Q.106 - R.28

COMMISSION INTERNATIONALE
DES GRANDES BARRAGES------VINGT SEPTIÈME CONGRÈS
DES GRANDES BARRAGESMARSEILLE, JUIN 2022-------SEISMIC PERFORMANCE VERIFICATION OF A ROCKFILL DAM AGAINSTLARGE DOUBLET EARTHQUAKES (∗)
Nario YASUDA
Head of Eng. Division 1,
JAPAN DAM ENGINEERING CENTER
Zengyan CAO
Senior Engineer,
J-POWER BUSINESS SERVICE CORPORATION,JAPAN

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. Based on the analysis results, the seismic performance of the dam was evaluated. The results clariﬁed that the change inthe dynamic characteristics of the dam in response to the ﬁrst event greatly affected
the behavior of the dam during the second 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, the reservoir is adjusted to a safe water level and maintainedat that level for a minimum of one week as an emergency response measure.

∗ Vériﬁcation des performances sismiques d’un barrage en enrochement contre des doublets
de séismes

DOI: 10.1201/9781003211808-123

449
報1-1

Q.106 - R.28

RÉSUMÉ

Le but de ce rapport est de clariﬁer le comportement d’un barrage en enrochement lors de doublet de grands tremblements de terre et de proposer une procédure
de vériﬁcation des performances sismiques des barrages en enrochement lors detels séismes. Impactées par le tremblement de terre d’Iwate-Miyagi Nairiku en 2008,les caractéristiques dynamiques du barrage d’Aratozawa ont changé temporairement de manière signiﬁcative. Le comportement du barrage soumis 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 sismiquedu barrage a été évaluée. Les résultats expliquent que le changement des caractéristiques dynamiques du barrage en réponse au premier événement a grandement
affecté le comportement dynamique du barrage lors du deuxième événement. De
plus, une méthode a été proposée aﬁn de prévoir l’affaissement résiduel ﬁnal dubarrage en additionnant le déplacement glissant provoqué par chaque séisme etl’affaissement lié aux secousses et au réarrangement des particules du sol. Il est
recommandé, après qu’un barrage ait subi un fort tremblement de terre, que leréservoir soit ajusté à un niveau d’eau sécurisé et maintenu à ce niveau pendant au
moins une semaine comme mesure d’intervention d’urgence.

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), the dynamic
characteristics of the Aratozawa Dam, a 74.4 m high rockﬁll dam, considerably deteriorated [1][2]. Approximately one week after the main shock, the natural frequenciesof 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 andMj 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 ashort period. Thus, it is necessary and beneﬁcial to dam engineering to investigate
the behavior of the Aratozawa Dam subject to a ground motion of JMA seismic intensity 7 before its dynamic characteristics fully recover from an earlier earthquake. The
situation mentioned here has not been addressed in the current “Guidelines of the
Seismic Performance Veriﬁcation of 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

450
報1-2

Q.106 - R.28

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 tothe shaking and rearrangement of soil particles are carried out considering thechange 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 by each 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 was completed
in 1992. Table 1 shows the speciﬁcations of the dam. The location, the plan view andthe standard cross-section of the dam and the locations of seismographs are shownin Fig. 1. The seismographs with three components (parallel and perpendicular tothe dam axis and vertical directions) are installed at the dam base (F), mid-heightof 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)

451
報1-3

Q.106 - R.28

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 located approximately
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. This is the largest
earthquake magnitude ever recorded at the base of a dam in Japan. During the earthquake, the natural frequency and acceleration ampliﬁcation factor of the dam sharply
decreased. Approximately 1 week after the main shock, the natural frequencies ofthe 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, the relationshipof the natural circular frequency ω, the stiffness k and the mass m are expressed as
Eq. [1].
k
(1)
ω2 =
m
The relationship between the three physical quantities in Eq. [1] is also generally satisﬁed in civil engineering structures such as rockﬁll dams. Because the massof 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 relationshipbetween the shear modulus G and the fundamental frequency is shown in Eq. [2].
f12

2
f10

=

G
G0

452
報1-4

(2)

Q.106 - R.28

Here, and 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 ofchange 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 thedam (T) and the dam base (F), and the frequency corresponding to the ﬁrst peakof the transfer function can be regarded as the fundamental frequency of the dam.
From the analysis of the records of the past small earthquakes, the fundamental
frequency of the Aratozawa Dam has been found to be 3.2 Hz [2]. To determine thefundamental frequency of the dam for each earthquake, the earthquake records ofrelatively 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 numberedin the order of occurrence.
Table 2
Earthquake records and the obtained results.
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19

