was divided into four test sites (7 ). All lanes consisted of a hot-mix asphalt (HMA) layer on an unbound dense-graded crushed aggre- gate base (CAB) of a 19.0-mm nominal maximum aggregate size diabase aggregate that met the Virginia Department of Transporta- tion Type 21A base course aggregate requirements, and a uni- formly prepared AASHTO A-4 subgrade soil. The total thickness of the HMA and CAB was 660 mm (26 in.). Lanes 1 through 7 were constructed with an HMA layer thickness of 100 mm (4.0 in.), whereas Lanes 8 through 12 had a thickness of 150 mm (6.0 in.) (Figure 2). The asphalt binders used in the ALF pavements are listed in Table 1. These binders consisted of an unmodified PG 70-22 asphalt binder, which was considered the control asphalt binder, the same binder with 0.3% polyester fibers by total mass of the aggregate, an air-blown asphalt binder, and the following five polymer-modified asphalt binders: an Arizona Department of Transportation (ADOT) wet-process crumb rubber asphalt binder (CR-AZ), a styrene- butadiene-styrene modified asphalt binder with linear grafting (SBS LG), a crumb rubber asphalt binder blended at the terminal (CR-TB), an ethylene terpolymer asphalt binder (Terpolymer), and an asphalt binder containing a blend of styrene-butadiene and styrene-butadiene-styrene (SBS), hereafter called SBS 64-40. The ALF machines have frames 29 m (95 ft) long with rails to direct rolling wheels. Each ALF machine was capable of applying an average of 35,000 wheel passes per week by using a half-axle load ranging from 33 to 84 kN (7,500 to 19,000 lbf). The load was applied in one direction to a 14-m (45-ft) length of pavement at a speed of 18 km/h (11 mph). The machines could allow testing with conventional dual truck tires or wide-based “super-single” tires and simulation of the real-world lateral distribution of truck loadings by using programmed transverse wheel wander. Under the current ALF experiment, both machines were equipped with super-single (425/65R22.5 wide base) tires. Since each pavement lane had four test sites, the full-scale pavement testing was and still is being conducted at two failure modes: rutting tests (Sites 1 and 2) at 64°C and 74°C, and fatigue cracking tests (Sites 3 and 4) at 19°C and 28°C. All rutting tests were conducted by using a wheel load of 44 kN (10,000 lbf) without transverse wander. On the other hand, all fatigue tests were conducted by using a wheel load of 74 kN (16,600 lbf) with transverse wander. An infrared heating system and thermocouples in the pavements provided the required pavement temperature (8). Mechanistic analyses to determine the fatigue and rutting primary responses under the ALF pavements were conducted in this study by using different available pavement analysis programs, including a finite element program (EVERFLEX) and multilayer elastic theory (MLET) programs, such as KENPAVE, WINLEA, and EVERSTRS. The MLET programs provide elastic solutions to the pavement Mechanistic Analyses of FHWA’s Accelerated Loading Facility Pavements Primary Response Ghazi Al-Khateeb, Nelson Gibson, and Xicheng Qi In-depth details are provided for mechanistic analyses conducted for the asphalt pavements of the FHWA accelerated loading facility (ALF) by using available programs, including KENPAVE, WINLEA, EVERSTRS, EVERFLEX, and VESYS 5W. These pavements were constructed by using highly modified and unmodified asphalt binders. The described analyses focused on primary response under the ALF pavements. This study included multilayer elastic theory (MLET) solutions, finite element analysis, and analysis using the VESYS 5W program. Predictions of the primary response for the fatigue mode included the horizontal tensile stress and strain at the bottom of the hot-mix asphalt (HMA) layer and for the rutting mode included the vertical compressive stress and strain on top of each pavement layer. The impact of loading frequency and stress sensitivity (nonlinearity) on fatigue primary response, rutting primary response, and principal stresses was investigated. The frequency did affect the fatigue tensile stress and strain, primarily at the bottom of the HMA layer. It also affected the major and minor principal stresses, par- ticularly at the bottom of the HMA layer. The frequency effect on the rut- ting compressive stress was insignificant, whereas it was considerable for the compressive strain within the HMA layer. The MLET solutions that used a linear elastic base provided reasonable predictions for the mea- sured tensile strains for highly modified and unmodified asphalt pave- ments with an absolute percentage error in the range of 0% to 15% percent in most cases. The solutions of the MLET and VESYS 5W pro- grams were capable of providing good predictions of the vertical defor- mation within the HMA layer that correlated well with the measured permanent deformation values. The mechanistic analyses in this paper were conducted on the accelerated loading facility (ALF) asphalt pavements and used available programs, including KENPAVE (1), WINLEA (2), EVERSTRS (3), EVERFLEX (4), and VESYS 5W (5, 6). Twelve asphalt pavement test lanes were constructed at the FHWA Pavement Testing Facility (PTF) of the Turner-Fairbank Highway Research Center in the summer of 2002. This facility was equipped with two ALF machines, and staff were trained to operate them. The two ALF machines are shown in Figure 1. Each pavement lane had a width of 4.0 m (13 ft) and a length of 50 m (165 ft) and G. Al-Khateeb, Department of Civil Engineering, Jordan University of Science and Technology, Irbid, 22110, Jordan. N. Gibson and X. Qi, FHWA, Turner-Fairbank Highway Research Center, 6300 Georgetown Pike, HRDI-11, McLean, VA 22101. Corresponding author: G. Al-Khateeb, [email protected]. Transportation Research Record: Journal of the Transportation Research Board, No. 1990, Transportation Research Board of the National Academies, Washington, D.C., 2007, pp. 150–161. DOI: 10.3141/1990-17 150
Transcript
was divided into four test sites (7 ). All lanes consisted of a hot-mixasphalt (HMA) layer on an unbound dense-graded crushed aggre-gate base (CAB) of a 19.0-mm nominal maximum aggregate sizediabase aggregate that met the Virginia Department of Transporta-tion Type 21A base course aggregate requirements, and a uni-formly prepared AASHTO A-4 subgrade soil. The total thicknessof the HMA and CAB was 660 mm (26 in.). Lanes 1 through 7 wereconstructed with an HMA layer thickness of 100 mm (4.0 in.),whereas Lanes 8 through 12 had a thickness of 150 mm (6.0 in.)(Figure 2).
