Disposition. Krympning och krypning av betong. Pantheon, Rom, 120 e Kr. Bakgrund. Luleå! Campus 11/12/2013

Transkript

1 11/12/213 Krympning och krypning av betong Lennart Elfgren Professor emeritus i konstruktionsteknik, LTU ELFORSK Workshop spännkablar i kärnkraftstillämpningar Arlanda, 12 november 213 Disposition Bakgrund Krympning Krypning Exempel - Sprickbildning - Infästningar - Broar Sammanfattning Bakgrund Pantheon, Rom, 12 e Kr K.W. Hatt (197): Notes on the effect of time element in loading reinforced concrete beams. Proc. ASTM, Vol 7, Prestressed Concrete, Eugene Freyssinet (1928- ) Fritz Dischinger (1937- ) Krister Cederwall (197 - ), Chalmers och LTU Adam M Neville (197 - ) Heinrich Trost (198 ) Folker H Wittman (198 -) Zedenek D Bazant (198-) Building of Nuclear Power Plants with prestressed concrete Luleå! Campus ACCEPT - Aging of concrete and civil structures in nuclear power plants 1

2 11/12/213 Avd BYGG (Byggkonstruktion och byggproduktion) Forskningsämnen och laboratorium Konstruktionsteknik, Stålbyggnad, Träbyggnad, Byggproduktion, Complab. Ca 8 personer, ca 65 MSEK, externfinansieringsgrad ca 7 % Avdelningschef Tekn. dr. Martin Nilsson Stålbyggnad Prof. Milan Veljkovic Byggproduktion Prof. Thomas Olofsson Konstruktionsteknik Prof. Mats Emborg Träbyggnad Prof. Lars Stehn Complab Fo.ing. Lars Åström Konstruktionsteknik Prof. /Lekt.: Mats Emborg, prof 6 % Jan-Erik Jonasson, prof 5 % Björn Täljsten, prof 2 % Lennart Elfgren, prof em 2 % Martin Nilsson, univ.lekt 7 % Ulf Ohlsson, univ.lekt Lennart Fransson, forskare Lars Bernspång, univ. lekt 3 % Hans Hedlund, adj professor 2 % Thomas Blanksvärd, bitr univ lekt 2% Gabriel Sas, univ adj 2 % Carina Hannu, FU koordinator, 2 % PhD students: Natalia Sabourova (föräldraledig) Peter Fjellström Johan Larsson Jonny Niilimaa Niklas Bagge Viktoria Bonath Aniket Patil Mohammed Majal Tarek Edress Majid Al-Gburi Katalin Orosz Rasoul Nilforoush - Elforsk Anders Hösthagen (6%) Niklas Johansson (6%) Cosmin Popescu Martin Persson (6%) Mohammad Hatem Mohammed Hasnan Igbal Faez Sayahi Jens Häggström MAINtenance, renewal and improvement of rail INfrastructure to reduce Economic and environmental impact, , 19 partners, 4,7 MEuro Björn Paulsson, UIC/TRV, Project Manager Lennart Elfgren, LTU, Scientific & Technical Coordinator Åby Älv Bridge Test to failure to calibrate assessment methods FEM model Test 12 Sept 213 Thermal Cracking of Concrete at LTU Basic Research Rilem TC 69 Impl. in Codes Rilem TC 119 Developm. of Tools EU: IPACS Modern Concr. (SCC, FA, Sl) Today Comb. T & RH : 9 PhD Thesis 8 Lic Thesis 5 IPACS Reports Material Testing Heat development Drying Temperature movements Moisture movements Creep (short-term test to long-term effects) Strength development (Compression and tension) Fracture condition (tension) Stresses at restraining 2

3 11/12/213 fib Model Code 21 Final Hard Copy Version 213 Tidsberoende deformationer Krympning Normalvärden för krympning Examples of too early and unwanted cracks in infrastructures 3

4 11/12/213 Krypning p g a s c (t o ) Den spänningsvarierande delen e cs (t, t o ) For linear conditions the constitutive equation may be written as Krypkoefficienten Normalvärden för krypkoefficienten Krister Cederwall (197) Reologiska grundmodeller Krypning i förspända pelare. Utgick från Franz Dischingers ekv (1937): ε = σ E 1 + φ dε dt = dσ/dt + σ dφ E E dt motsvarar (a) som är //BC medan betong mer motsvarar (b) som är //AB Krister Cederwall kompenserade för diskrepansen och tog fram uttryck för pelares knäcklast vid krypning ε I = σ I E ε II = σ II t η ε I = σ I E ε II = σ II E 4

