Flexible Pavements Dynamic Response under a Moving Wheel

Flexible Pavements Dynamic Response under a Moving Wheel Angel Mateos, Ph.D. 1, Pablo de la Fuente Martín Ph.D. P.E. 2 and Javier Perez Ayuso 1 This paper presents the results from a research study carried out in order to better understand the mechanic behavior of a pavement under the traffic loads. Experimental data comes from CEDEX Test Track, an outdoors research facility located to the north of Madrid. CEDEX is a Public Institution, attached to the Ministry for Public Works, that provide technical support and research in the different areas of the Civil Engineering. CEDEX facility can test six full-scale sections simultaneously; the load is applied by means of two automatic vehicles that continuously move along a 3 meters close track. Six full-depth sections were tested, consisting of a 15 mm asphalt concrete layer on different quality subgrades. The structural response was measured in terms of deflection, asphalt horizontal strains and vertical stresses and strains in granular layers, for different conditions of speed and temperature. A comprehensive in-situ testing and laboratory characterization were conducted as well. This research considers the different aspects of the pavement mechanic, like non-linearity of soils, wheel-asphalt contact surface modeling, border effects etc. and special emphasis were placed on the dynamic effects. As a result a model is proposed, and developed with ABAQUS finite element program. Pavement is modeled as a multilayer three-dimensional structure. The vehicle load is modeled as a loaded surface with variable position, and the problem is solved through a pseudo-dynamic analysis which does not take into account inertia forces (since these were found to be negligible for the typical range of traffic speed), but it does consider the frequency dependence of the mechanical properties of the asphalt mix. Numeric modeling predictions have been compared to actual response measured in the test track sections. This comparison shows the ability of the model to reproduce the fundamental aspects of the structural response of a flexible pavement. 1 Transport Research Center of CEDEX. Autovia de Colmenar Viejo, km 18.2, El Goloso, 2876 Madrid, Spain. email: amateos@cedex.es 2 Department of Mechanic of Continuous Media and Structures Theory, Technical University of Madrid. C/ Ramiro de Maeztu 7, 284 Madrid, Spain. email: pdelaf@caminos.upm.es

INTRODUCTION The CEDEX Test Track consists of two 75-m straight stretches joined by two circular curves with a radius of 25 m. A rail beam located on the inside perimeter of the track serves as a guide for two automatic vehicles. Figure 1. CEDEX Test Track The testing of the pavement sections is carried out in the straight stretches, and therefore the results are comparable to those obtained in other linear test tracks. Six 2-25 m long complete pavement sections can be tested simultaneously. Figure 2. Sketch of the Tested Sections A concrete test pit, 2.6 m deep and 8 m wide, enable the building of embankments of at least 1.25 m in height as well as the use of conventional machinery and the usual road-building procedures. The

purpose of using concrete test pits is to isolate the performance of the pavements from that of the surrounding ground, allowing homogeneous support to the pavements throughout each test and between different tests in such a way that the results are comparable. It also allows the subgrade to be flooded for testing under different groundwater conditions. Figure 3. Test Pit Loading is applied by means of two automatic vehicles running up to 6 km/h. The concrete rail beam located on the inside perimeter of the track serves as a guide and enables total control of the load path. Figure 4. Vehicle for Traffic Simulation Results presented in this paper come from a test carried out in order to evaluate the performance of different subgrades, and only the structural response measurements are used. Measurements were taken at the beginning of the test, when the structural deterioration of the sections was negligible.

The range of temperature and load-related variables is listed below: Asphalt Temperature: 5-3 ºC Speed: 35 km/h (additional tests were carried out to evaluate speed effect between 1 and 35 km/h for an asphalt temperature of 2 ºC approximately) Load: 65.7 kn Tire pressure: 785 kpa Twin wheels

