ABSTRACT
A research including a large experimental campaign on the thermo-mechanical behavior of different bituminous materials in the large strain amplitude domain is proposed. The primary goal of this paper is to identify and determine the links between the failure properties of bituminous binders and those of mixes at low temperatures.The thermo-mechanical behavior of bituminous binders was evaluated with the tensile strength at a constant strain rate and constant temperatures. The thermo-mechanical behavior of bituminous mixes has been studied by
performing measurements of the coefficient of thermal dilatation and contraction, tensile tests at constant temperatures and strain rates, and Thermal Stress Restrained Specimen Tests. Some pertinent links between fundamental properties of binders and mixes are established. Some characteristics which appear as pertinent and discriminating enough with regard to the low-temperature failure properties of bituminous mixes are presented.
Keywords : bitumens, bituminous mixes, rheological behavior, thermo-mechanical properties, failure properties, tensile strength, TSRST, low temperature, brittle, ductile, brittle/ductile transition temperature.
INTRODUCTION
The different domains of bitumen behavior can be illustrated according to the strain amplitude (_ε_) and the temperature (T), at a given strain rate. FIGURE 1 (drawn from (1) and (2)) points out :
• the brittle and ductile domains, where the tensile strength σp can be measured,
• the brittle failure, which could be characterized by the fracture toughness Kc (Linear Elastic Fracture
Mechanics),
• the linear elastic behavior, characterized by the moduli E and G,
• the linear viscoelastic domain, characterized by the complex moduli E* and G*,
• the purely viscous (Newtonian) behavior, characterized by the viscosity η,
• for strains of a few percent, the domain where the behavior is highly non-linear.
A bituminous mix has also a complex temperature-sensitive behavior. Its response to a given loading is strongly dependent on temperature and loading path. In addition, at a given temperature and a given strain rate, four main typical behaviors can be identified according to the strain amplitude (ε) and the number of applied cyclic loadings (N) (see FIGURE 2, from (3)).
This paper is aimed at providing an assessment of the work conducted to date within the framework of a partnership between the “Département Génie Civil et Bâtiment” of the Ecole Nationale des TPE, Appia and Eurovia. This study focused on the thermo-mechanical behavior of different bituminous materials in both the small strain domain and the large strain domain, at low and mid temperatures, when considering only a small number of loadings This paper only deals with the characterization of the failure properties (i.e. in the large strain amplitude domain) of bituminous materials, at low and mid temperatures. It may be underlined that this paper completes two previous papers which focused on the linear viscoelastic behavior of bituminous materials (i.e. in the small strain domain) at low and intermediate temperatures (2) and (4).
MATERIALS
Four very different bitumens have been tested : two pure bitumens (10/20 and 50/70 penetration grade), and two polymer modified bitumens with a high content of polymer, one with plastomer and one with elastomer. The polymer modified binders are named  hereafter  PMB1 and PMB2. TABLE 1 presents the results  of  the conventional tests (the Fraass brittle point, the Penetration at 25°C and the Softening Point Ring and Ball) initially performed on the different binders.
Four different bituminous mixes, made from the 10/20, 50/70, PMB1 and PMB2 bitumens with one type of  aggregate and grading, have been tested. The mixture samples had a continuous 0/10mm diorite grading, a 3±1% void content and a binder content of 6% by dry weight of aggregate.
TESTS ON BINDERS
SHRP Direct Tensile Tests (DTT)
As described in AASHTO TP3 and (5), the SHRP Direct Tensile Test consists in elongating 27mm high  bitumen  samples at 1mm/min and at constant temperatures. The corresponding strain rate (έ) equals 2.22m/m/h. At least six  repeats at each temperature were realized on unaged samples. Apart from the determination of the conventional temperature leading to failure at 1% strain, Tε=1%, our analysis also consists in characterizing a threshold temperature separating the brittle behavior and the ductile one. Moreover, the tensile strength  (maximum tensile stress)  and the
corresponding strain for each temperature are considered and represented in FIGURE 3.
In our opinion, the ranking of binders in function of their strain tolerance using the parameter Tε=1% does not seem to be really pertinent in the sense that this approach is rather empirical. This parameter will  be  hereafter  compared with a new concept of brittle/ductile transition temperature of binders, which is introduced at the studied strain rate. The determination of this brittle/ductile transition temperature of binders is explained in the next paragraphs.
