INCOLD

ICOLD Symposium on Sustainable Development of Dams and River Basins, 24th - 27th February, 2021, New Delhi

STUDY ON THE ENGINEERING BEDROCK AND
SEISMIC MOTION AT IT IN THE EARTHQUAKERESPONSE ANALYSIS OF A CONCRETE DAM
N. YASUDA
Japan Dam Engineering Center, Tokyo, Japan
Z. CAO
J-POWER Business Service Corporation, Tokyo, Japan
ABSTRACTIn Japan, the dam safety against large-scale earthquakes is verified by numerical analysis. Seismic motion
defined for verification of seismic performance of a dam is set based on the distance attenuation formula which
is obtained by statistical analysis of the earthquake records of many dams, the empirical Green’s function
method, and a method of adjusting ground motion record to the stipulated lower-limit acceleration response
spectrum for verification. Generally, the input seismic motion for the earthquake response analysis is preparedby pulling the seismic motion back to the engineering bedrock hypothesized by numerical analysis method.
However, lacking precise criteria for setting engineering bedrock for earthquake response analysis of a dam,
the appropriateness of the preparation method of the seismic motion and of the prepared input seismic motion
are not necessarily clarified. This study predicted seismic motion of deep bedrock using earthquake acceleration
records during the Tokachi-oki Earthquake in 2003 (M. 8.0) inside bedrock at a depth of 57 m below the bottomof the Satsunaigawa Dam which is equipped with 8 seismographs. Based on the research results, it was pointed
out that in the case of concrete gravity dams, the engineering bedrock should be set at a depth equal to about
1.5 times the dam height, and where the shear wave velocity of the bedrock should be no less than 2,000 m/s.
Then, a procedure of preparing input seismic motion for earthquake response analysis is proposed.

1 INTRODUCTION
Earthquake response analysis of a dam done to verify the seismic performance of the dam is often
carried out using the following flow: first estimating the seismic motion of the bottom surface ofthe dam or of the open bedrock applying the empirical method (Matsumoto et al. 2003) or thesemi-empirical method (Irikura1986, Boore 1983, Kamae et al. 1991) then predicting the seismic
motion of the engineering bedrock that was hypothesized by a pull-back calculation of the wave.
Naturally, the predicted seismic motion at the engineering bedrock is dependent on conditions of
the analysis model, and it is nothing more than a numerical analysis. The earthquake responses ofthe foundation bedrock, the natural ground and dam body excited by the input seismic motion are
not necessarily clarified. Furthermore, the verification of seismic performance of the dam basedon the analysis result has several matters to be resolved. Because, on the other hand, it is difficult
to directly measure seismic motion in deep bedrock, almost no efforts have been made in the fieldof dam engineering to verify the setting of seismic motion for engineering bedrock.
The Satsunaigawa Dam is a concrete gravity dam with height of 114 m. Three-direction component seismographs installed at the locations shown in Figure 1, have collected several earthquake records since the dam was completed in 1996. The seismograph at a depth of 57 m (equals
to half of the dam height) underneath the dam base in particular, has obtained valuable records
inside the bedrock. Besides, seismographs are also installed inside the rim-tunnels of both banks.

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報ٕ1Symposium on Sustainable Development of Dams and River Basins, 24th - 27th February, 2021, New Delhi

The dynamic properties and dynamic behavior of the dam were studied based on numerical analysis using earthquake records (Yasuda et al. 2007). This study aims to contribute to setting input
seismic motion in order to verify seismic performance of dams in the future. Based on earthquake
records obtained at multiple monitoring points on the Satsunaigawa Dam site, the seismic motionof the deep bedrock is predicted by a numerical analysis method. Simultaneously, the criteria forsetting engineering bedrock and preparation methods of input seismic motion for earthquake response analyses of the dam are investigated.
300 m

67 m

R2

T1

114 m

Right Bank

T2

T3

85 m

Left Bank

Vertical dir.

Stream dir.

F2
57 m

Axial dir.

R1

LegendSeismograph

F1

Figure 1. Locations of seismographs at the Satsunaigawa Dam (downstream side).

