rubble mound, caisson, piered?
clay, sand or rock foundation?
settlement of the foundation, core or armor?
short term settlement, creep, piping and erosion, seismic, liquifaction?
global instability, subsidence of toe berm?
suggest perhaps the following:
USACE EM 1110-1-1904 Settlement Analysis
USACE EM 1110-1-1905 Bearing Capacity Of Soils
USACE EM 1110-2-1902 Stability of Earth and Rock Fill Dams
I'd not get too concerned about settlement before you are sure it won't sink out of sight. A global stability evaluation would be the first step. For your soil data you need some information about relative density if sand soil. That will help with the stability check as well as estimating settlement. For a rubble breakwater, I's guess settlement won't be an issue even if some occurs, providing the stability check is OK.
with a sand foundation, you will have some consolidation which will occur quickly, but should not "sink out of sight". so global stability should be checked on the core material and using the weight of the armor or other superstructure as a surcharge loading. Estimate friction angle of your fill which I would assume is a well graded granular material, use fully saturated conditions and check for slope failure, check again for seismic and again for toe erosion, or provide an adequate toe berm. Finally, there will be some creep which should be estimated for your design life (50 years?). there will be some settlement and degradation of the armor, but really difficult to estimate that.
Assessing global stability can be done with the procedure for evaluating slopes or earth dams, as I see it. The slip circle technique is a common method. However, using some of the methods for determining bearing capacity based upon shear strength of the supporting soil also can be used. If you have not experience or training on how to use these, I'd suggest asking a practicing geotechnical engineer.
