Seismic Stability of Caisson Type Breakwater

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13 th World Conference on Earthquake EngineeringVancouver, B.C., Canada

August 1-6, 2004Paper No. 0588

VERIFICATION OF SEISMIC STABILITY OF CAISSON TYPEBREAKWATER

Ryuzo OZAKI 1 and Takashi NAGAO 2

SUMMARY

Seismic stability, which is on sliding and overturning, is verified for a design of a caisson type breakwaterif necessary. In the present Japanese design code for the port and harbor, the evaluation of seismic stabilityof the breakwater is based on the static method called as the seismic coefficient method, which doesnttake the dynamic response of the breakwater into account.

In this study, the framework of the performance-based earthquake resistant design for caisson typebreakwaters is presented. The procedure is as follows. The first step is to assess the necessity of theearthquake resistant performance by the schematic chart. The second step is to calculate the dimension ofthe breakwater for the evaluation of the earthquake resistant performance by the proposed method. Thefinal step is to verify the earthquake resistant performance by the methodology based on a single degree offreedom system.

INTRODUCTION

When designing a breakwater, which is one of the major facilities of the port and harbor, the principalconcern is its stability against waves, and its stability against earthquakes is often neglected (TechnicalStandards and Commentaries for Port and Harbour Facilities [1]). In contrast to quaywalls where loadsdirected toward the sea are dominant due to the action of earth pressure, with a breakwater there is nodominant loading action in a particular direction because the direction of loading action caused by inertialforces changes. The validity of the currently used design method has been proved by the fact that fewbreakwaters have suffered serious damage from strong motion during the past earthquakes. For example,the 1983 Nihonkai-chubu earthquake (Japan Society of Civil Engineers [2]) and the 1993 Kushiro-okiearthquake (Japan Society of Civil Engineers [3]) caused heavy damage to quaywalls and other port

structures, but little to breakwaters. The 1994 Sanriku-haruka-oki earthquake (Research Committee on theSanriku-haruka-oki Earthquake Damage [4]), however, caused the foundation to subside due to loss ofrigidity. The 1995 Kobe earthquake caused subsidence of the ground and sliding of breakwaters on the

1 Engineer, Chuo Fukken Consultants Co., Ltd., Osaka, Japan. Email: [email protected] Head of Port Design Standard Division, National Institute for Land and Infrastructure Management,Yokosuka, Japan. Email: [email protected]


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order of 0.3m (Committee for Research Report on the Great Hanshin-Awaji earthquake [5] and ResearchCommittee on the Great Hanshin Earthquake [6]).

Nevertheless, the earthquake resistant design of breakwaters is necessary, for example, in cases whendesign wave heights are low, and the caisson bodies do not need large weights for wave resistant stability.Since there has been no clear guideline on necessity of the earthquake resistant design of breakwaters, thedecision has been left to the design engineers. Furthermore, the actual earthquake resistant design employsthe seismic coefficient method that replaces the action of earthquake motion with static loading action. Italso uses a safety factor to evaluate the safety. In view of the trend toward performance-based designmethod, however, the introduction of the reliability-based design (Ministry of Land, Infrastructure andTransport [7]) which can evaluate the safety of structure quantitatively, or the design method which canevaluate the response of the structure to loading action concretely is necessary. To streamline theearthquake resistant design, the next-generation Japanese design code for port and harbor focus on adesign method to verify earthquake resistance based on the time history of earthquake ground motion(Nagao [8]). In this method, the design earthquake motion is not given by an area-wise seismic coefficientbut by the time history of the engineering bedrock (the soil layer which has a shear wave velocity of 300-400m/s). We therefore need to construct an earthquake resistant performance verification system that cancope with future changes in how the design earthquake ground motion is expressed.

This paper describes a proposed framework for the earthquake resistant performance design of caissontype breakwaters. Our major objective is to provide a chart for assessing whether to verify earthquakeresistant performance, a determination method of the cross sections for verification of earthquake resistantperformance, and a method of checking earthquake resistant performance. For verifying earthquakeresistant performance, we used a single degree of freedom system to evaluate the sliding and theoverturning of breakwaters caused by earthquakes. Herein, we focus on the cases in which the rubblemound is not damaged during earthquakes.

