A RELIABILITY BASED SIMULATION, MONITORING AND CODE CALIBRATION OF VEHICLE EFFECTS ON EXISTING BRIDGE PERFORMANCE

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1 A RELIABILITY BASED SIMULATION, MONITORING AND CODE CALIBRATION OF VEHICLE EFFECTS ON EXISTING BRIDGE PERFORMANCE C.S. Cai 1, Wei Zhang 1, Miao Xia 1 and Lu Deng 1 Dept. of Civil and Environmental Engineering, Louisiana State University, Baton Rouge, Louisiana 783, cscai@lsu.edu. ABSTRACT This paper summarizes the recent work by the first author s research group related to vehicle effects on existing bridges, using reliability based performance assessment. The first part presents a simulation framework of fatigue reliability assessment for existing bridges considering the effects of vehicle speed, road roughness condition, equivalent stress range and the constant amplitude fatigue threshold. The second part develops a framework to estimate the extreme structural response due to live load in a mean recurrence interval based on short-term monitoring of existing bridges. The Gumbel distribution of the extreme values was derived from extreme value theory and Monte Carlo Simulation. Studies have shown that the vehicle-induced dynamic allowance IM value prescribed by the AASHTO LRFD code may be underestimated under poor road surface conditions (RSCs) of some existing bridges. In addition, the IM, which is a random variable with certain statistical properties, was modeled as a deterministic constant in the code calibration process. In the third part of this paper, the reliability indices of a selected group of prestressed concrete girder bridges are calculated by modeling the IM explicitly as a random variable for different RSCs. Appropriate IM values are suggested for different RSCs in order to achieve a consistent target reliability index and a reliable load rating for existing bridges. KEYWORDS Vehicle effects, existing bridges, calibrations, reliability, extreme values. INTRODUCTION Due to the progressive deteriorations and accumulated fatigue damages of structures under dynamic loads such as vehicles, it is essential to ensure the structure safety and calculate fatigue reliabilities. In fatigue design, the load-induced fatigue effect should be less than the nominal fatigue resistance. Naturally, the fatigue requirement can also be stated as the fatigue life consumed by the load being less than the available fatigue life of the bridge detail. However, the vehicle speed and road roughness conditions are not considered in a typical fatigue analysis such as in the American Association of State Highway and Transportation Officials (AASHTO) specifications (27). It has been proven that these two factors have significant effects on the dynamic responses of short span bridges (Deng and Cai 21; Shi et al. 28). In the present study, the deterioration of the road surface due to environmental corrosions and passages of truckloads is considered. In addition, the road may be resurfaced when the road surface becomes unacceptable. Therefore, the road roughness coefficient is considered to change periodically with time. A limit state function is defined in the present study to calculate the fatigue reliability. Besides the random vehicle speeds and road profiles, the traffic increase rate is taken into account in the present study to compare their effects on the fatigue reliability index and fatigue life. Recently developed structural health monitoring (SHM) systems of bridges can provide useful information with which bridge performance can be assessed and predicted more precisely. Instead of measuring the weight of every vehicle passing through bridges, SHM techniques can more conveniently record structural response such as strains under routine service traffic loads. The procedure of reliability assessment using monitoring data includes collecting survey data, identifying the distribution type of live load effects and estimating its distribution parameters by curve fitting. The extreme load effects are derived from the response of a bridge directly including each possible combination of the number of loaded lanes multiplied by a corresponding multiple presence factor to account for the probability of simultaneous lane occupation (Orcesi and Frangopol 21). For reliability calculations, with the help of the monitored data, one can minimize the uncertainties and apply fewer assumptions in structural analysis, thus make the reliability calculation more rational. One of the aims of this study is to develop a methodology that can establish the maximum live load effects distribution for

