A review of rutting in asphalt concrete pavement

4.1 Traffic characteristics

Traffic characteristics is one of the most important factors affecting rutting, it includes tire contact pressure, vehicle speed, and the number of load repetitions (traffic volume).

The shape of the contact area between a tire and the road surface is approximately circular when the load applied is small relative to the recommended maximum for the tire, but it becomes increasingly elongated as the wheel load is increased at constant inflation pressure, this is shown in Figure 6, where the highest load considered is 50% above the tire manufacturer’s rating [19]. In calculating pavement stresses resulting from the passage of the traffic, it is usual to assume that the load carried by the wheel is uniformly distributed over a circular area and the radius of loading is calculated from the wheel load and the tire pressure [1], this is because it is assumed that the tire pressure is equal to the contact pressure (no effect for tire wall).

Figure 6

Tire prints for different loadings [19].

Higher tire pressures and weights of trucks since the AASHTO road testing have resulted in higher HMA rutting [18]. Responses to the 1987 AASHTO survey on the HMA rutting problem showed that 93% of those responding expressed that heavy truck tire pressure was a major cause of HMA rutting [2]. While the current 1993 AASHTO guide [17] for the design of pavement structure [17] is based on 18 kip loads and tire contact pressure of 75–80 PSI, recent studies [20,21] have shown that truck tire inflation pressure have increased and are now averaging around 100 PSI. Some researchers [20,22,23] reported truck tire pressures to be as high as 140 PSI. Chen et al. [24] stated in their field study using the Texas Load Simulator that such an increase in tire inflation pressure from 80 to 100 PSI leads to an increase in rut depth of about 43% after 1,600,000 axle load repetitions. In Dubai [26], after extensive laboratory and field studies, it was determined that the mixture and pavement had originally been well-designed according to existing methodologies. But the accelerated rutting (after 10 months of trafficking) appeared due to heavier than expected loads (up to 80,000 lb axle loads as compared to the 18,000 lb axle loads used for design) and higher tire pressures. Abbas et al. [27], in their study of the rutting in the oil tanks road located west of Baghdad, indicate that the increase in the tandem axle load by 61% leads to an increase in rut depth by 82%.

Another factor related to the traffic that significantly affects the rutting of asphalt concrete layers is the speed of traveling vehicles. When the viscoelastic approach is used to calculate the pavement response to the applied wheel load, speed is directly related to the duration of loading. If the elastic approach is used in the pavement response calculation, the elastic modulus of asphaltic concrete layers should be determined in commensurate with the vehicle speed. Generally, the greater the speed, the larger the modulus, and the lesser the deformation in the pavement [1]. Pereira et al. [28] investigated the effect of truck speed on the accumulation of permanent deformation; measurements of the development of actual rut depth were recorded as a function of truck speed (which decreased as the trucks climbed a steep hill) for the three sites in Portugal. The investigated roads pass through hilly terrain where long stretches of highways are on inclines and trucks frequently slow down to about 20 km/h. Schematic diagram for the location of highway and rutting severity is shown in Figure 7.

Figure 7

Schematic diagram showing the effect of vehicle speed along the grade on the rut depth [28].

Pereira stated that the rut depth at the end of the upward direction lane with 5% grade and 25 km/h average truck speed is 20 mm, while at the beginning of the grade, the rut depth is 10 mm. Also, Fwa and Tan [29] stated in their rutting survey on Singapore roads that rutting is commonly found in the slow lanes of major highways and in the approaches to the traffic-light junction. He also stated that this is an indication of the association of this problem with the slow-moving vehicles. Albayati and Saadi [30] in their research on some of the important rural highways connecting Baghdad with other governorates agreed with the above observation. They also found that all the observed highways suffer from rutting particularly on the slow-moving vehicle lane (right lane), which carries the bulk volume of the commercial vehicles.

The third component of the traffic that affect rutting is load repetition. In general, as the load repetition increases, the rutting increase. Specifically, the trend of this relationship is a function of several factors, such as temperature, loading conditions, and mixture parameters. Researchers [31,32] show that in most cases it follows the linear trend when plotted in log scale. Eisenmann and Hilmer [33], on the basis of wheel tracking test results, suggest the following relationship between the rut depth (Rd) and the number of load repetitions (N):

where a and b are laboratory determined parameters.

From the preceding discussion, it is apparent that the increased tire inflation pressure has placed the HMA mixture near the surface under high stresses, through increase in the probability of rutting. Therefore, more attention should be given to the selection of high-quality materials in designing the asphalt mixture and to quality control during the construction of the surface course of flexible pavement in order to minimize rutting.

