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• Healing efficiency theory developed based on geometric probability. • New self-healing capsules, called engineered aggregates, are introduced. • Self-healing efficiency calculated for different cracking conditions. • Effect of size, shape and dosage of capsules on healing efficiency is evaluated. This paper presents optimal self-healing configurations in concrete using a new concept referred to herein as engineered aggregates (EA). EA are hollow particles designed to carry healing agents into the cracks in concrete. The concept of EA has been developed by the authors as a cost-effective method for self-healing in conventional concrete without having to modify the existing materials or mixing procedures. EA have an internal brittle capsule carrying the healing agents and they are covered with a cementitious coating. They are similar in size to a concrete coarse aggregate and they are added during the mixing process replacing a portion of the coarse aggregates. Similar to other self-healing materials with cast in capsules, one of the basic requirements of EA is that when concrete cracks, the cementitious coating and the embedded brittle capsule break to release the healing agents into the cavity of the crack. The goal of this study is to identify the optimal shapes and sizes of EA that can be effectively used in self-healing concrete while minimizing the volume fraction of the added healing agent (and thereby EA). The tools of geometric probability are used to determine the probability of intersection of cracks with EA and the probability of healing of cracks with different geometries: a single crack, parallel cracks, mapping cracks and multiple discrete penny-shape cracks. As such, the optimal size and shape of EA are selected based on the density and type of cracking that might occur in concrete. [ABSTRACT FROM AUTHOR]