Issue 60

A. Taibi et alii, Frattura ed Integrità Strutturale, 60 (2022) 416-437; DOI: 10.3221/IGF-ESIS.60.29



) Ea RT

  ( ).exp( A

 

[1]

(1)

,R is the ideal gas constant, T is the temperature   K ,  is the hydration



 

 

1

where a E is the activation energy

. J mol

  ( ) A is the chemical affinity

   1 S given by

degree and

               2 3 4 5 6 ( ) A a b c d e f g (2) where a, b, c, d, e, f and g are constant material parameters which could be identified from a semi-adiabatic test. The energy balance equation, which includes the heat release due to hydration reaction is solved to obtain the temperature evolution [24]:





    ( ) C T k T L



(3)

  3 Jm ,k is the thermal conductivity 

   1 1 Wm K and C is the volumetric heat   

 

In which L is the latent hydration heat

capacity  3 1 Jm K , which is assumed constant. The boundary conditions are assumed to be of convective type. The convective heat flux       2 Wm reads:     

   (

) h Ts Text

(4)

   2 1 Wm K ,   

s T is the temperature on the

where h is the exchange coefficient including convection (after linearization)

surface   K and ext T is the ambient temperature   K [24]. The thermal strain is related to the temperature variation, due to the release of heat by hydration, and the coefficient of thermal expansion  (considered as constant):      TI th (5) As concrete hardens, autogenous shrinkage develops. The autogenous shrinkage is related to the evolution of hydration. Experimental results show that autogenous shrinkage evolution is linear with respect to the hydration degree. The autogenous shrinkage  au could be described by [23] :

        for > 0 k I au

(6)

The evolution of the mechanical parameters (Young's modulus, Poisson's ratio, tensile strength …) with respect to hydration process will be discussed after presenting the mechanical damage model.

D AMAGE PLASTICITY MODEL FOR THE NON - LINEAR BEHAVIOUR OF CONCRETE he non-linear mechanical behaviour of concrete is described by a damage model. The model used has been developed by [19]. The effective stress in the damaged material is related to the macroscopic stress. The relationship between stress and strain tensors is given by: T

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