Nonlinear concrete behaviour

Transcription

1 Universidad de la Costa From the SelectedWorks of Marian Sabau November, 2011 Nonlinear concrete behaviour Marian Sabau, Universidad de la Costa Traian Onet, Technical University of Cluj-Napoca Available at:

2 %# & NONLINEAR CONCRETE BEHAVIOUR SABU Marian*, ONE Traian, Technical University of Cluj-Napoca, Faculty of Civil Engineering, * (corresponding adress) A B S T R A C T This paper presents an overview of nonlinear behaviour in reinforced concrete structures. Structural concrete is a nonlinear material both at strength limit states and service loads. Are presented terms of effects that are primarily observed in concrete, steel or a combination of the two. When considering nonlinear behaviour, an important aspect is whether or not strain localization will occur as size effects. The model must first be validated by experiments and benchmark tests to ensure the safety and reliability criteria. In nonlinear finite element procedures, engineers must check their finite element discretization and modelling assumptions used in their analyses. Advanced analysis techniques including finite element method analysis have been increasingly utilized in various forms for the practice of design and construction of concrete structures in recent years. Received: October 2011 Accepted: October 2011 Revised: November 2011 Available online: November 2011 Keywords: finite element method, nonlinear analysis, smeared cracking, discret cracking, tension stiffening INTRODUCTION Nonlinear analysis is a tool gaining ground among engineers as a practical technique for design and verification of concrete structures. With nonlinear finite element analysis, a reliable solution can be obtained only after understanding the combination of multiple constitutive models, the treatment of analysis theories in the nonlinear processes, mathematical problems in applying to a softening material such as concrete, and so on. The judgment of the validity of modeling and analysis results has therefore been left to engineers with substantial experience. For some design and analysis problems, a linear analysis may not be sufficient when consider the requirement of satisfying a serviceability limit states such as calculating deflections and crack widths. For new structures a non-linear analysis may be performed on the structure after initial proportioning using a plasticity-based design procedure based on a linear elastic analysis. Nonlinear analysis can assist in the evaluation of complex geometry or poorly detailed structures where the effects of localized cracking, for example, may be poorly modelled by linear analysis. Situations where nonlinear analysis should be used: resistance of structures to extreme events, pushover analyses for structural capacity computation, resistance to fire, estimation of P- effects. MATERIALS AND METHODS Finite element analysis was first applied to the cracking of concrete structures by Clough (1962) [1] and Scordelis and his coworkers Nilson and Ngo [2], Nilson 1968 [3] as shown in fig

3 Fig.1. The first finite element model of a cracked reinforced concrete beam [2] The tables below (table 1, 2, 3, 4 and 5) presents important nonlinear effects observed in structural concrete. dependent Table 1. Behavioural effects Types of Behavioural Effects balance may need to be considered to fully model listed effect Elements must include variable stiffnesses to fully model the listed effect Indicates a discrete change in behaviour rather than a smooth transition Indicates that simple nonlinear elasticity may not provide a full solution Behaviour cannot be fully modelled with strain terms alone. Modelling also requires an absolute distance relationship such as a crack width Table 2. Behaviour of plain concrete Plain Concrete Behaviour Tension Compression Macrocracking Tension softening Cyclic response Creep Crack closing effect Shrinkage Crushing Nonlinearity at high Post-peak unloading Cyclic response Creep Rate of loading Bi or triaxial confinement Poisson s ratio Thermal effects 56

4 %# & Table 3. Behaviour of reinforcement Reinforcement Behaviour Tension Compression Shear Yielding Strain hardening Thermal effects Rate of loading Rupture Buckling Dowel action Table 4. Damage effects Damage Effects Material Damage Fatigue Table 5. Behaviour of combined concrete and reinforcement Combined Concrete and Reinforcement Behaviour Tension Bond Tension stiffening Tension splitting Compression softening Compression Shear Aggregate interlock 3. Concrete in compression Three important aspects of concrete compressive behaviour are presented: localization in compression, confinement of concrete, and compression softening. As concrete shows a decrease in stress for increasing beyond the strain associated with the compressive strength, localization of concrete in compression can be expected. Two primary effects will result from this: firstly larger specimens failing primarily in a compressive mode can be expected to show less ductility in the post-peak region than smaller specimens and, secondly, a size effect is predicted for some member types whereby larger elements in compression will be weaker in terms of stress than smaller elements. Some tests on specialized structural components confirm the presence of a size effect in unreinforced flexural compression zones [4]. Concrete can carry higher compressive stresses with larger deformations when it is laterally confined. Finite element models can require either biaxial or triaxial confinement relationships. One of the earlier 3D failure surface models that incorporated this strength enhancement was that of Ottosen [5] (fig. 2). 57

5 Fig. 2. Failure surface for Concrete One model which is often used in non-linear elasticity is the Kent and Park (1971) [6] model later modified by Scott et al. [7] to include the strength and ductility enhancement due to confinement effects and the effect of strain rate (fig. 3). Fig. 3. Modified Kent end Park model [7] As perpendicular to the direction of applied compression increase, this strength reduction effect, often called compression softening, becomes more severe. 4. Concrete in tension The most important aspect of concrete is cracking. There is more than one way to include tension in finite element analyses of concrete structures (table 6). Table 6. Level of analysis complexity Model concrete tension reinforcing bond element size Small-scale softening perfect bond very small Medium-scale stiffening/softening bond law medium Large-scale stiffening perfect bond large 5. Modelling of tension stiffening Modelling of tension stiffening can be done in two ways: the first is to modify the stiffness of reinforcing bars - the tensile stresses are transferred to concrete through bond, the second is to modify the concrete stiffness to carry the tension force after generation of cracks using the smeared crack model and the discrete crack model. 58