4.2 Temperature

Rutting is more prevalent in hot climate areas because the viscosity of the asphalt binder which is inversely related to rutting is significantly reduced with the increase in temperature resulting in a more rut susceptible HMA mix. Figure 8 shows the effect of temperature on log asphalt viscosity for a wide range of asphalt cement grades [34]. From the Figure, it is obvious that the viscosity of asphalts varies from less than one Poise to more than one trillion Poises. Within such an extreme viscosity range, asphalts are transformed from low viscosity Newtonian liquids to materials exhibiting shear-dependent visco-elastic behavior, where with decreasing temperature, the elastic component tends to be predominant. Thus, the gradually changing curvature of plots in Figure 8 indicates that the viscosity of asphalt tends to change more rapidly at low temperatures, and such change becomes far less pronounced at higher temperatures when the viscous behavior is predominant.

Figure 8

Relationship between viscosity and temperature for asphalt cements [34].

Figure 9

Effect of pavement temperature on rut depth [7].

Figure 10

Effect of asphalt cement penetration grade on rutting [40].

Hofstra and Klopm [7] showed from test wheel track measurements that rutting is significantly increased when testing temperature varies from 20 to 60°C. The obtained result is shown in Figure 9. The presented data indicate that the rut depth increases by a factor of 250 when the temperature increases from 20 to 60°C (from 68 to 140°F), this is consistent with Linden and Van der Heide [35] who reported a significant increase in rutting in Europe during the very hot summers of 1975 and 1976.

Célard [36], when testing cylindrical specimens (100 mm diameter × 200 mm height) in dynamic creep test, stated that the creep rate (percent deformation per million cycles) is increased by a factor of 2.5 when testing temperature changes from 25 to 35°C, under loading condition of 10 cycles per second and 70 PSI deviator stress.

Based on wheel tracking tests to evaluate some of the pavement mixtures conventionally used in Singapore, Fwa and Tan [29] state the following “after 10,800 passes of load, at 35 and 60°C test temperatures, the corresponding rut depth is 3.89 and 12.95 mm, respectively, i.e., 70% of rut depth was developed at 60°C.”

Tayebali et al. [37] carried out 36 repeated axial creep tests to evaluate the applicability of this test and some other tests in the assessment of rutting potential for a mixture containing modified binders. They found that the average plastic strain increased by a factor of 1.5 when the testing temperature increased from 40 to 60°C. This was observed at 20 PSI axial stress and 0.1 s load duration (60 cycles per minute).

Yassoub [3] stated that the time required to achieve 10 mm rut depth in asphalt concrete at 50°C is 72% shorter than that required at 40°C. Bonnot [38] selected a test temperature of 60°C for wearing-course asphalt concrete and 50°C for base courses. These temperatures were chosen to be relatively high to reproduce the most unfavorable conditions expected in France. Similarly, Mahboub [39] conservatively selected the hottest pavement profile to represent critical conditions. Based on the above, it can be concluded that the researchers have recognized the need to conduct laboratory tests at temperatures within the high-temperature range encountered in the field.

4.3 Asphalt concrete mixture components and properties

Speer [40] investigated the effect of different asphalt penetration grades on the rutting potential of asphalt concrete. His investigation was based on the laboratory test track and traffic simulator machine which have the capability for applying different tire pressures (30, 50, 70, and 90 PSI). Based on his experiments, he stated that asphalt cement with a softer grade (90) resulted in a rut depth more than that of penetration grade (40) by a factor of 1.5 at the end of one million repetitions of 90 PSI tire pressure. The comprehensive results of Speer are shown in Figure 10. However, Speer cautioned about the construction problems associated with the use of hard-grade asphalt due to the difficulty of mixing operation and pavement laydown process.

Leahy and Witczak [41] compared the performance of an AC-5 and AC-20 as related to the accumulated plastic strain in the repeated load test. They found that the plastic strain introduced to the asphalt mix by using AC-5 is 20% higher than that introduced by using AC-20 under the same loading and environmental conditions. On the basis of uniaxial static creep tests (1 h. loading time, 20°C testing temperature, and 14.5 PSI stress level), Mahboub [39], when investigating the performance of three types of asphalt cement (AC-5, AC-10, and AC-20), concluded that less viscous asphalts make the mixture less stiff and therefore more susceptible to irrecoverable deformation, i.e., rutting. Monismith et al. [42] made similar observations and recommended the use of harder (more viscous) asphalt cement on thicker pavements and hotter climates. Also, Decker and Goodrich [43] found that at a given temperature and loading rate, a high viscosity asphalt cement resulted in a stiffer mix which provides better rutting resistance, but they state such grade may cause low temperature cracking problems. Therefore, as they stated, a balance between the requirements of asphalt viscosity should always be maintained to ensure good performance of asphalt mixture during hot and cold ambient conditions. Hughes and Maupin [44] compared the performance of an AC-20 and AC-30 to prevent rutting. The researchers reported that the binder type was not as important as the aggregate gradation in minimizing early rutting. Keyser and Ruth [45] reported in a field study of pavements in Quebec, Canada that there was no good correlation between asphalt cement viscosity and rutting susceptibility. This conclusion, which is in contrast with that observed by the abovementioned researchers, may be attributed to the low ambient temperature encountered within this area which vanishes the effect of asphalt viscosity (mean annual temperature is −7.2°C, as listed in the World Index program [46]). Several researchers have tried to improve the rutting performance by using modifiers (polymers, micro fillers, etc.) to increase the viscosity of the asphalt cement at high temperatures without adverse effects at low temperatures. For example, Monismith and Tayebali [47] investigated the relative behavior of mixtures containing AR2000, AR8000 (AR refers to Aged Residue viscosity) and AR2000 modified by carbon black as micro filler. Based on both creep tests and repeated load triaxial tests, the latter two mixtures resulted in better resistance to permanent deformation at high temperatures than the mixture containing the AR2000 asphalt cement.

