1. INTRODUCTION
⌅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 (11.
ICPA - Instituto del Cemento Portland Argentino. (2014) Manual de
diseño y construcción de pavimentos de hormigón, ISBN 978-950-677-003-7,
Buenos Aires, Argentina, (2014)
), quality control and acceptance of pavements (22. NRMCA - National Ready Mixed Concrete Association. (2000) CIP 16- Flexural Strength Concrete. Concrete in Practice, https://www.nrmca.org/wp-content/uploads/2020/04/16pr.pdf
), which is determined by the standard methods
given in ASTM C78 (third-point loading) or ASTM C293 (center-point
loading) using a standardized 150 x 150 x 550 mm beam. However, this
test is susceptible to the effects of sample preparation, handling, and
the curing process (22. NRMCA - National Ready Mixed Concrete Association. (2000) CIP 16- Flexural Strength Concrete. Concrete in Practice, https://www.nrmca.org/wp-content/uploads/2020/04/16pr.pdf
). Also, the specimen is heavy, making it difficult to handle in the laboratory or the field (33.
Yusuf, I.T.; Jimoh, Y.A.; Salami, W.A. (2016) An appropriate
relationship between flexural strength and compressive strength of palm
kernel shell concrete. Alexandria Eng. J. 55 [2], 1553-1562. https://doi.org/10.1016/j.aej.2016.04.008
). Many road agencies have used compressive
strength as they consider it to be more reliable and convenient to
analyze the quality of the concrete and, later through correlation,
estimate its flexural strength. Although it is known that this
relationship is not a direct proportion, it is commonly held that the
compressive strength is approximately ten times the flexural strength,
which implies a fixed relationship between these two variables (44.
Ahmed, M.; El Hadi, K.M.; Hasan, M.A.; Mallick, J.; Ahmed, A. (2014)
Evaluating the co-relationship between concrete flexural tensile
strength and compressive strength. Int. J. Struct. Eng. 5 [2], 115-131. https://doi.org/10.1504/IJSTRUCTE.2014.060902
). Previous investigations have proposed empirical equations for this relationship, mainly of the form fs=afcun , where fs is the flexural strength of the concrete, fcu is the cube compressive strength of the concrete and a and n are correlation coefficients, as shown in Table 1. Most of these equations follow the square root form as an exponent (5-75.
Xiao, J-Zh.; Li, J-B.; Zhang, C. (2006) On relationships between the
mechanical properties of recycled aggregate concrete: An overview. Mater. Struct. 39, 655-664. https://doi.org/10.1617/s11527-006-9093-0
6. Ismeik, M. (2009) Effect of mineral admixtures on mechanical
properties of high strength concrete made with locally available
materials. Jordan. J. Civ. Eng. 3 [1], 78-90. https://www.iiste.org/Journals/index.php/JJCE/article/view/17874/18251
7. Ahmed, M.; Dad Khan, M.K.; Wamiq, M. (2008) Effect of concrete cracking on the lateral response of RCC buildings. Asian J. Civ. Eng. (Building Housing). 9 [1], 25-34. https://www.sid.ir/En/Journal/ViewPaper.aspx?ID=108211
). Other investigations have proposed equations
that do not follow the square root form to predict the flexural strength
of concrete (33.
Yusuf, I.T.; Jimoh, Y.A.; Salami, W.A. (2016) An appropriate
relationship between flexural strength and compressive strength of palm
kernel shell concrete. Alexandria Eng. J. 55 [2], 1553-1562. https://doi.org/10.1016/j.aej.2016.04.008
, 8-108. Uchechukwu, A.; Kabir, N. (2019) Flexural strength and compressive strength relations of spent foundry sand concrete. ACI Mater. J. 116 [6], 205-211. https://doi.org/10.14359/51718055
9. Bhanja, S.; Sengupta, B. (2005) Influence of silica fume on the tensile strength of concrete. Cem. Concr. Res. 35 [4], 743-747. https://doi.org/10.1016/j.cemconres.2004.05.024
10. Chhorn, C.; Hong, S.J.; Lee, S.W. (2018) Relationship
between compressive and tensile strengths of roller-compacted concrete. J. Traffic Transp. Eng. 5 [3], 215-223. https://doi.org/10.1016/j.jtte.2017.09.002
). It should be noted here that, in the equations
in ACI-2002 and ACI-2005, a conversion factor of 0.8 is applied to
convert the compressive strength of the cylinder to the cube, according
to (1111.
