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´                              F. Hernandez-Olivares et al. / Construction and Building Materials 21 (2007) 1918–1927     ...
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´                           F. Hernandez-Olivares et al. / Construction and Building Materials 21 (2007) 1918–1927        ...
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Fatigue Behaviour of Recycled Tyre Rubber-Filled Concrete and its implications in the Design of Rigid Pavements

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Fatigue Behaviour of Recycled Tyre Rubber-Filled Concrete and its implications in the Design of Rigid Pavements

  1. 1. Construction and Building Construction and Building Materials 21 (2007) 1918–1927 MATERIALS www.elsevier.com/locate/conbuildmat Fatigue behaviour of recycled tyre rubber-filled concrete and its implications in the design of rigid pavements a,* ´ F. Hernandez-Olivares , 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, Spain b ´ ´ Departamento de Arquitectura, Escuela Tecnica Superior de Arquitectura y Geodesia, Universidad de Alcala, ´ ´ C/Santa Ursula, 8, 28801 Alcala de Henares, Madrid, Spain c ´ Departamento de Arquitectura y Construcciones Navales, Escuela Tecnica Superior de Igenieros Navales, ´ Universidad Politecnica de Madrid, Arco de la Victoria, Ciudad Universitaria, Madrid 28040, Spain d 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 2006 Available online 22 September 2006Abstract 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.Ó 2006 Elsevier Ltd. All rights reserved.Keywords: Mechanical properties; Fatigue; Recycled rubber-filled concrete; Rigid pavements1. Introduction of the concrete–rubber composite, in relation with similar concrete samples without rubber. Recycled tyre rubber-filled concrete (RRFC) has There have also been proposed other uses for architec-become a matter of interest in the last few years, due to tural and building applications [3]. Besides, it has beenits good performance and as an alternative for tyre recy- experimentally shown that crumbed tyre rubber additionscling [1]. This new material provides a good mechanical in structural high strength concrete slabs improved its firebehaviour under static and dynamic actions and is being resistance, reducing its spalling damage under fire [4].used for road pavement applications. In a previous paper This paper presents the results of fatigue laboratory tests[2], the static and dynamic mechanical behaviour and per- on prismatic samples of similar rubber-filled concreteformance of RRFC from crumbed used tyres was assessed. described in [2,3] cut off from slabs of 90 · 60 · 5 cm, afterThe main conclusions were referred to the optimum crum- a long term exposition to natural weathering in Madridbed rubber fibre content, the compatibility and stability of (Spain) (one year ageing) are presented. From these exper-cement–rubber interface, the dynamic energy dissipation imental results, a mechanical analysis based on Westerg-and its better damping capacity and the stiffness reduction aard well known theory over flat plates on elastic foundation [5] has been developed to calculate the mini- * Corresponding author. Tel.: +34 913364245; fax: +34 913366560. mum thickness of RRFC for rigid pavements subjected ´ E-mail address: f.hernandez@upm.es (F. Hernandez-Olivares). to high density traffic, in order to assess the durability of0950-0618/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved.doi:10.1016/j.conbuildmat.2006.06.030
  2. 2. ´ F. Hernandez-Olivares et al. / Construction and Building Materials 21 (2007) 1918–1927 1919this rigid pavements under 106 cycles of 13 tons axle load, Table 2according with the generally established design rules based Some nominal properties of truck tyre rubber (after Waddell and Evans [14])on AASHTO test [6]. The Westergaard analysis has been previously success- Young modulus (vulcanized properties) @ 100% 1.97 MPafully applied by other authors who compared it with finite @ 300% 10 MPaelements methods and with AASTHO road experimental @ 500% 22.36 MPadata from rigid concrete pavements [7]. Tensile strength 28.1 MPa The results here presented are limited to N = 106 cycles Elongation to break 590%because the laboratory tests have been restrained to that Rebound resiliencelimit conditions. @ 23 °C 44% Fatigue behaviour of both conventional and porous @ 75 °C 55%concrete 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. Fig. 1. RRFC slab (90 · 60 · 5 cm3) into its mould and under wind of a Afterwards, increasing volumetric fractions (VF), from small fan (wind velocity 3.5 m/s) during the Kraai test (see text).0% to 13%, of fibre-shaped crumbed tyre rubber were Temperature and humidity data loggers were placed on the slab.added 