analysis of pavement damage and performance

95Vol. 11, No. 2 | July 2020

pISSN: 2093-8829, eISSN: 2234-1765LHI Journal 2020;11(2):95-104 • http://doi.org/10.5804/LHIJ.2020.11.2.95

Mechanistic Analysis of Pavement Damage and Performance Prediction Based on Finite Element Modeling with Viscoelasticity and Fracture of Mixtures

Mohammad Rahmani*·Yong-Rak Kim**·Yong Boo Park***· Jong Suk Jung****

Abstract

This study aims to explore a purely mechanistic pavement analysis approach where viscoelasticity and fracture of asphalt mixtures are considered to accurately predict deformation and damage behavior of flexible pavements. To do so, the viscoelastic and fracture properties of designated pavement materials are obtained through experiments and a fully mechanistic damage analysis is carried out using a finite element method (FEM). While modeling crack development can be done in various ways, this study uses the cohesive zone approach, which is a well-known fracture mechanics approach to efficiently model crack initiation and propagation. Different pavement configurations and traffic loads are considered based on three main functional classes of roads suggested by FHWA i.e., arterial, collector and local. For each road type, three different material combinations for asphalt concrete (AC) and base layers are considered to study damage behavior of pavement. A concept of the approach is presented and a case study where three different material combinations for AC and base layers are considered is exemplified to investigate progressive damage behavior of pavements when mixture properties and layer configurations were altered. Overall, it can be concluded that mechanistic pavement modeling attempted in this study could differentiate the performance of pavement sections due to varying design inputs. The promising results, although limited yet to be considered a fully practical method, infer that a few mixture tests can be integrated with the finite element modeling of the mixture tests and subsequent structural modeling of pavements to better design mixtures and pavements in a purely mechanistic manner.

Keywords: �Mechanistic�Pavement�Analysis,�Finite�Element�Modeling,�Viscoelasticity,�Fracture,�Performance�Prediction

1. Introduction

Several different approaches have been developed for pave-ment structure analysis and design in the past. The mechanistic- empirical pavement design guide (M-E PDG) was developed

under the National Cooperative Highway Research Program (NCHRP) 1-37A project (NCHRP, 2004) and adopted by AASHTO to update the AASHTO 1993 guide (AASHTO, 1993). The M-E PDG method is currently known as the Pave-ment ME Design and is implemented using AASHTOWare

* Graduate Student, Zachry Department of Civil & Environmental Engineering, Texas A&M University College Station, TX, USA (Main Author: [email protected])

**� �Professor,�Zachry�Department�of�Civil�&�Environmental�Engineering,�Texas�A&M�University�College�Station,�TX,�USA�(Corresponding�Author: [email protected])

*** Senior Researcher, Land and Housing Institute, Republic of Korea**** Senior Researcher, Land and Housing Institute, Republic of Korea

( Received: April 17, 2020 / Revised: July 20, 2020 / Accepted: July 23, 2020)

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Mohammad Rahmani·Yong-Rak Kim·Yong Boo Park·Jong Suk Jung

software program. Despite the significant improvements made by Pavement ME Design due to implementing mechanistic concepts for determining critical pavement response under traffic loads, it still employs database-dependent empirical equations to predict distresses in the structure making the method rely on limited field performance data and statistical approaches rather than damage prediction based on funda-mental material properties and mechanical behavior. Consid-ering the nature of transfer function along with the statistical calibration process, accurate prediction of distresses in asphalt pavements is limited in the approach. The mechanistic part is also limited in determination of mechanical response of pave-ment structures because it uses multi-layer elastic theory and therefore, cannot account for time-dependent behavior of highly viscoelastic asphalt concrete (AC) mixtures, nor stress-dependent stiffness in unbound layers. Furthermore, in Pavement ME Design, the main input data required for asphalt mixture is stiffness properties which are defined in the form of AC master curves. Using master curves to represent the stiffness behavior allows the design method to account for the effect of temperature and traffic speed on the response of asphaltic lay-ers, but it assumes AC as an elastic material. Including merely the stiffness characteristics of entire AC makes the design approach incapable of taking into account other important characteristics of asphalt mixtures that are not necessarily reflected only by stiffness properties (e.g., fracture properties).

