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Flexible Pavements Dynamic Response under a Moving Wheel

Angel Mateos, Ph.D. 1, Pablo de la Fuente Martín Ph.D. P.E. and Javier Perez Ayuso 1

2

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 300 meters close track. Six full-depth sections were tested, consisting of a 150 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, 28760 Madrid, Spain. email: [email protected]

Department of Mechanic of Continuous Media and Structures Theory, Technical University of Madrid. C/ Ramiro de Maeztu 7, 28040 Madrid, Spain. email: [email protected]

2

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 20-25 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 60 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: 5-30 ºC Speed: 35 km/h (additional tests were carried out to evaluate speed effect between 10 and 35 km/h for an asphalt temperature of 20 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

150 Asphalt Concrete Soil S3 500 250 Soil S0 150 250

Section 2

Asphalt Concrete Natural Granular Soil S1 Soil S0 150 200 300

Section 3

Asphalt Concrete Cement Stab. Soil (5%) Soil S1 Soil S0

1300

1300

1300

Concrete Text Pit

Concrete Text Pit

Concrete Text Pit

Section 4

150 Asphalt Concrete Soil S3 500 500 150

Section 5

Asphalt Concrete 150

Section 6

Asphalt Concrete Soil S3 500 geotextile

Soil S3

Soil S1 500

200

Lime Stab. Soil (3%) Soil S0

Soil S0

Soil S0 1100 800

1300

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 S0 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

AC

Section 1

l v t v AC ZN

Section 2

l t AC S-EST 3 v v

Section 3

l t

S3

S1 v

v

S1

v

v

v

(to the concrete pit)

(to the concrete pit)

(to the concrete pit)

AC

Section 4

l v t v AC

Section 5

l v t v AC

Section 6

l v t v

S3

S3

S3

S-EST 1 S1 v

v

(to the concrete pit) 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 250000 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

200

Longitudinal Strain (µ µ)

150

100

Sensor

long

50

22KL22

0

-50 -4000

-2000

0

2000

4000

Longitudinal Position (mm)

Figure 7.

Example of a Longitudinal Strain Record

Twin wheels (65.7 kN)

Section 1 - deflection -

v = 35 km/h

60.0

50.0

Deflection (mm/100)

40.0

Sensors

30.0

11DF01 12DF01

20.0

10.0

0.0 0 5 10 15 20 25 30

Temperature of the Asphalt Mix (ºC)

Figure 8.

Example of Deflection Evolution versus Temperature

Twin Wheels (65.7 kN)

Section 1 - deflection -

T: 15-20 ºC

60.0

50.0

Deflection (mm/100)

40.0

Sensors

30.0

11DF01 12DF01

20.0

10.0

0.0 0 10 20 30 40

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 10 that the confidence interval for the true response of the sensor is very narrow (e.g. ±0.2 mm/100 for the deflection at 20 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 10 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: ±10.5 mm/100. 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 Curve fit for each sensor

v = 35 km/h

80.0 70.0

95% confidence interval for the sensor true response 95% confidence interval for the mean response of the section

Deflection (mm/100)

60.0 Sensors 50.0 40.0 30.0 20.0 10.0 0.0 0 5 10 15 20 25 30

61DF01 62DF01 mean

Temperature of the Mix (ºC)

Figure 10. 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 (D0) 180 160 140

FWD tests were performed on the top of each layer after the construction

Modulus (MPa)

120 100 80 60 40 20 0 0 5 10 15 20 25 30 35 mean Soil S0 mean Soil S1 mean Soil S3 Natural Granular Soil

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 -

500

400

Deflection (µm)

300

200

D0 D200 D300 D450 D900

100

0 0 10 20 30 40 50 60 70 80 90 100

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 S0 120 MPa 2000 MPa 210 MPa 1500 MPa 75 MPa 110 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 : = 0

;

t0 (t ) 0

and the measured strain : = (t ) the Creep Compliance is : D(t ) =

Applied Load H0 H0 (t) Measured strain

time

(t)

delayed strain 0 (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:

D(t ) =

(t ) (t )

5.0

4.0

3.0

Actual Applied Load Theoretical Step Load

2.0

kN

1.0 0.0 0.350

0.400

0.450

0.500

0.550

time (s)