Pacheco, J.N.; de Brito, J.; Chastre, C.; Evangelista, L. (2019)
Probabilistic conversion of the compressive strength of cubes to
cylinders of natural and recycled aggregate concrete specimens. Materials. 12 [2], 280. https://doi.org/10.3390/ma12020280
).
| Equation | Comment | Reference |
|---|---|---|
|
| IS: 456-2000 (India) | (33.
Yusuf, I.T.; Jimoh, Y.A.; Salami, W.A. (2016) An appropriate
relationship between flexural strength and compressive strength of palm
kernel shell concrete. Alexandria Eng. J. 55 [2], 1553-1562. https://doi.org/10.1016/j.aej.2016.04.008
) |
|
| EC-02 (Europe) | (33.
Yusuf, I.T.; Jimoh, Y.A.; Salami, W.A. (2016) An appropriate
relationship between flexural strength and compressive strength of palm
kernel shell concrete. Alexandria Eng. J. 55 [2], 1553-1562. https://doi.org/10.1016/j.aej.2016.04.008
) |
|
| Ahmed et al. | (44.
Ahmed, M.; El Hadi, K.M.; Hasan, M.A.; Mallick, J.; Ahmed, A. (2014)
Evaluating the co-relationship between concrete flexural tensile
strength and compressive strength. Int. J. Struct. Eng. 5 [2], 115-131. https://doi.org/10.1504/IJSTRUCTE.2014.060902
) |
|
| ACI-2002 | (44.
Ahmed, M.; El Hadi, K.M.; Hasan, M.A.; Mallick, J.; Ahmed, A. (2014)
Evaluating the co-relationship between concrete flexural tensile
strength and compressive strength. Int. J. Struct. Eng. 5 [2], 115-131. https://doi.org/10.1504/IJSTRUCTE.2014.060902
) |
|
| ACI-2005 | (44.
Ahmed, M.; El Hadi, K.M.; Hasan, M.A.; Mallick, J.; Ahmed, A. (2014)
Evaluating the co-relationship between concrete flexural tensile
strength and compressive strength. Int. J. Struct. Eng. 5 [2], 115-131. https://doi.org/10.1504/IJSTRUCTE.2014.060902
) |
On the other hand, about 86% of Chile’s paved road network is built with hot mix asphalt (HMA) (1212. Dirección de Vialidad. (2020) Red Vial Nacional-Dimensionamiento y Características. Ministerio de Obras Públicas. http://www.vialidad.cl/areasdevialidad/gestionvial/Documents/RedVialNacional2019.pdf
). One of the most commonly used procedures for
the rehabilitation of these pavements is the milling of their asphalt
layers, producing reclaimed asphalt pavement material (RAP), which is
stored or sent to landfill. This material can be re-processed in plant
and separated into different sizes, usually into a fine fraction that
passes the No. 4 sieve (4.75 mm) and a coarse fraction represented by
the material retained on the No. 4 sieve (1313. Brand, A.S.; Roesler, J.R. (2015) Ternary concrete with fractionated reclaimed asphalt pavement. ACI Mater. J. 112 [1], 155-164. https://doi.org/10.14359/51687176
). Although restricted in the amount to be
incorporated, its use has focused primarily on producing new hot mix
asphalt (HMA) and warm mix asphalt (WMA) as a replacement for natural
virgin aggregates. For example, in Texas, U.S. RAP is limited to 10, 20,
and 30% replacement in the surface, mid and base layers, respectively (1414.
Copeland, A. (2011) Reclaimed asphalt pavement in asphalt mixtures:
state of the practice. Rep No FHWA-HRT-11-021, Federal Highway
Administration (FHWA), McLean, Virginia. https://www.fhwa.dot.gov/publications/research/infrastructure/pavements/11021/11021.pdf
, 1515.
Shi, X.; Mukhopadhyay, A.; Liu, K-W. (2017) Mix design formulation and
evaluation of Portland cement concrete paving mixtures containing
reclaimed asphalt pavement. Constr. Build. Mater. 152, 756-768. https://doi.org/10.1016/j.conbuildmat.2017.06.174
). In Chile, the Ministry of Public Works limited the incorporation of RAP for HMA to 20% replacement (1616. MOP - DGOP. (2019) Manual de carreteras de Chile. Vol. 5. Santiago de Chile, Ministerio de Obras Públicas de Chile, 2019
).