There is much in the literature on the relationship between asphalt cement content and asphalt concrete rutting susceptibility. Arabia [48] compared the results of cores from both good-performing and rutted areas of seven pavements in Saudi Arabia to identify the mix and material properties that caused rutting susceptibility. The author reported that the rutted areas had higher asphalt cement contents than the good-performing areas. Higher asphalt content is defined by the author as that produced air voids in a mix of less than 3%. Brown et al. [49] stated on the basis of laboratory test track that the addition of 0.5% asphalt beyond the optimum content increases the permanent deformation by approximately 50%. Mahboub and Little [50] indicated that higher asphalt cement contents which produce lower air voids increased rutting potential. They suggested that the reduction in air voids as a consequence of increased asphalt content is attributed to the fill of void space with asphalt. As a result, the increase in asphalt content is equivalent to the introduction of lubricants between aggregate particles otherwise separated by a very tight network of air voids. This phenomenon causes the mixture containing higher asphalt content to be more susceptible to permanent deformation induced by the viscous flow of asphalt between aggregate particles.

El-Basyouny and Mamlouk [51] studied the effect of aggregate gradations and asphalt contents on rutting potential using a cyclic creep test. The obtained results of tests were recorded as alpha and Mu for use as input to the VESYS3AM program for the purpose of rut depth calculation. The obtained results indicate that the optimum asphalt content (4.5%, for 19 mm aggregate maximum size) yields the minimum rut depth (10 mm) after six million standard axle load repetitions. This conclusion may provide further evidence to the earlier mentioned conclusion that an increase in asphalt content beyond optimum is equivalent to the introduction of lubricants between the aggregate particles with the consequence of increasing mix susceptibility to permanent deformation.

There have been numerous laboratory and field studies on the effect of aggregate characteristics (surface texture, shape, max size, and gradation) on the HMA rutting. Aggregate with rough surface texture provides higher internal friction and a stronger bond with the asphalt cement to provide better mix stability and rut resistance. Parker and Brown [52] investigated 13 pavements and rutting data from Alabama Highway Department road condition database to determine the aggregate properties that relate to rutting susceptibility. The authors concluded that the pavements with more angular, crushed particles experienced less rutting than pavements with more rounded aggregates.

Perdomo and Button [53] conducted a study to evaluate the effects of natural sands on permanent deformation and to quantify the influence on resistance to plastic deformation when natural sand is replaced with crushed fine aggregate. The study showed that the total deformation and rate of deformation increased as the percentage of natural sand increased. The shape and texture of the fine aggregate were major factors controlling plastic deformation in asphalt concrete mixtures. The authors recommended replacing natural sand with manufactured sand to increase the resistance of the asphalt concrete pavement to permanent deformation. Kalcheff and Tunnicliff [54] conducted a laboratory study to determine the effects of crushed aggregate size and shape on the properties of asphalt concrete mixtures. They specifically evaluated the effect of coarse aggregate gradations and the shape effects of fine aggregates. The laboratory specimens were produced with Marshall and Hveem methods using an aggregate blend composed of natural and manufactured sands. The authors reported that asphalt mixes having a higher percentage of coarse aggregate have less deformation; also, the authors found that asphalt concrete mixtures containing crushed fine aggregate were more resistant to permanent deformation from repeated loadings than comparable mixtures containing natural sand. The behavior of the asphalt concrete mixture was improved when manufactured sands replaced natural sands.

Brown et al. [55] reported that increasing the maximum aggregate size generally results in a tougher mix. Kandhal [56] and Brown and Bassett [57] believed that the use of larger aggregate size in asphalt mixes can minimize or eliminate rutting in HMA pavements. Dawley et al. [10] reported the results of a laboratory creep study which showed that mixes with larger max size, more crushed coarse aggregate, and less natural sand provide more resistance to permanent deformation than mixes with smaller max sized gravel and natural sands. Monismith et al. [42] reported that dense aggregate gradations are desired to mitigate the effects of rutting. Dense gradation (close to the 0.45 power curve) mixes tend to have higher stiffness and thus higher resistance to rutting. Moore and Welke [58] conducted numerous asphalt mix designs to determine the effect of fine aggregate on the Marshall stability. They stated that the asphalt concrete mixture gradation and aggregate angularity were very significant in increasing the stability of mixtures. They reported that as the mixture gradation approached the 0.45 curve for maximum density, the Marshall stability increased. They also stated that the more angular the fine aggregate, the higher the stability. The study concluded that rounded fine aggregate (natural sand) produced lower stabilities than the crushed fine aggregate.

