Statistical Mechanics of Safety Factors: From Atomic Scale to Structural Scale

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Abstract - Bazant, NWn U.Currently the strength reduction parts of safety factors areconsidered as fixed, determined purely from statistics of testdata. However, this is adequate only for purely brittle or ductilelimiting cases. Here the key idea is that, for the transitionalrange of quasibrittle structures (concrete structures, fibercomposites, rigid foams, ceramics, rocks, ice, soils, wood, etc.,and those on approach to nanoscale), the safety factor must dependon structure size and geometry, and that to ensure tolerablefailure probability, such as one in a million, the safety factormust be determined from extreme-value statistics based on stressdependence of activation energy of interatomic bonds. The strengthprobability distributions of material elements and of structure,deviations from power-law size effect, kinks on strengthhistograms, and dependence on temperature, loading rate andduration, are derived and exploited for verification andcalibration. Relevance and practical applications aredemonstrated by stochastic numerical analysis of documentedstructural disasters. Major implications for design codes andpractices for quasibrittle structures, as well as reliability ofmicro-nano-scale thin films and MEMS, are identified.