BFPartners...I assume you mean "pressure epoxy" instead of "pressure grouting". Grouting isn't done for typical cracks.
For flatwork, the method is usually to use a low viscosity epoxy, acrylic, or methacrylate sealer flowed into the crack by gravity. Since the top of the crack is most often wider than the bottom, you can gauge the type of material to use from the top width of the crack. The sealer manufacturers give guidelines for their particular sealers as they know the viscosity of their formulations.
The depth of the crack is relatively unimportant in this regard for slab cracks. Assume full depth cracks.
As to checking the effectiveness of the repair, the non-destructive methods are not yet sophisticated enough to give clear definition of repair depths. Coring is the only way to precisely know the effectiveness.