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MINISTRY OF EDUCATION AND TRAINING UNIVERSITY OF TRANSPORT AND COMMUNICATIONS NGUYỄN XUÂN LAM APPLICATION OF HOMOGENIZATION THEORY TO ANALYZE THE STAGE OF TEMPERATURE DISTRIBUTION AND STRESS DUE TO THE HEAT OF HYDRATION OF CEMENT IN REINFORCED CONCRETE WORKS Field: Transport Construction Engineering Mã số : 9.58.02.05 Major: Bridge and Tunnel Construction Engineering SUMMARY OF DOCTORAL THESIS HÀ NỘI – 2022 The thesis was completed at: University of Transport and Communications Người hường dẫn khoa học: PGS.TS Nguyễn Ngọc Long Academic Supervisors: Assoc Prof.Dr Nguyễn Ngọc Long Assoc Prof.Dr Nguyễn Duy Tiến Reviewer 1: ……………………………………… Reviewer 2: ……………………………………… Reviewer 3: ……………………………………… The thesis will be defended in frond of Doctoral – Level Evaluation Council at University of Transport and Communications At……,…….,…….2022 The thesis can be found at: University of Transport and Communications Library National Library INTRODUCTION I URGENCY OF THE SUBJECT Concrete is a widely used building material around the world because it has many features to meet the requirements of different types of structures, high formability, good structural properties and durability However, in the construction process, the formation of heat at early-age appears in reinforced concrete structures due to the influence of heat of hydration This is one of the important issues to study because the heat distribution has a direct influence on the stress-strain state of reinforced concrete structures at the construction stage In details, tensile stresses due to a combination of temperature differences, heat of hydration and ambient conditions, natural strains, and boundary conditions, often exert significant intrinsic effects on concrete structures Whenever such stress reaches the tensile strength of concrete, cracking will occur, which in turn can reduce the serviceability and durability of structures The handling, repair and overcoming of these cracks are costly in terms of money and cause difficulties in construction, as well as in maintenance and exploitation of works Thermal cracking in early-age concrete structures occurs frequently, such as large concrete blocks such as foundations, dams and bridge structures Thermal cracking of these structures is closely related to the binder content, the ambient temperature during construction, the temperature of fresh concrete and the geometrical characteristics of the structures The formation of a heat source in concrete structures depends on many factors, of which the important ones are concrete mix and construction technology In Vietnam, according to the standard TCVN 9341:2012 “Large concrete – Construction and acceptance” [1], to prevent the formation of cracks in concrete structures, we must ensure two factors: The temperature difference ∆T between points or areas in the concrete block does not exceed 20 o C: ∆T < 20o C; The temperature difference modulus M T between points in the concrete block is not more than 50 o C/m; M T< 50o C/m Currently, bridge works often use high-strength concrete (from 25MPa to 40MPa), so it needs to be reconsidered due to a number of factors as follows: High-strength concrete often contains large cement content (can be more than 400kg/m ) resulting in a much higher heat of hydration of cement than roller compacted concrete and hydraulic concrete Especially, the pier concrete structure uses reinforcement at the edge near concrete surface, so they change the coefficient of thermal conductivity and tensile strength on the surface of concrete Research on temperature sources and stress fields of concrete structures (temperature distribution and deformation) is of interest to many scholars However, the limitations of these studies are that researched structures are concrete blockes without reinforcement and the test mix is not suitable for the lower part of the structure bridge works (grades C30 and C35) Therefore, the topic: "Application of homogenization theory to analyze the state of temperature distribution and stress due to the heat of hydration of cement in reinforced concrete works" was chosen to study The research proposes a theoretical, verified computational model through field measurements to analyze and evaluate the behavior due to the heat of hydration of cement in the reinforced concrete structure II RESEARCH OBJECTIVES The first objective is: to determine equivalent thermal conductivity coefficient, influence range and equivalent material characteristics of reinforced concrete shells with some typical reinforcement diameters Next, the second objective is: to perform a chamber adiabatic test of some common concretes used for bridge construction to measure their adiabatic temperature curves Finally, the third objective is: to use the tested temperature generated values of the room and equivalent thermal conductivity coefficient, equivalent material characteristic of the material reinforced concrete to develop a program analysing temperature distribution and stress due to heat of hydration of cement in reinforced concrete structures III REASEARCH CONTENTS The thesis contents include: Literature review; Determination of equivalent thermal conductivity coefficient and equivalent material characteristics of reinforced concrete layer by homogenization method; Experimental study to determine the adiabatic temperature from the hydration process of cement for ordinary concrete used in bridge construction; Application of homogenization theory to analyze the state of temperature and stress distribution due to heat of cement hydration in reinforced concrete structures at early-age IV SCIENTIFIC AND PRACTICAL CONTRIBUTION  Firstly, develop a program to calculate the thermal characteristics of reinforced concrete using homogenization theory (TCon1 program): equivalent thermal conductivity coefficient, specific heat, homogenization range of reinforced concrete materials of typical reinforced concrete shell structures of bridge piers  Second, measure adiabatic curves for some concrete mixes used in the lower part of bridge structures (concrete C30, C35) according to the adiabatic method in the laboratory and the semi-adiabatic method in the field  Third, develop a program to calculate the distribution and change of temperature and stress over time due to the heat of cement hydration (Program TCon2) to compare with the actual measurement results in the field LITERATURE REVIEW 1.1 Overview of non-mechanical crack formation in reinforced concrete structures 1.1.1 Analysis of non-mechanical crack types The types of cracks caused by temperature in the cement hydration process, the shrinkage, the creep of concrete structures and by