The Characterisation of Fracture Resistance of Asphalt Mixtures Containing Rubber Modifiers and a Wax-Based Additive

Asphalt mixture modifcation with rubberised material frequently results in improved characteristics and extended service life in actual application. Tis research characterised the synergistic consequences of rubber modifers (crumb rubber powder (CRP) and natural rubber latex (NRL)) and wax-based admixtures (Tough Fix Hyper (TFH)) on the performance of the asphalt mixture from the fracture energy and laboratory fracture resistance perspectives. Semicircular bending (SCB) and indirect tensile strength (ITS) tests were conducted to assess the fracture properties of the asphalt mixture samples. To prepare asphalt mixture samples, the wet method was utilised. Higher CRP levels resulted in greater strength and a longer time to attain peak force for both control and mixtures containing wax admixture, as determined by SCB. Te interaction between the higher CRP or NRL content and the TFH additive enhanced the fracture resistance, indicating that the components are highly compatible. Te 10L +TFH additive produced the highest fraction of energy, indicating a more signifcant improvement than the counterpart mixes containing the CRP modifer. In addition, incorporation of the CRP and NRL increased the fracture plastic zone (FPZ), resulting in increased fracture toughness. Terefore, the gradient of fracture toughness and fracture energy in the asphalt mix depends on the rubber type, content, and TFH. Although the higher CRP, NRL, and TFH improve the fracture energy and cracking resistance, they increase the crack initiation and propagation velocities, whereby the high bitumen stifness makes the mixture more brittle than the control mixture. Caution should be exercised when selecting the content of rubber modifer and TFH for the asphalt pavements in low-temperature service. Also, there is a direct interconnection between fracture resistance and fracture energy in the mixtures containing CRP, NRL, and TFH. Such correlations can be used as the premise of predictive micro-and macro-models to evaluate mixture performance in terms of fracture resistance.


Introduction
Previous research has shown that the implementation of recycled crumb rubber and natural rubber latex biopolymer as asphalt modifers improves the performance of road surfacing materials [1][2][3][4].Rubber-modifed asphalt mixture has superior resistance to rutting, thermal cracking, fatigue damage, and stripping and lower temperature sensitivity [5][6][7].Compared to the conventional asphalt binder, using natural or synthetic polymers has signifcantly enhanced the binder properties [8,9].By enhancing the serviceability of the pavement, this approach has benefted the paving industry and provided forgiving road conditions for road users.
Te fracture distress of asphalt mixtures is an important factor in determining the serviceability of fexible pavements.Te fracture decreases the pavement's functional performance, eventually leading to structural failures.Subsequently, further costs for maintenance and rehabilitation would be incurred [10].Terefore, the analysis of fracture is important to characterise the failure mechanism of the pavement over its life span and to develop models for pavement management services [11][12][13].
If the fexural and shear stress/strain exceeds the resistance of the mixture components, cracking is inevitable in three modes at the crack tip as shown in Figure 1 [14].Te xaxis is perpendicular to the crack front, the y-axis being aligned to the crack plane, and the z-axis being aligned to the crack front.Te fundamental modes of three modes of cracking can be visualised in Figure 2. In the Mode I opening phase, tensile stress/strain results in cracking in the asphalt mixture's matrix.In Mode II, the shear stress fows through the weakened parts of the mix components, which are asphalt and mortar, during the sliding phase.In comparison, a fracture faces coarse aggregate particles in the fow track and the direction of the shear fow changes.In other words, shear stress fows to align with the crack plane and is perpendicular to the crack front.In Mode III, the crack propagation occurs in all three dimensions, as in the tearing phase.In other words, shear stress fows to align with the plane of the fracture and crack front.In Mode III, strain fow and shear stress pass through the weakened zone of an asphalt mixture matrix, similar to Mode II [14,15].Te weakened zones comprise a flm of asphalt binder, mortar, and aggregate particles that are not fully coated by asphalt binder.
To characterise and analyse the fracture in the asphalt mixtures, diferent methodologies, procedures, and apparatuses were developed.Tere are also numerous crack propagation micro-and macro-models with various inputs.For example, a laboratory and in-situ research at the University of Florida led to a viscoelastic cracking mechanicsbased model based on resting duration, microdamage, dispersion of the crack, and healing for stated loading situations and temperatures [16].In another laboratory research, Wei et al. [17] analysed the trend of cracking using an image-based numerical approach and acoustic emission.According to the model results, the crack begins as a weakened zone at the aggregate-mortar interface and then disperses slowly parallel to the surface [18].However, He et al. reported that about 10-15% of the fracture surface of the crack propagation passes, owing to the shattering of the densely packed aggregate particles.Tis range changes based on the failure mode.For example, Modes II and III have lower percentage drops in loading conditions and elevated testing temperatures.Compared to brittle and isotropic construction materials, asphalt mixtures with coarser aggregate gradation in the ligament exhibit a fracture pattern with signifcant variation at the midrange temperature [19].
Fracture toughness (K IC ) is one of the variables for analysing failure mechanisms; it is the material's resistance to crack propagation [18,20,21].Various experimental procedures existed to estimate the K IC of asphalt mixtures as follows: (i) Edge cracked rectangular beam loaded with threeor four-point bending [20,[22][23][24]  splitting fxture [35] (viii) Indirect diametral test [36] Generally, K IC is determined by temperature, loading rate, material, features, and sample geometry [37][38][39].Regardless of the test protocols and analytical methods, using diferent materials and building technologies may afect K IC [40].For example, Sabahfar et al. [41] evaluated the potential of cracking in the asphalt mixtures that accommodate 20% to 40% reclaimed asphalt pavement (RAP) supplied from diferent sources using simplifed viscoelastic continuum damage (S-VECD) tests, semicircular bending (SCB), dynamic modulus, and Texas overlay.Compared to other approaches, the S-VECD method produced more sensitive responses to changes in RAP content and characteristics.Furthermore, research conducted by Zarei et al. [42] showed that pure Modes I and II can characterise warm-mix asphalt (WMA) fractures.In addition, based on the observation, the distribution of coarse aggregate particles in the specimen's ligament section contributes signifcantly to the fracture property of the WMA mixture.It should be noted that the reduced stifness of the mixture results in improved fracture resistance.For instance, Kavussi and Motevalizadeh [43] found that the foam-WMA mixtures with a lower RAP content (up to 50%) have a higher resistance to fracture propagation, which is consistent with the results outlined by Yousef et al. [44].
Despite the fact that numerous studies on the fracture performance of various types of mixtures have been conducted, there is a scarcity of sound research focusing on the characterization of the interaction between materials and technology used in the production of asphalt mixes on 2 Advances in Materials Science and Engineering fracture performance.To fll a knowledge gap, this research investigates the interrelationship between rubber modifers and surfactant technology on mixture cracking performance using various test procedures.In addition, the test's purpose was to determine the efect of varying modifer concentrations on the cracking performance of asphalt mixtures.1.

