State-of-the-Art Review on Permanent Deformation Characterization of Asphalt Concrete Pavements

Abstract

Rutting is one of the significant distresses in flexible pavements. Examining the methods to decrease permanent deformation is of considerable importance to provide long service life and safe highways. The main objective of this paper is to undertake a state-of-the-art review to combine the existing work on the permanent deformation of asphalt concrete pavements. For this purpose, the review synthesizes the evolution of the permanent deformation models, the tests methods used to evaluate and quantify the rutting potential of asphalt mixtures with a particular focus provided on the stress sweep rutting test which is gaining popularity as it tackles the shortcomings of its predecessor for the exact characterization and prediction of permanent deformation. Additionally, some advanced computational intelligence methodologies such as finite element model and soft computing are reviewed. Furthermore, the most common permanent deformation solutions are reviewed. It was found that efforts are put towards improving either the rheological properties of base asphalt by using modifiers or asphalt mixture by using selected aggregates to enhance the aggregate interlock and by implementing semi-flexible asphalt pavements which is expected to be a promising method against permanent deformation. This state-of-the-art work is expected to supply a comprehensive perception of the available models, rutting test, and solutions, and to suggest future studying areas related to the rutting of asphalt pavements.

1. Introduction

Rutting, or permanent deformation, is one of the significant distresses in flexible pavement that can occur in the asphalt layer only, in the underlying unbound layers, or in both [1,2]. Permanent deformation appears as longitudinal depression in wheel paths [1]. The rutting performance strongly depends on traffic and weather conditions such as high temperatures, traffic densities, slow traffic, and heavy loads [3]. There are two major types of permanent deformation: deformation in the subgrade or underlying layers, and deformation due to inadequate mixture stability [4]. The first type of permanent deformation is known as a structural rutting failure where the whole pavement structure is deformed due to a weak subgrade or underlying layers [5]. On the other hand, the second form of permanent deformation is caused by the low shear strength of asphalt mixtures leading to the accumulation of irrecoverable strain from wheel load [6]. Several serviceability-related, social, and pavement problems are connected with permanent deformation such as hydroplaning, water spraying, and water intrusion [6,7,8]. Consequently, rutting not only decreases the pavement service life, but is considered a threat to the asphalt pavement safety performance [7].

Generally, three rutting modes that correspond to three different rutting stages are observed namely: decelerating, stationary, and accelerating stages. The rutting modes are: loss of material, densification, and lateral plastic flow which is known as shear-related deformation, respectively [9]. The first mode of rutting is generally manifested in low durable mixtures and leads to raveling along wheel paths. Additionally, the “loss of material” mode occupies a small proportion of the rutting depth [1]. The second and third modes of rutting are mainly the influential factors that control rutting accumulation [8,10,11,12]. While densification occurs in the early rutting stage, lateral plastic flow dominates the long-term rutting accumulation [13]. Densification refers to volume or air void change (volume contraction) while shear flow refers to deformation or translation with volume change [8,12]. An example of shear flow is the shear failure of soil under a foundation [14]. Consequently, the volume change in asphalt mixtures is due to densification only [11]. Generally, shear flow develops humps on the sides of the wheel paths, consequently, the volume under the wheel path is equal to the volume of the hump if densification did not occur [15,16,17].

In the decelerating or primary stage, strong aggregate skeleton and densification-related rutting occur as a result of the rapid increase in the accumulated permanent strain and the decrease in the strain rate [1,4]. In fact, the initial pavement deformation starts during the first two years of the service life of the pavement [18]. As a rule, asphalt concrete mixtures having higher air voids tend to cause higher densification-related rutting [1,19]. Shear flow greatly affects the permanent deformation of asphalt concrete pavements [15,16].

In the stationary or secondary stage, the accumulated permanent strain increases at a constant rate causing the deformation of the aggregate skeleton with a plastic lateral flow of asphalt concrete mixture. This can be a characterization of the combined effect of shear and densification deformation. In the accelerating or tertiary stage, shear failure of the mixture is manifested by the movement of the aggregates to the side upheavals. Shear flow deformation is the most crucial rutting stage and is considered a key role in rutting as the mixture is unable to resist the shear stresses from repetitive loading [1].

2. Objective and Scope

To deal with the permanent deformation and predict rut depth, several theoretical rutting models were developed providing guidelines for the design and analysis of asphalt pavement structures. There is a distinct lack of an in-depth review of the test methods addressing rutting susceptibility at the asphalt mixture level as well the high-temperature behavior of asphalt binder. The work presented here aims at providing a thoroughly comprehensive review and state-of-art information on the available literature on the most commonly used tests for the evaluation and characterization of (1) permanent deformation of asphalt concrete mixtures and (2) high-temperature rheological properties of asphalt binders. The review presented herein provides a complete comprehensive understanding and covers the findings of research studies and laboratory experience covering methods on the existing and most common permanent deformation test methods including simulative, dynamic, and monotonic-based loading tests. Moreover, a set of solutions were also provided and discussed for the reduction in the permanent deformation susceptibility of asphalt concrete mixtures.

3. Factors Affecting Permanent Deformation

Several factors influence the rutting resistance and performance of asphalt concrete pavement comprising material properties, weather conditions, traffic volume and density, heavy loads and axle type, traffic speed [20,21], and quality of construction [21] and mixture material [22]. In general, these factors can be grouped into three categories: (1) material properties, including binder properties, binder content, air voids [4], aggregate properties, internal structure, and skeleton; (2) weather and traffic; and (3) construction quality [21].

Zou et al. (2017) considered separately the asphalt binder type, mixture type, traffic loading weight, loading frequency, and temperature to study their influence on the rutting performance of asphalt pavements [21]. For this purpose, two types of asphalt binder were used, notably a conventional binder and a modified binder along with two types of aggregates and different gradations. Three testing temperatures were considered: 50 °C, 60 °C, and 70 °C. Additionally, four different categories of axle load were studied: single axle with single wheel, single axle with dual wheel, tandem axle with dual wheel, and tridem axle with dual wheel. Furthermore, three levels of loading frequency corresponding to 40 km/h, 50 km/h, and 60 km/h were evaluated. To assess the effect of the different mentioned factors on asphalt mixtures’ rutting performance, the wheel-tracking test was conducted on the different asphalt mixtures and dynamic stability was used as an indicator. The statistical outcomes of this study revealed that asphalt mixture type was the primary and most significant factor affecting the permanent deformation of asphalt mixtures followed by weather and temperature, then loading frequency or traffic speed and lastly, the loading magnitude. Additionally, the use of a modified asphalt binder improved the rutting resistance of the asphalt mixtures as compared to the conventional one.

Similarly, Ling et al. (2017) assessed the effect of asphalt bitumen modification type and the structure of the aggregate on the permanent deformation resistance of bituminous mixtures through modeling, experimentation, and image analysis. Binders with several levels of non-recoverable compliance and elastic recovery based on the multiple stress creep recovery test were selected. Different aggregate gradations were used in this study and a flow number test was performed on the asphalt samples to assess the rutting performance of the mixture. The results showed that aggregate gradation (packing) is the most important factor that affects the permanent strain of asphalt concrete mixtures. Additionally, the viscous component of the binder has a major effect; however, the elastic component is not important [23]. Sybilski et al. (2013) found that asphalt binder properties can be assigned to approximately 40% of the permanent deformation resistance of asphalt concrete mixtures [24]. Bańkowski et al. 2021, revealed that the effect of the binder type on the resistance of mixtures to permanent deformation can be attributed to findings at different temperatures [25]. Al-Khateeb et al., 2022 found that the properties of the asphalt binder play a major role in controlling the rutting performance of asphalt concrete mixtures [26].

Additionally, the findings of Sefidmazgi et al., (2012) revealed that the aggregate internal structure is crucial in the rutting performance of bituminous mixtures and aggregate packing is significantly affected by the asphalt binder properties at the temperature of compaction [27]. As a matter of fact, the shear strength, binder cohesion, and internal friction angle are related based on the Mohr–Coulomb failure theory expressed in Equation (1):

$$\tau f=C+\sigma tan\phi$$

(1)

where τf is the shear strength, C is the cohesion of the material, and σtanφ is the internal friction angle of the material being tested.

To enhance the shear strength of asphalt mixtures, efforts should be placed toward increasing the asphalt binder cohesion and the internal friction angle of aggregate [1,4]. As the cohesion of the aggregates is significantly low, thus the shear strength is greatly dependent on the inner particle friction and movement resistance [5]. Generally, asphalt mixtures with higher adhesion between aggregates and binders develop higher rutting resistance [28,29,30].

The shape and strength of aggregates affect significantly the durability, performance, and stiffness of asphalt concrete pavement. The aggregate shape develops the packing of the skeleton structure and the inside pavement resistance against deformation [31]. In order to resist permanent deformation, aggregates should be angular, and rough with a limited amount of elongated and flaky aggregates as they will tend to break down during the mixing and construction process [31,32].

The internal structure skeleton is directly affected by the aggregate shape, angularity, texture, and strength [24,33,34]. It is revealed that the configuration of asphalt concrete mixtures affects the contact characteristics, load transmission, and resistance to permanent deformation [35]. Pouranian and Haddock (2018) found that the rutting performance of asphalt concrete mixtures is strongly affected by effective aggregate skeleton [33].