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 (1717.
Huang, B.; Shu, X.; Li, G. (2005) Laboratory investigation of Portland
cement concrete containing recycled asphalt pavements. Cem. Concr. Res. 35 [10], 2008-2013. https://doi.org/10.1016/j.cemconres.2005.05.002
, 1818.
Singh, S.; Ransinchung, G.D.; Kumar, P. (2017) An economical processing
technique to improve RAP inclusive concrete properties. Constr. Build. Mater. 148, 734-747. https://doi.org/10.1016/j.conbuildmat.2017.05.030
). There is previous research regarding the
effects of RAP on the mechanical properties of concrete. In general,
there is evidence that the addition of RAP negatively impacts on the
fundamental mechanical properties of concrete, such as its compressive
strength (19-2319.
Berry, M.; Stephens, J.; Bermel, B.; Hagel, A.; Schroeder, D. (2013)
Feasibility of reclaimed asphalt pavement as aggregate in Portland
cement concrete pavements. FHWA/MT-13-009/8207. https://rosap.ntl.bts.gov/view/dot/24948
20. Brand, A.S.; Amirkhanian, A.N.; Roesler, J.R. (2014)
Flexural capacity of full-depth and two-lift concrete slabs with
recycled aggregates. Transp. Res Rec. 2456, 64-72. https://doi.org/10.3141/2456-07
21. Hossiney, N.; Tia, M.; Bergin, M.J. (2010) Concrete containing RAP for use in concrete pavement. Int. J. Pavem. Res. Technol. 3 [5], 251-258. http://www.ijprt.org.tw/files/sample/V3N5%284%29.pdf
22. Erdem, S.; Blankson, M.A. (2014) Environmental performance
and mechanical analysis of concrete containing recycled asphalt pavement
(RAP) and waste precast concrete as aggregate. J. Hazard. Mater. 264, 403-410. https://doi.org/10.1016/j.jhazmat.2013.11.040
23. Ben Saïd, S.E.E.; El Euch Khay, S.; Achour, T.; Loulizi, A.
(2017) Modelling of the adhesion between reclaimed asphalt pavement
aggregates and hydrated cement paste. Constr. Build. Mater. 152, 839-846. https://doi.org/10.1016/j.conbuildmat.2017.07.078
), flexural and splitting tensile strength (24-2824.
Getahun, M.A.; Shitote, S.M.; Gariy, Z.C.A. (2018) Experimental
investigation on engineering properties of concrete incorporating
reclaimed asphalt pavement and rice husk ash. Buildings. 8 [9], 115. https://doi.org/10.3390/buildings8090115
25. Chyne, J.M.; Sepuri, H.K.; Thejas, H.K. (2019) A review on recycled asphalt pavement in cement concrete. Int. J. Latest Eng. Res. Appl. 4 [2], 9-18. http://www.ijlera.com/papers/v4-i2/2.201902010.pdf
26. Singh, S.; Ransinchung, G.D.R.N.; Kumar, P. (2019) Feasibility study of RAP aggregates in cement concrete pavements. Road Mater. Pavem. Des. 20 [1], 151-170. https://doi.org/10.1080/14680629.2017.1380071
27. Al-Mufti, R.L.; Fried, A.N. (2017) Improving the strength properties of recycled asphalt aggregate concrete. Constr. Build. Mater. 149, 45-52. https://doi.org/10.1016/j.conbuildmat.2017.05.056
28. Singh, S.; Ransinchung, G.D.R.N. (2020) Laboratory and field evaluation of RAP for cement concrete pavements. J. Transp. Eng. 146 [2], 1-11. https://doi.org/10.1061/JPEODX.0000162
), and the modulus of elasticity (21-2321. Hossiney, N.; Tia, M.; Bergin, M.J. (2010) Concrete containing RAP for use in concrete pavement. Int. J. Pavem. Res. Technol. 3 [5], 251-258. http://www.ijprt.org.tw/files/sample/V3N5%284%29.pdf
22. Erdem, S.; Blankson, M.A. (2014) Environmental performance
and mechanical analysis of concrete containing recycled asphalt pavement
(RAP) and waste precast concrete as aggregate. J. Hazard. Mater. 264, 403-410. https://doi.org/10.1016/j.jhazmat.2013.11.040
23. Ben Saïd, S.E.E.; El Euch Khay, S.; Achour, T.; Loulizi, A.
(2017) Modelling of the adhesion between reclaimed asphalt pavement
aggregates and hydrated cement paste. Constr. Build. Mater. 152, 839-846. https://doi.org/10.1016/j.conbuildmat.2017.07.078
, 2929.
