Ohuchi, Hajime

Xi, Oh

Osaka City University Repository

Statistical Seismic Risk Analysis of the Highway Bridges
Xi OH'" and Hajime OHUCHI**
(Received September 30, 2009)
Synopsis
Lifecycle seismic risk of existing highway bridge piers which were retrofitted after the Hanshin Earthquake,
have been estimated by probability analysis. Hazard and fragility curves for the seismic risk analysis and also a
category of damage rank and recovery cost are explained practically, those are essentially required for the
estimation. The obtained results and also some issues to be solved for the near future are described consequently.
KEY WORDS: Seismic Risk, Hazard Curve, Fragility Curve, Execution Cost Estimation
1. Introduction
Cost minimum based strategy is strongly required nowadays for the maintenance of infrastructures. Life cycle
cost assessment is essential for decision making when and how to maintain and for priority which facility to
implement. The stages for the Iife cycle cost assessment are generally construction, maintenance and
reconstruction. In addition to those, it should be also essential to consider the possible impact of earthquake,
which might occur during service period.
In this paper, a seismic risk of highway bridges in urban area has been evaluated as value of money, which is
helpful for decision making. Money value quantifications of the possessing risk and of the countermeasure are
effective for the strategic maintenance program in practice. The seismic risk is generally consisted with direct cost
due to recovery of the infrastructure itself and indirect cost due to social loss by the deterioration of its network
function. The present study focuses only the former cost.
2. Seismic Risk Assessment Procedure
As shown in Fig.1, there are three essentials in the seismic risk analysis as follows: The first is a hazard curve
for ealihquake occurrence probability, the second is a fragility curve for damage rank and its probability of
structure due to earthquake, and the last is an expectable value loss relevant to each of the damage rank
The hazard curve used herein was as shown in Fig. 2, which has been proposed by JSCE available allover
Japan. Moreover, the fragility curve was obtained as follows: First, The strengths of existing highway bridge piers
were estimated considering confinement effect on concrete; Second, the displacement responses of the piers was
calculated by dynamic response analyses; Last, the fragility curve and also damage density distribution were
'" Student, Master Course of Dept. of Civil Engineering
** Professor of Civil Eengineering
-9-
Fragility Curve
Seismic Hazard
Curve
apital Costs at
Ranks
Damage and The
Probability
Seismic Risk
Figure 1. Flow of seismic risk estimation
drawn supposing that the displacement responses could accord to lognormal distribution. Furthermore the
expectable value loss was defined based upon the restoring expenses of highway viaducts, consisting piles and a
T-shaped pier at Hyogoken Nanbu Earthquake in 1995.
Max. acceleration
,.,
Max. acceleration
Figure 2. Seismic hazard curve3)
Consequently, the probability of the damage due to ealihquake was a product of the probabilitie of
occurrences of eatihquake by the hazard curve and damage by the fragility curve and the seismic risk can be
estimated by multiplying the obtained product by the expectable value lost.
3. Existing Bridge Piers to be analyzed
The structures to be analyzed are existing highway bridge piers in urban area, which have been already
retrofitted by steel jacketting due to sei mic code change after the HatlSin Earthquake, however, the focusing point
in the present stud is to estimate eismic risk against the larger earthquake in the future. The execution cost for
the piers reconstruction and strengthening due to earthquake damage a ear and fifty ser ice periods ere onl
considered, except for the cost for the girders due to earthquake damage and ordinary maintenance cost.
All the highway bridge pier for anal se are of reinforced concrete, while the corresponding bridge girders
are of reinforced concrete or steel. Various five piers among them, Ii ted in Tab. 1, were selected with deferent
height, cross-sectional size and the individuality which will be describe in section 5.2. The pier height at the
analysis was defined as the length from the bottom of deck slab to the top of foundation, in which an inetiia force
due to earthquake was applied at the top of the pier. Thu , the solution ha a safety margin because a gra ity
center of the superstructure is generally located above the bottom of the deck lab.