FRAMEWORK OF THE EARTHQUAKE RESISTANT PERFORMANCE DESIGN OFBREAKWATERS

Verification Method Figure 1 shows a flow for verifying the earthquake resistant performance of a breakwater. It is assumedthat the earthquake resistant performance is verified after conducting the wave resistant design. We firstassess whether the earthquake resistant performance needs to be verified based on the peak acceleration

Amax of the engineering bedrock and the specification parameters of the caisson. If the result shows suchverification is necessary, we compute the time history of the acceleration on the bottom surface of thebreakwater caisson by the earthquake response analysis of ground. After calculating the seismiccoefficient from the acceleration time history, we set the cross section for verifying the earthquakeresistant performance by the seismic coefficient method. The next step is to compare the calculatedcaisson width Beq of the cross section for verification with the width Bw obtained from the wave resistantdesign, and to choose the larger of the two as the caisson width for verification. Then a single degree of

freedom system is used to calculate the earthquake response of the breakwater, such as the sliding and theoverturning, and to verify the earthquake resistant performance. The step of setting the cross section forverification by means of the seismic coefficient method improves the efficiency of earthquake resistantperformance verification. We need to develop the new items surrounded by thick-lined boxes in Figure 1.By the way, the performance required to the breakwater is to keep the port calm. Therefore, based on thepast case examples, the limit state criterion of judgment with regard to the sliding is 50cm and the one tothe overturning is 90degree in this study.


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Method of Verifying Earthquake Resistant PerformanceA single degree of freedom system of the breakwater caisson is applied to evaluate the earthquake

response of the breakwater in order to verify the earthquake resistant performance. Sliding failure andoverturning failure are considered as failure modes. We numerically integrated the equation of motion in ahorizontal direction for the sliding mode, and the equation of angular motion around the edge of thebottom surface of the breakwater for the overturning mode (Sekiguchi [9]), when evaluating theearthquake response of the breakwater caisson based on Equations (1) and (2), respectively. Figure 2shows the load model of the breakwater. The water level used in this study is the synodic averaged highwater level (H.W.L.). This level gives the smallest ratio of the resistance force to the load effect. Thefriction coefficient between the concrete and the rubble is 0.6 (Technical Standards and Commentariesfor Port and Harbour Facilities [1]).

'222

W PW k

dt

x d g

W d h += (for the sliding safety) (1)

'222

cW bPW ak dt d

I d h +=

(for the overturning safety) (2)

where, 2127

H k P whd = (3)

( )3

22 h Bg

W I

+= (4)

Determination of caissonwidth Bw based on thewave resistant design

Assesment of

the necessity of earthquakeresistant design

Design conditions Amax etc.

Earthquake responseanalysis of the ground

Caluculation of seismic coefficient

Determination of caissonwidth for verification

Max( Beq Bw)

Seismic perfomanceverification

Deq< Dallow ?

End

D eq : Residual deformation D allow : Allowable deformation

Yes

Yes

No

No

W.L. W.L.

P d P d

W'

x

W

k h W

Figure 2 Load model of the breakwaterFigure 1 Flowchart for verifying the earthquake

resistant performance of a breakwater


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andk h : seismic coefficient (= / g) : acting acceleration (cm/s 2)g : acceleration of gravity (= 980cm/s 2)W : weight of the caisson of unit length (kN/m)P d : resultant dynamic water pressure of unit length (kN/m)W : effective weight of the caisson of unit length (kN/m)

H : water depth at the toe of caisson (m) w : unit weight of seawater (kN/m 3) : friction coefficient between the caisson and the rubble mound I : polar moment of inertia of unit length (kN m s2 /m)h : height of the caisson (m)a c : arm length of the load (m)

Application to One of the Disaster Cases Caused by the 1995 Kobe earthquakeWe applied the method described in previoussection to one of the breakwaters of Kobe port

that was damaged during the 1995 Kobeearthquake, in order to examine the validity ofthe analytical method. The object of study isthe seventh breakwater of Kobe port. It waslocated in an east-west direction roughlyperpendicular to the dominant direction (north-south direction) of the earthquake. The surveyconducted after the earthquake recorded amaximum displacement of 0.3m. Nooverturning occurred (Committee for ResearchReport on the Great Hanshin-Awaji earthquake[5]). Figure 3 shows the cross section of thebreakwater.

