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Abstract

Roller compacted concrete (RCC) is a kind of concrete that is used in pavement construction. RCC has the strength and performance of conventional concrete with the economy and simplicity of asphalt. Unfortunately, this type of concrete is less sensitive to cracking in relation with drying shrinkage and thermal stresses. In this way, reinforcement of RCC with fibers would be a useful solution. The main aim of this study was therefore investigating into thermal stress distribution in fiber-reinforced RCC (FRRCC) pavements. Firstly, the thermal stress induced in fiber-reinforced rigid pavements was modeled by using “thermal expansion law” in short fiber composite materials and “Eshelby’s model” extended from the “theory of elasticity”. Consequently, an instrument was developed to measure the heat gradient in FRRCC samples at different origin temperatures of 40℃, 60℃, and 80℃. Steel and polypropylene fibers were used to prepare FRRCC specimens. The analytical results showed that fiber modulus, fiber volume fraction, fiber Poisson’s ratio, and fiber coefficient of thermal expansion determine the induced thermal stress in FRRCC pavements. The analytical outcomes were straightly correlated with the experimental results.

Keywords

Roller compacted concrete pavement reinforcement polypropylene fiber steel fiber thermal stress

Introduction

Roller compacted concrete (RCC) has the same ingredients as conventional concrete mixture including cement, water, sand, and aggregates [1 –3]. But unlike conventional concrete, it is compacted by vibratory rollers [4]. RCC is typically constructed without joints. It needs neither forms nor finishing, nor does it contain dowels and/or steel bar reinforcing elements [5]. Today, RCC is used for any type of industrial or heavy-duty pavement because it has the strength and performance of conventional concrete with the economy and simplicity of asphalt. Compared to asphalt pavements, concrete pavements need lower maintenance [6,7], inferior energy consumption, and lower volume of aggregates used in construction [8].

Unfortunately, this type of concrete is less sensitive to cracking in relation with drying shrinkage and thermal stresses [9]. In this way, reinforcement of RCC with textile fibers would be a useful solution. For instance, researches show that adding fibers to concrete increases its ductility, tensile strength, ﬂexural strength and resistance against dynamic, impact loads [10,11] and fatigue strength [12]; furthermore, adding fibers reduces the possibility of spalling and scabbing failures, prevents crack propagation, and extends the softening region in the concrete matrix [13]. Steel and polypropylene (PP) fibers are the most useful fibers in this field [14]. For instance, the effects of two distinct types of steel fibers on RCC pavements were studied by Nanni and Johari [15]. They concluded that the effects of fibers on compressive strength and elasticity modulus were beyond expectation. Even after initial cracks, tensile and flexural strengths were significantly increased as a result of adding fibers.

It has been reported that the effect of steel fibers on compressive strength was often more significant than that of PP fibers, but neither steel nor did PP fibers contribute to increase in the rupture modulus independently from pozzolanic additives. In addition, the toughness indices increased when steel fibers were used [16].

An experimental and numerical study has been investigated to extract the effects of steel and PP fibers on impact resistance of fiber-reinforced concrete. The results show that steel fibers are more effective on increasing impact resistance than PP fibers [17].

Behnood and Ghandehari [18] concluded that the addition of 2 kg/m³ PP fibers can significantly promote the residual mechanical properties of high strength concrete (HSC) during heating. PP fiber can also enhance residual strength and fracture energy of concrete subjected to thermal shock induced by air cooling from high temperatures up to 600℃ to room temperature [19]. It is important to know that PP fibers due to their low tensile modulus cannot prevent the formation and propagation of cracks at high stress level but they can bridge large cracks [20,21].

As it can be seen, RCC pavement has many advantages compared to other types of pavements. However, the main problem is thermal cracking that is induced by thermal stresses. According to some researches, using fibers would be useful in this case. The main aim of this study is therefore the investigation of thermal stress distribution in fiber-reinforced RCC (FRRCC) pavements. In other words, this paper is going to answer how fibers can control the thermal gradient and induced thermal tensile stresses in FRRCC samples.

