Study of fatigue performance of a concrete mix for pavements reinforced with steel fibers

The behavior in flexural fatigue tests of concrete containing metal fibers has not been extensively studied. Therefore, this study was considered to determine the effect of incorporating metal fibers in concrete paving in flexural fatigue tests. A concrete mix was designed with modulus of rupture of 4.1 MPa at 28 days, which is dosed metal fibers 35 mm long and 0.5 mm in diameter in three proportions: 20 kg/m3, 40 kg/m3 and 80 kg/m3 and left to a non-corresponding control mixture addition. The fatigue tests were performed on 68 specimens of 100 x 100 x 350 mm, at a frequency of 8 Hz, and stresses between 80% and 90% of the modulus of rupture of each mixture. The Weibull probability distribution were used to calculate the fatigue curves with different failure probabilities. For the stresses ranges studied, the fatigue life does not increase for the mix with fiber content of 20 kg/m3 and increased by 6% to 40 kg/m3 (0.5%) and 25% to 80 kg/m3 (1%) compared to the Control mixture.


Introduction and background
Pavements are structures subjected to cyclic loading imposed by traffic and combined weather effects (Huang Yang, 2004;LCPC, 1997;Packard, 1984;Papagiannakis and Masad, 2008;Reyes, 2003).In concrete pavements, the concrete slab absorbs most of these stresses (Huang Yang, 2004;Packard, 1984) which are mainly compressive and flexural stresses (Huang Yang, 2004;Papagiannakis and Masad, 2008), where the latter is most critical for concrete, since the concrete flexural strength in concrete is lower than the compressive strength (Bentur and Sidney, 2007; Z. Li, 2011;Mehta and Monteiro, 2006).This concrete weakness is compensated by the steel reinforcement, which is incorporated to the concrete through corrugated steel bars (reinforced concrete) or metal fibers (fiber reinforced concrete) (Mehta and Monteiro, 2006).
The latter are frequently used with the additional purpose of increasing the fatigue strength (ACI Committee 544, 2009;Bentur and Sidney, 2007;Meda and Plizzari, 2004).Furthermore, they are easy to install and guarantee their dispersion throughout the whole concrete mass (Bentur and Sidney, 2007), something that corrugated steel bars cannot achieve.
The repeated action of flexural stress generates a progressive loss of the structural properties of concrete, a process known as material fatigue (Lee and Barr, 2004;Vassilopoulos, 2010).The mechanistic methods of pavement design use material fatigue laws to determine the capacity of pavement to resist stresses, deformations and deflections imposed by traffic volumes and the weather (Papagiannakis and Masad, 2008).Traditionally, concrete pavement designs use fatigue models such as the PCA model (Portland Cement Association) (Packard, 1984), the MEPDG (Mechanistic Empirical Pavement Design Guide) of the AASHTO (American Association of State Highway and Transportation Officials) (MEPDG, 2007), the mechanistic calibrated model (US Army Corps of Engineers) (Huang Yang, 2004), the French rational method (LCPC, 1997) and the zero maintenance model (Federal Highway Administration) (Huang Yang, 2004).It is important to mention that these models were developed under conditions and with materials that are not the same as in South American countries.Additionally, they were developed for non-reinforced concrete; therefore, it is necessary to develop fatigue models for non-reinforced concrete and steel fiber reinforced concrete with local materials that allow quantifying the effect of steel fibers in the materials fatigue life.
The interest to address the study of concrete fatigue dates back to the end of the XIX century in the United States, with the construction of reinforced concrete bridges for railways, which studied the concrete fatigue under compressive loading (Hsu, 1981).While the study of the fatigue performance of concrete in flexural tests started together with the development of the US highway system at the beginning of 1920 (Hsu, 1981;Shi, Fwa and Tan, 1993).
Concrete fatigue originates a kind of deterioration in concrete pavements that is evidenced by breaking of the concrete slab, thus generating a water inlet source and the subsequent erosion of the slab supporting material, which leads to the total destruction of the pavement structure (Huang Yang, 2004;Papagiannakis and Masad, 2008).
The concrete's fatigue performance is a relevant parameter in the design of concrete pavements for highways, airports and industrial facilities; therefore, it should be controlled, together with the erosion of the slab supporting materials (Huang Yang, 2004;Packard, 1984;Papagiannakis and Masad, 2008;Shi et al., 1993).The erosion of the supporting material is limited by using water-resistant materials, such as asphalt mixes or poor hydraulic concrete, which increase the stiffness of the concrete slab in order to reduce deflections transmitted to the support, and by using load transfer devices in the discontinuities of the slab (Huang Yang, 2004;Packard, 1984;Papagiannakis and Masad, 2008).In order to control the fatigue process of concrete, it is necessary to know the properties governing the performance of this phenomenon.
The fatigue performance is normally studied in terms of the stress applied, expressed as a percentage of the modulus of rupture (known as stress ratio) against the number of loading cycles applied to the failure (Johnston and Zemp, 1991;Shi et al., 1993).Results are represented in curves known as Whöler curves.In order to eliminate the influence of the water-cement ratio, type and grading of aggregates, and the type and quantity of cement in concrete, researches have chosen to use the stress ratio instead of the rupture stress (Huang and Zhao, 1995;Lee and Barr, 2004;Shi et al., 1993).
In general, parameters like loading conditions, loading frequency, stress level, number of cycles, composition of the matrix and the stress ratio will have an impact on the fatigue performance of the concrete specimen; however, there is no qualitative and quantitative consensus regarding how these parameters impact the fatigue performance of concrete (Lee and Barr, 2004).
Fatigue testing of concrete uses important resources of time and money.Therefore, the design of concrete pavements is commonly based on curves from road organizations, such as those developed by the PCA (Packard, 1984), the MEPDG of AASHTO (MEPDG, 2007), the mechanistic calibrated model (US Army Corps of Engineers) (Huang Yang, 2004), the French rational method (LCPC, 1997) and the FHWA zero maintenance model (Huang Yang, 2004).
Since the French rational method of pavement design characterizes fatigue curves with 2 parameters that are easily obtained, rupture stress for one million loading cycles σ 6 and slope of the fatigue curve b, it allows comparing results reported by different authors.Table 1 shows the parameters of the French rational method of the fatigue curves presented by some authors (Goel et al., 2012;Johnston and Zemp, 1991;Oh, 1991;Shi et al., 1993).These results will be the basis to compare the parameters obtained in this study.

