Construction and Building
MATERIALS
Construction and Building Materials 21 (2007) 1918–1927
www.elsevier.com/locate/conbuildmat
Fatigue behaviour of recycled tyre rubber-filled concrete and its implications in the design of rigid pavements F. Herna´ndez-Olivares
a,*
, G. Barluenga b, B. Parga-Landa c, M. Bollati d, B. Witoszek
e
a
b
Departamento de Construccio´n y Tecnologı´a Arquitecto´nicas, Escuela Te´cnica Superior de Arquitectura, Universidad Polite´cnica de Madrid, Avda. Juan de Herrera, 4, Madrid 28040, Spain Departamento de Arquitectura, Escuela Te´cnica Superior de Arquitectura y Geodesia, Universidad de Alcala´, ´ rsula, 8, 28801 Alcala´ de Henares, Madrid, Spain C/Santa U c Departamento de Arquitectura y Construcciones Navales, Escuela Te´cnica Superior de Igenieros Navales, Universidad Polite´cnica de Madrid, Arco de la Victoria, Ciudad Universitaria, Madrid 28040, Spain d Composites I+D, Pen˜a Sacra, 30, Galapagar, 28260 Madrid, Spain e Pavimentos Asfa´lticos 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 2006
Abstract This paper presents the results of fatigue bending tests on prismatic samples of recycled tyre rubber-filled concrete (RRFC) with different volumetric fractions (VF) of rubber (0%, 3.5% and 5%) after a long term exposition to natural weathering in Madrid (Spain) (one year ageing). From these experimental results, an analytical model based on classical Westergaard well known equations has been developed to calculate the minimum thickness of RRFC for rigid pavements subjected to high density traffic, in order to obtain a durability of these rigid pavements of 106 cycles of 13 tons (127 kN) axle load. In this investigation any value of the modulus of subgrade reaction for rigid 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) has become a matter of interest in the last few years, due to its good performance and as an alternative for tyre recycling [1]. This new material provides a good mechanical behaviour under static and dynamic actions and is being used for road pavement applications. In a previous paper [2], the static and dynamic mechanical behaviour and performance of RRFC from crumbed used tyres was assessed. The main conclusions were referred to the optimum crumbed rubber fibre content, the compatibility and stability of cement–rubber interface, the dynamic energy dissipation and its better damping capacity and the stiffness reduction *
Corresponding author. Tel.: +34 913364245; fax: +34 913366560. E-mail address: f.hernandez@upm.es (F. Herna´ndez-Olivares).
0950-0618/$ - see front matter 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.conbuildmat.2006.06.030
of the concrete–rubber composite, in relation with similar concrete samples without rubber. There have also been proposed other uses for architectural and building applications [3]. Besides, it has been experimentally shown that crumbed tyre rubber additions in structural high strength concrete slabs improved its fire resistance, reducing its spalling damage under fire [4]. This paper presents the results of fatigue laboratory tests on prismatic samples of similar rubber-filled concrete described in [2,3] cut off from slabs of 90 · 60 · 5 cm, after a long term exposition to natural weathering in Madrid (Spain) (one year ageing) are presented. From these experimental results, a mechanical analysis based on Westergaard well known theory over flat plates on elastic foundation [5] has been developed to calculate the minimum thickness of RRFC for rigid pavements subjected to high density traffic, in order to assess the durability of
F. Herna´ndez-Olivares et al. / Construction and Building Materials 21 (2007) 1918–1927
this rigid pavements under 106 cycles of 13 tons axle load, according with the generally established design rules based on AASHTO test [6]. The Westergaard analysis has been previously successfully applied by other authors who compared it with finite elements methods and with AASTHO road experimental data from rigid concrete pavements [7]. The results here presented are limited to N = 106 cycles because the laboratory tests have been restrained to that limit conditions. Fatigue behaviour of both conventional and porous concrete for rigid pavements has been widely studied, mainly under fracture mechanic analysis [8–10]. Nevertheless, RRFC cannot be classified as a simple porous concrete, mainly due to its dissipative and damping properties previously studied [2].