Modeling of thermal stresses in FRRCC structures

Calculation of coefficient of thermal expansion in short staple fiber-reinforced composites

The generation of thermal stresses is a well-known and major cause of early-age thermal cracking of massive concrete structures [22]. In RCC structures, the low thermal conductivity of concrete can induce a high thermal gradient in the interior mass and exterior surface of the structure. Due to the presence of interior and external restraints, this thermal gradient can cause significant thermal tensile stresses. If these thermal tensile stresses, in addition to the tensile stresses, exceed the tensile strength of RCC, cracks will be developed in the structure [23].

In this analytical study, we will use three types of analytical models including: (1) mixture law in composite materials [24]; (2) Eshelby’s model extended from “theory of elasticity” [25]; and (3) thermal analysis of rigid pavements [26]. The first is applied to predict the elastic modulus of FRRCC pavement; while the second is used to derive thermal expansion coefficient of randomly distributed fiber-reinforced concrete. The outcome of this analysis is to investigate thermal stress distribution in FRRCC structures and pavements. An analytical model is shown in Figure 1, where reinforcing short fibers are 3D randomly distributed in the matrix. The whole composite body D is assumed to subject to uniform temperature difference ΔT. The short fibers with aspect ratio of L_f/d_f in this figure are assumed to manifest 3D random orientation.

Figure 1.

An analytical model of 3D randomly distributed short fiber composite.

The first step is the derivation of the composite coefficient of thermal expansion (CTE). Let the domain of the composite body and fibers be noted by D and Ω, respectively. Therefore, the domain of the matrix will be D − Ω. The internal stress σ will be induced within the composite due to mismatch of CTE between reinforcing fibers and matrix under temperature difference ΔT. It is also assumed that fiber elastic modulus and coefficient of thermal expansion do not change with the environmental temperature invariants. Consequently, the volume average of σ which is shown by σ_av in the matrix domain D − Ω can be obtained through

(σ av) D - Ω = C m \bar{e}

(1) where C_m is the elastic constant of the matrix.

\bar{e}

denotes the volume-averaged distribution of strain in domain D − Ω. In the same way, the stress σ in fiber domain Ω is defined as

σ = C f (\bar{e} + e - α *)

(2) where C_f is the elastic constant of the fiber, while α* is the thermal strain due to mismatch between fiber and matrix CTEs given by

α * = (α f - α m) Δ T

(3)

By using Eshelby’s equivalent inclusion theory [25], we can convert the fiber with α* to the inclusion with C_m, e*, and α* in domain D in accordance with

σ = C m (\bar{e} + e - α * - e *)

(4) where e is the strain induced by α* + e* that can be obtained through

e = S (α * + e *)

(5)

It is noticed that e* is the fictitious strain called “eigenstrain” and/or “transformation strain” in “Eshelby’s theory”. This strain has some value in domain Ω, but vanishes in matrix domain D − Ω. Here S is the inclusion constant and/or Eshelby’s tensor in domain Ω calculated by the following expressions [25]

S 1111 = S 2222 = S 3333 = \frac{7 - 5 υ}{15 (1 - υ)} S 1122 = S 2233 = S 3311 = S 1133 = S 2211 = S 3322 = \frac{5 υ - 1}{15 (1 - υ)} S 1212 = S 2323 = S 3131 = \frac{4 - 5 υ}{15 (1 - υ)}

where ν is the Poisson’s ratio of the material. Using equations (4) and (5) gives σ in domain D − Ω

σ = C m [\bar{e} + α * (S - I) + (S - I) e *]

(6)

On the other hand, from equations (2) and (5), σ in domain Ω will be

σ = C f [\bar{e} + α * (S - I) + S e *]

(7) where I is the identity matrix. It is clear that the stress σ is equal in both domains Ω and D − Ω, therefore

C m [\bar{e} + α * (S - I) + (S - I) e *] = C f [\bar{e} + α * (S - I) + S e *]

(8) and the volume average of σ in domain D vanishes, so [27]

\bar{e} + v f (S - I) (α * + e *) = 0

(9) in which v_f is the fiber volume fraction defined for a wide range of 0 < v_f < 1. Consequently, substituting equations (8) into equation (9) leads to

[I - v f (S - I) {(C f - C m) (S - I) + C f} - 1 (C f - C m)] \bar{e} = - v f (S - I) {(C f - C m) (S - I) + C f} - 1 C f α *

(10)

