Zdeněk Bažant

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Zdeněk Pavel Bažant in 2015

Zdeněk Pavel Bažant (born December 10, 1937) is McCormick School Professor and Walter P. Murphy Professor of Civil Engineering and Materials Science in the Department of Civil and Environmental Engineering at Northwestern University's Robert R. McCormick School of Engineering and Applied Science.

Education, career and academic positions[edit]

Born on December 10, 1937, and educated in Prague, Bažant received the degree of Civil Engineer from the Czech Technical University (CTU) in Prague in 1960. While employed as Bridge Designer he earned in 1963 (as an external student) a PhD in engineering mechanics from the Czechoslovak Academy of Sciences, and in 1966 a postgraduate diploma in theoretical physics from Charles University, Prague. During 1964–67 he was research assistant professor at CTU, and obtained the degree of Docent habilitatis from CTU in 1967. After postdoctoral appointments at CEBTP Paris (1966–67) and University of Toronto (1967–68), he was in 1968–69 associate research engineer at the University of California, Berkeley. In 1969 he joined Northwestern University as an associate professor; he became professor of civil engineering in 1973. During 1981–87 he served as the founding director of Center for Geomaterials. Since 1990, he has held the distinguished W.P. Murphy Chair in Civil and Mechanical Engineering and Materials Science, and since 2002 simultaneously the chair of McCormick Institute Professor, the highest distinction at Northwestern. Bažant was the president of Society of Engrg. Science, and founding president of Int. Assoc. of Fracture Mech. of Concrete Structures (IA-FRAMCOS) and of Int. Assoc. of Concrete Creep and Durability Mechanics (IA-CONCREEP).[1] He served Division Director in IA-SMiRT (Struct. Mech. in Reactor Technology), as member of the US Nat. Comm. on Theor. and Applied Mech., and as editor-in-chief of Journal of Engrg. Mechanics of the Am. Soc. of Civil Engers. (ASCE). He is US regional editor of Int. J. of Fracture. Since 1971, he is an Illinois registered structural engineer (S.E.). In 1959, he patented in Czechoslovakia a safety ski binding which was in the early 1960s used by about one third of skiers in that country, and is exhibited in New England Ski Museum in Franconia, NH.

Research contributions and impact[edit]

Bažant, who is generally regarded as the world leader in research on scaling in the mechanics of solids,[1] is the author of six books dealing with concrete creep, stability of structures, fracture and size effect, inelastic analysis and scaling of structural strength. He is an Illinois registered Structural Engineer, and is one of the original top 100 ISI highly cited researchers in engineering (of all fields, worldwide). By June 2015, his H-index is 103, i10 is 496, and total citations 46,000 (on Google, minus self-citations).

Bažant, with his disciples, has made groundbreaking contributions to four areas of solid and structural mechanics.

Size effect, fracture and distributed damage[edit]

Bažant is a world leader in scaling research in solid mechanics. He is best known for discovering the size effect law for quasibrittle failure and the related nonlocal and crack band models. With the advent of computers in 1970, analysis of structures with distributed softening damage became feasible. But the pitfalls were not recognized. Bažant showed in 1976 that the computed structure strength was spuriously dependent on the chosen finite element (or mesh) size and that a characteristic material length serving as a localization limiter had to exist. The size effect on structural strength was recognized but was incorrectly attributed to material randomness and fracture mechanics was thought to be inapplicable. Bažant changed that. In a series of six landmark papers during 1976–1991, he revolutionized the theory of scaling of quasibrittle structure strength and demonstrated the applicability of quasibrittle fracture mechanics. In 1984, through asymptotic-matching arguments, he discovered the energetic (non-statistical) size effect law for quasibrittle failure — a deceptively simple law that bridges the small-size quasi-plastic behavior, exhibiting no size effect, to the large-size brittle behavior, exhibiting the maximum possible size effect. With his assistants, he amply verified his law experimentally. He showed that disregard of size effect was a major factor in the failures of Sleipner Oil Platform, viaducts in Kobe, Loma-Prieta and Norridge earthquakes, Schoharie Creek and Palau bridges, Shelby warehouse, St.-Francis and Malpasset dams, etc. Embodied in various standard recommendations, Bažant’s law is now widely used for sensitive large structures. A standardized fracture energy test (RILEM-FMT/1990) for concrete is based on his law.

After demonstrating in 1976 the inobjectivity and spurious mesh sensitivity of the classical stress-strain-based models for softening material damage, Bažant pioneered fracture-mechanics-based remedies - the crack-band model (1983) and nonlocal (1984, 1987) damage models, which introduced a material characteristic length as the basic characteristic of distributed damage, and transformed computer analysis of concrete structures and geomaterials, as well as load-bearing fiber composites for large structures such as aircraft and ships. His simple crack-band model today dominates in civil engineering industry and is incorporated in commercial software (e.g., ATENA, SBETA, OOFEM, DIANA). His more fundamental nonlocal damage model and second-gradient model spurned an avalanche of follow-up studies and became a vital check for sensitive designs. His books Fracture and Size Effect (with Planas), Inelastic Analysis (with Jirásek) and Scaling of Structural Strength became classics.

