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大桥 02 号桥 施工图 设计

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苏仙大桥（02号桥）施工图设计,大桥,02,号桥,施工图,设计

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Accepted Manuscript Not Copyedited 1 Uncertainty Analysis of Creep and Shrinkage Effects in Long-Span Continuous Rigid Frame of Sutong Bridge Zuanfeng Pan1, Chung C. Fu2, Fellow, ASCE and Yong Jiang3 Abstract: The long-term behavior of long-span prestressed concrete continuous rigid frame bridges are significantly sensitive to creep and shrinkage. Therefore, it is important to accurately estimate creep and shrinkage effects. In this paper, based on the creep and shrinkage models in the existing bridge code, modified prediction models, which are in well match with test results of the high-strength concrete used in the continuous rigid frame of Sutong Bridge, China, are presented. Results indicate that the accuracy of prediction of creep and shrinkage can be enhanced greatly by carrying out short-term creep and shrinkage measurements on the given concrete and modifying the prediction model parameters accordingly. Subsequently, the probabilistic analysis method of structural creep and shrinkage effects was studied. Uncertainty analysis of time-dependent effects in the preceding bridge was performed using the modified model, and results were compared with field test data. In addition, two approaches of mitigating deflections, which were used in the continuous rigid frame of Sutong Bridge, are introduced. Finally, the time-dependent deflection at mid-span due to creep and shrinkage was analyzed. CE database subject headings: Concrete; Long span bridge; Creep; Shrinkage; Prediction model; Uncertainty; Latin Hypercube Sampling. 1 Ph.D. Candidate, Department of Civil Engineering, Southeast University, Nanjing, China, 210096; and, Visiting Scholar and Research Assistant, The Bridge Engineering Software and Technology (BEST) Center, Department of Civil and Environmental Engineering, University of Maryland, College Park, MD 20742. Email: 2 Director and Research Professor, The Bridge Engineering Software and Technology (BEST) Center, Department of Civil and Environmental Engineering, University of Maryland, College Park, MD 20742. Email: ccfu 3 Design Engineer, China Zhongtie Major Bridge Engineering Group Co., LTD., Wuhan, 430050. Email: Journal of Bridge Engineering. Submitted October 26, 2009; accepted June 10, 2010; posted ahead of print June 15, 2010. doi:10.1061/(ASCE)BE.1943-5592.0000147Copyright 2010 by the American Society of Civil EngineersAccepted Manuscript Not Copyedited 2 Introduction Prediction of the creep and shrinkage effects is an intractable and crucial issue that needs to be resolved in the design of long-span concrete bridges. The main span of the studied bridge which is the auxiliary shipping channel bridge of Sutong Bridge (also called continuous rigid frame of Sutong Bridge) is 268m, among the longest spans of the world. It is a prestressed concrete continuous rigid-frame box girder bridge built by the balanced cantilever method, and was completed in 2007, shown in Fig. 1. In order to improve the strength and durability, high-strength and high-performance concrete was used in the bridge. The AASHTO LRFD Bridge Design Specifications (2007) emphasize that a “more precise estimate” of creep and shrinkage shall be made for segmentally constructed bridges, which is in consistent with what stated in the Chinese code JTG D62-2004 (2004). The objectives of this study are: 1. To obtain creep and shrinkage properties of the concrete used in the continuous rigid frame of Sutong Bridge; 2. To compare calculation results of the bridge model using the modified prediction models of creep and shrinkage with the field test results; 3. To perform uncertainty analysis of creep and shrinkage effects in the bridge using the modified creep and shrinkage models and to predict the long-term deflection of the bridge. Bazant and Baweja (1995a) pointed that, the influence of additive and mineral admixture on creep and shrinkage of concrete can be extrapolated by carrying out on the given concrete short-term creep and shrinkage measurements and adjusting the values of some model parameters accordingly. In this study, experiments on material properties, such as strength, modulus of elasticity, creep and shrinkage of the concrete used in the continuous rigid frame of Sutong Bridge, were conducted, and continued over more than one and a half years. The test results show that the creep and shrinkage prediction models in JTG D62-2004 (2004), in which CEB-FIP90 (1990) is adopted, can not accurately predict for the given concrete. The formulas of creep and shrinkage model in JTG D62-2004 (2004) can be seen in the Appendix A. Therefore, modified formulas of shrinkage strain and creep coefficient, which can be used for the concrete used in the continuous rigid frame of Sutong Bridge, are proposed in this paper. Moreover, the uncertainty of creep and shrinkage effects of the continuous rigid frame of Sutong Bridge was analyzed using the modified prediction model, considering modeling uncertainties and random properties of influencing factors. Also, two new methods used in the continuous rigid frame of Sutong Bridge are introduced emphatically for improving deflection problems. Journal of Bridge Engineering. Submitted October 26, 2009; accepted June 10, 2010; posted ahead of print June 15, 2010. doi:10.1061/(ASCE)BE.1943-5592.0000147Copyright 2010 by the American Society of Civil EngineersAccepted Manuscript Not Copyedited 3 Background Concrete creep and shrinkage may lead to cracks and excessive long-term deflection, and these cracks and excessive deflections would reduce the serviceability and durability of bridges. For example, the Koror-Babeldaob Bridge, Palau Islands, built by the cantilever method in 1977 is a segmental prestressed concrete box girder bridge with a hinge at mid-span, which had the maximum world-record span of 241m at that time. After 18 service years, the mid-span deflection reached 1.39m, and eventually collapsed. Bazant et al. (2008) concluded that the excessive deflections were mainly due to creep and prestress loss being higher than anticipated. They pointed out that a sound prediction model should be used for the bridge which was highly sensitive to creep and shrinkage. Therefore, the creep and shrinkage prediction models were necessary to be updated based on short-time tests of the given concrete. In addition, the Huangshi Yangtze River Bridge, China is a prestressed concrete continuous rigid-frame box girder bridge with the spans of 162.5m+3245m+162.5m. After 7 service years, the maximum deflection at mid-span reached 32cm higher than predicted (Zhan and Chen 2005). These lessons spurred on studies on the creep and shrinkage effects in the long-span concrete bridges. The emphasis here is on selecting proper creep and shrinkage prediction models for concrete if the structure is comparatively sensitive to creep and shrinkage. For the past several decades, about