## 3 Experimental Results
### Beam Performance  
The approach proposed in Section 2.3.2 for predicting the bending behaviour through reliability analysis allows the uncertainty in the behaviour to be quantified. To introduce this uncertainty, the populations of results obtained in the previous section were fitted to probabilistic distributions functions by performing goodness-of-fit tests. The candidate PDFs were selected based on physical considerations and other experimental campaigns with similar methodologies [33; 62]. To obtain a larger population size, both cylindrical and cubic sample values were used, applying conversion factor \(\gamma\) = 0.90. Considering that most of the data accepted all the tests, a lognormal distribution was chosen, including the mean and the deviation for each of the parameters, as shown in Table 2. In particular, after goodness-of-fit tests, a lognormal distribution was selected since, in contrast to the normal distribution, these physical parameters cannot reach negative values. Taking into account the model defined to obtain the maximum theoretical load, the variables related to the properties of the concrete were introduced as probabilistic variables, except for the tensile strength. In this case, due to its low value in relation to the steel used, the tensile strength of the concrete was not included in the calculation. In the case of the steel parameters, the properties corresponding to a B400S steel were used as a constant input. The ultimate strain of the recycled concrete was also used for the ultimate stress testing domain. With regard to the model for obtaining the deflection, the experimentally obtained compressive and tensile strengths and the modulus of elasticity were taken into account according to Equations (3) and (4). Due to the difficulty of knowing exactly the effective moment of inertia, a probabilistic coefficient of uniform distribution in the range of 30 to 50% was also introduced in this case and applied to the gross moment of inertia. The uniform distribution was chosen in this case due to the complexity of knowing this parameter and to achieve an equiprobable and uniform sampling. The higher uncertainty of this parameter is a handicap in accurately predicting the deflection result. In order to obtain a probabilistic density function for the maximum load and deflection supported by a beam manufactured with the recycled concrete studied, a total of \(10^{6}\) simulations were carried out using MCS for the previously defined model parameters. The distribution of the simulation results is shown in Figure 8 for the maximum load and in Figure 8 for the deflection. Both graphs show how the results are distributed according to a distribution that can be considered lognormal, with the modal value close to the mean. The most frequent value for the maximum load is 49.65 kN, while the most frequent value for the deflection is 9.32 mm. In order to validate the model and obtain the real behaviour of the recycled concrete bending beams, the experimental tests described in Section 2.3.1 were carried out. A total of six beams made of the studied recycled concrete were tested with the proposed configuration. A sample of six beams was used to strike a balance between representativeness of results and practical constraints such as available resources. This sample size ensures a variety of representative conditions from which meaningful conclusions can be drawn. This representative sample allows the model to be validated so that it can be scaled up and generalised to larger populations through further statistical analysis, such as Monte Carlo simulations. The results corresponding to the maximum load and deflection of each of the beams are also shown in Figures 8a and 8b, respectively. The DIC technique was also used to calculate the deflection experimentally. Due to the span of the beam, only a central ROI was selected where the largest displacements occur. A set of \(5\times 5\) px under the midpoint was then taken to obtain the average deflection.