Evan,
Welcome to this site. I’m sorry you didn’t get enough response on Eng-Tips to address your issues. As you noted, the sites have quite a few common members…we think we have the cream of the crop of common members on this site 
The article posted by SuperSalad is quite a good overview of conditions that can occur. Here are my comments to address your specific issues:
- Your coating is failing and you believe it to be an asphaltic coating.
Asphaltic coatings are sometimes used for concrete structures subjected to aggressive environments such as wastewater treatment plants. Asphaltic materials application onto concrete usually requires good surface preparation and a primer. When both are not present or poorly done, the coating will fail. Once failure of the coating occurs, the concrete beneath the coating will deteriorate in the aggressive environment.
Since coating failure has occurred, it will be necessary to remove the tank from service, re-route the influent to other tanks temporarily or to portable tanks as necessary, and then remove the existing coating so that a proper inspection of the exposed concrete can be done.
- You mentioned some friability in the exposed concrete surfaces.
This is a good example of deterioration of the surface due to either carbonation or chemical attack. Once you have the concrete exposed, you can determine the extent of the issue and take samples for a proper petrographic examination of the concrete.
You can also look at crack patterns in the concrete to see if those need to be repaired individually or whether only a better surface coating will take care of them. ACI 350 gives some guidelines on crack widths so that you can make that assessment.
You can also do a ground penetrating radar survey of the exposed and cleaned surface to determine the rebar pattern and approximate depth. In areas where the concrete cover over the rebar is shallow, you should physically remove the concrete to observe the rebar condition. If it has started to corrode, it will require specific remedial action including excavating the concrete at least 3/4 of an inch below the rebar, applying a rust inhibitor to the rebar and repairing with a high quality repair mortar.
Once you have surveyed the tank’s interior surface you will be in a better position to provide remediation specifications that include necessary crack repair, rebar repair and surface preparation for a new coating. Coal tar mastic is what I have used in the past for such applications. It is quite good for these applications and should give you years of protection for the concrete. One such product is Bitumastic 50 from Carboline (…for disclosure, I have no connection to Carboline other than having used and specified their coatings in the past)
Good luck with your project and if you need more info, don’t be shy about asking here. We have a good group of experienced engineers, some of whom have likely faced your very issues in the past.
Ron