Mechanical properties of young concrete: Part II: Determination of model parameters and test program proposals

Transcription

1 Materials and Structures/Matériaux et Constructions, Vol. 36, May 2003, pp Mechanical properties of young concrete: Part II: Determination of model parameters and test program proposals T. Kanstad 1, T. A. Hammer 2, Ø. Bjøntegaard 1 and E. J. Sellevold 1 1) Department of Structural Engineering, The Norwegian University of Science and Technology (NTNU), Trondheim, Norway 2) SINTEF, Civil and Environmental Engineering, Trondheim, Norway Paper received: October 23, 2001; Paper accepted: April 16, 2002 A B S T R A C T The paper concerns testing and modelling of the mechanical properties required as inpuo calculation programs made for crack risk estimation of hardening concrete structures. The results from several test series on mechanical properties of young concrete as described in Part I of this paper, are further evaluated. Model parameters for the modified CEB 1990 Model Code-equations, are determined for six concrete mixes, all having a w/b-ratio on 0.40, for compressive strength, tensile strength and E-modulus. To make the models applicable for young concrete, a t o -parameter is introduced to fix the time at which significant mechanical properties are present. A test program to determine the model parameters is proposed, based on the experience that compressive strength tests have the smallest statistical scatter and thahey are simpleso carry out. R É S U M É Ce rapport fait état des essais et de la modélisation concernant les propriétés mécaniques du béton, données nécessaires aux programmes de calcul pour l estimation des risques de fissuration des structures fraîchement coulées. Les résultats de plusieurs séries d essais sur les propriétés mécaniques du béton au jeune âge, décrits dans la première partie de ce rapport, font l objet d une analyse plus poussée. Les paramètres de modélisation pour l équation MC1990 modifiée sont déterminés, pour les six mélanges, dans le cas de la résistance en compression et en traction, et du module d élasticité. Pour que ces modèles puissent s appliquer au béton jeune, on introduit un paramètre t 0 représentant l instant à partir duquel on considère les propriétés mécaniques comme significatives. Il est proposé un programme expérimental visant à déterminer les paramètres de modélisation, basé sur le fait que les essais de résistance en compression montrent une très bonne reproductibilité et sont les plus simples à mettre en œuvre. 1. INTRODUCTION Assessment of cracking risk during concrete hardening requires reliable information about materials properties such as hydration heat, thermal conductivity, thermal dilation, autogenous deformation, creep and finally the mechanical properties; tensile strength and elastic modulus which are considered in this paper. The equations describing the property development used in this paper are based on the equation used in the CEB 1990 Model Code. A modification is introduction of the time t o defining a relevant startpoint for stress calculations, and ensuring consistent coupling between the different mechanical properties, including autogenous deformation and thermal dilation (thermal expansion and contraction), and between the hydration heat and the mechanical properties. The t o -parameter expresses that there is an equivalent concrete age (t o ), at which significant mechanical properties staro develop, and autogenous deformation and thermal dilation staro produce stresses. Based on the experimental results presented in Part I of this paper [1], model parameters to be used in calculation programs are determined for six concretes, and a set of default parameters is proposed. A minimum experimental program to quantify the development of the mechanical properties using as simple methods as possible is proposed. This program utilises the finding thahe development rate curves of the different mechanical properties can be related to each other, and that compressive strength test results have the smallest statistical scatter and are simpleso carry out. This paper is a part of a relatively large research programme which covers the field of early age concrete crack assessment ranging from basic materials research, Editorial Note Mr. Tor Arne Hammer and Dr. Øyvind Bjøntegaard are respectively Chairman and Secretary of RILEM TC DTD Recommendation for test methods for autogenous deformation and thermal dilation of early age concrete. Prof. Erik Sellevold participates in the above-mentioned RILEM TC DTD. All three are RILEM Senior Members /03 RILEM 226

