Compression failure in reinforced concrete columns and size effect

The size effect in the failure of columns or other reinforced concrete compression members is explained by energy release due to transverse propagation of a band of axial splitting cracks. According to their stress and strain states, three regions are distinguished in the column: cracking, unloading and invariable zones. The microslabs of the material between the axial splitting cracks are considered to buckle and undergo post-critical deflections. Based on the equality of the energy released from these regions and the energy consumed by formation of the axial splitting cracks in the band, the failure condition is formulated. It leads to a closed-form expression relating the characteristic size and the nominal strength of the structure. The results of laboratory tests of reduced-scale columns reported previously by Bazant and Kwon (1994) are analyzed according to the proposed formulation and are shown to be described by the proposed theory quite well. Although the present theory is formulated for a reinforced concrete column, it can be adapted to compression failures of other quasibrittle materials such as rocks, ice, ceramics or composites.