COMMISSION INTERNATIONALE
DES GRANDS BARRAGES------VINGT- QUATRIÈME CONGRÈS
DES GRANDS BARRAGES

Marseille, juin 2021-------SEISMIC PERFORMANCE VERIFICATION OF A ROCKFILL DAM
AGAINST LARGE DOUBLET EARTHQUAKES (*)
Nario YASUDA
Head of Eng. Division 1, JAPAN DAM ENGINEERING CENTER
Zengyan CAO
Senior Engineer, J-POWER BUSINESS SERVICE CORPORATION
JAPAN

1.

INTRODUCTION

In Japan, seismic performance verification of existing dams against large
earthquakes is being carried out via dynamic response analysis. In the dynamic
response analysis of these dams, engineers use the dam’s normal operating
conditions as the initial conditions for the analyses and suppose the dam subject
to a single earthquake. However, after the Iwate-Miyagi Nairiku Earthquake in 2008
(Mj 7.2, where Mj is the Japan Meteorological Agency (JMA) magnitude scale), thedynamic characteristics of the Aratozawa Dam, a 74.4 m high rockfill dam,considerably deteriorated [1][2]. Approximately one week after the main shock, thenatural frequencies of the dam were found to have nearly recovered. On the other
hand, during the 2016 Kumamoto earthquake of April 14 (21:26, Japan time) and
16 (01:25), (Mj 6.5 and Mj 7.3), Mashiki Town experienced ground motions of JMA
seismic intensity 7 twice within 28 hours [3]. Generally, large aftershocks often
occur after a strong inland earthquake. In the future, a dam may experience
multiple large seismic events in a short period. Thus, it is necessary and beneficial
to dam engineering to investigate the behavior of the Aratozawa Dam subject to aground motion of JMA seismic intensity 7 before its dynamic characteristics fully
recover from an earlier earthquake. The situation mentioned here has not beenaddressed in the current "Guidelines of the Seismic Performance Verification of(*)Vérification des performances sismiques d'un barrage en enrochement contre degrands tremblements de terre en doublet

報－1

Dams for Large-scale Earthquakes (draft)" [4]. Thus, this study clarifies the
behavior of rockfill dams subject to large doublet earthquakes and proposes a
seismic performance verification method and emergency response measures in
preparation for the occurrence of large doublet earthquakes in the future.
In this study, the authors modeled the response of the Aratozawa Dam to
two large earthquakes. The dynamic response analyses of the dam are performed
considering the variation in the dynamic characteristics of the dam during each
earthquake. The calculations of slip deformation and the deformation related to theshaking and rearrangement of soil particles are carried out considering the change
in the material properties of the dam. The final residual deformation of the dam
after the doublet earthquakes is predicted by summing the deformation induced byeach earthquake, and the seismic safety of the dam is verified via the residual
deformation. In addition, in preparation for large doublet earthquakes, emergency
response measures after large earthquakes are investigated for rockfill dams.

2.

2.1.

DAM SPECIFICATIONS AND EARTHQUAKE MONITORINGDAM SPECIFICATIONSThe Aratozawa Dam is a 74.4 m high rockfill dam with a central clay core on
the Kitakami River, Kurihara City, Miyagi Prefecture, and the dam body wascompleted in 1992. Table 1 shows the specifications of the dam. The location, theplan view and the standard cross-section of the dam and the locations ofseismographs are shown in Fig. 1. The seismographs with three components(parallel and perpendicular to the dam axis and vertical directions) are installed at
the dam base (F), mid-height of the core (M) and dam crest (T).
Table 1
Specifications of the Aratozawa Dam
Dam location
Dam type
Dam height
Crest length
Crest width
Crest elevation
Nonoverflow section elevation
Slope gradient
Embankment volume
Basin area
Reservoir storage volume
Design seismic coefficient

Kurihara City, Kurihara district, Miyagi Prefecture
Rockfill dam with central clay core
74.4 m (minimum ground elevation, EL. 205.0 m)
413.7 m10.0 mEL. 279.4 m
EL. 278.9 m
Upstream: 1: 2.7 downstream: 1: 2.13048000 m3
20.4 km2
13850000 m3
0.15 (dam body), 0.18 (intake tower), 0.16 (spillway)

報－2

10 m
155 m
2.5 m
2.5 m
HWS.EL276.9 mEL 279.4 m
181 m

T

Aratozawa Dam
T, M, F

Tokyo

M
F
EL 205.03m(a) Location of the dam● Seismographs(b) Plan view
T: Crest

27.2 m 3 m(c) Standard cross-section

M: Mid-height of core

F: Foundation bedrock

Fig. 1
Location of the dam and the locations of seismographs
Localisation du barrage et emplacements des sismographes

2.2.
NONLINEAR PROPERTIES OF EMBANKMENT MATERIALS EVALUATED FROM
EARTHQUAKE RECORDS
A large number of earthquakes since 1992, immediately after the dam bodycompletion, have been recorded. Of these, there were approximately 500
earthquakes with a maximum acceleration over 10 cm/s2 and 37 earthquakes over
100 cm/s2 at the dam base (F). On June 14, 2008, the Iwate-Miyagi Nairiku
Earthquake in 2008 (Mj 7.2) occurred. At the Aratozawa Dam locatedapproximately 15 km from the epicenter, the maximum acceleration of 1024 cm/s2
in the direction perpendicular to the dam axis was recorded at the dam base. Thisis the largest earthquake magnitude ever recorded at the base of a dam in Japan.
During the earthquake, the natural frequency and acceleration amplification factorof the dam sharply decreased. Approximately 1 week after the main shock, thenatural frequencies of the dam nearly fully recovered to their preearthquake values.
The decrease in the natural frequency of the dam implies a reduction in the
stiffness of the dam materials. In a single degree of freedom system, therelationship of the natural circular frequency ω, the stiffness k and the mass m areexpressed as Eq. [1].