Based on the strong motion record at the pointKp-79m of Port Island obtained by Kobe City,we performed a one-dimensional equivalentlinear earthquake response analysis, calculatingthe earthquake motion acting on the bottomsurface of the caisson. After analyzing the NS(north-south) and EW (east-west) components,we obtained the component in a directionperpendicular to the breakwater, considering adirection error (Gifu Univ. [10]) that occurredat the time of placing the seismograph.

Figure 4 shows the time history of theearthquake motion on the bottom surface of thebreakwater caisson and the caissons response.

The long period wave was predominant due tothe soft ground. As a result, the largedisplacement occurred at the peak acceleration

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Figure 3 Cross section of the seventh breakwater ofKobe port

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Figure 4 Input earthquake motion andcaissons response


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amplitude of 7sec. The residual displacement was 0.4m, nearly matching the actual deformation. Therotation angle at the peak acceleration amplitude was only 0.1degree. The results thus proved the validityof our method.

METHOD OF ASSESSING THE NECESSITY OF EARTHQUAKE RESISTANTPERFORMANCE VERIFICATION

Study MethodAs the constituent factors of the earthquake resistant performance verification system, we first studied theindices used for assessing the necessity of earthquake resistant performance verification. For theconvenience of design engineers, we used the peak ground acceleration produced in the engineeringbedrock instead of that on the bottom surface of the breakwater caisson. If it was judged to be unnecessaryto verify the earthquake resistant performance, the response analysis of the ground could be omitted. Sincethe width of the caisson was decided in the wave resistant design, we studied an assessment method usingthe following two parameters as the indices: the ratio of the width to the water depth ( B/H ) and the peakground acceleration on the engineering bedrock.

We selected the seven cross sections shown in Table 1 from the cross sections of breakwaters throughoutJapan, maintaining a balance among the values of water depths and the conditions of the ground. Nineearthquake motions were used in total. The waves actually observed in port and harbor areas were theHachinohe wave, the Ofunato wave, the Akita wave, and the Kobe wave used in previous chapter. Thefollowing simulated earthquake waves were also used: the strike wave and the dip wave caused byintraplate earthquakes; the subduction wave caused by interplate earthquake; and the earthquake motionrepresenting the level-1 and the level-2 earthquakes used for the analysis of railroad structures (RailwayTechnical Research Institute [11]) (hereafter referred to as the JR1 wave and the JR2 wave, respectively).

The reasons why these nine waves were selected are followings. Based on the present standard, the wavesthat are applied to the earthquake resistant design are the Kobe, Hachinone, Ofunato and Akita waves,which have been recorded during the earthquakes in port and harbor. Since the synthesized waves taking

the focal mechanism of earthquake, such as the intraplate and interplate earthquake, into account areadopted in next standard, the strike, dip and subduction waves are used. These waves were synthesized toconsider the three types of the focal mechanism which are the intraplate lateral fault, reverse fault andinterplate low angle reverse fault, respectively (Kagawa [12]). Furthermore, for the confirmation, the JR1and JR2 waves are applied because these two are for the earthquake resistant design of railroad structures.Table 2 shows the dominant frequencies of these waves. Figure 5 shows the Fourier spectra of theacceleration of the Hachinohe, Kobe and the subduction wave as examples. The spectra were smoothed bya 0.3Hz bandwidth Parzen window and their peak amplitudes were adjusted to 100Gal sec.

