LOT, Lifetime Optimisation Tool, Mastiek respons

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1 LOT, Lifetime Optimisation Tool, Mastiek respons M. Huurman & M.F. Woldekidan (Technische Universiteit Delft) J. Moraal & R.N. Khedoe (Technische Universiteit Delft) Samenvatting Zoab is de standaard deklaag op het Nederlandse hoofdwegennet. Rafeling is het meest maatgevende schadebeeld van zoab en in verreweg de meeste gevallen bepalend voor de levensduur. De levensduur van zoab is korter dan de levensduur van de rest van de verhardingsconstructie. Het is dus van groot maatschappelijk belang om de levensduur van zoab te verlengen. Binnen het Innovatie Programma Geluid van de DVS heeft rafeling in zoab daarom veel aandacht gekregen, hetgeen de ontwikkeling van LOT heeft mogelijk gemaakt. LOT is een meso-mechanische tool waarmee spanningen en rekken in het zoab-mengsel berekend worden. De tool beschouwt zoab als een constructie bestaande uit steentjes die met mastiek aan elkaar zijn geplakt. LOT berekent de belasting van de mastiek en van de hechtlaagjes tussen steen en mastiek en berekent de levensduur op basis hiervan. LOT rust op drie pijlers die gezamenlijk bepalend zijn voor de fenomenen die zich in zoab afspelen wielbelasting, gedrag van mastiek en hechtlaagjes steen-mastiek, mengsel geometrie. De bijdrage geeft inzicht in de mannier waarop het Visco-Elastische responsgedrag van mastiek is bepaald. Om op een eenvoudige manier aan mastiek te kunnen meten zijn nieuwe proeven bedacht. Deze proeven kunnen eenvoudig in de DSR (Dynamic Shear Rheometer) of DMA (Dynamic Material Analyser) worden uitgevoerd. Naast deze nieuwe proeven zijn ook bestaande DTT (Direct Tension Test) relaxatie proeven gedaan. Alle proeven zijn gemodelleerd om zo de resultaten voor de effecten van proefstukvorm te corrigeren. Het responsgedrag van mastiek is vervolgens bepaald op basis van de verkregen data-set.

2 . INTRODUCTION PA (Porous Asphalt Concrete) is the standard surfacing material on the Dutch primary road network. Approximately 7% of this network is surfaced with PA. This is mainly due to the advantages that follow from the application of PA, i.e. reduced traffic noise and no splash and spray in wet weather conditions. The main disadvantage of PA is its reduced ravelling resistance. Ravelling is the most significant type of damage in PA and in most cases by far decisive for PA service life. The Delft University of Technology is involved in meso-mechanical mechanistic modelling of asphaltic materials since the early 2 s (). In 22 the Dutch Road and Hydraulic Engineering Institute (DVS) of the Ministry of Transport, Public Works and Water Management started a 5 year research into PA ravelling. And, as part of that research the Delft University of Technology was contracted in 26 to develop a Lifetime Optimisation Tool (LOT) for PA. The LOT program aimed for the development of a meso-mechanical tool that gives insight into the phenomena that take place in PA mixtures during tyre passages. Use is made of Finite Element (FE) models. These models basically translate the PA surface load, the mixture geometry and the response behaviour of the mortar into signals of stress and strain at various locations in the PA mixture. By interpretation of the computed stress and strain signals the life expectancy of the modelled PA is estimated. As indicated, LOT is based on mechanical analysis of in-mixture phenomena. Such an approach requires information and modelling of; the PA mixture geometry, the PA mortar response, the load signals on individual stones at the PA surface, PA mortar fatigue behaviour and finally the fatigue behaviour of the PA stone-mortar adhesive zone. To enable the quantification of aging effects the various material component properties need to be known as a function of aging. Also the effects of water on material component properties need to be investigated so that the effects of water ingress on PA design life become known. This paper discusses the mortar response measurements that were done during the LOT project. The determination of the mortars Visco-Elastic properties on the basis of the measurements is also discussed. Finally it is explained how the response properties of the adhesive zone are determined on the basis of mortar response. 2. LOT LOT is a mechanistic tool that allows for insight into the phenomena that take place in a PA mixture during the passage of a tyre. The basics of LOT are explained in another contribution to the CROW Infradagen 28 (). Figure gives an impression of LOT. It gives an indication of in-mixture stresses that develop during the passage of a tyre. LOT distinguishes between three material components; mortar, stone and mortar-stone adhesive zones. A fourth component might be air enclosed in the PA voids. This component is however neglected since it is assumed that no stresses of magnitude may develop in the enclosed air. In LOT stone particles are modelled rigidly. As a result only the properties of mortar and the adhesive zone are relevant for LOT response calculations. LOT is based on three pillars that combined determine the mixture response; - Load insight into the wheel load stressing acting on the PA surface is required 2

