Advertisement

Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Prediction of autogenous shrinkage in concrete from material composition or strength calibrated by a large database, as update to model B4

  • 476 Accesses

  • 3 Citations

Abstract

In modern concretes, the autogenous shrinkage, i.e., the shrinkage of sealed specimens, is much more important than it is in traditional concretes. It dominates the shrinkage of thick enough structural members even if exposed to drying. A database of 417 autogenous shrinkage tests, recently assembled at Northwestern University, is exploited to develop empirical predictive equations, which improve significantly those embedded in RILEM Model B4. The data scatter is high and the power law (time)0.2 is found to be optimal for times ranging from hours to several decades of years, as the test data give no hint of upper bound. Statistics of data fitting yields the approximate dependence of the power law parameters on the water-cement and aggregate-cement ratios, cement type, additives such as the blast furnace slag and silica fume, and curing type and duration. Alternatively, the power law parameters can be reasonably well predicted from the compression strength alone. Since some database entries do not report all these composition parameters and others do not report the compressive strength, and since the concrete strength is often the only material property specified in design, two types of models are formulated—composition based, and strength based. Both are verified by statistical comparisons with individual tests, and optimized by nonlinear statistical regression of the entire database, so as to minimize the coefficient of variation of deviations from the data points normalized by the overall data mean. The regression is weighted so as to compensate for the bias due to crowding of data in the short-time range. Statistical comparisons with the prediction models in the JSCE code, Eurocode and CEB MC90-99 code (identical to fib Model Code 2010) show the present model to give significantly better data fits. Finally it is emphasized that, in presence of external drying and creep, accurate predictions will require treating the autogenous shrinkage as a consequence of pore humidity drop caused jointly by self-desiccation due to hydration and by moisture diffusion, and solving the time evolution of humidity profiles. The present model is proposed as an update for the autogenous shrinkage formula in model B4, although recalibration of the whole B4 would be needed.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

References

  1. 1.

    Bažant ZP, Hubler MH, Yu Q (2011) Excessive creep deflections: an awakening. Concr Int 33(8):44–46

  2. 2.

    Bažant ZP, Hubler MH, Yu Q (2011) Pervasiveness of excessive segmental bridge deflections: wake-up call for creep. ACI Struct J 108(6):766

  3. 3.

    Bažant ZP, Jirásek M, Hubler M, Carol I (2015) RILEM draft recommendation: TC-242-MDC multi-decade creep and shrinkage of concrete: material model and structural analysis Model B4 for creep, drying shrinkage and autogenous shrinkage of normal and high-strength concretes with multi-decade applicability. Mater Struct 48(4):753–770

  4. 4.

    Bažant ZP, Yu Q, Li G-H (2012) Excessive long-time deflections of prestressed box girders. I: Record-span bridge in Palau and other paradigms. J Struct Eng 138(6):676–686

  5. 5.

    Bažant Z, Najjar L (1972) Nonlinear water diffusion in nonsaturated concrete. Matériaux et Construction 5(1):3–20

  6. 6.

    Rahimi-Aghdam S, Bažant ZP, Qomi MA (2017) Cement hydration from hours to centuries controlled by diffusion through barrier shells of CSH. J Mech Phys Solids 99:211–224

  7. 7.

    Rahimi-Aghdam S, Rasoolinejad M, Bažant ZP (2019) Moisture Diffusion in Unsaturated Self-Desiccating Concrete with Humidity-Dependent Permeability and Nonlinear Sorption Isotherm. J Eng Mech 145(5):04019032

  8. 8.

    Baroghel-Bouny V, Mounanga P, Khelidj A, Loukili A, Rafai N (2006) Autogenous deformations of cement pastes: part II. W/C effects, micro–macro correlations, and threshold values. Cem Concr Res 36(1):123–136

  9. 9.

    Rasoolinejad M, Rahimi-Aghdam S, Bažant ZP (2018) Statistical filtering of useful concrete creep data from imperfect laboratory tests. Mater Struct 51(6):153

  10. 10.

    Lynam CG (1934) Growth and movement in Portland cement concrete. Oxford University Press, London

  11. 11.

    Davis HE (1940) Autogenous volume change of concrete. Proc ASTM 40:1103–1110

  12. 12.

    Jensen OM, Hansen PF (2001) Autogenous deformation and RH-change in perspective. Cem Concr Res 31(12):1859–1865

  13. 13.

    Tazawa E-I (2014) Autogenous shrinkage of concrete. CRC Press, Boca Raton

  14. 14.

    Holt EE (2001) Early age autogenous shrinkage of concrete, vol 446. Technical Research Centre of Finland, Espoo

  15. 15.