Asphalt Binder.
As the base binder, a 60/70 penetration grade binder was utilised.Table 2 summarises the asphalt binder's properties.

Crumb Rubber Powder.
Te origin of crumb rubber powder (CRP) was basically produced from scrap tires.Te acquired CRP was sieved to determine the distribution of particle size.Table 3 shows the CRP gradation.In order to retain the reliability and quality of the CRP, a single batch of the crumb rubber powder produced by a local supplier was used throughout this research.
Te existing crystalline phase and mineralogical composition of the CRP were determined using X-ray difraction (XRD) test.Table 4 presents the XRD result.
2.1.4.Natural Rubber Latex.Te natural rubber latex (NRL) obtained from a local vendor was used for this research.Basically, rubber hydrocarbon and nonrubber material are the two primary components of NRL.It has distinct chemical and physical characteristics that are considerably afected by the presence of the nonrubber constituent.Te physical and chemical properties of NRL must be maintained to certify the quality of the latex used for asphalt binder modifcation.Table 5 summarises the NRL properties.

Wax-Based Additive.
In this research, a wax-based additive was utilised to improve the bonding characteristics in the rubberised asphalt mixture.Te dosage of additive used in this research is 0.15% by the mass of the asphalt binder.Te properties of wax-based additive are summarised in Table 6.
2.1.6.Modifed Asphalt Binders.Prior to the preparation of the mixture samples, the CRP-and NRL-modifed asphalt binders with 0.15% TFH by mass of bitumen were blended in batches.Te CRP and NRL of 5% and 10% were used for modifcation purposes.Te asphalt binder was preheated in an oven at 160 °C for two hours, and a thermo-cell monitored the exact temperature during the blending process.A propeller mixer was used for the blending process, and the Advances in Materials Science and Engineering modifers asphalt binder was blended for 30 minutes.Te sample designation and types of asphalt mixtures assessed are summarised in Table 7. Figure 3 shows the physical appearance of modifers and additives used in this research.