2 a mean recurrence interval with extreme value theories based on short-term monitoring data of structural response. VEHICLE-INDUCED FATIGUE RELIABILITY ASSESSMENT OF EXISTING BRIDGES Prediction of vehicle induced bridge vibration To predict vehicle-induced vibrations for fatigue assessment, the vehicle is modeled as a combination of several rigid bodies connected by several axle mass blocks, springs and damping devices (Cai and Chen 24). The tires and suspension systems are idealized as linear elastic spring elements and dashpots. The equations of motion for the vehicle-bridge coupled system are as follows: Mb d b Cb Cbb Cbv db Kb Kbb Kbv db Fb G M v d C v vb C v d K v vb K (1) v dv Fc Fv where, [M b ] is the mass matrix, [C b ] is the damping matrix and [K b ] is the stiffness matrix of the bridge, {F b } is wheel-bridge contact forces on bridge; [M v ], is the mass matrix, [C v ], is the damping matrix and [K v ] is the stiffness matrix of the vehicle; {F G v } is the self-weight of vehicle; and {F c }is the vector of wheel-road contact forces acting on the vehicle. The terms C bb, C bv, C vb, K bb, K bv, K vb, F b and F v in Eq. (1) are due to the interactions between the bridge and vehicles. To demonstrate the methodology, a 12m long and 13 m wide slab-on-girder bridge is analyzed, which is designed in accordance with AASHTO LRFD bridge design specifications (AASHTO 27). In the present study, after conducting a sensitivity studying by changing the meshing, solid elements and nodes are used to build the finite element model of the bridge. The damping ratio is assumed to be.2. The present study focuses on the fatigue analysis at the longitudinal welds located at the conjunction of the web and the bottom flange at the mid-span. Since the design live load for the prototype of the bridge is HS2-44 truck, this three-axle truck is chosen as the prototype of the vehicle in the present study. In addition, only one vehicle in one lane is considered to travel along the bridge for fatigue analysis due to its short span length. Road surface roughness is an important parameter that causes dynamic effect and fatigue problem. It is generally defined as an expression of irregularities of the road surface and it is the primary factor affecting the dynamic response of both vehicles and bridges (Deng and Cai 21; Shi et al. 28). Road roughness condition is classically quantified using Present Serviceability Rating (PSR), Road Roughness Coefficient (RRC) or International Roughness Index (IRI). Various correlations have been developed between the indices (Paterson 1986; Shiyab 27). Based on the studies carried out by Dodds and Robson (1973) and Honda et al. (1982), the road surface roughness was assumed as a zero-mean stationary Gaussian random process and it could be generated based on the RRC through an inverse Fourier transformation as (Wang and Huang 1992): N r( x) 2 ( nk ) n cos(2 nk x k ) (2) k 1 where θ k is the random phase angle uniformly distributed from to 2; () is the power spectral density (PSD) function (m 3 /cycle/m) for the road surface elevation; n k is the wave number (cycle/m). Wang and Huang (1992) also suggested a concise power-spectrum-density function that was used in the present study: n 2 ( n) ( n )( ) (3) n where ( n) is the PSD function (m 3 /cycle) for the road surface elevation; n is the spatial frequency (cycle/m); n is the discontinuity frequency of 1/2 (cycle/m); and ( n ) is the RRC (m 3 /cycle) and its value is chosen depending on the road condition. In order to consider the road surface damages, a progressive deterioration model for road roughness is necessary. More specifically, it is essential to have such a model for RRC in order to generate the random road profile. Therefore, the RRC at any time after construction is predicted using the progressive deterioration model for IRI and the relationship between the IRI and RRC(Paterson 1986; Shiyab 27): 9 ( 5 6 ) exp 1.4 t n t e IRI 263(1 SNC) CESAL / t (4) Fatigue Assessment Based on Miner s rule, the accumulated fatigue damages could lead to bridge failures. According to Miner s rule, the accumulated damage is ni ntc Dt () (5) N N i i

