To meet the special requirements (for the strength and conductivity of concrete structures) that arise during the transmission of electricity to remote areas of the Russian Federation, a variant of using self-healing concrete is proposed. In this material, it is proposed to use microcapsules obtained by the physical method, consisting of sodium silicate and bentonite clay coated with ethyl cellulose with graphene. The mechanism of action of the capsule is as follows: after external mechanical destruction, access to graphene appears and it acts as a conductive medium, resulting in the cementing properties of the capsule core. In the course of the work, the optimal ratio of graphene and the capsule core was established, which was determined during several experiments and microstructure studies. The dependences of the compressive strength and conductivity of the composite on the graphene content in the capsule, the number of microcapsules in concrete, and the time of strength gain were also revealed. In the experiments, the average size of microcapsules was 1.25 mm, and the grain shape is predominantly spherical with a rough surface and dense structure. The optimal microcapsule content was 2% of the cement binder weight, which corresponds to 0.1% graphene oxide. With an increase in the graphene content, the conductivity of the concrete composite monotonically increases, and the compressive strength increases to a certain limit and then decreases. After partial destruction of the samples (discontinuity) at the micro level, the composite material recovered, while the recovery coefficient was 81%, and the recovery coefficient of compressive strength was 57%.