Fracture Behaviour Assessment via Semicircular
Bending (SCB) Test.Te SCB test was used to examine the fracture properties of the asphalt mixture following AASHTO TP105.Te specimen is prepared with a 15 mm notch depth and in the form of a half-disc.Formerly, the specimens were compacted to a thickness of 50 mm and a diameter of 150 mm.Before the SCB test, the specimens were preconditioned at 10 °C for 4 hours.Te maximum loading achieved and the deformation of the specimens were monitored.Tis test method evaluates the fracture energy (G f ) of the asphalt mixtures.Besides, this approach includes the procedures for calculating K IC and stifness (S).In addition, new fracture initiation and crack development rate parameters based on previous studies were also assessed.All the stated parameters above can be calculated using Equations ( 1) to ( 8).
(1) Calculation of fracture energy Fracture Energy, where G f � the fracture energy (J/m 2 ); W f � the work of fracture (J), where W f is Pdu; P � the applied load (N); u � the average load line displacement (m); Alig � the ligament area (m 2 ), where A lig is (r − a) × t; r � the specimen radius (m); a � the notch length (m); and t � the specimen thickness (m) Te total work of fracture is then calculated as the sum of W and W tail : where P i � the applied load (N) at the i load step application; P i+1 � the applied load (N) at the i+1 load step application; u i � the average LLD load line displacement (m) at the i step; and u i+1 � the average LLD load line displacement (m) at the i + 1 step:  Advances in Materials Science and Engineering where u � the integration variable equals to average load line displacement (m) and u c � the average load line displacement value at which the test stops (m).( 2) Calculation of fracture toughness At the critical load, P c , the fracture toughness, K IC , is obtained from the stress intensity factor, K I .It is presumed that the maximum load measured during testing represents the critical load.Te stress intensity factor, K I , is calculated using the following equation: where σ 0 � P/2rt; P � the applied load (MN); r � the specimen radius (m); t � the specimen thickness (m); a � the notch length (m); and Y I � the normalised stress intensity factor (dimensionless).
For the dimensionless SCB specimens used in this test method, Y I is calculated using the following equation: Y I(0.8) � 4.782 + 1.219 a r   + 0.063e (7.045(a/r)) . ( (3) Calculation of stifness Te stifness S is computed using the slope of the linear component of the ascending load-average load line displacement curve.(4) Calculation of fracture initiation velocity where V FI � the velocity of fracture initiation (J/m values can be used to evaluate the relative quality of asphalt mixtures and their resistance to rutting or cracking.A high tensile strain of a specimen at failure signifes that it can endure a higher strain before failing and is more resistant to cracking.Conforming to ASTM D693, the ITS test was conducted, and the specimens were stored at 15 °C for four hours before testing.Te ITS values of the specimens were calculated and analysed using equation ( 9): where P max � the maximum applied load in N; t � the height of specimen in mm; and d � the diameter of specimen in mm.

Fracture Resistance via Semicircular Bend (SCB)
Geometry.Only the Mode I loading condition has been adopted for assessment in this research.As a consequence of thermal stresses, the Mode I loading condition belongs to tension (bending).After the loading period, all the asphalt mixture samples were subjected to a validation test to ensure that crack propagation occurs within 10% of the specimen's diameter from the loading strip's centre.Figure 4 shows the validation test.Te 3D surface plots shown in Figures 5(a)-5(d) were used to investigate the correlation between a response variable (force) and two predictor variables (modifer content and time taken to reach peak load).Te plot shows the impact of modifer concentration on the force and time required to reach peak load.Te force presented in these 3D surface plots corresponds to the peak load obtained directly from the load versus displacement curve.From the 3D surface plot, the modifed asphalt mixture can sustain a more signifcant load, so it takes longer to achieve peak load before 6 Advances in Materials Science and Engineering failing.Also, this shows that the respective modifed asphalt mixture sample could sustain the applied load for an extended time before reaching its maximum load and failing.Te peak of each 3D surface plot reveals the best performance of the asphalt mixture.All the modifed asphalt mixtures, including those containing 10% rubber modifers, achieved the highest position on the 3D surface plot compared to the control asphalt mixture.Te incorporation of TFH and higher percentages of rubber modifers enhanced the performance of the asphalt mixture by achieving a higher load.Te higher force and longer duration ascribed to the higher modifer content reveal that the sample shows a sign of better fracture resistance in comparison to an asphalt mixture prepared without modifers and TFH.Even though all the results have a similar trend, the maximum force obtained from the load against the displacement curve needs to be more persuasive to be used as an indicator of fracture resistance because the calculated maximum force does not account for the geometry of asphalt mixtures.Advances in Materials Science and Engineering