The asphalt binders used in the ALF pavements are listed inTable 1. These binders consisted of an unmodified PG 70-22 asphaltbinder, which was considered the control asphalt binder, the samebinder with 0.3% polyester fibers by total mass of the aggregate, anair-blown asphalt binder, and the following five polymer-modifiedasphalt binders: an Arizona Department of Transportation (ADOT)wet-process crumb rubber asphalt binder (CR-AZ), a styrene-butadiene-styrene modified asphalt binder with linear grafting(SBS LG), a crumb rubber asphalt binder blended at the terminal(CR-TB), an ethylene terpolymer asphalt binder (Terpolymer),and an asphalt binder containing a blend of styrene-butadiene andstyrene-butadiene-styrene (SBS), hereafter called SBS 64-40.
The ALF machines have frames 29 m (95 ft) long with rails todirect rolling wheels. Each ALF machine was capable of applyingan average of 35,000 wheel passes per week by using a half-axleload ranging from 33 to 84 kN (7,500 to 19,000 lbf). The load wasapplied in one direction to a 14-m (45-ft) length of pavement at aspeed of 18 km/h (11 mph). The machines could allow testing withconventional dual truck tires or wide-based “super-single” tires andsimulation of the real-world lateral distribution of truck loadings byusing programmed transverse wheel wander.
Under the current ALF experiment, both machines were equippedwith super-single (425/65R22.5 wide base) tires. Since each pavementlane had four test sites, the full-scale pavement testing was and still isbeing conducted at two failure modes: rutting tests (Sites 1 and 2) at64°C and 74°C, and fatigue cracking tests (Sites 3 and 4) at 19°C and28°C. All rutting tests were conducted by using a wheel load of 44 kN(10,000 lbf) without transverse wander. On the other hand, all fatiguetests were conducted by using a wheel load of 74 kN (16,600 lbf) withtransverse wander. An infrared heating system and thermocouplesin the pavements provided the required pavement temperature (8).
Mechanistic analyses to determine the fatigue and rutting primaryresponses under the ALF pavements were conducted in this study byusing different available pavement analysis programs, including afinite element program (EVERFLEX) and multilayer elastic theory(MLET) programs, such as KENPAVE, WINLEA, and EVERSTRS.The MLET programs provide elastic solutions to the pavement
Mechanistic Analyses of FHWA’sAccelerated Loading Facility PavementsPrimary Response
Ghazi Al-Khateeb, Nelson Gibson, and Xicheng Qi
In-depth details are provided for mechanistic analyses conducted for theasphalt pavements of the FHWA accelerated loading facility (ALF) byusing available programs, including KENPAVE, WINLEA, EVERSTRS,EVERFLEX, and VESYS 5W. These pavements were constructed byusing highly modified and unmodified asphalt binders. The describedanalyses focused on primary response under the ALF pavements. Thisstudy included multilayer elastic theory (MLET) solutions, finite elementanalysis, and analysis using the VESYS 5W program. Predictions of theprimary response for the fatigue mode included the horizontal tensilestress and strain at the bottom of the hot-mix asphalt (HMA) layer andfor the rutting mode included the vertical compressive stress and strainon top of each pavement layer. The impact of loading frequency and stresssensitivity (nonlinearity) on fatigue primary response, rutting primaryresponse, and principal stresses was investigated. The frequency didaffect the fatigue tensile stress and strain, primarily at the bottom of theHMA layer. It also affected the major and minor principal stresses, par-ticularly at the bottom of the HMA layer. The frequency effect on the rut-ting compressive stress was insignificant, whereas it was considerable forthe compressive strain within the HMA layer. The MLET solutions thatused a linear elastic base provided reasonable predictions for the mea-sured tensile strains for highly modified and unmodified asphalt pave-ments with an absolute percentage error in the range of 0% to 15%percent in most cases. The solutions of the MLET and VESYS 5W pro-grams were capable of providing good predictions of the vertical defor-mation within the HMA layer that correlated well with the measuredpermanent deformation values.
The mechanistic analyses in this paper were conducted on theaccelerated loading facility (ALF) asphalt pavements and usedavailable programs, including KENPAVE (1), WINLEA (2),EVERSTRS (3), EVERFLEX (4), and VESYS 5W (5, 6).
Twelve asphalt pavement test lanes were constructed at theFHWA Pavement Testing Facility (PTF) of the Turner-FairbankHighway Research Center in the summer of 2002. This facility wasequipped with two ALF machines, and staff were trained to operatethem. The two ALF machines are shown in Figure 1. Each pavementlane had a width of 4.0 m (13 ft) and a length of 50 m (165 ft) and
G. Al-Khateeb, Department of Civil Engineering, Jordan University of Science andTechnology, Irbid, 22110, Jordan. N. Gibson and X. Qi, FHWA, Turner-FairbankHighway Research Center, 6300 Georgetown Pike, HRDI-11, McLean, VA 22101.Corresponding author: G. Al-Khateeb, [email protected].
Transportation Research Record: Journal of the Transportation Research Board,No. 1990, Transportation Research Board of the National Academies, Washington,D.C., 2007, pp. 150–161.DOI: 10.3141/1990-17
150
Al-Khateeb, Gibson, and Qi 151
BACKGROUND
Pavements are a major part of the nation’s infrastructure; there-fore, better understanding of their behavior and performance willlead to effective pavement designs and improved pavement reha-bilitation and maintenance strategies that will help extend the lifeof existing pavements. The analysis of existing pavements is anessential step toward understanding the behavior of pavements andoffering an accurate pavement design that is based on mechanisticapproaches.
