Complex modulus of cement-bitumen treated materials produced with different reclaimed asphalt gradations

The increasing attention over cold recycling technologies as sustainable paving solutions requires a proper characterisation in terms of complex modulus for supporting the pavement design. Among cold recycled materials, cement bitumen treated materials (CBTM) benefit from the presence of both bituminous and cementitious binders. This research aims at characterising the complex modulus of CBTM mixtures produced with three different gradations, modified bitumen emulsion and two types of cement. The complex modulus measurements were modelled considering the usual viscous dissipation behaviour, linked to the bituminous component of the mixtures, along with a time- and temperature-independent dissipation component. The results showed that both the aggregate skeleton and the composition of the fine aggregate matrix affected the rheological behaviour. Furthermore, the role played by the aged binder contained in the reclaimed asphalt aggregate was highlighted by the parameters of the rheological model.


Introduction
The global concern over the sustainability of the built environment is pushing policy makers towards new strategies for implementing high-quality recycling and reducing carbon and environmental footprints [1]. In pavement engineering, cold recycling techniques allow the reuse of high amounts of reclaimed asphalt (RA), generally between 50 and 100% of the total aggregate blend, and are carried out at ambient temperature. This may save up to 50% of fuel consumption compared to traditional hot mix asphalt (HMA) technologies [2,3] and reduce greenhouse gases and pollutants emissions [4][5][6][7].
Optimising the composition of CRM mixtures is the first step towards their wider implementation as a replacement for conventional HMA mixtures. In order to apply mechanistic-empirical design procedures to pavements including cold recycled material (CRM) layers [24], it is imperative to characterize their stiffness properties. This requires different testing and modelling approaches, depending on the composition of the mixture, in particular, the type and amount of binding agents. If cold recycling is carried out using only Portland cement, stiffness can be characterised using the approach employed for cement-treated materials (CTM) [25]. If bitumen is the main recycling agent a bitumen stabilised materials (BSM) is obtained, whose stiffness characterisation must take into account stress-dependency [26,27]. In pavement design, both CTM and BSM layers are considered time-and temperature-independent, and therefore the measurement of stiffness at different temperatures and loading frequencies is normally not of concern. On the other hand, cold recycled asphalt (CRA) and cementbitumen treated materials (CBTM) mixtures show a typical frequency-and temperature-dependent stiffness behaviour [28][29][30][31][32]. Therefore, their stiffness can be measured using complex modulus tests and modelled using linear viscoelastic (LVE) models [33,34]. The same experimental procedures and thermo-rheological models developed for conventional HMA mixtures are normally applied for CRA and CBTM mixtures [33,34]. However, these mixtures have some peculiarities that must be properly considered, like the interaction between the heavily aged RA binder and the fresh bitumen used as binding agent.
In this research we focused on the measurement and modelling of the complex modulus behaviour of CBTM mixtures produced with latex-modified bitumen emulsion and cement. Our main objective was to evaluate the effect of different grading curves on the complex modulus behaviour. The effects of RA content and cement type were also investigated. To tackle this objective, we applied a rheological modelling approach specifically developed for CBTM mixtures, which considers also non-viscous dissipation mechanisms. The paper is organised as follows: Sect. 2 presents a short review of current approaches for modelling the complex modulus of CBTM mixtures; Sect. 3 provides information on the tested mixtures, the complex modulus testing procedure and the proposed rheological modelling approach; Sect. 4 describes the experimental and model fitting results and Sect. 5 discusses the values of some rheological parameters and compares the results with those obtained from the review.

