自然災害科学 J. JSNDS 38 特別号 1 -23（2019 ）Investigation of the Tsujun Bridge
damage mechanism during the2016 Kumamoto earthquake
Aiko FURUKAWA1, Hiroki YOSHIKAWA1 and Junji KIYONO1

Investigation of the Tsujun Bridge damage mechanism
during the 2016 Kumamoto earthquake
Aiko FURUKAWA1, Hiroki YOSHIKAWA1 and Junji KIYONO1
Abstract
Tsujun Bridge, a stone arch bridge, suffered slight damage during the 2016 Kumamoto
earthquake. In this study, a microtremor observation was conducted, the natural frequencies ofthe bridge were estimated, and the horizontal-to-vertical (H/V) spectral ratios at Tsujun Bridge
and at a strong-motion observation site were calculated. The ground motion for Tsujun Bridge
was estimated based on H/V spectral ratios, and a numerical model was created based on theobserved natural frequencies. The seismic response of the numerical model was simulatedusing the reﬁned distinct-element method, and the damage mechanism during the Kumamoto
earthquake was investigated.
Key words： Tsujun Bridge; stone arch bridge; damage mechanism; 2016 Kumamoto earthquake; microtremor
observation; reﬁned distinct-element method

1. Introduction

the transverse direction. There are wall stones on

Tsujun Bridge is a stone arch bridge locatedboth sides and three stone pipes inside. The spac-in Yamato Town, Kumamoto Prefecture, Japanes between the stone pipes and those between the(Fig. 1(a)). This is a stone aqueduct bridge whose

wall stones and the stone pipes are ﬁlled with soil

construction was completed in 1854, and which(Yamato Town of Kumamoto Prefecture, 2015).

has since been designated as an important cultur-

During the foreshock and mainshock of theal property of Japan. The water pipe consists ofKumamoto earthquake on April 14 and 16 in 2016,

stones with a hole, as shown in Fig. 1(b). Fig. 1(c)Tsujun Bridge suffered slight damage. Althoughshows a sectional view of the top of the bridge instones did not fall, various wall stones were pushed1

Department of Urban Management, Graduate School ofEngineering, Kyoto University, Kyoto City, Japan1

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Investigation of the Tsujun Bridge damage mechanism during the 2016 Kumamoto earthquake

(a)

(b)

(c)
Fig. 1

Tsujun bridge: (a) appearance from the upstream side; (b) stone pipe; (c)section view of the top of the bridge in the transverse direction (revised
based on Yamato Town of Kumamoto Prefecture (2015)).

out in the transverse direction and cracks occurredstone pipes. The crack length has been reported toinside the soil ﬁlling the spaces between the wallbe approximately 1 to 2 cm (Yamato Town of Ku-

stones and the stone pipes, as shown in Fig. 2(a)mamoto Prefecture, 2016c).

(Yamato Town of Kumamoto Prefecture, 2016a).

Research regarding the damage to Tsujun

Fig. 2(b) shows a contour of movement displace-

Bridge is still insufﬁcient. Izuno et al. (2017) con-ment for the wall stones in the transverse direction

ducted microtremor obser vation on and around

during a series of Kumamoto earthquake vibrations

Tsujun Bridge to estimate the natural frequencies.

(Yamato Town of Kumamoto Prefecture, 2016b).

They also conducted simplified penetration test-

The displacement was calculated from the results

ing and estimated the stiffness of the supportingof a three-dimensional sur vey conducted before

ground. They modeled the bridge with a single-de-the earthquake in 2013 and after the earthquake

gree-of-freedom system based on the observed nat-in 2016. The red color indicates the maximum dis-ural frequencies, and conducted seismic response

placement. The displacement was small at the arch

analysis. They input the ground motion record

crown but larger between the arch support and theobserved at the nearest strong-motion observation

bridge deck edge. A maximum displacement of ap-

site (K-NET YABE) (NIED: National Research In-

proximately 15 cm was observed on the right-bankstitute for Earth Science and Disaster Resilience),side of the upstream side. In Fig. 2(c), the red line

which is 0.9 km from Tsujun Bridge. Hagiwara etindicates the location of the cracks observed insideal. (2017) conducted seismic response analysis

the soil (Yamato Town of Kumamoto Prefecture,

for Tsujun Bridge using the three-dimensional

2016c). Cracks in the soil were found between thefinite-element method. They modeled the bridgearch support and the bridge deck edge, but not atwith linear elements using the abovementioned ob-

the arch crown. Cracks in the soil were observed

served ground motion data as input. However, theyin the exterior soil between the wall stones and themodeled only the bridge and not the side ground.

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自然災害科学 J. JSNDS 38 特別号（2019 ）

(a)

(b)

(c)
Fig. 2

Damage to Tsujun Bridge caused by the Kumamoto earthquake: (a) movement of wall stones
and cracks in the soil (Yamato Town of Kumamoto Prefecture, 2016a); (b) contour of wall stone
displacement in the transverse direction (Yamato Town of Kumamoto Prefecture, 2016b); (c) locationsof crack occurrence in the soil (red color) (revised based on Yamato Town of Kumamoto Prefecture(2016c)).

In their results, the maximum displacement andstudy is to clarify the damage mechanism of Tsu-

maximum stress occur red at the arch crown,

jun Bridge during the Kumamoto earthquake. We

which is different from the actual damage. As men-used the reﬁned distinct-element method (reﬁned

tioned previously, the actual displacement of theDEM), which is suitable for three-dimensional elas-wall stones and the actual cracks in the soil weretic, failure, and collapse behaviors (Furukawa etobserved not at the arch crown but rather betweenal., 2011). We conducted microtremor observation

the arch support and the bridge deck edge. In thison the bridge and on the side ground surface, andregard, the damage mechanism of Tsujun Bridge

estimated their natural frequencies. The numeri-

has not yet been clariﬁed.

cal model was developed such that the analyticalGiven this background, the objective of thisnatural frequencies of the bridge and side ground4

Investigation of the Tsujun Bridge damage mechanism during the 2016 Kumamoto earthquake

matched the obser ved values. We also conduct-of the actual damage that occurred between theed microtremor obser vation on the base groundarch support and the bridge deck edge from thesurface of Tsujun Bridge and at the strong-motion

viewpoint of frequency characteristics. Moreover,obser vation site (K-NET YABE) to estimate thewe investigated the severity of ground motion re-horizontal-to-ver tical (H/V) spectral ratios. Be-

quired for the wall stones to fall and collapse of thecause the H/V spectral ratios at the two sites havearch system to occur.

different characteristics, intuition suggests that the
ground motion at Tsujun Bridge is different fromthat of K-NET YABE. Therefore, we estimated theground motion for Tsujun Bridge during the Kumamoto earthquake.

