Journal of JSCE, Vol. 7, 72-84, 2019
(Originally published in Journal of Japan Society of Civil Engineers, Ser. A1, Vol. 74, No. 3, 319-329, 2018 in Japanese)

LONG-TERM FLUCTUATION IN DYNAMIC
CHARACTERISTICS AND PROPAGATINGBEHAVIORS OF SEISMIC MOTION
IN A ROCKFILL DAM-FOUNDATION SYSTEM
Norihisa MATSUMOTO1, Nario YASUDA2 and Zengyan CAO3
1Fellow member of JSCE, Advisor, Japan Dam Engineering Center(2-9-7 Ikenohata, Taito-ku, Tokyo 110-0008, Japan)
E-mail: matsumoto@jcold.or.jp
2Member of JSCE, Dam Technology Research Institute, Japan Dam Engineering Center(2-9-7 Ikenohata, Taito-ku, Tokyo 110-0008, Japan)
E-mail: yasuda@jdec.or.jp
3Member of JSCE, Social and Environmental Eng. Dept., JP Business Service Corporation(2-2-18, Fukagawa, Koto-ku, Tokyo 135-8451, Japan)
E-mail: sou@jpbs.co.jp

With the earthquake records obtained during the last 23 years, analyses of transfer function,
cross-spectrum and coherence function have been performed for a rockfill dam named Aratozawa dam(74.4m high and with central clay core). Based on analysis results, the fundamental frequencies and acceleration amplification factors of the dam were investigated. It was found that the fundamental (firstnatural) frequencies and the acceleration amplification factors of the dam sharply decreased temporarily,
after being struck by the Iwate-Miyagi Nairiku Earthquake on June 14, 2008. However, these characteristics recovered almost to their original status about a week after the main shock. By investigating the
propagating behavior of seismic motion in the dam-foundation system, it has been pointed out that in the
low frequency range up to the fundamental frequency of the dam, the response of the dam crest mainly
depends on the seismic motion of the subjacent bedrock. On the other hand, in the higher frequency ranges,
the contribution of the seismic motion of both banks may become dominant depending on frequency.
Key Words: rockfill dam, earthquake record, dynamic characteristics, propagating behavior, crossspectrum, coherence function

gated the variation in shear wave velocity and shear
elastic modulus of the embankment materials of the
Aratozawa Dam based on earthquake records. They
also examined the variation in excessive pore waterpressure during and after the Iwate-Miyagi Nairiku
Earthquake in 2018 to study the nonlinear dynamic
properties of embankment materials. Mogi et al.3)
performed normalized input-output minimization
analysis (NIOM) on the earthquake records of thedam. The results clearly showed that shear wave
transmission time in the dam body increased abruptly
during the main motion of the earthquake, and thetime decreased as the amplitude declined after themain motion. Sato et al.4) evaluated the dynamic
deformation properties of a rockfill dam by analyzing
earthquake records and used the results to perform
reproduction analysis of the dynamic behaviors ofthe dam during the earthquake. Kondo et al.5) pre-1. INTRODUCTION
To ensure the seismic safety of dams, which areessential infrastructure facilities, monitoring theseismic behavior of dams during earthquakes andrelevant researches on applying such monitoring data
for maintenance and operation of dams are becoming
increasingly important. In recent years, spectral
analyses or statistical processions of earthquake
records have been performed to evaluate the dynamic
characteristics such as fundamental (first natural)frequency, acceleration amplification factors anddamping properties, or to assess the soundness ofdams. Matsumoto et al.1) obtained the fundamental
frequencies of dams based on earthquake records,
and presented these in their relationship to dam type,
dam height, and the maximum acceleration of thefoundation bedrock. Omachi and Tahara2) investi-

報－972

Table 1 Main features of the Aratozawa dam.

sented an approximate equation to show the relationship between the fundamental frequency of concrete gravity dam and the maximum acceleration offoundation bedrock and water level, etc. Ueshima etal. 6) clarified the effects of air temperature and reservoir level on the predominant frequency of an arch
dam by analyzing the monitoring data of microtremors and seismic motions for a period of
three-and-a-half years. This study demonstrates that
it is possible to evaluate the soundness of a dam withsuch monitoring data.
However, most of the studies concerning earthquake monitoring and relevant analyses so far mainly
survey with specific earthquakes or statisticallysurvey the seismic events of large number of dams.
This study has investigated the long-term fluctuationin the dynamic characteristics (fundamental frequency, acceleration amplification factor) of the
Aratozawa Dam by analyzing its earthquake records
over 23 years. Meanwhile, the influence of the
Iwate-Miyagi Nairiku Earthquake on the dynamic
characteristics of the Aratozawa Dam has been also
clarified.
Traditionally, the aseismic design of dams on theother hand, premises that seismic motion vertically
propagates uniformly from the bedrock under thedam. It does not consider the phase shifting at eachelevation of abutments and its effects on earthquake
responses of the dam. Therefore, in this study, analyses of transfer function between earthquake monitoring points, cross-spectrum and coherence function
were performed based on earthquake records of the
Aratozawa Dam, to investigate the correlation of theearthquake response of the dam crest with the seismic
motion of subjacent bedrock and those of both banks.
As a result, the contribution of the seismic motion of
the subjacent bedrock and those of both banks to theearthquake responses of the dam crest has been clarified.