2 INVESTIGATION METHOD AND CONDITIONS
2.1 Investigation Method
The following two points must be considered when setting the engineering bedrock.
(1) Seismic motion in engineering bedrock is almost immune to the effects of the dynamic
behavior of the upper ground structure and the dam, so that seismic motion at any location on the same elevation of the foundation bedrock is almost identical.
(2) When there are earthquake records at multiple monitoring points including natural
ground, it is possible to predict the seismic motion of the engineering bedrock based on
the earthquake record. Inversely, when the estimated seismic motion of the engineering
bedrock has been input, the dynamic response at all monitoring points must be reproduced.
According to the above premises, in this study, earthquake response analysis with a 3-D dam–foundation bedrock–reservoir system was performed to reproduce the behaviors of theSatsunaigawa Dam and its foundation bedrock during the Tokachi-oki Earthquake in 2003 (September, 26). Four items were considered concerning reproducibility: the maximum acceleration,
accelerogram, Fourier spectrum, and the transfer function. To improve the reproducibility of theobserved dynamic behavior, the physical properties of the dam and the foundation bedrock wererepeatedly adjusted. Through this process, the seismic motion of the engineering bedrock that was
assumed to be 171 m underneath the bottom surface of the dam was sequentially estimated. Figure
2 shows the investigation flow. By considering the seismic motion inside the bedrock when theearthquake record for each monitoring point was reproduced, setting criteria and appropriate
method of creating seismic motion at engineering bedrock for the earthquake response analysis
of a dam was proposed.

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報ٕ2Symposium on Sustainable Development of Dams and River Basins, 24th - 27th February, 2021, New Delhi

Setting or adjusting physicalproperties of foundation bedrock

Earthquake records

Preparing input seismic motion by pull-backEarthquake response analysisof the dam and foundation
Considering reproducibility
No

Reproduced?
Yes

Investigating seismic motionof deep bedrock
Evaluating suitability of setting of engineering bedrock
Figure 2. Investigation flow.

2.2 Investigation Conditions
2.2.1 Earthquake record
During the earthquake, acceleration records were obtained from each seismograph shown in Figure 1. The accelerations and Fourier spectra at the lower point of the bedrock (F1) are shown in
Figure 3(a) and Figure 3 (b) respectively as examples.
2.2.2 Model used for the investigation
Figure 4 shows the model used for this study. The geology and detailed topography of the foundation bedrock are taken into account in the analysis model. Viscous boundaries (Cao et al. 2012)were set as the side and bottom surface boundaries of the foundation bedrock model, and theextent of ground spreading infinitely outside the analysis range was considered.
2.2.3 Physical properties
For the dam concrete, as a linear material, its elastic modulus and damping coefficient were adjusted to most accurately reproduce the dam behavior during the earthquake. The damping coefficient was obtained by the half power method using the earthquake records (Yasuda et al. 2007),and the elastic modulus of the dam concrete was adjusted starting from the design value. Table 1
shows the physical properties of the dam concrete defined conclusively. Of these, the density andPoisson’s ratio are the results of quality control testing during the dam execution.
Table 1. Physical properties of dam concrete.
Elastic Modulus(N/mm2)
31200

Density(g/cm3)
2.4

Poisson’s ratio

Damping coefficient

0.2

2%

The foundation bedrock is also considered to be linear material. Its physical properties wereobtained from the seismic velocity (PS) logging and rock testing, but the damping coefficient was
finely adjusted so that it would be possible to most accurately reproduce the behavior of the monitoring points of the concerned foundation bedrock during the earthquake. Ultimately the physicalproperties were defined as shown in Table 2.

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0
-70
0

10 20 30 40 50 60 70 80

Fourier Spec.(cm/s)

Acc.(cm/s2)

Axial direction

0
-70
0
70

10 20 30 40 50 60 70 80

0-70
10 20 30 40 50 60 70 80

Time(s)Stream direction

10
1
0.1

1
Frequency(Hz)

100

10

Axial direction

10
1
0.1

Time(s)Vertical direction

0100

Time(s)70

Acc.(cm/s2)

Fourier Spec.(cm/s)

Stream direction

Fourier Spec.(cm/s)

Acc.(cm/s2)

70

1
Frequency(Hz)

100

10

Vertical direction

10
1
0.1

1
Frequency(Hz)10(a) Earthquake records(b) Fourier spectra
Figure 3. Earthquake records and Fourier spectra at the lower point of the bedrock (F1).

LegendCM Except for quartz, rock forming
minerals are somewhat softened.

CH Rock-forming minerals are weathered but the rock is relatively hard.

B Rocky hard, with no cracks or joints
and good adhesion.

Figure 4. Model used for the study.