2. Microtremor observation
2. 1

Overview

To investigate the vibration characteristics,
we conducted microtremor observation at Tsujun

According to the literature (Yabe Town ofBridge and at the strong-motion observation site.

Kumamoto Prefecture, 1984), the basement of

At the bridge, microtremors were observed at the

Tsujun Bridge seems to be attached to the bed-arch crown (point 1), at the mid-point between therock. Therefore, we computed the bedrock groundarch crown and the bridge deck edge on the right-

motion at K-NET YABE based on multiple-reflec-bank side (point 2), on the side ground surface ontion theory, and assumed it to be the input groundthe right-bank side (point 3), on the base groundmotion for Tsujun Bridge. We termed this groundsurface on the right-bank side (point 4), and on the

motion estimated ground motion 1. Additionally,base ground surface on the left-bank side (point 5).

we employed an empirical method to correct theMoreover, microtremors were observed at K-NET

observed ground motion using the H/V spectral

YABE, which is the strong-motion observation siteratios at the two sites (Nakamura et al., 2009). We

operated by NIED. K-NET YABE is 0.9 km fromtermed the ground motion estimated using thisTsujun Bridge. The observation point locations are

empirical method estimated ground motion 2.

shown in Fig. 3. The ﬁrst microtremor observation

Then, the seismic responses of Tsujun Bridge andwas conducted at points 1, 2, and 5 and at K-NET

the side ground during the Kumamoto earthquake

YABE on October 4, 2016. Considering that thewere simulated. We investigated the mechanism

modeling of side grounds is important, a second(a)Fig. 3(b)

Microtremor obser vation points: (a) measurement locations at Tsujun Bridge (Yamato Town ofKumamoto Prefecture, 2015); (b) location of Tsujun Bridge and K-NET YABE (Geospatial Information
Authority of Japan).

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自然災害科学 J. JSNDS 38 特別号（2019 ）microtremor observation was conducted at points

since mode shapes are difficult to draw with two

3 and 4 on November 1, 2017.

accelerometers. The damping ratios of the first

The measurement was conducted for 12

mode were estimated using the half-power method

minutes at each point. The sampling inter val forassuming that the input force is white noise. The

the measurement data was 0.01 s. The measured

damping ratios of the ﬁrst mode were determined

waveforms were corrected with regard to theas 0.029 for the longitudinal direction, 0.038 forbaseline and divided into segments of 4,096 data

the transverse direction, and 0.030 for the verticalpoints. Thus, their mean Fourier amplitudes weredirection.
The peak Fourier amplitudes were observed

computed. For smoothing, a Parzen window with afrequency bandwidth of 0.4 Hz was applied.

not at the ﬁrst-mode natural frequencies, but rather
at 11 Hz in the longitudinal direction and at 10 Hz

2. 2 Natural frequencies and damping ratios

in the transverse direction, because the predom-of Tsujun Bridge

inant frequency of the base ground was approxi-

Fig. 4 shows the Fourier spectra for the ac-mately 10-11 Hz, as will be explained later.

celerations observed at the bridge at points 1 and2. 3 Natural frequencies of the Tsujun Bridge

2 in three directions. Since the transfer functions

side groundat points 1 and 2 with regard to the base ground(point 4 or 5) were not observed, we estimate theFig. 5 shows the transfer function of the Tsu-ﬁrst-mode natural frequencies and damping ratios

jun Bridge side ground on the right-bank side,in three directions using the acceleration Fourier

which is obtained by taking the ratio of the Fourier

spectra at points 1 and 2 assuming that the input

spectra on the ground surface side (point 3) to thatforce is white noise.

on the base ground surface (point 4). The natural

From the figurs, the natural frequencies of thefrequencies of the side ground were estimated asﬁrst mode were estimated as 4.2 Hz for the longitu-

6.3 Hz in the east-west direction and 6.0 Hz in the

dinal direction, 2.4 Hz for the transverse direction,

north-south direction. Therefore, it was concluded

and 5.4 Hz for the vertical direction. It is possiblethat the natural frequency of the ﬁrst mode in thethat peak frequencies other than ﬁrst-mode natural

horizontal direction was approximately 6.0 Hz. The

frequencies are higher-mode natural frequencies,

first-mode natural frequency of the side ground

but it is dif ficult to determine the modal order

was found to be higher than that of the bridge.

(a)Fig. 4(b)(c)

Fourier spectra of microtremor obser vation records: (a) longitudinal direction; (b) transverse
direction; (c) vertical direction

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Investigation of the Tsujun Bridge damage mechanism during the 2016 Kumamoto earthquake

2. 4 H/V spectral ratios at Tsujun Bridge

The microtremor observation results are summarized in Table 1.

and K-NET YABE
Fig. 6 shows the H/V spectra ratios observedon the base ground sur face at Tsujun Bridge(points 4 and 5) and at K-NET YABE. The peak

3. Estimation of input ground motion for
Tsujun Bridge
3. 1

frequencies at Tsujun Bridge were approximately

Overview

10-11 Hz, even though there was little difference

By using microtremor observation, we foundbetween the right- and left-bank sides. On the oth-that the H/V spectral ratios at Tsujun Bridge ander hand, the peak frequency at K-NET YABE was

K-NET YABE had different characteristics, anddetermined as 7.2 Hz. The amplitude of the H/

that the ground motion at the two sites was also dif-

V spectra at Tsujun Bridge was smaller at 3-9 Hz

ferent. Therefore, this study estimated the groundand larger at 10-11 Hz in comparison with that at

motion for Tsujun Bridge using two methods. The

K-NET YABE. From these comparisons, it can be

ﬁrst method was to input the bedrock ground mo-

considered that the base ground vibration charac-tion at K-NET YABE as an input to Tsujun Bridge

teristics at the two sites were different even though(estimated ground motion 1). The second method

the two sites were very close with a straight dis-is empirical and was used to correct the groundtance of 0.9 km. Therefore, intuition suggests that

motion at K-NET YABE using the H/V spectral ra-

the ground motion at Tsujun Bridge has charac-

tios.

teristics that are different from those observed at
K-NET YABE.