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Table 2 Some nominal properties of truck tyre rubber (after Waddell and Evans [14]) Young modulus (vulcanized properties) @ 100% @ 300% @ 500% Tensile strength Elongation to break
1.97 MPa 10 MPa 22.36 MPa 28.1 MPa 590%
Rebound resilience @ 23 C @ 75 C
44% 55%
2. Materials and specimen preparation A plain concrete without crumbed rubber tyre has been done in order to fabricate the control slabs. The composition of this concrete labelled as ‘‘reference or plain concrete’’ is presented in Table 1 (per cubic meter of concrete). The aggregates gradation is non-continuous in order to obtain voids in the concrete for the easy arrange of crumbed tyre rubber particles in the mix, and to obtain also good drainage and noise absorbent concrete pavements. The polypropylene (PP) fibres (0.1% volumetric fraction) were added and mixed to reduce the early cracking of fresh concrete due to plastic shrinkage. Afterwards, increasing volumetric fractions (VF), from 0% to 13%, of fibre-shaped crumbed tyre rubber were added to fresh concrete fabricated with the reference concrete mix. Nevertheless, bending fatigue tests were accomplished only on concrete samples containing 0%, 3.5% and 5% VF of crumbed tyre rubber. The main physical properties of PP fiber and crumbed rubber tyres have been already presented [4]. That paper also contains a scanning electronic microscopy analysis (SEM) on the rubber-hydrated cement paste interface that shows good compatibility between those components. The nominal properties of truck tyre rubber are summarized in Table 2. The concrete slabs were cast in laboratory to perform the Kraai test of cracking of concrete due to plastic shrinkage, as described by Balaguru and Shah [11]. Each slab of 90 · 60 · 5 cm3 was demoulded after 24 h. During the first
Fig. 1. RRFC slab (90 · 60 · 5 cm3) into its mould and under wind of a small fan (wind velocity 3.5 m/s) during the Kraai test (see text). Temperature and humidity data loggers were placed on the slab.
8 h from the beginning of setting, the slabs into its own moulds were subjected to wind flow on its free face under room temperature and humidity conditions (22 C and 62% relative humidity, respectively). The wind velocity was 3.5 m/s measured on the middle of the slabs free surfaces position by mean of a calibrated anemometer. Surface temperature and humidity of slabs was continuously registered (Fig. 1). After demoulding, each slab was stored in laboratory for 28 days and in outer conditions for 11 months. Prismatic specimens of 5 · 5 · 25 cm3 were cut off from these aged slabs to be tested in fatigue bending. 3. Bending fatigue tests and results
Table 1 Reference concrete composition per cubic meter Cement CEM I-42.5R Coarse aggregate, 12–18 mm Sand, 3–6 mm Water (w/c = 0.4) Water reducing admixture (Sikament 500) Set retarding admixture (Bettoretard) Polypropylene fiber fibermesh (0.1% vol)
360 kg 1103 kg 699 kg 147 kg 7.20 kg 1.07 kg 900 g
Bending fatigue tests were run in the CEDEX (Road Research Center) Laboratory (Spain) on a servohydraulic dynamic test facility MTS 810 (Fig. 2). Prismatic specimens of 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 accomplished with load control, supports span 20 cm, and frequency of
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F. Herna´ndez-Olivares et al. / Construction and Building Materials 21 (2007) 1918–1927
main specimen dimension). Each fatigue test was immediately stopped after complete cracking of the respective specimen been tested. Three series of ten (10) concrete specimens for each recycled 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 samples batch. 3.1. Concrete specimens without recycled tyre rubber (0% VF)
Fig. 2. Dynamic MTS 810 facility from CEDEX Laboratory (Madrid) used in this research for fatigue bending tests. A three point bending RRFC sample (3.5% VF crumbed rubber content) is on place. Supports span: 20 cm.
