  We investigate the dust structure of gravitationally unstable disks
undergoing mass accretion from the envelope envisioning the application to
Class 0/I young stellar objects (YSOs) We find that the dust disk quickly
settles into a steady state and that, compared to a disk with interstellar
medium (ISM) dust-to-gas mass ratio and micron-sized dust, the dust mass in the
steady-state decreases by a factor of 1/2 to 1/3, and the dust thermal emission
decreases by a factor of 1/3 to 1/5. The latter decrease is caused by dust
depletion and opacity decrease owing to dust growth. Our results suggest that
the masses of gravitationally unstable disks in the Class 0/I YSOs are
underestimated by a factor of 1/3 to 1/5 when calculated from the dust thermal
emission assuming an ISM dust-to-gas mass ratio and micron-sized dust opacity,
and that a larger fraction of disks in Class 0/I YSOs is gravitationally
unstable than was previously believed. We also investigate the orbital radius
$r_{\rm P}$ within which planetesimals form via coagulation of porous dust
aggregates and show that $r_{\rm P}$ becomes $\sim 20$ AU for a gravitationally
unstable disk around a solar mass star. Because $r_{\rm P}$ increases as the
gas surface density increases and a gravitationally unstable disk has a maximum
gas surface density, $r_{\rm P}\sim 20$ AU is the theoretical maximum radius.
We suggest that planetesimals formation in the Class 0/I phase is preferable to
that in the Class II phase because large gas surface density is expected and
large amount of dust is supplied by envelope-to-disk accretion.
