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Theoretical and Applied Mechanics Program Northwestern University Ranked No. 1 by the Chronicle of Higher Education Where to apply? http://www.tam.northwestern.edu/ 24 Faculty: J. D. Achenbach, O. Balogun, Z.P. Bazant,T.Belytschko,C.Brinson, J.Cao, W.Chen. I.M. Daniel, S.H. Davis, G. Dvorak, H.D. Espinosa, S. Ghosal, Y.Huang, L.M. Keer, S. Keten, S.Krishnaswamy, S. Lichter, W.-K. Liu, R..Lueptow, N.A. Patankar, J.Qu, J.W. Rudnicki, J. Wang, J. Weertman.. 7 NAE, 3 NAS and 5 AAAS members

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PERVASIVENESS OF CONCRETE CREEP PROBLEMS IN STRUCTURES: WAKE-UP CALL FOR DESIGN CODES AND CONSEQUENCES OF NANO-POROSITY ZDENĚK P. BAŽANT COLLABORATORS: QIANG YU, MIJA HUBLER AND ROMAN WENDNER SPONSORS: NSF, DoT UNIVERSITY OF MIAMI, CORAL GABLES, 11//06/2011

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1. Clue from Tragic Collapse in Palau 1996 1. Clue from Tragic Collapse in Palau 1996

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Box Girder of World Record Span 241 m, Palau, 1977 Segmental Cantilever Construction Eugène Freyssinet 1879 – 1962 Ulrich Finsterwalder 1897 - 1988

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Koror-Babeldaob Bridge in Palau Built 1977, failed 1996 Delamination creep buckling of top slab. Sudden loss of prestressing force ~20,000 ton, emits wave. Babeldaob side (failed first)

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Trigger of Collapse: Delamination creep buckling of top slab 3 months after remedial prestressing 1. Delamination in top slab 2. Box girder fails in compression- shear 3. Load from Babeldaob side transmitted 4. Bridge lifts up and hold-down bars fracture 5. Section at pier overloaded and fails in compression 6. Side span slams back on end pier and fails in shear Babeldaob Koror Top slab subjected to longitudinal compressive forces Crack Delamination buckling Longit. force 190 MN (21400 tons) from 316 tendons in 4 layers 1 layer buckling releases about 5000 tons

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18 years later: Deflection 1.61 m (compared to design camber)

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2. Release of Data on Litigated Failure Sealed in Perpetuity 2. Release of Data on Litigated Failure Sealed in Perpetuity

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1) The structural engineers gathered at their 3rd World Congress deplore the fact that the technical data on the collapses of various large structures, including the Koror-Babeldaob Bridge in Palau, have been sealed as a result of legal litigation. 2) They believe that the release of all such data would likely lead to progress in structural engineering and possibly prevent further collapses of large concrete structures. 3) In the name of engineering ethics, they call for the immediate release of all such data. Palau: Legal litigation (1996-1998) didn’t establish the causes of excessive deflections and collapse. All data sealed in perpetuity! Nov. 2007: Resolution, proposed by Bažant, adopted by 3rd World Congress of Structural Engineers: 2 months later: Attorney General of Palau agreed to controlled release of the data!

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Withholding of technical data on any real or potential disaster is prohibited by law, as well as international agreements. Contrast: Commercial Aviation

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3. Why the creep deflections of KB Bridge were so excessive? 3. Why the creep deflections of KB Bridge were so excessive?

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Diaphragms Three-Dimensional Mesh for Prestressed Box Girder 5036 eight-node isoparametric (hexahedral) elements and 6764 steel bar elements

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Algorithm Utilizing ABAQUS From B3 (or ACI, CEB, GL) obtain axial and transverse compliance functions for each finite element, as function of D, h T. Use Widder’s formula to calculate discrete spectrum moduli for each finite element and each time step. Specify for ABAQUS the (yield) strength limit of each finite element. Loop on time steps Loop of finite elements. From Δt and the current strains of Kelvin units, calculate for each finite element the incremental moduli E ijrs and inelastic (quasi-thermal) strain increments Δε rs ” for each finite element. Supply the quasi-elastic stress strain relation Δσ rs = E ijrs (Δε rs – Δε rs ”) with inelastic strains Δε rs ” to each finite element of ABAQUS, along with the current stress. End of loop on finite elements. Apply load and prescribed displacement increments, if any. Run ABAQUS, heeding the strength limits. End of loop on time steps: Obtain incremented nodal displacements, strains and stresses, go to 4, and start a new time step.

