What I've learned from those failures is I should create 2 things.
1 A soil bed with no pebbles and soil mass
2 An elevated soil bed for avoiding carrots from water soaking
Now it's in the middle of a hot summer with record-high temperature but I decided to create an special soil bed spending 2 hours! The height of the pad is about 30 cm (15 inches) so it's high enough to avoid flood.
A measure against bugs is also important to grow carrots. Young worms of a swallowtail butterfly is a big enemy for carrots so I covered the bed with a insect screen to ward off the butterfly.
Watering is another issue for gardeners growing carrots in this season in Japan. Carrot's germination requires watering everyday to keep the bed wet. So I used rice bran as you can see it on the photos shown below. Of course, I have to water them everyday through the hot summer,,,,.