the restraining deformation in concrete blocks at early-age are the types of cracks that are not directly affected by mechanical impact Tensile stresses due to a combination of temperature differences, heat of hydration and ambient conditions, natural deformations and boundary conditions, often exert significant intrinsic effects on concrete structures Whenever such stress reaches the tensile strength of concrete, cracking will occur, which in turn can reduce the serviceability and durability of structures Thermal cracking in early-age concrete structures occurs frequently, such as large concrete blocks including foundations, dams and bridge structures Thermal cracking ability of these structures is closely related to binder content, ambient temperature during construction and the temperature of fresh concrete, the geometrical characteristics of the structures 1.1.2 Concept of heat of hydration of cement in concrete The heat of hydration is the heat released during the cement hydration process, which causes an increase in the temperature of concrete blocks during the first 72 hours The heat of cement hydration increases the uneven temperature in the concrete mass, creating a temperature Gradient and thermal expansion, which is one of the possible causes of cracking of reinforced concrete structures The hydration of cement caused by the constituent minerals generates a certain amount of heat That heat can be monitored and measured with an isothermal device Under normal conditions, the heat generated during the hydration of cement is classified into stages Figure 1 Hydration heat release of Portland cement 1.1.3 Regulations on non-structural crack control for bridge contructions in Vietnam According to TCVN 11823:2017: “Design standard for motorway bridges” [2] to control the temperature due to the heat of hydration of cement that forms non-structural cracks: For concrete used for saltwater and coastal structures, the water/cement ratio should not exceed 0.45; The total amount of Portland cement and other cement-containing materials must not exceed 475 kg/m of concrete, except for high-performance concrete, the amount of Portland cement and other cements shall not exceed 593 kg/m According to the standard TCVN 9341:2012 [1], using ordinary Portland cement, the amount of heat of hydration after days is not more than 70cal/g; low heat Cement, with heat of hydration after days not exceeding 60 Cal/g; pozzolan and Portland cement, or Portland- slag cement should be used for construction projects in coastal areas that are exposed to acidic water 1.2 Methods of analyzing the formation of heat of hydration of cement in reinforced concrete structures at early-age around the world and in Vietnam 1.2.1 Methods around the world One of the complete approaches to estimating the size of a texture mass is hydrothermal diffusion characterization proposed by Ulm and Coussy [55], which considers both the dimensional size of structures and its thermal conductivity characteristics Another approach is related to the geometry of structures [12] Besides, De Schutter and Taerwe [26] studied the American Concrete Institute (ACI) concepts of block size and proposed to use the equivalent thickness as a measure of the size of structures, where M is the mass of the structure and γ a is the form factor with respect to heat flow A thermo-mechanical analysis using the finite element method to evaluate the structural safety based on the FIB Model Code 2010 [24] by nonlinear analysis [23] to evaluate the safety for the wind power pylon foundation using highstrength concrete and reinforced or non-reinforced concrete tunnels with the formation of heat of hydration of cement at early-age 1.2.2 Methods in Vietnam A study on the influence of bulk concrete structure size on the formation of temperature field and cracks due to cement hydration of [3] examined the effect of concrete block size on the temperature field at early age However, it was a pure concrete block without reinforcement inside the structure Another study on the degree of hydration and strength development in high-strength concrete [7] based on the degree of hydration determined from the adiabatic temperature experiment However, these studies still have limitations as the structure is simply a concrete block without reinforcement and the test concrete mix is not suitable for the lower part of bridge works The above studies can use the finite element method or experimental methods, or actual data investigation methods, but none of them mentioned the method of homogenizing reinforced concrete materials of the structural shell 1.3 Some solutions to prevent and limit non-mechanical crack in concrete and reinforced concrete structures of abutments at the construction stage A number of solutions have been applied in practice, including: methods of cooling down aggregates, using less heat-emitting cement, curing concrete, controlling concrete temperature during construction and using mineral additives 1.4 Conclusion for Chapter This chapter gives the overview of non-mechanical crack formation in reinforced concrete structures and the causes of cracks in large-sized constructions Next, the author reviews methods to evaluate the formation of cracks, analyze and handle these types of cracks The analysis and evaluation can be done by field experiment method and simulation method through structural analysis software (FEM/FEA) DETERMINATION OF EQUIVALENT THERMAL CONDUCTIVITY COEFFICIENT AND MATERIAL CHARACTERISTICS OF REINFORCED CONCRETE LAYERS BY HOMOGENIZATION METHOD 2.1 Overview of material homogenization method 2.1.1 Material behavior Establishing the rule of material behavior by building theoretical prediction rules on the basis of establishing macro-micro relationship More specifically, the material properties at the building equipment level (macro level) are related to and determined by the physical properties, structures and laws at the smaller material level (micro level) 2.1.2 Multi-level concept Multi-level model is a research direction in which different models at different levels (quantum mechanics, molecular dynamics mechanics, continuum mechanics ) are used simultaneously to describe the behavior of physical systems 2.1.3 The concept of homogenization The multi-level material homogenization method considers the material at the level obeys the laws of continuous environmental mechanics At the macro level (structure level) the building is considered as a continuum characterized by theoretical elementary volume, the volume element is infinitely small of considered material system More specifically, if we denote L and l are the dimensions of the building and the volume element respectively, then l