Fracture Energy of Asphalt Mixtures (G f ).
Instead of utilising the force computed directly from the loaddisplacement curve, the asphalt mixture fracture properties are easily explained by the fracture energy (G f ) approach through linear elastic fracture mechanics (LEFM).To calculate the fracture energy using the LEFM method, it is necessary to account for the area below the curve of the loaddisplacement graph.Fracture energy signifes the external energy needed for a crack to evolve.Te fracture energy is used as a metric to distinguish asphalt mixtures with improved crack It is also the fundamental metric employed in more sophisticated investigations involving the fctitious fracture (cohesive zone).Figure 6 illustrates the fracture energies of every asphalt mixture.
Figure 6 demonstrates that the modifed CRP-and NRLbased asphalt mixture exhibited higher fracture energy.Higher fracture energy requires more energy to generate a crack surface area.Higher fracture energy is observed in an asphalt mixture prepared with a stifer asphalt binder.Te fracture energy of the control asphalt mixture is observed at the lowest value of 788.73 J/m 2 , indicating that the fracture resistance is very low during the crack propagation phase due to the softer asphalt binder.Te fundamental principle of the fracture mechanism is that cracking occurs only in the area of the crack tip (notch tip) if the energy accumulated exceeds the fracture energy.Te addition of TFH and the higher content of rubber modifers resulted in a higher fracture energy value.As can be seen, the 10L + TFH has the best resistance against fracture, with the highest fracture energy of 2939.95J/m 2 , which is 3.75 times greater than the control mixture (CB).Figure 6 also depicts the efect of CRP or NRL content on the G f .For example, the G f of a mixture containing 10L + TFH is 750 J/m 2 , which is higher than the G f of a mixture containing 5L + TFH, indicating that more than 5% NRL resulted in an extra 750 J/m 2 in G f .Another example is that the mixture containing 5% CRP and TFH (5CR + TFH) has 200 J/m 2 G f less than the counterpart mix containing 10% CRP.In other words, an extra 5% of NRL resulted in 750 J/m 2 , while the extra 5% of CRP led to 200 J/ m 2 , indicating that the NRL outperforms CRP in increasing G f .As a result of this interaction, higher percentages of NRL and TFH can result in a higher G f compared to CRP and TFH.

Fracture Toughness (KIC) of Asphalt Mixtures.
Figure 7 indicates various asphalt mixtures with their respective fracture toughness (K IC ).Te fracture toughness of asphalt mixtures with enhanced cracking resistance was also used as an index factor.Fracture toughness can be referred to as the stress intensity factor.It is highly dependent on the asphalt mixture geometry.Te stress intensity factor will reach its maximum value and cause crack propagation, causing failure to initiate at the notch tip.Te asphalt mixture's fracture toughness can be calculated using the LEFM-developed equation.As expected, fracture toughness has a similar trend to fracture energy.Te properties of the asphalt mix incorporated with the modifed asphalt binders have improved its fracture toughness.Te reduced fracture toughness of an asphalt mixture results in crack propagation being perpendicular to the substantial tensile stress in the applied load direction.Te fracture toughness increases when a higher concentration of rubber modifers and TFH is applied.Te control asphalt mixture demonstrated more brittle behaviour with a low fracture toughness value.Tis verifes that the addition of rubber modifers and TFH improves the cracking resistance at low temperatures.
According to LEFM, crack initiation begins with the fracture plastic zone (FPZ) in the region of the weak zone (notch tip), which is mainly caused by plastic deformation in the material [45].Te FPZ for an elastic material is typically microscale and has a minor impact on the process of fracture analysis.However, the LEFM is used in this case because the asphalt mixture behaves as a quasi-brittle viscoelastic material and the higher magnitude of FPZ causes the fracture process [46].Enhanced fracture toughness can reduce the occurrence of strain hardening, microcrack growth, and high scale yielding near the crack tip (notch tip) in order to resist cracking.Te viscosity of the CRP-and NRL-modifed asphalt mixtures is higher, resulting in a greater FPZ at the notch tip.Tis process contributes to a stress-relieving phenomenon.Te higher FPZ helps in managing efective stress at the notch tip by viscoelastic stress relaxation and consequently exhibits superior fracture resistance [46].A higher FPZ results in higher fracture energy to maintain continuous crack development activity, whereas the control asphalt mixture's viscosity is constrained to create a higher FPZ.Terefore, the control asphalt mixture has a very low fracture toughness value (0.394 MPa × m 0.5 ).