For three-dimensional characterization of fracturing, Bažant conceived in 1983 the microplane model in which the constitutive law, formulated in terms of vectors rather than tensors, is based on the concepts of crack opening and frictional slip, with their orientation, and the stress tensor is obtained from stress vectors by a variational principle. With his assistants, he developed microplane models for concrete, rocks, fiber composite laminates, braided composites, rigid foam, clays, granular solids, shape memory alloys, fiber reinforced concrete and annulus fibrosus. He demonstrated the ‘vertex’ effect in concrete (e.g., stiffness drop in torsion after previous compression in softening range) and showed that the microplane model can capture it. Bažant’s microplane models M4 and M7 became favored tool for simulating the effects of terrorist explosions, missile impact and groundshock. Ramifications include the load-carrying capacity of sea ice, forces on oil platforms, snow-avalanche triggering, borehole breakout, size effect in metallic thin films, etc. He discovered experimentally and explained theoretically that material strain softening reverses to hardening when the loading rate suddenly increases, which is important for shock wave propagation.

Uncertainty of structural strength[edit]

Important for structural safety is Bažant’s nano-mechanics–based calculation of probability distribution of strength and lifetime of quasibrittle structures. Based on statistics of interatomic bond breaks he derived the distribution of strength and crack growth rate on the atomic scale and discovered a surprisingly simple multiscale transition to the representative volume element of material on the macro-scale. Thus he showed that, for quasibrittle materials, which are characterized by a fracture process zone whose size is not negligible compared to structural dimensions, the strength distribution is a combination of Weibull and Gaussian distributions varying with the structure size. This causes that the safety factors of quasibrittle structures must vary with structure size, too. Recently, he demonstrated a similar distribution for static and fatigue lifetimes of quasibrittle structures.

Creep and durability[edit]

Bažant is also a leading world authority in creep and shrinkage of concrete. In 1972 he derived the age-adjusted effective modulus (AAEM) method which became the industry stardard for simplified analysis of creep and shrinkage effects in concrete structures and has been a standard recommendation of ACI in America and fib in Europe. Motivated initially by problems of nuclear reactor containments, and later by large-span box-girder bridges and super-tall buildings, Bažant achieved fundamental advances in nano-poro-mechanics, and particularly the long-term creep and diffusion processes. By 1970, there was a host of unexplained conflicting observations—e.g., why concrete creep increases during drying whereas, at thermodynamic equilibrium, a lower pore water content gives lower creep; or why the decrease of creep with the age at load application continues for decades whereas chemical hydration terminates within a year. During 1970–1997, Bažant with his assistants answered these questions by formulating a consistent theory based on surface thermodynamics and disjoining pressure in adsorbed nano-pore water. He based on it his models B3 and B4 for practical prediction of concrete creep and shrinkage, which he calibrated by assembling, with his assistants, a vast world-wide database of laboratory tests. Model B3 became an international standard (RILEM-CGS/1995, endorsed also in ACI-209/2008 Guide, and B4 is being evaluated for a new RILEM standard). More recently, beginning with his analysis of the ill-fated record-span bridge in Palau, Bažant showed how the multi-decade concrete creep prediction can be updated by data on dozens of excessively deflecting large-span prestressed bridges, which he compiled with his assistants.

Aging creep computations at transient environment were facilitated by Bažant’s conversion of history integrals to a rate-type creep law, and by his 1971 invention of the unconditionally stable exponential algorithm for aging creep of concrete, now widely used in finite element programs. By discovering that a pore humidity decrease causes moisture diffusivity to drop by an order of magnitude, he formulated a nonlinear diffusion equation for concrete which has become the mainstay of computer programs and is part of the CEB-fib Model Code. Bažant’s further work dealt with Bayesian updating and quantified the effects of randomness of creep and environment.

Creep, drying shrinkage, permeability and pore water pressure increase due to heating above 100 C, while strength, fracture energy and stiffness decrease. Concrete spalls and may explode. Temperatures up to 600 C are of major concern for the survival of tunnel linings and tall buildings in fire, and of containments in nuclear accidents. Studying these phenomena, Bažant documented a 100-fold increase of concrete permeability upon surpassing 100 C, and formulated a comprehensive theory used to evaluate the safety of nuclear concrete structures at Argonne NL and EDF in France, and to analyze the ‘Chunnel’ fire. With Kaplan, he published a widely read book on Concrete at High Temperatures. Bažant also pioneered chemo-mechanics of reinforcement corrosion, freeze-thaw, salt ingress and, especially, alkali-silica reaction, whose prediction is essential for sustainability of concrete structures.

