KSCE Journal of Civil Engineering (2013) 17(3):556-567 DOI 10.1007/s12205-013-0007-8
Load Rating and Assessment of Bridges
www.springer.com/12205
Load Rating of Highway Bridges by Proof-loading Joan R. Casas* and Juan D. Gómez** Received January 10, 2013/Accepted February 19, 2013
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Abstract Aging and lack of maintenance are a matter of increasing concern for most bridges that are part of the road and railway systems of the European Union. Many of these bridges are very old and without documentation and as a consequence load rating by analytical tools is not possible. This paper explains how a possible way to assess their capacity is by means of a so-called “proof load test”. The work was developed as part of the Project ARCHES (Assessment and Rehabilitation of Central European Highway Structures) funded by the VI Framework Program of the European Union. A methodology of proof load testing for existing highway bridges is proposed and applied to the traffic conditions of several European Countries. The final objective is to provide guidance on the appropriate target proof load to be used based in very simple parameters of the bridge as span-length and percentage of heavy traffic. Keywords: bridges, assessment, structural reliability, field testing, loads, nondestructive testing ···································································································································································································································
1. Introduction Existing bridges in several parts of the world, including Europe, are aging. This is because of the great expansion in road and railway construction occurred during the post-World War period, the fifties and sixties. For this reason the assessment and maintenance of the existing structures is every day more and more important. The increase of traffic and specifically of the vehicles load capacity causes a greater effect on bridges. This increase along with a deficient maintenance has caused in some countries the deterioration of these structures. The consequences are serious in main highway bridges and can be enhanced due to fatigue, corrosion and other forms of material deterioration. During the last years, new codes for the assessment of existing bridges have been developed in several European countries as UK, Denmark and Switzerland. Building on the experience from the various national codes and recent research developed in different European Projects (BRIME, 2001; COST345, 2004; SAMARIS, 2006; SUSTAINABLE BRIDGES, 2007; ARCHES, 2009), the possibility of developing a new Eurocode for Bridge Safety Assessment is under consideration. This Code should be based on the most advanced techniques for load rating and assessment of existing bridges and therefore, must include the following key elements: 1) the possibility of directly using reliability-based methods, 2) the inclusion of structural system redundancy and robustness, 3) the use of site-specific live loads and dynamic amplification factors, 4) the incorporation of field
measurements and diagnostic test data and 5) the use of proof load testing. Development of items 1 to 4 has been carried out elsewhere (Casas, 2000; Casas, 2010; Wisniewski et al., 2009a,b; Casas and Wisniewski, 2011; Ghosn and Casas, 1996; Rodrigues et al., 2011; Cavaco et al., 2011; Cavaco et al., 2013; Anitori et al., 2011; Anitori et al., 2012; Anitori et al., 2013). The objective of the present paper is to deal with proof load testing, explaining the safety background behind the method and then showing its implementation in a practical case. The load rating of a bridge tries generally: a) to confirm the maximum load that the structure can support under acceptable safety conditions or b) to increase the service load limit. Nevertheless, usually the standard theoretical methods used in the capacity assessment give very conservative results and the actual resistance is usually much higher. This is because many of the methods do not exactly reflect the complex structural behavior. The normal methods for calculating the bridge resistance tend to be conservative and often do not take into account some reserve capacity that comes from additional and/or hidden sources of strength (composite action between slab and girders in bridges that were designed as non-composite, rigid or semi-rigid connections that were designed as flexible, …). Thus, the objective of load testing is to optimize bridge assessment by finding hidden reserves in the load carrying capacity. Savings in such optimized assessment and, consequently, in less severe rehabilitation measures on deteriorating structures, can be significant. Another problem when evaluating old structures is the difficulty to identify the actual properties, as well as the selection of a
*Professor, Dept. of Construction Engineering, Universitat Politècnica de Catalunya (UPC), 08034 Barcelona, Spain (Corresponding Author, E-mail:
[email protected]) **Engineer, Integral S.A., Carrera 46 52-36 Piso 10. Medellín, Colombia (E-mail:
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Load Rating of Highway Bridges by Proof-loading
suitable safety level, especially considering the load regulations of new trucks. All these situations are an actual problem at the European Union (EU) as consequence of incorporation of New Member States (NMS), many of them from East Europe. The increasing volume of European transport urgently requires an effective road and rail system in Central and Eastern European countries. To bring this transport infrastructure up to modern European standards will require an immense investment (estimated by the European Commission to be about €100 billion), and therefore difficult to achieve in the medium term taking into account the actual economic situation. New motorways will be required with many new bridges, but, more important, numerous existing bridges will need to be assessed, and a large portion of them improved or replaced. Thus, it takes great importance the development of more appropriate bridge capacity assessment techniques and procedures to avoid unnecessary interventions (repairs/replacements) in the existing road network. One of these techniques can be obtained by means of a proof load test where existing bridges are proven (Moses et al., 1994). During the proof load test performed, often, the structure reveals resistance reserves, due to the contribution of nonstructural elements, supports behavior, better materials properties, etc. (Minervino et al., 2004). The main difficulty in the execution of a proof load test is in the estimation of the value of the proof load to apply during the test, so that this is sufficiently representative to evaluate the capacity of the bridge with an appropriate safety level, and without causing irreversible damages or the collapse of the structure. In this paper, proof loading is presented. The correct application of the method should combine an accurate execution and monitoring of the loading process and the accurate estimate of the actual traffic in the bridge. This can be achieved by the most advanced WIM techniques available, also developed and applied within the ARCHES project (ARCHES-D08, 2009).