Shi, X.; Mukhopadhyay, A.; Zollinger, D.; Huang, K. (2021) Performance
evaluation of jointed plain concrete pavement made with portland cement
concrete containing reclaimed asphalt pavement. Road Mater. Pavem. Des. 22 [1], 59-81. https://doi.org/10.1080/14680629.2019.1616604
).
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 user-friendly 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, semi-circular 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.
2. MATERIALS
⌅A commercial Portland cement type A, with a density of 2.9 g/cm3,
and fresh tap water were used for all concrete mixtures. This water is
considered suitable for use in concrete under the standard NCh1498 (3030. NCh1498 (2012) Concrete and mortar - Mixing water - Classification and requirements. Chilean Standard
). The fine and coarse virgin aggregates used in this research conformed to the requirements for concrete aggregates. Table 2
shows the combined gradation of the aggregate; this remained constant
for RAP’s different replacement rates of virgin aggregates. The physical
properties of the aggregates used in this investigation are shown in Table 3.
The RAP used in this research was from a section of urban highway in
Santiago de Chile. The RAP was processed in a hammer crusher and
separated into two sizes: a fine fraction, represented by the material
passing the No. 4 sieve (4.75 mm), and a coarse fraction, represented by
the material retained in the No. 4 sieve. The fine and coarse
aggregates of RAP contained 7% and 4% asphalt by weight, respectively.
It is worth noting that the RAP material was not washed before its use
in the concrete mixtures.
| 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/m3 | 2.74 | 2.80 | 2.76 | 2.30 | 2.40 |
| Dry bulk specific gravity | t/m3 | 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 |
3. EXPERIMENTAL METHODS
⌅3.1. Mixing Design and Mixing Procedures
⌅A grade H35 concrete (35 MPa) was dosed according to NCh 170 (3131. NCh170 (1985) Concrete - General requirement. Chilean standard
),
the minimum recommended by the Code Standards and Technical
Specifications of Paving Works of the Ministry of Housing and Urban
Planning for concrete pavements (3232.
Ministry of Housing and Urbanism. (2018) Código de normas y
especificaciones técnicas de obras de pavimentación, Editora e imprenta
MAVAL S.P.A., Santiago de Chile, 1-340 p, (2018)
). To
investigate the different effects of RAP on concrete properties, four
groups of concrete mixtures with different RAP contents were prepared:
0% (control), 20%, 50% and 100% replacement of fine and coarse
aggregate, by weight. These mixtures were designated R0, R20, R50, and
R100, respectively. A total of four mixtures were prepared, one for each
RAP content. For determining the proportions of the materials in the
mixtures, the modified Faury method was used. Table 4 shows the proportions in the mixtures studied. In all mixtures, 160 kg/m3
of water was used and the water to cementitious material ratio of 0.44
was kept constant. The concrete mixtures were prepared using a
mechanical mixer and compacted by a vibrating table. The samples were
cured in immersion, to guarantee the correct hydration of cementitious
materials until they were tested at a temperature of 23±2°C in
accordance with that recommended by NCh1017 (3333.
NCh1017 (2009) Concrete-Making in the field and curing specimens for
compression, flexural and spitting tensile tests. Chilean Standard
).
| Mix Type | Mix Description | Materials (kg/m3) | |||
|---|---|---|---|---|---|
| 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 |
3.2. Testing program
⌅Hardened concrete was tested for compressive strength and flexural strength. Table 5 provides a summary of the tests, ages, and standards. The tests were replicated three times for the samples at each of the different curing times and different RAP contents: a total of 144 specimens tested.
| Hardened concrete properties | ||||
|---|---|---|---|---|
| Compressive strength | Flexural strength | Flexural strength | Flexural strength | |
| Standard | NCh 1037 | NCh 1038 | NCh 1038 | EN 12697-44 |
| Specimen size (mm) | 150x150x150 | 150x150x550 | 75x75x120 | 100x50x50 |
| Shape | Cube | Beam | Modified beam | Semi-circular |
| 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 (3434. NCh 1037 (2009) Concrete - Test for compressive strength of molded cubes and cylinders. Chilean Standard
), by testing the specimens at 7, 14, and 28 days of cure at 20±2°C and applying a load rate of 0.35 N/m2/s.
