  We present the first part of our DARTTS-S (Disks ARound TTauri Stars with
SPHERE) survey: Observations of 8 TTauri stars which were selected based on
their strong (sub-)mm excesses using SPHERE / IRDIS polarimetric differential
imaging (PDI) in the J and H bands. All observations successfully detect the
disks, which appear vastly different in size, from $\approx$80 au in scattered
light to $>$400 au, and display total polarized disk fluxes between 0.06% and
0.89% of the stellar flux. For five of these disks, we are able to determine
the three-dimensional structure and the flaring of the disk surface, which
appears to be relatively consistent across the different disks, with flaring
exponents $\alpha$ between $\approx$1.1 and $\approx$1.6. We also confirm
literature results w.r.t. the inclination and position angle of several of our
disk, and are able to determine which side is the near side of the disk in most
cases. While there is a clear trend of disk mass with stellar ages ($\approx$1
Myr to $>$10 Myr), no correlations of disk structures with age were found.
There are also no correlations with either stellar mass or sub-mm flux. We do
not detect significant differences between the J and H bands. However, we note
that while a high fraction (7/8) of the disks in our sample show ring-shaped
sub-structures, none of them display spirals, in contrast to the disks around
more massive Herbig Ae/Be stars, where spiral features are common.
