Deviation with the scale in the theories of elastic or plastic structures
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Remnants of the Malpasset Dam in Maritime Alps, France, which failed at its first filling in 1959 and caused a giant flood that wiped out the town of Frejus, with several hundred fatalities. This dam, the tallest and slenderest at that time, failed because of an excessive horizontal slip in the gneissic abutment. The tolerable displacement considered in design is not known but, if calculated today, the size effect would reduce it to about one half of the value according to the design procedures in the 1950s.
According to the classical theories of elastic or plastic structures made from a material with non-random strength (ft), the nominal strength (σN) of a structure is independent of the structure size (D) when geometrically similar structures are considered.[1] Any deviation from this property is called the size effect. For example, conventional strength of materials predicts that a large beam and a tiny beam will fail at the same stress if they are made of the same material. In the real world, because of size effects, a larger beam will fail at a lower stress than a smaller beam.
The structural size effect concerns structures made of the same material, with the same microstructure. It must be distinguished from the size effect of material inhomogeneities, particularly the Hall-Petch effect, which describes how the material strength increases with decreasing grain size in polycrystalline metals.
The size effect can have two causes:
statistical, due to material strength randomness, likelihood of a critical flaw occurring in a high-stress location, and increasing volume increasing the probability of a serious flaw.
energetic (and non-statistical), due to energy release when a large crack or a large fracture process zone (FPZ) containing damaged material develops before the maximum load is reached.
^The nominal strength of a structure (σN) has units of stress and is related to the maximum load (Pmax) that the structure can support. For structures that can be approximated as two-dimensional, σN = Pmax/bD where b is the thickness of the two-dimensional structure. For three-dimensional structures, σN = Pmax/D2. Any structure dimension can be chosen for D but it must be homologous for every size.
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