Marker [59] and Crawford [60] concluded that particle shape and the amount of material passing the No. 4 sieve were major factors contributing to the tenderness of an asphalt concrete mixture. They showed that most tender pavements have an excess of middle-sized sand particles (No. 8 to No. 100) in the aggregate gradation. This excess of mid-sized sand particles is revealed as a hump in the curve when the gradation is plotted as percent passing vs the sieve size raised to the 0.45 power. Tenderness is generally most critical when this hump is near No. 30 sieve. This condition is generally combined by a relatively low amount of filler. The authors also stated that rounded, uncrushed aggregates are more likely to contribute to tender mixes, especially as the amount of uncrushed material passing the No. 4 sieve increases. Brown and Cross [61] conducted a study to evaluate aggregate properties that affect pavement rutting. Samples from 42 pavements that had rutted in less than 5 years or been in service for more than 5 years without rutting were tested to determine aggregate and mixture properties. The authors concluded that aggregate properties do not significantly affect the rutting potential when in-place air voids are below 2.5% since the mixtures tend to rut regardless of aggregate properties. They stated that the percentage of fractured faces of the coarse aggregate affected the rate of rutting. The rate of rutting increased as the percentage of crushed faces decreased. They concluded that higher percentages of crushed coarse aggregate and crushed fine aggregate reduced the potential for rutting. The effect of aggregate characteristics on rutting has also been demonstrated from field studies of the following researchers: Miller et al. [62], Huber and Heiman [63], Grau [64], and Carpenter [65], all of these authors reported less rutting occurred in HMA pavements with more crushed coarse aggregate and manufactured fine aggregate than that in HMA pavements constructed using rounded aggregate and natural sand.

A portion of the mineral filler (particles greater than asphalt film thickness) contributes to the interlocking of the aggregate. The other portion of the filler (particles less than asphalt film thickness) is suspended in the asphalt cement and acts as part of the binder in the mix. The resulting filler-asphalt binder can increase the stiffness by more than 100 times depending on the types and sizes of the mineral filler [66,67]. Dukatz and Anderson [68] reported that creep compliance is greatly increased by the stiffening of the filler. Brown et al. [55] reported that there is evidence that the optimum amount of filler content is between 4 and 8% for well-graded asphalt concrete to improve its resistance to permanent deformation.

Asphalt mixture volumetric properties (air voids, voids in mineral aggregate [VMA], and voids filled with asphalt [VFA]) have an essential role in the rutting susceptibility of HMA mixes [69]. The importance of air voids in HMA mixes is well documented in the literature. The Federal Highway Administration (FHWA) Technical Advisory on Asphalt Concrete Mix Design and Field Control [70] recommended that pavements have an in-place air voids content of 3–5% after densification by traffic. To achieve this air void content, the Technical Advisory recommends that asphalt mixes be designed with 3–5% voids at optimum asphalt content. This requirement is adopted by the Iraqi specification for HMA concrete [71].

Ford and Ford [72] studied the relationship between in-place air voids and rutting. Thirty-eight pavement sites were selected to represent various types of HMA pavements in the state of Arkansas. The pavement structure age ranged from 0.5 year to 22.7 years and the number of total accumulated 18 kip equivalent single axle loads ranged from 130,000 to 3,100,000. The rut depth of each pavement was measured before taking three inside wheel path cores using a 101.6 mm (4 in) core machine. The author stated that rutting is more severe for pavements with air voids significantly less than 3% [72].

Brown and Cross [73] observed low voids in their prematurely rutted pavements and they observed in other studies [61] that when the in-place voids were below 3%, the probability of having premature rutting was much higher than if the voids were above 3%. Huber and Heiman (1986) found no direct correlation between voids and rutting; however, they reported that 4% voids appeared to be a threshold value with unacceptable rut depths occurring as voids fell below 4%. The relationship between voids and rutting was not well defined by Kandhal et al. [74]. However, they did report that pavements that rutted prematurely had lower in-place voids than pavements that did not rut prematurely.

Several researchers related the importance of the mix design void content to an unacceptable rate of rutting. The U.S. Army Corps of Engineers recognized the importance of voids when they developed their specifications for the Marshall mix design method. The original requirements [75] specified that the HMA should have between 3 and 5% voids at optimum asphalt content, which is still recommended today by SCRB [71]. Dawley et al. [10] concluded that HMA should be designed at 4% voids to prevent low voids in-place and hence an unacceptable rate of rutting. Miller et al. [62] concluded that the mix design void content should be raised from 2.5 to 4% to prevent premature rutting in Illinois. Ford and Hensley [76] concluded that premature rutting in Arkansas pavements was related to low mix design air void contents. Kandhal et al. [77] reported that Pennsylvania HMA with higher mix design voids experienced lower rates of rutting.

