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Asymptotic temporal and spatial scaling of coupled creep, aging, diffusion and fracture processes

The paper reviews the scaling aspects of various physical mechanisms involved in concrete creep and durability problems. Understanding of these aspects, and especially the asymptotic scaling, is essential for developing realistic materials models valid over a broad range of response times and structure sizes, which are of particular concern for extrapolating from reduced-scale short-time laboratory tests to the full structure sizes and design lifetimes. The scaling aspects are discussed in relation to the coupling of creep with aging, hygro-thermal processes and diffusion processes in concrete. The mathematical structures of the recently developed micro prestress-solidification theory of concrete creep and of model B3 are explained by various scaling considerations. The interplay with . the spatial scaling of cracking and fracture phenomena is also discussed. The benefit of setting the time scale in shrinkage prediction by means of weight load measurements is pointed out. The mathematical approach to the stresses and early fracturing of a nuclear containment wall due to hydration heat is discussed. Finally, the question as to why many ancient masonry towers either collapse or are endangered after centuries of faultless existence is considered. Based of numerical simulations relevant to the collapse in 1989 of the Civic Tower of Pavia in Italy, it is proposed that the explanation must be sought in the interaction drying times, creep rates and size effect in compression failure.