Equation (10) provides a solution to calculate $\bar{e}$ . Consequently, e* can be obtained by using equation (9), while α* is calculated by equation (3). Currently, the fiber orientation distribution is assumed to be axisymmetric about the x₃ axis independent of angle ϕ (see Figure 1). Therefore, the fiber volume element dψ will be [28]

d ψ = ρ (θ) \sin θ d θ d ϕ

(11) where ρ(θ) is the probability density function of fibers representing the number of reinforcing elements at angle θ within the composite domain D. It is clear that the thermal expansion coefficient of the composite α_c is [29]

α c = α m + (γ D / Δ T)

(12) where γ_D is the volume average of the induced strain in composite domain D in accordance with

γ D = \frac{1}{V D} \int D [\bar{e} + S (e * + α *)] d v

(13) in which V_D is the volume of domain D, i.e. the whole composite volume. Noting that

γ D = γ D - Ω + γ Ω

(14) where γ_D_− Ω and γ_Ω are the volume average of the induced strain in matrix and fiber domains, respectively. Therefore

γ D - Ω = \frac{1}{V D - Ω} \int D - Ω [\bar{e} + S (e * + α *)] d v = \bar{e}

(15)

γ Ω = \frac{1}{V Ω} \int ψ \int Ω [\bar{e} + S (e * + α *)] d v d ψ = (\sum_{i = 0}^{π / 2} ρ (θ i) \sin θ i) \times [\bar{e} + S (e * + α *)]

(16)

Thermal stresses in concrete pavements

In concrete pavements, during the day, when the temperature on the top of the structure is greater than that at the bottom, the top tends to expand with regard to the neutral axis, while the bottom tends to contract. However, the weight of the slab restrains it from expansion and contraction; thus, compressive stresses are induced at the top, tensile stresses at the bottom. At night, when the temperature on the top of the slab is lower than that at the bottom, the top tends to contract with respect to the bottom; therefore, tensile stresses are induced at the top and compressive stresses at the bottom. These phenomena lead to curling stresses in concrete pavement that is shown in Figure 2.

Figure 2.

Curling stresses in concrete pavements during the day (the right) and at night (the left).

When planar bending occurs in both the x and y directions, as is the case for temperature curling in RCC pavement, the stresses in both directions (σ_x and σ_y) must be superimposed to obtain the total stress. Therefore, the maximum stress in an infinite slab due to temperature curling can be obtained by assuming that the slab is completely restrained in both x and y directions. Let ΔT = T₂ − T₁ be the temperature differential between the top and the bottom of the slab and α_c be the coefficient of thermal expansion of fiber-reinforced RCC structure. If the RCC slab is free to move and the temperature at the top is greater than that at the bottom, the top will expand by a strain of “α_cΔT/2” and the bottom will also contract by the same strain, as shown in Figure 2. This means that

ɛ x = ɛ y = α c Δ T / 2

(17)

Using the generalized Hooke’s law gives the strain in x direction ɛ_x

ɛ x = σ x / E c - υ c σ y / E c

(18) where E_c and υ_c are elastic modulus and Poisson’s ratio of fiber-reinforced RCC, respectively. It is clear that when an infinite plate is bent in the x direction, ɛ_y should be equal to 0 because the plat is so wide and well restrained that no strain could ever occur. Consequently

σ y = υ c σ x

(19)

Merging equations (19) and (17) with equation (18) gives

σ x = 0.5 E c α c Δ T / (1 - υ c 2)

(20)

Because equation (20) is also the stress in the y direction due to bending in the y direction, from equation (19), the stress in the x direction due to bending in the y direction $σ x /$ will be

σ x / = 0.5 υ c E c α c Δ T / (1 - υ c 2)

(21)

The total stress in the x direction σ_tx is the sum of equations (20) and (21)

σ tx = σ x + σ x / = 0.5 E c α c Δ T / (1 - υ c)

(22)

It is clear that the total stress in the y direction σ_ty is equal with σ_tx. Herein, α_c can be derived from the previous section. It is proved that for most practical purposes, the elastic modulus of randomly distributed fiber-reinforced composites E_c can be approximated reasonably closely by [24]

E c = 3 / 8 E L + 5 / 8 E T

(23) where E_L and E_T are calculated longitudinal and transverse modulus for a unidirectional fiber-reinforced composite in accordance with [24]

E L = v f E f + (1 - v f) E m

(24)

1 / E T = v f / E f + (1 - v f) / E m

(25) where E_f and E_m are fiber and matrix elastic modulus, respectively. An analogous approximate expression can be obtained for the shear modulus of a random short fiber composite G_c

G c = 1 / 8 E L + 1 / 4 E T

(26)

Consequently, randomly distributed fiber-reinforced composites can be considered as an isotropic. Therefore, according to the elasticity theory, the Poisson’s ratio υ_c will be

υ c = (0.5 E c / G c) - 1

(27)

On the whole, equation (12) and equations (22) to (27) give the total induced curling stresses in both x and y directions.