Pan et al. 2021 found that construction quality has a considerable influence on asphalt pavement rutting performance. One index in construction quality is the degree of compaction of the asphalt pavement. The higher the compaction degree the higher and stronger the durability and strength of the pavement and the lower the pavement deterioration and permanent deformation [36].

Flexible pavements are typically susceptible to moisture damage because water causes the asphalt binder to separate from the surface of the aggregate. Stripping and other premature distresses might occur separately or concurrently due to this condition. Damage from moisture in asphalt mixture results in major issues such as loss of strength and durability and increased repair and maintenance expenses of asphalt pavements. Moisture-related harms include the breakdown of asphalt binder aggregate, raveling, the formation of potholes, and cracking [37].

One of the main issues impacting the durability of hot mix asphalt (HMA) pavements is stripping. To lessen the asphalt’s susceptibility to moisture in HMA pavements, a variety of liquid anti-stripping agents have been developed [38].

A study by Xiao and Huang researches the moisture susceptibility of aged HMA, both in the short term and long term. The study concluded that both aging methods increased the debonding potential per unit contact area. The lower wettability of aged binders was the main cause of the decrease in moisture resistance of combinations prepared with preaged asphalts. However, if the aging of the asphalt took place on the surface of the aggregate, the total moisture resistance was similarly correlated with the length of time the asphalt and aggregate were in contact. After a brief period of aging, more asphalt could be absorbed into the aggregate’s pores thanks to an enhanced wettability of the asphalt that was linked to the coating quality. In other words, the surface area of contact between the asphalt and aggregate grew over time, increasing total adhesion. Even though the asphalt degraded, the asphalt mixes after brief age showed greater moisture resistance. As a result of the asphalts’ severe deterioration and excessively high stripping potential per unit area caused by prolonged age, their moisture resistance was significantly reduced [39].

The performance of asphalt mixtures against moisture can generally be improved with the use of anti-stripping additives; however, the type and percentage of these additives should be chosen based on the type of aggregate, the type of bitumen, and the characteristics of the mix design of the asphalt mix. According to the suggested model by Nejad et al., mixtures’ capacity to resist moisture is improved by increases in cohesion-free energy, adhesion-free energy, aggregate bitumen wettability, aggregate surface area, and apparent asphalt film thickness on the aggregate surface. Debonding energy, saturation level, and permeability, on the other hand, have a detrimental impact on the asphalt mixture’s capacity to withstand moisture damage [40].

Another study by Xiao et al. looked into the moisture damage mechanism and material selection of hot-mix asphalt (HMA) with an amine-based antistripping agent (ASA). By reducing the nonpolar components and boosting the polar components, the application of amine ASA altered the thermodynamic characteristics of asphalt, improving the adhesion work between asphalt and aggregate and lowering the free energy generated in the presence of water. The use of ASA agents also increased the wettability of asphalt over aggregate. All of those adjustments resulted in a higher energy ratio (ER), which shows that materials are more compatible and better able to withstand wetness. Due to the lower dry adhesion energy and higher free energy released with moisture, asphalt mixes containing acidic aggregate showed more severe moisture degradation. The choice of appropriate asphalt-aggregate combinations appeared to be more successful than the application of amine ASA to increase moisture resistance [41].

4. Evolution of Rutting Prediction Models

Different rutting prediction models have been developed in an attempt to accurately predict the viscoplastic strain, thus the permanent deformation of asphalt concrete pavements. Some of these models are too simple to illustrate the permanent deformation behavior of asphalt concrete and other models are too complicated and need high calibration costs for the prediction of permanent deformation. The existing mathematical prediction models can be grouped into (1) power law-type models, (2) rigorous mechanical models, and (3) advanced models developed at North Carolina State University, respectively.

4.1. Power Law Type Models

Power law-type models are simple models that necessitate less calibration effort than other rigorous mechanical models and are derived from RLPD tests [11]. The classical power law describes a perfectly linear log–log scale and thus can precisely predict the stationary stage where the accumulated permanent strain increases at a constant rate causing the deformation of the aggregate skeleton with a plastic lateral flow of asphalt concrete mixture. However, the behavior in the decelerating or primary stage is not covered when using the pure power law or exponential models due to the fact that the strain increases at a rapid rate in the primary stage, and therefore, other models are needed to capture the rutting behavior during the decelerating stage [11].

Table 1. Permanent deformation models [11].

Model	Equation	Definitions
Classical Power Law	${ϵ}_p=a{N}^b$	N = number of cycles a, b = regression parameters
[30]	${ϵ}_p=A{N}^B+C\left(e^{DN}-1\right)$	N = number of cycles A, B, C, D = regression parameters
[42]	${ϵ}_p={ϵ}_0·e^{-{\left(\raisebox{1ex}{$\rho $}\!\left/ \!\raisebox{-1ex}{$N$}\right.\right)}^b}$	N = number of cycles ${ϵ}_0$, $\rho$, b = regression parameters
[43]	${ϵ}_p={\theta }_1·\left(1-e^{{\theta }_{2}N}\right)+{\theta }_3·\left(e^{-{\theta }_{4}N}-1\right)$	${\theta }_1$,${\theta }_3$ = primary and tertiary strains ${\theta }_2$,${\theta }_4$ = rates of curvature of primary and tertiary zones
MEPDG (2002)	$\frac{{ϵ}_p}{{ϵ}_r}={10}^{k_1}·T^{k_2}·N^{k_3}$	N = number of cycles ${ϵ}_r$ = the resilient strain T = the temperature k1, k2, k3 = regression parameters
[44]	${ϵ}_p=\delta \left(T\right)N^a{\sigma }^{n-1}\left[{\sigma }_z-0.5\left({\sigma }_x+{\sigma }_y \right)\right]$	$\delta \left(T\right)$ = temperature function a = coefficient N = number of load cycles T = load time $\sigma$ = equivalent stress defined as a function of principal stress
[45]	${ϵ}_p={\left(q/a\right)}^{b}N$	${ϵ}_p$ = permanent shear strain q = deviatoric stress a, b = coefficient N = number of load cycles
[46]	$\frac{{ϵ}_p}{N}=A_a{N}^{-m}$	Aa = material property. Function of resilient modulus and applied stress m = material parameter

below summarizes the existing most common power law and exponential-type models. The main focus of the classical power law model is the stationary stage whereas the model developed by [30,42] can predict the decelerating stage better than the other models however, the fitted strain diverges from the measured one [11].

4.2. Rigorous Mechanical Models

Rigorous mechanical models are models that use plastic or/and viscoelastic concepts for the prediction of rutting as a function of several conditions. Despite that, these models necessitate considerable computation time and calibration efforts. Additionally, these models are considered too complicated to understand [8]. These rigorous mechanical models comprise the simple strain-hardening model (p-q-Y model), HiSS model implemented by Delft University of Technology, and HiSS Model by the University of Maryland.

4.2.1. Simple Strain-Hardening Model (p-q-Y Model)

The simple strain-hardening model, known as the (p-q-Y model), is a uniaxial mechanistic model used for the viscoplastic strain prediction for compressive and tensional uniaxial loading in terms of stress function and time and is developed by [47,48]. The viscoplastic strain rate is dependent on the stress function and the coefficient of viscosity of the material and is expressed in Equation (2).

$$\epsilon vp=\frac{g\left(\sigma \right)}{\eta \left(\epsilon vp\right)}$$

(2)

where,

• εvp is defined as the viscoplatic strain,
• g($\sigma )$ is the stress function, and
• η(εvp) is the material’s coefficient of viscosity.

Supposing that the viscosity follows the power law in the viscoplastic strain equation, thus the viscoplastic strain rate can be represented by Equation (3)

$$\mathsf{\epsilon }vp=(\frac{p+1}{Y}{)}^{\frac{1}{p+1}}{({\int }_0^t{\sigma }^{q}dt)}^{\frac{1}{p+1}}$$

(3)

where,

• p, q, and Y are pressure dependent models, and
• εvp is defined as the viscoplatic strain.

This model is characterized via creep and recovery tests using viscoplastic strains [11]. Although the implementation of the model is simple, however, the description of rutting behavior is not adequate when using this model as it simulates the stress effect only with time [11]. The p-q-Y model has been utilized for the prediction of viscoplastic strain in asphalt concrete mixtures for compressive and tensile uniaxial loading [49].

4.2.2. Hierarchical Single Surface (HiSS) Model Implemented by Delft University of Technology

The HiSS model was introduced by [36] and can express the viscoplastic behavior of asphalt materials by using the flow rule when subjected to monotonic loading [11]. Despite that, numerical problems remain for the determination and prediction of permanent deformation. This model is based on the assumption of continuity; thus, it cannot account for discontinuities [50]. Additionally, the calibration of the HiSS model used the constant strain rate which is not easy to simulate the asphalt behavior under discontinuous loading [11]. It is important to shed light on the fact that although the use of this model is difficult for both compressive and tensile stress conditions, the HiSS model can be formulated for both conditions by getting testing parameters from separate tension and compression tests. More details can be found in [51,52,53].

4.2.3. Hierarchical Single Surface (HiSS) Implemented by the University of Maryland

A simplified model of the HiSS implemented by Delft University of Technology was suggested by [54] using Perzyna’s flow rule and the time–temperature superposition principle. Using the time–temperature superposition principle led to a reduction in the number of tests to be conducted for the model calibration and widened its range of applicability. Another advantage of the Maryland HiSS model is that the creep and recovery tests are applied for the characterization of the model [55]. The Maryland HiSS model can effectively predict the lateral strain as it is a three-dimensional model.

