AN APPROXIMATE DAMAGE MODEL FOR CONCRETE. UNDER FINITE DEFORMATION

S. Khajehpour1, G. D. Morandin and R. G. Sauve

Computational Mechanics Development Reactor Engineering Services Atomic Energy of Canada Ltd.

2251 Speakman Dr.,
Mississauga, On, Canada L5K 1B2

Abstract

As the computing power of computers is constantly increasing, more accurate finite element analysis and detailed modelling of structures are sought. The critical issue of concern at hand is the characterization of complex material constitutive behaviour using numerical techniques. Finite element analysis of reinforced concrete structures under severe and reversible loadings requires a proper representation of concrete material behaviour. Abnormal loads such as impact, blast and seismic are generally reversible and cause structures to vibrate. To arrive at a reasonable approximation of damage in reinforced concrete structures under abnormal loading, the cracking of the concrete and its direction must be addressed. The inclusion of a mechanism that accounts for crack closure should be considered to include the compression strength of the cracked concrete if the load direction is reversed and the crack is closed. Thus, development of an improved material model for concrete and its implementation in a non-linear finite element code that is well suited to this class of problem is undertaken. In the work described in this paper, the methodology used in the development of this new material model for concrete is discussed. A sample case is analysed and the results of these FE analyses are discussed. The new concrete material model predicts the location and the direction of the cracks accurately and also allows for the inclusion of the compression strength of the cracked material in directions parallel to crack plane. In addition the closure of the crack and re­activation of the compression strength of the concrete orthogonal to the crack plane when the crack is closed is achieved.

1. Introduction

The work described in this paper covers the methodology used to evaluate the structural integrity of a reinforced concrete structure (shown in Figure 1) following a postulated handling accident scenario. To achieve this objective, a material model that approximately represents true behaviour of concrete material is developed. The primary structure considered in this work will be used for the purpose of facilitating the loading of a special container with radiated waste material. It is postulated that during the various handling operations, a loading accident occurs when the container is suspended over the structure at a certain vertical position above the water surface. The objective of this work is to determine, using full-scale explicit transient analysis with modelling of reinforced concrete, if the mentioned reinforced structure is capable of withstanding the pressure pulse generated by the accidental drop of the container onto the surface of the water contained in the loading bay. The loading considered in this work arises from dropping the container from the maximum handling height of 0.354 m onto the surface of the water assuming that the concrete structure is filled with water. This evaluation was achieved by employing the concrete material model described in this paper as part of the state-of-the-art three-dimensional non-linear continuum computer code H3DMAP (Sauve, R. G. et al. 2004) for the numerical simulation of the fluid-structure interaction response of the container drop-generated shock wave. Pertinent modelling details include the hydrodynamic and acoustic

khaiehpours@aecl. ca, Corresponding author

87

M. Pandey et al. (eds), Advances in Engineering Structures, Mechanics & Construction, 87-98. © 2006 Springer. Printed in the Netherlands.

effects of the fluid with surface waves, discrete attachments, finite deformation material constitutive laws (i. e., large displacement and large strain), concrete reinforcing bar and large motion sliding/contact surfaces between the water and containing structures. Description of the proposed concrete material model, the method of analysis, key assumptions, and detailed results are presented in this paper.

’Stainless Steel Liner

Container

Pool*

Silent

Figure 1: Overall View of Reinforced Concrete Structure (FE Model)