3 - Material behaviour knowledge of the behaviour of the mixture components is required. - Geometry the geometry of the mixtures structure needs to be known. Within LOT effort was made to represent each of the pillars with ample accuracy. In this paper the emphasis is on the response behaviour of mortar and the adhesive zones. 2 Figure General impression of the LOT mechanistic tool. 3. MORTAR RESPONSE 3. Constitutive model Pavements and pavement materials alike have a service life that in realistic cases is no shorter than for instance 5 load repetitions. From this it is concluded that the amount of damage that accumulates during a single load cycle is negligible in any realistic case. For that reason it was chosen to compute in-mixture damage development on the basis of PA response calculations in which damage development is neglected. Ofcourse accurate PA response calculations demand for accurate modelling of mortar response. Combining the previous it was concluded that the mortar response can be described by application of a linear visco-elastic model. The following 2-term Prony series constitutive model was applied in LOT. t t () t t2 E t = E α e α2 e and υ =constant () Where E(t) Stiffness as function of time [MPa]; E Instantaneous stiffness [MPa]; α, α 2 stiffness reduction parameters [-]; t time [s]; t, t 2 time constants [s] It was decided to make use of the Prony series model with two terms because only with two terms the Prony series model is capable in describing the fast initial relaxation in combination with slower long term relaxation. 3

4 3.2 Direct Tension Tests Accurate determination of the five stiffness parameters (E, α, α 2, t and t 2 ) is possible by consideration of direct tension relaxation test data. Such tests are done on T-bone shaped specimens, see figure 2. The specimens are 6 mm high, 2.75 mm wide and 3.4 mm thick. Frictionless contact between pin and end cap. steel pin end cap mortar end cap steel pin Figure 2 Impressions of DTT relaxation test. Fe-model (left), real test (middle), specimens (right). Figure 3 gives an impression of a typical DTT relaxation test. The figure indicates that the 2- term Prony series model is very well capable in describing the initial response (E), the initial relaxation (α, t ) and long term relaxation (α 2, t 2 ). In the DTT relaxation test the T-bone specimen is elongated at a preset rate over a short period of time. Thereafter elongation is kept constant. The resistance of the specimen against elongation and the relaxation of stress after elongation is kept constant are measured. In most cases by far a very good fit between measured specimen response and the back calculated 2- term Prony response is obtained. Figure 3 gives an example of test results (green stress response line) in combination with the 2-term Prony response (red stress response line). Figure 3 Impressions of DTT relaxation test. Test results and back calculation (left), FE simulation (right). It should be noted that the FE models are used to help interpret the measurement data. As stated the LOT project is based on the insight that response depends on the trinity of load, material behaviour and geometry. The same principle holds for material tests. It is simply not possible to measure the response of a material. It is however possible to measure the response 4

5 of a structure that (mainly) consists of a certain material, the specimen. In that case however measurement data needs to be corrected for the geometry of that structure, the T-bone specimen in this case. In the LOT project effort is made to determine accurate transfer functions for each individual test by utilisation of FE modelling. The transfer functions relate structural specimen response to material response, i.e force [N] and displacement [mm] are translated into stress [MPa] and strain [-]. In total 25 DTTs were done (56 Short Term Aged mortar, 7 retained STA mortar and 52 LTA mortar) at temperatures of -, and 2 C. The applied rate of elongation varied from. to 3 mm/min. It was found that there is a strong dependency between t and t 2, equation 2. Secondly it was found that α 2 is related to temperature, equation 3, and finally a relation between α and α 2 was derived, equation 4. t = a (2) t 2 f T d exp b e α = 2 + c α = b + c α 2 Table 2 Parameters to be used in equations 2, 3 and 4 a [-] b [-] c [-] d [-] e [K] f [-] STA mortar LTA mortar The effects of hour water submersion in a vacuum vessel remained limited if existent at all. 3.3 DSR & DMA frequency sweeps The described DTT measurements give all 2-term Prony parameters at distinct combinations of temperature and rate of elongation. In order to generalise the DTT relaxation test data a total of frequency sweep tests were done on STA, STA retained, LTA and LTA retained specimens. Three types of frequency sweep tests were done 6 x Dynamic Shear Rheometer, DSR G* measurements, 2 x Dynamic Material Analyser, DMA dual cantilever E* measurements, 2 x Dynamic Material Analyser, DMA uniaxial E* measurements. It was chosen to do a combination of DSR G * and DMA E * tests since the Poisson s ratio may be estimated by combination of results. For DSR shear testing and DMA uniaxial testing a new type of specimen was developed. A photo of the specimens used in the DSR shear and DMA uniaxial tests is given in figure 4 that also gives an impression of the FE model developed to properly take into account specimen geometrical effects. As indicated the specimen has a radius of 6 mm and a height of 2 mm. At the ends the specimen widens and is enclosed in steel rings allowing clamping the specimen into DSR or DMA. (3) (4) 5

