Skip to main content
SpringerLink
Log in

Stochastic and recursive estimation of the hygro-thermo-chemical-mechanical parameters of concrete through Monte Carlo analysis and extended Kalman filter

  • Research Paper
  • Published:
Structural and Multidisciplinary Optimization Aims and scope Submit manuscript

Abstract

Hygro-thermo-chemical-mechanical models, used to determine the variations over time of temperature, relative humidity and shrinkage induced deformations in concrete components, are characterised by the presence of a large number of input parameters. Some of these parameters can be evaluated on the basis of the concrete mix specifications or from literature data, while the others present a large variability and, in some cases, do not have a precise physical meaning and, for this reason, require the implementation of proper identification strategies. The experimental work involved for this characterisation can be time-consuming and costly because based on the long-term monitoring of the time evolution of the field quantities in specific positions within concrete components. The aim of this paper is to propose and validate recursive identification strategies that exploit, in a step by step fashion, the information coming from the experimentation for the identification of the model input parameters. The influence of different exposure conditions and of different concrete thicknesses are investigated and, for each scenario considered, the expected identification error of each parameter is estimated, within a stochastic context implemented through Monte Carlo analyses and Kalman Filter, as a function of the monitored time.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

Abbreviations

a, b :

Parameters associated with the variation of the degree of cement hydration over time

A c1,A c2,η c :

Parameters associated with the variation of the degree of cement hydration over time

c :

Cement content per unit volume

c t :

Concrete specific heat

D h :

Moisture diffusion coefficient

D 0, D 1, n:

Parameters that control the moisture diffusion and depend on the specific concrete mix

g 1 :

Parameter that governs the shape of the sorption curve

h :

Relative humidity

k c :

Parameter associated with non-evaporable water

k sh :

Parameter that relates the change over time of the free shrinkage deformation to the rate of the relative humidity

\( {\dot{Q}}_{\mathrm{c}} \) :

Rate of heat generation due to cement hydration

\( {\overset{\sim }{Q}}_{\mathrm{c}}^{\infty } \) :

Total heat content per unit cement mass due to cement hydration

RHe :

Ambient relative humidity

T :

Temperature

T e :

Ambient temperature

T 0 :

Reference room temperature

w/c :

Water-to-cement ratio

w n :

Non-evaporable water

w 0 :

Initial water content

α c :

Degree of cement hydration

\( {\alpha}_{\mathrm{c}}^{\infty } \) :

Final value of the cement hydration degree

γ c :

Ratio of the hydration activation energy over the universal gas constant

ε el :

Elastic deformation

ε sh :

Shrinkage deformation

ε tot :

Total deformation

\( {\kappa}_{\mathrm{vg}}^{\mathrm{c}} \) :

Parameter that governs the amount of water contained in the cement gel pores

λ :

Concrete heat conductivity

ρ:

Concrete mass density

References

  • Abyaneh SD, Wong HS, Buenfeld NR (2013) Modelling the diffusivity of mortar and concrete using a three-dimensional mesostructure with several aggregate shapes. Comput Mater Sci 78:63–73

    Google Scholar 

  • Abyaneh SD, Wong HS, Buenfeld NR (2016) Simulating the effect of microcracks on the diffusivity and permeability of concrete using a three-dimensional model. Comput Mater Sci 119:130–143

    Google Scholar 

  • Al-deen S, Ranzi G (2015) Effects of non-uniform shrinkage on the long-term behavior of composite steel-concrete slabs. Int J Steel Struct 15:415–432

    Google Scholar 

  • Azenha M, Sousa C, Faria R, Neves A (2011) Thermo–hygro–mechanical modelling of self-induced stresses during the service life of RC structures. Eng Struct 33:3442–3453

    Google Scholar 

  • Bažant ZP, Najjar LJ (1972) Nonlinear water diffusion in nonsaturated concrete. Mater Constr 5:3–20

    Google Scholar 

  • Benboudjema F, Meftah F, Torrenti JM (2005) Interaction between drying, shrinkage, creep and cracking phenomena in concrete. Eng Struct 27:239–250

    Google Scholar 

  • Bittanti S, Maier G, Nappi A (1985) Inverse problems in structural elastoplasticity: a Kalman filter approach. In: Sawczuk A, Bianchi C (eds) Plasticity today. Elsevier Appl. Sci. Publ, pp 311–329

  • Bocciarelli M, Maier G (2007) Indentation and imprint mapping method for identification of residual stresses. Comput Mater Sci 39:381–392

    Google Scholar 

  • Bocciarelli M, Ranzi G (2018a) Identification of the hygro-thermo-chemical-mechanical model parameters of concrete through inverse analysis. Constr Build Mater 162:202–214

    Google Scholar 

  • Bocciarelli M, Ranzi G (2018b) An inverse analysis approach for the identification of the hygro-thermo-chemical-mechanical model parameters of concrete. Int J Mech Sci 138–139:368–382

    Google Scholar 

  • Bocciarelli M, Bolzon G, Maier G (2005) Parameter identification in anisotropic elastoplasticity by indentation and imprint mapping. Mech Mater 37:855–868