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% and 8 h from the beginning of setting, the slabs into its own5% VF of crumbed tyre rubber. moulds were subjected to wind flow on its free face under The main physical properties of PP fiber and crumbed room temperature and humidity conditions (22 °C andrubber tyres have been already presented [4]. That paper 62% relative humidity, respectively). The wind velocityalso contains a scanning electronic microscopy analysis was 3.5 m/s measured on the middle of the slabs free sur-(SEM) on the rubber-hydrated cement paste interface that faces position by mean of a calibrated anemometer. Sur-shows good compatibility between those components. face temperature and humidity of slabs was continuously The nominal properties of truck tyre rubber are summa- registered (Fig. 1).rized in Table 2. After demoulding, each slab was stored in laboratory The concrete slabs were cast in laboratory to perform for 28 days and in outer conditions for 11 months. Pris-the Kraai test of cracking of concrete due to plastic shrink- matic specimens of 5 · 5 · 25 cm3 were cut off from theseage, as described by Balaguru and Shah [11]. Each slab of aged slabs to be tested in fatigue bending.90 · 60 · 5 cm3 was demoulded after 24 h. During the first 3. Bending fatigue tests and resultsTable 1 Bending fatigue tests were run in the CEDEX (RoadReference concrete composition per cubic meter Research Center) Laboratory (Spain) on a servohydraulicCement CEM I-42.5R 360 kg dynamic test facility MTS 810 (Fig. 2). Prismatic specimensCoarse aggregate, 12–18 mm 1103 kgSand, 3–6 mm 699 kg of 5 · 5 · 25 cm3 were cut off from Kraai test slabs (0%,Water (w/c = 0.4) 147 kg 3.5% and 5% volumetric fractions of recycled tyre rubber)Water reducing admixture (Sikament 500) 7.20 kg exposed to natural weathering for one year.Set retarding admixture (Bettoretard) 1.07 kg Three point bending fatigue tests were accomplishedPolypropylene fiber fibermesh (0.1% vol) 900 g with load control, supports span 20 cm, and frequency of
  3. 3. 1920 ´ F. Hernandez-Olivares et al. / Construction and Building Materials 21 (2007) 1918–1927 main specimen dimension). Each fatigue test was immedi- ately stopped after complete cracking of the respective specimen been tested. Three series of ten (10) concrete specimens for each recy- cled crumbed tyre rubber VF composition (0%, 3.5% and 5%) were tested in bending. Fatigue strain on the lower face of each specimen was measured and registered; flexural strength and Young modulus were registered every ten load cycles. 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 flexuralFig. 2. Dynamic MTS 810 facility from CEDEX Laboratory (Madrid) strength and the number of load cycles of the concreteused in this research for fatigue bending tests. A three point bending specimens without crumbed rubber (plain concrete). TheRRFC sample (3.5% VF crumbed rubber content) is on place. Supports scatter of these experimental measurements is usual in sim-span: 20 cm. ilar data presented by other researchers (see, for instance, the results collected by Lee and Barr on plain and fibreload 10 Hz. In order to avoid stress concentrations near the reinforced concrete [10]). In any case a linear regressionbearings and the load head, three metallic pieces cut from plot is included into the chart of Fig. 4, that correspondshollow tubes of mild steel (2 · 2 cm2, 2 mm thickness) were to the following equation:epoxy-bonded to the specimens for load transmission as it rflexural strength; 95% ðMPaÞ ¼ À0:2 Log10 ðN Cycles Þ þ 5:4 ð1Þis shown in Fig. 3. This figure also shows a specimen afterfailure by complete cracking. If this fatigue law is strictly applied, it asserts that our Due to the rigid behaviour of RRFC (with regard to plain concrete could resist 106 loading cycles of 4.2 MPahigh modulus bituminous mixtures) a load controlled pro- flexural stress. It must be pointed out that this Eq. (1)cedure was used on fatigue tests. Load head longitudinal is not representative of the mechanical fatigue behaviourdisplacement was measured, and a 50-mm gage-length of all the specimens tested, due to the wide scatter ofMTS extensometer was placed on the lower side of the the experimental results, obtained by testing under flex-specimen to register transversal strain (longitudinal in the 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 the plain concrete. To be sure about the flexural fatigue strength of plain concrete a confidence percentage must be introduced. Here it is proposed to consider a confi- dence percentage of 95%, in such a way that under this assumption, the new fatigue law for plain concrete is the following (see Fig. 4): rflexural strength; 95% ðMPaÞ ¼ À0:2 Log10 ðN Cycles Þ þ 5:1 ð2Þ Then, it can be considered that the