Report - PEER - University of California, Berkeley

More documents

Recommendations

Info

MODELING CONSIDERATIONS IN PROBABILISTIC PERFORMANCEBASED SEISMIC EVALUATION OF HIGHWAY BRIDGESSashi K. KUNNATH 1 and Leah I. LARSON 2ABSTRACTLimitations associated with deterministic methods to quantify demands and develop rationalacceptance criteria have led to the emergence of probabilistic procedures in performance-basedseismic engineering (PBSE). The Pacific Earthquake Engineering Research (PEER)performance-based methodology is one such approach. In this paper, the impact of certainmodeling decisions made at different stages of the evaluation process is examined. Modeling,in the context of this paper, covers hazard modeling, structural modeling, damage modeling andloss modeling. The specific application considered in this study is a section of an existingviaduct in California: the I-880 interstate highway. Several simulation models of the viaduct aredeveloped, a series of nonlinear time history analyses are carried out to predict demands,measures of damage are evaluated and the closure probability of the viaduct is estimated for thespecified hazard at the site. Results indicate that the assessment is particularly sensitive to thedispersion in the demand estimation, which in turn is influenced by the ground motion scalingprocedure.Keywords: Bridge; Fragility functions; Nonlinear time-history analysis; Performancebasedseismic engineering; Seismic evaluation; Soil-foundation interaction.1. INTRODUCTIONEarly attempts in probabilistic seismic evaluation can be traced to the developmentand application of fragility curves. A formal implementation utilizing a probabilisticapproach in seismic evaluation and design materialized with FEMA-350 (2000). ThePEER performance-based framework may be regarded as an extension and anenhancement of the procedure developed for FEMA-350 (Cornell et al., 2002). Aconceptual description of the methodology, based on the total probability theorem, isexpressed as follows:ν ( DV ) = ∫∫G(DV | DM ) dG( DM | EDP ) dG( EDP | IM ) dλ(IM ) (1)1 Professor, Civil & Environmental Engineering, University of California, Davis, CA 956162 Graduate Student, Civil & Environmental Engineering, University of California, Davis, CA 9561665
where ν ( DV ) is the probabilistic description of the decision variable (for example,the annual rate of exceeding a certain repair cost), DM represents the damagemeasure, EDP represents the engineering demand parameter (drift, plastic rotation,etc.) and IM represents the intensity measure (characterizing the hazard). Theexpression of the form P(A|B) is essentially a cumulative distribution function or theconditional probability that A exceeds a specified limit for a given value of B. Theterms that appear in the above equation can be deaggregated using the totalprobability theorem that assumes that each operation is mutually independent. Oneuseful application of Equation (1) is to derive the mean annual probability ofexceeding a DV given an IM.While probabilistic methods offer distinct advantages over deterministicapproaches, it is important to be cognizant of the assumptions that underlie theframework. A closer look at the PEER methodology indicates that the resultingevaluation is a function of four separate modeling tasks: hazard, demand, damage anddecision-making. Suppositions and simplifications are often introduced at variousmodeling phases that can impact the final outcome of the assessment. This paperattempts to investigate the sensitivity of modeling assumptions introduced at differentstages of a performance-based evaluation using the PEER framework.2. APPLICATION OF THE PEER METHODOLOGY TO AN EXISTINGVIADUCT IN CALIFORNIAThe expected seismic performance of a section of the I-880 viaduct constructed in themid-1990s as part of the California Department of Transportations (CALTRANS)Cypress Replacement Project in Oakland, California, is evaluated using the PEERPBSE framework. The specific issues investigated include: modeling of the sitehazard and issues related to scaling the ground motions; modeling of the system, thelevel of detail that is needed to establish reliable estimates of performance, and issuesrelated to soil-foundation-structure interaction (SFSI) and P-delta effects;considerations in damage modeling; and finally, the significance of subjectivedecisions made by bridge inspectors in post-earthquake reconnaissance.2.1 Description of the ViaductThe rebuilt segment of the I-880 (Figure 1) is a seven-frame structure consisting of 26spans and a total length of approximately 1140 m. The site is located within 7-8 kmof the Hayward Fault. The soils on the site near the San Francisco Bay consist ofdense fill, Bay mud and sand, covering deep clay deposits. The superstructure iscomposed of 7 cast-in place reinforced concrete box girders, approximately 21.8 mwide, 2.0 m tall and 0.3 m in depth. All columns of the viaduct have rectangularcross-sections with circular reinforcement. While a majority of the columns havecontinuous moment connections at the column-deck and column-pile-cap region,some bents have pinned connections at either the column-pile-cap or column-deck66
Page 2 and 3:
PERFORMANCE-BASED SEISMIC DESIGNCON
Page 4 and 5:
CONTENTSTable of Contents..........