Any isothermal direct tensile test yields much more data than just failure strain or stress values. In  particular, the  brittle-like  or the ductile-like shape of the stress-strain curve can be examined at each temperature. Athigh temperatures, binders have a purely ductile behavior, whereas at very low temperatures their behavior is purely fragile. Following the considered temperature, the bitumen behavior sweeps from ductile (high temperature) to brittle (low temperature). Nevertheless, at intermediate temperatures, there is a slow evolution of the behavior from a ductile
one to a brittle one when decreasing the temperature. Thus, practically, there is no determining an accuratetransition temperature directly from the examination of the shape of the stress-strain curve. In the best case, it is just possible to determine a more or less wide temperature range which corresponds to this slow transition of the
physical properties of binders.
From our results, we introduce a brittle/ductile transition temperature of binders at the studied strain rate,Tbdb, which is the temperature at which the tensile strength peaks in the axes tensile strength-temperature (FIGURE3). This makes the determination of Tbdb easier and more accurate since the maximum of the tensile strength may be clearly identified. King et al. (5) have already noticed that when the temperature drops below about -15°C, the tensile strength of bituminous mixtures decreases and the tensile specimen fractures at low strain as a brittle failure.
The brittle/ductile transition temperature, hereafter named Tbdb (for a strain rate of 2.22m/m/h), can be  considered as  a pertinent,  handy and  alternative low-temperature parameter. Its physical meaning is directly linked to the type of fracture process of specimens, which influences the shape of the stress-strain curves.
The values of Tbdb are presented in TABLE 1 along with the temperature corresponding to a strain of 1% at failure, Tε=1%. Tbdb and Tε=1% are highly correlated with each other (r2=0.977). Nevertheless, further investigations on
other bituminous binders are still needed before any definitive conclusion can be drawn.
As shown in FIGURE 3, the failure stress results are noticeably scattered at low temperatures, where the behavior is brittle. However, the performance of such a test at intermediate and high temperatures leads to a minor scatter of results. Therefore, from our results on four very different binders, the maximum tensile stress (tensile
strength) seems to be all the more repeatable than the temperature is high (FIGURE 3). As assumed by Largeaud et al. (7), the scattering at low temperature could be explained by the detrimental influence of occlusions of air bubbles in the small section of binder samples.
TESTS ON MIXES
Direct Tensile Tests (DTT)
DTT results on mixes
These tests were performed at constant temperatures between 5°C to -46°C at constant strain rate. Two very different strain rates (300 and 45000μm/m/h) were chosen so as to study the influence of strain rate upon the failure properties of bituminous mixtures. 220mm high cylindrical (diameter=80mm) samples were tested in tension using a servo-hydraulic press at the Eurovia laboratory. The strain in the sample was considered as the mean value of the measures given by three transducers placed at 120° around the sample. Two or three test replicates were performed
at each temperature.
On one hand, as previously shown by Di Benedetto et al. (8) (9), the experimental results on the four studied bituminous mixtures evidence that the stress at failure (viscoplastic flaw) is highly dependent on the strain rate in the ductile domain (high temperature). On the other hand, the obtained stress at failure only slightly depends upon the strain rate in the brittle domain (low temperature). So, as a first approximation, the tensile strength in the brittle domain can be considered as independent of the chosen strain rate. This point is of primary importance since a high strain rate can be used in the brittle domain in order to save time. Nevertheless, it is noteworthy that Stock and Arand (10) previously stated that in the brittle domain, at very low temperatures, the tensile strength slightly decreases while increasing the strain rate.  This  point  needs to be deepened  with  further investigation.
Furthermore, in reference to the transition temperature concept presented for binders, we introduced the brittle/ductile transition temperature of bituminous mixes, Tfdm, which depends on the applied strain rate (). The  difference for the two considered strain rates (300 and 45000μm/m/h) can reach 9°C. This low-temperature
parameter is reported in TABLE 1 for the two considered strain rates.
As illustrated in FIGURE 4 where all replicate results are plotted, the scatter of results is rather small whatever the strain rate and the temperature. The repeatability of such a test on mixes appears as especially good, as well in the fragile domain as in the ductile domain.
FIGURE 5 sums up the influence of both the temperature and the strain rate on the brittle/ductile behavior for tensile tests at constant strain rate on binders and mixes.