Methodology
In order to meet the objectives of this study, a physical and chemical characterization of the gravel, sand and cement was made.These materials were used in the design of a concrete pavement mixture, according to the ACI-211.1 method, that would comply with a minimum flexural strength of 4.1 MPa at 28 days and slump at 125 mm.Concrete mixtures with steel fiber contents of 20 kg/m 3 , 40 kg/m 3 , 80 kg/m 3 , and plain control mixes were manufactured.Each mixture in the plastic state was subjected to slump, air content and unit mass tests.In the hardened state, compressive strength and modulus of elasticity were measured in cylinders of 150 mm diameter and 300 mm height, and the modulus of rupture, in beams of 150 mm x 150 mm x 550 mm.Flexural fatigue tests were carried out in a MTS dynamic system, on specimens measuring 100 mm x 100 mm x 350 mm.The load was applied at the middle third of the clear span and magnitudes were 90% and 80% of the maximum load of the modulus of rupture.Dynamic loading was applied at a speed of 8 Hz and the ratio between minimum stress and maximum stress applied by loading cycle was set at 0.01.Loading cycles tested to rupture at each loading stress applied were statistically processed to adjust them to a Weibull distribution function and thus incorporate parameters of failure probability to predict loading cycles to rupture for a specific failure probability.These values were used to draw fatigue curves and calculate rupture stresses for one million loading cycles (σ 6 ) and the slopes of fatigue laws b.