Empirical design methods have long been used in pavements. Thesemethods are based on empirical relationships developed to best relateobserved pavement performance to field and laboratory test results andother variables, including traffic, load, and environmental conditions.However, purely empirical models suffer because the accuracy andvalidity of prediction from these models outside the range of the dataused to develop them are not known and can be questionable.
The focus on mechanistic–empirical design methods thereforebecame essential in pavement technology for their advantages overpurely empirical methods in providing more accurate pavementdesigns and realistic predictions and better understanding of pavementperformance. The first step in a mechanistic–empirical design methodis to conduct a mechanistic analysis of the pavement to determine thestresses and strains the pavement perceives under traffic loading.
Any mechanistic model used for predicting pavement response isan approximation to the actual pavement system, and the predictedpavement response can be significantly different from the actual mea-sured values under the pavement. For this reason, it is important tocompare these predictions with measured values on controlled pave-ment sections that are similar to real existing pavements with similartraffic and environmental conditions. It is also critical to define themost significant inputs, including material properties for pavementanalysis programs and software, which have the greatest effect on thepredicted response. Hence, in general, sensitivity analyses for suchprograms are essential to determine the critical input variables andthe accuracy required in measuring or determining their values foraccurate analysis and predictions.
Various factors affect pavement behavior under loading as wellas response predictions. Among the loading-related factors are typeof tire (single versus dual versus wide base), axle configuration,and loading amplitude. Elseifi et al. quantified pavement damagecaused by dual and wide-base tires (9). They found that the first newgeneration of single wide-base tires would cause relatively greater
FIGURE 1 FHWA pavement testing facility and ALF machines.
primary response under loading. The EVERSTRS program offers aniterative solution for the primary response in case stress sensitivity(nonlinearity) of the base or subgrade layers is used as an input.
The EVERFLEX program offers a finite element analysis (FEA)package to analyze the primary response of asphalt pavements. It alsohas the ability to model cracks, slip between layers, and nonlinearmaterial behavior. The VESYS 5W program, which was developed bythe FHWA’s Office of Infrastructure Research and Development (6),provides three types of analyses:
1. Type I primary response analysis under single-load axle,2. Type II primary response analysis under multiple-load axle,
and3. Type III pavement performance analysis.
In this paper, a Type I analysis was conducted by using VESYS 5Wto determine pavement primary response.
The input variables needed for the analysis included material-related properties (such as modulus and Poisson’s ratio), loading data(amount of applied load, contact pressure and area or radius, and dis-tribution of load), pavement structural data (thickness of each layer),and environmental data (mainly temperature).
pavement damage than conventional dual tires, and the secondsize new generation of wide-base tires would induce similar pave-ment damage as the conventional dual tires. Chatti and El Mohtarstudied the effect of different axle configurations on fatigue life ofasphalt concrete mixtures (10). They compared the predicted fatiguelife by using the single load pulse with the measured one from thedifferent axle groups and trucks and found that the normalizeddamage per load carried decreased with an increasing number ofaxles within an axle group.
Yoo et al. investigated flexible pavement responses to differentloading amplitudes (11). They concluded that use of continuous load-ing amplitudes and nonuniform pressure distribution to simulate amoving wheel, surface shear forces, and appropriate layer interfacefriction may significantly improve the capability of finite elementmodels to predict pavement response to vehicular loading.
OBJECTIVES
The main objectives of this study are as follows:
1. To predict pavement fatigue and rutting primary responses ofthe ALF pavements;
2. To determine the appropriate material properties that yieldconsistent predictions of the measured tensile strains and permanentdeformations at the ALF pavements;
3. To analyze the ALF pavements for stresses, strains, anddeformations;
4. To compare the predicted pavement fatigue and rutting primaryresponses with the measured responses at the ALF sites;
5. To compare linear elastic solutions with nonlinear solutions;6. To evaluate available programs and software used for pavement
analysis; and7. To investigate the effect of stress sensitivity (nonlinearity) on
the pavement primary response predictions.
FATIGUE AND RUTTING PRIMARY RESPONSE
As described previously, the MLET programs used in the analysiswere KENPAVE, WINLEA, and EVERSTRS. The horizontal ten-sile stress and strain at the bottom of the HMA layers were predictedat 19°C as fatigue primary responses, whereas the vertical compres-sive stress, strain, and deformation at the top of each pavement layerwere predicted at 64°C as rutting primary responses.
For the HMA layer, the dynamic modulus obtained from the sim-ple performance tester (SPT) dynamic modulus testing was used asthe modulus of elasticity. The SPT dynamic modulus testing was con-ducted on laboratory-produced, laboratory-compacted specimens ofasphalt mixtures similar to those used in the construction of the ALF
pavements according to the procedures described in NCHRP Report465 (12).
The dynamic modulus values at 19°C and 64°C were used inthe analysis of the fatigue and rutting primary responses, respec-tively. To study the effect of loading frequency on the fatigue andrutting primary responses with depth, two loading frequencieswere used in the analysis programs, 7 and 1.66 Hz. The 7-Hz fre-quency was chosen because this value was the outcome of thecosine fit of the predicted vertical stress profiles that are shownin the next section, whereas the 1.66-Hz frequency value wasselected because it corresponded to the loading speed of the ALFmachines of 18 km/h (11 mph).
To investigate the impact of material stress sensitivity (nonlinear-ity) on the predictions of the fatigue and rutting primary responses,linear elastic base (LEB) and stress-sensitive base (SSB) were usedin the analysis. Moduli values of the base and the subgrade layerswere backcalculated from the falling weight deflectometer (FWD)test data. The FWD tests were conducted on top of the subgrade andbase layers, respectively.