Materials

The constituent materials used in this study were prepared from local sources. Ordinary Portland cement of C53 grade conforming to the requirements of ASTM C 642-82 type I was procured from Sepahan Cement Company, Isfahan, Iran. Physical characteristics and chemical compositions of the cement were found to satisfy the requirements of ASTM C 618 which are given in Table 1.

Table 1.

Chemical properties (%) of cement used in this study.

SiO₂	Al₂O₃	Fe₂O₃	CaO	MgO	SO₃	Loss on ignition
22.1	5.71	3.59	62.3	2.26	2.36	1.07

Well-graded steel slag aggregates finer than 25 mm was used. The aggregate grading is shown in Figure 3. Locally available potable water was used for mixing and curing of specimens.

Figure 3.

The aggregate grading used in this study to produce RCC and/or FRRCC samples.

Two types of fibers were chosen to produce FRRCC samples including PP and steel fibers. PP fibers were selected due to their excellent consistency with cement while steel fibers were applied in experimental design to investigate the effect of fiber CTE. The general properties of fibers have been illustrated in Table 2.

Table 2.

General properties of PP and steel fibers used in this study.

Fiber specification	Fiber type
Fiber specification	Polypropylene (PP)	Steel
Specific gravity (g/cm³)	0.91	7.8
Diameter (µm)	22	−
Cross section	Round	Round
Tensile strength (MPa)	350–400	1050
Elastic modulus (GPa)	1.6	210
Melting point (℃)	160–170	1510
Thermal conductivity (m/m℃)	150 × 10⁻⁶	13 × 10⁻⁶
Length (mm)	15	15 and 30
Poisson's ratio	0.3	0.2

Experimental work

Sample preparation

Samples of RCC and/or FRRCC were manufactured as cubes of approximately 200 mm × 200 mm × 60 mm. A 4.536 kg compactor was used as a standard compacting technique. Compacting was conducted by dividing the sample into two layers of 30 mm thickness. Each layer was compacted by 145 knocks. Atmospheric curing was carried out in a temperature and humidity-controlled room (23 ± 2℃; 50 ± 5% RH) before casting for 28 days. Figure 4 shows details of the manufacture of samples using the vibrating compactor.

Figure 4.

Manufacturing of RCC and/or FRCC samples using the vibrating compactor.

Three specimens were manufactured for each treatment. The experimental design is shown in Table 3 in which PP and steel fibers were used as reinforcing elements. Steel fibers due to their high modulus and PP fibers because of excellent consistency with the cement matrix mixtures are used to reinforce concrete pavements. It is noticed that both PP and steel fibers for each treatment were blended with cement, water, and aggregate by using a mechanical blender. Consequently, the compaction process was carried out on mixture to produce RCC and/or FRRCC sample.

Table 3.

The experimental design used in this study.

Treatment no.	Fiber type	Fiber length (mm)	Fiber content (%)	Bottom temperature (℃)
1	–	–	–	40, 60, and 80
2	Polypropylene	15	0.1	40, 60, and 80
3	Polypropylene	15	0.2	40, 60, and 80
4	Polypropylene	15	0.4	40, 60, and 80
5	Steel	15	0.4	40, 60, and 80
6	Steel	35	0.4	40, 60, and 80

Heat transition measurements

Various types of laboratory equipment have been invented since the early 1980s to reproduce thermal stress in simulated structures. In this study, a thermo-electrical device was originally developed to generate thermal stress under a prescribed temperature history. The schematic of the apparatus is shown in Figure 5.

Figure 5.

The schematic of the thermo-electrical device developed to generate thermal stress in FRRCC samples.

