Is it permissible to take pebbles and sand from the site of a cancelled dam, knowing that these materials were extracted from the same land where the dam was to be built?

If gravel and sand are extracted from land you own, and nothing is extracted from outside your land, then it is your property, and you may dispose of it as you wish, because it is considered an increase arising from your ownership. An example of this is what Al-Sarakhsi said in Al-Mabsut regarding a usurped slave girl who gains weight.

However, if the aforementioned quantity or some of it is extracted from outside your land, but there is no benefit in it for the usurper, then you may take it without compensation, by analogy with small crops that have no benefit for the usurper, as Al-Mawaq mentioned from Ibn Al-Qasim and Ashhab.

However, if it is beneficial in the latter case, you may not take it except with compensation that is disbursed to public welfare projects or to the poor.