curing and temperature sensitivity of cement … curing and temperature sensitivity of...

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Post-print version Published version available from http://www.tandfonline.com/toc/gpav20/current#.VDBZ3-eaVD4 http://dx.doi.org/10.1080/10298436.2014.966710 Curing and temperature sensitivity of cement-bitumen treated materials Fabrizio Cardone Department of Civil and Building Engineering and Architecture, Università Politecnica delle Marche, Ancona, Italy Andrea Grilli Department of Economics and Technology, University of the Republic of San Marino, Republic of San Marino Maurizio Bocci Department of Civil and Building Engineering and Architecture, Università Politecnica delle Marche, Ancona, Italy Andrea Graziani (corresponding author) Department of Civil and Building Engineering and Architecture, Università Politecnica delle Marche, Ancona, Italy [email protected]

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Page 1: Curing and temperature sensitivity of cement … Curing and temperature sensitivity of cement-bitumen treated materials In the present study, the curing process of cement-bitumen treated

Post-print version Published version available from http://www.tandfonline.com/toc/gpav20/current#.VDBZ3-eaVD4 http://dx.doi.org/10.1080/10298436.2014.966710

Curing and temperature sensitivity of cement-bitumen treated materials

Fabrizio Cardone

Department of Civil and Building Engineering and Architecture, Università Politecnica delle Marche, Ancona, Italy

Andrea Grilli

Department of Economics and Technology, University of the Republic of San Marino, Republic of San Marino

Maurizio Bocci

Department of Civil and Building Engineering and Architecture, Università Politecnica delle Marche, Ancona, Italy

Andrea Graziani (corresponding author)

Department of Civil and Building Engineering and Architecture, Università Politecnica delle Marche, Ancona, Italy

[email protected]

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Curing and temperature sensitivity of cement-bitumen treated materials

In the present study, the curing process of cement-bitumen treated materials

(CBTM) was investigated by analysing the influence of cement dosage and

curing temperature on moisture loss and evolution of complex modulus.

Moreover, the study aimed to characterize the thermo-rheological behaviour of

cured CBTM. Results showed that moisture loss by evaporation controls the

increase in stiffness of the mixtures. However, excessive evaporation can hinder

the full potential of the cement hydration process. Results also showed that the

quantitative effects of curing time and loading frequency on stiffness can be

superposed. Similar to hot-mix asphalt, CBTM showed a viscoelastic and

thermo-dependent response. In particular, results suggested that, at higher

frequencies, the iso-thermal viscoelastic response is mainly affected by the aged

binder whereas, at lower frequencies, the response of the mixtures depended

mainly from the behaviour of the fresh binder.

Keywords: cold recycling; cement-bitumen treated materials; curing; temperature

sensitivity; complex modulus.

Introduction

The growing social and political awareness about environmental issues is moving towards the development of low-energy and low-emission technologies for the production and laying of bituminous mixtures. At the same time, the limited availability of natural aggregates and the increasing disposal costs of milled materials is supporting the worldwide diffusion of recycling technologies for pavement construction and rehabilitation (EAPA 2008, ARRA 2001). In this context, cold recycling is becoming one of the most attractive rehabilitation technologies since it allows high-performance mixtures with low environmental impact to be produced (Stroup-Gardiner 2011).

Basically, cold recycling consists of milling a distressed bituminous pavement and combining the milled material with one or more binding agents to produce a new pavement layer without reheating. Bituminous binders (paving grade bitumen or modified bitumen, either as foam or emulsion), hydraulic binders (Portland cement, hydrated lime and fly ash) and chemical additives (recycling agents, rejuvenators) are employed to cover the mechanical deficiencies of the cold recycled mixes and to achieve the required structural and durability properties (Kearney 1997, Stroup-Gardiner 2011).

A wide range of mixtures can be produced by cold recycling techniques depending on the composition of the recycled aggregate mix and the type and dosages of the binding agents. In current practice, the term cold-recycled asphalt mixture (CAM) indicates a mixture consisting of reclaimed asphalt pavement (RAP) treated with a high dosage of bituminous binder. Usually, RAP is blended with virgin aggregate to meet grading requirements. In most cases, bituminous emulsion or expanded (foamed) bitumen is employed, while cementitious (hydraulic) binders can also be added as “active” fillers to improve the short-term properties of the mix. The high dosage of residual binder (fresh bitumen) and a ratio between bituminous and cementitious

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binder normally greater than one (B/C > 1), confers to CAM asphalt-like mechanical properties like loading rate and temperature susceptibility (Kim and Lee 2012, Stimilli et al. 2013).

The cold recycled mixture composition changes when RAP is blended with reclaimed aggregates (RAg) coming from the underlying base or subbase layers, either unbounded or hydraulically-bounded (Bocci et al. 2011, Bocci et al. 2012, Thompson et al. 2009). As such, three main types of mixtures can be distinguished: bitumen stabilised materials (BSM), cement treated materials (CTM) and cement–bitumen treated materials (CBTM).

BSM can be obtained with the addition of bituminous binders, either as bitumen emulsion or foamed bitumen (Asphalt Academy 2009). BSM are characterized by lower bitumen dosage with respect to CAM and by a limited dosage of active fillers. As a consequence, the mechanical properties of BSM show a stress–dependent behaviour with improved shear resistance if compared to unbound granular materials (Fu and Harvey 2007).

CTM are produced using only cement as stabilising agent and typically show brittle behaviour characterized by susceptibility to shrinkage cracking and great permanent deformation resistance (Xuan et al., 2012, Grilli et al., 2013b).

CBTM are characterized by higher dosages of cementitious binder with respect to BSM (generally B/C ! 1) which leads to an increase in stiffness and strength properties (Grilli et al. 2012). From a mechanical point of view, CBTM are stiffer and less prone to permanent deformation as compared to BSM and show reduced cracking susceptibility with respect to conventional CTM (Bocci et al. 2011).

Regardless of aggregate nature, binder type and dosage, a distinctive feature of cold recycled mixtures is the requirement for a certain curing period to develop the ultimate mechanical properties (strength and stiffness).When both bituminous and cementitious binders are employed, the curing process actually results from diverse mechanisms: emulsion breaking, moisture loss and hydration of cementitious compounds (Asphalt Academy 2009, Bocci et al. 2011, Kavussi and Modarres 2010).

