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Modification of existing shape factor models for self-compacting concrete strength by means of Bayesian updating techniques

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Abstract

In this paper, the existing formulas for the shape factors for uniaxial compressive strength of vibrated concrete, in which the influence of the shape, size and damage due to drilling has been included, are adapted for powder-type self-compacting concrete. An extensive test program was executed and Bayesian updating techniques were applied in order to calculate posterior distributions of the parameters involved in the conversion formulas for shape factors. Using this method, differences between the shape factor formulas of vibrated and self-compacting concrete could be analysed despite the large variability in the experimentally obtained test results. The methodology developed in this paper for the Bayesian updating of shape factor formulas can also be applied to other material properties of self-compacting concrete and even other materials, especially in cases where a limited number of samples are available or in cases where a considerable variability in the test data is observed.

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Abbreviations

A :

The horizontal cross section of the test specimen

B :

The parameter vector space

d :

The lateral dimension of the test specimen (i.e. the core diameter or side length)

h :

The height of the test specimen

\( f_{\text{c}} \) :

The compressive strength determined on a standard cylinder with diameter 150 mm and height 300 mm

\( f_{\text{c\;x}} \) :

The compressive strength determined on a non-standard specimen of type x

\( f_{\text{c\;cub}} \) :

The compressive strength determined on a cube

f c cyl :

The compressive strength determined on a cylinder

\( f_{\text{c\;prism}} \) :

The compressive strength determined on a prism

f :

A distribution function

β :

The damage by drilling, defined as the ratio of the strength of a drilled specimen to the strength of a casted specimen with the same shape

\( \underline{\beta } \) :

The parameter vector

\( \underline{{\widetilde{\beta }}} \) :

The candidate vector space

\( \mu_{{f_{\text{c}} }} \) :

The mean compressive strength

\( \sigma_{{f_{\text{c}} }} \) :

The standard deviation of the compressive strength \( f_{\text{c}} \)

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Authors and Affiliations

  1. Magnel Laboratory for Concrete Research, Department of Structural Engineering, Ghent University, Technologiepark-Zwijnaarde 904, 9052, Ghent, Belgium

    Farid Van Der Vurst, Robby Caspeele, Pieter Desnerck, Geert De Schutter & Jonathan Peirs

  2. Center of Infrastructure and Engineering Studies, Missouri University of Science and Technology, Rolla, MO, USA

    Pieter Desnerck

Authors
  1. Farid Van Der Vurst
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  2. Robby Caspeele
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  3. Pieter Desnerck
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  4. Geert De Schutter
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  5. Jonathan Peirs
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Correspondence to Farid Van Der Vurst.

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Van Der Vurst, F., Caspeele, R., Desnerck, P. et al. Modification of existing shape factor models for self-compacting concrete strength by means of Bayesian updating techniques. Mater Struct 48, 1163–1176 (2015). https://doi.org/10.1617/s11527-013-0222-2

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