Literature review
This review focuses on studies where the complex modulus of CBTM mixtures, or at least the stiffness modulus (i.e. the absolute value of the complex modulus, also known as dynamic modulus), was measured and modelled applying analogical or mathematical models. Table 1 summarises the literature sources and includes information on the composition of the mixtures, the curing protocol and the rheological modelling approach. The RA content of those mixtures varied between 20 and 100% and the fines content varied between 1.8 and 9.6%. As regards their volumetric properties, the air voids content varied between 8.9 and 18.0%. As regards the binding agents, the dosage of fresh bitumen (residual from the emulsion or foamed) varied between 1.2 and 3.8%, whereas the dosage of cement varied between 1.0 and 4.0%. The dosages of fresh bitumen and cement are reported in Fig. 1, where the tentative composition limits for the four families of CRM mixtures described in the Introduction are also outlined.
In all the literature sources, the time-temperature superposition principle (TTSP) was applied to obtain the master curves of the stiffness modulus. To compare among different papers, we shifted the master curves to the same reference temperature T ref = 25°C using the reported shift factors (Fig. 2). Only the master curves of mixtures from 19 to 28 (Table 1) refer to T ref = 21.1°C because the shift factors values were not provided [33]. As can be observed, the curves show a high dispersion, which is not surprising, given the wide range of compositions, voids content and curing conditions. The equilibrium moduli (E e ) and glassy moduli (E g ) reported in the literature sources are also listed in the last two columns of Table 1. The dispersion is particularly high for E e that varies between 10 -5 and 1479 MPa. Such a dispersion is also due to the calibration of the adopted models. In fact, the rheological models' equations were fitted within the range of reduced frequencies covered by the experimental data. Therefore, we may expect lower precision when predicting the behaviour of the mixtures at the asymptotic conditions represented by E e and E g .

Materials
The RA aggregate had a nominal maximum aggregate size (NMAS) of 16 mm (RA 0/16). In the laboratory, two fractions were further separated using the 2 mm sieve: RA 0/2 and RA 2/16. The virgin fine aggregate was crushed limestone sand with NMAS of 2 mm, and the filler was a finely ground limestone dust. Table 2 lists the main properties of the aggregates and Fig. 3a depicts their gradations. For the RA aggregate, the socalled ''black curve'' is reported. The bitumen emulsion was a commercial cationic slow-setting type, specifically designed for cold recycling applications, and classified C 60 BP 10 according to the European standard EN 13808. The emulsion was modified with Styrene-Butadiene-Rubber latex, and its residual bitumen content was 60%. Two types of cementitious binders were used, coded C2 and C3 [23], both are characterised by high compressive strength after 28 days according to EN 196-1.

Mixtures
The mixtures tested in this research were designed to be used in binder courses of medium-to-high traffic roadways. Three gradations with NMAS of 16 mm ( Fig. 3b) were evaluated: • A dense-graded gradation (DG) derived from the Fuller-Thompson curve with exponent 0.45. The RA aggregate content was 80%; • A gap-graded gradation (GG) whose coarse fraction (particles retained on the 2 mm sieve) was constituted by the RA 2/16, whereas the fine fraction (particles passing to the 2 mm sieve) was natural sand and filler; • A gap-graded gradation, with RA aggregate content of 95% (GGRA).  Table 1 and identification of CRM mixtures families  Table 1: a mixtures produced with bitumen emulsion; b mixtures produced with foamed bitumen The DG gradation fits within the gradation limits specified by Italian technical guidelines for cold recycling [42,43]. The two gap-graded gradations fit within the limits specified by Italian technical guidelines for stone mastic asphalt (hot) mixtures [43]. Figure 4a shows that the GG and GGRA gradations had the same coarse RA aggregate skeleton but different compositions in terms of fine aggregate. The GG gradation comprised only virgin fine aggregate, whereas the GGRA gradation comprised mostly fine RA aggregate particles. Figure 4b shows the relative volume fractions of the fresh bitumen from the emulsion and the aged bitumen from RA 2/16 and RA 0/2. It is highlighted that the fine fraction of the GG gradation does not contain RA. Table 3 summarises the composition by mass of the mixtures in terms of fresh bitumen from the emulsion, aged bitumen from RA aggregate and cement.
For all mixtures, the emulsion dosage was 5.0% (residual bitumen 3%) and the cement dosage was 2.5% by dry aggregate mass, resulting in a B/C ratio of 1.2. The mixtures can be classified as CBTM according to the scheme proposed in Fig. 1, even though the fresh bitumen dosage is slightly higher than those typically characterising these materials.
The total water dosage, comprising the emulsion water and the pre-wetting water, was 4.5% for the DG gradation and 4.0% for the two gap-graded gradations. The target voids content, which included the volume of air and intergranular water, was 9.0%, comparable to the lower values found in the literature (Table 1). A total of six mixtures was investigated by combining the three gradations (DG, GG, GGRA) and the two cement types (C2, C3). Two replicate specimens (R1 and R2) were tested for each mixture.