TESTED PAVEMENT SECTIONS Six different alternatives for a high quality subgrade were tested. Section 1 was the reference section, as it was included in the Spanish Design Catalog. Three groups of alternatives were considered: Section 3, were the capping layer was substituted by a high quality cement-stabilized soil. Sections 4, 5 and 6, were an improved support was added under the capping layer. Section 2, were the capping layer was substituted by other granular materials. In terms of bearing capacity, only Section 3 significantly improved the reference one (Section 1). For the other 4 solutions, the bearing capacity was very similar to the reference one. Section 1 Section 2 Section 3 15 Asphalt Concrete 15 Asphalt Concrete 15 Asphalt Concrete 5 Soil S3 25 25 Natural Granular Soil S1 2 3 Cement Stab. Soil (5%) Soil S1 Soil S Soil S Soil S 13 13 13 Concrete Text Pit Concrete Text Pit Concrete Text Pit 15 Section 4 Asphalt Concrete 15 Section 5 Asphalt Concrete 15 Section 6 Asphalt Concrete 5 Soil S3 5 Soil S3 5 Soil S3 geotextile 5 Soil S1 2 Lime Stab. Soil (3%) Soil S Soil S Soil S 13 8 11 Concrete Text Pit Concrete Text Pit Concrete Text Pit Layer Thickness in mm (values correspond to design thickness; actual measured thickness was used for modeling) Figure 5. Tested Sections Soils are classified, according to the Spanish Catalogue, into 4 categories; Atterberg limits, granulometry, CBR, harmful materials contents etc. are established for each type of soil. The number indicates a relative quality, being the soil S3 the best and the soil S the worse.

INSTRUMENTATION AND DATA COLLECTION Sections were instrumented with sensors in order to measure the structural response under the moving loads of the traffic simulator vehicles. The following variables were measured: Deflection Horizontal strain at the bottom of the asphalt layers Vertical stresses in soils at different levels Vertical strain in soils at the top of the subgrades δ Section 1 Section 2 Section 3 δ δ AC ε l ε t AC ε l ε t AC ε l ε t S3 σ v ε v ZN S-EST 3 S1 σ v ε v S1 σ v ε v σ v σ v σ v (to the concrete pit) (to the concrete pit) (to the concrete pit) δ Section 4 δ Section 5 δ Section 6 AC ε l ε t AC ε l ε t AC ε l ε t S3 σ v ε v S3 σ v ε v S3 σ v ε v S1 S-EST 1 σ v σ v (to the concrete pit) σ v (to the concrete pit) (to the concrete pit) LVDT sensor for Defection Strain gages for the horizontal strain in asphalt (longitudinal y transversal) Pressure cell LVDT sensor for vertical strain Figure 6. Instrumentation of the Sections

Data was collected by means of a specially design software that allowed the acquisition and treatment of more than 25 registers through the complete test. A complete register is recorded for each sensor under the pass of the traffic simulator vehicles, and the peak response value was calculated from that. The peak values could be plotted versus temperature or speed, as shown in Figures 8 and 9. Twin wheels (65.7 kn) Section 2 - longitudinal strain - (asphalt mix) v = 35 km/h T: 15 ºC 2 Longitudinal Strain (µε µε) 15 1 5 ε long Sensor 22KL22-5 -4-2 2 4 Longitudinal Position (mm) Figure 7. Example of a Longitudinal Strain Record Twin wheels (65.7 kn) Section 1 - deflection - v = 35 km/h 6. 5. Deflection (mm/1) 4. 3. 2. 1. Sensors 11DF1 12DF1. 5 1 15 2 25 3 Temperature of the Asphalt Mix (ºC) Figure 8. Example of Deflection Evolution versus Temperature

Twin Wheels (65.7 kn) Section 1 - deflection - T: 15-2 ºC 6. 5. Deflection (mm/1) 4. 3. 2. 1. Sensors 11DF1 12DF1. 1 2 3 4 Speed (km/h) Figure 9. Example of Deflection Evolution versus Speed The automatic data management system allowed the acquisition of a large number of measurements. Several hundreds records were registered for each sensor at the regular test speed of 35 km/h; that allowed the accurate definition of its response. Consequently, the variability of the response of each sensor did not mean a problem, since it was overcome with a large number of measurements. It can be seen in Figure 1 that the confidence interval for the true response of the sensor is very narrow (e.g. ±.2 mm/1 for the deflection at 2 ºC). But the variability from one sensor to another was significant, and it could not be overcome with a large number of sensors; usually, only two sensors were available for each variable in one section. It can be seen in Figure 1 how the variability from one sensor to another throws a significant uncertainty on the true value for the section. In terms of deflection, for example, the confidence interval for the true value is relatively wide: ±1.5 mm/1. So, for each response variable, the sections were classified into different groups, and the mean value for the group was calculated. That helped reducing significantly the margin of error. The mean value for the group was used for the evaluation of the model, but previously, it was verified that the model resulted in the same grouping as the measured variables.

