EVALUATION OF THE MATERIAL PROPERTYAND SEISMIC PERFORMANCE OF A ROCKFILLDAM DURING LARGE DOUBLET EARTHQUAKES
Nario YASUDA1, Zengyan CAO2 and Kosuke NAKAMORI3
1Member of JSCE, Eng. Division 1, Japan Dam Engineering Center (JDEC)(2-9-7 Ikenohata, Taito-ku, Tokyo 110-0008, Japan)
E-mail: yasuda@jdec.or.jp (Corresponding Author)
2Member of JSCE, J-POWER Business Service Corporation (4-6-4, Tsukiji, Chuo-ku, Tokyo 104-0045, Japan)
E-mail: sou@jpbs.co.jp
3Member of JSCE, Department of Prefectural Land Development, Mie Prefecture(Komie 13, Tsu-city, Mie 514-8570. Japan)
E-mail: nakamk27@pref.mie.lg.jp

The relationship between the shear modulus and shear strain of embankment materials is evaluated basedon earthquake records. When the average shear strain of a dam body is less than approximately 2.0×10-4,
the decreased stiffness of the embankment materials can be promptly recovered. However, when the shear
strain exceeds 1.0×10-3, one week or more may be necessary for the stiffness to be recovered. Using theevaluated nonlinear properties, the behaviors of the Aratozawa dam during an assumed large doublet
earthquake are investigated through numerical analyses. The results indicate that the change in the dynamic
characteristics of the dam in response to the first event considerably influences the dynamic behaviors ofthe dam during the second event. In addition, a procedure to evaluate the seismic performance of rockfill
dams during doublet earthquakes is proposed. In this approach, the variation in the material properties in
the first and second events is considered. The final residual subsidence of the dam is predicted by summing
the sliding displacements caused by each earthquake and subsidence related to the shaking and rearrangement of soil particles. Furthermore, as a precautionary measure for assumed large doublet earthquakes, after a dam experiences a large earthquake, it is recommended that the reservoir be adjusted to asafe water level and maintained at that level for at least one week as an emergency response measure.
Key Words : rockfill dam, dynamic behavior, seismic performance evaluation, doublet earthquake

1. INTRODUCTION
In Japan, the seismic performance evaluation ofexisting dams during large earthquakes (maximum
design earthquakes1)) is conducted by performing
dynamic response analyses. In the dynamic response
analysis and seismic performance evaluation of thesedams, engineers consider the normal operating conditions of the dams as the initial conditions for the
analysis and assume the dam to be subjected to asingle earthquake. However, after the Iwate-Miyagi
Nairiku Earthquake in 2008 (Mj 7.2, where Mj is theJapan Meteorological Agency (JMA) magnitude
scale), the dynamic characteristics of the Aratozawa
dam, a 74.4 m high rockfill dam located approximately 15 km from the epicenter, deteriorated considerably2), 3),4). Approximately one week after themain shock, the natural frequencies of the dam were
found to be nearly recovered. This phenomenon has

not yet been reported in dam engineering. Furthermore, during the 2016 Kumamoto earthquake (Mj 6.5
and 7.3 on April 14 and 16, respectively), Mashiki
town experienced ground motions of JMA seismic
intensity VII two times within 28 h5). Based on thesefacts, it is reasonable to assume that in the future, adam may experience multiple large seismic events ina short period. Such situations have not been addressed in the current “Guidelines of the Seismic
Performance Evaluation of Dams for Large-Scale
Earthquakes (draft)” 6). Thus, it is significant in thecontext of dam engineering to clarify the behaviorsof rockfill dams subjected to multiple earthquakes
and establish a method to address this issue. In thisstudy, the behavior of the Aratozawa dam subjected
to ground motions of JMA seismic intensity VII,
before the corresponding dynamic characteristics
fully recover from the state after the Iwate-Miyagi
Nairiku Earthquake in 2008, is examined. Further-

報－22

more, to realize dam management during earthquakes, appropriate emergency measures must be
established to suitably respond to large doublet
earthquakes. The dynamic response analysis andseismic performance evaluation methodologies of
rockfill dams subjected to large doublet earthquakes
have emerged as key research subjects in dam safety
management. Thus, this study clarifies the behaviorof a rockfill dam subjected to a large doublet earthquake and proposes a seismic performance evaluation method and emergency response measures in
preparation for the occurrence of large doublet
earthquakes in the future.
In this study, the responses of the Aratozawa dam
to two large earthquakes (“Earthquake A”: theIwate-Miyagi Nairiku Earthquake in 2008; “Earthquake B”: a synthetic local earthquake) are analyzed.
The dynamic response analyses of the dam are performed considering the variation in the dynamic
characteristics and material properties of the dam
during each earthquake. The sliding deformation anddeformation related to the shaking and rearrangement of soil particles (a phenomenon in which thevolume shrinks as the soil particle arrangementchanges due to vibrations) are calculated considering
the change in the material properties of the dam. The
final residual deformation of the dam after the doublet earthquake is predicted by summing the deformations induced by each earthquake. Moreover, theseismic safety of the dam is verified considering theresidual deformation. In addition, in preparation forlarge doublet earthquakes, emergency response
measures are recommended for rockfill dams subjected to large earthquakes.

Table 1 Main features of the Aratozawa dam.