ten prediction models for creep and shrinkage had been presented by researchers based on large numbers of creep and shrinkage tests, which can be divided into three types. The first one is to describe the overall development of creep, such as CEB-FIP90 (1990), ACI 209-82, ACI 209-92 (1992), AASHTO (2007), GZ (Gardner and Zhao 1993), GL2000 (Gardner and Lockman 2001); the second one is dividing creep into basic creep and drying creep, such as BP-KX, BP-2, B3 (Bazant and Baweja 1995b); the last one is separating the recovery creep from the unrecoverable creep, such as CEB-FIP78. In recent years, high-strength concrete has been widely used in long-span prestressed concrete bridges, resulting in tremendous changes in material properties and reduced material costs. Most of the existing prediction models for concrete creep and shrinkage are generally derived through statistical regression analysis of test data largely which are mostly from normal strength concrete, and their applicability on the high-strength concrete needs to be evaluated. Moreover, due to using high-strength concrete, deflection becomes a more crucial issue as structural components become more slender. In addition, creep and shrinkage in concrete structures are the most uncertain properties of concrete, considering inherent material variations and modeling uncertainties. Past studies focused on inputting Journal of Bridge Engineering. Submitted October 26, 2009; accepted June 10, 2010; posted ahead of print June 15, 2010. doi:10.1061/(ASCE)BE.1943-5592.0000147Copyright 2010 by the American Society of Civil EngineersAccepted Manuscript Not Copyedited 4 determinate values of the factors affecting creep and shrinkage to obtain the structural response. However, studies of uncertainty of creep and shrinkage effects in concrete structures have increasingly gained interest in recent years (Madsen and Bazant 1983; Takcs 2002; Yang 2007; Bazant and Li 2008). The change of environmental conditions, the variation of the quality and the mix composition of the materials of the concrete, and the variation due to inherent mechanism of creep and shrinkage are the main causes of uncertainty. Time-dependent deformations and redistribution of sectional forces of long-span prestressed concrete cantilever bridges are highly sensitive to concrete creep and shrinkage. Therefore, the random properties of these factors should be taken into account in analysis of creep and shrinkage effects. To minimize the risk of excessive deflections, the long-span prestressed box girder bridges should be designed for response values representing not the mean values but 95% confidence limits (Bazant and Baweja, 1995b). Modified Prediction Models of Creep and Shrinkage Component materials and mechanical properties of concrete Table 1 shows the mixture ratio of concrete used in the continuous rigid frame of Sutong Bridge. The Portland cement (P.II.52.5) is produced in Huaxin Cement Co., Ltd., and the first-grade fly ash takes its source at Jianbi power station in Zhenjiang. The manufacturing location of the sand is Ganjiang in Jiangxi Province. Aggregate is taken from limestone of Maodi in Zhenjiang, and the size grading is 510mm and 1020mm, of which the proportion is 2:3, correspondingly. The concrete admixture is JM-PCA concrete water-reducer produced by Jiangsu Subote New Materials Co., Ltd. The cubic compressive strength, prism compressive strength and modulus of elasticity in standard curing conditions are tabulated in Table 2. The cubic standard cure strength specimens were cast in 150mm150mm150mm steel molds; while prism strength and modulus specimens were cast in 100mm100mm300mm steel molds. The experimental results demonstrate that the 28-day cubic compressive strength is 79.6MPa after being mixed with high-quality fly ash and concrete water reducer, which is higher than the 60MPa designed. The cubic strength is increased by 9.0MPa from 28 days to 90 days, and the strength develops a little later. The modulus of elasticity at 28 days is more than the 36GPa designed in JTG D62-2004, and it increased slightly after 28 days. Creep and shrinkage tests The purpose of the experiment is to determine the time-dependent properties of high-strength and high-performance concrete used in the continuous rigid frame of Sutong Bridge. The creep prism specimens were cast in 100mm100mm300mm steel molds, along with the strength, modulus and shrinkage Journal of Bridge Engineering. Submitted October 26, 2009; accepted June 10, 2010; posted ahead of print June 15, 2010. doi:10.1061/(ASCE)BE.1943-5592.0000147Copyright 2010 by the American Society of Civil EngineersAccepted Manuscript Not Copyedited 5 specimens. After casting, the creep and shrinkage specimens were stored in a moist room where the ambient temperature was 202 and the relative humidity was approximately 95%. The creep specimens were moist cured until they were loaded in the creep frames in a constant-temperature and constant-humidity room where the ambient temperature was 202 and the relative humidity was approximately 60%. A factor which greatly affects creep is the age of concrete at loading. In the experiment, two groups of creep specimens were stacked in two creep frames separately, and loaded to 40% of their after-cure compressive strength. The ages of the two groups at loading were 7 days and 14 days, respectively. Loading the specimens at 7 days was to simulate the prestress tensioning situation of each segmental box girder in the continuous rigid frame of Sutong Bridge. Each group had two specimens. The size of creep specimens and other test conditions are tabulated in Table 3. The strains of all creep specimens were measured using a gauge with a 150mm gauge length, and each gauge had a dial gauge mounted on a frame. There were two gauges for each specimen, and the average of the two strain readings was regarded as the strain of each specimen. Also, there were three shrinkage specimens together with each group of creep specimens. Therefore, when determining the creep strain at any time, the shrinkage strains were subtracted from total strains directly. A total of 9 shrinkage specimens in three groups were tested. The shrinkage specimens were exposed to the same ambient conditions as creep specimens. Table 4 lists the size of shrinkage specimens and other test conditions. In the surface of each specimen, the brass inserts were cast into each shrinkage prism, so that two gage points separated by 250mm could be attached after curing. The YB-250 hand-held strainmeter produced by Tianjin Construction Instruments Co., Ltd. was used for measuring the shrinkage strains. To improve the measuring precision, there were three specimens for each group, with two pairs of brass inserts for each specimen. Subsequently, the average of the measured data was regarded as the shrinkage strain of each specimen. Modified prediction model of shrinkage Using the form of the shrinkage prediction model in JTG D62-2004, a modified prediction model of shrinkage is presented through shrinkage tests. 