TimeDependent Behavior Prediction, Serviceability and Sustainability Problems for HighPerformance Concrete Bridges
Abstract
The posttensioned concrete Igirder superstructure bridge made by highperformance concrete (HPC) typically exhibits deceptive timedependent behavior issues with age of concrete. The most common changes are observed deformation, top and bottom fiber stress variation and loss of prestress in Igirder due to the secondary effects of shrinkage and creep in concrete. However, in design optimistic expectation of the timedependent behavior of several posttensioned concrete Igirder bridges are premature by the existing bridge code, design specification and available prediction models. Nevertheless, about 1–10 years the timedependent behavior is observed inaccurate in prediction and introduced serviceability and sustainability problems. Consequently, more study is needed toward the timedependent behavior prediction of the concrete bridges using HPC shrinkage and creep dataset and existing material prediction models. In the present study author’s own an experimentally measured HPC shrinkage and creep database is considered from the literature Gedam et al. 2015 and for same shrinkage and creep are predicted using existing material models such as the American Concrete Institute (ACI), the fib model code 2010 (fib), the Bazant and Bawaja (B3) and the Gardner and Lockman (GL). The results experimentally measured of the shrinkage and creep and predicted by existing material models are incorporated in incremental timestep analysis method to obtain timedependent behavior results of the simply supported posttensioned Igirder up to 800 days. Furthermore, outcome longterm behavior results from both an experimental and models are comparatively studied. It has been observed in comparative studies that the existing shrinkage and creep prediction models are not found sophisticated in prediction of the HPC shrinkage and creep properties. Also, it has a probability that in the conventional analysis, design and regional construction, use of any one out of the four existing material models may be produced serviceability and sustainability issues in longterm behavior prediction. In fact, these material models needed reevaluation and modification, especially local environmental condition and indigenously sourced concrete materials properties.
Nomenclature
The following symbols are used in this paper:
 c_{1}
Top fiber neutral axis depth
 c_{2}
Bottom fiber neutral axis depth
 M_{o} and M_{l}
Midspan moment due to superimposed dead load and live load
 Pi
Initial prestress
 S_{t} and S_{b}
Section moduli with respect to the top (I _{ c } /c _{ 1 }) and bottom (I _{ c } /c _{ 2 }) surface of the girder
 n − 1
Beginning of a particular time step
 n
End of the aforementioned time step
 φ_{pi}
First term is the instantaneous curvature occurring immediately upon the application of initial prestress Pi
 d_{φ1}
Second term is a change in curvature corresponding due to loss of prestress considered PCI Committee report (1975) and Maguru et al. (1965) from creep, shrinkage, and relaxation coefficient and time funtions
 d_{φ2}
Third term is a change in curvature resulting from the direct effect of concrete creep under sustained loading and service conditions
 r
Radius of gyration (I _{ c } /A _{ c })
1 Introduction
2 Objective and Scope
In this study, to prove the importance of an appropriate material model in prediction of timedependent behavior of the posttensioned Igirder bridge. An analytical study is carried out using an experimental measured HPC shrinkage and creep database, and existing material models, namely ACI, fib, B3, GL. Basically, the timedependent shrinkage and creep of HPC and relaxation of the prestressed steel are responsible for the timedependent behavior, serviceability and sustainability of posttensioned Igirder PCI DH (1975). Therefore, an incremental timestep analytical method procedure is adopted on excel platform, which has been used to predict timedependent behavior of posttensioned Igirder. The algorithm used for prediction of the timedependent response has been validated using an experimental results reported in the literature Nilson (1987). In conclusion, the timedependent behavior of posttensioned Igirder bridge for M50 grade HPC mix properties is investigated using an experimental and prediction models of shrinkage and creep, and discussion on outcome results for serviceability and sustainability issues of the HPC bridge is presented.
3 Experimental Data Consideration
HPC mix proportions for shrinkage and creep measurement
HPC mix composition  Unit  HPC mix proportion 