load 10 Hz. In order to avoid stress concentrations near the bearings and the load head, three metallic pieces cut from hollow tubes of mild steel (2 · 2 cm2, 2 mm thickness) were epoxy-bonded to the specimens for load transmission as it is shown in Fig. 3. This figure also shows a specimen after failure by complete cracking. Due to the rigid behaviour of RRFC (with regard to high modulus bituminous mixtures) a load controlled procedure was used on fatigue tests. Load head longitudinal displacement was measured, and a 50-mm gage-length MTS extensometer was placed on the lower side of the specimen to register transversal strain (longitudinal in the
Fig. 4 depicts the relationship between failure flexural strength and the number of load cycles of the concrete specimens without crumbed rubber (plain concrete). The scatter of these experimental measurements is usual in similar data presented by other researchers (see, for instance, the results collected by Lee and Barr on plain and fibre reinforced concrete [10]). In any case a linear regression plot is included into the chart of Fig. 4, that corresponds to the following equation: rflexural strength; 95% ðMPaÞ ¼ 0:2 Log10 ðN Cycles Þ þ 5:4
If this fatigue law is strictly applied, it asserts that our plain concrete could resist 106 loading cycles of 4.2 MPa flexural stress. It must be pointed out that this Eq. (1) is not representative of the mechanical fatigue behaviour of all the specimens tested, due to the wide scatter of the experimental results, obtained by testing under flexural 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 confidence 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 0:2 Log10 ðN Cycles Þ þ 5:1
Fig. 3. RRFC specimen (5 · 5 · 25 cm3) before and after fatigue bending test with strain control. Metallic epoxy-bonded hollow tubes 2 · 2 cm2 square section, made of mild steel 2 mm thickness.
ð1Þ
ð2Þ
Then, it can be considered that the plain concrete flexural failure stress for 106 cycles of load is 3.9 MPa, with a confidence interval of 95%. Similar analysis is applied to Young modulus measurements for the three points fatigue bending tests of the concrete specimens without recycled rubber (plain concrete) 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 specimens tested. Again, it is proposed here to consider not the linear regression equation for the Young modulus E of plain concrete, that is to say
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y = -0.2x + 5.4 R2 = 0.2044
Flexural Stress (MPa)
5
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 concrete specimens (without rubber additions). The continuous line indicates the linear regression and the dashed line shows the lower limit for a confidence interval of 95%.
35
30
E (GPa)
y0.95 (dashed) = 0.03x + 25.0
25 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
but, the following Eq. (4), that incorporates a confidence interval of 95%: Eflexural ðGPaÞ ¼ 0:03 Log10 ðN Cycles Þ þ 25:0
ð4Þ
As the stiffer concrete transmits greater flexural tensile stress. Because of that, the Young modulus value of plain concrete that has to be considered for rigid pavement design must be defined by mean of the upper limit equation of the 95% confidence interval (25.1 GPa). This criterion corresponds to the worst case. It must be notice that the flexural failure stress value was determined for the lower limit equation of the 95% confidence interval. Fig. 6 depicts the relationship between the failure flexural strain and the number of loading cycles obtained in
bending fatigue tests on plain concrete specimens (without rubber additions). Each maximum strain value represents the maximum admissible plain concrete flexural strain for its linked number of load cycles. The linear regression equation is as follows: eflexural ðldefÞ ¼ 7:2 Log10 N Cycles þ 225:6 ð5Þ Again, the scatter of data collected suggests to use a 95% confidence interval for the design strain. The following equation represents this lower limit (see Fig. 6) for the maximum flexural strain related to the corresponding number of load cycles: eflexural; 95% ðldefÞ ¼ 7:2 Log10 ðN Cycles Þ þ 212:0
ð6Þ
Under this criterion, the plain concrete flexural failure strain for 106 cycles of load is 169 ldef.