- 10 -
Table 1. Detail of bridge piers
Square
Static nonlinear individuality
Bridge Height Yielding Yielding Maximum Maximum Ultimate
Beam cross-Section
Piear (m) load Seismic load Seismic displacement(111m)
(kN) Intensity* (kN) Intensity* (111111 )
T1 RC 12.7 2400 2577 0.35 3696 0.50 302
T2 Steel 11.2 2000 1864 0.40 2612 0.55 272
T3 Steel 11.2 2000 1781 0.36 2228 0.45 438
T4 Steel 11.2 2300 2582 0.47 3700 0.67 304
T5 Steel 11.1 2300 2256 0.47 3181 0.66 354
• Failure seismic intensity is defined as the ratio between failure load and weight, while maximum seismic intensity is defined as the ratio between
maximum load and weight
4. Seismic Hazard Curve
In Fig.2, the left graphic shows seismic hazard curve in the 246 places distributed around Japan. For each
acceleration, a curve which has larger probability than the 84% curves was drawn, and named as 0.84. At this
research, considering the reinforcement, the curve named 0.16 was chosen to estimate the min. seismic risk.
5. Fragility Curve
5.1 Confinement effect of concrete
In an ordinary structural design of concrete, the uniaxial stress and strain relation as broken line in Fig. 3.
However, an alternative solid line in the figure was recommended lately in the specification of highway bridge
design in Japan, which was reflected on the confinement effect of concrete due to shear reinforcement. The effect
can lead the improvement of the strength and defonnability of reinforced concrete structural members. The
maximum effect was expected in this study, because the referred existing bridges had a sufficient shear
reinforcement.
Confined concrete p
(J C B A As
member
d
,
~ Unconfined
concrete member
E 8
Figure 3. Example of uniaxial Figure 4. Dal11age rank on
stress-strai n curve for confined load-displacement curve
concrete
- 11 -
5.2 Load-deflection curves and hysteresis of the piers
FigA shows the idealized multi linear load-deflection curve introduced by a nonlinear analysis program used
herein. Each slope were determined as follows: First, at the point a in the figure, cracking of concrete initiates;
Second, at point b, tensile reinforcement yielded and the yielding load achieved; Third, at point c, maximum
strength attains; Last, at point d of ultimate state defined by the compressive failure of concrete. Furthermore, four
damage ranks according to deflection level were categorized into C, B, A and As.
5.3 Time response analysis
Time response analysis is a kind of dynamic analysis, with the proper period and ground motion due to
earthquake as parameters. To raise the reliability of the analysis, number of practical pier models with various and
reasonable proper periods were derived from the existing five piers, altering their yielding intensity. In Fig.5, in
actually the piers with the same shear strength have different bending strength from each other around 10%,
accordingly we changed yielding intensity among ex ± 0.1 (ex as the initial yielding intensity). The alteration
results are shown in Fig.6.
As the another parameter, 6 kinds of design seismic waves for the second-category foundation have been
prescribed by the existing specifications for highway bridges, in which three of them are called Type 1, and the
rest are called Type 2. We adjusted the earthquake intensity from 100gai to 1000gai with 100gai increment in
between. Thus, there are 60 seismic waves available.
The estimation results of the pier T5 are shown in Fig.7.
Bending strenght
350100 150 200 250 300
8(mm)
50
5000 ,--------------.....,
4500 I------~~·~·~· .;-;.:-:-c------I
~ . . ... , .
4000 t--------:o,J~/~--,---..~.=_,..,-.-. -_-I
." .' ~
-:::: ;-~~.:- :.~~ ~.--~ =~ -.