3 where n i is number of observations in the predefined stress-range bin S ri, N i is the number of cycles to failure corresponding to the predefined stress-range bin; n tc is the total number of stress cycles and N is the number of cycles to failure under an equivalent constant amplitude loading (Kwon and Frangopol 21): m N A S re (6) where S re is the equivalent stress range and A is the detail constant taken from Table in AASHTO (AASHTO, 27). Either using the Miner s rule or Linear Elastic Fracture Mechanics (LEFM) approach, the equivalent stress range for the whole design life is obtained through the following equation (Chung 26): 1/ m n m Sre i Sri (7) i1 where α i is the occurrence frequency of the stress-range bin, n is the total numbers of the stress-range bin and m is the material constant that could be assumed as 3. for all fatigue categories (Keating and Fisher 1986). Since each truck passage might induce multiple stress cycles, two correlated parameters were essential to calculate the fatigue damages done by each truck passage, i.e. the equivalent stress range and numbers of cycle per truck passage. In the present study, a new single parameter, S w, is introduced for simplifications to combine the two parameters on a basis of equivalent fatigue damage; namely, the fatigue damage of multiple stress cycles is the same as that of a single stress cycle of S w. For truck passage j, the revised equivalent stress range is defined and derived as: 1/m S N S (8) j j j w c re where N j c is the number of stress cycles due to the j th j truck passage, and S re is the equivalent stress range of the stress cycles by the j th truck. When D(t) is 1, the structure approaches to fatigue failure based on the Miner s rule. Correspondingly, the limit state function (LSF) is defined (Nyman and Moses 1985): g( X ) Df D( t) (9) where D f is the damage to cause failure and is treated as a random variable with a mean value of 1; D(t) is the accumulated damage at time t; and g is a failure function such that g< implies a fatigue failure. In the present study, the typical representative vehicle speed ranges (i.e. vehicle speed from 1m/s to 6m/s), lane numbers (i.e. the fast lane or the slow lane) and road roughness conditions (i.e. from very good to very poor) are defined. The overall fatigue damages are a summation of damages done by the trucks under all vehicle speed ranges, lane numbers and road roughness conditions. Therefore, the accumulated damage D(t) is: j n m 1 1 m truck Nc j j j D() t n m truck Sw A ntr A p j Sw j (1) j A S j j re where p j means the probability of case j, and here case j is defined as a combination of vehicle speed, road roughness condition and lane numbers. Based on such a definition, a combination of the six vehicle speed ranges, five road roughness conditions and two lane numbers leads to 6 cases. For fatigue assessment, all the random variables in the LSF for predicting fatigue reliabilities are assumed to follow certain distributions, which are detailed as the following: D f, the accumulated damage at failure, is considered as a random variable. Its mean and COV value is assumed as 1. and.15, respectively. The COV value are chosen to ensure that 95% of variable amplitude loading tests have a life within 7-13% (±2 Standard deviation) of the Miner s rule prediction (Nyman and Moses 1985). The ADTT for trucks often varies greatly for bridges at different sites and causes the variations of the estimated fatigue life and fatigue reliability. The ADTT can be calculated and predicted from filed monitoring data. As discussed earlier, the ADTT for the trucks HS2-44 is assumed as a deterministic parameter that equals to 2 in the first year. The ADTT number might remain the same or increase if a traffic increase is considered (i.e. α = %, 3% or 5%). The present study is concerned with the fatigue cracks that may develop at the longitudinal welds located at the conjunction of the web and the bottom flange at the mid-span, which falls into fatigue detail Category B (AASHTO 27). When the fatigue detail coefficient A is assumed to follow a lognormal distribution, the mean and COV values can be calculated based on the test results of welded bridge details. Based on the tests performed by Keating and Fisher (1986), the mean and COV are calculated as and.34. S w, the revised equivalent stress range, is calculated for given combinations of vehicle speed and road roughness condition. In the present study, the chi-square goodness-of-fit test is used to check the distribution type of the parameter S w for each combination of vehicle speed and road roughness condition. Based on Sturges rule, the number of intervals is seven for a 5-data bin and the degree of freedom is four. If a 5% significance level is chosen, the test limit for the Chi-Square test is calculated as C.95,4 = As demonstrations in the present study, six out of the total thirty groups of cases are employed to verify the distribution type. Both normal and lognormal are acceptable for revised equivalent stress range S w based on the Chi-Square test.

