The riprap calculation in the current version of HEC-RAS follows the approach described in the USACE Engineering Manual EM 1110-2-1601: Hydraulic Design of Flood Control Channels (USACE, 1994). The design approach is outlined in Chapter 3 and is based on the work of Dr. Stephen Maynord.
https://www.publications.usace.army.mil/Portals/76/Publications/EngineerManuals/EM_1110-2-1601.pdf
See also, Maynord (1992) "Riprap Resistance Tests From a Large Test Channel"
https://erdc-library.erdc.dren.mil/jspui/bitstream/11681/10724/1/MP-HL-92-5.pdf
and
Maynord S., Ruff, J., and Abt, S. (1989) Riprap Design, ASCE Journal of Hydraulics..
https://ascelibrary.org/doi/abs/10.1061/%28ASCE%290733-9429%281989%29115%3A7%28937%29
They were based on a series of experiments in the ERDC (formerly Waterways Experimentation Station – WES) Riprap Test Facility, which measured rock stability in a series of bends in a mesoscale flume (pictured below).

The general workflow of the USACE riprap design approach is illustrated in the figure below:

Future versions of HEC-RAS will include other Riprap sizing methods.