𝜔

1

The relationship between the three physical quantities in Eq. [1] is also
generally satisfied in civil engineering structures such as rockfill dams. Because
the mass of the dam body does not change, considering that the stiffness is
proportional to the shear modulus G of the dam material through Poisson’s ratio,
the relationship between the shear modulus G and the fundamental frequency 𝑓
is shown in Eq. [2].
𝑓
𝑓

𝐺
𝐺

2

報－3

Here, 𝐺 and 𝑓 are the initial shear modulus of the material in the small
strain status and the initial fundamental frequency of the dam, respectively.
Therefore, the rate of change in the shear modulus of the materials can be obtained
from the rate of change in the fundamental frequency of the dam using Eq. [2] [5].
In addition, the transfer function of the dam can be obtained from the earthquake
records at the crest of the dam (T) and the dam base (F), and the frequency
corresponding to the first peak of the transfer function can be regarded as thefundamental frequency of the dam. From the analysis of the records of the pastsmall earthquakes, the fundamental frequency of the Aratozawa Dam has beenfound to be 3.2 Hz [2]. To determine the fundamental frequency 𝑓 of the dam foreach earthquake, the earthquake records of relatively large acceleration amplitude
are extracted, focusing on the Iwate-Miyagi Nairiku Earthquake in 2008 and its
aftershocks. The list of the extracted earthquake records is shown in Table 2.
These earthquake records (Nos. 1-19) are numbered in the order of occurrence.
On the other hand, using the earthquake records of the dam, it is possible tocalculate the average shear strain of the dam according to the procedure shown in
Fig. 2.
From each earthquake record, the fundamental frequency of the dam in the
direction perpendicular to the dam axis and the average shear strain are calculated
and summarized in Table 2. The value of 𝐺 ⁄𝐺 is calculated according to Eq. [2]𝛾and plotted with the average shear strain γ in Fig. 3. Depending on the 𝐺 ⁄𝐺
relationship and the occurrence time of the earthquakes, this seismicity can bedivided into the following 3 periods.
Period I. Earthquake 1 to earthquake 5
Period II. Earthquake 6 to earthquake 14
Period III. Earthquake 15 to earthquake 19
The 𝐺 ⁄𝐺 -γ relationship in Period I can be approximated by a curve and isclearly different from that in Period II. In response to the Iwate-Miyagi Nairiku
Earthquake in 2008 (No. 5), it is clear that the material properties of the Aratozawa
Dam had significantly changed temporarily. Thus, during the earthquake response
analysis and seismic performance evaluation of the dam in Period II, the dynamic
characteristics and material properties of the dam during this period must be
considered. In addition, the 𝐺 ⁄𝐺 -γ relationship in Period III can be estimated tohave nearly recovered to the relationship exhibited in Period I. The solid line
showing the 𝐺 ⁄𝐺 -γ relationship of the dam in Period I and Period III is very similar
to that of ordinary soil materials. The shear strain corresponding to 𝐺 ⁄𝐺 =0.5 is
2.9×10-4, which substantially coincides with the reference shear strain (3.0×10-4)
identified by a reproduction analysis of a past earthquake of the Aratozawa Dam[6]. In Period II, there are no data reflecting a shear strain of 10-4 or more, but whenthe existing data are fitted with a hyperbolic line, the relationship indicated by thebroken line is obtained.

報－4

Table 2
Earthquake records and the obtained results
Time ofoccurrence

No.

Focal Max. acc. at the Fundamental Averagedepth
dam base※1
freq. of the shear strain(km)
dam (Hz)of dam body(cm/s2)

M

1
1996/08/11 03:12
6.1
9
28
2.930
5.320E-05
2
1996/08/11 08:10
5.8
10
36
2.830
3.920E-05
3
1996/08/11 15:01
4.9
10
30
3.027
6.600E-06
4
2003/05/26 18:24
7.1
72
114
2.637
1.727E-04
5
2008/06/14 08:43
7.2
8
1024
1.514
1.566E-03
6
2008/06/14 09:00
4.2
11
99
2.344
3.700E-06
7
2008/06/14 09:01
4.0
7
482
1.953
7.760E-05
8
2008/06/14 09:14
3.6
4
151
2.246
1.660E-05
9
2008/06/14 09:20
5.7
7
76
2.051
7.980E-05
10
2008/06/14 10:40
4.8
7
120
2.148
5.960E-05
11
2008/06/14 12:09
4.1
8
92
2.246
2.840E-05
12
2008/06/14 12:10
4.8
9
79
2.344
2.480E-05
13
2008/06/14 19:11
4.1
8
229
2.148
5.170E-05
14
2008/06/16 23:14
5.3
7
76
2.246
3.760E-05
15
2008/07/24 00:26
6.8
108
27
2.600
6.530E-05
16
2008/09/25 15:04
4.1
6
119
2.539
7.000E-05
17
2011/03/11 14:46
9.0
24
102
2.307
1.858E-04
18
2011/04/07 23:32
7.2
66
120
2.344
2.405E-04
19
2015/05/1306:13
6.8
46
18
2.942
1.350E-05
Note: ※ 1 The maximum value of the three directional components of the dam base (F)Acceleration record → displacement → relative displacement → shear strain