6 4 mm steel ring, Inner diameter 7 mm mm central part Cylinder with 6 mm diameter 4 mm steel ring, Inner diameter 7 mm Figure 4 Impressions of the specimens used in the DMA uniaxial tests and in the DSR G* measurement. Real specimen (left), FE DMA simulation (right). The DMA dual cantilever tests performed in LOT are the standard DMA dual cantilever tests. In these tests beams that are 6 mm wide, 3 mm high and 6 mm long are tested. The test is geometrically complex and a FE model was again developed to obtain insight into test mechanics. Figure 5 gives an impression of the DMA dual cantilever test and the FE model thereof. Figure 5 Impressions of the DMA dual cantilever test. FE model (left), real set-up (right). By combination of G* and E* measurements it was concluded that.45 is a very realistic Poisson s ratio for mortar. Figure 6 gives the E* master curve obtained on the basis of a G* measurement assuming a Poisson s ration of.45 compared to two E* master curves measured in the DMA. The curves are all obtained from STA mortar. As indicated a good agreement exists between the various master curves E*. This strongly suggests that a Poisson s ratio of.45 is appropriate for the mortar. 6

7 .E+4.E+3 E* DSR 8 E* DMA-bending E* [MPa].E+2.E+ E* DMA-tension Φ DSR Φ DMA- bending Φ DMA- tension 6 4 Φ [ ].E+ 2.E-.E-5.E-2.E+.E+4.E+7.E+.E+3 Reduced frequency [Hz] Figure 6 E* master curves with indication of phase angle measured directly in the DSR compared with the E* master curve obtained by translation of a G * master curve by assuming a Poisson s ratio of.45. It is stated explicitly that the dimensions of all specimens are in the order of millimetres; as such the scale of the specimens equals the scale of the mortar bridges in PA. This is especially important with respect to the effects of water ingress. On the basis of E* measurements on specimens made from STA and LTA mortar that were not subjected to water ingress the following master curves have been derived. Again the effects of water ingress on response remained limited if existent at all G*[MPa] 4 Φ[ ] G* [MPa] 4 Φ [ o ] 2 2.E-4.E-2.E+.E+2.E+4.E+6 Reduced Frequency[Hz] Figure 7.E-4.E-2.E+.E+2.E+4.E+6 Reduced frequency [Hz] Indication of representative master curves for STA mortar (left) and LTA mortar T reference = C. The master curves have been constructed by use of the following equations. δh R T T s α T = e so that f r = α T f Where α T shift factor [-]; δh Apparent activation energy [KJ/mole]; R Universal gas constant [J/K/mole]; T Temperature [K]; T s Reference Temperature [K]; f frequency [Hz]; f r reduced frequency, i.e. frequency corrected for temperature [Hz]. (5) 7