Fig. 5

Fig. 6
Transfer function of the side ground onright-bank side.

Table 1
Location

H/V spectral ratios on the base groundsur face at Tsujun Bridge and K-NET
YABE.

Summary of microtremor observation results.

Tsujun bridge
Transverse VerticalSide ground of
Tsujun Bridge

Base ground of
Tsujun Bridge

Base ground of
K-NET YABE

Horizontal

Horizontal

Horizontal

Direction

BridgeNaturalfrequency

4.2 Hz2.4 Hz5.4 Hz6.0 Hz

10-11 Hz

7.2 HzDamping ratio

0.029

0.038

0.030

−

−

−

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自然災害科学 J. JSNDS 38 特別号（2019 ）3. 2 Method 1: Bedrock ground motion at

Here, subscripts O and E indicate the observation

K-NET YABE (estimated ground motion 1)

point and estimation point, respectively; super-

From the literature (Yabe Town of Kumamoto

scripts M and E indicate the microtremors andPrefecture, 1984), the Tsujun Bridge basement

earthquake, respectively; and COmax and CEmax are

seems to be attached to the bedrock. Therefore, we

the maximum amplitudes of the microtremor H/

computed the bedrock ground motion at K-NET

V spectral ratios at the observation and estimation

YABE based on multiple-reﬂection theory, and con-points, respectively. In summary, modiﬁcation fac-sidered it as the input ground motion for Tsujun

tors βO and βE were obtained by dividing the normal-

Bridge. We termed this ground motion estimatedized microtremor H/V spectral ratios by the H/Vground motion 1.

spectral ratios of the earthquake ground motion.

The soil profile of the sur face ground at

By introducing modification factors βO and

K-NET YABE is presented in Table 2 (NIED). We

βE, the microtremor H/V spectral ratio at the ob-assumed that the height of the bedrock surface

servation and estimation sites can be obtained as

was 5 m. The natural frequency of the ﬁrst mode offollows.

the SH wave was calculated as 7.2 Hz, which is in（2）

good agreement with that obtained from the H/Vspectral ratio. The material was assumed to belinear and the damping ratios for the surface soil
were assumed to be 0.05.

From the above equation, the horizontal Fourier earthquake amplitudes at estimation site HEE
were obtained using the earthquakeʼs horizontal

3. 3 Method 2: Empirical method proposed
by Nakamura et al. (estimated ground

Fourier amplitudes at obser vation site H OE andmodiﬁcation factor α, as follows:

motion 2)（3）

The second method is empirical and has been
proposed by Nakamura et al. (2009). This method
corrects the obser ved ground motion using the
H/V spectral ratios at two sites. We termed theModiﬁcation factor α can be estimated as follows:

ground motion estimated using this empiricalmethod estimated ground motion 2.

（4）

In this method, modiﬁcation factors βO and βE
are deﬁned as follows:

In the above equation, to estimate modification factor α, all parameters except modification（1）

factor βE and the spectral ratio of vertical groundmotions γE/O can be computed from the H/V spec-

Table 2tral ratios. However, modification factor βE andSoil profile of the surface ground at
K-NET YABE (NIED).
3

Depth Density (ton/m )Shear wave velocity(m/s)

Soil type

0-3 m

1.63

90

Clay

4-5 m

2.00

230

Gravel

5m

2.16

810

Rock

the spectral ratios of vertical ground motions γE/O
cannot be obtained without the earthquake groundmotion records at the estimation site. Nakamura etal. (2009) proposed empirical equations to estimate
these unknown parameters.
First, we explain how to estimate modiﬁcation

8

Investigation of the Tsujun Bridge damage mechanism during the 2016 Kumamoto earthquake

factor βE. Nakamura et al. (2009) repor ted that
there is a positive correlation between average βO

3. 4 Comparison of observed ground motionand estimated ground motion

and average βE between the period from 0.1 s to 2

Fig. 7 indicates the acceleration time historys at nearby stations. They proposed to obtain aver-of the obser ved ground motion at K-NET YABE

age βO of the observation site from 0.1 s to 2 s, and(observation), estimated ground motion 1 (estima-

use it as modification factor βE for the estimation

tion 1), and estimated ground motion 2 (estimation

site.

2). Because the two methods can be used only for
Next, we explain how to estimate the spectral

horizontal ground motion, the obser ved verticalratio of vertical ground motion γE/O. Nakamura et

ground motion at K-NET YABE was used with theal. (2009) proposed the following estimation equa-

estimated horizontal ground motion. Fig. 7 shows

tions:

the ground motion used as input for the numericalanalysis conducted in this study. We combined theforeshock at 21:26 on April 14 and the mainshock（5）

at 1:25 on April 16 into one continuous groundmotion. The time history consisted of 0 gal for 1
s to maintain stability against gravitational force,

Here, γI
E/O

is an estimation equation when the

predominant frequency of the obser vation siteʼs
H/V spectral ratio is higher than that of the estimation site, and γ IIE/O is an estimation equation when
the obser vation siteʼs predominant H/V spectral
ratio frequency is lower than that of the estimationsite. Moreover, γE/O can be estimated for each peri-(a)od T, and Tg is the larger value of the predominantnatural H/V spectral ratio periods for the microtremors between the observation and estimationsites. The estimation equation for C’ max is as follows:（6）(b)
The Fourier amplitudes of the ear thquake
ground motion for Tsujun Bridge were estimatedby Nakamuraʼs method. The Fourier phase cannot
be estimated by this method; thus, the Fourierphase of the obser ved ground motion at K-NET
YABE was used for the Tsujun Bridge site. Finally,
the vertical ground motion cannot be estimated bythis method.

(c)Fig. 7

Acceleration time histories: (a)longitudinal direction; (b) transverse
direction; (c) vertical direction.

9

自然災害科学 J. JSNDS 38 特別号（2019 ）foreshock for 22.5 s, 0 gal for 1.5 s to dissipate

the observed ground motion, because the natural

the vibration caused by the foreshock and restore

frequency of the K-NET YABE ground surface wasstability, and mainshock for 25 s. The obser ved

7.2 Hz. Estimated ground motion 2 had a smaller

motion had the largest peak ground acceleration

amplitude at approximately 3-9 Hz and a larger am-(PGA), while estimated motion 2 had the smallest

plitude at approximately 10-11 Hz, in comparison

PGA.

with the obser ved ground motion, owing to theFig. 8 shows a comparison of the accelera-difference in the H/V spectral ratios.

tion Fourier spectra in the horizontal directions.
Estimated ground motion 1, which is the bedrock
ground motion at K-NET YABE, had a smaller amplitude at approximately 7 Hz, in comparison with

Fig. 8

(a)

(b)

(c)

(d)

Fourier acceleration amplitudes: (a) foreshock in the longitudinal direction; (b) mainshock in thelongitudinal direction; (c) foreshock in the transverse direction; (d) mainshock in the transverse
direction.