AT

UT
Integration

H

UTF= UT-UF

γ=UTF/HUF

AF

Integration

Fig. 2
Procedure for calculating the shear strain of the dam from the recordings
Procédure de calcul de la déformation de cisaillement du barrage à partir desenregistrements
1.0
0.9

19

0.8

1
2

G/G0

0.7
6

12
8

0.4

11

14 10
13

17
9

18

approximate
curve during
normal conditions

7

0.3

5

0.2

approximate
curve during
aftershocks period

0.1
0.0
1.0E-06

4

15
16

0.6
0.5

1～ 4 Before the mainshock
5
Mainshock
6～14 1 week after the mainshock
15～19 1 month after the mainshock3

1.0E-05

1.0E-04

γave

1.0E-03

1.0E-02

Fig. 3
G/G0-γ relationship obtained from the records of relatively strong earthquakes
G/G0-𝛾 relation obtenue à partir des enregistrements de tremblements de terre
relativement forts

報－5

3.

3.1.

CONSIDERED EVENTS AND STUDY METHODSCONSIDERED EVENTSIn this study, it is assumed that the Aratozawa Dam will subject to a doublet
earthquake similar to the 2016 Kumamoto Earthquake. The foreshock (Mj 6.5) of
the 2016 Kumamoto Earthquake occurred on April 14, and the main shock (Mj 7.3)
occurred on April 16 of the same year. Mashiki Town, Kumamoto Prefecture,experienced the ground motion of JMA seismic intensity 7 (the maximum seismic
intensity ever observed in Japan) twice within 28 hours. In this study, the terms"Earthquake A" and "Earthquake B" are used instead of the terms "foreshock" and"main shock", respectively. For the Aratozawa Dam, the Iwate-Miyagi Nairiku
Earthquake in 2008 is considered Earthquake A in the following analysis. Before
the dynamic characteristics of the dam recover, an earthquake of Mj 6.5 is modeledto occur directly underneath the dam (Earthquake B).
The acceleration records obtained at the dam base will be used directly as
the input ground motions of Earthquake A. For Earthquake B, artificial seismic
waves will be created with the earthquake records obtained at the dam base during
the aftershocks immediately after Earthquake A. The ground motions at the dambase for Earthquake B are created by fitting the earthquake records of anaftershock equivalent to an Mj 6.5 earthquake to the lower limit spectra defined in
the verification guidelines of dams during large earthquakes [4].

3.2.

STUDY METHODSThe earthquake response analysis of the dam will be performed with anequivalent linearization method, which is a commonly available analysis method,
instead of nonlinear analysis. The main influencing factors for the seismic behavior
and seismic safety verification of dams include the ground motion, material
properties such as strength and elastic modulus, and reservoir conditions. If thematerial properties of the dam have changed due to Earthquake A, the variation
should be reflected in the response analysis of the dam to Earthquake B. As shownin Fig. 3, the initial shear modulus and the 𝐺 ⁄𝐺 -γ relationship in Period II are
clearly different from those of the other periods. Therefore, to predict theearthquake responses of the dam to Earthquake B within approximately one week
after Earthquake A, the initial shear modulus G0 and the shear strain dependenceof the materials during the period are considered. The residual deformation of thedam due to the doublet earthquake is predicted by summing the deformations
calculated separately for each earthquake. The deformation includes the sliding
component and the subsidence associated with soil particle oscillation. Figure 4
shows the earthquake response analysis and the seismic performance verification
procedure for rockfill dams subject to a large doublet earthquake used in this study.

報－6

Analysis model

Relationship

G/G0～γofEarthquake A

based on earthquake records(Iwate-Miyagi Nairiku Earthquake)(1)

Response analysis(Equivalent linearization method)(2) Subsidence associatedwith shaking(3) Slip deformation(4) Deformation due toEarthquake A (=(2)＋(3))

Relationship
based

on

of

G/G0～γEarthquake B

aftershock(artificial waves)records of Earthquake A(5) Response analysis(Equivalent linearization method)(6) Subsidence associatedwith shaking(7) Slip deformation(8) Deformation due toEarthquake B (= (6) + (7))(9) Total residual deformation(= (4) + (8))(10) Seismic performanceverification of the dam

Fig. 4
Verification of the seismic performance of rockfill dams for doublet earthquakes
Vérification de la performance sismique des barrages en enrochement pour lestremblements de terre « doublet »

4.

4.1.

RESPONSE OF THE DAM TO EARTHQUAKE A

REPRODUCTION ANALYSIS

Figure 5 shows the 3D analysis model of the dam-reservoir-foundation
system. Considering the influence of the vibration of the free fields outside the報－7

analysis region, viscous boundary conditions are used at the perimeter and bottom
boundaries of the foundation rock and the upstream end of the reservoir model. In
the static stress analysis before the earthquake, the influence of the reservoir wateron the water level (EL 270.1 m) during the earthquake and that of the pore waterpressure inside the dam are considered. However, the influence of thehydrodynamic pressure is neglected in the earthquake response analysis since theinteraction between embankment material and reservoir water is not yet fully
understood.

