.17 s, and 0.089 s [3,4]. The mode shapes were obtained by plotting the 

modal amplitudes measured in the tests. 

It appears that no attempt was made to estimate modal damping directly from 

the test data using methods such as half-power bandwidth or other similar 

ones, presumably because the resonance curves were not smooth enough. 

Instead a simulation analysis of the tests, employing an analytical model 

with certain assumed physical constants, was performed [3,4]. Apparently 

the physical constants were adjusted until the analytical resonance curves 

and mode shapes agreed with corresponding test data. This analysis gave the 

modal damping, as a percentage of critical damping, to be 33.7, 8.4, and 5.4 

respectively for the three modes. 

The analytical model employed in the simulation of the test with the 

excitation along the N-S axis was the same as the one used in the dynamic 
5 

analysis to simulate the response to a 1970 earthquake, and is described in 

[6]. This lumped-mass, spring-element model essentially consisted of 

straight and branched stick models of the building walls. Both bending and 

shearing stiffnesses of the walls were taken into account. The masses were 

lumped at each floor level. Springs in horizontal planes modeled the 

relatively flexible floors. The foundation was divided into three elements 

with rotational and translational springs representing the soil behavior. 

This model also predicted natural periods and mode shapes that agreed well 

with the ones obtained from the vibration tests. 

Among the physical cons tants used in the simulation analysis, the Young's 

modulus for the soil had to be taken as 45 t/ cm2 in order to get good 

comparison with the test records. This value is significantly different 

from the value of 18 t/cm2, presumably determined directly from field 

tests. Tanaka, whose investigation of the 1978 earthquake is discussed 

later, is of the opinion [7] that the value of 45 t/cm2 for the soil Young's 

modulus is too large. However, he notes that the authors' use of the higher 

value in a formula for the determination of the soil spring constant based 

on static loading yields approximately the same soil spring constants when a 

lower value for soil Young's modulus is substituted in a formula based on 

dynamic loading. Also Tanaka considers [7] the Young's modulus for 

concrete, taken by the authors to be 520 t/cm2 to be too high, but he does 

not consider it a significant error as he thinks that this value should be 

considered in association with the method and assumptions used for modeling 

the building. Thus it is probable that other material property values 

employed in the simulation analysis also do not represent the true physical 

constants, but are actually only mathematical equivalents that depend on the 

characteristics of the analytical model. If indeed the material parameters 

had been adjusted without regard to their actual values (determined directly 

by tests or obtained from engineering practice), the objectivity of the 

model is open to challenge. 

Comparing the periods obtained from the peaks of the resonance curves of the 

test data with those obtained from the analytical model, we note that the 

first and third mode periods (i .e. 0.25 sand 0.089 s)agree exactly while 

the second mode period from test data (0.17 s) is slightly different from 
6 

that of the model (0.18 s). Since the method used for identifying the 

periods from test data is probably a visual selection, this difference in 

the second mode frequency is probably of no significance. 

Mode shapes for the first three modes were also computed by the authors of 

[3,4] from the analytical model and were compared with the corresponding 

mode shapes directly obtained from the test data. The comparison is 

generally very good, and the only significant difference occurs in the 

first-mode mode shape vector at one location in the roof. 

4.0 EARTHQUAKE OF 1970 

In May 1970, only a few months after the forced vibration tests, a minor 

earthquake, whose center was located 50 km offshore at a depth of 50 km, 

occurred. As seismographs had been installed in the building two months 

before the earthquake, the North-South response of the building at the 

following six locations was recorded: basement floor, 3rd floor, 5th floor, 

roof, and the top and bottom of the gamma shield wall. The peak 

accelerations recorded at any of these locations are not given in [6,8]. 

However, the response spectra with 5% damping show peaks of the order of 

0.03 - 0.06 g at the building locations. 