Controlling the breaking process is particularly important when bitumen emulsion is employed because it must occur after the completion of the mixing and compaction phases. Afterwards, the presence of water inside the cold recycled mixtures delays the attainment of the ultimate mechanical properties. Moisture loss, by means of drainage or evaporation, ensures mixture hardening and bonding between the bituminous mortar (i.e., fine aggregate particles bonded by the bituminous binder) and the coarse aggregate skeleton.

Hydration of cementitious materials is linked to various chemical and physical phenomena. Starting from the early curing stages, it accelerates the emulsion breaking process, increases the rate of bitumen coalescence and reduces the amount of evaporable water (Brown and Needham 2000, Giuliani 2001). At low cement content, the hydration products disperse inside the bituminous mortar increasing its viscosity and improving the resistance of the mixture to permanent deformations. At higher cement content, the volume of hydration products grows forming a stiffer matrix that connects coarser aggregate particles (Garcia et al. 2012).

It is particularly important to remark that while the curing process of bituminous binders, either emulsion or foam, is strictly linked to moisture loss, the chemical reactions that take place during the hydration of cementitious binders require the presence of water and do not entail any moisture loss.

Laboratory curing of cold recycled mixtures aims to simulate field curing conditions while trying to accelerate the attainment of ultimate properties (Jenkins et al. 2008). However, the factors that influence field curing are extremely difficult to standardize and reproduce since they are related to composition (binder types and dosage) of the mixture, construction features (degree of compaction, layer thickness, drainage conditions, construction phases) and environmental factors (temperature, humidity, wind). Therefore, a rational laboratory curing procedure should: consider the relevant curing mechanisms which arise from mixture composition (emulsion breaking/moisture loss and cement hydration), define specimen shape, dimensions and boundary conditions and control curing temperature and relative humidity.

In the present laboratory study, the curing process of CBTM is investigated by measuring the evolution of moisture and stiffness. Specifically, uniaxial cyclic compression tests were carried out to measure complex modulus at different curing ages. Our main objective

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was to analyse the stiffness evolution of CBTM considering the influence of mixture and environmental factors (cement dosage and curing temperature).

Another objective of the study was to characterize the thermo-rheological behaviour of cured CBTM using the procedure which is normally employed for hot-mix asphalt (HMA). Therefore, complex modulus tests were performed on 28-day cured mixtures and the results were analysed to compare the effects of temperature and loading frequency.

Experimental program

Materials

The samples of CBTM tested in this study were prepared in the laboratory using RAP, virgin aggregates, bituminous emulsion, Portland cement and water.

The RAP was sampled from a cold recycling jobsite after milling the aged asphalt layers (Bocci et al. 2010). Its average size distribution, obtained by wet sieving, is reported in Figure 1. As can be observed, the maximum size of the RAP particles is 32 mm, and the fine content is low because the finer aggregate particles, including filler, are bounded to larger aggregate particles forming RAP lumps. The average bitumen content of RAP was 4.6 % by aggregate weight (EN 12697-1), and the maximum size of the extracted aggregate was 12 mm. The RAP was designated as 32 RA 0/12 according to the European standard EN 13108-8. Two crushed coarse aggregate sizes, 6/12 and 12/20, and a fine aggregate size, 0/4 having the same mineralogy (limestone) were blended with the RAP in order to obtain the final mixture grading (Figure 1). The main physical and geometrical properties of RAP and virgin aggregate particles are summarized in Table 1.

The aggregate blend was prepared by mixing 50% of RAP, 10% of 12/20, 5% of 6/12 and 35% of 0/4. These proportions were selected in order to meet the Italian specification for a subbase course (Figure 1).

A cationic, slow-setting bituminous emulsion with a 60 % nominal binder content was employed (Table 2). The emulsion, designated as C60B5 according to the European standard EN 13808, is specifically formulated for cold recycling. In fact, it is characterised by high mixing stability with cement (over-stabilised emulsion) and allows good workability during the mixing and compaction phases. The employed emulsion dosage was 3 % by dry aggregate weight, corresponding to 1.8 % of residual (fresh) bitumen.

A Portland limestone cement (PLC) type II/B-LL, strength class 32.5 R (EN 197-1) was employed. Its composition is a combination of clinker (65 % - 79 %) and limestone dust (35 % - 21 %). Mixtures with two cement dosages (1 % and 2 % by dry aggregate weight) were produced and referred to as M3B1C and M3B2C, respectively.

The mixing water content was 5 % by dry aggregate weight; this amount was determined in a preliminary mix-design study and includes emulsion water and extra water which is added to the fresh mix in order to improve compactability (Grilli et al. 2012).

Specimen preparation

Before mixing and compaction, virgin aggregates and RAP were dried at 105 °C and 40 °C, respectively. The dry aggregate blend was preliminarily mixed with a water amount corresponding to the absorption of the constituent particles. In order to obtain a homogeneous moisture, the wet aggregate blend was stored in a sealed plastic bag for 12 hours, at room temperature. Afterwards, each blend was thoroughly mixed, gradually adding water, cement and emulsion, in this sequence. After mixing by hand for at least two minutes, a visual evaluation was made to check for homogeneity and to verify that emulsion breaking had not taken place.

Various types of compaction equipment are currently employed for the preparation of cold-recycled specimens in the laboratory (Tebaldi et al. 2014). The procedure adopted in the

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present study was developed in Italy, based on several years of field experience (Santagata et al. 2009, Bocci et al. 2011, Grilli et al. 2012). In particular, specimens were compacted by means of a shear gyratory compactor in a 100 mm diameter mould with a constant pressure of 600 kPa, a gyration speed of 30 rpm and a constant angle of inclination of 1.25°. For each specimen, the weight of the loose mixture (about 2.4 kg) was adjusted to attain a bulk density of about 2,1 kg/m3 and a specimen height of 150 ± 2 mm after 180 gyrations. After compaction, specimens were sufficiently stable to allow immediate extrusion.

Curing procedure

The curing conditions were fixed and controlled to study the evolution of the material properties as a physical phenomenon. Compacted specimens were cured in a climatic chamber at constant relative humidity (70 ± 5 %) and at two curing temperatures (20 ± 2 °C and 40 ± 2 °C). The relative humidity value was considered a reasonable compromise in order to achieve curing of the bituminous components, which is essentially based on moisture loss, and the curing of cementitious components, which instead requires a moist environment. The temperature of 20 °C was considered a reference value, while the temperature of 40 °C was selected to obtain accelerated curing.

Complex modulus testing procedure

Complex modulus testing was conducted to measure the stiffness evolution arising from the curing process and to characterize the thermo-rheological behaviour of the CBTM mixtures at their final curing stage (28 days).

