Properties of early-age concrete relevant to cracking in massive concrete
Introduction
The temperature of mass concrete may increase substantially due to the combination of heat liberation caused by cement hydration and thermal boundaries that for very thick members may even approach adiabatic conditions. This temperature increase results in thermal deformation of structural members made of concrete and it influences both the kinetics of cement hydration and the phase assemblage of the hydration products.
When the temperature of mass concrete increases and then decreases again, thermal strain (expansion upon heating and contraction upon cooling) occurs. Due to temperature gradients in the cross-section of a concrete member, the core of the member (experiencing higher temperature) will initially expand more than the outer skin (at lower temperature). Tensile stresses will consequently arise in the skin, which may cause surface cracks. These cracks occur in the phase when the temperature is still increasing. They are normally relatively thin and will close later when the temperature of the whole concrete member equilibrates. In the presence of external restraint (e.g. any adjoining structure or the subgrade), compressive stresses will arise in the mass concrete core when the temperature increases. These compressive stresses will eventually turn into tensile stresses when the temperature decreases to equilibrate with the external environment. This is mainly caused by the difference of Young's modulus of concrete during temperature increase and during temperature decrease. The initial compressive stresses are quite low because of the low Young's modulus and high stress relaxation of the concrete in the heat liberation phase. When the temperature decreases, the degree of hydration of the concrete is higher and with it the Young's modulus, while relaxation/creep decreases with the degree of hydration. Another reason why the tensile stresses will exceed the initial compressive stress is the presence of other types of contraction, for instance autogenous shrinkage. Finally, if the temperature of the fresh concrete is higher than the equilibrium temperature of the environment during the cooling phase, the temperature difference during expansion will be smaller than that during cooling. Additionally, the coefficient of thermal expansion (CTE) might be at a minimum at setting and then increase with self-desiccation. A schematic illustration about the process of cracking in massive concrete structures is shown in Fig. 1.
Even though, cracks will be present by design in reinforced concrete, cracking due to volume change will enlarge the crack width and such cracks may jeopardize the durability of concrete. Therefore, the risk of cracking needs to be evaluated and mitigation strategies need to be implemented.
To predict the risk of thermal cracking at any age, it is necessary to calculate the self-induced stresses (stresses induced by either self-restraint or external restraint to deformations of the concrete) and compare them with the tensile strength of the concrete at that age. For a 1D configuration (which is always ideal and in practice needs to be adapted to the actual geometry), the stress can be computed as [1]:where Ec(t) is the Young's modulus at time t, the dot indicates derivative respect to time and ε is the total strain defined as:where e indicates elastic, sh shrinkage, th thermal and cr creep. The thermal strain and the shrinkage are the driving forces of cracking, while the creep strains act to reduce the magnitude of self-induced stresses at early ages.
In some cases, Eq. (1) is modified by introducing the effect of damage on the Young's modulus as (1 − D) · Ec(t), where D is the damage coefficient due to cracking (see e.g. [2]); this approach is followed especially when the cracking behavior is considered numerically. Eq. (2) is modified by introducing the plastic strain εpl, which occurs when the Young's modulus evolves (e.g., due to hydration or damage of concrete) under sustained load, when the stress history results in irreversible creep, or when the thermal expansion coefficient changes under temperature variation.
As already mentioned, Eq. (1) is valid only for the ideal 1D case. For actual, complex geometries the strains and the stresses need to be calculated in 2D or 3D with a finite element model (FEM). It is remarked here that in the general case, the elastic stresses will also depend on the Poisson's ratio. For typical geometries (e.g., walls, piers, layer structures), the Japan Concrete Institute (JCI) Guidelines [3] and Architectural Institute of Japan [4] already provide equations to evaluate the cracking risk. Also for typical geometries, reference can be made to this ACI report [5]. It must be remarked that also for these simplified approaches, the knowledge of the mechanical properties and of the volume changes of the concrete is essential.
The definition of mass concrete is complex because it depends both on the (thermal) boundary conditions and on the material properties of the concrete. Mass concrete is defined in ACI 116R [6] as “any volume of concrete with dimensions large enough to require that measures be taken to cope with generation of heat from hydration of the cement and attendant volume change to minimize cracking.” While this definition may be useful in cases of litigation (e.g., if cracks in a structure are identified as thermal cracks, it may be inferred that not enough measures have been taken), it cannot be used to identify dangerous situations beforehand. Ulm and Coussy developed a definition of mass concrete that depends on a combination of concrete properties, including heat liberation, heat transport, volume change of concrete (thermal deformation strain, shrinkage strain, and creep strain), and physical property development (especially Young's modulus and tensile strength) [7]. Following this approach, relatively thin elements made of high-performance concrete, with rapidly developing stiffness and high heat liberation, may qualify as mass concrete just like much thicker sections of normal strength concrete.