Stifness of Asphalt Mixtures.
Te asphalt mixture's stifness (S) is presented in Figure 8.Using the gradient at the linear portion of the increasing load-displacement curve, the asphalt mixture's stifness is calculated.Te stifness demonstrated a correlation with the elastic modulus of the asphalt mixture at lowered temperatures.As it is strongly related to pavement distress, such as fatigue and low-temperature cracking, the elastic modulus is a crucial design parameter for pavement structures.Te elastic modulus of an asphalt mixture is not a measure of its strength but rather its behaviour.
Fundamentally, temperature changes signifcantly impact the elastic modulus of the asphalt mixture.However, in this case, various types of asphalt mixtures would be evaluated at the same temperature.According to the fndings, adding rubber modifers and TFH signifcantly improved the elastic modulus of the asphalt mixture.Tis fnding is consistent with the rheological properties of asphalt binder (complex shear modulus, phase angle, and viscosity), which are rapidly changed by rubber modifers and the additive.Te addition of TFH results in a slight decrease in stifness in the CB + TFH and 10L + TFH samples.However, the general trend shows that the modifcation process improved the stifness of all asphalt mixtures, and the stifness values are comparable with no signifcant diferences.However, the maximum stifness values for the NRL-modifed asphalt mixtures without and with TFH were 4. 57   Advances in Materials Science and Engineering A higher elastic modulus implies that the asphalt mixture is resistant to elastic deformation under force application, indicating the viscoelastic behaviour of rubber-modifed asphalt binder.As expected, the control asphalt mixture exhibited the lowest stifness with 3.52 kN/mm and 3.48 kN/ mm, without and with TFH, respectively.It must be noted that the elastic range of the asphalt mixture is obtained from the ascending linear part of the load-displacement curve.In this curve region, if the asphalt mixture sample is loaded with any force, it will return to its previous shape and no crack will form.However, once the asphalt mixture reaches the limit of its elastic range, cracks will begin to develop, indicating that it has reached its failure stage.Terefore, the rubber-modifed asphalt mixture demonstrated higher loading resistance without immediate cracking and exhibited higher fatigue and low-temperature cracking resistance compared to the control asphalt mixture.8 show the fracture initiation and crack growth velocities.Several parameters, such as the fracture behaviour of the asphalt mixture, have been previously discussed.Numerous studies have proposed alternative methods for assessing cracking behaviour, such as fracture initiation and crack growth velocity [37].Te velocity of fracture initiation (V FI ) is the rate at which a crack initiates upon reaching its failure limit.While the velocity of crack growth (V CG ) refers to the velocity of the crack after its initiation, the crack growth velocity is obtained from the linear gradient of the descending part of the load-displacement curve.Te steeper slope would result in a higher velocity value.Te outcome indicates that the asphalt mixture prepared with a modifed asphalt binder (stifer asphalt binder) has higher V FI and V CG compared to the asphalt mixture prepared using a control asphalt binder (softer asphalt binder).Despite the fact that there is a slight decrease in V FI and V CG in some instances, the general trend indicates that the increment in rubber modifer percentages and the addition of TFH result in increased V FI and V CG .

Velocity of Fracture Initiation (VFI) and Crack Growth (VCG) of Asphalt Mixtures. Te results tabulated in Table
Compared to the CRP-modifed asphalt mixture, the NRL-modifed asphalt mixture has the highest V FI and V CG .Yet, both the NRL-and CRP-modifed asphalt mixtures outperform the control asphalt mixture.Tese results may contradict other parameters, such as fracture energy, fracture toughness, and stifness, which show that asphalt mixtures made with modifed asphalt binders have superior fracture resistance.Te higher the stifness of the modifed asphalt binder in nature, the greater the brittleness at low temperatures.Terefore, the increased V FI and V CG are associated with the brittleness of modifed asphalt binder due to the low temperature.It can be concluded that higher energy is needed to initiate a crack in the modifed asphalt mixture; nevertheless, once the threshold of load-bearing is exceeded, the fracture initiation and crack growth velocity are rapid due to the brittleness of the material.Tis is due to the elastic energy stored in the specimen during the loading phase, and the rubber-modifed asphalt mastic exhibits a ductile failure [47].

