Materials and Structures

, Volume 49, Issue 10, pp 4217–4227 | Cite as

Sensitivity analysis of creep models considering correlation

Original Article


Correlations between the parameters involved in creep models are relatively complex, resulting in difficulties to identify the contribution of each parameter on the predicted creep and reduce creep uncertainty. Sensitivity analysis is a method to quantify the contribution of those parameters. Based on six creep models, B3, B4, ACI-209, MC90, fib MC 2010 and GL2000, the sensitivity of eight parameters, water cement ratio w/c, aggregate cement ratio a/c, cement content c, 28-day compressive strength f cm, 28-day elasticity modulus E 28, effective thickness of specimen D, temperature T, and relative humidity H, to the models was analyzed. An updated creep database, NU database, was used to obtain the statistical characters and correlation matrix of the parameters. For these six creep models, direct and indirect path coefficients of each parameter were calculated by using Path Analysis and the path diagrams of the six creep models were obtained. It can be found that there are still some issues in the existing creep models, that coupling relation between the parameters has not been paid enough attentions. Furthermore, concerning the nonlinear relation between parameters, sensitivity of the creep to the parameters were decomposed into correlated and uncorrelated parts by using back propagation artificial neural network. The sensitivity of the six models to each parameter differs from each other, and the basic parameters are identified in the six models by using path analysis and sensitivity analysis.


Concrete Creep models Sensitivity decomposition Path analysis BP ANN 



The authors gratefully acknowledge the financial support by Natural Science Foundation of China (Grant Nos. 51078027 and 51278037) and the Fundamental Research Funds for the Central Universities (Grant No. 2013JBM011).


  1. 1.
    Ang AHS, Tang WH (1975) Probability concepts in engineering planning & design, vol I—basic principles. Wiley, New YorkGoogle Scholar
  2. 2.
    Keitel H, Dimmig-Osburg A, Vandewalle L, Schueremans L (2012) Selecting creep models using Bayesian methods. Mater Struct 45(10):1513–1533CrossRefGoogle Scholar
  3. 3.
    Pan ZF, Li B, Lu ZT (2013) Re-evaluation of CEB-FIP 90 prediction models for creep and shrinkage with experimental database. Constr Build Mater 38:1022–1030CrossRefGoogle Scholar
  4. 4.
    Saltelli A, Ratto M, Andres T, Campolongo F, Cariboni J, Gatelli D, Saisana M, Tarantola S (2008) Global sensitivity analysis. The primer. Wiley, New YorkMATHGoogle Scholar
  5. 5.
    Bazant ZP, Baweja S (1995) Justification and refinements of model B3 for concrete creep and shrinkage—statistics and sensitivity. Mater Struct 28(7):415–430CrossRefGoogle Scholar
  6. 6.
    Teplý B, Keršner Z, Novák D (1996) Sensitivity study of BP-KX and B3 creep and shrinkage models. Mater Struct 29(8):500–505CrossRefGoogle Scholar
  7. 7.
    Keitel H, Dimmig-Osburg A (2010) Uncertainty and sensitivity analysis of creep models for uncorrelated and correlated input parameters. Eng Struct 32(11):3758–3767CrossRefGoogle Scholar
  8. 8.
    American Concrete Institute (ACI) (1997) Prediction of creep, shrinkage, and temperature effects in concrete structures. Manual of Concrete Practice, Farmington HillsGoogle Scholar
  9. 9.
    Fédération Internationale du Béton, Comite Euro-Internationaldu (1993) CEB-FIP model code 1990: design code. No. 213 214Google Scholar
  10. 10.
    Fédération Internationale du Béton (1999) Structural concrete: textbook on behaviour, design and performance: updated knowledge of the CEB-FIP model code 1990 (vol 1). FIB-Féd. Int. du BétonGoogle Scholar
  11. 11.
    Fédération Internationale du Béton (2012) Model code 2010 final draft, vol 1, Bulletin 65, and vol 2, Bulletin 66, Lausanne, SwitzerlandGoogle Scholar
  12. 12.
    Gardner NJ, Lockman MJ (2001) Design provisions for drying shrinkage and creep of normal-strength concrete. ACI Mater J 98(2):159–167Google Scholar
  13. 13.
    Bazant ZP, Baweja S (1995) Creep and shrinkage prediction model for analysis and design of concrete structures-model B3. Mater Struct 28(6):357–365CrossRefGoogle Scholar
  14. 14.
    Bazant ZP, Hubler MH, Wendner R (2015) Model B4 for creep, drying shrinkage and autogenous shrinkage of normal and high-strength concretes with multi-decade applicability. Mater Struct 48:753–770CrossRefGoogle Scholar
  15. 15.
    Hubler M, Wendner R, Bažant ZP (2015) Comprehensive database for concrete creep and shrinkage: analysis and recommendations for testing and recording. ACI Mater 112(4):547–558. doi: 10.14359/51687452 Google Scholar
  16. 16.
    Bazant ZP, Li GH (2008) Comprehensive database on concrete creep and shrinkage.
  17. 17.
    Bazant ZP, Li GH (2008) Unbiased statistical comparison of creep and shrinkage prediction models. ACI Mater J 105(6):610–621Google Scholar
  18. 18.
    Hoyle RH (1995) Structural equation modeling: concepts, issues, and applications. Sage Publications, Thousand OaksGoogle Scholar
  19. 19.
    Adam I, Mahmoud M, Reda T (2011) Identifying the significance of factors affecting creep of concrete: a probabilistic analysis of RILEM database. Int J Concr Struct Mater 5(2):97–111CrossRefGoogle Scholar
  20. 20.
    Sobol IM (1993) Sensitivity estimates for nonlinear mathematical model. Math Model Comput Exp 1:407–414MathSciNetMATHGoogle Scholar
  21. 21.
    Abdollahi F, Patel RV, Khorasani K (2010) Neural network-based state estimation of nonlinear. Springer, BerlinMATHGoogle Scholar

Copyright information

© RILEM 2015

Authors and Affiliations

  • Bing Han
    • 1
  • Hui-Bing Xie
    • 1
  • Dian-Jie Zhang
    • 2
  • Xiao Ma
    • 1
  1. 1.School of Civil EngineeringBeijing Jiaotong UniversityBeijingPeople’s Republic of China
  2. 2.Central Research Institute of Building and Construction Co., Ltd., MCCBeijingPeople’s Republic of China

Personalised recommendations