The flexural strength of pavement concrete is generally deduced by testing beams or by applying empirical equations. In this investigation, concrete mixtures were manufactured, incorporating 0, 20, 50 and 100% Reclaimed Asphalt Pavement (RAP), by weight, as a replacement for natural aggregates. The compressive strength was measured using cubic specimens and the flexural strength was measured for three types of specimens; beam, semicircular (SCB) and modified beam. This study proposes logarithmic and power equations that allow the estimation of the flexural strength of a concrete mix that incorporates RAP as a function of its compressive strength. Linear or power models are proposed to predict beam flexural strength from SCB specimens and a logarithmic model for modified beam specimens. Statistical analyses show that the proposed prediction models can be considered sufficiently accurate and their use is justified.
La resistencia a la flexión de un concreto para pavimentos generalmente se estima ensayando vigas o aplicando ecuaciones empíricas. En esta investigación se fabricaron mezclas de concreto incorporando 0, 20, 50 y 100% de material asfáltico recuperado (RAP) como reemplazo por peso de los agregados naturales. Se midieron las resistencias a la compresión de probetas cúbicas y a la flexión para tres tipos de probetas; viga, semicircular (SCB) y viga modificada. Este estudio propone ecuaciones logarítmica y potencial para estimar la resistencia a la flexión de un concreto que incorpora RAP en función de su resistencia a la compresión. Para predecir la resistencia a la flexión de viga a partir de probetas SCB se propone el modelo lineal o potencial y para probetas de viga modificada el modelo logarítmico. Los análisis estadísticos muestran que los modelos de predicción propuestos pueden considerarse lo suficientemente precisos y su uso está justificado.
Flexural strength is a measure of the tensile strength of a concrete and is expressed in terms of the Modulus of Rupture (MOR). This parameter is used in structural design (
Equation  Comment  Reference 


IS: 4562000 (India)  ( 

EC02 (Europe)  ( 

Ahmed et al.  ( 

ACI2002  ( 

ACI2005  ( 
On the other hand, about 86% of Chile’s paved road network is built with hot mix asphalt (HMA) (
In recent years, the incorporation of RAP in the manufacture of new concrete mixtures for pavements has been explored with two main objectives: to achieve greater dissipation of fracture energy, by reducing a possible abrupt and fragile failure of the concrete, and reducing the exploitation of natural resources, by promoting a lower consumption of virgin aggregates using a material that still retains good physical properties and is considered to be an artificial source of aggregates (
Based on the literature review, it was possible to establish that there is no consensus for estimating flexural strength from compressive strength. There are proposals for various equations that provide different results. Few laboratory studies have been carried out to propose a userfriendly correlation equation to estimate the modulus of rupture of concrete incorporating RAP, as a substitute for natural virgin aggregates in pavement applications. The main objective of this study was to characterize concrete mixtures with different RAP contents in the laboratory, measuring the compressive strength of cubes and the flexural strength by testing three types of specimens; beam, semicircular beam (SCB), and modified beam. The results of this research propose different empirical equations to estimate the flexural strength of concrete with RAP from its cubic compressive strength, according to the type of test specimen. It also proposes correlation equations for estimating the modulus of rupture of concrete with RAP for a standardized beam, from laboratory results using the semicircular and modified beam specimens.
Road agencies in Chile will be able to use the results of this research to study the possible adoption of the use of concrete with RAP aggregates for pavements in its construction standards, by applying the precepts of the circular economy, promoting the reduction of construction waste, reducing the use of natural resources and limiting energy consumption. This study also promotes the feasibility of using other geometries and test modes, such as SCB, to estimate the modulus of rupture of concrete by implementing a simple, fast test with different advantages compared to the traditional beam test.
A commercial Portland cement type A, with a density of 2.9 g/cm^{3}, and fresh tap water were used for all concrete mixtures. This water is considered suitable for use in concrete under the standard NCh1498 (
Sieve size (mm)  40  25  20  12.5  10  5  2.5  1.25  0.63  0.315  0.16  0.08 
% passing  100  76  62  53  47  32  25  20  15  6  1  0 
Property  Unit  Sand  Gravel 1  Gravel 2  Fine RAP  Coarse RAP 