Kurihara City, Miyagi Prefecture
Rockfill dam with central claycore
74.4 mDam height413.7 mCrest length
10.0 mCrest width
EL. 279.4 m
Crest elevation
Upstream: 1:2.7
Slope gradient
Downstream: 1:2.1
Embankment volume 3,048,000 m3
Basin area
20.4 km2
Total water volume 13,850,000 m3
Design seismic coef- 0.15 (dam body), 0.18 (intake
ficient
tower, bridges), 0.16 (spillway)
Dam location
Dam type

Legend:●: Seismograph
M: Middle of the core(a) location of the dam

T: Crest
F: Dam base(b) plan view

2. EVALUATION OF NONLINEAR MATERIAL PROPERTIES BY ANALYZINGEARTHQUAKE RECORDS(1) Dam specifications
The Aratozawa dam is a 74.4 m high rockfill dam
with a central clay core in the Kitakami river, Kurihara city, Miyagi prefecture. Table 1 summarizes
the main features of the dam. The location, planview, and standard cross-section of the dam and thelocations of seismographs are shown in Fig. 1. Notably, seismographs with three components (perpendicular to the dam axis, parallel to the dam axis,
and vertical directions) are installed at the dam base(F), mid-height of the core (M), and dam crest (T).
(2) Evaluation of nonlinear properties by considering earthquake records
Since 1992, immediately after the dam bodycompletion, many earthquakes have been recorded.

(c) standard cross-sectional viewFig. 1 Location, plan view, and standard cross-section of thedam and locations of the seismographs.

Among these earthquakes, approximately 500 and 37
earthquakes were recorded with a maximum acceleration of over 10 cm/s2 and 100 cm/s2 at the dambase (F), respectively. On June 14, 2008, theIwate-Miyagi Nairiku Earthquake (Mj 7.2) occurred.
At the Aratozawa dam, located approximately 15 km
from the epicenter, a maximum acceleration of 1024
cm/s2 in the direction perpendicular to the dam axis
was recorded at the dam base. This earthquake corresponds to the highest intensity earthquake everrecorded at the base of a dam in Japan. During the

報－23

𝑓
𝑓

𝐺
𝐺

1

Here, 𝐺 and 𝑓 denote the initial shear modulus of
the material under a small strain and initial fundamental frequency of the dam, respectively. Therefore, the rate of change in the shear modulus of thematerials can be obtained from the rate of change inthe fundamental frequency of the dam by using
Equation (1) 7). In addition, the transfer function of
the dam can be obtained by analyzing the earthquake
records at the crest of the dam (T) and dam base (F),and the frequency corresponding to the first peak of
the transfer function can be regarded as the fundamental frequency of the dam. An example is shownin Fig. 2. According to the analysis of the records ofpast small earthquakes, the fundamental frequency of
the Aratozawa dam can be calculated as 3.2 Hz 2). To
obtain the fundamental frequency 𝑓 of the dam
during each earthquake, earthquake records of different acceleration amplitudes are selected, focusing
on the Iwate-Miyagi Nairiku Earthquake in 2008 andits aftershocks. The selected earthquake records arelisted in Table 2. These earthquake records (Nos.
1–20) are numbered in the order of occurrence. On
the other hand, by integrating the acceleration records obtained at the crest and dam base, the relative
displacement of the dam body is calculated. Furthermore, by dividing the relative displacement by
the dam height, the average shear strain 𝛾 of thedam can be obtained.

Table 2 Earthquake records and obtained results.
No. Time of occurrenceM

Amax※1

f1 ※2

𝛾

※3

(cm/s2) (Hz) (10128
1996/08/11 03:12 6.1
2.93
5.32
2
36
1996/08/11 08:10 5.8
2.83
3.92
3
30
1996/08/11 15:01 4.9
3.03
0.66
4
114
2003/05/26 18:24 7.1
2.64
17.27
5
2008/06/14 08:43 7.2 1024
1.51
156.6
6
99
2008/06/14 09:00 4.2
2.34
0.37
7
482
2008/06/14 09:01 4.0
1.95
7.76
8
151
2008/06/14 09:14 3.6
2.25
1.66
9
76
2008/06/14 09:20 5.7
2.05
7.98
10
120
2008/06/14 10:40 4.8
2.15
5.96
11
92
2008/06/14 12:09 4.1
2.25
2.84
12
79
2008/06/14 12:10 4.8
2.34
2.48
13
229
2008/06/14 19:11 4.1
2.15
5.17
14
76
2008/06/16 23:14 5.3
2.25
3.76
15
9
2008/06/21 12:19 2.8
3.03
0.17
16
27
2008/07/24 00:26 6.8
2.60
6.53
17
119
2008/09/25 15:04 4.1
2.54
7.00
18
102
2011/03/11 14:46 9.0
2.31
18.58
19
120
2011/04/07 23:32 7.2
2.34
24.05
20
18
2015/05/1306:13 6.8
2.94
1.35
Note: ※ 1 Maximum value of the three directional componentsof the dam base (F)※ 2 Frequency corresponding to the first peak of thetransfer function obtained from the earthquake records※ 3 Average shear strain obtained from the relative
displacement determined by integrating the acceleration records of earthquakes
30
Amplification