Twin Wheels (65.7 kn) Deflection - Section 6 - v = 35 km/h Deflection (mm/1) 8. 7. 6. 5. 4. 3. 2. Curve fit for each sensor 95% confidence interval for the sensor true response 95% confidence interval for the mean response of the section Sensors 61DF1 62DF1 mean 1.. 5 1 15 2 25 3 Temperature of the Mix (ºC) Figure 1. Margin of Error for Deflection in Section 6

MATERIAL CHARACTERIZATION Soils Soils were evaluated during the construction, after the placement of each layer. A falling weight deflectometer test series was carried out for different load levels. Soils showed an stress dependent behavior as expected, with the stiffness increasing for low levels of load. Equivalent Modulus - central deflection (D) - FWD tests were performed on the top of each layer after the construction 18 16 Modulus (MPa) 14 12 1 8 6 4 mean Soil S mean Soil S1 mean Soil S3 Natural Granular Soil 2 5 1 15 2 25 3 35 Applied Load (kn) Figure 11. Modulus from the FWD Test for Different Load Levels Nonetheless, the series of FWD tests performed after the construction, on the asphalt layer, showed a behavior that did not separate significantly from the linearity, as can be seen in Figure 13. All the sections performed the same in this sense. Section 2 Load Level Effect - Falling Weight Deflectometer - 5 4 Deflection (µm) 3 2 1 D D2 D3 D45 D9 1 2 3 4 5 6 7 8 9 1 FWD Load (kn) Figure 12. Linear Response under the FWD Load

Soils moduli were finally obtained by means of FWD backcalculation from tests performed on the asphalt layer, after the construction of the sections. Values are included in Table 1, and they correspond with the values that would be expected from the layer testing with FWD during the construction. Table 1. FWD Backcalculated Moduli Soil S3 Cement Stabilized Soil S-EST 3 Natural Granular Soil Lime Stabilized Soil S-EST 1 Soil S1 Soil S 12 MPa 2 MPa 21 MPa 15 MPa 75 MPa 11 MPa Asphalt Mix Frequency dependency of the asphalt mixture is usually considered by means of the complex modulus or the creep compliance. Both were estimated in the laboratory from 18 cores extracted from the pavements. In the creep compliance test, a step load is applied to the core and the deformation is measured as a function of time. The interpretation of the creep compliance is as follows: If the applied stress is : and the measured strain : the Creep Compliance is : σ = σ ε = ε ( ) D t ; ( t) ε = σ t ( t) Applied Load H H ε(t) Measured strain time ε(t) delayed strain ε (instantaneous stain) time Figure 13. Creep Compliance Test

Applying a step load is very complicated, and in practice, there will be always a short period of time or ramp before the load gets constant, as can be seen in Figure 14. The quasi-elastic approximation is applied, and the creep compliance is calculated from: ε D ( t) = σ ( t) ( t) 5. 4. kn 3. 2. Actual Applied Load Theoretical Step Load 1...35.4.45.5.55 time (s) Figure 14. Actual Step Load Tests were carried out under the following conditions: - Temperature (3 levels): 1 / 2 / 3 ºC - Reference (zero) load:.25 kn (σ = 32 kpa) - Step load: 1 ºC 4. kn (σ = 59 kpa) 2 ºC 4. kn (σ = 59 kpa) 3 ºC 2. kn (σ = 255 kpa) An explicit creep function was used: D(t) = D + D 1 t n, and results are presented in Table 2. Table 2. Results from Creep Compliance Tests Parameter Temperature D D 1 n 1 ºC 2 ºC 3 ºC mean 57.5 124.331 Std. Error 2.4 3.4.6 C.I. (95 %) [47. ; 68.] [18 ; 139] [.3 ;.362] mean 74.5 367.425 Std. Error 16.6 76.9.34 C.I. (95 %) [66.2 ; 82.7] [328 ; 45] [.48 ;.442] mean 164.7 1365.526 Std. Error 4.2 294..21 C.I. (95 %) [144. ; 185.3] [1214 ; 1516] [.516 ;.537]