In recent years, several studies have attempted to develop somewhat more mechanistic pavement design approaches that could address some of the empirical aspects with Pavement ME Design. Although most of these approaches have been devel-oped based on finite element modeling rather than multi-layer elastic theory, they have utilized different methods to predict damage in the pavement structure. Al-Rub et al. (2010; 2011) and Darabi et al. (2013) developed a mechanistic-based mod-el, named the PANDA (Pavement Analysis Using Nonlinear Damage Approach). It uses a nonlinear damage approach by having global damage-associated responses obtained from laboratory tests such as creep and recovery or constant strain tests to predict damage behavior of asphaltic pavements. A micro-damage healing model was also include in order to improve the ability of model to predict the fatigue life of

asphalt pavements. Repeated creep-recovery tests conducted in different loading times and rest periods in both tension and compression mode were then used for validation of healing model. The results of this study suggested that the ability of the constitutive model to predict fatigue life of pavement could be significantly enhanced by incorporating the micro-damage healing model. Al-Rub et al. (2011) also used a prediction technique for determining rutting in an attempt to reduce the computational cost associated with 3D finite element modeling under many loading cycles. In this extrapolation technique, the 3D modeling is first conducted for a small number of load-ing cycles, and then the modeling is extended through 2D finite element modeling for a large number of cycles. Gungor et al. (2016) developed a mechanistic-based pavement design using a 3D finite element model and validated their pavement model response with field instrument responses in terms of vertical pressure and horizontal tensile strains. Although the accurate prediction of pavement responses was found to be sensitive to proper material characterization, their study concluded that FE modeling is a promising technique that could address the shortcomings of layered elastic theory. Wang et al. (2016) used a mechanistic model to predict fatigue cracking and the rut-ting performance of pavement structures. A program named layered viscoelastic pavement design for critical distresses (LVECD) program developed at North Carolina State Univer-sity was used. It employs 3D viscoelastic finite element analysis with moving loads and a simplified viscoelastic continuum damage (S-VECD) to predict damage in pavement structures. In their study, a comparison between model prediction results and those of the pavement ME program indicated a good agreement between their mechanistic design approach and field performance data.

All mechanistic approaches aforementioned are based on continuum damage mechanics. The continuum damage mechanics typically represents damage as reduced mixture stiffness due to multiple micro- and macro-scale changes in mixture integrity. The continuum damage mechanics has been widely used in the pavement modeling community since it can provide a good computational stability and is easy to be implemented into a finite element method. It is also powerful to catch critical locations in pavements due to loading and

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Mechanistic Analysis of Pavement Damage and Performance Prediction

other factors and can accurately model initiation of damage. However, the continuum damage mechanics modeling is usu-ally limited to accurately model how cracks evolve to an ulti-mate failure in a progressive manner, because the damaged body is considered to be a homogeneous continuum on a scale that is much larger than that of the size of the cracks. Damage in the body is typically represented by phenomenological internal state variables (ISVs) that are determined by matching damage evolution characteristics from laboratory testing results through regression analyses.