VERTICAL STRESS AND TENSILE STRAIN PROFILES
Vertical stress profiles under the pavement theoretically shouldlook similar to those shown in Figure 3. Typically, the stress ampli-tude decreases with depth and distributes over a wider area in thepavement called the influence zone. The stress profiles predictedfrom the pavement analysis programs showed that although the
152 Transportation Research Record 1990
TABLE 1 Asphalt Binders Used in ALF Pavements
Asphalt Binder Type PG 70-22 Air-Blown SBS LG CR-TB Terpolymer SBS 64-40
Lane 1 (bottom), 2, and 8 3 and 10 4 and 11 5 6 and 12 9
FIGURE 3 Theoretical stress profiles under pavement.
Al-Khateeb, Gibson, and Qi 153
stress amplitude decreased with depth in the HMA layer, the stresswas distributed over the same area within the pavement HMAlayer, as shown in Figure 4. These stress profiles were fitted byusing the following equation:
where
σ = vertical stress,f = stress frequency,t = time or distance from the center of load,
A and B = constants, andφ = constant that represents the shift of the maximum
stress from the centerline of the applied load (fixed inthis case = 0).
Similarly, the predicted tensile strain profiles within the HMAlayer were plotted in Figure 4. The strain was in compression inthe upper half of the HMA layer and in tension in the lower part.In the middle of the HMA layer, the strain value was neutral, andthe maximum value was obtained at the bottom of the layer, asshown in Figure 4.
σ π φ= +( ) +A ft Bcos ( )2 1
The influence zone in case of the predicted vertical stress andtensile strain did not change with depth within the HMA layer(constant with depth, about 280 mm). Cosine function fits (Equa-tion 1) of the predicted vertical stress and tensile strain throughoutthe entire depth of the HMA layer showed similar frequency ( f ),which implied the same conclusion. For all ALF pavements, includ-ing the 150-mm and 100-mm pavements, it was found that the fre-quency f for the fitted curves of the vertical stress and tensile strainwas 7.0 Hz within the HMA layer, as obtained from KENPAVE,WINLEA, and EVERSTRS.
EFFECT OF FREQUENCY ON PREDICTEDPRIMARY RESPONSE
Fatigue Primary Response
The tensile stress and strain responses with depth were similar,particularly in the HMA layer. The highest tensile stress and strainwere obtained at the bottom of the HMA layer. The difference intensile stress between the 7- and 1.66-Hz cases was significant atthe bottom of the HMA layer with a maximum value of 17% and
FIGURE 4 Predicted stress and strain profiles under ALF pavements at 19�C Lane 8: (a) vertical stress and (b) tensile strain.
150% for the LEB and SSB (Lane 8), respectively. The tensile stressfor the 7-Hz case was higher than that of the 1.66-Hz case for bothLEB and SSB. The difference in tensile stress or strain betweenthe two frequencies was higher in the case of the SSB than that forthe LEB.
As discussed previously, stresses and strains were compressive inthe upper half of the HMA layer and inverted to tensile in the lowerpart of the layer. The rate of increase or decrease in the tensile stressor strain was relatively sharp within the HMA layer compared to thatin the base and subgrade layers, where the rate became approximatelyzero, as shown in Figure 5.
The difference in tensile stress or strain between the two fre-quencies decreased from its highest value at the bottom of the HMAlayer with depth, particularly in the subgrade layer (Figure 5). Thisdifference was evident for the LEB and SSB. The difference intensile strain was consistent with depth for the SSB but was higherand inconsistent with depth for the LEB (Figure 5b). The valuereached its maximum of 24% and 35% for these two cases, respec-tively (Lane 8). The tensile strain in the 7-Hz case was lower thanthat in the 1.66-Hz case for the LEB. An opposite result, however,was obtained for the SSB; higher tensile strain resulted in the 7-Hzfrequency case than that in the 1.66-Hz frequency case because of
154 Transportation Research Record 1990
the stress-hardening effect of the base layer, which obviously dom-inated the effect of the modulus differences between the LEB andthe SSB (Figure 5b).
Rutting Primary Response
The vertical stress response decreased with depth. The vertical stressreduction had the highest rate in the HMA layer and a slower rate inthe base layer until the curve reached a plateau in the subgrade layer(Figure 6). No significant difference in the vertical stress was foundbetween the two frequencies (7 and 1.66 Hz) and between the LEBand SSB, particularly within the base and subgrade layers. Yet thehighest differences were predicted at the bottom of the HMA layerand decreased with depth dramatically (Figure 6a).
There was significant difference in vertical strain between the twofrequencies within the HMA layer, as shown in Figure 6b. The high-est difference was obtained somewhere within the HMA layer, anddecreased significantly with depth in the base and subgrade layers.The difference in vertical strain between the LEB and the SSB wasinsignificant. The vertical stress and strain responses were higher forthe 1.66 Hz than for the 7 Hz.
(b)
(a)
LEB-7 Hz
LEB-1.66 Hz
SSB-7 Hz SSB-1.66 Hz
0
20
40
60
80
100
3000 2000 1000 0 -1000 -2000 -3000
Dep
th (
cm)
0
20
40
60
80
100
4003002001000-100-200-300-400
Dep
th (
cm)
LEB-7 HzLEB-1.66 HzSSB-7 HzSSB-1.66 Hz
FIGURE 5 Predicted stress and strain within pavement layers at 19�C Lane 8: (a) tensile stress (kPa) and (b) tensile strain (��).
Al-Khateeb, Gibson, and Qi 155
EFFECT OF STRESS SENSITIVITY ONPREDICTED PRIMARY RESPONSE
The stress sensitivity (nonlinearity) of the base was considered inthe analysis using the EVERSTRS program. For granular bases, itimplies that the resilient modulus of the base is a function of the bulkstress, as shown in the following equation:
where
Mr = resilient modulus,θ = bulk stress, and
K1, K2 = constants.
By using historical data of the crushed aggregate base layer at theALF pavements (13), the K1 and K2 constants were found to be 8,534and 0.80, respectively. Therefore, Equation 2 for the ALF base layermaterial became as follows:
Mr = ( ) ′8 534 20 80
, ( ).
θ
M Kr
K= ( )1
2 2θ ( )
In this case, an iterative approach in the EVERSTRS programwas used in which the modulus of the base layer was changedaccording to Equation 2′ by using the maximum allowed numberof iterations in the program until a converged value of the modu-lus was reached.