    Tazawa E-I, Miyazawa S, Kasai T (1995) Chemical shrinkage and autogenous shrinkage of hydrating cement paste. Cem Concr Res 25(2):288–292

  16. 16.

    Gawin D, Pesavento F, Schrefler BA (2006) Hygro-thermo-chemo-mechanical modelling of concrete at early ages and beyond. Part I: Hydration and hygro-thermal phenomena. Int J Numer Methods Eng 67(3):299–331

  17. 17.

    Grasley ZC, Leung CK (2011) Desiccation shrinkage of cementitious materials as an aging, poroviscoelastic response. Cem Concr Res 41(1):77–89

  18. 18.

    Hua C, Acker P, Ehrlacher A (1995) Analyses and models of the autogenous shrinkage of hardening cement paste: I. Modelling at macroscopic scale. Cem Concr Res 25(7):1457–1468

  19. 19.

    Luan Y, Ishida T (2013) Enhanced shrinkage model based on early age hydration and moisture status in pore structure. J Adv Concr Technol 11(12):360–373

  20. 20.

    Lura P, Jensen OM, van Breugel K (2003) Autogenous shrinkage in high-performance cement paste: an evaluation of basic mechanisms. Cem Concr Res 33(2):223–232

  21. 21.

    Bažant ZP, Donmez A (2016) Extrapolation of short-time drying shrinkage tests based on measured diffusion size effect: concept and reality. Mater Struct 49(1–2):411–420

  22. 22.

    Dönmez A, Bažant ZP (2016) Shape factors for concrete shrinkage and drying creep in model B4 refined by nonlinear diffusion analysis. Mater Struct 49(11):4779–4784

  23. 23.

    Bentz DP (1997) Three-dimensional computer simulation of Portland cement hydration and microstructure development. J Am Ceram Soc 80(1):3–21

  24. 24.

    Bentz DP, Garboczi EJ (1990) Digitised simulation model for microstructural development. Ceram Trans 16:211–226

  25. 25.

    Di Luzio G, Cusatis G (2009) Hygro-thermo-chemical modeling of high performance concrete. I: Theory. Cem Concr Compos 31(5):301–308

  26. 26.

    Di Luzio G, Cusatis G (2009) Hygro-thermo-chemical modeling of high-performance concrete. II: Numerical implementation, calibration, and validation. Cem Concr Compos 31(5):309–324

  27. 27.

    Jennings HM, Johnson SK (1986) Simulation of microstructure development during the hydration of a cement compound. J Am Ceram Soc 69(11):790–795

  28. 28.

    Lin F, Meyer C (2009) Hydration kinetics modeling of Portland cement considering the effects of curing temperature and applied pressure. Cem Concr Res 39(4):255–265

  29. 29.

    Navi P, Pignat C (1996) Simulation of cement hydration and the connectivity of the capillary pore space. Adv Cem Based Mater 4(2):58–67

  30. 30.

    Pathirage M, Bentz DP, Di Luzio G, Masoero E, Cusatis G (2018) A multiscale framework for the prediction of concrete self-desiccation. In: Computational modelling of concrete structures: proceedings of the conference on computational modelling of concrete and concrete structures (EURO-C 2018), Feb 26–March 1, 2018, Bad Hofgastein, Austria. CRC Press, pp 203

  31. 31.

    Nishiyama M (2009) Mechanical properties of concrete and reinforcement. J Adv Concr Technol 7(2):157–182

  32. 32.

    Holt E, Leivo M (2004) Cracking risks associated with early age shrinkage. Cem Concr Compos 26(5):521–530

  33. 33.

    Schiessl P, Beckhaus K, Schachinger I, Rucker P (2004) New results on early-age cracking risk of special concrete. Cem Concr Aggreg 26(2):1–9

  34. 34.

    Sellevold E (1994) High performance concrete: early volume change and cracking tendency. In: Thermal cracking in concrete at early ages, pp 229–236

  35. 35.

    Tazawa E (1992) Autogeneous shrinkage caused by self desiccation in cementitious material. In: 9th International congress on the chemistry of cement, New Delhi, pp 712–718

  36. 36.

    Ziegeldorf S, Müller H, Plöhn J, Hilsdorf H (1982) Autogenous shrinkage and crack formation in young concrete. In: International conference on concrete of early ages, pp 83–88

  37. 37.

    Igarashi S, Bentur A, Kovler K (1999) Stresses and creep relaxation induced in restrained autogenous shrinkage of high-strength pastes and concretes. Adv Cem Res 11(4):169–177

  38. 38.