Page 6 and 7:
REAL-TIME DYNAMIC HYBRID TESTING OF
Page 8 and 9:
PREFACEThe workshop on “Seismic D
Page 10 and 11:
LIST OF PARTICIPANTSSergio M. Alcoc
Page 12 and 13:
RESOLUTIONSThe International Worksh
Page 14 and 15:
CONCLUSIONS AND RECOMMENDATIONSThe
Page 16 and 17:
nonlinear dynamic) and when they sh
Page 18 and 19:
exists to develop testing protocols
Page 20 and 21:
to be sent soon to the 28 members o
Page 22 and 23:
factor γ I is 1.4 or 1.2 for essen
Page 24 and 25:
i. The well-known relation µ θ -
Page 26 and 27:
γ s =1.15. Values less than 1.0 me
Page 28 and 29:
efore (factor α in Eq.(4)). Materi
Page 30 and 31:
the force demand from the analysis,
Page 32 and 33: OVERVIEW OF A COMPREHENSIVE FRAMEWO
Page 34 and 35: ground motion Intensity Measure (IM
Page 36 and 37: 2.2 Simulation of Engineering Deman
Page 38 and 39: describing the economic losses asso
Page 40 and 41: practice the localized gravity load
Page 42 and 43: Whereas financial and insurance org
Page 44 and 45: AN OUTLINE OF AIJ GUIDELINES FOR PE
Page 46 and 47: (7) a method of performance evaluat
Page 48 and 49: where, T: natural period of structu
Page 50 and 51: 6. DAMAGE AND LIMIT DEFORMATIONSThe
Page 52 and 53: The limit inter-story deformations
Page 54 and 55: DirectionX-directionY-directionSkew
Page 56 and 57: HAZARD, GROUND MOTIONS AND PROBABIL
Page 58 and 59: of events with [X1>x 1 , X 2 >x 2 ,
Page 60 and 61: 2.4 Option C: Sufficient IMs: Estim
Page 62 and 63: predictions and hence required samp
Page 64 and 65: PEER has put forward PBSA methodolo
Page 66 and 67: 3.2.1 A DCF Displacement-Based Form
Page 68 and 69: parameter k (the slope of the hazar
Page 70 and 71: POST-EARTHQUAKE FUNCTION OF HIGHWAY
Page 72 and 73: ln( EDP) a b ln ( IM )= + (1)Probab
Page 74 and 75: terms of global and local bridge pe
Page 76 and 77: Figure 3. Bridge column component d
Page 78 and 79: 5.2 Method B: MDOF Residual Displac
Page 80 and 81: calculated using a 2 dimensional mu
Page 84 and 85: location. Transverse reinforcement
Page 86 and 87: 2.50.1000Spectral Accel. (g)2.01.51
Page 88 and 89: Results indicate that 33% of the re
Page 90 and 91: 4.1.2 Elastic vs. Inelastic ModelsF
Page 92 and 93: The increased dispersion leads to h
Page 94 and 95: AN ANALYSIS ON THE SEISMIC PERFORMA
Page 96 and 97: The survey stood on the condition t
Page 98 and 99: who decide the design force levels
Page 100 and 101: It is interesting to clarify whethe
Page 102 and 103: concluded that the dependence of in
Page 104 and 105: Table 10. Problems of performance-b
Page 106 and 107: DEVELOPMENT OF NEXT-GENERATION PERF
Page 108 and 109: ground shaking hazard, probable str
Page 110 and 111: Vulnerability of buildings to losse
Page 112 and 113: Peak Interstory Drfit Ratio0.120.10
Page 114 and 115: Conditional Probability ofDamage St
Page 116 and 117: Probability of Non-Exceedance10.80.