0( , )()cssshcssst ttt (1) The calculation methods of cs0 and s(t-ts) can be found in JTG D62-2004. In order to determine the value of sh, the measured shrinkage strain at each time is regarded as the value, cs(t,ts), and the developing curve of shrinkage strain, s(t-ts) is assumed to be the same as that in JTG D62-2004, so we can get the value of shcs0. Journal of Bridge Engineering. Submitted October 26, 2009; accepted June 10, 2010; posted ahead of print June 15, 2010. doi:10.1061/(ASCE)BE.1943-5592.0000147Copyright 2010 by the American Society of Civil EngineersAccepted Manuscript Not Copyedited 6 Then, the value of sh can be obtained through shcs0 dividing by cs0, which is calculated by the method in JTG D62-2004. The measured concrete strength in Table 2 is applied in the function. For each measured time, we can get a value of sh; therefore, there are many values of sh. Using the statistical method, the modified coefficient sh of shrinkage model is obtained and expressed as: 1.52sh (2) Figs. 2 to 4 show the estimated curves and test data of shrinkage strains of Group S1 to Group S3. The shrinkage prediction values of the shrinkage model in JTG D62-2004 are also plotted in Figs. 2 to 4. Modified prediction model of creep Using the form of the creep prediction model in JTG D62-2004, a modified prediction model of creep is presented through creep tests. 0( , ),crctt (3) Based on previous researches, there are two definitions of creep coefficient, one is as follows, ( , )( , )( )/(28)cccttE (4) The other is defined as follows, ( , )( , )( )/( )cccttE (5) The difference between the two expressions is the use of the modulus of elasticity. In this study, Eq. (5) is used. The calculation methods of 0 and c(t,) can be seen in JTG D62-2004. For the purpose of getting cr, the measured creep coefficient at each time is regarded as the value, (t,), and the developing curve of creep coefficient, c(t,), is assumed to be the same as that in JTG D62-2004, so the value of cr0 can be obtained. Then, through cr0 dividing by 0, which is calculated by the method in JTG D62-2004, the value of cr at each time is obtained. The measured concrete strength is applied in the function. It is worth noting that the creep coefficient in JTG D62-2004 is defined in the form of Eq. (4), so we need convert it into the second definition, Eq. (5) through multiplying Ec()Ec(28). Using the same statistical method as the process of the shrinkage test, the modified coefficient of creep model is obtained and expressed as: 0.754cr (6) Figs. 5 and 6 show the estimated curves and test data of creep coefficient of Group C1 and Group C2. The creep coefficients calculated by JTG D62-2004 are also plotted in Figs. 5 and 6 for comparison. Journal of Bridge Engineering. Submitted October 26, 2009; accepted June 10, 2010; posted ahead of print June 15, 2010. doi:10.1061/(ASCE)BE.1943-5592.0000147Copyright 2010 by the American Society of Civil EngineersAccepted Manuscript Not Copyedited 7 Five current prediction models of creep and shrinkage Various prediction models have been developed to predict the creep and shrinkage of concrete in the past. Five creep and shrinkage prediction models are introduced in this paper. The five models are ACI 209-82 model, AASHTO (2007), JTG D62-2004, B3, and GL2000. It is well known that all these models are empirical or semi-theoretical formulas, and the parameters in these models are obtained through test data fitting. The limitations of the influence factors considered in each model, as well as the test data which each model is based on may result in larger variability between the predicted values and the measured of a certain concrete. In this paper, the discussion is concentrated on the evaluation accuracy of the five models through comparing the predicted results with the test results of the high-strength concrete used in the continuous rigid frame of Sutong Bridge. Comparison of shrinkage models Figs. 2 to 4 show the comparison of the five shrinkage models mentioned above and the modified model with the test data of Group S1 to Group S3. From the test results of Groups S1 and S2, the test shrinkage curves are very close, which means if the time of initial moist curing is more than 7 days, it would have little effect on the drying shrinkage strains. After drying for a month, the shrinkage strains of the three groups developed only a little. The results of Groups S1 and S3 indicate that the ultimate shrinkage strains of different sizes of specimens tend to have different values. Smaller the specimen size is, greater the ultimate shrinkage strain becomes. The prediction shrinkage model in JTG D62-2004 obviously underestimates the shrinkage strains of concrete used in the continuous rigid frame of Sutong Bridge. As a result, if the shrinkage model in JTG D62-2004 is applied to the bridge, there is a risk in underestimating the long-term deflection of the bridge. For Groups S1, S2 and S3, the modified model matches the test data well, and the correlations between the calculated values of the modified shrinkage model and test data are 0.962, 0.965, and 0.933, respectively. Although in the beginning of the period of test, the prediction value is a little smaller than the measured value, while in the late days it is more than the measured value. ACI 209-82, AASHTO and GL2000 models all overestimate largely the shrinkage strains of the high-strength concrete, while the predicted values of B3 model are close to the test data, because B3 model is established on the moisture diffusion theory and takes account of the mixture proportions of concrete in detail. However, B3 model, in contrast to the others, raises the concern of complexity for the engineers. Moreover, the B3 Coefficient of Variation Method which was developed by Bazant and Baweja (1995c) was used in this study for evaluating the accuracy of the five current models and the modified model. For the Journal of Bridge Engineering. Submitted October 26, 2009; accepted June 10, 2010; posted ahead of print June 15, 2010. doi:10.1061/(ASCE)BE.1943-5592.0000147Copyright 2010 by the American Society of Civil EngineersAccepted Manuscript Not Copyedited 8 three groups of shrinkage specimens, the coefficients of variations for ACI 209-82, JTG D62-2004, GL2000, B3, AASHTO, and the modified model are 83.0%, 36.7%, 50.1%, 21.4%, 84.7% and 14.2%, respectively. Comparison of creep models Figs. 5 and 6 show the comparison of the five current creep models and the preceding modified creep model with the test data of the tested concrete. From Figs. 5 and 6, the creep coefficients develop fast in the beginning period of loading, especially in the initial 30 days. Subsequently, the development becomes a little slower, and keeps stable growth. Within 150 days, the development of creep coefficients is relatively faster. After loading for 150 days, the development is slow. Using the modified creep model, the calculated values match the test data very well, and the curve tendency is also very close to test data. For Groups C1 and C2, the correlations between the