DTT on binders Vs DTT on mixes
As can be seen in FIGURE 6, the tensile strength of binders found with the SHRP Direct Tensile Tests at 1mm/min (2.22m/m/h) is quite close to the tensile strength of mixes at 300μm/m/h. This point is noticeable and needs further
investigation. Indeed, as testing bituminous mixtures is very expensive and time-consuming, one of the current great issues is to determine methods in which the properties of mixes could be evaluated with enough accuracy from the properties of the binder and from the mix composition. To confirm these results, next steps could consist in testing another strain rate for binders (150mm/min, i.e. 333m/m/h, if possible) and also different mix compositions.
In addition, in the brittle domain at very low temperatures, and only as a first approximation (lack of repeatability), the previous observations (cf. FIGURE 6) allow to consider that the tensile strength of binders equals the tensile strength of mixes which does not depend on the strain rate (FIGURE 4). To our knowledge, this statement which is sometimes supposed to be valid has been but little experimentally checked. Moreover, this statement is of the utmost importance since the failure in mixes could be predicted, as a first approximation, from the failure in binders. For instance, as regards the current  revision of the  AASHTO low  temperature specification MP1 (MP1A), the failure stress from DTT on binders is incorporated in a comprehensive model to calculate and predict the socalled critical cracking temperature of pavement (11) (12).
Coefficient of thermal dilatation/contraction of bituminous mixes
The linear coefficient of thermal dilatation/contraction “α” depends on the thermal characteristics of the components of the bituminous mixture (binder, aggregate and air). It especially highly depends on the binder content since the
coefficient of linear thermal dilatation/contraction of bitumen is some 30 times greater than that of the mineral aggregate (13) (14) (15). In our study, as only one mix design is considered, the influence of the amount of binder and aggregate can not be evaluated.
Parallelepipedic asphalt samples (L*W*H = 16*4*4 cm3) of the four types of investigated mixes were laid on their length on a layer of small glass marbles coated with a silicone spray. This base provides nearly frictionless movement. Each sample was submitted to different plateaus of temperature in the range of +24 to –26°C. The
temperature was held constant for about three-hour periods after each increment of around three degrees Celsius.
Two identical strain gages are used for each test : the first one is glued on the upper part of the asphalt beam, the second one on the lower part, for not taking into account the flexion of the beam during the test. The average value is considered. A third strain gage was glued on a reference titanium silicate beam, of known α-value
(0.03μm/m/°C), in order to account for and correct the effect of temperature. In addition, a temperature probe was used to measure the temperature at the surface of asphalt samples.
The thermal strain ε can be written as follows :
ε=α∆T [1]
where α : linear coefficient of thermal dilatation/contraction (m/m/°C)
∆T : change in temperature (°C)
Thermal equilibrium
After each temperature change, the temperature is held constant during 3 hours so as to allow the specimen, the titanium silicate beam and the three strain gages to equilibrate at the considered temperature. At the onset of this plateau of temperature, a transitional period is first observed, in which each element is contracting (or dilating) until thermal equilibrium. The transitional period of each element depends i)on its dimensions (the strain gage reaches more quickly the thermal equilibrium than the mix sample), ii)on its thermo-physical coefficients, iii)on the temperature change amplitude, iv)etc. From our results, this transitional period lasts about 1 hour.
Experimental coefficients
FIGURE 7 shows that the thermal dilatation coefficient of mixes and their thermal contraction coefficient are really close (see also (16)). The two coefficients are hereafter considered as equal. Moreover, FIGURE 7 highlights that the four different mixes have very close thermal contraction coefficients over the considered range of temperature (from -26 to +24°C). As Di Benedetto and Neifar (16), using a specially designed test method, and Serfass et al. (17) have already shown, a linear relationship between the thermal contraction coefficient and the temperature can be
considered, as a first approximation, below 5°C. These coefficients vary slowly from around 30 to 15μm/m/°C while decreasing temperature from 5° to –26°C. The thermal contraction coefficient appears as nearly constant at temperatures above 5°C, but the excessive creep of the sample makes the measurements inaccurate.
The environmental chamber did not allow to investigate temperatures lower than –26°C so that no glass transition point (change in the slope of α-T curve) could have been identified from our results.
It is noteworthy that Di Benedetto & Neifar (16) previously pointed out the anisotropic behavior of mixes.They measured on cylindrical samples the coefficients of both radial and axial thermal contraction. These latter were found to be different (30 to 50%).