Predominantfrequency(Hz)

Hachinohe wave 0.39Ofunato wave 2.34

Kobe wave 2.88Akita wave 0.44Strike wave 1.66

Di wave 0.68Subduction wave 0.60

JR1 wave 0.78JR2 wave 1.34

Water depth(-m)

Caissonwidth(m)

Front widthof mound(m)

case1 11.5 7.5 6.5case2 8.9 6.6 6case3 12.2 5.5 6.5case4 11.1 9.5 11case5 11.8 7.5 5case6 9.05 5 3.5case7 11.05 5 4.5

Table 1 Cross sections used for the study

Table 2 Dominant frequencies ofearthquake waves used for the study


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As for the analysis, the peak acceleration amplitudes were adjusted to 120, 250, 400, 600, 800, 1000,1200, 1400, and 1600 Gal of 2E wave (which has twice amplitude of incident wave), and the one-dimensional equivalent linear earthquake response analysis code Dyneq (Yoshida [13]) was used tocalculate the earthquake motion produced on the bottom surfaces of the breakwater caissons for each crosssection shown in Table 1. Figure 6 shows the relationship between the PGA on the bedrock, and that ofthe bottom surface of the breakwater caisson, using case 1 as an example. The amplification factors of thePGA were small due to the soft ground. The differences in the amplification factors of different waveswere large. The acceleration amplification factor of the subduction wave was the highest, and that of theOfunato wave was the lowest. The other cases showed similar results.

We next changed the caisson width by a step of 0.5m from the original design caisson width, using the

single degree of freedom system shown in previous chapter to evaluate the response of the breakwatercaisson. Figure 7 shows the contour maps of the residual displacements caused by the subduction wave(a), the Hachinohe wave (b), and the Kobe wave (c), focusing on case 6. The horizontal axis represents theratio of the caisson width to the water depth ( B/H ), and the vertical axis the peak acceleration on theengineering bedrock. Figure 7 indicates that different waves give different displacement deformationseven under the same condition of the peak bedrock acceleration and that the subduction wave gave thelargest residual displacement. One of the reasons is that the acceleration amplification factor of thesubduction wave was the highest, as shown in Figure 6. Another reason is that the direction of the slidingdeformation of the breakwater caisson caused by the subduction wave did not change often in response tothe change of the direction of the inertial force. Next chapter describes the difference in the patterns ofsliding of the breakwater.

Even when the residual displacement of the caisson was very small, there was a possibility that a verylarge displacement was produced during the earthquake, causing the breakwater caisson to slip down therubble mound. We hence studied the relationship between the residual displacement of the caisson and themaximum displacement in the earthquake-responding process. The results showed that the percentage ofthe maximum displacement caused by the Kobe wave was the largest with respect to the residualdisplacement. Figure 8 shows the contour map of the maximum displacements caused by the Kobe waveof case 6. The residual displacement necessary for breakwater caissons to be classified as disaster-strickenis usually about 50cm, but comparison with Figure 7 (c) indicates that in some cases, maximum

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Dip wave

Strike wave

Subductionwave

Figure 5 Fourier spectra of the acceleration

Figure 6 Relationship between PGA on bedrockand PGA of response motion of bottom surface

of the caisson

Hachinohe waveKobe waveSubduction wave


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displacements of about 150cm were produced when the residual displacements were smaller than about50cm. In other cases, maximum displacement of 400cm were sometimes produced when the residualdisplacements were 50cm, but all of them remained within the front width of the mounds shown in Table1 and were not large enough to cause the caisson to slip down the mounds. It is therefore concluded thatwe only need to consider the residual displacement when evaluating the sliding failure for judging thenecessity of earthquake resistant performance verification. The maximum deformations of about 400cmwere produced when the PGA were about 1000Gal. With different earthquake waves, the PGA smallerthan 1000Gal gave a residual displacement exceeding 50cm.

We then compared the sliding failure with the overturning failure, and found that the overturning failureonly occurred when the PGA was very large. As results of studies by the ground motion giving stricterconditions of overturning than those of sliding, focusing on the subduction wave (see Figure 9) showedthat overturning only occurred when the ratios of the caisson width to the water depth ( B/H ) wereextremely small and the produced residual displacements were larger than about 300cm. We thereforeconcluded that the conditions for overturning breakwaters did not need to be verified, and so the followingsections focus on sliding failure.

