Abstract
In order to analyze the optimal dosage of capsule pre-embedded in concrete materials, this article simplified the irregular cracks generated in concrete materials into linear regular hexagonal cracks in two-dimensional plane and planar cracks in three-dimensional space. Then, the probability model describing the interaction between the cracks and capsules was established using the probability theory of integral geometry. The theoretical solutions for the required capsule dosage for the two- and three-dimensional cases were derived. Finally, the calculated results for the theoretical model were compared with those provided by the computer simulation software. The results indicated that the model is suitable for analyzing and optimizing the capsule dosage required to repair cracks in concrete materials. It can provide a theoretical basis for the design of self-healing materials.
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