Specimen preparation
Before mixing, aggregates were dried until reaching constant mass. Next, a quantity of water equal to the  water absorption was added to the dry aggregate blend, and the wet samples were sealed in plastic bags for at least 12 h at room temperature to reach the saturated surface dry (SSD) condition. Then, cement, water and bitumen emulsion were gradually added to the SSD aggregate and mixed using a mechanical mixer, alternated with hand-mixing. Immediately after mixing, the specimens were compacted at the target voids content with a gyratory compactor, using a mould with diameter of 150 mm, a pressure of 600 kPa, a gyration speed of 30 rpm and an external angle of gyration of 1.25°(internal angle 1.16°). The specimens were extracted from the mould right after compaction. Curing was carried out in a climatic chamber for 28 days at (25 ± 2)°C and (70 ± 5)% relative humidity. At this point, the samples were cored to obtain specimens with a diameter of 75 mm. Then, curing was extended for additional 180 days at (25 ± 2)°C and (70 ± 5)% relative humidity.

Complex modulus testing and rheological modelling
Cyclic uniaxial compression tests were carried out using an AMPT PRO testing system (Fig. 5). The target peak-to-peak strain amplitude was 30•10 -6 mm/mm [34]. The testing frequencies were 10, 5, 1, 0.5 and 0.1 Hz, and twenty loading cycles were applied at each frequency. The sequence of where r 0 and e 0 are the steady-state amplitudes of the measured stress and strain signals, j is the imaginary unit, u is the phase angle, describing the delay of strain with respect to the stress, E 0 is the stiffness modulus, E 1 and E 2 are the storage and loss moduli, respectively. Thermo-rheologically modelling was carried out starting from the application of the TTSP. The reference temperature T ref = 25°C was selected, and the reduced frequency (fr) was calculated using the closed-form shifting (CFS) algorithm based on the minimisation of the overlapping area between two successive isothermal curves of the stiffness modulus E 0 [44]. The temperature dependency of the shift factors (a Tref T ð Þ) was modelled using the Williams-Landel-Ferry (WLF) equation: where C 1 , C 2 are constants obtained by least-squares fitting [45]. Rheological modelling of the complex modulus data was carried out with an approach specifically developed for CBTM mixtures. In addition to the viscous dissipation due to the bituminous binding agent, which is normally considered in LVE models, a hysteretic dissipation component was considered. The model is described as follows: where E Ã LVE is the LVE complex modulus model simulating a frequency-and temperature-dependent dissipation and exp ju HY ð Þ is a correction term that adds a constant phase angle u HY [31,34]. Physically, u HY describes time-independent (non-viscous) and temperature-independent dissipation phenomena which affect the CBTM behaviour during cyclic loading. Hysteretic dissipation is generally used to describe the dynamic behaviour of granular soils or cement concrete [46,47]. In CBTM mixtures, the hysteretic dissipation may be linked to the presence of cementitious bonds and internal friction caused by an incomplete coating of the aggregate. In the present research the analogical 2S2P1D model [48] was used to simulate the LVE behaviour: where x ¼ 2pf r is the angular frequency, d, h, k and b are binder-related dimensionless shape parameters and s is the characteristic time parameter. The dimensionless parameter b can be written as follows: Considering the full testing temperature and frequency range, the gap-graded mixtures were stiffer and showed a lower thermal sensitivity with respect to the dense-graded mixtures (the variability of E 0 across the entire temperature and frequency range was less than one order of magnitude). Based on the composition data shown in Fig. 4 and Table 3, we observe that the difference in stiffness is not related to the bitumen (either fresh or aged) or cement content. However, we can hypothesize that gap-graded mixtures were stiffer because of the higher volume of coarse RA aggregates resulting in an improved stone-on-stone contact. We highlight that the measurements carried out in the present research fall within the stiffness modulus range outlined in Fig. 2.
As regards the phase angle, the lowest values were also measured at 5°C and 10 Hz. In these conditions, considering all the specimens, the average value (standard deviation) was 5.1°(1.1°). Increasing the temperature/reducing the frequency, the phase angle increased, reaching a maximum at 45°C or 55°C. For the DG specimens, we obtained a maximum of 21.0°( 2.4°), whereas for the GG and GGRA specimens together, we obtained 15.5°(2.54°). These maximum values are lower than typical HMA ones [50] because of the lower frequency and thermal sensitivity of CRM mixtures, whose dissipation behaviour is affected by the presence of both the aged RA bitumen and the cementitious bonds. Similar values of the maximum phase angle were also found in the references listed in Table 1.