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Investigation of the Tsujun Bridge damage mechanism during the 2016 Kumamoto earthquake

4. Development of a numerical model for
Tsujun Bridge
4. 1

Refined DEM

Before failure, the continuous elements are connected by the restoring springs, and the elastic
behavior can be simulated. Structural failure is

The reﬁned DEM (Furukawa et al., 2011) is amodeled as the breakage of the restoring spring,

numerical analysis method that simulates three-di-at which time the restoring spring is replacedmensional elastic, failure, and collapse behaviors.

with a contact spring and a contact dashpot. Fig.

This method is a refined version of the three-di-9(d) shows a spring and a dashpot for computing

mensional DEM. The points of difference from thethe contact force (contact spring and dashpot).

original DEM (Cundall, 1998) are the arrangement

These model the contact, separation, and recontactof springs, and that the spring constant is theoreti-

between the elements. The dashpots were intro-

cally determinable from the material properties.

duced to represent the energy dissipation caused

In the refined DEM, a structure is modeledby the contact. Thus, the interaction between theas an assembly of rigid elements, as in the original

elements is modeled using multiple springs andDEM. However, unlike the original DEM, the sur-

multiple dashpots attached to the surface of theface of an element is divided into small segments,

elements.

as shown in Fig. 9(a). The black points indicate theThis method enables the simulation of elastic

representative point of each segment. One restor-

behavior and is suitable for simulating large dis-ing spring and a combination of a contact spring

placement behaviors such as failure and collapse.

and a dashpot are attached to one segment (Fig.
9(b)) at each of the representative points shown

4. 2

Numerical modelin Fig. 9(a). This segmentation enables the spring

For the bridge, the area surrounded by theconstant to be derived theoretically based on the

red frame in Fig. 10(a) was modeled. The bridge

three-dimensional stress-strain relationship of the

span was 72.9 m, the width was 6.6 m, and thematerial and segment area.

height was 21.6 m. The entire view of the numer-

Fig. 9(c) shows a spring for computing the re-ical model and the view of the bridge from abovestoring force (restoring spring). This spring mod-are shown in Fig. 10(b, c). The longitudinal direc-

els the elasticity of the elements. The restoringtion and transverse direction are deﬁned as the x-

spring is a set between the continuous elements.

and y-axis, respectively.

(a)Fig. 9

(b)

(c)

(d)

Model of the spring and dashpot in refined DEM: (a) segments and contact points; (b) multiple
springs and multiple dashpots attached to the surface; (c) restoring spring; (d) contact spring anddashpot.

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自然災害科学 J. JSNDS 38 特別号（2019 ）In Fig. 10(b, c, d), all stones except the stone

m for water to pass through. Although we used apipes are shown with brown elements. The ele-

rectangular element without a hole, we consideredment size of the stones was approximately 1 m (x)the effect of the hole by applying a smaller appar-

×1 m (y) ×1 m (z), which is larger than the actual

ent density.

size of approximately 0.6 m (x) ×0.6 m (y) ×0.6 m

There is soil between the wall stones and(z), owing to the limited computational resources.

stone pipes, and between the stone pipes, as indi-

The stone pipe is modeled by a rectangular ele-

cated by the red element in Fig. 10(d). To express

ment with a size of 0.6 m (x) ×0.8 m (y) ×0.8 m (z),the crack, the soil was divided into two elements inas shown for the yellow element in Fig. 10(c). The

the transverse direction.

actual stone pipe has an interior hole of 0.3 m ×0.3

The surrounding ground is also modeled andindicated by the light gray elements. The groundsurrounding the bridge from the upstream anddownstream sides is modeled with the same sizeas the stones. The side grounds of 40 m (x) × 70
m (y) ×21.6 m (z) on both the right- and left-bank(a)sides were also modeled to express the vibration
characteristics. The side grounds were divided
roughly into elements with a size of 8 m (x)×7.8 m(y) × 5.4 (z). The dark gray elements indicate thebase ground. From the literature (Yabe Town ofKumamoto Prefecture, 1984), the basement of Tsujun Bridge seems to be attached to the bedrock.

(b)

Therefore, the dark gray elements were assumed
to be ﬁxed.
The total number of elements was 8,204. The
surface of each element was divided into nine segments.

(c)

4. 3

Material properties

The material properties used in the analysis
are listed in Table 3.
With regard to the side ground, the shear
modulus was determined such that the analyticalnatural frequency of the first mode matches the(d)natural frequency obtained by microtremor obser-

Fig. 10 Numerical model: (a) front view of thebridge and modeled area (Yamato Town
of Kumamoto Prefecture, 2015); (b)birdʼs-eye view of the numerical model;(c) plan view of the Tsujun Bridge
model; (d) cross section of the top of thebridge.

ing that Poissonʼs ratio is 0.3. We used the samevation. Youngʼs modulus was estimated by assumparameters for the ground surrounding the bridgefrom the upstream and downstream sides. With regard to the bedrock, the same properties as thoseof the K-NET YABE bedrock were used.

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Investigation of the Tsujun Bridge damage mechanism during the 2016 Kumamoto earthquake

Table 3

Material properties of the numerical model.
Density (kg/m3)

Youngʼs modulus (N/m2)

Poissonʼs ratio

Stone (not comprising the arch ring)3

2.7×107.2×1080.25

Stone (comprising the arch ring)

2.7×103

6.0×1090.25

Stone pipe

2.3×103

2.0×108

0.25

Soil

1.8×103

7.5×1070.30

Surrounding ground

1.8×103

1.44×1090.30

Bedrock

2.16×103

3.68×109

0.30

Table 4Comparison of natural frequencies between microtremor observation and the numerical model.

