Accumulative response of large offshore steel bridge under severe earthquake and ship impact due to earthquake-induced tsunami flow

Engineering Structures 134 (2017) 190–204

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Accumulative response of large offshore steel bridge under severe earthquake and ship impact due to earthquake-induced tsunami flow Lan Kang a,c, Kazuya Magoshi b,c, Hanbin Ge d,⇑, Testuya Nonaka e a

School of Civil Engineering and Transportation, South China University of Technology, Guangzhou 510640, China Seismic Analysis Research Inc., Nagoya 466-0059, Japan c Meijo University, Japan1 d Department of Civil Engineering, Meijo University, Nagoya 468-8502, Japan e Department of Civil Engineering, Nagoya Institute of Technology, Nagoya 466-8555, Japan b

a r t i c l e

i n f o

Article history: Received 21 March 2016 Revised 21 October 2016 Accepted 23 December 2016

Keywords: Tsunami propagation analysis Drifting object Impact analysis Seismic response analysis Accumulative response

a b s t r a c t During the 2011 Great East Japan earthquake occurring at the north-east pacific region, serious secondary disasters caused by collision of drifting containers or ships occurred in various structures when tsunami came. Disaster deterioration caused by earthquake and drifting object impact during earthquake and tsunami has become another problem. This study presents an effective method to evaluate the accumulative response of steel bridge under earthquake and large drifting object impact due to tsunami flow, and the earthquake and tsunami come from the same fault motion. The main innovation has to do with the quantification of the earthquake effect and the ship-impact effect due to earthquake-induced tsunami directly into ductility demands, a phenomenon which has not been studied in the past. A series of seismic response analysis and impact analysis are carried out, and damage to the main tower of bridge is evaluated by means of elastic-plastic finite element analysis. This study shows that piers of main tower of bridge can be severely damaged due to the earthquake and ship impact effect compared to only impact effect. An effective evaluated method that could be useful for evaluating damage of lifeline engineering under such mega earthquake and tsunami is proposed. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction Previous studies on the behavior of reinforce concrete (RC) columns due to impact loads have been mainly in the area of vehicle impact on RC columns [1,2] and barge impact on bridge piers and offshore platforms [3,4]. During the 2011 Great East Japan earthquake occurring at the north-east pacific region, except for damaging coast facilities, flushing away bridges and inundating buildings, serious secondary disasters caused by collision of drifting containers or ships occurred in various structures when tsunami came [5– 9]. Tsunami reconnaissance surveys have reported that buildings, bridges, and other coastal infrastructure were damaged or had completely collapsed due to wave forces, scouring, and impact of massive objects carried by the tsunami flow [6]. Several large ships and fishing boats which were moored in ports drifted onto land as the area became inundated [6]. An effective method for evaluating drifting object collisions with large steel bridges due to tsunami

⇑ Corresponding author. 1

E-mail address: [email protected] (H. Ge). Formerly.

http://dx.doi.org/10.1016/j.engstruct.2016.12.047 0141-0296/Ó 2016 Elsevier Ltd. All rights reserved.

flow was proposed in our previous study to investigate the impact behavior of a steel bridge subjected to large ship impact due to tsunami [10]. In the authors’ previous investigation [10], it is assumed that a large drifting ship collides with a long-span bridge in the gulf line during a tsunami, and tsunami propagation analysis and nonlinear dynamic finite element analyses of the whole bridge during collision are performed. Based on the collision force calculations, an approximate analytical method using elastic-plastic solid element model is proposed, and the maximum mass of drifting object which can result in the collapse of the whole bridge structure is calculated using this method. Meanwhile, the damage to the impacted pier is assessed. The technical specification for roads and bridges – Part V: earthquake-resistant design was revised on the March 2012 [11], in which the corresponding provisions about tsunami were added based on the devastating disasters to structures in a large area in east Japan due to the tsunami during the 2011 Great East Japan earthquake. The impact of waterborne shipping containers is one of the major threats to buildings located in the vicinity of industrial ports in tsunami inundation zones, and the similar observations have been reported in other references [5,6,12–15]. Besides, the

L. Kang et al. / Engineering Structures 134 (2017) 190–204

boundary of mega earthquake in the south ocean is changed, which assumes four earthquakes occur simultaneously, that is, Tokai earthquake in east ocean, Tonankai earthquake in southeast ocean, Nankai earthquake and Hyuganada earthquake in south ocean. The forecast of such great earthquake (four earthquakes occurring simultaneously) is based on the historical record and the fact that south ocean of Japan is at the boundary of the earth’s plates (Pacific plate and Eurasian plate). It is reported that great earthquakes frequently occurred here. Four earthquakes occurring simultaneously is the hypothesis that the seismic damage is maximized as a worst case. In addition, the acceleration response spectrum of this mega earthquake is amplified to 1.2–2.0 times. These revisions lead to a re-understanding ship-impact resistant design induced by earthquake-induced tsunami for the structures located in this area [16]. The previous study only focused on the behavior of bridge structures due to large drifting object impact loads during tsunami, however, the response of offshore bridges in the gulf line subjected to both mega earthquake and following tsunami has not been systematically studied in the past. The main objective of this study is to evaluate the damage of an offshore long-span steel bridge induced by both earthquake and following large ship impact due to tsunami flow, in which such two actions come from the same fault movement. Tsunami wave pressure on bridge is not taken into account because the response of bridge subjected to tsunami wave pressure is greatly smaller than that of bridge subjected to earthquake force and impart force [17]. In which, two cases are taken into account. One of them is that the tsunami waves inundate caisson surface, and the other one case is that the tsunami waves do not inundate caisson surface. The response of bridge in the two cases are very small and can be neglected [17]. Seismic analysis of this steel bridge subjected to such mega earthquake and impact analysis of it subjected to large ship impact due to tsunami flow are carried out using nonlinear finite element code SeanFEM (ver.1.22). In this study, the response of the offshore bridge under such actions including earthquake and ship impact induced by earthquake-induced tsunami is called as the accumulative response including earthquake response and impact response due to earthquake-induced tsunami. The damage of this offshore bridge includes the damage resulted from earthquake and the damage due to large drifting object impact during tsunami. Such damage is named as the accumulative damage. Both the earthquake and the ship impact due to tsunami are considered in this study. 2. Evaluation procedure The evaluation procedure for complex numerical simulation of the whole steel bridge subjected to both mega earthquake and large drifting object impact loading during tsunami induced by earthquake from the focal fault to the bridge position is stated as follows (as shown in Fig. 1).

