Construction

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Construction and Building Materials 21 (2007) 1918–1927

and Building

MATERIALS

Fatigue behaviour of recycled tyre rubber-filled concrete andits implications in the design of rigid pavements

F. Hernandez-Olivares a,*, G. Barluenga b, B. Parga-Landa c, M. Bollati d, B. Witoszek e

a Departamento de Construccion y Tecnologıa Arquitectonicas, Escuela Tecnica Superior de Arquitectura,

Universidad Politecnica de Madrid, Avda. Juan de Herrera, 4, Madrid 28040, Spainb Departamento de Arquitectura, Escuela Tecnica Superior de Arquitectura y Geodesia, Universidad de Alcala,

C/Santa Ursula, 8, 28801 Alcala de Henares, Madrid, Spainc Departamento de Arquitectura y Construcciones Navales, Escuela Tecnica Superior de Igenieros Navales,

Universidad Politecnica de Madrid, Arco de la Victoria, Ciudad Universitaria, Madrid 28040, Spaind Composites I+D, Pena Sacra, 30, Galapagar, 28260 Madrid, Spain

e Pavimentos Asfalticos de Salamanca, S.L. Avda. de Salamanca, 264-268, Salamanca 37004, Spain

Received 27 September 2005; received in revised form 19 June 2006; accepted 28 June 2006Available online 22 September 2006

Abstract

This paper presents the results of fatigue bending tests on prismatic samples of recycled tyre rubber-filled concrete (RRFC) with dif-ferent volumetric fractions (VF) of rubber (0%, 3.5% and 5%) after a long term exposition to natural weathering in Madrid (Spain) (oneyear ageing). From these experimental results, an analytical model based on classical Westergaard well known equations has been devel-oped to calculate the minimum thickness of RRFC for rigid pavements subjected to high density traffic, in order to obtain a durability ofthese rigid pavements of 106 cycles of 13 tons (127 kN) axle load. In this investigation any value of the modulus of subgrade reaction forrigid pavement design have been considered.� 2006 Elsevier Ltd. All rights reserved.

Keywords: Mechanical properties; Fatigue; Recycled rubber-filled concrete; Rigid pavements

1. Introduction

Recycled tyre rubber-filled concrete (RRFC) hasbecome a matter of interest in the last few years, due toits good performance and as an alternative for tyre recy-cling [1]. This new material provides a good mechanicalbehaviour under static and dynamic actions and is beingused for road pavement applications. In a previous paper[2], the static and dynamic mechanical behaviour and per-formance of RRFC from crumbed used tyres was assessed.The main conclusions were referred to the optimum crum-bed rubber fibre content, the compatibility and stability ofcement–rubber interface, the dynamic energy dissipationand its better damping capacity and the stiffness reduction

0950-0618/$ - see front matter � 2006 Elsevier Ltd. All rights reserved.

doi:10.1016/j.conbuildmat.2006.06.030

* Corresponding author. Tel.: +34 913364245; fax: +34 913366560.E-mail address: f.hernandez@upm.es (F. Hernandez-Olivares).

of the concrete–rubber composite, in relation with similarconcrete samples without rubber.

There have also been proposed other uses for architec-tural and building applications [3]. Besides, it has beenexperimentally shown that crumbed tyre rubber additionsin structural high strength concrete slabs improved its fireresistance, reducing its spalling damage under fire [4].

This paper presents the results of fatigue laboratory testson prismatic samples of similar rubber-filled concretedescribed in [2,3] cut off from slabs of 90 · 60 · 5 cm, aftera long term exposition to natural weathering in Madrid(Spain) (one year ageing) are presented. From these exper-imental results, a mechanical analysis based on Westerg-aard well known theory over flat plates on elasticfoundation [5] has been developed to calculate the mini-mum thickness of RRFC for rigid pavements subjectedto high density traffic, in order to assess the durability of

Table 2Some nominal properties of truck tyre rubber (after Waddell and Evans[14])

Young modulus (vulcanized properties)

@ 100% 1.97 MPa@ 300% 10 MPa@ 500% 22.36 MPaTensile strength 28.1 MPaElongation to break 590%

Rebound resilience

@ 23 �C 44%@ 75 �C 55%

Fig. 1. RRFC slab (90 · 60 · 5 cm3) into its mould and under wind of asmall fan (wind velocity 3.5 m/s) during the Kraai test (see text).Temperature and humidity data loggers were placed on the slab.