4.3. Models Developed at North Carolina State University (NCSU)

Researchers at NCSU have suggested some advanced mathematical models for the behavior prediction of asphalt concrete mixtures that are imported to the pavement performance prediction program: FlexPave^TM. FlexPave^TM carries out a three-dimensional viscoelastic analysis in order to simulate the behavior of asphalt concrete, in other words, the percentage of cracking and rutting depth in flexible pavements can be predicted under various conditions [56]. In general terms, some of the mathematical models developed by NCSU, namely the rest period-induced softening, incremental model, and shift models, are presented in this section below.

4.3.1. Rest Period-Induced Softening

Yun (2008) revealed that the rate-dependent softening behavior of asphalt material is strongly due to the rest period length and should be included in the permanent deformation model due to the fact that as the period of rest is longer, the permanent strain is greater at the test termination. This is referred to as rate-dependent softening [57]. Although the model considers the effect of rate-dependent softening in addition to the concept of viscoelastic for viscoplastic modeling, however, it is a complicated model that necessitates long computation time and many tests [11].

4.3.2. Rate Model

Subramanian et al. (2013) proposed a rate model that can accurately predict the stress-dependent behavior of asphalt materials [58]. In fact, the values of the viscoplastic creep compliance are comparable to the value used in viscoelasticity; however, these values are not associated with the properties of viscoelasticity [11]. In addition, the model calibration necessitates a minimum of 9 loading conditions, loading time, and stress levels which makes the process expensive in terms of computation [11]. For this purpose, a simplified version is introduced to overcome the shortcomings of the other existing models known as the incremental model.

4.3.3. Incremental Model

The incremental model is a simplified version of the rate model that is used for the viscoplastic strain prediction while considering the stress-dependent behavior of asphalt materials [58]. The incremental model suggests that the steady state condition begins at the first load for the reason that all the effective stress decreases the zero from the first loading cycle supposing that the rest period is long enough [11]. Under the condition of a steady state, the incremental growth of the convolution integral becomes constant thus an incremental model can be acquired from the rate form model comprising the loading history as expressed in Equation (4).

$${ϵ}_{vp}=\frac{A+BN}{{\left(C+N\right)}^{\alpha }}$$

(4)

where,

• α is defined as a parameter for hardening evolution,
• N is the number of cycles,

$$A=\frac{{ϵ}_{vp,ini}^0}{{\left(I_H\left(t_l,t_r,{\sigma }_d\right)\right)}^{\alpha }}, B=\frac{I_{vp}\left(t_l,t_r,{\sigma }_d\right)}{{\left(I_H\left(t_l,t_r,{\sigma }_d\right)\right)}^{\alpha }}, \mathrm{and} C=\frac{H_{ini}}{I_H\left(t_l,t_r,{\sigma }_d\right)}$$

H_ini is the initial hardening of a specimen, and ${ϵ}_{vp,ini}^0$ is defined as the initial permanent strain.

It is important to note that A, B, and C are loading time related, stress related, and rest period related. However, A is dependent on the initial permanent strain, C on the hardening increment of the specimen at the start of testing, and B is defined as the ratio of incremental strain to incremental hardening at the steady state.

4.3.4. Shift Model

The shift model was proposed by [11] in accordance with the incremental model form and takes into account the deviatoric stress, load time, and temperature effect on permanent strain in addition to the time–temperature superposition and time–stress superposition concepts. One permanent strain master curve and two shift functions are the basis of the shift model, thus representing a viscoplastic strain master curve. Another advantage of the shift model is that it perfectly fits and covers the decelerating (primary) and stationary (decelerating) stages of the asphalt behavior [11]. The viscoplastic strain can be predicted using the mathematical expression expressed in Equation (5).

$${ϵ}_{vp}=\frac{{ϵ}_0.N_{red}}{{\left(N_I+N_{red}\right)}^{\beta }}$$

(5)

where,

• ${ϵ}_{vp}$ is the viscoplastic/permanent strain,
• ${ϵ}_0,N_I$, β are incremental model parameters, and
• Nred is defined as the reduced number of cycles at reference loading conditions expressed as

$$N\ast {10}^{a_{total}}$$

where,

$$a_{total}=a_{{\sigma }_v}+a_{{\xi }_p}$$

$a_{{\sigma }_v}$ and $a_{{\xi }_p}$ are the vertical stress and reduced load time shift factors, respectively.

The vertical stress shift factors can be computed as in Equation (6)

$$a_{{\sigma }_v}=D\times \left(log\left(\raisebox{1ex}{${\sigma }_v$}\!\left/ \!\raisebox{-1ex}{$P_a$}\right.\right)-0.877\right)$$

(6)

where ${\sigma }_v$ and $P_a$ are the applied vertical stress and the atmospheric pressure for stress normalization, respectively.

$$D=d_1\times T+d_2$$

• $d_1$ and $d_2$ are parameters of vertical stress shift factor, and
• $T$ is the testing temperature.

The reduced load time shift factor can be computed as in Equation (7)

$$a_{{\xi }_p}=p_1\times log\left({\xi }_p\right)+p_2$$

(7)

where

$${\xi }_p=\raisebox{1ex}{$\xi $}\!\left/ \!\raisebox{-1ex}{$a_T$}\right.$$

• $p_1$ and $p_2$ are parameters of reduced load time shift factor,
• ${\xi }_p$ is defined as the reduced load time,
• $\xi$ is referred to as the actual load time, and
• $a_T$ is the time–temperature shift factor for the given temperature.

4.4. Laboratory Performance Tests for Permanent Deformation Evaluation of Asphalt Concrete Mixtures

In the course of time, asphalt concrete mix design has continuously evolved after being developed based on specific tests and protocols for the purpose of determining the optimal asphalt binder content for a specific mixture [59]. The Superpave mix design method is currently the primary methodology for asphalt mix design after being inducted from the limitations of its predecessor methods [60]. Despite the fact that the Superpave mix design method comprised a performance-based mix design system to improve the pavement in-service performance, however, the application of its performance-based mix design system showed to be less effective [61]. The Superpave mix design method was abbreviated into a volumetric process that relies on properties from component materials (aggregate shape and physical properties) and consensus mixture properties (air voids, voids in mineral aggregates, and voids filled with asphalt) [61,62]. Efforts have been placed towards developing tests that capture the durability of asphalt concrete mixtures at high temperatures and serve as qualitative methods providing performance-indicating indices. For this purpose, different tests have been emerged and proposed along with performance-indicating indices [63,64,65,66,67]. In general terms, three testings can be categorized into three testing types, namely: simulative loading tests, dynamic loading tests, and monotonic loading tests.

4.4.1. Simulative Based Loading Tests

Simulative-based loading tests are defined as simple tests that relatively mimic the effect of traffic load on the asphalt pavement by tracking a wheel load on the tested asphalt mixtures. As a result, the accumulated deformation is measured per wheel load cycle enhancing the understanding of the performance of asphalt mixtures in the decelerating stage, stationary stage, and accelerating stage.

French Rutting Tester

The French rutting tester (FRT) developed by Laboratoire Central des Ponts et Chaussées (LCPC) has been utilized in France for over 15 years to assess the permanent deformation characteristics of hot mix asphalt mixtures that are subjected to heavy traffic and has no performance history or including materials that are susceptible to rutting [68]. It is a substantial part of the LC26-410 method developed by the Quebec Ministry of Transportation [69]. The FRT machine tests asphalt slabs having dimensions of 180 × 50 × (20–100) mm that are compacted with a French plate compactor for rutting using a reciprocating loaded pneumatic tire of 415 mm diameter and 110 mm width at a constant testing temperature of 60 °C. Samples are conditioned for 12 h at the testing temperature. Two slabs can be tested at the same time and loaded with a 5000 N pneumatic tire inflated to 600 kPa [68]. The tested samples are loaded at 1 cycle/s and the testing duration is around 9 h. The samples should be aged at room temperature prior to testing for 7 days [70]. Rutting depth is defined as the deformation expressed as a function of the initial slab thickness. A “Zero” rut depth is defined as the deformation at the initial loading for 1000 cycles at the testing temperature [66,68]. Rut depth is measured at 100, 300, 1000, 3000, 10,000, and 30,000 cycles and is calculated as the average of 15 measurements. A test is considered successful if the rut depth is less than or equal to 10% of the original slab thickness after 30,000 cycles. Although FRT is proven to differentiate between good and poor rutting performance [70], however, it is not applicable for asphalt mixtures having a nominal maximum aggregate size larger than 20 mm as these mixtures may be restricted from shearing upward and outward and are not properly compacted by the French Plate Compactor [71]. Additionally, the width of the slab is considered somehow small compared to the width of the tire. A research study conducted by Özen (2011) assessed the permanent deformation of different asphalt concrete mixtures notably hydrated lime and SBS-modified mixtures using the French rutting tester known as LCPC. LCPC wheel-tracking compaction effort was examined with field roller compaction in the LCPC loading system. It was concluded that the original LCPC compactor correlated well with field roller compaction [72]. Additionally, the results were also in agreement with the findings of Aschenbrener (1994) and Visser et al. (2002) who revealed that French rutting tester and actual rutting depths had a very good correlation and LCPC performed well at predicting the pavement performance [73,74].