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— use a continuous retardation spectrum Advantage: Continuous retardation spectrum D( ) is unique (1995), defined by Laplace transform inversion, easily obtained by Widder’s formula. Discrete approximation D i of continuous spectrum, different in each time step, yields Kelvin chain moduli – easy step-by-step integration. EE 11 11 11 11 Continuous Spectrum discrete spectrum Age t’ 2 EE E1E1 11 11 11 E Compliance log (t-t ' ) J Age t ‘ 1 = 28 days Age t ‘ 2 = 365 days Age t’ 1 Replace history integrals by rate equations for internal variables (partial strains) (a concept pioneered by Biot)

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Concrete creep and shrinkage models compared in new ACI Guide 209.2R-08 ( 2008): ——————————————————————————————————————— 1) B3 (Bažant & Baweja 1995, 2000; update of BP Model 1978) 2) ACI 1971, reapproved in 2008 (sole dissenting vote: Bažant) 3) CEB-fib (or CEB-FIP Model Code 1990, fib 1998, fib Draft 2010) 4) GL (Gardner & Lockman 2001) (similar to Bažant & Panula 1978) 5) JSCE and JRA (Japan) — all rated in ACI Guide as approximately equivalent!

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Two Questions in Comparing Various Models 1. Prediction: How do the predictions of various models differ from observations? 2. Credible Explanation: Can the observations be explained and matched with realistic parameter values?

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Parameter Sets Considered for Model B3 Set 1 (prediction): q 1 = 0.146, q 2 = 1.04, q 3 = 0.045, q 4 = 0.053, q 5 = 1.97 x 10 -6 /psi, λ 0 = 1 day, ε k = 0.0013, k t = 19.2 = empirical estimates from design strength f’ c and mix composition Set 2 (explanation) : q 2, q 5, ε k , λ 0, k t = same (from composition) but q 1 = 0.188 based on E- modulus from truck load test q 3 = 0.262, q 4 = 0.140 x10 -6 / psi = long-time parameters updated from Brooks (1984, 2006) 30-year creep data (Univ. of Leeds)

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Does Model B3 (Set 2) match any real concrete? It does – Brooks (1984, 2006) 30-year data 140 0.1 280 10 1 100 1000 10000 J(t,t’) x 10 -6 / MPa t-t’ (log. scale, days) B3 (Set 2) w/c = 0.56 w/c = 0.67 t’ = 14 days Brooks, 1984 (University of Leeds)

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1D beam element model in commercial software SOFiSTiK 3D element model for ABAQUS Fig. 6 0 2000 4000 6000 8000 0 -0.8 -1.2 -1.6 t, time from construction end, days Mean Deflections (m) ACI (3D) CEB (3D) GL (3D) JSCE (3D) B3 (3D) (set1) B3 (3D) (set2) -0.4 CEB (1D, SOFiSTiK) 1 100 1000 10000 100000 0 -1.5 -2.0 log t, time from construction end, days -0.5 -2.5 10 CEB (3D) GL (3D) JSCE (3D) B3 (3D) (set1) B3 (3D) (set2) CEB (1D, SOFiSTiK) ACI (3D) Deflections [in m ] predicted by 3D finite elements using models ACI, CEB, GL, JSCE, and B3 (Sets 1, 2) KB BRIDGE

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0 2000 4000 6000 8000 0 -0.8 -1.2 -1.6 t, time from construction end, days Mean Deflections (m) ACI (3D) CEB (3D) GL (3D) JSCE (3D) B3 (3D) (set1) B3 (3D) (set2) -0.4 CEB (1D, SOFiSTiK)

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Prestress loss (MN) in tendons at main pier predicted by 3D finite elements using models ACI, CEB, GL, JSCE, and B3 (Sets 1, 2) Detailed report: Google “Bazant”, download “…Palau…” KB BRIDGE IN PALAU

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New I-35W Bridge in Minneapolis (allegedly designed using SOFiSTiK or similar)

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Mean response (m) and 95% confidence limits of Model B3 in normal and logarithmic scales (based on expected CoV of q 1, q 2, q 3, q 4, q 5, k t,, and humidity) Calculated from 8 deterministic runs for random (Latin Hypercube) samples of input pararameters

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Relaxation in Prestressing Steel Tendons 2. Effect of Temperature Ignored Temperature in top slab Temperature Location in Slab (mm) time (s), log scale The first layer of tendon reaches 30ºC in about 2.5 hours 55ºC max. 20ºC Tropical sun 1. Effect of Varying Strain in Steel Ignored: top bottom - The strain in the tendons decreased by 30 %. - A rate-type viscoplastic model must be used for prestressing steel. Temperature (ºC) Relaxation (%) fib Model Code Draft 2010 The initial strain in concrete is 0. After prestress and self-weight is applied, it is about 0.00056. After 20 years, the total strain in concrete is about 0.00103 due to creep and shrinkage. The concrete strain is almost doubled in 20 years. The initial strain in steel is about 1% ? So the strain in prestr. Steel drops by about 10% of the initial value.