Among bridge designers, Bažant is known for clarifying the grossly excessive deflections of the ill-fated record-span prestressed concrete bridge in Palau and showing that they were the consequence of incorrect standard recommendations for long-term creep rather than lapses of quality control.

Stability of structures[edit]

Bažant was the first to resolve decades-long controversies about stability and critical loads of three-dimensional structures. Since 1910, there have been incessant polemics about the theories of Southwell, Hencky, Truesdell, Rivlin, Biot, Engesser, Haringx, etc., based on different choices of finite strain tensor and of objective stress rate, yielding critical load estimates differing even by >100%. These polemics were resolved in 1971 by Bažant’s (1971) variational derivation of objective stress rates which led him to formulate the work conjugacy criteria of finite strain tensors and stress rates. He showed that different tensors are mutually equivalent, that a transition from one to another can be effected by a certain stress-dependent transformation of the tangential stiffness tensor, and that only one particular finite strain tensor is admissible when the material stiffness is considered constant. Recently he demonstrated that non-conjugate rates, which are used in many commercial programs, can lead to errors of >50% in critical loads of highly compressible or highly orthotropic structures soft in shear (e.g., foam core sandwich shells, fiber composites, orthotropically cracked bodies). Bažant wrote (with Cedolin) a lucid and the most comprehensive treatise on stability of structures, treating in a unified manner not only the elastic and plastic theories, but also the fracturing, damage and creep theories.

Forensic Engineering[edit]

He explained scientifically what did, and what did not , cause the 9/11 collapse of WTC towers in New York in 2001, and what caused the enormous deflections with ensuing fatal collapse of the world-record prestressed box girder bridge in Palau (see related publications).

Honors and awards[edit]

Bažant was elected to US National Academy of Sciences in 2002, US National Academy of Engineering in 1996, and American Academy of Arts and Sciences in 2008. He is a foreign member of the Royal Society of London (2015), Austrian Academy of Sciences, Academy of Engrg. of Czech Rep., Italian National Academy (dei Lincei, Rome), Spanish Royal Academy of Engrg., Istituto Lombardo (Milan), Academia Europaea (London) and European Acad. of Science and Arts. His honors include 7 honorary doctorates: CTU Prague (1991), TU Karlsruhe (Fredericiana, 1997), UC Boulder (2000), Politecnico di Milano (2001), INSA Lyon (2004), TU Vienna (2006), and Ohio State University (Dec. 2011). He is a Honorary member of Am. Soc. of Mechanical Engineers (ASME), Am. Soc. of Civil Engineers (ASCE), Am. Concrete Institute (ACI), RILEM, Paris (Int. Union of Res. Lab. In Mat. & Str.), Czech Soc. of Mechanics, Czech Soc. of Civil Engineers, Czech Concrete Society, and Building Res. Institute of Spain. He has given almost one hundred plenary conference lectures and over thirty distinguished university lectures. His honors include:

  • Timoshenko Medal (ASME)
  • Worcester Reed Warner Medal (ASME)
  • Nadai Medal (ASME)
  • von Karman Medal (ASCE)
  • Newmark Medal (ASCE)
  • Biot Medal (ASCE)
  • Mindlin Medal (ASCE)
  • Croes Medal (ASCE)
  • Lifetime Achievement Award (ASCE Ill. Section)
  • W.L. Huber Prize (ASCE)
  • TY Lin Award (ASCE)
  • Prager Medal (Soc. of Engrg. Science, SES)
  • Roy Award (Am. Ceramic Society, ACS)
  • L’Hermite Gold Medal (RILEM, Paris)
  • Wilhelm Exner Medal (Austria Gov.-Industry Assoc. awarded by Austrian President)
  • Šolín Medal (CTU Prague)
  • Medal of Czech Soc. for Mech.
  • Stodola Medal (Bratislava)
  • Zdenek Bazant, Sr., Medal (CTU Prague)
  • Outstanding Contributions Award (IACMAG)
  • ICOSSAR Lecture Award
  • Best Engrg. Book of the Year (Assoc. of Am. Publishers)
  • Publication Merit Award (SEAOI)
  • Outstanding paper award (REILM)
  • In 2015, ASCE established Z.P. Bazant Medal for Failure and Damage Prevention


