Highway Engineering
KSCE Journal of Civil Engineering Vol. 10, No. 2 / March 2006 pp. 97~104
Viscoelastic Continuum Damage Finite Element Modeling of Asphalt Pavements for Fatigue Cracking Evaluation By Sungho Mun*, Murthy N. Guddati**, and Y. Richard Kim*** ···································································································································································································································
Abstract This paper documents the findings from the study of fatigue cracking mechanisms in asphalt pavements using the finite element program (VECD-FEP++) that employs the viscoelastic continuum damage model for the asphalt layer and a nonlinear elastic model for unbound layers. Both bottom-up and top-down cracks are investigated by taking several important variables into account, such as asphalt layer thickness, layer stiffness, pressure distribution under loading, and load level applied on the pavement surface. The cracking mechanisms in various pavement structures under different loading conditions are studied by monitoring a damage contour. Preferred conditions for top-down cracking were identified using the results from this parametric study. The conjoined damage contours in thicker pavements suggest that the through-the-thickness crack may develop as the bottom-up and top-down cracks propagate simultaneously and coalesce together, supporting observations from field cores and raising the question of the validity of traditional fatigue performance models that account for the growth of the bottom-up cracking only. Keywords: viscoelasticity, Continuum damage, finite element modeling, asphalt fatigue cracking ···································································································································································································································
1. Introduction A traditional approach to dealing with fatigue cracking in asphalt pavements is based on the assumption that cracks initiate at the bottom of the asphalt layer due to tensile stresses developed from the flexure of the layer and propagate to the pavement surface under repeated load applications (so-called bottom-up cracking). However, recent field studies also suggest that fatigue cracks can also initiate at the pavement surface and propagate downward under traffic (so-called top-down cracking). Myers et al. (2001) used linear elastic finite element analysis to conclude that the major cause of top-down cracking is due to tensile stresses resulting from the interaction between truck tires and the pavement surface. In order to accurately determine the initiation location and cause of the fatigue cracking, it is imperative to use realistic constitutive models for different pavement layers because the cracking behavior of asphalt concrete is closely associated with the stress-strain response of the material. In recent years, there has been some success in developing a mechanistic constitutive model of asphalt concrete. A series of experimental/analytical studies by Kim et al. (1997), Daniel and Kim (2002), and Chehab et al. (2002) has resulted in the viscoelastic continuum damage (VECD) model that is based on the elastic-viscoelastic correspondence principle using pseudo strain, continuum damage mechanics, and time-temperature superposition principle with growing damage. To take full advantage of this model’s strength, the VECD model is implemented into the finite element code,
FEP++, developed by Guddati (2001). For aggregate base and subgrade, the nonlinear stress-state dependent model is used. The resulting VECD-FEP++ program is used in this study to investigate the top-down and bottom-up cracking mechanisms in various combinations of pavement structures, layer stiffnesses, and loading conditions.
2. Viscoelastic Continuum Damage Model Kim et al. (1997) developed a uniaxial viscoelastic continuum damage model by applying the elastic-viscoelastic correspondence principle based on pseudo strain to separate out the effects of viscoelasticity and then employing internal state variables based on the work potential theory to account for the damage evolution under cyclic loading and the microdamage healing during rest periods. From the verification study, it was found that the constitutive model has the ability to accurately predict the stressstrain behavior of asphalt concrete under varying loading rates, random rest durations, multiple stress/strain levels, and different modes of loading (controlled-stress versus controlled-strain). A continued effort in refining this model resulted in the work by Daniel and Kim (2002) in which a unique damage characteristic curve between the normalized pseudo stiffness (C) and the damage parameter (S) was discovered regardless of the applied loading conditions (cyclic versus monotonic, amplitude/rate, and frequency). This characteristic curve describes the reduction in material integrity (C) as damage (S) grows in the asphalt concrete specimen. In addition, Chehab et al. (2002) demonstrated that
*Member, Senior Researcher, HTTI, Korea Highway Corporation, Korea (Corresponding Author, E-mail:
[email protected]) **Assistant Professor, Campus Box 7908, Department of Civil, Construction & Environmental Engineering, North Carolina State University, Raleigh, NC, U.S.A. (E-mail:
[email protected]) ***Professor, Campus Box 7908, Department of Civil, Construction & Environmental Engineering, North Carolina State University, Raleigh, NC, U.S.A. (E-mail:
[email protected]) Vol. 10, No. 2 / March 2006
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the time-temperature superposition principle is valid not only in the linear viscoelastic state, but also with growing damage. This finding allows the prediction of mixture responses at various temperatures from laboratory testing at a single temperature. The damage characteristic curve and the time-temperature superposition principle with growing damage are the foundations of the VECD model employed in this study. The major contribution of the VECD model is the significant reduction in testing requirements for the determination of input parameters. The model allows the prediction of the material’s behavior at any temperature from a test result obtained from a single temperature and the time-temperature shift factors obtained from temperature sweep complex modulus tests, as long as the viscoplastic response is minimal in the stress-strain behavior (i.e., low to intermediate temperature and intermediate to fast loading rates). That is, one can perform a simple strength test at a single temperature and dynamic modulus tests at multiple temperatures and predict the cyclic fatigue life of the mix under different testing conditions (i.e., load amplitudes and frequencies, loading time, and temperatures). More detailed descriptions of the VECD model can be found
in (Kim et al., 1997, Daniel and Kim, 2002, and Mun, 2003). The finite element implementation of the VECD model was verified using the uniaxial tension test results (Mun, 2003).
