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Three-dimensional nonlinear finite element model of railway prestressed concrete sleeper has been developed in this study. The general purpose finite element package, ANSYS 10, is employed for the numerical analyses. Using SOLID65 solid element, the compressive crushing of concrete is facilitated using plasticity algorithm while the concrete cracking in tension zone is accommodated by the nonlinear material model. Since the section of concrete sleeper is fully prestressed by nature, the smeared crack analogy is impracticable. Discrete reinforcement modeling with truss elements, LINK8, is then more suitable to utilize. The pre-tensioning is modeled via an initial strain in the tendon elements. Perfect bonding between concrete and  pre-stressing wires is assumed herein. Comparison with experimental load-deflection response is presented for the prestressed
concrete sleeper. Convergence of both analytical and experimental results is showed.

Concrete structural components require the understanding into the responses of those components to a variety of loadings. There are a number of methods for modeling the concrete structures through both analytical and numerical approaches. Finite element analysis (FEA) is a numerical one widely applied to the concrete structures based on the use of the nonlinear behavior of materials. FEA provides a tool that can simulate and predict the responses of reinforced and prestressed concrete members. A number of commercial FEA codes are available in e-markets, along with the advanced modules for complex analyses. The use of FEA has increased because of progressing knowledge and capability of computer package and hardware. Any attempts for engineering analyses can be done conveniently and fast using such versatile FEA packages. These result in the modernization of structural modeling by newgeneration practical engineers, in order to verify their structural designs. Nonlinear material models
have been integrated in many of general purpose finite element codes, i.e. ABAQUS, ANSYS, STRAND7, or MSC.NASTRAN. Those nonlinear models play a vital role in nonlinear response analyses since each material component tends to possess the  complicated stress-strain behaviors. Among those packages, ANSYS [1] provide a three-dimensional element (Solid65) with the nonlinear model of brittle materials similar to the concrete materials. The element features in a smeared crack analogy for cracking in tension zones and a plasticity algorithm to take into account the concrete crushing in compression zones. It is an eight nodded solid isoparametric element with the integration points for the cracking and crushing checks. The linear elastic behavior governs the analyses until exceeding either the specified tensile or compressive strengths. Once the principal stresses at the integration points reach the tensile and compressive strength, the cracking or crushing of concrete elements can be formed. Then, the cracked or crushed regions will form in perpendicular with the locally redistributed residue stresses to the direction of principal stress. These require the nonlinear iterative solver with high performance computer [2-4]. Railway sleeper is an important component of track structure. It mainly helps distribute loads from the rail foot to underlying ballast bed. It has been found that most of loading on tracks are dynamic loads that have effects on the deterioration of the railway tracks’ components and undermine the load resistant performance of the railway concrete sleepers [5-8]. Understanding into relationships between static and dynamic responses is mandatory.

There are few studies related to the modeling of prestressed concrete sleepers. Most of them predicted the static sagging behaviors of the concrete sleepers [5, 9]. Prediction of the rotational and translational behaviors under normal track loading, which creates the hogging moment, has rarely been found in literature. The objective of this study was to develop a numerical model where nonlinear material properties of concrete sleepers can be included in the detailed analyses for static and dynamic investigations in the future. Due to its availability to industry, a commercial FEA package is preferable in order to use the model in general design practice. A three-dimensional nonlinear finite element model of a railway prestressed concrete sleeper was developed by a general purpose finite element analysis package, ANSYS10. Concrete section was modeled using SOLID65 solid element where the compressive crushing of concrete is facilitated using plasticity algorithm and the concrete cracking in tension zone is accommodated by the nonlinear material model. In normal practice, the railway concrete sleeper is designed to resist prestressing force fully throughout the whole cross section. This makes the smeared crack analogy unsuitable for the replacement of prestressing tendons in the fully prestressed concrete sleeper. The use of a truss element, LINK8, for discrete reinforcement modeling, is then more practicable. An initial strain real-constant feature in ANSYS appropriately substituted the pre-tensioning forces in the tendon elements. However, it was assumed that perfect bonding between concrete and pre-stressing wires occurs during loading exposure. The static full-scale experiment was conducted to validate this FE model [8]. The experimental details were based on the associated Australian Standards [10, 11]. Comparison with experimental load-deflection response and rotational capacity are presented for a specific type of prestressed concrete sleepers.

The analytical solutions of the concrete sleeper due to only prestressing force (Stage I) are illustrated in Figure 3. Both top and bottom fibre stresses are identical to those calculated manually [8]. The results from various material models are similar since only the initial linear parts of elasticity were employed in this early stage. The effect of self weight in Stage 2 is quite small when added up to the displacement due to the pre-tension. The comparison of experimental load-deflection responses is plotted with the finite element results in Figure 4.

Figure 3. Pre-camber, displacement, and fibre stress diagrams due to pre-tensioned strain

Figure 4. Load-deflection responses.

From Figure 4, it is found that MAT1 model can predict the linear range (from 0 to 65 kN of loading) of static behaviors of the concrete sleeper. The nonlinear material models, MAT2 and MAT3, give similar results in the same loading range. However, it can be found in the nonlinear range that MAT2 model seems to well represent the experimental load-deflection curve, while MAT3 model yields slightly smaller than MAT2 model when subjected to larger displacements (after 10-15mm). To obtain the deflection of 15 mm, the static loads of about 126 and 125 kN are needed in MAT2 and MAT3 models, which are, respectively, at 4.5% and 5.3% differences from the experimental results. When using both cracking and crushing model into MAT4, it is noticed that the analytical results are far from the experimental ones because of the low tensile strength of concrete used. This causes the loaddeflection response much lower than others.

This paper demonstrates the finite element modeling to investigate the static behaviors of railway prestressed concrete sleeper, with the uses of nonlinear material properties. Commercial package, ANSYS10, was employed in this study, for which it would be benefit for the industry. The finite element model of the prestressed concrete sleeper was developed. The concrete bricks and prestressing wires were modeled using SOLID65 and LINK8 elements, respectively. The prestressing was applied using the initial strain to LINK8 elements in the discrete manner. Applied displacement method was used in the analyses due to the fast and smooth convergence of numerical iterations. The hogging moment test of railway concrete sleeper was carried out, to evaluate its performance under such loading. It was found that only known compressive strength of concrete, measured from exacted cores, and existing formulas are sufficient to model the prestressed concrete sleeper. Apparently, the nonlinear material models can well capture the nonlinear static behaviors of concrete sleeper. The results also show that the tensile strength based on 0.4(f'c)^0.5 is unsuitable for the high strength concrete.

Authors: S. Kaewunruen and A. Remennikov

Source: Faculty of Engineering - University of Wollongong - 2006

Paper: http://ro.uow.edu.au/cgi/viewcontent.cgi?article=1320&context=engpapers