2. Proof Load Testing This test is used to verify component and system performance under a known external load and is normally aimed to provide a complementary assessment methodology to the theoretical assessment. The use of such tests, due to the risks of collapse or of damaging essential elements of the structure, must be restricted to bridges that have failed to pass the most advanced theoretical assessment and are therefore condemned to be posted, closed to traffic or demolished. It is also important that the bridge has a high level of redundancy to be a good candidate. Furthermore, some balance has to be found between the risk of failure under the test load and the benefit of an updated reliability of the bridge. In some cases when the bridge is in poor condition due to lack of maintenance or because of an extreme loading event, such as flooding or impact, the actual resistance of the remaining bridge is difficult to assess without a detailed inspection, but it can still Vol. 17, No. 3 / April 2013
carry a high percentage of design load. The actual resistance of the bridge is difficult to assess without a detailed inspection. Even in the case that this information is provided thanks to an inspection process, the theoretical models to obtain bridge resistance can be hardly adopted. In such cases, a proof load can be also of interest to define the allowable load in the bridge. Of course, to follow up the loading sequence and the bridge response accurately and not produce more damage in the bridge or even its failure, it is mandatory to use an accurate monitoring system. The use of this type of test may be also recommended in the case of bridges with high redundancy level and where an accurate theoretical model of behavior or an accurate definition of geometry and material properties is not possible due to lack of information (no drawings). This can be, for instance, the case of old masonry arch bridges. If the failure could be sudden, without warning, proof testing should not be used. In this test, the bridge is loaded with a high percentage of the design loading to prove that its behavior is in compliance with the design or to a high percentage of the actual traffic to prove that the bridge can carry the existing traffic. One of the main concerns when executing a proof load tests is the level of damage and risk due to the high load applied. The load is applied incrementally and the most important decision is when the loading increase must stop in order not to permanently damage the bridge or even cause a failure. The way to control the risk is by appropriate monitoring during the test. However, it should be pointed out that the possibility of incurring permanent damage with the test is extremely small (of the more than 250 bridge tests conducted in Ontario, not a single bridge suffered any damage because of testing), providing the test is planned and executed carefully and methodically monitored (ISIS, 2001). Proof load testing provides an alternative to analytically computing the load rating of a bridge. A proof test “proves” the ability of the bridge to carry its full dead load plus some “magnified” live load. Normally, a higher load than the live load the bridge is expected to carry is placed on the bridge. This is done to provide a margin of safety in the event of an occasional overload during the normal operation of the bridge. Before the execution of the test, the target proof load has to be defined. The maximum target load should be applied in several increments while observing structural response. Also in this case, the measurement of the temperature during the period of execution is necessary to correct the results of the test according to the temperature variations. The first-stage loading should not exceed 25% of the target proof load, and the second stage loading should not exceed 50%. Smaller increments will be implemented when the applied proof load approaches the target load. Before a new loading scheme is applied, it is mandatory to remove from the deck all loads corresponding to the previous loading scenario. This is not necessary in the case of simply supported bridges. The bridge is carefully and incrementally loaded in the field until the bridge materials approaches their elastic limit, but never
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exceeding it. At this point, the loading is stopped and the maximum applied load and its position on the bridge is recorded. The maximum applied load can be lower than the target proof load and the percentage of total traffic loading according to that maximum can be evaluated. Monitoring at critical locations should be performed during the loading increase to determine the onset of non-linear behavior. Once any non-linearity is observed, the bridge should be unloaded immediately and the deflection recovery recorded. The strain in the materials in the most critical sections of the bridge should also be measured in order to guarantee that the elastic limit of the materials (if known) is not reached. The load is applied in accordance to a loading scheme and held for a certain time period. Loads must be moved to different positions to check all load path components. Upon execution of a proof load test and load removal, the bridge should be inspected to see that no damage has occurred (excessive crack width, deflection, opening of cracks in prestressed concrete structures…) The personnel in charge of the execution should have a proved qualification and experience in the execution of similar tests. In certain situations, safety shoring may be erected underneath the bridge to provide safety in case of failure.
3. Safety Assessment by Proof Load Testing The proof load level should be sufficiently higher to ensure the desired level of safety if the bridge passes the test. A load higher than the one the bridge is expected to carry along its entire service life is placed on the bridge. This account for uncertainties, in particular the possibility of bridge overloads during the normal operation and the impact factor, because proof load tests are normally executed in a static way. Different alternatives are available to define both representative loads (target and maximum proof load) as presented in AASHTO – LRFR (2003) and DAfStb (2000). The method proposed in the ARCHES project (ARCHESD16, 2009) is based on the same philosophy as for the AASHTO recommendations. The idea is to use a reliability-based approach to obtain the target proof load that guarantees a required safety level on the bridge against the actual traffic. However, the method is not restricted to the assumption of Normal distributions for all variables involved. In particular, the traffic action is considered as Gumbel distributed. The final objective was to derive a simple method based on figures, charts and tables that a bridge evaluator without specific knowledge of reliability theory can easily apply and obtain calibrated target proof load factors to derive the load level to be reached, depending on the safety level also prescribed by himself. 3.1 Theoretical Background The assessment via proof load test is analyzed from a reliabilitybased perspective. If R and S are the resistance and action variables respectively, the limit state function is defined as:
G ( x ) = R – S = R – G – Q = R′ – Q
(1)
And the failure probability: Pf = P ( R – S ≤ 0 ) = P ( Z ≤ 0 )
(2)
Where R, G and Q are the resistance and the effects of the permanent and variable actions respectively. R' = R-G is the margin of resistance for additional variable actions. If R and S are independent variables with Normal distributions, the reliability index β can be defined in function of the inverse normal probability distribution as:
µR – µs β = Φ–1 ( –Pf ) = ------------------2 2 σR + σS
(3)
R is the resistance, S = actions effect and µ, σ = mean and standard deviation of the variable. Once the safety level in the bridge is defined through the definition of a target reliability index, it is possible to obtain the required resistance and the corresponding target value of the proof load for a predefined level of traffic load. Of course, first, the type of distribution as well as the main parameters (mean and standard deviation) of the variables involved should be defined. For example, in the case that both resistance and actions are defined as Normal variables, the target value of the proof load, can be calculated from Eq. (3) as follows: ( µR – µD ) – ( µQ + µDad ) β = --------------------------------------------------σ 2R + σ 2D + σ 2Q + σ 2Dad
(4)
