The article presents designe of rapid-hardening, non-shrinking cementitious mixtureses, which allows solving the problem of rehabilitation of concrete structures and has a positive effect of environmental sustainability. To ensure the maximum dense packing of the cement mixture, the granulometric composition of the sand was optimized. Mathematical models of physical and technical indicators of repair mixtures based on Portland limestone cement and optimized sand composition were obtained, which quantitatively characterize the action of high-alumina fly ash, sodium hydroaluminate, polycarboxylate ethers with increased rapid hardening, early strength, adhesive strength and reduction of shrinkage deformations. A combination of Portland limestone cement, fly ash, polycarboxylate ethers and alkaline activator ensures the intensification of early structure formation due to the formation of hydrocarboaluminates and alkaline hydroaluminosilicates; larger fractions of limestone particles and fly ash act as a microfiller, which in the complex contributes to increasing the early strength and stability of the cementitious matrix.