On the contrary, an increasing number of researchers have recently used fracture mechanics approaches, such as the cohesive zone modeling (Kim and Buttlar, 2009; Baek and Al-Qadi, 2009; Dave and Buttlar, 2010; Kim et al., 2010; Kim, 2011; Ahmed et al., 2013; Ban et al., 2017), to repre-sent cracks in the mixtures and pavements. Since the cohesive zone modeling is based on the fracture mechanics, it can effec-tively study the response and failure of structures as a conse-quence of crack initiation and propagation. Fracture mechan-ics approaches directly deal with discrete internal boundaries (cracks) in a body, and damage evolution is characterized by employing certain fracture criteria (material properties) gov-erning the prediction of internal boundaries. As one of frac-ture mechanics-based methods, the cohesive zone modeling approach has received increased attention from the asphaltic materials and pavement mechanics community. It is a well-es-tablished way to model crack development in monolithic and composite materials not only because it removes the stress sin-gularity at the crack tip but also because it provides a powerful and efficient tool that can be easily implemented in various computational methods, such as FE method. Moreover, the cohesive zone approach can model both brittle failure and duc-tile failure, which are frequently observed in asphaltic materi-als due to the wide range of service temperatures and loading rates. In comparison, the typical elastic fracture mechanics theories are limited to modeling damage evolution of materials that show different levels of brittleness (or ductility).

2. Study Objective and Scope

This study explores a purely mechanistic pavement analysis

approach where viscoelasticity and fracture of asphalt mixtures are considered to accurately predict deformation and damage behavior of flexible pavements. To that end, this study uses finite element modeling technique along with the cohesive zone fracture to predict damage. An in-house finite element code, MIDAS was used for predicting viscoelastic deformation and fracture in mixtures and pavements in this study. Asphalt mixtures are treated as a viscoelastic material with cohesive zones so that the time-, rate-, and temperature-dependent deformation and fracture of mixtures are better represented when the effects of moving traffic loads and environment are associated. In order to examine the effectiveness of the mecha-nistic pavement modeling, different pavement configurations and traffic loads are considered based on three main functional classes of roads suggested by FHWA i.e., arterial, collector and local. For each road type, three different material combi-nations for asphalt concrete (AC) and base layers are consid-ered to study damage behavior of pavement. A concept of the approach is presented and a case study where three different material combinations for AC and base layers are considered is exemplified to investigate progressive damage behavior of pavements when mixture properties and layer configurations are altered.

3. Pavement Configurations and Finite Element Models

Fig. 1 presents three different pavement configurations: arterial, collector and local road types. The FEM mesh of arte-rial is exemplified in Fig. 2. A critical zone is assumed under the tire loads where damage occurrence is more likely. Within this zone, in order to have a more accurate calculation of stress field over the elements and to get the damage status, finer mesh with automatic insertion of cohesive elements are employed.

For arterial and collector roads, loadings are assumed to be 80 kN per axle and for local road, 6.7kN single axle load was applied. To specify how the prescribed loads evolve in time, sine pulse time function was used. Regarding boundary conditions for the pavements, horizontal displacements at two sides of transverse cross section as well as vertical displacements

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at the bottom of subgrade layer were fixed in finite element model.

4. Viscoelasticity and Cohesive Zone of Asphalt Mixture

Asphalt mixture in this method is considered viscoelastic with damage caused by cracks. This makes the response be highly dependent on time, loading rate, and temperature, and allows the development of cracks at different lengths. Unlike the Pavement ME Design that uses the stiffness of the AC mix-ture varying at different temperatures and frequencies (usually referred to as the dynamic modulus), the complex viscoelastic damage behavior of asphalt concrete is taken into account by considering viscoelastic deformation and damage evolution as a result of the cracking. To address the viscoelastic response of

AC, the linear viscoelastic relaxation modulus is necessary as a material property. The isotropic linear viscoelastic constitutive behavior can be expressed in the following convolution inte-gral form:

��

� ��

��

�

��

��

�

ij ijkk

t

ijt

E t d

E t d

��

��

�

��

�

�

�

�

( )( )( )

( )

1 1 2

1

1

0

0

(1)

where E(t)=viscoelastic stress relaxation modulus, ν=Pois-son’s ratio, δij=Kronecker delta, and τ=integration variable.

