This question is impossible to answer with the details you have given. All land is different. If you were to do a soil test on ten different barren lands, you’d get ten different results, probably vastly different. Even if you were to make the grossly over generalized assumption that a sample from one area of a barren land would represent the whole land (you would be better off averaging samples from different locations in the same area), you’d need the specific data to make this analysis.
This is because you can’t figure the absorption capacity without the numbers to work with. There’s an actual formula for figuring out such things, but it’s very complicated and mathematical. If you would like to run some tests yourself on some land you have legal access to, however, the formula is included in the citations!
I’m sorry I could not give you a better answer, but I hope this puts you on the right track!
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