(c)

(d)

(e)

(f)

(g)

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simultaneously, that is, Tokai earthquake in east ocean, Tonankai earthquake in southeast ocean, Nankai earthquake and Hyuganada earthquake in south ocean (Mw = 9.0, Mw here means moment magnitude) [18]. The flow direction and velocity are obtained by tsunami propagation analysis, and then the impact direction and velocity of large drifting object, which collides with the long-span bridge, are obtained. The impact load on the main tower of bridge induced by the large ship collision is adopted as a wave-form force. The wave form of impact force on the steel bridge pier is determined to be normal distribution, and the maximum value occurs at the half of the impact time. The maximum impact force on the pier is assumed to be equal to the ultimate bearing capacity of the main tower, and the maximum ship mass can be obtained based on the maximum impact force. Based on the above assumed seismic source model in the step (b), the simulation of short-period ground motions is performed using the empirical Green’s function, longperiod ground motions from source faults are deterministically calculated using the 3D finite-difference method. The seismic wave under such ground motions is inversed using equivalent linear method (SHAKE). The fiber model [19,20], which is commonly used in the seismic analysis of bridge structures, is adopted considering material nonlinearity. The nonlinear seismic wave is input based on the above step (e). Based on the damaged state caused by the earthquake, the impact analysis (elastic-plastic finite element analysis) is performed by inputting the impact force wave.

For the impact analysis, there are four important factors: impact velocity, impact direction, impact force and impact time. The impact direction in the step (c) can be determined using the result of tsunami propagation analysis, besides, the value of impact force on the steel bridge pier varies with the mass of large drifting ship and the impact time, which are based on the following ultimate assumptions. In which, the maximum value of impact force wave is assumed to be equal to the ultimate bearing capacity of the main tower in this study. A pushover analysis (static elastic-plastic finite element analysis) is conducted in displacement control in order to obtain the ultimate bearing capacity of collided member by applying the lateral impact load. The ultimate bearing capacity and ultimate displacement, which are used to determine the peak impact force wave, can be obtained through this pushover analysis. Besides, all of strain, stress states, displacements and damages of the whole bridge induced by earthquake before the ship impact due to tsunami flow are considered to be initial conditions during the impact analysis.

3. Impact velocity and direction of drifting objective (a) Bridge adopted in the analyses is shown in Fig. 2, which is a 1000 m long (250 + 500 + 250) long-span cable-stayed bridge and is assumed to be built in the east gulf coast of Osaka Gulf where many large ships go in and out every day. The distance between ship nose and ocean surface is 11.3 m. The distance between ocean surface and bridge tower base surface is 1 m, however, it becomes 2.7 m when tsunami comes. Consequently, the large ship nose hits the position of bridge pier 13 m away from the bridge base. (b) Tsunami propagation analyses are conducted by employing tsunami wave source model proposed by the investigation committee on models of strong earthquakes at south ocean trench, which assumes four earthquakes occur

3.1. Tsunami propagation analysis 3.1.1. Analytical conditions Tsunami propagation analyses are conducted by employing tsunami wave source model proposed by the investigation committee on models of strong earthquakes at south ocean trench, which assumes four earthquakes occur simultaneously, that is, Tokai earthquake in east ocean, Tonankai earthquake in southeast ocean, Nankai earthquake and Hyuganada earthquake in south ocean (Mw = 9.0) [18]. The fault parameters and magnitude scale of the above assumed four earthquakes occurring simultaneously are listed in Table 1.

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Seismogenic fault assumption: strong earthquakes at south ocean trench, which assumes four earthquakes occur simultaneously

Ground motion synthesis by broadband hybrid method

Tsunami propagation analysis using nonlinear long wave theory

Ground wave

Flow direction and velocity at the analytical bridge position

Obtain ground surface wave by equivalent linear method (SHAKE)

Elastic-plastic finite element analysis of the analytical bridge

Ground surface wave

Ultimate bearing capacity and displacement of the analytical bridge

Seismic wave input Seismic analysis of a large-span offshore steel bridge

Maximum impact force of large drifting object obtained from the ultimate bearing capacity

Stress state after mega earthquake

Impact force wave Impact direction Impact velocity

It is considered as initial conditions

Numerical analysis of large-span offshore steel bridge subjected to impact force due to large drifting object during tsunami

Evaluation of steel bridge under earthquake and ship impact due to earthquake-induced tsunami during extreme disaster Fig. 1. The flowchart of damage evaluation for long-span offshore steel bridge subjected to actions including earthquake and following ship impact due to earthquakeinduced tsunami flow.

Association and Geospatial Information Authority of Japan, and the data between meshes can be obtained by interpolation. Manning’s friction coefficient of sea bottom is 0.025. The tsunami propagation analyses are carried out according to the assumed wave source model, water level changes of ocean surface which are ocean bottom ground changes calculated by the Mansinha and Smylie method [21], two-dimensional shallow water-flow model and differential method-based nonlinear long-wave theory. The interval of analytical time is 0.1 s, and the analytical time is 6 h from earthquake occurrence. In addition, mean half-monthly rising tide level of water close to the bridge during typhoon season T.P. +0.9 m (O.P. +2.20 m) is taken into account.

