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FE MODELING OF DEFORMATION AND FRACTURE PROCESSES WHEN PULLINGOUT BAR REINFORCEMENT FROM CONCRETE BLOCK Benin^{ }A., Bogdanova G. Petersburg State Transport University, 190031, Russia, St. Petersburg, Moskovsky pr. 9 Pulling ribbed bars out of concrete blocks is one of the critical problems of structural mechanics. The solution of this problem can advance strength assessment of reinforced concrete structures that have macro fractures. To find a proper solution for the defined class of problems, we have to employ reliable models that describe actual concretetosteel interaction realized through the power of cohesion. One of the main factors that enable joint performance of the reinforcement and concrete in structures thus enabling the reinforced concrete to behave as a seamless solid element is the adhesion between concrete and reinforcement. Reduced adhesion between reinforcement and concrete will lead to excessive crack opening, reduced stiffness and bearing capacity of structures. The concretetosteel bond can be defined with the following key factors:
3. Adhesive and molecular adhesion ("bonding") of the reinforcement to concrete due to adhesive ability of the cement gel (about 10% of the total shear resistance). Each of the three abovementioned factors refers to different adhesive forces shown schematically in Fig. 1. The total resistance to pullingout for plain reinforcing bars is about 23 times lower than that for corrugated bars since the mechanical engagement of bars with a plain surface is negligibly small. Adhesion strength increases in the higher grades of concrete, where watercement ratio is reduced and the age of concrete is increased. An important role for the concretetosteel bond has the form and shape of the reinforcing bar surface: the greatest adhesion is attributed to round corrugated bars while bars with a square or rectangular cross section can be characterized by a smaller adhesion (up to 40% in some cases). The adhesion value is significantly influenced by the type of the stress state in the contact area between the reinforcing bar and concrete block. Compressive stresses caused by external loads and acting in the direction perpendicular to the rebar substantially increase the adhesion stresses. The adhesion is also influenced by the direction of stresses in reinforcing bars (thus, the forces that tend to press the bar into concrete (longitudinal compression) exceed the forces that tend to pull the bar out of concrete). Fig. 1 – Schematic diagram of different power factors the cumulative effect of which characterizes the concretetosteel bond phenomenon: 1 – collapse and shear resistance forces conditioned by the presence of the reinforcing bar protrusions; 2 – friction forces; 3 – adhesive interaction forces In the general case, finite element calculations for reinforced concrete structures with discrete arrangement of reinforcing bars require to choose the laws describing the behavior of concrete, steel and their bonding material. The main characteristics describing their nonlinear properties are concrete and steel deformation curves, as well as the adhesion tangential stresses versus reinforcementagainstconcrete displacement curve. The adhesion tangential stresses versus reinforcementagainstconcrete displacement curve can be determined experimentally. There are a lot of various options for the experimental determination of the concretetosteel bond strength. The main of them (as the most reliable ones) are the pulling of a reinforcing bar out of the concrete specimen or forcing of a reinforcing bar throughout the concrete specimen. The boundary value problem of pulling a corrugated reinforcing bar out of a concrete block assumes various approaches to the solution which varies by the way in which the adhesion phenomena is addressed. Differences arise in the method of description of discontinuities that arise in the process of destruction of bonding links which can be entered explicitly (by separate consideration of reinforcement and concrete motions in the presence of special bonding, by explicit introduction of a system of cracks) or indirectly (by changing effective properties of materials in the adhesion zone, by making adjustments for continual disturbances). Below is given initial data which is common for all FE models used below. Specific data representing distinctive features of the models is discussed in relevant sections. We consider pulling of corrugated reinforcing bars out of a concrete block in the monotonic loading conditions. The height of the concrete class B25 cube is 200 mm, the reinforcement diameter d_{s} = 14 mm, corrugation c/c spacing is 10 mm, corrugation height is 2 mm. The load is applied to the reinforcing bar bottom end. The displacement has been measured on the reinforcement upper end. The loading conditions and the member geometry comply with the requirements of RILEM/CEB/FIB. One of the most attractive options for describing the process of concretetosteel bond failure in the context of the problem about pulling a reinforcing bar out of a concrete block is the approach based on finite element modeling that takes into account the possibility of concrete microcracking in the process of deformation. The adhesion discontinuity is not set explicitly but is taken into account indirectly through the change in effective elastic properties of concrete in accordance with the level and type of load. This approach allows taking into account actual failure mechanisms occurring in the process of pulling the reinforcing bar out of concrete, and can be applied for random loading conditions and variations of the reinforcement geometry. The research has aimed, as before, at obtaining the forcedisplacement and adhesion stressdisplacement curves, as well as the analysis of the pattern of microcrack distribution in concrete. The problem has been addressed in the context of the following three statements:
concrete; • pulling out of a corrugated rebar with an allowance for the contact interaction with concrete. The problem was addressed in the ANSYS system where there is a special element (SOLID65) to model the nonlinear concrete behavior which allows taking into account the effects of microcracking and fracture in the combined stress. These effects are introduced to the model through modification of the stiffness matrix. Table 1 shows the distribution patterns of microcracks in concrete for corrugated reinforcing bars (the plane of the circle coincides with the plane of the crack). The models were loaded by moving down the reinforcing bar bottom end. Table 1 – Crack development when pulling out plain and corrugated reinforcing bars The obtained images correlate well with the experimentally observed systems of crack. First, a system of conical cracks develops and then, as the load increases, radial cracks come up. Fig. 2 shows the development of von Mises stress intensity fields σ_{i} for three levels of loads: A (u_{y} = 3 µm), B (u_{y} = 6 µm), C (u_{y} = 25 µm) when pulling out corrugated bars. Fig. 2 –Development of the von Mises stress intensity field ffjfor three levels of loads A, B, C when corrugated reinforcement is being pulled out We have found that, both for plain and corrugated bars, the area with microcracks will grow from bottom to top as the load increases. One can quite precisely define the frontline position for this area which separates the cracked concrete (that bears nearly no load) from the undisturbed one (that keeps bearing the load). The abovementioned results have provided the basis for the following diagrams: displacement versus pullingout force and displacement versus adhesion tangential stresses which allow comparison with the experimental data. Conclusions 1. The use of the concrete deformation model that includes microcracking and failure effects allows making a qualitatively correct description of the process of pulling a reinforcing bar out of a concrete block. 2. The design level of peak values for tangential stresses on the adhesion curve is lower than that observed experimentally which requires adjustments of the concrete stiffness parameters at cracking, as well as consideration of adhesive and frictional forces of adhesion. 3. The modeling has employed only the material constants obtained through standard tests which in its turn makes this method of describing the process more valuable since there is no need to set up further experiments. 