Page 118 and 119: APPLICATIONS OF PERFORMANCE-BASED E
Page 120 and 121: PRACTICAL ADAPTATION FOR STAKEHOLDE
Page 122 and 123: cost premium for the more expensive
Page 124 and 125: The future techniques will improve
Page 126 and 127: Benefit-cost ratio(BCR) 2.5UC Berke
Page 128 and 129: motivation to change the way they w
Page 130 and 131: CHANGING THE PARADIGM FOR PERFORMAN
Page 132 and 133:
Ideally, the preliminary design of
Page 134 and 135:
ModelM1M2M3Table 1. Description of
Page 136 and 137:
Sample results from the response-hi
Page 138 and 139:
In FEMA 273/356, the intersection o
Page 140 and 141:
(M8 and M9) and the isolated frames
Page 142 and 143:
THE ATC-58 PROJECT PLAN FOR NONSTRU
Page 144 and 145:
The development of next-generation
Page 146 and 147:
for these flexible nonstructural co
Page 148 and 149:
spectra is several times larger tha
Page 150 and 151:
The variability is associated with
Page 152 and 153:
functions for a wide variety of non
Page 154 and 155:
SIMPLIFIED PBEE TO ESTIMATE ECONOMI
Page 156 and 157:
One can show (Porter et al. 2004) t
Page 158 and 159:
( )FDM| EDP= xdm = 1 −FRdm , + 1,
Page 160 and 161:
1. Facility definition. Same as in
Page 162 and 163:
Table 1. Approximation of seismic r
Page 164 and 165:
The EAL values shown in Figure 3 mi
Page 166 and 167:
ASSESSMENT OF SEISMIC PERFORMANCE I
Page 168 and 169:
where e -λτ is the discounted fac
Page 170 and 171:
IDR 3[rad]σPFAIDR34(g)σ PFA4media
Page 172 and 173:
Figure 3a, shows an example of frag
Page 174 and 175:
P(C LVCC i |IM )1.00.80.60.40.20.00
Page 176 and 177:
E [ L T | IM ]$ 10 M$ 8 M$ 6 M$ 4 M
Page 178 and 179:
SEISMIC RESILIENCE OF COMMUNITIES
Page 180 and 181:
2. RESILIENCE CONCEPTSResilience fo
Page 182 and 183:
quantification tools could be used
Page 184 and 185:
structure remains elastic. This is
Page 186 and 187:
of Figure 7a will be used. It is as
Page 188 and 189:
Nigg, J. M. (1998). Empirical findi
Page 190 and 191:
acceleration with a 475-year return
Page 192 and 193:
limit states, the suggestions given
Page 194 and 195:
∆NSLsi= SϑH(5)iTFor column-sway
Page 196 and 197:
Pinto et al., 2004). The probabilit
Page 198 and 199:
The main difficulty in assigning a
Page 200 and 201:
Crowley, H., R. Pinho, and J. J. Bo
Page 202 and 203:
analytical models generally have si
Page 204 and 205:
Figure 2. Structure of the response
Page 206 and 207:
can be used as a random variable of
Page 208 and 209:
4. DERIVATION OF THE VULNERABILITY
Page 210 and 211:
5. CONCLUSIONSDerivation of vulnera
Page 212 and 213:
REFERENCESAbrams, D. P., A. S. Elna
Page 214 and 215:
In general, these types of bench-mo
Page 216 and 217:
where & x&(t ) = acceleration at th
Page 218 and 219:
science building. The lateral load-
Page 220 and 221:
emain the same, the magnitude of sl
Page 222 and 223:
of sliding thresholds, are desirabl
Page 224 and 225:
Retrofit of Nonstructural Component
Page 226 and 227:
was developed to accommodate these
Page 228 and 229:
tested by Meinheit and Jirsa are us
Page 230 and 231:
where D is the maximum drift and N
Page 232 and 233:
in predicting damage as well as rep
Page 234 and 235:
4.2.2 Modeling the Data Using Stand
Page 236 and 237:
that the defining demand using a no
Page 238 and 239:
• The influence on the dynamic re
Page 240 and 241:
deviations σ and correlation coeff
Page 242 and 243:
The first three modes of vibration
Page 244 and 245:
Details about the ten records selec
Page 246 and 247:
to allow a quantitative assessment
Page 248 and 249:
Cornell A. C., F. Jalayer, R. Hambu
Page 250 and 251:
limited possibilities of overcoming
Page 252 and 253:
uildings, up to five stories high (
Page 254 and 255:
Efficiency η, %100806040203D-RWBW-
Page 256 and 257:
Table 1. Performance criteria for c
Page 258 and 259:
Because the analytical model strong
Page 260 and 261:
REFERENCESAguilar, G., R. Meli, R.
Page 262 and 263:
tests of its type ever conducted. T
Page 264 and 265:
end work-point to work-point). And
Page 266 and 267:
Fig. 5 shows the actual application
Page 268 and 269:
3Roof Disp. (mm)250200150100500-50-
Page 270 and 271:
Base Shear (kN)Base Shear (kN)40002
Page 272 and 273:
8. CONCLUSIONSBased on the test and
Page 274 and 275:
REAL-TIME DYNAMIC HYBRID TESTING OF
Page 276 and 277:
:::::2004) can be formulated using
Page 278 and 279:
The structure to be simulated is di
Page 280 and 281:
measurements, to the modeling of th
Page 282 and 283:
Figure 8. Two stories (left) and hy
Page 284 and 285:
ROLES OF LARGE-SCALE TEST FOR ASSES
Page 286 and 287:
mid-height in the third story, at w
Page 288 and 289:
cycles were repeated for each ampli
Page 290 and 291:
the tests with ALC panels were excl
Page 292 and 293:
the relationship between the moment
Page 294 and 295:
attachment details adopted for inst
Page 296 and 297:
FULL-SCALE LABORATORY TESTING: STRA
Page 298 and 299:
economic losses resulting from the
Page 300 and 301:
4. OBJECTIVES AND OUTCOME OF STRUCT
Page 302 and 303:
15001000500Shear [kN]0-8.0 -6.0 -4.