22500 'I~"/~"" - ..
a. H~'l'-;;r'f....--=-...._._.._' --1---0.34
2000 .IV,
,1' - . - . '025
1500 1.' - --- .0,3
1000 H,I'-------------j '0,4
500 1/------------1
- - - -0.45
Ol.-------'---...J...--.........- .......~~~_LJ
o
o
..
o
22000 ,------------------",
20000 0 Bending failure ;//
6 Shcnring fnilufc •••••0••/·/·
18000 • 11l1cnsc bending failure
...... 16000 ... Intense shearing l'ailurc ."0'
-sn5 14000 0 //
~ 12000 -9:;4..' to 0
g> 10000 0 ~.c. ..0
~ 8000 ~~~
~ :~~~ @E~~~O ....
2000 .-=
a ./
o 4000 8000 12000 16000 20000
Figure 5. Shear and bending strengths
of existing highway bridge piers in
Hanshin earthquake5)
Figure 6. The alteration results of
yielding seismic intensity
- 12 -
800 ,,----------------,j
ij 700; •j 600! ;-1! 500 : -+ _. I
1,"0· i+h
:i ::: I-I-~.-:3~ 100 ---,--1- .e-------
0' • ,
o 200 400 600 800 1000
Max. ground acceleration (gal)
20 r··..···..·_······..·__·_·..__·_..·····..· ·..· ·..·..· ··- _ ..
18
16
14
V> 12
~ 10
8
6
4
2
o
191 219248276304333361 389418446
seismic t'esponse diaplacement
Figure 7. Distribution of response
displacement
Figure 8 Distribution of displacements
5.4 Seismic fragility curve
It is essential, for the five existing piers, the corresponding damage rank previously described in section 5.2.
Table.2 shows the definition of the damage ranks.
For each of the prescribed acceleration on ground surface, the corresponding series of the calculated
responses displacement, take the results of 700gal shown in Fig.7 as an example, were approximated to be
distributed lognormally, as shown in Fig.8. The approximated distribution were, further more, subdivided into four
of the damage ranks of As, A, Band C as shown in Fig.9, in which the subdivided curves were integrated as to be
the occurrence probability of each damage rank. The fragility curves shown in Fig.! 0 have been obtained as the
whole results of the probabilities, ca'Tying out the same procedure as to data in Fig.7 of other accelerations.
probability distnbution of700gal's results
0.007 r..· .,....·· · ,. · · · · ,
seismic response displacement
1000200 400 600 800
max. grOlmd acceleration
1.000 (/
0.900
0.800 /
.0 0.700 /OJ C B A As.D 0.600 i0
0. /00 0.500
"0 OAOO !
-"OJ /<.> 0.300
"-..>
0.200
0.100
0.000
600500400300200
OL-..;...,e:...-__L- -=:~~
100
0.001
0.002
0.005
i::'
'= 0.004
.D
'".De 0.003
Q.
0.006 B
Figure 9 Lognormal distribution Figure 10 Fragility Curve
- 13 -
Table 2. Category of damage rank based upon displacement states
Damage
Displacement Definition
Rank
As Ultimate Collapsed or seriously deformation
A at The Maximum Load Rupture ofre-bars and Significant deformation
B At Yielding Load ofre-bars Crack and partial peeling of cover concrete
C Elastic Minor damage, i.e., crack initiation
6. Cost at Ranks of Seismic Damage and Seismic Risk
According to reference 4, the restoring method and cost for each damage rank were indicated and shown in
Tab.3. From chapter 4 to 6, all of three essentials were prepared, P(a) as the probability of earthquake, p(bla) as
the probability of level b damage when earthquake a occurs, at last cost(b) as the repairing cost of level b
indicated at Tab.3. The seismic risk is able to be calculated with the equation I and 2. The results are in TabA with
the interest rate 0.02.