Analysis of Variance of the SCB Test Results.
Statistical analysis was conducted to validate the obtained results of fracture energy and verify the contribution of the CRP modifer, the NRL modifer, and the TFH additive towards the fracture properties of the asphalt mixture.Te efect of diferent factors on the fracture energy of asphalt mixtures was evaluated by conducting an ANOVA and using the general linear model.Te results are shown in Table 9. Te efect of the selected factors on the fracture behaviour of the asphalt mixture is considered signifcant if the P-value is <0.05.In addition to evaluating each individual factor, the interaction between the modifer and TFH was also evaluated.
Referring to the variance analysis, it can be summarised that all of the listed factors are statistically signifcant and contributed to the fracture energy, as their P values are below 0.05.However, the interaction factor between rubber modifers and TFH does not signifcantly change the asphalt mixture's fracture properties.It is concluded that diferent modifer contents and types, as well as the addition of TFH, increased the crack resistance of the asphalt mixtures.Te percentage of contributions is based on the estimates of the variance components, refecting the degree of efect on the crack resistance properties.Terefore, as shown in Table 9, 52.08% of the total variation in the measurements is due to the NRL content.It is evident from the results that the inclusion of the NRL modifer at various percentages signifcantly enhanced the crack resistance properties.Te percentages of contribution for CRP contents and the wax-based additive are 9.10% and 17.91%, respectively.Te contribution due to the interaction between modifer content and TFH can be assumed to be less signifcant.Figure 9 shows the normal plots of residuals.Te normal probability plot of residuals is used to verify that residuals have a normal distribution.Te general linear model can evaluate the impact of various factors on the response of results based on the normal distribution of residuals along the ftting line.Te indirect tensile strength (ITS) test was conducted to determine the tensile properties of the asphalt mixtures based on the cracking characteristics of pavement.Te ITS test is widely used to characterise the internal resistance of compacted asphalt mixtures.As one of the input factors in the asphalt pavement transverse cracking model utilised in the Pavement Mechanistic-Empirical (ME) Design Guide, the ITS test is a widely acknowledged test method [48].Figure 10 shows the individual value plot of the asphalt mixture's tensile strength.All the asphalt mixtures were tested at 15 °C to measure the strength and stifness of the entire asphalt mixture rather than the strength of the asphalt binder itself.At a higher temperature, such as 25 °C, the testing will only induce stress on the layer of asphalt binder within the restrained asphalt mixture specimens rather than on the aggregates and asphalt binder.Figure 10 shows that the black circular point on each asphalt mixture type refects the associated mean tensile strength value.Incorporating CRP and NRL modifers in asphalt mixtures improves their tensile strength substantially.Te mixture's volume increases when rubber modifers are added to asphalt mixtures of all varieties.Te tensile strength of the CRP-modifed asphalt mixture increased by 17.32% and 32.40%, respectively, with the addition of 5% and 10% modifers.Te NRL-modifed asphalt mixture increased by 17.88% with the 5% modifer and 30.17% with the 10% modifer.
Due to the higher tensile strength observed with the incorporation of TFH, it can be deduced that TFH facilitates enhancing the tensile strength of asphalt mixtures in this research.Te addition of TFH into the control asphalt binder improved the tensile strength from 1.79 MPa to 1.99 MPa.In comparison, the CRP-modifed asphalt mixture increased from 2.10 MPa to 2.26 MPa and from 2.37 MPa to 2.60 MPa for 5% and 10% modifer content, respectively.NRL-modifed asphalt mixture with 5% modifer content rose from 2.11 MPa to 2.25 MPa and from 2.33 MPa to 2.52 MPa for 10% modifed content with the incorporation of TFH.In addition, the increased indirect tensile strength suggests that the improved asphalt mixtures can withstand substantially bigger tensile strains before cracking or failing.Typically, asphalt mixtures with a low tensile strength are expected to break more than those with higher tensile strength.However, previous research has demonstrated that air voids in asphalt mixture, the aging process, moisture damage, and the freeze-thaw process also signifcantly infuence the tensile strength of asphalt mixture and its service life [49].
Te ITS of modifed asphalt mixtures increases due to improved asphalt binder-aggregate adhesion, which enhances the toughness.Polymer efciency on the ITS properties of asphalt mixtures is dependent on the asphalt source, polymer type, and polymer content [50][51][52].In this case, the polymer type and polymer content are important in  Advances in Materials Science and Engineering determining the tensile strength of the asphalt mixture.In comparison to plastomers, elastomers have a loosely crosslinked structure, which is responsible for their high tensile strength during chain stretching to a great extent [53,54].Terefore, the use of elastomer facilitated the improvement of the tensile strength of the asphalt mixture, and the addition of polymer content improved the tensile properties.
In addition to the infuence of elastomers on tensile strength, the increased viscosity of the modifed asphalt mixes contributed to the rise in indirect tensile strength.Te increased viscosity is a result of the addition of rubber modifers.Physical asphalt mixture hardening refects an increase in stifness.Also, the incorporation of TFH increased the asphalt binder's viscosity.Te crystallisation of TFH wax was the additional element responsible for the physical hardening of the asphalt mixtures, which boosted their indirect tensile strength.
Teoretically, the rubber-modifed asphalt binder experiences a glass transition state due to the changes in its mechanical, optical, and thermodynamic properties [55].At this stage, the asphalt binder stifens or hardens, which contributes to the asphalt mixture's strength.Te time-and temperature-dependent viscoelastic behaviour of rubbermodifed asphalt binders usually includes all four regions, namely, glassy, transition, plateau, and fow [56,57].Te plateau is only possible if the asphalt binder has a polymeric network.However, the unmodifed asphalt binder does not exhibit rubber-like behaviour, and their transition occurs directly from the glassy region to the fow region, with no glass transition stage or plateau region [58][59][60].Tis might be the source of the control asphalt mixture's insufcient strength compared to the modifed asphalt mixtures.Te concept of the glass transition stage is applicable in this case, as it is widely used to research the rheological properties of the asphalt binder at below room temperature, which is the temperature adopted in this test.In conclusion, the addition of elastomer improves the resistance to cracking by enhancing the asphalt mixture's rheological and mechanical properties, especially its tensile strength.

