Rubble Stockpiles are Industry Stockpiles produced by Kapaku after they have researched the Siege Engineering technology. Like standard Industry Stockpiles, the base amount of Industry they yield is 100 , but researching Unskilled Labor and Organized Labor will raise this amount by 500 and 1000 respectively. However, unlike Industry Stockpiles, Rubble Stockpiles cannot be traded via Diplomacy, and cannot be bought or sold on the Marketplace.
Rubble Stockpiles are generated by accruing points in the Siege Damage Counter that appears on the empire screen when Siege Engineering is researched; the meter accrues 1 point for percent of a given city's fortifications you damage - for example, dealing 15 points of damage to a city with 150 points of fortification will increases the meter by 10. Once the meter reaches 100, a rubble stockpile is created.
This is a stockpiles of debris, broken mortar, and fortification scraps, to be used one time to boost a city's Industry points.