  We examine the backreaction effect of the enhanced small-scale scalar
perturbations from the sound speed resonance (SSR) mechanism for primordial
black hole formation in Dirac-Born-Infeld (DBI) inflation on background as well
as curvature perturbation, which can generate a considerable amount of
primordial black holes (PBH) in the radiation-dominated epoch. Within the
perturbative regime, the backreaction effect of perturbations on the background
dynamics can be described by an effective action after integrating out the
perturbation sector. Starting with the effective field theory of a specific DBI
inflation model that incorporates SSR, we obtain the one-loop effective action
by integrating out the scalar perturbations at the quadratic level. Using the
effective Friedmann equations derived from this one-loop effective action, we
solve the Hubble parameter with backreaction and the effective perturbation
dynamics on this background as well. Our numerical findings reveal that, for a
viable parameter space, the backreaction effect results in a relative
correction to the Hubble parameter of approximately $10^{-7}$, whereas the
relative correction to the slow-roll parameter can vary between $-0.3$ and
$0.1$, before gradually converging to $10^{-7}$. Furthermore, our results show
that the backreaction effect on SSR sound speed causes a slight reduction in
the resonant peak of the curvature power spectrum, and the subsequent PBH
formation predicted by the SSR mechanism remains almost unchanged.
