Prediction of cracking within early-age concrete due to thermal, drying and creep behavior
Introduction
It is well known that continuously casting concrete may result in cracking propagation within structures. Researchers and engineers have noticed that high thermal stresses happen within mass concrete members when pouring a thick foundation base or constructing a dam. Preventive measures, such as using less quantity and low-heat cement, adding proper additives, cooling down, insulating surface and placing rebars, had been developed since the middle of the past century. Wang and Dilger [1] compiled a program to predict temperature distribution in hardening concrete, and RILEM recently published a proceeding to summarize such works [2].
Recently, rapid and massive placing of wall/slab type structure as a whole has become more common due to advanced concrete pumping techniques. Cracking in this situation, unavoidably, becomes a main concern. Meanwhile, evidences showed that occurrence of cracks may be controlled through detailed preparations. Although microcracks cannot be prevented completely, the methodology to have it under control, however, is still unavailable.
Generally, early-age deformation in young concrete leads to excessive distortions, damage and even cracking. Subsequently, problems were encountered, such as deterioration in structural integrity, waterproof requirement and high costs in repair or replacement. Concrete deformation must be supported as far as possible by the quantification of its intensity and spatial distribution. Stress states resulting from deformations and long-term evolution of early-age reaction are the main consideration.
Simple empirical equations have been used in the past for estimation of the shrinkage of concrete. Roelfstra and Salet [3] completed a model to describe heat and moisture transport. Jonasson et al. [4], based on some essential models, studied early features of moisture and thermal effects and set up a linear relationship between shrinkage and relative humidity. Sellevold [5] summarizes Norway's results on a number of investigation. These approaches are easy to apply. A suitable and precise prediction approach involving structural detail, time-dependent variation, environmental conditions, and evaluation of stress distributions within structures would be expected. Bazant [6], [7] gave a general concept on numerical simulation of concrete material and a series of publications focused on the microcracking mechanism according to fracture mechanics.
The major task here is to develop an accurate and applicable prediction method for structural behaviors suffering from early-age reactions. The methodology should be in accordance with the following requirements: (a) The effects of concrete materials and mix proportions on drying shrinkage were to be considered in terms of differences in pore structures. (b) Variations in boundary and environmental conditions, including temperature, humidity, support and load, together with the curing conditions, were also to be considered. (c) Prediction of fields of thermal, moisture and deformation with age was needed. To satisfy these requirements, a macroscopic moisture distribution model had been combined with a micromechanical drying shrinkage model.
A theoretical numerical modelling procedure, based on the characteristics of concrete at both material level and micromechanical level, has been developed to simulate the whole process after concrete setting. Transient temperature and relative humidity fields and their influence to stress (strain) field of cast structure must be exactly matched. A compiled three-dimensional finite element and finite difference (3D-FE-FD) program conforms to this complex time-dependent process including thermal expansion, drying shrinkage and creep behavior. To verify the effectiveness of the proposed numerical procedure, a comparison with specific shrinkage test results is presented and a good agreement was obtained.
Section snippets
The mathematical model
For computational purposes, any point is subjected to three-dimensional strain. To predict the response of structure member in the early period of construction, a step-by-step method is necessary. At the beginning of each time step, deformation due to thermal variation (hydration and environment), drying shrinkage and creep during the current time interval is imposed. This imposed incremental strain on any point at ith time interval is defined as (Eq. (1))where, Δεsh is
Thermodynamical equilibrium of vapor and liquid water
Without considering adsorption and adhesive wetting of water molecules on solid capillary walls, the relation of the equilibrated partial pressure of vapor in fine pores and the interface between the gas and liquid phases can be described by the Kelvin equation (Eq. (4)):where pV is the partial pressure of vapor (Pa), pV0 is the saturated partial pressure of vapor (Pa), pV/pV0 equals to relative humidity h, MW is the molecular mass of water (kg/mol), R is the gas
Heat diffusion within concrete
After concrete is placed in the field, it will be sustained in a thermal environment different from mixing. At early age, a great deal of heat will be generated with the hydration of cement. With day after night, temperature would be varied with time. With the help of heat conduction theory, heat diffusion within concrete is easily expressed in a differential equation (Eq. (8)):where T is temperature of concrete (K), kx, ky and kz are the diffusion
Numerical implementation
A three-dimensional numerical program CCC (Concrete Cracking Control) has been developed for the above nonlinear analysis of concrete. An eight-node serendipity isoparametric element coped with the effects of reinforcement is assumed. At each node of an element, three degrees of freedom are specified, corresponding to three displacements at that node. Stress and strain are evaluated at Gauss integration points within each element. The program is compiled in the format of Visual C++ code as
General
The proposed model was verified based on the experimental data presented by J.-K. Kim and C.-S. Lee [13], which was used to verify the prediction of differential drying shrinkage of some specific concrete specimens.
Outline of the experiments
The specimens as shown in Fig. 2 were exposed to a constant-temperature and constant-humidity room of 20±1 °C and 68±2% RH after moist curing for 7 days. Five sides of the specimen were sealed with paraffin wax to ensure the uniaxial moisture diffusion. The embedded strain gauges
Conclusions
This paper proposed an analytical model to predict potential cracking of early-age concrete. The model could account for the effects of hydration, moisture transport and environmental influences. Verification states the following conclusions.
- 1.
The analytical model proposed here incorporates many of the key influential parameters governing the performance of premature concrete and enables simulation and prediction of development in drying shrinkage and thermal expansion in young concrete under
Acknowledgements
The research presented here was partially supported by the Natural Science Foundation of China (Grant No. 59778031). The authors also appreciate the comments and help of Professor David A. Lange, University of Illinois at Urbana-Champaign.
References (13)
- et al.
Prediction of differential drying shrinkage in concrete
Cem. Concr. Res.
(1998) - et al.
Prediction of temperature distribution in hardening concrete
- et al.
Modelling of heat and moisture transport in hardening concrete
- et al.
Modelling of temperature and moisture field in concrete to study early age movements as a basis for stress analysis
High-performance concrete: Early age cracking, pore structure, and durability