Your question is vague. What's your role in the project? I've worked on a lot DOT projects, the specs list the safety requirements, eg, competent persons, demolition and erection procedures, comply with OSHA, no drinking or drug use on the site; PPE, porta-Johns, etc, and require the contractor to submit a plan explaining how they will comply with said requirements. It's the contractor's responsibility to ensure that his work force complies with the requirement. The specs give the owner's representative the authority to stop any part or all of the work if the contractor is violating the safety plan. Of course, OSHA can walk in at any time unannounced and issue citations or shut things down independent of the owner.
If you're on the owner's side of the fence, your contract has to spell out the safety requirements. If you're on the other side, you better have a safety program in place. Not only does it save you money on worker's comp premiums but you don't want OSHA coming down on you.