Dam location
Dam type
Dam height
Crest length
Crest width
Crest elevation
Slope gradients
Dam volume
Basin area
Reservoir capacity
Design seismic
coefficient

Aratozawa, Miyagi Prefecture
Rockfill dam with central claycore
74.4 m (Lowest ground elevation: EL205.0 m)
413.7 m10.0 mEL.279.4 m
Upstream: 1:2.7
Downstream: 1:2.1
3,048,000 m3
20.4 km2
13,850,000 m3
0.15 (dam body), 0.16 (spillway)

N

Seismograph
T CrestF Bottom gallery
G Right bank●(a) Plan view(b) Typical cross-section
Fig. 1 Locations of seismographs at the Aratozawa Dam.

2. DAM USED IN THE STUDY(2) Outline of earthquake monitoring
A total of about 1,700 earthquakes from 1992
immediately after the completion of the dam embankment to 2015 were recorded. Of these, in thefoundation bedrock, earthquakes with maximum
acceleration 10 cm/s2 or more and earthquakes with100 cm/s2 or more were recorded 500 times and 37
times, respectively. Particularly, the Iwate-Miyagi
Nairiku Earthquake (M7.2, below referred to as “themain shock”) occurred on June 14, 2008, a maximum
acceleration of 1,024 cm/s2 in the stream direction at
the foundation bedrock was recorded. This is thebiggest earthquake record at dam foundation bedrockin Japan so far.

(1) Dam specifications
The Aratozawa Dam is a rockfill dam with a central clay core 74.4 m high and completed in 1998.
Table 1 shows the main features of the dam. Figure
1 is the plan view and the typical cross-section of thedam, and the locations of seismographs are shown in
the figure. Seismographs are installed in three directions (stream, dam-axial, and vertical directions) ateach monitoring point of the foundation (F), dam
crest (T) and natural ground on the right bank (G),respectively.

報－10
73

Stream Direction40

3.42 Hz

20

0

5

10
15
Frequency(Hz)

20

0

20

Dam-axial Direction
3.22 Hz

40
20
0
0

5

10
15
Frequency(Hz)20

Amplification

4.69 Hz20

3.32 Hz

40
20
0

5

10
15
Frequency(Hz)20

Vertical Direction

60

40
20

10
15
Frequency(Hz)Dam-axial Direction

0

Vertical Direction

60

5

60

Amplification

60

Amplification

3.52 Hz40

00Amplification

Stream Direction

60

Amplification

Amplification

60

40

4.73 Hz

20
0

0
0

5

10
15
Frequency(Hz)020Earthquake A (1992/12/29 11:08)

5

10
15
Frequency(Hz)20Earthquake B (1993/02/18 16:20)

Fig. 2 Examples of transfer functions based on earthquake records.

if the amplitude of the acceleration record is not sufficiently large, inaccuracy in analysis results will be
relatively large. On the other hand, if the amplitudeof the acceleration record is too large, nonlinear
properties of the embankment materials, i.e., thedecrement of the stiffness and the shift of the fundamental frequency of the dam will appear. Therefore, in this study, the records with maximum acceleration in the stream direction at the dam crest within
the range of 10 to 20 cm/s2 were selected. The
measurement is thought to be precise, and the nonlinearity of the materials can be neglected. A total of
38 earthquake records were selected from earthquake
records covering 23 years with consideration of theirdistribution in time. However, there was no earthquake record that satisfied the above selection criteria
during the two days immediately after the main shock.
As an exception, two earthquake records with the
maximum acceleration in the stream direction at the
crest of 123 cm/s2 and 139cm/s2 were selected as theobjects of analysis.
Fourier spectra of the selected earthquake records
were found and transfer functions of the dam (Fourier
spectrum ratio between the crest (T) and foundation
bedrock (F)) were obtained. Figure 2 shows theexamples obtained from the first two earthquake
records in time series. The frequency corresponding
to the first peak of the transfer function in each

3. LONG-TERM FLUCTUATION IN THE
DYNAMIC CHARACTERISTICS OF
THE DAMThe earthquake records of a dam reflect the dynamic characteristics (fundamental frequencies, acceleration amplification factors) of the dam. Therefore, it is possible to clarify the long-term fluctuationin the dynamic characteristics of the dam by analyzing the earthquake records of about 23 years
mentioned above. The investigation focuses on thelong-term fluctuation in fundamental frequency andacceleration amplification factor of the dam in eachdirection based on the analysis of earthquake records.
(1) Fluctuation in fundamental frequencies
Based on acceleration records at the foundation
bedrock (F) and crest (T) of the dam, accelerationtransfer functions of the dam were found. By examining the variation in the transfer functions, thefluctuation, if any, in the fundamental frequency ofthe dam in each direction and the trends of thisfluctuation were studied. It is important to appropriately select the earthquake records to be used forfinding the transfer function. With the considerationof microtremors (max. 1 cm/s2 is assumed) and theresolution of measurement instruments (0.01cm/s2),

報－11
74

The horizontal axis shows the time the earthquake occurred.
For example, 1992 year
12 month
29 day11 hour
08 minuteFreqency(Hz)― Average of the fundamental frequency
Stream Direction

4

3

2
1
21993
3 19944 1995
5
6
1992
12
29
11
08

02
18
16
20

12
17
12
19

12
29
05
52

12
23
08
15

04
05
17
40

7

04
07
06
16

81996
9

08
11
05
39

08
11
10
59

10

08
27
00
40

11

11
30
11
51

12
14 2000
15
16
17
1997131999
2001

02
20
05
21

12
07
12
50

11
15
10
34

02 03
18 21
22 06
38 56

06
14
09
20

18

06
14
10
40

Freqency(Hz)