8 G * = G low + ( G G ) high low e γ g fr β g E or * = E low + ( E E ) high low e γ g fr β g γφ fr (7) β = + ( ) φ φ φlow φhigh φlow e Where G * Complex G-modulus [MPa]; G low G * at very low frequencies; G high G * at very high frequencies; E * Complex E-modulus [MPa]; E low E * at very low frequencies; E high E * at very high frequencies; β model parameter [Hz]; γ model parameter [-]; φ phase angle [degr.]; φ low phase angle at very low frequencies [degr.]; φ high phase angle at very high frequencies [degr.]; The following parameters were determined. Table 3 Master curve parameters for LOT computational use. Virgin aged mortar Aged mortar Complex modulus Phase angle Complex modulus Phase angle Master curve Master curve Master curve Master curve Emin [ MPa] Emin [ MPa] Emax [MPa] Emax [MPa] Gmin [MPa] φmin 8.58 [] Gmin [ MPa] φmin.92 [] G [MPa] 9. [] 47.2[ MPa] [] max φmax Gmax φ max γ.5292 [-] γ.89[-] γ.422 [-] γ.49 [-] β [-] β.99 [-] β [-] β.4243 [-] R2.7 R2.87 R2.95 R2.98 δ H [KJ/mole] δ H 27.3 [KJ/mole] 3.4 Determination of 2-term Prony parameters for LOT The combined measurements discussed in section 3.2 and 3.3 allow for the determination of the appropriate 2-term Prony series parameters for any combination of frequency and temperature. Hereto first the E* and phase angle are determined by application of equations 5, 6 and 7. The obtained E* and phase angle are then translated into E, α, α 2, t and t2 taking into account equations 2, 3 and 4. In this process the most appropriate frequency for parameter determination is calculated as follows. f = 2 t (8) t Where f most appropriate frequency for parameter determination, t t time for tyre food print to pass. Figure 8 gives an impression of the results of the above described procedure. The two plots give the average measurement results (darker scattered points) in combination with the master curve fitted trough data (contentious line). The red dots indicate the response that follows by application of the 2-term Prony series model in combination with parameters obtained as per 8 (6)

9 discussed procedure. The figures indicate a good fit, which guaranties that mortar response is modelled with ample precision in LOT response calculations. 8 8 E* [ MPa ] Master curve E* Prony series E* Average measured E* Master curve Φ Prony series Φ Average measured Φ 6 4 Φ[ o ] E* [ MPa ] Mas ter curve E* Prony series E* Average measured E* Mas ter curve Φ Prony series Φ Average measured Φ 6 4 Φ [ o ] 2 2.E-4.E-2.E+.E+2.E+4.E+6.E+8 Figure 8 Reduced freqency [Hz] LOT mortar response (red dots) in relation to interpreted measurement data. Right STA, left LTA. Reference temperature C 4. ADHESIVE ZONE RESPONSE The adhesive zone is very thin,. mm (). As a result there is hardly any material that can deform. This implies when two adjacent stones in the PA mixture translate or rotate relatively especially the mortar bridge is deformed. Deformation over the ultimately thin adhesive zone remains limited. The response of the thin adhesive zone is thus of limited effect on the system stiffness. For that reason it was decided that the adhesive zone may be modelled using a high stiffness linear interface. An estimate of the stiffness can be made by consideration of the E* that follows from application of the mortar representative master curves by application of the following equations. * E k n = (9). mm * G k s = (). mm Where k n normal stiffness of the adhesive zone [MPa/mm], k s shear stiffness of the adhesive zone [MPa/mm],. mm thickness of the adhesive zone. 5. CONCLUSIONS.E-4.E-2.E+.E+2.E+4.E+6 Reduced freqency [Hz] On the basis of the previous the following conclusions are drawn. - LOT is based a mechanistic tool determination of the ravelling resistance of PA. - With LOT the ravelling resistance is determined on interpretation of in-mixture stresses and strains that develop during the passage of a tyre. This implies that accurate calculation of mixture response is the basis of LOT. - LOT is founded on the insight that the response of any structure, including asphalt concrete mixture structures, depends on the trinity of; load, geometry and material behaviour. - In the LOT project effort is made to continuously respect this trinity. In the laboratory measurements discussed here this is shown by two things. First each test that is performed in the LOT project is FE-modelled so that results can be corrected for the effects of test geometry. Secondly all tests are done on a scale that equals the scale of the issue at hand. This limits scale effects, if any. 9

10 - In LOT a 2-term Prony series model is applied for mortar. - The discussed tests and interpretation give ample insight into the parameters of this model. A procedure was developed that guaranties that the most appropriate parameters are applied in LOT calculations. - A Poisson s ratio of.45 is applicable. - Mortar response is dependent on the effects of aging. The effects of water ingress on mortar response remain limited if existent at all. - Ample insight into mortar response exists to allow determination of PA-mixture response under passing tyres. LITERATURE M. Huurman, L.T. Mo, M.F. Woldekidan, Ont-rafeling van zoab, LOT, Lifetime Optimisation Tool, CROW Infradagen 28, Delft