Several researchers reported good correlations between VFA and rutting susceptibility. Huber and Heiman [63] reported that the in-place VFA should be a maximum of 70% to minimize rutting; however, they qualified their statement for VFA as being lower than usually suggested and recommended further study. Ford and Ford [72] found a relationship between VFA and rutting susceptibility which showed that higher VFA lead to an increased rate of rutting. The US Army of Corps of Engineers [75] recommended that VFA be between 75 and 80% for 50 blow mixes, and 70–80%, for 75 blow mixes, based on laboratory and field studies. However, neither the FHWA [70] nor SCRB [71] gives recommendations for voids filled with asphalt cement.

The volume contained between aggregate particles in a compacted paving mix is termed the VMA. It is composed of air voids and effective asphalt volume [78]. For asphalt concrete with an aggregate maximum size of 19 mm, the SCRB specifications recommended 14% as a minimum [71]. Pradhan [79] presented data related to VMA for permanent deformation of asphalt concrete mixes, he stated that as VMA decreased, the resistance to permanent deformation increased. Huber and Heiman [80] found that HMA pavements with high VMA have higher rutting than pavements with low VMA and reported a VMA of 13.5% for mixes with an aggregate top size of 16 and 18 mm.

5.1 Laboratory test methods

The overall objective of materials testing should be to reproduce as closely as practical in situ pavement conditions, including the general stress state (stress magnitude and duration), temperature, and general condition of the material. Laboratory tests usually used to characterize the permanent deformation response of asphalt concrete are typically categorized as uniaxial, triaxial, or diametral. Within those three general categories, loading may be static (creep), repeated, or dynamic [81].

Before the discussion about the properties of each test and how much it can simulate the field conditions, it is necessary to highlight the stress condition (magnitude and duration) within the pavement under the effect of moving loads. The stress condition within the asphalt concrete surface layer is varying according to the location with respect to both the axis of loading and the neutral axis. For an element away from the axis of loading symmetry, the element is subjected to three normal stresses in the direction of x, y, and z, also there are three tangential shear stresses acting on the surfaces of the equilateral element. Under these three-dimensional states of stress, unfortunately, no testing equipment is currently available which can simulate these stress conditions. Therefore, some simplification is required, if an element on the axis of load symmetry is being considered, then two simplifications will bring the stress conditions in line with those occurring in the triaxial test. The principal stresses will become vertical and horizontal (no shear stresses) and the two stresses acting horizontally in the direction of x and y will be equal. Further, along the axis of load symmetry, the state of stress varies according to the location with respect to the neutral axis, as shown in Figure 11. Also, from the same Figure, it can be shown that the vertical stress remains in a compressive state, while the horizontal stress varies from the compression above the neutral axis to tension below the neutral axis.

Figure 11

Average theoretical stress state for 26.67 cm (10.5 in) thick full-depth asphalt concrete pavement under the axis of loading [90].

Application of tensile stresses to reproduce the theoretical stress condition in the bottom of the layer is quite difficult and not suitable for use in a routine design method for characterizing the permanent deformation [82]. Also, when an element of asphalt concrete in the tensile zone starts to deform laterally in the direction of the tensile stress, passive resistance would be encountered due to the presence of surrounding materials; therefore, the lateral tensile stress developed in the field would be less than that calculated by the layered theory [82]. Near the center of the asphalt concrete at the neutral axis, the lateral stress is zero and an axial compressive state exists similar to that in the unconfined compression test [82].

The existence of a simple unconfined compressive stress state near the center of the layer suggests that such a condition can be reasonably close to the average of the tensile and compressive stress state within the entire asphalt concrete layer. This can be a practical alternative to using considerably more complicated stress states involving both tension and compression which require more sophisticated test equipment with a possibly high cost that makes attaining them by most testing laboratories difficult [81] . For the above reason, the uniaxial load test may be more practical than that of the triaxial test in characterizing the permanent deformation of the asphalt concrete.

On the other hand, the diametral test can also be used for characterizing permanent deformation, but its use does not seem promising for two major reasons:

The state of stress is nonuniform and strongly dependent on the shape of the specimen [83]. At high temperatures or high loads, permanent deformation produces changes in the specimen shape that significantly affect both the state of stress and test measurements.

Its use is restricted to relatively low testing temperatures (less than 40°C) and for low-stress levels (less than 20 PSI) [84]. Accordingly, the diametral test may be better suited to the repeated load testing associated with modulus measurements than to the longer time periods associated with the permanent deformation characterization [84].