4 Based on the assumption that all the variables (i.e. A, D f and S wj ) follow a certain distribution, the fatigue reliability index is obtained using the method in the literature (Estes and Frangopol 1998). Based on such a method, an arbitrary initial design point can be chosen and the solving process for the complex equation of g()= can be avoided. After several iterations, convergence can be achieved without forcing every design points to fall on the original failure surface. In order to investigate the effects of the vehicle speed and road roughness condition on the fatigue reliability, the fatigue reliability are calculated for all the 3 combinations of 6 vehicle speeds from 1m/s to 6m/s and 5 road roughness conditions from very good to very poor. The limit state function for a given combination of vehicle speed and road roughness condition is simplified as: m ntr Sw g( X ) Df (11) A Based on the LSF function, the fatigue reliability index, β, can be derived, assuming that all random variables (i.e. A, D f and S w ) are lognormal, as follows: m ln n f w ( m ) D A S tr Df A Sw where D f, A, S and w D, f A, S denote the mean value and standard deviation of ln(a), ln(d w f ) and ln(s w ), respectively. Generally, the fatigue reliability indices are found to decrease with the increase of vehicle speed and road roughness coefficient. If a 5% failure probability, i.e., a 95% survival probability is assumed, the corresponding reliability index is 1.65 (Kwon and Frangopol 21). When the vehicle increase rate is %, the reliability index in all the thirty cases is larger than the target index of Accordingly, the survival probability of all the thirty cases is larger than 95%. When the vehicle increase rate is 3% or 5%, seven or eight cases are found with a fatigue reliability index less than 1.65, i.e., the probability of fatigue failure for the bridge is larger than 5% during its 75 years life. In addition, when the vehicle increase rate is 5% and the road roughness condition is very poor, the reliability index is negative, which suggests the bridge would be more likely to suffer fatigue failure than to survive in its 75 years life. In general, the higher vehicle speed, the smaller reliability index and the higher probability of failure the structure will have in most cases. The deteriorated road surface seems to accelerate fatigue damages due to the dynamic effects from vehicles, which implies the importance of road surface maintenances for existing bridges. Table 1 Fatigue reliability index and Fatigue life Α β (for Fatigue life of 75 years) (12) Fatigue life for target β=1.65 (unit: years) % % % In the real circumstances, vehicle speeds vary for different trucks and road surface conditions deteriorate with time. By treating the vehicle speed and road roughness as random variables as discussed earlier, the fatigue reliability index is calculated and listed in Table 1 for different traffic increase rate, i.e., α= %, 3% and 5%. The fatigue life corresponding to a target fatigue reliability of 1.65 is also presented in the table. As expected, the predicted fatigue life is longer than that if we assume the road roughness is poor or very poor and shorter than that if we assume the road roughness is good or very good. For the current modeling of the vehicle speed and road surface deteriorations, the fatigue life of the bridge components is comparable with the case with a 6m/s vehicle speed and an average road-roughness condition. ESTIMATE THE EXTREME STRUCTURAL RESPONSE This section is focus on the estimation of the extreme structural response based on monitoring data. At present, the live load applied to calculate the reliability index was computed based on the live load models that were developed by Nowak (1993) and used in the calibration of the early version of AASHTO LRFD Bridge Design Specifications (AASHTO 1994). The models were derived from the available statistical data on 9,25 selected truck surveys, and weigh-in-motion measurements. For a structure with a given capacity, its reliability index is only related to the maximum load effect distribution corresponding to the structure s service life. Assuming a normal distribution for the individual truck load, the maximum live load effects (moment or shear) for various time periods were determined by extrapolation as follows. Let the live load effects following certain distribution Ω, and the number of trucks in the surveying interval is. Then, the total number of trucks passing through the bridge in an expected service life, will be

5 The maximum live load effects corresponding to any expected bridge service life is ( ) where is the inverse of the standard distribution function. According to AASHTO specifications, the expected service life for a new bridge is 75 years. According to Orcesi and Frangopol (21), the extreme value distribution of SHM data is assumed to approach a Gumbel probability distribution (Gumbel 1958). ( ( )) where is the cumulative distribution function of Gumbel probability distribution, both μ and σ are constants to be determined from the measured data. Thus, the extreme values of the SHM data in a mean recurrence interval,, ( is longer than the monitoring period), can be predicted as [ ( )] Using these methods to estimate the extreme value of load effects in a mean recurrence interval, the information of the number of the trucks running through the