Component

Direction

Microtremor Observation (Hz)

Numerical analysis (Hz)BridgeLongitudinal direction

4.2

4.7

0.48

BridgeTransverse direction

2.4

2.3

−0.05

BridgeVertical direction

5.4

5.3

−0.09

6.0

6.2 (x-direction)
5.9 (y-direction)

0.16
−0.06

Side ground

Horizontal

Difference (Hz)By determining the material properties of theto obtain the free vibration of the side ground.

ground in advance, the material properties for the

Table 4 shows the comparison of the ﬁrst modeʼsremaining elements, i.e., stone (not comprising

natural frequencies, which were obtained by mi-

the arch ring), stone (comprising the arch ring),

crotremor observation and numerical analysis.

stone pipe, and soil, were determined. By referringWith regard to Tsujun Bridge, the analyticalto the material properties in the literature (NIED;

natural frequencies of the first mode are in good

Asai et al., 2009), we set the material properties

agreement with the observed ones, particularly insuch that the analytical natural frequencies of thethe transverse direction and in the vertical direc-

bridge matched the natural frequencies obtainedtion. Regarding the side ground, the analytical nat-by microtremor observation.

ural frequencies were 6.2 Hz in the x-direction and
5.9 Hz in the y-direction, which were close to the

4. 4 Verification of the numerical model for
linear analysis
The natural frequencies of the ﬁrst mode forthe bridge and the side ground were simulated

observed natural frequency of 6.0 Hz. From thesecomparisons, we considered that the numericalmodel and determined material properties wereapplicable to a linear analysis of Tsujun Bridge.

to verify the developed numerical model and thematerial properties determined for linear analysis.

4. 5

Strength between elements

An acceleration of 100 gal was input for a duration

Next, we determined the strength betweenof 0.01 s, and the response was computed as a freethe elements to express failure and sliding between

vibration in each direction. The strength between

the elements. The strength values are listed in

the elements was set to be strong enough such that

Table 5. Since the actual strength is not available,

failure could not occur. The acceleration response

we assumed the strength values in the following

was computed at the yellow circle point shown inmanner.

Fig. 10(c) to obtain the free vibration of the bridge,

The strength between the stone pipes is theand at the yellow circle point shown in Fig. 10(b)strength of the mortar. The mortar was placed at

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自然災害科学 J. JSNDS 38 特別号（2019 ）Table 5Strength between elements to model tensile and shear failure.
Tensile strength (N/m2) Bond strength (N/m2)

Friction coefﬁcient

Stone pipe-Stone pipe (mortar)

1.0×105

1.0×105

0.584

Stone-Stone/Stone-Stone pipe

1.0×102

1.0×1020.669

Stone-Soil/Stone-Ground

1.0×102

1.0×102

0.584

Soil-Soil/Soil-Ground

1.0×1022.5×104

0.372

Ground-Ground

Failure not considered

the notch shown in Fig. 1(b). The area where theConversely, the material non-linearity of the side

mor tar was placed is ver y small in comparison

ground was considered by introducing equivalent

with the section area of the stone pipe. Because

linear analysis.

experimental data were not available, we used thestrength value recommended as the design spec-

4. 6

Non-linearity of the side groundification for masonr y (Architectural Institute of

The non-linearity of the side ground wasJapan, 1964) and modiﬁed the value by considering

investigated using equivalent linear analysis. By

the area where the mortar was placed and the area

inputting the material properties of the ground andof the stone pipe element.

bedrock (listed in Table 3), equivalent linear anal-

With regard to the strength between theysis was conducted for the three ground motions

stones and the strength between the stone and thein the transverse direction (y). The bedrock wasstone pipe, the actual strength was equal to zero

assumed to be linear, and the dynamic deforma-because there was no mortar in between. However,tion characteristics proposed by the Public Works

to obtain numerical stability against gravity, a small

Research Institute (PWRI, 1982) were used for thevalue was used for the tensile strength and bondside ground.

strength.

The equivalent shear modulus and equivalent

In the same manner, a small tensile strength

damping ratios were obtained, and the equivalent

was used between the soils and between the soil

shear modulus was transformed into the equiva-

and the ground. Regarding the bond strength

lent Youngʼs modulus. The results are presented inand friction coefﬁcient, the value was determined

Table 6. The equivalent Youngʼs modulus became

assuming that the N value of the standard penetra-

smaller and the equivalent damping ratio becametion test was approximately equal to 2. Since there

larger as the PGA increased. In the seismic re-are no physical data available for the soil stiffness,sponse analysis, the equivalent Youngʼs modulus

we assumed the N value to be 2 based on the ﬁnd-and damping ratio were used for the ground ele-

ings that the soil settled almost 30 cm by two-stepments.

jumps due to the weight during the survey on October 4, 2016.
The friction coefﬁcient was determined by referring to previous research (Asai, 2009).

4. 7

Damping ratio

In the refined DEM, structural damping canbe considered as mass-propor tional damping.

Thus, a non-linear model was developed for

Because the vibration in the transverse direction

the bridge by considering the failure between the(y) was dominant, the damping ratio of the bridge

elements. Regarding the non-linearity of the side

components (stone, stone pipe, and soil) was

ground, failure was not considered because failureassumed to be 0.038, which is the damping ratio

did not occur during the Kumamoto earthquake.

obtained by microtremor observation in the y-di-14

Investigation of the Tsujun Bridge damage mechanism during the 2016 Kumamoto earthquake

Table 6Equivalent Youngʼs modulus and damping ratio of the ground.

Input ground motion

PGA (y-direction)

Equivalent Youngʼs modulus (N/m2)

Equivalent damping ratio

Observed motion

626 gal1.24 × 109

0.053

Estimated motion 1

346 gal1.25 × 109

0.043

Estimated motion 2

207 gal1.33 × 109

0.039

rection. For the damping ratio of the side ground,the equivalent damping ratio described in 4.6 andpresented in Table 6 was used.

5. Seismic response analysis of Tsujun
Bridge5. 1

Analysis Output

Fig. 11 shows the locations where the re-(a)sponses were computed. We computed the displacement response for a gravity center of 150
elements at the top of the bridge. We focused on 15
rows from row A to row O in the longitudinal direction, and 10 columns from column 1 to column 10
in the transverse direction. In total, 150 elements(15 rows ×10 columns) were considered. The elements were named by combining the letter indicating the row and the number indicating the column.
For example, the wall stone at the arch crown on
the upstream side is termed H1. The elements(b)Fig. 11 Locations to output displacement
responses: (a) rows and columns to
output responses (view from above);(b) rows to output responses (side view
from the upstream side).

in the 1st and 10th columns are the wall stones, andTable 7the elements from the 2nd to the 9th columns are thesoils.