Fatigue Primary Response
Stress sensitivity of the base layer affected the results of the tensilestress and strain responses predominantly at the bottom of theHMA layer. The difference in the tensile stress between the LEBand the SSB was substantial at the bottom of the HMA layer (Fig-ure 5a). This difference decreased with depth until it disappearedin the subgrade layer. The same finding was obtained for the ten-sile strain, but as the difference decreased with depth it was stillconsiderable in the subgrade layer, as shown in Figure 5b. Tensilestresses and strains were higher for the LEB than those for the SSBfor both 7 and 1.66 Hz, because of the higher modulus of the SSB.However, the difference in tensile strain between the LEB and theSSB decreased as the frequency increased.
(b)
(a)
LEB-7 HzLEB-1.66 HzSSB-7 HzSSB-1.66 Hz
20
0
40
60
80
100
0 1000 2000 3000 4000 5000
Dep
th (
cm)
LEB-7 Hz LEB-1.66 Hz SSB-7 Hz SSB-1.66 Hz
20
0
40
60
80
100
0 200 400 600 800 1000 1200
Dep
th (
cm)
FIGURE 6 Predicted vertical compressive strain and stress within pavement layersat 64�C Lane 8: (a) vertical stress (kPa) and (b) vertical strain (��).
Rutting Primary Response
Stress sensitivity of the base layer also affected the vertical stressand strain with depth. The vertical stress as it decreased with depthwas higher for the SSB than that for the LEB, as shown in Figure 6a,but the difference was insignificant. It declined with depth. In con-trast, the vertical strain difference between the LEB and the SSBwas noticeable in the HMA layer and then started to shrink withdepth into the pavement layers, as shown in Figure 6b.
IMPACT OF FREQUENCY AND STRESSSENSITIVITY ON PRINCIPAL STRESSES
The effect of loading frequency and stress sensitivity on principalstresses with depth was investigated. As the major principal stressdecreased with depth (Figure 7), the rate of decrease was higher inthe HMA layer than that in the base and subgrade layers.
Differences in major principal stress between the two frequencies(7 and 1.66 Hz) and between the LEB and the SSB were consider-
able at the surface and at the bottom of the HMA layer (Figure 7b),and they decreased considerably in the base and subgrade layers.
The minor principal stress at the surface of the HMA layer wasequal to the applied loading or pressure (827.3 kPa in compression)under the centerline of the wheel. This value decreased until it reachedzero somewhere within the HMA layer, then it reversed from com-pression to tension and started to increase until it reached a maximumvalue at the bottom of the HMA layer, where it started to decreaseagain with depth in the base layer and reached a zero value again atabout a 50-mm depth in the base layer. The zero value of the minorprincipal stress continued with depth into the base and the subgradelayers, as shown in Figure 7c.
Differences in minor principal stress between the two frequenciesand between the LEB and the SSB were significant at the bottom ofthe HMA. The difference in major or minor principal stress betweenthe two frequencies was higher for the SSB than for the LEB, andbetween the LEB and SSB it was higher for the 1.66 Hz than for the7 Hz (Figure 7). These differences decreased with depth until theydisappeared in the subgrade layer.
156 Transportation Research Record 1990
0
20
40
60
80
100
-300
0-2
000
-100
00
Dep
th (
cm)
LEB-7 Hz
LEB-1.66 Hz
SSB-7 Hz
SSB-1.66 Hz
(a)
(c)
0
20
40
60
80
100
Dep
th (
cm)
-300
0-2
000
-100
00 10
0020
0030
00
(d)
0
5
10
15
-300
0-2
000
-100
00 10
0020
0030
00
Dep
th (
cm)
(b)
-300
0-2
000
-100
00
0
5
10
15
Dep
th (
cm)
FIGURE 7 Predicted principal stresses, kPa, within pavement layers at 19�C Lane 8: (a) majorprincipal stress within pavement layers, (b) major principal stress within HMA layer, (c) minorprincipal stress within pavement layers, and (d) minor principal stress within HMA layer.
Al-Khateeb, Gibson, and Qi 157
CHANGES IN PREDICTED VERTICAL DEFORMATION
Pavement permanent deformation is the accumulation of verticaldeformation in each layer. Hence, prediction of vertical deformationwithin each pavement layer is important to understand the ruttingbehavior of pavements.
The vertical deformation decreased with depth. The difference invertical deformation between the 7 and 1.66 Hz frequencies washighest at the surface of the HMA layer, and it decreased signifi-cantly with depth, as shown in Figure 8. The vertical deformationfor 1.66 Hz was higher than that for 7 Hz, as expected. Except forthe surface of the pavement, the difference in vertical deformationbetween the two frequencies was insignificant.
FINITE ELEMENT ANALYSIS
FEA was conducted by using the EVERFLEX FEA program. Onlysquare loading instead of typical circular loading was allowed inthis program. A three-dimensional finite element mesh was con-structed to represent the three-layered pavements of the ALF. Auniform load distribution (ULD) and a nonuniform load distribu-tion (NLD) were used in the analysis. In the case of NLD, a nor-malized load distribution with an overall load intensity that isequal to that of the uniform distribution was used. A linear elasticbase as well as a stress-sensitive base were used in the analysis.Results of different combinations using the two types of load dis-tribution and the two types of base behavior were obtained fromFEA. The FEA program provided a plane stress–strain analysis inall cases. These results from FEA are discussed along with theresults from the previous analyses conducted by using the MLETprograms in the following sections.
