The International Basic Safety Standards on the protection of radiation has specified the limitations on radiation exposure as for occupation and public exposure. Since there is no mention on the rationale of these values, I wonder if they are based on experimentally determined radiation dose.
Perhaps you should start with a journal such as Health Physics, which has existed since 1958 and bills itself as
The journal along with its quarterly supplement, Operational Radiation Safety, provides features that allow readers to understand more about the topics that interest them. These features include original papers, technical notes, articles on advances in practical applications, editorials, and correspondence that report on the latest findings in theoretical practical and applied disciplines, of epidemiology and radiation effects; radiation biology and radiation medicine; fate and transport of radioactive materials in biological systems to name just a few. Scientists, physicians and engineers alike will find useful information regarding radiation safety.
It is the official journal of the Health Physics Society, a professional society of radiation protection folks.
The bottom line is that there is a long history of radiation measurements, impact on human health, and so forth. These get codified in industry, national and international standards. While it might be fascinating to go back and delve in to the history of how we got here, it is quite clear that the standards are backed up by experimental evidence.