Grade of concrete  Grade  M50 
Cement  kg/m^{3}  425 
Fine aggregate  kg/m^{3}  709 
Coarse aggregate  kg/m^{3}  1150 
Water  kg/m^{3}  148.75 
Superplasticizer G51  kg/m^{3}  1.7 
w/c  –  0.35 
Slump  mm  120 ± 5 
v/s of cylinder  mm  38 
fck _{28 days} of cube  MPa  61.18 
E _{28 days} of cylinder  MPa  33484 
t _{ 0 } and t _{ s }  Days  28 
4 Incremental TimeStep Method
A reasonably accurate estimation of the timedependent behavior is an important parameter to ensure that the structure built in such concrete performs satisfactorily specially in longterm and service. Hence, the incremental timestep analysis method is adopted on excel platform to evaluate the timedependent behavior of the HPC girder.
4.1 Incremental TimeStep Fiber Stress Distribution
The stresses variation at top and bottom fiber in girder can be calculated with respect to time as follows:
Top fiber stress
Bottom fiber stress
4.2 Incremental TimeStep Deformations
The timedependent deformations variation is calculated on the basis of curvature equations and for computational purpose the timedependent change in curvature after prestress losses have been considered in three parts by using the following equations from Nilson (1987). The general expression to obtain the total curvature φ _{ pt } after losses at the end of a time intervals at any section can be expressed as follows:
Curvature after losses
4.3 Prestress Tendon
In incremental timestep method, total prestress losses for Igirder member is computed as per conventional practice. The losses included due to shrinkage and creep of concrete, friction, anchorage slip, elastic shortening and steel relaxation, respectively. All losses are interdependent phenomenon, and therefore, to deal with such complex problem the relaxation of steel is evaluated using the following equation which was proposed by Maguru et al. (1964) and still applicable for all existing code and design specification.
Loss of stress in the steel due to relaxation
4.4 TimeDependent Material Models
The four existing material models ACI, fib, B3 and GL predicted results for HPC M50 grade concrete are implemented in incremental timestep analysis method to predict the timedependent behavior of HPC Igirder Gedam et al. (2014). In practice, the existing material models result in either underestimation/overestimation of the actual timedependent behavior of HPC Igirder. Hence, the experimental measured shrinkage and creep database has also been used in incremental timestep analysis method for a critical appraisal Gedam et al. (2013). Thus, predicted timedependent behavior of girder is based on the required material models as well as experimental data based.
4.5 Posttensioned IGirder Details
5 Results and Discussion
The analytical procedure of incremental timestep method for simply supported posttensioned Igirder on excel platform is used to compute timedependent deformation response, fiber stress variation and prestress losses in HPC Igirder at the age of 0 days to 800 days. The predicted results of timedependent behavior with the help of experimental and material models, and the model’s error percentage difference worked out with the reference of HPC mix experimentally investigated.
5.1 Deformations
Timedependent midspan camber of Igirder at age of 800 days under LC
HPC mix  Initial prestressing (f _{ pi }) in MPa  Tendon area (A _{ p }) in mm^{2}  Camber (mm) as per exp. properties  Predicted camber (mm) as per existing material models and difference (%)  

ACI  fib  B3  GL  
Val.  Diff.  Val.  Diff.  Val.  Diff.  Val.  Diff.  
M50 grade  1460  7ply × 9^{*} = 630  −17  −10  +41  −25  −47  −40  −135  +0.4  +98 
5.2 Stress Distribution
Summary of stress distribution in Igirder for LC using experimental data
HPC mix  Top fiber stress (MPa)  Bottom fiber stress (MPa)  

0 day  800 days  % diff.  0 day  800 days  % diff.  
M50 grade  10.86  10.75  1.01  3.94  1.40  64.46 
Summary of bottom fiber stress distribution of Igirder for LC using material models at age 800 days
HPC mix  Stress (MPa) as per experimental properties  Predicted stress (MPa) as per existing material models at the age of 800 days and the difference (%)  

ACI  Diff.  fib  Diff.  B3  Diff.  GL  Diff.  
M50 grade  1.40  1.69  −20.7  0.81  +42.1  −0.3  +121  1.87  −33.5 
5.3 Prestress Losses
Summary of prestress loss in Igirder under LCII at age 800 days
HPC mix  Prestress loss (MPa) as per experimental properties  Predicted prestress loss (MPa) as per existing material models at the age of 800 days  

ACI  % diff.  fib  % diff.  B3  % diff.  GL  % diff.  
MixII  395  365  +7.60  456  −15.4  543  −37.5  346  +12.4 
6 Conclusions

The percentage error in predicting camber is observed for each model are +41% for the ACI model, −47% for the fib model, −135% for the B3 model and +98% for the GL model at the age of 800 days. The ACI and GL models usually underestimate the camber while the fib and B3 models overestimate.

The percentage error in predicting of bottom fiber stress of Igirder at the age of 800 days is −20.70% for the ACI model, +42.10% for the fib model, +121% for the B3 model and −33.5% for the GL model.

The average percentage error in predicting of the prestress loss at the age of 800 days is +7.60% for the ACI model, −15.4% for the fib model, −37.5% for the B3 model and +12.4% for the GL model respectively.
An appropriate material model in the analysis process to meet the demand of optimistic design expectations with efficient and scientifically sound in very important. In fact, due to the scattered results and higher percentage error in prediction, it is very difficult to say which model is the best of the timedependent properties prediction for HPC concrete bridges. Therefore, more study and improvement is needed in the prediction models, especially indigenous source concrete material properties.
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