Figure 10 shows the conditions for each of the studied breakwater cross sections, with the change of thecaisson width by a step of 0.5m from the original design caisson width, to cause the subduction wave toproduce a residual displacement of larger than 50cm. The values of case 6 represent the lower limits. Thecurve connecting the lower limits is the assessment criterion of verifying the sliding failure of thebreakwater. Even when the ratio of the caisson width to the water depth ( B/H ) reached 2.0, sliding failureswere produced under certain conditions. This was because the increase of the caisson width caused theincrease of the sliding resistance force as well as the increase of the inertial force. For reference, Figure 10also shows the lower limit values for the Hachinohe wave to produce a residual displacement of 50cm.Since the lower limit curves depend largely on the earthquake motions, attentions should be paid whenusing other waves.

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Figure 7 Relationship between peak bedrock acceleration and sliding failures(a) Subduction wave (b) Hachinohe wave (c) Kobe wave


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PROCEDURE FOR SETTING THE CROSSSECTIONS FOR VERIFICATION

Comparison between Residual Displacementand Maximum DisplacementThe next subject is setting the cross section forverification when it is judged that the

earthquake resistant performance of abreakwater needs to be verified. The basicprocedure is to use the caisson width calculatedfrom the result of the wave resistant design toverify the earthquake resistant performance. Ifthe resultant displacement exceeds theassessment criterion, the next step is to increasethe caisson width and repeat the calculation.This procedure is repeated until the optimum solution is obtained. For design engineers convenience, westudied another method of setting the optimum cross section for verification.

As already examined in Figure 7, the relationship between the PGA on engineering bedrock and the

residual displacement of the caisson differed largely depending on the input motions, so we studied therelationship between the PGA of the bottom surface of the caisson and the residual displacement. Usingthe Hachinohe wave, the Kobe wave, the JR2 wave, and the subduction wave under the conditions of case1 ( B/H = 0.65), we plotted in Figure 11 the relationship between the ratio of the caisson width to the waterdepth ( B/H ) and the PGA on the bottom surface of the caisson when the residual displacement of thebreakwater caisson was 50 cm. This figure shows that the relationship between the PGA on the bottomsurface of the caisson and the residual displacement also differed greatly depending on the groundmotions. The other cases gave similar results. We conclude that it is inappropriate to use the PGA on the

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Figure 8 Relationship between peak bedrockacceleration and sliding failures (Maximum

displacement of Kobe case)

Figure 9 comparison between the slidingfailure and the overturning failure

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case1

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Hachinohewave(case2)

Subduction wave

Hachinohe w ave

Figure 10 Chart for assessing the necessity ofverifying earthquake resistant performance


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bottom surface of a breakwater caisson for calculating the seismic coefficient directly. We tried to studythe application of the peak velocity amplitudes and obtained the same result.

Focusing on cases 1 and 4 which have the contrasting groundcondition with each other, we analyzed the reason in detail, usingFigure 12. We plotted the time histories of the earthquake motionon the bottom surfaces of the caissons and those of thedisplacements of the breakwaters, with the PGA of input motionadjusted to give a residual displacement of 40cm. Figure 13 showsthe Fourier amplitude spectra of the input motion on the bottomsurfaces of the caissons. From the frequency characteristics shownin Figure 13, we found that the Fourier amplitude spectrum of theKobe wave was dominant at all frequencies except the lowfrequency side of case 4. Since the residual displacements were thesame, the frequency characteristics alone cannot evaluate theamount of residual displacements.

In the case of the residual displacement caused by the Hachinohewave of case 1 shown in Figure 12, the first and the seconddisplacement accumulated to form the residual displacement. In thecase of the subduction wave, the shape of the residual one wasformed almost at once. In the case of the Kobe wave, repeatedpositive and negative deformation formed the residualdisplacement, which was smaller than the maximum one. Thewaves showed no specific tendencies. For example, in the case ofthe Hachinohe wave of case 4, the residual displacement wasformed almost at once.