Analysis of Variance of the Indirect Tensile Strength Test
Results.Te asphalt mixture's tensile strength increased due to the infuence of modifer content and TFH, as measured by indirect tensile strength.Terefore, statistical analysis was carried out to determine the signifcance of the CRP modifer, NRL modifer, and TFH additives on the asphalt mixtures' performance.ANOVA was employed to formulate the efect of various factors on the indirect tensile strength of asphalt mixtures.Table 10 summarises the results of the analysis of variance using the general linear model.Te efect of various factors on the stifness properties of an asphalt mixture is considered signifcant if the P value is <0.05.In addition to evaluating the individual components, the efect of interaction between the modifer and the TFH additive was also evaluated.
As the P values were less than 0.05, the analysis of variance demonstrated that all individual factors were statistically signifcant and contributed to the tensile strength of asphalt mixtures.However, the interaction factors had no signifcant efect on the performance.Te P values of the interaction factors were higher than 0.05.Te percentage of contribution is based on the estimates of the variance components, indicating the degree of infuence on the tensile strength properties.Terefore, as shown in Table 10, the NRL content accounted for 46.10% of the total variation in the measurements.Te results showed that the addition of the NRL modifer at various percentages substantially increased the tensile strength properties compared to modifed asphalt mixtures with CRP.Te percentages of contribution     for CRP content and TFH are 26.37% and 13.68%, respectively.Owing to the low contribution percentages of 0.24% and 0.20% for the CRP and NRL modifers, respectively, the contribution due to the interaction between modifer content and TFH can be anticipated to be less signifcant.Figure 11 shows the normal plots of residuals.Te normal probability plot of residuals refects that the residuals have a normal distribution.Te general linear model estimates the efects of various factors on the response of results based on the normal distribution of residuals.A normal probability plot of the residuals should follow a straight line.

Correlations between ITS and Fracture Energy of Asphalt
Mixtures.Tis analysis shows a signifcant correlation between the ITS of the asphalt mixture and the asphalt mixture's fracture energy as determined by the SCB test.Te ITS of asphalt mixture is commonly used to evaluate the potential cracking in compacted asphalt mixture.Meanwhile, the fracture energy represents the asphalt mixture's resistance to fracture.Te ITS and fracture energy are interconnected with each other to secure good mechanical performance.
Figures 12(a)-12(d) show the 3D surface plot of the correlation.Te analysis showed that ITS was directly proportional to the asphalt mixture's fracture energy, indicating a strong correlation relationship.Te asphalt mixture's fracture energy increases as the ITS increases, which is attributed to the presence of rubber modifers and a TFH additive.A higher ITS signifes that the asphalt mixture is resistant to cracking, and therefore, has greater fracture energy.Regardless of the presence of TFH, all types of asphalt mixture demonstrated similar attributes and tendencies.Te correlation between the results of the ITS test and those of the SCB test indicated that the SCB test's fndings are plausible.