3. Structures, Material Properties, and Loading Conditions In this study, the VECD-FEP++ program is used to investigate the effects of asphalt layer thickness, layer stiffness, contact pressure distribution, and load level on the stresses and fatigue cracking mechanisms in aggregate base pavements. Combinations of these variables are selected so that the effects of individual variables on stress and damage states can be evaluated separately and effectively. Values selected for each variable are summarized in Table 1. Only one base thickness of 50 cm and infinite subgrade was selected for this study. The Prony series constants and a damage function, shown in Table 1, were obtained from the experimental study by Chehab et al. (2002) in which the Maryland Superpave 12.5 mm mix was tested in uniaxial tension. The base and subgrade material parameters of the nonlinear universal model
Table 1. Layer thicknesses and properties selected in this study Pavement Layer
Thickness (cm) (Poisson’s Ratio)
Material Parameter** AC I Prony Coefficients, Em (kPa)
Relaxation Time, Um
Prony Coefficients, Em (kPa)
0.02
4908141.9
0.02
1258989.3
0.2
5735749.4
0.2
2214693.3
2
4955029.9
2
3621321.1
Relaxation Time, Um
Asphalt Concrete
7.6, 17.8, 30.5 (0.30)
AC II
20
2956638.2
20
5136030.7
200
1261172.2
200
5729228.2
2000
446992.8
2000
4459729.9
157584.1
20000
20000
Ef: 58269.0 kPa
2317303.2 Ef: 155243.0 kPa
Damage Function: 50 (0.35)
Base
Infinite (0.40)
Subgrade
** E t = Ef +
Type
k1
k2
k3
Stiff
5764.0
0.420
-0.240
Weak
354.0
0.484
-0.403
Type
k1
k2
Stiff
474.0
-0.366
Weak
771.0
-0.169
Type
k1
k2
Combination
Type of Base
Type of Subgrade
Modulus SS
Stiff
Stiff
Modulus SW
Stiff
Weak
Modulus WS
Weak
Stiff
Modulus WW
Weak
Weak
M
¦ Emexp –t e Um
m=1
where Ef, Um, and Em are infinite relaxation modulus, relaxation time, and Prony coefficients, respectively. 98
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Viscoelastic Continuum Damage Finite Element Modeling of Asphalt Pavements for Fatigue Cracking Evaluation
that were used are found in Santha (1994) and Garg et al. (1998). A moving load was represented by the haversine load with peak magnitudes of 20 and 40 kN. A loading duration of 0.03 sec and a rest period of 0.97 sec were selected. For a tire-pavement contact pressure distribution on the pavement surface, both uniform and nonuniform contact pressure distributions were studied. The uniform contact pressure has been used most widely for pavement response evaluation. However, recent studies (Sebaaly and Tabatabaee, 1993, Groenendijk et al., 1997, and Miradi et al., 1997) have revealed that the contact pressure is nonuniform and that the effect of the nonuniform distribution of the contact pressure is crucial in actual pavement response computation. For the nonuniform tire pressure, the tire pressure measured by Sebaaly (1992) and Siddharthan et al. (2002) was selected for this study.