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Relaxation in Prestressing Steel 2. Traditionally: Effect of temperature ignored Temperature in top slab Temperature Location in Slab (mm) time (s), log scale The first layer of tendons reaches 30ºC in about 2.5 hours 55ºC max. 20ºC Tropical sun 1. Up to now: Effect of varying strain ignored: top bottom - But the strain in tendons can decrease by 30 %. - Hence, a rate-type viscoplastic model must be used for prestressing steel. Time (hours) Relaxation (%) Normal relaxation grade (Shinko, Japan) 80 ºC 60 ºC 40 ºC 20 ºC

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A T = Arrhenius factor Q = activation energy k B = Boltzmann constant Reduced time (due to temperature): Steel Relaxation Generalized to Variable Strain & Temp. Main features: 1)Relaxation terminates when stress reaches certain level 2)No crossing for relaxation curves under different initial stress + T Proposed for varying strain and T : Constant strain and T :

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Comparison with Tests: Variable Strain 0.1 110 100 1000 1400 1200 log t (hours) Stress (MPa) 0.1 110 100 1000 1500 1250 log t (hours) Stress (MPa) SR9-5 and SR10-5 (Buckler & Scribner 1985) SR14-10 (Buckler & Scribner 1985) 0.1 110 100 1000 1150 1320 1235 Stress (MPa) 0.1 110 100 1000 1120 1420 1270 Stress (MPa) SR9-5 and SR10-5 (Buckler & Scribner 1985) SR14-10 (Buckler & Scribner 1985) CEB (rate-type) Fit by proposed formula

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Comparison with Tests: Step-Wise T History Time (hours) Stress (MPa) Rostasy & Thienel, 1991 Proposed formula (constants calibrated by relaxation test at 20 ºC) Time (hours) Stress (MPa) Rostasy & Thienel, 1991 T (ºC) 20 ºC 70 ºC 130 ºC T (ºC) 45 ºC 70 ºC 130 ºC 20 ºC Time (hours)

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Programs for Structural Creep Analysis Programs now in use (e.g. SOFiSTiK) are based on the state of the art 40 years ago – history integrals of linear aging viscoelasticity, computed in time steps — obsolete, misleading. Reasons: 1) Poor material model. 2) Beam-type analysis instead of 3D 3) Variation of drying effects due to thickness variation 4) Cracking (which is not hereditary), nonlinear deformations 5) Gradual prestress relaxation (nonlinear viscoplasticity) 6) Variable environment Required: Rate-type creep law in which the history is taken into account by current values of internal variables (partial strains).

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Causes of Error 1.Incorrect standard recommendations on concrete compliance and shrinkage functions (esp. for > 3 years, and on prestressing steel relaxation. 2.Differential shrinkage and drying creep compliance due to: a) plate thickness, b) temperature (both CEB 1972, 1990 and ACI 1972, 2008 are incorrect). 3.Beam elements instead of 3D FEM 4.No updating by short-time tests. 5.No statistical estimate (95% confidence limit). Dead load Prestress

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4. Aren’t Other Presstressed Segmentally Errected Bridges Behaving Similarly? 4. Aren’t Other Presstressed Segmentally Errected Bridges Behaving Similarly?

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Completion 1982 Age 26years Max. span 84.5m Tsukiyono Bridge After Y. Watanabe, Shimizu Constr. Co., Concreep 2008

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Time dependent deflection –Tsukiyono Bridge CONCREEP8CONCREEP8 11010 10 0 100 0 10,00 0 0 50 10 0 15 0 Data courtesy Y. Watanabe, Chief Engineer, Shimizu Constr. Co., 2008 JSCE

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Koshirazu Bridge Completion1987 Connected1997 Age10 years Max. span59.5m After Y. Watanabe, Chief Engineer, Shimizu Constr. Co., Concreep 2008

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Time dependent deflection – Koshirazu Bridge CONCREEP8CONCREEP8 11010 10 0 100 0 10,00 0 0 20 40 60 80 10 0 Data courtesy Y. Watanabe, Chief Engineer, Shimizu Constr. Co., 2008 JSCE

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Konaru Bridge 0 200 400 2000 40006000800010000 Elapsed days 0 200 400 10 100100010000 Deflection (mm) Data courtesy Y. Watanabe, Chief Engineer, Shimizu Constr. Co., Concreep 2008 JSCE

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Děčín Bridge, Continuous Box Girder No Hinge at Midspan over Elbe River, Northern Bohemia