19

06
16
15
57

21
22
2008

20

06
16
17
11

06
16
21
15

06
18
07
42

23

06
18
21
17

24

06
20
11
10

25

06
21
12
19

262009
27

07
14
04
24

28
29
2010

09 04
21 24
18 00
57 41

03
03
23
01

30 2011
31

03
11
16
04

03
11
20
57

32

33201234 201335
36
201437

03
12
23
43

06
08
14
24

04
01
20
57

03 03
31 13
14 06
14 16

04
03
08
22

38 2015
39

40

02
26
10
11

05
13
06
13

02
17
08
07

Dam-axial Direction

4

3

2
1
21993
3 19944 1995
5
6
1992
12
29
11
08

02
18
16
20

12
17
12
19

12
29
05
52

12
23
08
15

04
05
17
40

7

81996
9

10

11

12
14 2000
15 2001
16
17
1997131999

04
07
06
16

08
11
05
39

08
27
00
40

11
30
11
51

02
20
05
21

08
11
10
59

12
07
12
50

11
15
10
34

02 03
18 21
22 06
38 56

06
14
09
20

18

19

20

21
2008222324

25262009
27

06
14
10
40

06
16
15
57

06
16
17
11

06
16
21
15

06
18
07
42

06
18
21
17

06
20
11
10

06
21
12
19

07
14
04
24

28
29
2010

09 04
21 24
18 00
57 41

03
03
23
01

302011
31

32

03
11
20
57

03
12
23
43

03
11
16
04

33
34 2013
35
2012

04
01
20
57

03 03
31 13
14 06
14 16

36
37
2014

04
03
08
22

06
08
14
24

382015
39

40

02
26
10
11

05
13
06
13

02
17
08
07

Vertical Direction

6

Frequency(Hz)■ Fundamental frequency

5
4
3
1
21993
3 19944 1995
5
6
1992
12
29
11
08

02
18
16
20

12
17
12
19

12
29
05
52

12
23
08
15

04
05
17
40

7

81996
9

10

11

12
14 2000
15
16
17
2001
1997131999

04
07
06
16

08
11
05
39

08
27
00
40

11
30
11
51

02
20
05
21

08
11
10
59

12
07
12
50

11
15
10
34

02 03
18 21
22 06
38 56

06
14
09
20

18

19

20

21
22
2008

23

24

25

262009
27

06
14
10
40

06
16
15
57

06
16
17
11

06
16
21
15

06
18
07
42

06
18
21
17

06
20
11
10

06
21
12
19

07
14
04
24

28
29
2010

09 04
21 24
18 00
57 41

03
03
23
01

30 2011
31

32

03
11
20
57

03
12
23
43

03
11
16
04

33201234 201335
36
201437

04
01
20
57

03 03
31 13
14 06
14 16

04
03
08
22

06
08
14
24

38 2015
39

40

02
26
10
11

05
13
06
13

02
17
08
07

Fig. 3 Variation in the fundamental frequencies of the dam.

Table 2 Variation in the fundamental frequencies.

shock of 10:40, the fundamental frequencies recovered slightly, but in the stream direction, it was 2.8
Hz, which is much lower than that before the main
shock. It should be kept in mind that the acceleration
amplitude of these two aftershocks were slightly
larger than those of the other earthquakes and thestiffness softening caused by nonlinearity of theembankment materials is included. During the twodays immediately after the main shock, aftershocks
exceeding 200 cm/s2 at the foundation bedrock occurred several times. About one week until June 20 of
the same year, the fundamental frequencies in three
directions fluctuated, but decreased significantly
from those before the main shock. This reveals that
because of the main shock, the fundamental frequencies of the dam decreased sharply.
b) Recovery of the decreased fundamental frequency
Then, from June 18 until June 20, a recovery tendency was seen in the horizontal fundamental frequencies. The average values before and after themain shock and its aftershocks are summarized inTable 2 and shown by the solid line in Fig. 3. After

Direction
Before(Hz)After(Hz)*1
Variation*2
Stream
3.2
3.0
-6.2%
Dam-axial
3.1
2.8
-9.7%
Vertical
4.6
4.8
+4.3%
Note: *1 a week after the main shock*2 Variation = (After – Before) / Before

direction (stream, dam-axial, and vertical direction)is considered as the fundamental frequency of thedam, and the results were organized in order of timeof occurrence of the earthquakes in each direction asshown in Fig. 3.
a) Decrement of the fundamental frequency
caused by strong ground motion
The main shock occurred at 8:43 on June 14, 2008.
As shown in Fig. 3, the fundamental frequency of thedam in the stream direction obtained from theearthquake record of an aftershock at 9:20 on thesame day shows a sharp decrement from 3.2 Hz before the main shock to 2.2 Hz. This decreasing trend
is similar for all three directions. At the next after-

報－12
75

Table 3 Specifications of the earthquakes analyzed.
PGA*1
Depth
(km)
(cm/s2)
A
1996/08/11 03:12
6.1
9
28
B
1996/08/11 08:10
5.8
10
36
C
1996/08/11 15:01
4.9
10
30
D
2003/05/26 18:24
7.1
72
114
E
2008/06/14 08:43
7.2
8
1024
F
2008/06/14 09:00
4.2
11
99
G
2008/06/14 09:01
4.0
7
482
H
2008/06/14 09:14
3.6
4
151
I
2008/06/14 09:20
5.7
7
76
J
2008/06/14 10:40
4.8
7
120
K
2008/06/14 12:09
4.1
8
92
L
2008/06/14 12:10
4.8
9
79
M
2008/06/14 19:11
4.1
8
229
N
2008/06/16 23:14
5.3
7
76
O
2008/07/24 00:26
6.8
108
27
P
2008/09/25 15:04
4.1
6
119
Q
2011/03/11 14:46
9.0
24
102
R
2011/04/07 23:32
7.2
66
120
S
2015/05/13 06:13
6.8
46
18
Note: *1 The maximum acceleration of the three directional
components of the foundation

No.