The mathematical model, noted in the previous section, was used in the 

dynamic analysis to simulate the earthquake response. The measured basement 

motion was applied as the base excitation to the model. The physical 

constants of the model (Young's modulus, Poisson's ratio, and a viscous 

damping coefficient) were adjusted until the computed response agreed 

closely with the recorded accelerations at different locations in the 

superstructure. Comparing the physical constants needed to correctly 

simulate the vibration test response with those for the correct simulation 

of earthquake response, we find that the only difference occurs in the 

viscous damping coefficient for the reactor pressure vessel and the primary 

containment vessel. (The damping coefficient is the ratio of 

proportionality between stiffness and damping matrices of an element.) The 

coefficient is 0.00032 s for the vibration tests and 0.00016 s for the 
7 

earthquake. Whereas it is obvious that the lower damping value gave a 

better comparison with the recorded earthquake, it is not clear what 

physical reasoning would justify a lower damping coefficient for the steel 

vessels in the anlaysis for earthquake response. The authors of [3,4,6,8] 

do not give any explanation for this. 

By considering the damped free vibrations of the analytical model, the 

authors of [6,8], also determined the natural periods, damping ratios, and 

the mode shapes for the eight lowest modes. The damped natural period of 

the first three modes and the damping ratio for the first two modes were 

identical to the corresponding values obtained for the vibration-test 

model. The damping ratio for the third mode was, however, obtained to be 

1.6%, in the case of the earthquake response analysis whereas it was 

determined to be 5.4% in the case of vibration test response analysis. This 

is clearly a consequence of reducing the values for the physical constant 

representing damping in the steel reactor vessel and containment, as the 

third mode is the dominant mode of the reactor pressure vessel. 

The authors show the first eight analytically determined mode shapes in 

[6]. In the first mode (period: 0.25 s) the building and the basemat 

vibrated in the same direction. In the second mode (period: 0.18 s) the 

concrete and steel parts of the structures were out of phase, with the 

amplitude of the steel truss being dominant. The third mode (period: 0.89 

s) was predominantly a local mode - the first mode for the reactor pressure 

vessel. In the fourth mode (period: 0.077 s) the translation and rocking 

of the foundation mat were very pronounced and the roof vibrated out-ofphase with the base. (The authors [6] noted that this mode may be 

considered the second mode of the system. This would seem to imply that the 

mode with a period of 0.18 s is a local mode of the steel truss). The fifth 

mode, (period: 0.051 s), is a local torsional mode of the steel truss. The 

sixth mode (period: 0.050 s) has two nodes along the height and is noted by 

the authors of [6] to be the third mode of the system. The seventh mode 

(period: 0.048 s) is a local translational mode of the truss. The eighth 

mode (period: 0.045 s) is a local mode, being the first mode of the gamma 

shield wall. (Note that the sixth and seventh modes referred to above are 

incorrectly designated as seventh and sixth, respectively, by the authors [6].) 
8 

As there was no direct mode shape estimation from the recorded earthquake 

response, it is not possible to make a comparison of the analytical and 

"measured" mode shapes. However, it is possible to make a visual comparison 

of the mode shapes of the analytical model based on earthquake response with 

those directly determined from tests. As only three lower modes were 

determined from the test data (see [3,4]) only the first three lower-mode 

mode shapes computed analytically (see [6]) are useful for this 

comparison. The comparison shows that the analytical mode shapes from the 

earthquake simulation analysis were generally close to the test-determined 

mode shapes. 

5. MIYAGlKEN-OKI EARTHQUAKE OF 1978 

On June 12, 1978, about nine years after the vibration testing, the 

Fukushima plants experienced a strong earthquake. This earthquake, of 

Richter magnitude 7.4, had its epicenter at about 95 km from the coast of 

Miyagi prefecture of Japan. The approximate epicentral distance to 

Fukushima was 140 km. The peak horiz'ontal ground acceleration recorded at 

the Fukushima plant site was 0.13 g and the duration of the strong gound 

motion was about 30 sec. 