Although researchers agree that the non-recoverable deformation of an asphalt concrete layer in a pavement structure can be best characterized by the axial compression test, they differ on the type of loading that should be used in this test. In order to best simulate the moving wheel loads, most of the researchers prefer the use of a repetitive loads test rather than the static creep test for permanent deformation characterization, others prefer the latter due to the simplicity of the testing device. Shell researchers [13,85] who pioneered the use of the static creep test have developed their creep and rutting criteria based on the static compressive creep. Others have presented their rutting prediction models based on the repetitive load test. The VESYS model [86] and the modified ILLIPAVE model [87] are two examples of predictive models which require repetitive load testing. Researchers at the Australian Road Research Board investigated both the static creep and repetitive load tests [88]. They showed that although the magnitude of plastic deformation will be different depending on the type of loading, the irrecoverable deformation trends are similar. This conclusion is in agreement with that made by Van Der Poel [89] who describes the dynamic and static responses of bitumen. Barksdale and Miller [90] reported that a repeated load test is more sensitive to mixture variables than the creep tests. On the basis of shell creep tests, they showed that the increase in the asphalt content of a particular mixture from 4.5 to 5.5 does not have any significant effect on the rut depth. However, the results of the repeated load tests on the same mixture indicated that such an increase in asphalt content could increase the rut depth by 16% (Figure 12). When comparing his results with laboratory test track data, McLean [15] found that his creep test results under-predicted permanent deformation by a factor on the order of 25.

Figure 12

Comparison of rut depth predictions from repeated load and creep tests [90].

Some creep testing was also undertaken by Snaith [91] using repeated load tests. The applied vertical stresses and temperatures were similar to those used in the repeated load tests. The objective was to determine if the relatively simple creep test could be used to predict permanent deformation under the more complex repeated load situation. At low stresses, he found that the static and repeated load test results were similar. However, at a higher stress level, he observed that a static stress of about 65% of the repeated stress value would be required to produce the same strain at a particular time. When plotting log strain vs either log time (static creep test) or log cycle (repeated load test), Snaith found that the slope factor was the same for similar test conditions. He concluded that any difference in the strain behavior due to the manner of loading would be shown in the intercept value alone. He related the intercept values for the two types of tests by the equation shown below:

where a = intercept value for repeated load test and a _s = intercept value for static creep test.

Chen et al. [24] indicated that the repetitive compressive test gives a more reasonable estimate for the field rutting than the creep test. He attributed this conclusion to the better simulation of the repetitive loading test to the field condition than that of the creep test, also he recommended the use of pulse time as close as possible to that occuring in the field. For laboratory testing, the shape of the load-time trace is commonly one of three forms [92]: sine, square, or triangular. Using elastic finite element theory to evaluate the shape and duration of the stress pulse, Barksdale [93] found that the vertical compressive stress pulse varies from an approximately sinusoidal one at the surface to a more nearly triangular pulse for elements near the subgrade. More specifically, for conventional pavements with surfaces up to a thickness of about (12.5 cm), a sinusoidal stress pulse should be applied. For thicker, deep-strength, or full-depth pavements, a sinusoidal stress pulse should be used for the upper parts of the pavement. At the middle and bottom, a triangular-shaped pulse more nearly approximates the actual shape. Figure 13 shows the variation in vertical stress pulse with vehicle velocity and depth. Additionally, some of the techniques used to define the time of loading are shown in Table 2.

Figure 13

Speed–loading time relationship [93].

Finally, the researchers of SHRP [78] summarized the tests that were used to characterize the permanent deformation as presented in Table 3.

5.2 Predictive models

Numerous studies have been made to characterize the permanent deformation response of asphalt concrete materials due to repeated load applications. The studies used the repeated compressive load test to investigate the variables that influence the relationship between the number of load applications (N), and the permanent strain (ε _p). Rather than reviewing each in detail, the more recent research efforts are presented in tabular form (Table 4) to facilitate ease of revisions.

6.1 Layer-strain procedure

The layer-strain approach uses either linear or nonlinear elastic theory to analyze the pavement structure and estimate rut depths using permanent deformation features identified from laboratory studies. The basic idea behind this approach was first put forth by Barksdale [111] and Romain [112]. Although nonlinear elastic theory should produce more accurate findings [97], it has not been applied widely because of its extra complexity. Each pavement structure layer is divided into several sublayers, and the stress state is calculated at the center of each sublayer immediately beneath the wheel load using elastic analysis (Figure 14). This allows for predicting the amount of permanent deformation that would occur after a specific number of wheel load applications. Results of laboratory experiments can be used to determine the axial plastic strain associated with the average stress state at the center of each sublayer. The average plastic strain that occurs in the center of each sublayer and the corresponding sublayer thickness are added together to provide the overall rut depth for a specified number of load repetitions.

where Δp is the total rut depth, ε _pi is the average plastic strain in the center of the ith sublayer, Δz _i is the thickness of the ith sublayer, and n is the total number of sublayers. This approach has been adopted in various forms by many researchers and, as noted above, the Shell design methodology represents a practical example of the use of this procedure, also, the VESYS elastic approach represents another example of this method. The layer-strain method is considered a simplified engineering approach for predicting rut depth which permits the flexibility of using either linear or nonlinear elastic analysis. The following sections provide a description of the Shell and the approach used in the VESYS program.

Figure 14

Diagram of pavement system used to estimate permanent deformation [78].

