The matter orbiting black holes (BHs) in microquasars or active galactic nuclei forms toroidal accretion disk structures, and multiple torus structures have been recently described as ringed accretion disks (RADs) in a full general relativistic approach. Here we realize full general relativistic magnetohydrodynamic (GRMHD) numerical simulations related to double toroidal structure immersed in the equatorial plane of the gravitomagnetic field of a central Schwarzschild BH in an asymptotically uniform magnetic field. We study the merging dynamics of an initial RAD structure constructed by two corotating or counterrotating tori, where accretion of matter from the outer torus is assumed onto the inner torus, using the 2.5D GRMHD simulation schemes with the HARM numerical code. We study the dynamics of the system assuming various initial conditions, and we have demonstrated that the initial matter density is the relevant factor governing the system evolution.