Complex modulus tests were also carried out on the same cores, and values were compared to those obtained from the creep test. The creep compliance defines the frequency dependent behavior of the mix, and the complex modulus can be obtained from it, by using the following relation: E * ( ω) where D*(ω) is the Laplace transformation of D(t). 1 = D * The comparison from both tests shows similar results (in relative terms) for the high frequencies, but for the low frequencies the stiffness is higher from the complex modulus test. It must be considered that for the very low frequency of.1 Hz the contribution of the aggregate interlock can be significant, and the cores were subjected to a higher deformation during the complex modulus test. ( ω) Dynamic Modulus Tª: 2 ºC 12 1 E* (MPa) 8 6 4 Complex Modulus Test Creep Test 2.1.1 1 1 1 Frequency (Hz) Figure 15. Comparison between Creep Test and Complex Modulus Test Time-temperature superposition principle was verified for the mix, and a relation on the following form was assumed: log ( a ) = β ( T ) T T where a T is the time scale and β depends on the mix type. The β value was obtained from the creep compliance functions obtained in the laboratory for 1, 2 and 3 ºC, as can be seen in Figure 16.

Superposition time-temperature 6 5 β =.124 Corrected cruve by means of a compression in time scale D(t) (µε µε/mpa) 4 3 2 Error: ε = 7.4 % β =.137 1 ºC 2 ºC 3 ºC ε = 1. % 1..2.4.6.8 1. 1.2 time (s) Figure 16. Comparison between Creep Test and Complex Modulus Test

MODELING ABAQUS finite element program was used for the modeling. A series of initial considerations was necessary in order to adequately model the problem. Dynamic Nature of the Problem The structural response of a flexible pavement under the pass of a moving wheel falls directly into the dynamic of structures. The dynamic nature of the problem clearly shows up when observing two phenomena: Increase in the structural response when the vehicle speed decreases (e.g. Figure 17). Longitudinal asymmetry of the registered signals under the moving wheel (e.g. Figure 18). Both aspects have been widely described in the literature and mainly attributed to the time-dependent mechanical properties of asphalt mix. Nonetheless, whether or not the inertial forces are significant in this problem is an issue that requires further considerations. Twin Wheels (65.7 kn) Section 1 - vertical stress - (soil S3) T: 15-2 ºC.2 Vertical Stress (MPa).15.1.5 Sensors 11CT31 12CT31. 1 2 3 4 Speed (km/h) Figure 17. Example of Speed Effect on Pavement Response Twin wheels (65.7 kn) Section 1 - vertical stress - (soil S3) v = 35 km/h T: 15 ºC.15 Vertical Stress (MPa).1.5. -.5-4 -2 2 4 Longitudinal Position of the Vehicle (mm) Figure 18. Longitudinal Asymmetry of the Structural Response

Linearity of the Response Linearity of the response was observed from the FWD tests conducted at different load levels, from 12.5 kn to 7 kn, as previously shown in Figure 12 for Section 2. The same pattern was observed for all the sections: the deflections (under the load plate and at certain distances up to 9 mm) increased linearly with the load level. Creep compliance tests at different load levels were also performed on 18 cores extracted from the pavements. This comparison was carried out for 2ºC, and the results show that the response of the mix was almost linear for this range of load. Creep Compliance T: 2 ºC 5 4 µε/mpa 3 2 Load applied on Cores 2 kn (255 kpa) 4 kn (59 kpa) 1..1.2.3.4.5.6.7.8.9 1. time (s) Figure 19. Effect of Load Level on Creep Compliance Geometry of the Problem The pavement sections were built in a concrete test pit, so they are horizontally confined to the walls of the test pit, as shown in Figure 2. In order to evaluate the effect of the horizontal confinement at 3.3 meters, a multilayer linear elastic calculation was carried out with Bisar. A representative section was modeled and the structural response was calculated for different depth levels. Some of the results are shown in Figure 21, and it can be noted that the structural response is negligible for distances farther than 2 meters. In terms of modeling, this means that a conventional multilayer linear elastic program, where infinite horizontal extension is assumed, could be used for the Test Track sections. In terms of finite element modeling, this means that the boundary of the modeled space should be 2 meters far from the load. The dimensions of the modeled space are shown in Figure 22. This figure also shows the symmetry plane located between both tires of the twin wheels, where the displacements in the perpendicular direction are restricted. For the bottom plane, all movements are restricted an for the vertical plane, the horizontal displacements were restricted.