R is the resistance, Q = variable actions effect (traffic); D = Effect of the permanent actions and self-weight during the test load, Dad = additional dead load effect expected to be added to the bridge after the proof-load test, such as that of an overlay; µ, σ = mean and standard deviation of the variable. According to Eq. (4), once the target safety level is defined (β), then, the target proof load to introduce in the bridge to guarantee a mean value of the resistance can be easily estimated provided that the rest of parameters have been also defined. This is the case when all random variables involved are Gaussian-type. In the present study, the aim is to obtain the target value in the case that the traffic action is modeled with more appropriate distributions (Lognormal, Gumbel) and for different values of the target reliability index. The objective is also to define the target proof load depending on the actual traffic load in the bridge obtained by WIM techniques or similar, and not on a nominal value defined in the Code that many bridges in the road network will never experience. The actual traffic load can take into account the characteristics of the traffic composition depending on the bridge location (site-specific or country-specific). For this reason, the objective is also to develop the target values for five different traffics (one from Western Europe and the rest from Central and Eastern European Countries (CEEC), representative of the traffic in CEEC and the possible differences of traffic patterns between new and old Member States in Europe. The countries considered are: The Netherlands, Czech Republic,
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Poland, Slovakia and Slovenia. The case where the statistical distribution of R is available or may be evaluated (thanks to existence of drawings, inspections …) as well as the case where it is un-known, will be considered. 3.2 Definition of the traffic action The target proof load achieved should guarantee the normal operation of the bridge under the traffic action with a predefined (by the user) level of safety. Therefore, two important requirements arise concerning an accurate assessment of the bridge capacity by proof load testing: An accurate estimate of the actual traffic action in the bridge A statistical definition of the traffic action, allowing the definition of the required safety level with a certain level of confidence. Both requirements need the recording and analysis of several days or weeks of traffic measured in the bridge. Nowadays this can be effectively achieved by the use of Weigh-In-Motion (WIM) systems (Ghosn and Moses, 1984). Several procedures exist for estimating the maximum expected load effect due to traffic on a highway bridge. For a safety assessment, deterministic models are not of interest. The statistical models include methods based on the probability convolution approach, extreme value distributions, Monte Carlo simulations and simplified statistical projection techniques (Sivakumar et al., 2009). These procedures explain how site-specific truck weight and traffic data collected using Weigh-in-Motion Systems (WIM) can be used to obtain estimates of the maximum live load for the design life of a bridge. The models require as input the WIM data collected at a site after being filtered to remove WIM measurement errors. Within the European Project ARCHES, WIM data from five different countries has been analyzed and the corresponding traffic models were derived according to the methods and algorithms described in ARCHES-D08 (2009). It was necessary to estimate as accurately as possible the probable maximum bridge load effects (bending moments, shear forces) over a selected lifetime. For assessment, this can be 5 to 10 years, whereas for design it may be between 75 to 100 years. The approach used in ARCHES was to build a detailed Monte Carlo simulation model, without any restrictive assumptions, and to calibrate it against extensive WIM data collected for over half a million trucks at each of two European sites in the Netherlands and Slovakia in 2005 and 2006. The model is designed to extrapolate both vehicle weights and types (axle configurations), and while this extrapolation is based on assumptions which will influence the results, it is considered to give a more realistic estimate of lifetime loading. The model is then applied to WIM data collected in three other Central European countries (Czech Republic, Slovenia and Poland) and is used to calculate lifetime load effects within a certain reference period for typical bridges. As an example, in Table 1 are presented the main values (mean and coefficient of variation COV) corresponding to the mid-span bending moment of simply-supported bridges with different span lengths. The
Table 1. Lifetime Load Effects for Traffic Recorded in 5 European Countries. Simply-supported Spans Site
The Netherlands
● ●
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Czech Republic
Slovenia
Poland
Slovakia
Mid-span Moment (kNm) Lane Span 50-year Factors (m) Characteristic 50-Year Value Mean COV 15 4095 3714 5.9% 25 8877 8023 5.9% High 35 14274 12926 5.9% 45 20518 18238 6.2% 15 3113 2917 3.4% 25 7195 6706 4.5% Low 35 11755 10874 4.7% 45 16881 15733 4.3% 15 3131 2832 5.6% 25 6773 6129 5.6% High 35 10766 9853 4.9% 45 15170 13877 4.8% 15 2878 2604 5.2% 25 5855 5419 4.2% Low 35 9539 8592 5.2% 45 13671 12322 5.3% 15 3051 2756 5.5% 25 6584 5797 6.3% High 35 10548 9383 6.2% 45 14800 13097 6.3% 15 2766 2513 5.2% 25 5630 5240 4.2% Low 35 8905 8220 4.4% 45 12893 11497 6.4% 15 3091 2853 4.4% 25 6388 5951 4.4% High 35 10202 9441 4.7% 45 14413 13170 5.2% 15 2674 2449 4.7% 25 5656 5160 4.6% Low 35 8631 8136 3.3% 45 12208 11396 3.9% 15 2995 2643 6.2% 25 6233 5573 6.7% High 35 9862 8776 6.9% 45 13806 12112 7.3% 15 2731 2506 4.7% 25 5341 5001 3.8% Low 35 8368 7864 3.5% 45 11885 11035 4.1%
characteristic value corresponds to the 1000 year return period. According to the definition of the characteristic value of the traffic action in the Eurocode, this corresponds to a value that is exceeded only 5% of the times in the distribution of the maximum traffic effect over a period of 50 years. Similar values were obtained for shear in simply supported bridges as well as hogging moment for two-span continuous bridges. In Table 1, the lane factor measures the effect that the vehicle in one lane produces in the adjacent lane. It depends basically on the cross-
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sectional properties of the bridge. The WIM data corresponds to a two lane bridge with the traffic in the same direction (except for Slovenia) and is recorded in a highway location representative of the most heavy traffic conditions within each country. Therefore, the values can be assumed as representative of the country. However, they may be excessive when looking at second class or local roads. To take into account this possibility, simplified traffic loads that can use WIM data specifically recorded in a particular location were also developed and checked (ARCHES-D08, 2009). 3.2.1 Definition of the General Traffic Action As shown in Gómez and Casas (2008), the coefficient of variation of the traffic action has a higher influence than the type of distribution (Normal, Lognormal, Gumbel). In addition, Gumbel distribution produces the highest values of the target proof load. Therefore, the Gumbel distribution is used to characterize the randomness in the traffic action. The next step is to obtain the two parameters (or alternatively the mean and coefficient of variation) of the Gumbel distribution representing the traffic load. Ghosn and Moses used a convolution method to calibrate an empirical formula that is valid for the calculation of maximum traffic effects in a reference period for typical US traffic patterns on two-lane highway bridges (Ghosn and Moses, 1984). The proposed formula is: M = amW95 H
(5)
M is the median of the maximum expected lifetime moment, a is the moment effect of a representative vehicle with a typical configuration and a one unit total gross weight. a is a deterministic value and can be calculated from the influence line of the bridge. It was found that for typical US truck traffic composition, it is best to use a representative semi-trailer truck configuration for spans greater than 15 meters, while a single unit truck gives more consistent results for the shorter span lengths. m is a random variable representing the variation of the effect of a random truck from the effect of the representative truck. If the representative vehicle has the configuration of an average truck, m is then close to 1.0 with a coefficient of variation that varies from 15 to 4% depending on the span length. W95 is the characteristic value representing the intensity of the gross weight histogram. The 95 percentile value was chosen as the representative gross weight. For the spans where the single unit trucks dominate the response, i.e., spans less than 15 m for typical US sites with 20% single unit trucks, W95 is obtained from the gross weight histograms of the single trucks. For longer spans, the gross weight histogram of the semi-trailer trucks is used. H is the headway multiplicative factor. It reflects the number of typical trucks with the W95 weight needed to produce the maximum lifetime load effect. H was found to be a function of the span length and traffic composition reflecting the fact that the longer the span length the more