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Residual Dis p.=50cm

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JR2 wave

Figure 11 Relationshipbetween the PGA on thebottom surface of the caissonand the residual displacement

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Figure 12 Input motion on the bottom surface of the breakwater and the deformation of thebreakwater

(a) case1 (b) case4


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Clearly, the preliminary estimation of therelationship between the maximum displacementand the residual one is important for properlyverifying earthquake resistant performance. Thisstudy of all cases showed that the ratio of theresidual displacement and the maximumdisplacement ( Rdef ) can be estimated from theresult ( Racc ) of dividing the absolute value of thesum of the positive and negative peakacceleration amplitudes ( acc max and acc min ,respectively) by the larger one of the absolute values ofthose. As shown in Figure 14, we defined the maximumvalue of the differences between the variable points of thedisplacement vectors as the maximum displacement. Racc isexpressed as:

( )minmaxminmax

,max accacc

accacc Racc

+= (5)

Figure 15 shows the relationship between Racc and Rdef .Considering that the limit state criterion of judgment withregard to the sliding is 50cm, the 106 cases in which theresidual displacement lie between 30 and 100cm werepicked up from our studied all cases. Although the data werewidely scattered, Rdef tended to increase as Racc increased.Using the result of linear regression of the relationship

between the two (the straight line in the figure and Equation(6)), we estimate Rdef from the acceleration time history.

44.087.0 += accdef R R (6)

We also conducted a multiple regression including not only Racc but also indices such as the dominantfrequency, but the correlation coefficient did not increase significantly, so we estimated Rdef from thepositive and negative peak acceleration alone for simplification and convenience.

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Figure 13 Fourier spectrum of the input motion on the bottom surface of the breakwater(a) case1 (b) case4

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Figure 14 Definition of the maximum deformation

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Figure 15 Relationship between R acc and R def


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Procedure for Setting the Cross Sections for VerificationWe then studied the procedure for setting thecross section of breakwater caissons forverification. Since we could estimate the targetmaximum displacement for the target residualdisplacement (50cm) from the acceleration timehistory of the bottom surface of a breakwatercaisson, we studied the method of estimating thecross section necessary for producing the targetmaximum displacement. Instead of using actualearthquake waves having various frequencycomponents, we used sine waves for our study.As shown in Figure 16, we examined the peakacceleration amplitude necessary for giving apredetermined value of D max . One cyclesdisplacement due to the sine wave would bealmost constant after the third to fifth cycle. However, themaximum displacement of an actual breakwater caissoncaused by an earthquake could not occur in the constantcondition. Therefore, the displacement due to the second cyclewas regarded as the maximum displacement Dmax here. Thestudy conditions were set as follows: frequency of earthquakemotion = 0.110Hz; and B/H for cross section of breakwatercaisson = 0.4, 0.6, and 0.8 (in case 1). We first examined thepeak acceleration amplitudes that produced a value of D max of25-200cm. Figure 17 shows the results for D max of 25cm.Different values of B/H of the breakwater gave different peakamplitudes. Dividing the amplitudes by the acceleration of

gravity, and dividing the resultant by a limit seismiccoefficient corresponding to a safety factor of displacement of just over 1.0, we obtained the values ( Rkh) shown in Figure 18.The relationships were almost constant regardless of thevalues of B/H . The relationships are expressed as:

( ) ( ) 1max2max ++= f Db f Da Rkh ( ) 0035.00178.0 maxmax = D Da (7)( ) 8174.00095.0 maxmax += D Db

where, f = frequency (Hz).

Since this study used a sinusoidal earthquake wave, the valuesof Rkh in Figure 18 correspond to the Fourier spectra of theacceleration. We multiplied the Fourier spectrum of theacceleration on the bottom surface of the breakwater caissonby a filter F so as to make the amplitude at each frequency thesame as that at a frequency of 0Hz (1.0). We then obtained thespectrum (uniform-target maximum displacement spectrum)

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-200

0

200

400600

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5Time(s)

-120

-100

-80-60

-40

-20

0

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5Time(s)

Maximum displacement D max One cycle's displacementof continuous wave inthe steady state

Figure 16 Study method

Figure 17 PGA of input motionagainst frequency

0

50

100

150

200

250

300

0 1 2 3 4 5 6 7 8 9 10Frequency of input motion(Hz)

25cm

50cm

75cm

100cm

125cm

150cm

Figure 18 Seismic coefficient ratioagainst frequency


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corresponding to the target maximum displacement at anyfrequency component. From the reciprocal plot of Equation(7), the filter F is expressed as (See Figure 19):

( ) ( )1

1

max_

2

max_ ++

=

f Db f DaF

t t

(8)

where, Dmax_t : target maximum displacement (cm) f : frequency (Hz)a (), b() : same with Equation (7).