Time ofoccurrence
1996/08/11 03:12
1996/08/11 08:10
1996/08/11 15:01
2003/05/26 18:24
2008/06/14 08:43
2008/06/14 09:00
2008/06/14 09:01
2008/06/14 09:14
2008/06/14 09:20
2008/06/14 10:40
2008/06/14 12:09
2008/06/14 12:10
2008/06/14 19:11
2008/06/16 23:14
2008/07/24 00:26
2008/09/25 15:04
2011/03/11 14:46
2011/04/07 23:32
2015/05/1306:13

M
6.1
5.8
4.9
7.1
7.2
4.2
4.0
3.6
5.7
4.8
4.1
4.8
4.1
5.3
6.8
4.1
9.0
7.2
6.8

Focal
depth
(km)
9
10
10
72
8
11
7
4
7
7
8
9
8
7
108
6
24
66
46

Max. acc. at thedam base1(cm/s2 )
28
36
30
114
1024
99
482
151
76
120
92
79
229
76
27
119
102
120
18

Fundamental
freq. of thedam (Hz)
2.930
2.830
3.027
2.637
1.514
2.344
1.953
2.246
2.051
2.148
2.246
2.344
2.148
2.246
2.600
2.539
2.307
2.344
2.942

Averageshear strainof dam body5.320E-05
3.920E-05
6.600E-06
1.727E-04
1.566E-03
3.700E-06
7.760E-05
1.660E-05
7.980E-05
5.960E-05
2.840E-05
2.480E-05
5.170E-05
3.760E-05
6.530E-05
7.000E-05
1.858E-04
2.405E-04
1.350E-05

Note: 1 The maximum value of the three directional components of the dam base (F).

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/G0 is calculated according to Eq. [2]and plotted with the average shear strain γ in Fig 3. Depending on the G/G0 -γ

453
報1-5

Q.106 - R.28

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.

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.
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/G0 -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

454
報1-6

Q.106 - R.28

characteristics and material properties of the dam during this period must be considered. In addition, the G/G0 -γ relationship in Period III can be estimated to havenearly recovered to the relationship exhibited in Period I. The solid line showing the
G/G0 -γ relationship of the dam in Period I and Period III is very similar to that ofordinary soil materials. The shear strain corresponding to G/G0 = 0.5 is 2.9 × 10−4 ,which substantially coincides with the reference shear strain (3.0 × 10−4 ) identiﬁedby 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 when the existingdata are ﬁtted with a hyperbolic line, the relationship indicated by the broken line is
obtained.

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 modeled to 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 theaftershocks immediately after Earthquake A. The ground motions at the dam basefor Earthquake B are created by ﬁtting the earthquake records of an aftershock
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 an equivalent linearization method, which is a commonly available analysis method, insteadof nonlinear analysis. The main inﬂuencing factors for the seismic behavior and seismic safety veriﬁcation of dams include the ground motion, material properties such

455
報1-7

Q.106 - R.28

as strength and elastic modulus, and reservoir conditions. If the material propertiesof the dam have changed due to Earthquake A, the variation should be reﬂectedin the response analysis of the dam to Earthquake B. As shown in Fig. 3, the initial shear modulus and the G/G0 -γ relationship in Period II are clearly different fromthose of the other periods. Therefore, to predict the earthquake responses of the dam
to Earthquake B within approximately one week after Earthquake A, the initial shear
modulus G0 and the shear strain dependence of the materials during the period areconsidered. The residual deformation of the dam due to the doublet earthquake isFig. 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”.

456
報1-8

Q.106 - R.28

predicted by summing the deformations calculated separately for each earthquake.
The deformation includes the sliding component and the subsidence associatedwith soil particle oscillation. Figure 4 shows the earthquake response analysis andthe seismic performance veriﬁcation procedure for rockﬁll dams subject to a large
doublet earthquake used in this study.

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 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 water on thewater level (EL 270.1 m) during the earthquake and that of the pore water pressure
inside the dam are considered. However, the inﬂuence of the hydrodynamic pressure is neglected in the earthquake response analysis since the interaction between
embankment material and reservoir water is not yet fully understood.

Fig. 5
Analysis model.
Modèle d’analyse.