earthquake, the natural frequency and acceleration
amplification factor of the dam sharply decreased.
For example, in the direction perpendicular to thedam axis, the fundamental frequency of the dam
decreased from 3.2 Hz to 2.2 Hz. Approximately one
week after the main shock, the natural frequencies ofthe dam nearly fully recovered to theirpre-earthquake values. The mechanism of this variation has been discussed to a certain extent in a previous study2). Furthermore, many small aftershocks
occurred after the main shock. It is presumed that thematerial particles loosened by the main shock were
promoted to mesh by the micro vibration of the aftershocks, and the recovery of the shear modulus of
the embankment material was accelerated. However,there are insufficient data to explain the contributionsof other factors, such as creep and material relaxation. Therefore, the detailed recovery mechanism of
the shear modulus requires further investigation.
A decrease in the natural frequency of the dam
corresponds to a reduction in the stiffness of theembankment materials. The relationship between theshear modulus G and fundamental frequency 𝑓 isshown in Equation (1).

First peak

20
10
0
0

5

10
Freq. (Hz)15

20

Fig. 2 Sample transfer function obtained from earthquake
records.

From each earthquake record, the fundamental
frequency of the dam in the direction perpendicular
to the dam axis and average shear strain are calculated and summarized, as shown in Table 2. The
value of 𝐺 ⁄𝐺 is calculated according to Equation(1) and plotted with the average shear strain 𝛾 in
Fig. 3. In Fig. 3, the results obtained from theearthquake records at the crest and the middle of thecore are indicated by ● and ○, respectively. It is obvious that the results based on the earthquake records
at different elevations are approximately the same.
The results based on the earthquake records at the
crest are numbered 1 – 20 in the figure, which will be

報－24

1 - 4 Before the mainshock
6 - 14 Within 1 week after the mainshock

5 Mainshock
15 - 20 One week after the mainshock

1.0
0.9

Hyperbolic model

3

15

20

0.8

1
2

G/G0

0.7

0.3

12

6

0.5
0.4

4

16
17

0.6
8

Approximate curve
during aftershocks

14
11

13

18
10

19

Approximate curve during
normal conditions

9

7
5

0.2
0.1

Crest (T) - Dam base (F)Middl of core (M) - Dam base (F)0.0
1.0E-06

1.0E-05

Aecovery potential

1.0E-04

γave

1.0E-03

1.0E-02

Fig. 3 G/G0-γ relationship obtained from earthquake records.

used in the subsequent studies. The figure indicatesthat the decreased stiffness of the embankment materials is immediately recoverable when the average
shear strain 𝛾 caused by an earthquake is less thanapproximately 2.4×10-4 (the value corresponding toearthquake 19 in Table 2). The stiffness may recoverwith the potential indicated by the solid arrow in the
figure. However, when 𝛾 exceeds 15.7×10-4 (thevalue corresponding to earthquake 5 in Table 2), thedecreased stiffness recovers at different potentials
indicated by the dashed arrow. Therefore, it is presumed that there exists a limit value of the shear
strain between the abovementioned two values.
Shear strain can be recovered when it is less than thelimit value. Furthermore, the knowledge obtained
from this case and limit value of the recoverable
shear strain are applicable for other rockfill dams. It
is noted that 𝐺 can recover to only 58% of its origrelationshipinal value. Based on the 𝐺 ⁄𝐺𝛾
and the occurrence time of the earthquakes, theseismicity can be divided into the following three
periods:
Period I. Earthquake 1 to earthquake 5
Period II. Earthquake 6 to earthquake 14
Period III. Earthquake 15 to earthquake 20
The 𝐺 ⁄𝐺𝛾 relationship in Period I can beapproximated by a curve (solid line), which is inclose agreement with the normal hyperbolic model
represented by the dashed line in the same figure.
However, this relationship is considerably different
from that in the aftershock period (Period II). In response to the Iwate-Miyagi Nairiku Earthquake in2008 (No. 5), the material properties of the Aratozawa dam significantly changed, although temporarily. Thus, in the earthquake response analysis andseismic performance evaluation of the dam in Period
II, the dynamic characteristics and material properties of the dam during this period must be consideredinstead of the initial conditions. In addition, the𝐺 ⁄𝐺𝛾 relationship in Period III can be estimated to have nearly recovered to the relationshipexhibited in Period I. Although the mechanism of thestiffness recovery cannot be concretely described, theconsolidation effect of the loosened coarse-grainedmaterial is the primary reason. Approximately one
week was required for the recovery to occur for the
rockfill dam, which is a large soil structure. The shear
strain corresponding to 𝐺 ⁄𝐺 = 0.5 is 2.9×10-4 issimilar to the reference shear strain (3.0×10-4) determined by conducting a reproduction analysis of apast earthquake experienced by the Aratozawa dam3).
In Period II, no data corresponding to a shear strainof 10-4 or more are present; however, when the existing data are fitted with a hyperbola, the relationship represented by the dotted line is obtained. These
nonlinear characteristics are considered in the subsequent seismic response analyses of the dam.