Uniaxial cyclic compression tests (CCT) were performed using a servo-pneumatic testing equipment in control strain mode; a sinusoidal (haversine) axial strain with 15 µ" amplitude was applied at various frequencies. The deformation was measured by means of two LVDT transducers, fixed to the lateral surface of the specimen 180° apart; a 70 mm measurement base was adopted to reduce end effects and to provide a more accurate deformation reading. The axial load was measured using a 20 kN load cell. A total of 110 strain cycles were applied at each frequency, and the complex modulus E* was calculated as follows:

E*= E0 exp( j! ) (1a)

E0 =! 0

"0 (1b)

! = 2" f!t (1c)

where E0 is the absolute value (norm) of the complex modulus, also called the stiffness (or dynamic) modulus, ! is the phase (or loss) angle, f is the test frequency (Hz), and j is the imaginary unit (j2 = -1). The amplitude of the measured stress and strain signals ("0, #0) and the time lag between the two waves were calculated performing a sinusoidal regression on the last ten loading cycles.

The test procedure was adapted from those available for HMA mixtures (EN 12697-26, AASHTO T 342-11). Although higher strain amplitudes (up to 100 µ") are currently applied to test HMA in the linear viscoelastic domain, a reduced strain level was employed since the

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presence of cementitious components may reduce the linearity field and also to avoid specimen damage due to local brittle behaviour, as observed in previous studies (Bocci 2009).

Summary of test programme

The complex modulus test programme is summarized in Table 3. Two CBTM were analysed, characterized by 3 % emulsion dosage and two cement dosages: 1 % and 2 % (coded M3B1C and M3B2C, respectively). For each mixture, two series of six replicate specimens were prepared. The first series was cured at 20 °C and the second at 40 °C. For each series, four specimens were subjected to CCT whereas two control specimens were used as reference to check moisture loss due to evaporation.

In order to evaluate the curing effect on stiffness, CCT were carried out at 20 °C and six frequencies (0.1, 0.3, 1, 3, 10 and 20 Hz) at curing times of 1, 3, 7, 14, 21 and 28 days. Specimens cured at 40 °C were conditioned for 4 hours at 20 °C before mechanical testing.

The thermo-rheological behaviour of the studied CBTM mixtures was analysed by performing CCT on the specimen series cured at 20 °C for 28 days, at four temperatures (5, 20, 35, 50 °C) and six test frequencies (0.1, 0.3, 1, 3, 10 and 20 Hz).

Results and discussion

Moisture Loss

Moisture loss by evaporation was measured by weighing the control specimens, and results are reported in Figure 2 where the curing time axis is in log scale. As can be observed, moisture loss was particularly high in the first hours and, after one curing day, exceeded 50 % of the initial water content for all specimens.

As expected, raising the curing temperature from 20 °C to 40 °C accelerated the rate of evaporation of both mixtures. In particular, specimens cured at 40 °C reached an equilibrium water content WEQ after 7 days, while specimens cured at 20 °C required about 14 days. The value WEQ appears to be influenced by the cement content of the mixture. In fact, after 28 days of curing, mix M3B2C retained about 7 % of the initial water content, corresponding to WEQ = 0.35 %, while mix M3B1C retained about 10 % of the initial water content, corresponding to WEQ = 0.50 %.

In order to analyse the moisture loss data, it should be considered that the equilibrium water content WEQ contains the water required by the cement hydration process WHY that is not available for evaporation. Part of WHY (about 23 % of cement weight) is chemically bound and becomes part of the calcium-silicate-hydrate (C-S-H) gel; another part (about 19 % of cement weight) is adsorbed by the C-S-H nano-porosity and can be removed only at extremely low relative humidity values (below 50 %) (Mehta and Monteiro 1993).Therefore, the amount of water required by the hydration process can be estimated as:

WHY = (0.23 + 0.19) · $ · k · c0 (2)

where $ is the degree of hydration of the cement paste, c0 is the cement dosage relative to the dry aggregate weight (1 % for mix M3B1C, 2 % for mix M3B2C) and k is the fraction of Portland cement clinker in the cement (0.72 was assumed as the average value of the clinker content range).

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Considering a degree of hydration $ = 0.9, which may be a reasonable assumption after 28 days of curing (Garcia et al 2012), equation (2) gives: WHY = 0.27 % and WHY = 0.54 % for mixtures M3B1C and M3B2C, respectively.

This indicates that, for the M3B1C mixture, the measured equilibrium water content (WEQ = 0.50 %) still contains a residual fraction of potentially evaporable water (WEQ !WHY= 0.23 %); this residual amount may be contained inside the larger-sized (capillary) pores of the hydrated cement paste or inside the surface porosity of the aggregates. Furthermore, the residual water amount may form water bubbles inside the bituminous mortar, as shown by Garcia et al.(2012), influencing the mechanical behaviour of the mixture.

For the M3B2C mixture, the estimated amount of water required by hydration (WHY = 0.54 %) exceeded the measured equilibrium water content (WEQ = 0.35 %). This implies that the actual degree of hydration after 28 day was well below the previously hypostasized value ($ = 0.9). In fact, assuming that all the equilibrium water content was employed in the hydration process(WHY = WEQ), equation (2) would yield a degree of hydration $ = 0.54, indicating that for the M3B2C mixture moisture loss by evaporation stopped the hydration process at about one half of its potential.

Curing effects

Stiffness modulus

The stiffness modulus E0, measured at 20 °C and at curing times starting from 1 day to 28 days (average of four replicate specimens), is reported in Figure 3 and Figure 4, as a function of test frequency, obtaining iso-curing curves. For each curing period, stiffness increases with increasing test frequency, at both curing temperatures. This typical viscoelastic response, similar to the response of HMA (Di Benedetto and de la Roche 1998), is generally measured on cold recycled mixtures produced with both emulsion (Kim and Lee 2012) and foamed bitumen (Van de Ven et al.2007). Fresh bituminous binder plays a major role in the viscoelastic response, but the aged binder in the RAP also gives its contribution to the time- (and temperature) dependent response (Grilli et al. 2013a).

Higher stiffness was measured with longer curing times, regardless of the curing temperature. However, it was observed that beyond 14 days the distance between iso-curing lines tends to vanish, suggesting that stiffness is approaching its ultimate value. This observation can be directly related to the moisture loss trend of the mixtures (Figure 2). In particular, it should be noted that all mixtures showed a noticeable increase in stiffness between 7 and 14 days even if no significant moisture loss due to evaporation occurred. This can be explained by cement hydration that carried on using the residual water still present inside the bituminous mortar or absorbed by the surface porosity of aggregates.