calculated values of the modified creep model and test data are 0.997 and 0.994, respectively. The measured creep coefficients are lower than the predicted values by JTG D62-2004, GL2000 and B3 creep models, while ACI 209-82 and AASHTO model are relatively close to the test data, especially AASHTO model. Gardner and Zhao (1993) pointed that ACI 209-82 creep model generally underestimates the creep coefficient. We feel that Gardner and Zhao got the conclusion aiming at normal strength concrete, because ACI 209-82 creep model is not sensitive to the strength of concrete and its prediction precision may be better for the high-strength concrete instead of normal strength concrete. However, the applicability of ACI 209-82 and AASHTO creep models for wider scope of the high-strength concrete needs to be studied further. Besides, AASHTO model and ACI 209-82 model have the same time-progress curves, and in the beginning, the creep coefficients, or shrinkage strains develop very fast, but later, they progress very slow as close to a straight line. Therefore, if using the ACI 209-82 model or AASHTO model, there is a risk in underestimating the increment of deflection of the bridge. For the two groups of creep specimens, the B3 coefficients of variations for ACI 209-82, JTG D62-2004, GL2000, B3, AASHTO, and the modified model are 18.0%, 46.2%, 99.6%, 52.0%, 15.2% and 12.5%, respectively. Therefore, the modified creep model can well reflect creep property of the high-strength concrete used in the continuous rigid frame of Sutong Bridge. Using this model, the analysis precision of the time-dependent behavior of the bridge can be improved. Journal of Bridge Engineering. Submitted October 26, 2009; accepted June 10, 2010; posted ahead of print June 15, 2010. doi:10.1061/(ASCE)BE.1943-5592.0000147Copyright 2010 by the American Society of Civil EngineersAccepted Manuscript Not Copyedited 9 Uncertainty Modeling of Creep and Shrinkage Prediction Models An important but usually neglected property of creep and shrinkage models, which usually predict the mean value, is the expected error of the prediction. In reality, the coefficients of creep and shrinkage strains should be considered as statistical variables. Model uncertainty factors are used for defining uncertainty of creep and shrinkage prediction models. So, the equation for modified prediction of shrinkage strain is as follows: 10( , )()cssshcssst ttt (7) The equation for modified prediction of creep coefficient is as follows: 02( , ),crctt (8) Ang and Tang (1975) introduced a method for how to calculate the uncertainty of concrete creep and shrinkage prediction models, which is as follows: *ii （i=1, 2） (9) Where *1 and *2 are prediction error terms that account for the uncertainty inherent in the theoretical model and the uncertainty of the micro-mechanism of shrinkage and creep that have been neglected. Those two prediction error terms can be obtained by comparing the prediction value of the model with experimental data. Referring to studies on uncertainty of the concrete creep and shrinkage prediction model by Bazant and Baweja (1995c), the mean values and coefficients of variation of *1 and *2 for the modified prediction model are assumed as the same as the CEB-FIP90 model, respectively, and they are *1()1E，*1()0.463V (10a) *2()1E，*2()0.353V (10b) The factors to be used in Eq. (7) and Eq. (8) are prediction model uncertainty 1 and 2, and the coefficients of variation in Eq. (10a) and Eq. (10b) must therefore be revised. The factors in Eq. (9) are assumed to be independent, and the relation between the coefficients of variation is (Ang and Tang 1975) 2*222(1()(1()(1()(1()iiVVVV (i=1, 2) (11) The research by Reinhardt et al. (1982) indicates that a value between 0.06 and 0.10 for ()V is reasonable for test specimens, and 0.08 is chosen in this study. The coefficient of variation ()V is estimated as 0.05 by Madson and Bazant (1983). The following corrected values are obtained based on Eq. Journal of Bridge Engineering. Submitted October 26, 2009; accepted June 10, 2010; posted ahead of print June 15, 2010. doi:10.1061/(ASCE)BE.1943-5592.0000147Copyright 2010 by the American Society of Civil EngineersAccepted Manuscript Not Copyedited 10(10a), Eq. (10b) and Eq. (11). 1()1E, 1()0.45V (12a) 2()1E, 2()0.34V (12b) Latin Hypercube Sampling (LHS) Method for Uncertainty Analysis In response to the uncertainty of creep and shrinkage effects in a structure, an alternative method, which can yield more precise estimates, is to use the constrained Monte Carlo Sampling method. But the Monte Carlo Sampling method may be limited by intensive calculation work, a long wait and computer capability in the time-dependent analysis of a large bridge. Latin Hypercube Sampling method was adopted to improve sampling precision and decrease sampling numbers in the random simulation. Latin Hypercube Sampling method was suggested by Mckay and Conover (1979), which was developed from the Stratified Sampling method. This method consists of two steps. It is assumed that there are N statistical variables. The first step is partitioning each input variable into K non-overlapping intervals on the basis of equal probability, so the probability of each interval is correspondent to 1/K. Only one sample is insured to be implemented from each interval in the analysis. If the number of intervals, K is greater than the number of variables, N, the centroid of each interval can be taken as a representative value of the sample, shown in Fig.7, that is ()1 2kiF xkK (k=1,2,K) (13) The second step is coupling input variables with tables of random permutations of rank numbers, and the table of K rows and N columns will then be obtained. Each statistical variable, xi, is described by its known cumulative distribution function with the appropriate statistical parameters. The kth row of the table is used on the kth computer run of the structure model. Therefore, the corresponding value Yk of is obtained on the kth computer run. From K computer runs, we can get a column vector, 12,.,TKYY YY of the structural response. Through statistically assessing the column vector, the expectation value and variance of the structural response can be obtained. Comparing with other sampling methods, the significant advantage of the LHS method is that the number of computer runs can be considerably reduced to achieve the same level of precision. Furthermore, the computer efficiency of the LHS method is improved greatly as the number of variables, N, increases. Bazant and Liu (1985) applied the LHS method in the analysis of creep effect, and pointed out that the accuracy requirement can be met if the number of computer runs is twice the number of the random variables, K=2N. Journal of Bridge Engineering. Submitted October 26, 2009; accepted June 10, 2010; posted ahead of print June 15, 2010. doi:10.1061/(ASCE)BE.1943-5592.0000147Copyright 2010 by the American Society of Civil EngineersAccepted Manuscript Not Copyedited 11 Uncertainty Analysis of Creep and Shrinkage Effects in Continuous Rigid Frame of