# The Size Effect on Flexural Fracture of Polyolefin Fibre-Reinforced Concrete
## 4 Discussion
### Size Effect and Strength-CMOD Curves
Figure 11: \(Cont.\)  
Figure 10: Plots of average values of proportionality limit strength (\(f_{LOP}\)), minimum strength at the end of discharging branch (\(f_{MIN}\)), CMOD opening of 0.5 mm (\(f_{R1}\)) and CMOD of 2.5 mm (\(f_{R3}\)) versus the total specimen depth \(D\). The analysis of the relationship of residual strengths versus number of fibres also confirms the existence of the size effect. Figure 12 was prepared to analyse the size effect by using the plot residual strength versus number of fibres which shows the superior behaviour in terms of strength of the small specimens compared with the larger sizes. Considering all the sizes and fitting the lines passing through the origin, the tendency of each size could be found. If the figure is observed in detail, for a specific number of fibres in the fracture surface the strength obtained follows the size effect expected tendency. That is to say, the larger the size the lower is the strength for the same number of fibres. In such a way, the size effect existence was observed by decoupling the influence of the fibre distribution on the fracture surface. Figure 12 shows the values of \(f_{R1}\),\(f_{R3}\),\(f_{min}\) and \(f_{REM}\) as a function of the number of fibres in the fracture surface. As can be seen, keeping constant the volume fraction, the number of fibres in the fracture surface in the smallest specimens is about 50, in the medium-sized specimens around 100 and close to 200 for the largest specimens. To assess the size effect in \(f_{min}\), Figure 12 was performed. In this figure, the results of Figure 11a were extended by a linear fitting for the comparison with the same number of fibres. It has been shown [33] that residual strength in fibre-reinforced concrete is directly related with the number of fibres in the fracture surface. Figure 12 shows that with the same number of fibres there is a clear size effect. Considering, for example, 50 fibres the strength of the large specimens  
Figure 11: Tendency lines of the distinct residual strength values in relation to the number of fibres for the three specimen sizes: (**a**) for the minimum strength (\(f_{MIN}\)), (**b**) for CMOD of 0.5 mm (\(f_{R1}\)), (**c**) for CMOD of 2.5 mm (\(f_{R3}\)) and (**d**) for the maximum residual post-cracking strength (\(f_{REM}\)). Figure 12: Fitting lines of the relationship average minimum residual strength versus number of fibres. (point A) corresponds to a minimum value of 0.48 MPa, whereas this value increases to 0.78 MPa (point B) for medium-size specimens and reaches 1.11 MPa (point C) in case of small specimens. This data means a 231% strength increment in the small specimens in relation to the big specimens. Again, this behaviour confirmed that the size effect occurred for PFRC elements, according to the classical theory of size effect for quasi-brittle materials [32]. With this procedure it was possible to conclude that the size effect took place not only in the strength values depending on the concrete matrix (\(f_{LOP}\)) but also in the post-cracking strength values.