    Google Scholar 

  • Bocciarelli M, Buljak V, Moy CKS, Ringer SP, Ranzi G (2014) An inverse analysis approach based on a POD direct model for the mechanical characterization of metallic materials. Comput Mater Sci 95:302–308

    Google Scholar 

  • Bui HD (1994) Inverse problems in the mechanics of materials: an introduction. CRC Press, Boca Raton FL

    Google Scholar 

  • Cervera M, Oliver J, Prato T (1999) Thermo–chemo–mechanical model for concrete. I: hydration and aging. J Eng Mech ASCE 125:1018–1027

    Google Scholar 

  • Coleman TF, Li Y (1996) An Interior Trust-Region Approach for Nonlinear Minimization Subject to Bounds. SIAM J Optim 6(2):418–445

    MathSciNet  MATH  Google Scholar 

  • Corigliano A, Mariani S (2004) Parameter identification in explicit structural dynamics: performance of the extended Kalman filter. Comput Methods Appl Mech Eng 193:3807–3835

    MATH  Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  • Di Luzio G, Cusatis G (2013) Solidification–microprestress–microplane (SMM) theory for concrete at early age: theory, validation and application. Int J Solids Struct 50:957–975

    Google Scholar 

  • Du M, Jin X, Ye H, Jin N, Tian Y (2016) A coupled hygro-thermal model of early-age concrete based on micro-pore structure evolution. Constr Build Mater 111:689–698

    Google Scholar 

  • Gasch T, Malm R, Ansell A (2016) A coupled hygro-thermo-mechanical model for concrete subjected to variable environmental conditions. Int J Solids Struct 91:143–156

    Google Scholar 

  • Gawin D, Pesavento F, Schrefler BA (2006) Hygro-thermo-chemo-mechanical modelling of concrete at early ages and beyond, part I: hydration and hygrothermal phenomena. Int J Num Methods Eng 67:299–331

    MATH  Google Scholar 

  • Gelb A (1974) Applied optimal estimation. MIT Press, Cambridge, MA

    Google Scholar 

  • Havlásek P, Jirásek M (2016) Multiscale modeling of drying shrinkage and creep of concrete. Cem Concr Res 85:55–74

    Google Scholar 

  • Jirásek M, Havláseka P (2014) Microprestress–solidification theory of concrete creep: reformulation and improvement. Cem Concr Res 60:51–62

    Google Scholar 

  • Jooss M, Reinhardt HW (2002) Permeability and diffusivity of concrete as function of temperature. Cem Concr Res 32:1497–1504

    Google Scholar 

  • Kim JK, Lee CS (1999) Moisture diffusion of concrete considering self-desiccation at early ages. Cem Concr Res 29:1921–1927

    Google Scholar 

  • Kopp RE, Orford RJ (1963) Linear regression applied to system identification for adaptive control systems. AIAA J 1:2300–2306

    MATH  Google Scholar 

  • Ljung L (1979) Asymptotic behavior of the extended Kalman filter as a parameter estimator for linear systems. IEEE Trans Autom Control AC 24:36–50

    MathSciNet  MATH  Google Scholar 

  • Ljung L (1999) System identification. Theory for the user, 2nd edn. Prentice Hall, Englewood Cliffs, NJ

    MATH  Google Scholar 

  • Mariani S, Ghisi A (2007) Unscented Kalman filtering for nonlinear structural dynamics. Nonlinear Dyn 49:131–150

    MATH  Google Scholar 

  • Mroz Z, Stavroulakis GE (2005) Identification of materials and structures. In: CISM Lecture Notes, vol 469. Springer-Verlag, Wien

    Google Scholar 

  • Nguyen T-T, Waldmann D, Bui TQ (2019) Computational chemo-thermo-mechanical coupling phase-field model for complex fracture induced by early-age shrinkage and hydration heat in cement-based materials. Comput Methods Appl Mech Eng 348:1–28

    MathSciNet  Google Scholar 

  • Oh BH, Cha SW (2003) Nonlinear analysis of temperature and moisture distributions in early-age concrete structures based on degree of hydration. ACI Mater J 100:361–370

    Google Scholar 

  • Pantazopoulo SJ, Mills RH (1995) Microstructural aspects of the mechanical response of plain concrete. ACI Mater J 92:605–616

    Google Scholar 

  • Quarteroni A (2000) Modellistica numerica per problemi differenziali. Springer-Verlag, Italia, Milano

    MATH  Google Scholar 

  • Rahimi-Aghdama S, Bažant ZP, Abdolhosseini Qomic MJ (2017) Cement hydration from hours to centuries controlled by diffusion through barrier shells of C-S-H. J Mech Phys Solids 99:211–224

    Google Scholar 

  • Stavroulakis G, Bolzon G, Waszczyszyn Z, Ziemianski L (2003) Inverse analysis. In: Karihaloo B, Ritchie RO, Milne I (eds) Comprehensive structural integrity. Elsevier Science Ltd., Kidlington (Oxfordshire)