F. Herna´ndez-Olivares et al. / Construction and Building Materials 21 (2007) 1918–1927
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300
Flexural Strain ( μdef)
250
y = -7.2x + 225.6 R2 = 0.171
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 (without rubber additions). The continuous line is the linear regression and the dashed line shows the lower limit for a confidence interval of 95%.
lower limit equation of the 95% confidence interval of the linear regression fit
3.2. Concrete specimens with 3.5% VF of recycled tyre rubber The reasoning above can be repeated here to study the fatigue behaviour of the rubber–concrete specimens. The particular values obtained for this new batch of samples are simply shown here, omitting those paragraphs which are similar. Fig. 7 depicts the relationship between the failure stress and the number of cycles obtained in the bending fatigue tests on RRFC specimens (3.5% VF). The continuous line indicates the linear regression and the dashed line shows the lower limit for a confidence interval of 95%. As described for the reference concrete results, the fatigue law for flexural strength of RRFC with 3.5% VF of recycled crumbed tyre rubber is better described using the
rflexural strength; 95% ðMPaÞ ¼ 0:3 Log10 ðN Cycles Þ þ 5:4
ð7Þ
According with this equation, the bending failure stress for 106 cycles of load is 3.8 MPa, this value is slightly lower than the one obtained for plain concrete without rubber. Fig. 8 depicts the Young modulus results obtained from of the fatigue bending tests of the concrete specimens with 3.5% VF of recycled rubber. Again, the Young modulus considered for a rigid pavement design is defined by the upper limit equation of the 95% confidence interval of the linear regression fit, as described above 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
Flexural Stress (MPa)
6 5 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 line indicates the linear regression and the dashed line shows the lower limit for a confidence interval of 95%.
F. Herna´ndez-Olivares et al. / Construction and Building Materials 21 (2007) 1918–1927
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35 y0.95 (dashed) = 1.9x + 16.1
30
E (GPa)
25 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). The continuous 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 27.4 GPa. This value fits with the dynamic Young modulus obtained in compression dynamic tests at 60 C [4]. The maximum flexural strain measured in the fatigue bending tests of the concrete specimens with 3.5 VF of recycled rubber are presented in Fig. 9. Once more, it is considered the lower limit equation of the 95% confidence interval, that is to say, the following equation:
Fig. 10 depicts the fatigue flexural stress test results of the concrete specimens with 3.5% VF of recycled crumbed tyre rubber. As for the plain concrete and the 3.5% rubber–concrete results, the fatigue law for flexural strength of RRFC with 5% VF of recycled crumbed tyre rubber is better described using the lower limit equation of the 95% confidence interval of the linear regression fit
e3:5; flexural; 95% ðldefÞ ¼ 32:4 Log10 ðN Cycles Þ þ 340:8
rflexural strength; 95% ðMPaÞ ¼ 0:1 Log10 ðN Cycles Þ þ 3:6
ð9Þ
Under this criterion, the 3.5% VF rubber concrete flexural failure 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 the 5% VF rubber–concrete specimens is presented below.
ð10Þ
According to this equation, the bending failure stress for 106 cycles of load is 3.0 MPa. This value is much lower than 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 obtained from the fatigue bending tests of the concrete specimens with 5% VF of recycled crumbed tyres rubber. Again, the
400 y = -32.4x + 363.5 R2 = 0.5991
Flexural Strain (μdef)
350 300 250 200 150
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). The continuous line indicates the linear regression and the dashed line shows the lower limit for a confidence interval of 95%.
F. Herna´ndez-Olivares et al. / Construction and Building Materials 21 (2007) 1918–1927
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4.5 y = -0.1x + 3.9 R2 = 0.0917
Flexural Stress (MPa)
4 3.5 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). The continuous 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
E (GPa)
20
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
Flexural Strain (mdef)
300
y = -23.1x + 307.4 R2 = 0.2063
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). The continuous line indicates the linear regression and the dashed line shows the lower limit for a confidence interval of 95%.