F. Hernandez-Olivares et al. / Construction and Building Materials 21 (2007) 1918–1927 1919

this rigid pavements under 106 cycles of 13 tons axle load,according with the generally established design rules basedon AASHTO test [6].

The Westergaard analysis has been previously success-fully applied by other authors who compared it with finiteelements methods and with AASTHO road experimentaldata from rigid concrete pavements [7].

The results here presented are limited to N = 106 cyclesbecause the laboratory tests have been restrained to thatlimit conditions.

Fatigue behaviour of both conventional and porousconcrete for rigid pavements has been widely studied,mainly under fracture mechanic analysis [8–10]. Neverthe-less, RRFC cannot be classified as a simple porous con-crete, mainly due to its dissipative and dampingproperties previously studied [2].

2. Materials and specimen preparation

A plain concrete without crumbed rubber tyre has beendone in order to fabricate the control slabs. The composi-tion of this concrete labelled as ‘‘reference or plain con-crete’’ is presented in Table 1 (per cubic meter ofconcrete). The aggregates gradation is non-continuous inorder to obtain voids in the concrete for the easy arrangeof crumbed tyre rubber particles in the mix, and to obtainalso good drainage and noise absorbent concrete pave-ments. The polypropylene (PP) fibres (0.1% volumetricfraction) were added and mixed to reduce the early crack-ing of fresh concrete due to plastic shrinkage.

Afterwards, increasing volumetric fractions (VF), from0% to 13%, of fibre-shaped crumbed tyre rubber wereadded to fresh concrete fabricated with the reference con-crete mix. Nevertheless, bending fatigue tests were accom-plished only on concrete samples containing 0%, 3.5% and5% VF of crumbed tyre rubber.

The main physical properties of PP fiber and crumbedrubber tyres have been already presented [4]. That paperalso contains a scanning electronic microscopy analysis(SEM) on the rubber-hydrated cement paste interface thatshows good compatibility between those components.

The nominal properties of truck tyre rubber are summa-rized in Table 2.

The concrete slabs were cast in laboratory to performthe Kraai test of cracking of concrete due to plastic shrink-age, as described by Balaguru and Shah [11]. Each slab of90 · 60 · 5 cm3 was demoulded after 24 h. During the first

Table 1Reference concrete composition per cubic meter

Cement CEM I-42.5R 360 kgCoarse aggregate, 12–18 mm 1103 kgSand, 3–6 mm 699 kgWater (w/c = 0.4) 147 kgWater reducing admixture (Sikament 500) 7.20 kgSet retarding admixture (Bettoretard) 1.07 kgPolypropylene fiber fibermesh (0.1% vol) 900 g

8 h from the beginning of setting, the slabs into its ownmoulds were subjected to wind flow on its free face underroom temperature and humidity conditions (22 �C and62% relative humidity, respectively). The wind velocitywas 3.5 m/s measured on the middle of the slabs free sur-faces position by mean of a calibrated anemometer. Sur-face temperature and humidity of slabs was continuouslyregistered (Fig. 1).

After demoulding, each slab was stored in laboratoryfor 28 days and in outer conditions for 11 months. Pris-matic specimens of 5 · 5 · 25 cm3 were cut off from theseaged slabs to be tested in fatigue bending.

3. Bending fatigue tests and results

Bending fatigue tests were run in the CEDEX (RoadResearch Center) Laboratory (Spain) on a servohydraulicdynamic test facility MTS 810 (Fig. 2). Prismatic specimensof 5 · 5 · 25 cm3 were cut off from Kraai test slabs (0%,3.5% and 5% volumetric fractions of recycled tyre rubber)exposed to natural weathering for one year.