The equivalent linearization method is used in the analysis to consider theinﬂuence of nonlinear material properties. The initial shear moduli of the embankment materials are set according to Sawada’s equation [7], which is based on the

457
報1-9

Q.106 - R.28

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 thefundamental frequency of the dam obtained from eigenvalue analysis is consistent
with the result estimated for past small earthquakes. The approximate curve in thenormal status shown in Fig. 3 is used for considering the shear strain dependenceof the shear moduli.
The damping is evaluated by Eq. [3] and considered to be classical Rayleighdamping.
[C]e = α[M ]e + β[K]e(3)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 = 1.4hω1

β = 0.6h/ω1(4)where ω1 is the fundamental angular frequency of the dam; and the damping ratio
h is evaluated by Eq. [5], which considers its shear strain dependence.
h = hmaxγ+ h0
γ + γr(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 pastearthquakes [6]. γ is the effective shear strain (2/3 of its maximum value). γr isthe 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 thedam are listed in Table 4.

Table 3Damping factors identiﬁed by the reproduction analysis of dynamic
behavior of the dam during past earthquakes.
Classiﬁcation
A: Lower part of the core
B: Upper part of the core
C: Filter: Transition
E: Rock (inner): Rock (outer)Maximum damping ratio hmax
20%
30%
30%
20%

Initial damping ratio h05%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 as

458
報1-10

Q.106 - R.28

Fig. 6
Zoning of the properties (refer to Table 3).
Zonage des propriétés (se reporter au Tableau 3).

Table 4
Density of the materials used in the analysis.
Classiﬁcation
Core
FilterTransition
Upstream rockDownstream rock

Inner
Outer
Inner
Outer

Spillway concrete
Bedrock

Wet
2.04
2.34
2.24
2.15
2.15
2.18
2.13

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

a 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, theearthquake records (shown by the solid line in Fig. 7(c)) obtained at the dam base(F) during the Iwate-Miyagi Nairiku Earthquake in 2008 are used. The input groundmotions at the bottom boundary of the model (as shown in Fig. 5) are created byinverse analysis of the earthquake records at the dam base.
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, the response waveforms are
generally coincident. Good reproducibility is obtained in the acceleration response
histories. The waveforms from 0 sec to 4 sec in the acceleration response historiesof 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 thoseof the analysis results. This is thought to be due to the fact that in the equivalent

459
報1-11

Q.106 - R.28

Fig. 7
Acceleration response of Earthquake A.
Réponse d’accélération du tremblement de terre A.

460
報1-12

Q.106 - R.28

linearization method, the stiffness of the embankment materials is a constant value
for the whole history, but in the actual dam, the rigidity of 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

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 barrage.

461
報1-13

Q.106 - R.28

functions of the acceleration responses at the dam base and 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 the higher frequency range, the deviation
between the analysis results and earthquake records gradually increases as thefrequency increases. This ﬁnding may also be due to the continuous change in thephysical properties of the real dam, while the physical properties in the analysis
are treated as constant values. As a result, the physical properties suitable for the
principle motion, which mainly include the low-frequency components, lead to thedifferences 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 by numericalanalysis. Using the analysis results, the residual deformation of the dam causedby Earthquake A is calculated. The residual deformation of the dam caused by
the earthquake will be calculated separately via two methods according to the two
deformation mechanisms, sliding and subsidence.
First, 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 “D3Group”. Fig 9(a) shows the arcs of the U2 Group as an example. Table 5 shows thestrength parameters of the embankment materials based on the results of material
tests during dam construction.
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 arcof the minimum safety factor in the 6 arc groups is summarized in Table 6, andthe positions of the corresponding arcs are shown in Fig. 10. For the sliding arcs
with safety factors lower than 1, the sliding displacement is calculated and shownin Table 6. In the local surface layer of the downstream slope of the dam (the No.
4 arc), 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

462
報1-14

Q.106 - R.28

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.
DivisionCore
FilterTransition
Upstream rock zone
Downstream rock zone

Inner
Outer
Inner
Outer

Cohesion
(MPa)
0.049
0.078
0.039
0.049
0.049
0.049
0.049

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

Evidence
Based on triaxial compression test

Table 6
The results of sliding deformation for Earthquake A.
Slip direction
To the upstream side