    Shah SP, Weiss WJ, Yang W (1998) Shrinkage cracking-can it be prevented? Concr Int 20(4):51–55

  39. 39.

    Japan Society of Civil Engineers (JSCE) (2007) Standard specification for concrete structures. Structural performance verification

  40. 40.

    Comité Européen de Normalisation (2004) Design of concrete structurespart 1-1: general rules and rules for buildings. Eurocode 2, EN 1992-1-1: 2004: E

  41. 41.

    Fédération Internationale Du Béton (1999) Structural concrete: textbook on behaviour, design and performance: updated knowledge of the CEB/FIP Model Code 1990

  42. 42.

    Beverly P (2013) Fib model code for concrete structures 2010. Ernst & Sohn, Hoboken

  43. 43.

    Neville AM (1995) Properties of concrete, vol 4. Longman, London

  44. 44.

    Swayze M (1960) Discussion on: Volume changes of concrete. In: Proceedings of 4th international symposium on the chemistry of cement, pp 700–702

  45. 45.

    Bennett E, Loat D (1970) Shrinkage and creep of concrete as affected by the fineness of Portland cement. Mag Concr Res 22(71):69–78

  46. 46.

    Miyazawa S, Tazawa E (2005) Prediction model for autogenous shrinkage of concrete with different type of cement. In: Proceedings of the fourth international research seminar, Gaithersburg, Maryland, USA

  47. 47.

    Tazawa E-I, Miyazawa S (1995) Influence of cement and admixture on autogenous shrinkage of cement paste. Cem Concr Res 25(2):281–287

  48. 48.

    Eppers S, Muller C (2008) Autogenous shrinkage strain of ultra-high-performance concrete (UHPC). In: Proceeding of the 2nd international symposium on ultra high performance concrete. Kassel University Press, Kassel, pp 433–441

  49. 49.

    Jensen M, Hansen PF (1996) Autog enous deformation and change of the relative humidity in silica fume-modified cement paste. Mater J 93(6):539–543

  50. 50.

    Jensen OM, Hansen PF (1995) Autogenous relative humidity change in silica fume-modified cement paste. Adv Cem Res 7(25):33–38

  51. 51.

    Persson B (1997) Self-desiccation and its importance in concrete technology. Mater Struct 30(5):293–305

  52. 52.

    Zhang M, Tam C, Leow M (2003) Effect of water-to-cementitious materials ratio and silica fume on the autogenous shrinkage of concrete. Cem Concr Res 33(10):1687–1694

  53. 53.

    Buil M, Delage P (1987) Some further evidence on a specific effect of silica fume on the pore structure of Portland cement mortars. Cem Concr Res 17(1):65–69

  54. 54.

    Igarashi S-I, Watanabe A, Kawamura M (2005) Evaluation of capillary pore size characteristics in high-strength concrete at early ages. Cem Concr Res 35(3):513–519

  55. 55.

    Meddah MS, Tagnit-Hamou A (2009) Pore structure of concrete with mineral admixtures and its effect on self-desiccation shrinkage. Mater J 106(3):241–250

  56. 56.

    Jiang Z, Sun Z, Wang P (2005) Autogenous relative humidity change and autogenous shrinkage of high-performance cement pastes. Cem Concr Res 35(8):1539–1545

  57. 57.

    Lee K, Lee H, Lee S, Kim G (2006) Autogenous shrinkage of concrete containing granulated blast-furnace slag. Cem Concr Res 36(7):1279–1285

  58. 58.

    Tazawa E, Miyazawa S (1997) Influence of constituents and composition on autogenous shrinkage of cementitious materials. Mag Concr Res 49(178):15–22

  59. 59.

    Eppers S, Mueller C (2007) On the examination of the autogenous shrinkage cracking propensity by means of the restrained ring test with particular consideration of the temperature influences. VDZ concrete technology reports, 2009, pp 57–70

  60. 60.

    Yan P, Chen Z, Wang J, Zheng F (2007) Autogenous shrinkage of concrete prepared with the binders containing different kinds of mineral admixture. In Proceedings of the 12th international conference on chemistry of cement, Canada

  61. 61.

    Feldman RF (1983) Significance of porosity measurements on blended cement performance. Spec Publ 79:415–434

  62. 62.

    Staquet S, Espion B (2004) Evolution of the thermal expansion coefficient of UHPC incorporating very fine fly ash and metakaolin. In: International RILEM symposium on concrete science and engineering: a tribute to Arnon Bentur. RILEM Publications SARL

  63. 63.