bridge must be available. However, sometimes it is not easy to identify the number of trucks only by dealing with the recorded strain data. Even the number of the trucks is known, some cases whose maximum structural response is induced by multiple presences of vehicles side by side or one after another in a same span are still excluded in the reliability calculation. The aim of this part is to develop a methodology that can establish the maximum live load effects distribution for a mean recurrence interval with extreme value theories based on short-term monitoring data of structural response. Extreme Value Theory Since only the maximum structure response is concerned, it is reasonable to use extreme theories to estimate the long-term maximum response from the short-term records of structure response monitoring. In this study, the Gunbel distribution is used to model the extreme values of long (finite) sequences of independent, identically distributed random variables. Gumbel distributions also known as Type I extreme value distribution within the extreme value theory. Let the variable be the maximum of independent random variables. Since the inequality implies for all i, it follows that The probabilities are referred to as the initial distributions of the variables. In the particular case in which all the variables have the same probability distribution, the probability distribution of becomes If the number becomes large enough, the cumulative distribution of the largest values approach limits known as Type I or Type II extreme value distributions if the initial distributions are of the exponential or of the Cauchy type, respectively (Simiu and Scanlan 1986). Probabilistic Modeling of Maximum Live Load Effects for a Mean Recurrence Interval For simplification, let s use the yearly maximum live load effects as a demonstration. The yearly maximum live load effect is the extreme value of live load effects the structure is subjected in a year. A year can be divided into time segments; the maximum live load effects in each time segment,, is a variable and can be obtained with bridge health monitoring system. The extreme values are assumed to be independent with each other and have the same distribution with a cumulative distribution function. The probabilities,, is referred to as the initial distribution. The distribution of yearly maximum live load effect can be derived according to Eqs. (17) and (18) as: The accuracy of the estimation of the yearly maximum live load effects probability distribution depends on the accuracy of the distribution of the initial population and the number of the intervals. For different number of time segments and (or different length of time segments, seg_1 and seg_2), initial distribution and can be obtained. The distribution of the extreme live load effects in a mean recurrence interval can be derived in terms of and as follow:

6 Probability Density Function Probability Density Function Probability Density Function Probabilily Density Function The 5th Cross-strait Conference on Structural and Geotechnical Engineering (SGE-5) For example, the yearly extreme structure response distribution can be derived from initial distributions based on time segments of an hour or a minute as: (21) where and are initial distributions and they represent the maximum structure response cumulative distribution function for 1 hour and 1 minute, respectively. The initial distribution can be derived by distribution fitting of the monitored data. It shows in Eq. (2) and Eq. (21) that the yearly maximum live load distribution is unique; the initial distributions corresponding to different length of time segments are not unique. To estimate a reasonable number of intervals or to determine the length of the time segment requires that the following two principles are satisfied (Duan et al. 22): 1. The time segment is long enough so that the maximum live load in every interval satisfies independence requirement. 2. The length of the time segment is reasonable so that the maximum live loads in every interval follow the same distribution. These two conditions require the length of the time segments is long enough so that the structural response record in every time segment is a stationary and ergodic process. The property of stationarity of a stochastic process always refers to the process being unchanged when shifting along the time axis (Lutes and Sarkani 24). For an ergodic process, its statistical properties (such as its mean and variance) can be deduced from a single, sufficiently long sample (realization) of the process. In other words, statistical properties obtained from a single time-series will approach definite limits independent of the particular series as the length of the series increases. Once the initial distribution of the parent population is determined, the maximum distribution in any mean recurrent intervals can be derived from Eq. (2) and Eq. (21). Case Study With time segment of 8s With time segment of 5s Strain (1.E-6) Strain (1.E-6).25 With time segment of 9s With time segment of 3s Strain (1.E-6) Strain (1.E-6) Fig. 1 Initial distribution fitting using Gumbel distribution: time segment of (a) 8s; (b) 5s; (c) 9s; (d) 3s Time history record of strains at the mid-span of a steel girder in the CORIBM Bridge on route LA 7 in District 61, Assumption Parish, Louisiana, were recorded. Since only three hours monitoring data is available, it is not