3. EVENTS CONSIDERED AND STUDYMETHODS(1) Events considered
In this study, the terms “Earthquake A” and“Earthquake B” are used instead of “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 (Earthquake B) is
assumed to occur directly underneath the dam. The
seismic behaviors of the Aratozawa dam subjected tosuch a large doublet earthquake are predicted, and thedam safety is evaluated considering the analysis results. In addition, the possibility of liquefaction of thedam and foundation must be determined according to
the evaluation guidelines pertaining to embankment
dams. However, since the Aratozawa dam is a rockfill dam constructed using modern technology, therisk of liquefaction is extremely low; thus, the liquefaction is not discussed in this paper.
The acceleration records obtained at the dam base(F) in Earthquake A are considered to generate theinput ground motions. For Earthquake B, artificial
seismic waves are generated considering the earthquake records obtained at the dam base during theaftershocks that occur immediately after Earthquake
A. The ground motions are created by fitting theacceleration records to the lower limit spectra defined in the evaluation guidelines of dams during
large earthquakes6), assumed to be equivalent to an
Mj 6.5 earthquake.
(2) Study methods
The earthquake responses of the dam are analyzed
using the equivalent linearization method, which is acommonly available analysis method, instead of thesequential nonlinear analysis technique. The main報－25

Fig. 5 Analysis model.

4.

Fig. 4 Procedure of the response analysis and performance
evaluation of rockfill dams subjected to large doublet
earthquakes.

factors influencing the seismic behavior and seismic
safety evaluation of dams include the ground motion,material properties such as strength and elastic
modulus, and reservoir conditions. If the material
properties of the dam change due to Earthquake A,
the variation should be considered when analyzing
the response of the dam to Earthquake B. As shownin Fig. 3, the initial shear modulus and 𝐺 ⁄𝐺𝛾relationship in Period II are considerably different
from those in the other periods. Therefore, to predict
the earthquake responses of the dam to Earthquake B
in approximately one week after Earthquake A, therelainitial shear modulus 𝐺 and 𝐺 ⁄𝐺
𝛾tionship of the materials during this period are considered.
The residual deformation of the dam due to the
doublet earthquake is predicted by summing the deformations calculated separately for each event. The
deformation includes the sliding component andsubsidence associated with soil particle oscillation.
Figure 4 shows the procedure of the earthquake response analysis and seismic performance evaluation
for rockfill dams subjected to the considered large
doublet earthquake. The material properties (i.e., step[2] in Fig. 4) considered in the analyses of the two
events are different.

RESPONSE OF
EARTHQUAKE A

THE

DAM

TO

(1) Reproduction analysis
Figure 5 shows the 3D analysis model of thedam–reservoir–foundation system. The earthquake
response analysis program “UNIVERSE” 8) is used
for the analysis. Considering the influence of thevibration of the free fields outside the analysis model,
viscous boundary conditions9) are applied at the perimeter and bottom boundaries of the foundation
rock. In the static stress analysis before the earthquake, the influence of the reservoir water on thewater level (EL 270.1 m) during the earthquake andthat of the pore water pressure inside the dam areconsidered. However, the influence of the hydrodynamic pressure and excessive pore water pressure areneglected in the earthquake response analysis since
the interaction between the embankment material
and reservoir water is not yet fully understood.
A strong nonlinearity likely occurred in the dam
during Earthquake A. However, the equivalent linearization method is used in this study as it is a generally feasible analysis method to consider the influence of nonlinear material properties. The initialshear moduli of the embankment materials are set
according to Sawada’s equation10), which is based on
the compressional and shear wave logging (P-S logging) of several rockfill dams. To enhance the accuracy of the initial shear moduli, the values are slightly
adjusted to ensure that the fundamental frequenciesof the dam obtained from eigenvalue analysis are
consistent with the results estimated from past small
earthquakes. The approximate curve in the normal
state (solid line) shown in Fig. 3 is used to consider
the shear strain dependence of the shear moduli of theembankment materials.
The damping is evaluated as the Rayleigh damping
proportional to the mass and stiffness, and thedamping ratio h is determined using Equation (2).

報－26Table 3 Damping ratios determined through the reproduction
analysis of the past earthquakes3).
Max. damping
ratio hmax

Classification*1
A: lower part of the core20%

B: upper part of the core

30%

Table 4 Density of the materials considered in the analysis.
Classification

Init. damping
ratio h0Core
FilterTransition
Inner
Upstream
rock
Outer
Inner
Downstream
rock
Outer
Spillway concrete
Bedrock

C: filter
5%30%
D: transition
E: rock (inner)20%
F: rock (outer)
Note: ※ 1 Classifications A, B, etc. are shown in Fig. 6.

Fig. 6 Zoning of the materials.

ℎ

ℎ

𝛾
𝛾

𝛾

ℎ

2

denote the damping ratio, its
where ℎ, ℎ , and ℎinitial value (in the range of small strain), and its
maximum value, respectively. The values of ℎ andlisted in Table 3 and Fig. 6 are determinedℎthrough the reproduction analysis of the dynamic
behavior of the dam during past earthquakes3).
Value 𝛾 is the effective shear strain (2/3 of the
maximum value obtained in the previous iteration of
the calculation). Value 𝛾 is the reference shear strain,
which can be determined from Fig. 3 to be 2.9×10-4
when 𝐺/𝐺 = 0.5. Poisson's ratios of the embankment materials are set according to Sawada’s equation10). The densities of the embankment materials,
foundation rock, and spillway concrete, as determined from the construction quality control tests ofthe dam (listed in Table 4), are used.
Spillway concrete is treated as a linear material
with an elastic modulus of 30000 N/mm2 and a
Poisson's ratio of 0.2. Furthermore, the foundationrock is modeled as a linear material. The shear
modulus of this rock is 5500 N/mm2, determinedthrough conversion from the average shear wave
velocity of the rock (𝑉 = 1440 m/s). The Poisson's
ratio of the foundation rock is 0.25, which is estimated to be the average value for the rock.
In terms of the input ground motions, since
Earthquake A is a real earthquake, the input groundmotions at the bottom boundary of the model (asshown in Fig. 5) are generated by performing theinverse analysis of the earthquake records at the dambase (F).
As an example of the earthquake responses of theDensity (g/cm3)
Wet
Saturated
2.04
2.10
2.34
2.43
2.24
2.33
2.15
2.29
2.15
2.32
2.18
2.32
2.13
2.30
2.40
2.60