4. Investigation of Macrocrack Initiation Mechanisms The research performed in this study focuses on investigating the fatigue failure mechanism(s) of top-down and bottom-up
cracking modes by monitoring the state of stresses and structural damage. One unique feature of the VECD-FEP++ program is its ability to determine the amount of damage in the asphalt layer as the number of loading cycles increases. The amount of damage is represented by a damage parameter calculated from the VECD model. This feature of the VECD-FEP++ program is quite different from typical finite element analysis based on fracture mechanics, such as the studies done by Jenq et al. (1991, 1993) and Myers et al. (2001). In their studies, an artificial crack was introduced before the load was applied and critical stresses that contribute most to the macrocrack propagation were identified. In this study, the approach allows the investigation of the location and mechanisms of microcracks without any initialized artificial cracks in the pavement structure. The pavement structure is modeled by an axisymmetric finite element model. Fig. 1(a) shows radial stress-strain curves at the bottom of the asphalt concrete layer under nonuniform contact pressure in the cyclic mode. The hysteresis loops shifted to the right side, demonstrating the increase of radial strain in tension as the damage in the asphalt layer increases. Fig. 1(b) presents
Fig. 1. VECD-FEP++ Analysis of a Pavement with Thick Asphalt Layer Thickness: (a) Cyclic Hysteresis Behavior; (b) Damage Contours at Different Cycles Vol. 10, No. 2 / March 2006
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Sungho Mun, Murthy N. Guddati, and Y. Richard Kim
the damage contours at different numbers of cycles. It is noted that the intensity of damage increases as the number of cycles increases. In Fig. 1(b), significant damage is found at the pavement surface near the load center where the compressive stress is the greatest. In the current formulation of the VECD-FEP++ program, the damage parameter is calculated from the absolute value of stresses. Therefore, the damage observed at the pavement surface around the load center is the damage computed from the compressive stress and, therefore, should be ignored as an error. This error can be corrected by assigning the damage value of zero when the stress is in compression. It was found that the comparison of stress and damage contours at the peak load of the 1,000th cycle yields similar conclusions to those made from longer cycles. For this paper, therefore, stress and damage contours at the peak load of the 1,000th cycle are used for comparison. Fig. 2 to Fig. 6 show the contours of damage and stresses for all the pavement structures and loading conditions selected in this study. Fig. 2 to Fig. 5 were generated using the soft asphalt stiffness (i.e., AC I) only, and the effect of asphalt layer stiffness is shown in Fig. 6. 4.1. Effect of Asphalt Layer Thicknesses The level of damage is found greatly affected by the asphalt layer thickness. In Fig. 2, the damage value decreases signi-
ficantly as the asphalt layer thickness increases. For example, the increase of the asphalt layer thickness from 7.6 to 17.8 cm results in the decrease in the damage level by about 60 times, as seen in the comparison between the maximum values of the contour legends shown in Fig. 2. The most important observation from Fig. 2 is the change in the location of crack initiation as a function of the asphalt layer thickness. When the thinnest layer is modeled in Fig. 2, the severe damage is found at the bottom of the layer with negligible damage at the top of the asphalt layer. As the asphalt layer becomes thicker, damage right under the tire edge starts to emerge, in addition to that at the bottom of the asphalt layer. In the thickest asphalt layer case, the intensity of damage under the tire edge is as high as that at the bottom of the asphalt layer. This result can be attributed to the increased localization of punching shear stresses in thicker pavements under the edge of the load. The different cracking mechanisms between thin and thick asphalt layers can be seen more effectively when Fig. 1(b) and Fig. 3 are compared. In Fig. 3, for the thin asphalt layer, the damage evolution is governed mostly by the damage that started from the bottom of the asphalt layer. However, in Fig. 1(b), for the thick asphalt layer, damage initiates from both the bottom of the asphalt layer and right under the tire edge, and propagates simultaneously to form a conjoined damage contour. This conjoined damage contour, shown in Fig. 1(b) and Fig. 2 for the
Fig. 2. Damage Contours in Varying Asphalt Layer Thicknesses Under Nonuniform 40 kN Load for: (a) MODULUS SS; (b) MODULUS SW; (c) MODULUS WS; (d) MODULUS WW 100
KSCE Journal of Civil Engineering
Viscoelastic Continuum Damage Finite Element Modeling of Asphalt Pavements for Fatigue Cracking Evaluation
Fig. 3. Damage Evolution in the Thin Asphalt Layer
Fig. 4. Damage Contours in Varying Asphalt Layer Thicknesses Under Uniform 40 kN Load for: (a) MODULUS SS; (b) MODULUS SW; (c) MODULUS WS; (d) MODULUS WW Vol. 10, No. 2 / March 2006
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Sungho Mun, Murthy N. Guddati, and Y. Richard Kim
Fig. 5. Damage Contours in the Thin Asphalt Layer Under Nonuniform and Uniform 20 kN Load for: (a) MODULUS SS; (b) MODULUS SW; (c) MODULUS WS; (d) MODULUS WW