Sutong Bridge Description of the continuous rigid frame of Sutong Bridge The continuous rigid frame of Sutong Bridge is a segmental, cast-in-place concrete cantilever bridge completed in 2007, and the span distribution is 140m+268m+140m, among the longest spans of the world. Fig. 8 shows the bridge in construction. The width of the top slab of the box girder is 16.4m, and width of the bottom slab is 7.5m. The height of the box girder varies from 15m at the piers to 4.5m at mid-span. The thickness of the bottom slab varies from 1700mm at piers to 320mm at mid-span. The web thickness varies in steps from 1000mm at the piers to 450mm at mid-span. Fig. 9 shows the arrangement of the box girder in the bridge, and Fig. 10 shows the segments and layout of longitudinal tendons including the cantilever webs bent-down tendons. The central span consists of 63 segments while the two side spans consist of 33 segments each, and the entire span is constructed in balanced cantilevers. The detailed construction process of the bridge is tabulated in Appendix B. Two Approaches to Mitigate Deflection To mitigate deflections of mid-span, two effective approaches are applied in the bridge. One is the longitudinal jacking construction technology in the central span, shown in Fig. 11. There are four horizontal jacks between the two cantilever ends along the longitudinal direction, and the total jacking force of the four jacks is 720t. After jacking, the closure segment was cast in site. The devices and components of jacking and anchoring would be removed after the compressive concrete strength of the closure segment reached 50% of the designed value. The other one is pre-setting internal tendons in the bottom slabs of the box girder which would be applied during the bridges service. As shown in Fig. 10, there are a total of 15 couples of continuity tendons in the bottom slab in the main span. Z1 to Z5, Z7 to Z9, Z11 to Z13, and Z15 were tensioned after casting the closure segment in the main span. The rest couples of tendons are Z6, Z10 and Z14 anticipated to be tensioned in one year after the completion of the bridge. Obviously, this approach can effectively improve the stress states and deflections of the bridge. Statistical Properties of Input Variables Because tendons play an important part in the deformation and the stress state of the bridge, and their effects also couple with the creep and shrinkage, the tension-control stress of tendons is thereby regarded as a Journal of Bridge Engineering. Submitted October 26, 2009; accepted June 10, 2010; posted ahead of print June 15, 2010. doi:10.1061/(ASCE)BE.1943-5592.0000147Copyright 2010 by the American Society of Civil EngineersAccepted Manuscript Not Copyedited 12statistical variable in the uncertainty analysis of creep and shrinkage effects. In summary, in the present study, five model parameters are considered as statistical variables and accordingly, five uncertainty factors, 1x,2x,3x, 4x, 5x are introduced into the numerical model. The first two uncertainty factors are meant to consider the potential prediction error in the shrinkage and creep models while the other two uncertainty factors are assigned to model parameters such as relative humidity and concrete strength to take into account the statistical variation and estimation error. The last uncertainty factor is assigned to tension-control stress of tendons. The uncertainty factors are assumed to follow normal distribution with the mean value of one. Table 5 shows the values for the mean and the coefficient of variation of the five input variables. The assumptions of the coefficients of variation of the humidity and the tension control stress were made based on consulting the designers of the bridge who have years of experiences in the design of the bridges under the similar environment. Also, the prestress loss has large effects on the structural time-dependent behavior. However, this paper focuses on creep and shrinkage effects of concrete; therefore, the calculated method of the prestress loss is based on the specifications in JTG D62-2004, and the parameters for calculating the prestress loss are provided by the designers and construction organization. The FE model for the continuous rigid frame of Sutong Bridge was built, in which the modified creep and shrinkage prediction models were used to calculate the structural time-dependent behavior. In order to verify the rationality of the modified model, three-class experiments were conducted. On the whole, the specimens are grouped in three classes, which are respectively prismatic plain concrete specimens mentioned above, reinforced concrete specimens, and a small-scale segmental concrete cantilever beam under natural environment which is close to that of the studied bridge. Test results show that a good agreement is observed between the test data and the calculated values using the modified prediction models. In this study, the number of computer runs were chosen to be K =3N =15 for the N =5 random variables to ensure the accuracy. The fifteen computer runs furnished fifteen values for structural response. Then, the statistical properties of the structural response, such as the mean value and the coefficient of variation, could be estimated. Comparison between Results and Measured Data in the Construction Stage Figs. 12 and 13 show the stresses of top slab and bottom slab of rear-end box girder section of 2# segment in the main span. The number of 15 to 31 in abscissa represents that the measured values (China Zhongtie Major Bridge Engineering Group Co., Ltd. 2007) are obtained from transducers after casting the corresponding number of segment, and No. 32 means the measured values are obtained after tensioning the continuity tendons in the main span. The development trend of calculated stress tallies closely with the Journal of Bridge Engineering. Submitted October 26, 2009; accepted June 10, 2010; posted ahead of print June 15, 2010. doi:10.1061/(ASCE)BE.1943-5592.0000147Copyright 2010 by the American Society of Civil EngineersAccepted Manuscript Not Copyedited 13measured values. The deviations of stress of the top slab between calculation values and measured values are around 1.4MPa, and the greatest deviation, 2.2MPa occurs in casting 18# segment. The deviation of stress of bottom slab between calculation values and measured values is around 1.2MPa, and the greatest deviation, 1.75MPa occurs in casting 18# segment. Figs. 14 and 15 show the stresses of top slab and bottom slab of rear-end box girder section of 10# segment in the main span. The number of 17 to 31 in abscissa represents the measured values that are obtained from the transducers after casting the corresponding number of segment, and No. 32 means the measured values are obtained after tensioning the continuity tendons in central span. The development trend of calculated stress tallies closely with the measured values. The deviation of stress of top slab between calculation values and measured values is around 2MPa, and the greatest deviation, 2.65MPa occurs in