The pattern of iso-curing modulus curves shown in Figure 3 and Figure 4 closely resembles the pattern of iso-thermal stiffness values obtained in routine frequency sweep tests on HMA. This suggests that the quantitative effects of curing time and loading rate on E0 could be superposed, and a unique master curve could be obtained by selecting a reference curing time and shifting the iso-curing values parallel to the frequency axis. This is equivalent to defining a curing-reduced loading frequency fr,c:

fr,c =f

ac,R (tc ) (3)

where f is the actual test frequency and ac,R(tc) is a curing shift factor whose value at each curing time tc depends on the stiffness variation between tc and the reference curing time tc,R.

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A similar approach, based on the definition of an age-reduced time, has been used to characterize the creep and relaxation response of polymeric and bituminous materials subjected to physical aging (Struik 1978, O’Connell and McKenna 1997, Barbero and Julius 2004, Canestrari et al. 2013). The use of a shift function has also been proposed to model the creep behaviour of aging concrete (Bazant and Wu 1974). In this perspective, the curing of cement-bitumen treated materials may be considered a sort of short-term aging.

In the present study, a four-parameter sigmoidal function was adopted to represent the curing master curve:

logE0 ( fr,c ) = ! +"

1+ exp(# +$ ! log fr,c ) (4)

where $, %, & and ' are shape parameters that were estimated by the curve fitting of experimental data, allowing a free variation of the curing shift factors.

Equation (4) is extensively employed to represent the stiffness master curve of HMA (Pellinen 2003) obtained by superposing the effects of loading frequency and temperature (time-temperature superposition principle, TTSP). It is worth noting that the TTSP is applied with the implicit assumption that HMA is a non-aging material and that its rheological properties do not change with time (e.g., binder aging is fixed).In the present study, the same mathematical procedure was applied to analyse curing by superposing the effects of loading frequency and curing time, fixing the loading temperature at 20° C. The influence of test temperature on stiffness was separately considered on the 28-day cured mixtures.

The stiffness modulus master curves at 20° C and at the reference curing time of 28 days are shown in Figure 5. Excellent fitting of the experimental data was obtained with equation (3)(Table 4).The adequacy of the sigmoidal model was checked with a residuals analysis. Plotting the standardized residuals against the independent variable (log E), it is observed that the values show a random pattern and fall in the interval (-2, +2) (Figure 6a). Moreover, in the Q-Q plot (Figure 6b), the residuals are distributed approximately along the 45-degree reference line. These plots indicate that residuals may be considered uncorrelated random variables with normal distribution and therefore the proposed model shows no severe inadequacies.

The logarithm of curing shift factors are plotted in Figure 7 as a function of curing time (shifting function); the values log ac,28(tc) are proportional to the horizontal shift of the iso-curing lines on the log-frequency scale and therefore may be used to measure the curing level at each test frequency with respect to the 28 days condition.

From Figure 5, it can be observed that raising the curing temperature from 20° C to 40°C, a lower stiffness is obtained at 28-day curing, especially with 2 % cement content. A similar reduction in stiffness at long curing times was also measured on CBTM by means of indirect tensile tests (Bocci et al. 2011). This effect can be related to the structural and morphological characteristics of the hydrated cement. In particular, at higher curing temperatures the density of the hardened cement can be less uniform and have higher porosity (Verbeck and Helmuth 1969), leading to lower mechanical properties.

From Figure 7, it can be observed that at fixed cement content lower shift factors were obtained when the curing temperature was raised from 20 °C to 40 °C. This confirms that higher temperature accelerated the curing process. In fact, lower values of the curing shift factors (ac,28) at a specific curing time (tc) indicate higher stiffness with respect to the 28-day reference curing state, denoting a higher curing level.

Starting from 14 days, the shifting functions tend to overlap, indicating that in this second phase specimens cured at 20 °C show a higher rate of stiffness increase. This behaviour can be related to the amount of water present in the mixture (Figure 2): at 40°C evaporation is almost complete after 7 days while at 20°C some residual water is still present in the mixture, allowing cement hydration to proceed.

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At fixed curing temperature, higher shift factors were obtained for the M3B2C mix compared to the M3B1C mix. This indicates that cement addition resulted in a slower increase of curing level, especially in the short-term (1 to 7 days). Beyond 14 days, the shifting functions tend to overlap which indicates that in this phase specimens with a higher cement content show a faster increase in curing level.

Additional information on the mechanisms that control the curing process (evaporation and hydration) can be obtained by plotting the curing shift factors versus moisture loss by evaporation (Figure 8). As can be observed, for M3B1C mixtures the relationship between curing shift factors and moisture loss is almost perfectly linear regardless of the curing temperature. This suggests that the curing level, as measured by stiffness increase, is controlled by the amount of moisture loss through evaporation, whereas the curing temperature controls the rate of curing level increase.

The development of stiffness for M3B2C mixtures is analogous, as the increase can be basically explained by the amount of moisture loss. However, at fixed moisture loss, M3B2C mixtures showed higher ac,28 values, and therefore lower curing level, compared to the M3B1C mixture. This indicates that the curing level of M3B2C results from the combined effect of moisture loss and cement hydration. In fact, when moisture content gets closer to its equilibrium value, the curing shift factors trend is no longer a function of moisture loss. At this point, an increase in the curing level is not related to moisture loss anymore but can be explained by cement hydration.

These findings suggest that an improved curing for CBTM could be obtained by a two-phase procedure. In the initial phase, environmental conditions should facilitate moisture loss by evaporation to achieve curing of the bituminous binder (low relative humidity); in the second phase, once the equilibrium moisture value has been reached, curing should aim to obtain the maximum degree of hydration of the cementitious binder using the non-evaporable water possibly present in the mixture or even providing a moist environment. The relative duration of the two phases should be related to environmental conditions and to the initial moisture content of the CBTM, which is usually established in order to obtain optimal compaction.

Phase angle

The phase angle (!) can be used to evaluate the balance between the elastic and viscous response of CBTM and how such a balance is affected by curing. As an example, iso-curing curves of ! measured at 20 °C are reported in Figure 9 for M3B2C (the same trend was observed for M3B1C). For each curing period, the ! values decrease with increasing test frequency at both curing temperatures. This behaviour is consistent with the stiffness modulus variation and can be related to the viscoelastic response of the fresh and aged bituminous binder.

