3
Mechanical properties of the hardened concrete

3.1 General

Owing to its dense microstructure, ultra high performance concrete (UHPC) has both a high strength and also a greater stiffness (expressed by the modulus of elasticity) when compared with normal- and high-strength concretes. It is well known that the behaviour of concrete becomes more brittle as its strength increases. This effect is particularly evident with UHPC. However, this disadvantage can be countered effectively by adding fibres, e.g. high-strength steel fibres, which bring about a considerable improvement in the post-peak behaviour in compression and tension, and that in turn means a more favourable response generally and better warnings when failure is pending. Further, the utilizable strength can be increased, especially for tension actions. Compared with the brittle matrix, activating the fibres (basically a form of reinforcement) can also help UHPC handle tension more reliably. Various mechanical properties of the hardened concrete are discussed below in so far as they are relevant, also with respect to the influence of adding fibres. However, the local distribution of the fibres and their orientation must always be considered, see Section 2.7.2. Some of the information below is drawn from the state of the art report on UHPC [22].

3.2 Behaviour in Compression

3.2.1 UHPC without Fibres

UHPC, compared with normal- and high-strength concrete, is characterized by the fact that, in a uniaxial compression test, it exhibits an essentially linear elastic behaviour for a relatively long time – until shortly before reaching its compressive strength and before the formation of microcracks signal the transition to failure. This effect has been observed essentially irrespective of the maximum grain size. The modulus of elasticity generally lies in the range 45–55 GPa. Adding bauxite can increase this figure significantly, to approx. 70 GPa. Without fibres, brittle failure is the result (see Figure 3.1), which in compression tests – as described in Section 2.7.2 – is very often in the form of a sudden, explosive failure. A similar effect has been observed in UHPC from values as low as about 90 N/mm2.

Fig. 3.1 Stress–strain diagram for UHPC without fibres in a uniaxial compression test

The addition of fibres has very little influence on the ascending portion of the stress–strain diagram. The increase in strength with typical fibre contents of up to approx. 2.5% by vol. is of minor importance, likewise the influence on the modulus of elasticity. However, this and the strain upon reaching the strength clearly depend on the grading of the aggregate. In the case of fine-grained concretes with max. 2 mm particle size, we can typically expect 4.0–4.4‰ [57,58], whereas in coarse-grained concretes, figures in the region of 3.5‰ have been observed.

Generally, the value of the modulus of elasticity of UHPC is underestimated by the equations given in DIN 1045-1 and CEB-FIP Model Code 90 [59]. Following tests carried out at the University of Leipzig [58], the following relationships between the modulus of elasticity Ec and the cylinder compressive strength fc have been proposed for fine- and coarse-grained UHPC (see Figure 3.2):

Fig. 3.2 Relationship between modulus of elasticity and cylinder compressive strength [22]

with Ec and fc in N/mm2.

As in EN 1992 [61,62] and DIN 1045-1,

can be assumed.

Poisson's ratio ν was found to lie between 0.18 and 0.19 for fine-grained UHPC in the elastic zone [60] and to be approx. 0.21 for coarse-grained UHPC (basalt chippings with max. 5–8 mm particle size). It is therefore very similar to the figure of 0.2 typically assumed for normal-strength concrete. As can be seen from the stress–strain diagram, a departure from the linear elastic response takes place fairly late due to the formation of microcracks, which is reflected in the late rise in Poisson's ratio (see Figure 3.3). At failure, ν = 0.3 can be assumed unless more accurate data is available for the respective mix.

Fig. 3.3 Development of Poisson's ratio ν as the compressive stress increases [22]

3.2.2 UHPC with Steel Fibres

The addition of high-strength steel fibres can bring about a distinct improvement in the post-peak structural behaviour. However, this has hardly any effect on the ascending portion of the stress–strain curve. By contrast, the descending portion of the curve is influenced to a great extent by the following parameters:

1. – Fibre content
2. – Fibre geometry (length, diameter), also when compared with the maximum particle size
3. – Fibre orientation
4. – Bond between fibre and matrix (surface properties, any profiling, etc.)
5. – Stiffness of the fibres, specifically in combinations of different fibres.

It is, however, hardly possible to predict the course of the descending portion of the stress–strain curve by means of simple relationships. Therefore, appropriate laboratory studies are generally necessary for a certain UHPC. It should also be remembered that the fibre content and fibre orientation in a component can vary locally and be influenced by concreting activities. During concreting, the large majority of the fibres is aligned with the direction of flow, primarily parallel with any nearby formwork surface. As an example, Figure 3.4 shows a number of measured stress–strain curves for Ductal® [63] (measured on 200 × 100 × 100 mm prisms) and according to [11] (measured on 300 × 150 × 150 mm cylinders). The figure clearly shows how the post-peak behaviour can be considerably improved and controlled by adding fibres. However, the measured stress–strain curves for the post-peak range (descending portion of curve) exhibit much more scatter than the ascending portion. This is illustrated schematically in Figure 3.5.

Fig. 3.4 Compression stress–strain relationships for UHPC with fibres [22,63]

Fig. 3.5 Compression stress–strain diagram (schematic) for UHPC with variation in the behaviour in the descending portion depending on fibre content, fibre type and fibre orientation [22]

Up to about 2% by vol. fibres, no significant influence on the compressive strength was observed. According to [11], a rise in the compressive strength amounting to approx. 15%, compared with an otherwise identical mix without fibres, was noted at a content of 2.5% by vol.

3.2.3 Further Factors Affecting the Compressive Strength

3.2.3.1 Geometry of Test Specimen and Test Setup

The results available regarding the influences of the test specimen geometry are inconsistent. From the mechanics of materials viewpoint, it is the way the loading platens restrict the lateral strain that is responsible for this. Normally, cylindrical specimens with a slenderness ratio (height/diameter) of 2 should be used to determine the compressive strength. The diameter should be at least 100 mm. The French guideline [64] recommends cylinders with dimensions of 70 mm dia. × 140 mm high or 110 mm dia. × 220 mm high.

Quite often, the high strength of UHPC means that the test specimen dimensions have to be chosen to suit the capacity of the testing machine. In the case of UHPC without fibres in particular, it is especially important that the surfaces of the specimen are exactly parallel and that stress concentrations due to misalignment or deformation of the loading platens are avoided.

3.2.3.2 Heat Treatment

Curing with the help of heat can increase the strength of UHPC and accelerate the strength development. Temperatures of approx. 80–90 °C are typical, which are applied for 1–2 days. According to [11,25,65], heating at only 90 °C for just 48 h leads to higher strengths than storing in water for 28 days at 20 °C. Heat treatment at 250 °C influences not only the reaction rate of the setting process, but also leads to the formation of other mineral phases and hence to a change to the microstructure that results in much higher strengths being reached.

3.3 Behaviour in Tension

3.3.1 Axial (Concentric) Tension Loads

Axial tension tests represent a direct way of shedding light on how UHPC behaves in tension. Tests on unnotched specimens are suitable for determining the tensile strength, whereas tests on notched specimens are more appropriate for determining the stress–crack width relationship of fibre-reinforced UHPC. The latter is regarded as characteristic for the response of brittle materials or materials with a softening post-peak behaviour. Typical tensile strength values for UHPC lie in the range 7–11 N/mm2. Fehling et al. [11] and Tue/Dehn [60] did not observe any significant differences between fine- and coarse-grained concretes without fibres. However, the tensile strength is mainly influenced by the addition of silica fume to the mix.

Without fibres, very brittle failure can be expected in tension. It is therefore very difficult to measure any stable descending portion in the force–deformation diagram, or stress–crack width diagram....