Which model of the internal social structure of the city explains that a city grows outward from a central area in a series of five rings, like the growth rings of a tree?

The answer is the concentric model
the concentric model was first created by a sociologist named Erness Burgest in 1925. This model divided each areas into several zones depending on their functions. He proposed 6 different zones for his initial model, which are:  Commuter zone,  Residential zone , Working class zone , Zone of transition  ,Factory zone , and Central business Zone