7 Probability Density Function m (1.E- 6) The 5th Cross-strait Conference on Structural and Geotechnical Engineering (SGE-5) advisable to estimate extreme strain distribution for a very long mean recurrence interval. The extreme strain distribution (Gumbel distribution) for mean recurrence intervals of 1 day, 1 days, 3 days, 18 days and one year were estimated using maximum likelihood estimation method as shown in Fig. 1. The yearly extreme strain distribution can be derived from the initial distributions with time segments of 9s or 3s as where the initial distributions and have been obtained from distribution fitting previously. It is difficult to prove directly that Eq. (22) is tenable and it is difficult to derive the parameters of yearly extreme response distribution through an analytical method. An alternative method is to generate samples using Monte Carlo simulation following the distribution functions on the right side of Eq. (22), and then, fit the generated samples with the selected distribution function, Gumbel distribution (maximum cases). The factors derived from distribution fitting were shown in Fig. 2. From Fig. 2, it is seen that both the location factor μ and the scale factor σ show converging property as the length of time segment increases. For different mean recurrence intervals, μ converges to different values, but σ converges to a fixed value. The location factor μ determines the mode value of the distribution while the shape factor σ determines the variance or the standard deviation of the distribution. Its location shifts to the right direction as the mean recurrence interval increases. The distributions have different mode values but same variance for different mean recurrence intervals. The PDF of extreme strain distribution for mean recurrence intervals of 1 day, 1 days, 3 days and one year are shown in Fig day 1 days 3 days one year day 1 days 3 days one year Time Segment (s) Time Segment (s) Fig. 2 Extreme strain distributions parameter, μ, σ, derived from different initial distributions Mean recurrence interval of 1 day Mean recurrence interval of 1 days Mean recurrence interval of 3 days Mean recurrence interval of 18 days Mean recurrence interval of one year Extreme Strain (1.E-6) Fig. 3 PDF of extreme strain distribution for mean recurrence intervals of 1 day, 1 days, 3 days and one year

8 CALIBRATION OF IMPACT FACTOR FOR EXISTING BRIDGES Impact factors of existing bridges may be significantly different from code specified values. Therefore, in the present study the impact factor of existing bridges is calibrated through a reliability approach. The following design equation, recommended by the current LRFD code (AASHTO 24) for considering situations with only dead loads and vehicle live loads, was used in the calibration process. φr 1.25DC 1.5DW 1.75LLl 1.75(1 IM ) LL t (23) where R = nominal value for the resistance, DC = effects due to design dead loads excluding the weight of wearing surface, DW = effects due to wearing surface weight, LL = effects due to design lane load, LL = effects due to the most demanding between truck and tandem load, IM LL t LL -1=.33 denotes the l, dyn t dynamic load allowance(impact factor), in which LL t, = effects due to the most demanding between truck dyn and tandem load including the dynamic effects, and φ = resistance factor. For prestressed-concrete bridges, the current AASHTO LFRD code suggests a resistance factor of 1. and.85 for moment and shear, respectively, based on the study by Nowak (1995). In order to calibrate the impact factors for existing bridges, a group of seven prestressed concrete girder bridges were selected as benchmark bridges in this study. The detailed configurations and properties of the seven prestressed concrete girder bridges are described in Deng and Cai (21). By assuming certain statistical properties of the impact factors under different road surface conditions (RSCs) and explicitly modeling the IM as an individual random variable, calibrations can be performed with respect to different RSCs (Deng et al. 211). The proposed IMs have been chosen with the aim of balancing three different needs, i.e., (1) obtaining reliability indices consistent with the target reliability index of 3.5 for all bridges under any RSC, (2) ensuring as much as possible consistency with the AASHTO LRFD code (24), and (3) minimizing the modifications to the IM values suggested by the AASHTO LRFR manual (23). Table 2 provides, for all the RSCs considered, (1) the minimum values of IM required to reach the target reliability index of 3.5 for both moment and shear strength limit states for all the bridges considered here, (2) the proposed values of IM for rating of existing bridges, and (3) the values of IM proposed by two of the authors in a previous study (Deng and Cai 21). From Table 2, it is observed that the IMs proposed in the present study are close to those proposed in Deng and Cai (21), except for the case of very poor RSC. Table 2. Comparison between the proposed dynamic load allowance IMs in the present study and those by Deng and Cai (21) Deng and Cai (21) Present study Road Surface Theoretical Minimum Condition Proposed IMs Proposed IMs IMs Very Poor Poor Average Good Very Good To verify whether the proposed IM can lead to a consistent reliability index of 3.5 for all RSCs, the reliability