Figure 14. Actual Step Load

Tests were carried out under the following conditions: Temperature (3 levels): Reference (zero) load: Step load: 10 ºC 20 ºC 30 ºC 10 / 20 / 30 ºC 0.25 kN ( = 32 kPa) 4.0 kN ( = 509 kPa) 4.0 kN ( = 509 kPa) 2.0 kN ( = 255 kPa)

n

An explicit creep function was used: D(t) = D0 + D1·t , and results are presented in Table 2. Table 2. Results from Creep Compliance Tests

Temperature

D0

mean Std. Error C.I. (95 %) mean Std. Error C.I. (95 %) mean Std. Error C.I. (95 %)

Parameter D1

124

30.4 [108 ; 139]

n

0.331

0.060 [0.300 ; 0.362]

57.5

20.4 [47.0 ; 68.0]

10 ºC 20 ºC 30 ºC

74.5

16.6 [66.2 ; 82.7]

367

76.9 [328 ; 405]

0.425

0.034 [0.408 ; 0.442]

164.7

40.2 [144.0 ; 185.3]

1365

294.0 [1214 ; 1516]

0.526

0.021 [0.516 ; 0.537]

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* () =

1 D* ()

where D*() is the Laplace transformation of D(t). 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 0.1 Hz the contribution of the aggregate interlock can be significant, and the cores were subjected to a higher deformation during the complex modulus test.

Dynamic Modulus

12000

Tª: 20 ºC

10000

8000

|E*| (MPa)

6000

Complex Modulus Test Creep Test

4000

2000

0 0.01

0.1

1

10

100

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 T ) = - (T - T0 )

where aT is the time scale and depends on the mix type. The value was obtained from the creep compliance functions obtained in the laboratory for 10, 20 and 30 ºC, as can be seen in Figure 16.

Superposition time-Temperature

600 Corrected cruve by means of a compression in time scale 500 = 0.124 400

D(t) (µ µ/MPa)

Error:

= 7.4 %

300 = 0.137 200

10 ºC 20 ºC 30 ºC

= 1.0 %

100

0 0.0 0.2 0.4 0.6 0.8 1.0 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: 15-20 ºC

0.20

Vertical Stress (MPa)

0.15 Sensors 0.10

11CT31 12CT31

0.05

0.00 0 10 20 30 40

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

0.15

Vertical Stress (MPa)

0.10

0.05

0.00

-0.05 -4000

-2000

0

2000

4000

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 70 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 900 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 20ºC, and the results show that the response of the mix was almost linear for this range of load.

Creep Compliance

500

T: 20 ºC

400

µ/ MPa

300

Load applied on Cores

2 kN (255 kPa) 4 kN (509 kPa) 200

100

0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

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 20. 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.

3300 mm

8000 mm 2000 mm

Figure 20. Distance between the Wheel Load and the Concrete Wall

Deflection

50

Level 1 (Suface)

0.02

Vertical Stress

40

0.00

(mm/100)

30

-0.02

V (MPa)

20

-0.04

Level 4

10

-0.06 Level 3: Top of the Subgrade Level 4: Top of the Embankment

0

-0.08

Level 3

-10 0 500 1000 1500 2000 2500 3000

-0.10 0 500 1000 1500

2000

2500

3000

Distance to the Load (mm)

Distance to the Load (mm)

Figure 21. Attenuation of the Structural Response with Horizontal Distance

Tire Print

z x

Asphalt Concrete Subgrade

y

e lan yP etr 0 m = ym x S

Concrete Test Pit

4 meters

2 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: 14400 Nº nodes: 16359 Nº degrees of freedom: · total: 49077 (3 d.o.f. per node) · restricted in boundary: - 6201 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 ±20% 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' = 0

Tire Load

Y' = -1.5 m

St dif ruct fer ura en l r t d es ep po ths ns e

ca lcu lat ion at

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: 0 = 0.15. 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

8.0 Normalized D(t) (Shear Modulus, G) 6.0

Normalized D(t) (elastic modulus, E) 4.0

2.0

1.0

0.0 0 0.2 0.4 0.6 0.8 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

Longitudinal Strain

- Asphalt Mix -

ABAQUS Modeling T: 20ºC

250 200 150

L (µ)