Due to the short period (typically a couple of days to a few days) in which the temperature of mass concrete first reaches its peak and then decreases to approach the ambient temperature and the small surface to volume ratio of mass concrete, the contribution of drying shrinkage to deformations and cracking can be considered negligible. On the other hand, in the case of high-performance concrete, substantial autogenous shrinkage will develop at the same time as the thermal deformations and the combined self-induced stresses might exceed the tensile strength and result in cracking. In addition, both the autogenous shrinkage and the CTE are controlled by self-desiccation, the decrease of internal relative humidity due to chemical shrinkage.
To evaluate the risk of thermal cracking, it is necessary to understand a number of interrelated phenomena, including:
1) the hydration process of the cement with varying temperature (rate of hydration, activation energy of hydration, phases formed at different temperatures, heat liberation, the final degree of hydration);
2) the heat capacity of the concrete, which combined with the potential heat of hydration of the cement allows to calculate the adiabatic temperature rise (the theoretical maximum increase of temperature with no heat losses, useful as an engineering approximation);
3) the thermal boundary conditions and the thermal conductivity of the concrete, which determine both how much lower the maximum temperature in the concrete will be compared to the adiabatic temperature and also how large the temperature gradients will be within the concrete member;
4) the CTE of the concrete, including its dependence on self-desiccation. In addition, the CTE of the different components within the concrete (matrix and aggregates, and also steel reinforcement) will induce self-induced stresses at the mesoscale that may result in microcracking;
5) the autogenous shrinkage of the concrete, which depends both on the self-desiccation (governed by cement hydration) and on the temperature of the concrete;
6) the elastic properties of the concrete, which governs the magnitude of the self-induced stresses that may induce cracking. The Young's modulus depends on the degree of hydration or the maturity of the concrete. A different porosity or phase assemblage at higher temperature will affect the Young's modulus, as well as microcracking arising e.g. from differential thermal expansion or autogenous shrinkage;
7) the stress relaxation will reduce the magnitude of the self-induced stresses in the concrete compared to the elastic stresses. The stress relaxation is also affected by the degree of hydration/maturity, by the phase assemblage and by the temperature;
8) the tensile strength of the concrete. The tensile strength is affected by the maturity and by the temperature. Moreover, the tensile strength during a long-term sustained load might be different from the short-term tensile strength;
9) Modeling and predicting boundary conditions for numerical calculation. Numerical calculation results are greatly affected by the modeling and settings of boundary conditions. For the thermal problem, both the temperature at the construction site and that at the production plant should be predicted; due to the uncertainties of this prediction, the obtained results should be evaluated from statistical point of view;
10) When crack opening is of concern, early-age bond behavior (time development of bond properties, bond behavior change under varying of loads, including bond creep under variation of stress, developments of cracks around rebar due to autogenous shrinkage and temperature change).
This contribution addresses mainly the mechanical properties and the volume changes, while the hydration process, the resultant heat production and the thermal properties (in particular specific heat and thermal conductivity) have been covered elsewhere [[8], [9], [10], [11], [12], [13]]. The main aims of this paper are 1) improving the current understanding of cracking in massive concrete and 2) presenting improved strategies for numerical modeling of the risk of cracking, such as the JCI guidelines [3]. To evaluate the crack width in massive concrete, it is necessary to take into account the interaction between reinforcement bars and concrete; such structural aspects are not covered by this contribution. Drying is also an important issue for the quality of surface concrete, but this problem is also not covered here because it is not essential to understand cracking in massive concrete.
Section snippets
Strength and elastic modulus
The physical properties of concrete at early ages evolve with cement hydration. At the same time, they are also influenced by the temperature increase due to the exothermic reaction of cement with water and by temperature changes in the surrounding environment (including daily cycles) and by drying after demolding. The prediction of the properties of concrete is necessary for performance-based design of reinforced concrete [14], especially for long-term in-service performance and durability
Autogenous deformation
In High-Performance Concrete at early ages, due to the low w/b (typically lower than 0.40) a substantial decrease in the internal relative humidity (RH) occurs without any external drying. For very low w/b, the internal RH can even drop to about 80–75% within a few days [135].
When cement hydrates in concrete, the capillary pores are progressively refined. At the same time, chemical shrinkage empties the pores and causes a drop of internal RH, also called self-desiccation [136]. According to
Conclusions
The properties of concrete related to crack formation in mass concrete have been discussed in this paper. The main conclusions are listed below:
- 1.
To obtain a comprehensive collection of data directly useful for engineers, the concrete properties need to be related to the degree of hydration of the cement. Convenient experimental methods for determining the hydration degree of the concrete are desired. The relationships between cement hydration as well as phase composition and physical properties
Acknowledgement
IM thanks Dr. Atsushi Teramoto (Hiroshima University) and Dr. Go Igarashi (The University of Tokyo) for contributing discussion. PL thanks Dr. Mateusz Wyrzykowski (Empa) for critical reading of the manuscript.
Declaration on conflict of interest
The authors declare that they have no conflict of interest.
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