Nineteen concrete mixtures with multi wall carbon nano tube (MWCNT), graphene, nano scale (waste of steel industry, iron oxide) and suspensions of nano sized iron, zinc, and a composite suspension of nano sized iron, silver, copper, zinc were designed with different volume percent. The electrical resistivity decreased 229%, 176%, 113%, 251% with additions of graphene, MWCNT, nano scale, composite suspension of nano-sized iron, silver, copper, zinc, respectively. The compressive strain sensitivity of the mixtures increased 244%, 211%, 311% with addition of graphene, MWCNT, nano zinc suspension, respectively. Tensile strain and crack length sensitivities of reference and graphene added mixtures which had the highest compressive strain sensitivity were determined. Strong linear relationships between compressive strain, tensile strain and crack length versus electrical resistance change were observed. Detailed phenomenological models were presented for relationship between the graphene amount, tensile strain and crack sensitivities.