Intrinsic scatter of FRC: an alternative philosophy to estimate characteristic values

TLDR: In this paper, an extensive parametric study is conducted with more than 35,000 models, each one unique in terms of fibre distribution. And an alternative formulation is defined to estimate the characteristic value of the FRC considering the real structure in which it will be applied, and the results derived from this study represent a contribution towards a more efficient design of structures and the reduction of the nonconformities in the quality control of the fiber reinforced concrete.

Abstract: The results from small-scale laboratory tests of fibre reinforced concrete (FRC) usually show a high scatter. However, several studies indicate that the real scatter on the post-cracking response of the material reduces considerably with the increase of the size of the elements tested. Such observations highlights a possible contradiction in the design of FRC since the characteristic values estimated from small-scale tests might not be representative of large-scale structures. This could penalize the material, leading to higher fibre consumption, less competitive solutions and problems in the quality control. The main objective of the present study is to address this fundamental issue. The aim is to evaluate the scatter that is intrinsic to the FRC and how it is affected by the size of the element, the type of concrete, the type and content of fibre. For that, a novel numerical approach is proposed for the simulation of the material and its variability. Then, an extensive parametric study is conducted with more than 35,000 models, each one unique in terms of fibre distribution. Based on this analysis, equations are proposed to estimate the intrinsic scatter depending on several parameters. Finally, an alternative formulation is defined to estimate the characteristic value of the FRC considering the real structure in which it will be applied. The results derived from this study represent a contribution towards a more efficient design of structures and the reduction of the non-conformities in the quality control of the FRC.

Figures

Figure 8.- CVI for IC (a) and for AC (b)

Figure 17.- Influence of the result of the bending test on the final RSCV (a) and the fR,k (b)

Figure 3.- Methodology to estimate the scatter

Figure 13.- Relation between the CVI of fR,4 and the CV of number of fibre (a), embedded length (b) and angle (c) for elements with AC and 60 kg/m³

Table 2.- Parameters k depending on the number of specimens tested

Figure 1.- Coefficient of variance measured in the bending test EN 14651

Frequently asked questions

Q1. What are the contributions mentioned in the paper "Materials and structures intrinsic scatter of frc: an alternative philosophy to estimate characteristic values" ?

The main objective of the present study is to address this fundamental issue. The aim is to evaluate the scatter that is intrinsic to the FRC and how it is affected by the size of the element, the type of concrete, the type and content of fibre. The results derived from this study represent a contribution towards a more efficient design of structures and the reduction of the non-conformities in the quality control of the FRC. 

Q2. What are the properties of the material that are calculated according with the Eurocode 2?

Theother properties of the material such as elastic modulus and tensile strength were calculated according with the formulations proposed in the Eurocode 2. 

Q3. How many models were used to calculate the scatter?

For instance, in the simulation of the bending test with 30 kg of hooked fibres, 1000 models were analysed in order to calculate a single value of scatter. 

Q4. What is the effect of the larger number of fibres on the CVI?

the reduction in the variation due to the bigger number of fibres is compensated by the decrease on the average angle, leading practically to the same CVI for IC and AC. 

Q5. What is the way to estimate the load-crack opening curve?

The application of these models require the execution of at least one pull-out test of a single fibre aligned with the load direction in order to obtain the key points of the load-crack opening curve. 

Q6. How many models are needed to obtain representative values of scatter for different fibre contents?

Notice that in the present work, tens of thousands of models should be processed in order to obtain representative values of scatter for different fibre contents and geometries. 

Q7. What is the effect of the real scatter on the post-cracking behaviour of FRC?

Several authors indicate that the real scatter on the post-cracking behaviour of FRC reducesconsiderably with the increase of the cracking surface, which is especially evident when real-scale elements are tested [5-10]. 

Q8. What is the intuitive result of the diagram?

The most intuitive result would be to observe an increase in the scatter as the CMOD increases since part of the fibres are pulled out of the concrete matrix, thus reducing the number of fibres that contribute to the residual strength. 

Q9. What is the effect of the degree of anisotropy of concrete on the CVI?

This suggests that the degree of anisotropy of concrete has a major influence on the CVI of the number of fibres and much less influence on the CVI of the angle.