This research involved evaluating flexural strength using three
different specimens: standard beam, modified beam, and Semi-Circular
Beam (SCB). The standard specimen for flexural strength testing is
normally specified as a 150 x 150 x 550 mm beam. In this case, the
flexural strength was measured according to NCh 1038 (3535. NCh1038 (2009) Concrete - Test for flexural tensile strength. Chilean Standard
), by applying a third point load at a load application rate of 0.016 N/m2/s.
It was possible to obtain the so-called modified beam specimens from
the standard beam, once tested, using the two halves resulting from the
breakage. The 75 x 75 x 120 mm specimens were cut and tested in
accordance with NCh 1038 (3535. NCh1038 (2009) Concrete - Test for flexural tensile strength. Chilean Standard
),
by applying a center point load. The semi-Circular Beams were obtained
from the cutting of sliced concrete cylinders, which were cut in half,
obtaining specimens that were 100 mm in diameter, 50 mm thick and 50 mm
high. Flexural strength for SCB specimens was measured under EN 12697-44
(3636.
EN 12697-44 (2011) Bituminous mixtures - Test methods - Part 44: Crack
propagation by semi-circular bending test. Spanish standard
), as recommended for asphalt mixtures. The loading application rate for the SCB specimens was 5 mm/min. Figure 1 shows the different specimens used and the configuration of each of the tests.
4. RESULTS AND ANALYSIS
⌅4.1. Hardened Properties of Concrete
⌅
Figure 2
presents the results of compressive strength and flexural strength,
with the relationship between them for the different curing periods of
concrete mixes. Error bars indicate standard errors for 95% confidence.
The results show a systematic reduction in the compressive strength of
concrete mixtures made with RAP, compared to the control mix; this is
consistent with the literature (1313. Brand, A.S.; Roesler, J.R. (2015) Ternary concrete with fractionated reclaimed asphalt pavement. ACI Mater. J. 112 [1], 155-164. https://doi.org/10.14359/51687176
, 1717.
Huang, B.; Shu, X.; Li, G. (2005) Laboratory investigation of Portland
cement concrete containing recycled asphalt pavements. Cem. Concr. Res. 35 [10], 2008-2013. https://doi.org/10.1016/j.cemconres.2005.05.002
, 37-3937. Al-Mufti, R.L.; Fried, A.N. (2017) Improving the strength properties of recycled asphalt aggregate concrete. Constr. Build. Mater. 149, 45-52. https://doi.org/10.1016/j.conbuildmat.2017.05.056
38. El Euch Ben Said, S.; El Euch Khay, S.; Loulizi, A. (2018) Experimental investigation of PCC incorporating RAP. Int. J. Concr. Struct. Mater. 12, 8. https://doi.org/10.1186/s40069-018-0227-x
39. Abraham, S.M.; Ransinchung, G.D.R.N. (2018) Influence of RAP
aggregates on strength, durability and porosity of cement mortar. Constr. Build. Mater. 189, 1105-1112. https://doi.org/10.1016/j.conbuildmat.2018.09.069
).
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
micro-cracking within the concrete matrix. Another possible reason could
be the weak link between the asphalt film and the concrete matrix (1717.
Huang, B.; Shu, X.; Li, G. (2005) Laboratory investigation of Portland
cement concrete containing recycled asphalt pavements. Cem. Concr. Res. 35 [10], 2008-2013. https://doi.org/10.1016/j.cemconres.2005.05.002
). Moreover, compressive strength increases with a
longer cure time for the specimens. However, this increase gets smaller
as the RAP content in the mixtures increases. Also, the incorporation
of RAP into the mixture reduced the flexural strength of the concrete,
which is consistent with the literature (1313. Brand, A.S.; Roesler, J.R. (2015) Ternary concrete with fractionated reclaimed asphalt pavement. ACI Mater. J. 112 [1], 155-164. https://doi.org/10.14359/51687176
, 1818.
