Analytical solution on dosage of self-healing agents in cementitious materials: Long capsule model

Crack-repairing technology via embedded capsules with healing agents is becoming a promising approach to sustain the performance of cementitious materials. In this article, the practical crack patterns in cementitious materials caused by various mechanisms are simplified to be the linear cracks in two-dimensional plane and the planar cracks in three-dimensional space, respectively. Then, based on the assumption that the length of the capsules embedded is larger than the average spacing between the adjacent cracks, via the theory of geometrical probability, the analytical solutions on the exact dosage of capsules required are developed for the different types of crack pattern models in a probabilistic point of view. Furthermore, the reliability of these analytical solutions is verified via computer simulation.