Three point bending fatigue tests were accomplishedwith load control, supports span 20 cm, and frequency of

Fig. 2. Dynamic MTS 810 facility from CEDEX Laboratory (Madrid)used in this research for fatigue bending tests. A three point bendingRRFC sample (3.5% VF crumbed rubber content) is on place. Supportsspan: 20 cm.

1920 F. Hernandez-Olivares et al. / Construction and Building Materials 21 (2007) 1918–1927

load 10 Hz. In order to avoid stress concentrations near thebearings and the load head, three metallic pieces cut fromhollow tubes of mild steel (2 · 2 cm2, 2 mm thickness) wereepoxy-bonded to the specimens for load transmission as itis shown in Fig. 3. This figure also shows a specimen afterfailure by complete cracking.

Due to the rigid behaviour of RRFC (with regard tohigh modulus bituminous mixtures) a load controlled pro-cedure was used on fatigue tests. Load head longitudinaldisplacement was measured, and a 50-mm gage-lengthMTS extensometer was placed on the lower side of thespecimen to register transversal strain (longitudinal in the

Fig. 3. RRFC specimen (5 · 5 · 25 cm3) before and after fatigue bendingtest with strain control. Metallic epoxy-bonded hollow tubes 2 · 2 cm2

square section, made of mild steel 2 mm thickness.

main specimen dimension). Each fatigue test was immedi-ately stopped after complete cracking of the respectivespecimen been tested.

Three series of ten (10) concrete specimens for each recy-cled crumbed tyre rubber VF composition (0%, 3.5% and5%) were tested in bending. Fatigue strain on the lower faceof each specimen was measured and registered; flexuralstrength and Young modulus were registered every ten loadcycles.

The results obtained are presented below for each sam-ples batch.

3.1. Concrete specimens without recycled tyre rubber (0%

VF)

Fig. 4 depicts the relationship between failure flexuralstrength and the number of load cycles of the concretespecimens without crumbed rubber (plain concrete). Thescatter of these experimental measurements is usual in sim-ilar data presented by other researchers (see, for instance,the results collected by Lee and Barr on plain and fibrereinforced concrete [10]). In any case a linear regressionplot is included into the chart of Fig. 4, that correspondsto the following equation:

rflexural strength; 95% ðMPaÞ ¼ �0:2Log10ðNCyclesÞ þ 5:4 ð1ÞIf this fatigue law is strictly applied, it asserts that ourplain concrete could resist 106 loading cycles of 4.2 MPaflexural stress. It must be pointed out that this Eq. (1)is not representative of the mechanical fatigue behaviourof all the specimens tested, due to the wide scatter ofthe experimental results, obtained by testing under flex-ural stress different samples cut from the same slab.Because of this, it should be wrong to consider Eq. (1)as the right law to describe the fatigue behaviour of theplain concrete. To be sure about the flexural fatiguestrength of plain concrete a confidence percentage mustbe introduced. Here it is proposed to consider a confi-dence percentage of 95%, in such a way that under thisassumption, the new fatigue law for plain concrete isthe following (see Fig. 4):

rflexural strength; 95% ðMPaÞ ¼ �0:2Log10ðNCyclesÞ þ 5:1 ð2Þ

Then, it can be considered that the plain concrete flexuralfailure stress for 106 cycles of load is 3.9 MPa, with a con-fidence interval of 95%.