    Khayat K, Mitchell D (2009) Self-consolidating concrete for precast, prestressed concrete bridge elements, vol 628. Transportation Research Board, Washington, DC

  64. 64.

    Hobbs D (1974) Influence of aggregate restraint on the shrinkage of concrete. J Proc 71(9):445–450

  65. 65.

    Shah SP, Ahmad SH (1994) High performance concrete. Properties and applications. McGraw-Hill, New York

  66. 66.

    Bjøntegaard Ø, Hammer T, Sellevold EJ (2004) On the measurement of free deformation of early age cement paste and concrete. Cem Concr Compos 26(5):427–435

  67. 67.

    Jensen OM, Hansen PF (1999) Influence of temperature on autogenous deformation and relative humidity change in hardening cement paste. Cem Concr Res 29(4):567–575

  68. 68.

    Loukili A, Chopin D, Khelidj A, Le Touzo J-Y (2000) A new approach to determine autogenous shrinkage of mortar at an early age considering temperature history. Cem Concr Res 30(6):915–922

  69. 69.

    Kamen A, Denarie E, Brühwiler E (2007) Thermal effects on physico-mechanical properties of ultra-high-performance fiber-reinforced concrete. ACI Mater J 104(4):415

  70. 70.

    Staquet S, Boulay C, DAloïa L, Toutlemonde F (2006) Autogenous shrinkage of a self-compacting VHPC in isothermal and realistic temperature conditions. In: 2nd International RILEM symposium on advances in concrete through science and engineering, pp 361. RILEM Publications SARL

  71. 71.

    Turcry P, Loukili A, Barcelo L, Casabonne JM (2002) Can the maturity concept be used to separate the autogenous shrinkage and thermal deformation of a cement paste at early age? Cem Concr Res 32(9):1443–1450

  72. 72.

    Baroghel-Bouny V, Mounanga P, Loukili A, Khelidj A (2004) From chemical and microstructural evolution of cement pastes to the development of autogenous deformations. Spec Publ 220:1–22

  73. 73.

    Bjøntegaard Ø, Sellevold E (2001) Interaction between thermal dilation and autogenous deformation in high performance concrete. Mater Struct 34(5):266–272

  74. 74.

    Lura P, van Breugel K (2003) Effect of curing temperature on autogenous deformations of cement paste and high performance concrete for different cement types. In: 11th International congress on the chemistry of cement: proceedings, South Africa, pp 1616–1625

  75. 75.

    Mounanga P, Baroghel-Bouny V, Loukili A, Khelidj A (2006) Autogenous deformations of cement pastes: part I. Temperature effects at early age and micro–macro correlations. Cem Concr Res 36(1):110–122

  76. 76.

    Mounanga P, Loukili A, Bouasker M, Khelidj A, Coué R (2006) Effect of setting retarder on the early age deformations of self-compacting mortars. In: International RILEM conference on volume changes of hardening concrete: testing and mitigation, pp 311–320. RILEM Publications SARL

  77. 77.

    Persson B (2005) On the temperature effect on self-desiccation of concrete. In: Proceedings of the 4th international research seminar on self-desiccation and its importance in concrete technology, Gaithersburg, Maryland, USA. Division Building Materials, Lund Institute of Technology, Lund, Sweden, pp 101–124

  78. 78.

    Bažant ZP, Baweja S (1995) Justification and refinements of model B3 for concrete creep and shrinkage 1. statistics and sensitivity. Mater Struct 28(7):415–430

  79. 79.

    Collins TM (1989) Proportioning high-strength concrete to control creep and shrinkage. Mater J 86(6):576–580

  80. 80.

    Bažant Z, Panula L (1978) Practical prediction of time-dependent deformations of concrete. Matériaux et Construction 11(5):317–328

  81. 81.

    Bažant ZP, Li G-H (2008) Comprehensive database on concrete creep and shrinkage. ACI Mater J 105(6):635–637

  82. 82.

    Hubler MH, Wendner R, Bažant ZP (2015) Comprehensive database for concrete creep and shrinkage: analysis and recommendations for testing and recording. ACI Mater J 112(4):547

  83. 83.

    Wendner R, Hubler MH, Bažant ZP (2015) Optimization method, choice of form and uncertainty quantification of model B4 using laboratory and multi-decade bridge databases. Mater Struct 48(4):771–796

  84. 84.

    Troxell G (1958) Log-time creep and shrinkage tests of plain and reinforced concrete. ASTM 58:1101–1120

  85. 85.

    Brooks J (2000) Elasticity, creep, and shrinkage of concretes containing admixtures. Spec Publ 194:283–360

  86. 86.