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Mid-Span Deflection of Děčín Bridge Days, linear scale Deflection (cm) 2000 4000 6000 0 15 30 Prediction Measurements Days, log scale 100 1000 10000 0 15 30 Prediction Measurements 100000 Deflection (cm) Data courtesy Dr. Vrablik, CTU Prague

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5. Wake-Up Call: Excessive deflections are not isolated but endemic to this kind of bridges

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KB Bridge 241 m Palau, 1977 Konaru Bridge 101.5 m Japan, 1987 Parrots Ferry Bridge 195 m U.S.A., 1978 Nordsund Bru 142 m Norway, 1971 Pelotas River Bridge 189 m Brazil, 1966 Tunstabron 107 m Sweden, 1955 Urado Bridge 230 m Japan, 1972 Zvíkov-Otava Bridge Hinge 1 84 m Czech Rep., 1962 Zvíkov-Otava Bridge Hinge 2 84 m Czech Rep., 1962 Zvíkov-Vltava Bridge Hinge 4 84 m Czech Rep., 1963 Zvíkov- Vltava Bridge Hinge 3 84 m Czech Rep. 1963 Maastricht Bridge 112 m Netherlands, 1968 Savines Bridge Span l 77 m France, 1960 Savines Bridge Span k 77 m France, 1960 Savines Bridge Span j 77 m France, 1960 Savines Bridge Span h 77 m France, 1960 Savines Bridge Span g 77 m France, 1960 Savines Bridge Span f 77 m France, 1960 Savines Bridge Span c 77 m France, 1960 Savines Bridge Span b 77 m France, 1960 Alnöbron Hinge 1 134 m Sweden, 1964 Alnöbron Hinge 2 134 m Sweden, 1964 Källösundsbron Hinge 1 107 m Sweden, 1958 Källösundsbron Hinge 2 107 m Sweden, 1958 Alnöbron Hinge 3 134 m Sweden, 1964 Alnöbron Hinge 4 134 m Sweden, 1964 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 0.8 0.4 0 0.2 0 0.6 0.3 0 0.4 0.2 0 1 0.5 0 0.26 0.13 0 0.24 0.12 0 0.2 0.1 0 0.2 0.1 0 0.2 0.1 0 0.2 0.1 0 0.2 0.1 0 0.2 0.1 0 0.3 0.15 0 0.2 0.1 0 0.2 0.1 0 0.2 0.1 0 0.2 0.1 0 0 0.2 0.1 0 0.2 0.1 0 0.16 0.08 0 0.1 0.05 0.14 0.07 0 0.16 0.08 0 0.12 0.06 0 0.1 0.05 0 [Deflection/Span (%) ] vs. Time Elapsed (days, log-scale) 56 Bridges: Excessive Deflections. Any Bound? -1 Alnöbron Bridge Hinge 5 134 m Sweden, 1964 10 2 10 3 10 4 0.1 0.05 0 Grubben- vorst Bridge 121 m Netherlands, 1971 10 2 10 3 10 4 0.16 0.08 0

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Wessem Bridge 100 m Netherlands, 1966 Empel Bridge 120 m Netherlands, 1971 Ravenstein Bridge 139 m Netherlands, 1975 Koshirazu Bridge 59.5 m Japan, 1987 Narrows Bridge 97.5 m Australia, 1960 Gladesville Arch 300 m Australia, 1962 Captain Cook Bridge 76.2 m Australia, 1966 Art Gallery Bridge Australia, 1961 Macquarie Bridge Australia 1969 Victoria Bridge Australia, 1966 Želivka Bridge, Hinge 1 102 m Czech Rep., 1968 Želivka Bridge, Hinge 2 102 m Czech Rep., 1968 Děčίn Bridge 104 m Czech Rep. 1985 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 0.1 0.05 0 0.14 0.07 0 0.12 0.06 0 0.2 0.1 0 0.07 0.035 0 0 0.08 0.04 0 0.12 0.06 0 0.05 0.025 0 0.12 0.06 0.016.008 0 0.02 0.01 0.016.008.06.03 0 [Deflection/Span (%) ] vs. Time Elapsed (days, log-scale) Konaru Bridge 101.5 m Japan, 1987 10 2 10 3 10 4 0.4 0.2 0 Stenungs - undsbron 94 m Sweden 10 2 10 3 10 4 0. 2 0 0.4 Tsukiyono Bridge 84.5 m Japan, 1982 10 2 10 3 10 4 0.2 0.1 0 La Lutrive Bridge Hinge 2 131 m Switzerland, 1973 La Lutrive Bridge Hinge 3 131 m Switzerland, 1973 10 2 10 3 10 4 10 2 10 3 10 4 0.14 0.07 0 0.12 0.06 0 Heteren Bridge 121 m Netherlands, 1972 10 2 10 3 10 4 0.1 0.05 0 Zuari Bridge Span C 120 m Goa, 1986 10 2 10 3 10 4 0.08 0.04 0 Zuari Bridge Span E 120 m Goa, 1986 10 2 10 3 10 4 0.08 0.04 0 Zuari Bridge Span F 120 m Goa, 1986 Zuari Bridge Span H 120 m Goa, 1986 Zuari Bridge Span J 120 m Goa, 1986 10 2 10 3 10 4 0.08 0.04 0 10 2 10 3 10 4 10 2 10 3 10 4 0.08 0.04 0 0.08 0.04 0 Zuari Bridge Span L 120 m Goa, 1986 Zuari Bridge Span M 120 m Goa, 1986 Zuari Bridge Span O 120 m Goa, 1986 Zuari Bridge Span P 120 m Goa, 1986 10 2 10 3 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 0.14 0.07 0 0.1 0.05 0 0.1 0.05 0 0.1 0.05 10 4 0 56 Bridges: Excessive Deflections. Any Bound? -2

