Bayesian Inverse Modelling of Early-Age Stress Evolution in GGBFS Concrete Due to Autogenous Deformation and Aging Creep

Minfei Liang*, Erik Schlangen, Branko Šavija

*Corresponding author for this work

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Stress evolution of restrained concrete is directly related to early-age cracking (EAC) potential of concrete, which is a tricky problem that often happens in engineering practice. Due to the global objective of carbon reduction, Ground granulated blast furnace slag (GGBFS) concrete has become a more promising binder comparing with Ordinary Port-land Cement (OPC). Although GGBFS concrete produces less hydration heat which further prevents thermal shrinkage, the addition of GGBFS highly increases the autogenous shrinkage and thus increases EAC risk. This study presents experiments and numerical modelling of the early-age stress evolution of GGBFS concrete, considering the development of autogenous deformation and creep. Temperature Stress Testing Machine (TSTM) tests were conducted to obtain the autogenous deformation and stress evolution of restrained GGBFS concrete. By a self-defined material sub-routine based on the Rate-type creep law, the FEM model for simulating the stress evolution in TSTM tests was established. By characterizing the creep compliance function with a 13-units continuous Kelvin chain, forward modelling was firstly conducted to predict the stress development. Then inverse modelling was conducted by Bayesian Optimization to efficiently modify the arbitrary assumption of the codes on the aging creep. The major findings of this study are as follows: 1) the high autogenous expansion of GGBFS induces compressive stress at first hours, but its value is low because of high relaxation and low elastic modulus; 2) The codes highly underestimated the early-age creep of GGBFS concrete. They performed well in prediction of stress after 200 h, but showed significant gaps in predictions of early-age stress evolution; 3) The proposed inverse modelling method with Bayesian Optimization can efficiently adjust the aging terms which produced best modelling results. The adjusted creep compliance function of GGBFS showed a much faster aging speed at early ages than the one proposed by original codes.

Original languageEnglish
Title of host publicationSSCS 2022
Subtitle of host publicationNumerical Modeling Strategies for Sustainable Concrete Structures
EditorsPierre Rossi, Jean-Louis Tailhan
Number of pages11
Publication statusPublished - 2023
EventNumerical Modeling Strategies for Sustainable Concrete Structures - Marseille, France
Duration: 4 Jul 20226 Jul 2022

Publication series

NameRILEM Bookseries
ISSN (Print)2211-0844
ISSN (Electronic)2211-0852


ConferenceNumerical Modeling Strategies for Sustainable Concrete Structures
Abbreviated titleSSCS 2022
Internet address

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.


  • Autogenous shrinkage
  • Bayesian Optimization
  • Concrete
  • Creep
  • Early age cracking
  • Relaxation

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