You are going to have trouble getting an answer to this question because it is not well constructed. I'm a PhD'ed academic who taught in a southern US state prison for 3 years so I can speak from some expertise, though US incarceration isn't particularly mine. The United States has both federal and state prisons, and each will accordingly have its own histories and cultures derived from numerous factors that will affect violence and reports of infractions at facilities. Your question assumes a homogeneity among prisons that doesn't exist as every facility is basically going to be different.

In east Texas you can have adjacent facilities for long-term incarceration like Ramsey, Terrel, and Strinfegllow that each share some resources, but are separately governed at the prison level. Among them, there are high-security facilities for very dangerous criminals, and then there are segregated accommodations and facilities for the "trustee camp" convicts who live in annexed facilities for non-violent convicts. Compare this to a facility like Rikers in NY that does both long-term incarceration and pretrial detention of all sorts of people with a huge history of abuses (not that Texas or any others don't have their own).

A better way to approach what you want to know is to ask is to specify, how did a prison like ___ [Rikers, Folsom, San Quentin...] receive the reputation or history of the kind(s) of violence you ask about. Because the answer is going to have at least as much to do with local/state history as it is going to have with pan-national history.