Similar analysis is applied to Young modulus measure-ments for the three points fatigue bending tests of theconcrete specimens without recycled rubber (plain con-crete) which are collected in Fig. 5. The mean value keepspractically constant, independently of the number of loadcycles. Nevertheless, the linear regression presents a verylow value for R2 = 0.0003, which shows the great scatterof the Young modulus measurements for the different spec-imens tested. Again, it is proposed here to consider not thelinear regression equation for the Young modulus E ofplain concrete, that is to say

y = -0.2x + 5.4R2 = 0.2044

y0.95 (dashed)= -0.2x + 5.1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7

log10(N. Cycles)

Fle

xura

l Str

ess

(MP

a)

Fig. 4. Relationship between failure flexural stress and the number of loading cycles obtained in the three points bending fatigue tests on plain concretespecimens (without rubber additions). The continuous line indicates the linear regression and the dashed line shows the lower limit for a confidence intervalof 95%.

y= 0.03x + 23.7R2 = 0.0003

y0.95 (dashed) = 0.03x + 25.0

10

15

20

25

30

35

0 1 2 3 4 5 6 7

Log10(N.Cycles)

E (

GP

a)

Fig. 5. Relationship between dynamic Young modulus and number of loading cycles obtained in the flexural fatigue tests on plain concrete specimens(without rubber additions). The continuous line indicates the linear regression and the dashed line shows the upper limit for a confidence interval of 95%.

F. Hernandez-Olivares et al. / Construction and Building Materials 21 (2007) 1918–1927 1921

Eflexural ðGPaÞ ¼ 0:03Log10ðNCyclesÞ þ 23:7 ð3Þbut, the following Eq. (4), that incorporates a confidenceinterval of 95%:

Eflexural ðGPaÞ ¼ 0:03Log10ðNCyclesÞ þ 25:0 ð4Þ

As the stiffer concrete transmits greater flexural tensilestress. Because of that, the Young modulus value of plainconcrete that has to be considered for rigid pavement de-sign must be defined by mean of the upper limit equationof the 95% confidence interval (25.1 GPa). This criterioncorresponds to the worst case. It must be notice that theflexural failure stress value was determined for the lowerlimit equation of the 95% confidence interval.

Fig. 6 depicts the relationship between the failure flex-ural strain and the number of loading cycles obtained in

bending fatigue tests on plain concrete specimens (withoutrubber additions). Each maximum strain value representsthe maximum admissible plain concrete flexural strain forits linked number of load cycles. The linear regressionequation is as follows:

eflexural ðldefÞ ¼ �7:2Log10 NCycles

� �þ 225:6 ð5Þ

Again, the scatter of data collected suggests to use a 95%confidence interval for the design strain. The followingequation represents this lower limit (see Fig. 6) for the max-imum flexural strain related to the corresponding numberof load cycles:

eflexural; 95% ðldefÞ ¼ �7:2 Log10ðN CyclesÞ þ 212:0 ð6ÞUnder this criterion, the plain concrete flexural failurestrain for 106 cycles of load is 169 ldef.

y = -7.2x + 225.6R2 = 0.171

y0.95 (dashed) = -7.2x + 212.0

0

50

100

150

200

250

300

0 1 2 3 4 5 6 7

Log10(N.Cycles)

Fle

xura

l Str

ain

(μd

ef)

Fig. 6. Relationship between failure flexural strain and number of loading cycles obtained in bending fatigue tests on plain concrete specimens (withoutrubber additions). The continuous line is the linear regression and the dashed line shows the lower limit for a confidence interval of 95%.

1922 F. Hernandez-Olivares et al. / Construction and Building Materials 21 (2007) 1918–1927

3.2. Concrete specimens with 3.5% VF of recycled tyrerubber

The reasoning above can be repeated here to study thefatigue behaviour of the rubber–concrete specimens. Theparticular values obtained for this new batch of samplesare simply shown here, omitting those paragraphs whichare similar.

Fig. 7 depicts the relationship between the failure stressand the number of cycles obtained in the bending fatiguetests on RRFC specimens (3.5% VF). The continuous lineindicates the linear regression and the dashed line showsthe lower limit for a confidence interval of 95%.

As described for the reference concrete results, the fati-gue law for flexural strength of RRFC with 3.5% VF ofrecycled crumbed tyre rubber is better described using the

y = -0.3x + 5.8R2 = 0.1891

y0.

