Variable Engagement Model for the Design of Fibre Reinforced Concrete Structures

In this paper a model is developed to describe the behaviour of randomly orientated discontinuous fibres in reinforced composites subject to uniaxial tension. The model is built by integrating the behaviour of single, randomly oriented, fibres over 3D space and is capable of describing the peak and post-peak response of fibre-cementbased composites in tension. The model is used to form a constitutive law for use in finite element analysis of reactive powder concrete members with a prestressed reactive powder beam failing in shear analysed. A good correlation between the theoretical and experimental results attained. Introduction The idea of using discrete, ductile, fibres to reinforce brittle materials such as concrete is not new with many studies having been undertaken over the past four decades. Early studies by Romualdi and Batson (1963) indicated that the tensile strength of concrete can be improved by providing suitably arranged and closely spaced wire reinforcement. The low tensile strength of concrete matrix is primarily due to the propagation of internal cracks and flaws. Romualdi and Batson hypothesized, that, if these flaws can be locally restrained from extending into the adjacent matrix, the initiation of tension cracking can be retarded and a higher tensile strength of the material achieved. By adding fibres to a concrete mix the objective is to bridge discrete cracks providing for some control to the fracture process and increase the fracture energy. The current understanding of the behaviour of fibre-matrix interfacial mechanics is based on a number of pullout studies using single or multiple fibres where steel fibres are ------------------1 Research Student, School of Civil and Environmental Engineering, The University of New South Wales, UNSW Sydney, 2052, Australia; phone +61 (2) 9385 5055; fax +61 (2)9385 6139; Jackie @civeng.unsw.edu.au 2 Associate Professor, School of Civil and Environmental Engineering, The University of New South Wales, UNSW Sydney, 2052, Australia; phone +61 (2) 9385 5055; fax +61 (2) 9385 6139; S.Foster@unsw.edu.au 1 Voo and Foster: Variable Engagement Model for the Design of Fibre Reinforced Conc Published by ECI Digital Archives, 2003 2 embedded within a cementitious matrix. In spite of a belief sometimes expressed (Banthia and Trottier, 1994) that no correlation exists between the behaviour of a single fibre pullout test and the behaviour of bulk fibres in a real composite matrix, the effectiveness of a fibres as a medium of stress transfer is often assessed using fibre pullout tests where slip between the fibres and the matrix is monitored as a function of the applied load. It is well established that for quasi-brittle materials, such as concrete, loaded in tension that localization dominates the behaviour beyond the peak load and that this behaviour can be described by the load versus crack opening displacement (w) as shown in Figure 1. In this paper a deterministic model is developed for uniaxial tension based on experimental observations and probability for randomly oriented fibres in three dimensions. The model developed within is named the Variable Engagement Model.