Hamburg Wheel-Tracking Device

The Hamburg wheel-tracking device (HWTD) was manufactured by Helmut-Wind in Germany during the 1980s [73,75,76] and gained interest among state highway agencies [77,78]. It evaluates the combined rutting and shearing resistance failure using a rolling steel wheel of 47 mm width applying a load of 705 N that goes backward and forward on asphalt slabs of 320 mm length, 260 mm width, and 40 mm height or cylinder of 150 mm diameter and 62 mm height submerged in hot water [79,80]. The test is conducted according to AASHTO T324 [81]. The tested slab is compacted to 7 ± 1% air voids using a kneading compactor. The water bath temperature ranges from 25 °C to 70 °C with 50 °C being the most common testing temperature [1,82]. The test is stopped and accumulated rutting is measured when a deformation of 20 mm, measured by Linear Variable Differential Transformers at 11 points along the length of the specimen, is reached or 20,000 passes are applied [79,83]. The test outputs retrieved from the HWTD comprise creep slope, rut depth, stripping slope, and stripping inflection point. The creep slope is the inverse of the deformation rate in the linear zone of the curve of deformation. The stripping slope is the inverse of the deformation in the linear zone of the curve of deformation. The stripping inflection point corresponds to the number of passes at which the stripping and creep slopes are intersected. The inflection point is used to evaluate the moisture susceptibility of asphalt mixtures [84].

Despite the fact that the outcomes of the HWTD and the field rut depth did not strongly correlate [22], the permanent deformation potential of asphalt mixtures is still assessed by using the HWTD [85,86,87].

Georgia Loaded-Wheel Tester

The Georgia loaded-wheel tester (GLWT) was manufactured in the mid-1980s with the cooperation of the Georgia Department of Transportation and Georgia Institute of Technology [88,89]. It consists of rolling a steel wheel of 445 N load across a pneumatic hose having a pressure of 690 kPa placed on top of an asphalt specimen at a testing temperature of 41 °C [90]. Testing specimens can be asphalt cylindrical specimens having dimensions of 150 mm diameter and 75 mm height or asphalt beam specimens having dimensions of 125 mm width, 300 mm length, and 75 mm height compacted to 4 or 7% air voids. Specimens are conditioned for 24 h at room temperature and conditioned for 24 more hours at the testing temperature prior to testing. When the test is accomplished, i.e., attaining 8000 loading cycles, the rutting depth value can be measured by determining the average difference in surface profile before and after testing and compared to a maximum criteria of 5 or 7.5 mm [87]. To evaluate the correlation between and field rutting performance, a testing program was conducted by Collins et al. (1995) using three different asphalt concrete mixtures having different rutting resistance. The rut depth findings revealed a strong correlation between the field and the tested samples [91,92]. This conclusion was in agreement with the one of Miller et al. (1995) who assessed the feasibility of predicting permanent deformation using GLWT [93].

Asphalt Pavement Analyzer

The Asphalt Pavement Analyzer (APA) is the second generation of GLWT conducted according to AASHTO T340 used to assess the fatigue, rutting, and moisture susceptibility of asphalt concrete mixtures [94,95]. APA follows the same testing procedure as the GLWT as it is a newer modified version of the GLWT [1,68]. APA consists of running a loaded wheel backward and forward across a pressurized linear hose over asphalt samples to induce permanent deformation. The wheel load and the number of cycles, and the hose pressure values remain the same as for the GLWT. The testing samples can be asphalt beam compacted to 7% air voids by the asphalt vibratory compactor or cylindrical specimens compacted to 4 or 7% air voids by the Superpave gyratory compactor (SGC). Testing temperatures range from 40.6 °C to 64 °C depending on the performance grade of the asphalt binder being used [12]. Huang et al. (2017) found that the APA overestimated the rut depth in the field [96]. Along with the HWT are considered the most commonly used rutting tests for the balanced mixed design concept in the US [61,66,75,97,98,99].

Despite the fact that these tests are simple and have been proven to correlate well with the field performance to assess the rutting potential of asphalt mixtures [12,90,98,100], these simulative-based tests suffer from a common limitation which is developed by the fact that these simulative-based tests run a loaded wheel backward and forward (two directional loadings) over the tested asphalt specimen leading to a deviation in mimicking the actual field conditions. Actually, the load generated from traffic on the pavement is considered to be one-directional loading inducing a shearing plane in the asphalt sample and causing plastic flow, whereas the two-directional loading develops two different shearing planes [12,98]. Additionally, simulative-based loading tests cannot provide mechanical parameters of the tested asphalt mixtures that are used in asphalt pavement design and prediction models [101,102]. Consequently, there is a need to rely on other test types to reinforce the correlations between the rut depth experimentally measured and that from the field. Such a need can be accomplished through the use of dynamic or monotonic-based loading rutting tests [66,99].

Wheel-Tracking Test

Since 1998, the wheel-tracking test has been the primary indicator of asphalt surface deformation resistance in the UK [103]. It determines the susceptibility of bituminous materials to rut under wheel loads. The device consists of a loaded wheel that repeatedly passes over a sample that is firmly kept on a fixed table. The pace at which ruts form on the specimen surface is being watched by a connected instrument. To ensure that the test specimen’s temperature is at a constant ±1 °C throughout the testing process, a temperature control device is needed [104].

Wheel with a track width of (110 + 5) mm and a 6.00-R9 pneumatic tire without a tread pattern is used. The pneumatic tire’s travel with respect to the specimen must be (700 + 5) mm. The total travel time (both directions) must be (2.5 ± 0.5) s. The test specimen will be subjected to a rolling load of (10,000 ± 100) N at its center, measured at least while the apparatus is static [105].

The loaded wheel is brought into contact with the compacted specimen after it has been placed in the wheel-tracking machine, and an automated displacement measurement system keeps track of how the rut develops. The chamber’s temperature is maintained constant. The associated data-collecting equipment receives automated transfers of the determined rut depth at intervals of 100 cycles from the displacement measuring device. Ten thousand cycles of tracking are performed, or until the desired rut depth is attained [104].

4.4.2. Dynamic Based Loading Tests

Dynamic-based loading tests are tests that apply sinusoidal loading cycles on the asphalt concrete sample. The outputs of the tests can be translated into deformation to evaluate the rutting potential of asphalt concrete mixes as the results exhibit the rutting and shear resistance level of asphalt concrete mixtures.

Dynamic Modulus, Flow Number and Flow Time Tests

The dynamic modulus (DM) test is a non-damaged test that is considered to be a stress-controlled test that embraces the application of repetitive sinusoidal dynamic compressive axial load to an unconfined asphalt sample over a range of various testing temperatures and different loading frequencies [106]. The DM test can be performed according to AASHTO TP62 [107] and is accomplished at a variable number of cycles that are preset per stress level per frequency per temperature [108,109]. The stress level ranges from 3.4 kPa to 1725 kPa. The DM test is conducted to characterize the stiffness of asphalt concrete mixtures, measured as a function of the dynamic complex modulus which is the absolute value of the complex modulus, in addition to the viscoelastic properties of the mixture [110]. At any temperature and loading frequency, the modulus of the asphalt mixture can be measured by constructing the master curve using the time–temperature superposition principle at a reference temperature. The NCHRP Project 9-19 recommended the use of the DM along with the flow time and flow number tests as the top three candidates for simple performance test methods of the permanent deformation evaluation of asphalt concrete mixtures [111]. The tested cylindrical asphalt sample is compacted to 7% air voids using an SGC having dimensions of 150 mm height and 100 mm diameter.

Although several studies have proven a good correlation between the results of the DM tests and the field rutting performance [109,110,112,113,114], however, a study conducted by Jiang et al. (2016) suggested that the DM test could not quantify the actual field characteristics of rutting as the strain levels of the DM are too small; consequently, there is a need for careful interpretation of the DM test outcomes [115].

The flow number (FN) test was proposed in the NCHRP 9-19 Project to assess the susceptibility of asphalt mixtures to permanent deformation [98,110]. The test consists of applying repeated compressive haversine loads and recording the cumulative permanent deformation in terms of the number of cycles at a testing temperature ranging from (37.8 °C to 54.4 °C) in unconfined conditions with a vertical deviatoric stress ranging between 68.9 kPa and 206.8 kPa [115]. As the DM is a non-damaged test, the same sample can be tested for the FN test. The FN test is terminated after completing 10,000 load repetitions or when achieving an accumulation of 30,000 microstrains. The FN test results comprise: (1) the number of cycles at which the accelerating/tertiary flow starts, known as the FN, (2) the accumulated permanent strains at the onset of tertiary flow, (3) the time to onset of tertiary flow, and (4) the ratio between accumulated permanent strains at the onset of tertiary flow and the FN [116]. The FN test is a promising test method as several research studies have demonstrated that the findings of the FN test correlate well with the actual field rutting performance [112], as well with the DM test results [109,112,115,117,118,119,120]. Nevertheless, there are some limitations in using the FN test such as the cost and the complicated equipment, and the long testing time that may take up to 3 h to run [106,118]. For this purpose, Witczak et al., (2002) proposed the dry HWTT in lieu of the FN test to assess the permanent deformation resistance of asphalt concrete mixtures and revealed that these two tests had a good correlation [112]. Additionally, Walubita et al. (2013) suggested a new FN index parameter from the original FN test method which is considered a potential to replace the HWTT [121]. Another limitation of the FN test is that is it based on a pass/fail protocol which considers fixed testing conditions prohibiting the evolution of rutting prediction for different field conditions [122].