(Unit: m) Fig. 2. The layout of the steel long-span cable-stayed bridge.

The tsunami propagation analytical conditions are listed in Table 2, six analytical regions A-F are shown in Fig. 3, and the assumed bridge is located in Osaka Gulf. The analytical region takes Osaka Gulf as center and the nested mesh model is to gradually connect 6-steps mesh model with minimum intervals of 10 m. All of terrain data is provided by Japan Hydrographic

3.1.2. Analytical results Shown in Fig. 4 are contour colors indicate uplift and subsidence of the ocean surface, when the earthquake happens and 30 min after the earthquake, calculated by the wave source model. 30 min later, tsunami reaches Osaka Gulf from the Pacific Ocean though Kiisuido Channel. Because the location of the evaluated bridge is inside the gulf and the tsunami reflects from the complex

Table 1 Assumed mega earthquake fault parameters and earthquake magnitude scale. Earthquake type

Fault position

Fault length L (km)

Fault width W (km)

Fault area S (km2)

Moment magnitude Mw

Strong earthquakes at south ocean trench

Tokai earthquake Tonankai earthquake Nankai earthquake North South

115 174 295 64 75

82 91 125 48 54

9400 15,800 37,000 3082 4079

8.2 8.4 8.8 7.7 7.8

Hyuganada earthquake Four earthquakes occurring simultaneously

9.0

L. Kang et al. / Engineering Structures 134 (2017) 190–204 Table 2 Tsunami propagation conditions. Item

Content

Calculated mesh size

Area A 2430 m (510
300) Area B 810 m (417
300) Area C 270 m (408
327) Area D 90 m (471
336) Area E 30 m (363
237) Area F 10 m (624
426) Nonlinear long wave theory Area A is free The level and flow of other areas are continuous Manning roughness factor: 0.025 Non-reflecting boundary conditions for all mesh models

Base equation Marine boundary conditions Seabed friction Land boundary conditions Initial wave shape Terrain data

Tidal conditions Calculated interval time Calculated duration time

Mansinha and Smylie ETOPO2a, MIRC-JTOPO30b, Seabed terrain data M7000c, Terrain data download from Geographical Survey Institute of Japand T.P. +0.9 m 0.1 s 6 h after earthquake occurring

a

1. NOAA National Geophysical Data Center. 2. Japan, MIRC JTOP030(Copyright(c) Marine Information Research Center, Japan Hydrographic Association). c 3. Japan Hydrographic Association coastal, contour line data. d 4. Geographical Survey Institute of Japan, information. b

geographical shapes, wave height distribution is very difficult to be determined.

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to right is positive, and the north direction is regarded as 0°. The first wave arrives at the bridge approximately 90 min after earthquake and the maximum tsunami height was recorded as 2.702 m 114 min later (as shown in Fig. 6(a)), the resultant flow velocity reaches to 1.14 m/s 109 min later (as illustrated in Fig. 6 (b)), and at the moment of 109 min, the flow direction is 30.7°. It is assumed that the bridge is built in the direction of 150°, so the impact direction with large ship is 60.7° relative to the bridge (as shown in Fig. 7). The wave height, impact direction and impact velocity are obtained based on the results of tsunami propagation analysis in the reference [10] and the bridge location. This is the worst-case scenario of bridge at this location under such earthquake and earthquake-induced tsunami. The maximum tsunami height of Konohana-ku in Osaka city is 4 m based on the latest report published in Central Disaster Prevention Meeting, which was held on August 29th, 2012. It is noted that the maximum tsunami height near the bridge calculated in this tsunami propagation analysis is about 1.3 m less than that published in the above report. The main reason is that the bridge position is different to the location recorded in the above report. When the tsunami height of recorded position in the above report of Central Disaster Prevention Meeting is about 3.5 m, tsunami arrival time is 90–120 min. The corresponding tsunami height of the steel bridge position is simulated to be 1 m in the tsunami propagation analysis of this study, when the tsunami arrival time is 114 min. Consequently, the assumed tsunami disaster in the tsunami propagation analysis of this study covers the disaster assumption of Central Disaster Prevention Meeting.

4. Impact force wave used in ship-impact analysis 3.2. Impact direction and velocity of drifting object 4.1. Drifting ship impact force model Referring to Fig. 5, the contour map of water level change in Osaka Gulf and the horizontal vector diagram of current velocity near the bridge at the maximum flow are illustrated. The histories of tsunami height, resultant flow velocity and flow direction near the bridge are illustrated in Fig. 6. Here, the north direction turning

The impact load on the pier of main tower of bridge induced by the large ship collision is adopted as wave-form force in the following finite element analysis. If the large ship is completely stopped due to the collision, the kinetic energy of the striking ship is equal

Area A Area B

Area E

Area C

Area F Area D

Evaluated bridge

Fig. 3. Analytical regions of tsunami propagation analysis.

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(a) Just after the earthquake

(b) 30 minutes after the earthquake

Fig. 4. The contour map of water level change.