33 mm 8 mm 2 mm Figure 2. Distance between the Wheel Load and the Concrete Wall Deflection Level 1 (Suface) Vertical Stress 5.2 4. δ (mm/1) 3 2 1 σv (MPa) -.2 -.4 -.6 Level 4 -.8 Level 3 Level 3: Top of the Subgrade Level 4: Top of the Embankment -1 5 1 15 2 25 3 Distance to the Load (mm) -.1 5 1 15 2 25 3 Distance to the Load (mm) Figure 21. Attenuation of the Structural Response with Horizontal Distance Tire Print z x Asphalt Concrete y Subgrade Symmetry Plane x = Concrete Test Pit 2 meters 4 meters Figure 22. Modeled Geometric Space

Element Meshing Figure 23 shows the meshing for Section 1. Similar ones were used for the rest of the sections. The main characteristic of this mesh are listed below: - Type of element: linear isoperimetric tetrahedron (C3D8I; ABAQUS denomination) - Nº Elements: 144 - Nº nodes: 16359 - Nº degrees of freedom: total: 4977 (3 d.o.f. per node) restricted in boundary: - 621 d.o.f. 42876 C3D8I is a linear element with internal modes of deformation, that improves the performance of linear elements almost to a quadratic level and eliminates the shear locking effect, with reduced computation requirements. The mesh was validated by comparison with the results from Bisar for a static linear elastic problem. Figure 23. Finite Element Meshing Load of the Vehicles Wheel load was modeled by circular areas with constant vertical stress (735 kpa). The tire-pavement mean contact stress was obtained from actual measured tires imprints, and it resulted slightly lower than actual tire air pressure, that was 785 kpa. Axel loads are known to vary around the death weight due to the irregularities of the pavement and the effect of the suspension. This variation can be significant, and values up to ±2% have been reported for normal traffic speed on pavements in good conditions. In this case, the speed was relatively low, 35 km/h, so this fluctuation was expected to be lower; besides, the structural measurements were considered at the beginning of the test, when the pavement surfaces were in good condition. The variation around the dead weight was estimated by accelerometers, and values below ±5% were obtained. So, the magnitude of the load was assumed to be constant.

The position of the load, though, does vary along the pavement, and the modeling can result cumbersome, since nodal forces change as the load moves. In order to simplify this modeling, the surface contact utility from ABAQUS was used. Tire load was modeled by a circular area with a constant vertical stress applied on it. The area is placed on the pavement surface, that is considered to be the master surface. Then, a movement is imposed to the tire area, resulting in a constant stress circular surface moving along the pavement. Figure 24. Tire Load Modeling Y = +1.5 m Tire Movement Y = Tire Load Y = -1.5 m Structural response calculation at different depths Figure 25. Movement of Tire Load In the real pavement, the initial conditions of the system are different from zero; wheel load is approaching, so when it gets to Y=-1.5, a primary response exists. If the load were applied directly from Y=-1,5 in a dynamic analysis, an oscillation in the vertical movement would be introduced, and it would disturb the calculated response. In order to get rid from that, an initial step was introduced where the load was applied in a static analysis.

Consequently, analysis was carried out in three steps: Step 1: applied load (static analysis) Step 2: constant acceleration, in order to reach 35 km/h (from Y=-1.5 to Y=-1) Step 3: constant speed from Y=-1 to Y=+1.5 meters Viscoelasticity of the Asphalt Mix Viscoelastic nature of the asphalt mix is more related to the deformation rather than to the compressibility. In fact, it has been frequently assumed for modeling a constant bulk modulus K and a frequency-dependent shear modulus G. Only the E modulus (or the Creep Compliance) was measured in the laboratory tests, but not the Poisson ratio. So, an assumption had to be made for the instantaneous Poisson ratio, based on literature reference values: υ =.15. Once this value has been estimated, and assuming an elastic K, the creep function for the shear modulus can be estimated from the creep function for the elastic modulus. Normalized Creep Functions 8. Normalized Dγ(t) (Shear Modulus, G) 6. 4. Normalized D(t) (elastic modulus, E) 2. 1...2.4.6.8 1 time (s) Figure 26. Normalized Creep Functions Type of Analysis The asphalt mix mechanical stiffness strongly depends on the frequency of the load, and this dependency makes the flexible pavement response increases when the vehicle speed decreases and also makes the signal registered under a moving wheel to be asymmetric. Both aspects have been frequently described in the literature as well as observed for the six sections considered in this study. But it is not clear whether or not the inertial forces must be considered or could be neglected in the analysis. In order to assess this inertial forces effect, a pavement section representing Section 1 was