Page 304 and 305:
5.1 3D Tests on a Torsionally Unbal
Page 306 and 307:
Non-linear substructuring was recen
Page 308 and 309:
PERFORMANCE BASED ASSESSMENT — FR
Page 310 and 311:
4 x 50 m = 200 mC1 C2 C3h u = 7 mh
Page 312 and 313:
some procedures are (contrary to th
Page 314 and 315:
5 th floor disp. [cm]0.60.0-0.6CC =
Page 316 and 317:
While the global drift of the build
Page 318 and 319:
the use of such connections in eart
Page 320 and 321:
I d = 0.25elastic limitmaximum resi
Page 322 and 323:
As regards the influence of differe
Page 324 and 325:
ON GROUND MOTION DURATION AND ENGIN
Page 326 and 327:
time between the first and last acc
Page 328 and 329:
FyFyFyFFFkk0.03kδδδcover a large
Page 330 and 331:
T5b, T13a, T13b, T20a and T20b can
Page 332 and 333:
Tabled results show that in the cas
Page 334 and 335:
0 0.25 0.5 0.75 1Dkin PfSa[g]0 0.25
Page 336 and 337:
ON DRIFT LIMITS ASSOCIATED WITH DIF
Page 338 and 339:
BehaviourElasticInelasticCollapseDa
Page 340 and 341:
Other factors such as the applied l
Page 342 and 343:
4. MOMENT RESISTING FRAMES4.1 Ducti
Page 344 and 345:
5Ductility factor432100 0.2 0.4 0.6
Page 346 and 347:
5.1 Flexural Structural WallsAn exa
Page 348 and 349:
MODAL PUSHOVER ANALYSIS: SYMMETRIC-
Page 350 and 351:
Floor963SeattleNonlinear RHAFEMA1st
Page 352 and 353:
The peak modal demands r n are then
Page 354 and 355:
9BostonSeattleLos AngelesFloor63RSA
Page 356 and 357:
5. EVALUATION OF MPA: UNSYMMETRIC-P
Page 358 and 359:
Without additional conceptual compl
Page 360 and 361:
AN IMPROVED PUSHOVER PROCEDURE FOR
Page 362 and 363:
for a response governed by the fund
Page 364 and 365:
2.2 Modal ScalingThe principal aim
Page 366 and 367:
2.3 Pushover-History AnalysisSubsti
Page 368 and 369:
(3) Calculate cumulative scale fact
Page 370 and 371:
46.4 58 58 58 58 58 58 58 58 58 58
Page 372 and 373:
EXTENSIONS OF THE N2 METHOD — ASY
Page 374 and 375:
The strength reduction factor due t
Page 376 and 377:
The relations apply to SDOF systems
Page 378 and 379:
in X-direction pushover curves prac
Page 380 and 381:
As an example, an idealized force-d
Page 382 and 383:
The IN2 curve can be used in the pr
Page 384 and 385:
HORIZONTALLY IRREGULAR STRUCTURES:
Page 386 and 387:
Dutta and Das (2002, 2002b and refs
Page 388 and 389:
They tested the procedure on three
Page 390 and 391:
Table 1. Properties of the 4 WallsW
Page 392 and 393:
The following is a summary of two s
Page 394 and 395:
ectangular concrete deck supported
Page 396 and 397:
REFERENCESAlmazan, J. L., and J. C.