For each loading frequency, lower phase angles were measured at longer curing times. In particular, it was observed that beyond 7 days, curing the distance between iso-curing curves tends to vanish similar to stiffness modulus (Figure 4). Considering the observed moisture loss trend (Figure 2), the higher viscous response of the mixture at short curing times can be related to the presence of water inside the mortar composed of fresh bitumen, fine aggregate and cement, which binds the coarser aggregate particles (virgin or recycled).

Similar to the stiffness modulus, an attempt was made to superpose the effects of frequency and curing time for the phase angle. However, the shape of the ! iso-curing lines clearly did not allow acceptable results to be obtained (i.e., a unique master curve).

Overall viscoelastic response

The overall influence of curing on E* can be analysed in the Black space where the stiffness modulus is plotted versus the phase angle (Figure 10). As can be observed, a unique curve cannot be obtained, indicating that it is not possible to superpose the effects of load frequency

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and curing time. As shown above, this is mainly due to the phase angle and therefore to the viscous component of the material response.

The combined effect of loading frequency and curing on E0 and ! is summarized in Figure 11.The dashed curves represent the variability of E* with the load frequency, that is the viscoelastic response which is due to the fresh bituminous binder and the aged binder in the RAP. On the other hand, the continuous lines indicate the variability of E* with the curing age which is due only to the curing dependent mortar (fresh bituminous binder and cement).

A stiffness increase can be obtained with higher test frequencies (path F) or longer curing times (path C). However, in the second case, the reduction in viscous response is smaller (smaller phase angle reduction) because it is related only to mortar curing.

From a phenomenological point of view, the effects of curing (stiffness increase, phase angle reduction) may be considered opposite of the effects of non-linearity (path N) that results in stiffness reduction and a phase angle increase (Gauthier et al. 2010). Opposite effects can be explained by opposite physical phenomena: in the first case, curing leads to the formation of stable micro-structural bonds through the hardening of the fresh bituminous phase and cement hydration; in the second case, non-linearity occurring with large and/or repeated strains, brings to a progressive destruction of supra-molecular structures and networks (Gauthier et al 2010).

Temperature susceptibility

Stiffness modulus

The stiffness modulus of the studied CBTM measured after 28 days of curing at 20 °C (average of the four replicate specimens), is reported in Figure 12. Iso-thermal curves at 5, 20, 35 and 50°C show an increase in stiffness with increasing test frequency and decreasing temperature. This viscoelastic and thermo-dependent response is analogous to the response of HMA mixtures. Applying the TTSP, the stiffness modulus master curve was obtained by fitting the experimental data using the sigmoidal function described by equation (4). In this case, the temperature-reduced frequency is defined in the usual way:

fr,T = aT,R (T ) ! f (5)

where f is the actual test frequency and aT,R(T) is a shift factor whose value, at each temperature T, depends on the stiffness variation between T and the reference temperature TR.

The stiffness modulus master curves at reference temperature TR = 20° C are shown in Figure 13. Excellent fitting of the experimental data was obtained with equation (4), allowing a free variation of the curing shift factors. It can be noticed that by increasing the cement content from 1 % to 2 %, the mixture stiffness increased only moderately. This is also confirmed by the values of the equilibrium (static) modulus Ee and glassy modulus Eg obtained from the sigmoidal regression parameters. In particular, the Eg values (10307 MPa and 14270 MPa for M3B1C and M3B2C, respectively) are low if compared to the Eg values of conventional HMA. This can be related to the partial aggregate bonding produced by the emulsified bitumen and by the lower density of the mixtures. The modest stiffening effect produced by the increase in cement dosage is consistent with the low degree of hydration that was previously estimated for the M3B2C mixture. In addition, the shape of the two master curves is similar (Figure 13) which results in similar values of the shape parameters % and ' (Table 5). This suggests that cementitious bonds between the coarse aggregates do not appear to influence the stiffness behaviour probably because cement hydration products were incorporated into the fresh bituminous matrix.

The logarithm of temperature shift factors, plotted in Figure 14 as a function of test temperature, were fitted using the Arrhenius relation:

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loga20 (T ) =C1T!1TR

"

#$

%

&' (5)

where C (°K) is a material constant that is related to the thermal sensitivity of the bituminous binder and temperatures (T, TR) are expressed in °K. The calculated C values were 10980 °K and 10110 °K for M3B1C and M3B2C mixtures, respectively. These values are analogous to the values obtained from HMA (Di Benedetto and De la Roche 1998, Pellinen et al. 2003) indicating that the thermal sensitivity of the tested mixtures is the same as that of HMA.

Viscoelastic response

The influence of temperature on the viscoelastic behaviour of the tested CBTM was analysed in the Black space (Figure 15). As can be observed, the values of E0 and ! measured at different temperatures do not form a unique curve indicating that, as regards E*, it is not possible to superpose the effects of load frequency and temperature. Since the application of TTSP was acceptable for E0, the thermo-rheologically complex behaviour of E* is due to the phase angle and therefore to the viscous component of the material response.

The analysis of the Black space plots shows that at higher frequencies of the iso-thermal E* curves become almost flat and parallel, indicating that frequency variation has a limited effect on E0 in this range. A similar pattern was observed on E* iso-thermal Black curves obtained on cement-bound mixtures containing high percentages of reclaimed asphalt and no fresh bitumen (Figure 16, from Grilli 2013a). The outlined behaviour suggests that the iso-thermal viscoelastic response of CBTM at high frequencies is mainly related to the response of the aged binder contained in the reclaimed asphalt. On the other hand, temperature variations highlight the effect of the fresh binder; in fact, an increase in temperature results in lower glassy values (intercept at ! = 0) of the modulus.

At lower frequencies, the measured E* values tend to overlap forming a unique envelope curve: the effect of temperature and frequency can be superposed. This suggests that at lower frequencies, the response of the mixtures, particularly their viscous component, arises mainly from the fresh binder, while the RAP behaves only as a “black” aggregate.

These phenomenological considerations are further illustrated in Figure 17. In the high-frequency range, a stiffness increase can be obtained by increasing frequency (path F’) or reducing temperature (path T’); however, in the second case, the reduction in the phase angle is smaller as it is only due to the fresh binder. In the low-frequency range, an increase in frequency (path F’’) or a decrease in temperature (path T’’) has a similar quantitative effect which indicates that the fresh binder controls the viscoelastic response.