modeled with ABAQUS and an elastic material was used for the asphalt layer. Two types of analysis were carried out: Pseudo-dynamic. Inertial forces are not considered. Dynamic; 35 km/h. Inertial forces as well as damping are considered (a 5% artificial damping was assumed). The response was calculated in both cases for the different variables considered in this study: deflection, horizontal strain in the asphalt layer and vertical stresses and strains in soils at different depth levels. In all cases the results were the same: there is no difference between both analysis, which means the inertial forces are negligible for this type of pavement for a speed of 35 km/h. An example is shown in Figure 27. Twin Wheels 25 Longitudinal Strain - Asphalt Mix - ABAQUS Modeling T: 2ºC 2 15 εl (µε) 1 5 Pseudo-dynamic Dynamic (35 km/h) -5-2. -1.5-1. -.5..5 1. 1.5 2. Longitudinal Position (m) Figure 27. Pseudo-dynamic versus Dynamic (Section 1) Consequently, a pseudo-dynamic analysis was carried out, that does not take into account the inertial forces but it does consider the time-dependency of the mechanical properties of the asphalt mix. Dynamic Effects for High Speeds The speed of 35 km/h is relatively low when compared to typical traffic speed. So the later comparison was extended to a much higher range of velocities. The results are shown in Figure 28 for the different response variables. It can be observed that the dynamic amplification is negligible for the typical traffic speeds, even for the highest speed trucks can reach on roads. It must be bear in mind that the calculations were performed for Section 1, but it seems clear that the results can be extrapolated to most typical road pavements, so a pseudo-dynamic analysis can be used to model the structural response of a flexible pavement under a moving wheel, even for the highest speeds that can be reached on roads. It was considered appropriated, though, to evaluate the effect of the concrete rigid layer under the pavement (due to the test pit), so the same exercise was carried out without this layer, assuming a semi-infinite embankment. This was modeled by using infinite elements in ABAQUS, whose shape

functions set to zero in a theoretical boundary that is placed at infinite depth. Results are presented in Figure 29, and are quite similar to the previous results. Twin Wheels 13% Speed Effect ABAQUS Modeling T: 2ºC 36 km/h Dynamic Response / Static Response 12% 11% 1% 9% 8% 7% 35 6 12 18 24 Deflection Longitudinal Strain Transverse Strain Vertical Stress (top subgrade) Vertical Strain (top subgrade) Vertical Stress (top embankment) Vertical Strain (top embankment) 6% 5 1 15 2 25 3 35 4 Speed (km/h) Pavement with a Rigid Bottom Layer (Concrete Test Pit) Figure 28. Dynamic Amplification of the Structural Response (Section 1) Twin Wheels 14% Speed Effect ABAQUS Modeling T: 2ºC Dynamic Response / Static Response 13% 12% 11% 1% 9% 8% 7% 35 6 12 18 24 36 km/h Deflection Longitudinal Strain Transverse Strain Vertical Stress (top subgrade) Vertical Strain (top subgrade) Vertical Stress (top embankment) Vertical Strain (top embankment) 6% 5 1 15 2 25 3 35 4 Pavement with a Semi-infinite Embankment Velocidad (km/h) Figure 29. Dynamic Amplification of the Structural Response (Section 1; with a semiinfinite embankment)

MODEL EVALUATION Next Figures show the comparison between the measured response in the Test Track and the results from ABAQUS modeling. It must be bear in mind that the sections were classified into groups according to the measured response, and a confidence interval was calculated for the mean response of each group; that reduced significantly the margin of error. It must be also bear in mind that ABAQUS material parameters were estimated from FWD testing in the case of the soils and from laboratory testing in the case of the asphalt mix. A rational procedure was established for determining those parameters, so no readjustment was allowed in order to fit the measured response. The variables considered for the comparison are listed below: Deflection. Longitudinal strain at the bottom of the asphalt layer. Vertical stress at the top of the subgrade. Vertical strain at the top of the subgrade. Vertical stress at the top of the embankment. Sections 1, 5 and 6 7 6 Deflection 95% Confidence Interval for the mean response v = 35 km/h 61.4 δ (mm/1) 5 4 3 2 33.4 31.2 36.5 4.8 36.4 46.4 53.3 46.2 1 5 1 15 2 25 3 35 Temperature of the Asphalt Mix (ºC) Measured Response ABAQUS Modeling Figure 3. Model Evaluation ~ Deflection