6 %# & 6. Modelling of concrete cracks In finite element models the cracks can be considered either as smeared throughout the element or only present at finite element boundaries wich is known as discrete cracking Discrete crack models In the finite element method (FEM), discrete cracks are usually modeled by altering the mesh to accommodate propagating cracks. A zone of inelastic material behavior, called the fracture process zone (FPZ), exists at the tip of a discrete crack, in which the two sides of the crack may apply tractions to each other. One of the development of finite element modeling of nonlinear discrete fracture has been the implementation of the fictitious crack model (FCM) (Hillerborg et al. 1976) [8], in which the crack is considered to be a strain softening zone modeled by cohesive nodal forces or by interface elements. There are situations in which even the FCM seems inadequate to model realistic concrete behavior in the FPZ, in this case a smeared crack model must be used Smeared crack models The smeared crack approach was introduced by Rashid (1968) [9]. It is much more convenient to represent cracks by changing the constitutive properties of the finite elements than to change the topography of the finite element grid. Localization problems can occur for smeared cracking problems (fig. 4). Fig. 4. Localization in FEM 7. Modelling of reinforcement Reinforcing bars in structural concrete are assumed to be one-dimensional line elements without transverse shear stiffness nor flexural rigidity. Reinforcement in a nonlinear concrete analysis can be treated as either discrete or smeared. Discrete reinforcement involves the inclusion of individual axial or axial-flexural elements into the finite element mesh that model each layer of reinforcement explicitly. Smeared reinforcement involves calculating an average stress-strain relationship that applies to the entire element area and is included directly as part of the overall concrete element stiffness matrix. CONCLUSIONS Nonlinear finite element modelling can be an extremely useful and powerful approach in determining the behavioural response of complex concrete structures but extreme care is needed in the setting up of the models, in the verification of the model, in assessing the models capability to correctly identify critical behaviour and in the interpretation of results. Non-linear finite element analysis based on advanced constitutive models can be well used for the simulation of a real 59

7 behaviour of reinforced concrete structures. Using the nonlinear finite element method can greatly contribute to improve construction quality and safety performance of actual structures. REFERENCES 1. CLOUGH, R. W. (1962), The Stress Distribution of Norfolk Dam, Series 100, Issue 19, Institute of Engineering Research, University of California, Berkeley, Aug. 2. NGO, D., and SCORDELIS, A. C. (1967), Finite Element Analysis of Reinforced Concrete Beams, ACI Journal, Proceedings V. 64, No. 3, Mar., pp NILSON, A. H. (1968) Nonlinear Analysis of Reinforced Concrete by Finite Element Method, ACI JOURNAL, Proceedings, V. 65, No. 9, Sept., pp KIM, J.-K., YI, S.-T., YANG, E.I. (2000), effect on flexural compressive strength of concrete specimens, ACI Structural Journal, 97(2), pp OTTOSEN N. S. (1977), A failure criterion for concrete, Journal of Engineering Mechanics, ASCE, 103, pp KENT, D.C., and PARK, R. (1971), Flexural members with confined concrete, ASCE J. of Struct. Engng., 97(ST7), pp SCOTT, B.D., PARK, R., and PRIESTLEY, M.J.N. (1982), Stress-Strain Behavior of Concrete Confined by Overlapping Hoops at Low and High Strain Rates, ACI Journal Proceedings, 79(1), pp HILLERBORG, A., MODEER, M. and PETERSSON, P. E. (1976), Analysis of Crack Formation and Crack Growth in Concrete by Means of Fracture Mechanics and Finite Elements, Cem. and Conc. Res., V. 6, pp RASHID, Y. R. (1968), Ultimate Strength Analysis of Prestressed Concrete Pressure Vessels, Nuclear Engineering and Design, V. 7, pp *** (1997) ACI 446.3R-97, Finite Element Analysis of Fracture in Concrete Structures: Stateof-the-Art, reported by ACI Committee *** (2008) JCI, Technical Committee on Utilization of Nonlinear Finite Element Method, Committee Report: JCI- TC064A. 12. *** (2010) FIB bulletin 55 and 56, Model Code 2010 for Concrete Structures, International Federation for Structural Concrete. 13. *** (2008) FIB bulletin 45, Practitioners guide to finite element modelling of reinfroced concrete structures, International Federation for Structural Concrete. 14. *** (2006) ASME, Guide for Verification and Validation in Computational Solid Mechanics, American Society of Mechanical Engineers, PTC 60 Committee. 15. PRYL D., CERVENKA J., PUKL R. (2010), Material model for finite element modelling of fatigue crack growth in concrete, Procedia Engineering, pp , Elsevier (ISI). 16. CERVENKA J., PAPANIKOLAOU V. K. (2008) Three dimensional combined fracture plastic material model for concrete, International Journal of ity 24, pp , Elsevier (ISI). 17. CERVENKA V., CERVENKA J., SISTEK M. (2011), Verification of global safety assisted by numerical simulation, fib Symposium Prague, Proceedings ISBN RABCZUK T., ZI G., BORDAS S., NGUYEN-UAN H. (2008), A geometrically non-linear three-dimensional cohesive crack method for reinforced concrete structures, Engineering Fracture Mechanics 75, pp , Elsevier (ISI). 19. NG. PUI-LAM (2007), Constitutive modelling and finite element analysis of reinforced concrete structures, Ph.D. Thesis, The University of Hong Kong. 60