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Autonomous healing of cracks using capsule-based systems is emerging as a promising solution to restore the durability and strength of damaged structures. For satisfactory self-healing efficiency, both capsule geometry and dosage are to be determined for the concrete mix proportion. With previous research being performed on self-healing efficiency using different capsule shapes and crack patterns, his paper introduces quantitative numerical solutions on the optimal dosage of the capsules required to completely repair cracks in a three-dimensional model of a cementitious matrix. Four different sizes of spherical capsules ranging between 0.6mm to 4.75mm embedded within a mortar matrix were tested in the model and the model results were validated using previous experimental findings. As the capsules could carry powder or liquid self-healing agents, three different scenarios were considered in this work to calculate the volume of the healing agent in the crack. It was found that the smaller the capsules the more homogenous and uniform the distribution of capsules is. However, the bigger sizes of the capsules are much preferable in terms of the amount of self-healing materials supplied to the cracked vicinity. For instance, capsules of 2-4mm size could fill 80% of the crack volume but were localised and unevenly distributed on the planes of the crack. Overall, the developed model in this study provides a robust and efficient tool to quantitively design the proportions of cement-based self-healing systems. Based on the results of the geometric model, an ANN model was also developed to calculate healing volume in terms of the volume fraction of the healing agents and the size of capsules. Results showed very close values to those obtained by the numerical model.