  It is important to clarify where and when rocky and icy planetesimals are
formed in a viscously evolving disk. We wish to understand how local runaway
pile-up of solids occurs inside or outside the snow line. We assume an icy
pebble contains micron-sized silicate grains that are uniformly mixed with ice
and are released during the ice sublimation. Using a local one-dimensional
code, we solve the radial drift and the turbulent diffusion of solids and the
water vapor, taking account of their sublimation/condensation around the snow
line. We systematically investigate effects of back-reactions of the solids to
gas on the radial drift and diffusion of solids, scale height evolution of the
released silicate particles, and possible difference in effective viscous
parameters between that for turbulent diffusion ($\alpha_{\rm tur}$) and that
for the gas accretion rate onto the central star ($\alpha_{\rm acc}$). We study
the dependence on the ratio of the solid mass flux to the gas ($F_{\rm p/g}$).
We show that the favorable locations for the pile-up of silicate grains and icy
pebbles are the regions in the proximity of the water snow line inside and
outside it, respectively. We found that runaway pile-ups occur when both the
back-reactions for radial drift and diffusion are included. In the case with
only the back-reaction for the radial drift, no runaway pile-up is found except
for extremely high pebble flux, while the condition of streaming instability
can be satisfied for relatively large $F_{\rm p/g}$ as found in the past
literatures. If the back-reactions for radial diffusion is considered, the
runaway pile-up occurs for reasonable value of pebble flux. The runaway pile-up
of silicate grains that would lead to formation of rocky planetesimals occurs
for $\alpha_{\rm tur} \ll \alpha_{\rm acc}$, while the runaway pile-up of icy
pebbles is favored for $\alpha_{\rm tur} \sim \alpha_{\rm acc}$.