Viscous boundary(Free field is considered)

Viscous boundary(Free field is considered)Fig. 5
Analysis model
Modèle d'analyse
The equivalent linearization method is used in the analysis to consider the
influence of nonlinear material properties. The initial shear moduli of theembankment materials are set according to Sawada’s equation [7], which is basedon the compressional and shear wave logging (P-S logging) of a number of rockfill
dams. To improve the accuracy of the initial shear moduli, they are adjusted slightly
so that the fundamental frequency of the dam obtained from eigenvalue analysis
is consistent with the result estimated for past small earthquakes. The approximate
curve in the normal status shown in Fig. 3 is used for considering the shear strain
dependence of the shear moduli.
The damping is evaluated by Eq. [3] and considered to be classical Rayleighdamping.


𝐶

𝛼𝑀

3

𝛽𝐾

where [C], [M], and [K] are the damping matrix, mass matrix and stiffness matrix,
respectively. Superscript e indicates that these matrices belong to each element.
α and β are the parameters defined by Eq. [4].
α

1.4ℎ𝜔

𝛽

0.6 ℎ⁄𝜔

4

where 1 is the fundamental angular frequency of the dam; and the damping ratioℎ is evaluated by Eq. [5], which considers its shear strain dependence.

報－8

h

ℎ

𝛾
𝛾

ℎ

𝛾

5

where h , h0 and hmax are the damping ratio, its initial value and its maximum
value, respectively. The values of h0 and hmax are listed in Table 3 and Fig. 6 are
identified by the reproduction analysis of the dynamic behavior of the dam during
past earthquakes [6].  is the effective shear strain (2/3 of its maximum value).  ris the reference shear strain, which can be found from Fig. 3 to be approximately
2.9×10-4 when G/G0 = 0.5. The Poisson's ratios of the embankment materials are
set according to Sawada’s equation [7]. The densities of the embankment
materials, foundation rock and spillway concrete from construction quality control
tests of the dam are listed in Table 4.
Spillway concrete is treated as a linear material with an elastic modulus of
30000 N/mm2 and a Poisson's ratio of 0.2. The foundation rock is also modeled asa linear material. Its shear modulus is 5500 N/mm2, which is obtained by convertingfrom the average shear wave velocity of the rock (Vs = 1440 m/s). The Poisson's
ratio of the foundation rock is 0.25, which is estimated to be the average value ofthe rock.
As for the input ground motions, since Earthquake A is a real earthquake,the earthquake records (shown by the solid line in Fig. 7(c)) obtained at the dambase (F) during the Iwate-Miyagi Nairiku Earthquake in 2008 are used. The input
ground motions at the bottom boundary of the model (as shown in Fig. 5) arecreated by inverse analysis of the earthquake records at the dam base.
B

F
E

F
D

A

D

E

C

Fig. 6
Zoning of the properties (refer to Table 3)
Zonage des propriétés (se reporter au Tableau 3)
Table 3Damping factors identified by the reproduction analysis ofdynamic behavior of the dam during past earthquakes
Maximum damping
ratio hmax

Classification
A: Lower part of the core20 %B: Upper part of the core30 %C: Filter

D: Transition

30 %E: Rock (inner) F: Rock (outer)

20 %

報－9

Initial damping ratio
h05%Table 4
Density of the materials used in the analysis
Classification

Wet
2.04
2.34
2.24
2.15
2.15
2.18
2.13

Core
FilterTransition
Upstream rockDownstream rock

Inner
Outer
Inner
Outer

Spillway concrete
Bedrock

Density (g/cm3)
Saturated
2.10
2.43
2.33
2.29
2.32
2.32
2.30
2.40
2.60

Figure 7 shows the acceleration response histories of the earthquake
monitoring stations. Although there is some difference in the maximum
acceleration values between the analysis results and earthquake records, theresponse waveforms are generally coincident. Good reproducibility is obtained in
the acceleration response histories. The waveforms from 0 sec to 4 sec in theacceleration response histories of the crest have approximately the same phase.
In contrast, in the waveforms after 4 sec, the peak values of the earthquake records
appear slightly later than those of the analysis results. This is thought to be due tothe fact that in the equivalent linearization method, the stiffness of the embankment
materials is a constant value for the whole history, but in the actual dam, the rigidityof the dam decreased after the principal motion of the earthquake, which resulted
in a decelerating wave propagation. Figure 8 shows the comparison of the Fourier
spectra and the transfer functins of the acceleration responses at the dam baseand crest. In the frequency range up to 2 Hz, the Fourier spectra and transfer
functions between the earthquake records and analysis results are similar. In thehigher frequency range, the deviation between the analysis results and earthquake
records gradually increases as the frequency increases. This finding may also be
due to the continuous change in the physical properties of the real dam, while thephysical properties in the analysis are treated as constant values. As a result, thephysical properties suitable for the principle motion, which mainly include the lowfrequency components, lead to the differences in the high-frequency seismic
responses in the analysis.

4.2.