Firstly, the heat generator was set to warm up the steel plate to achieve the prescribed temperature. In this way, three prescribed and/or primary temperatures were selected in experimental design including 40℃, 60℃, and 80℃ to simulate moderate, warm, and hot climatic conditions, respectively. All surface temperatures were measured by using a laser-base thermometer (Kiray, France) with the accuracy of ±0.1℃. After that, the RCC and/or FRRCC sample was put on the steel plate, and the laser-base thermometer was located above the sample to measure the thermal gradient. It is important to know that the chamber was isolated by an aluminum–wool stone–aluminum sandwich panel to prevent heat loss during the measurements. The temperature on the top of the sample was measured at five points (the middle and four corners) and reported each 10 min for time duration of 120 min. Therefore, a graph comprised of temperature increase rate on the top of the sample could be drawn based on the prescribed bottom temperature of the sample during the time of the experiment.

Results and discussions

Figures 6 and 7 show the plot of thermal stress σ_t versus fiber volume fraction v_f and fiber modulus E_f, respectively.

Figure 6.

Thermal stress σ_t vs. fiber volume fraction v_f for PP fiber-reinforced RCC.

Figure 7.

Thermal stress σ_t vs. fiber modulus E_f for v_f = 0.1 and ν_f = 0.3.

Equation (22) has been used to draw the plots at different temperature differentials of 10℃, 30℃, and 50℃. Figure 6 states that as the PP fiber volume fraction increases, the induced thermal stress will be raised in FRRCC pavement. The key point to explain this trend is the higher value of CTE for PP fibers compared to the concrete, i.e. 150 × 10⁻⁶m/m/℃ for PP against 9 × 10⁻⁶m/m/℃ for concrete. According to equation (22), the more the fiber CTE, the more induced thermal stress will be resulted in FRRCC pavement. In addition, by increasing the temperature differential ΔT from 10℃ to 50℃, the enlargement rate of the thermal stress increases specially at ΔT = 50℃. It is clear from Figure 7 that increase of fiber modulus leads to enhancement of induced thermal stress in FRRCC sample.

The growth rate of the thermal stress increases when the temperature differential ΔT increases from 10℃ to 50℃. It is important to know that the fiber modulus E_f influences directly both the coefficient of thermal expansion α_c and tensile modulus E_c of FRRCC. For instance, the coefficient of thermal expansion of a unidirectional fiber-reinforced composite α_cu can be obtained through [24]

α 1 = (E f v f α f + E m v m α m) / E c

(28)

As it can be seen, E_f is straightly correlated with α_cu. On the other hand, combination of equations (24) and (25) with equation (23) gives

E c = 3 / 8 (v f E f + v m E m) + 5 / 8 [E f E m / (v m E f + v f E m)] = \frac{1}{8 (v m E f + v f E m)} \times (3 v f v m E f 2 + 3 v f 2 E m E f + 3 v m 2 E m E f + 3 v m v f E m 2 + 5 E m E f)

(29)

Based on the above equation, the composite elastic modulus E_c can be rewritten as a function of fiber modulus E_f in accordance with

E c = \frac{cE f 2 + dE f + e}{aE f + b}

(30) where the constants of a, b, c, d, and e are calculated from

a = 8 v m, b = 8 v f E m, c = 3 v f v m d = 3 v f 2 E m + 3 v m 2 E m + 5 E m and e = 3 v m v f E m 2

Figure 8 shows the diagram of E_c against E_f for a randomly distributed fiber-reinforced RCC for v_f = 0.1 and E_m = 26 GPa.

Figure 8.

Diagram of E_c vs. E_f for a randomly distributed fiber-reinforced RCC.

From the figure, it is interesting to know that by increasing the fiber modulus E_f up to the matrix modulus E_m, i.e. concrete modulus (26 GPa), the FRRCC modulus will strictly increase. After that as the fiber modulus increases from 26 GPa to 210 GPa, the growth rate of FRRCC modulus will become so slowly.

The plot of thermal stress σ_t versus fiber CTE α_f has been drawn in Figure 9.

Figure 9.

Thermal stress σ_t vs. fiber CTE α_f for v_f = 0.1 and E_f = 20 GPa.

One can find out that increase in fiber CTE α_f leads to more induced thermal stress. In this case, the same trend can be seen regarding v_f and E_f. However, herein the plot of α_f versus induced thermal stress is almost linear. This is due to the fact that is supposed the fiber modulus is constant to drawing the plot in Figure 9, i.e. α_f is independent of E_f, meanwhile this assumption seems to be far from the real.

