Actions during hardening 87
induced in the hardening wall and tensile stresses in the floor. At this point,
the cracking risk will be low, as the floor already has fully developed tensile
strength and the hardening wall is in compression. (However, when the
wall thickness is high, a thermal gradient can occur in the wall itself, possibly leading to surface cracks in the wall, as explained in the previous case
of internal restraint.)
A more dangerous situation is obtained during the cooling phase. The
thermal contraction of the hardening wall will be restrained by the floor.
At this stage, tensile stresses occur in the wall and compressive stresses in
the floor. Through cracks can occur in the hardening wall, going from one
surface to the other. This type of crack formation can have important consequences for water tightness and durability of the wall.
In case no thermal cracking occurs, thermal stresses will remain in the
hardened concrete element as eïgenstresses or self-stresses. These eïgenstresses have to be duly considered as the initial state when further mechanically loading the element.
4.4.1.3 Importance of evolving mechanical properties
In order to better understand the phenomenon of early-age thermal
cracking in hardening concrete elements, it is important to study the
role of the evolving mechanical properties. By means of some elementary
theoretical example, it will be illustrated here that a Young’s modulus
which varies in space and in time (due to the evolution of the hydration
process) has a specific influence on the occurrence of and possible continual thermal stresses.
Consider an elastic body consisting of two halves as illustrated in
Figure 4.12. Both halves have the same time-independent Young’s modulus,
E, but undergo a different temperature variation at time t, namely Δθ 1 and
Δθ 2 . It is supposed that the deformation of the two halves can only happen in one dimension (no transversal expansion, no rotation). It is further
supposed that both halves have a unit length and a unit section, so that
equilibrium equations can further be based on stresses and strains directly.
If both halves were able to deform independently, the situation shown
in Figure 4.12b would occur, showing different thermal dilation and no
stresses. The thermal strains ε 1 and ε 2 can be obtained by:
ε
θ α
1
1
= ∆ ⋅ t
(4.3)
ε
θ α
2
2
= ∆ ⋅ t
(4.4)
in which α t is the coefficient of thermal expansion (CTE), which is considered to be the same for both halves.
induced in the hardening wall and tensile stresses in the floor. At this point,
the cracking risk will be low, as the floor already has fully developed tensile
strength and the hardening wall is in compression. (However, when the
wall thickness is high, a thermal gradient can occur in the wall itself, possibly leading to surface cracks in the wall, as explained in the previous case
of internal restraint.)
A more dangerous situation is obtained during the cooling phase. The
thermal contraction of the hardening wall will be restrained by the floor.
At this stage, tensile stresses occur in the wall and compressive stresses in
the floor. Through cracks can occur in the hardening wall, going from one
surface to the other. This type of crack formation can have important consequences for water tightness and durability of the wall.
In case no thermal cracking occurs, thermal stresses will remain in the
hardened concrete element as eïgenstresses or self-stresses. These eïgenstresses have to be duly considered as the initial state when further mechanically loading the element.
4.4.1.3 Importance of evolving mechanical properties
In order to better understand the phenomenon of early-age thermal
cracking in hardening concrete elements, it is important to study the
role of the evolving mechanical properties. By means of some elementary
theoretical example, it will be illustrated here that a Young’s modulus
which varies in space and in time (due to the evolution of the hydration
process) has a specific influence on the occurrence of and possible continual thermal stresses.
Consider an elastic body consisting of two halves as illustrated in
Figure 4.12. Both halves have the same time-independent Young’s modulus,
E, but undergo a different temperature variation at time t, namely Δθ 1 and
Δθ 2 . It is supposed that the deformation of the two halves can only happen in one dimension (no transversal expansion, no rotation). It is further
supposed that both halves have a unit length and a unit section, so that
equilibrium equations can further be based on stresses and strains directly.
If both halves were able to deform independently, the situation shown
in Figure 4.12b would occur, showing different thermal dilation and no
stresses. The thermal strains ε 1 and ε 2 can be obtained by:
ε
θ α
1
1
= ∆ ⋅ t
(4.3)
ε
θ α
2
2
= ∆ ⋅ t
(4.4)
in which α t is the coefficient of thermal expansion (CTE), which is considered to be the same for both halves.