Is the jack arch (shallow arch) a single span, spanning the width of the bridge. If so, then unless there is some restraint at the ends of the jack arch, it will likely behave as a beam. If it is constrained, then it will have very high thrusts that must be accommodated.
I don't know of any publications, but the arches should be readily analised using FEM or something similar. Strut and tie also would work nicely.
Dik