Figure 10 shows the maximum thermal stress induced in different RCC samples. It is important to know that the average between longitudinal and transverse CTE of the unidirectional fiber-reinforced concrete was calculated instead of using probability density function in calculations. The Poisson’s ratio of concrete was selected as 0.15 [26].

Figure 10.

The maximum thermal stress (kPa) induced in different RCC/FRRCC samples.

The differential temperature ΔT has been also measured through the method described in previous section; consequently, the induced thermal stress was calculated by using equation (22). It can be found that by increasing the primary temperature at the bottom of the sample from 40℃ to 80℃, the thermal stress will rise in all RCC and FRRCC treatments. This trend shows good consistency with equation (22), where σ_tx is directly influenced by ΔT. Another outcome of taking an accurate look at Figure 10 illustrates that using both PP and steel fibers lead to more induced thermal stress in FRRCC samples compared to unmodified RCC and/or neat sample. This concept will be amplified as the PP fiber volume content increases from 0.1% to 0.4%. In addition, the FRRCC sample reinforced with 0.4% steel fiber comprised the most induced thermal stress among all samples. As it was previously discussed, the CTE is 150 × 10⁻⁶ for PP fibers; meanwhile, this parameter is 9 × 10⁻⁶ for the concrete. On the other hand, the modulus of elasticity is 210 GPa for steel fibers while that is 26 GPa for the unmodified concrete. Therefore, according to equation (22), the more tensile stress will be induced in FRRCC samples compared to neat concrete sample. The same trend will be found for the minimum induced thermal stress in RCC and/or FRRCC samples which is shown in Figure 11.

Figure 11.

The minimum thermal stress (kPa) induced in different RCC/FRRCC samples.

The minimum thermal stress is an important parameter showing the value of the curling stress at the final time of the experiment, i.e. after 2 h. Once more it can be seen that FRRCC samples contain more residual thermal stress with regard to the RCC sample. But the most vital point is that the bending stiffness (BS) of FRRCC samples is more than that of RCC sample based on the following formula [30]

BS = E \times I

(31) where E and I are the elastic modulus and momentum of inertia, respectively. Therefore, FRRCC samples show more resistance against thermal cracking and/or local failure. So, it can be concluded that both PP and steel fibers induce more thermal stress within the composite RCC pavement; meanwhile, these fibers increase the bending strength of the structure. It means that PP and steel fibers induce more thermal stress in FRRCC pavements, but at the same time they will resist against thermal cracking of the pavement and crack development within the pavement.

Conclusion

The main aim of this study was the investigation of thermal stress distribution in FRRCC pavements. The study was divided in two sections including experimental part and modeling section. In the experimental section, two types of fibers were chosen to produce FRRCC samples including PP and steel fibers. The differential temperature between bottom and top of the samples was measured by a device developed in this study. In the analytical section of the study, three types of analytical models were used including: (1) mixture law in composite materials; (2) Eshelby’s model extended from “theory of elasticity”; and (3) thermal analysis of rigid pavements. Consequently, the induced thermal stress was calculated by using experimental results and model outputs. The insight research finding of this paper is that both PP and steel fibers induce more thermal stress within the FRRCC samples compared to RCC sample, meanwhile these fibers increase the bending strength and thermal cracking resistance of the structure. The key point to explain this phenomenon is the higher value of coefficient of thermal expansion for PP fibers compared to the concrete. On the other hand, the modulus of elasticity is 210 GPa for steel fibers while that is 26 GPa for the unmodified concrete. Therefore, more tensile stress will be induced in FRRCC samples with regard to neat concrete sample.

It is recommended to use and to investigate the role of other fibers, e.g. poly vinyl alcohol (PVA) fibers, in FRRCC structures in future works. In this work, the fiber volume fraction v_f was limited to 0.1%, 0.2%, and 0.4%, therefore an effort seems to be required to determine the optimized v_f in the future. Recycling of PP-reinforced RCC pavements is a novel idea that should be focused in the upcoming researches.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

References

Courard

Michel

Delhez

. Use of concrete road recycled aggregates for roller compacted concrete. Constr Build Mater 2010; 24: 390–395.