Enlarged view of dam area

Time of occurrence

M

Table 4 Average of the amplification factor.
Mainshock &After theaftershocks
earthquake*1
1.29
3.36
Stream3.33(-61.3%)*2(0.9%)
1.85
4.30
Dam-axial
4.89(-62.2%)(-12.1%)
2.11
3.23
Vertical
2.85(-26.0%)(13.3%)
Note: *1 a week after the main shock*2 Values in parentheses = (Current – Before) / Before
Direction

Aratozawa Dam
A–S: Epicenter of earthquakes■

Before theearthquake

Fig. 4 Epicenters of earthquakes analyzed.

The above reveals that, as a result of the main
shock, the fundamental frequencies of the Aratozawa
Dam in each direction, or in other words its stiffness,
temporarily decreased sharply. The fundamental
frequencies recovered to nearly their original status
about a week after the main shock. On the other hand,
restoration effect is anisotropic and the vertical fundamental frequency of the dam recovered to evenhigher than its original value.

June 21st, the situation was relatively stable at 3.0 Hz
in stream direction, 2.8 Hz in dam-axial direction,
which are 0.2 Hz and 0.3 Hz lower, respectively, thanthose before the main shock.
c) Fluctuation in the vertical fundamental frequency
On the other hand, the vertical fundamental frequency of the dam also decreased temporarily. It
recovered about a week after the main shock, andeven increased by 4.3% from the average value before the main shock. It is thought that the stiffness ofthe embankment materials softened because of thestrong ground motion, then recovered due to restoration effect. However, the recovery of the stiffness
caused by the restoration effect differed between thehorizonal and vertical directions and was remarkablein the vertical direction. This indicates that the influence of the strong ground motion differed according to its direction.

(2) Fluctuation in the acceleration amplification
factorEarthquake records with relatively large acceleration amplitudes were selected before and after themain shock of June 14, 2008 and its aftershocks.
With these earthquake records, the fluctuation in theacceleration amplification factor of the dam and its
fluctuation process were investigated. Table 3 shows
the selected earthquakes, and Fig. 4 shows the epicenter position of each earthquake and the location of
the Aratozawa Dam.

報－13
76

The ratios of the maximum acceleration of thecrest (T) and that of the foundation bedrock (F) ineach direction were found as the amplification factors, and their temporal fluctuation is shown in Fig. 5.
In this figure, the fundamental frequencies of the dam
before May 26, 2003 and those after July 24, 2008
are the values shown in the Table 2, respectively, as
the average values before and after the main shock.
The average values of the fundamental frequencies ofthe dam during the main shock and approximately aweek afterwards are obtained from records of aftershocks during this period shown in Fig. 3. The following can be mentioned based on Fig. 5.
a) Decrement of the acceleration amplification
factor caused by the strong ground motion
As a result of the main shock at 8:43 on June 14,
the acceleration amplification factors of the dam ineach direction decreased sharply. In the aftershocks
that occurred a few days, although the maximum
acceleration of the ground motion of the aftershocks
was much smaller than that of the main shock, theacceleration amplification factor in each direction
overall, remained low. The average values of theacceleration amplification factors in two horizontal
directions during this period dropped to less than halfof their values before the main shock. And in verticaldirection, it was also lower than that before the main
shock. One cause of this decrement is, as shown in
Fig. 5, that the predominant frequency (frequency
corresponding to the peak of the Fourier spectrum of
the acceleration record at the foundation bedrock (F))
of earthquakes during this period was higher thanthose of other periods, and the average value of thefundamental frequency of the dam (in this figure,shown by the dotted lines) decreased as describedabove. Another cause is the nonlinearity that reduced
the stiffness and increased the damping of the embankment materials, with the occurrence of large
strain of the materials under the strong ground motion during this period.
Figure 6 shows the relationship of the acceleration
amplification factor and the maximum acceleration(the maximum value of three direction components)of the foundation bedrock (F). This figure reveals
that as one of the effects of material nonlinearity(decline in stiffness and increase in damping due tostrain increment), the higher the maximum acceleration of the foundation bedrock, the lower the acceleration amplification factor of the dam.
b) Recovery of the reduced acceleration amplification factor
The average values of the acceleration amplification factors in each direction before and after themain shock and aftershocks are found, and the results
are shown by the dash-dotted line in Fig. 5. The av-

erage values of each period are summarized in Table
4. Although the acceleration amplification factors in
the two horizontal directions are scattered after theearthquake, the average values recovered almost to
their original levels before the earthquake.
c) Different fluctuation tendency of the amplification factors in the horizontal direction andthe vertical direction
As shown in Table 4 and Fig. 5, as a result of themain shock, the acceleration amplification factors ofthe dam reduced about 61% horizontally, but only
about 26% vertically. Moreover, compared with therecovery condition of the acceleration amplification
factors in the two horizontal directions after theearthquake, the amplification factor in the verticaldirection completely recovered to the state before themain shock. This shows a similar fluctuation trend
like that of the fundamental frequency of the dam in
the vertical direction as described in Section (1).