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6. Why have the standard recommendations for concrete creep been so incorrect, for 40 years? 6. Why have the standard recommendations for concrete creep been so incorrect, for 40 years?

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Criteria for Selecting Material Creep Model a) Ability to fit individual compliance and shrinkage curves of one concrete — essential validation b) Statistical comparison with laboratory database for all kinds of concretes — code committees’ way c) Correct prediction of multi-decade deflection of structures — additional essential validation d) Theoretical foundation — essential — only this is discussed today

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Histograms of Data Points in New NU-ITI Database 11821 creep data points Loading Duration log(t-t’) DAYS Effective SizeAge at Loading log t’ 8326 shrinkage data points Drying Duration log(t-t 0 ) Effective Size

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Examples of Almost Useless Statistical Comparisons for Creep, NU-ITI Database, Unweighted Data (1/MPa) Calculated MeasuredMPa -1 Why so little difference among models? — Because all data points got equal weights.

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Almost Useless Comparisons of Residuals (Errors) After Al-Manaseer & Lam, ACI Mat.J. 2005 Time [days] shrinkage creep

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i =1 2 3 4 6 7 8 9 11 12 13 14 5 10 15 i =16 17 18 19 20 21 22 n i =1 2 3 4 5 6 7 8 9 10 11 12 n log (t-t') log t' (age of loading) (or thickness,or humidity h ) y=J(t,t') m i = number of all points in box i How to optimize and compare models?—By multivariate regression statistics, countering bias by proper weights 1D Boxes (Intervals)2D Boxes y=J(t,t') m i = number of all points in interval i x=log (t-t') t'=t' 1 t' 2 t' 3 points j=1,2,…m i y ij Y ij Standard Error of Regression, s : Weighted mean of all data points Number of all data points Weights: Problem with multi- dimensional boxes: Some contain only 0 or 1 point.

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27.3 42.6 31.030.241.9 50 2D boxes of log(t-t’) and H Comparisons by Weighted Least-Square Regression Coefficients of Variation (C.o.V.) of Errors 28.5 42.3 47.431.044.4 28 2D boxes of log(t-t 0 ) and a) Complianceb) Shrinkage The differences are as marked as those for Palau

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10 -2 Wittmann et al.,1987 d s∞ sh (mm) 10 -3 (days) 83 0.891 120.7 1600.893 264.3 300 0.812 699.7 d = 83 mm d = 300 mm d = 160 mm Strain (×10 -3 ) 10 -1 10 0 10 1 t-t' (days) 0.8 0.0 0.4 10 2 10 3 Hansen and Mattock,1966 RH = 50% t 0 = 8 Days T = 21°C I-section 11.5 × 4.25 in. 23 × 8.5 in. 46 × 17 in. 10 1 t-t 0 (days) 10 2 10 3 1.0 0.0 0.5 Essential Criterion: Capability to Fit All Test Curves for One and the Same Concrete Strain (×10 -3 ) J ( t, t' ) (×10-6/psi) 10 0 10 1 10 2 10 3 10 -2 10 -1 0.5 0.1 0.3 Kommendant et al., (b),1976 sealed Optimum fit t' = 28 days t' = 270 days t' = 90 days t' = 2 days t' = 7 days t' = 28 days t' = 365 days t' = 90 days 10 0 10 1 10 2 10 3 0.9 0.1 0.5 0.3 0.7 Canyon Ferry Dam,1958 Optimum fit Creep Shrinkage

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(helped by new RILEM TC-MDC) 7. Idea: Exploit box girder deflections for inverse analysis to calibrate multi-decade material model for creep (helped by new RILEM TC-MDC)

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Inverse FE Creep Analysis of Multi-Decade Prestressed Box Girder Deflections Objective: Find functions predicting 9 material creep and shrinkage parameters of model B3 from the composition parameters of concrete. Ideally: 56 multi-decade bridge deflection records fitted jointly with the short-time database of >1000 lab tests. However, collecting the data for most bridges proved difficult, exasperating. a) Minimize sum of weighted squared errors. b) Or Bayesian posterior fitting of database with bridge data as incomplete prior.