F. Herna´ndez-Olivares et al. / Construction and Building Materials 21 (2007) 1918–1927
Young modulus considered for a rigid pavement design is also defined by the upper limit equation of the 95% confidence interval of the linear regression fit E5; flexural; 95% ðGPaÞ ¼ 1:1 Log10 ðN Cycles Þ þ 15:0
ð11Þ
6
Therefore, the Young modulus for 10 cycles of load is 21.6 GPa. This value is clearly lower than the dynamic Young modulus obtained in compression dynamic tests at any testing temperature [4]. As it has been shown for the 3.5% VF of recycled rubber concrete depicted in Fig. 8, Young modulus increases with the number of load cycles. Comparison of Fig. 5 with Figs. 8 and 11 shows that stiffness increases under cyclic load for those concretes filled with recycled crumbed tyres rubber. The reference concrete (Fig. 5) shows no stiffness increase under cyclic load. Fig. 12 depicts the maximum flexural strain measured in the fatigue bending tests of the concrete specimens with 5 VF of recycled rubber. It has been also considered the lower limit equation of the 95% confidence interval, that is to say, the following equation: e3:5; flexural; 95% ðldefÞ ¼ 23:1 Log10 ðN Cycles Þ þ 293:3
ð12Þ
Under this criterion, the 5% VF rubber concrete flexural failure strain for 106 cycles of load is 155 ldef. 4. Design implications for rigid pavements In order to determine design implications for rigid pavements of RRFC, the maximum tensile stress produced by a 13 tons simple axle of a truck (127 kN) was evaluated, considering the most adverse load location. The rigid pavement was modelled as a plate placed on an elastic subgrade. Several values for the modulus of elastic reaction for the foundation, from 50 to 150 MPa/m, were used. A tyre pressure of 7 bar (0.7 MPa) was considered for evaluating the radius of the load circle on the concrete slab, according to the Westergaard method. The Westergaard theoretical equations [5] evaluate the load configurations that produce the maximum tensile stress rmax on the concrete slab pavements, comparing the application point of the load. Three different cases can be evaluated [12]: Case I: rmax I
load applied on the center of the slab 3 W ð1 þ mÞ Le ¼ ln þ 0:6159 2pt2 R0
Case II: rmax II
load applied on the edge of the slab 0:863W ð1 þ mÞ Le ¼ ln þ 0:207 t2 R0
ð13Þ
Case III: rmax III
load applied on the vertex of the slab " 0:6 # 3W R0 ¼ 2 1 1:083 t Le
ð14Þ
ð15Þ
1925
where W is the load applied, t is the concrete slab thickness, m is the concrete Poisson ratio, Le is the characteristic length and R0 is the contact radius between tyre and pavement. Le can be calculated using equation [12] sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Et3 4 Le ¼ 12ð1 m2 Þk
ð16Þ
where k is the modulus of subgrade reaction, E is the concrete Young modulus, t is the concrete slab thickness and m is the concrete Poisson ratio. R0 can be obtained from the applied load W and the tyre pressure, rP using the next equation [8] rffiffiffiffiffiffiffiffi W R0 ¼ ð17Þ prP However, when considering a concrete rigid pavement mad, as the RRFC described, R0 can be substituted by R, by means of the following equation [13, p. 372 in Spanish Edition]: 2 ð18Þ R ¼ R0 þ t 3 As a result of the previous equations, and according with the fatigue behaviour test results, a systematic calculation of the maximum tensional stress on a RRFC slab of any thickness and on several elastic foundation with different modulus subgrade reaction can be run. The maximum tensional stress on the RRFC corresponds to the load Case II described above (load applied on the edge of the slab). Thus, the results of such a systematic calculation for Case II are represented in Fig. 13, for a RRFC with the three different VF of recycled rubber (0%, 3.5% and 5%) and three values of the modulus of subgrade reaction have been considered. It is shown in Fig. 13 the relationship between the Maximum tension stress on the edge of the concrete slab (Westergaard equations, Case II) and the thickness of the slab for 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), for applied load of 127 kN. Fig. 13 shows that the modulus of subgrade reaction has a great influence on the slab thickness necessary to limit the maximum tensional stress achieved: the lower the modulus of subgrade reaction, the larger the maximum tensional stress. This feature is according to the rigid behaviour of the RRFC pavement. It is also observed a dependence of the maximum tensional stress on the volume fraction and thus on the Young modulus. RRFC with a 3.5% VF of recycled rubber show the largest tensional stress for a fixed modulus of subgrade reaction and slab thickness. This value is slightly higher than that shown by the reference concrete. It must be taken into account that the Young modulus considered in the Westergaard equations corresponds to