RESIDUAL DEFORMATION CAUSED BY EARTHQUAKE A

The seismic performance of rockfill dams is evaluated via residual
deformation under the current guidelines [4]. In the previous section, the seismic
behavior of the Aratozawa Dam in response to Earthquake A was reproduced bynumerical analysis. Using the analysis results, the residual deformation of the damcaused by Earthquake A is calculated. The residual deformation of the dam causedby the earthquake will be calculated separately via two methods according to thetwo deformation mechanisms, sliding and subsidence.

報－10

(cm/s2)
1000

Record：max 525
Analysis：max 661

Direction perpendicular to dam axis

500
0
-500
-1000
0

2

(cm/s2)
1000

4

6

8

10

(Sec.)

Record：max 455
Analysis：max 558

Direction parallel to dam axis

500
0
-500
-1000
0

2

4

(cm/s2)
1000

6

8

10

(Sec.)

Record：max 622
Analysis：max 414

Vertical direction

500
0
-500
-1000
0

2

4

6

8

10

(Sec.)(a) Crest (T)Record：max 535
Analysis：max 330

Direction perpendicular to dam axis

(cm/s2)
1000
500
0
-500
-1000
0

2

(cm/s2)
1000

4

6

8

10

(Sec.)

Record：max 478
Analysis：max 312

Direction parallel to dam axis

500
0
-500
-1000
0

2

4

(cm/s2)
1000

6

8

10

(Sec.)

Record：max 470
Analysis：max 367

Vertical direction

500
0
-500
-1000
0

2

4

6

8

10

(Sec.)(b) Middle of Core (M)(cm/s2)
1000

Record：max 1024
Analysis： max 993

Direction perpendicular to dam axis

500
0
-500
-1000
0

2

(cm/s2)
1000

4

6

8

10

(Sec.)

Record：max 899
Analysis：max 860

Direction parallel to dam axis

500
0
-500
-1000
0

2

4

(cm/s2)
1000

6

8

10

(Sec.)

Record：max 691
Analysis：max 540

Vertical direction

500
0
-500
-1000
0

2

4

6

8

10

(Sec.)(c) Dam Base (F)Fig. 7
Acceleration response of Earthquake A
Réponse d'accélération du tremblement de terre A

報－11

Crest (T)Fourier Spectra (cm/s)

400

RecordAnalysis
200

0
0

2

8

10

Dam Base (F)400
Fourier Spectra (cm/s)

4
6Frequency (Hz)RecordAnalysis
200

0
0

2

4
6
Frequency (Hz)810Transfer Functions

4

RecordAmplitude

Analysis
2

0
0

2

4
6
Frequency (Hz)8

10

Fig. 8
Fourier spectra and transfer function of the acceleration response in the direction
perpendicular to the dam axis
Spectre de Fourier et fonction de transfert de la réponse d'accélération
perpendiculairement à l'axe du barrageFirst, the deformation due to sliding is calculated. Here, the method proposedby Watanabe and Baba [8] is used, which is based on the sliding block assumption
and the stress results of the earthquake response analysis. A 2D calculation is
performed with the standard cross-section extracted from the 3D model shown in
Fig. 5. In total, 1235 arcs are set up, covering all the possible sliding zones. To
fully investigate the stability of the dam, the arcs sliding toward the upstream side
are divided into 3 groups. The arcs for which both ends pass through only the
upstream surface of the dam are referred to as the "U1 Group". Those with their
upper end at the crest and lower end at the upstream surface are categorized into
the “U2 Group”. In addition, the arcs that cut the core zone are referred to as the“U3 Group". Similarly, the arcs sliding downstream are divided into the "D1 Group","D2 Group" and "D3 Group". Fig. 9(a) shows the arcs of the U2 Group as an
example. Table 5 shows the strength parameters of the embankment materials
based on the results of material tests during dam construction.

報－12

Fig. 9Arcs of the U2 Group (as an example of sliding arcs)
Arcs du groupe U2 (comme exemple d'arcs glissants)
Table 5Strength parameters of the embankment materials
Cohesion
(MPa)
0.049
0.078
0.039
0.049
0.049
0.049
0.049

DivisionCore
FilterTransition
Upstreamrockzone
Downstream rock
zone

Inner
Outer
Inner
Outer

Friction angle(degrees)
33.2
42.2
39.9
42.7
43.4
40.2
42.7

Evidence
Basedontriaxial
compression
test

As a result, except for one arc each near the upstream and downstream toesof the dam, the safety factors of all of the other arcs are greater than 1. The arc of
the minimum safety factor in the 6 arc groups is summarized in Table 6, and thepositions of the corresponding arcs are shown in Fig. 10. For the sliding arcs withsafety factors lower than 1, the sliding displacement is calculated and shown in
Table 6. In the local surface layer of the downstream slope of the dam (the No. 4arc), the sliding safety factor is 0.847, but nearly no sliding displacement occurs(0.04 cm). This result suggests that the sliding in the Aratozawa Dam did not occur
during Earthquake A (the Iwate-Miyagi Nairiku Earthquake in 2008). This result is
consistent with the field survey after the earthquake [9], which reported that no slip
phenomenon was found to be due to the earthquake.
Table 6
The results of sliding deformation for Earthquake A
Slip direction
To the upstream side

To the downstream side

Arc group

Arc No.