4. INVESTIGATION ON PROPAGATIONBEHAVIOR OF SEISMIC MOTION IN
DAM-FOUNDATION SYSTEM
In aseismic design and earthquake response analysis of a dam, it is usually assumed that seismic motion propagates vertically from subjacent bedrock. In
other words, seismic motion propagates while varying its phase in the abutment and the influence of thison the earthquake response of the dam is neglected. It
will be significant for the aseismic design and analysis of dams to clarify the propagation behavior ofseismic motion of the dam site. Therefore, the contribution of the seismic motion propagating from thesubjacent bedrock and that transmitted through thenatural ground of both banks on the earthquake response of the dam crest are investigated here. In thisstudy, transfer function analysis, cross-spectral
analysis and coherence function analysis7) are performed on the earthquake records of the Aratozawa
Dam shown in Fig. 4 and Table 3. Based on theanalysis results, the propagating behavior of seismic
motion in dam-foundation system and the influenceof the main shock are investigated.
(1) Analysis method
In a dam-foundation system, because of irregularnatural topography and complex distribution of rockgeology as well as zoned non-uniform embankment
materials and so on, seismic motion overlaps with the
disturbance of scattered waves. Hence, the propagation of seismic motion is extremely complex. However, investigating the correlation of the earthquake

報－14
77

The horizontal axis shows the time the earthquake occurred.
For example, 1992 year
12 month
29 day11 hour
08 minuteIn● Peak acceleration of foundation▲ Predominant freq. of earthquake
Average of predominant freq. of earthquakes
Fundamental freq. of the dam■ Acceleration amplification factor
Average of amplification factors

1000

Acc. (cm/s2)

Main shock
100
10Freq. (Hz)128

3.0 Hz4

3.2 Hz0

Amplification

6
5
4
3
2
1
0

2003

1996
08
11
03
12

08
11
08
10

2.7 Hz

08
11
15
01

05
26
18
24

2008
06
14
08
43

06
14
09
00

06
14
09
01

06
14
09
14

06
14
09
20

06
14
10
40

2011
06
14
12
09

06
14
12
10

06
14
19
11

06
16
23
14

07
24
00
26

09
25
15
04

03
11
14
46

2015
04
07
23
32

05
13
06
13

Stream Direction

Amplification

Freq. (Hz)Acc. (cm/s2)

1000

Main shock
100
10
12
8
4

3.1 Hz

0
6
5
4
3
2
1
0

1996
08
11
03
12

08
11
08
10

2.7 Hz2.8 Hz

2003
08
11
15
01

05
26
18
24

2008
06
14
08
43

06
14
09
00

06
14
09
01

06
14
09
14

06
14
09
20

06
14
10
40

2011
06
14
12
09

06
14
12
10

06
14
19
11

06
16
23
14

07
24
00
26

09
25
15
04

03
11
14
46

2015
04
07
23
32

05
13
06
13

Dam-axial Direction

Amplification

Freq. (Hz)Acc. (cm/s2)

1000

Main shock
100
10
12

4.8 Hz84

4.6 Hz

0
6
5
4
3
2
1
0

1996
08
11
03
12

08
11
08
10

4.1 Hz

2003
08
11
15
01

05
26
18
24

2008
06
14
08
43

06
14
09
00

06
14
09
01

06
14
09
14

06
14
09
20

06
14
10
40

2011
06
14
12
09

06
14
12
10

06
14
19
11

Vertical Direction

Fig. 5 Fluctuation in acceleration amplification factors.

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06
16
23
14

07
24
00
26

09
25
15
04

03
11
14
46

2015
04
07
23
32

05
13
06
13

Main shock & aftershocks
Other earthquakes－－Regression line of all the earthquakes●◆

Stream direction
Amplification factor

65Fig. 7 Axial cross-section of the dam and schematization of
the propagation path of seismic motion.

4
3
Main shock2

influence of the seismic motion propagated from thesubjacent bedrock and that transmitted through thenatural ground of both banks on the earthquake response of the dam crest. The analysis results werecomprehensively examined in comparison with theresults of transfer function analysis between any twomonitoring points.
During an earthquake, seismic motion propagates
through arbitrary position of abutment to a dam.
However, in order to clearly distinguish the propagating path, the path from the monitoring point (F) of
the foundation bedrock to the monitoring point (T) of
the dam crest shown in Fig. 7 (below referred to as
Path “F-T”) and the path from the monitoring point(G) of the natural ground on the right bank to themonitoring point (T) of the dam crest (below referred
to as Path “G-T”) were schematized. The following
analyses were performed on the earthquake recordsof each propagating path.

1
0
10

100

1000

The max. acc. of foundation(cm/s2)
Dam-axial direction

Amplification factor

6
5
4
3

Main shock

2
1
0
10

1000

Transfer function:

Vertical direction

6
Amplification factor

100
The max. acc. of foundation(cm/s2)

DTi = ST/Si (i = F, G)

5

Cross-spectrum:

4

WTi = STꞏSi (i = F, G)

3

Main shock2

Coherence function:
C2Ti = | WTi |2 /(WTTꞏWii) (i = F, G)

1
0
10

100

where, S represents the Fourier spectra of the acceleration records of each monitoring point, and D indicates the transfer function between the monitoring
points of the propagating path. W and C2 represent
cross-spectrum and coherence function, respectively.
T, F, and G indicate the monitoring points: crest (T),foundation bedrock (F), and right bank (G) in turn.
The study in the previous section reveals that thedam showed different vibration characteristics during
the three periods, i.e., before the main shock, about
one week beginning at the main shock, and from then
to 2015. Therefore, the 19 earthquake records shownin Table 3 were analyzed and the results were examined by grouping them according to the variation
timing of the vibration characteristics of the dam as
follows.
Group 1: From completion of the dam construction
to just before the main shock