Similarly, the flow time (Ft) test has shown a promising potential to correlate well with field performance [84,112,123,124,125,126]. Ft consists of applying creep loads on asphalt samples having dimensions of 150 mm height and 100 mm height in unconfined or confined conditions [112]. However, the confined condition is shown to simulate the actual field conditions more than the unconfined conditions [120]. The confining stress is selected to be 276 kPa with a deviator stress of 1380 kPa and the testing temperature depends on the average monthly pavement temperature [112]. The Ft test corresponds to the minimal rate of change of permanent axial strain during the static creep test by fitting the data obtained to the Fracken model expressed in Equation (8) [120].

εp = AnB + C (eDn − 1)

(8)

where,

• εp is the permanent strain expressed in %,
• n is the time, and
• A, B, C, and D are fitting coefficients.

Repeated Load Permanent Deformation

The repeated load permanent deformation (RLPD) test characterizes the rutting response of asphalt concrete mixtures by applying, in unconfined conditions, a repeated compressive haversine loading at two different testing temperatures specifically 40 °C and 50 °C [109,116,126,127]. The RLPD is similar to the FN test; however, the load magnitudes are different [109,126]. The RLPD test is considered to be a more comprehensive research-oriented test as it provides information about the quality of the mixture design and pavement modeling [106]. Witczak (2005) and Hu et al., (2011) demonstrated that the findings of the RLPD tests correlate well with the field performance. Despite that, the complexity of the equipment for lateral confinement may limit the application of this test [7,128]. Additionally, this test does not take into consideration the primary stage, hence the results might not yield precise predictions [12]. As a result, Zhu et al., (2016) proposed a simplified triaxial repeated load test (STRT) that is easy to conduct for the characterization of permanent deformation resistance of bituminous mixtures through in situ confinement simulation encountered in actual asphalt pavement and found out that the simplified test results have good relevance with rutting performance of asphalt pavements [7].

Repeated Load Axial Test

The repeated load axial test has been used in order to evaluate the creep behavior of bituminous mixtures. The test applies a dynamic compressive load, repeated load axial, of a set magnitude of 150 kPa, 250 kPa, or 350 kPa for one hour at various testing temperatures, notably 40 °C, 45 °C, 50 °C, 55 °C, and 60 °C, on cylindrical asphalt samples having a diameter of 101 mm and height of 70 mm. The vertical deformation is measured by LVDTS and in each test, the samples are placed under confinement pressure of 10 kPa for 600 s prior to the application of 150 kPa, 250 kPa, or 350 kPa for 1000 cycles with one second rest period and one second pulse period. The creep parameters are determined using the repeated load axial test in order to predict and model the permanent deformation behavior of asphalt concrete mixtures [129]. Özen (2011) assessed the rutting behavior of hydrated lime and SBS-modified mixtures using LCPC and repeated load axial test. The results revealed that LCPC results were in agreement with the results of repeated tests. Additionally, the findings revealed that repeated test is a good indicator of SMA mixtures or stony skeleton mixtures [130,131]. Moreover, it was found that repeated load axial tests correlate better than static tests with the actual field asphalt pavement rutting [72].

Superpave Shear Tester

The Superpave shear tester (SST) is considered a fundamental shear test to capture the shear properties and resistance of asphalt concrete mixtures [111,132,133]. It was developed under the Strategic Highway Research Program. The test applies a biaxial load on a sample having 150 mm diameter and 50 mm height, using a dual actuator feature that applies vertical axial and shear loads with testing temperatures ranging from 0 °C to 70 °C [85]. Three tests can be performed using the SST for providing information related to stiffness, shear deformation, and rutting resistance, namely: the frequency sweep at a constant height (FSCH), a repeated shear at a constant height (RSCH), and a simple shear at a constant height (SSCH). The FSCH and RSCH tests are the most two common tests used for the assessment and prediction of permanent deformation of asphalt concrete mixtures [111].

Uniaxial Shear Tester

The uniaxial shear tester (UST) was introduced as a cooperation between the University of California Pavement Research Center and Czech Technical University for the evaluation of the shear resistance of bituminous mixtures. A hollow cylindrical asphalt sample 150 mm in diameter and 50 mm in height is placed inside a steel cylinder and the load is applied through the knee joint on a steel insert placed in the center of the asphalt specimen and pushed down to provoke shear load in the mixture [134]. The UST test applies 30,000 cycles of haversine shape pulses at 69 kPa for 0.1 s followed by 0.6 s of rest periods at a constant temperature of 50 °C [4,134]. The outcomes of the study conducted by Zak et al., (2017) revealed that the UST test correlated well with the RSCH test results and provided promising results. However, the loading frame may be one of the shortcomings of the UST test [4].

Triaxial Stress Sweep Test

The triaxial stress sweep (STT) test is introduced by [135] as an optimized test method for the evaluation of the rutting performance of asphalt mixtures under confining stress [135,136]. The test protocol consists of using a shift model resulting from an incremental viscoplastic model that takes into consideration the temperature, loading time, and deviatoric stress effect with a constant confining pressure of 69 kPa on rutting [58,137]. This model is developed by using the time–temperature superposition principle and the time–stress principle [138]. Actually, the prediction of the permanent deformation of the asphalt pavement is insured by the application of the shift model on the layered viscoelastic continuum damage (LVECD) software [138,139]. The cyclic compression test is adopted by different advanced models for permanent deformation as it provides specific material characteristics [57,58,137,138,139,140,141]. The TSS test comprises three loading groups, each of 200 loading cycles, applied under three deviatoric stresses (483 kPa, 689 kPa, and 896 kPa) that are altered between the loading groups in an increasing order while keeping a 69 kPa confining pressure [11]. The TSS test is conducted in two phases and in different samples. The first phase is the triaxial RLPD and the second phase is the multiple stress sweep test [135]. In their research study, Choi and Kim (2014) verified that the TSS test acts as a material characterization test, the shift model acts as a rutting model, and the LVECD software acts as pavement analysis software, having the potential of predicting the rut depth in the field. At the end of each of the loading blocks, the recorded permanent strains can be shifted to construct the permanent strain master curve. However, conducting the TSS test requires four inherent tests along with two replicates to reduce variability which makes its application impractical as the testing time along with conditioning time is around two days for a single asphalt mixture [141]. Therefore, in an effort to reduce the testing efforts, a simplification of this test was introduced by [8] as a stress sweep rutting (SSR) test conducted according to the AASHTO TP134 [142].

Stress Sweep Rutting Test

The basic origin of the stress sweep rutting (SSR) test goes back to a research study conducted under NCHRP 9-19 for better characterization of the effect of stress level and loading time on the rutting of asphalt concrete [112]. Despite that, the reference point for the SSR test developed at present was [137] who suggested using the TSS test for the calibration of the permanent deformation shift model for the purpose of overcoming the shortcomings of the original TSS test by decreasing the testing time and number of samples for the accurate characterization and prediction of rutting of asphalt concrete mixtures [141]. An advantage of this test is that it measures the rutting characteristics of bituminous mixtures in terms of three deviatoric stress, loading duration, and temperature as each of these factors differs with depth and time in the pavement structure [143]. Despite the fact that the TSS test takes into consideration the effects of temperature, loading time, and deviatoric stress and effectively characterizes the shift model; however, it necessitates a reference test carried at the high temperature: RLPD, in addition to the long testing time as three stress sweep tests should be conducted at low, intermediate and high temperature. In order to decrease the testing time, Jeong et al., (2021) removed the reference test and reorganized the stress levels in the SSR test at the high temperature only [141]. The updated version of the TSS test was known as the SSR test [56].

Two different temperatures, notably low and high temperatures, are required to conduct the SSR test according to AASHTO TP 134. The outcomes of the test are used to develop and calibrate the rutting shift model which describes the rutting behavior of the asphalt concrete mixture at the material level and thus facilitates the prediction of the viscoplastic strain and the long-term rutting performance of asphalt pavements [143]. The implementation of the shift factor into FlexPAVETM, a finite element program, facilitates the prediction of permanent deformation of asphalt layers under different loading times conditions, climatic conditions, and stress levels in terms of pavement depth over its entire design life [56].

Additionally, the compressive cyclic loading test is performed under a constant confined pressure of 69 kPa with 200 cycle haversine loading blocks for each of the three deviatoric stress levels. For the low temperature, the load pulse is 0.4 s for each cycle with a rest period of 1.6 s and the stress deviatoric levels are applied in an ascending order notably 483 kPa, 689 kPa, and 896 kPa. Concerning the high temperature, the rest period is increased to 3.6 s, whereas the deviator stress levels are applied in a reserve loading block as follows: 689 kPa, 483 kPa, and 896 kPa. Kim and Kim (2017) revealed that the findings from the reverse loading blocks at high-temperature testing could be effectively used to remove the reference test and thus decrease the number of replicates from eight to six [141]. Furthermore, the elimination of the intermediate temperature was also assessed by Kim and Kim (2017) who found that the rutting depth predicted using FlexPAVE^TM was not considerably altered. Consequently, the last SSR protocol test discarded the intermediate temperature, resulting in a total of four SSR tests, two replicates at each temperature, for the calibration of the permanent deformation shift model.