0

1

2

3

4

5

6

7

0 1 2 3

Log10

Fle

xura

l Str

ess

(MP

a)

Fig. 7. Relationship between failure stress and number of cycles obtained in theindicates the linear regression and the dashed line shows the lower limit for a

lower limit equation of the 95% confidence interval of thelinear regression fit

rflexural strength; 95% ðMPaÞ ¼ �0:3Log10ðNCyclesÞ þ 5:4 ð7Þ

According with this equation, the bending failure stress for106 cycles of load is 3.8 MPa, this value is slightly lowerthan the one obtained for plain concrete without rubber.

Fig. 8 depicts the Young modulus results obtained fromof the fatigue bending tests of the concrete specimens with3.5% VF of recycled rubber.

Again, the Young modulus considered for a rigid pave-ment design is defined by the upper limit equation of the95% confidence interval of the linear regression fit, asdescribed above

E3:5; flexural; 95% ðGPaÞ ¼ 1:9 Log10ðN CyclesÞ þ 16:1 ð8Þ

95 (dashed) = -0.3x + 5.4

4 5 6 7 8

(N.Cycles)

bending fatigue tests on RRFC specimens (3.5% VF). The continuous lineconfidence interval of 95%.

y = 1.9x + 13.5R2 = 0.2553

y0.95 (dashed) = 1.9x + 16.1

0

5

10

15

20

25

30

35

0 1 2 3 4 5 6 7 8

Log10(N.Cycles)

E (

GP

a)

Fig. 8. Relationship between dynamic Young modulus (E) and number of cycles obtained in the bending fatigue tests on RRFC specimens (3.5% VF). Thecontinuous line indicates the linear regression and the dashed lines shows the upper limit for a confidence interval of 95%.

F. Hernandez-Olivares et al. / Construction and Building Materials 21 (2007) 1918–1927 1923

Therefore, the Young modulus for 106 cycles of load is27.4 GPa. This value fits with the dynamic Young modulusobtained in compression dynamic tests at 60 �C [4].

The maximum flexural strain measured in the fatiguebending tests of the concrete specimens with 3.5 VF ofrecycled rubber are presented in Fig. 9. Once more, it isconsidered the lower limit equation of the 95% confidenceinterval, that is to say, the following equation:

e3:5; flexural; 95% ðldefÞ ¼ �32:4Log10ðNCyclesÞ þ 340:8 ð9ÞUnder this criterion, the 3.5% VF rubber concrete flexuralfailure strain for 106 cycles of load is 146 ldef.

3.3. Concrete specimens with 5% VF of recycled crumbed

tyre rubber

Following the same scheme the fatigue behaviour of the5% VF rubber–concrete specimens is presented below.

y = -32.4x + 363.5R2 = 0.5991

0

50

100

150

200

250

300

350

400

0 1 2 3

Log10

Fle

xura

l Str

ain

(μd

ef)

Fig. 9. Relationship between failure tension strain and number of cycles obcontinuous line indicates the linear regression and the dashed line shows the l

Fig. 10 depicts the fatigue flexural stress test results ofthe concrete specimens with 3.5% VF of recycled crumbedtyre rubber.

As for the plain concrete and the 3.5% rubber–concreteresults, the fatigue law for flexural strength of RRFC with5% VF of recycled crumbed tyre rubber is better describedusing the lower limit equation of the 95% confidence inter-val of the linear regression fit

rflexural strength; 95% ðMPaÞ ¼ �0:1Log10ðNCyclesÞ þ 3:6 ð10ÞAccording to this equation, the bending failure stress for106 cycles of load is 3.0 MPa. This value is much lowerthan the one obtained for plain concrete without rubber(3.9 MPa) and RRFC with 3.5% VF of recycled rubber(3.8 MPa).

