Self-healing capsules in early-age cementitious composites: A deterministic-probabilistic multi-scale approach

• Inherent variability affects capsule failure and effective properties of matrix. • Failure probability changes greatly with evolving early age concrete properties. • Reliability index for optimization of capsule design. • Neglecting drying creep effect overestimates probability of capsule rupture. Capsules for healing early-age concrete cracks should possess multi-functional properties to ensure shell rupture and release of healing agents rather than debonding from the cementitious matrix when intercepting a crack. A deterministic-probabilistic multi-scale model is developed to determine the probability of capsule rupture versus interfacial debonding induced by early age volume change. A micromechanical model along with a probabilistic model are employed for determining the maximum tensile stresses in capsule shell, radial tensile stresses on the capsule-matrix interface, and the corresponding probability index of capsule rupture and debonding. The matrix is modeled as an equivalent homogeneous medium with effective properties determined from a homogenization scheme. The influence of crack is accounted for implicitly. The model results are qualitatively in agreement with results reported in the literature.