Modelling
For all tested specimens, the (E 0 , u) and (E 1 , E 2 ) pairs described unique curves in the Black and Cole-Cole diagrams (Fig. 6). Therefore, we considered the material behaviour to be thermo-rheologically simple and applied the TTSP to obtain the master curves of stiffness modulus and phase angle as a function of the reduced frequency (T ref = 25°C). Figure 7 shows the calculated temperature shift factors along with the fitted WLF models (Eq. 2). Mixtures DG and GGRA had similar values of C 1 and C 2 , whereas the values for mixture GG were smaller. Practically, for the latter mixture, the slope of the WLF curve was somewhat lower, indicating a lower temperature dependency. Considering the data shown in Table 3, this different thermal sensitivity can be linked to the lower ratio between the aged RA bitumen and the fresh bitumen that characterised the mixtures GG. Table 4 summarises the corrected 2S2P1D model (herein named 2S2P1D-HY) fitting parameters for all specimens, whereas Fig. 8 shows the fitted model for specimens DG-C3_R2 and GGRA-C2_R2 as an example. Figure 8 also shows the effect of the hysteretic correction u HY by plotting the 2S2P1D model without correction (dashed curves). Both 2S2P1D and 2S2P1D-HY models provide the same, good fitting of the stiffness modulus master curves (Fig. 8c), as the hysteretic correction u HY produces a rotation in the complex plane, without altering the length of the E 0 vector [18]. On the contrary, it is quite evident that the 2S2P1D-HY model results in an enhanced fitting of the phase angle master curves (Fig. 8d) and the experimental data plotted in the Cole-Cole and Black diagram ( Fig. 8a and b). In particular, for the specimen DG-C3_R2, u HY was 2.2°, corresponding to the 40% and 11% of the minimum and maximum phase angle measurements, respectively. For the specimen GGRA-C2_R2, u HY was 0.9°, corresponding to the 20% and 6% of the minimum and maximum phase angle measurements, respectively. Thus, although the hysteretic correction was small, at intermediate and low temperatures, it represented a non-negligible part of the phase angle for CBTM mixtures. To give a synthetic overview of the deviation between the measurements and the 2S2P1D-HY model predictions we calculated the following parameters: Du ¼ u measured À u model ð6bÞ Adopting the 2S2P1D-HY model, DE 0 values were generally lower than 10% (Fig. 9a) and Du values were generally lower than 3° (Fig. 9b), confirming the good accuracy of the fitting. Due to the hysteretic correction, we also observe that, at f r higher than 0.1 Hz, the 2S2P1D-HY model predicted the phase angle with an error lower than 1°.