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Fig. 13. Relationship between the Maximum tension stress on the edge of the concrete slab (Westergaard equations, Case II) and the thickness of the slab for 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 tendency (Fig. 8) that makes its Young modulus at 106 load cycles higher than that exhibited by the reference concrete at 106 cycles (25.1 GPa) depicted in Fig. 5. According to the experimental fatigue results and the analytical study presented, the relations obtained can be used for the calculation of RRFC pavement thickness, as a function of the modulus of subgrade reaction, for 106 cycles of a 13 tons simple axle load. For different load traffic density, the equivalent durability in years can be also calculated.
of RRFC with a 5% VF of recycled rubber on an elastic foundation with a modulus of subgrade reaction of 150 MPa/m, with a 95% confidence level, for 106 cycles of a 13 tons simple axle load. From Fig. 13, a good fitted curve (R2 = 0.999) can be obtained for a RRFC with a 5% VF and a modulus of subgrade reaction of 150 MPa/m
4.1. Example of design implication. Application to a rubberfilled concrete rigid pavement
A pavement slab thickness of 24.3 cm is obtained from the data and equations shown above. The same problem can be solved for a rigid pavement of RRFC with a 3.5% VF of recycled rubber on an elastic foundation with a modulus of subgrade reaction of 150 MPa/m. In this case, the maximum tensile stress in
The slab thickness should be defined to guarantee a maximum tensile stress lower than 2.9 MPa, the maximum achieved in the bending fatigue tests for a rigid pavement
rmax II ðMPaÞ ¼ 258:43t 1:405 1 1:405 258:43 t ðcmÞ ¼ rmax II ðMPaÞ
ð19Þ
Concrete slab thickness (cm)
30
25
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 of subgrade reaction: 150 MPa/m.
F. Herna´ndez-Olivares et al. / Construction and Building Materials 21 (2007) 1918–1927
the bending fatigue tests is 3.8 MPa, with a 95% confidence level, for 106 cycles of a 13 tons simple axle load is. Again, from Fig. 13, a good fit (R2 = 0.999) can be obtained to relate maximum tensile stress with the pavement thickness for a RRFC with a 3.5% VF and a modulus of subgrade reaction of 150 MPa/m rmax II ðMPaÞ ¼ 294:62t 1:4312 1 1:4312 294:62 t ðcmÞ ¼ rmax II ðMPaÞ
ð20Þ
Now, the pavement slab thickness obtained, is 21.1 cm. From a design point of view, an improvement of the fatigue behaviour of RRFC with 3.5% VF of recycled rubber with regard to 5% VF is obtained. The slab thickness is 3 cm thinner for the same conditions and durability. The better fit (R2 = 0.999), from Fig. 13, between maximum tensile stress and concrete thickness for the reference concrete and a modulus of subgrade reaction of 150 MPa/m is rmax II ðMPaÞ ¼ 280:45t 1:4213 1 1:4213 280:45 t ðcmÞ ¼ rmax II ðMPaÞ
ð21Þ
For the maximum tensional stress in fatigue of 4.0 MPa (106 cycles of a 13 tons simple axle load) the pavement slab thickness obtained is 19.9 cm. From a design point of view this value means a reduction of thickness of only 1 cm with regard 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 pavements design of road construction is based on experimental results obtained from laboratory tests and analytical calculations, according to Westergaard equations for flat plates on elastic foundations, that here are recovery. It has be shown that it is a powerful design tool. The results of recycled tyre rubber-filled concrete (RRFC) under fatigue loads and the analytical study presented in this paper show the feasibility of using this cement based composite material as a rigid pavement for roads on elastic subgrade. The scatter of fatigue experimental results that is usual in the concrete laboratory tests, has been overcome by means of the utilization of a 95% confidence level in the analytical calculations for the strength and stiffness of the concrete pavement. It can be used too for maximum strain design implications.