ALF-MEASURED FATIGUE AND RUTTINGPRIMARY RESPONSES
Sixty H-bar type strain gauges (Figure 9a) were installed under the12 lanes of the ALF pavements during construction in the summer of2002. In each lane, five strain gauges were embedded at the bottomof the HMA layer (Figure 9b) in one test site (typically, Site 3 plannedfor fatigue failure mode testing). Three of these gauges were alignedlongitudinally and two transversely. The strain responses were mea-
sured in all 12 ALF pavements under the moving wheel loading ofthe two ALF machines early in 2003. Besides the eight differentbinders used for construction of the ALF pavements and the two dif-ferent pavement thicknesses, other variables were considered in thestrain gauge measurements, including two load levels, three temper-atures (19°C, 28°C, and ambient temperature), three offset distances(0, 150, and 300 mm), two gauge orientations, and one to four loadingspeeds (18 km/h for all tests and 5, 7, and 13 km/h for no-offset tests).
Typical strain responses from the installed strain gauges areshown in Figures 9c and 9d. This strain response was caused by awheel load passing directly over the gauge. Figures 9c and 9dshow strain responses from three longitudinal strain gauges andtwo transverse strain gauges, respectively. In these figures, ten-sion is positive and compression is negative. Strain reversal couldbe observed in the longitudinal strain responses. The gaugeshowed compression first when the load was approaching, thentension when the load was moving over the top of the gauge.(Variation in peak strains from the three longitudinal gaugescould also be observed.) On the other hand, the transverse strainwas consistently in tension and decreased slowly to zero after theload passed. If the subsequent load passed before the recoverywas completed, then tension would accumulate. This accumula-tion would be more noticeable at higher pavement temperaturesand slower wheel speeds.
Initial measurements of the peak strains obtained from each of thestrain gauges were recorded. These initial tensile strains were com-pared with the predicted tensile strains by using the different analy-sis methods described previously. Details of these comparisons arepresented in the following sections.
During loading, pavement layer permanent deformation datawere collected through differential rod and level surveys on eightsets of reference plates installed at the time of construction along thecenterline of each test site. The plates were located at the surface ofthe pavement and on top of the crushed aggregate base to measurethe permanent deformation at these two locations at predeterminedALF wheel loading passes. The difference between these twomeasurements yielded the permanent vertical deformation withinthe HMA layer.
FATIGUE PRIMARY RESPONSE COMPARISONS
The predicted fatigue tensile strains were compared with the tensilestrains measured by the strain gauges at the bottom of the HMAlayer of the ALF pavements (Figure 10).
Seven different cases were considered in the comparison betweenthe predicted and measured fatigue tensile strains at the bottom ofthe HMA layer:
• MLET using LEB and 7 Hz,• MLET using LEB and 1.66 Hz,• MLET using LEB and 0.1 Hz,• MLET using SSB and 7 Hz,• FEA using ULD and 7 Hz,• FEA using NLD and 7 Hz, and• VESYS 5W using 7 Hz.
As shown in Figure 10, in most cases the analysis programs under-predicted the ALF-measured tensile strains, which implied thatthese programs provided stiffer pavements and stronger foundation
0
20
40
60
80
100
0 500 1000 1500 2000
Dep
th (
cm)
Linear Elastic Base-7 Hz
Linear Elastic Base-1.66 Hz
FIGURE 8 Predicted vertical deformation (1�10�6 m) withdepth at 64�C Lane 8.
under loading, which resulted in lower tensile strains at the bottomof the HMA layer. However, the MLET using LEB and 0.1 Hzprovided reasonable predictions of the tensile strains with a max-imum absolute percentage error of approximately 46%. This errorin most of the lanes, particularly for the 150-mm pavements, was inthe range of 0% to 15%.
The ALF machines apply loading at slower speeds, the highestbeing 18 km/h (11 mph). The frequency that corresponds to thisspeed is 1.66 Hz, as discussed previously. However, the actual load-ing frequency of the ALF machine was measured to be approximately0.1 Hz. Therefore, the MLET using LEB and 0.1-Hz loading fre-quency provided predictions that were favorably compared to theALF-measured values.
The tensile strain predictions from the FEA, the MLET using LEB,and the VESYS 5W program were found to be similar when the sameloading frequency was used, as shown in Figure 10. The NLD in theFEA had insignificant impact on the tensile strain predictions whencompared with those using the ULD. The MLET using SSB solutionprovided the extreme case of the tensile strain predictions. The SSByielded stiffer base (higher base modulus) because of the stress-hardening property of the granular materials. This made the tensilestrain predictions of the SSB the lowest (Figure 10).
In all these cases the correlation between the predicted and mea-sured tensile strains was high, particularly for the 150-mm pavementswith a coefficient of determination (R2) of 0.99 in most cases. For
the 100-mm pavements, the correlation was still significant with anR2 value in the range of 0.72 to 0.87, despite the difference betweenthe predicted and the measured tensile strains.
For the 150-mm pavements, the difference between the predictedand measured tensile strains was lower than that for the 100-mmpavements. Nearly all the 150-mm pavements showed exceptionalresults provided by the solution of the MLET using LEB and 0.1-Hzfrequency with a considerably low absolute percentage error in therange of 0% to 10%, except for the pavement of Lane 9 (SBS 64-40),which also had a relatively low error of 29%. On the other hand, the100-mm pavements showed an absolute error in the range of 4%to 46%. In general, the MLET using LEB and realistic loadingfrequency could provide satisfactory predictions of the measuredfatigue tensile strains.
RUTTING PRIMARY RESPONSE COMPARISONS
The predicted vertical (permanent) deformation within the HMAlayer was compared with the measured permanent deformation at theALF sites. The predictions of the HMA layer permanent deformationfrom the MLET using LEB and 0.1-Hz frequency (EVERSTRS) andfrom the VESYS 5W program were used (Figure 11).
The variation in vertical deformation on top of the subgradebetween the ALF pavements of the different lanes was not significant(Figure 11a). However, there was considerable difference in vertical
158 Transportation Research Record 1990
(a) (b)
5 Gauges atSite 3 for
Each Lane
CTLH-Bar Strain Gauge
(d)
-200
0
200
400
600
800
0.8 1.2 1.6 2.0Time (sec)
Str
ain
(μεμε
)
(c)
-200
0
200
400
600
800
0.8 1.2 1.6 2.0Time (sec)
Str
ain
(μεμε
)
Directionof Loading
FIGURE 9 Strain gauges used for ALF pavements with their response signals from Lane 2: (a) H-bar-type strain gauge, (b) strain gauges covered with HMA, (c) three longitudinal straingauges (19�C), and (d) two transverse strain gauges (19�C).