Multiplying the spectrum of an actual earthquake motion bythis filter and performing inverse-Fourier transformation,and dividing the resultant peak acceleration amplitude by theacceleration of gravity, we can obtain the seismic coefficientfor verification corresponding to the target displacement.

Figure 20 shows the flow of calculating the seismiccoefficient for verification.

Verification of the Validity of the Proposed MethodHere we verify the validity of the method of setting the crosssection for verification described above. Using our methodto calculate the seismic coefficient for verification on the106 cross sections in which the correlation between Racc and

Rdef was examined shown in Figure 15, we set the crosssection giving a safety factor of 1.0 by using the calculatedseismic coefficient. We then evaluated the displacement ofthe breakwater caisson having the cross section set above.

Figure 21 shows the relationship between the peakacceleration on the bottom surface of the breakwater caissonand the caisson weight ratio ( Rweight ) of the cross section forthe verification of the earthquake resistant performance to that for the wave resistant design. Differentsymbols were used depending on whether the residual displacements were less than 50cm. In the caseswhere Rweight < 1.0, the verification was actually made based on the cross section obtained from the waveresistant design, i.e. based on the cross section in the case of Rweight = 1.0. It is clear from the figure thatsome of the values of Rweight calculated by the proposed method were equal to or larger than 3.0. Furtherstudy showed that the displacements produced in such cases were smaller than the target amount of 50cm,giving uneconomical cross sections. It is therefore appropriate to set the upper limit of Rweight at about 3.0after calculating the caisson width from the seismic coefficient for verification.

We thus calculated the residual displacements for the modified caisson weights in the range of0.30.1 weight R . Figure 22 shows the frequency distribution of the residual displacements. The residual

displacements were distributed in a relatively narrow range of 0-100cm. The resultant average residualdeformation was about 40cm, which was slightly smaller than the target amount of 50cm. This wasinfluenced by the cases where the cross sections designed from the standpoint of wave resistance werelarger than those designed from that of earthquake resistance. Also, there are some cases in which the

0.001

0.01

0.1

1

0 1 2 3 4 5 6 7 8 9 10Frequency(Hz)

25cm

50cm

75cm

100cm

125cm

150cm

Reading of PGA from time

history on the bottom surfaceof the caisson

Setting of the target maximumdisplacement Dmax_t based on Racc

Filter processingcorresponding D max_t

Inverse-Fourier transformationCalculation of the seismic coefficient

for verification from PGA

FourierTransformation

Figure 19 Filter for calculating theseismic coefficient for verification

Figure 20 Flowchart for calculatingthe seismic coefficient for verification


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residual displacement is much larger than 50cm. In such cases, it is necessary to repeat the procedure untilthe optimum solution is obtained.

As shown in Figure 15, the procedure of setting the cross sections for verification has 50% of possibilitythat the residual displacement would be over the allowable displacement of 50cm. In other words, it isdifficult to determine the optimum cross section without some trial and error, because the data werewidely scattered in Figure 15. However, it is possible to estimate the cross section required from theaspects of seismic stability with some degree of accuracy and to verify the earthquake resistantperformance conveniently. In contrast with our proposed method, the numerical analysis approach byEquation (1) needs to repeat lots of trial and error in order to obtain the optimum cross section.

CONCLUSIONS

This paper shows the methodology of performance-based design for seismic stability of the caisson typebreakwater. The conclusions are summarized as follows.

1 A method of verifying the earthquake resistant performance of caisson type breakwaters is developed.The method uses a single degree of freedom system to evaluate the sliding and overturningdeformation of caissons. Using the method, we successfully evaluated the response of one of thebreakwaters of Kobe port during the 1995 Kobe earthquake.