Analysis cases.

Case

Input ground motion

PGA (y-direction)

In this study, we focused on the two main

Case 1

Observed ground motion

626 galdamage types caused to Tsujun Bridge by theCase 2Estimated ground motion 1

346 gal

Case 3

Estimated ground motion 2

207 galKumamoto ear thquake; namely, the movementof the wall stones in the transverse direction, andthe cracks in the soil that did not occur at the arch

tween the 2nd and 3rd columns, 4th and 5th columns,

crown but rather between the arch support and6th and 7th columns, and 8th and 9th columns.

the bridge deck edge. The movement of the wallstones was investigated by the displacement history in the y-direction of the top wall stones in the 1

st

5. 2

Seismic response analysis（1）Analysis cases

and 10th columns. The cracks in the soil were inves-

The analytical cases are listed in Table 7. In

tigated by the relative displacement history in thecases 1-3, the seismic behaviors against the threey-direction between the two adjacent soil elements.

input ground motions are compared. Assuming

Thus, we obtained the relative displacement be-that the ground accelerations at the base ground15

自然災害科学 J. JSNDS 38 特別号（2019 ）are uniform at both the left- and right-bank sides,

This analytical result is an overestimation because

ground accelerations as inertia forces are input tono wall stones actually fell during the Kumamoto

the gravity centers of all movable elements belong-earthquake.

ing to the stone bridge and the side grounds. A
time interval of 2.0×10−4s was employed.

Fig. 13 indicates the contour of the residual
displacement of the wall stones in the transverse
direction at 50 s. The positive value indicates move-（2）Results: Case 1

ment in the outward direction. It should be noted

Fig. 12 indicates the displacement history ofthat the top wall stones that had already fallen are

the top wall stones in the transverse direction (y).

not shown. Therefore, the movement of the soil

On the upstream side, the negative displacement

elements is shown instead. There were many wall

indicates movement in the outward direction. On

stones with a displacement larger than 20 cm.

the downstream side, the positive displacement

However, the analytical result overestimated theindicates movement in the outward direction.

actual damage shown in Fig. 2(b).

On the upstream side, almost all of the top wall

Next, the relative displacements of the ad-stones moved outward during the foreshock, thejacent soil elements between the 2 nd and 3rd col-stones in the middle from C1 to M1 fell during theumns, and between the 4th and 5th columns on theforeshock, and the remaining stones (A1, B1, N1,

upstream side are shown in Fig. 14. The positive

and O1) fell during the mainshock. Similarly, allvalue indicates the separation between adjacentof the top wall stones fell on the downstream side.

soil elements. Similar results were obtained for thesoils on the downstream side. In the analytical result, cracks in the soil occurred in almost all areas,
which is an overestimation of the actual situation,
wherein cracks were only observed between thearch support and the bridge deck edge, as shownin Fig. 2(c). Since no soil elements fell, the relative
displacement exceeding 5 cm just means that thecrack width in the soil is larger than 5 cm.

(a)In summary, the results of case 1 overestimated the actual damage. Therefore, it can be said thatthe obser ved ground motion at K-NET YABE is(b)
Fig. 12 Displacement of the top wall stones inthe transverse direction (case 1): (a)wall stones on the upstream side; (b)wall stones on the downstream side.

Fig. 13 Residual displacement of wall stones inthe transverse direction (case 1).

16

Investigation of the Tsujun Bridge damage mechanism during the 2016 Kumamoto earthquake

(a)

(a)

(b)

(b)

Fig. 14 Relative displacement between adjacentsoil elements (case 1): (a) relative
displacement between columns 2 and3; (b) relative displacement between
columns 4 and 5.

Fig. 15 Displacement of the top wall stones inthe transverse direction (case 2): (a)wall stones on the upstream side; (b)wall stones on the downstream side.

different from the actual ground motion that affected Tsujun Bridge.
（3）Results: Case 2
Fig. 15 shows the displacement histor y of
the top wall stones in the transverse direction (y).
As can be seen, more than half of the stones remained. The top wall stones fell from row F to row
M on the upstream side, and from rows G and I torow K on the downstream side.

Fig. 16 Residual displacement of wall stones inthe transverse direction (case 2).

Fig. 16 shows the residual displacement contour for the wall stones in the transverse direction

ered an overestimation.

at 50 s. The positive value indicates movement in

Next, the relative displacement of the adjacent

the outward direction. Note that the top wall stones

soil elements between the 2nd and 3rd columns andthat had already fallen are not shown. Therefore,

between the 4th and 5th columns on the upstream

the movement of the soil elements is shown in-side are shown in Fig. 17. Case 2 has a smaller

stead. In comparison to the actual displacement

relative displacement in comparison with case 1;

shown in Fig. 2(b), the result of case 2 is consid-

however, cracks occurred in all rows.

17

自然災害科学 J. JSNDS 38 特別号（2019 ）

(a)

(a)

(b)

(b)

Fig. 17 Relative displacement between adjacentsoil elements (case 2): (a) relative
displacement between columns 2 and3; (b) relative displacement between
columns 4 and 5.

Fig. 18 Displacement of top wall stones in thetransverse direction (case 3): (a) wallstones on the upstream side; (b) wallstones on the downstream side.

From the results presented above, it was determined that case 2 overestimated the actual damage.
（4）Results: Case 3
Fig. 18 shows the displacement histor y forthe top wall stones in the transverse direction (y).
These stones first moved during the foreshock,and moved further during the mainshock. However, none of these wall stones fell.
Fig. 19 shows the contour of the residual

Fig. 19 Residual displacement of wall stones inthe transverse direction (case 3).

displacement for the wall stones in the transverse

cm on the downstream side. The displacement

direction at 50 s. If we focus on the top part of aof approximately 15 cm shown in Fig. 2(b) was

bridge, displacement cannot be seen at the archmeasured on October 20, 2016. Thus, intuition sug-crown but rather between the arch support and thegests that the wall stones moved not only because

bridge deck edge. This tendency is in good agree-of the foreshock and mainshock, but also because

ment with the actual situation shown in Fig. 2(b).

of the earthquakes between the foreshock and the

The largest displacement determined by numericalmainshock and aftershocks that occurred before

analysis was 8 cm on the upstream side and 10

October 20, 2016. Additionally, the final displace-

18

Investigation of the Tsujun Bridge damage mechanism during the 2016 Kumamoto earthquake

ment reached up to 15 cm. Therefore, the displace-tive displacement between the 4th and 5th columns

ments of 8 cm and 10 cm were smaller than theon the interior side. The residual relative displace-

actual displacement (approximately 15 cm) shown

ment was smaller than 1 cm at all locations on thein Fig. 2(b).

inner side. This means that the relative displace-

Next, the relative displacement of the adjacentment of the soil on the inner side was smaller thansoil elements between the 2nd and 3rd columns andthat of the soil on the outer side. This tendency is

between the 4 and 5 columns on the upstream

in good agreement with the actual situation, where-side is shown in Fig. 20. First, we consideredin cracks occurred in the soil on the outer side, as

the relative displacement between the 2

shown in Fig. 2(c).

th

th

nd

and 3

rd

columns, which occurred on the outer side. The
large relative displacement in the soils occurred（5）Discussion

from row A to row E and from row K to row O.