likely it is to have many heavy vehicles simultaneously on the bridge. Similarly, the heavier the truck traffic is the more likely it is to have many heavy vehicles on the bridge. Values of H are tabulated for different span lengths, truck traffic intensities and projection periods (or service lifespan). A model such as the one proposed in Eq. (5) is extremely powerful for traffic load modelization because of its flexibility and adaptability to any individual bridge site, local, state or national jurisdiction. For this reason Ghosn and Casas (1996) checked if the proposed model, although calibrated for US traffic conditions, could be also extrapolated to the traffic in other parts of the world. As presented in Ghosn and Casas (1996), the model predicts very accurately (maximum error = 6%, average error = 3%) the results of the simulation of the maximum traffic action in a period of 50 years for the traffic conditions in 3 European countries: The Netherlands, Switzerland and Spain. Within the scope of ARCHES project, the model was checked again with the results of the simulation of traffic actions with updated parameters of the traffic obtained via WIM in five different countries: Czech Republic, Holland, Poland, Slovakia and Slovenia. The results were obtained for a 1000 year return period and for a simply supported bridge with different span lengths ranging from 15 to 35 meters. The results obtained by simulation (Table 1) were compared with those obtained with Eq. (5). With the mean value of the maximum traffic action derived according to Eq. (5), the coefficient of variation of the traffic effect distribution should be estimated to derive the 1000 year return period value. The results accuracy show a high dependence on the COV used. The values of H and the coefficient of variation of H are those proposed in Ghosn and Moses (1984), 10% for short spans and 7% for spans longer than 20 m. The coefficient of variation of W95 is taken as 15% for short spans (2 axle trucks dominate) and 10% for longer spans (more than 20 m, where the 5 axle trucks control), as proposed in the same reference. This results on a total COV of the traffic actions of 18% for spans up to 20 m and 12% for longer spans. From the results obtained in the comparison carried out within the ARCHES project (ARCHESD16, 2009), it may be concluded that the traffic model represented by Eq. (5) is not only general in space (valid for different countries) but also in time, as far as the main parameters of actual traffic (mainly the COV) are introduced. In fact, the model gives good results in the case of The Netherlands, both for the traffic data from 1978 (Ghosn and Casas, 1996) as well as for the traffic data collected in the year 2003 by the team of the University College Dublin (Getachew and O´Brien, 2007). The sites were R04 highway (Amsterdam), R16 highway (Utrecht) and R12 highway (Dordrecht). 3.2.2 Definition of Specific Traffic Action The differences between the simplified model represented in Eq. (5) and the simulation (Table 1) are due to the assumed coefficients of variation for the traffic action because equation
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(5) only gives the mean value of the distribution, but not the coefficient of variation. In fact, the values of COV used in the comparison (12 and 18%) are those obtained in the study carried out in the US and proposed by Ghosn and Moses (Ghosn and Moses, 1984). However, the coefficients of variation are site specific, mainly the one corresponding to W95, and those derived in the US in the 1980s cannot longer apply to nowadays traffic conditions in European countries. For this reason, a simplified method to obtain a more accurate value of the coefficient of variation of the traffic action for a specific site supported by a particular bridge is proposed here. The methodology is as follows: ●
●
●
●
The most representative vehicle for the bridge is defined from the obtained WIM data and the effect on the bridge is evaluated (calculation of am) From the WIM data the value W95 for the most representative vehicle is obtained With the previous calculated values and the values defined in Ghosn and Moses (1984) for H calculate the mean value of the maximum traffic effect for 50 year reference period using Eq. (5). H is a function of the average daily truck traffic and span length, which data can be also easily obtained on site Use the simplified method proposed by Getachew and O´Brien (2007) to obtain the 1000 year return period effect.
●
This corresponds to the characteristic value (percentile of upper 10%) of the maximum traffic effect for a 50 year time period. The simplified method requires only the values of the 1000 year and 1 week return period Gross Vehicle Weight (GVW). These values can be easily obtained by extrapolation on the WIM data available for a period of some weeks or months. Assuming that the random variable “maximum traffic action within a period of 50 years” is of the Gumbel type, the coefficient of variation of the distribution can be calculated from the mean and characteristic values previously calculated.
As an example, in Table 2 are presented the results of the application of the method to the traffic WIM data from Slovakia. As can be seen, the actual value of COV of the traffic action, calculated in the way that the values in the columns for the 1000 year return period and Getachew and Obrien coincide, is in the order of magnitude of 14% for the short spans and 7% for the longer spans. In this case is in quite good agreement with the values obtained in US (18% and 12% respectively). In Table 3, a similar calculation is carried out for the traffic data from The Netherlands. In this case, the coefficient of variation of the actual traffic action is around 11% for short spans and 5% for longer spans. These values are lower than those reported in the US traffic and in the case of Slovakia.
Table 2. Traffic Action in Slovakia (Adjustment of COV of Ghosn & Moses model with Getachew & O'Brien model.) Span (m)
H
10 15 20 25 30 35
2.7 2.8 2.8 2.9 2.9 3.0
W95 (kN) 443 443 443 443 443 443
amH W95 (kNm) 1424 2479 3891 5515 7235 9097
COV (adjusted) 0.146 0.109 0.095 0.080 0.053 0.054
Mean (kNm) 1459 2524 3953 5589 7298 9178
1000 year Return (kNm) 1858 3040 4657 6424 8015 10104
Getachew ( kNm) 1858 3040 4657 6424 8015 10104
Table 3. Traffic Action in The Netherlands (Adjustment of COV of Ghosn & Moses model with Getachew & O´Brien model.) Span (m) 10 15 20 25 30 35
H 2.7 2.8 2.8 2.9 2.9 3.0
W95 (kN) 656 656 656 656 656 656
amH W95 (kNm) 2110 3671 5726 8149 10695 13472
COV (adjusted) 0.113 0.061 0.075 0.058 0.036 0.035
Mean (kNm) 2149 3708 5796 8228 10759 13550
1000 year Return (kNm) 2603 4130 6607 9121 11477 14436
Getachew ( kNm) 2603 4130 6607 9121 11477 14635
Fig. 1. L: Crane with 10 Axles and Total Weight of 1100 kN, R: Low-loader with 12 Axle and Total Weight of 1650 kN Vol. 17, No. 3 / April 2013
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A correction factor equal to 1.56 has been considered in the definition of the value of W95 for the 5-axle truck (656 = 1.56 × 420.5) in the case of the Dutch traffic. This factor takes into account the fact that in the simplified model of Getachew and O´Brien (2007), the load is notional and not intended to reflect a realistic loading scenario. As in the Dutch traffic many nonstandard vehicles are present (see Fig. 1): 1) “low loaders” which are characterized by a set of closely spaced front axles, followed by a large axle spacing (about 11 m) and completed by a second set of closely spaced axles, and 2) cranes and crane-type vehicles characterized by a small value for the maximum axle spacing (typically 3 m or less), the extrapolation to find the characteristic 1 week and 1000 year values generates unrealistically heavy 5 axle-vehicles. However, in the model of Eq. (5), the possibility of such rare vehicles is not considered. It must be pointed out that these exceptional loads are present in the normal traffic flow, not being escorted. Therefore, both models cannot be compared directly in the case of Dutch traffic. This problem can be solved in 2 ways: removing from the traffic data all this “rare” vehicles and perform a new simulation process to define new values of 1 week and 1000 year return periods, or, alternatively, use a virtual value of W95 that reflects this situation. This last option has been considered here. The calculation of the correction factor has been as follows: In the simplified model of Getachew and O´Brien (2007), the 1000 year return period 5-axle truck has a weight of 1530 kN and 980 kN for the traffic data in Holland and Slovakia respectively. Because the standard 5-axle truck has a very close configuration in axle-loads and axle-spacing in both countries, as was found from the gathered WIM traffic data, then a similar coefficient 1530/980 = 1.56 can apply to the W95 values for the two traffics. In ARCHES-D16 (2009) and Gómez (2010) are obtained similar results to those of Tables 2 and 3 for the site-specific COV obtained in Poland, Slovenia and Czech Republic. It should be pointed out that in all cases, the 5-axle truck is the one producing the highest bending moment at mid-span, for all spanlengths, even for the short ones.
