PERMANENT DEFORMATION AND COMPLEX MODULUS: TWO DIFFERENT CHARACTERISTICS FROM A UNIQUE TEST

Transcription

1 316 6th RILEM Symposium PTEBM'3, Zurich, 23 PERMANENT DEFORMATION AND COMPLEX MODULUS: TWO DIFFERENT CHARACTERISTICS FROM A UNIQUE TEST Mondher Neifar, Hervé Di Benedetto, Berthe Dongmo Département Génie Civil et Bâtiment, Ecole des TPE, France. Abstract A new test was developed at the Département Génie Civil et Bâtiment (DGCB) of the Ecole Nationale des Traux Publics de l Etat (ENTPE) to study permanent deformation of bituminous mixes. The experimental program was realised in co-operation with the Laboratoire Centrale des Ponts et Chaussées (LCPC) of Nantes. This test which is homogeneous provides direct information for the determination of the rheological law of the bituminous mixes. A specific equipment was developed in order to carry out the measurements of the accumulated permanent deformation (which can reach some 1-2 m/m) and the cyclic deformation for each small cycle (some 1 5 m/m). Cyclic deformation data allow to calculate the complex modulus for the considered frequency, temperature and stress amplitude. Experimental tests were carried out in order to contribute with the comprehension of the phenomena and the formulation of a thermovisco-plastic law adapted for the rutting phenomenon modelling. 1. Introduction The present investigation was undertaken in order to contribute to the development of a thermovisco-plastic law adapted to predict the rutting phenomenon of bituminous mixes. It deals with the characterization of permanent deformation during cyclic loading tests. Some studies were previously made by several authors (Brown & Gibb 1996, Celard 1977, Francken & Hampson 1972, Molenaar & Molenaar 2). The permanent deformation characterization is obtained from cyclic loading test. This characterization of permanent deformation is associated with the determination of small strain behiour. This paper describes a new test developed, which is homogeneous and provides direct information for the determination of the rheological law of the bituminous mixes. The principle of the test consists in applying an ial hersine compressive stress to a cylindrical specimen. The permanent deformations, which can reach some 1-2 m/m, and the cyclic deformation for each small cycle (around some 1-5 m/m) are measured in the same time. Data are proposed for a /14 bituminous mixes with pure 35/5 bitumen at 6.8 ppc. Three temperatures (15 C, 25 C and 35 C), two frequencies (1Hz and 1Hz), and five stress amplitudes (.1 MPa,.2MPa and.3mpa in compression and.5 and.1 in traction) are analyzed.

2 Performance Testing and Evaluation of Bituminous Materials The new developed test 2.1 Experimental procedure The chosen experiment is a compression or extension test on cylindrical samples, whose height is 12cm and diameter 8cm (Neifar & al. 22, Neifar & Di Benedetto 2). The stress and strain fields can be considered as homogeneous during this type of test. The principle of the test is to apply a hersine (compression or extension) load (ial stress) and to measure, both, permanent deformation and small strain appearing at each cycle. Due to the large difference between the two measured strain levels, a new system was developed. This system is represented in Figure 1. Specimen =.8cm h=12cm Axial targets Load cell Axial non contact transducers Non contact transducer fixed Capteur sans to contact the (Système de fixation sample Cf. figure 4) Compression spring Ressort de compression Temperature chamber Target Cible 2 nd cogwheel 2ème roue dentée Lock nut Contre écrou 1 st cogwheel 1ère roue dentée Moteur miniature Miniature motor Tige filetée la base de la Threaded rod Press actuator radial non contact transducers Axial non contact transducer support fixed to the sample Axial targets Radial Targets Figure 1. Experimental system. Two non-contact transducers placed at 18, whose range is 1 mm, are used to measure radial strain. They give with an accuracy of.5 m (1, in strain) the variation of the sample diameter. The target is an aluminium plate glued on the sample. To measure ial strain, four noncontact transducers, whose range is.5 mm, are used. Two transducers placed at 18 give the displacement of an upper material plane perpendicular to the sample symmetrical e, and two transducers also placed at 18 give the displacement of a lower material plane perpendicular to the sample symmetrical e. The two planes are situated at 2,5 cm from the upper respectively lower boundary of the sample. The relative displacement of these two planes, which is calculated from the transducers output give the ial strain. The use of two diametrically opposed systems allows obtaining an erage value of strain. The transducers were chosen with a small range to