1000

The max. acc. of foundation(cm/s2)

Fig. 6 Relationship between the acceleration amplification
factor and the maximum ground acceleration.

records of any two monitoring points may clarify thecausal relationship or the magnitude of the mutual
influence of the seismic motion between the twopoints. Cross-spectrum shows the correlation of two
signals for each frequency. Coherence function
quantitively shows the correlation of two waveforms
for each frequency. Coherence function takes a value
from 0 to 1, and in case of 1 it indicates that output
signals are all due to input signals in this frequency.
In this study, cross-spectral analysis and coherencefunction analysis were carried out to analyze the

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Spectrum(cm2/s2)

Earthquake K is chosen from Group 2 since it is theaftershock that occurred on the same day as the main
shock. Earthquake S is chosen from Group 3 since itis the most recent earthquake record available. Table
5 lists the chosen earthquakes and indicates the reasons for their selection.
Figure 9 shows the analysis results of the chosen
earthquakes.
The cross-spectrum and coherence function results
show that there are generally common features inGroup 1 and Group 3, respectively. However, regarding Group 2, i.e., the main shock and aftershocks
during the week immediately after the main shock,the variation in the results is relatively large.
a) From completion of the dam construction tojust before the main shock
Figure 9(A) shows the analysis results of anearthquake that occurred on August 11, 1996 shortly
after the completion of the construction of the dam.
In the stream direction, up to the primary predominant frequency (2.93Hz) of the transfer function,
both the cross-spectrum and coherence function ofpath “F-T” were higher than those of path “G-T,” andhence, it is thought that within the low frequency
range up to this first predominant frequency, thecontribution of the seismic motion of the subjacentbedrock to the earthquake response of the dam crest
was larger than that of the seismic motion of thenatural ground of both banks. In the frequency range
higher than the first predominant frequency, themagnitude relationship of coherence functions between the two paths varied alternately according to
the frequency, but the cross-spectrum was always ahigher value in path “G-T.” This suggests that theseismic motion of the natural ground of both banks is,
as a result of amplification of ground acceleration,
larger than the seismic motion of the subjacent bedrock. Therefore, at the frequency (where both thecoherence function and cross-spectrum are large), thecontribution of the seismic motion of the natural
ground of both banks may be larger than that of the
subjacent bedrock. In other words, for the earthquake
response of the dam crest in the stream direction, in
the low frequency range up to the fundamental frequency of the dam, the contribution of the seismic
motion of the subjacent bedrock is relatively large.
Whereas in the higher frequency range, the influenceof the seismic motion of the subjacent bedrock andthe natural ground of both banks varies according tofrequency. There are also cases where the contribution of the seismic motion of the natural ground ofboth banks is relatively larger than that of the subjacent bedrock.
The mechanism of the above phenomena is considered as follows. Using the three-dimentional

Cross-spectrum

1000
100
10
1
0.1
0.01

Coherence function

1
0.8
0.6

A

0.4

C

B
D

0.2
0

1

2

3

4
5
6
Frequency(Hz)

7

8

9

10

Fig. 8 Example of cross-spectrum and coherence function(Group 1, Path “F-T”, in stream direction).
Table 5 Earthquakes selected for investigation.
No

Occurrence timeA

1996/8/11
03:12

K

2008/6/14
12:09

S

2015/5/13
06:13

State of the dam
From completion of
the dam construction
to just before themain shock
From the main shock
to about a week later
From about a week
after the main shock
to 2015

Reason for
selection
Record showing the initialstate of the dam
Just after themain shock
Record showing the current
state of the dam

Group 2: From the main shock to about a week
laterGroup 3: From about a week after the main shock
to 2015(2) Analysis results
As an example, Fig. 8 shows the results of thecross-spectrum and coherence function of the path
“F-T” of Group 1 in the stream direction. Because theacceleration of the foundation bedrock of Earthquake
D is the highest in this group, the cross-spectrum also
shows a relatively high value. However, the four
earthquakes show generally common features. For
example, in the frequency range of 2.1 - 2.6 Hz, all
the earthquakes show their respective large spectrum
values. Common features of the coherence functions
are even clearer. For example, in the frequency rangeof 0.2 - 1.6 Hz, the coherence functions are almost 1
for all the earthquakes. In the frequency range up to
2.6 Hz, except a few individual frequencies, thevalues are 0.9 or larger. To show the results clearly,
for each group one earthquake is chosen here, withthe consideration of the time of occurrence of theearthquake and the number of data in the record (longduration time). Earthquake A is chosen from Group 1
since it reflects the original status of the dam.

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10
5

10
1
0.1
0.01

Coherence function

1

10
5

10
1
0.1
0.01

Coherence function

1

0.6
0.4

0.2

0.2
4 5 6 7Frequency(Hz)

8

9 10

0.2
0

1

F-T

10
Cross-spectrum

Spectrum(cm2/s2)

10
1
0.1
Coherence function

1

4 5 6 7Frequency(Hz)

8

9 10

0

Transfer function
2.73Hz

30
25
20
15
10
5
0

G-T
F-T

10
1
0.1
0.01

Coherence function

1

0.01

0.4

0.2

0.2
0

1

(b) Dam-axial direction

23

4 5 6 7Frequency(Hz)

8

9 10

0

F-T

5

F-T

10
0

Cross-spectrum

Spectrum(cm2/s2)