Seismographs and moving-coil accelerometers installed in and near the 

containment building of Unit 1 of the Fukushima nuclear plant complex 

recorded the earthquake motions of the soil and the building. The 

acceleration records used in the simulation analysis discussed below [9] 

were the horizontal N-S motions (the direction parallel to the coast line) 

obtained from seismographs installed at the following five locations: 

basement floor, 3rd floor, 5th floor, top floor, and in the soil buried at 

an elevation of -40 m (i.e., 36 m beneath the foundation) on the vertical 

axis of the building. The maximum acceleration recorded at the basement was 

about 0.08 g, and that at the fifth floor was about 0.15 g. 

Adopting an approach similar to those reported in [3,4,6,8] Tanaka and 

Nakahara [9] performed a simulation analysis of the structural response to 

the earthquake, instead of applying an inverse method to identify a dynamic 
9 

model from recorded earthquake response. However, the mathematical model 

devised by Tanaka and Nakahara [9] was quite different from that used in 

[3,4,6,8]. In this model, the soil surrounding the building was modeled 

with much greater detail and refinement. The soil region of the model had 

a depth of about 50 m (corresponding to the deepest earthquake observation 

point at the elevation of -40 m), length of about 190 m, and a width of 

about 63 m. The length direction was parallel to the N-S direction, the 

direction of earthquake motions considered. The soil was divided into 

vertical columns, each of which was idealized as a lumped-mass shear beam. 

The vertical soil columns were assumed to be fixed at their botton boundary 

and were interconnected at other nodes by horizontal springs. The building 

was represented by two vertical cantilevers (having the shear and bending 

stiffness equivalent to the outer and inner walls), with lumped masses and a 

horizontal connecting spring at each floor level. Rotational springs also 

connected the foundation to the soil. The building nodes had horizontal 

translation (N-S) and rotational degrees of freedom while the soil nodes had 

only the translational degree of freedom. 

The shear wave velocity in the soil was taken to be 180 mls for the top 

layer of 5 m depth, 270 mls for the next layer of 5 m depth and 530 mls for 

the third layer of 40 m depth. Tanaka [7] notes that of these values, those 

for the surface layers were assigned on the basis of measurements made at a 

different location of the same site and that the average measurement for the 

supporting mudstone layer was actually 610 mls but was adjusted down to 530 

m/s. Though Tanaka justifies the adjustment by pointing out that it lies 

within the range of measurements, he implies that the reason for the 

adjustment was that the adjusted value resulted in a better simulation. 

The first part of the analysis was the determination of natural frequencies, 

modal damping ratios, mode shapes and participation factors. The authors 

give the periods, participation factors, and modal damping values for ten 

modes. The periods for the ten modes are 0.396 s, 0.322 s, 0.260 s, 

0.210 s, 0182 s, 0.163 s, 0.159 s, 0.153 s, 0.137 s, and 0.109 s. The 

corresponding damping ratios, as a percentage of critical damping are 10.08, 

10.15, 8.84, 8.12, 6.98, 11.32, 10.27, 10.47, 10.27, and 10.40. They also 

give the mode shapes for the first, third, and the fifth modes. They note 
10 

that the first mode (period: 0.396 s) is the fundamental mode of the site 

model, the third mode is the fundamental mode of the building (period: 0.26 

s) and the fifth mode (period: 0.182 s) is predominantly the motion of the 

steel structure of the containment building. 

The second part of the analysis was the simulation of response to the 1978 

earthquake. The recorded acceleration at the -40 m elevation was used as 

the base excitation for the model. The. computed acceleration histories at 

the basement floor, third floor, and fifth floor were compared with the 

corresponding earthquake records. According to the authors the agreement 

between computed history and recorded history is good for the basement floor 

and the third floor. From the acceleration history figures given in [9], it 

appears that the fifth floor response is not as well simulated by the 

model. However, a comparison based on the acceleration response spectra 

(for 5% damping), shown in [9], seems to indicate that the simulation is 

satisfactory for response at the basement, third floor, and fifth floor. On 

the other hand, this comparison indicates that the response of the roof 

truss at frequencies greater than 4 Hz is not well simulated by the model. 

