#### 3.1.1. Viscoelastic Properties

The relationship between the applied shear stress amplitude (

${\tau}_{max,0}$) and the corresponding initial value of the norm of the complex shear modulus (

${\left|{G}^{*}\right|}_{0}$) is depicted in

Figure 7. The equation used for calculating the amplitude of the applied shear stress (

${\tau}_{max,0}$) is shown in the following:

The initial value

${\left|{G}^{*}\right|}_{0}$ is assumed as the norm of the complex shear modulus evaluated at the 50th cycle, because at this stage of the test, the double-layered specimen is not damaged yet and, at the same time, the induced stress–strain field can be considered not affected by the initial perturbation (i.e., steady). The results presented in

Figure 7 show that the initial norm of the complex shear modulus (

${\left|{G}^{*}\right|}_{0}$) depends on the applied shear stress amplitude (

${\tau}_{max,0}$), i.e., the interface displays nonlinear viscoelastic behavior within this loading range. In particular, the measured

${\left|{G}^{*}\right|}_{0}$ decreases as the applied shear stress amplitude increases. It can be also observed that the presence of a geogrid at the interface leads to smaller initial values of the norm of the complex shear modulus (

${\left|{G}^{*}\right|}_{0}$). Besides, due to the presence of the asphalt concrete layers,

${\left|{G}^{*}\right|}_{0}$ increases as testing temperature decreases (from 20 to 10 °C) for the FG interface type.

The damage of the specimen was analyzed by using the evolution of the phase angle (

φ) and the normalized norm of complex shear modulus (

${\left|{G}^{*}\right|}_{n}$). The latter is given by the following equation:

where

${\left|{G}^{*}\right|}_{N}$ is the norm of the complex shear modulus calculated at any given number of loading cycles (N).

The results of specimen FG_7 tested with a torque amplitude

${T}_{0}$ = 55 Nm at 10 Hz and 10 °C are presented herein as a typical example. In

Figure 8, the normalized norm of complex shear modulus (

${\left|{G}^{*}\right|}_{n}$) and the phase angle (

φ) are presented as a function of the number of cycles. It is interesting to observe in

Figure 8 that

${\left|{G}^{*}\right|}_{n}$ decreases with the number of cycles, indicating a progressive weakening of the interface properties during the test characterized by a typical three-phase fatigue curve [

51,

52,

58,

59], whereas the phase angle (

φ) increases during the cyclic test and drops suddenly approaching the end of the test. Four phases can be identified for the phase angle curve. The first phase consists of a quick increase in the phase angle; this is attributable to bulk reversible phenomena (e.g., self-heating) that tend to appear during the initial test cycles. The second phase is associated with a quasi-linear increase in the phase angle. In the third phase, irreversible phenomena (e.g., fatigue damage) appear and the phase angle quickly increases until a sudden drop (fourth phase). During the fourth phase, macro-cracks propagate at the interface, generating a not homogeneous distribution of stresses and strains. According to Reese [

54], the maximum point of the phase angle defines the point at which the location of the damage begins.

Figure 9 shows the evolution of the normalized norm of complex shear modulus (

${\left|{G}^{*}\right|}_{n}$) of the FG interface type at various torque amplitudes (

${T}_{0}$) at 10 Hz and 10 °C. It is possible to note that

${\left|{G}^{*}\right|}_{n}$ decreases faster with the number of loading cycles as the applied torque amplitude increases.

Figure 10 shows the evolution of the phase angle (

φ) of the FG interface type at 10 Hz and two testing temperatures (10 and 20 °C). It is possible to note that, for both temperatures,

φ increases faster with the number of loading cycles by applying higher torque amplitude values. Besides, the phase angle values at 20 °C are greater than those at 10 °C because, as expected, asphalt materials are more viscous at higher temperatures. This observation is in agreement with a previous study [

60], and the measured values of the phase angle are also comparable.

After the test, the failure occurred exactly at the interface for all the specimens, i.e., a complete detachment between the two layers of the specimen was observed. In particular, the failure for the FG interface type was on the polyester knitted veil side, denoting that the veil could be an obstacle to bonding the two layers in contact (

Figure 11).

#### 3.1.2. Interlayer Shear Fatigue Curve

The interlayer shear fatigue curves of the tested interface types are shown in a log–log plane from

Figure 12,

Figure 13,

Figure 14 and

Figure 15. A typical power-law model was used to obtain the relationship between the amplitude of the applied shear stress amplitude (

${\tau}_{max,0}$) and the number of cycles to failure (

${N}_{f}$) according to the following equation:

where parameters

a and

b are regression coefficients. In particular,

b represents the slope of the linear regression in a log–log plane.

In each plot, interlayer shear fatigue curves obtained by using the classical fatigue criterion (

${N}_{50}$) were compared to those established by considering more appropriate failure criteria (

${N}_{70}$ and

${N}_{\phi max}$). The corresponding regression coefficients for the power-law model (

a and

b) are also presented in

Table 2, as well as the coefficient of determination (R

^{2}).

Looking at the experimental results, it can be seen that the obtained interlayer shear fatigue curves are very similar by applying the failure criteria

${N}_{70}$ and

${N}_{\phi max}$, whereas in some cases, the

${N}_{50}$ failure criterion is not always in agreement with the previous ones (UN and FG interface types at 20 °C,

Figure 12 and

Figure 14, respectively). As a consequence, the traditional failure criterion (

${N}_{50}$) can probably lead to a misleading ranking, since it is not capable of quantifying the damage mechanisms that occur within the interface. Meanwhile, the maximum phase angle (

${N}_{\phi max}$) and the 70% failure criterion (

${N}_{70}$) can better correlate the number of cycles to failure with the damage process at the interlayer because they are related to a change in the inner behavior of the specimen. For example, once the specimen becomes severely damaged at the interface, the strain response curve in a stress-controlled test varies significantly from an actual sinusoidal function and this distortion is responsible for the drop in phase angle. These results also confirm the effectiveness of the 70% failure criterion already highlighted in a previous study carried out on unreinforced asphalt interlayers [

51]. Thus, considering the weakness of the traditional approach, these results illustrate that the maximum phase angle and the 70% failure criterion provide similar results and can offer an accurate shear fatigue life prediction.

