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This study addresses the contradiction between the strict requirements of vibration speed control in existing operating tunnels and the difficulties of tunnel excavation in hard rock strata, as well as the lack of theoretical basis for blasting vibration speed control standards in adjacent tunnels. Based on the energy principle, this study establishes the energy balance equation in a single cycle of the low frequency band of blasting vibration wave curve, and proposes to replace the maximum elastic strain energy accumulated in concrete by twice the kinetic energy corresponding to the peak vibration speed under blasting action (the "Twice the Peak Kinetic Energy Method") according to the conversion relationship between the input energy of concrete mass unit and the elastic strain energy and kinetic energy. On the basis of this method, the formulae of safe vibration velocity of blasting in two states were derived by combining the energy criteria corresponding to the damage and destruction states of concrete. It is verified in a new tunnel under existing operating railway section in hard rock stratum in Xiamen area. The results show that the maximum principal stress and displacement reach the maximum value in the cycle when the peak vibration speed decays close to zero for the first time in the low frequency band; the elastic strain energy also reaches the maximum value in the cycle when the kinetic energy decays close to zero; affected by a small amount of dissipation energy, the kinetic energy corresponding to the peak vibration speed is slightly less than twice the maximum elastic strain energy, which verifies the reasonableness of the theoretical analysis. Finally, the safe vibration speed corresponding to different concrete grades is given based on the design value of tensile strength.

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