plain concrete flexural failure 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 the concrete specimens without recycled rubber (plain con- crete) which are collected in Fig. 5. The mean value keeps practically constant, independently of the number of load cycles. Nevertheless, the linear regression presents a very low value for R2 = 0.0003, which shows the great scatter of the Young modulus measurements for the different spec-Fig. 3. RRFC specimen (5 · 5 · 25 cm3) before and after fatigue bending imens tested. Again, it is proposed here to consider not thetest with strain control. Metallic epoxy-bonded hollow tubes 2 · 2 cm2 linear regression equation for the Young modulus E ofsquare section, made of mild steel 2 mm thickness. plain concrete, that is to say
  4. 4. ´ F. Hernandez-Olivares et al. / Construction and Building Materials 21 (2007) 1918–1927 1921 6 y = -0.2x + 5.4 R2 = 0.2044 5 Flexural Stress (MPa) 4 y0.95 (dashed)= -0.2x + 5.1 3 2 1 0 0 1 2 3 4 5 6 7 log10(N. Cycles)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%. 35 30 y0.95 (dashed) = 0.03x + 25.0 25 E (GPa) y= 0.03x + 23.7 R2 = 0.0003 20 15 10 0 1 2 3 4 5 6 7 Log10(N.Cycles)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%.Eflexural ðGPaÞ ¼ 0:03 Log10 ðN Cycles Þ þ 23:7 ð3Þ bending fatigue tests on plain concrete specimens (without rubber additions). Each maximum strain value representsbut, the following Eq. (4), that incorporates a confidence the maximum admissible plain concrete flexural strain forinterval of 95%: its linked number of load cycles. The linear regressionEflexural ðGPaÞ ¼ 0:03 Log10 ðN Cycles Þ þ 25:0 ð4Þ equation is as follows: À Á eflexural ðldefÞ ¼ À7:2 Log10 N Cycles þ 225:6 ð5ÞAs the stiffer concrete transmits greater flexural tensilestress. Because of that, the Young modulus value of plain Again, the scatter of data collected suggests to use a 95%concrete that has to be considered for rigid pavement de- confidence interval for the design strain. The followingsign must be defined by mean of the upper limit equation equation represents this lower limit (see Fig. 6) for the max-of the 95% confidence interval (25.1 GPa). This criterion imum flexural strain related to the corresponding numbercorresponds to the worst case. It must be notice that the of load cycles:flexural failure stress value was determined for the lower eflexural; 95% ðldefÞ ¼ À7:2 Log10 ðN Cycles Þ þ 212:0 ð6Þlimit equation of the 95% confidence interval. Fig. 6 depicts the relationship between the failure flex- Under this criterion, the plain concrete flexural failureural strain and the number of loading cycles obtained in strain for 106 cycles of load is 169 ldef.
  5. 5. 1922 ´ F. Hernandez-Olivares et al. / Construction and Building Materials 21 (2007) 1918–1927 300 250 y = -7.2x + 225.6 R2 = 0.171 Flexural Strain ( μdef) 200 150 y0.95 (dashed) = -7.2x + 212.0 100 50 0 0 1 2 3 4 5 6 7 Log10(N.Cycles)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%.3.2. Concrete specimens with 3.5% VF of recycled tyre lower limit equation of the 95% confidence interval of therubber linear regression fit rflexural strength; 95% ðMPaÞ ¼ À0:3 Log10 ðN Cycles Þ þ 5:4 ð7Þ The reasoning above can be repeated here to study thefatigue behaviour of the rubber–concrete specimens. The According with this equation, the bending failure stress forparticular values obtained for this new batch of samples 106 cycles of load is 3.8 MPa, this value is slightly lowerare simply shown here, omitting those paragraphs which than the one obtained for plain concrete without rubber.are similar. Fig. 8 depicts the Young modulus results obtained from Fig. 7 depicts the relationship between the failure stress of the fatigue bending tests of the concrete specimens withand the number of cycles obtained in the bending fatigue 3.5% VF of recycled rubber.tests on RRFC specimens (3.5% VF). The continuous line Again, the Young modulus considered for a rigid pave-indicates the linear regression and the dashed line shows ment design is defined by the upper limit equation of thethe lower limit for a confidence interval of 95%. 95% confidence interval of the linear regression fit, as As described for the reference concrete results, the fati- described abovegue law for flexural strength of RRFC with 3.5% VF ofrecycled crumbed tyre rubber is better described using the E3:5; flexural; 95% ðGPaÞ ¼ 1:9 Log10 ðN Cycles Þ þ 16:1 ð8Þ 7 y = -0.3x + 5.8 R2 = 0.1891 6 5 Flexural Stress (MPa) 4 y0.95 (dashed) = -0.3x + 5.4 3 2 1 0 0 1 2 3 4 5 6 7 8 Log10(N.Cycles)Fig. 7. Relationship between failure stress and number of cycles obtained in the bending fatigue tests on RRFC specimens (3.5% VF). The continuous lineindicates the linear regression and the dashed line shows the lower limit for a confidence interval of 95%.
