There is a way to weigh broken concrete that doesn't involve shoveling it onto a scale. It is possible to determine the weight of broken concrete by first figuring out the weight of the concrete slab it was part of before it was broken. This requires that you measure the area covered by the slab and know the thickness of the slab before it was broken.
Measure the space the concrete was taken from. Note the length and width of the slab area. Measure the depth of a piece of the broken slab to determine the depth of the slab itself. These measurements will allow you to figure out the volume of the concrete before it was broken.
Multiply the length, width and depth of the slab for the size in cubic meters. For example, if the slab is 10 m long by 5 m wide and 0.15 meters deep , the volume is 7.5 cubic meters.
Multiply the total by the density of concrete, which is rated as 2,400 kg per cubic meter for poured concrete and 3,000 kg for standard, rebar-reinforced concrete. For example, 7.5 x 2,400 = 18,000 kg and 7.5 x 3,000 = 22,500 kg.