Conclusion

In the present study, the curing process of CBTM was investigated by measuring moisture loss and complex modulus, considering the influence of cement dosage and curing temperature. In addition, the influence of temperature on the complex modulus of 28-day cured mixtures was evaluated. Tests were carried out on laboratory compacted specimens, considering a dosage of 3 % of bituminous emulsion and two different cement dosages (1 – 2 %).

As regards moisture loss, the following conclusions can be drawn:

• The moisture loss rate by evaporation increased with an increase in curing temperature; in particular, specimens cured at 20 °C reached an equilibrium water content value WEQ within 14 days, while specimens cured at 40 °C required less than 7 days;

• Raising the cement dosage from 1 % to 2 % reduced WEQ; for the M3B1C mixture, the WEQ value suggests that complete cement hydration was reached, whereas for the

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M3B2C mixture moisture loss by evaporation stopped the hydration process at about one half of its potential;

As regards the curing effects on complex modulus E*, the following conclusions can be drawn:

• The increase in stiffness modulus E0 due to curing was mainly related to moisture loss and higher temperature which accelerated the curing process;

• The quantitative effects of curing time and loading frequency on E0 can be superposed, and a unique master curve was obtained by selecting a reference curing time and shifting the iso-curing values parallel to the frequency axis (curing-reduced frequency); a four-parameter sigmoidal function was able to model the curing master curves at the reference curing time of 28 days;

• The curing shift factors ac,R can be considered a measure of the curing level; in particular, ac,R values clearly highlight the role of moisture loss and cement hydration in the curing level;

• When plotted on the Black diagram, the E* values measured at different curing times do not form a unique curve because of the viscous component (!) of the material response; in particular, while test frequency affects the response of both the aged binder from RAP and the fresh binder from emulsion, the curing process (moisture loss and cement hydration) only affects the properties of the fresh binder.

As regards the effects of temperature on E*, the following conclusions can be drawn:

• Similar to HMA, CBTM exhibited a viscoelastic and thermo-dependent response; the TTSP was applied to obtain a master curve for the stiffness modulus E0, and the temperature dependence of the shift factors was analogous to that of HMA;

• The cement content had a moderate effect on stiffness and on the temperature shift factors confirming that the amount of cement hydration products was very similar because of moisture loss by evaporation;

• When plotted on the Black diagram, the E* values suggest that at higher frequencies, the iso-thermal viscoelastic response is mainly affected by the fresh aged binder, while at lower frequencies, the response of the mixtures, in particular their viscous component, arises mainly from the fresh binder, whereas the RAP behaves only as a “black” aggregate.

References

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Asphalt Recycling and Reclaiming Association (ARRA), 2001. Basic Asphalt Recycling Manual [online]. Available from http://www.mdt.mt.gov/publications/docs/brochures/research/toolbox/ARRA/BARM%20-%20B/1-124-BARM1.pdf [Accessed 22 April 2013].

Barbero, E.J. and Julius, M.J., 2004. Time-Temperature-Age Viscoelastic Behavior of Commercial Polymer Blends and Felt Filled Polymers. Mechanics of Advanced Materials and Structures, 11(3), 287-300.

Bazant, Z.P. and Wu S.T., 1974. Thermoviscoelasticity of Aging Concrete. Journal of the Engineering Mechanics Division, 100(EM3), 575-595.

Bocci, M., Canestrari, F., Grilli, A., Pasquini, E. and Lioi D., 2010. Recycling Techniques and Environmental Issues relating to the Widening of an High Traffic Volume Italian Motorway. International Journal of Pavement Research and Technology, 3 (4), 171-177.

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Bocci, M., Grilli, A., Cardone, F. and Graziani A., 2011. A study on the mechanical behaviour of cement-bitumen treated materials. International Journal of Construction and Building Materials, 25 (2), 773-778.

Bocci, M., Grilli, A., Cardone, F. and Ferrotti G., 2012. Full Depth Reclamation for the Rehabilitation of Local Roads: a Case Study. International Journal of Pavement Engineering, 15(3), 191-201.

Brown, S. F., and Needham, D., 2000. A Study of Cement Modified Bitumen Emulsion Mixtures. Journal of the Association of Asphalt Paving Technologists, 69, 92–116.

Canestrari, F., Graziani, A., Pannunzio, V. and Bahia H.U., 2013. Rheological Properties of Bituminous Binders with Synthetic Wax. International Journal of Pavement Research and Technology, 6(1), 15-21.

Di Benedetto, H. and de la Roche, C., 1998. State of the art on stiffness modulus and fatigue of bituminous mixtures. In L. Franken ed. Bituminous Binders and Mixes. RILEM Report 17, E & FNSpon, London.

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Garcia, A., Lura P., Partl, M.N., and Jerjen, I., 2012. Influence of cement content and environmental humidity on asphalt emulsion and cement composites performance. Materials and Structures, DOI 10.1617/s11527-012-9971-6.

Gauthier, G., Bodin, D., Chailleux, E. and Gallet, T., 2010. Non Linearity in Bituminous Materials during Cyclic Tests, Road Materials and Pavement Design, 11:sup1, 379-410.

Giuliani, F., 2001. X-Ray diffraction method for studying cement-modified bitumen emulsion mixtures in asphalt pavement cold recycling. 1st international Symposium on subgrade stabilization and in-situ pavement recycling using cement. Salamanca, Spain. Paper n. 6.

Grilli, A., Graziani, A. and Bocci, M., 2012. Compactability and Thermal Sensitivity of Cement-Bitumen Treated Materials. Road Materials and Pavement Design, 13 (4), 599-617.

Grilli, A., Bocci, E. and Graziani A., 2013a. Influence of reclaimed asphalt content on the mechanical behaviour of cement-treated mixtures. Road Materials and Pavement Design, 14 (3), 666-678.

Grilli, A., Bocci, M. and Tarantino A. M., 2013b. Experimental investigation on fiber-reinforced cement-treated mixtures using reclaimed asphalt. Construction and Building Materials, 38, 491–496.

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Kim, Y. and Lee, H.D., 2012. Performance Evaluation of Cold In-place Recycling Mixtures Using Emulsified Asphalt Based on Dynamic Modulus, Flow Number, Flow Time, and Raveling Loss. KSCE Journal of Civil Engineering, 16(4), 586-593.

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Advances in Materials Characterization and Modeling of Pavement Systems. 15th Engineering Mechanics Division Conference, ASCE, 83-101.