3 318 6th RILEM Symposium PTEBM'3, Zurich, 23 obtain a good accuracy for small strain appearing at each cycle ( m/m). But due to large number of applied cycles, the mobile target has to be moved. Figure 1.shows a general view of the test and the principle of the mechanical system developed to move the ial targets. 2.2 Experimental program The aim of the experimental program is to help with the comprehension of the phenomena and the formulation of a thermo-visco-plastic law adapted to the rutting phenomenon. One more particular objective is to dissociate the recoverable viscous component and the viscoplastic component. For this purpose, cyclic loading periods and recovery period (=) are successively applied. The evolution of permanent deformation, strain after recovery, erage volume variation, complex modulus and complex Poisson ratio, with respect to Temperature, frequency and amplitude of the cyclic stress are analyzed Stress path history The test consist in applying to the specimen a hersine compression load during a time t 1, then in applying a period (=) during a time t 2. This sequence is repeated i times for various t 1 and t 2 (t 1i respectively t 2i ). Chosen t 1i times are the following: t 11 =35s ; t 12 =1s ; t 13 =3s ; t 14 =1s ; t 15 =3s and t 16 =1s The t 2i duration is selected long enough in order to obtain of a "quasi" stabilisation of permanent deformation (Cf Fig. 2 and Fig. 3). Fig. 3 shows the evolution of permanent deformation obtained for test with a temperature of 25 C, a frequency of 1 Hz, and a mimal loading stress of.4 MPa. During loading, the permanent deformation increases with time (or number of cycles) and three s can be observed : - a first with a decreasing rate of permanent deformation. - a second showing a linear evolution of permanent deformation with the number of cycles (constant permanent ial strain rate). - a third with a fast evolution and an increasing rate of permanent ial deformation, which carries out towards the failure. The third was observed only for tests at 35 C and for all the tests in extension.

4 Performance Testing and Evaluation of Bituminous Materials 319 Stress m =.2 MPa or.4 MPa or.6 MPa in compression m =.1 MPa or.2 MPa in extention f = 1Hz or 1 Hz m T= 15 C or 25 C or 35 C 1st cyclic loading duration : 35 s 2 nd cyclic loading duration : 1 s 3rd cyclic loading duration : 3 s 4 th cyclic loading duration : 1 s 5th cyclic loading duration : 3 s 6th cyclic loading duration : 1 s 7th cyclic loading duration more than 1 s Sequence 1 Sequence 2 Sequence 3 Sequence 5 Sequence 6 Sequence 7 Time Figure 2. Applied stress path history. Axial strain (%) Rest periods Cyclic loading periods Time (s) Figure 3. Permanent deformation obtained for test with T=25 C, f=1hz and m =.4Mpa. 3. Results 3.1 Permanent deformation The ial strain is calculated from the 4 ial strain transducer signals and approximated by a continuous curve which equation is given in (1). The parameters of this equation are obtained by a minimization of the square distance. N, t) (N) t (N) (N) *sin t (N) (1) ( t 2T T is the period of the cyclic loading and =2/T (N) is the ial permanent deformation and (N) is the amplitude of ial sinusoidal strain component at cycle N. It can be considered as the amplitude of the linear viscoelastic response when creep is eliminated (complex modulus). (N) is the slope of erage permanent deformation at cycles N (and N+1).

5 32 6th RILEM Symposium PTEBM'3, Zurich, 23 The evolution of the ial permanent deformation with the cumulated number of cycles, obtained during the tests, highlight the effect of the increase in loading. As expected, an increase of loading creates an increase in permanent deformation. The results obtained show the great sensitivity of the permanent deformations to the temperature. An increase in the temperature involves an increase in the permanent deformation. For all the tests, the deformations obtained for the same number of cycles at a frequency of 1Hz are higher than those obtained at a frequency of 1 Hz. It is also of inte to plot these evolutions according to the time of loading. Figure 4 shows the curves obtained for the tests at 25 C and m =.4 MPa. It is noted that the deformation at 1Hz remains always lower than the deformation at 1Hz (this is checked for all the tests). This means that a cycle applied during 1 second generates more deformation than 1 cycles hing the same amplitude applied during the same time. This result shows clearly the cyclic effects of loading. The results of Figure 4 imply that the law can't be a linear viscoelastic one. In addition, a classical viscoplastic law of the type : vp f ( ) also appears as not adapted. (2) Axial strain (%) Hz 1 Hz Number of cycles Axial strain (%) Hz 1 Hz loading tim e (s) Figure 4. Evolution of permanent deformation according to number of cycles and loading time (T=25 C ; m =.4 MPa; period eliminated). 3.2 Normalised deformation The normalised permanent deformation is introduced as the ratio of by the amplitude of the linear viscoelastic response : ( N Norm ) ( N) (3) Norm Figure 5. shows that evolution for the different loading conditions are situated inside tow narrow zones, one in compression and another one in traction. Then it can be written : ( N) f ( N) where takes into account for the temperature, stress and frequency effects. When failure appears, the normalised deformation lees this narrow zone as shown for tests at 35 C in compression. We observe clearly that failure in traction appear earlier than failure in compression

