Temperature Boundary Condition Models for Concrete Bridge Members

The temperature development of mass concrete elements is strongly dependent on constituent materials and mixture proportions, as well as the formwork type, geometry, and environmental conditions. This paper presents a method to account for the effects of convection, radiation, and shading on the surface temperature of mass concrete. Solar radiation, atmospheric radiation, surface-emitted radiation, and formwork radiation exchange were considered. Wind speed, ambient temperature, and surface roughness were included in the convection model. The model described was incorporated into a mass concrete temperature prediction model. The predicted temperatures were then compared with measured near-surface concrete temperatures. The ability of the model to predict the maximum temperature and maximum temperature difference were also examined. The results show that the model accurately estimates the near-surface concrete temperatures, the maximum temperature, and maximum temperature difference of the 12 concrete members instrumented.

Keywords: formwork; mass concrete; temperature prediction.

(ProQuest-CSA LLC: ... denotes formulae omitted.)

INTRODUCTION

Large quantities of heat are released during the exothermic hydration process in concrete, which in turn raises the concrete temperature. In recent years, larger bridge members, increased cement fineness, and greater amounts of cement in concrete mixtures have increased the temperature rise in concrete bridge members. Concern over thermal cracking and delayed ettringite formation (DEF)1 in these members has spurred interest in developing temperature prediction models for mass concrete bridge members.

Heat transfer and temperature prediction of a concrete member involves a number of interrelated mechanisms, none of which has a closed-form solution. Each of these mechanisms must be modeled, and a solution determined iteratively. The analysis may be divided into three main components: the heat generation from the hydration process, the heat conduction in the concrete, and the heat exchanged at the boundary of the structural element. This paper will focus on the heat exchange with the environment and boundary conditions as they pertain to mass concrete elements.

There is a body of literature2,3 that deals with methods to account for the heat generated by cement hydration. The most commonly used method combines the equivalent age maturity method and an exponential degree of hydration curve to characterize the rate of heat generation. This method is well documented in other papers, and is shown in Eq. (1)2,3

... (1)

where Q^sub h^ is the rate of heat generation (J/h/m^sup 3^); H^sub u^ is the total amount of heat generated at 100% hydration (J/kg); C^sub c^ is the total amount of cementitious materials (kg/m^sup 3^); τ is the hydration time parameter, in hours; t^sub e^ is the concrete equivalent age at the reference temperature, in hours; β is the hydration slope parameter; α^sub u^ is the ultimate degree of hydration (unitless); E is the activation energy (J/mol); R is the universal gas constant (J/mol/K); T^sub r^ is the reference temperature (°C); and T^sub c^ is the concrete temperature (°C).

The conductive properties of concrete are well covered in literature. Heat conduction in the concrete is dependent on the moisture content, density, specific heat, and thermal conductivity of the concrete. The specific heat and thermal conductivity of concrete is dependent on the mixture proportions, temperature, and degree of hydration of the concrete.3 Aggregates play an especially important role in the conductive properties of concrete.

The discussion of boundary conditions in literature is less thorough. Most of the work reported has been done on horizontal surfaces, mainly bridge decks and pavements.4-6 The boundary conditions of the concrete member are the most complex and variable portion of the heat transfer analysis. The modeling of the concrete heat exchange with the environment is dependent on the surrounding features such as walls and ground surfaces, formwork, curing blankets, ambient conditions, orientation of the element, and heat conduction from the concrete interior.7 Radiation and convection are especially dependent on these parameters. A review of the theory behind these heat transfer mechanisms is thus warranted and is provided in this paper.

Radiation exchange with the environment involves incoming and outgoing components. Solar radiation, radiation from the atmosphere, radiation from the surrounding surfaces, and radiation from the formwork bracing can all impact the surface temperature of the concrete and can be considered heat sources. Irradiation (radiation emitted by the formwork) and reflected radiation act as heat sinks. Figure 1 illustrates the different radiation and convection surface boundary conditions from the environment to the outside formwork of a column.

Convection transfer on the outside of concrete members consists of free and forced convection. Free convection is the heat transfer due to bulk fluid movement (due to buoyancy forces from the temperature differences in the air during heat exchange) and diffusion of the fluid (usually air or water for concrete members) around the member. Forced convection is the heat transfer from bulk fluid movement caused by the wind.8