Finite element modelling of voided slab bridge decks using orthotropic plate theory - De Kock, Warrick (Department of Civil Engineering, 2017)
Circular voids are often incorporated into concrete bridge decks to reduce their self-weight without greatly reducing the flexural stiffness. Incorporating voids within a slab offers many advantages over a conventional solid concrete slab, for example a lower total cost of construction, reduced material use, and enhanced structural efficiency. The advantages of this topology are obvious, however the voids within the slab complicate the analysis of the structure. The incorporation of the voids within the slab results in different flexural stiffness in the longitudinal and transverse directions, resulting in an orthotropic slab. Another feature which distinguishes voided slabs from other common bridge types is the deformable nature of their cross-sections, which influences the load distribution of the structure. The need for a method of analysis which accounts for the orthotropic behaviour and deformable nature of the cross-section has been suggested by many in the past. The idealisation of voided slabs as an orthotropic plate has been the subject of extensive research. When modelling a voided slab as an orthotropic plate, it is necessary to calculate the reduction in the longitudinal and transverse stiffness due to the presence of the voids. Several equivalent plate parameters, which take on numerous forms, have been suggested by various authors to account for the effect of the voids. No research has been reported in technical literature to compare these different methods employing orthotropic plate parameters. Key shortcomings to these methods include the lack of definition of the suggested equivalent plate parameters, and the geometrical parameters of voided slabs which influence their behaviour. In an attempt to address these limitations, the aim of this study is to verify and validate the effect of the void diameter ratio and void spacing on the structural behaviour of voided slabs, which are the main influences on the orthotropic behaviour and cross-section deformation. The different methods of analysis using orthotropic plate theory suggested by various authors employing equivalent plate parameters are compared and discussed. The objectives of the study were achieved based on the finite element approach using ABAQUS. Finite element models with a void diameter to slab depth ratio range of 0.5 to 0.9, and a void spacing range of 0.9m to 2.7m were considered and analysed. Comparisons were made of the longitudinal and transverse stress distribution results from these models in order to draw conclusions. Results from solid models using both isotropic and orthotropic materials based on the equivalent plate parameters suggested from literature are also presented for comparison in order to verify the methods suggested by the technical literature for the analysis of voided slab bridge decks. Results of the finite element modelling show that the addition of voids causes large variations to the transverse stress distribution from the typical parabolic transverse stress distribution shape, leading to large peak transverse stresses in the flanges above and below the voids. These variations are due to the deformable nature of the cross-section. The voids also lead to a stress raising effect on the longitudinal stresses. It was found that an increase in void diameter to slab thickness ratio results in a rapid increase in both the longitudinal and transverse stresses, which shows that there is an increase in orthotropic behaviour and deformation of the cross-section with an increase in void diameter ratio. From the results, it can be concluded that the optimal void diameter ratio is between 0.6 and 0.8. This range of void diameter ratios allow for greater efficiency due to reduced dead load and material use, without generating excessive stresses due to cellular distortion resulting from excessively thin and flexible flanges above and below the voids. The spacing of the voids was found to have minimal effect on the stress distributions for a logical void spacing. These results show that the orthotropic behaviour and deformation of the cross-section are more sensitive to variations in void diameter ratio than the spacing of the voids. The void diameter ratio should therefore form the basis of the equivalent plate parameters for the use of orthotropic plate theory. The use of a solid orthotropic plate to idealise a voided slab showed reasonable agreement with the results from three-dimensional models, with some discrepancies in the different authors' methods noted. The net effect of using a two-dimensional analysis is the averaging out of the stress transverse distribution, which cannot predict the peak stresses around the voids. The orthotropic models compared more favourably with the 3D model than the isotropic models with increasing void diameter ratio. The results presented have shown that the incorporation of voids begins to affect the structural behaviour of the slab once the void diameter ratio exceeds 0.6, and the orthotropic behaviour becomes considerable. The stress raising effect of the voids should therefore be accounted for in the analysis of a voided slab once the void diameter ratio exceeds 0.6. It is recommended that a solid isotropic slab can be used to idealise a voided slab when the void diameter to slab depth ratio is less than 0.6. When the void diameter ratio is greater than 0.6, the transverse stiffness should be evaluated independently from the longitudinal stiffness, and orthotropic models are more suitable. For higher void diameter ratios, the method employed by Sen et al. (1994), which employs a reduced depth solid orthotropic slab in conjunction with stress multipliers, was found to be the most accurate method for idealising voided slabs. It is evident from this study, that while a three-dimensional finite element model may be too complex for everyday use, it may be extremely valuable for determining the local effects due to the presence of the voids.