Al-Khateeb, Gibson, and Qi 159
deformation within the HMA layer between the different pavements,as shown in Figure 11b. The predicted vertical deformations withinthe HMA layer correlated highly with the ALF-measured HMA per-manent deformations, as shown in Figures 11c and 11d, with an R2
value of 0.65 and 0.67 for the MLET and VESYS 5W, respectively.However, the surface (total) vertical deformations did not correlatewell with the measured surface permanent deformations at the ALFsites. The MLET programs provided initial prediction values of pri-mary response, whereas VESYS 5W could provide primary responsepredictions at progressing load cycles.
The predictions of the total permanent deformation depend on therutting model used in the MLET program to calculate the total per-manent deformation. If the model takes into account the verticalstrain–stress on top of each layer to calculate the total permanentdeformation, more accurate predictions can be obtained. However,if it considers only the vertical strain–stress on top of the subgrade,inaccurate predictions are expected. Huang reported that underheavy traffic with a thicker HMA layer, most of the permanentdeformation occurs in the HMA layer, rather than in the subgradelayer (14). Therefore, predictions of the pavement total permanentdeformation that are based only on the compressive stress or defor-mation on top of the subgrade layer are inaccurate, especially for
thick pavements under heavy traffic loadings. This is why the pre-dictions of the HMA permanent deformation were found to corre-late well and better than the total permanent deformation with thosemeasured at the ALF sites.
CONCLUSIONS
On the basis of the results of the fatigue primary response predictions,the following conclusions are drawn:
1. The fitted frequency of the predicted vertical stress profilesthroughout the depth in the HMA layer was found to be 7 Hz.
2. The highest difference in tensile stress–strain between 7 Hz and1.66 Hz was obtained at the bottom of the HMA layer. It decreasedwith depth, particularly in the subgrade layer.
3. The tensile stress for 7 Hz was higher than that of 1.66 Hz forboth the LEB and the SSB but the difference was more pronouncedfor the SSB.
4. The tensile strain for 7 Hz was lower than that in the 1.66 Hzcase for the LEB. The opposite result was obtained for the SSB;higher tensile strain was acquired for 7 Hz because of the stress-hardening effect of the base layer, which dominated the effect of themodulus differences between the two frequencies.
5. The difference in tensile stress–strain between the LEB andSSB was substantial at the bottom of the HMA layer. It decreasedwith depth until it disappeared in the subgrade layer, particularly forthe tensile stress.
6. The tensile stress and strain for the LEB were higher than thosefor the SSB for both 7 Hz and 1.66 Hz.
7. The rates of change in major and minor principal stress weresignificantly high in the HMA layer and reduced dramatically inthe base and subgrade layers until it reached a plateau at which theprincipal stresses had zero values.
8. The difference in major principal stress between the LEB andthe SSB was significant at the surface and bottom of the HMA layer.This difference decreased with depth until it nearly vanished in thesubgrade layer. The difference in minor principal stress between theLEB and the SSB was significant at the HMA layer.
9. A significant difference in major and minor principal stresswas also observed between 7 Hz and 1.66 Hz in the HMA layer, par-ticularly for the SSB with the highest difference at the surface andbottom of the HMA layer, respectively.
The following conclusions are drawn from the rutting primaryresponse predictions:
1. No significant difference in vertical stress was found between7 Hz and 1.66 Hz and between the LEB and SSB, particularlywithin the base and subgrade layers. Yet the highest differenceswere predicted at the bottom of the HMA layer and decreased withdepth dramatically. The vertical stress for the SSB was higher thanthat for the LEB.
2. There was significant difference in vertical strain between 7 Hz and 1.66 Hz in the HMA layer with the highest not necessar-ily at the bottom of the layer. It decreased sharply in the base andsubgrade layers.
3. The vertical strain differences between the LEB and SSBand between 7 Hz and 1.66 Hz were noticeable in the HMA layer,particularly at the surface, and then started to decrease with depth.
FIGURE 10 ALF-measured versus predicted tensilestrains at bottom of HMA layer at 19�C: (a) tensilestrains for ALF 150-mm pavements and (b) tensilestrains for ALF 100-mm pavements.
4. The difference in the vertical deformation between 7 Hz and1.66 Hz was the highest at the surface of the HMA layer and decreasedsignificantly with depth. However, this difference was insignificantexcept at the surface of the HMA layer.
On the basis of the comparison between the predicted and theALF-measured primary response, the following conclusions arepresented:
1. The MLET using LEB solution provided reasonable and real-istic results for the tensile strains with an absolute percentage errorin the range of 0% to 15% in most cases. The predictions comparedwell with the ALF-measured tensile strains.
2. The actual loading frequency at the ALF sites was estimated tobe about 0.1 Hz, which favored the MLET solution using the 0.1-HzHMA dynamic modulus over the dynamic modulus at other loadingfrequencies.
3. The tensile strain predictions from the FEA, the MLET usingLEB, and the VESYS 5W program were found to be similar whenthe same loading frequency was used.
4. The effect of NLD in the FEA was insignificant on the tensilestrain predictions when compared with those that used ULD.
5. The solution of the MLET using SSB provided the extremecase of the tensile strain predictions with the highest deviation fromthe measured values.
6. For the 150-mm asphalt pavements, the difference in the pre-dicted and measured tensile strains was lower than that of the 100-mmpavements. Nearly all the 150-mm pavements showed exceptionalresults by using the LEB and 0.1-Hz frequency with a significantly lowabsolute percentage error in the range of 0% to 10%, except for thepavement of Lane 9 (SBS 64-40), having a relatively low error of 29%.The correlations between the two showed exceptional high R2 valuesof 0.90 and 0.72 for the 150-mm and 100-mm pavements, respectively.