  6. 6. ´ F. Hernandez-Olivares et al. / Construction and Building Materials 21 (2007) 1918–1927 1923 35 y0.95 (dashed) = 1.9x + 16.1 30 25 E (GPa) 20 15 y = 1.9x + 13.5 R2 = 0.2553 10 5 0 0 1 2 3 4 5 6 7 8 Log10(N.Cycles)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%.Therefore, the Young modulus for 106 cycles of load is Fig. 10 depicts the fatigue flexural stress test results of27.4 GPa. This value fits with the dynamic Young modulus the concrete specimens with 3.5% VF of recycled crumbedobtained in compression dynamic tests at 60 °C [4]. tyre rubber. The maximum flexural strain measured in the fatigue As for the plain concrete and the 3.5% rubber–concretebending tests of the concrete specimens with 3.5 VF of results, the fatigue law for flexural strength of RRFC withrecycled rubber are presented in Fig. 9. Once more, it is 5% VF of recycled crumbed tyre rubber is better describedconsidered the lower limit equation of the 95% confidence using the lower limit equation of the 95% confidence inter-interval, that is to say, the following equation: val of the linear regression fite3:5; flexural; 95% ðldefÞ ¼ À32:4 Log10 ðN Cycles Þ þ 340:8 ð9Þ rflexural strength; 95% ðMPaÞ ¼ À0:1 Log10 ðN Cycles Þ þ 3:6 ð10ÞUnder this criterion, the 3.5% VF rubber concrete flexural According to this equation, the bending failure stress forfailure strain for 106 cycles of load is 146 ldef. 106 cycles of load is 3.0 MPa. This value is much lower than the one obtained for plain concrete without rubber3.3. Concrete specimens with 5% VF of recycled crumbed (3.9 MPa) and RRFC with 3.5% VF of recycled rubbertyre rubber (3.8 MPa). Fig. 11 depicts the Young modulus results obtained Following the same scheme the fatigue behaviour of the from the fatigue bending tests of the concrete specimens5% VF rubber–concrete specimens is presented below. with 5% VF of recycled crumbed tyres rubber. Again, the 400 y = -32.4x + 363.5 R2 = 0.5991 350 300 Flexural Strain (μdef) 250 200 150 y0.95 (dashed)= -32.4x + 340.8 100 50 0 0 1 2 3 4 5 6 7 8 Log10(N.Cycles)Fig. 9. Relationship between failure tension strain 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 line shows the lower limit for a confidence interval of 95%.
  7. 7. 1924 ´ F. Hernandez-Olivares et al. / Construction and Building Materials 21 (2007) 1918–1927 4.5 y = -0.1x + 3.9 4 R2 = 0.0917 3.5 Flexural Stress (MPa) 3 2.5 y0.95 (dashed) = -0.1x + 3.6 2 1.5 1 0.5 0 0 1 2 3 4 5 6 7 8 Log10(N.Cycles)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%. 30 25 y0.95 (dashed) = 1.1x + 15.0 20 E (GPa) 15 y = 1.1x + 12.4 R2 = 0.0785 10 5 0 0 1 2 3 4 5 6 7 8 Log10(N.Cycles)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%. 350 300 y = -23.1x + 307.4 R2 = 0.2063 Flexural Strain (mdef) 250 200 150 y0.95 (dashed) = -23.1x + 293.3 100 50 0 0 1 2 3 4 5 6 7 8 Log10(N.Cycles)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%.
