We present the first part of our Disks ARound TTauri Stars with SPHERE ( DARTTS-S ) survey : observations of eight TTauri stars that 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 80Â au in scattered light to > 400Â 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 with regard to the inclination and position angle of several of our disks 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 1Â Myr to > 10Â 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 substructures , none of them display spirals , in contrast to the disks around more massive Herbig Ae/Be stars , where spiral features are common .