Conclusions
Te synergistic outcomes of adding CRP, NRL, and synthetic wax to the asphalt mixtures' fracture energy and fracture resistance characteristics were evaluated based on SCB and ITS tests.Te 3D plots clearly showed that the higher CRP and NRL improved cracking resistance.In addition, the fracture energy was improved by 1.75-3.75times, depending on the use of TFH, CRP, and NRL content.Notably, the mixture with 10% NRL and TFH had the highest fracture energy.A similar pattern was discovered for fracture toughness and stifness.
Although higher fracture energy and cracking resistance are positive aspects, they might have an adverse efect on the other aspects.Analysis of V FI and V CG showed that the incorporation of CRP and TFH improved crack propagation speed as a result of the stifness of the binder, which made the mixture more brittle in contrast to the control mix.Statistical analysis through a general linear model showed that the modifer (CRP and NRL) contents signifcantly afect the fracture energy.In addition, the model outputs showed that the percentages of contributions for CRP content and TFH additive in terms of crack resistance property were 9.10% and 17.91%, respectively, while the contribution due to the interaction between modifer content and TFH additive was less signifcant.Furthermore, the fracture energy, fracture toughness, and indirect tensile strength of mixtures containing 5% NRL were comparable with those containing 5% CRP (with or without TFH), while the mixtures containing 10% NRL showed higher fracture energy and stifness than their counterpart mixtures with 10% CRP.As a result, the selection of the rubber type is a critical criterion for the fracture properties of rubbermodifed mixtures.
All modifed binder samples exhibit a direct correlation between the fracture energy determined by the SCB test and the cracking resistance shown by the ITS test.Changes in fracture energy and crack resistance can be attributed to diferent chemical structures and crystallisation processes, material sources, and binder additives.In conclusion, the interaction of CRP or NRL with TFH improves the structural adequacy of asphalt mixtures.However, the appropriate percentage of each material should be selected for better performance.

Figure 1 :
Figure 1: Local coordinate system on a crack tip of fracture asphalt mixture.

Figure 2 :
Figure 2: Tree modes of cracking of asphalt mixture under fexural load: (a) mode I (tensile on x-axis):opening phase, (b) mode II (shear stress align to crack plane on y-axis and 90 °to crack front on x-axis):sliding phase, and (c) mode III (shear stress parallel on crack plane and crack front on y-axis and z-axis):tearing phase.

Figure 3 :
Figure 3: Physical appearance of the modifers and additive used: (a) crumb rubber powder, (b) natural rubber latex, and (c) wax-based additive.

Figure 5 :Figure 4 :
Figure 5: Surface plot of asphalt mixtures on efects of modifer content on the force and duration taken to reach the peak load: (a) CRPmodifed asphalt mixture without TFH, (b) CRP-modifed asphalt mixture with TFH, (c) NRL-modifed asphalt mixture without TFH, and (d) NRL-modifed asphalt mixture with TFH.

Figure 6 :Figure 7 :Figure 8 :
Figure 6: Fracture energy of various asphalt mixtures with percentage diference compared to the control binder.

Figure 9 :
Figure 9: Normal probability plot of residual for fracture energy.

Figure 11 :
Figure 11: Normal probability plot of residual for ITS test.

Table 1 :
Physical properties of granite aggregates.

Table 2 :
Properties of asphalt binder.

Table 4 :
Mineralogy compounds of crumb rubber powder.

Table 6 :
Properties of the TFH wax-based additive.
°C 4Advances in Materials Science and Engineering

Table 7 :
Sample designation and types of asphalt binder.
ΔF � the load decrement (kN) from the peak to the total failure occurrence; and Δt � elapsed time from peak to the end.
2 s); P � the load; G fpeakand0 � the fracture energy at peak and test initiation (J/m 2 ); and t � the elapsed time.(5) Calculation of crack growth velocity 2.2.2.Indirect Tensile Strength Test.In conjunction with laboratory mix design testing, indirect tensile strength (ITS)

Table 8 :
Velocity of fracture initiation and crack growth of various asphalt mixtures.

Table 9 :
ANOVA data of fracture energy.

Table 10 :
ANOVA analysis of indirect tensile strength.