Table 3. Restoring method and cost for each damage rank
Retrofitting design
Damage rank
New-Construction Repairing
Recovery cost
Strengthening
As Removal of existing
pier and Construct
new pier with - - 15.8
A sufficient seismic
performance
Removal of
damaged concrete,
Steel or concrete
B - Repair of deformed 2.8
re-bars and Fill up
jacketing
of cracks with resin
C None 0
New construction I
rOOOgal f.
risk = 1 P(a)x LLP(b!a)xcosl(b)]
!Jam
risk50 = iJiSk/(1 + O.02Y]
1=0
- 14-
Table 4. Estimation results
Tag
Percentage of average cost Percentage of total cost for 50 years
Yearly(risk) usage(risk50)
T1 4.07% 125%
T2 4.40% 136%
T3 4.43% 134%
T4 3.57% 110%
T5 3.38% 104%
The damage possibilities of the existing highway bridge piers in the urban area due to earthquake and also
the relevant cost for recovery.
As Fig.11 showed, as to the tendency of estimated cost a year for each damage rank, it was naturally found
that the cost for damage ranks As and A was expensive. It was due to the need of the rernoval and reconstruction
based on the practical experience at the Hanshin Earthquake.
While Fig.12 shows us the seismic risks of different piers, it also could be pointed out that the seismic risk
of the pier under eccentric vertical load was relatively less occasionally designed with larger ultimate strength.
The contain of seismic risks for different piers as shown in Fig.13 and the list of the cost for the rank A and
B categories took larger percentage.
T5
1.2
50403010 20
-total seismic risk
o "",I'--_'--_-L_---J'___....L-L---'
o
~
<0
~OA
<0
-:;:; 0.2
-:;:; 1
o
~ 08
<l.>
~ 06
years
Figure 11. Seismic Risk by Ranks
I~B- lilAmAs
l
-I
T5T4T3T2TI
1;) 0.8
<3
~
~ 0.6
~
~ 0.4
1.2 .
504030
years
2010
....... T1 (RG beam)
1.2 T2(Steel beam)
T3 (Steel beam)
T4(Steel beam, eccentric) ---/
-'-'-T5(Steelbeam,eccentric) /' .·1I-:========~Lc~/:"'-'-"~"~"~i
0.81- /'.....!
0.4 I------~,.'-----,:r"''--------j
0.2 l----ft'-7"O"-----------j
0.6 I--------;;>~'-------cc~"'i
Figure 12. Seismic Risk by years Figure 13. Contents of Seismic Risk of
7. Concluding Remarks Different Pillars
- 15 -
In this paper, with detail expectation of hazard curve, fragility curve and prospective recovery cost, the min.
seismic risk of the highway bridges, which are supposed to be adequately strengthened, were estimated. From
the results, it can be seen that
(1) the piers of steel beam have larger seismic risk than the ones of concrete beam.
(2) It is also obviously that A and B ranks take the larger percentage of the total seismic risk..
(3) The total risk will increases with a yearly reduced pace.
As issues to be solved, first, load-displacement relationship of the bridge piers should be improved
considering foundation. Second, definition of both damage rank and corresponding cost should be more
precisely considered. Last, hazard risk should be improved reflecting locality.
References
1) Yltoh and M.Wada: Study on Lifecycle Evaluation Method of Transportation Infrastructures Considering
Natural Events. Proceedings ofJapan Society of Civil Engineers. v.745, n.1-65, pp.131-142, 2003
2) H.Yoshigawa and K.otaki: Seismic Fragility Curve and Damage Function in Earthquake Risk Analysis.
Concrete Joumal, VolA, No.lO, pp26-34 2007.10
3) Japan Association for Earthquake Engineering: Japan Activity Report on Level II earthquake motions, 2000
4) Y.Adachi and G.Shoji: Restoration Cost of Seismically Damaged Expressway Bridges Due to
Hyogoken-Nanbu Earthquake. Joumal of Japan Society of Civil Engineers, Vo1.27, No.189, 2003
5) Japan Society of Civil Engineers: Research Reports on Hanshin-Awaji Great Earthquake -Damage of Civil
Engineering structures-, 1997
6) Japan Road Association: Specification for Highway Bridges, 2002
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Statistical Seismic Risk Analysis of the Highway Bridges

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Statistical Seismic Risk Analysis of the Highway Bridges

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