Fig. 11 depicts the Young modulus results obtainedfrom the fatigue bending tests of the concrete specimenswith 5% VF of recycled crumbed tyres rubber. Again, the

y0.95 (dashed)= -32.4x + 340.8

4 5 6 7 8

(N.Cycles)

tained in the bending fatigue tests on RRFC specimens (3.5% VF). Theower limit for a confidence interval of 95%.

y = -0.1x + 3.9R2 = 0.0917

y0.95 (dashed) = -0.1x + 3.6

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 1 2 3 4 5 6 7 8Log10(N.Cycles)

Fle

xura

l Str

ess

(MP

a)

Fig. 10. Relationship between failure tension stress and number of cycles obtained in the bending fatigue tests on RRFC specimens (5% VF). Thecontinuous line indicates the linear regression and the dashed line shows the lower limit for a confidence interval of 95%.

y = 1.1x + 12.4R2 = 0.0785

y0.95 (dashed) = 1.1x + 15.0

0

5

10

15

20

25

30

0 1 2 3 4 5 6 7 8

Log10(N.Cycles)

E (

GP

a)

Fig. 11. Relationship between dynamic Young modulus (E) and number of cycles obtained in the three points bending fatigue tests on RRFC specimens(5% VF). The continuous line indicates the linear regression and the dashed lines shows the upper limit for a confidence interval of 95%.

y = -23.1x + 307.4R2 = 0.2063

y0.95 (dashed) = -23.1x + 293.3

0

50

100

150

200

250

300

350

0 1 2 3 4 5 6 7 8

Log10(N.Cycles)

Fle

xura

l Str

ain

(m

def

)

Fig. 12. Relationship between failure tension strain and number of cycles obtained in the bending fatigue tests on RRFC specimens (5% VF). Thecontinuous line indicates the linear regression and the dashed line shows the lower limit for a confidence interval of 95%.

1924 F. Hernandez-Olivares et al. / Construction and Building Materials 21 (2007) 1918–1927

F. Hernandez-Olivares et al. / Construction and Building Materials 21 (2007) 1918–1927 1925

Young modulus considered for a rigid pavement design isalso defined by the upper limit equation of the 95% confi-dence interval of the linear regression fit

E5; flexural; 95% ðGPaÞ ¼ 1:1Log10ðN CyclesÞ þ 15:0 ð11ÞTherefore, the Young modulus for 106 cycles of load is21.6 GPa. This value is clearly lower than the dynamicYoung modulus obtained in compression dynamic testsat any testing temperature [4].

As it has been shown for the 3.5% VF of recycled rubberconcrete depicted in Fig. 8, Young modulus increases withthe number of load cycles.

Comparison of Fig. 5 with Figs. 8 and 11 shows thatstiffness increases under cyclic load for those concretesfilled with recycled crumbed tyres rubber. The referenceconcrete (Fig. 5) shows no stiffness increase under cyclicload.

Fig. 12 depicts the maximum flexural strain measured inthe fatigue bending tests of the concrete specimens with 5VF of recycled rubber. It has been also considered thelower limit equation of the 95% confidence interval, thatis to say, the following equation:

e3:5; flexural; 95% ðldefÞ ¼ �23:1Log10ðNCyclesÞ þ 293:3 ð12ÞUnder this criterion, the 5% VF rubber concrete flexuralfailure strain for 106 cycles of load is 155 ldef.

4. Design implications for rigid pavements

In order to determine design implications for rigid pave-ments of RRFC, the maximum tensile stress produced by a13 tons simple axle of a truck (127 kN) was evaluated, con-sidering the most adverse load location.

The rigid pavement was modelled as a plate placed onan elastic subgrade. Several values for the modulus of elas-tic reaction for the foundation, from 50 to 150 MPa/m,were used. A tyre pressure of 7 bar (0.7 MPa) was consid-ered for evaluating the radius of the load circle on the con-crete slab, according to the Westergaard method.