Piarc, France. Use of roller compacted concrete for roads. Tech Committee for Concrete Roads, 1993.

Guerinet M. Roller compacted concrete. Ecole Nationale des Ponts et Chaussées. Ponts formation edition 1997, pp. 17–29 (in French).

Burns Cecil

Saucier Kenneth

. Vibratory compaction study of zero-slump concrete. ACI J 1978; 75(3): 86–90.

Tremblay S. Design methods for roller compacted concrete and effect of air entraining agents on consistency. Master Thesis, Université Laval (Qc), Canada, 1997, pp. 16–80 (in French).

Thomas D. Choosing between asphalt and concrete pavement. Public Works Magazine 2006.

Sullivan E. Update: Paving, new realities. Flash report – breaking analysis of the economy, Construction and Cement Industries. PCA: Washington, DC, 2009.

Dellate

. Concrete pavement design, construction and performance, London: Taylor & Francis, 2008.

Hazaree

Ceylan

Wang

. Inﬂuences of mixture composition on properties and freeze–thaw resistance of RCC. Constr Build Mater 2011; 25: 313–319.

10.

Pakravan

Jamshidi

Latifi

. Investigation on polymeric fibers as reinforcement in cementitious composites: Flexural performance. J Ind Text 2012; 42: 3–18.

11.

Halvaei M, Jamshidi M and Lataifi M. Application of low modulus polymeric fibers in engineered cementitious composites. J Ind Text 2012.

12.

Graeff

Pilakoutas

Neocleous

. Fatigue resistance and cracking mechanism of concrete pavements reinforced with recycled steel fibres recovered from post-consumer tyres. Eng Struct 2012; 45: 385–395.

13.

Farnam

Mohammadi

Shekarchi . Experimental and numerical investigations of low velocity impact behavior of high-performance fiber-reinforced cement based composite. Int J Impact Eng 2010; 37: 220–229.

14.

Yao

. Mechanical properties of hybrid fiber-reinforced concrete at low fiber volume fraction. Cem Concr Res 2003; 33: 27–30.

15.

Nanni

Johari

. RCC pavement reinforced with steel fibers. Concr Int Des Constr 1989; 11(3): 64–69.

16.

Madhkhan

Azizkhani

Torki Harchegani

. Effects of pozzolans together with steel and polypropylene fibers on mechanical properties of RCC pavements. Constr Build Mater 2012; 26: 102–112.

17.

Alavi Nia

Hedayatian

Nili

. An experimental and numerical study on how steel and polypropylene fibers affect the impact resistance in fiber-reinforced concrete. Int J Impact Eng 2012; 46: 62–73.

18.

Behnood

Ghandehari

. Comparison of compressive and splitting tensile strength of high-strength concrete with and without polypropylene fibers heated to high temperatures. Fire Safety J 2009; 44: 1015–1022.

19.

Al Qadi ANS and Al-Zaidyeen SM. Effect of fibre content and specimen shape on residual strength of polypropylene fibre self-compacting concrete exposed to elevated temperatures. J King Saud Univ Eng Sci 2013.

20.

Qian

Stroeven

. Development of hybrid polypropylene–steel fibre-reinforced concrete. Cem Concr Res 2000; 30: 63–69.

21.

Karahan

Atis

. The durability properties of polypropylene fiber reinforced fly ash concrete. Mater Des 2011; 32: 1044–1049.

22.

Amin

Kima

Lee

. Simulation of the thermal stress in mass concrete using a thermal stress measuring device. Cem Concr Res 2009; 39: 154–164.

23.

Noorzaei

Bayagooba

Thanoonb

. Thermal and stress analysis of Kinta RCC dam. Eng Struct 2006; 28: 1795–1802.

24.

Harris

. Engineering composite materials, London: The Institute of Metals, 1999.

25.

Gao

. Green’s function and Eshelby’s tensor based on a simplified strain gradient elasticity theory. Acta Mech 2009; 207(3–4): 163–181.

26.

Huang

. Pavement analysis and design, 2nd edn. London: Prentice Hall, 2003.

27.

Mori

Tanaka

. Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metallurigica 1973; 21: 571–574.

28.

Hatta

Takei

Taya

. Effects of dispersed microvoids on thermal expansion behavior of composite materials. Mater Sci Eng 2000; 285: 99–110.

29.

Takao