10
1
0.1
0.01

Coherence function

1

10
1
0.1
0.01

Coherence function

1

1

0.01

0.6

0.4

0.4

0.2

0.2
9 10

(c) Vertical direction(A) Earthquake A (1996/8/11 03:12)

Coherence function

1

0.4
8

Cross-spectrum

0.1

0.8

4 5 6 7Frequency(Hz)

F-T

10

0.6

3

G-T

100

0.8

2

9 10

10

0.6

1

8

Transfer function

0
Cross-spectrum

100

4 5 6 7Frequency(Hz)

20

0.8

0

3

30

Spectrum(cm2/s2)

0

G-T

20

2

(b) Dam-axial direction

Transfer function

30

Amplification

G-T

100

1

(b) Dam-axial direction

Transfer function

10

Coherence function

1

0.2

15

Cross-spectrum

1

0.6

20

F-T

0.1

0.4
9 10

G-T

10

0.4
8

Transfer function
2.61Hz100

0.8

4 5 6 7Frequency(Hz)

9 10

10

0.6

3

8

20

0.8

2

4 5 6 7Frequency(Hz)

30

0.6

1

3

0

Cross-spectrum

100

2

40

0.8

0

1

(a) Stream direction

Spectrum(cm2/s2)

G-T

20

0.01

3

(a) Stream direction

Transfer function
3.03Hz100

2

Amplification

3

Coherence function

1

0.4

Amplification

Amplification

0.1
0.01

0.4

0

Spectrum(cm2/s2)

1

0.8

30

Amplification

10

0.6

2

Cross-spectrum

100

0.8

(a) Stream direction

Spectrum(cm2/s2)

20

0.6

1

F-T

40

0.8

0

G-T

60

0

Cross-spectrum

100

Transfer function
2.95Hz80

Spectrum(cm2/s2)

Cross-spectrum

100

F-T

0

Spectrum(cm2/s2)

Spectrum(cm2/s2)

0

15

G-T

Amplification

F-T

Transfer function
2.34Hz20

Amplification

Amplification

15

G-T

Amplification

Transfer function
2.93Hz

20

0.2
0

1

2

3

4 5 6 7Frequency(Hz)

8

9 10

(c) Vertical direction(B) Earthquake K (2008/6/14 12:09)

0

1

2

3

4 5 6 7Frequency(Hz)

81

9 10

(c) Vertical direction(C) Earthquake S (2015/5/13 06:13)

Fig. 9 Transfer functions, cross-spectra and coherence functions before and after the main shock.

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eigenvalue analysis of the dam including the natural
ground, the first mode as shown in Fig. 10 reflects
the overall shaking of the dam body and can be represented two-dimensionally in each direction. It canbe easily understood that the restriction effect of theabutment is relatively weak in the first mode. In addition, the length of the path “F-T” is relatively short.
These factors indicate that within the low frequency
range up to the fundamental frequency, the contribution of the seismic motion of the subjacent bedrockis larger than that of the natural ground of both banks
to the earthquake response of the dam. On the other
hand, the restriction effect of the abutment on thesecondary and higher modes becomes larger as themode order increases. In higher mode, the seismic
motion of the natural ground of both banks may
propagate more easily than that from the subjacentbedrock. In addition, as shown in Fig. 1 and Fig. 7, a
spillway exists on the right bank side, and a part ofthe dam on the right bank side is composed of original natural ground. Thus, the real propagation pathof seismic motion from the right bank to the middleof the dam crest is thought to be much shorter than
“G-T.”In the dam-axial direction, the coherence functionof path “F-T” in the low frequency range up to 2.5 Hz
shows a high value (approximately 1), indicatinghigh agreement between the earthquake response of
the crest and the seismic motion of the subjacentbedrock. At the frequency near the fundamental
frequency (3.0Hz) in the dam-axial direction, thecoherence functions of the two paths show similarvalues, but the cross-spectrum shows a larger value inthe path “G-T.” Based on this, it is presumed thatnear the fundamental frequency of the dam in the
dam-axial direction, the contribution of the seismic
motion of the natural ground of both banks to theearthquake response of the dam crest in the dam-axial
direction is probably larger than that of the subjacentbedrock. In the frequency range higher than thefundamental frequency, the cross-spectra and coherence functions of both paths show tendencies likethose in the stream direction. That is, thecross-spectrum of path “G-T” was always a higher
value and the magnitude relationship of coherencefunctions between the two paths varied alternately
depending on frequency. It can be stated that thecontribution of the seismic motion of the subjacentbedrock and that of the natural ground of both banks
to the earthquake response of the dam crest in the
dam-axial direction are alternately dominant depending on frequency.
In vertical direction, in the low frequency range up
to nearly the first predominant frequency of thetransfer function, the cross-spectra of both paths(a) First mode(b) Second mode(c) Third mode(d) Fourth mode

Fig. 10 Natural vibration modes of the dam by eigenvalue
analysis.

show similar values, and the coherence function of
the path “F-T” is a little higher. Therefore, it isthought that in the low frequency range, the contribution of the seismic motion of the subjacent bedrockto the earthquake response of the dam crest is a little
larger than that of the path “G-T.” In the frequency
range higher than this, the cross-spectrum and thecoherence function of both paths show tendencies
generally the same as those in the results for the
stream direction and dam-axial directions describedabove.
Based on the above investigation, it can be concluded that the contribution of the seismic motion of
the subjacent bedrock and that of the natural groundof both banks to the earthquake response of the dam
crest varies depending on the vibration direction.
However, generally, in the low frequency range up to
the fundamental frequencies of the dam, the contribution of the seismic motion of the subjacent bedrockis larger, and in the higher frequency range, the contribution of the seismic motion of the natural groundof both banks may become dominant according tofrequency.
b) From the main shock to about a week later
Figure 9(B) shows the analysis results of the aftershock at 12:09 just after the main shock. Up to thefirst predominant frequency (2.34Hz) of the transfer
function in the stream direction, the coherence function of path “F-T” is obviously lower than that before
the main shock, and the cross-spectrum increases
approximately in proportion to the frequency from an
extremely low value. From this fact, it is presumed
that in the low frequency range, the contribution of
the seismic motion of the subjacent bedrock to theearthquake response of the dam crest in stream direction decreased sharply, compared with that before
the main shock. In the frequency range higher than

