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Supermassive black holes (SMBHs) are observed in active galactic nuclei interacting with their environments, where chaotical, discontinuous accretion episodes may leave matter remnants orbiting the central attractor in the form of sequences of orbiting toroidal structures, with strongly different features as different rotation orientations with respect to the central Kerr BH. Such ringed structures can be characterized by peculiar internal dynamics, where co-rotating and counter-rotating accretion stages can be mixed and distinguished by tori interaction, drying-feeding processes, screening effects, and inter-disk jet emission. A ringed accretion disk (RAD) is a full general relativistic model of a cluster of toroidal disks, an aggregate of axi-symmetric co-rotating and counter-rotating disks orbiting in the equatorial plane of a single central Kerr SMBH. In this work, we discuss the time evolution of a ringed disk. Our analysis is a detailed numerical study of the evolving RAD properties formed by relativistic thin disks, using a thin disk model and solving a diffusion-like evolution equation for an RAD in the Kerr spacetime, adopting an initial wavy (ringed) density profile. The RAD reaches a single-disk phase, building accretion to the inner edge regulated by the inner edge boundary conditions. The mass flux, the radial drift, and the disk mass of the ringed disk are evaluated and compared to each of its disk components. During early inter-disk interaction, the ring components spread, destroying the internal ringed structure and quickly forming a single disk with timescales governed by ring viscosity prescriptions. Different viscosities and boundary conditions have been tested. We propose that a system of viscously spreading accretion rings can originate as a product of tidal disruption of a multiple stellar system that comes too close to an SMBH.