medium and thick asphalt pavements, supports the findings from field studies of top-down cracking (Gerritsen et al., 1987); that is, the top-down cracks are found in asphalt pavements with an asphalt layer thicker than 25 to 30 cm. Also, the conjoined damage contour suggests that the throughthe-thickness crack may develop as these bottom-up and topdown microcracks propagate further and coalesce together. Gerritsen et al. (1987) reported that they found field cores with top-down cracking for about 10 cm, about 5 cm with no cracking at all, and about 10 cm bottom-up cracking in the same core. The conjoined damage contour in Fig. 1(b) and Fig. 2 explains the reason behind this observation. This finding clearly demonstrates the problem associated with the traditional approach to fatigue performance prediction in which the tensile strain at the bottom of the asphalt layer is related to the fatigue life of the pavement. This approach cannot account for the additional crack growth from the top of the pavement and, therefore, overestimates the fatigue life of the pavement. 4.2. Effect of Contact Pressure Distributions Sebaaly (1992) presented the nonuniform contact pressure distribution measured from a moving surface load. Fig. 2 and Fig. 4 show the results from the nonuniform and uniform contact pressures, respectively. One observation that can be made from the comparison of the figures is that the nonuniform pressure distribution results in a greater amount of damage in all the cases. For example, Fig. 2, with the nonuniform contact pressure, shows greater damage than Fig. 4 with the uniform contact pressure when the values of the contour legends are compared. This difference suggests that the pavement responses, calculated in the traditional way of treating the tire pressure as uniform, may underestimate the actual damage in the field and thereby overestimate the pavement service life. Also, it needs to be noted that the propensity of top-down cracking becomes greater under nonuniform pressure than under uniform pressure. This
observation supports findings from laboratory tests conducted by Groenendijk et al. (1997) and Miradi et al. (1997) who showed that a nonuniform load causes large stresses at the pavement surface. Fig. 6 presents the medium thick asphalt layer cases for uniform and nonuniform pressures and clearly shows the same observation. 4.3. Effect of Load Levels Damage contours under 20 kN loading are plotted in Fig. 5 for the nonuniform and uniform contact pressures, respectively. Compared to the damage contours in Fig. 2 and Fig. 4 for the 40 kN load, the magnitude of damage is dramatically reduced for thin pavements due to the reduction of the load. Comparing the values of contour legends for the thin asphalt layer cases in Fig. 2 to Fig. 5 reveals that a reduction in the load level by a factor of two results in the reduction in the damage by more than five times, regardless of structures, contract pressure distribution, or layer properties. One major use of the damage values calculated from different load levels is the development of the Equivalent Axle Load Factor (EALF). Traditionally, the damage under a load was either represented by critical pavement responses or calculated by performance equations. Using the damage computed from the VECD-FEP++ program, one can directly determine the damage ratios of different load levels and, therefore, EALFs. 4.4. Effect of Base and Subgrade Moduli The effect of base and subgrade moduli can be evaluated by comparing four subfigures under each response parameter in each figure. First of all, it is found in and Fig. 4 that the effect of the subgrade modulus on damage states is much less than the effect of the base modulus. Regarding the crack initiation location, the weaker base and/or weaker subgrade increases the intensity of damage under the tire edge and, therefore, the propensity of top-down cracking. In the thickest asphalt layer,
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Viscoelastic Continuum Damage Finite Element Modeling of Asphalt Pavements for Fatigue Cracking Evaluation
Fig. 6. Damage Contours in the Medium Thick Asphalt Layer: (a) Nonuniform Pressure and AC I Stiffness; (b) Nonuniform Pressure and AC II Stiffness; (c) Uniform Pressure and AC I Stiffness; (d) Uniform Pressure and AC II Stiffness.
the weaker base resulted in more damage in general, but this trend was more evident in the damage under the tire edge. 4.5. Effect of Asphalt Layer Stiffness Fig. 6 presents the damage contours calculated using two asphalt layer stiffnesses (AC I and AC II in Table 1) under both nonuniform and uniform pressure distributions. It can be concluded from this figure that the damage under the tire edge becomes slightly greater as the stiffness of the asphalt layer increases. This observation may become important when the aging of the asphalt layer is considered. It is known that aging is more severe at the top portion of the asphalt layer. The stiffening effect of aging, therefore, makes the top portion of the asphalt layer stiffer than the rest of the layer, which in turn increases the tendency of top-down cracking. Vol. 10, No. 2 / March 2006
5. Conclusions It is demonstrated that the VECD-FEP++ program, with a damage characteristic curve determined from a single monotonic test and the time-temperature shift factor determined from the complex modulus test, may be used to study the cracking mechanisms of asphalt pavements. The findings from this study show the effect of various pavement and load factors on pavement responses as well as damage in the asphalt layer. It was found that the propensity of top-down cracking increases as: (1) the asphalt layer becomes thicker; (2) the contact pressure becomes nonuniform; (3) base and/or subgrade become less stiff; and (4) the asphalt layer becomes stiffer. The conjoined damage contours in thicker pavements suggest that the through-the-thickness crack may develop as these
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bottom-up and top-down cracks propagate simultaneously and coalesce together. This observation raises a serious question of the validity of the traditional fatigue performance prediction approach in which only the tensile strain at the bottom of the asphalt layer is considered in predicting the fatigue life of asphalt pavements.
