Captain reported while on the RNAV approach to Runway 36 at BHM Airport; the aircraft crossed a ridge only by 500 ft. The Captain states there is no alert or warning regarding the ridge and believes there should be some type of notation.

Narrative

Weather was excellent day VMC. Because of our arrival track we opted to use Runway 36. The pilot flying (PF) decided to back up the approach with the RNAV 36. In the briefing we noted it was not a LPV or VNAV approach; but that the approach met the criteria for a Continuous Descent Final Approach (CDFA) approach. We were cleared down to I believe 3000 ft. prior to being cleared for the approach; and we intercepted well outside of the FAF. In accordance with SOP; the PF armed approach and VNAV. The approach was normal and the airplane was exactly on the VGP (Vertical Glide Path); however; descending from the FAF we crossed the ridge south of the airport at a mere 500 feet. Surprisingly we did not get a GPWS warning; and the PF disconnected the autopilot to shallow out the descent before rejoining on the other side. Doubling checking; the only notes on that runway is that it is not authorized at night. There is no mention of the terrain. Looking at online sources; 121 operators have experienced GPWS alerts while conducting CDFA approaches on this approach.There should at least be ops notes about this ridge; and consideration should be given to restricting or modifying this approach. Longer term; improving the chart to depict the terrain would also be helpful.