The Miyagiken-Oki earthquake response of Fukushima Unit 1 was also used in 

another investigation sponsored by NRC/RES for correlating the results of 

the standard Soil Structure Interaction (SSI) methods of analysis with 

measured response. Miller et al. [10] performed a number of different SSI 

analyses using lumped parameter and finite element methodologies. As all 

these studies focused on response prediction aspects of different SSI 

models, the modal charachertistics of the models were not determined in all 

cases. In fact modal parameters were determined only for two cases of 

lumped parameter models. In one of these two cases, the model had only free 

boundaries for the superstructure with the SSI represented by nodal 

forces. Because of this the modes of this model do not correspond to the 

modes of the full soil-structure system. In the other case, the lumpedparameter model of the superstructure was attached to spring and dashpot 

elements representing the SSI. Therefore the modal parameters of this model 

can be considered to be that of the. full soil-structure system. Thus only 

this case is pertinent to the purposes of the present study and is discussed 

below. 
11 

The superstructure was modeled as four vertical beams, all lying in the E-W 

plane (i.e., normal to direction of earthquake excitation) with masses 

lumped at floor levels and connected by horizontal beams. Horizontal 

translation in the N-S direction and rotation about the E-W axis were the 

two degrees of freedom allowed at the nodes. The SS! was accounted for by 

spring and damper elements connected to the nodes in the base and side 

walls. Frequency-independent spring and damper constants (termed standard 

interaction parameters) were determined by averaging the frequency-dependent 

parameters derived from analytical solutions for steady-state vibrations of 

rigid foundations resting on a homogeneous elastic half-space. 

The material properties used for steel and concrete were identical to those 

used by Tanaka and Nakahara [9]. However, the shear wave velocity in the 

soil was assumed to be 490 mis, which is slightly smaller than the .530 mls 

used by Tanaka and Nakahara for the mudstone layer. The damping values for 

the elements connected to the base was 38.5% of critical for translation and 

7.58% critical for rocking; those for the elements connected to the sidewall 

were 129.2% of critical for translation and 51.8% of critical for rotation. 

The authors note that if the structure is taken to be rigid, the natural 

frequencies associated with SSI occur at 3.6 Hz (period: 0.277 s) and at 

10.5 Hz (period: 0.094 s). On the basis of amplifications of the spectral 

peaks in the measured response, the authors state that the interaction 

springs are consistent with measured data. 

Natural frequencies, mode shapes, and damping ratios are given for the first 

12 modes, though actually 15 modes were used in the analysis according to 

the authors. The natural frequencies of these 12 modes are (in Hz) 2.51, 

4.13, 4.44, 8.32, 10.21, 12.47, 12.63, 14.77, 16.46, 17.02, 18.49, and 

19.96. The damping ratios (expressed as percentage of critical) for the 12 

modes are: 17, 6, 6, 37, 5, 4, 11, 6, 6, 5, 7, and 5. Significant 

interaction effects were noted to occur at modes 1, 4, 7, 10, and 11. 

The response to Miyagiken-Oki earthquake ~as computed by subjecting the base 

of the lumped parameter model to input motions. Different cases of input 

motions were applied to the base though only two are of interest in the 
12 

present context. In one case the free field motion measured directly under 

the basemat was used as input. In the other case, the input motion used was 

derived from a convolution analysis where the motion measured at the -40 m 

elevation was propagated up through the soil to the basemat location. In 

calculating this input motion, a soil damping of 10% of critical was 

assumed. The other cases considered by the authors of [10] are not 

considered here because for these cases (in which the interaction spring 

and/or damper parameters were varied to obtain a best fit between computed 

and measured data) no corresponding modal parameters of the lumped-parameter 

model were given. 

Comparisons of computed spectra with measured 

measurement locations in the building are shown. 

spectra for the four 

For the case where the 

measured pulse under the basemat was used as input, the agreement is good at 

the basemat but significant differences are noticed at the other 

locations. Specifically, the frequencies at which spectral peaks occur in 

the computed and measured spectra are noticeably different. For the other 

case where the calculated pulse was used as input, the comparisons at all 

four measurement locations is even less satisfactory. The authors conclude 

that the standard interaction parameters are correct while the convolution 

analysis is responsible for the differences. But the discrepancies noted in 

the comparisons of the former case do not support this conclusion in our 

view. Though the computed responses may be considered as acceptable 

approximations of measured responses, the lack of coincidence of the 

spectral peaks leads us to question whether the modal parameters of the 

lumped-parameter model with standard interaction parameters are actually the 

best approximations to the modal parameters of the physical system. 