Several interesting findings can be drawn also looking at the results listed in

Table 2. By comparing the fatigue law parameters at 20 °C for the

${N}_{70}$ and

${N}_{\phi max}$ criteria, it is possible to observe that the FG interface shows the lowest and highest values for

a and

b, respectively. In general, coefficients of determination (R

^{2}) are greater than 0.9 for all the interface types, which indicates a very good correlation between measured data and the linear fatigue law. Nevertheless, R

^{2} values increase as the temperature decreases (greater than 0.99) for the FG interface, indicating that the specimen-to-specimen interlayer shear variability increases at higher temperatures. Meanwhile, the parameter

b values decrease as the testing temperature decreases, indicating a clear thermo-dependency for the interlayer shear fatigue properties.

In order to rank the different interface types (UN, CF and FG) and to investigate the influence of testing temperature on the FG interface, interlayer shear fatigue curves are represented in

Figure 16 according to 70% norm of the complex shear modulus reduction criterion (

${N}_{70}$). Since the asphalt mixture and compaction method of the tested specimens are the same, it can be asserted that the resistance to shear fatigue damage is only a function of the interface type.

Figure 16 shows that UN and CF interfaces provide very similar results in term of interlayer shear fatigue life, although it appears that UN interface guarantees slightly higher performance at a lower shear stress level than the CF interface. Moreover, for a given shear stress amplitude, FG reinforced specimens are characterized by a number of cycles to failure considerably lower than unreinforced and CF reinforced specimens (

Figure 16). For example, with

${\tau}_{max,0}$ = 0.15 MPa (i.e.,

${T}_{0}$ = 30 Nm) as input level (orange dotted line in

Figure 16), the FG interface requires less than 30,000 cycles to failure at 20 °C, whereas the other CF reinforced interface undergoes more than 700,000 cycles at the same temperature.

Starting from these results, it is expected that the CF geogrid is able to perform well in the field since the debonding effect highlighted by shear-torque fatigue loading is not so evident compared to the unreinforced interface UN. The fairly good performance of this type of geogrid has already been observed in previous studies by performing static shear tests on specimens reinforced with a similar geogrid [

13,

45]. This could be due to the presence of the pre-coating and the fact that the grid knots are not fixed, which allows the grid structure to move freely during the laying and compaction of the asphalt mixture ensuring the achievement of an optimal interlocking. Besides, the presence of the film applied on the underside of the CF geogrid, which is burned before installation, further improves the bonding properties on the underlying layer. On the contrary, the FG geogrid provides the lowest performance with respect to the other two interface types (UN and CF). This could be due to the presence of the polyester knitted veil and the fixed knots of the FG geogrid (unlike the CF geogrid), which probably hinder the achievement of an optimal bonding and interlocking between the two asphalt layers in contact as already observed in

Figure 11.

As far as the testing temperature is concerned, the FG interface at 10 °C provides higher shear fatigue performance compared to those at 20 °C for the same reinforcement (

Figure 16). This is in accordance with previous investigations carried out with various shear tests in cyclic modality on unreinforced specimens [

34,

39,

61] and in static modality on reinforced specimens [

45], where an improvement of interlayer resistance was measured at low temperatures. Therefore, it can be assumed that as the temperature decreases, since the asphalt concrete is a thermo-dependent material, the interlayer becomes stiffer and more loading cycles of the same stress intensity are needed to cause the failure of the specimen.

To allow a better comparison between the different interface types (UN, CF and FG), it is possible to calculate, from the power-law models reported in

Figure 16, the parameter

${\tau}_{6}$ shown in

Figure 17. The parameter

${\tau}_{6}$ is defined as the shear stress level that leads to a fatigue life of 1 million cycles (

${N}_{f}$ = 10

^{6}) in a cyclic shear test and it is inspired by

${\epsilon}_{6}$, defined as the strain level leading to specimen failure for 1 million cycles, which is used to calculate the admissible strain in asphalt pavement layers in the French pavement design method [

34,

62]. Lower

${\tau}_{6}$ implies lower shear fatigue performance. As shown in

Figure 17, the values of

${\tau}_{6}$ confirm the outcomes previously discussed in

Figure 16, but the comparison of

${\tau}_{6}$ allows to easily rank the different interface types (UN, CF and FG), denoting that it can be a useful parameter to characterize the interlayer bonding in cyclic shear tests.

In synthesis, the obtained results demonstrate that an appropriate choice of the most suitable interlayer reinforcement system could increase the cyclic shear fatigue resistance strictly linked to the debonding effect. Moreover, shear-torque fatigue tests could provide useful guidance for the selection of the most appropriate reinforcement because the results are clearly sensitive to the testing parameters (i.e., type of interface and testing temperature). However, further work is needed to adopt a method for selecting effective torque levels because different reinforcement and/or type of interface experience different levels of sensitivity to changes in stress level. Furthermore, another shortcoming is that shear-torque fatigue tests are highly time-consuming, especially at very low stress–strain levels. On the other hand, the analysis of failure of fatigue curves could help for a better understanding of the experimental results obtained with routine testing protocols such as static (i.e., monotonic) shear tests for the evaluation of the interlayer shear strength (ISS or ${\tau}_{peak}$).