6.1.1 Shell method

Shell researchers [14,108] have developed a practical procedure, utilizing layer-strain concepts, to predict rutting in the asphalt-bound layer. These concepts are used in a pavement design procedure to determine the plastic strain which is input to equation (6). This procedure requires (1) detailed information on mixture components, traffic, and the pavement environment; (2) a layered elastic analysis; and (3) data from a simple uniaxial creep test on a specimen representative of the mixture. The basic premise is that the development of deformation in an asphalt pavement is related to that occurring in a laboratory creep test [11]. The Shell researchers have presented the results of creep tests in the form shown in Figure 15 and have demonstrated that mixture stiffness (S _mix) and bitumen stiffness (S _bit) are uniquely related, regardless of the temperature, since S _bit is a function of both time of loading and temperature. If a value of S _bit can be found corresponding to the field conditions under which the deformation occurs, the resulting S _mix can be found from the test curve (like those shown in Figure 15).

Figure 15

Stiffness characteristics of mixture [85]. (a) Range of mixtures. (b) Representative mixtures.

In this methodology, it is argued [14] that the required bitumen stiffness is the viscous component of the total stiffness, (S _bit)_Vis, which can be determined as follows:

(4) ( S bit ) vis = 3 η N t w ,

where N is the total number of load applications, t _w is the loading time for one load application (s), and η is the viscosity of bitumen (N s/m²).

A nomograph is provided by Shell for estimating the viscosity which requires as input the pavement temperature together with the penetration index and the temperature corresponding to 800 pen. for the asphalt. To estimate permanent deformation in the asphalt-bound layer, the following variation in equation (3) is used:

(5) Δ h = C m h σ av S mix ,

where σ _av is the average stress in the bituminous layer and determined from σ _av = Zσ◦; h is the thickness of the bituminous layer; Δh is the change in thickness of the bituminous layer; S _mix is the value of the mixture stiffness for S _bit determined from equation (4) and obtained from a curve like that shown in Figure 15; Cm is a correction factor; Z is a coefficient determined using layered elastic analysis; and σ◦ is the contact stress between tire and pavement.

The procedure for using equation (5) [85] requires that σ _av is determined by applying a “Z” factor (determined using the BISAR program for computation of stresses and strains in a multilayer elastic system) to σ◦, the contact stress between tire and pavement. Also, the method divides the bituminous layer(s) into three sublayers (h1 = 4 cm, h2 = 4 cm, and h3 = total asphalt thickness = 8 cm) and calculates the deformation in each, requiring appropriate S _mix and σ _av values for each of the sublayers.

As emphasized by Claessen et al. [85], a considerable error could result if an inappropriate S _mix vs S _bit curve is used. The S _mix vs S _bit should be determined from a creep test on a core of material, or by correlations between laboratory specimens and field cores. In the event that such data are not available, the Shell researchers have presented three creep curves representative of different mixture types, the selection of one of these curves for the analysis depends on the judgment of the designer. Mahboub [39] stated that there are two major drawbacks associated with the Shell prediction equation, these are as follows:

1. The stiffness parameter, S _mix, is a pseudo-elastic parameter, and it is used in a Hook’s law format as follows:

   (6) Strain = Stress ( Z σ ∘ ) Stiffness ( S mix ) .

   It is extremely important to remember that the above format only holds true for elastic (recoverable) deformations. As a result, using the total stiffness parameter, S _mix, which represents the combination of elastic, plastic, viscoelastic, and viscoplastic responses in a Hook’s law format for rutting prediction, is not valid [39].

2. Another serious consequence of using a Hookean constitutive relationship for permanent deformation characterization is the assumption of linearity. Mahboub [39] states that the accumulation of permanent strains is not linearly proportional to the stress level, further he states that this relationship is of log-linear form.

6.1.2 VESYS method

The FHWA, Austin Research Engineers, and Massachusetts University of Technology all contributed to the ongoing development of VESYS, a probabilistic and mechanistic flexible pavement analysis system [1]. Primary response, general response, damage, and performance model are the four main interaction models that are included. The basic response model uses either the elastic approach (material characterized by resilient modulus and Poisson’s ratio) or the viscoelastic method to determine the layered system response (stress, strain, and deflection) (material characterized by creep compliance). The damage model includes three sub-models for the prediction of cracking, rut depth, and roughness under static loading, which incorporates the influence of moving load using Boltzmann's principles. To determine how the PSI will change over the analysis period, the calculated values for these distresses are used as input for the performance model [1]. The VESYS system is a computer software; VESYS 5, is the most recent version. The layer and system rutting options are available in this version's rut depth predictive sub-model. The system rutting option takes into consideration subgrade rutting. It uses the total deflection in the pavement surface to determine the total rut depth for the entire system, as opposed to the layer rutting option, which calculates the rut depth for each layer in the pavement structure [113].

Based on the power relationship of εp-N of the asphalt concrete shown in equation (7), below

(7) ε p = a N b ,

where ε _p = permanent strain, N = number of stress applications, a = intercept coefficient, b = slope coefficient,

the permanent strain for the Nth repetition can be calculated as follows [92]:

(8) ε p ( N ) = ε t ( N ) − ε r ( N ) = ε r μ N − α ,

where ε _p(N) = permanent strain for Nth repetition, ε _t(N) = total strain for Nth repetition, ε _r(N) = resilient strain for Nth repetition (assumed to be independent of N).

