Non-clastic rocks have chemical or organic origins. Names of non-clastic rocks are based on their compositions. A calcite-rich rock with many fossils is called a fossiliferous limestone. ... Sedimentary rocks with non-clastic texture include fossiliferous limestone (above left), chert (above right) and coal (right).Clastic sedimentary rocks such as breccia, conglomerate, sandstone, siltstone, and shale are formed from mechanical weathering debris. Chemical sedimentary rocks, such as rock salt, iron ore, chert, flint, some dolomites, and some limestones, form when dissolved materials precipitate from solution.