The Eos family, composed of two objects of about 90 km diameter, plus a few of around 50 km and many smaller chunks, was larger, around 550 km diameter by current estimates. The dynamics of an asteroid collision could produce a variety of results, ranging from complete dispersal to formation of mixed bodies. However, most collisions between asteroids in the solar system today would result in dispersal of the vast majority of material, since escape velocities are so low for most asteroids. Much more frequent than big asteroids hitting each other are small impacts which serve to chip away at the outside surface of a large asteroid, with the crater ejecta escaping the asteroid's feeble gravitational field. In fact, telescopic spectroscopy reveals a few large asteroids apparently with large quantities of free metal at the surface, possibly the result of the stony exterior being chipped away over the eons to expose the mantle and core.
Asteroids are likely to be crumbly material due to all the shock waves of impacts.
Whatever material was not blown off is likely to be pulverized. Photographs of Mars' two tiny moons, which are themselves captured asteroids between 8 km and 28 km wide, show pulverized surface material, cracks, and steam tubes from volatiles that vaporized from the energy of impacts. One of Mars' moons, Deimos, is U-shaped when viewed from one angle. As one can see, there are a great variety of sources for asteroidal material. Next, we look at the composition of meteorites that fell to Earth's surface, since this is largely what we have to go on when we think of designing space industrialization around asteroidal materials.