  8. 8. ´ F. Hernandez-Olivares et al. / Construction and Building Materials 21 (2007) 1918–1927 1925Young modulus considered for a rigid pavement design is where W is the load applied, t is the concrete slab thickness,also defined by the upper limit equation of the 95% confi- m is the concrete Poisson ratio, Le is the characteristicdence interval of the linear regression fit length and R0 is the contact radius between tyre and pave-E5; flexural; 95% ðGPaÞ ¼ 1:1 Log10 ðN Cycles Þ þ 15:0 ð11Þ ment. 6Therefore, the Young modulus for 10 cycles of load is Le can be calculated using equation [12]21.6 GPa. This value is clearly lower than the dynamic sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiYoung modulus obtained in compression dynamic tests 4 Et3 Le ¼ ð16Þat any testing temperature [4]. 12ð1 À m2 Þk As it has been shown for the 3.5% VF of recycled rubberconcrete depicted in Fig. 8, Young modulus increases with where k is the modulus of subgrade reaction, E is the con-the number of load cycles. crete Young modulus, t is the concrete slab thickness and m Comparison of Fig. 5 with Figs. 8 and 11 shows that is the concrete Poisson ratio.stiffness increases under cyclic load for those concretes R0 can be obtained from the applied load W and the tyrefilled with recycled crumbed tyres rubber. The reference pressure, rP using the next equation [8] rffiffiffiffiffiffiffifficoncrete (Fig. 5) shows no stiffness increase under cyclic Wload. R0 ¼ ð17Þ prP Fig. 12 depicts the maximum flexural strain measured in However, when considering a concrete rigid pavementthe fatigue bending tests of the concrete specimens with 5 mad, as the RRFC described, R0 can be substituted byVF of recycled rubber. It has been also considered the R, by means of the following equation [13, p. 372 in Span-lower limit equation of the 95% confidence interval, that ish Edition]:is to say, the following equation: 2e3:5; flexural; 95% ðldefÞ ¼ À23:1 Log10 ðN Cycles Þ þ 293:3 ð12Þ R ¼ R0 þ t ð18Þ 3Under this criterion, the 5% VF rubber concrete flexural As a result of the previous equations, and according withfailure strain for 106 cycles of load is 155 ldef. the fatigue behaviour test results, a systematic calculation of the maximum tensional stress on a RRFC slab of any4. Design implications for rigid pavements thickness and on several elastic foundation with different modulus subgrade reaction can be run. In order to determine design implications for rigid pave- The maximum tensional stress on the RRFC corre-ments of RRFC, the maximum tensile stress produced by a sponds to the load Case II described above (load applied13 tons simple axle of a truck (127 kN) was evaluated, con- on the edge of the slab). Thus, the results of such a system-sidering the most adverse load location. atic calculation for Case II are represented in Fig. 13, for a The rigid pavement was modelled as a plate placed on RRFC with the three different VF of recycled rubber (0%,an elastic subgrade. Several values for the modulus of elas- 3.5% and 5%) and three values of the modulus of subgradetic reaction for the foundation, from 50 to 150 MPa/m, reaction have been considered.were used. A tyre pressure of 7 bar (0.7 MPa) was consid- It is shown in Fig. 13 the relationship between the Max-ered for evaluating the radius of the load circle on the con- imum tension stress on the edge of the concrete slab (West-crete slab, according to the Westergaard method. ergaard equations, Case II) and the thickness of the slab The Westergaard theoretical equations [5] evaluate the for different VF of recycled rubber (0%, 3.5% and 5%)load configurations that produce the maximum tensile and three different values of the Modulus of Subgradestress rmax on the concrete slab pavements, comparing Reaction (k = 50, 100 and 150 MPa/m, respectively), forthe application point of the load. Three different cases applied load of 127 kN.can be evaluated [12]: Fig. 13 shows that the modulus of subgrade reaction has a great influence on the slab thickness