If you speak about a circular SRR with a inner ring, then the resonance frequency of the SRR structure behaves as the resonance frequency of an LC circuit, where L is given by the length and width of the line, and total C is given by the two gaps capacitance.
Compared to a simple ring resonator, the circular SRR resonance frequency is affected by the external radius, by the gaps distance, and by the angle of rotation of the inner ring.