    Google Scholar 

  • The Math Works Inc, USA, User’s Guide and Optimization Toolbox, Release 9.3, Matlab 2017

  • Toropov VV, Yoshida F, van der Giessen E (1997) Material parameter identification for large deformation plasticity models. In: Sol H, Oomens H, Cees WJ (eds) Material identification using mixed numerical experimental methods. Kluwer Academic, Dordrecht, pp 81–92

    Google Scholar 

  • Ulm FJ, Coussy O (1995) Modeling of thermo-chemical–mechanical couplings of concrete at early age. J Eng Mech ASCE 121:785–794

    Google Scholar 

  • Wan L, Wendner R, Liang B, Cusatis G (2016) Analysis of the behavior of ultra high performance concrete at early age. Cem Concr Compos 74:120–135

    Google Scholar 

  • Wang Y, Zhou X, Kou M (2018a) Numerical studies on thermal shock crack branching instability in brittle solids. Eng Fract Mech 204:157–184

    Google Scholar 

  • Wang Y, Zhou X, Kou M (2018b) A coupled thermo-mechanical bond-based peridynamics for simulating thermal cracking in rocks. Int J Fract 211:13–42

    Google Scholar 

  • Wang Y, Zhou X, Kou M (2019) An improved coupled thermo-mechanic bond-based peridynamic model for cracking behaviors in brittle solids subjected to thermal shocks. Eur J Mech A Solids 73:282–305

    MathSciNet  MATH  Google Scholar 

  • Wittmann FH (1982) Creep and shrinkage mechanics. In: Bažant ZP, Wittmann FH (eds) Creep and shrinkage of concrete structures. John Wiley & Sons Ltd., Hoboken, pp 129–161

    Google Scholar 

  • Zhou XP, Bi J (2018) Numerical simulation of thermal cracking in rocks based on general particle dynamics. J Eng Mech 144(1):04017156

    Google Scholar 

Download references

Funding

The work in this article was supported by the Australian Research Council through its Future Fellowship scheme (FT140100130).

Author information

Authors and Affiliations

  1. Architecture, Built environment and Construction engineering Department, Politecnico di Milano (Technical University), Milan, Italy

    Massimiliano Bocciarelli

  2. School of Civil Engineering, The University of Sydney, Sydney, NSW, Australia

    Gianluca Ranzi

Authors
  1. Massimiliano Bocciarelli
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gianluca Ranzi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Massimiliano Bocciarelli.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Responsible Editor: Mehmet Polat Saka

Publisher’s note

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

Appendix

Appendix

1.1 Matrices and vectors of the system in (8) are defined as follows

$$ \mathbf{W}=\underset{e}{\cup}\underset{\varOmega_e}{\int }{\mathbf{N}}_e^T\frac{\partial {w}_e}{\partial h}{\mathbf{N}}_e\mathrm{d}\varOmega $$
(A1)
$$ \mathbf{D}=\underset{e}{\cup}\underset{\varOmega_e}{\int }{\mathbf{B}}_e^T{D}_h{\mathbf{B}}_e d\varOmega $$
(A2)
$$ \mathbf{F}=-\underset{e}{\cup}\underset{\varGamma_e}{\int }{\mathbf{N}}_e^T{\mathbf{n}}^T\mathbf{j}\ \mathrm{d}\varGamma -\underset{e}{\cup}\underset{\varOmega_e}{\int }{\mathbf{N}}_e^T\left(\frac{\partial {w}_e}{\partial {\alpha}_c}+\frac{\partial {w}_n}{\partial {\alpha}_c}\right){\dot{\alpha}}_c d\varOmega $$
(A3)
$$ \mathbf{C}=\underset{e}{\cup}\underset{\varOmega_e}{\int }{\mathbf{N}}_e^T\rho {c}_t{\mathbf{N}}_e d\varOmega $$
(A4)
$$ \boldsymbol{\Lambda} =\underset{e}{\cup}\underset{\varOmega_e}{\int }{\mathbf{B}}_e^T\lambda {\mathbf{B}}_e d\varOmega $$
(A5)
$$ \mathbf{Q}=-\underset{e}{\cup}\underset{\varGamma_e}{\int }{\mathbf{N}}_e^T{\mathbf{n}}^T\mathbf{q}\ \mathrm{d}\varGamma +\underset{e}{\cup}\underset{\varOmega_e}{\int }{\mathbf{N}}_e^T{\dot{Q}}_c d\varOmega $$
(A6)

where symbol \( \underset{e}{\cup } \) refers to the assembly operation typical of the finite element approach, and matrices Ne and Be collect shape functions and their spatial derivatives, respectively.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bocciarelli, M., Ranzi, G. Stochastic and recursive estimation of the hygro-thermo-chemical-mechanical parameters of concrete through Monte Carlo analysis and extended Kalman filter. Struct Multidisc Optim 61, 91–110 (2020). https://doi.org/10.1007/s00158-019-02347-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00158-019-02347-y

Keywords

Search

Navigation