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The stiffness increase due to fatigue load implies a slight increase 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 the used tyres, the low cost of this solid waste and the better damping capacity of the rubber–concrete composite. Acknowledgements The authors want to acknowledge J. Garcı´a Carretero of the Roads Laboratory of CEDEX (Spain) his collaboration in performing the fatigue tests. References [1] Siddique R, Naik TR. Properties of concrete containing scrap-tyre rubber – an overview. Waste Manage 2004;24(5):563–9. [2] Herna´ndez-Olivares F, Barluenga G, Bollati M, Witoszek B. Static and dynamic behaviour of recycled tyre rubber-filled concrete. Cement Concr Res 2002;32(10):1587–96. [3] Herna´ndez-Olivares F, Barluenga G. High strength concrete modified with solid particles recycled from elastomeric materials. In: Ko¨nig G, Dehn F, Faust T, editors. Proceedings of the 6th international symposium on high strength/high performance, Leipzig, Germany, 2002. p. 1067–77. [4] Herna´ndez-Olivares F, Barluenga G. Fire performance of recycled rubber-filled high-strength concrete. Cement Concr Res 2004;34(1):109–17. [5] Westergaard HM. Stresses in concrete pavements computed by theoretical analysis, public roads, US Department of Agriculture, Bureau of Public Roads 1926;7(2). [6] American Association of State Highway and Transportation Officials (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): 507–18. [8] Bollati MR, Talero R, Rodrı´guez M, Witoszek B, Herna´ndez F. Porous high performance concrete for road traffic. In: Dhir RK, Henderson NA, editors. Concrete for infrastructure and utilities. London: E&FN Spon; 1996. p. 589–99. [9] Pindado MA, Aguado A, Josa A. Fatigue behaviour of polymermodified porous concretes. Cement Concr Res 1999;29(7):1077–86. [10] Lee MK, Barr BIG. An overview of the fatigue behaviour of plain and fiber reinforced concrete. Cement Concr Compos 2004;26(4): 299–305. [11] Balaguru PN, Shah SP. Fiber-reinforced cement composites. New York: MacGraw-Hill; 1992. [12] Young WC. Roark’s formulas for stress and strain [Rev. ed. of: Raymond J. Roark. Formulas for stress and strain, 5th ed., 1975]. 6th ed. New York: McGraw-Hill; 1989. pp. 473–474 (Table 26). [13] Hahn J. Vigas continuas, po´rticos, placas y vigas flotantes sobre terreno ela´stico, Gustavo Gili Si.A., Barcelona, Spain, 1982 (in Spanish, from: J. Hahn, ‘‘Durchlauftra¨ger, Rahmen, Platte und Balken auf elastischer Bettung’’, Werner-Verlag, Du¨sseldorf, Germany, 13th ed., 1981 in German). [14] Waddell WH, Evans LR. Use of nonblack fillers in tire compounds. Rubber Chem Technol 1996;69(3):377–423.