U1
U2
U3
D1
D2
D3

1
2
3
4
5
6

報－13

SafetySlip disp.

factor
0.994
1.469
1.478
0.847
1.239
1.407

(cm)
0.0001
0.04
-

3
2
6
5

1

4

Fig. 10
Arcs with the minimum safety factor of each arc group for Earthquake A
Arcs avec un facteur de sécurité minimum de chaque groupe d'arc pour letremblement de terre A
It has been noted that, in addition to sliding, subsidence may be caused by
the shaking and rearrangement of the soil particles in fill dams due to strong
earthquakes. Such deformation can be regarded as a result of the decrease in therigidity of the dam. Subsidence can be conveniently evaluated by deformation
calculation due to dead load, using the shear moduli of the embankment materials
before and after the earthquake (Railway Technical Research Institute 1997). Here,the rigidities of the embankment materials before Earthquake A are evaluated by
the initial shear moduli used in the earthquake response analysis, and those after
the earthquake are evaluated by the converged shear moduli with the equivalentlinearization method. The 3D model shown in Fig. 5 is used for this analysis. The
difference in the deformation before and after the earthquake can be regarded as
the residual deformation caused by the earthquake. That is,
𝑈

𝑈

𝑈

6

where U r is the residual deformation caused by the earthquake and U b and U a
are the deformations due to dead load before and after the earthquake,
respectively.
Figure 11 shows the deformation due to this mechanism after Earthquake A.
In the standard cross-section of the dam, the maximum value of subsidence is 5.44
cm. The maximum subsidence of 5.53 cm occurs at the crest of the dam in thedam axial section.
During an earthquake, sliding and subsidence related to the shaking andrearrangement of soil particles may occur simultaneously. However, the sliding
displacement of a rigid block cannot be directly added to the calculated subsidence
results. As an estimation of the possible maximum subsidence at the crest, thevertical component of the slippage at the crest can be summed with the subsidence
related to the shaking and rearrangement of the soil particles. Since no sliding
behavior was observed during Earthquake A, the residual deformation of the damcaused by Earthquake A equals that related to the shaking and rearrangement of

報－14

soil particles, with a maximum value of 5.53 cm at the crest of the dam. According
to the field survey after Earthquake A, the subsidence at the crest of the Aratozawa
Dam was approximately 20 cm (Shimamoto et al. 2008). However, since the survey
was conducted 16 days after the mainshock, the measured subsidence includes
the contributions of many aftershocks, and other events since December 4, 2007.
Therefore, the exact residual deformation caused by Earthquake A itself cannot be
confirmed.
Subsidence 5.44 cm

Subsidence 5.53 cm(a) Standard cross-section(b) Dam axial section

Fig. 11
Subsidence related to the shaking and rearrangement of the soil particles causedby Earthquake A
Affaissement lié aux secousses et au réarrangement des particules du sol
provoqués par le tremblement de terre A

5.

5.1.

RESPONSE OF THE DAM TO EARTHQUAKE B

EARTHQUAKE RESPONSE ANALYSIS

Using the same model shown in Fig. 5 but with the material properties
exhibited after Earthquake A, the response of the Aratozawa Dam to the
Earthquake B is analyzed with the equivalent linearization method. As shown in
Fig. 3, after Earthquake A, the shear moduli of the embankment materials dropped
to approximately 58 % of those before Earthquake A (G/G0=0.58 corresponding to
the shear strain 1.0×10-6) for approximately one week. In consideration of thenonlinearity of the materials, the earthquake response analysis is performed by theequivalent linearization method using the approximate curve in the aftershock
period, as shown in Fig. 3. The damping is thought to increase with the decreasein the material rigidity. Because the quantitative variation is unknown, the values
shown in Table 3 and Eq. [5] are used to obtain a conservative evaluation.
For setting Earthquake B, it is assumed that a potential fault exists directly
under the dam, causing an Mj 6.5 earthquake. The ground motion at the dam baseis created by fitting an earthquake record of a past earthquake to the lower limit
response spectrum specified in the current guidelines (MLIT 2005). Here, theearthquake record at the dam base (F) in the aftershock that occurred 62 hours
after the Iwate-Miyagi Nairiku Earthquake in 2008 is used. Figure 12 shows theacceleration waveforms and the spectra of the created ground motions.

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Direction perpendicular to dam axis

-400
5

0

-400

10

0

5

Time (sec.)

-400

10

0

5

Target SP
Created Wave
1

10

Vertical direction

1000

100
Target SP
Created Wave
10
0.01

0.1

Period (sec.)

1

10

Acc. Resp. Spec.(cm/s2)

100

10

Time (sec.)

Direction parallel to dam axis
Acc. Resp. Spec.(cm/s2)

Acc. Resp. Spec.(cm/s2)

Direction perpendicular to dam axis

0.1

0Time (sec.)

1000

10
0.01

Vertical direction

400

Acceleration(cm/s2)

00

Direction parallel to dam axis

400

Acceleration(cm/s2)

Acceleration(cm/s2)

400

1000

100
Target SP
Created Wave
10
0.01

0.1

Period (sec.)

1

10Period (sec.)

Fig. 12Synthetic ground motion at the dam base during Earthquake B (by fitting theearthquake record of an aftershock to the lower limit response spectrum)
Mouvement synthétique du sol à la base du barrage pendant le tremblement deterre B (en ajustant l'enregistrement du tremblement de terre d'une réplique au
spectre de réponse de limite inférieure)

5.2.