Fig. 5. The contour map of water level change in Osaka Gulf and the horizontal vector diagram of flow velocity near the evaluated bridge at maximum flow.

to the elastic-plastic absorbed energy by the main tower of bridge. The wave form of impact force is very complex, and some simplified assumptions are developed for practical engineering application [22]. Many impact force profiles are proposed as shown in Fig. 8. Based on some impact experimental results [6,23,24], the impact histories in these tests are more like a normal distribution shape, as demonstrated in Fig. 8. The wave form of impact force are determined to be normal distribution, and the maximum value occurs at the half of the collision time dt. The integral of the kinetic energy of the striking ship during the collision time dt is equal to 99.73% of the whole collision energy, and 3r (r is standard error) is equal to half of the collision time dt. By employing the mass of the large ship m and the velocity v calculated by tsunami simulation, the wave form equation of ship impact force F(t), as a function of time t, can be expressed as follows:

ðtlÞ2 mv  FðtÞ ¼ pffiffiffiffiffiffiffi  e 2r 2 2p  r

l¼ r¼

dt 2

l 3

ð1aÞ

ð1bÞ ð1cÞ

In which, l is a mean value. The maximum value Fmax of the force wave form F(t) occurs when t = l, therefore:

mv F max ¼ pffiffiffiffiffiffiffi 2p  r

ð2Þ

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dt 0 ¼

The peak impact force is related to the mass of large drifting object based on Eq. (2), and the maximum mass can be obtained

Based on Eq. (3), the collision time is calculated to be dt0 = 2.46 s.

(m)

4.2. Ultimate bearing capacity of collided member and impact force wave

Tsunami height

The force out of the impact time is equal to zero and the force during the impact time is assumed to be a normal distributed force. The total time of force wave is 10.0 s, and 1.0 s of zero force exists before the impact of drifting large ship.

if the maximum peak impact force is identified. Because this impact is a low velocity impact (impact velocity less than 10 m/ s), the response of low velocity impact is assumed to be same to the quasi-static response [24–26]. The impact velocity of this study is 1.1 m/s (less than 10 m/s), and for such low velocity impact, the maximum mass of large drifting object depends on the ultimate bearing capacity of collided member obtained from pushover analysis. In other words, it is assumed that the ultimate bearing capacity of collided member is equal to the maximum value of peak impact force, and the impact force larger than the ultimate bearing capacity of collided member will not appear forever. Once the ultimate bearing capacity of collided member is obtained by pushover analysis, the maximum mass of drifting object can be calculated through the above assumption. This assumption may be very simple, and needs to be verified by experimental investigations in the future. Elastic-plastic finite element model including shell and beam elements as shown in Fig. 9(a) is adopted to calculate the ultimate bearing capacity of main tower of bridge. The impact direction is obtained from the above tsunami propagation analysis. Detailed analytical model and numerical method have been stated in the previous reference [10]. Based on the above pushover analysis, the Mises stress distribution when reaching to the ultimate bearing capacity is illustrated in Fig. 9(b). As shown in the load-displacement curve of pushover analysis (Fig. 10), the ultimate bearing capacity Pm = 163,157 kN, the displacement at the ultimate bearing capacity dm = 676 mm. It is assumed that both the collision object and collided object have the same deformation induced by local buckling, and they have the same linear motion with constant acceleration from collision to complete stop. Thus, the collision time can be determined by employing the displacement dm at the maximum load obtained from pushover analysis and the velocity v obtained from tsunami simulation:

hmax = 2.702 m [114.0 min]

4.0 3.0 2.0 1.0 0.0 -1.0

t (min) 0

60

120

240

300

360

vmax =1.14m/s [109.0 min]

2.0 Flow Speed (m/s)

180

1.0 0.0

t (min)

-1.0 -2.0 0

60

120

Flow Direction ()

360

180

=30.7

240

300

360

[109.0 min]

240 120

t (min) 0 0

60

120

180

240

300

360

Fig. 6. The response histories of tsunami near the bridge.

2d

v

¼

4dm

ð3Þ

v

30.7°

150° 60.7°

Evaluated bridge

Large ship

Large ship

Impact position 13m

Fig. 7. The location and direction of drifting ship collision.

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L. Kang et al. / Engineering Structures 134 (2017) 190–204

Mountain wave

Rectangular wave Pulse distribution

Half sine distribution

Trapezoid distribution

Normal distribution Logarithmic normal distribution

F

F Fmax

A normal distribuon

Fmax Area=Impulse

Area=Impulse dt

dt

Ship impact force –time history

Fig. 8. Determination of ship impact force profile.

( σy = 450MPa) σ σy

a

Scale : 2 (a) Analytical model

(b) Mises stress distribution

Fig. 9. The finite element model and the Mises stress distribution at the maximum bearing capacity of collided member.

In addition, supposing Fmax = Pm, the mass M of largest drifting object, which is determined based on the ultimate bearing load

250

P (x1000kN)

M¼

Pm =163,157kN [ 676mm] Pu =140,599kN [ 1678mm]

200 150

P

100 50 δ

140 mm

0 0

500

1000

1500

of the collided member, can be calculated through Eq. (4) as the following equation:

(mm) 2000

Fig. 10. Load-displacement curve of the pushover analysis.

pffiffiffiffiffiffiffi 2p  r

v

 F max

pffiffiffiffiffiffiffi 2 2p dm  Pm ¼  v2 3

ð4Þ

Based on Eq. (4), the maximum mass of drifting object M = 152.4
106 kg is obtained. The drifting object is a large-scale petroleum tanker which is approximately 270 m long (Suezmax). Depending on the above analysis and calculation, the force wave form is obtained as illustrated in Fig. 11, and the parameters of impact force wave form are listed in Table 3. 5. Surface ground motion response spectrum and seismic response analysis The damage, strain and stress states of structures due to mega earthquake are considered as the initial conditions or states to

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L. Kang et al. / Engineering Structures 134 (2017) 190–204

Fmax = 163,157kN [2. 23 s]

F (x1000kN)

200

100

Engineering E ineeeerin Engine ng ground 0.4
50 0

Surface ground

Surface ground

150

t (s) 0

2

4

6

8

Deep ground

10

Fig. 11. Force wave form Fm(t) (M = 152.4
106 kg, dt0 = 2.46 s).