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Approximate Multi-Decade Extrapolation of Creep Deflections of Prestressed Box Girders w 1000 – measured deflection at 1000 days J(t,t’) – model creep function (ACI, CEB, or B3) t a – average age at load application t c – average age at closing of the bridge span Hypothesis: After 1000 days, the complex effects of drying, construction sequence, differences in age, thickness and environmental exposure, etc., almost die out. 0 10 2 10 3 10 4.8.4.6.2 Defl. / Span (%) Time Elapsed (days, log-scale) region where models agree 10 1 B3 ACI CEB Data

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Mean deflection of the Koror-Babeldaob Bridge in Palau (1977) calculated by the ACI, CEB, and B3 models based on a 3D finite element model: Verification of Approximate Extrapolation Formula by Accurate Solutions for KB Bridge Extrapolation for each model is based on the given material properties. 0 10 2 10 3 10 4 ACI model.8.4.6.2 CEB model B3 model tata tctc Defl. / Span (%) Time Elapsed (days) log-scale In the following slides: Long-term estimates of 55 bridges based on average material properties. psi lb/yd 3 (400 kg/m 3 ) lb/yd 3 (2300 kg/m 3 ) In the following slides: Some bridges are deleted because of: 1. Insufficient data 2. Deflections were not excessive, or span was unknown. 3. Straight line regime not yet entered after 1000 days. 0 10 2 10 3 10 4.8.4.6.2 tata tctc 0 10 2 10 3 10 4.8.4.6.2 tata tctc Humidity, h, based on location of bridge. extrapolation FEM ASSHTO & CEB limit

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Mean= 1.6 Std. dev.= 0.74 10 2 10 3 10 4 10 1.4 0 Defl. / Span (%) Time Elapsed (days) δ ξ = optimized Model B3 scaling factor such that mean error → 0 Coeff. of Var.= 0.45 Scaling up Long-Term Slope of Model B3 KB Bridge, Palau 0 0.5 1 1.5 2 2.5 3 3.5 Error Histogram from 55 bridges (n = 0.1) ξ = 1.6 Asymptotic Slope = nq 3 + q 4 q 3 ← ξ q 3, q 4 ← ξ q 4

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Zvíkov- Vltava Bridge Hinge 3 84 m Czech Rep. 1963 Long-Term Deflections Extrapolated by Various Models: ACI ( ), CEB ( ), GL ( ), and B3 ( ) 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 0.8 0.4 0 0.6 0.3 0 0.4 0.2 0 1 0.5 0 0.26 0.13 0 0.24 0.14 0 0 0.2 0.1 0 0.2 0.1 0 0.2 0.1 0 0.2 0.1 0 0.2 0.1 0 0.3 0.15 0 0.2 0.1 0 0.2 0.1 0 0.2 0.1 0 0.2 0.1 0 0.2 0.1 0 [Deflection/Span (%) ] vs. Time Elapsed (days, log-scale) KB Bridge 241 m Palau, 1977 Parrots Ferry Bridge 195 m U.S.A., 1978 Nordsund Bru 142 m Norway, 1971 Pelotas River Bridge 189 m Brazil, 1966 Tunstabron 107 m Sweden, 1955 Urado Bridge 230 m Japan, 1972 Zvíkov-Otava Bridge Hinge 1 84 m Czech Rep., 1962 Zvíkov-Otava Bridge Hinge 2 84 m Czech Rep., 1962 Zvíkov-Vltava Bridge Hinge 4 84 m Czech Rep., 1963 Maastricht Bridge 112 m Netherlands, 1968 Savines Bridge Span l 77 m France, 1960 Savines Bridge Span k 77 m France, 1960 Savines Bridge Span j 77 m France, 1960 Savines Bridge Span h 77 m France, 1960 Savines Bridge Span g 77 m France, 1960 Savines Bridge Span f 77 m France, 1960 Savines Bridge Span c 77 m France, 1960 0.2 0.1 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4