requires the statistical definition of the random variables involved as well as the calculation of the reliability indices. This may be a difficult and cumbersome task for a professional engineer not directly involved and used to such approach. Therefore, in order to facilitate the work to the bridge evaluator, a calibration procedure has been developed with the objective to obtain the target proof load from charts and figures using very few and simple parameters of the bridge under investigation. The calibration has been developed taking into account the following parameters: − Safety level: Target values of reliability index considered are: 2.3, 3.6, 5.0. These are feasible values. The lower one takes into account an inspection every two years and is the value assumed by AASHTO in USA. A value of 3.6 is similar to the required safety level for the design of a new bridge as defined in the Eurocode, for instance. The value 5.0 can be seen as an upper value when a relatively high safety level needs to be considered. − Span length: 10, 15, 20, 25, 30, 35 m. This covers most of the span lengths in standard bridges encountered in the European highway network. − Bridge type: The longitudinal profile is a simply supported structure. Concrete bridges with pre-cast beams with upper slab, massive and voided slab and box-girder cross-sections are considered. This covers most of the encountered cross-sections in concrete bridges for the span lengths accounted for. The parameter considered is the ratio between the effects (bending moment at mid-span) of the permanent load (G) and the traffic load (Q) as defined in the Eurocode of actions on highway bridges (EN, 1991-3). Depending on the defined cross-section type, the values presented in Table 4 for the ratio moment due to permanent load/ moment due to traffic action in EC-1 were obtained. Therefore, a range of values from 0.5 to 3.5 were taken into consideration in this study. − Traffic action: Two traffic scenarios have been considered, one representative of Western Europe (The Netherlands) and other representative of Central and Eastern Europe (Czech Republic, Poland, Slovakia and Slovenia). Therefore, five different country-specific traffics were studied. The traffic from the Netherlands comes from A12 (E25/E30) highway, near Woerden, 30 km east of the port of Rotterdam. 20 weeks of traffic were recorded in 2 lanes in the same direction, from 7th February to 25th of June, 2005. A total of
4. Application to European Highway Network With the coefficients of variation of all variables involved (including traffic as explained in 3.2), the corresponding reliability index related to the proof load execution can be calculated using a FORM (Fist Order Reliability Method) algorithm or similar. (Nowak and Collins, 2000). Alternatively, if a target reliability index is previously defined, the target proof load to be introduced in the test to guarantee the passage of the actual traffic with the previously defined safety level can be also calculated by and iterative use (trial and error) of a FORM algorithm (Gómez, 2010; Gómez and Casas, 2010; Casas, 2010). In section 3.1, the reliability-based methodology has been explained to derive the target value of the proof load according to the traffic characteristics present in the bridge. The method
Table 4. Ratio of MG/MQEC-1 for Different Cross-section Types Type Precast beam + upper slab Slab (concentrated stiffness) Slab (distributed stiffness) Box-girder
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10 0.32 0.42 0.47 0.4
15 0.45 0.68 0.90 0.59
Span-length (m) 20 25 30 0.61 0.83 1.06 0.98 1.30 1.63 1.42 2.02 2.68 0.78 0.98 1.18
35 1.32 1.99 3.39 1.39
KSCE Journal of Civil Engineering
Load Rating of Highway Bridges by Proof-loading
646,548 trucks were recorded, which represents and Average Daily Truck Traffic (ADTT) equal to 4,618 trucks/day. In Slovakia, the traffic corresponds to the 4-lane D1 (E50) highway near the eastern entrance to the Branisko tunnel, between the towns of Levoca and Presov. The traffic data corresponds to the slowest lanes in opposite directions. Data was provided for a 19 month period, from 1st June 2005 to 31st December 2006. A total of 748,338 trucks were recorded in this case, giving ADTT = 1,313 trucks per day. In Slovenia, the traffic corresponds to 2 same-direction lanes (slow and fast) in the location of Vransko with a total of 142,131 trucks in lane 1 and 5,621 trucks in lane 2. In Poland, the traffic corresponds to 2 same-direction lanes (slow and fast) in the location of Wroclaw with a total of 398,044 trucks in lane 1 and 31 636 trucks in lane 2. In Czech Republic, the traffic corresponds to 2 same-direction lanes (slow and fast) in the location of Sedlice with a total of 684,345 trucks in lane 1 and 45 584 trucks in lane 2. The coefficient of variation of the traffic action depends on the site location as well as the span-length (Casas and Gómez, 2010). For a specific measurement site, the values vary in the range from 5 to 15%. The gathering of traffic data from other locations will derive in larger coefficients of variation due to the traffic variability from site to site. To take into account this effect, according to other traffic studies (Sivakumar et al., 2009), in the present report the analysis and calculation of target proof load factors have been done with a coefficient of variation of the traffic effect of 20%. Of course, in the case that particular traffic data from a specific bridge site would be available, the simplified method presented in 3.2.2 can be used to derive a more accurate