Although ASME B31.1 does not address ground settlement, ASME B31.3 does in section 319.2.1 (c). This section clearly states that this is a displacement strain. It also allows stresses due to settlement to exceed normal displacement stress allowables providing “due consideration if given to avoidance of excessive localised strain and end reactions”.
As for the sustained case with settlement, this is no different to any system with displacement loads including thermal effects. B31.3 requires the sustained stresses to be checked in all operating positions. Supports that lift off due to settlement should be treated the same as supports that lift off due to thermal deflections (ie a “Hot Sustained” case).