necessary to limit the Case I: load applied on the center of the slab maximum tensional stress achieved: the lower the modulus 3 W ð1 þ mÞ Le of subgrade reaction, the larger the maximum tensionalrmax I ¼ ln þ 0:6159 ð13Þ stress. This feature is according to the rigid behaviour of 2pt2 R0 the RRFC pavement. Case II: load applied on the edge of the slab It is also observed a dependence of the maximum ten- 0:863W ð1 þ mÞ Le sional stress on the volume fraction and thus on the Youngrmax II ¼ ln þ 0:207 ð14Þ modulus. RRFC with a 3.5% VF of recycled rubber show t2 R0 the largest tensional stress for a fixed modulus of subgradeCase III: load applied on the vertex of the slab reaction and slab thickness. This value is slightly higher 0:6 # 3W R0 than that shown by the reference concrete.rmax III ¼ 2 1 À 1:083 ð15Þ It must be taken into account that the Young modulus t Le considered in the Westergaard equations corresponds to
  9. 9. 1926 ´ F. Hernandez-Olivares et al. / Construction and Building Materials 21 (2007) 1918–1927Fig. 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.106 load cycles. RRFC (3.5% VF) shows a stiffness increase of RRFC with a 5% VF of recycled rubber on an elastictendency (Fig. 8) that makes its Young modulus at 106 load foundation with a modulus of subgrade reaction ofcycles higher than that exhibited by the reference concrete 150 MPa/m, with a 95% confidence level, for 106 cyclesat 106 cycles (25.1 GPa) depicted in Fig. 5. of a 13 tons simple axle load. According to the experimental fatigue results and the From Fig. 13, a good fitted curve (R2 = 0.999) can beanalytical study presented, the relations obtained can be obtained for a RRFC with a 5% VF and a modulus of sub-used for the calculation of RRFC pavement thickness, as grade reaction of 150 MPa/ma function of the modulus of subgrade reaction, for 106cycles of a 13 tons simple axle load. rmax II ðMPaÞ ¼ 258:43tÀ1:405 !1:405 1 ð19Þ For different load traffic density, the equivalent durabil- 258:43ity in years can be also calculated. t ðcmÞ ¼ rmax II ðMPaÞ4.1. Example of design implication. Application to a rubber- A pavement slab thickness of 24.3 cm is obtained from thefilled concrete rigid pavement data and equations shown above. The same problem can be solved for a rigid pavement of The slab thickness should be defined to guarantee a RRFC with a 3.5% VF of recycled rubber on an elasticmaximum tensile stress lower than 2.9 MPa, the maximum foundation with a modulus of subgrade reaction ofachieved in the bending fatigue tests for a rigid pavement 150 MPa/m. In this case, the maximum tensile stress in 30 25 Concrete slab thickness (cm) 20 15 10 5 0 0 1 2 3 4 5 6 Recycled Rubber VF (%)Fig. 14. Design values of the concrete slab thickness for different recycled rubber VF, for N = 106 load cycles (13 tons simple axle load). Modulus ofsubgrade reaction: 150 MPa/m.
  10. 10. ´ F. Hernandez-Olivares et al. / Construction and Building Materials 21 (2007) 1918–1927 1927the bending fatigue tests is 3.8 MPa, with a 95% confidence The stiffness increase due to fatigue load implies a slightlevel, for 106 cycles of a 13 tons simple axle load is. increase of the slab pavement thickness with RRFC (3.5% Again, from Fig. 13, a good fit (R2 = 0.999) can be VF) with regard to concrete without rubber of around 5%.obtained to relate maximum tensile stress with the pave- Nevertheless, it can be compensated by the recycling of thement thickness for a RRFC with a 3.5% VF and a modulus used tyres, the low cost of this solid waste and the betterof subgrade reaction of 150 MPa/m damping capacity of the rubber–concrete composite.rmax II ðMPaÞ ¼ 294:62tÀ1:4312 !1:4312 1 Acknowledgements 294:62 ð20Þt ðcmÞ ¼ rmax II ðMPaÞ ´ The authors want to acknowledge J. Garcıa Carretero ofNow, the pavement slab thickness obtained, is 21.1 cm. the Roads Laboratory of CEDEX (Spain) his collabora-From a design point of view, an improvement of the fati- tion in performing the fatigue tests.gue behaviour of RRFC with 3.5% VF of