5 Deformation /Pa Coefficients a1 & a2, 1/log(time) Relaxation stress, GPa Deformation, 1-12 /Pa Deformation, 1-12 /Pa 11/12/213 Maxwell-kedja LLM (Linear Logarithmic Model) Creep Formula ε = σ E + σ η E σ = σ e η t + ηεconst 1 E e η t τ μ = η μ Retardation time E μ σ μ = σ μ + E μ ε Linear Logaritmic Model, LLM, Jan-Erik Jonasson Mårten Larsson (2) Short-term tests: Creep part in linear time scale 16 KW3_1d, t=.87 d KW3_7d, t= 5.89 d 14 KW3_28d, t= 28 d KW5_1d, t= 1.12 d 12 KW5_7d, t= 6.5 d KW5_28d, t= 28 d 1 KW1_1d, t=.82 d Time after loading, days Creep part in logarithmic time scale Time after loading, days Very young concrete Hardening concrete Mature concrete KW3_1d, t=.87 d KW3_7d, t= 5.89 d KW3_28d, t= 28 d KW5_1d, t= 1.12 d KW5_7d, t= 6.5 d KW5_28d, t= 28 d KW1_1d, t=.82 d From individual fittings to Continuous formualation Robust after conversion to Long-Term Relaxation (Superposition) 12 1 Individual a1& a Solid lines: Creep tests 2 Dashed lines: Individual fitting Time after loading, d 7 a1, Eq. 5 6 a2, Eq. 5 Mix 1 5 Mix 2 4 Mix 1 Mix Equivalent time at loading, d t = 54.1d t =.37d t.25d (6h) t =.25 d t =.37 d t =.54 d t =.79 d t = 1.2 d t = 1.7 d t = 2.5 d t = 3.7 d t = 5.4 d t =7.9 d t = 11.6 d t = 17.1 d t = 25.1 d t = 36.8 d t =54.1 d Note: No stress change-over! Time of setting Time after applied strain, d Example Crack-Free Planning Svinesund Bridge between Sweden and Norway (ready 25) Creep in Bonded Anchors Test Set-up in Borås and Luleå Span width 247m Total bridge length 74m Elevation 5

6 11/12/213 Creep to failure curves for tests in Luleå Creep to failure curves for tests in Borås 6

7 11/12/213 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 1. Clue from Tragic Collapse in Palau 1996 SPONSORS: NSF, DoT UNIVERSITY OF MIAMI, CORAL GABLES, 11//6/211 Box Girder of World Record Span 241 m, Palau, 1977 Segmental Cantilever Construction Koror-Babeldaob Bridge in Palau Built 1977, failed 1996 Babeldaob side (failed first) Ulrich Finsterwalder Eugène Freyssinet Delamination creep buckling of top slab. Sudden loss of prestressing force ~2, ton, emits wave. Trigger of Collapse: Delamination creep buckling of top slab 3 months after remedial prestressing 2. Box girder fails in compression- shear Babeldaob 1. Delamination in top slab 3. Load from Babeldaob side transmitted 5. Section at pier overloaded and fails in compression Top slab subjected to longitudinal compressive forces Delamination buckling 6. Side span slams back on end pier and fails in shear Koror 4. Bridge lifts up and hold-down bars fracture 2. Release of Data on Litigated Failure Sealed in Perpetuity Crack Longit. force 19 MN (214 tons) from 316 tendons in 4 layers 1 layer buckling releases about 5 tons 7

8 Compliance Mean Deflections (m) 11/12/ Why the creep deflections of KB Bridge were so excessive? Diaphragms Three-Dimensional Mesh for Prestressed Box Girder 536 eight-node isoparametric (hexahedral) elements and 6764 steel bar elements Replace history integrals by rate equations for internal variables (partial strains) J (a concept pioneered by Biot) 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. 1 E 1 E s s E s 1 1 s Continuous Spectrum E Age t Age t log (t-t ' ) discrete spectrum Deflections [in m] predicted by 3D finite elements using models ACI, CEB, GL, JSCE, and B3 (Sets 1, 2) 3D element model for ABAQUS B3 (3D) (set2) t, time from construction end, days Fig. 6 KB BRIDGE CEB (1D, SOFiSTiK) JSCE (3D) -.5 ACI (3D) CEB (3D) GL (3D) -1. B3 (3D) (set1) D beam element model in commercial software SOFiSTiK CEB (1D, SOFiSTiK) JSCE (3D) ACI (3D) CEB (3D) GL (3D) B3 (3D) (set1) B3 (3D) (set2) log t, time from construction end, days Summary of Theoretical and Physical Foundations of Model B3 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 si Ei ( t) ei, not si Ei ( t) ei. But s k k ( t) ek 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 Pores capillary 4. Capillarity and surface tension of liquid pore water nanopores 5. Processes controlled by activation energy Q Q / kt In C-S-H gel: Rate of interatomic bond breaks e sinh( s / kt) size effect on drying half-time D 2 Sammanfattning Krympning Uttorkning och hydratisering av cement (autogen) Krypning Lastberoende deformationer Fenomenologiska modeller med empiriska koefficienter Allt bättre modeller för allt bättre betong Fortsatt uppföljning och kalibrering 7. Rate of chemical processes causing autogeneous volume change 8