Keywords: concrete slabs, arching action, compressive membrane action, finite element, damaged plasticity, explicit analysis.

Work at Queen's University has looked at exploiting arching action or Compressive Membrane Action (CMA) which occurs when restraint is provided at the boundary of slabs [1]. By exploiting CMA it should be possible to arrive at designs for bridge decks that require less reinforcement, and allow the reinforcement to be placed in a position within the slab where it is protected from the penetration of chloride ions. As a further alternative the steel reinforcement could be replaced by another material which is not liable to corrosion.

The focus of this particular work was to attempt to use the Abaqus finite element package to simulate the arching effect. If this could be established, then finite element analysis could be used to optimise the design of slabs, leading to efficient and cost effective solutions, and achieving the objective of a sustainable structure.

Abaqus offers a choice of constitutional material models for simulating the behaviour of the concrete. The first model, the smeared crack model [2], has been offered by the Abaqus package for many years, however, Abaqus has recently provided an alternative, the damaged plasticity model [3]. A third brittle material model is also available, but although the tensile characteristics are appealing, it only allows for linear compressive behaviour which would be inadequate for this particular application and hence is not considered in this work. In addition to the differing material models, the analysis can be undertaken using either implicit or explicit analysis. The implicit method is the traditional method where the non-linear equations are solved using a Newton Raphson approach and the explicit method involves dynamic analysis where the deformations at the next time step are derived from integrating the accelerations at the current time step.

The permutations given in the previous paragraph form the areas under investigation in this work. The objective was to establish, which method, if any, can best be used to simulate the arching effect in restrained slabs.

The results have shown that the smeared crack and the damaged plasticity models provide similar results. Convergence proved more difficult with the damaged plasticity model but analysis near to failure could be achieved through the appropriate selection of tension stiffening parameters. Both models were capable of modelling the arching effect, with the strength of the slab being greatly enhanced with increasing restraint. The predicted failure loads showed good correlation with experimental results. Although it was the damaged plasticity model that experienced the most severe convergence problems, both methods did not converge easily using the implicit method. The problem being modelled was not easy to analyse, with large areas of the slab cracked under tension. It was hoped that the explicit method would offer a solution to the convergence problems associated with the damaged plasticity model and this proved to be the case, as the explicit method demonstrated itself to be extremely computational efficient. However there wss some doubt regarding the explicit method's ability to model softening of the slab.

1

Taylor, S.E., Rankin G.I.B., Cleland, D.J, "Arching Action in High Strength Concrete Slabs", ICE proceedings - Structures and Buildings, 146, 353-362, 2001. doi:10.1680/stbu.146.4.353.45453

2

Hillborg, A. , Modeer, M., Petersson, P.E., "Analysis of Crack Formation and Crack Growth by Means of Fracture Mechanics and Finite Elements", Cement and Concrete Research, 6, 773-782, 1976. doi:10.1016/0008-8846(76)90007-7

3

Lubliner, J., Oliver, S., Oller, S., Onate, E., "A Plastic-Damage Model for Concrete", International Journal of Solids and Structures, 25, 299-329, 1989. doi:10.1016/0020-7683(89)90050-4

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