2 Kanstad, Hammer, Bjøntegaard, Sellevold laboratory testing and materials modelling to finite element analysis and field testing [1-6]. 2. MATERIALS MODELS AND MODEL PARAMETERS 2.1 Materials models In general the type of equation chosen to describe the property development versus maturity, as defined in Part I [1], is not a major point, buhe following Equations (1ac), which are based on the expressions in the CEB-FIP Fig. 1 Relative strength and stiffness development for the 1990 Model Code [7] briefly presented in the Appendix, BASIC-5 Concrete according to the materials models (Equation are quite convenient for practical use. A modification is (1a-c)). introduction in the form of a parameter t o, which is the time when the strength and stiffness are Table 1 Model parameters for the compressive strength defined to be zero [8, 9], but after which significant values develop. The parameter ensures consistent coupling between the different mechanical REF-A Concretes: f c (MPa) s t o (hours) St.dev. (MPa) Coeff. of var.* properties (also including autogenous deformation BASIC and thermal dilation), and between the hydration BASIC heat and strength development. Such a parameter (t o ) is useful if the materials BASIC models have to be adjusted to take into account REF STD different setting times because of different mix REF FA temperature or the use of retarding/accelerating admixtures. t o is probably close to the point of MARIDALEN final set, and for the concretes reported in this * The coefficient of variation is normalized to the -day strength. paper it varies typically between 9 to 12 hours at 20 C (maturity time), which corresponds to a degree of hydration of 15-20% (defined as relative heat development). Consequently the t o -concept expresses that a two parameters to be determined from the tensile from compressive tests. This approach leaves then only certain hydration musake place before the concrete strength (f t and nt) and the modulus of elasticity (E c starts to achieve mechanical properties. The choice of t o and ne) tests. This makes the test programme smaller has significant impact on the calculated cracking risk and also more accurate for t o, since it is simple to perform many compressive tests at very early ages. The because the parameter defines how much of the thermal- and autogenous strains that are to be included into parameters nt and ne are different in order to express the the stress calculation. Our choice of t o is based on extensive data from tests where early self-induced stress is three material properties as shown in Fig. 1. fachahe time functions have different shapes for the recorded under conditions of full restraint [9]. Compressive strength: 2.2 Model parameters fc( te)= fc s (1a) The model parameters determined from the compressive tests, including specimens exposed to both isothermal Tensile strength: and realistic temperature histories, are presented in Table 1. nt The model parameters are determined by means of the least square sum of the deviations between the model and ft( te)= ft s (1b) the experimental results. Tables 2 and 3 give the additional parameters for the tensile strength and the modulus of elasticity. The splitting strength results were firsransformed Modulus of elasticity: ne to uniaxial tensile strength by means of Equation (1) presented in Part I [1]. Part I also gives the concrete composi- Ec( te)= Ec s (1c) tions; they all have water-to-binder ratios of 0.40, the numbers 5, 10 and 15 indicates the dosages of silica fume. One basic idea is thahe parameter t o, and the parameter s, which describes the curvature of the compres- the different properties. It is clearly seen thahe statistical Fig. 2 shows predicted versus experimental values for sive strength development versus time, are common for scatter is smaller for the compressive strength test results all three equations, and therefore may be determined than for the tensile strength and E-modulus. The tensile 227

3 Materials and Structures/Matériaux et Constructions, Vol. 36, May 2003 Table 2 Model parameters for the tensile strength Concretes: f t (MPa) nt St.dev. (MPa) Coeff. of var.* REF-A BASIC BASIC BASIC REF STD REF FA * The coefficient of variation is normalized to the -day strength. Table 3 Model parameters for the E-modulus Concretes: E c (GPa) ne St.dev. (GPa) Coeff. of var.* REF-A BASIC BASIC BASIC REF STD REF FA * The coefficient of variation is normalized to the -day strength. strength results for three of the concretes are presented in Fig. 3, while Fig. 4 shows similar results for the E-modulus. The statistical variations are given in Tables 1-3, showing coefficients of variations in the range 2-9%. 3. PROPOSED TEST PROGRAM FOR CRACK RISK ESTIMATION Fig. 1 showed the relative development of the mechanical properties for the BASIC-5 concrete expressed by the material models. Although the model parameters depend on the concrete mix, the relations between the three properties look quite similar also for the other concretes. This observation can be utilised to define a minimum test programme to quantify the necessary mechanical properties in order to calculate the crack risk of a given concrete. Fig. 5 shows the relative development of the tensile strength and the modulus of elasticity versus the compressive strength development for six different concretes. Based on these figures, and the previously described results, the following test programme is proposed: Compressive strength tests on specimens exposed to isothermal (20 C) and realistic temperature histories ahe following ages: 0.6, 1, 3, 7 and days. E-modulus and tensile strength tests on specimens exposed to isothermal conditions (20 C) awo ages: 2 and days. The parameters s and t o are determined from the compressive strength test results, while the parameters nt and ne are determined from the tensile strength and the E-modulus test results, respectively. Default values for nt (=0.59) and ne (=0.37) might probably be used without significant loss of accuracy. The temperature sensitivity factor (activation energy) is determined from the compressive test results [1]. The -day compressive strength values will also warn if the Fig. 2 Model versus experimental results for all tests, (a) compressive strength, (b) tensile strength, and (c) E-modulus. strength loss due to elevated temperature curing is significant for the particular concrete and if so more tests must be carried out on tensile strength before realistic crack risk assessment can be carried out. To determine t o from compressive test results is probably the simplest (and most accurate) method. Alternatively can this parameter also be directly determined from stress measurements in a temperature-stress testing machine where the concrete specimen is fully or partly restrained and exposed to isothermal or realistic temperature histories. It can also be indirectly determined from heat of hydration measurements, or by methods based on ultrasonic pulse velocity. 2

