Mathematical Models to Predict the Critical Conditions for Bacterial Self-healing of Concrete

  • Serguey V. Zemskov
  • Henk M. Jonkers
  • Fred J. Vermolen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7125)


Two mathematical models for bacterial self-healing of a crack are considered. The study is embedded within the framework of investigating the potential of bacteria to act as a catalyst of the self-healing process in concrete, that is the ability of concrete to repair occurring cracks autonomously. The first model concerns an analytic formalism to compute the probability that a crack hits an encapsulated particle. Hence, it predicts the probability that the self-healing process starts. The second model of the self-healing process is based on a moving boundary problem. A Galerkin finite-element method is used to solve the diffusion equations. The moving boundaries are tracked using a level set method.


Mathematical modeling Moving boundary problem Self-healing 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Serguey V. Zemskov
    • 1
  • Henk M. Jonkers
    • 1
  • Fred J. Vermolen
    • 1
  1. 1.Delft University of TechnologyDelftThe Netherlands

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