  Tidal dissipation, which is directly linked to internal structure, is one of
the key physical mechanisms that drive systems evolution and govern their
architecture. A robust evaluation of its amplitude is thus needed to predict
evolution time for spins and orbits and their final states. The purpose of this
paper is to refine recent model of the anelastic tidal dissipation in the
central dense region of giant planets, commonly assumed to retain a large
amount of heavy elements, which constitute an important source of dissipation.
The previous paper evaluated the impact of the presence of the static fluid
envelope on the tidal deformation of the core and on the associated anelastic
tidal dissipation, through the tidal quality factor Qc. We examine here its
impact on the corresponding effective anelastic tidal dissipation, through the
effective tidal quality factor Qp. We show that the strength of this mechanism
mainly depends on mass concentration. In the case of Jupiter- and Saturn-like
planets, it can increase their effective tidal dissipation by, around, a factor
2.4 and 2 respectively. In particular, the range of the rheologies compatible
with the observations is enlarged compared to the results issued from previous
formulations. We derive here an improved expression of the tidal effective
factor Qp in terms of the tidal dissipation factor of the core Qc, without
assuming the commonly used assumptions. When applied to giant planets, the
formulation obtained here allows a better match between the an elastic core's
tidal dissipation of a two-layer model and the observations.