Bulk unit weight  t/m^{3}  2.74  2.80  2.76  2.30  2.40 
Dry bulk specific gravity  t/m^{3}  2.58  2.66  2.68  2.24  2.31 
Relative specific gravity (SSD)  2.64  2.71  2.71  2.26  2.35  
Absorption  %  2.30  1.90  1.00  1.10  1.55 
Asphalt content  %        7.0  4.0 
A grade H35 concrete (35 MPa) was dosed according to NCh 170 (
Mix Type  Mix Description  Materials (kg/m^{3})  

Cement  Water  Aggregate  RAP  
R0  100% virgin aggregates  364  160  1902.0  0.0 
R20  80% virgin aggregates + 20% RAP aggregates  364  160  1521.6  380.4 
R50  50% virgin aggregates + 50% RAP aggregates  364  160  951.0  951.0 
R100  100% RAP aggregates  364  160  0.0  1902.0 
Hardened concrete was tested for compressive strength and flexural strength.
Hardened concrete properties  

Compressive strength  Flexural strength  Flexural strength  Flexural strength  
Standard  NCh 1037  NCh 1038  NCh 1038  EN 1269744 
Specimen size (mm)  150x150x150  150x150x550  75x75x120  100x50x50 
Shape  Cube  Beam  Modified beam  Semicircular 
Testing age, d  7, 14, 28  7, 14, 28  7, 14, 28  7, 14, 28 
The compressive strength of 150 mm cubes was measured according to NCh 1037 (
The reduction in strength could be due to the asphalt layer around the RAP particles being softer than the concrete and aggregate matrix. The presence of a soft binder can induce stress concentration and cause microcracking within the concrete matrix. Another possible reason could be the weak link between the asphalt film and the concrete matrix (
A regression analysis of the relationship between cubic compressive strength and flexural strength was performed for three different specimens. All curing periods were taken into account for this analysis. Linear, logarithmic, and power regression models were analyzed to evaluate the prediction equations that best fit the experimental data. From the regression analysis, the equations presented in
Test mode  Model Regression Equations  

Linear  Logarithm  Power  
Beam 


SCB  
Modif Beam 
where
The goodness of fit and the performance of the models were evaluated using statistical procedures. The coefficient of determination (
where
From
% RAP  Age (days)  Experimental data (MPa) 







Beam model  SCB model  Modified Beam model  
Linear  Logarithm  Power  Linear  Logarithm  Power  Linear  Logarithm  Power  
0  7  25.03  2.30  3.26  4.88  2.70  2.76  2.76  3.89  3.95  3.92  7.36  7.53  7.37 
14  28.53  2.82  4.18  8.70  2.88  2.89  2.92  4.14  4.12  4.13  8.13  8.06  8.09  
28  35.17  3.18  4.62  9.79  3.23  3.10  3.20  4.61  4.39  4.48  9.61  8.91  9.39  
20  7  14.33  2.13  2.75  4.28  2.14  2.20  2.15  3.13  3.22  3.16  4.98  5.27  4.97 
14  16.20  2.63  3.73  6.26  2.24  2.33  2.27  3.26  3.38  3.31  5.39  5.76  5.42  
28  20.45  2.82  4.06  7.18  2.46  2.56  2.52  3.56  3.69  3.63  6.34  6.71  6.39  
50  7  12.37  1.78  2.49  4.01  2.04  2.06  2.02  2.99  3.03  2.98  4.54  4.67  4.47 
14  14.50  2.27  3.25  5.79  2.15  2.22  2.17  3.14  3.24  3.17  5.01  5.31  5.01  
28  16.03  2.52  3.60  6.61  2.23  2.32  2.26  3.25  3.37  3.30  5.35  5.72  5.38  
100  7  8.03  1.52  2.23  3.00  1.81  1.63  1.67  2.68  2.46  2.52  3.57  2.92  3.29 
14  9.23  1.68  2.97  3.47  1.87  1.77  1.77  2.77  2.65  2.66  3.84  3.48  3.63  
28  9.93  2.02  3.09  4.17  1.91  1.84  1.83  2.81  2.74  2.74  4.00  3.78  3.83  