recycled rubberwith regard to 5% VF is obtained. The slab thickness is References3 cm thinner for the same conditions and durability. The better fit (R2 = 0.999), from Fig. 13, between max- [1] Siddique R, Naik TR. Properties of concrete containing scrap-tyre rubber – an overview. Waste Manage 2004;24(5):563–9.imum tensile stress and concrete thickness for the reference ´ [2] Hernandez-Olivares F, Barluenga G, Bollati M, Witoszek B. Staticconcrete and a modulus of subgrade reaction of 150 MPa/m and dynamic behaviour of recycled tyre rubber-filled concrete.is Cement Concr Res 2002;32(10):1587–96. ´ [3] Hernandez-Olivares F, Barluenga G. High strength concrete modifiedrmax II ðMPaÞ ¼ 280:45tÀ1:4213 with solid particles recycled from elastomeric materials. In: Konig G, ¨ !1:4213 1 ð21Þ Dehn F, Faust T, editors. Proceedings of the 6th international 280:45 symposium on high strength/high performance, Leipzig, Germany,t ðcmÞ ¼ rmax II ðMPaÞ 2002. p. 1067–77. ´ [4] Hernandez-Olivares F, Barluenga G. Fire performance of recycledFor the maximum tensional stress in fatigue of 4.0 MPa rubber-filled high-strength concrete. Cement Concr Res(106 cycles of a 13 tons simple axle load) the pavement slab 2004;34(1):109–17.thickness obtained is 19.9 cm. From a design point of view [5] Westergaard HM. Stresses in concrete pavements computed by theoretical analysis, public roads, US Department of Agriculture,this value means a reduction of thickness of only 1 cm with Bureau of Public Roads 1926;7(2).regard to RRFC with 3.5% VF of recycled rubber. [6] American Association of State Highway and Transportation Officials Fig. 14 depicts the results of this example of design. (AASHTO). Guide for design of pavement structures. Edition 1993. [7] Ramsamooj DV, Lin GS, Ramadan J. Stresses at joints and cracks in highway and airport pavements. Eng Fract Mech 1998;60(5–6):5. Conclusions 507–18. ´ [8] Bollati MR, Talero R, Rodrıguez M, Witoszek B, Hernandez F. ´ The methodology presented in this paper for rigid pave- Porous high performance concrete for road traffic. In: Dhir RK,ments design of road construction is based on experimental Henderson NA, editors. Concrete for infrastructure and utilities.results obtained from laboratory tests and analytical calcu- London: EFN Spon; 1996. p. 589–99. [9] Pindado MA, Aguado A, Josa A. Fatigue behaviour of polymer-lations, according to Westergaard equations for flat plates modified porous concretes. Cement Concr Res 1999;29(7):1077–86.on elastic foundations, that here are recovery. It has be [10] Lee MK, Barr BIG. An overview of the fatigue behaviour of plainshown that it is a powerful design tool. and fiber reinforced concrete. Cement Concr Compos 2004;26(4): The results of recycled tyre rubber-filled concrete 299–305.(RRFC) under fatigue loads and the analytical study pre- [11] Balaguru PN, Shah SP. Fiber-reinforced cement composites. New York: MacGraw-Hill; 1992.sented in this paper show the feasibility of using this [12] Young WC. Roark’s formulas for stress and strain [Rev. ed. of:cement based composite material as a rigid pavement for Raymond J. Roark. Formulas for stress and strain, 5th ed., 1975]. 6throads on elastic subgrade. ed. New York: McGraw-Hill; 1989. pp. 473–474 (Table 26). The scatter of fatigue experimental results that is usual ´ [13] Hahn J. Vigas continuas, porticos, placas y vigas flotantes sobrein the concrete laboratory tests, has been overcome by ´ terreno elastico, Gustavo Gili Si.A., Barcelona, Spain, 1982 (in Spanish, from: J. Hahn, ‘‘Durchlauftrager, Rahmen, Platte und ¨means of the utilization of a 95% confidence level in the Balken auf elastischer Bettung’’, Werner-Verlag, Dusseldorf, Ger- ¨analytical calculations for the strength and stiffness of the many, 13th ed., 1981 in German).concrete pavement. It can be used too for maximum strain [14] Waddell WH, Evans LR. Use of nonblack fillers in tire compounds.design implications. Rubber Chem Technol 1996;69(3):377–423.

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