indices are recalculated for the seven bridges designed following Eq. (23) while employing the proposed IM values. These results confirm that using the proposed IM values produce more consistent reliability indices that are very close to the target reliability index of 3.5, regardless of what the actual RSC is. It is noteworthy that, when the RSC is below average, the proposed IM values are greater than the value of.33 suggested by the current LRFD code. In particular, the IM value proposed for very poor RCS is significantly larger than.33 (i.e., more than seven times larger). Since a significant portion (i.e., more than 17%) of all bridge decks in the United States belong to fair or worse RSCs, it is concluded that the use of different IMs, which account for the different RSCs, is necessary for accurate performance evaluation of existing bridges. SUMMARY AND CONCLUSIONS This paper summarizes the research group s work related to vehicle effects on existing bridges, using reliability based performance assessment. The first part presents a simulation framework of fatigue reliability assessment for existing bridges considering the effects of vehicle speed, road roughness condition, equivalent stress range and the constant amplitude fatigue threshold. The second part develops a framework to estimate the extreme t

9 structural response due to live load in a mean recurrence interval based on short-term monitoring of existing bridges. The Gumbel distribution of the extreme values was derived from extreme value theory and Monte Carlo Simulation. In the third part of this paper, the reliability indices of a selected group of prestressed concrete girder bridges are calculated by modeling the IM explicitly as a random variable for different RSCs. Appropriate IM values are suggested for different RSCs in order to achieve a consistent target reliability index and a reliable load rating for existing bridges. REFERENCES American Association of State Highway and Transportation Officials (AASHTO) (24). LRFD bridge design specifications, Washington, DC. American Association of State Highway and Transportation Officials (AASHTO). (27). LRFD bridge design specifications, Washington, DC. Cai, C. S., and Chen, S. R. (24). "Framework of vehicle-bridge-wind dynamic analysis." Journal of Wind Engineering and Industrial Aerodynamics, 92(7-8), Chung, H.-Y., Manuel, L., and Frank, K. H. (26). "Optimal Inspection Scheduling of Steel Bridges Using Nondestructive Testing Techniques." Journal of Bridge Engineering, 11(3), Deng, L, and Cai, C. S. (21). Development of dynamic impact factor for performance evaluation of existing multi-girder concrete bridges. Engineering Structures, 32, Deng, L., and Cai, C. S. (21). "Development of dynamic impact factor for performance evaluation of existing multi-girder concrete bridges." Engineering Structures, 32(1), Deng, L., Cai, C.S., and Barbato, M. (211). Reliability-based dynamic impact factor for prestressed concrete girder bridges. Journal of Bridge Engineering, ASCE. In press. doi:1.161/(asce)be Dodds, C. J., and Robson, J. D. (1973). "The Description of Road Surface Roughness." Journal of Sound and Vibration, 31(2), Duan,Z., Ou,J., and Zhou, D. (22). "Optimal probability distributions of extreme wind speeds" China Civil Engineering Journal, 35(5), Estes, A. C., and Frangopol, D. M. (1998). "RELSYS: A computer program for structural system reliability." Structural Engineering and Mechanics, 6(8), 91. Gumbel, E. J. (1958). Statistics of extremes, Columbia University Press, New York. Honda, H., Kajikawa, Y., and Kobori, T. (1982). "SPECTRA OF ROAD SURFACE ROUGHNESS ON BRIDGES." Journal of the Structural Division, 18(ST-9), Keating, P. B., and Fisher, J. W. (1986). "Evaluation of Fatigue Tests and Design Criteria on Welded Details." NCHRP Report 286, Transportation Research Board, Washington, D.C. Kwon, K., and Frangopol, D. M. (21). "Bridge fatigue reliability assessment using probability density functions of equivalent stress range based on field monitoring data." International Journal of Fatigue, 32(8), Lutes, L. D., and Sarkani, S. (24). Random vibrations : analysis of structural and mechanical systems, Elsevier, Amsterdam ; Boston. Nowak, A. S. (1993). "Live load model for highway bridges." Structural Safety, 13(1-2), Nowak, A. S. (1995). Calibration of LRFD bridge code. Journal of Structural Engineering, 121(8), Nyman, W. E., and Moses, F. (1985). "Calibration of Bridge Fatigue Design Model." Journal of Structural Engineering, 111(6), Orcesi, A. D., and Frangopol, D. M. (21). "Inclusion of crawl tests and long-term health monitoring in bridge serviceability analysis." Journal of Bridge Engineering, 15(3), Paterson, W. D. O. (1986). "International Roughness Index: Relationship to Other Measures of Roughness and Riding Quality." Transportation Research Record 184, Washington, D.C. Rackwitz, R. and Fiessler, B. (1978). "Structural Reliability under Combined Random Load Sequences." Computer and Structures, 9, Shi, X., Cai, C. S., and Chen, S. (28). "Vehicle Induced Dynamic Behavior of Short-Span Slab Bridges Considering Effect of Approach Slab Condition." Journal of Bridge Engineering, 13(1), Shiyab, A. M. S. H. (27). "Optimum Use of the Flexible Pavement Condition Indicators in Pavement Management System." Ph.D Dissertation, Curtin University of Technology.

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