Section 3 4 35 Deflection 95% Confidence Interval for the mean response v = 35 km/h 3 29.6 δ (mm/1) 25 2 15 17. 16.4 17.9 19.6 18.3 22.1 25.4 22.3 1 5 5 1 15 2 25 3 35 Temperature of the Asphalt Mix (ºC) Measured Response ABAQUS Modeling Figure 31. Model Evaluation ~ Deflection (Section with cement-stabilized soil) Sections 1, 2, 4, 5 and 6 Longitudinal Strain - Bottom of Asphalt Mix - v = 35 km/h 6 5 95% Confidence Interval for the mean response 4 389.5 εl (µε µε) 3 2 1 135.6 143.9 158.3 195. 187.6 245.8 31.6 38. 5 1 15 2 25 3 35 Temperature of the Asphalt Mix (ºC) Measured Response ABAQUS Modeling Figure 32. Model Evaluation ~ Longitudinal Strain in Asphalt

Sections 1, 4, 5 and 6 Vertical Stress - Top of Subgrade - v = 35 km/h -.2 -.15 95% Confidence Interval for the mean response -.154 σv (MPa) -.1 -.5 -.61 -.67 -.71 -.86 -.82 -.14 -.127 -.113. 5 1 15 2 25 3 35 Temperature of the Asphalt Mix (ºC) Measured Response ABAQUS Modeling Figure 33. Model Evaluation ~ Vertical Stress (top of subgrade) Sections 1, 4, 5 and 6 Vertical Strain - Top of Subgrade - v = 35 km/h -14-12 95% Confidence Interval for the mean response -1-93.7-183.8 εv (µε µε) -8-6 -589.6-634.2-76. -84.8-751.3-4 -423. -525.4-2 5 1 15 2 25 3 35 Temperature of the Asphalt Mix (ºC) Measured Response ABAQUS Modeling Figure 34. Model Evaluation ~ Vertical Strain (top of subgrade)

Sections 1, 2 and 6 Vertical Stress - Top of Embankment - v = 35 km/h -.8 -.7 -.6 95% Confidence Interval for the mean response σv (MPa) -.5 -.4 -.3 -.2 -.27 -.27 -.3 -.33 -.31 -.37 -.42 -.37 -.46 -.1. 5 1 15 2 25 3 35 Temperature of the Asphalt Mix (ºC) Measured Response ABAQUS Modeling Figure 35. Model Evaluation ~ Vertical Stress (top of embankment) The overall conclusion is that there is a general agreement between the measured response and the ABAQUS modeling results for low temperatures: 1 ºC. But, as the temperature increases, the measured response increases more than the model does, resulting in an underestimation of the response for the highest temperature of 3 ºC. With the exception of the vertical strain at the top of the subgrade, model predictions underestimate the measured response in 5-15% for 1 ºC; for 3 ºC the underestimation is higher: 15-25%. Besides, when observing the evolution versus temperature, the measured response also changed more rapidly than model predictions; an example can be seen in Figure 36. This seems to indicate a problem with asphalt modeling. So, additional considerations were necessary in order to evaluate the appropriateness of the linear viscoelastic model used for the asphalt mix. It was carried out by looking at the unloading branch of the creep test records. The model underestimated the vertical strain for all temperatures, with values around 3% lower than the measured response. This could be partly related to the asphalt modeling as stated before, but also seems to indicate some needs related to the soil modeling.

Sections 1, 2, 4, 5 and 6 Longitudinal Strain - Bottom of Asphalt Mix - T: 2 ºC 3% εl (%) compared to 35 km/h 25% 2% 15% 1% 5% 28.6% 17.2% 25.3% 7.3% % 5 1 15 2 25 3 35 Velocidad (km/h) Measured Response ABAQUS Modeling Figure 36. Model Evaluation ~ Evolution of Asphalt Strain versus Speed A linear viscoelastic model was used for the asphalt mix, but the comparison between measured and predicted structural response seems to indicate some problem with this type of modeling. As the temperature increases the model tends to underestimate the actual measured response. Besides, the measured response changes with the speed faster than the model does. So, an additional consideration has been carried out by looking at the unloading branch of the creep test. The linear viscoelastic parameters of the mix model were determined by adjusting the actual strain measured in the creep test, by using a function of the type D(t) = D + D 1 t n. The agreement was very good; the type of function reproduced very well the strain in the loading part. The load step of the creep test took 1 second, and strain was also recorded afterwards. The strain in the unloading branch was only recorded, but it was not used for the calibration of the model. The Figures 37 to 39 show the model predictions for the unloading branch. After the loading step, the strain recuperates more slowly than the model predictions, and this difference is relatively small for 1 ºC, but it increases with temperature: 4% / 9% / 29% for 1 / 2 / 3 ºC respectively. This reveals non resilient deformation, probably due to plastic effects, that the model does not consider. The observed differences can explain the underestimation of the measured response, specially for high temperatures.