6. COMPARISONS 

As the same mathematical model was not used in all the three investigations, 

a direct comparison of the physical parameters (e.g., stiffnesses) assumed 

in the models is not possible. Even the physical constants (e.g., elastic 

modulus of concrete or the soil) were different in different models because 

these were in some cases equivalent material properties that were influenced 
13 

by the modeling assumptions. Moreover the physical constants were adjusted, 

within the limits of available direct test data [7], to obtain good 

simulations of dynamic tests or earthquake response. Therefore it is more 

appropriate to use the modal parameters (e.g., natural periods) as the basis 

for comparisons. 

A difficulty arises even in comparing the modal parameters. The different 

models gave rise to modes that are not the same. This difficulty is 

compounded by the fact that without analyzing the numerical data for the 

mode shapes, it is not possible for the present authors to decide whether 

two modes determined from different models are the same on the basis of a 

visual examination of the mode shapes sketched. Therefore the original 

authors' description of the mode, the frequency at which the mode occurs and 

the sketch of the mode shape were all taken into account in making the 

comparison. Table I shows the natural periods identified from the test 

data, and the natural periods and damping ratios computed for the four 

different analytical models simulating the test and earthquakes. The modes 

are arranged in the order of descending periods and each mode is identified 

by a serial number for the sake of convenience. It must be noted that in 

almost all cases the serial number is different from the mode number 

assigned to the mode by the original authors. When a mode is identified by 

a number in the following, it is this serial number that is referred to. 

A glance at Table I will demonstrate the difficulty noted above in making 

this comparison. The number of modes given by various authors ranged from a 

minimum of 3 to a maximum of 12. But since the modes obtained from 

different models could not be identified to be the same except in a few 

instances, there are actually a total of 27 modes, with periods varying from 

0.398 s to 0.045 s, that were determined from different models. As is clear 

from the table there is a great deal more difference than similarity between 

the modal parameters of the various models. 

Since the two simulation models for the 1969 tests and 1970 earthquake were 

almost identical, the mode shapes for the two models agreed very well. Only 

two of the mode shapes (Le., 3 and 7) obtained by Tanaka and Nakahara [9] 

can be identified to be similar to two determined by Muto et ale 
14 

[3,4,6,8]. Even though the model of the former is very different from that 

of the latter, the description of three of the ten mode shapes given by the 

former made it possible to identify these as common modes. Tanaka also 

confirmed this subsequently [7]. As for the mode shapes given by Miller et 

al. [10], it was not possible to relate any except their first mode with any 

of the modes determined by others. Miller et al. [10] stated that their 

first mode was identical to that determined by Tanaka and Nakahara. Even 

for their modes with a period very close to that determined by anyone of 

the other authors, the mode shapes do not seem to agree. 

Furthermore there is strong evidence to consider the first two modes given 

by Tanaka and Nakahara [9] to be fictitious (in the sense that these are 

merely the consequence of modeling assumptions) and not actual modes of the 

physical system. The soil boundary at the level of -40 m was assumed to be 

fixed in their model. Tanaka admitted [7] that "since the actual site soil 

profile does not have the distinct boundary at the corresponding level 

(i.e., at -40 m), the above mode does not actually exist." While no such 

admission regarding mode 2 has been made, it appears to us that this mode 

also is peculiar to the site model and does not exist for the physical 

system. 

It is somewhat surprising that Miller et al. [10] also determined a mode at 

about the same period (i.e., mode 1) and claimed it to be the same as those 

given by Tanaka and Nakahara, despite the lack of a fixed soil boundary in 

the model of Miller et al. [10]. As Miller et al. do not model the soil as 

a continuum, 

deformations. 

their mode shapes contain only the superstructure 

On the other hand Tanaka and Nakahara [9] have only two beam 

elements to model the superstructure but an elaborate set of elements to 

model the site. Thus it is difficult to be sure that mode 1 of [10] is the 

same as mode 1 of [9]. 