Earthquake ground rthquake thqua quakee groun roun o Vs>3 km/s

Seismogenic fault

Table 3 Parameters of impact force wave form.

Upper crust

Name

Variable

Unit

Value

Ultimate bearing capacity Displacement at ultimate bearing capacity Distance until stopping Impact velocity Weight Mass Impact time Mean value Standard deviation Variance Maximum impact force Duration time of force wave Time at maximum impact force

Pm dm d v W M dt0

kN m m m/s t kg s s – – kN s s

163,157 0.676 1.353 1.1 152,395 152,395,129 2.46 1.23 0.410 0.168 163,157 10.00 2.23

l r r2 Fmax T t

input into impact analysis. Analytical model is elastic-plastic nonlinear finite element model, before impact analysis, seismic response analysis is conducted to obtain the first damage, namely, earthquake damage (or seismic damage). 5.1. Ground motion synthesis using hybrid method Strong earthquake evaluation methods are divided into theoretical method, empirical method, semi-empirical method and so on [27]. In order to improve earthquake prediction accuracy, shortperiod ground motions are synthesized by statistical analysis using semi-empirical green function method [28], and a theory stiffnessmatrix method is employed to synthesize long-period ground motion. In another word, a broadband hybrid method is applied to synthesizing ground motion in this research. Based on the ground surface motion obtained, seismic wave is calculated by equivalent linear method (SHAKE) [29]. Fig. 12 illustrates the ground model in this study and the surface ground model is listed in Table 4. Only SH wave is considered, and the effects of water saturation and water layer on ground motions are not taken into account in this study. The flowchart for this simulation procedure is stated in Fig. 13. 5.1.1. Short-period ground motion wave (statistical semi-empirical green function method) Short-period component of ground motion wave propagation is easy to be affected by non-uniform feature of propagation medium, and so it is difficult to be recorded by using empirical Green’s function method during mid-small earthquake. In this study, statistical semi-empirical green function method improves the calculation accuracy of earthquake wave. In details, the acceleration response spectrum less than 1 s can refer to the previous research, pulse time of fault parameters [30], fracture propagation velocity [31] and random phase angle [32] are respectively selected to parameters. For example, 5 pulse times of fault parameters (0.67 times, 0.83 times, 1.0 times, 1.17 times and 1.33 times of mean pulse time); six fracture propagation velocity (0.72 km/s, 0.756 km/s, 0.792 km/s, 0.828 km/s, 0.864 km/s, 0.9 km/s), 10 random phase

Fig. 12. Ground model.

Table 4 Surface ground model. Depth D (m)

Velocity of S wave Vs (m/s)

Density q (tf/m3)

0–10 10–17 17–37 37–50 50

110 190 225 320 400

1.60 1.65 1.65 1.70 1.80

Short-period ground motion wave obtained by statistical semiempirical green function method

Long-period ground motion wave obtained by stiffness-matrix method

Ground motion synthesis using hybrid method Ground surface response spectrum synthesized using equivalent linear method (SHAKE) Fig. 13. Surface ground motion response spectrum synthesis.

angles (0–2p), total 300 acceleration response spectrums are obtained by changing these parameters. The acceleration response spectrum of seismic wave should be the one which is equal to the average acceleration response spectrum of 300 those plus 2r (r: standard deviation). The average acceleration response spectrum, average acceleration response spectrum plus r, and average acceleration response spectrum plus 2r are shown in Fig. 14. 5.1.2. Long-period ground motion wave (stiffness-matrix method) For long-period ground motion wave, the theoretical stiffnessmatrix method is based on kinematic fault model and horizontal layered medium model to synthesize ground motion wave. The wave equation of this method is related to earthquake focus features, propagation path characteristics and discrete frequency. This theoretical method has an advantage that it is more easily employed than other numerical methods. In this study, the acceleration response spectrum more than 1 s is obtained by this method. 5.1.3. Full-period synthetic ground motion wave (hybrid method) A hybrid method for synthesizing ground motion wave in fullperiod is employed. In which, the short-period ground motion

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short-period ground motion wave. Finally, the surface ground motion response spectrum under such ground motion waves is synthesized using equivalent linear method (SHAKE).

Acceleration response spectrum (gal)

Average

5.2. Seismic response analysis

Period (s) Fig. 14. Acceleration response spectrum of short-period ground motion wave.

wave is calculated by function method, and obtained by the [16,29,33,34]. For the 1.0–1.2 s, filtration is

using the statistical semi-empirical green the long-period ground motion wave is theoretical stiffness-matrix method long-period ground motion wave during employed to successfully connect with

5.2.1. Analytical model of whole steel cable-stayed bridge Shown in Fig. 15(a) is the finite element analytical model of the whole steel cable-stayed bridge, which mainly consists of elasticplastic fiber beam nonlinear element and tension-only cable element. The cross section of main tower in fiber beam element is illustrated in Fig. 15(b). The material model employed is a bilinear hardening elastic-plastic model, and plastic modulus is E/100 (E: elastic modulus). Multi-node cable element is employed to accurately predict deflection and tension force during strong earthquake and impact. Dead load and cable tension of each member are considered as initial stress state of the bridge. Analytical details can refer to references [10,19], as shown in Fig. 15(a), the longitudinal direction and transverse direction of the evaluated bridge are denoted as X and Y, respectively. 5.2.2. Eigenvalue analysis Based on the results of eigenvalue analysis, the mode shapes of evaluated bridge in the longitudinal and transverse directions are illustrated in Fig. 16. Natural vibration periods of evaluated bridge

Analytical frame model

Integral point M M Y

X M P1

P4

P3

M

P2 Cross section model

(a) Analytical finite element model

(b) Cross section of main tower

Fig. 15. Finite element analytical model of whole cable stayed bridge.