Table 2. Physical properties of foundation bedrock.
Rock class
CM
CH
B
Grounds

Elastic modulus(N/mm2)
13620
29180
52530
PS logging

Density (g/cm3)

Poisson’s ratio

2.74

0.28

Rock testing

PS logging

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Damping coefficient
5%2%
1%
by analysis

Symposium on Sustainable Development of Dams and River Basins, 24th - 27th February, 2021, New Delhi

2.2.4 Input seismic motion
The input seismic motion at the bottom surface of the model (hypothesized engineering bedrock)
was prepared based on the pull-back method (Yasuda et al. 2018, Cao et al. 2016) of the threedimensional seismic motion using earthquake records of the lower points of the bedrock (F1)which is immune to the effects of the vibration of the dam and natural ground. Figure 5 shows theprocedure image, and the detailed description is given in references (Yasuda et al. 2007, Yasuda
et al. 2018).

{FF1}, {FB} is the Fourier spectrum of
F1 and B, respectively.
[T] is the transfer function between F1 and B.

F1B
Figure 5. Preparing the input seismic motion.

3 RESULTS OF REPRODUCTION ANALYSIS OF DYNAMIC BEHAVIOR OF THE
DAM AND FOUNDATION BEDROCK
The earthquake motions at each monitoring point on the dam body and foundation bedrock weresuccessfully reproduced by numerical analysis at relatively good precision. The maximum accelerations at each monitoring point are summarized in Table 3. Here, as examples, Figure 6 shows
the acceleration response time histories at the dam crest (T2) and upper point of the bedrock (F2),and Figure 7 shows the Fourier spectra and transfer functions of these acceleration responses.
The differences of the maximum acceleration responses and recorded accelerations at the dam
crest (T2) and upper point of the bedrock (F2) are scattered according to direction, but as shownin Figure 6, the accelerograms generally are similar. Figure 7 shows that the Fourier spectra andtransfer functions of calculated acceleration response and recorded accelerations at these two locations conform extremely closely. The calculated and recorded results for the left bank (T1) andthe right bank (T3) conform closely, and calculated results those generally reproduced both thenatural ground on the left bank (R1) and the right bank (R2) were obtained. The reasons for thegood reproducibility of the analysis are assumed to be the fact that the analysis model reflects
detailed topographical and geological information, and the physical properties were precisely defined.
4 SEISMIC MOTIONS INSIDE BEDROCK AND AT ENGINEERING BEDROCK
4.1 Seismic motions inside bedrock
When the earthquake motions of all monitoring points on the dam body and inside the foundation
bedrock had been reproduced by numerical analysis, it is assumed that the earthquake response
deep in the foundation bedrock model approximated the actual seismic motion without effects ofthe vibrations of dam body and natural ground. Accelerations at a total of 18 points on two horizontal planes shown in Figure 8 were calculated. The time histories and Fourier spectra of calculated accelerations at each location considered in the stream direction and axial direction (see Fig.
8(b)) were compared on each plane. Since the seismic motion inside the bedrock includes thewave propagates from the lower layer and the reflection from above layer, it is marked as E+F
wave in Figure 8. The seismic motion at the engineering bedrock is obtained by inverse analysis
using the earthquake records of monitoring points. The seismic motion is defined at an open
ground, so it is marked to be 2E wave in Figure 8.

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Table 3. Maximum accelerations at each monitoring point found by reproduction analysis.
SeismographObserved (cm/s2)

Direction

Analyzed (cm/s2)

Acc(cm/s2)

674
672
Stream Dir.
T2
Axial Dir.
310
402
Vertical Dir.
214
256
Stream Dir.
61
80
F2
Axial Dir.
67
90
Vertical Dir.
58
73
Stream Dir.
53
53
F1
Axial Dir.
67
67
Vertical Dir.
47
47
Stream Dir.
68
94
R1
Axial Dir.
68
86
Vertical Dir.
71
83
Stream Dir.
202
161
T1
Axial Dir.
222
182
Vertical Dir.
114
110
Stream Dir.
213
191
T3
Axial Dir.
195
204
Vertical Dir.
157
149
Stream Dir.
79
106
R2
Axial Dir.
98
90
Vertical Dir.
99
110
Note: *Error = (analysis value – observed value)/observed value
Stream Direction

800

Error [%]*
0
30
20
33
34
27
0
0
0
39
26
16
-20
-18
-3
-10
5
-5
35
-8
11

Record, max:554.7ࠉmin:-674.3
Analysis, max:672.3ࠉmin:-655.0

T2

0

-800
0

20

40

60

80

Acc(cm/s2)

