Triple-sheath structures and temporal evolution of the dust grain-charge in a dusty plasma with the trapped dust grains are investigated by numerical calculation. Trapped dust grains modify the shape of the sheath and give rise to the triple-electric field structures. The sheath width becomes narrower than that of the Boltzmann distributed dust grains due to the existence of trapped dust grains. It is found that trapped dust grains play an important role in the formation of the new sheath structure and shorten the charging time.

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