7. The MLET using LEB appeared to have the capability of pre-dicting the primary response including the fatigue tensile strain atthe bottom of the HMA layer regardless of the type of material ofthat layer, whether it was an unmodified or highly modified asphaltmaterial, especially for the 150-mm asphalt pavements.
8. The MLET using LEB and VESYS 5W programs providedgood predictions for the ALF-measured permanent deformationswithin the HMA layer for the 150-mm and 100-mm asphalt pavements
160 Transportation Research Record 1990
(a) (b)
0.0
0.5
1.0
1.5
2.0
Ver
tica
l Def
orm
atio
n o
nT
op
of
Su
bg
rad
e (m
m)
2 3 4 5 6 8 9 10 11 12
Lane No.
7-Hz Frequency
0.1-Hz Frequency
0.0
1.0
3.0
2.0
4.0
5.0
2 3 4 5 6 8 9 10 11 12
Lane No.
Ver
tica
l Def
orm
atio
n a
tS
urf
ace
(mm
)
7-Hz Frequency
0.1-Hz Frequency
(d)
y = 1.4461x - 6.2789R2 = 0.67
ALF-Measured HMA PermanentDeformation at 25000 Wheel Passes
(mm)
Pre
dic
ted
Ver
tica
l Def
orm
atio
n a
t 25
000
Lo
ad C
ycle
s (m
m)
Within HMA Layer
Top of Subgrade
0.0
10.0
20.0
30.0
0.0 10.0 20.0 30.0
(c)
y = 0.132x - 0.366R2 = 0.65
0.0
1.0
2.0
3.0
0.0 10.0 20.0 30.0
ALF-Measured HMA PermanentDeformation at 25000 Wheel
Passes (mm)
Pre
dic
ted
Init
ial V
erti
cal D
efo
rmat
ion
(m
m)
Within HMA Layer
Top of Subgrade
FIGURE 11 ALF-measured versus predicted vertical deformations within HMA layer at 64�C: (a) MLETpredictions on top of subgrade, (b) MLET predictions at surface, (c) MLET, and (d) VESY 5W.
Al-Khateeb, Gibson, and Qi 161
with a relatively high correlation between the two (R2 = 0.65 and0.67, respectively).
ACKNOWLEDGMENTS
The authors thank Nadarajah Sivaneswaran of the FHWA Officeof Infrastructure Research and Development for his review andcomments. The authors also thank M. Emin Kutay of the Turner-Fairbank Highway Research Center for help in conducting theFEA, and the authors thank the ALF staff, Dennis Lim and MarioTinio, for providing the primary response data measured at theALF sites.
REFERENCES
1. Huang, Y. H. Kenlayer Computer Program. In Pavement Analysis andDesign, Prentice Hall, Englewood Cliffs, N.J., 1993, pp. 100–167.
2. WinJULEA. Engineering Research and Development Center, Vicksburg,Miss., 2003.
3. Everstress Version 5.0 for Windows. Washington State Department ofTransportation, Olympia, 1999.
4. Wu, H. Parallel Methods for Static and Dynamic Simulation of FlexiblePavement Systems. PhD dissertation. University of Washington, Seattle,2001.
5. VESYS 5Ws User Manual. Office of Infrastructure Research and Devel-opment, FHWA, U.S. Department of Transportation, 2003.
6. Hufferd, W. L., and J. S. Lai. Analysis of n-Layered Viscoelastic PavementSystems. FHWA-RD-78-22. FHWA, U.S. Department of Transportation,1978.
7. Qi, X., G. G. Al-Khateeb, T. Mitchell, K. Stuart, and J. Youtcheff. TheConstruction of Pavements with Modified Asphalt Binders. Office ofInfrastructure Research and Development, FHWA, U.S. Department ofTransportation, 2004.
8. Qi, X., G. G. Al-Khateeb, A. Shenoy, T. Mitchell, N. Gibson, J. Youtcheff,and T. Harman. Performance of the FHWA’s ALF Modified-BinderPavements. Presented at 10th International Conference on AsphaltPavements, Quebec, Canada, 2006.
9. Elseifi, M. A., I. L. Al-Qadi, P. J. Yoo, and I. Janajreh. Quantificationof Pavement Damage Caused by Dual and Wide-Base Tires. In Trans-portation Research Record: Journal of the Transportation ResearchBoard, No. 1940, Transportation Research Board of the National Acad-emies, Washington, D.C., 2005, pp. 125–135.
10. Chatti, K., and C. S. El Mohtar. Effect of Different Axle Configurationson Fatigue Life of Asphalt Concrete Mixture. In Transportation ResearchRecord: Journal of the Transportation Research Board, No. 1891, Trans-portation Research Board of the National Academies, Washington, D.C.,2004, pp. 121–130.
11. Yoo, P. J., I. L. Al-Qadi, M. A. Elseifi, and I. Janajreh. Flexible PavementResponses to Different Loading Amplitudes Considering Layer InterfaceCondition and Lateral Shear Forces. International Journal of PavementEngineering, Vol. 7, No. 1, 2006, pp. 73–86.
12. Witczak, M. W., K. Kaloush, T. Pellinen, M. El-Basyouny, and H. V.Quintus. NCHRP Report 465: Simple Performance Test for SuperpaveMix Design. TRB, National Research Council, Washington, D.C., 2002.
13. Anderson, D. A., W. P. Kilareski, and Z. Siddiqui. Pavement TestingFacility-Design and Construction. FHWA-RD-88-059. Office ofEngineering and Highway Operations, FHWA, U.S. Department ofTransportation, 1987.
14. Huang, Y. H. Flexible Pavement Design-Rutting Models. In PavementAnalysis and Design, Prentice Hall, Englewood Cliffs, N.J., 1993, pp. 531–594.
The Full-Scale and Accelerated Pavement Testing Committee sponsored publicationof this paper.