Singh, S.; Ransinchung, G.D.; Kumar, P. (2017) An economical processing
technique to improve RAP inclusive concrete properties. Constr. Build. Mater. 148, 734-747. https://doi.org/10.1016/j.conbuildmat.2017.05.030
, 2121. Hossiney, N.; Tia, M.; Bergin, M.J. (2010) Concrete containing RAP for use in concrete pavement. Int. J. Pavem. Res. Technol. 3 [5], 251-258. http://www.ijprt.org.tw/files/sample/V3N5%284%29.pdf
). The flexural strength reduction pattern
presented the same trend as that of compressive strength. However, the
rate of strength reduction in RAP mixtures was significantly lower than
for compressive strength in all test modes. It was also shown that there
was a systematic increase in flexural strength with specimen age, for
all mixtures. Figure 2
also illustrates the compressive strength to flexural strength ratio.
As the RAP content increased, there was a decrease in the strength
ratio, which is due to the higher rate of reduction in the concrete’s
compressive strength, compared to the reduction in its bending strength.
These values tend to get closer in all three test specimens, with
increasing RAP in the mixtures. For the control mix, the average values
of the strength ratio for 7, 14 and 28 days’ curing of the beam, SCB and
modified beam tests were 10.7, 7.4 and 4.0, respectively. This
indicates that the relationship depends on the shape of the specimen and
RAP content in the mixture.
Figure 3
shows the compressive and flexural strength reductions in mixtures R20,
R50, and R100 with respect to the standard mixture, R0. It was observed
that the reductions in the studied mixtures’ compressive strength at
different testing ages were of the same order of magnitude, obtaining an
average of 42.6%, 51.4%, and 69.1% for the mixtures R20, R50, and R100,
respectively. This indicates that, as the amount of RAP in the mixture
increased, the loss of compressive strength also increased, compared to
the standard mixture. Compressive strength decreased sharply when using a
20% RAP replacement rate. Its reduction was higher than 10 MPa. As can
be seen, for the same mixture at different test ages, the reduction
percentage is relatively constant, which suggests that the RAP and
cement matrix’s chemical bonds do not improve over time. This coincides
with the findings reported by (1313. Brand, A.S.; Roesler, J.R. (2015) Ternary concrete with fractionated reclaimed asphalt pavement. ACI Mater. J. 112 [1], 155-164. https://doi.org/10.14359/51687176
). A reduction in flexural strength after 28 days
of curing can also be seen for all three specimens. As RAP increases,
there is a higher flexural strength reduction compared to the standard
mixture (0% RAP). This reduction is minor compared to that presented by
the compressive strength tests, indicating that the flexural strength
property is less affected by the incorporation of RAP aggregates in the
mix. It is also possible to observe that the flexural strength depends
on the specimen used and the test mode in the laboratory. However, a
similarity was found in the flexural strength reduction values for the
beam and SCB specimens.
4.2 Relationship between compressive and flexural strengths
⌅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 Table 6 were obtained.
| Test mode | Model Regression Equations | ||
|---|---|---|---|
| Linear | Logarithm | Power | |
| Beam |
| ||
| SCB | |||
| Modif Beam | |||
where fs beam is the flexural strength, obtained from a standardized beam; fs SCB is the flexural strength obtained from a semicircular specimen; fs MB is the flexural strength obtained from a beam of smaller dimensions to the standardized beam, and fcu is the cubic compressive strength.
The
goodness of fit and the performance of the models were evaluated using
statistical procedures. The coefficient of determination (R2), Pearson correlation coefficient (r), Sum Square Error (SSE), Root Mean Square Error (RMSE), and the Mean Magnitude of the Relative Error (MMRE)
of predicted flexural strength to experimental flexural strength values
were calculated. Some of these parameters were estimated using Equations [1] to [3]Equations [1], [2], [3]. The lower the SSE and RMSE
values, the better the model is at predicting them; values closer to
zero indicate a better fit. Furthermore, a model can be considered
accurate enough for most purposes when the value of the MMRE parameter is less than 0.25 (4040. Ardiansyah, A.; Mardhia, M.M.; Handayaningsih, S. (2018) Analogy-based model for software project effort estimation. Int. J. Adv. Intell. Informatics. 4 [3], 251-260. http://doi.org/10.26555/ijain.v4i3.266
).
where xi is the experimental value observed for data i, x*i is the estimated value for each data i and n is the total number of data.
