The Mathematica Book
Mathematical models to predict the critical conditions for bacterial self-healing of concrete
MMCP'11 Proceedings of the 2011 international conference on Mathematical Modeling and Computational Science
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The present study is performed in the framework of the investigation of the potential of bacteria to act as a catalyst of the selfhealing process in concrete, i.e. their ability to repair occurring cracks autonomously. Spherical clay capsules containing the healing agent (calcium lactate) are embedded in the concrete structure. Water entering a freshly formed crack releases the healing agent and activates the bacteria which will seal the crack through the process of metabolically mediated calcium carbonate precipitation. In the paper, an analytic formalism is developed for the computation of the probability that a crack hits an encapsulated particle, i.e. the probability that the self-healing process starts. Most computations are performed in closed algebraic form in the computer algebra system Mathematica which allows to perform the last step of calculations numerically with a higher accuracy.