After a 35-Year Push, Bažant’s Size Effect Law Adopted for ACI Design Code

For 35 years, Zdeněk P Bažant relentlessly argued in the American Concrete Institute (ACI) for adopting his non-statistical energetic size effect law, based on quasibrittle fracture mechanics, for ACI design code specifications. His advocacy finally succeeded. According to the new ACI-318/2019 Standard, to be published in June, the concrete shear strength of reinforced concrete beams and slabs (including the strut-and-tie approximation) must now be adjusted according to Bažant law, i.e., the shear strength obtained by classical limit analysis must, from now on, be multiplied by the size effect factor λs = C (1 + d/d0)-1/2 (if < 1); d = structure size (beam or slab depth), C = 21/2 and d0 = 10 in.

Bažant’s theoretical derivation of this factor was published in 1984 (ACI Struct. J. p. 518). In that year, Bažant, with his student J.-K. Kim, also proposed it to ACI for shear design (ditto, p. 579). Adoption eventually required many years of more-detailed theoretical studies, extensive computational modeling, failure probability analyses, and extensive experimental verifications, including the collection of a vast worldwide database of the results of uncoordinated experiments and its filtered statistical interpretation. For a long time, Bažant was the lone proponent, but in the last few years major and decisive support in the relevant ACI committees came from Bažant’s former students Jia-Liang Le, Mija Hubler, Qiang Yu and Christian Hoover, and from collaborators Gianluca Cusatis and Christian Carloni (current and past chairs of ACI fracture mechanics committee) as well as other ACI committee members (D. Sanders, A. Belarbi, G. Klein, D. Kuchma, L. Novak, R. Frosch, T. Hsu, A. Cladera, H.-G. Park and others).

Prior to 1984, Weibull’s statistical size effect law based on material strength randomness was the only known size effect on structural strength. But Bažant showed it to be inapplicable to reinforced concrete. More generally, he showed that his nonstatistical (energetic) size effect is exhibited by all quasibrittle materials, including fiber composites, tough ceramics, rocks, stiff soils, bone, dental ceramics, rigid foams, sea ice, wood, etc., and all brittle materials on the micrometer scale.

By adopting the Bažant law, ACI becomes the first concrete society to introduce quasibrittle fracture mechanics into its design code. This major innovation is bound to improve structural safety. Historically, very large concrete structures have been failing with the frequency of about 1 in a thousand, which is excessive by far. But the new code should make the failure probability close to 1 in a million per lifetime, which is the maximum generally considered acceptable for all engineering structures (including aircraft, bridges, MEMS, etc.).

While ultimately successful, this experience should also be a cautionary tale on civil engineering education. One may wonder why it took 35 years for the fracture-mechanics based size effect law to be adopted by practitioners. The answer is fairly simple – civil engineers are not properly trained in fracture mechanics, which finds its way into only few civil engineering curricula, and only at the graduate level, that is, PhD level. Fracture mechanics should be taught, albeit at an elementary level, in undergraduate mechanics of materials courses alongside the strength theories. And Northwestern University, where the quasibrittle fracture mechanics for concrete was invented, should lead the way.