1. MOISTURE CURLING OF CONCRETE SLABS FOR AIRFIELD APPLICATIONS ILLINOIS University of Illinois at Urbana-Champaign PIs: David A. Lange Jeffery R. Roesler RAs: Chang Joon Lee Yi-shi Liu Benjamin F. Birch November, 2005

2. OUTLINE Objective of the Project Computer Modeling Laboratory Tests for FAA Material Prediction of NAPTF Single Slab Technology Transfer of Results Future Works

3. OBJECTIVE OF PROJECT To develop a better understanding of concrete material behavior that leads to moisture curling To develop guidelines for future concrete materials selection for airport pavement applications.

4. COMPUTER MODELING

5. WHY IS OUR MODELING CONCEPT USEFUL? ABAQUSDIANAICON Gradient excitations YES Aging concrete properties NOYES Hygrothermal model for shrinkage NO YES Aging effect on creep NOSIMPLESOLIDIFYING NOTE: Assessments are based on the built-in functions of the codes

6. “Instantaneous” response - Static “Delayed” response - Creep Hygrothermal Model Material Models Concrete is an Aging Material Linear Elastic Continuum Solidification Theory [Bazant 1977] “Hygrothermal” response - Shrinkage & Thermal Expansion

7. Stress is a function of porosity and humidity 1m1m 50 nm Drying shrinkage is a mechanical response of porous microstructure to the capillary pressure due to internal humidity reduction

8. Kelvin-Laplace Equation relates RH directly to capillary pressure  – surface tension r – mean pore radius RH – Relative humidity R – Universal gas constant T – Temperature v’ – molar volume of water Capillary pore pressure as a function humidity

9. Two concepts for hygrothermal models Stress Approach: Internal stress based hygrothermal model Strain Approach: Strain based hygrothermal model

10. Internal stress based hygrothermal model

11. Average stresses in porous media: Converts pore pressure to average bulk stress! σ average = p x p c = (pore pressure) x (porosity) P c = 9% σ average = 90.1psi P c = 16.3% σ average = 162.8psi P c = 22.5% σ average = 225.2psi NOTE: σ average = average hydrostatic stress assuming that out-of-plan behavior of the porous medium shows the same behavior with the in-plan behavior pore pressure = 1000psi,

12. Stress in concrete for a given humidity & porosity As applied to Concrete… Where,

13. 1/8 model Finite Element Analysis for a free drying prism Aging Material properties (Porosity, Elastic & Creep response) Humidity History at different depth from drying surface

14. 1/8 model, stress in z direction at age of 30days Deformation and stress distribution in a free drying prism

15. Best fit with the parameter P cal Free drying shrinkage of prism

16. Strain based hygrothermal model

17. Strains in a solid with spherical pores under negative pore pressure (A linear elastic solution) [ Grasley et al., 2003] P

18. Saturation factor (Approximation) [Bazant & Kim, 1991]

19. Fit to experimental data (RH, T, shrinkage) NOTE: simple linear model for shrinkage 

20. LABORATORY TESTS TO CALIBRATE MODEL FOR FAA HIGH-FA CONCRETE

21. Lab Test: Strength Development Rate Uniaxial Compressive StrengthSplit Tensile Strength

22. Lab Test : Stress-strain & Young’s modulus Uniaxial compressive test with axial & lateral strains Stress-strain Stress-lateral dilation Young’s modulus 28 days 7 days 28 days 7 days

23. Lab Test: Temperature, RH & shrinkage Free drying shrinkage test + internal temperature & relative humidity Drying Internal temperature Drying shrinkage Internal humidity

24. Lab Test - Creep Sealed testExposed to ambient Drying Sealed Basic creep Total deformation

25. PREDICTION OF NAPTF SLAB

26. “Instantaneous” response - Static “Delayed” response - Creep Material Models for Prediction Shrinkage & Thermal Expansion Linear Elastic Model Bazant ’ s Solidification Theory Const. creep Poisson ’ s ratio Strain based Hygrothermal Model for Shrinkage Different shrinking & expanding rates for drying & wetting Linear relation for thermal expansion

27. ¼ modeling using symmetric boundary conditions INPUTS – Finite Element Mesh & Boundary Conditions 7.5ft 11 in. Non-linear spring for base contact

28. INPUTS – Material Parameters from Lab. tests Parameters for the material model set were calibrated based on the Lab. material test results. BASIC CREEP ELASTIC MODULUS SHRINKAGE

29. INPUTS – Internal Temperature & RH from NAPTF test TEMPERATURERELATIVE HUMIDITY Internal humidity and temperature measured at the NAPTF were applied to the FE model

30. OUTPUTS - Deformation & Stresses A B Age = 68days, Mag. = 100xAge = 68days Deformation map Max. Principle stress 234 psi

31. Lift-off displacement Deformation Comparison A VD-1 VD-4 CL-3 VD-5 CL-4 CL-2 CL = Clip gauge VD = Vertical Displacement Transducer CL VD

32. Lift-off displacement Deformation Comparison B VD-2

33. TECHNOLOGY TRANSFER OF RESULTS

34. Finite Element Analysis Code

35. ICON ver 0.1.0 Finite Element Analysis Code 1.ICON is a FEA code written in C++ for deformation and stress prediction.  OOP (Object Oriented Programming)  Effective in code maintenance, update 2.ICON is specialized for aging concrete & time dependent excitations  Material properties as functions of time  Internal humidity & temperature as functions of time  Loads & BCs, as functions of time 3. ICON is a Standalone code  Previous version required MATLAB engine for a sparse matrix solver.  Current version uses TAUCS( a library for a sparse matrix solver). ICON can be run as a standalone program.

36. ICON ver 0.1.0 Finite Element Analysis Code ELEMENTS: 20-node solid element 8-node solid element 2-node spring 2-node bar-element

37. ICON ver 0.1.0 Finite Element Analysis Code MATERIAL: Linear elastic Solidifying material model for creep Internal stress based hygrothermal model Strain based hygrothermal model

38. Structure of ICON input file

39. 1. NODE section  nodal coordinates 2. ELEMENT section  element connectivity, properties 3. GROUP section  group info. (node & element set) for easy access to the model 4. MATERIAL section  material info. 5. CONDITION section  loads, BCs, RH, temperature, age 6. ASSIGN section  CONDITIONs are ASSIGNed to GROUPs 7. CONTROL section  analysis duration, time interval, convergence criterion, etc. Structure of ICON input file

40. NODE: … ELEMENT: … GROUP: … … Input file format

41. MATERIAL: for for [ ] CONDITION: … ASSIGN: … Input file format

42. CONTROL: … Input file format

43. Modeling Procedure MSC.Patran- modeling geometry model.inp ICON – Finite Element Analysis Generate mesh data for ICON Read input file model.res Write analysis results MSC.Patran- graphical postprocessing Read result file Add materials & other conditions(BC, RH, T)

44. Modeling Procedure MSC.Patran- modeling geometry

45. Modeling Procedure model.inp

46. Modeling Procedure ICON – Finite Element Analysis

47. Modeling Output File model.res

48. Modeling Results MSC.Patran- graphical post-processing

49. FUTURE WORK

50. Lab Tests: Drying/Wetting test Scale-down single slab test Computer Modeling: Modeling Twin slabs Application with the models using various drying scenario Technology Transfer of Results: Users Manual for ICON Anticipated Completion: Summer 2006 Future Features? Prediction of internal temperature & humidity Graphical pre- and post-processor user interface