Discussion
First, we investigate the link between the rheological parameters listed in Table 4 and the composition of the mixtures described in Fig. 4 and Table 3. Considering all the specimens, the hysteretic correction u HY varied from 0.5°to 2.7°and, on average, specimens DG and GG were characterised by higher values with respect to specimens GGRA. Mixtures DG and GG also had a lower total bitumen content (fresh ? aged). This confirms that u HY is linked to dissipation mechanisms that are not related to the bituminous component of the mixtures and thus are frequency and temperatureindependent.
The gradation of the mixtures had a clear effect on the equilibrium and glassy moduli, and thus on the elastic component of the rheological behaviour. In particular, GG and GGRA specimens had higher values of E e , which could be related to an improved stone-to-stone contact in the gradation. Moreover, the GG specimens were characterised, on average, by the highest values of E e and E g . In terms of composition, the GG mixtures were characterised by a fine aggregate matrix (FAM) containing only virgin sand (no RA). This favoured the development of cementitious bonds within the FAM, leading to higher stiffness at all temperatures and frequencies. The DG specimens were also characterised by the lowest values of E e . Since the equilibrium modulus is linked to the properties of the aggregate skeleton, this highlights the stiffening role played by the coarse stone-on-stone contact, which is prevalent in the gap-graded gradations GG and GGRA. The values of E e and E g were also affected by the cement type. In fact, with the same gradation, the mixtures produced with cement C2 were generally stiffer than those produced with cement C3. This is particularly evident for mixtures GG that, as highlighted above, were characterised by a cementdominated FAM.
The parameters h, k, d and b of the 2S2P1D model are linked to the LVE response of the bituminous component of the mixtures that, in the present case, comprises both fresh emulsion bitumen and aged RA bitumen. In particular, h and k must be comprised between 0 and 1, with lower values representing a more elastic behaviour and higher values representing a more viscous behaviour. In our model fitting, we used the same values of h (0.38, 0.40 and 0.33) and k (0.12, 0.13 and 0.12) for specimens characterised by the same gradation (DG, GG, GGRA, respectively), and thus by the same bitumen content. Even though the values of h and k were not specifically optimised  for each specimen, a good precision was obtained (Fig. 9). As shown in Fig. 10a, the values of h and k found in the present research were similar to those obtained for other CRM mixtures [30,31,34] but significantly lower than those commonly obtained for conventional hot and hot-recycled asphalt mixtures [48,49]. This suggests that the RA binder affects the rheological behaviour of CRM mixtures by reducing the values of h and k, but with a different mechanism than in hot recycled mixtures. We highlight that this phenomenological interpretation does not imply any reactivation of the aged RA binder nor its blending with the emulsion residue. In fact, cold recycling is carried out at ambient temperature, where the RA binder is still viscoelastic but can hardly be considered ''active''. Neither it can be assumed that the RA binder significantly blends with the emulsion residue, generating a new ''reactivated'' binder. Figure 10b shows the relation between the characteristic time s and the Newtonian viscosity parameter g. Specimens GGRA had the highest values of both s and g indicating lower viscous relaxation ability and higher ageing degree with respect to the mixtures DG and GG. This result can also be linked to the content of aged binder in the mixtures (Table 3). Figure 11 compares the measured stiffness modulus values with the range of data obtained from the literature review (Fig. 2a, Table 1). At high reduced frequencies (f r ¼ 10 6 Hz), the tested mixtures had stiffness modulus values comparable to those of the On the other hand, at low reduced frequencies (f r ¼ 10 À4 Hz), the stiffness modulus E 0 10 À4 ð Þ of the tested mixtures was comprised between 343 and 2920 MPa. In contrast, the literature data varied from 66 to 2356 MPa. This suggests that the use of high-strength cements in relatively high dosage (2.5%) did not lead to an excessive stiffness at low temperatures that could result in a cracking-prone behaviour. On the other hand, the material was still quite stiff at high temperatures suggesting a good permanent deformation resistance. However, we highlight that these results refer to the small-strain behaviour and extrapolation to the failure behaviour must be supported by specific experiments.

Conclusions
In this paper we evaluated the effect of different grading curves, RA contents and cement types on the complex modulus behaviour of CBTM mixtures. The analysis of experimental data was based on a rheological modelling approach specifically developed for CBTM mixtures, which considers also a hysteretic  • Gap-graded gradations lead to a stiffness increase, especially at high temperatures with respect to dense graded gradations. This is due to a higher number of coarse stone-to-stone contact points. • The cement type affects the elastic component of the rheological behaviour, and in particular, the values of the asymptotic moduli E e and E g . This effect is particularly evident in the mixtures with a cement-dominated FAM. • The 2S2P1D-HY model allows an excellent fitting of the complex modulus results and the hysteretic correction angle u HY is higher for mixtures having lower bitumen content (fresh ? aged) confirming that u HY is linked to dissipation mechanisms that are frequency and temperature-independent. • CBTM mixtures are characterised by values of the rheological parameters h and k that are well below those of hot recycled mixtures. This could be related to the fact that in cold recycling, contrary to hot recycling, the fresh bituminous binder and the aged RA binder do not blend. Funding Open access funding provided by Università Politecnica delle Marche within the CRUI-CARE Agreement.

Declarations
Conflict of interest The authors have no relevant financial or non-financial interests to disclose.
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