0.859  0.896  0.890  0.834  0.841  0.827  0.877  0.878  0.883  

0.738  0.803  0.793  0.695  0.708  0.684  0.769  0.771  0.780  

0.745  0.559  0.631  1.698  1.626  1.623  11.388  11.257  11.138  

0.249  0.216  0.229  0.376  0.368  0.368  0.974  0.969  0.963  

0.097  0.080  0.085  0.106  0.103  0.105  0.150  0.132  0.141 
Standardized 150 x 150 x 550 mm beams, that can reach a weight of up to 30 kg, have traditionally characterized the flexural strength property of concrete for pavement applications. The flexural strengths were measured from semicircular, smaller beam specimens (75 x 75 x 120 mm) obtained from standardized beams. A possible correlation between the flexural strength values for the three types of specimens was studied. Linear, logarithmic, and power regression models were analyzed to evaluate the prediction equations that best fit the experimental data. From the regression analysis, the equations presented in
Model  Model Regression Equations  

Linear  Logarithm  
Beam 


SCB  
Modif Beam 
% RAP  Age (days) 




Beam  SCB  Modified beam  SCB model  Modified Beam model  
Linear  Logarithm  Power  Linear  Logarithm  Power  
0  7  2.30  3.26  4.88  2.24  2.29  2.24  2.12  2.19  2.14 
14  2.82  4.18  8.70  2.87  2.85  2.87  3.00  2.97  3.02  
28  3.18  4.62  9.79  3.17  3.07  3.16  3.25  3.12  3.24  
20  7  2.13  2.75  4.28  1.89  1.91  1.89  1.98  2.01  1.97 
14  2.63  3.73  6.26  2.56  2.59  2.56  2.44  2.52  2.48  
28  2.82  4.06  7.18  2.79  2.78  2.78  2.65  2.71  2.69  
50  7  1.78  2.49  4.01  1.72  1.69  1.71  1.92  1.92  1.90 
14  2.27  3.25  5.79  2.24  2.29  2.23  2.33  2.42  2.37  
28  2.52  3.60  6.61  2.47  2.51  2.47  2.52  2.59  2.56  
100  7  1.52  2.23  3.00  1.54  1.44  1.54  1.69  1.53  1.60 
14  1.68  2.97  3.47  2.04  2.08  2.04  1.80  1.73  1.74  
28  2.02  3.09  4.17  2.12  2.17  2.12  1.96  1.97  1.94  

0.960  0.952  0.947  0.959  0.977  0.970  

0.923  0.907  0.896  0.920  0.954  0.941  

0.220  0.265  0.221  0.228  0.130  0.177  

0.135  0.149  0.136  0.138  0.104  0.121  

0.046  0.051  0.046  0.057  0.041  0.049 
A laboratory study was developed to evaluate the mechanical properties of concrete with and without the incorporation of RAP. Cube compression strength and flexural strength tests were carried out, applying three test modes representing different shapes and sizes of specimens (beam, SCB, and modified beam). Based on the analysis of the test results, it is possible to draw the following conclusions:
Compressive strength and flexural strength decrease with increasing RAP in the mix. Compressive strength decreases dramatically from 20% RAP incorporation. The flexural strength for all threetest modes decreases steadily with RAP incorporation into the mixture. It can be considered a less susceptible property compared to the compressive strength. The flexural strength depends on the shape and size of the specimen and the type of test.
Representative equations are proposed to relate the compressive strength properties to the flexural strength for the three test specimens. This relationship depends on the shape of the test specimen used and the amount of RAP incorporated in the mixture, but it is considered to be constant during the curing time. The logarithmic and power models are the most appropriate and accurate to use. For these models, the Pearson correlation coefficient between the two types of strength is greater than 0.80, which indicates that they are wellcorrelated and fit satisfactorily with the experimental data.
The power equation proposed to relate the compressive strength and the flexural strength of standardized beams shows the same trend as the equation proposed by ACI2002, practically obtaining the same results.
In this research, correlation equations are proposed between flexural strengths for the three types of tests used. Linear and power models are suggested for tests with SCB specimens and a logarithmic model for tests with modified specimens. These models have a Pearson correlation coefficient higher than 0.9, which means a very high association of strength and explains a large part of the variability of the response, indicating that they are the most adequate and accurate to represent the experimental data. The models can be used to estimate the flexural strength of concrete obtained for a standardized beam from the values obtained in the laboratory using more easily manipulated and safer specimens, both in the laboratory and in the field.