COV for the bridge site and a reliability analysis executed to define a more accurate target proof load factor. − Permanent additional load: The additional dead load that may appear in the bridge after the execution of the proof load, is modeled with a Normal random variable with mean equal to the nominal value (BIAS factor = 1) and a coefficient of variation of 25%. This additional permanent load normally reflects the increment of the pavement thickness due to repaving. − Existing bridge documentation: Two cases are considered: the existence or not of bridge documentation and information (drawings, materials specifications, …) to calculate the nominal value of the resistance and dead load at the time of test execution, or the parameters (mean and standard deviation) of the variables R and D assumed as Normally distributed. In the case that the nominal value of the resistance is unknown the assumption is that the proof load introduced in the bridge with the test execution is precisely the nominal value. 4.1 Bridge Documentation Available In this case from the information on bridge geometry and materials available from the design documentation and drawings, it is possible to calculate the nominal value of the Resistance (R). Vol. 17, No. 3 / April 2013
Considering this actual resistance as a certain percentage of the value Rn, defined as: Rn = γD Gn + γL Q
(6)
with Gn, Qn = nominal value of permanent and traffic load, and γD , γL the partial safety factors for permanent and traffic action (1.35 and 1.50 respectively), the ratio R/Rn is obtained as a parametric value. The nominal value of traffic action, Qn, is obtained according to the Eurocode 1 (EN 1991-3). The limit state function: Z = R – G – Q – D ad = R′ – Q – Dad
(7)
is used to obtain the target reliability index defined, being the target proof load (or the target proof load factor, γPL) the corresponding variable. In the calculation of the reliability index corresponding to limit state in Eq. (7), the following values are considered: R/Rn ranging from 0.5 to 1.0 G is a random variable normally distributed with BIAS= 1.05 and COV= 0.10. The nominal value of G, Gn, can be obtained from the bridge documentation. However, in the case of concrete bridges for span-lengths from 10 to 35 m, a range of values of Gn between 0.5 and 3.5 times Qn was considered (Table 4). Therefore, a range Gn/Qn from 0.5 to 3.5 was investigated. R is a random variable normally distributed with BIAS = 1.12 (reinforced concrete in bending) and COV = 0.14 R' is a random variable normally distributed and truncated in the lower part by the value γPLQn (see Fig. 2), where γPL is the target proof load factor, which indicates the number of times that the nominal value of the live load has to be applied in the bridge during the proof load test. The mean value and standard deviation of R' is the corresponding to the random variable R-G. Q is a Gumbel random variable with a mean value calculated according to Eq. (5) and a COV = 0.20 to take into account site to site variability of traffic action within the same country. Dad is a normally distributed random variable with BIAS = 1.0 and COV = 0.25. The nominal value corresponds to a 10 cm pavement overlay (density = 23 kN/m3). ● ●
●
●
●
●
●
Fig. 2. Reliability Model (Load and resistance distributions: Documentation available)
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Fig. 3. Target Proof Load Factors for Slovak Traffic (Reliability level = 5.0/Span-length = 15 m)
Fig. 4. Target Proof Load Factors for Dutch Traffic (Reliability level = 3.6/Span-length = 25 m)
The results show a very low dependence on the Gn/Qn ratio, that represents the different bridge types (beams, slab, boxgirder) independent of the ratio R/Rn and the span-length (Gómez, 2010). As an example, in Figs. 3 and 4 are presented two cases obtained from the traffic in Slovakia and Holland. According to this result, the values in Table 4, and the fact that most concrete bridges are of the type precast girder+upper slab, the variable G/Q (cross-section type) was eliminated from the
parametric study, adopting in each case the most unfavourable value in order to get values in the safe side In Tables 5 to 9 is presented a summary of the results obtained for all safety levels considered in the study, the span-length in meters and the ratio R/Rn for the five studied countries. A complete description of the results can be found in Gómez (2010). As seen in Table 7, the target proof load factors obtained for the Dutch traffic are much higher than in the rest of the
Table 5. Target Proof Load Factors for Czech Republic Traffic and Reliability Levels = 2.3, 3.6 and 5.0
R/Rn 1.0 0.9 0.8 0.7 0.6 0.5
10 0.08 0.48 0.59 0.67 0.73
β=2.3 Span-length (m) 15 20 25 30 0.19 0.33 0.38 0.48 0.53 0.61 0.66 0.72 0.64 0.73 0.78 0.84 0.72 0.81 0.87 0.93 0.78 0.86 0.93 0.97
35 0.50 0.73 0.85 0.94 0.98
R/Rn 1.0 0.9 0.8 0.7 0.6 0.5
10 0.66 0.76 0.86 0.94 1.00 1.04
β=3.6 Span-length (m) 15 20 25 30 0.72 0.81 0.87 0.94 0.81 0.92 0.99 1.10 0.91 1.04 1.12 1.20 1.00 1.12 1.20 1.25 1.05 1.16 1.24 1.30 1.08 1.18 1.26 1.31
35 0.95 1.11 1.20 1.26 1.29 1.31
R/Rn 1.0 0.9 0.8 0.7 0.6 0.5
10 1.27 1.34 1.40 1.43 1.45 1.47
β=5.0 Span-length (m) 15 20 25 30 1.33 1.49 1.59 1.67 1.40 1.55 1.65 1.71 1.45 1.59 1.69 1.75 1.48 1.61 1.71 1.77 1.50 1.63 1.73 1.78 1.51 1.64 1.74 1.78
35 1.66 1.71 1.74 1.76 1.78 1.78
Table 6. Target Proof Load Factors for Poland Traffic and Reliability Levels = 2.3, 3.6 and 5.0
R/Rn 1.0 0.9 0.8 0.7 0.6 0.5
10 0.44 0.55 0.63 0.69
β=2.3 Span-length (m) 15 20 25 30 0.28 0.45 0.55 0.59 0.58 0.69 0.78 0.82 0.69 0.82 0.94 0.96 0.78 0.92 1.00 1.04 0.84 0.96 1.04 1.07