    Bažant ZP, Li G-H (2008) Unbiased statistical comparison of creep and shrinkage prediction models. ACI Mater J 105(6):610

  87. 87.

    Bažant ZP, Jirásek M (2018) Creep and hygrothermal effects in concrete structures, vol 225. Springer, Berlin

  88. 88.

    Bažant ZP, Rahimi-Aghdam S (2016) Diffusion-controlled and creep-mitigated ASR damage via microplane model. I: Mass concrete. J Eng Mech 143(2):04016108

  89. 89.

    Rahimi-Aghdam S, Bažant ZP, Caner FC (2016) Diffusion-controlled and creep-mitigated ASR damage via microplane model. II: Material degradation, drying, and verification. J Eng Mech 143(2):04016109

  90. 90.

    Hubler MH, Wendner R, Bažant ZP (2015) Statistical justification of model B4 for drying and autogenous shrinkage of concrete and comparisons to other models. Mater Struct 48(4):797–814

  91. 91.

    Bažant Z, Dönmez A, Masoero E, Aghdam SR (2015) Interaction of concrete creep, shrinkage and swelling with water, hydration, and damage: nano-macro-chemo. In: CONCREEP 10. ASCE, Washington, DC, pp 1–12

  92. 92.

    Loukili A, Khelidj A, Richard P (1999) Hydration kinetics, change of relative humidity, and autogenous shrinkage of ultra-high-strength concrete. Cem Concr Res 29(4):577–584

  93. 93.

    Persson B (2002) Eight-year exploration of shrinkage in high-performance concrete. Cem Concr Res 32(8):1229–1237

  94. 94.

    Rahimi-Aghdam S, Bažant ZP, Cusatis G (2018) Extended microprestress-solidification theory for long-term creep with diffusion size effect in concrete at variable environment. J Eng Mech 145(2):04018131

  95. 95.

    Mazloom M, Ramezanianpour A, Brooks J (2004) Effect of silica fume on mechanical properties of high-strength concrete. Cem Concr Compos 26(4):347–357

  96. 96.

    Rahimi-Aghdam S, Masoero E, Rasoolinejad M, Bažant ZP (2019) Century-long expansion of hydrating cement counteracting concrete shrinkage due to humidity drop from selfdesiccation or external drying. Mater Struct 52(1):11

  97. 97.

    Ulm F-J, Coussy O (1996) Strength growth as chemo-plastic hardening in early age concrete. J Eng Mech 122(12):1123–1132

  98. 98.

    Pickett G (1956) Effect of aggregate on shrinkage of concrete and a hypothesis concerning shrinkage. J Proc 52(1):581–590

  99. 99.

    Grasley Z, Lange D, Brinks A, DAmbrosia M (2005) Modeling autogenous shrinkage of concrete accounting for creep caused by aggregate restraint. In: Proceedings of the 4th international seminar on self-desiccation and its importance in concrete technology, NIST, Gaithersburg, MD, pp 78–94

  100. 100.

    Bažant ZP, Panula L (1980) Creep and shrinkage characterization for analyzing prestressed concrete structures. PCI J 25(3):86–122

  101. 101.

    Bažant ZP, Yu Q (2005) Designing against size effect on shear strength of reinforced concrete beams without stirrups: II. Verification and calibration. J Struct Eng 131(12):1886–1897

  102. 102.

    Videla C, Carreira DJ, Garner N et al (2008) Guide for modeling and calculating shrinkage and creep in hardened concrete. ACI report, p 209

  103. 103.

    Comite Euro International du Beton (1993) CEB-FIP Model Code 1990. Thomas Telford Publishing. https://doi.org/10.1680/ceb-fipmc1990.35430

  104. 104.

    Nakanishi H, Tamaki S, Yaguchi M, Yamada K, Kinoshita M, Ishimori M, Okazawa S (2003) Performance of a multifunctional and multipurpose superplasticizer for concrete. Spec Publ 217:327–342

Download references

Funding

This study was funded by partial financial support from the U.S. Department of Transportation, provided through Grant 20778 from the Infrastructure Technology Institute of Northwestern University, and from the NSF under Grant CMMI-1129449.

Author information

Correspondence to Zdeněk P. Bažant.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Rasoolinejad, M., Rahimi-Aghdam, S. & Bažant, Z.P. Prediction of autogenous shrinkage in concrete from material composition or strength calibrated by a large database, as update to model B4. Mater Struct 52, 33 (2019). https://doi.org/10.1617/s11527-019-1331-3

Download citation

Keywords

  • Autogenous shrinkage
  • Swelling
  • Predictive model
  • Concrete composition
  • Concrete strength
  • NU database