dam, Fig. 7 shows the acceleration response historiesof the dam crest (T). Although a certain difference
exists in the maximum acceleration values between
the analysis results and earthquake records, the response waveforms are generally coincident. A highreproducibility is obtained in the acceleration response histories, except for the period from 5.4 s to
6.8 s in the direction perpendicular to the dam axis.
Furthermore, the waveforms from 0 s to 4 s in theacceleration response histories have approximately
the same phase, or the peak values pertaining to theearthquake records appear slightly earlier than thoseof the analysis results. In contrast, in the waveforms
after 4 s, the peak values pertaining to the earthquake
records appear slightly later than those of the analysis
results. This phenomenon likely occurs because in
the equivalent linearization method, the stiffness ofthe embankment materials is a constant for the whole
history; however, in the actual dam, the rigidity of thedam decreased after the principal motion of theearthquake, which resulted in decelerated wave
propagation. Figure 8 shows the comparison of theFourier spectra of the acceleration responses at thedam crest. This figure shows that the behavior of thedam during Earthquake A can be effectively reproduced.
(2) Residual deformation caused by Earthquake A
The seismic performance of rockfill dams isevaluated considering the residual deformation under
the current guidelines6). As described in the previous
section, the seismic behavior of the Aratozawa damin response to Earthquake A is reproduced through a
numerical analysis. Using the analysis results, theresidual deformation of the dam caused by Earthquake A can be calculated.
The residual deformation of the dam caused by theearthquake is calculated using two methods corresponding to the two simultaneous deformation
mechanisms: sliding and subsidence. To consider the
deformation due to sliding, the method proposed by
Watanabe and Baba12) is used, which is based on the報－27

Acc. (cm/s2)
1000

Record: 525
Analysis: 661

Direction perpendicular to dam axis

500
0
-500
-1000
0

2

4

Acc. (cm/s 2)
1000

Time (s) 68

10Record: 455
Analysis: 558

8

10
Record: 622
Analysis: 414

Direction parallel to dam axis

500
0
-500
-1000
0

2

4

Acc. (cm/s 2)
1000

Time (s)6

Vertical direction

5000Fig. 9 Sample sliding arcs.

-500
-1000
0

2

4

Time (s) 6810Table 5 Strength parameters of the embankment materials
used in the sliding deformation calculation11).
Cohesion Friction
Division
Evidence(MPa)angle (°)
Core
0.049
33.2
Based ontriaxial
Filter0.078
42.2
compression
Transition
0.039
39.9
tests
Upstream
Inner
42.7

Fig. 7 Acceleration response determined by the reproduction
analysis and earthquake records at the dam crest.
Direction perpendicular to the dam axis

Fourier Spectra (cm/s)

400

RecordAnalysis200

rock
Downstream
rock

0
0

2

4
6
Frequency (Hz)8

10

Fig. 8 Fourier spectra and transfer function of the acceleration
response at the dam crest.

sliding block assumption and use of the accelerationand stress results of the earthquake response analysis.
In general, 3D sliding calculations have not yet been
applied; therefore, a 2D calculation is performed
using the standard cross-section extracted from the
3D model shown in Fig. 5. In total, 1235 arcs are
established, covering all the possible sliding zones.
Figure 9 shows an example of the arcs with the upper
end at the center of the crest. To fully investigate thestability of the dam, the arcs sliding toward the upstream side are divided into three groups. The arcs
for which both ends pass through only the upstream
surface of the dam are referred to as the “U1 Group.”
The arcs for which the upper and lower ends lie at the
crest and upstream surface are categorized to be in
the “U2 Group.” In addition, the arcs that cut the corezone correspond to the “U3 Group.” Similarly, thearcs sliding downstream are divided into the “D1Group,” “D2 Group,” and “D3 Group.” Table 5shows the strength parameters of the embankment
materials based on the results of material tests during
dam construction.
Except for one arc each near the upstream anddownstream toes of the dam, the safety factors of all
the other arcs are greater than 1. The minimum sliding safety factor is 0.847; however, nearly no sliding
displacement occurs in the sliding analysis (themaximum value is 0.04 cm). This result suggests that

Outer
Inner
Outer

43.4
40.2
42.7

0.049

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 survey13) after the earthquake, which reported that no
sliding phenomenon due to the earthquake was observed.
In addition to sliding, subsidence may be causedby the shaking and rearrangement of the soil particles
in earthfill dams due to strong earthquakes14). Suchdeformation can be attributed to the decrease in therigidity of the dam. The subsidence can be conveniently evaluated by calculating the deformation due
to the dead load by using the shear moduli of theembankment materials before and after the earthquake15). The rigidities of the embankment materials
before Earthquake A are evaluated considering theinitial shear moduli used in the earthquake response
analysis, and those after the earthquake are evaluatedfor each element considering the converged shear
moduli during Earthquake A with the equivalentlinearization method. The 3D model shown in Fig. 5
is used for this analysis. The difference in the deformations before and after the earthquake can be
regarded as the residual deformation caused by theearthquake. Specifically,
𝑈

𝑈

𝑈

3

where 𝑈 is the residual deformation caused by theearthquake, and 𝑈 and 𝑈 denote the deformations

報－28

Acceleration(cm/s2 )400

Fig. 10 Deformation near the crest caused by Earthquake A.