We found that the analytical results of case 3,

These correspond to the location between the archwhich used estimated ground motion 2 as input,

support and the bridge deck edge and are in good

had the best agreement with the actual situationagreement with the actual locations of crack oc-

amongst all three cases. Case 1 using the observed

currence shown in Fig. 2(c). The residual relative

motion as input, and case 2 using estimated grounddisplacement was approximately 1-3 cm, with the

motion 1 as input both overestimated the damage.

exception of row B. Then, we considered the rela-In the next section, we will discuss why case 3 wasable to simulate the actual situation.
5. 3

Influence of input ground motion frequency characteristics（1）Overview
Amongst cases 1-3, the analytical results ofcase 3 (estimated ground motion 2) are in good
agreement with the actual situation, whereas case(a)1 (observed ground motion) and case 2 (estimatedground motion 1) overestimated the damage. Because the PGAs of case 1 and case 2 were larger
than those of case 3, as shown in Table 7, intuition suggests that the damage caused by case 1
and case 2 was larger than that caused by case 3.
However, the frequency characteristics of the input
ground motion also affect the results.
In this section, the ef fect of the frequency
characteristics of the input ground motion are(b)Fig. 20 Relative displacement between adjacentsoil elements (case 3): (a) relative
displacement between columns 2 and3; (b) relative displacement between
columns 4 and 5.

discussed. Additional analytical cases are presented in Table 8. In case 4, the PGA of the groundmotion observed in the y-direction was modified
to 207 gal. In case 5, the PGA of estimated groundmotion 1 in the y-direction was modiﬁed to 207 gal.

19

自然災害科学 J. JSNDS 38 特別号（2019 ）The amplitudes in the three directions were scaled

23 and 24.

down using the same scaling factor. For cases 3-5,

Figs. 21 and 23 show the displacement of

the effects of the difference in the frequency char-

the top wall stones in the transverse direction (y).

acteristics of the input ground motion on seismic

In both cases, one top wall stone fell at the archbehavior are compared.

crown (stone of row I on the downstream side forcase 4; stone of row J on the upstream side for case（2）Results

5).

The results of case 4 are presented in Figs. 21

Figs. 22 and 24 show the residual displace-and 22, while those of case 5 are presented in Figs.
Table 8 Analysis cases to investigate the effectof frequency characteristics of input
ground motion.
Case

Input ground motion

PGA(y-direction)

Case 3

Estimated ground motion 2

207 gal

Case 4

Amplitude-modiﬁed observed
ground motion

207 gal

Case 5

Amplitude-modiﬁed estimatedground motion 1

207 gal(a)Fig. 22 Residual displacement of wall stones inthe transverse direction (case 4).

(a)

(b)

(b)

Fig. 21 Displacement of top wall stones in thetransverse direction (case 4): (a) wallstones on the upstream side; (b) wallstones on the downstream side.

Fig. 23 Displacement of top wall stones in thetransverse direction (case 5): (a) wallstones on the upstream side; (b) wallstones on the downstream side.

20

Investigation of the Tsujun Bridge damage mechanism during the 2016 Kumamoto earthquake

point 1 (arch crown) had a larger amplitude thanpoint 2 (mid-point between the arch crown andthe bridge deck edge) at 3.5-9.0 Hz, where theobser ved ground motion and estimated groundmotion 1 had a larger amplitude than estimatedground motion 2. Conversely, as shown in Fig.
4(b), point 2 had a larger amplitude than point 1 at
approximately 10 Hz where estimated ground moFig. 24 Residual displacement of wall stones inthe transverse direction (case 5).

tion 2 was dominant. Therefore, the displacement
at the arch crown was maximum for the observed
ground motion and estimated ground motion

ment contour for the wall stones in the y-direction

1, while the area between the arch support andafter the mainshock (50 s). In both cases, the dis-bridge deck edge increased for estimated groundplacement of the wall stones was maximum above

motion 2. Therefore, the analytical results using

the arch, which is different from the actual situa-

estimated ground motion 2 (case 3) are in goodtion. The movement of the wall stones occurred inagreement with the actual damage.

an area wider than that in case 3 (Fig. 19).
5. 4 Seismic performance investigation for（3）Discussion
Cases 4 and 5 had the same PGA as that of

Tsujun Bridge（1）Overview

case 3 in the y-direction. However, the top wall

In this section, we describe the seismic perfor-stone above the arch fell. Moreover, the displace-

mance evaluation of Tsujun Bridge using incremen-ment of the wall stones was maximum above thetal dynamic analysis (IDA) (Vamvatsikos, 2002).

arch, and could not simulate the actual damage that

Two seismic performances were considered. The

occurred between the arch support and the bridgeﬁrst one is that wall stones do not fall. The second

deck edge. This can be explained by comparing theone is that the arch system does not collapse. Wa-

Fourier spectra of the microtremors observed at

ter leakage occurrence is also an important seis-

the bridge (Fig. 4) and the Fourier spectra of themic performance, but we did not consider it since

input ground motion (Fig. 8). The input ground

it is difﬁcult to estimate using the current reﬁned

motion of case 3 (estimated ground motion 2) had

DEM. The seismic performance was evaluated bya smaller amplitude at 3.5-9.0 Hz and a larger am-

the PGA of the input ground motion up to which

plitude at approximately 10 Hz, in comparison withperformance is guaranteed. We generated a suitethe other input ground motions (observed groundof ground motions by multiplying the scale factor

motion and estimated ground motion 1). This isby the amplitudes of estimated ground motion 2,

because estimated ground motion 2 was modiﬁed

whose PGA was 207 gal. The same scale factor wasby using the H/V spectral ratios shown in Fig. 6.

used for all three directions.

