Concrete creep is one of the most important properties for concrete structures, especially prestressed concrete. Therefore, an accurate prediction of concrete creep is required for the design of the structures. Due to the limited time and economic condition, long-term creep is mostly predicted using parameter estimation of creep models based on the short-term experimental results. However, the prediction results are significantly different according to the model which is used for prediction. In this paper, improving method for creep prediction is presented to reduce the model uncertainties.


Creep is the time-dependent deformation of concrete under a sustained load(Neville et al. 1983). It is one of the most important properties to design concrete structures(Rao and Jayaraman 1989). Numerous studies on creep have been performed to predict concrete creep, and many prediction models were proposed(American Association of State Highway and Transportation Officials. Subcommittee on Bridges and Structures 2011; Korea Concrete Institute 2009; Walraven and Bigaj 2011). However, as concrete creep is significantly affected by mix proportion as well as curing conditions, the prediction results are different according to the predictive models.

To overcome the limitation, predictive models are calibrated based on the experimental results, and the long-term creep is predicted by the calibrated models. However, even though the predictive models are calibrated, it shows large deviation when the long-term creep is predicted, i.e., extrapolation due to ignoring model uncertainties(Smith 2013).

In this study, improved prediction method is proposed to provide reliable and better predictions over both calibration(interpolation) and evaluation(extrapolation).

Bayesian inference for predictive density

Bayesian inference is one of the method to estimate model parameters and their uncertainties(Higdon et al. 2008). Based on Bayes' theorem of conditional probability, our prior belief on the model parameter (θ) is updated using given measurement (Ycal). The updated parameter (posterior density) is obtained as


where, π(θ|Ycal) is posterior density, π(θ) is prior density, π(Ycal|θ) is likelihood, π(Ycal) is normalizing constant, and can be ignored for parameter estimation. Therefore, Eq. (1) can be expressed as


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