Scaling in size, time and risk—The problem of huge extrapolations and remedy by asymptotic matching

Zdeněk P. Bažant*, Hoang T. Nguyen, A. Abdullah Dönmez

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


The scaling of structural response of concrete structures to large structure sizes, to long service lives and to tolerable failure probabilities is a problem of order-of-magnitude extrapolations, which are intractable by AI and machine learning and require significant theoretical advances. The present review, based on a lecture at Yonggang Huang's 60th birthday symposium in Houston, summarizes the recent advances, with a focus on those achieved at Northwestern University. Reliable extrapolation requires two-sided asymptotic matching. Most existing databases provide support on only one extreme of the range of size, time or failure probability, but theoretical support can be obtained for the asymptotic behaviors on both sides of the range. The advantage is that the asymptotics are much simpler than the behavior in the central, transitional, range. In closing it is explained that realistic extrapolations are required to mitigate the calamitous CO2 emissions from cement and concrete industry.

Original languageEnglish
Article number105094
JournalJournal of the Mechanics and Physics of Solids
Publication statusPublished - Jan 2023
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2022 Elsevier Ltd


Partial financial support, under National Science Foundation, United States of America grant CMMI-202964 and ARO, United States of America Grant W911 NF-19-1-0039 , both to Northwestern University, are gratefully acknowledged.

FundersFunder number
National Science FoundationCMMI-202964
Army Research OfficeW911 NF-19-1-0039
Northwestern University


    • Cement hydration
    • Concrete structures
    • Creep and shrinkage
    • Experimental databases
    • Failure probability
    • Fracture mechanics
    • Size effect on strength
    • Water diffusion


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