Physical and chemical characterization of the materials and mix design
The materials for producing the concrete used in the fatigue tests were based on their compliance with the requirements of the specification No. 600-11 of the Urban Development Institute of Bogota, Colombia.Gravels and sands came from an alluvial source of the Department of Tolima.
The cement used was type 1M (according to the Colombian Standard NTC-30), with 15% slag addition, which complies with NTC-4018.The cement tests are those mentioned in the standards NTC-121 and NTC-321.The water used for mixing and curing the samples comes from the Bogota D.C. aqueduct for human consumption.Two additives were used, a high-range plasticizer and a water reducer, which comply with NTC-1299 and ASTM C-494, respectively.These additives were not subjected to control tests, since they were delivered with certification from the supplier.The metal fibers were made of cold-drawn low carbon steel, non-galvanized, whose tensile strength, according to the manufacturer's report, is 1100 MPa; they were 35 mm long with a diameter of 0.55 mm and the ends were bent in the form of a hook.Fibers were joined by an adhesive that melted when entering into contact with the mixing water.These fibers were manufactured according to the ASTM-A820 specification.
The concrete mix design followed the procedure of ACI-211.1.As input data for the concrete mix design, a flexural strength of 4.1 MPa at 28 days with a slump of 125 mm was established.This concrete strength considered the fact that it is the most used in pavement construction in the city of Bogota.It should be noted that, in the ACI-211.1 procedure, the input data is the compressive strength; therefore, equation 1 was used, which expresses a correlation taken from the Colombian regulations for earthquake-resistant construction (2010).
Where, MR is the required modulus of rupture in MPa and f'c is the required compressive strength in MPa.The fiber quantities considered for manufacturing the specimens were 20 kg/m 3 , 40 kg/m 3 and 80 kg/m 3 .These proportions were set to cover from the minimum required by the manufacturer of the fiber to twice the maximum recommended by the manufacturer of the fiber.Moreover, control samples without fibers were made to quantify the variations in the studied properties.

Tests in the plastic state and mechanical tests in the hardened state
The laboratory test program established two moments of the concrete mixture; the first corresponds to the plastic state or freshly mixed, and the second to the hardened state of the mix at different ages.Tests were run for concrete in the plastic state, as shown in Table 3, and in the hardened state in Table 4.
Slump tests of concrete reinforced with fibers followed the procedure of the NTC-396 and not the ASTM-C995, considering the indications of the ACI-544 Committee (quoted by Bentur and Sidney, 2007), which states that once a satisfactory handling is achieved with a fiber reinforced concrete, and the control has been made with the slump test, the latter can be used to monitor the consistency of the fiberreinforced mixture.This allowed keeping a comparison parameter with the control sample.

Fatigue tests
Fatigue tests were carried out on prismatic specimens of 100 mm x 100 mm x 350 mm.Prior to the test, these specimens underwent a curing process immersed in water under controlled conditions, according to NTC-550.Consequently, at the time of the fatigue test, specimens were moist.
Then, it was verified that the minimum dimension was 3 times bigger than the maximum gravel size, which was 25 mm, so the minimum dimension should be 75 mm.However, considering that the length of the steel fiber was 35 mm, this dimension was extended to 100 mm to avoid being orientated in the sense of the fibers.
The number of manufactured joists was 96, from which 28 were tested in the static mode (monotonic loading) to obtain the modulus of rupture of the prismatic beams of 100 mm x 100 mm x 350 mm, and 68 were tested in the dynamic mode (cyclic load) to find the number of loading cycles to failure.In order to obtain the modulus of rupture in the prismatic beams of 100 mm x 100 mm x 350 mm, a monotonic load was applied at a standardized speed of 1 MPa/min until rupture.
Once the rupture under load was obtained, this value was used for finding the reference load for the specimens subjected to fatigue, which corresponds to 90% to 95% and 80 to 85% of the rupture under load.Specimens were subjected to a controlled stress-loading mode applied at the third points of the span at a frequency of 8 Hz.The ratio between the minimum stress and the maximum stress applied by loading cycle was set at 0.01.
The equipment used for the fatigue tests was a MTS system with loading capacity of 100 kN.

Statistical analysis of results
Fatigue results were processed with the Weibull probability distribution, considering the indications of Gumble (quoted by Singh and Kaushik, 2000), who mentioned that the hazard function of the lognormal distribution decreases as time or life increases.
In order to obtain the Weibull probability distribution function, it is necessary to find the shape parameters of function (α) and the scale parameter (µ), based on Equations 2 and 3.
Where, COV is the coefficient of variation of the number of cycles to failure under a specific load.
In equation 3, µ is the average of the number of cycles to failure under load; Gamma is the statistical function, and α was previously defined.
Equation 4 was adopted to include the failure probability (P f ) in the calculation of the number of cycles to failure under load, according to the model proposed by Singh and Kaushik (2000): Where n is the number of cycles to failure under a load applied for failure probability.For each curve, the rupture stress for one million loading cycles (σ 6 ) and the slope of the fatigue law b were calculated.

