Rambam Hilchos Avel 6 (13) refers to washing with sand:
ומכבס כסותו במים אבל לא בנתר ולא בחול
He may wash his clothes in water, but not with soap or using sand.
Is there an explanation of the cleaning power of sand and how was it used?
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As explained in the parallel thread on History.SE, sand is an abrasive. I’ll let them do the talking for me:
Sand is an "abrasive". As such, it is good for dislodging/removing dirt, etc. trapped in clothes.
But after you do this, you have to wash out the sand.
Soap does a similar job in a different way (using "chemical," rather than "mechanical" means).