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10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 0.2 0.1 0 0.16 0.08 0 0.1 0.05 0 0.12 0.06 0 0.1 0.05 0 0.1 0.05 0 0 0.16 0.08 0 0.16 0.08 0 0.1 0.05 0 0.14 0.07 0 0.12 0.06 0 0.2 0.1 0 0.07 0.035 0 0.12 0.06 0 0.08 0.04 0 0.06 0.03 0 [Deflection/Span (%) ] vs. Time Elapsed (days, log-scale) 0.14 0.07 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 Savines Bridge Span b 77 m France, 1960 Alnöbron Hinge 1 134 m Sweden, 1964 Alnöbron Hinge 2 134 m Sweden, 1964 Alnöbron Hinge 3 134 m Sweden, 1964 Alnöbron Hinge 4 134 m Sweden, 1964 Alnöbron Bridge Hinge 5 134 m Sweden, 1964 Källösundsbron Hinge 1 107 m Sweden, 1958 Källösundsbron Hinge 2 107 m Sweden, 1958 Grubbenvorst Bridge 121 m Netherlands, 1971 Wessem Bridge 100 m Netherlands, 1966 Empel Bridge 120 m Netherlands, 1971 Ravenstein Bridge 139 m Netherlands, 1975 Koshirazu Bridge 59.5 m Japan, 1987 Narrows Bridge 97.5 m Australia, 1960 Captain Cook Bridge 76.2 m Australia, 1966 Gladesville Arch 300 m Australia, 1962 Děčίn Bridge 104 m Czech Rep. 1985 Continued: Deflections Extrapolated by Various Models: ACI ( ), CEB ( ), GL ( ), and B3 ( ) 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 10 2 10 3 10 4 0 0

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Long-Term Deflections Extrapolated by Original Model B3 ( ) and Scaled Model B3 ( ) [Deflection/Span (%) ] vs. Time Elapsed (days, log-scale)

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Further Long-Term Deflections Extrapolated by Original Model B3 ( ) and Scaled Model B3 ( ) ˇˇ ˇ

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h P M y/h pp LL DD pp DD LL pp DD LL margin Strength limit ft*ft* ft*ft* ft*ft* fc*fc* a)Small span -- creep deflection upwards b) Large span -- no margin on f t *, deflection downwards c) Large span -- big margin on f t *, no deflection -- + + Precautionary Design Design Making Maximum Use of Strength Limit Dimensionless Coordinate Note: Not all segmental bridges deflect excessively!

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8. Theoretical Foundation: Intriguing Consequences of Nanoporosity

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A fundamental theory of multi-decade creep requires clarifying the NANO-SCALE CREEP MECHANISM Shear breaks and restorations of interatomic bonds bridging nano-pores in C-S-H*, controlled by MICROPRESTRESS or DISJOINING PRESSURE generated by: unequal chemical volume changes during hydration any change of pore humidity and temperature (due to differences in chemical potential of nano-pore water); and gradually relaxed by thermally activated processes (which cause long-term aging); 5) insensitive to applied load. _______________ *low density C-S-H?

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Intriguing Consequences of Nano-Porosity with Strongly Hydrophyllic Surfaces Hysteretic sorption isotherms, disjoining presures in nano-pores, and diffusion equation Picket effect, or drying creep Transitional thermal creep Multi-year (multi-decade) aging, or hardening ~20-fold permeability drop at decreasing humidity Delayed thermal dilatation and its humidity dependence 100-fold permeability jump when exceeding 100 o C

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BET (Brunauer-Emmett-Teller) isotherm for multi-layer adsorption: —is reversible! Why?—Longitudinal interactions ignored Typical Isotherms of Adsorbate Content versus Relative Vapor Pressure REALITY

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Classical Examples of Hysteresis of Desorption-Sorption Isotherms of Adsorbate Mass vs. Relative Vapor Pressure For > 60 years, the hysteresis has been attributed to ”nano-pore collapse”. — Can that be true? cement compacts hardened cement paste

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Chemical potentials per unit mass: Free Hindered Continuum Thermodynamics of Hindered Adsorption Disjoining pressure (typically > 100 MPa)

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By integration: Longitudinal and transverse (disjoining) pressures in free and hindered adsorption layers: Introduce pressure ratio: Disjoining pressure by continuum thermodynamics: (free layer, biaxial stress) (hindered layer, triaxial stress)

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Interatomic or Intermolecular Potential and Repulsive or Attractive Forces

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Different numbers of adsorption layers with the same chemical potential per molecule Two or three layers: One or two layers:

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Jumps of misfit disjoining pressure Δp d at filling of continuously diverging nanopore Continuum disjoining pressure Misfit disjoining pressure Misfit tension 3

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Misfit transverse pressure: Can the chemical potentials per adsorbate molecule be equal for n and n+1 layers in the pore? f