The low testing temperature is selected based on the performance grade of the binder whereas the high testing temperature is selected from the degree days parameter derived from the LTPPBind with 98% reliability for the area of interest and can be calculated as expressed in Equation (9) [144].

$$T_{\mathit{high}}0.87\times (58+7\frac{DD}{100}-15\times log\left(H+45\right))$$

(9)

where,

• DD is the number of degrees days that are greater than 10 °C and,
• H is 0 for the surface layer and design depth to top of layer for base layers, mm.

The asphalt concrete samples to be tested are cylindrical samples having 150 mm height and 100 mm diameter compacted to 7% air voids using an SGC. The test can be conducted in a universal triaxial cell (UTC) or asphalt mixture performance tester (AMPT) that performs the requirement confinement. Two greased latex friction reducers are placed between the asphalt specimen and the top and bottom platens. Then, a membrane is stretched over the specimen and the platens and is attached to the platens by O-ring seals.

The Rutting Strain Index (RSI) is”defi’ed as the ratio of the permanent deformation in an asphalt layer to the thickness of the layer at the end of the pavement service life with 30 million 18-kip standard axle load repetitions for a standard structure [145]. The RSI is directly calculated from the SSR data by the FlexMATTM-Rutting analysis tool. An asphalt concrete mixture with a higher RSI value has lower rutting resistance [143]. The predicted field results were in agreement with the results of the SSR test results and FlexMAT^TM simulations, which proves that the SSR test can be applied outside the United States [122]. Additionally, Jeong et al., (2021) found a strong relationship between the values of the RSI and the predicted rut depth [143].

4.4.3. Monotonic Based Loading Tests

Monotonic-based loading tests are tests that apply (1) a high level of strain to the bituminous mixture for the purpose of capturing its resistance to rutting and (2) a constant rate of strain till reaching the peak load.

Marshall Stability Test

Marshall stability (MS), introduced in the 1940s, is known as the maximum load that can be applied to the asphalt sample just before its fracture under the Marshall testing frame, and flow is defined as the specimen compression before this fracture [146]. MS is conducted according to ASTM D5581 [147]. The ratio of MS (kN) to the flow (mm) is defined as the Marshall quotient (MQ) expressed in kN/mm. This parameter was used to indicate the rutting resistance of asphalt mixtures. A lower value of MQ indicates less resistance to permanent deformation [148]. The MS test is performed by applying a constant compression load rate of 51 mm/min on cylindrical asphalt samples having dimensions of a diameter of 101.6 mm and a height of 63.5 mm at a constant temperature of 60 °C [84]. Nevertheless, it was revealed that the indicators of the MS test were poorly correlated with actual pavement rutting performance [149].

Hveem Stabilometer Test

The Hveem stabilometer test indicates the ability of asphalt mixtures to develop rutting resistance under compressive loading at a constant temperature of 60 °C compacted using a California kneading compactor [84,123]. The test is applied to a cylindrical specimen having dimensions of a diameter of 101.6 mm and a height of 63.5 mm. The Hveem stabilometer test is considered an empirical test to measure the internal friction within a mixture [123]. The values of the internal friction measurements reflect more the aggregate properties, characteristics, and binder content than the asphalt binder grade [150]. Additionally, this test was replaced with Superpave thus it is no more considered a performance test [123].

Indirect Tensile Strength

The indirect tensile strength test is considered a method in order to determine the tensile properties of asphalt concrete mixtures which are related to permanent deformation properties of asphalt concrete mixtures [151]. The test is conducted at 25 °C where cylindrical asphalt samples are placed between two strips and a compression load is applied along the diametrical plane of the sample until failure. This compressive force is able to generate a uniform tensile stress perpendicular to the applied load plane. It was found that the results obtained from the indirect tensile strength test correlated well with the permanent deformation of asphalt concrete mixtures [150,152,153,154].

IDEAL Shear Rutting Test

The IDEAL shear rutting test (IDEAL-RT) was recently introduced by Zhou et al., (2020) as a monotonic-based loading test for the shear resistivity evaluation of asphalt concrete mixtures. IDEAL-RT is conducted in a similar way as the indirect tensile test with the difference that a shear fixture is used instead of an indirect tensile test fixture [60].

IDEAL-RT was proven to show good correlation and validation with other frequently used rutting field tests, specifically APA and HWTD, which makes it a suitable and practical test for asphalt pavement rutting performance as it takes into consideration the key components of asphalt concrete mixtures [155,156]. The cylindrical samples of 150 mm diameter and 62 mm height, compacted to 7% air voids, are subjected to axial displacement of a constant rate of 50 mm/min on their diametrical plane at a temperature of 50 °C [60].

For the quantification of the potential of permanent deformation, a rutting tolerance index is calculated using Equation (10) from a maximum load.

$$\mathit{RTindex}=\frac{6.618\times 10-5\times 0.0356\times Pmax}{t\times w}$$

(10)

where,

• Pmax is the maximum load, expressed in Newtons (N),
• t is the thickness of the asphalt specimens, expressed in meters (m), and
• w is the upper loading strip width which is equal to 0.0191 m.
• The lower the RTindex, the lower the resistance to shear deformation.

Simple Punching Shear Test

Faruk et al., (2015) introduced a new experimental rutting shear test known as the Simple Punching Shear Test (SPST) as a complementary test to the available rutting test [6]. The SPST is a monotonic loading-based test that characterizes and quantifies the shear properties of the asphalt concrete mixture against permanent deformation [108]. The SPST is performed using a lateral confinement pressure of 137.9 kPa and an axial compressive load using a steel punching head at a constant rate of 0.2 mm/s. The test is stopped when the steel head penetrates the total asphalt sample thickness of 63.5 mm with a run time of around an hour [6]. The sample to be tested has a diameter of 152.4 mm and a height of 63.5 mm, compacted to 7% air voids. The SPST revealed promising potential for the characterization and differentiation of the shear resistance properties of asphalt concrete mixtures as it is sensitive to the key mix variables of asphalt mixtures [6].

5. Laboratory Test Methods for the Characterization and Quantification of the High-Temperature Rheological Properties of Asphalt Binders

The rutting performance of asphalt concrete pavements is strongly affected by the asphalt binder properties [157]. As a matter of fact, hot mix asphalt rutting is dominant in high-temperature regions, specifically on roads having high traffic volume, heavy axle load, and slow-moving vehicles [158,159]. Consequently, the adequate laboratory measurement, characterization, and quantification of the high-temperature rheological properties of asphalt concrete binders during the material selection stage and mix design stage is a key factor to ensure satisfactory rutting performance of asphalt pavements [160]. This section covers the commonly used laboratory test methods and devices for the quantification of the high-temperature rheological properties of asphalt binders.

5.1. Superpave Rutting Parameter

Some basic asphalt binder indicators were often used for the performance description of the high temperature such as penetration, softening point, and rotational viscosity [1,161]. However, in the early 1990s, the Strategic Highway Research Program proposed a new specification known as the Superior Performing Asphalt Pavements (Superpave) that relates the physical properties of binders to the field performance [1,162]. The Superpave rutting parameter defined as (|G*|/sinδ) was considered one of the earliest rheological parameters commonly used to assess the rutting potential of asphalt binders [163,164]. The two parameters: dynamic shear modulus G* and phase angle δ, are measured from the Dynamic Shear Rheometer. Thus, to achieve higher resistance to rutting, a higher G* or lower phase angle (higher elasticity) should be attained. (|G*|/sinδ) is limited to 1 kPa for unmodified biners and 2.2 kPa for rolling thin-film oven-aged binders in order to determine PG-high temperature grade [165]. Despite the fact that this rutting parameter is commonly used, however, it was questioned for its inaccuracy with the emergence of modified asphalt binders as the Superpave experimental data based comprised tests conducted on unmodified asphalt binders [164,166,167,168]. In fact, Bahia et al., (2001) found a poor correlation between the results obtained from the experimentally measured mixes rutting and the results obtained from the application of non-linear viscoelasticity and energy dissipation concepts [169]. Additionally, the dynamic shear rheometer performs reversible load which is not in agreement with the rutting mechanism that occurs in actual pavements leading to the separation of strain energy dissipated in viscous flow from the total strain energy [168]. Furthermore, the loading cycle number is considered inadequate for the binder to reach a steady state behavior [168]. In an effort to resolve these deficiencies, refinements and new parameters have recently evolved to substitute the Superpave rutting parameter for the accurate rutting quantification of modified asphalt binders such as non-recoverable creep compliance [169,170], Shenoy’s rutting parameter [171], zero shear viscosity [172,173], and low shear viscosity [3,20,174].

5.2. Zero Shear Viscosity

Zero shear viscosity is a theoretical approach and is defined as the measured viscosity when the shear rate is zero [175]. This method was used to quantify and evaluate the rutting resistance of the mixture. However, it was substituted by another indicator, namely: low shear viscosity, due to the unrealistically high value of zero shear of modified asphalt binders [172,176] for the characterization of rutting resistance of asphalt pavements [3,177].

5.3. Repeated Creep and Recovery Test

The repeated creep and recovery test was proposed as a novel method to substitute the Superpave rutting parameter for better estimation of the rheological properties of modified asphalt binders [178]. The test method consists of measuring the permanent strain accumulated in the asphalt binder after a total of 100 cycles of repeated creep (of stress level ranging between 30 kPa and 300 kPa) and recovery, (1 s loading followed by 9 s unloading) for the purpose of representing the real loading features on the asphalt pavement [169,178]. The repeated creep and recovery test is conducted with the Dynamic Shear Rheometer and is considered an indication of the resistance to rutting, thus, the lower the permanent shear strain, the higher the resistance. On the other hand, it was demonstrated that the rheological behavior of binders in the non-linear viscoelastic zone was dependent on the applied stress and strain, and rather than the temperature and loading time which questions the potential of this test in predicting the modified binders’ rutting resistance under different loading levels [178,179].