2 A chart for assessing whether the earthquake resistant performance of a breakwater needs to beverified is prepared. The assessment chart uses the PGA on the engineering bedrock and the ratio ofthe caisson width to the water depth. The failure mode of the breakwater is assumed to be sliding, as

the overturning mode is not regarded to be a dominant factor.

3 The method of setting the cross section for verification is described when earthquake resistantperformance needs to be verified. Using the positive and negative peak values of the acceleration onthe bottom surface of the breakwater caisson to set the target maximum displacement, we calculatedthe seismic coefficient corresponding to the target maximum displacement.

4 Using the results above, we proved the effectiveness of the verification of the earthquake resistantperformance of caisson breakwaters. The upper limit of the caisson weight ratio of the cross section

0

1

2

3

4

5

6

7

8

0 200 400 600 800 1000 1200PGA at the bottom of breakwater caisson(Gal)

Smaller than 50cm

Equal to orlarger than 50cm

10 30 50 70 900

5

10

15

20

25

Residual displacement(cm)

Average: 37.1cm

Figure 21 Relationship between the peakacceleration produced on the bottom of thebreakwater and Rweight

Figure 22 Frequency distribution of theresidual displacement


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for the verification of the earthquake resistant performance to that obtained from the wave resistantdesign is 3.0.

The results of this study will be useful for the rational earthquake resistant design of breakwaters, whichhas traditionally been based on the method that the earthquake response of the breakwaters are not takeninto account. When this report was written, area-wise earthquake motion was not given in the form of atime history. Design engineers who use this method should therefore select an earthquake motion forperformance verification after examining differences in the earthquake responses of the caisson producedby different motions.

ACKNOWLEDGMENT

We are grateful to Mr. Masaki Fujimura, a researcher at the National Institute for Land and InfrastructureManagement, for his help with the analysis.

REFERENCES

1. The Overseas Coastal Area Development Institute of Japan, Technical Standards andCommentaries for Port and Harbour Facilities in Japan, 1999

2. Japan Society of Civil Engineers, Research Report on the 1983 Nihonkai-chubu EarthquakeDamage, 1986

3 Japan Society of Civil Engineers, Research Report on the 1993 Kushiro-oki Earthquake Damage,1994

4 Research Committee on the Sanriku-haruka-oki Earthquake Damage, Research Report on the 1994Sanriku-haruka-oki Earthquake Damage, The Japanese Geotechnical Society, 1996

5 Committee for Research Report on the Great Hanshin-Awaji earthquake, Research Report on theGreat Hanshin-Awaji earthquake: Damage to Civil Engineering Structures, Chapter 5: Port,Harbor, and Coast Structures, Japan Society of Civil Engineers, 1997

6 Research Committee on the Great Hanshin Earthquake, Research Report on the Great Hanshin

Awaji Earthquake: Reference Materials, Vol. 1, The Japanese Geotechnical Society, 19967 Ministry of Land, Infrastructure and Transport, Basis of the Design on Civil Engineering andArchitecture, 2002

8 Nagao T. Trend in the Revision of the Standards for Port and Harbor Facilities, Proceedings of the5th Symposium on Steel Structures and Bridges, Steel Structure Committee, The Japan Society ofCivil Engineers, 2002: 9-20

9 Shibata T. and Sekiguchi H. Bearing Capacity of the Ground, Kajima Institute Publishing Co.,Ltd., 1995

10 Civil Engineering Department, Gifu University and Development Bureau, Kobe City, Analysis ofthe Strong Motion Record at the Vertical Array Observation Point of Port Island, 1995

11 Railway Technical Research Institute, Design Standards for Railway Structures: EarthquakeResistant Design, Maruzen Co., Ltd., 1999

12 Kagawa T. and Ejiri J. Estimation of Ground Motion in Near-Field of Focal Region considering theRupture Process of Causative Fault Proceedings of Symposium Discussing the Level-2 GroundMotion for the Seismic Design of Soil Structure, 1998: 1-6

13 Yoshida N. and Suetomi I. DYNEQ: Earthquake Response Analysis Program Based on theEquivalent Linear Method for the Horizontal Stratification Ground, Technical Laboratory Report,Sato Kogyo Co., Ltd., 1996: 61-70

Seismic Stability of Caisson Type Breakwater

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