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Transverse pressure at critical coordinate makes a jump: Equality occurs at critical coordinates: Transverse pressures at critical coordinates: Misfit chemical potential + continuum chemical potential = total chemical potential

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Δp d and in a diverging nanopore Sequential snapthroughs of chemical potential Mass content Misfit disj. pressure Misfit chem. potential ΔμdΔμd

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Humidity Snapthroughs of adsorbate mass h w Sequential Snapthroughs During Desorption and Sorption

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Analogy with snap-through buckling of an arch or shell

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Misfit disjoining pressure in step-wise nanopore Disj. Pressure Chem. Potential Adsorbate Mass

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Snapthrough in a system of nanopores communicating through vapor phase

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Superposition of hysteretic loops from many nanopores

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1.Processes without characteristic time and asymptotic limit combination of power laws. Transitions by asymptotic matching. 2. Solidification process – Thermodynamic restriction on layers solidified on pore walls in stress-free state 3.Disjoining pressure and microprestress relaxation (load-bearing hindered adsorbed water, its diffusion in nanopores): …a) sorption hysteresis, b) drying creep, c) long-term aging, d) transitional thermal creep 4. Capillarity and surface tension of liquid pore water 5. Processes controlled by activation energy Q – size effect on drying half-time 7.Rate of chemical processes causing autogeneous volume change Summary of Theoretical and Physical Foundations of Model B3 In C-S-H gel: Rate of interatomic bond breaks Pores capillary nanopores D2 D2

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Without collapse and fatalities, and without the ethics resolution of SEW Congress, these results might have never become known, and old practice would continue. Many engineers do not care about troubles >20 years later. Ethics codes of engrg. societies must be updated. 55 min. Thank you. Questions? EPILOGUE Google “Bazant”, download pdf’s: 498, 504, P216 and detailed report. For background: S43, 54, 243, 326, 365, 436 (.pdf) 0 2000 4000 6000 8000 0 -0.8 -1.2 -1.6 t, time from construction end, days Mean Deflections (m) ACI (3D) CEB (3D) GL (3D) JSCE (3D) B3 (3D) (set1) B3 (3D) (set2) -0.4 CEB (1D, SOFiSTiK)

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flow viscoelastic Model B3 (1995) Based on Solidification Theory (1988 ) Compliance rate: b) Creep and Shrinkage at Variable h and T : Alt. I. Approximate mean over wall thickness: aging nonaging = stress duration) asymptotic elastic drying creep a) Basic Creep Compliance: ( Mean drying creep (Pickett effect): Mean shrinkage: Half-time:

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1) Microprestress-Solidification Theory (NU 1996) Relaxation of microprestress: s(x,t) Reduced time for creep rate: 3) Free shrinkage rate: Henry Eyring 1901-1981 Drying creep (Pickett effect) Replace: 2) Processes controlled by activation energy Reduced time for hydration: h = h(x,t) = R.H. in pores from the diffusion equation s = consequence of nanoporosity Alt. II. Point constitutive law:

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EXCESSIVE CREEP DEFLECTIONS OF PRESTRESSED SEGMENTAL BRIDGES: A WAKE-UP CALL FOR DESIGN CODES AND CONSEQUENCES OF NANO-POROSITY ZDENĚK P. BAŽANT COLLABORATORS: QIANG YU, MIJA HUBLER AND ROMAN WENDNER SPONSORS: NSF, DoT UNIVERSITY OF WISCONSIN, MILWAUKEE, 10/28/2011

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Stepwise loading 2.5 m 0.25 m Analytical (CEB 90) Rate-type (ABAQUS) Integral-type (SOFiSTiK) 1 10 100 1000 10000 1.4 2.8 Time (days) Deformation (mm) 0 Creep after 30 years Plain concrete column Fig. 5

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Deflections [in m ] predicted by 3D finite elements using models ACI, CEB, GL, JSCE, and B3 (Sets 1, 2) ACI: Recommendation 1971, reapproved 2008; CEB (fib): Eur. Concrete Comm.; JSCE: Japan Soc. of Civil Engrs.; GL: Gardner & Lockman (Canada); B3: Bazant & Baweja 1995, 2000 (Northwestern). 0 2000 4000 6000 8000 0 -0.4 -0.8 -1.2 -1.6 t, time from construction end, days Deflection (m) ACI CEB GL JSCE B3 (Set 1) B3 (Set 2) CEB-72 prediction in design 100 1000 10000 0 -0.4 -0.8 -1.2 -1.6 t, days, log scale Deflection (m) 10 1 ACI CEB GL JSCE B3 (Set 1) B3 (Set 2)

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