5.4. Multiple Stress Creep Recovery Test

The multiple stress creep recovery (MSCR) test was developed by D’Angelo et al., (2007) in order to take into account the creep recovery behaviors of asphalt binders in the non-linear viscoelastic regime [180]. To assess the high-temperature performance of asphalt binders, two major parameters were proposed: non-recoverable compliance (Jnr) and the percent recovery (R). (Jnr) is an indicator of the asphalt binder resistance to rutting under repeated loading conditions measured at 3.2 kPa, whereas, (R) is a parameter used for the identification of the presence of elastic response and stress dependence of the binder [165,181]. It has been shown that the (Jnr) correlated well with the resistance to permanent deformation of asphalt mixtures [164,182,183]. Although this method was considered to be the most effective method for the assessment of the rutting resistance of modified binders at high temperature [184,185] and the (R) successfully distinguished the modified and unmodified binders, the stress level between 0.1 kPa and 3.2 kPa failed to present the non-linear features of the binder [181,183,186,187,188]. For the purpose of enhancing the MSCR test, (1) increase in creep time only, (2) increase in recovery time only, and (3) increase in creep and recovery time were used. It was recommended to use 30 cycles of creep and recovery in order to comprise the steady-state behavior of binders [165]. Additionally, increasing the stress level to 12.8 kPa was proposed for the accurate characterization of asphalt binder viscoelasticity [189].

A new parameter namely: the change in non-recoverable creep compliance to an incremental change in applied stress was proposed by [190] for the quantification of the stress sensitivity of the binder instead of the percent difference. This parameter was found to be able to accurately characterize the relationship between the predicted rut depth variation and the change in non-recoverable compliance.

Table 2. Some rheological parameters used to assess the rutting performance of asphalt binders.

Binder Rutting Test	Parameters	Literature	Results
Superpave rutting parameter	Dynamic shear modulus |G*|/and Phase angleδ (|G*|/sinδ)	[163,166,167,168,169,182]	Poor correlation between the results obtained and the results from the application of non-linear-viscoeelasticity and energy dissipation method.
Zero shear viscosity	Rut rate and viscosity	[173,180,191,192,193]	Time consuming and extensive effort should be placed to tested at very low shear rates. High sensitivity to molecular weight that may overestimate the rutting performance of binders.
Repeated creep and recovery Test	Elastic creep compliance, Je Delayed elastic creep compliance Jde and Gv viscous component of the creep stiffness	[169,178,180,194,195]	Testing at one stress did not take into consideration the stress dependency of modified binders.
Multiple stress creep recovery test	Non-recoverable creep compliance Jnr and percent recovery R	[165,180,181,183,186,187,188,189,190,196]	MSCR is found out to be the best and accurate method to predict rutting susceptibility of asphalt binders, very good correlation with other test results.

presents some rheological parameters used to assess the permanent deformation performance of asphalt binders and

Table 3. Correlation between MSCR test results and laboratory asphalt mixture rutting [165].

Literature	Stress Level	Temperature	Test Method	Conclusion
[197]	11 levels (25 to 25,600 Pa)	60	Wheel-tracking test	Jnr correlated better to the mixture rutting than (|G*|/sinδ), softening point and penetration.
[181]	11 levels (25 to 25,600 Pa)	58 to 70	Hamburg wheel-tracking test	Jnr correlated better to the mixture rutting than (|G*|/sinδ).
[186]	11 levels (25 to 25,600 Pa)	40, 50 and 60	Hamburg wheel-tracking test	Jnr correlated better to the mixture rutting than (|G*|/sinδ).
[164]	0.1 and 3.2 kPa	50	Wheel-tracking test	Jnr accurately predicted the binder’s contribution to asphalt mixture rutting, and with the compliance calculated from the unconfined dynamic creep test.
[164]	0.1 and 3.2 kPa	64	Unconfined dynamic creep	Jnr accurately predicted the binder’s contribution to asphalt mixture rutting, and with the compliance calculated from the unconfined dynamic creep test.
[198]	0.1 and 3.2 kPa	64	Flow time test	Jnr correlated well with the mixture rutting performance measured by flow time test.
[199]	0.1 and 3.2 kPa	64, 70, and 76	Hamburg wheel-tracking test and Repeated loading permanent deformation	Jnr, Hamburg wheel-tracking test and repeated loading permanent deformation test showed excellent correlation.
[200]	0.1 and 3.2 kPa	64	Flow number test	MSCR correlated well with the flow number test results.
[201]	0.1 and 3.2 kPa	60	Wheel-tracking test	MSCR is found out to be the best method to predict rutting susceptibility of asphalt binders.
[202]	0.1 and 3.2 kPa	70	Hamburg wheel-tracking test	Hamburg wheel-tracking test showed that rutting resistance based on Jnr is more accurate.
[163]	9 levels (100 to 25,600 Pa)	60	Wheel tracking-test	Jnr correlated very well with other binder rutting parameters.

shows the correlation of the MSCR binder rutting test results with the asphalt mixtures’ experimental rutting results.

6. Advanced Computational Intelligence Methodologies

Despite the fact that several researchers have worked in the field of prediction of permanent deformation in asphalt pavements, the physics and mechanics of the permanent deformation problem are still not fully understood which makes it complicated to explain it mathematically [203]. Lately, efforts have been placed towards the use of different techniques for developing a rutting prediction model that takes into consideration various effective factors. Consequently, advanced recognition techniques such as finite element model, soft computing, and machine learning techniques are being examined.

6.1. Finite Element Method

The application of the finite element method to stimulate asphalt pavement is rapidly increasing due to the non-linear relationship between stress and strains, thus the use of 3D models is necessary for the accurate and realistic characterization of asphalt concrete pavement responses [204,205]. In the finite element method, the pavement structure is divided into many finite, small, and discrete elements that are solved simultaneously [205]. Different finite element models have been elaborated for stimulating the behavior of asphalt concrete mixtures and analyzing the asphalt pavement responses and determining the contribution of each layer of the pavement structure to the rut depth [205,206,207,208,209,210,211]. Various methods for permanent deformation prediction are available notably finite difference methods [207], analytical methods [212], multilayer elastic theory, hybrid methods [213], and finite element methods [206,214]. Gu et al., (2016) assessed the mitigation effect of geogrid-reinforced asphalt pavements on the rutting damage through a finite element model. The findings revealed that reinforced asphalt pavements resisted permanent deformation better than unreinforced asphalt pavements [215]. The findings of Fussl et al., (2018) who developed a finite element model to predict asphalt pavement performance correlated well with the field-tested findings [216]. Liu et al., (2022) proposed a constitutive finite element model using ABAQUS software to predict the rutting behavior of asphalt pavements [217]. Wang et al., (2022) applied FlexPAVE^TM a finite element analysis software with moving loads in order to predict the asphalt pavement rutting performance. The outcomes showed a very good correlation between the predicted performance and field observations [218].

6.2. Machine Learning and Soft Computing Methods

Machine learning is considered to be the most popular technique to develop performance-based predictive models from empirical data in order to predict the performance of different materials such as asphalt concrete [219,220,221]. Machine learning has been used to reach different objectives such as pavement distress [222], performance prediction, evaluation of viscoelastic behavior of asphalt [217], and rutting prediction [223].

6.2.1. Artificial Neural Network

Artificial neural network was first inspired by the biological neural network of the human brain and have shown to be a powerful yet accurate tool for the realistic prediction of different parameters without any limitation. Meanwhile, artificial neural network has been employed to conduct non-linear statistical modeling. Neural Networks are able to identify complex non-linear relationships between the variables (dependent and independent) and thus have the ability to identify all interactions between those variables. Different investigations have been executed in this field. Mirzahosseini et al. (2011) examined the permanent deformation potential of asphalt concrete mixtures by applying a multilayer perceptron technique [224]. Oh and Barham (2011) revealed that the artificial neural network backpropagation algorithm is considered an effective technique for capturing the non-linear modeling functions to predict the rutting of asphalt materials [225]. Shafabakhsh et al. (2015) found that the backpropagation algorithm is a suitable approach to predict rutting for asphalt mixtures with nano-additives [226]. Amin and Amadorr-Jimenez (2017) applied the backpropagation neural network algorithm to model the pavement condition index [227]. Mirabdolazimi and Shafabakhsh (2017) concluded that their developed artificial neural network model for the prediction of rut depth correlated very well with the experimental results [228]. Haddad et al. (2021) developed a permanent deformation model by employing a deep neural network on data extracted from the LTPP database. The outcomes revealed that the elaborated model enhanced predictive power when comparing it to the models present in the existing literature [229].