10 0.61 0.86 1.04 1.11 1.14
β=2.3 Span-length (m) 15 20 25 30 0.18 0.38 0.70 0.84 1.07 1.16 0.98 1.14 1.26 1.31 1.12 1.26 1.33 1.37 1.18 1.28 1.37 1.41 1.20 1.30 1.39 1.44
35 0.31 0.61 0.84 0.98 1.05 1.09
R/Rn 1.0 0.9 0.8 0.7 0.6 0.5
10 0.62 0.72 0.80 0.88 0.94 0.98
β=3.6 Span-length (m) 15 20 25 30 0.78 0.94 1.08 1.16 0.89 1.10 1.23 1.28 1.01 1.21 1.32 1.36 1.10 1.28 1.37 1.40 1.14 1.30 1.39 1.43 1.17 1.32 1.41 1.45
35 1.17 1.29 1.37 1.41 1.44 1.45
R/Rn 1.0 0.9 0.8 0.7 0.6 0.5
10 1.16 1.25 1.31 1.35 1.37 1.39
β=5.0 Span-length (m) 15 20 25 30 1.47 1.71 1.85 1.89 1.53 1.77 1.89 1.93 1.57 1.79 1.91 1.95 1.60 1.81 1.93 1.97 1.62 1.82 1.94 1.98 1.63 1.82 1.95 1.99
35 1.89 1.93 1.95 1.97 1.98 1.99
Table 7. Target Proof Load Factors for Dutch Traffic and Reliability Levels = 2.3, 3.6 and 5.0
R/Rn 1.0 0.9 0.8 0.7 0.6 0.5
35 0.49 1.22 1.35 1.41 1.44 1.46
R/Rn 1.0 0.9 0.8 0.7 0.6 0.5
10 1.34 1.45 1.51 1.55 1.57 1.59
β=3.6 Span-length (m) 15 20 25 30 1.45 1.61 1.74 1.80 1.54 1.68 1.80 1.85 1.59 1.73 1.84 1.89 1.63 1.76 1.86 1.91 1.65 1.77 1.88 1.93 1.66 1.77 1.89 1.94 − 564 −
35 1.84 1.89 1.93 1.95 1.96 1.97
R/Rn 1.0 0.9 0.8 0.7 0.6 0.5
10 2.17 2.20 2.22 2.23 2.25 2.26
β=5.0 Span-length (m) 15 20 25 30 2.26 2.43 2.57 2.63 2.29 2.45 2.59 2.65 2.30 2.47 2.61 2.67 2.32 2.46 2.62 2.68 2.34 2.48 2.63 2.69 2.35 2.48 2.64 2.70
35 2.67 2.69 2.72 2.73 2.73 2.74
KSCE Journal of Civil Engineering
Load Rating of Highway Bridges by Proof-loading
Table 8. Target Proof Load Factors for Slovenian Traffic and Reliability Levels = 2.3, 3.6 and 5.0
R/Rn 1.0 0.9 0.8 0.7 0.6 0.5
10 0.44 0.55 0.63 0.69
β=2.3 Span-length (m) 15 20 25 30 0.17 0.31 0.37 0.47 0.51 0.59 0.65 0.72 0.63 0.71 0.77 0.83 0.70 0.79 0.86 0.92 0.76 0.85 0.92 0.96
35 0.50 0.73 0.84 0.93 0.98
R/Rn 1.0 0.9 0.8 0.7 0.6 0.5
10 0.62 0.72 0.80 0.88 0.94 0.98
β=3.6 Span-length (m) 15 20 25 30 0.70 0.79 0.86 0.93 0.80 0.90 0.98 1.08 0.89 1.01 1.10 1.18 0.98 1.10 1.18 1.24 1.03 1.14 1.22 1.28 1.06 1.16 1.25 1.30
35 0.94 1.09 1.19 1.25 1.28 1.30
R/Rn 1.0 0.9 0.8 0.7 0.6 0.5
10 1.16 1.25 1.31 1.35 1.37 1.39
β=5.0 Span-length (m) 15 20 25 30 1.30 1.46 1.56 1.65 1.37 1.52 1.62 1.69 1.42 1.56 1.66 1.73 1.45 1.59 1.69 1.75 1.48 1.61 1.71 1.77 1.49 1.62 1.72 1.79
35 1.65 1.70 1.73 1.75 1.76 1.77
Table 9. Target Proof Load Factors for Slovakian Traffic and Reliability Levels = 2.3, 3.6 and 5.0
R/Rn 1.0 0.9 0.8 0.7 0.6 0.5
10 0.15 0.51 0.63 0.72 0.78
β=2.3 Span-length (m) 15 20 25 30 0.19 0.40 0.49 0.54 0.53 0.66 0.72 0.77 0.65 0.78 0.85 0.90 0.74 0.88 0.94 0.99 0.80 0.92 0.99 1.03
35 0.58 0.80 0.94 1.02 1.06
R/Rn 1.0 0.9 0.8 0.7 0.6 0.5
10 0.71 0.82 0.92 1.01 1.07 1.10
β=3.6 Span-length (m) 15 20 25 30 0.74 0.88 0.97 1.04 0.84 1.02 1.14 1.19 0.95 1.14 1.23 1.28 1.05 1.20 1.29 1.33 1.10 1.24 1.32 1.36 1.12 1.26 1.34 1.38
35 1.10 1.24 1.32 1.37 1.39 1.41
R/Rn 1.0 0.9 0.8 0.7 0.6 0.5
10 1.37 1.44 1.49 1.52 1.54 1.55
β=5.0 Span-length (m) 15 20 25 30 1.42 1.62 1.73 1.78 1.49 1.67 1.77 1.82 1.53 1.70 1.80 1.85 1.56 1.76 1.83 1.87 1.58 1.74 1.84 1.89 1.59 1.76 1.85 1.89
35 1.82 1.86 1.88 1.90 1.92 1.93
Table 10.Target Proof Load Factors of Concrete Bridges in Bending Proposed for CEEC as Function of Actual Resistance and Spanlength (Reliability index β = 2.3, 3.6 and 5.0) R/Rn 1.0 0.9 0.8 0.7 0.6 0.5
10 0.15 0.51 0.63 0.72 0.78
β=2.3 Span-length (m) 15 20 25 30 -0.28 0.45 0.55 0.59 0.58 0.69 0.78 0.82 0.69 0.82 0.94 0.96 0.78 0.92 1.00 1.04 0.84 0.96 1.04 1.07
35 0.31 0.61 0.84 0.98 1.05 1.09
R/Rn 1.0 0.9 0.8 0.7 0.6 0.5
10 0.71 0.82 0.92 1.01 1.07 1.10
β=3.6 Span-length (m) 15 20 25 30 0.78 0.94 1.08 1.16 0.89 1.10 1.23 1.28 1.01 1.21 1.32 1.36 1.10 1.28 1.37 1.40 1.14 1.30 1.39 1.43 1.17 1.32 1.41 1.45
35 1.17 1.29 1.37 1.41 1.44 1.45
R/Rn 1.0 0.9 0.8 0.7 0.6 0.5
10 1.37 1.44 1.49 1.52 1.54 1.55
β=5.0 Span-length (m) 15 20 25 30 1.47 1.71 1.85 1.89 1.53 1.77 1.89 1.93 1.57 1.79 1.91 1.95 1.60 1.81 1.93 1.97 1.62 1.82 1.94 1.98 1.63 1.82 1.95 1.99
35 1.89 1.93 1.95 1.97 1.98 1.99
countries, due to the presence of exceptional non-escorted vehicles in the traffic flow. The analysis of results presented in Tables 5, 6, 8 and 9, corresponding to the traffic characteristics in CEEC are used to derive global factors representative of CEEC conditions as presented in Table 10. 4.2 Bridge Documentation Not Available The same limit state function (Eq. 7) is used for the calibration of the target proof load factor. However, because in this case the nominal value of the variable R' = R-G can not be evaluated due to the lack of information, it is assumed that it corresponds to the target value achieved in the proof test: γPLQn (Fig. 5). The methodology is similar to the one presented in Eq. (4) where all variables are assumed Normally distributed. However, this is not the case of the present study, where the traffic action is considered as Gumbel distributed, what makes necessary an iterative procedure to obtain the target proof load factor, γPL, as a function of the target reliability index β assumed. The characteristics of the rest of variables assumed in the present study are the same as for Vol. 17, No. 3 / April 2013
Fig. 5. Reliability Model (Load and resistance distributions: Documentation not available)
the case of bridge documentation available. The values presented in Table 11(a to f) were obtained for the considered countries. According to the small differences obtained for the 4 CEEC (Czchec Republic, Poland, Slovenia and Slovakia), the values in Table 11(f) are recommended as representative of the traffic conditions in these countries.