casting 17# segment. The deviation of stress of bottom slab between calculation values and measured values is around 1.2MPa, and the greatest deviation, 2.12MPa occurs in tensioning the continuity tendons of the central span. Predicting Long-Term Deflection Considering the uncertainty of the preceding five random variables, the increment of deflection at mid-span after completing the bridge was calculated using the modified model, and Fig. 16 shows the mean and the 95% confidence intervals for the deflection increment at mid-span. Also, the predicted values are compared with that produced by other models. The increments of deflection at mid-span after completing the bridge were predicted using the modified model, the model in JTG D62-2004 and the ACI 209-82 model. Furthermore, the 95% confidence limits of the deflection increment are calculated using the modified model. From the predicted results, we can see that the predicted deflection by the modified model is close to that predicted by the model in JTG D62-2004, and that is because the creep model in JTG D62-2004 overestimates the measured creep coefficients, while the shrinkage model underestimates the tested shrinkage strains. In the mass, their predicted values are similar. However, in the 15 years after completing the bridge, the predicted increment of deflection by JTG D62-2004 is a little higher than that predicted by the modified model. On the other hand, it may underestimate the long-term deflection increment using the ACI 209-82 model, which is the same as that Bazant (2008) concluded. It is well known that the methods of determining creep and shrinkage in AASHTO (2007) are based on the recommendation of ACI 209-82 as modified by additional published data. AASHTO model and ACI 209-82 model have the same time-progress curves, and in the beginning, the creep Journal of Bridge Engineering. Submitted October 26, 2009; accepted June 10, 2010; posted ahead of print June 15, 2010. doi:10.1061/(ASCE)BE.1943-5592.0000147Copyright 2010 by the American Society of Civil EngineersAccepted Manuscript Not Copyedited 14coefficients, or shrinkage strains develop very fast, but later, they progress very slow as close to a straight line. Therefore, if using the ACI 209-82 model or AASHTO model, there is a risk in underestimating the increment of deflection of the long-span concrete bridge. From Fig. 16, the mean increment of deflection at mid-span would be 36mm in one year after completing the bridge using the modified creep and shrinkage models. Tensioning the pre-setting internal tendons in the central span would induce a camber of 22mm at mid-span. Hereby, pre-setting internal tendons is effective to mitigate the excessive deflection problems. The mean increment of deflection at mid-span would be 58mm in ten years after completing the bridge while it would be 85mm in thirty years. With regard to the confidence limit, the probability band width of structural response is increased with time, which means the prediction uncertainty is increased with time. Based on the 95% confidence intervals, the maximum increment of deflection at mid-span would be 140mm in thirty years after completing the bridge, while the minimum one is 35mm. So the design of long-span concrete cantilever bridge should be deliberated with the confidence limit to ensure the long-term serviceability. In our opinions, according to the lower limit of the mid-span deflection induced by the uncertainty of the creep and shrinkage effects, we can design required number of pre-setting internal tendons or preparatory external tendons tensioned during the service years of the bridge to avoid the excessive deflections. Conclusions High-strength and high-performance concrete exhibits different material properties, especially creep and shrinkage, from those of normal concrete. Experimental study on the creep and shrinkage of concrete used in the continuous rigid frame of Sutong Bridge shows that the measured coefficient of creep is lower than the prediction value of the creep model in JTG D62-2004, while the shrinkage prediction model in JTG D62-2004 underestimates shrinkage strains. The new modified factors are introduced to reflect the studied concrete, and the modified prediction models for creep and shrinkage match the test data very well. The method to reduce the prediction uncertainty is to conduct short-time tests and use them to modify the values of the material parameters in the current model, so the modified model can be specific only for the tested concrete. This approach can improve the accuracy of the prediction models of creep and shrinkage. Creep and shrinkage are the most uncertain mechanical properties of concrete. The stochastic aspects of these physical phenomena therefore should be taken into account in structural design. In view of some problems commonly found in long-span concrete bridges, the deformation should rather be considered as statistical variables and the calculated deformation should be considered with a certain confidence limit. Journal of Bridge Engineering. Submitted October 26, 2009; accepted June 10, 2010; posted ahead of print June 15, 2010. doi:10.1061/(ASCE)BE.1943-5592.0000147Copyright 2010 by the American Society of Civil EngineersAccepted Manuscript Not Copyedited 15Comparing with other sampling methods, the LHS method can considerably reduce the samples of variables in order to achieve the same level of precision in the uncertainty analysis of creep and shrinkage effects. Using the modified creep and shrinkage prediction models, the calculated stress in the top slabs and bottom slabs of a box girder section dovetails well with the field test data, and the deviations are mostly less than 2MPa. The results of uncertainty analysis of creep and shrinkage effects indicate that long-term deformation is stochastic due to the five random variables. The mean value of increment of mid-span deflection is 85mm in thirty years after completing the bridge, and the upper limit of 95% confidence limit is 35mm, while lower limit is 140mm. Moreover, to avoid the excessive deflections, according to the lower limit of the mid-span deflection induced by the uncertainty of creep and shrinkage of concrete, we can design required number of pre-setting internal tendons or preparatory external tendons tensioned during the service years. Two new approaches used in the continuous rigid frame of Sutong Bridge to mitigate the deflections ensure the serviceability of the bridge, which are longitudinal jacking construction technology for the closure segment in the central span and pre-setting internal tendons in girders tensioned during the bridges service. They can be referred to in the similar bridges. Acknowledgements This research work is mainly conducted at the Southeast University, China sponsored by the Headquarter of Sutong Bridge; finalized at the University of Maryland, College Park, USA. The authors acknowledge the funding support of Research Plan of Transportation Science in Jiangsu Province of China (Grant No. 05y02) and the BEST Center, University