6.2.2. Genetic Programming

Genetic programming is defined as a supervised machine learning technique that searches a program space instead of a data space and is known as another approach for the analysis of the permanent deformation potential [230,231]. It was first introduced by Koza (1992) [231]. In genetic programming, an arbitrary population of trees (known as computer programs) is elaborated to get higher diversity. Several investigations have assessed genetic programming for the purpose of finding any complex and complicated relationships between experimental data [232,233,234,235]. Gandomi et al. (2010) elaborated new models for the prediction of the flow number of asphalt concrete number using genetic programming [236]. Additionally, Hossein Alavi et al. (2010) used genetic programming along with simulated annealing algorithms to find new prediction models for the flow number [237]. Furthermore, multi-expression programming is a new approach to genetic programming using a linear representation of chromosomes. Multi-expression programming is able to encode several computer programs of a problem in a single chromosome [224]. However, multi-expression programming has been applied in limited areas related to civil engineering [238,239].

7. Enhancing the Permanent Deformation Resistance of Asphalt Concrete Pavements

To reduce the permanent deformation of asphalt pavements, measurements can be grouped into four categories namely: Binder-based technologies and mixture improvement methods, aggregate-based methods, structure-based techniques, and cooling methods.

7.1. Binder-Based Technologies and Mixture Improvement Methods

On the asphalt binder level, asphalt binder properties contribute to around 40% of the permanent deformation performance of asphalt pavements [24]. For the purpose of mitigating rutting in asphalt pavements, enhancement of the rheological properties of the asphalt binder was considered. The typical means of improving the high-temperature rheological properties comprised the addition of different modifiers into base asphalt binder such as ethylene copolymer [240], styrene–butadiene–styrene (SBS) [241], Trinidad Lake asphalt [242], high modulus modifier [243]. Additionally, a wide variety of additives is used to improve the anti-rutting performance of asphalt binders such as nanomaterial particles [244], anti-rutting additives [245], epoxy resin [246], crumb rubber [157], fiber and furan resin [247]. Additionally, some composite modifiers are used such as SBS/nano-clay composites [248], anti-rutting agents, polyethylene [249], etc.

On the other hand, and on the mixture level, the asphalt binder extracted from Reclaimed Asphalt Pavements (RAP) was found to have a viscosity higher than that of the traditional one. Consequently, to enhance the rutting resistance of asphalt mixtures, RAP was added to the asphalt concrete mixture. However, its proportion should be monitored as the addition of high percentages of RAP often led to other distresses such as thermal cracking, poor fatigue performance, and secondary aging [250,251]. Additionally, different types of wastes and powders were introduced into asphalt concrete mixtures as a replacement for aggregates or mineral filler which demonstrated to have higher rutting resistance than that of the control mix when using it in a specific proportion range such as municipal solid waste incineration fly ash [252], municipal solid waste incineration bottom ash [253], brick debris [254], zeolite tuffs [255], construction demolition waste [256], glass waste powder [257], coal waste powder [258], and rice husk ash [259]. It should be noted that the majority of the previously mentioned technologies to enhance the rutting resistance of asphalt mixtures fall within the hot mix asphalt (HMA) mix type [1].

7.1.1. Warm Mix Asphalt

Warm mix asphalt (WMA) is recently gaining popularity by virtue of its savings in energy and reduction in carbon dioxide emission during the process of production and placing [1]. As revealed by several research studies, the permanent deformation resistance of WMA was commonly higher than that of the control HMA mixture for the reason of reducing mixing temperature and binder aging [260,261]. The improvement in the rutting performance of WMA was affected by the type of warm additive: mixes having additives such as Asphamin^® and Evotherm^® revealed comparable rutting resistance to the control mixture [262]. In contrast, mixes having 3% Sasobit and 2% Rheofalt showed improvement in the non-recoverable compliance by 82% and a maximum recovery of 28% [263,264]. Additionally, crumb rubber, steel slag, nanoclay, and glass fiber were shown to enhance the rutting resistance when added to WMA [18,262,265]. However, the findings of some studies revealed that WMA mixes were harder to compact and thus were susceptible to rutting [261,262].

7.1.2. Half-Warm Mix Asphalt

In practice, the mixing temperatures of half-warm mix asphalt (HWMA) are below 100 °C whereas the mixing temperatures for WMA are between 120 °C and 130 °C. For HWMA, the aggregates are considered to have a substantial amount of moisture. This new technique is rapidly gaining popularity as a sustainable alternative to HMA [18,266]. The outcomes of research studies have shown that the presence of moist aggregates resulted in better rutting resistance than that of the control mix, especially with the use of recycled materials [267,268].

7.1.3. Cold Mix Asphalt

Cold mix asphalt (CMA) is more sustainable and energy-efficient than HMA, WMA, or HWMA as it is placed in ambient temperatures and can be either cement-based CMA or asphalt emulsion-based CMA [1]. It was revealed that CMA stabilized with cement had developed higher resistance to permanent deformation than CMA stabilized with emulsified asphalt [269]. Furthermore, the resistance of the CMA mix to permanent deformation was significantly observed when SBS-modified asphalt emulsion and limestone filler were used [270,271].

7.2. Aggregate-Based Methods

One way to mitigate excessive shear strain and enhance the rutting resistance of asphalt concrete mixtures is by optimizing the aggregate gradation and properties [29,46]. As a matter of fact, aggregates contribute to the majority of the mixture and thus the internal friction angle makes up around 80% of the shear strength [272]. Thus, adjusting the aggregate gradation, commonly coarse or gap gradation [273], and optimizing the properties of the aggregates used to be high friction aggregates, angular and rough surface texture [274,275], strengthen the aggregate interlock resulting in improvement in rutting resistance. The failure proneness of asphalt mixtures significantly increased when using fine aggregate instead of crushed particles [276,277]. Furthermore, using a dense gradation and larger aggregate size contributed to higher aggregate interlock and therefore considerably dissipated the shear stresses leading to higher shear resistance [13].

7.3. Structure-Based Optimization Techniques

Structure-based optimization techniques, including geosynthetic materials or sheets that are placed at the bottom of the asphalt layer or between asphalt overlays, are proven to enhance the bearing capacity and stiffness of the pavement structure and decrease the shear strain and thus the permanent deformation of the entire pavement structure [278,279]. Additionally, it was shown that the use of semi-flexible pavements, which are composed of asphalt mixture having 20–35% air voids filled with cement slurry, enhances the mechanical performance of the mixture and consequently enhances its rutting resistance [280,281].

7.4. Cooling Methods

The aim of the use of cooling measures and thermal regulation in asphalt pavements, known as cooling pavement, is to reduce the development of rutting distress [282,283,284]. Three categories of cooling measures were used to reduce the accumulation of heat in flexible pavements, namely: heat-reflective and heat-resistant materials [285,286], phase change materials and solar energy collector pavement [287,288], and permeable and water-retentive asphalt pavement [289]. The first category of cooling measure is used to mitigate the solar absorption of flexible pavements whereas the second category is used to absorb the accumulation of heat and the third category is used to discharge the accumulation of heat by the evaporation of water.

Although these thermal regulations have great cooling effects, some of these methods cannot be used to reduce permanent deformation. In fact, phase change materials affected negatively the mechanical performance of asphalt pavements [290,291]. Additionally, energy collector materials altered the distribution of the stress in the asphalt pavement which increase the proneness to permanent deformation [292]. Consequently, a thorough review is needed about these cooling methods to suggest some recommendations to improve their use for the aim of reducing the rutting performance of asphalt concrete pavements.

8. Conclusions and Recommendations Discussion

Permanent deformation occurs in asphalt concrete layers as a result of three modes: loss of materials, densification, and shear-related deformation known as the lateral plastic flow, namely. The third mechanism makes up the greater part of the research conducted to address permanent deformation. Although the occurrence of permanent deformation in flexible pavements has become a principal distress mode, rutting can lead to many serviceability-related, social, and structural problems. Despite the fact that aggregates constitute the largest part and are crucial to the shear strength of the mixture, the existing studies commonly address the permanent deformation performance of the pavement by finding effective measures to improve the rutting resistance of the mixtures or by modifying the asphalt binder for the purpose of enhancing its rheological properties such as adding rubber, fibers, wastes, RAP, polymers, etc.

Along with modifying the asphalt binder or mixture and enhancing the aggregate interlock to improve the rutting resistance, pavement structure-based optimization techniques were used to decrease the sensitivity of pavements to permanent deformation. Although the Superpave rutting parameter (|G*|/sinδ) has been used extensively for the evaluation of the rheological properties of asphalt binder, the multiple stress creep recovery was considered to be the best approach to test the rheological properties of modified and unmodified asphalt binders. Although simulated-based loading tests have been widely used to assess the permanent deformation response, these tests cannot accurately supply the mechanical parameters of the mixture to be tested; thus, the stress sweep rutting test is recently developed and gaining popularity as it tackles the shortcomings of its predecessor tests for the exact characterization and prediction of permanent deformation of asphalt mixtures. Efforts have been placed towards the use of different techniques for developing a rutting prediction model that takes into consideration various effective factors. Consequently, advanced recognition techniques such as finite element model, soft computing, and machine learning techniques are being examined for accurate and realistic characterization of the behavior of asphalt concrete mixtures and the stimulation of asphalt pavements due to the non-linear relationship between stress and different types of strains.

Based on the findings of the existing literature, and the knowledge and experience of the authors, a set of recommendations and suggestions were discussed to enhance the rutting resistance of asphalt concrete pavements. Semi-flexible pavement is proposed as an anti-rutting solution fighting this type of distress in asphalt concrete pavements as it has high mechanical properties without altering the pavement flexibility. Additionally, cooling measures are considered a promising method to improve the resistance to permanent deformation of asphalt pavements.