Once a private airstrip has been certified, do you have to get faa approval to make changes to the runway such as adding crossings, access etc…?
The only requirement for a private airfield is to notify the FAA using form 7480-1. There are exceptions for otherwise regulated (these would not be private), temporary (less than 30 days), and intermittent (less than 3 days/week for less than one year) VFR use of an site that is not an airport. What you describe is a permament, civil, private use airport so you have to notify 90 days before activating or making a change.
Title 14 Code of Federal Regulations Part 157 requires all persons to notify the FAA at least 90 days before construction, alteration, activation, deactivation, or change to the status or use of a civil or joint-use (civil/military) airport. (As used herein, the term “airport” means any Landing or Takeoff Area, e.g. Airport, Heliport, Vertiport, Gliderport, Seaplane Base, Ultralight Flightpark, or Balloonport.) Notice is not required for:
- An airport subject to conditions of a Federal agreement that requires an approved current airport layout plan to be on file with the Federal Aviation Administration.
- Establishment of a temporary airport at which operations will be conducted under visual flight rule (VFR) and will be used for less than 30 days with no more than 10 operations per day.
- Intermittent use of a site that is not an established airport, which is used for less than one year and at which flight operations will be conducted only under VFR. (Intermittent use means the use of the site for no more than 3 days in any one week and for no more than 10 operations per day.)