Santagata, F.A., Bocci, M., Grilli, A. and Cardone, F., 2009. Rehabilitation of an Italian Highway by Cold In-Place Recycling Techniques. Proceedings of the 7th International RILEM Symposium ATCBM09 on Advanced Testing and Characterization of Bituminous Materials, Vol. 2, pp. 1113-1122, Rhodes, Greece.

Stimilli, A., Ferrotti, G., Graziani, A. and Canestrari, F., 2013. Performance evaluation of cold recycled mixture containing high percentage of reclaimed asphalt. Road Materials and Pavement Design, 14(sup.1), 149-161.

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Tebaldi, G., Dave, E. V., Marsac, P., Muraya, P., Hugener, M., Pasetto, M., ... & Canestrari, F., 2014. Synthesis of standards and procedures for specimen preparation and in-field evaluation of cold-recycled asphalt mixtures. Road Materials and Pavement Design, 15(2), 272-299.

Thompson, M.R., Garcia, L.and Carpenter, S.H., 2009. Cold in-place recycling and full-depth recycling with asphalt products (Report no. FHWA-ICT-09-036). Illinois Center for Transportation.

Van de Ven, M.F.C., Jenkins, K. J., Voskuilen, J. L. M. and Van den Beemt, R., 2007. Development of (half-) warm foamed bitumen mixes: state of the art, International Journal of Pavement Engineering, 8(2), 163-175.

Verbeck, G. and Helmuth, R.H., 1969. Structures and physical properties of cement pastes. In: Proc. of the 5th international symposium on the chemistry of cement. Part III: properties of cement paste and concrete, Tokyo.1–32.

Xuan, D.X., Houben, L.J.M., Molenaar, A.A.A. and Shui, Z.H., 2012. Mechanical properties of cement-treated aggregate material – a review. Materials & Design, 33, 496–502.

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Figure 1. Gradation of virgin aggregates (0/4, 6/12, 12/20), RAP (32 RA 0/12) and CBTM mixtures.

Figure 2. Moisture loss by evaporation during the curing phase.

0

25

50

75

100

0.01 0.1 1 10 100

Pass

ing

(%)

Sieve size (mm)

0/4

6/12

12/20

32 RA 0/12

CBTM mix

0

20

40

60

80

100

0.1 1 10 100

Moi

stur

e lo

ss (%

)

Curing time (days)

M3B1C curing at 20°C M3B1C curing at 40°C M3B2C curing at 20°C M3B2C curing at 40°C

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(a)

(b)

Figure 3. Stiffness modulus E0 at 20 °C for M3B1C mixtures:(a) curing at 20 °C and (b) curing at 40 °C.

1000

10000

0.01 0.1 1 10 100

Stiff

ness

mod

ulus

(MPa

)

Frequency (Hz)

1 % cement - curing at 20°C

28 days 21 days 14 days 7 days 3 days 1 day

1000

10000

0.01 0.1 1 10 100

Stiff

ness

mod

ulus

(MPa

)

Frequency (Hz)

1 % cement - curing at 40°C

28 days 21 days 14 days 7 days 3 days 1 day

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(a)

(a)

Figure 4. Stiffness modulus E0 at 20 °C for M3B2C mixtures: (a) curing at 20 °C and (b) curing at 40 °C.

1000

10000

0.01 0.1 1 10 100

Stiff

ness

mod

ulus

(MPa

)

Frequency (Hz)

2 % cement - curing at 20°C

28 days 21 days 14 days 7 days 3 days 1 day

1000

10000

0.01 0.1 1 10 100

Stiff

ness

mod

ulus

(MPa

)

Frequency (Hz)

2 % cement - curing at 40°C

28 days 21 days 14 days 7 days 3 days 1 day

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(a)

(b)

Figure 5. Curing master curves of E0 at 20 °C at reference curing time tc,R = 28 days:

(a) M3B1C mixtures;(b) M3B2C mixtures.

1000

10000

1.0E-05 1.0E-03 1.0E-01 1.0E+01 1.0E+03

Stiff

ness

mod

ulus

(MPa

)

Curing-reduced frequency (Hz)

M3B1C curing at 20°C

M3B1C curing at 40°C

1000

10000

1.0E-05 1.0E-03 1.0E-01 1.0E+01 1.0E+03

Stiff

ness

mod

ulus

(MPa

)

Curing-reduced frequency (Hz)

M3BC2 curing at 20°C

M3BC2 curing at 40°C

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(a)

(b)

Figure 6. Residual analysis for the E0 curing master curve models: (a) Residuals vs.

fitted values and (b) Q-Q plot.

-4

-2

0

2

4

3.0 3.2 3.4 3.6 3.8 4.0

Stan

dard

ised

res

idua

ls

Fitted values (log E0)

M3B2C curing at 40°C M3B2C curing at 20°C

M3B1C curing at 40°C M3B1C curing at 20°C

-4

-2

0

2

4

-4 -2 0 2 4

Stan

dard

ised

res

idua

ls

Theoretical Quantiles

M3B2C curing at 40°C M3B2C curing at 20°C M3B1C curing at 40°C M3B1C curing at 20°C

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Figure 7. Curing shift factors ac,28(tc) vs. curing time tc.

Figure 8. Curing shift factors ac,28vs. moisture loss.

-1.0

0.0

1.0

2.0

3.0

4.0

1 10 100

log a c

,28

Curing time (days)

M3B1C curing at 20°C

M3B1C curing at 40°C

M3B2C curing at 20°C

M3B2C curing at 40°C

y = -0.078x + 7.586 R! = 0.950

y = -0.084x + 7.878 R! = 0.982

y = -0.062x + 5.608 R! = 0.969

y = -0.061x + 5.485 R! = 0.994

-1.0

0.0

1.0

2.0

3.0

4.0

50 60 70 80 90 100

log a c

,28

Moisture loss (%)

M3B2C Curing at 40°C

M3B2C Curing at 20°C

M3B1C Curing at 40°C

M3B1C Curing at 20°C

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(a)

(b)

Figure 9. Phase angle at 20 °C for M3B2C mixtures: (a) curing at 20 °C and (b) curing

at 40 °C.

0.0

5.0

10.0

15.0

20.0

0.01 0.1 1 10 100

Phas

e an

gle

(deg

ree)

Frequency (Hz)

2 % cement - curing at 20°C

28 days 21 days 14 days 7 days 3 days 1 day

0.0

5.0

10.0

15.0

20.0

0.01 0.1 1 10 100

Phas

e an

gle

(deg

ree)

Frequency (Hz)

2 % cement - curing at 40°C

28 days 21 days 14 days 7 days 3 days 1 day

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(a)

(b)

Figure 10. Black curves for M3B2C mixtures: (a) Curing at 20 °C and (b) Curing at

40 °C.