0

-400
0

2

4

6

8

10

Time (sec.)

5.

RESPONSE OF
EARTHQUAKE B

THE

DAM

TO

(1) Response analysis
Using the same model shown in Fig. 5 and thematerial properties exhibited after Earthquake A, theresponse of the Aratozawa dam to Earthquake B isanalyzed. In the analysis, the equivalent linearization
method is used for the same reason mentioned in theanalysis of Earthquake A, although a stronger nonlinearity of the embankment materials is considered
to occur in Earthquake B.
As shown in Fig. 3, after Earthquake A, the shear
moduli of the embankment materials dropped toapproximately 58% of those before Earthquake A(G/G0 = 0.58 corresponding to a shear strain of 10-6)
for approximately one week. To consider the nonlinearity of the materials, earthquake response analysis is performed considering the approximate curve
during the aftershocks, as shown in Fig. 3. The(a) Acceleration history
Acc. Resp. Spec.(cm/s2 )due to the dead load before and after the earthquake,
respectively.
It is observed that the maximum subsidence of
5.53 cm occurs at the crest. The deformation near the
crest is shown in Fig. 10. Since the core zone androck zone are continuous in the analysis model, asmooth deformation is calculated. However, theamount of subsidence of the core zone is larger thanthat of the rock zone. Since no sliding behavior wasobserved during Earthquake A, the residual deformation of the dam caused by Earthquake A equals
that related to the shaking and rearrangement of soil
particles, with a maximum value of 5.53 cm at the
crest of the dam. According to the field survey13) after
Earthquake A, the subsidence at the crest of the
Aratozawa dam was approximately 20 cm. However,since the survey was conducted 16 d after themainshock, the measured subsidence includes thecontributions of many aftershocks and the incrementfrom half a year ago (since December 4, 2007).
Therefore, the exact residual deformation caused by
Earthquake A itself cannot be confirmed. Nevertheless, the calculated maximum subsidence can beconsidered to be consistent with that of the measured
subsidence.

1000

100
Target SP
10
0.01

Created Wave
0.1

1

10

Period (sec.)(b) Acceleration response spectrum
Fig. 11 Ground motion at the dam base during Earthquake B(the component perpendicular to the dam axis).

damping is thought to increase with the decrease in
the material rigidity. Because the quantitative variation is unknown, the values shown in Table 3 andEquation (2) are used to obtain a conservative evaluation.
A notable issue is the setting of the ground motion
at the dam base during Earthquake B. It is assumed
that a potential fault exists directly under the dam,causing an Mj 6.5 earthquake. The three-directional
ground motions at the dam base are created by fitting
the acceleration records of a past earthquake to thelower limit response spectra specified in the current
guidelines6). Earthquake records at the dam base in
the aftershock that occurred 62 h after the
Iwate-Miyagi Nairiku Earthquake in 2008 are considered. Figure 11 shows the created acceleration
waveform and acceleration response spectrum of thecomponent in the direction perpendicular to the dam
axis as an example. The input ground motions at thebottom of the foundation rock model are created by
performing the 3D inverse analysis using the groundmotions defined at the dam base.
Figure 12 shows the acceleration response histories at the dam crest (T) to Earthquake B. The acceleration amplification factor is only 0.77, which isan abnormal value for a rockfill dam that is 74.4 m
high and constructed using modern construction
technologies. Figure 13 shows the Fourier spectra of
the acceleration responses at the crest. The acceleration responses at the crest have nearly no frequency
components of 3 Hz or higher. The high-frequency
components cannot propagate in the dam body since

報－29

Direction perpendicular to dam axis

Acc. (cm/s 2)

400
200
0
-200
-400
0

2

4

6

8

10

8

10

8

10

Direction parallel to dam axis

400
Acc. (cm/s 2)

Time (Sec.)