Time(s)Axial Direction

800

Record, max:289.3ࠉmin:-309.6
Analysis, max:341.0ࠉmin:-402.3

0

-800
0

20

40

60

80

Acc(cm/s2)

Time(s)Vertical Direction

800

Record, max:211.7ࠉmin:-213.7
Analysis, max:255.8ࠉmin:-237.0

0
-800
0

20

40

60

80

Acc(cm/s2)

Time(s)(a) The Crest (T2)
Stream Direction

800

Record, max:60.6ࠉmin:-59.9
Analysis, max:67.4ࠉmin:-80.5

0

-800
0

20

40

60

80

Acc(cm/s2)

Time(s)Axial Direction

800

Record, max:64.2ࠉmin:-67.1
Analysis, max:89.7ࠉmin:-62.1

0

Acc(cm/s2)

-800
0

20

40

Time(s)Vertical Direction

800

60

80

Record, max:57.9ࠉmin:-50.2
Analysis, max:73.3ࠉmin:-72.5

0

-800
0

20

40

60

80

Time(s)(b) The Upper Point of Foundation(F2)Figure 6. Comparison of acceleration at dam crest and dam base in reproduction analysis.

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F2

Symposium on Sustainable Development of Dams and River Basins, 24th - 27th February, 2021, New Delhi    
Stream Direction

1

Axial Direction

1

Vertical Direction

1

Frequency(Hz)Axial Direction

10

1

Amplitude

1

Frequency(Hz)10

Axial Direction

100

10

10
1

0.1

Frequency(Hz)10Vertical Direction

1000

10

1

Frequency(Hz)1Fourier Spec.(cm/s)

100

1

0.1

100

10

10

10

1

100
10
1

Frequency(Hz)10Vertical Direction

100

Amplitude

Frequency(Hz)

1

1000

10

1

10

1

Fourier Spec.(cm/s)

100

Fourier Spec.(cm/s)

Frequency(Hz)

100

10

Stream Direction

100

Amplitude

10

1

Stream Direction

1000

Fourier Spec.(cm/s)

Fourier Spec.(cm/s)

100

Fourier Spec.(cm/s)

  ̿̿̿ Earthquake record   ̿̿̿ Analysis

10
1

0.1
1

Frequency(Hz)(a) F210

1Frequency(Hz)10(b) T2            (c) T2/F2

Figure 7. Comparison of Fourier spectra and transfer functions at dam crest and the upper point of bedrock (Recorded and calculated).

LegendLocations where
seismic motion isconsideredF1 plane
E+F
2E

Bottom surfaceof model(a) Depth of the plane considered     

 (b) Points on each plane considered

Figure 8. Locations of calculated accelerations inside the bedrock.

In order to clearly compare the accelerograms at different locations, 10 seconds (20.01 to 30.0
seconds) of main motion was extracted from the total time history (length 81.92 seconds). Figure
9 shows the main motions of three components at three locations on the F1 plane (depth of 57m
from bottom surface of dam) of the dam axis section. Comparing with the lower point of the
bedrock (F1), the accelerations at both sides (L1 and R1) are a little larger in three directions, andthe phase difference appeared partially in time histories. This result is assumed to be the disturbance of the seismic motion in the bedrock of this depth by the influence of the dynamic behaviorof the dam and the natural ground on both sides. Figure 10, on the other hand, shows the main
motion at three locations on the bottom plane of the model (depth of 171 m below the bottom
surface of the dam). At this depth, the relative error of the maximum acceleration at three locations
was quite small, and its phases conformed throughout almost the entire time history. For thisreason, it is assumed that the depth of the engineering bedrock for analysis should be set at least
1.5 times the dam height (in this model, 171 m), and that the seismic motion at this location willbe almost unaffected by the behavior of the dam and natural ground during the earthquake.