1000

10000

0 5 10 15 20

Stiff

ness

mod

ulus

(MPa

)

Phase angle (degree)

2 % cement - curing at 20°C

28 days 21 days 14 days 7 days 3 days 1 day

1000

10000

0 5 10 15 20

Stiff

ness

mod

ulus

(MPa

)

Phase angle (degree)

2 % cement - curing at 40°C

28 days 21 days 14 days 7 days 3 days 1 day

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Figure 11. Schematic representation of loading frequency and curing time effects on E* components: increase in loading frequency (F); increase in curing time (C); non linearity effect (N).

Stiff

ness

mod

ulus

Phase angle

Effect of loading frequency

Effect of curing time

F

C

N

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(a)

(b)

Figure 12. Stiffness modulus E0 after 28 days of curing at 20 °C: (a) M3B1C mixtures; (b) M3B2C mixtures.

100

1000

10000

0.01 0.1 1 10 100

Stiff

ness

mod

ulus

(MPa

)

Frequency (Hz)

1 % cement

5 °C

20 °C

35 °C

50°C

100

1000

10000

0.01 0.1 1 10 100

Stiff

ness

mod

ulus

(MPa

)

Frequency (Hz)

2 % cement

5 °C

20 °C

35 °C

50°C

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Figure 13. Stiffness modulus master curves (curing for 28 days at 20°C), reference

temperature T0 = 20 °C

Figure 14. Temperature shift factors.

100

1000

10000

100000

1.0E-06 1.0E-04 1.0E-02 1.0E+00 1.0E+02 1.0E+04

Stiff

ness

mod

ulus

(M

Pa)

Temperature-reduced frequency (Hz)

M3B2C

M3B1C

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(a)

(b)

Figure 15. Black curves for mixtures cured for 28 days at 20 °C:(a) M3B1C mixtures; (b) M3B2C mixtures. (Eg values estimated using equation (4))

Eg = 10307

300

3000

30000

0 5 10 15 20

Stiff

ness

mod

ulus

(MPa

)

Phase angle (degree)

1 % cement

5 °C

20 °C

35 °C

50 °C

Eg = 14270

300

3000

30000

0 5 10 15 20

Stiff

ness

mod

ulus

(MPa

)

Phase angle (degree)

2 % cement

5 °C 20 °C 35 °C 50 °C

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Figure 16. Iso-thermal E* Black curves obtained from cement-bound mixtures containing 3 % cement: without RAP (3C-00RA); 50 % RAP (3C-50RA) and 80 % RAP (3c-80RA) (from Grilli et al. 2013a).

Figure 17. Analysis of E* Black curves for the studied mixtures: increase in loading frequency (F’ and F’’); increase in temperature (T’ and T’’).

To that hand, measured values of complex modulus norm |E*| and phase angle ! of the studied mixtures are reported in Figure 4 (Black Diagram). As it can be noticed, low values of ! (0° ÷ 6°) were obtained for CTM with no RA, which can be related to the viscous properties of the cement paste (Sun et al., 2006).

As expected, CTMs containing RA showed higher phase angles (up to 10°) on increasing RA content, highlighting the influence of the bitumen component on time-dependent behaviour. However, since a unique curve was not obtained from measurements at different temperatures, the validity of the TTSP for the complex modulus E* was not proved.

Figure 4. Black diagram of CTMs

Even if the tested CTMs were not strictly thermo-rheologically simple materials,

for practical uses it is possible to apply the partial time-temperature superposition (Olard et al., 2002) and represent only the complex modulus norm as a function of frequency or temperature. As shown in Figure 5, measured |E*| versus frequency can be shifted along the frequency axis to build a single master curve at the reference temperature of 20 °C. The master curve can be mathematically modelled by a 4-parameter sigmoidal function:

!"# !!!! ! ! ! !! ! !!!! !"#!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

where !!!! !!and ! are material parameters representing the rheological behaviour and fr is the reduced frequency defined as follows:

!! ! ! ! !! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

3.0E+03

3.0E+04

0 2 4 6 8 10 12

|E*|

[MPa

]

! [°]

T = 10°CT = 20°CT = 30°C3C-00RA

3C-50RA

3C-80RA

Stiff

ness

mod

ulus

Phase angle

Effect of loading frequency

Effect of loading temperature

F'

T'

F'' ! T''

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Table 1. Main physical properties of the used aggregates.

Material Particle density (Mg/m3)

Water absorption at 24 h (%)

32 RA 0/12 2.50 0.5 12/20 (coarse) 2.69 0.9 6/12 (coarse) 2.69 1.0 0/4 (fine) 2.73 1.8

Table 2. Properties of bituminous emulsion and residual bitumen.

Emulsion Property Test procedure Value Polarity EN 1430 Positive Water content EN 1428 40 % pH EN 12850 3 Breaking value EN 13075-1 180 Settling tendency at 7 days EN 12847 8 % Mixing stability with cement EN 12848 2 g Residual binder property Penetration EN 1426 70 # 10-1 mm Softening point EN 1427 50 °C Fraass breaking point EN 12593 -10 °C

Table 3. Complex modulus testing program

Curing effect Temperature effect

Material codes M3B1C, M3B2C M3B1C, M3B2C

Curing temperatures (°C) 20, 40 20

Curing time (days) 1, 3, 7, 14, 21, 28 28

Testing temperatures (°C) 20 5, 20, 35, 50

Testing frequencies (Hz) 0.1, 0.3, 1, 3, 10, 20 0.1, 0.3, 1, 3, 10, 20

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Table 4. Shape parameters of the stiffness modulus curing master curve at 20 °C

(reference curing time tc,R = 28 days).

Mixture code Curing Temperature (°C)

" # $ % R2

M3B1C 20 2.875 1.201 -0.639 -0.459 0.999 M3B1C 40 2.880 1.115 -0.691 -0.513 0.999 M3B2C 20 2.984 1.031 -0.784 -0.534 0.999 M3B2C 40 2.659 1.405 -0.772 -0.377 0.999

Table 5. Shape parameters of the stiffness modulus master curve after 28 days of curing,

(reference temperature: T0 = 20 °C).

Mixture code Curing Temperature (°C)

" # $ % R2

M3B1C 20 2.652 1.360 -1.066 -0.472 0.999 M3B2C 20 2.498 1.656 -0.943 -0.380 0.999