X

X Y

Y

(a) TX = 4.01s

(b) TY = 3.27s Fig. 16. Mode shapes of evaluated bridge.

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in the longitudinal and transverse directions are TX = 4.01 s and TY = 3.27 s, respectively. Meanwhile, the damping ratios corresponding to these mode shapes can be obtained. The selected number of mode shapes should depend on results of the seismic response analysis. 5.2.3. Input seismic wave and analytical conditions The NS and EW directions of input seismic wave calculated in Section 5.1 are shown in Fig. 17. The input directions of seismic wave are the longitudinal and transverse directions of evaluated bridge. The acceleration wave and acceleration response spectrum of input seismic wave in X and Y directions (damping ratio is 5%) are shown in Fig. 18. In the acceleration waveform, the maximum accelerations in the X and Y directions is 391.5 Gal and 335.3 Gal, the interval time between the two maximum accelerations is 20– 150 s. The acceleration values corresponding to natural vibration periods TX and TY is 190 Gal and 185 Gal, respectively. The input seismic waves consist of digital data with the same interval time 0.01 s. Besides, the input seismic wave include wave damping data with duration time of 300 s (5 min). In this study, 0.0 s of input seismic wave is earthquake occurrence time. Taking Tonankai earthquake as one example, the distance between the earthquake fault position and the evaluated bridge position is 160 km, the seis-

The longitudinal direction of bridge

Large ship

Fig. 17. Relationship between input direction of seismic wave and evaluated bridge.

mic wave arrives the evaluated bridge position after 20 s, when S wave velocity (Vs) is 3.8 km/s. Based on the tsunami propagation analytical results in Section 3.2, the occurrence time of drifting object impact is 109 min later. The duration time of seismic wave is 300 s (5 min), the evaluated bridge with damping ratio of 0.05 converges to zero before large drifting object-bridge impact. The duration time of seismic response analysis is taken as 600 s based on a pre-analysis in which the end of vibration due to earthquake was confirmed. Finite element software SeanFEM ver.1.22 is employed to conduct seismic response analysis, in which the Updated Lagrange method is utilized considering geometric nonlinearity and small strain.

5.2.4. Seismic response analysis The ground motions are assumed uniform at all the bridge supports. Multi-point earthquake excitations for long-span bridges may be investigated in the future because the purpose of this study is to evaluate the cumulative damage of steel bridge subjected to earthquake and ship impact due to earthquake-induced tsunami. X- and Y-direction seismic waves are input simultaneously. Shown in Fig. 19 are the displacement-time histories for top of main tower P2 and center of main girder in bridge. For the top of main tower, the maximum displacements in X- and Y-direction are 1.316 m and 0.937 m, respectively. Besides, the main deformation state of evaluated bridge in dynamic response is similar to the natural vibration mode as shown in Fig. 16(a). The main vibration mode for the input wave was also founded in TX because the predominant frequencies of the top point of main tower and the center point of main girder in TX by Fourier transforms were founded in the natural mode of TX. Therefore, it is confirmed that selected stiffness proportional damping of mode TX is suggested because it is reasonable to evaluate the vibration of seismic response. The cyclic motion response in Y-direction continues until about 150 s (see Fig. 19), however, the cyclic motion response in Xdirection continues until about 250 s. X- and Y-direction displacements for the top of main tower P2 are illustrated in Fig. 20. In

Acceleration Response Spectrum (gal)

Acceleration (gal)

10000

X max= -391.5gal[54.32s] Y max= 335.3gal[53.93s]

600 300 0 -300

X Y

TY 1000

100

TX

t (s)

Period (s)

10

-600 0

50

100

150

200

250

0.1

300

(a) Acceleration waveform

1

10

(b) Acceleration response spectrum (Damping ratio: 5%) Fig. 18. Input seismic wave.

Displacement (m)

1.0 0.0 -1.0

a : 246 mm

-2.0

0

100

200

300

400

500

t (s)

X max= 0.752m[128.90s] Y max= 0.987m[54.00s]

2.0 Displacement (m)

X max= -1.316m[126.80s] Y max= 0.937m[110.70s]

2.0

1.0

0.0 -1.0

t (s)

-2.0

600

0

(a) Top of main tower

100

200

300

400

(b) Center of main girder Fig. 19. Displacement-time histories.

500

600

200

L. Kang et al. / Engineering Structures 134 (2017) 190–204

Y-Direction (m)

however, there is the residual displacement of 246 mm at the top of main tower. Fig. 22 is the strain response of base of main tower P2. As shown in Fig. 22(a), the maximum strain is 0.82ey less than yield strain, but the minimum strain is 1.17ey more than yield strain. It is observed that the compression strain is more than tension strain. It is concluded that the yield state of bridge within the yield region will be considered as the initial state during impacting, and the tower pier within this yield region may be damaged firstly. The displacement and strain response results of main tower P3 are symmetrical to those of P2.

0 - 150 s 150 - 300 s 300 - 600 s

2.0 1.0 0.0

Y

-1.0 X

-2.0 -2.0

-1.0

0.0

1.0

2.0

P2

X-Direction (m) 6. Impact analysis Fig. 20. X- and Y-direction displacements for top of main tower P2.