4 Kanstad, Hammer, Bjøntegaard, Sellevold Fig. 3 Tensile strength development. Direcensile tests or splitting tests on cylinders and cubes. The specimens were exposed to isothermal (20 C) or realistic temperature histories. (a) REF-A, (b) BASIC-5, (c) BASIC SUMMARY Fig 4. E-modulus development. Tensile or compressive testing. The specimens were exposed to isothermal (20 C) or realistic temperature histories. (a) REF-A, (b) BASIC-5, (c) BASIC-10. The paper (Part I and Part II) presents results of several test series on mechanical properties of young high strength concrete all having a w/b-ratio on Six different concrete mixes were tested systematically and a number of other concretes less extensively. The paper describes the test methods and evaluates the results in part I, while model equations for the mechanical properties and a minimum test program to determine their parameters for a given concrete are proposed in part II. The model parameters for the modified MC1990- equation to be used in calculation programs are determined for the six concretes tested. The t o parameter is introduced into the models to fix the time at which significant mechanical properties are present, and to ensure consistent coupling between the different mechanical properties, the volume changes and the hydration heat development. A set of default values for the model parameters are proposed. For the high performance concretes with water-to-binder ratios around 0.4 reported in this paper, t o varies typically between 9 to 12 hours maturity time. 229

5 Materials and Structures/Matériaux et Constructions, Vol. 36, May 2003 Fig 5. (a) Tensile strength development vs compressive strength development for six different concrete mixes. (b) E-modulus development vs compressive strength development for the same concrete mixes. Finally a minimum test program to determine the model parameters is proposed. This programme is based on the experience that compressive strength tests have the smallest statistical scatter, and thahey are simpleso carry out. It is proposed thahe compressive strength should be determined at least at five different ages both for specimen cured under isothermal and realistic temperature histories. Experimental determination of E-modulus and tensile strength can then be limited to 2 ages, for instance 2 and days for specimen stored under isothermal conditions only. ACKNOWLEDGEMENT This paper is a product of the Brite-Euram Project IPACS 1 (Contract BRPR-CT ) and the associated Norwegian NOR-IPACS 2 project. The financial contributions of the European Comission and the Norwegian Research Council are gratefully acknowledged. REFERENCES [1] Kanstad, T., Hammer, T.A., Bjøntegaard, Ø. and Sellevold, E.J., Mechanical properties of young concrete: Part I: Experimental results related to test methods and temperature effects, Mater. Struct. 36 (258) (2003) [2] Bjøntegaard, Ø., Thermal dilation and autogenous deformation as driving forces to self-induced stresses in high performance concrete, Dr. ing. thesis, Department of Structural Engineering (The Norwegian University of Science and Technology, NTNU, Trondheim, 1999). [3] Bosnjak, D., Self-induced cracking problems in hardening concrete structures, Dr.ing. thesis, Department of Structural Engineering (The Norwegian University of Science and Technology, NTNU, Trondheim, 2000). [4] Atrushi, D., Bjøntegaard, Ø., Bosnjak, D., Kanstad, T. and Sellevold, E.J., Creep deformations due to self-stresses in hardening concrete, effect of temperature, in Proceedings of the 6th International RILEM Conference on Creep, Shrinkage & Durability Mechanics of Concrete and other Quasi-Brittle Materials (Concreep6), Cambridge, USA, Aug. 2001, (Elsevier Science Ltd., Oxford, 2001) [5] Hammer, T.A., Effect of silica fume on the plastic shrinkage and pore water pressure of high-strength concretes, Mater. Struct. 34 (2001) [6] Kanstad T., Bjøntegaard, Ø., Sellevold, E.J., Hammer, T.A. and Fidjestøl, P., Effect of silica fume on early age crack sensitivity of high performance concrete, Concrete International, The Magazine of the American Concrete Institute 23 (12) (2001) [7] CEB-FIP Model Code 1990, CEB Bulletin No.203, (Comité Euro-International du Béton, Lausanne, Switzerland, 1991). [8] Kanstad, T., Early age behaviour of concrete and reinforced concrete structures, Report, The Department of Structural Engineering, (The Norwegian University of Science and Technology, NTNU, Trondheim 1994). [9] Bjøntegaard, Ø., Kanstad, T., Sellevold, E.J. and Hammer, T.A., Stressinducing deformations and mechanical properties of high performance concrete at very early ages, in Proceedings of the 5th International Symposium on Utilization of High Strength/ High Performance Concrete, Sandefjord, Norway, June 1999 (The Norwegian Concrete Association, Oslo, 1999) APPENDIX: STRENGTH DEVELOPMENT ACCORDING TO CEB-FIP 1990 MODEL CODE [7] The compressive strength can be determined according to the following equation: fcm ( te)= fcm s t (A1) e In which the parameter s is 0.20 for rapid hardening high strength cements, 0.25 for normal and rapid hardening cements, and 0.38 for slowly hardening cements. Correspondingly the E-modulus can be determined as: 05. Ec( te)= Ec s t (A2) e For both properties the equivalent age (or maturity), t e, can be determined by Equation (2a) in part I of this paper [1], using a fixed value for temperature sensitivity parameter E r =4000 K. 1 IPACS Partners are Scancem AB (project leader), Selmer ASA, TU Delft, ENEL, TU Luleå, NCC AB, Skanska Teknik AB, TU Braunschweig, Ismes, Norwegian Public Roads Directorate, Elkem ASA Materials, Norcem AS and NTNU. 2 NOR-IPACS Partners are: Selmer ASA (project leader), Elkem ASA Materials, Norcem AS, Fesil ASA, Norwegian Public Roads Directorate and NTNU. 230