Axial Strain - Creep Test - T: 1 ºC 12 1 8 µε 6 Measured Model 4 2 Load Unload Linear Viscoelastic Model 1. 1.5 2. 2.5 3. 3.5 4. 4.5 5. 5.5 6. Core 4 time (s) Figure 37. Asphalt Model Evaluation ~ Unloading Branch of the Creep Test (1 ºC) Axial Strain - Creep Test - T: 2 ºC 18 16 14 12 µε 1 8 Measured Model 6 4 Linear Viscoelastic Model 2 Load Unload..5 1. 1.5 2. 2.5 3. 3.5 4. 4.5 5. Core 2 time (s) Figure 38. Asphalt Model Evaluation ~ Unloading Branch of the Creep Test (2 ºC)

Axial Strain - Creep Test - T: 3 ºC 4 35 3 25 µε 2 15 Measured Model 1 Linear Viscoelastic Model 5 Load Unload Core 3 1. 1.5 2. 2.5 3. 3.5 4. 4.5 5. 5.5 6. tiempo (s) Figure 39. Asphalt Model Evaluation ~ Unloading Branch of the Creep Test (3 ºC)

CONCLUSIONS Six pavement sections have been considered in this study. All the sections consisted of a 15 mm asphalt concrete layer on different alternatives of a high quality subgrade. The sections were instrumented with sensors in order to measure the structural response under the pass of the moving vehicles that simulate traffic in the CEDEX Test Track. The following variables were measured: Deflection Horizontal strain at the bottom of the asphalt layers Vertical stresses in soils at different levels Vertical strain in soils at the top of the subgrades Soils moduli were obtained by means of FWD backcalculation from tests performed on the asphalt layer, after the construction of the sections. Moduli were consistent with the values that would be expected from the layer testing with FWD during the construction. Asphalt mix was characterized in the laboratory from the creep test, but additional complex modulus tests were also carried out. The comparison from both tests shows similar results (in relative terms) for the high frequencies, but for the low frequencies the stiffness is higher from the complex modulus test. This result is probably related to the contribution of the aggregate interlock to the mix stiffness. ABAQUS finite element program was used for the modeling. Soils were assumed to be linear elastic and asphalt mix to be linear viscoelastic, with a constant bulk modulus k and a time-dependent shear modulus G. the meshing was validate by comparison with BISAR results for a multilayer linear elastic section. The asphalt mix mechanical stiffness strongly depends on the frequency of the load, and this dependency makes the flexible pavement response increases when the vehicle speed decreases and also makes the signal registered under a moving wheel to be asymmetric. Both aspects have been frequently described in the literature as well as observed for the six sections considered in this study. But an specific study was conducted in order to evaluate whether or not the inertial forces must be considered or could be neglected in the analysis. The results show that inertial forces are negligible and can be omitted for regular traffic speeds. Consequently, a pseudo-dynamic analysis was carried out, that does not take into account the inertial forces but it does consider the time-dependency of the mechanical properties of the asphalt mix. Tire load was modeled by a circular area with a constant vertical stress applied on it. The area is placed on the pavement surface, that is considered to be the master surface by the ABAQUS surface contact utility. Then, a movement is imposed to the tire area, resulting in a constant stress circular surface moving along the pavement. The model predictions were compared to actual measured response. There is a general agreement for low temperatures. But, as the temperature increases, the measured response increases more than the model does, resulting in an underestimation of the response for the highest temperature. With the exception of the vertical strain at the top of the subgrade, model predictions underestimate the measured response in 5-15% for 1 ºC; for 3 ºC the underestimation is higher: 15-25%. This underestimation seems to be related to the linear viscoelastic model used for the asphalt mix. This model overpredicted the recovered strain after the load step in the creep test, being the difference small for 1 ºC and much higher for 3 ºC. This reveals non resilient deformation, probably due to plastic effects, that the model does not consider, and can explain the underestimation of the measured response, specially for high temperatures.

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