The phrase "encroached up on" refers to a situation where something is slowly and steadily intruding into a particular space or area. Some synonyms for the phrase include "invaded," "trespassed," "penetrated," "infringed," "overstepped," and "obtruded." These words all imply a sense of violation or overreaching, whether it's in terms of physical boundaries or personal space. Other terms to describe this phenomenon might include "eroded," "encumbered," "enclosed," "overran," or "occupied." No matter which word is used, the underlying idea is that something has crossed a line, exceeded its limits, and is now imposing itself on someone or something else.