The force wave form Fm(t) obtained in Section 4.2 and the earthquake damage obtained in Section 5.2 are input before the following dynamic elastic-plastic finite element analysis.

which, the displacements are divided into the following three sections: 0–150 s is duration time of seismic wave inputting (blue line), 150–300 s is after earthquake (green line), and 300–600 s is up to end of seismic response analysis. 0–150 s, both the Xdirection displacement and the Y-direction displacement are main component; 150–300 s, the displacement mainly consists of the Xdirection displacement. This phenomenon mainly results from characteristics of input ground motion, X- and Y-direction stiffness of evaluated bridge. The maximum strain distribution of main tower and the yield region in cross section of right pier due to earthquake are shown in Fig. 21. The maximum strain appears at the bottom of main tower of bridge. Meanwhile, the maximum strain (2641l, 1.17ey, steel of SM570) occurs at the compression side of tower. The yield region is less than non-yield region,

6.1. Initial stress state of impact analysis considering the damage due to earthquake The residual stresses induced by earthquake are applied to the model during impact analysis as the initial stress state. The residual stresses are obtained from the last step of earthquake analysis. For the impact analysis, the initial stress state of bridge is the stress state at 600 s of the seismic response analysis. The residual displacement, plastic strain, and yield regions of the base of P2, P3 main towers are considered at the beginning of impact analysis as shown in Fig. 23.

Fig. 21. The maximum strain distribution of main tower and the yield region in cross section of right pier due to earthquake.

1,000

10,000 Strain (μ)

5,000

Stress (kN/m2)

εmax= 0.82 εy [47.50s] εmin= -1.17 εy [47.60s]

0 -5,000

500 0 -500

t (s)

-10,000 0

100

200

300

400

500

600

Strain(μ)

-1,000

-10,000

(a) Strain-time curve Fig. 22. Strain response of the base of main tower P2.

-5,000

0

5,000

(b) Stress-strain curve

10,000

201

L. Kang et al. / Engineering Structures 134 (2017) 190–204

246mm

P3

P2

X

Fig. 23. Final deformation result (600 s after earthquake, scale: 50).

6.2. Impact analytical result The strain distribution of collision part at the maximum impact force is illustrated in Fig. 24. Fig. 25 is displacement histories of key

points in the bridge (as shown in Fig. 24), in which key points including the top and the base of main tower P2, the center of main girder and the top of main tower P3. The maximum X- and Y-direction displacements of collision part appear firstly at 2.35 s and 2.53 s, which are 0.149 m and 0.178 m, respectively. And then, the maximum displacement propagation path is from the collision part to the top of main tower P2, to the center of main girder, and finally up to the top of main tower P3. Besides, the deformation shape of bridge when the center of main girder reaches to maximum Y-direction displacement is the same as the second mode shape (TY = 3.27 s), based on the impact vibration characteristics. The strain response of collision part of main tower P2 is shown in Fig. 26, in which the arrow means the impact force and d means the position of response result, the strain-time curve is illustrated in Fig. 26(a) and the stress-strain curve of d position is shown in Fig. 26(b). The maximum compression strain of collision part is 3552l (=1.58ey, steel of SM570), which appears after the maximum impact force occurrence. similarly, the strain response of base of main tower P2 is shown in Fig. 27. Almost simultaneously (close to the occurrence time of the maximum strain of collision part), the maximum compression strain of base of main tower P2 is 8390l (= 3.73ey, steel of SM570), and the maximum tension

( Scale : 50 )

b

d c

Y P2

X

a

(σ y = 450 MPa )

P3

−1.2 −1.0 P2

1.2

0

Compression

ε εy

1.2

Tension

X max= -0.149m[2.35s] Y max= 0.178m[2.53s]

2.0 1.0 0.0 -1.0

t (s)

-2.0 0

2

4

6

8

Displacement (m)

Displacement (m)

Fig. 24. Strain distribution of collision part at the maximum impact force.

t (s)

-2.0 0

2

4

6

(c) Center of main girder (Point c in Fig. 23)

8

t (s)

-2.0 0

10

Displacement (m)

Displacement (m)

0.0 -1.0

0.0 -1.0 2

4

6

8

10

(b) Top of main tower P2 (Point b in Fig. 23)

X max= -0.163m[6.79s] Y max= 0.425m[6.25s]

1.0

1.0

10

(a) Collision part (Point a in Fig. 23) 2.0

X max= -0.459m[7.45s] Y max= 0.855m[2.85s]

2.0

X max= 0.261m[9.09s] Y max= -0.577m[8.04s]

2.0 1.0 0.0 -1.0

t (s)

-2.0 0

2

4

6

(d) Top of main tower P3 (Point d in Fig. 23)

Fig. 25. Displacement histories of key points in the bridge.

8

10

L. Kang et al. / Engineering Structures 134 (2017) 190–204

ε max =

Strain ( )

10,000

1,000

1.15 εy [ 2.39 s ]

ε min = − 1.58 εy [ 2.36 s ]

5,000

500

Stress (kN/m2)

202

0 -5,000

0 -500

t (s)

-10,000 0

2

4

6

8

-1,000 -10,000

10

(a) Strain-time curve

-5,000

0

5,000

10,000

(b) Stress-strain curve

Fig. 26. Strain response of collision part of main tower P2.