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4.2 Seismic motion at engineering bedrockAcc.(cm/s2)

As stated in the previous section, the seismic motion on the bottom surface of the model at a depthof 171 m is almost immune from the influence of the dynamic behavior of the dam or natural
ground, so this depth (Fig. 8(a)) can be set as the engineering bedrock. Figure 11 shows the responses of this location obtained by reproduction analysis. This is considered to be similar toseismic motion actually generated in deep bedrock by the Tokachi-oki Earthquake in 2003. Figure11(a) shows the ground motion on the open bedrock surface (Fig. 8(a)) at this location. It is possible to reproduce the dynamic behavior at each monitoring point on the dam body and on thefoundation bedrock by inputting this wave, so this wave can be considered to be the seismic motion at the engineering bedrock.
L1 max:53.4ࠉmin:-58.0 㸪

100
0
-100

Acc.(cm/s2)

20

22

24

26

28

Time(s)(a) Stream Direction
L1 max:68.0ࠉmin:-76.3 㸪

100

30

F1 max:61.2ࠉmin:-67.4 㸪 R1 max:64.1ࠉmin:-70.4

0
-100
20

Acc.(cm/s2)

F1 max:48.8ࠉmin:-53.0 㸪 R1 max:48.3ࠉmin:-55.1

22

24

28

Time(s)(b) Axial Direction

L1 max:56.2ࠉmin:-57.9 㸪

100

26

L1

F1

R1

L2

M

R2

30

F1 max:47.4ࠉmin:-37.7 㸪 R1 max:57.4ࠉmin:-50.4

0
-100
20

22

24

26

28

Time(s)(c) Vertical Direction30

Acc.(cm/s2)

Figure 9. Comparison of seismic motion on F1 plane.
L2 max:62.6ࠉmin:-55.3 㸪

100
0
-100

Acc.(cm/s2)

20

22

24

26

28

Time(s)(a) Stream Direction
L2 max:77.8ࠉmin:-70.2 㸪

100

30

M max:79.3ࠉmin:-71.5 㸪 R2 max:76.9ࠉmin:-76.6

0
-100
20

Acc.(cm/s2)

M max:53.7ࠉmin:-57.7 㸪 R2 max:66.1ࠉmin:-52.7

22

24

Time(s)(b) Axial Direction
L2 max:58.3ࠉmin:-44.5 㸪

100

26

28

30

M max:50.5ࠉmin:-46.8 㸪 R2 max:42.9ࠉmin:-51.5

0
-100
20

22

24

26

28

Time(s)(c) Vertical Direction

Figure 10. Comparison of seismic motion on bottom of model.

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Symposium on Sustainable Development of Dams and River Basins, 24th - 27th February, 2021, New Delhi

The hypocenter of the Tokachi-oki Earthquake in 2003 was 45 km deep at an epicentral distance of 150 km downstream from the Satsunaigawa Dam. Figure 12 shows the relative locational
relationship of the hypocenter and the Satsunaigawa Dam. The vibration components of stream
direction and vertical direction at the dam site are based on a synthesis of P waves and SV wavesof the seismic motion, and the axial direction is almost exactly parallel to the vibration directionof the earthquake’s SH wave. Thus, as shown in Figure 11(a) and Figure 11(b), the seismic main
motion in the stream direction and vertical direction at the Satsunaigawa Dam appear to havearrived a little earlier than the axial direction component. On the other hand, the amplitude ofseismic motion of axial direction, or in other words of the SH wave component, was a little larger
than the other two components.
From the above, it is assumed that at the Satsunaigawa Dam, the appropriate location of theengineering bedrock for earthquake response analysis is in deep bedrock at a depth 1.5 times thedam height, and where the shear wave velocity is approximately 2,000 m/s (the elastic modulusof rock class CH in Table 2 is calculated with Vs = 2000 m/s). The preparation method of theseismic motion at the engineering bedrock hypothesized is to identify the analysis model by reproducing the earthquake records at multiple monitoring points following the investigation flowin Figure 2, then performing the pull-back calculation of the seismic motion as explained in Section 2.2.4. Rightly, the analysis model used must reflect the geology and topography of the foundation bedrock.
For the past analysis related to verification work of seismic performance of a dam, the input
seismic motion was prepared by a method of the dam distance attenuation formula, or the empirical Green’s function method, or the method of adjusting an earthquake record to the lower-limit
acceleration response spectrum for verification. Seismic motion at foundation bedrock obtained
through this study can contribute to the verification of these preparation methods of input seismic
motion.
Acc.(cm/s2)

max:53.7ࠉmin:-57.7

0
-150
0

10

20

30

40

50

60

70

Stream Direction

150

Acc.(cm/s2)

Stream Direction

150

0
-150

80

0

10

20

30

Time(s)