Results and discussion
The results of the execution of each of the activities defined in the work methodology are described below.

Physical and chemical characterization of the materials and mix design
Table 5 shows the results of the gravel tests.Figure 1 shows the obtained grading.Table 6 shows the results of the sand tests and Figure 2 indicates the obtained grading.
Table 7 shows the results of the chemical tests in cement and Table 8 shows results of the physical and mechanical tests in cement.
The concrete mix design followed the procedure of ACI-211.1, which was adjusted with a water reducer additive (0.45% of the cement weight) and a high-range plasticizer (0.15% of the cement weight).The proportion of the additives followed the recommendation of the manufacturer.The proportions used in the concrete mix are indicated in Table 9.
The design verification was made by testing beams of 150 mm x 150 mm x 550 mm at 3 days, 7 days and 28 days, and the results are shown in Figure 3.

Tests in the plastic state and mechanical tests in the hardened state
Table 10 shows the results of the tests in samples in the plastic state.
Whereas Table 11 shows the test results the hardened state in cylinders of 150 mm and 300 m height, and beams of 150 mm x 150 mm x 550 mm.

tests
The obtained during the fatigue tests in the specimens 100 mm x 100 mm x 350 mm with different fiber quantities and the control sample are shown in Figures 4, 5, 6 and 7.The rupture stress for 1 loading cycle corresponds to that obtained in the specimens of 100 mm x 100 mm x 350 mm.

Statistical analysis of the results
The parameters of the Weibull distribution α, µ and the prediction of the number of cycles with a 50%, 80% and 90% of failure probability for each rupture stress (n), is shown in 12.
this information, curves were graphed for each using different failure probabilities.These curves are shown in Figures 8, 9, and 10, along with the bestfitted regression Equation .It is necessary to find the rupture stress for one million cycles (σ 6 ) and the slope of the fatigue curve (b), from each one of the curves.These parameters were obtained by applying the regression equation for one million loading cycles and taking the negative inverse of the exponent of the regression equation.The parameters obtained for each considered failure probability are shown in 13, 14 and 15.The column named σ 6 variation is the result of comparing the rupture stress for one million cycles (σ 6 ) of the mixtures with fibers, with the rupture stress for one million cycles (σ 6 ) of the control mix.
The average of the variation of the rupture stress for one million cycles (σ 6 ) of the mixtures with fibers compared with the control sample, is shown in Table 16.
This section of the paper will address the analysis of the results obtained in this research compared with results reported by researches with similar goals.Table 17 shows the equivalence between metal fiber contents in kg/m 3 and in volume percentages.This conversion will be useful to compare results from different authors.First, results obtained from the measurements of the material's basic properties in the plastic and hardened states are analyzed, and then, the results of the fatigue curves.The analysis is based on curves reported by other researchers, whose parameters used the rational French design method to characterize fatigue curves of cementitious materials, rupture stress for one million cycles (σ 6 ), and slope of the fatigue law (b).
The slump of concrete mixes showed a decrease of 25 mm for fiber content of 40 kg/m 3 (0.5%) and 35 mm in the mix with 80 kg/m 3 (1.0%); the latter is consistent with the slump decrease reported by Jun and Stang (1998), who worked with the same steel fiber content.In general, slump losses found in this research are within the reduction range reported by ACI 544.1R (2009), which mentions that the incorporation of steel fibers between 0.25% and 1.5% will reduce slump between 25 mm and 102 mm Air content measurements show that concrete mixes reinforced with steel fibers increase the air content as metal fibers are incorporated, which is consistent with the reports of ACI 544.1R (2009).
The modulus of rupture increased with the incorporation of steel fibers by 9% for a fiber content of 20 kg/m 3 (0.25%), 13% in the mix with 40 kg/m 3 (0.5%), and 33% in the mix with 80 kg/m 3 (1.0%),compared with the control mix.These figures are within the range of increases of the modulus of rupture between 10% and 35% for fiber contents between 0.5% and 1%, found by Johnston and Zemp (1991), Huang and Zhao (1995), Jun and Stang (1998), Naaman and Hammoud (1998), Singh et al. (2005) and Goel et al. (2012).
The elasticity modulus measured in this research increased by 10% for the mix with 20 kg/m 3 (0.25%), 20% in the mix with 40 kg/m 3 (0.5%), and 28% in the mix with 80 kg/m 3 (1.0%),compared with the control mix.According to ACI 544.1R, under 2% of fiber, the elasticity modulus does not increase significantly.However, ACI 544.1R (2009) does not indicate the orders of magnitude of the elasticity modulus.
The average fatigue life variation in the considered failure probabilities indicates that the fatigue life does not increase in the mix with fiber content of 20 kg/m 3 (0.25%), while it does increase by 6% for the mix with 40 kg/m 3 (0.5%) and 25% in the mix with 80 kg/m 3 (1.0%),compared with the control mix.These results show the effect of incorporating steel fibers on the concrete's fatigue life, which entails a better performance under cyclic loads when the steel fiber content is higher than 40 kg/m 3 (0.5%).
As mentioned earlier in the theoretical framework, the comparison made with data reported by different publications is focused on knowing the orders of magnitude and the trends of the fatigue curves, because in the absence of a universal test standard to measure fatigue, test conditions differ from one research to another.Among these differences, the following should be highlighted: load types, dimensions of tested specimens, fiber type, fiber quantities, modulus of rupture of concrete, and the range of stresses applied for measuring fatigues.
The parameters that characterize the fatigue curves in the French rational method (stresses for one million cycles (σ 6 ), and the slope of the fatigue law (b), were calculated with published data.Regarding concretes without fibers, Table 18 shows the results taken from the references (Goel et al., 2012;Johnston and Zemp, 1991;Oh, 1991;Shi et al., 1993).
It can be observed that the rupture stress for one million cycles (σ 6 ) is higher than that reported by quoted references.However, if divided among the modulus of rupture, it is evidenced that results are similar.Table 19 shows the results taken from the references for concretes reinforced with steel fiber contents of 40 kg/m 3 (0.5%) (Goel et al., 2012;Singh and Kaushik, 2003).It is evidenced that the value of σ 6 found experimentally in this research is higher than the values reported by Singh and Kaushik (2003) and Goel et al. (2012).However the σ 6 /MR ratios are similar.
For 1% steel fiber contents, Table 20 shows data taken from the references (Goel et al., 2012;Huang and Zhao, 1995;Johnston and Zemp, 1991;Jun and Stang, 1998;Singh and Kaushik, 2003;Singh et al., 2005), which show that the orders of magnitudes of the σ 6 /MR ratios are similar.