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the first predominant frequency of the transfer function, except those near 3.0Hz (2.2 – 3.5Hz), the coherence functions of the two paths show similarvalues. Whereas, the cross-spectrum of path “G-T” isa little larger, it indicates that in the frequency rangeof 3.5Hz and higher, the contribution of the seismic
motion of the natural ground of both banks is a little
larger.
In the dam-axial direction, up to the first predominant frequency of the transfer function, thecross-spectrum and coherence function show similar
trends like those in the stream direction, revealingthat the contribution of the seismic motion of the
subjacent bedrock to the earthquake response of thedam crest has changed because of the influence of themain shock. In the frequency range higher than this,the cross-spectra of both paths are in the same order,
but the magnitude relationship of the coherencefunctions of the two paths varies depending on frequency.
The results in the vertical direction show similar
trends with those in the dam-axial direction. Compared with the analysis results of the original status of
the dam, the dependency of the earthquake responseof the dam crest on the seismic motion of the subjacent bedrock and that of the natural ground of bothbanks is obviously weakened by the main shock.
c) From about a week after the main shock to2015
Figure 9(C) shows the analysis results of the mostrecent aftershock (06:13 on May 13, 2015). Thisshows that compared with Fig. 9(A), the propagation
characteristics of seismic motion in the dam underpresent conditions shows almost the same trends inall directions as before the main shock. In the low
frequency range up to the fundamental frequency of
the transfer function, for example, the coherencefunction of path “F-T” is almost 1, and in the higher
frequency range, the magnitude relationship withpath “G-T” alternates according to frequency. The
cross-spectra tend to change in a similar way to thoseof the results before the main shock.

horizontal fundamental frequencies of the dam
were, on the average, slightly lower than those
before the main shock, but they had recovered toa stable status. The vertical fundamental frequencies, on the other hand, dropped temporarily
immediately after the main shock, but later
completely recovered, and even rose about 4%
higher than that before the main shock. In otherwords, strong seismic motion caused the stiffnessof the dam to decline, but later, as time passed,
the stiffness of the dam recovered under restoration effect. However, the state of this recovery
was more remarkable in the vertical direction
than in the horizontal directions.
2) After being struck by the main shock of the
Iwate-Miyagi Nairiku Earthquake, the acceleration amplification factors of the dam in each direction also decreased temporarily. It is thoughtthat this phenomenon resulted from the fact thatthe predominant frequencies of the main shock
and of the aftershocks were relatively high. Also,
the nonlinearity of the stiffness decrement anddamping increment of the embankment materials
occurred as a result of large strain.
3) Regarding the propagation characteristics ofseismic motion in a dam-foundation system, inthe low frequency range up to approximately thefundamental frequency of the dam, the contribution of seismic motion of the subjacent bedrock to the earthquake response of the dam crestis larger than that of the natural ground of bothbanks. In the frequency range higher than this,the contribution of seismic motion of the natural
ground of both banks may be larger than that of
the seismic motion of the subjacent bedrock according to frequency. Also, as a result of the
Iwate-Miyagi Nairiku Earthquake, the correlation of the earthquake response of the dam crestand the seismic motion of the subjacent bedrockand that of the natural ground of both banks
temporarily weakened. According to the analysis
results of the earthquake records of 2015, it canbe judged that the propagation characteristics ofseismic motion in the present dam-foundation
system recovered to its original status before themain shock.
In future studies, the relationship between vibration intensity and compaction effect of embankment
materials should be clarified with material testing.
And based on wave theory, the influence of seismic
motion of the dam site on the earthquake response of
the dam should be studied.

5. CONCLUSIONS
The following conclusions are obtained from thisstudy.
1) Based on the earthquake records over a 23-year
period, long-term fluctuation of the fundamental
frequency of the dam was investigated. Afterbeing struck by the Iwate-Miyagi Nairiku
Earthquake on June 14, 2008, the fundamental
frequencies of the dam dropped sharply.
Whereas, about a week after the main shock, the

ACKNOWLEDGMENT: This study was conducted using valuable earthquake records and in-

報－20
83

formation about the dam contributed by the Kurihara
Regional Dam Office in Miyagi Prefecture and theJapan Commission on Large Dams. The authors wish
to express their gratitude to these two organizations
for their support.

5)

6)

REFERENCES
1)

2)
3)

4)

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rockfill dam, Dam Engineering, Vol. 25, No. 4, pp.
218-229, 2015 (in Japanese).
Sato, N., Soda, H. and Sai, A.: Estimation of and applica-

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bility of measured dynamic deformation properties according to earthquake records of rockfill dams, Dam Engineering, Vol. 25, No. 4, pp. 230-239, 2015 (in Japanese).
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earthquakes, Collected Papers of the Japan Association for
Earthquake Engineering, Vol. 15, No. 7 (Special Issue),2015 (in Japanese).
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(Received December 19, 2018)報－2184