Thus it would be appropriate to exclude the modal parameters of Miller et 

al. [10] from further comparisons due to lack of any COmmon ground between 

them and the rest. Even among the rest, the comparison has to be limited to 

modes 3 and 7 which were the only ones determined independently by two 

different models by two different set of investigators. There is agreement 
15 

that mode 3 is the fundamental mode of the soil-building system and that 

mode 7 is a local bending mode of the steel truss [3,6,9]. Comparing the 

natural frequencies for these modes, the slight difference in the 

calculated values between [6] and [9] is not significant. The change in 

period of mode 7 from 0.17 s (identified from test data) to 0.18 s 

(determined from models) could also not be considered as representing any 

true softening of the system. Thus the tests may be considered as 

successful 1n identifying the periods of these two modes. 

Concerning the damping ratios, it must first be emphasized that none of the 

values in this table were identified directly from the test or earthquake 

response data through a parameter identification procedure. Thus these 

values have to be considered to be dependent on the analytical modeling 

assumptions involved in the three models. These results probably are 

directly related more to the assumed damping properties of the materials 

than to the other aspects influencing energy dissipation. Considering the 

fundamental mode of the soil-building system, the large difference between 

the values of the 1969/1970 models [3,6] on the one hand and the 1978 model 

on the other, is explained by Tanaka [7] as due to the difference in the 

nature of the two models. His explanation may be interpreted to be that the 

damping value of 33.7% given by the 1969/1970 models includes all the 

dissipative effects of soil-structure interaction, whereas the 8.84% given 

by the model of [9] does not include the energy dissipation within the 

soil. When one consideres that the latter model gave modal damping values 

of 10.08% and 10.15% for its first two modes that are physically 

unrealizable, the combined dissipative effect of the first three modes of 

this model might be equivalent to a high damping value indicated by the 

1969/1970 models for the first mode indicated by them. 

No explanation is available for the differences' between the damping values 

for the other common mode. From a practical point of view all the above 

damping values should be treated with caution and only an analysis of the 

measured response data might help to identify acceptable damping values. 
16 

7. CONCLUSIONS 

The low-level dynamic tests appear to have successfully identified the first 

mode and the fundamental period of the Fukushima Uni t 1 reactor building. 

This period has not shifted during the relatively small 1970 earthquake. 

There is a slight increase in its value, from 0.25 s to 0.26 s for the 

larger 1978 earthquake. On the basis of available information, it is not 

possible to determine whether this small increase in the period is due to a 

softening of the system or due to modeling assumptions. The difference in 

damping values obtained from the models simulating the different events are 

significant enough to cast doubt on the practical validity of any of the 

damping values. 

This exercise at comparison of test and earthquake dynamic characteristics 

has also raised a question as to the utility of simulation models for 

predicting any responses to excitations other than the ones they were 

originally devised for. One of the simulation models for the 1978 

earthquake [9] has shown that it could simulate the 1978 earthquake response 

correctly despite the physically unrealistic assumption of a fixed boundary 

in the soil at the level of -4Om. It is not known whether this model could 

successfully simulate the 1970 earthquake or the 1969 tests. The other 

analytical model [10] response to simulating the 1978 earthquake was not 

even as successful in simulating this earthquake. Similar criticism also 

applies to the simulation models of the 1969 tests and 1970 earthquakes in 

which the choice of the material constants seem to have been "adjusted" to 

obtain good simulations without any effort to relate these constants to 

physical constants obtained from direct tests. 

The objective of this study would have been better achieved had the modal 

parameters been determined from measured response through a parameter 

estimation analysis. Employing the parameters of simulation models was 

resorted to only because the data were not available to us. Based on this 

experience the use of simulation analyses in lieu of parameter estimation 

methods is not recommended. 
17 

REFERENCES 

1. Srinivasan, M. G., Kot, C. A. Hsieh, B. J., "Feasibility of Dynamic 

Testing of As~built Nuclear Power Plant Structures: An Interim 

Evaluation," NUREG/CR-1937, ANL-CT-81-5, Argonne National Laboratory, 

May 1981. 