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Table 11. Proposed Target Proof Load Factors for Non-documented Bridges a. Czech traffic conditions Span length (m) 10 15 20 25 30 35
b. Polish traffic conditions
β 2.3 0.79 0.84 0.92 0.98 1.01 1.02
3.6 1.07 1.12 1.21 1.29 1.33 1.34
5.0 1.49 1.54 1.66 1.76 1.81 1.82
Span length (m) 10 15 20 25 30 35
d. Slovak traffic conditions Span length (m) 10 15 20 25 30 35
3.6 1.13 1.19 1.29 1.36 1.40 1.44
2.3 0.75 0.89 1.01 1.08 1.11 1.12
3.6 1.02 1.20 1.36 1.4 1.46 1.48
5.0 1.41 1.65 1.85 1.97 2.00 2.01
Span length (m) 10 15 20 25 30 35
e. Dutch traffic conditions
β 2.3 0.83 0.89 0.97 1.03 1.06 1.09
c. Slovenian traffic conditions
β
5.0 1.57 1.64 1.77 1.87 1.91 1.95
Span length (m) 10 15 20 25 30 35
3.6 1.61 1.67 1.80 1.91 1.95 1.99
5.0 2.25 2.33 2.51 2.64 2.70 2.75
Span length (m) 10 15 20 25 30 35
5. Conclusions
16332 are highly acknowledged.
Proof load testing has been proved as very efficient in the capacity assessment of existing bridges. The target proof load to be introduced in the bridge during the test can be evaluated on the basis of reliability theory as many variables involved are of random nature. The target proof load can be obtained as the nominal traffic load described in the Code of actions multiplied by a so-called target proof load factor. In the present study, the Code considered was the Eurocode 1. In order to get values of the target proof load factor representative for several countries from Central and Eastern Europe to facilitate the execution of such tests, actual traffic data is mandatory. The paper shows how the traffic data from 5 European countries, obtained via WIM, has been used to propose a set of target proof load factors applicable to the existing bridge in those countries or in a group of them. In order to be general, they are based on the most heavy traffic conditions that can be encountered. Therefore, the proposed target proof load factors may become too conservative for many bridges located in local or secondary roads that will never experience such level of loading. For this reason, additionally, the paper presents a simplified method that with very common traffic data easily recordable by WIM systems may predict accurately the most critical traffic actions for any specific bridge under assessment. The paper shows a simple method, based in figures and tables, that helps to calculate the target load to be introduced in a proof load test for bridge assessment.
References
Acknowledgements The financial support provided by the European Commission through ARCHES Project and the Spanish Ministry of Education through grants INNPACTO-IPT-370000-2010-29 and BIA2010-
3.6 1.02 1.11 1.20 1.2 1.31 1.33
5.0 1.42 1.51 1.64 1.74 1.77 1.79
f. CEEC countries
β 2.3 1.18 1.23 1.33 1.40 1.45 1.49
β 2.3 0.75 0.82 0.90 0.97 1.00 1.02
β 2.3 0.83 0.89 1.01 1.08 1.11 1.12
3.6 1.13 1.20 1.36 1.44 1.46 1.48
5.0 1.57 1.65 1.85 1.97 2.00 2.01
AASHTO LRFR (2003). Guide manual for condition evaluation and Load and Resistance Factor Rating (LRFR) of highway bridges, American Association of State Highway and Transportation Officials, Washington, USA. Anitori, G., Casas, J. R., and Ghosn, M. (2011). “Reliability and redundancy of bridge systems under lateral loads.” Proc. ASCE Structures Congress, Las Vegas, USA. Anitori, G., Casas, J. R., and Ghosn, M. (2013). “Redundancy and robustness in the design and evaluation of bridges: European and north american perspectives.” Journal of Bridge Engineering, ASCE (Submitted). Anitori, G., Casas, J. R., Ghosn, M., and Jurado, S. (2012). “Enhancement of bridge redundancy to lateral loads by FRP strengthening.” Proc. 6th International conference on bridge maintenance, Safety and Management, IABMAS’ 12. Stresa, Italy. ARCHES-D08 (2009). Recommendations on the use of results of monitoring on bridge safety assessment and maintenance, Deliverable D08 [On line]. ARCHES Project. VI EU Framework Program. Brussels. [cited 16 Feb, 2010], Available from Internet: . ARCHES-D10 (2009). Recommendations on dynamic amplification allowance, Deliverable D10 [On line]. ARCHES Project. VI EU Framework Program. Brussels. [cited 16 Feb, 2010], Available from Internet: . ARCHES-D16 (2009). Recommendations on the use of soft, diagnostic and proof load testing, Deliverable D16 [On line]. ARCHES Project. VI EU Framework Program. Brussels. [cited 16 Feb, 2010], Available from Internet: . ARCHES (2009). ARCHES Newsletter, [On line]. ARCHES Project. VI EU Framework Program. Brussels. [cited 16 Feb, 2010], Available from Internet: . BRIME (2001). Guidelines for assessing load carrying capacitydeliverable D10, Bridge Management in Europe-IV EU Framework
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Load Rating of Highway Bridges by Proof-loading
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