  • Bažant, Zdeněk P. (1966). Creep of Concrete in Structural Analysis. Prague: State Publishers of Technical Literature (SNTL). 
  • Bažant, Zdeněk P.; Luigi Cedolin (1991). Stability of Structures: Elastic, Inelastic, Fracture and Damage Theories. New York: Oxford University Press. pp. 1011 pages. ISBN 0-486-42568-1. 
  • Bažant, Zdeněk P.; Maurice F. Kaplan (1996). Concrete at High Temperatures: Material Properties and Mathematical Models. London: Longman (Addison-Wesley). pp. 412 pages. ISBN 0-582-08626-4. 
  • Bažant, Zdeněk P.; Jaime Planas (1998). Fracture and Size Effect in Concrete and Other Quasibrittle Materials. Boca Raton and London: CRC Press. pp. 616 pages. ISBN 0-8493-8284-X. 
  • Jirásek, Milan; Zdeněk P. Bažant (2002). Inelastic Analysis of Structures. London and New York: J. Wiley & Sons. pp. 735 pages. 
  • Bažant, Zdeněk P. (2002). Scaling of Structural Strength. London: Hermes Penton Science. ISBN 1-56032-984-X. 
  • Bažant’s list of publications: http://www.civil.northwestern.edu/people/bazant/PDFs/publicat.pdf



  • J. P. Dempsey and G. Pijaudier-Cabot, Guest Editors (1998), Preface in “ Special Topics in Structural Mechanics of Geomaterials”, “A Volume in Honor of Professor Z. P. Bažant”, Special Issue of Int. J. of Solids & Structures 35 (31-32), 4019-4350.
  • G. Pijaudier-Cabot, Z. Bittnár and Bruno Gérard, Editors (1999), Preface in “Mechanics of Quasi-Brittle Materials and Structures,” “A Volume in Honour of Professor Z.P. Bažant 's 60th Birthday”, Hermes Science Publications, Paris (446 pp.).
  • V. Červenka (2002). “Profesor Bažant becomes member of US National Academy of Sciences” (in Czech). Beton (Prague) 2 (5), p. 54.
  • Editorial, “Prof. Bažant Visiting CTU (Czech Technical University) in Prague” (in Czech), Prazska Technika 2003 (No. 2), 10-11.
  • S. Karlowski (2003), “Dr. Bažant receives the Structural Group Lifetime Achievement Award”, ASCE Illinois Section News, Vo. 44 (6), 2003, pp. 1 and 4.
  • C. Kisor (2003), “Tough Shoulders”. Pilot (Evanston Northwestern Healthcare) 67 (2), 10-11.
  • L. Bundesen (2004), “Biography of Zdeněk P. Bažant.” Proc., National Academy of Sciences 101 (37), 13397-13399.
  • V. Křístek (2005), “Prof. Ing. Z.P. Bažant, Ph.D., Dr.h.c.” (in Czech) Aula-Review of Academic and Science Policy (Prague) Vol. 13 (No. 2), 34-35.
  • G.J. Dvorak, Guest Editor (2006), Preface and Special Issue in Honor of Professor Z.P. Bažant, Intern. Jour. of Fracture 137 (1-4), pp. 1-294.
  • C.K.Y. Leung and K. Willam, Guest Editors (2007), Preface and Special Issue dedicated to Z.P. Bažant, Engineering Fracture Mechanics 74 (1-2), pp. 1-280 (20 papers).
  • Ta-Peng Chang and Jenn-Chuan Chern (2007). Preface and Proc., Asian Special Workshop on Concrete Technology in Honor of the 70th Birthday of Prof. Z.P. Bažant,” National Taiwan University of Science and Technology, Taipei, Nov. 2
  • V. Křístek (2007). Prof. Z. P. Bažant 70 Year Anniversary (in Czech).” Beton (Prague), Vol. 7, No. 6 (Dec.), pp. 54-55.
  • A13. Sarah Ostman, “Concrete Results” (Bažant ‘s life and achievements), McCormick Magazine, Fall 2012, Northwestern University, Evanston.
  • A14. F.-J. Ulm, Preface and Tribute to Z.P. Bažant, Proc., CONCREEP-9 (9th Intern. Conf. on Creep, Shrinkage and Durability Mechanics of Concrete, held in 2014 at MIT, Cambridge); F.-J. Ulm, Editor, publ, by ASCE, Washington, D.C.
  • Bundesen, Liza Q. (September 14, 2004). "Biography of Zdeněk P. Bažant" (PDF). Proceedings of the National Academy of Sciences 101 (37): 13397–13399. doi:10.1073/pnas.0405856101. PMC 518768. PMID 15353582. Retrieved August 24, 2007. 
  • Dvorak, George J.; White-Traut, R.; Studer, T.; Meleedy-Rey, P.; Murray, P.; Labovsky, S.; Kahn, J. (January–February 2006). "Preface to Special Issue In Honor of Professor Zdeněk P. Bažant" (PDF). International Journal of Fracture 137 (1–4): 1–7. doi:10.1007/s10704-006-7350-4. PMID 12032792. Retrieved August 25, 2007.