6. References Chehab, G.R., Kim, Y.R., Schapery, R.A., Witczak, M.W., and Bonaquist, R. (2002). “Time-temperature superposition principle for asphalt concrete mixtures with growing damage in tension.” Journal of Association of Asphalt Paving Technologists, Vol. 71, pp. 559593. Daniel, J.S. and Kim, Y.R. (2002) “Development of a simplified fatigue test and analysis procedure using a viscoelastic continuum damage model.” Journal of Association of Asphalt Paving Technologists, Vol. 71, pp. 619-650. Garg, N. and Thompson, M.R. (1998) Mechanistic-Empirical Evaluation of the Mn/ROAD Low Volume Road Test Sections, Illinois Cooperative Highway and Transportation Research Program Report FHWA-IL-UI-262, Urbana, IL. Gerritsen, A.H., Van Gurp, C.A.P.M., Van der Heide, J.P.J., Molenaar, A.A.A., and Pronk, A.C. (1987). “Prediction and prevention of surface cracking in asphalt pavements.” 6th International Conference on Structural Design and Asphalt Pavements, The University of Michigan, Ann Arbor, MI, pp. 378-391. Guddati, M.N. (2001) FEP++: A Finite Element Program in C++, Input Manual, Department of Civil Engineering, North Carolina State University. Groenendijk, J., Vogelzang, C.H., Molenaar, A.A.A., Mante, B.R. and Dohmen, L.J.M. (1997). “Linear tracking response measurements: determining effects of wheel-load configurations.” Transportation Research Record 1570, TRB, National Research Council, Washington, D.C., pp. 1-9. Jenq, Y.S., and Perng, J.D. (1991). “Analysis of crack propagation in asphalt concrete using cohesive crack model.” Transportation
Research Record 1317, TRB, National Research Council, Washington, D.C., pp. 90-99. Jenq, Y.S., Liaw, C.J., and Liu, P. (1993). “Analysis of crack resistance of asphalt concrete overlays - A fracture mechanics approach.” Transportation Research Record 1388, TRB, National Research Council, Washington, D.C., pp. 160-166. Kim, Y.R., Lee, H.J., and Little, D.N. (1997) “Fatigue characterization of asphalt concrete using viscoelasticity and continuum damage theory.” Journal of the Association of Asphalt Paving Technologists, Vol. 66, pp. 520-569. Miradi, A., Groenendijk, J., and Dohmen, L.J.M. (1997) “Crack development in linear tracking test pavements from visual survey to pixel analysis.” Transportation Research Record 1570, TRB, National Research Council, Washington, D.C., pp. 48-54. Mun, S. (2003). Nonlinear Finite Element Analysis of Pavements and Its Application to Performance Evaluation. Ph.D. Dissertation, Department of Civil Engineering, North Carolina State University, 2003. Myers, L.A., Roque, R., and Birgisson, B. (2001). “Propagation mechanisms for surface-initiated longitudinal wheel path cracks.” Transportation Research Record 1778, TRB, National Research Council, Washington, D.C., pp. 113-122. Santha, B.L. (1994). “Resilient modulus of subgrade soils: Comparison of two constitutive equations.” Transportation Research Board 1462, TRB, National Research Council, Washington D.C., pp. 7990. Sebaaly, P.E. (1992). Dynamic Forces on Pavements: Summary of Tire Testing Data. Report on FHWA Project DTFH 61-90-C-00084. Sebaaly, P.E. and Tabatabaee, N. (1993). “Influence of vehicle speed on dynamic loads and pavement response.” Transportation Research Board 1410, TRB, National Research Council, Washington D.C., pp. 107-114. Siddharthan, R.V., Krishnamenon, N., El-Mously, M., and Sebaaly, P E. (2002). “Investigation of tire contact stress distributions on pavement response.” Journal of Transportation Engineering, Vol. 128, No. 2, ASCE, pp. 136-144.
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(Received September 8, 2005/Accepted February 8, 2006)
KSCE Journal of Civil Engineering