Microtremors were obser ved at point 1 andTo investigate the performance with no wall

point 2 at the bridge. Point 1 is at the arch crownstones falling, we generated input ground motions

and corresponds to row H. Point 2 is a mid-point

whose PGA in the y-direction was 220 gal, 240 gal,

between the arch crown and the bridge deck edge

260 gal, and 280 gal.

and corresponds to row L. As shown in Fig. 4(b),To investigate the performance with the arch

21

自然災害科学 J. JSNDS 38 特別号（2019 ）system not collapsing, we generated input groundof estimated motion 2, which is equal to 207 gal.

motions whose PGA in the y-direction was 300 gal,

Therefore, the analysis result suggests that Tsujun

400 gal, 500 gal, 600 gal, 700 gal, 800 gal, 900 gal,

Bridge had a large allowance against collapse of

1,000 gal, and 1,100 gal.

the arch system.

（2）Results

6. Conclusion

The wall stones did not fall under 260 gal;In this study, the damage mechanism of Tsu-

however, the top wall stone of C1 on the upstream

jun Bridge during the Kumamoto earthquake wasside fell at 280 gal, as shown in Fig. 25. Note thatinvestigated by numerical analysis using the re-

280 gal is approximately 1.35 times the PGA of

ﬁned DEM.

estimated motion 2, which is equal to 207 gal.

First, the natural frequencies of Tsujun Bridge

Therefore, the analysis result indicates that Tsujun

and the side ground were obtained by microtremor

Bridge did not have a large allowance against theobservation. Then, a numerical model was devel-

falling wall stones.

oped such that the analytical natural frequencies of

The arch system of Tsujun Bridge did notcollapse under 1,000 gal; however, the arch system

the bridge and the side ground were in agreementwith those obtained by microtremor observation.

collapsed at 1,100 gal, as shown in Fig. 26. Note

Next, the H/V spectral ratios were obtainedthat 1,100 gal is approximately 5.3 times the PGA

at the base ground surface of Tsujun Bridge andat K-NET YABE. Because the H/V spectral ratios
were different at each site, it was found that the
ground motion at Tsujun Bridge was dif ferent
from the obser ved ground motion at K-NET
YABE. Therefore, the ground motions at Tsujun
Bridge were estimated using two methods. The
first method was to use the bedrock ground motion at K-NET YABE as the input ground motion
for Tsujun Bridge, assuming that the bridge wasFig. 25 Residual displacement of wall stones inthe transverse direction (280 gal).

(a)Fig. 26

constructed on the bedrock. This ground motion
was termed estimated ground motion 1. The(b)

Collapse of arch systems (1,100 gal): (a) front view; (b) view from above.

22

Investigation of the Tsujun Bridge damage mechanism during the 2016 Kumamoto earthquake

bedrock ground motion was estimated by multi-

bridge is our future work. In this study, only theple-reﬂection analysis. The second method was toeffects of the foreshock and aftershock were con-modify the observed ground motion at the surface

sidered, and the effects of the other aftershocksof K-NET YABE using the H/V spectral ratios atwere not considered. In future works, we would

the two sites. This motion was termed estimatedlike to consider the effects of other aftershocks

ground motion 2.

on the failure behavior of Tsujun Bridge. Further-

Subsequently, seismic response analysis

more, we would like to conduct a numerical anal-

was conducted by inputting the ground motion

ysis based on the actual material properties andobserved at K-NET YABE and the two estimatedstrength values evaluated by the experiment using

ground motions into the developed numericalactual materials.

model. The damage simulated by inputting the observed ground motion and estimated ground mo-

Acknowledgmentstion 1 overestimated the actual damage. Converse-

We would like to express our sincere appre-ly, the damage simulated by inputting estimatedciation to Ms. Kyoko Otsuyama and the Board ofground motion 2 was in good agreement with the

Education, Yamato Town, Kumamoto Prefecture.

actual damage. In the actual situation, wall stones

Additionally, we thank Professor Kazuyuki Izuno

did not fall and the observed damage did not occur

from Ritsumeikan University for providing us withat the arch crown but rather between the arch sup-useful information. The K-NET strong-groundport and the bridge deck edge. Damage was not

motion record was used in this study. Part of theobserved between the arch support and the bridge

present work was supported by the Japan Society

deck edge because estimated ground motion 2 wasfor the Promotion of Science (JSPS) grant-in-aid

dominant at a high frequency of approximately 10(17H01287 and 18K04323). This support is greatly

Hz, where the vibration between the arch support

appreciated.

and the bridge deck edge was dominant in comparison with the arch crown.
Finally, the seismic performance of Tsujun
Bridge was investigated based on the critical
PGAs, where the wall stones fall and the archsystem collapses. Thus, it was found that the wallstones fall when the ground motion is 1.35 times aslarge as estimated ground motion 2. Additionally,
it was found that the arch system collapses when
the ground motion is approximately 5.3 times aslarge as estimated ground motion 2. Thus, the archsystem of Tsujun Bridge was found to have hadsatisfactory seismic performance against the Kumamoto earthquake.
This research introduced a methodology to
explain the damage occurrence mechanism of astone bridge due to earthquakes. The proposal of aseismic reinforcement method suitable for a stone

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（投 稿 受 理：2019年 3 月 1 日
訂正稿受理：2019年 7 月 3 日）

旨2016年熊本地震により，熊本県山都町に位置する重要文化財「通潤橋」には，壁石のはらみ出し，
盛土の亀裂，通水管からの漏水などの被害が発生した。壁石のはらみ出しは最大15 cm 程度で，その発生位置はアーチ中央部ではなくアーチ端部と橋端部の間であった。本研究では，まず，微動計測により通潤橋と周辺地盤の振動特性を明らかにした。次に，通潤橋と近傍の強震観測
点での地盤の卓越周期が大きく異なることから，通潤橋地点の地震動を推定した。 続いて，微動計測により明らかにした固有振動数に一致するように通潤橋の解析モデルを作成し，地震応
答解析を行った。その結果，観測地震動を入力したときはアーチ中央部が破壊したのに対し，
推定地震動を入力したときはアーチ端部と橋端部の間で壁石のはらみ出しが大きくなり，実被害を良好に再現することができた。