Conclusions
The incorporation of steel fibers in concrete for pavements does not increase the fatigue life for fiber contents of 20 kg/m 3 (0.25%), while it does increase by 6% with 40 kg/m 3 (0.5%) and 25% with 80 kg/m 3 (1.0%),compared with concrete without fibers, on average.The slopes of fatigue curves increase when reinforcing concrete with steel fibers.Were it not for the increase of the modulus of rupture of concrete by the incorporation of steel fibers, the fatigue life would not show improvements compared with the control mix.
The variation coefficients of data obtained in the fatigue tests are on average 100%; therefore, it is highly relevant to use the Weibull probability distribution for processing the fatigue test results, which, in this research, provided fatigue curves with regression coefficients over 0.90.It is important to mention that the regression coefficients increased as the failure probability increased.

Figure 5 .Figure 6 .Figure 7 .Rupture
Figure 5. Fatigue test results of sample with fiber content of 20 kg/m 3

Table 2 .
Indicates the tests carried out with gravels

Table 3 .
Tests of freshly mixed concrete

Table 4 .
Tests of hardened concrete

Table 7 .
Results of chemical tests in cement

Table 6 .
Sand test results

Table 8 .
Results of physical and mechanical tests in cement

Table 9 .
Concrete Mix Design

Table 10 .
Test results for freshly mixed concrete

Table 11 .
Test results for hardened concrete

Table 12 .
Weibull parameters for each type of mix Figure 9. Fatigue curves with 80% failure probability

Table 13 .
Parameters of the fatigue curves with 50% failure probability

Table 14 .
Parameters of the fatigue curves with 80% failure probability

Table 15 .
Parameters of the fatigue curves with 90% failure probability

Table 17 .
Equivalence between steel fiber contents

Table 16 .
Average of the σ 6 variation of the failure probabilities considered

Table 18 .
Properties of fatigue curves of mixes without fibers

Table 19 .
Properties of fatigue curves of mixes with 0.5% fiber

Table 20 .
Properties of fatigue curves of mixes with 1.0% fiber