of Maryland. The writers would like to thank Professor Zhitao L and Zhao Liu of the Department of Civil Engineering, Southeast University for their advice, and also thank the design engineers of the studied bridge in CCCC Highway Consultants Co., Ltd. Appendix A Creep and shrinkage models in JTG D62-2004, which were modified from CEB-FIP90, are as follows. Shrinkage strain 0( , )()csscssst ttt (A.1) 0()csscmRHf (A.2) 60160 10910scmcmcmfscff (A.3) 301.55 1RHRH RH (A.4) Journal of Bridge Engineering. Submitted October 26, 2009; accepted June 10, 2010; posted ahead of print June 15, 2010. doi:10.1061/(ASCE)BE.1943-5592.0000147Copyright 2010 by the American Society of Civil EngineersAccepted Manuscript Not Copyedited 160.51201()350ssssttttth httt (A.5) Creep coefficient 0( , ),ctt (A.6) 0()( )RHcmf (A.7) 0130110.46RHRH RHh h (A.8) 0.505.3()cmcmcmfff (A.9) 0.211( )0.1t (A.10) 0.311()cHttttt (A.11) 1800150 11.22501500HRHhRHh (A.12) Appendix B The detailed construction process of the preceding bridge is tabulated as follows. No. Construction contents Duration 1 Piers 100 days 2 0# and 1# segments 70 days 3 Tensioning of T1 and F1 tendons 3 days 4 Installation of the form travelers for 2# segments 30 days 5 Casting of 2# segments 3 days 6 Curing of concrete 7 days 7 Tensioning of T2 and F2 tendons 1 day 8 Moving forward of the form travelers 1 day 9 Casting of 3# segments 3 days 10 Curing of concrete 7 days 11 Tensioning of T3 and F3 tendons 1 day 1295 4# to 24# segments 12 days for each segment Journal of Bridge Engineering. Submitted October 26, 2009; accepted June 10, 2010; posted ahead of print June 15, 2010. doi:10.1061/(ASCE)BE.1943-5592.0000147Copyright 2010 by the American Society of Civil EngineersAccepted Manuscript Not Copyedited 1796 Casting of the B3 deviation blocks 0.1day 97108 25# to 27# segments 12 days for each segment 109 Casting of the B2 deviation blocks0.1 day 110121 28# to 30# segments 12 days for each segment 122 Casting of the B1 deviation blocks0.1 day 123 Moving forward of the form travelers 1 day 124 Casting of 31# segments 3 days 125 Curing of concrete 7 days 126 Tensioning of T31 and F31 tendons 1 day 127 Casting of the A1 and A2 deviation blocks 0.1 day 128 Casting of the straight segments in both side spans using brackets 1 day 129 Moving forward of the form traveler in side spans, and refitting them into the hoisting baskets 3 days 130 40 tons of the ballast weight on 31# segments in the side spans, while 35 tons of the ballast weight on 31# segments in the central span, and installation of the stiff steel framework. 3 days 131 Casting of the closure segments in the side spans, and remove the balance weights 10 days 132 Curing of concrete 7 days 133 Tensioning of T32, T33, and B1B7 tendons in the side spans 5 days 134 Removing the brackets in the side spans 1 day 135 Moving forward of form travelers in the central span, and refitting them into the hoisting baskets 3 days 136 Jacking longitudinally in the central span, and installing the stiff steel framework 5 days 137 Casting of the closure segment in the central span, and remove the balance weights 10 days 138 Curing of concrete 7 days 139 Tensioning of Z1 to Z5 tendons 10 days 140 Tensioning of Z7 to Z9 tendons 5 days 141 Tensioning of Z11 to Z13, and Z15 tendons 5 days 142 Removing the hoisting baskets in both side spans and the central span 10 days 143 Bridge deck pavement 60 days 144 Tensioning of the rest tendons Z6, Z10 and Z14 one year after completing the bridge 10 days Notation The following symbols are used in this paper: (28)cE = modulus of elasticity at 28 days; Journal of Bridge Engineering. Submitted October 26, 2009; accepted June 10, 2010; posted ahead of print June 15, 2010. doi:10.1061/(ASCE)BE.1943-5592.0000147Copyright 2010 by the American Society of Civil EngineersAccepted Manuscript Not Copyedited 18( )cE = modulus of elasticity at loading; fcm = average cubic compressive strength of concrete at 28 days (MPa); fcm0 = 10MPa; ( )iF x = the cumulative distribution function of ix; h = effective thickness to account of volume/surface ratio (mm); h0 = 100mm; K = partitioning each input variable into K non-overlapping intervals on the basis of equal probability; N = number of statistical variables; RH = relative humidity (%); RH0 = 100%; t = time (days); t1 = 1day; ts = age of curing (days); ix = the ith statistical variable; Y = the column vector of the structural response; ,ct = creep coefficient as time progresses; ()sstt = shrinkage strain function as time progresses; sc = coefficient to describe type of cement, equal to 5.0 for general portland-type cement or rapid hardening cement; cr= modified coefficient for creep model; sh= modified coefficient for shrinkage model; = age of concrete at loading (days); ( , )t = creep coefficient; 0 = ultimate creep coefficient; ( , )csst t = shrinkage strain, mm/mm; 0cs= ultimate shrinkage strain; Journal of Bridge Engineering. Submitted October 26, 2009; accepted June 10, 2010; posted ahead of print June 15, 2010. doi:10.1061/(ASCE)BE.1943-5592.0000147Copyright 2010 by the American Society of Civil EngineersAccepted Manuscript Not Copyedited 191 = model uncertainty factor for the shrinkage model; 2 = model uncertainty factor for the creep model; *1 = prediction error term that accounts for the uncertainty inherent in the theoretical model and the uncertainty of the micro-mechanism of shrinkage that has been neglected; *2 = prediction error term that accounts for the uncertainty inherent in the theoretical model and the uncertainty of the micro-mechanism of creep that has been neglected; = factor due to internal uncertainty; = factor due to measurement errors and uncertainty in the laboratory (or site) environment. References ACI 209R-92. (1992). Prediction of creep, shrinkage and temperature effects in concrete structures. ACI Manual of Concrete Practice. Part 1. Detroit. American Association of State Highway and Transportation Officials (AASHTO). (2007). AASHTO LRFD Bridge Design Specifications, 4th Ed., Washington, D.C. Ang, H.S. and Tang, W.H. (1975). Probability concepts in engineering planning and design. Vol. 1, Basic Principles. Wiley, New York. Bazant, Z.P. and Liu, K.L. (1985). “Random creep and shrinkage in structures: sampling.” Journal of Structural Engineering, 111(5), 1113-1134. Bazant, Z.P. and Baweja, S. (1995a). “Justification and refinements of model B3 for concrete creep and shrinkage. 2. updating and theoretical basis.” Materials and Structures, 28(182), 488-495. Bazant, Z.P. and Baweja, S. (1995b). Creep and shrinkage prediction model for analysis and design of concrete structures: Model B3. Materials and Structures, 28(180), 357-365. Bazant, Z.P. and Baweja S. (1995c). “Justification and refinements of model B3 for concrete creep and shrinkage. 1. Statistics and sensitivity.” Materials and Structures, 28(181), 415-430. Bazant, Z.P., Li, G. et al. (2008). “Explanation of excessive long-time deflections of collapsed record-span Journal of Bridge Engineering. Submitted October 26, 2009; accepted June 10, 2010; posted ahead of print June 15, 2010. doi:10.1061/(ASCE)BE.1943-5592.0000147Copyright 2010 by the American Society of Civil EngineersAccepted Manuscript Not Copyedited 20box girder bridge in Palau.” 