Page 398 and 399:
Rosenblueth, E. (1957). “Consider
Page 400 and 401:
instantaneous period of vibration a
Page 402 and 403:
value of the maximum plastic deform
Page 404 and 405:
(a) elastic-perfectly plastic type(
Page 406 and 407:
where a is the constant peculiar to
Page 408 and 409:
Referring to Eq. (15), the natural
Page 410 and 411:
-The effective period obtained by u
Page 412 and 413:
eal damage data, rather than theore
Page 414 and 415:
liquefaction-induced damage. This i
Page 416 and 417:
Figure 5. Selected damage distribut
Page 418 and 419:
Figure 6. Idealized capacity spectr
Page 420 and 421:
I’ for the ductile case, as expec
Page 422 and 423:
This study has shown that a modific
Page 424 and 425:
thickness of the inner wall is usua
Page 426 and 427:
4. EARTHQUAKE GROUND MOTION INPUT A
Page 428 and 429:
5.2 Performance Levels and Limit St
Page 430 and 431:
where λ I jis the occurrence rate
Page 432 and 433:
intensity VI because the number of
Page 434 and 435:
and thus are not considered in seis
Page 436 and 437:
The values of the displacement modi
Page 438 and 439:
constant amplitude loading (CA) or
Page 440 and 441:
deterioration. These are the type o
Page 442 and 443:
members, is the main feature of the
Page 444 and 445:
RESULTS, DISCUSSIONS AND CONCLUSION
Page 446 and 447:
systems, where FEMA estimations are
Page 448 and 449:
The case study is a Hospital in the
Page 450 and 451:
Table 1. Dimensions and amount of r
Page 452 and 453:
4.2 Incremental AnalysisBase shear
Page 454 and 455:
When adding jackets to columns, the
Page 456 and 457:
storyShear in interior Column [ton]
Page 458 and 459:
PERFORMANCE-BASED SEISMIC ASSESSMEN
Page 460 and 461:
2. HYBRID FRAME BUILDINGSTwo precas
Page 462 and 463:
15’ - 0” 15’ - 0”Hybrid fra
Page 464 and 465:
and maximum residual inter-story fr
Page 466 and 467:
As the first step in understanding
Page 468 and 469:
Table 3. Comparison of calculated m
Page 470 and 471:
NEW MODEL FOR PERFORMANCE BASED DES
Page 472 and 473:
(a) interior beam-column joint(b) k
Page 474 and 475:
yxVN =VADjDBABLD jDOV cOVCN= VLV bV
Page 476 and 477:
3.3.2 B-modeThe equilibrium conditi
Page 478 and 479:
3.6 Failure ModeBased on the calcul
Page 480 and 481:
Name ofSpecimenTable 2. Comparison
Page 482 and 483:
EARTHQUAKE ACTIONS IN SEISMIC CODES
Page 484 and 485:
examination of the risk implication
Page 486 and 487:
Bozorgnia and Campbell (2004) find
Page 488 and 489:
structure, the results of inelastic
Page 490 and 491:
hazard curves will often vary throu
Page 492 and 493:
large uncertainties associated with
Page 494 and 495:
A PRAGMATIC APPROACH FOR PERFORMANC
Page 496 and 497:
Relative Height20118160.8140.6 1210
Page 498 and 499:
Yield Strength Coefficient, Cy2.01.
Page 500 and 501:
Yield Strength Coefficient, Cy*1.61
Page 502 and 503:
2.6 Preliminary DesignIn the preced
Page 504 and 505:
4. CONCLUSIONSIn the space availabl
Page 506 and 507:
EXAMINATION OF THE EQUIVALENT VISCO
Page 508 and 509:
of the bilinear model with the ener
Page 510 and 511:
3. STUDY PARAMETERS AND ASSESSMENT
Page 512 and 513:
decided to investigate the accuracy
Page 514 and 515:
DISPLACEMENT(m)DISPLACEMENT (m)DISP
Page 516 and 517:
The results for all 100 earthquake
Page 518 and 519:
CONTRASTING PERFORMANCE-BASED DESIG
Page 520 and 521:
Conceptual design is greatly facili
Page 522 and 523:
2. The availability of cost-of-repa
Page 524 and 525:
There are many questions to be answ
Page 526 and 527:
assess expected NSASS losses. For t
Page 528 and 529:
3.2.2 Design for Tolerable Mean Ann
Page 530 and 531:
THE PERFORMANCE REQUIREMENTS IN JAP
Page 532 and 533:
2.1 Law Enforcement and InspectionT
Page 534 and 535:
Splices and development of reinforc
Page 536 and 537:
as for the rising part of continuou
Page 538 and 539:
compressive stress of concrete is t
Page 540 and 541:
MOLIT Notification No. 1461 outline
Page 542 and 543:
AUTHOR INDEXH. Akiyama.............
Page 544 and 545:
F. Taucer .........................
Page 546 and 547:
PEER 2003/06PEER 2003/05PEER 2003/0
Page 548 and 549:
PEER 2001/13PEER 2001/12Modeling So
Page 550:
PEER 1999/04 Adoption and Enforceme
show all

Report - PEER - University of California, Berkeley

Create successful ePaper yourself

Delete template?

Save as template?