100 50 0 -50 -2.0

Pseudo-dynamic Dynamic (35 km/h)

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

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

130%

Speed Effect

360 km/h

ABAQUS Modeling T: 20ºC

Dynamic Response / Static Response

120%

240 120 180

110%

35 60

100%

90%

Deflection Longitudinal Strain Transverse Strain Vertical Stress (top subgrade) Vertical Strain (top subgrade) Vertical Stress (top embankment) Vertical Strain (top embankment)

80%

70%

60% 0 50 100 150 200 250 300 350 400

Speed (km/h)

Pavement with a Rigid Bottom Layer (Concrete Test Pit)

Figure 28. Dynamic Amplification of the Structural Response (Section 1)

Twin Wheels

140%

Speed Effect

ABAQUS Modeling T: 20ºC

Dynamic Response / Static Response

130% 120% 110%

180 240 120 360 km/h

100% 90% 80% 70% 60% 0

35

60

Deflection Longitudinal Strain Transverse Strain Vertical Stress (top subgrade) Vertical Strain (top subgrade) Vertical Stress (top embankment) Vertical Strain (top embankment)

50

100

150

200

250

300

350

400

Velocidad (km/h)

Pavement with a Semi-infinite Embankment

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

70 60 50

Deflection

95% Confidence Interval for the mean response

53.3

v = 35 km/h

61.4

(mm/100)

46.4

40

36.5 33.4

40.8 36.4 31.2

46.2

30 20 10 0 0 5

10

15

20

25

30

35

Temperature of the Asphalt Mix (ºC)

Measured Response

Figure 30. Model Evaluation ~ Deflection

ABAQUS Modeling

Section 3

40 35 30

Deflection

95% Confidence Interval for the mean response

v = 35 km/h

29.6 25.4 22.1

(mm/100)

25 20

17.0 17.9 18.3 16.4 19.6

22.3

15 10 5 0 0 5

10

15

20

25

30

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

600 500 400

Longitudinal Strain

- Bottom of Asphalt Mix 95% Confidence Interval for the mean response

v = 35 km/h

389.5 310.6 308.0 245.8

L (µ)

300 200

158.3 135.6 195.0 187.6

100 0 0 5

143.9

10

15

20

25

30

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

-0.200

Vertical Stress

- Top of Subgrade v = 35 km/h

95% Confidence Interval for the mean response -0.150

-0.154 -0.127

V (MPa)

-0.100

-0.086 -0.071 -0.061

-0.104

-0.113

-0.082

-0.050

-0.067

0.000 0 5 10 15 20 25 30 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

-1400 -1200 -1000

Vertical Strain

- Top of Subgrade v = 35 km/h

95% Confidence Interval for the mean response

-1083.8 -930.7

V (µ µ)

-800

-706.0

-804.8 -634.2 -525.4 -423.0 -751.3

-600 -400 -200 0 0 5

-589.6

10

15

20

25

30

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

-0.080 -0.070 -0.060

Vertical Stress

- Top of Embankment v = 35 km/h

95% Confidence Interval for the mean response

V (MPa)

-0.050 -0.040 -0.030 -0.020 -0.010 0.000 0 5 10 15 20 25

-0.033 -0.027 -0.030 -0.031 -0.027 -0.042 -0.037

-0.046

-0.037

30

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: 10 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 30 ºC. With the exception of the vertical strain at the top of the subgrade, model predictions underestimate the measured response in 5-15% for 10 ºC; for 30 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 30% 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

30%

28.6%

Longitudinal Strain

- Bottom of Asphalt Mix -

T: 20 ºC

L (%) compared to 35 km/h

25% 20% 15% 10% 5% 0% 0 5

25.3%

17.2%

7.3%

10

15

20

25

30

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 n measured in the creep test, by using a function of the type D(t) = D0 + D1·t . 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 10 ºC, but it increases with temperature: 4% / 9% / 29% for 10 / 20 / 30 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 120

T: 10 ºC

100

80

60

Measured Model

µ

40

20

Load Unload

Linear Viscoelastic Model

0 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0

Core 4

time (s)

Figure 37. Asphalt Model Evaluation ~ Unloading Branch of the Creep Test (10 ºC)

