Probability Characteristics of a Crack Hitting Spherical Healing Agent Particles: Application to a Self-Healing Cementitious System

A geometric model is developed to statistically study the probability characteristics of crack intersecting self-healing capsules with a structured random distribution in a cement paste mix. To evaluate the probability of a crack intersecting encapsulated particles, the fill ratio of the crack, and the depth of the first-hit capsule, Monte Carlo simulations are performed. The variables are the crack geometry, i.e., width, length, depth, orientation, skewness, and so on; the size and mass fraction of healing capsules; and the agglomeration of capsules. Models based on statistical analyses for hit probability Ph, crack fill ratio Rf-95 at 95% confidence level, and first hit depth h0-95 at 95% confidence level are expressed as functions of capsule size and mass fraction, as well as crack geometry. The model assumptions and results are evaluated using data reported in the literature. The data include results from experimental and theoretical studies.