For clean sands one can use Hazen's equation:
k = C.(D10)^2
D10 = diameter for 10% finer
You can use an average value for C, C = 1.
If you take D10 in mm, your k value will come out as cm/s.
If you have even small amount of fines (clays/silts) this may reduce your k dramatically. So Hazen's k...
Preloading can be a good idea when dealing with peats. There is a good paper "Secondary Compression of Peat with or without Surcharging" (1997) by Professor Mesri at the University of Illinois at Urbana-Champaign, who has done extensive work on peats. I recommend contacting him if you need...