RESIDUAL DEFORMATION CAUSED BY EARTHQUAKE B

As in the case of Earthquake A, the sliding deformation is calculated for the
standard cross-section. The stiffness of the embankment materials was greatly
reduced due to Earthquake A. Therefore, the residual strength of the embankment
materials should be used in the calculation due to Earthquake B. The results oftriaxial compression tests of Shichigasyuku Dam materials [10], which are similar
to the materials of the Aratozawa Dam, are used here. The residual strength factors
used in the slippage calculation are shown in Table 7. The calculation results are
summarized in Table 8 and Fig. 13. Compared with the upstream side, the slip
displacement on the downstream side is larger overall. This is presumed to be dueto the difference in the slope angle of the upstream and downstream and thestrength of the materials. The slope of the upstream surface is 1:2.7, while that ofthe downstream surface is 1:2.1. In addition, as shown in Table 7, the frictional
angles of the downstream rock zones are slightly smaller than those of the
upstream side.
Table 7
Residual strength parameters of embankment materials
for the calculation of sliding deformation caused by Earthquake B
Classification
Core
FilterTransition
Upstream rockzone
Downstreamrock zone

Cohesion (MPa)

Inner
Outer
Inner
Outer

0.0

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Friction angle(deg.)
22.1
28.1
26.6
28.5
28.9
26.8
28.5

Notes
As the residual strengthparameters, cohesionis set to be zero, andfrictional angle is 2/3 ofthe peak value.

Table 8
Results of sliding calculations for Earthquake B
Sliding dir.
To theupstreamside
To thedownstream
side

Group
U1
U2
U3
D1
D2
D3

No.
1
2
3
4
5
6

2

Safety factor
0.384
0.935
1.279
0.700
0.789
0.950

Max. sliding disp. (cm)
2.80
0.04
－
46.20
76.76
1.71

3
6

Max.subsidence (cm)
1.99
0.02
－
32.91
49.80
1.10

5

4

1

Fig. 13
The arcs with the maximum slippage in each group caused by Earthquake B
Les arcs avec le glissement maximum dans chaque groupe provoqué par letremblement de terre B
Subsidence 25.66 cm

Subsidence 26.40 cm(a) Standard cross-section(b) Dam axial section

Fig. 14
Residual deformation related to the shaking and rearrangement of the soil
particles caused by Earthquake B
Déformation résiduelle liée aux secousses et au réarrangement desparticules du sol provoqués par le tremblement de terre B
The sliding deformations to the upstream side are generally judged to bepermissible. To the downstream side, although the sliding section of the No. 4 arc
exhibits a displacement of 46.20 cm, it is very localized in the vicinity of thedownstream toe. The sliding section of the No. 5 arc passes through the crest witha sliding displacement of 76.76 cm. The subsidence at the crest accompanying thesliding reaches 49.80 cm.
Figure 14 shows the residual deformation of the dam associated with theshaking and rearrangement of soil particles caused by Earthquake B. Regarding
the maximum potential subsidence of the dam crest caused by Earthquake B, it ispossible to sum the vertical components calculated by the above two methods.
This sum is estimated to be 76.20 cm (49.80 cm + 26.40 cm) at the crest.

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5.3.

RESIDUAL DEFORMATION CAUSED BY THE DOUBLET EARTHQUAKEThe deformation caused by the doublet earthquake is calculated by summing
the deformation induced by Earthquake A and Earthquake B. As the maximum
possible subsidence at the dam crest, the vertical components of the slipe
deformation and that related to the shaking and rearrangement of the soil particles
can be summed directly as long as the location used for each estimate remains
the same. The maximum possible subsidence at the dam crest caused by the
doublet earthquake is predicted to be 81.27 cm. By comparing the subsidence
calculated above with the dam freeboard (200 cm), it is considered that theearthquake may not induce immediate overflow. However, the subsidence of thecrest reaches an amount that requires detailed investigation, for example, via
elastic-plastic analysis.

5.4.

PROPOSAL OF EMERGENCY MEASURES AFTER A LARGE EARTHQUAKE

Even rockfill dams constructed by modern construction techniques are not
likely to suffer from liquefaction due to a large earthquake, but the following eventsare considered to occur.
1) Overflow due to the excessive subsidence of the crest2) Concentrated seepage along the slip surface cross the core3) Water penetration through cracks4) Increment of the amount of seepage flow and the generation of turbidity of
seepage water
Since these phenomena may cause dam failure, emergency inspection
immediately after a large earthquake is essential. As revealed in this study, there
is potential risk that the seismic performance of a rockfill dam may temporarily
decline due to the change in the dynamic characteristics and material properties
after a large earthquake. Therefore, in preparation for a large earthquake that may
occur later, it is proposed to lower the reservoir water to a safe level and keep it fora week. The counter measure is also needed to prevent the infiltration of water into
the cracks. In addition, careful monitoring of the dam body and timely analysis ofrecords are recommended.

6.