The Westergaard theoretical equations [5] evaluate theload configurations that produce the maximum tensilestress rmax on the concrete slab pavements, comparingthe application point of the load. Three different casescan be evaluated [12]:

Case I: load applied on the center of the slab

rmax I ¼3 W ð1þ mÞ

2pt2ln

Le

R0

� �þ 0:6159

� �ð13Þ

Case II: load applied on the edge of the slab

rmax II ¼0:863W ð1þ mÞ

t2ln

Le

R0

þ 0:207

� �ð14Þ

Case III: load applied on the vertex of the slab

rmax III ¼3Wt2

1� 1:083R0

Le

� �0:6" #

ð15Þ

where W is the load applied, t is the concrete slab thickness,m is the concrete Poisson ratio, Le is the characteristiclength and R0 is the contact radius between tyre and pave-ment.

Le can be calculated using equation [12]

Le ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiEt3

12ð1� m2Þk4

sð16Þ

where k is the modulus of subgrade reaction, E is the con-crete Young modulus, t is the concrete slab thickness and mis the concrete Poisson ratio.

R0 can be obtained from the applied load W and the tyrepressure, rP using the next equation [8]

R0 ¼ffiffiffiffiffiffiffiffiWprP

rð17Þ

However, when considering a concrete rigid pavementmad, as the RRFC described, R0 can be substituted byR, by means of the following equation [13, p. 372 in Span-ish Edition]:

R ¼ R0 þ2

3t ð18Þ

As a result of the previous equations, and according withthe fatigue behaviour test results, a systematic calculationof the maximum tensional stress on a RRFC slab of anythickness and on several elastic foundation with differentmodulus subgrade reaction can be run.

The maximum tensional stress on the RRFC corre-sponds to the load Case II described above (load appliedon the edge of the slab). Thus, the results of such a system-atic calculation for Case II are represented in Fig. 13, for aRRFC with the three different VF of recycled rubber (0%,3.5% and 5%) and three values of the modulus of subgradereaction have been considered.

It is shown in Fig. 13 the relationship between the Max-imum tension stress on the edge of the concrete slab (West-ergaard equations, Case II) and the thickness of the slabfor different VF of recycled rubber (0%, 3.5% and 5%)and three different values of the Modulus of SubgradeReaction (k = 50, 100 and 150 MPa/m, respectively), forapplied load of 127 kN.

Fig. 13 shows that the modulus of subgrade reaction hasa great influence on the slab thickness necessary to limit themaximum tensional stress achieved: the lower the modulusof subgrade reaction, the larger the maximum tensionalstress. This feature is according to the rigid behaviour ofthe RRFC pavement.

It is also observed a dependence of the maximum ten-sional stress on the volume fraction and thus on the Youngmodulus. RRFC with a 3.5% VF of recycled rubber showthe largest tensional stress for a fixed modulus of subgradereaction and slab thickness. This value is slightly higherthan that shown by the reference concrete.

It must be taken into account that the Young modulusconsidered in the Westergaard equations corresponds to

Fig. 13. Relationship between the Maximum tension stress on the edge of the concrete slab (Westergaard equations, Case II) and the thickness of the slabfor different VF of recycled rubber (0%, 3.5% and 5%) and three different values of the Modulus of Subgrade Reaction (k = 50, 100 and 150 MPa/m,respectively). Applied load 127 kN.

1926 F. Hernandez-Olivares et al. / Construction and Building Materials 21 (2007) 1918–1927

106 load cycles. RRFC (3.5% VF) shows a stiffness increasetendency (Fig. 8) that makes its Young modulus at 106 loadcycles higher than that exhibited by the reference concreteat 106 cycles (25.1 GPa) depicted in Fig. 5.

According to the experimental fatigue results and theanalytical study presented, the relations obtained can beused for the calculation of RRFC pavement thickness, asa function of the modulus of subgrade reaction, for 106

cycles of a 13 tons simple axle load.For different load traffic density, the equivalent durabil-

ity in years can be also calculated.

