Modeling and sensitivity analysis the thermal behaviour of mass concrete with finite volume method

Abstract

Concrete is one of the most widely used materials in the world, second only to water. As the population grows and available land becomes limited, there is a growing need for large structures such as dams and bridges and towers to meet the demands of water management, transportation, and accommodation. To ensure the strength and durability of these structures, high-performance concrete is often used. However, a major challenge in such concrete structures is thermal cracking, which occurs due to temperature gradients within the concrete. Concrete has low thermal conductivity, meaning that heat does not dissipate quickly throughout the material. As a result, the outer layer of concrete cools faster than the inner layer, creating thermal gradients. These temperature differences cause differential thermal expansion, if there is no restriction for these movements, there is no problem. But as soon as these movements are stopped by internal or external restrictions, the development of stress will start. When these stresses exceed the tensile strength of the concrete, cracks form. These cracks can result in issues such as water penetration, reduced structural integrity, durability problems (such as corrosion of embedded reinforcement), and aesthetic concerns. Different standards define limitations on the maximum temperature reached within concrete and the maximum temperature gradient within concrete elements, in Turkish standards (TS 13515 ) these limitations are 65 C and 25 C respectively. These specifications are designed to minimize the risk of thermal cracking by ensuring that concrete structures are maintained within safe temperature ranges throughout their service life. The finite volume modeling technique is used in the current model, which was developed in Python. The concrete element is separated into nodes in this manner, and for each node, a control volume according to its location is considered. Convection and conduction are taken into account as boundary conditions in the model, with the flexibility to include other heat transfer processes such as radiation and solar loads. Additionally, an equivalent convection coefficient is derived and employed in the model to account for the impact of formwork and insulation using the analogy of electrical resistance. The governing equation, which is developed from energy balance principles, is then applied to each node. This energy balance takes into consideration all of the energy that enters, is produced, is lost, and is stored inside the concrete. The present model is capable of accepting the ambient temperature using a predictive method, or it may also take actual temperature-time histories as input to improve its accuracy and dependability. The model incorporates the concept of maturity and calculates the heat generated during cement hydration using the Arrhenius maturity function. To simulate the heat generation, Schindler's S-shaped function is employed, requiring curve fitting techniques to determine two important hydration parameters: the slope parameter and time parameter. Unlike previous models that use a single set of hydration parameters, which fails to capture the behavior of blended cement, the current model addresses this limitation by utilizing the superposition of two S-shaped functions. This approach accurately catch all the points on the released heat curve for blended cement. By considering the behavior of blended cement, the model effectively captures the heat generation characteristics. From the S-shaped function, the generated heat rate function can be easily obtained. Additionaly, the model has the capability to accept the generated heat rate as an input. Accurately determining the generated heat rate function is crucial in simulating the thermal behavior of mass concrete, ensuring that the model accurately represents the actual heat generation process. During the experimental phase, data obtained from the Bursa Beton factory was employed. In Chapter 3 of the thesis, the experiment setup is described in detail, and the resulting outcomes are presented. This particular chapter focuses on investigating the impact of insulation on the temperature gradient within the concrete, as well as the influence of different concrete mixtures. The analysis of the collected data revealed noteworthy findings. When a thick layer of insulation was applied around the concrete, the temperature development recorded by the thermocouples placed inside the concrete exhibited similar behavior on both the right and left sides. However, in cases where no insulation was present and the concrete samples were exposed to the environment, distinct temperature profiles were observed between the right and left side sensors. This disparity in temperature can be attributed to the microclimate effect, which includes factors such as wind speed and solar loading on the concrete surface. It is worth noting that this effect has often been overlooked in previous models. The model has been developed in both 2-D and 3-D. The 3-D version is validated by simulating Bursa Beton samples and comparing the findings with experimental data, whereas the 2-D model is validated by comparing its results with the Ballims model. The 3-D model is additionally validated using data from a study carried out at West Virginia University. The model constantly exhibits sufficient accuracy in every validation instance, creating trust in its abilities and allowing sensitivity analysis to be carried out. Additionally, a sensitivity analysis is carried out to examine the impact of different variables on the temperature profile of mass concrete. The initial temperature of the concrete, the size of the concrete element, and the usage of supplemental cementitious materials (SCMs) in place of cement in blended cement are among the changes that have been taken into consideration. The results of the analysis show that the final temperature profile is significantly influenced by both the initial temperature and the size of the concrete part. However, the addition of SCMs to the concrete mixture lessens this sensitivity, especially when fly ash is used instead of some part of cement. Furthermore, when considering the utilization of different replacement levels of supplementary cementitious materials (SCMs), the findings demonstrate significant reductions in both the maximum temperature and maximum temperature gradient within the concrete. The results indicated that the usage of fly ash led to a greater reduction in the maximum temperature and temperature gradient compared to using GGBFS. Additionally, the presence of GGBFS resulted in a delay in the time required for the concrete to reach its maximum temperature. This suggests that adding fly ash to mass concrete lessens its sensitivity to changes in size while at the same time reducing the maximum temperature and thermal gradient inside the concrete. Furthermore, the degree of hydration affects the thermal properties of concrete, including its thermal conductivity and specific heat capacity. As the hydration reaction advances, the amount of available water or moisture inside the concrete drops, which causes a decrease in thermal conductivity and specific heat capacity. In earlier models, these thermal properties were frequently assumed to have constant values. A sensitivity analysis comparing the modeling results with constant thermal properties to those considering variations with hydration reveals that assuming constant specific heat capacity significantly impacts the final results. However, assuming a constant thermal conductivity does not cause substantial changes. In conclusion, the developed model offers a simple yet effective approach to predict the temperature distribution within concrete elements using the finite volume method. It accounts for various boundary conditions, considers the generation of heat during cement hydration, and incorporates the behavior of blended cement using a superposition of S-shaped functions. The model's accuracy is validated through comparisons with experimental data and existing models. Sensitivity analysis provides insights into the influence of different parameters and variations on the temperature profile. By addressing the thermal cracking issue, the model contributes to ensuring the safety, durability, and cost-effectiveness of concrete structures.