How deep to place a deadman anchor for a slackline?
It’s based on the 1) angle of repose, and 2) weight of soil, and 3) length of deadman. 

7-8kn equals about 1500 - 1,800 lbs. 

If the angle of repose is about 45 degrees and your soil weighs about 80 lbs. per cubic foot, then you’ll need about 2,000 lbs. (safety factor) resisting. 

Therefore, you need to bury your deadman about 3’ deep if the deadman is 3’ long. (I’d compact all material in the ground.) 

I’d worry about a 2” diameter deadman getting pulled through the soil and compacting the soil immediately adjacent to the deadman. You’ll need a wider diameter deadman, such as a 12” wide x 3’ long steel plate welded onto your 2” pipe. 

Adjust accordingly for your 15-17kn.