Axial Strain - Creep Test 180 160 140 120

T: 20 ºC

µ

100 80 60 40

Linear Viscoelastic Model

Measured Model

20 0 0.0 0.5

Load

Unload

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

Core 2

time (s)

Figure 38. Asphalt Model Evaluation ~ Unloading Branch of the Creep Test (20 ºC)

Axial Strain - Creep Test 400 350 300 250 200 150 100 50 0 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0

T: 30 ºC

Measured Model

µ

Linear Viscoelastic Model

Load

Unload

Core 3

tiempo (s)

Figure 39. Asphalt Model Evaluation ~ Unloading Branch of the Creep Test (30 ºC)

CONCLUSIONS

Six pavement sections have been considered in this study. All the sections consisted of a 150 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 10 ºC; for 30 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 10 ºC and much higher for 30 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.

REFERENCES

Alavi, S. H. and C. L. Monismith. "Time and Temperature Dependent Properties of Asphalt Concrete Mixes tested as Hollow Cylinders and Subjected to Dynamic Axial and Shear Loads". Journal of the Association of Asphalt Paving Technologist, Vol. 63, 1994. Barbour, I. A. and W. H. Newton. "Multiple-Sensor Weight-In-Motion". First European Conference on Weight-In-Motion of Road Vehicles, Zurich, 1995. Chatti, K. and T. Kim. "Effect of Frequency-dependent Asphalt Concrete Layer Moduli on Pavement Response". Nondestructive Testing of Pavements and Backcalculation of Moduli: Third Volume, ASTM STP 1375, S. D. Tayabji and E. O. Lukanen, Eds., American Society for Testing and Materials, West Conshohocken, P.A., 2000. European Commission. "Action COST 333: Development of New Bituminous Pavement Design Method". Final Report. European Commission, Brussels, 1999. European Commission. "AMADEUS project: Advanced Models for Analytical Design of European Pavement Structures". European Commission, Brussels, 2000. Daniel, Jo Sias and Y. Richard Kim. "Relationships among rate-dependent stiffnesses of asphalt concrete using laboratory and field test methods". Transportation Research Record 1630, TRB, National Research Council, Washington, D.C., 1998. Foinquinos, R., J. M. Roesset and K. H. Stokoe II. "Response of Pavement Systems to Dynamic Loads Imposed by Nondestructive Tests". Transportation Research Record 1504, TRB, National Research Council, Washington, D.C., 1995. Huang, Y. H. "Pavement Analysis and Design". Prentice Hall, New Jersey, 1993.

Kim, Y. R., Y. C. Lee and H. J. Lee. "Correspondence Principle for Characterization of Asphalt Concrete". Journal of Materials in Civil Engineering, Vol. 7, 1995.

Mamlouk, M. S. "Use of dynamic analysis in predicting field multilayer pavement moduli". Transportation Research Record 1043, TRB, National Research Council, Washington, D.C., 1985. Mamlouk, S. M. and P. P. Khanal. "Bimodular Analysis of Asphalt Pavements". Proceedings of the 8th International Conference on Asphalt Pavements, Seattle, Washington, 1997. Mateos, A. "Load Equivalency Factors from the Structural Response of Flexible Pavements". Master's Thesis, University of Minnesota, Department of Civil Engineering, Minneapolis, 2000. Mateos, A. and M. B. Snyder. "Validation of Flexible Pavement Structural Response Models Using Mn/ROAD Data". Annual Meeting of the Transportation Research Board, Washington, D.C., 2002. Mateos, A. "Modeling the Structural Response of Flexible Pavements from Full Scale Test Track Experimental Data". Ph.D. Thesis, Technical University of Madrid, Department of Mechanics of Continuum Media and Theory of Structures, Madrid, 2003. Nazarian, S. and K. M. Boddapati. "Pavement-Falling Weight Deflectometer Interaction Using Dynamic Finite-Element Analysis". Transportation Research Record 1482, TRB, National Research Council, Washington, D.C., 1995. Sivaneswaran, N., L. M. Pierce and J. P. Mahoney. "EVERCALC Pavement Backcalculation Program". Materials Laboratory, Washington State Department of Transportation, 1999. Ullidtz, P. "Pavement Analysis". Elsevier Science, New York, 1987.

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