To the downstream side

Arc group
U1
U2
U3
D1
D2
D3

Arc No.
1
2
3
4
5
6

Safety factor
0.994
1.469
1.478
0.847
1.239
1.407

Slip disp. (cm)0.0001–
0.04––

consistent with the ﬁeld survey after the earthquake [9], which reported that no slip
phenomenon was found to be due to the earthquake.
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 the rigidityof the dam. Subsidence can be conveniently evaluated by deformation calculation

463
報1-15

Q.106 - R.28

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.

due to dead load, using the shear moduli of the embankment materials before andafter the earthquake (Railway Technical Research Institute 1997). Here, the rigidities of the embankment materials before Earthquake A are evaluated by the initialshear moduli used in the earthquake response analysis, and those after the earthquake are evaluated by the converged shear moduli with the equivalent linearization
method. The 3D model shown in Fig. 5 is used for this analysis. The difference inthe deformation before and after the earthquake can be regarded as the residual
deformation caused by the earthquake. That is,

Ur = Ua − Ub(6)where Ur is the residual deformation caused by the earthquake and Ub and Ua 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.

464
報1-16

Q.106 - R.28

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.

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, the vertical 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 ofsoil 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.

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 the nonlinearity ofthe materials, the earthquake response analysis is performed by the equivalent linearization method using the approximate curve in the aftershock period, as shown in

465
報1-17

Q.106 - R.28

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).

Fig. 3. The damping is thought to increase with the decrease in 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 dambase is 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.

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

466
報1-18

Q.106 - R.28

Table 7
Residual strength parameters of embankment materials for the calculation ofsliding deformation caused by Earthquake B.
Cohesion Friction angle(MPa)(deg.)
Notes
0.
22.1
As the residual strength parameters, cohesionis set to be zero, and frictional angle is 2/3 ofthe peak value.
Filter
28.1
Transition
26.6
Upstream rock zone
Inner
28.5
Outer
28.9
Downstream rock zone Inner
26.8
Outer
28.5
Classiﬁcation
Core

Table 8Results of sliding calculations for Earthquake B.
Sliding dir.
To the upstream side

To the downstream side

Group
U1
U2
U3
D1
D2
D3

No.
1
2
3
4
5
6

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

Max.subsidence (cm)
1.99
0.02
32.91
49.80
1.10

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.

467
報1-19

Q.106 - R.28

displacement on the downstream side is larger overall. This is presumed to be due tothe difference in the slope angle of the upstream and downstream and the strengthof the materials. The slope of the upstream surface is 1:2.7, while that of the downstream surface is 1:2.1. In addition, as shown in Table 7, the frictional angles of thedownstream rock zones are slightly smaller than those of the upstream side.
The sliding deformations to the upstream side are generally judged to be permissible. 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 the downstream toe. The sliding section of the No. 5 arc passes through the crest with asliding 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. Thissum is estimated to be 76.20 cm (49.80 cm + 26.40 cm) at the crest.

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 des particules dusol provoqués par le tremblement de terre B.

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 slip deformation and that related to the shaking and rearrangement of the soil particles can besummed 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 the earthquake may not induce

468
報1-20

Q.106 - R.28

immediate overﬂow. However, the subsidence of the crest 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)
2)
3)
4)

Overﬂow due to the excessive subsidence of the crest
Concentrated seepage along the slip surface cross the core
Water penetration through cracks
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 ispotential 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 for a 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 of records arerecommended.

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 is clariﬁed by analyzing 19 earthquake records. The material properties of rockﬁll dams
may change temporarily in response to strong seismic motion. If another large earthquake occurs before the dynamic characteristics of the dam and the properties ofthe embankment materials recover, the subsidence of the dam may increase signiﬁcantly. From the viewpoint of dam safety management, it is necessary to quickly
lower the reservoir water to a safe level and keep it at the lower 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, careful

469
報1-21

Q.106 - R.28

frequent monitoring is necessary. Moreover, early remedial action to ﬁx the damaged
portion of the dam body is needed.

ACKNOWLEDGEMENTS

Many thanks to the Miyagi Prefecture Kurihara Dam Management Ofﬁce and
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,
227–238.

[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 andearthquake 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, Journalof Disaster Research, Vol.13 No.1, 2018, 205–315.

[7]

Railway Technical Research Institute. Design standards of railway structures,
Maruzen Publishing Co., Ltd., 1997 (in Japanese).

[8]

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).

470
報1-22

Q.106 - R.28

[9]

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.

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

471
報1-23