200
0
-200
-400
0

2

4

Time (Sec.)6

Acc. (cm/s2)

Vertical direction
400
200
0
-200
-400
0

2

4

Time (Sec.)6

Fig. 12 Acceleration responses of the crest to Earthquake B.
Direction perpendicular to dam axis

Fourier Spec. (cm/s)

300
200
100
0
0

2

Fourier Spec. (cm/s)

8

10

8

10

8

10

Direction parallel to dam axis

300
200
100
0
0

2

4
6
Frequency (Hz)Vertical Direction

300

Fourier Spec. (cm/s)

4
6Frequency (Hz)

200
100
0
0

2

4
6
Frequency (Hz)Fig. 13 Fourier spectra of acceleration response at the crest.

the rigidities of the embankment materials decreased
due to Earthquake A. In Earthquake B, the rigiditiesof the embankment materials further decreased. The
shear strains generated in the rock zones during
Earthquake B range from 0.02%–1.0%. As the shear
moduli of the rock materials decrease, the damping
ratio increases. This aspect also explains the extremely small value of the acceleration amplificationof the dam.
(2) Residual deformation caused by Earthquake
B
Using the abovementioned analysis results, theresidual deformation of the Aratozawa dam causedby Earthquake B is calculated using the same

methods as those applied for Earthquake A. The
deformation due to sliding and that related to theshaking and rearrangement of soil particles are calculated separately. Next, the vertical components ofthe two kinds of deformation are summed to find the
maximum possible subsidence of the dam caused by
Earthquake B.
Although slippage did not occur due to Earthquake
A, the dam was heavily loaded, and the stiffness ofthe embankment materials was considerably reduced. Therefore, the use of the decreased strength ofthe embankment materials was considered in thecalculation of the sliding deformation due to Earthquake B. To set the strength parameters, the results ofpast experimental studies were applied. After Tatsuoka et al.16), a higher density corresponds to agreater decrease in the strength (internal friction
angle), as indicated by the plane strain compression
test. The strength is affected by the anisotropy of thespecimens and reduced at most by approximately
20% at 10% of the axial strain. Sasaki et al.17) investigated the strength and deformation properties ofcoarse-grained materials by performing cyclic andmonotonic loading triaxial compression tests undervarious conditions. The static peak strength after
cyclic loading reduced by approximately 20%. According to the results of the large-scale triaxial tests
with quartz andesite18), which are similar to the construction materials of the Aratozawa dam, the deviator stress reduced by 30% compared to the peakstress. In this work, considering the variability of theexperimental results and to perform a conservativeevaluation, the ratio of the declined strength to thepeak strength is set as 2/3. The cohesion is set aszero, and the frictional angles are two-thirds theirpeak values. Moreover, similar to the stiffness of thedam, it is presumed that the decrease in strength
likely recovered one week after the mainshock.
The calculation results show that sliding mainly
occurs on the downstream slope. The sliding arcs
with the maximum slip displacements are extracted
from each arc group and summarized in Table 6. The
corresponding sliding arcs are shown in Fig. 14.
Compared with the results on the upstream side, theslip displacements on the downstream side are larger.
This phenomenon likely occurs owing to the difference in the upstream and downstream slope gradientsand strength of the materials. The slope of the upstream and downstream surfaces of the dam is 1:2.7
and 1:2.1, respectively. In addition, as shown in Table 5, the frictional angles of the downstream rockzones are slightly smaller than those of the upstreamside.
Arc No. 1 is small and limited to the area near the
upstream toe of the dam with a displacement of 2.80
cm. Even if this type of sliding occurs, the effect on

報－30

Table 6 Results of sliding deformation for Earthquake B.
Sliding
direction

Arc
No.
group

Safetyfactor

Slip
disp.
(cm)

Subsidence(cm)

Upstream
side

U1

1

0.384

2.80

1.99

U2

2

0.935

0.04

0.02

U3

3

1.279

-

-

Downstream
side

D1

4

0.700

46.20

32.91

D2

5

0.789

76.76

49.80

D3

6

0.950

1.71

1.10

(a)

(b)

Standard cross-section

Dam axial section

Fig. 15 Residual deformation related to the shaking and rearrangement of the soil particles caused by Earthquake B.

cm (49.80 cm + 26.40 cm) at the crest.

Fig. 14 Arcs with the minimum safety factor of each arcgroup for Earthquake B.

the stability of the dam is limited. The sliding sectionof arc No. 2 passes through the crest but does notreach the core, and the slip displacement is only 0.04
cm. No slippage occurs in the U3 arc group. Thus,
the sliding deformations to the upstream side are
judged to be permissible. Toward the downstreamside, although the sliding section of arc No. 4 exhibits a displacement of 46.20 cm, the displacement ishighly localized in the vicinity of the downstream
toe. The sliding section of arc No. 5 passes throughthe crest with a sliding displacement of 76.76 cm.
The subsidence at the crest accompanying the sliding
reaches 49.80 cm. The sliding section of arc No. 6
cuts through the core. The maximum slip displacement is 1.71 cm, and the subsidence at the upper endof the arc is 1.10 cm.
To determine the deformation associated with theshaking and rearrangement of soil particles, the calculation process used for Earthquake A is implemented using Equation (3) and the results of the response analysis of Earthquake B. The shear moduli
of the embankment materials before and after
Earthquake B are considered. The results are shownin Fig. 15. At the crest of the dam, a maximum subsidence of 26.40 cm is predicted.
Due to the differences between the two kinds ofdeformation mechanisms, the deformation due toslippage cannot be simply added to the deformation
related to the shaking and rearrangement of soil particles. However, in terms of the maximum potential
subsidence of the dam crest, caused by Earthquake B,
the vertical components calculated using the two
methods can be summed to obtain a value of 76.20(3) Residual deformation caused by the doublet
earthquake
The deformation caused by the doublet earthquake
can be determined by summing the deformations
induced by Earthquakes A and B. As the maximum
possible subsidence at the dam crest, the verticalcomponents of the two kinds of deformation can besummed directly if the location considered for eachestimate is the same. Since no slippage occurred due
to Earthquake A, the sliding deformation of the damby the doublet earthquake equals that caused by
Earthquake B. The maximum subsidence at the dam
crest is 49.80 cm. In contrast, the deformation related
to the shaking and rearrangement of the soil particles
caused by the doublet earthquake can be determinedby summing the deformations induced by Earthquakes A and B. It should be noted that the locationsof maximum subsidence due to Earthquake A andEarthquake B are not necessarily the same. The
maximum subsidence occurs at the crest with a valueof 31.47 cm. Therefore, the maximum possible subsidence at the dam crest caused by the doublet
earthquake is predicted to be 81.27 cm, which is thesum of the subsidence induced by sliding (49.80 cm)
and shaking and rearrangement of the soil particles(31.47 cm).
The comparison of the subsidence calculated using
the dam freeboard indicates that the earthquake may
not induce an immediate overflow. However, thesubsidence of the crest reaches a value that requires
detailed investigation, for example, by performing asequential nonlinear analysis.
(4) Seepage failure evaluation
In the calculation of the sliding deformation by