Assuming linear stress–strain behavior during the loading and unloading cycles with Eloading ≠ Eunloading, the total and resilient strain can be written as follows:

(9) ε t z = 1 E lo ( N ) [ σ z − γ ( σ x + σ y ) ] = σ z ' E lo ( N ) ,

(10) ε r z = 1 E un ( N ) [ σ z − γ ( σ x + σ y ) ] = σ z ' E un ( N ) ,

where ε _tz = total axial strain for Nth repetition, ε _rz = resilient axial strain for Nth repetition, σ _z = axial stress, σ _x and σ _y = radial stresses, E _lo(N) = modulus during loading cycle for Nth repetition, E _un = modulus during unloading cycle, γ = Poisson’s ratio, and σ z ' = resultant axial stress.

By substitution of equations (9) and (10) in equation (8), we get

(11) σ z ' 1 E lo ( N ) − 1 E un = σ z ' E un μ N − α .

By solving equation (11) for E _lo(N) yields the following:

(12) E lo ( N ) = E un 1 + μ N − α .

The main assumptions included in the program are:

1. Poisson’s ratio is constant for both loading and unloading conditions.

2. ε _r, and consequently E _un, is independent of the number of load repetitions.

The model of equation (12) is used to evaluate rutting in the asphalt concrete layer as follows:

1. Determine the value of resilient modulus, E _un.

2. For a specific value of N, determine the value of E _lo(N).

3. Using E _lo(N) in a multilayer elastic solution, compute the deflections due to loading (δ _lo(N)) and unloading (δ _un).

4. Compute the rut depth for the Nth load repetition, Rd(N) = δ _lo(N) − δ _un.

5. Repeat steps 2 through 4 for the specific value of N.

6. Compute the total rut depth for N repetitions as follows:

(13) R d = ∫ i = 1 N R d ( N ) d N .

Omer [114] states that the use of the VESYS sub-model for rut depth prediction of full depth asphalt concrete over silty clay subgrade yield results that are compared favorably with the measured rut depth, as shown in Figure 16.

Figure 16

Rut depth prediction [114].

6.2 Viscoelastic approach

In this approach, moving wheel loads can be considered in conjunction with time-dependent material properties to define the states of stress and strain at particular points in the pavement structure. Material properties can be defined either in terms of models consisting of finite numbers of Maxwell and/or Kelvin elements in various arrangements or in terms of generalized compliance relationships. An important advantage of this approach is that moving wheel loads can be considered directly. This results in the correct time rate of loading to be applied to each material element and permits estimates to be made of the lateral plastic flow of material from beneath the moving wheel. While nonlinear viscoelastic response characteristics may provide a more realistic estimate of pavement response, the associated mathematical complexities have limited past analyses to linear characterizations [115,116]. In this approach, material properties within a given layer are assumed to be the same throughout the layer regardless of whether the material is in tension or compression. Another example of this methodology is embodied in the VESYS procedure [99]. If a viscoelastic analysis is used, a generalized linear viscoelastic response is tractable, and several authors have used or proposed this method [117]. The calculations tend to be time-consuming; however, the assumption of linearity itself is questionable [100]. A nonlinear viscoelastic model seems even more prohibitive, in terms of both computational effort and the scale of laboratory work necessary to establish appropriate nonlinear, time-dependent constitutive equations. A viscoplastic theory, coupled with the use of finite-element methods [100] seems to have the same drawbacks. More recently, Thrower et al. [118] and Nunn [119] have suggested that using estimates of the accumulation of permanent deformation on viscous properties of asphalt concrete has the potential to provide reasonable estimates of rutting.

6.3 Artificial neural network approach

An artificial neural network is a parallel information processing system that has certain performance characteristics similar to biological neural networks. A neural net consists of a large number of simple processing elements called neurons. Each neuron is connected to other neurons by means of directed links, each directed link has a weight associated with it. The weights acquired through the training process represent abstracted information from the dataset, which is used by the net to solve a particular problem. In order to construct a neural network for solving a particular problem, three key components need to be determined first. They are (1) architecture, (2) learning method, and (3) neuron activation function [120,121].

According to Oh and Barham [122], an efficient method for capturing the non-linear modeling functions to predict the rutting of asphalt materials is the artificial neural network backpropagation algorithm. In their study [123], Mirabdolazimi and Shafabakhsh found that their constructed artificial neural network model for the prediction of rut depth corroborated the experimental findings quite well. The pavement condition index was modeled by Amin and Amador-Jimenez [124] using the backpropagation neural network technique. According to Shafabakhsh et al. [125], rutting for asphalt mixtures containing nano-additives can be predicted using the backpropagation algorithm. A permanent deformation model was created by Haddad et al. [126] using data taken from the LTPP database and a deep neural network. When compared to models found in the current literature, the results showed that the extended model had improved predictive power.