8th International Conference on Creep and Shrinkage of Concrete, Ise-Shima, Japan. China Zhongtie Major Bridge Engineering Group Co., LTD. (2007). Report of construction control of continuous rigid frame of Sutong Bridge. Wuhan. (in Chinese) Comit Euro-International du Bton (CEB). (1990). CEB-FIP model code for concrete structures, Lausanne, Switzerland. Gardner, N.J and Zhao, J.W. (1993). “Creep and shrinkage revisited.” ACI Materials Journal, 90(3), 236246. Gardner, N.J. and Lockman, M.J. (2001). “Design provisions for drying Shrinkage and Creep of normal-strength concrete.” ACI Materials Journal, 98(2), 159167. JTG D62-2004. (2004). Code for design of highway reinforced concrete and prestressed concrete bridges and culverts, Peking. (in Chinese) Madsen, H.O. and Bazant, Z.P. (1983). “Uncertainty analysis of creep and shrinkage effects in concrete structures.” ACI Journal, 82(2), 116-127. McKay, M. D., Beckman, R. J. and Conover, W. J. (1979). “A comparison of three methods for selecting values of input variables in the analysis of output from a computer code.” Technometrics, 21(2), 239-245. Reinhardt, H.W., Pat, M. and Wittmann, F.H. (1982). “Variability of creep and shrinkage of concrete.” Symposium on fundamental research on creep and shrinkage of concrete. Hague, 75-94. Takcs P. F. (2002). “Deformation in concrete cantilever bridges: observations and theoretical modeling.” Ph.D. dissertation, Norwegian University of Science and Technology, Tronheim, Norway. Yang, I. H. (2007). “Uncertainty and sensitivity analysis of time-dependent effects in concrete structures.” Engineering Structures, 29(7), 1366-1374. Journal of Bridge Engineering. Submitted October 26, 2009; accepted June 10, 2010; posted ahead of print June 15, 2010. doi:10.1061/(ASCE)BE.1943-5592.0000147Copyright 2010 by the American Society of Civil EngineersAccepted Manuscript Not Copyedited 21Zhan, J. and Chen H. (2005). “Analysis of causes of excessive deflections and cracking of box girder in long-span continuous rigid-frame bridges.” Journal of China & Foreign Highway, 25(1), 56-58. (in Chinese) Journal of Bridge Engineering. Submitted October 26, 2009; accepted June 10, 2010; posted ahead of print June 15, 2010. doi:10.1061/(ASCE)BE.1943-5592.0000147Copyright 2010 by the American Society of Civil EngineersAccepted Manuscript Not CopyeditedFig. 1. The continuous rigid frame of Sutong Bridge Fig. 2. Comparison between predicted values and test data of Group S1 Fig. 3. Comparison between predicted values and test data of Group S2 Fig. 4. Comparison between predicted values and test data of Group S3 Fig. 5. Comparison between predicted values and test data of Group C1 Fig. 6. Comparison between predicted values and test data of Group C2 Fig. 7. K intervals for equiprobability of the statistical variable Fig. 8. Construction of the continuous rigid frame of Sutong Bridge Fig. 9. Typical section of the box girder (cm) Fig. 10. Segments and layout of tendons in the continuous rigid frame of Sutong Bridge Fig. 11. Longitudinal jacking construction technology for closure segment Fig. 12. Comparison between calculated values and measured values of top slab stress Fig. 13. Comparison between calculated values and measured values of bottom slab stress Fig. 14. Comparison between calculated values and measured values of top slab stress Fig. 15. Comparison between calculated values and measured values of bottom slab stress Fig. 16. Increment of deflection at mid-span after completing the bridge Figure Captions ListJournal of Bridge Engineering. Submitted October 26, 2009; accepted June 10, 2010; posted ahead of print June 15, 2010. doi:10.1061/(ASCE)BE.1943-5592.0000147Copyright 2010 by the American Society of Civil EngineersAccepted Manuscript Not CopyeditedTable 1. Mixture proportions of concrete (kg/m3) Table 2. Mechanical properties of concrete Table 3. Test conditions of creep specimens Table 4. Test conditions of shrinkage specimens Table 5. Statistical properties of variables for modified CEB-FIP90 model Journal of Bridge Engineering. Submitted October 26, 2009; accepted June 10, 2010; posted ahead of print June 15, 2010. doi:10.1061/(ASCE)BE.1943-5592.0000147Copyright 2010 by the American Society of Civil Engineers Fig. 1. The continuous rigid frame of Sutong Bridge.pdfAccepted Manuscript Not CopyeditedJournal of Bridge Engineering. Submitted October 26, 2009; accepted June 10, 2010; posted ahead of print June 15, 2010. doi:10.1061/(ASCE)BE.1943-5592.0000147Copyright 2010 by the American Society of Civil Engineers050100150200250300350050100150200250300350400450500550600Shrinkage microstrainsDrying time (days) Measured data ACI 209-82 Shrinkage model in JTG D62-2004 GL2000 B3 AASHTO Modified model Fig. 2. Comparison between predicted values and test data of Group S1.pdfAccepted Manuscript Not CopyeditedJournal of Bridge Engineering. Submitted October 26, 2009; accepted June 10, 2010; posted ahead of print June 15, 2010. doi:10.1061/(ASCE)BE.1943-5592.0000147Copyright 2010 by the American Society of Civil Engineers050100150200250300350-50050100150200250300350400450500550600Shirnkage microstrainsDrying time (days) Measured data ACI 209-82 Shrinkage model in JTG D62-2004 GL2000 B3 AASHTO Modified model Fig. 3. Comparison between predicted values and test data of Group S2.pdfAccepted Manuscript Not CopyeditedJournal of Bridge Engineering. Submitted October 26, 2009; accepted June 10, 2010; posted ahead of print June 15, 2010. doi:10.1061/(ASCE)BE.1943-5592.0000147Copyright 2010 by the American Society of Civil Engineers050100150200250300350050100150200250300350400450500550600Shrinkage microstrainsDrying time (days) Measured data ACI 209-82 Shrinkage model in JTG D62-2004 GL2000 B3 AASHTO Modified model Fig. 4. Comparison between predicted values and test data of Group S3.pdfAccepted Manuscript Not CopyeditedJournal of Bridge Engineering. Submitted October 26, 2009; accepted June 10, 2010; posted ahead of print June 15, 2010. doi:10.1061/(ASCE)BE.1943-5592.0000147Copyright 2010 by the American Society of Civil Engineers01002003004005006000.00.81.01.82.02.8Creep coefficientDuraiton of loading (days) Measured data ACI209-82 Creep model in JTG D62-2004 GL2000 B3 AASHTO MOdified model Fig. 5. Comparison between predicted values and test data of Group C1.pdfAccepted Manuscript Not CopyeditedJournal of Bridge Engineering. Submitted October 26, 2009; accepted June 10, 2010; posted ahead of print June 15, 2010. doi:10.1061/(ASCE)BE.1943-5592.0000147Copyright 2010 by the American Society of Civil Engineers01002003004005006000.00.81.01.82.0Creep coefficientDuration of loading (days) Measured data ACI 209-82 Creep model in JTG D62-2004 GL2000 B3 AASHTO Modified model Fig. 6. Comparison between predicted values and test data of Group C2.pdfAccepted Manuscript Not CopyeditedJournal of Bridge Engineering. Submitted October 26,