報－31

Earthquake B, arc No. 6 cuts through the core with aslip displacement of 1.71 cm. Since the elevation of
the upper end of the arc is lower than the normal
water level of the reservoir, it is necessary to examine
the risk of seepage failure6) (failure due to piping
along the slip surface).
The risk of seepage failure is evaluated considering the hydraulic gradient calculated using Equation
(4):
i

𝐻 ⁄𝐿

4

where H is the pressure head (difference between thewater level of the reservoir and elevation of thedownstream end of the sliding arc in the core zone),and L is the residual length of the sliding section of
the arc in the core zone. The hydraulic gradient of thesliding section of arc No. 6 in the core zone is approximately 0.91 according to Equation (4). Thisvalue is less than 1, which is generally regarded as
the limit value for the occurrence of seepage failure6)(a higher value corresponds to a more critical situation). Nevertheless, this value is relatively large;
thus, a more detailed study is necessary. It is desirable to adopt appropriate precautions to prevent
seepage failure.

6.

PROPOSALOFMEASURESAFTER
EARTHQUAKEEMERGENCYA
LARGE

Although rockfill dams constructed using modern
construction techniques are unlikely to suffer fromliquefaction due to a large earthquake, the occurrenceof the following events must be considered:
1) Overflow due to the excessive subsidence ofthe crest
2) Concentrated seepage along the slip surface
across the core3) Water penetration through cracks4) Increased seepage flow and the generation of
turbid seepage water
Since these phenomena may cause dam failure, itis necessary to perform an emergency inspection
immediately after a large earthquake. As clarified inthis study, the seismic performance of a rockfill dam
may temporarily decline due to the change in the
dynamic characteristics and material properties after
the occurrence of a large earthquake. Therefore, in
preparation for a large earthquake that may occur
later, the reservoir water should be lowered to a safe
level and maintained at this level for at least a week.
Moreover, before the discharge is realized, it is necessary to exchange information and coordinate withthe related organizations, such as the local govern-ments in the downstream area, and subsequently
release the reservoir water according to the operation
manual of the dam. Future work to respond tolarge-scale doublet earthquakes can be aimed at revising the dam operation manual and constructing thedam operation supporting system. Furthermore, acountermeasure must be implemented to prevent the
infiltration of water into the cracks. In addition,
careful monitoring of the dam body and timely
analysis of the inspection records are recommended.

7. CONCLUSIONS
The following conclusions were derived throughthis study:1) The relationship between the shear modulus of
the embankment materials and average shear
strain evaluated based on the earthquake records can be approximately expressed by aconventional hyperbolic model. When thegenerated average shear strain is less than approximately 2.0×10-4, the stiffness of the embankment materials can be promptly recovered.
However, when the shear strain exceeds
1.0×10-3, the decreased stiffness requires additional time to recover. In the case of Aratozawa dam, the shear moduli of the embankment materials decreased to 58% of their
original values and recovered in approximately one week.
2) The earthquake response and seismic performance of a rockfill dam subjected to a large
doublet earthquake were evaluated. Moreover,a practical evaluation procedure was proposed.
3) The material properties of rockfill dams maychange temporarily in response to strong
seismic motion. These variations induced by
the first event may significantly affect the responses of the dam to the second event. The
decreased stiffness is expected to result in an
increased subsidence related to the shaking
and rearrangement of soil particles. The decreased strength is expected to result in an increased slip deformation.
4) To ensure dam safety immediately after a large
earthquake, the reservoir water level should be
rapidly reduced to a safe value and maintainedat this value for at least one week in preparation for a large doublet earthquake. Careful
and frequent monitoring of the dam body andtimely analysis of inspection records must be
ensured.
In this paper, the effect of the pore water pressure
was not considered in the earthquake response analyses, and the permanent displacements of the dam

報－32

due to earthquakes were predicted using a simplified
method. Future work may be aimed at using an advanced dynamic nonlinear analysis method thatconsiders the effects of the pore water pressure.
ACKNOWLEDGMENT: We appreciate the
Miyagi Prefecture Kurihara Dam Management Office and Japan Commission on Large Dams forproviding us with the earthquake records and information regarding the dam considered in the present
study.
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報－33(Received December 7, 2020)(Accepted May 22, 2021)