4.1. Example of design implication. Application to a rubber-filled concrete rigid pavement

The slab thickness should be defined to guarantee amaximum tensile stress lower than 2.9 MPa, the maximumachieved in the bending fatigue tests for a rigid pavement

0

5

10

15

20

25

30

0 1 2

Recycled R

Co

ncr

ete

slab

th

ickn

ess

(cm

)

Fig. 14. Design values of the concrete slab thickness for different recycled rusubgrade reaction: 150 MPa/m.

of RRFC with a 5% VF of recycled rubber on an elasticfoundation with a modulus of subgrade reaction of150 MPa/m, with a 95% confidence level, for 106 cyclesof a 13 tons simple axle load.

From Fig. 13, a good fitted curve (R2 = 0.999) can beobtained for a RRFC with a 5% VF and a modulus of sub-grade reaction of 150 MPa/m

rmax II ðMPaÞ ¼ 258:43t�1:405

t ðcmÞ ¼ 258:43

rmax II ðMPaÞ

� � 11:405 ð19Þ

A pavement slab thickness of 24.3 cm is obtained from thedata and equations shown above.

The same problem can be solved for a rigid pavement ofRRFC with a 3.5% VF of recycled rubber on an elasticfoundation with a modulus of subgrade reaction of150 MPa/m. In this case, the maximum tensile stress in

3 4 5 6

ubber VF (%)

bber VF, for N = 106 load cycles (13 tons simple axle load). Modulus of

F. Hernandez-Olivares et al. / Construction and Building Materials 21 (2007) 1918–1927 1927

the bending fatigue tests is 3.8 MPa, with a 95% confidencelevel, for 106 cycles of a 13 tons simple axle load is.

Again, from Fig. 13, a good fit (R2 = 0.999) can beobtained to relate maximum tensile stress with the pave-ment thickness for a RRFC with a 3.5% VF and a modulusof subgrade reaction of 150 MPa/m

rmax II ðMPaÞ ¼ 294:62t�1:4312

t ðcmÞ ¼ 294:62

rmax II ðMPaÞ

� � 11:4312 ð20Þ

Now, the pavement slab thickness obtained, is 21.1 cm.From a design point of view, an improvement of the fati-gue behaviour of RRFC with 3.5% VF of recycled rubberwith regard to 5% VF is obtained. The slab thickness is3 cm thinner for the same conditions and durability.

The better fit (R2 = 0.999), from Fig. 13, between max-imum tensile stress and concrete thickness for the referenceconcrete and a modulus of subgrade reaction of 150 MPa/mis

rmax II ðMPaÞ ¼ 280:45t�1:4213

t ðcmÞ ¼ 280:45

rmax II ðMPaÞ

� � 11:4213 ð21Þ

For the maximum tensional stress in fatigue of 4.0 MPa(106 cycles of a 13 tons simple axle load) the pavement slabthickness obtained is 19.9 cm. From a design point of viewthis value means a reduction of thickness of only 1 cm withregard to RRFC with 3.5% VF of recycled rubber.

Fig. 14 depicts the results of this example of design.

5. Conclusions

The methodology presented in this paper for rigid pave-ments design of road construction is based on experimentalresults obtained from laboratory tests and analytical calcu-lations, according to Westergaard equations for flat plateson elastic foundations, that here are recovery. It has beshown that it is a powerful design tool.

The results of recycled tyre rubber-filled concrete(RRFC) under fatigue loads and the analytical study pre-sented in this paper show the feasibility of using thiscement based composite material as a rigid pavement forroads on elastic subgrade.

The scatter of fatigue experimental results that is usualin the concrete laboratory tests, has been overcome bymeans of the utilization of a 95% confidence level in theanalytical calculations for the strength and stiffness of theconcrete pavement. It can be used too for maximum straindesign implications.

The stiffness increase due to fatigue load implies a slightincrease of the slab pavement thickness with RRFC (3.5%VF) with regard to concrete without rubber of around 5%.Nevertheless, it can be compensated by the recycling of theused tyres, the low cost of this solid waste and the betterdamping capacity of the rubber–concrete composite.

Acknowledgements

The authors want to acknowledge J. Garcıa Carretero ofthe Roads Laboratory of CEDEX (Spain) his collabora-tion in performing the fatigue tests.

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