Keywords: steel fibres, high performance concrete, three dimensional finite element modelling.

It is well known that the main drawback of concrete is its low tensile strength. Due to this fact, the concrete tends to crack even under relatively low forces and for this reason, it is used mainly in the form of reinforced concrete. It has been proved by many researchers that the overall behaviour of concrete can be improved by the addition of steel fibres to the concrete mix. The positive effect of the steel fibres is not profound until the first crack occurs in the concrete. After this point, the behaviour of the fibre reinforced concrete is completely different from that of unreinforced concrete.

Various researchers have studied the behaviour of fibre reinforced concrete and the various parameters that affect the effectiveness of the steel fibres. The first steel fibres that were used for the production of fibre reinforced concretes were straight. A lot of analytical models were developed for the explanation of their beneficial participation. Later, steel fibres of improved shape were introduced, such as hemi-circular, curved, waved and hooked shapes. It was demonstrated by various researchers that the use of these steel fibres of improved shape lead to better performance with respect to straight vibres in terms of compressive concrete strength [1,2], flexural strength [2,3,4] and shrinkage [5]. Intuitively, the main reason for this improved performance is the mixed friction-plastification mechanism that is developed during the fibre pull-out on either side of the crack. However, the analytical study of the pull-out mechanism seems to be a difficult task as many nonlinear effects should be accurately taken into account.

The aim of the present paper is to understand the pull-out mechanism of hooked fibres from a high strength matrix. For this reason, various two-dimensional and three-dimensional models were formulated. All the numerical models take effectively into account the various nonlinearities which are present in the physical model, such as the unilateral contact between the steel fibre and the matrix, the frictional mechanism and the plastification of the steel fibre.

In order to understand the pull-out mechanism a parametric analysis was performed, by modifying the various quantities governing the structural behaviour as:

• The yield stress of the steel fibre
• The geometry of the steel fibre
• The compressive strength of the concrete matrix
• The friction coefficient between the steel fibre and the concrete matrix

Although three-dimensional modelling was mainly used for the computation of the results, the fact that the computational time was enormous, led to the development of simple two-dimensional models. The paper presents certain tips for the development of the simplified models, which, under certain circumstances may lead to acceptable results. Finally, the last part of the paper is dedicated to the study of the effect of different fibre geometries to the load-displacement behaviour during the pull-out test.

1

D.E. Otter and A.E. Naaman. Fiber Reinforced Concrete Under Cyclic and Dynamic Compression Load. Research Report, No. UMCE 88-9, Department of Civil Engineering, University of Michigan, Ann Arbor, 178 pp., 1988.

2

S. Ezeldin and S.R. Lowe. "Mechanical Properties of Steel Fiber Reinforced Rapid-Set Materials", ACI Materials Journal, Jul-Aug, Vol. 88, No. 4, pp. 384-389, 1991.

3

V. Ramakrishnan, G.Y. Wu, and G. Hosalli. "Flexural Behavior and Toughness of Fiber Reinforced Concretes", Transportation Research Record, No. 1226, 1989, pp. 69-77, 1989.

4

P.N. Balaguru, R. Narahari, and M. Patel. "Flexural Toughness of Steel Fiber Reinforced Concrete", ACI Materials Journal, Nov-Dec, Vol. 89, No. 6, pp. 541-546, 1992.

5

M. Pailleve, M. Buil, and J.J. Serrano. "Effect of Fiber Addition on the Autogenous Shrinkage of Silica Fume Concrete", ACI Materials Journal, Mar-Apr, Vol. 86, No. 2, pp. 139-144, 1989.

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