2. Srinivasan, M. G., Kot, C. A., Hsieh, B. J., "Dynamic Testing of AsBuilt Civil Engineering Structures: A Review and Evaluation," 

NUREG/CR-3649, ANL-CT-83-20, Argonne National Laboratory, January 1984. 

3. Muto, K., Hayashi, T., Omatsuzawa, K., Ohta, T., Uchida, K., and Kasai, 

Y., "Comparative Forced Vibration Test of Two BWR-Type Reactor 

Buildings," Paper No. K 5/3, Transactions of the Second International 

Conference on Structural Mechanics in Reactor Technology, Berlin 1973. 

4. Muto, K., Hayashi, T., Omatsuzawa, K., Ohta, T., Uchida, K., and Kasai, 

Y. , "Comparative Forced Vibration Test of Two BWR-Type Reactor 

Buildings," Nuclear Engineering and Design, 27, 220-227, 1974. 

5. Muto, K., Uchida, K., Kasai, Y, Ohta, T., and Adachi, N., "A New 

Measuring Method of Vibration Using Correlation Technique," Proceedings 

of the Fifth World Conference on Earthquake Engineering, Rome, V. 2, 

1412-1421, 1973. 

6. . Muto, K. and Omatsuzawa, K., "Earthquake Response Analysis for a BWR 

Nuclear Power Plant Using Recorded Data," Nuclear Engineering and 

DeSign, 20, 385-392, 1972. 

7. Tanaka, H., Private Communications. 

8. Muto, K., and Omatsuzawa, K., "The Earthquake Response Analysis for a 

BWR Nuclear Power Plant Using Recorded Data," Paper No. K2/1, 

Transactions of the First International Conference on Structural 

Mechanics in Reactor Technology, Berlin, 1971. 

9. Tanaka, H. and Nakahara, M., "Investigation of Soil-Building 

Interaction Behavior of a BWR Plant During Miyagiken-Oki Earthquake of 

1978," Proceedings of the Seventh World Conference on Earthquake 

Engineering, Istanbul, V.6, 73-80, 1980. 

10. Miller, C. A., Constantino, C. J., Philippacopolous, A. 

Reich, M. , "Verification of Soil-Structure Interaction 

NUREG/CR-4182, Brookhaven National Laboratory, May 1985. 

J., and 

Methods, 
-

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. 

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3: 

I 

lLJ 

(.!) 

u.. -
Serial 

No. 

Description/characteristics of mode as 

given by authors of noted reference 

1 I Fundamental mode of site (9), significant 

interaction effects (10)** 

2 

3 Fundamental mode of soil-building system [3,6,9 

4 

5 

: ILoCS. bend1.g of ., ... 'ru •• [3.6.'1 

9 

10 

111 12 Significant interaction effects (10) 

13 

14 

15 Local mode of reactor vessel [3,6] 

16 

17 Significant interaction effects (10) 

18 Translation and rocking of basemat 

(second global mode of system) [6] 

19 I 

20 21 Significant interaction effects [10] 

22 Significant interaction effects [10] 23 Local torsional mode of steel truss [6] 24 Third global mode of system [6] 25 26 ILocal translational mode of steel truss [1) 27 Local mode of shield wall [6) 

!able I. Co.parison of Modal Para.eters 

from measured 

frequency 

response of 

1969. tests 

(Ref (3) 

0.25 

0.17 

0.089 

llatural Period. in seconds 

from analytical model simulating 

__ of 

1970 

(Ref (6) 

0.25 

0.18 

0.089 

0.077 

0.051 

0.050 0.048 

0.045 

1978 

(Ref [91> I (Ref (10)*) 

0.396 0.322 

0.26 

0.21 

0.182 

0.163 

0.159 

0.153 

0.137 

0.109 

0.398 0.242 

0.225 

0.120 

0.098 0.080 

0.079 

0.068 

0.061 

0.059 

0.054 

0.050 

*The analytical model is the lumped parameter model with standard interaction parameters 

**Authors of (10) state this mode is identical to that given by (9) 

1969 

Tests 

(Ref (3» 

33.7 

8.4 

5.4 

Da..,i

from a

simula

1970 

(Ref [6 

33.7 

8.4 

1.6 

70.4 

2.4 

35.9 

2.9 

4.3 
20 

Distribution for NUREG/CR-4432 (ANL-85-67) 

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R. A. 