6 Performance Testing and Evaluation of Bituminous Materials 321 / 35 C-1Hz-.2MPa 2 35 C-1Hz-.6MPa 35 C-1Hz-.4MPa Num ber of cycles C-1Hz-.1MPa C-1Hz-.2MPa Compression Traction Figure 5. Evolution of the normalised permanent deformation with number of cycles for different tests. 3.3 Volume variation Axial permanent deformation and radial permanent deformation give volume variation and deviatoric deformation using the following equations : v rad 2 (4) q rad (5) 5 v(%) Traction Compression q (%) Figure 6. Volumic variation versus deviatoric deformation; same tests as Figure 5. Curves of v versus q for different tests as are plotted Figure 6. The analysis of this curves shows : - a slight contractant behiour (positive variation of volume) at the beginning of each loading period, - a of significant dilatant behiour after the contracting. Due to the existence of confining pressure, it should not be of this importance on roadway, - a dilatant at the beginning of the periods, - a contractant behiour after the dilatant during the period Complex modulus The complex modulus gives the viscoelastic properties and characterizes the bituminous mixes behiour in the small strain domain. It is calculated by considering stress signal and the sinusoidal component of the ial strain (1). The complex modulus of material is : i E* e (6)

7 322 6th RILEM Symposium PTEBM'3, Zurich, 23 with : the stress amplitude, the amplitude of the cyclic component of the ial strain, the angle ( ). le*l (MPa) 1 15 C 25 C 35 C Number of cycles Figure 7. Modulus of complex modulus evolution versus number of cycles. f=1hz ; m =.4 MPa). Figure 7.shows the modulus of complex modulus E* versus the number of cycles, corresponding to the tests at 1Hz and.4mpa. It is generally noticed that the modulus increases at the beginning of each cyclic loading. This increase could be due to the total ial strain increase which can creates an increase in the contact area between the aggregates in direction 1. Then, a decrease of the modulus is observed. This decrease is more significant during the tests at 25 C and 35 C. This phenomena is also observed during fatigue tests (Di Benedetto & al. 1998). It can be due to the heating of bituminous mixes induced by dissipated energy or to the tixotropy of the bitumen. It is generally noticed that the angle decreases at the beginning of each cyclic loading. After this decrease, a stabilisation or a very slight increase is observed. 4. Conclusion The new test developed to study viscoplastic behiour of bituminous mixes revelled to be a good tool to study permanent deformation and complex modulus evolutions. The accumulated permanent deformations (which can reach some 1-2 m/m) and the cyclic deformation for each small cycle (some 1 5 m/m) are measured in the same time. Some results presented in this paper show the effect of temperature, frequency and applied stress on permanent deformation, volume variation, and complex modulus. An increase in frequency creates less permanent deformation for the same time of loading. This implies that the law can't be a linear viscoelastic or a classical viscoplastic one. Norm A normalized deformation ( ) is considered. It allows to model the irreversible strain evolution in a unified way with the use of the linear viscoelastic strain obtained for each cycle. Volume variations show a slight contractant behiour (positive variation of volume) and a of significant dilatant behiour. This behiour is qualitatively the same as the one observed for monotonic compression tests.

8 Performance Testing and Evaluation of Bituminous Materials References [1] Brown S. & Gibb M. Validation experiments for permanent deformation testing of bituminous mixtures. Annual Meeting of the Association of Asphalt Ping Technologist, Baltimore 18-2 Mars p. [2] Celard B. Esso road design technology. Proceeding of the 4th International conference Structural Design of Asphalt Pements, Michigan, Août p [3] Francken L., & Hampson A.H. Appareilage de compression sous charge répétées. La Technique Routière. Revue de l association des congrès belges de la route. Vol. XVII, n 1, mars p [4] Molenaar J.M.M. & Molenaar A.A.A. Susceptibility to permanent strain of asphalt in the dynamic triial compression creep test. Proceeding of the 2 nd Eurasphalt & Eurobitume Congress, Barcelona September 2. p [5] Neifar, M., Di Benedetto H., Piau, J.M., Odéon H. Permanent deformation of bituminous mixes : monotonous and cyclic contributions. 6 th international conference on the Bearing Capacity of Roads, Railways and Airfields, Lisbon June 22. [6] Neifar, M., & Di Benedetto H. "Etude de l'orniérage des mélanges bitumineux : mise au point d un dispositif expérimental et campagne d'essais". Rapport de synthèse du contrat LCPC n 97/259. ENTPE-DGCB, novembre 2. 6 p. [7] Di Benedetto, H., De La Roche, C. State of the art on stiffness modulus and fatigue of bituminous mixtures. Bituminous binders and mixtures: state of the art and interlaboratory tests on mechanical behiour and mix design, E&FN Spon, Ed. L. Francken, 1998, p ,.