-150
10

20

30

40

50

60

70

0

10

20

30

30

40

max:137.5ࠉmin:-135.0

50

60

70

50

60

70

max:80.2ࠉmin:-77.1

-150

80

0

10

20

30

40

50

60

70

Time(s)(1)ࠉAcceleration(1) Acceleration
100

Fourier Spec.(cm/s)

100

10StreamAxial
Vertical

1
0.1

80

0

Time(s)Fourier Spec.(cm/s)

40

Vertical Direction

150

Acc.(cm/s2)

Acc.(cm/s2)

max:50.5ࠉmin:-46.8

-150
20

80

-150

80

0

10

70

Time(s)Vertical Direction

0

60

0

Time(s)150

50

Axial Direction

150

Acc.(cm/s2)

Acc.(cm/s2)

max:79.3ࠉmin:-71.5

0

0

40

Time(s)Axial Direction150

max:104.5ࠉmin:-112.9

10
StreamAxial
Vertical11Frequency(Hz)

0.1

10

1

Frequency(Hz)(2) Fourier Spectrum(2) Fourier Spectrum(a) at intra-layer of 171 m deep(b) at engineering bedrock

Figure 11. Seismic motion at intra-layer of 171 m deep and engineering bedrock.

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80

Vertical dir.

Symposium on Sustainable Development of Dams and River Basins, 24th - 27th February, 2021, New Delhi

Stream dir.

P waves are longitudinal waves that oscillate
in the direction in which the waves travel
and transmit expansion and contraction.
150 kmSH waves are the shear components that oscillate parallel to the ground surface.
SV waves are shear components perpendicular to SH waves.

Figure 12. Relationships of seismic motion directions and orientations of the dam.

5 CONCLUSIONSThis study clarified the followings.
(1) The physical properties of the Satsunaigawa Dam were identified by preparing an analysis
model based on detailed topographical data and geological information to perform reproduction analysis of dynamic behavior during the earthquake. The analysis succeeded inprecisely reproducing the earthquake records at multiple monitoring points on the dam
body and the foundation bedrock, and in predicting the seismic motion at deep bedrock,particularly at the engineering bedrock.
(2) As the criteria for setting the position of the engineering bedrock, in the case of a concrete
gravity dam, the engineering bedrock should be set at a depth equal to 1.5 times the damheight, and where the shear wave velocity is at least 2,000 m/s.
(3) The seismic motion at the engineering bedrock should be prepared by pull-back calculationof the seismic motion using an analysis model identified by the reproduction of the earthquake records at multiple monitoring points.
(4) The seismic motion at engineering bedrock produced by this study can help verify theseismic motion preparation methods that have been in wide use for the verification of seismic performance of dams.
REFERENCES
Boore, D. M. 1983. Stochastic Simulation of High Frequency Ground Motions based on SeismologicalModels of Radiated Spectra, Bulletin of the Seismological Society of America Vol.73, No.6, pp.18651894.
Cao, Z. and Saotome A. 2012. Analytic Method of Method of 3D Soil-Structure System with the Viscous
Boundaries Considering the Vertical Motion, 15th World Conference on Earthquake Engineering,
No.0598.
Cao, Z., Matsumoto, N., Tardieu, B., Fry, J. J., Bourdarot, E., and Robbe, E. 2016. Practical guide forselection seismic parameters and numerical models in earthquake analysis of dams, Proc. of international symposium on qualification of dynamic analysis of dams and their equipment and probabilistic
assessment of seismic hazard in Europe, No.1-4.
Irikura, K. 1986. Prediction of strong acceleration motions using empirical Green’s function, The Seventh
Japan Earthquake Engineering Symposium, pp.151-156. (in Japanese)
Kamae K., Irikura K., and Fukuchi Y. 1991. Prediction of strong ground motion based on scaling law ofearthquake, Journal of Structural and construction engineering, No.430, pp.1-9.
Matsumoto, N., Yoshida, H., Sasaki, T. and Annaka, T. 2003. Response Spectra of Earthquake Motion at
Dam Foundation, Proc. 21st International Congress on Large Dams.
Yasuda, N., Shimamoto, K., et al. 2007. 3D-seismic response analysis of concrete gravity dam –Satsunaigawa dam analysis -, Memorandum of National Institute for Land and Infrastructure Management, No.429. (in Japanese)
Yasuda, N., Matsumoto, N. and Cao, Z. 2018. Study on the Mechanism of the Peculiar Behaviors of Aratozawa Dam in the 2008 Earthquake, Journal of diaster research, Vo.13, No.1, pp.205-215.

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