R. S. 

P. R. 

C. A. 

Till 

Valentin 

Zeno 

Huebotter 

Kot (2) 

M. G. Srinivasan (25) 

B. J. Hsieh (2) 

S. Zussman 

C. K. Youngdahl 

ANL Patent Dept. 

ANL Contracts File 

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Components Technology Division Review Committee: 

P. Alexander, Flopetrol Johnston Schlumberger, P.O. Box 36369, Houston 

Texas 77236 

D. J. Anthony, General Electric Co., 175 Curtner Ave., San Jose, 

Calif. 95125 

A. A. Bishop, U. Pittsburgh, Pittsburgh, Penn. 15261 

B. A. Boley, Northwestern U., Evanston, Ill. 60201 

R. N. Christensen, Ohio State U., Columbus, Ohio 43210-1321 

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IIIRC FOR ... 136 u.s. ~UC\"lA" RIQULATOAY COMMI$SION I HcPOH. T J'o4UMI:JEA /Au'IMd b'l rlDc. #(J(J VpI No, d #n".J 

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3201, J]()] BIBLIOGRAPHIC DATA SHEET ANL-85-67 SEE .NSTRUCT.O .... S ON T .... E REVERSE 

] TlTL.E A""O SUBTITLE J LEAVE BLANK 

Comparison of Dynamic Characteristics of Fukushima 

Nuclear Power Plant Containment Building Determined 

From Tests and Earthquakes 4 DATE REPORT COMPLETED 

MO ..... TH I yEA.R 

S AUTp;OR(SI September 1985 

tj DATE REPORT 'SSuED 

M. C. Srinivasan, C. A. Kot, and B. J. Hsieh MONTH I YEAR 

October 1985 

1 "ERFORM .... G OR~A,..,IZAT 10 .... ""A"'E AND MA1LI .... G ADDRESS (If1CllJtH Z,P CcxhJ B PROJECT/TASK/WORK UNIT NUMBER 

Argonne National Laboratory 

9700 S. Cass Avenue 9 FIN OR GRANT NUMBER 

Argonne, IL 60439 A2217 

10 SPO"'SORI~G ORGAN.ZATION ... A .... E ANO MAILING ADDRESS flnelll*Z,p COIhJ 1 h. TYPE OF REPORT 

Division of Engineering Technology Formal Technical 

Office of Nuclear Regulatory Research 

U.S. Nuclear Regulatory Commission b. PERIOD COVEREO (lnC/'IIIII. rMr.,J 

Oct. 1983 - Sept. 1985 

11 SUPPLE .... E~TARY NOTES 

13. 4BSTRACT (200 WOt"tJ, Or '.uJ 

Modal parameters determined from response measured in dynamic tests and from 

analytical models for simulating the tests and two subsequent earthquakes 

experienced by the containment building of Unit 1 of the Fukushima Power 

Station complex in Japan are compared for the purpQse of evaluating the 

effectiveness of the dynamic tests in earthquake response prediction. The 

tests are found to have led to the correct identification of a fundamental 

frequency. The lack of agreement between test- and earthquake-determined 

modeshapes and damping is attributable more to the shortcomings of the 

simulation models than to differences in actual behavior. 

14 OOCUMEJ'04T ANAL '(SIS • I(EvWOADSIOESCRIPTORS IS AVAILABIL.TY 

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Dynamic tests, Earthquakes, Nuclear Power Plant Building, 

Simulation models, Modal Parameters, Comparisons. Unlimited 

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