Thermal Stress Restrained Specimen Tests (TSRST)
Typically, restrained cooling tests (or TSRST) are considered as an accelerated performance test to predict lowtemperature cracking of bituminous mixtures. These tests were carried out at a cooling rate of 10°C/h from an initial temperature of 5°C using a servo-hydraulic press at the Eurovia laboratory and were run in duplicate or triplicate on 250mm high samples (diameter=60mm). A temperature probe was used to measure the temperature at the surface of asphalt samples. The thermal regulation is directly realized from the measured surface temperature. The air in the
environmental chamber is circulated with a fan so that the temperature distribution is uniform. The strain in the sample was considered as the mean value of the values given by three transducers placed at 120° around the sample.This strain ε is kept equal to zero during the whole test. As the material is restrained, its tendency to shorten results in the development of a tensile stress that produces failure. The strain ε can be modeled as the sum of a “thermal” strain and a “mechanical” strain :
with: mechanical strain, described by the DBN viscoplastic model (24-25) (not developed in this paper);
: thermal strain which is equal to α.∆Τ (cf. equation [1]).
Moreover, as the coefficients of thermal contraction of the four mixes vary from 30 to 15μm/m/°C when the temperature drops from 5° to -30°C (FIGURE 8), the equivalent mechanical strain rate () ranges from300 to 150μm/m/h during the restrained cooling tests (since ε =0). It is noteworthy that aluminum caps were used to
fix samples to the MTS hydraulic press in order to avoid excessive shear stresses at the top and at the bottom of samples. The standard value of the coefficient of thermal contraction of aluminum is around 23μm/m/°C, which is close to that of mixes over the considered range of temperatures.
From our results, failure occurs in the brittle domain when the induced thermal stress equals the tensile strength obtained at 300μm/m/h (FIGURE 8). This means that the strength of the bituminous mixes seems to be a function of the temperature (18) and the strain rate only, and does not depend upon the previous followed stress and temperature paths. Moreover, to the extent that the tensile strength only slightly depends on the strain rate in the fragile domain (FIGURE 4), it seems possible to forecast the thermal cracking in the brittle domain by means of the tensile strength curve obtained at any strain rate. The temperature which corresponds to failure, the so-called fracture temperature TTSRST, is given in TABLE 1.
For equivalent changes in temperature, the lower the thermally induced tensile stress, the better the mix behavior. Likewise, the colder the TSRST fracture temperature, the greater the mix resistance to low-temperature cracking. Therefore, among the four considered bituminous mixes, the two polymer modified mixtures are the best
regarding their resistance to low-temperature cracking.
Moreover, the performance ranking of the four considered mixtures which were made from the same mix
design and four different binders is very discriminating. Thus, for the considered mix design, this confirms that the
bitumen property appears as a key factor regarding the resistance to low-temperature cracking of bituminous mixes.
The influence of the cooling rate has not been studied during this laboratory work. Mixtures resistance to
thermal cracking has been measured under very severe conditions (-10°C/h). It is of particular interest to note that
more realistic pavement surface cooling rates are generally in the range from about 0.5 to 2°C/h (19) (20). Amid the
results drawn from the literature, Fabb (21) previously showed that the cooling rate has little effect on the fracture
temperature and the fracture strength when the rate was greater than 5°C/h. From the results of Jung and Vinson (22)
(23), when considering cooling rates of 1°C/h and 10°C/h, the relative difference between the amplitudes of induced
thermal stresses can reach 100% near the fracture temperature. Typically, TTSRST is coldest at 1°C/h, which can be
easily simulated by the “DBN” law (27). Notwithstanding this fact, the ranking of bituminous materials does not
seem to be influenced by the chosen cooling rate. Therefore, the TSRST with a cooling rate of 10°C/h can still
provide rather quickly pertinent information regarding to the low-temperature cracking properties of bituminous
mixtures.
Eventually, the thermally induced stress of the given mixes may also have been predicted using the law
described by Di Benedetto et al. (24-26) and Neifar et al. (27-28). The prediction is given by the general viscoplastic
“DBN law” (Di Benedetto and Neifar) using the results of i)complex modulus tests, ii)the tensile strength of mixes
and iii)the knowledge of the thermal contraction coefficient. This procedure consists in a very effective alternative to
the widespread procedures which are based only on the linear viscoelastic properties of these materials. The
influence of non linearities for the prediction of the TSRST has been previously evidenced with the DBN law (25)
(28). Then, the cracking temperature can be determined from the intersection of the cooling and tensile strength
curves (27-28). For more details, the reader is referred to the following references (24-28).