From Table 7, it can be seen that all r
values are greater than 0.8, which shows a high association strength,
indicating that changes in the predictors are related to changes in the
response variable and that the obtained prediction models explain much
of the variability of the response. It can also be seen that all MMRE
values are less than 0.25 for all prediction models, which is
considered to be sufficiently accurate, and, therefore, their use is
justified. From a general comparison of SSE, RMSE and MMRE,
the equations that best fit the experimental data are the logarithmic
and power models, considered to be the most suitable for this research.
These models allow the estimation of the flexural strength of concrete
from its cubic compressive strength, for the range studied in this
research. It can also be seen that, for the same value of compressive
strength, there is a different value of flexural strength, which
indicates that this property depends on the size and shape of the sample
and the type of test applied. Figure 4
presents the relationships between the compressive strength of cubes
and the flexural strength of concrete using the equations in Table 1 and those obtained in this investigation, described in Table 6.
Only power equations are shown for the corresponding comparison. It was
observed that the proposed regression equation for the beam specimens
coincided with the equation of the ACI-2002, in terms of trend and
values. The SCB specimen regression equation shows a similar trend to
the equations proposed by IS: 456-200 and Ahmed et al. (44.
Ahmed, M.; El Hadi, K.M.; Hasan, M.A.; Mallick, J.; Ahmed, A. (2014)
Evaluating the co-relationship between concrete flexural tensile
strength and compressive strength. Int. J. Struct. Eng. 5 [2], 115-131. https://doi.org/10.1504/IJSTRUCTE.2014.060902
), while the modified beam regression equation shows results much superior to all the equations shown.
| % RAP | Age (days) | Experimental data (MPa) | Predicted flexural strength - fs (MPa) | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| fcu Cube | fs Beam | fs SCB | fs MB | 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 | |
| r | 0.859 | 0.896 | 0.890 | 0.834 | 0.841 | 0.827 | 0.877 | 0.878 | 0.883 | |||||
| R2 | 0.738 | 0.803 | 0.793 | 0.695 | 0.708 | 0.684 | 0.769 | 0.771 | 0.780 | |||||
| SSE | 0.745 | 0.559 | 0.631 | 1.698 | 1.626 | 1.623 | 11.388 | 11.257 | 11.138 | |||||
| RMSE | 0.249 | 0.216 | 0.229 | 0.376 | 0.368 | 0.368 | 0.974 | 0.969 | 0.963 | |||||
| MMRE | 0.097 | 0.080 | 0.085 | 0.106 | 0.103 | 0.105 | 0.150 | 0.132 | 0.141 | |||||
4.3 Relationship between flexural strengths
⌅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 Table 8 were obtained. The goodness of fit and the performance of the models were evaluated using the same statistical parameters previously applied. Table 9 shows that all the r values are greater than 0.9, which means a very high association strength and that the prediction models obtained explain much of the variability of the response. It can also be observed that all MMRE values are less than 0.25 for all prediction models, being considered sufficiently accurate, and their use is justified. From a general comparison of SSE, RMSE, and MMRE, the equations that best fit the experimental data are the linear and power models for the SCB specimens. The logarithmic model for the modified beam specimen is the most appropriate in this research. These models allow the estimation of the flexural strength of the concrete beam from SCB or Modified Beam specimen tests. It is possible to observe that the values predicted by the linear, logarithmic, and potential models for the SCB and modified beam test specimens are close to those obtained in the laboratory for the flexural strength of a standardized beam. This indicates a relationship between the flexural strength values that is independent of the shape of the specimens tested and that allows the estimation of this property for a standard-size beam, using smaller specimens that are easily manipulated and consume less materials.
| Model | Model Regression Equations | |
|---|---|---|
| Linear | Logarithm | |
| Beam |
| |
| SCB | ||
| Modif Beam | ||
| % RAP | Age (days) | Experimental data of flexural strength - fs(MPa) | Predicted flexural strength - fs (MPa) | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 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 | |
| r | 0.960 | 0.952 | 0.947 | 0.959 | 0.977 | 0.970 | ||||
| R2 | 0.923 | 0.907 | 0.896 | 0.920 | 0.954 | 0.941 | ||||
| SSE | 0.220 | 0.265 | 0.221 | 0.228 | 0.130 | 0.177 | ||||
| RMSE | 0.135 | 0.149 | 0.136 | 0.138 | 0.104 | 0.121 | ||||
| MMRE | 0.046 | 0.051 | 0.046 | 0.057 | 0.041 | 0.049 | ||||
5. CONCLUSIONS
⌅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 three-test 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 well-correlated 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 ACI-2002, 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.