CONCLUSIONSThe seismic performance verification of a rockfill dam for a large doublet
earthquake was tested. A practical verification procedure was proposed.
The variation history of the material properties of the Aratozawa Dam isclarified by analyzing 19 earthquake records. The material properties of rockfill
dams may change temporarily in response to strong seismic motion. If anotherlarge earthquake occurs before the dynamic characteristics of the dam and the

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properties of the embankment materials recover, the subsidence of the dam may
increase significantly. From the viewpoint of dam safety management, it isnecessary to quickly lower the reservoir water to a safe level and keep it at thelower level for at least 1 week in preparation for a large doublet earthquake.
The stiffness of the rockfill dam that experiences a strong earthquake may
recover to its normal status after approximately 1 week. During this period, carefulfrequent monitoring is necessary. Moreover, early remedial action to fix thedamaged portion of the dam body is needed.

ACKNOWLEDGEMENTS
Many thanks to the Miyagi Prefecture Kurihara Dam Management Officeand the Japan Commission on Large Dams for providing us with the earthquake
records and the information about the dam used in the present study.

REFERENCES[1] OHMACHI T. and TAHARA T. Nonlinear earthquake response characteristics
of a central clay rockfill dam, Soils and Foundations, Vol.51, No.2, 2011, 227238[2] MATSUMOTO N., YASUDA N., and CAO Z. Investigation on the long-term
fluctuation of the dynamic characteristics and transmitting behaviors of seismic
waves in a rockfill dam – foundation system, Journal of Structural Mechanics
and earthquake Engineering, JSCE, No.74 / I-3, 2018, 319-329[3] Earthquake Engineering Committee, Japan Society of Civil Engineers (JSCE).
Report on the damage surveys and investigations following the 2016
Kumamoto Earthquake, Maruzen Publishing Co., Ltd., 2017 (in Japanese)[4] Ministry of Land, Infrastructure, Transport and Tourism (MLIT), River
Bureau. Guideline for seismic performance verification of dams against
large earthquakes in Japan (draft), 2005 (in Japanese)[5] YASUDA N. and MATSUMOTO N. Comparisons of deformation characteristicsof rockfill materials using monotonic, cyclic loading and in-situ tests, Canadian
Geotechnical Journal, Vol.31, No.2, 1994, 162-174[6] YASUDA N., MATSUMOTO N., and CAO Z. Study on the Mechanism of thePeculiar Behaviors of the Aratozawa Dam During the 2008 Earthquake,
Journal of Disaster Research, Vol.13 No.1, 2018, 205-315[6] Railway Technical Research Institute. Design standards of railway structures,
Maruzen Publishing Co., Ltd., 1997 (in Japanese)[7] SAWADA Y. and TAKAHASHI T. Study on the material properties and theearthquake behaviors of rockfill dams, 4th Japan Earthquake Engineering
Symposium, 1975, 695-702 (in Japanese)[8] WATANABE H. and BABA K. A Study of sliding stability evaluation method
based on the dynamic analysis of fill dams, Large Dam, No.97, 1981, 25-38

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[9] SHIMAMOTO K., SATO N., OMACHI T., et al. Report on damage to damscaused by the 2008 Iwate/Miyagi inland earthquake, 2008[10] HOJO K., HARITA K. and OGAWA M. Large-scale tri-axial test for thecharacteristics of filldam materials, Technical memorandum of PWRI, No.1507,
Public Works Research Institute, Ministry of Construction, 1979

SUMMARY
The purpose of this study is to clarify the behavior of a rockfill dam during
large doublet earthquakes and to propose a procedure for verifying the seismic
performance of rockfill dams during such earthquakes. Impacted by a strong
earthquake, the dynamic characteristics of the Aratozawa Dam significantly
changed temporarily. The behavior of the dam subject to another strong
earthquake before its dynamic characteristics had recovered was predicted. Basedon the analysis results, the seismic performance of the dam was evaluated. The
results clarified that the change in the dynamic characteristics of the dam in
response to the first event greatly affected the behavior of the dam during thesecond event. In addition, a method was proposed for predicting the final residual
subsidence of the dam by summing the sliding displacement caused by each
earthquake and the subsidence related to the shaking and rearrangement of soil
particles. It is recommended that after a dam experiences a strong earthquake, thereservoir is adjusted to a safe water level and maintained at that level for aminimum of one week as an emergency response measure.
RÉSUMÉ
Le but de cette étude est de clarifier le comportement d' un barrage enenrochement lors de grands tremblements de terre « doublet » et de proposer une
procédure de vérification des performances sismiques des barrages enenrochement lors de tels séismes. Impactées par le tremblement de terre d'IwateMiyagi Nairiku en 2008, les caractéristiques dynamiques du barrage d'Aratozawa
ont changé temporairement de manière significative. Le comportement du barragesoumis à un autre puissant tremblement de terre avant que ses caractéristiques
dynamiques se soient rétablies a été prévu. Sur la base des résultats de l'analyse,
la performance sismique du barrage a été évaluée. Les résultats expliquent que lechangement des caractéristiques dynamiques du barrage en réponse au premierévénement a grandement affecté le comportement dynamique du barrage lors dudeuxième événement. De plus, une méthode a été proposée afin de prévoir
l'affaissement résiduel final du barrage en additionnant le déplacement glissantprovoqué par chaque séisme et l'affaissement lié aux secousses et auréarrangement des particules du sol. Il est recommandé, après qu'un barrage ait
subi un fort tremblement de terre, que le réservoir soit ajusté à un niveau d'eau
sécurisé et maintenu à ce niveau pendant au moins une semaine comme mesured'intervention d'urgence.

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KEYWORDS; Aratozawa Dam, rockfill dam, seismic resistance, numerical model

報－21