The mixtures resistance to thermal cycles remains to be tested soon in a complementary study or,
alternatively, can be theoretically predicted by means of the “DBN law” for instance. Finding that the rankings of
mixtures regarding to either low-temperature cracking or cyclic thermal resistance are similar could be in particular
of great interest.
ANALYSIS – DISCUSSION
The parameters Tε=1%, Tbdb, Tbdm(300μm/m/h), Tbdm(45000μm/m/h) and the failure temperature at the TSRST,
named TTSRST, are presented in TABLE 1 for the four studied bituminous materials. TABLE 2 gathers the correlation
coefficients between all the previously introduced parameters.
First, Tbdb and Tε=1% are highly correlated with each other (r2=0.977). One must bear in mind that the
physical meaning of the introduced Tbdb is directly linked to the type of fracture process of specimens, which
influences the shape of the stress-strain curves. That is why this pertinent parameter could be associated to the
current low-temperature specification for asphalt binders based up to now on Tε=1%.
Second, for the considered mix design, Tbdm(300μm/m/h) and Tbdm(45000μm/m/h) exhibit pretty good
correlation with Tbdb (resp. r2=0.936 and 0.908) and Tε=1% (resp. r2=0.929 and 0.925). Moreover, the correlation
between Tbdb and TTSRST is r2=0.992. This evidences that, at low temperatures, the failure properties of bituminous
mixtures can be predicted from those of bitumens.
These correlation coefficients between mixes and binders properties still need to be confirmed by
additional tests with other binders and especially other mix compositions.
For the considered set of binders, the Softening Point Ring and Ball and the Fraass Brittle Point are not
good indicators of the low-temperature cracking properties of bituminous mixtures. Indeed, the correlation
coefficients of these two traditional parameters with Tε=1%, Tbdb, Tbdm(300μm/m/h), Tbdm(45000μm/m/h) and TTSRST are not good. Eventually, the correlation coefficients of the Penetration at 25°C with Tε=1%, Tbdb, Tbdm(300μm/m/h), Tbdm(45000μm/m/h) and TTSRST appear as not so good. Indeed, as far as the authors know, in the literature, except the results of Jung and Vinson (23) (29) that evidenced pretty good correlation between TTSRST and the Penetration at15°C, poor correlation is usually emphasized (5).
Finally, as the Penetration at 25°C, the Softening Point Ring and Ball and the Fraass Brittle Point are concerned, these conventional tests do not bring relevant information nor do they provide a very accurate ranking regarding to the failure behavior of the bituminous materials at low temperatures. Let’s add that the Penetration at 25°C and the Softening Point Ring and Ball are not well correlated with the low-temperature criterions since, obviously, they are not associated with the same domain of temperature.
CONCLUSIONS
A rational approach which consists in comparing the properties of binders and mixes only in the same domain of behavior (the large strain domain up to failure) has been considered in this paper. From our results, the following conclusions can be drawn :
• A new way of determining the brittle/ductile transition temperature related to the peak of the tensile strength/temperature response curve (at a given strain rate) is proposed. This makes the determination of such a transitional temperature easier and more accurate.
• For the considered set of binders, the tensile tests on binders and mixes rank the materials in the same manner regarding the rate-dependent brittle/ductile transition temperatures of binders and mixes.
• As a first approximation, the tensile strength of mixes can be considered as independent of the strain rate in the brittle domain (at very low temperatures). This point is of primary importance since a high strain rate can be used in the brittle domain so as to save time.
• Only as a rough approximation, in the brittle domain (at very low temperatures), the tensile strength of binders and mixes can be considered as close. This point needs further investigation.
• An expanded laboratory testing program is recommended to further explore the effects of strain rate and mixdesign on the tensile strength of bituminous binders and mixes.
• Parameters such as i)the temperature leading to failure at 1% strain at the SHRP tensile tests on binders, ii) and iii)the fragile/ductile transition temperatures of binders and mixes (for given strain rates) and iv)the failure temperature obtained at the TSRST tests have been determined for each material. It has been shown that these
low-temperature parameters well correlate with each other. This series of parameters ranks in the same manner the bituminous materials regarding to their low-temperature properties. That means that these four parameters can be good surrogates to each other.
• Concerning the relevancy of the traditional parameters (the Penetration at 25°C, the Softening Point Ring and Ball and the Fraass Brittle Point), as many other authors have previously stated, bad correlation between the latter parameters and more rational characteristics have been found herein.