ε max =

10,000

Stress (kN/m2)

ε min = − 3.7 ε y [2.37 s ]

5,000 Strain ( )

1,000

2.71ε y [2.38 s ]

0 -5,000

1.48ε y − 2 . 39 ε y

-10,000 0

2

4

6

8

500 0 -500

t (s) Strain( )

-1,000 -10,000

10

(a) Strain-time curve

-5,000

0

5,000

10,000

(b) Stress-strain curve

Fig. 27. Strain response of base of main tower P2.

strain is 6104l (= 2.71ey). Finally, the residual compression and tension strains are 5384l (= 2.39ey) and 3333l (= 1.48ey), respectively. For the impact damage evaluation, an elastic-plastic shell finite element model is employed to evaluate local the impact damage of steel bridge. The maximum displacement of collision part in impact direction is 140 mm as shown in Fig. 28, in which the arrow is the impact direction. As illustrated in the load-displacement curve of pushover analysis of Fig. 10, the collision part just enters into plastic state. The Von Mises stress distribution of shell finite element model at d = 140 mm is shown in Fig. 28. It is observed from the stress distribution and deformation of inter-pier longitudinal and lateral stiffed plates that such large drifting object impact

Cross section deformation at impact region

Impactregion P

= 140mm σ σy

leads to obvious local buckling of steel bridge pier although longitudinal and lateral stiffed plates can resist impact loading. The final accumulated damage of base of main tower P2 consists of not only impact damage but also earthquake damage. It is confirmed that the earthquake damage has significant effect on the final accumulated damage of base of main tower. The residual displacement of 325 mm appears at the top of main tower P2. Consequently, the accumulative damage can be effectively evaluated by the method proposed in this study. 7. Evaluation of accumulative responses of steel bridge under the accumulative effect including earthquake and large drifting object impact In previous research, only drifting object impact effect due to tsunami flow was considered. In this study, both the earthquake loading and the drifting object impact loading are taken into account. The comparisons of displacement and strain distribution of main tower only considering the impact effect and those considering the accumulative effect (including the earthquake effect and the ship impact effect due to earthquake-induced tsunami) are conducted. As shown in Fig. 29, the maximum X-direction displacement of main tower top considering the accumulative effect

Displacement (m)

1.5

( Scale:50 ) Fig. 28. Von Mises stress distribution of shell finite element model.

1.0

Only impact effect

0.5

X max = − 0.121m [3.19s ]

0.0 -0.5 0

2

4

6

8

-1.0 -1.5 -2.0

10

t (s)

X max = − 0.459m [7.45s]

Accumulative effect

Fig. 29. Comparison between X-direction displacement histories of main tower top only considering impact effect and that considering accumulative effect.

L. Kang et al. / Engineering Structures 134 (2017) 190–204

Accumulative effect 1.0

Y-Direction (m)

Only impact effect 0.5

0.0

203

which, s means that the start moment, and d means that the moment of maximum displacement. Similarly, the same trend is observed in the strain distribution of main tower P2. As shown in Fig. 31, the maximum compression strain is 3.73ey instead of 2.66ey only considering the impact effect. The accumulative damage considering the accumulative effect is larger than the damage only including the impact effect.

Y X

8. Conclusion and summary

-0.5

-1.0

P2 -0.6

-0.3

0.0

0.3

Fm (t )

0.6

X-Direction (m) Fig. 30. Comparison between X- and Y-direction displacements of main tower top only considering impact effect and those considering accumulative effect.

is 459 mm, more than 121 mm only considering the impact effect, because of the initial X-direction displacement of 246 mm due to earthquake. On the one hand, the maximum X-direction displacement considering the accumulative effect is 338 mm large than that only considering the impact effect; on the other hand, the occurrence time of maximum X-direction displacement considering the accumulative effect is 4.26 s later than only considering the impact effect. Fig. 30 demonstrates the comparison between X- and Y-direction displacements of main tower top only considering impact effect and those considering accumulative effect. In

In this study, the accumulative effect is taken into account to evaluate the accumulative damage of a long-span cable-stayed steel bridge subjected to both earthquake and drifting object impact due to tsunami flow, in which earthquake and tsunami come from the same fault motion. A novel evaluated method used for quantitatively evaluating accumulative damage of steel bridge structures under both earthquake and tsunami is present. First of all, the impact force wave is calculated by the method proposed in previous reference [10]. Impact direction and velocity can be obtained by the tsunami propagation analysis due to four earthquakes occurring simultaneously (Mw = 9.0). The maximum mass of drifting object can be calculated by assuming the maximum impact force in this impact force wave equal to ultimate bearing capacity of the pier of main tower. Besides, a broadband hybrid method is employed to synthesize ground motion in this research, in which the short-period ground motion wave calculated by statistical semi-empirical green function method and the long-period ground motion wave obtained

Fig. 31. Comparison between maximum strain distribution of main tower P2 considering impact effect and those considering accumulative effect.

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L. Kang et al. / Engineering Structures 134 (2017) 190–204

by stiffness-matrix method are synthesized. The seismic wave under such ground motions is inversed using equivalent linear method (SHAKE). The earthquake damage can be evaluated by seismic response analysis, the maximum strain of 1.17ey at the base of main tower and the residual displacement of 246 mm at the top of main tower are considered as initial state and initial condition during the following impact analysis. Furthermore, 1.58ey at the collision part of main tower and 3.73ey at the base of main tower are obtained by the impact analysis using shell element model, and at the same time local buckling occurs. In addition, the accumulative damage and only impact damage of bridge are made comparison in this study. It is observed that the response including residual strain and residual displacement of key points considering the accumulative effect is great larger than those only considering impact effect. It is found that the accumulative effect strongly affects the response of structures and leads to greater structural damage. Such accumulative damage cannot be ignored especially for lifeline engineering. Future studies are underway by the authors to extend this numerical study to experimental investigation. Although there are many challenges of conducting experimental tests considering the accumulative effect, it may be necessary to characterize and simulate the accumulation damage by experimental method. The method proposed in this study may need revision based on future experimental results. Despite all this, the present method and numerical results also provide how to describe the possible response results of structures subjected both earthquake and large drifting object impact due to tsunami flow.

Acknowledgements The study is supported in part by grants from the Advanced Research Center for Natural Disaster Risk Reduction, Meijo University, which supported by Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan. Besides, the first author also wishes to thank the Science and Technology Planning Project of Guangdong Province of China for providing support for the author to conduct this study (Grant No. 2014A020218002).

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