The linear viscoelastic relaxation modulus E(t) is deter-mined by performing laboratory constitutive tests such as static creep/relaxation tests or dynamic modulus tests where testing is performed within the limits of linear viscoelasticity. These

Fig. 2. Finite element mesh with tire loads of arterial road

Fig. 1. Pavement configurations: Arterial road, collector road, and local road



testing results can be represented by a mathematical form, such as a Prony series, based on the generalized Maxwell model. The linear viscoelastic stress relaxation modulus can be expressed as:

E t E E ts

ss

M

( ) exp� � ��

��

�

��

�� 1

(2)

where E∞ and Es are spring constants in the generalized Maxwell model, ρs is the relaxation time, and M is the number of Maxwell units in the generalized Maxwell model.

To account for the damage evolution due to cracking, the cohesive zone model can be used among various approaches to model crack initiation and propagation in the material. A gen-eral cohesive zone model for cracking shows the fracture as a gradual phenomenon that occurs in a potential damage zone ahead of a crack tip (see Fig. 3). According to the model con-cept, the fracture is resisted by cohesive tractions that vary from a maximum value Tmax, where the maximum traction is reached and cracks start to open, to 0 (zero), where the open-ing displacement reaches critical displacement.

In this study, a nonlinear viscoelastic cohesive zone model in Eq. (3) (Yoon and Allen, 1999) was used to simulate the cracking behavior of AC mixtures and AC layer in pavements.

T ttu t

t E t dii

ii

t

t

� � � � ��

� � ��

��

��

��

�1

1

0�

� � �

�

(3)

where Ti(t) is cohesive zone traction, ui(t) is cohesive zone displacements, λ(t) is Euclidean norm of the cohesive zone displacements, δi is cohesive zone material length parameter, α(t) is internal damage parameter, σi is required stress level to initiate cohesive zone damage, E(t) is relaxation modulus of the cohesive zone, and i=n (normal), or s (shear) for two- dimensional objects.

A phenomenological form of damage evolution, expressed in Eqs. (4) and (5) can be used to evolve crack propagation. The damage evolution law can reasonably represent the rate-dependent fracture of viscoelastic materials such as asphaltic materials.

� � � �� A tm, when and0 1 (4)

� � 0, when or� �� 0 1 (5)

where A and m are micro scale material constants which govern damage evolution behavior.

Fig. 3. Cohesive zone crack modeling of mixture and its application to pavement cracking

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5. Mixture Tests and Properties

In order to obtain the viscoelastic stiffness of AC surface and base mixtures, dynamic modulus tests were performed on two sets of virgin and 30% RAP asphalt mixtures. Figs. 4 and 5 present the dynamic modulus test results. To obtain damage properties of AC surface mixtures, indirect tensile test (IDT) were performed at the temperature of 25°C and finite element

simulation of the IDT with the same geometry and boundary conditions was carried out to calibrate the cohesive zone mod-el parameters. Prony series parameters obtained from dynam-ic modulus testing were used for the viscoelastic properties of each mixture. Fig. 6 presents the IDT comparisons between test results with model simulation results, which show a good agreement. Fig. 7 shows an exemplary contour plot with hori-zontal stresses distributed in the IDT specimen at four different

(a) AC surface mixture (without RAP) (b) AC surface mixture (with 30% RAP)

Fig. 4. Dynamic modulus test results and Prony fit for viscoelastic stiffness

(a) AC base mixture (without RAP) (b) AC base mixture (with 30% RAP)

Fig. 5. Dynamic modulus test results and Prony fit for viscoelastic stiffness



stages: initial to failure.

The underlying layers of pavement structures (i.e., subbase and subgrade) were modeled as isotropic elastic. Elastic mod-uli of the layers were back-calculated from falling weight deflectometer measurements with some necessary calibration.

Resulting Young’s moduli of subbase layers for arterial, collec-tor, and local roads were 308 MPa, 250 MPa, and 430 MPa, respectively. Subgrade moduli used for arterial, collector, and local roads were 35 MPa, 35 MPa, and 44 MPa, respectively. A constant Poisson’s ratio of 0.45 was used for all cases.

Fig. 6. IDT comparisons: test results vs. model simulation results

(a) AC mixture without RAP (b) AC mixture with 30% RAP

Fig. 7. Contour plots of IDT model simulations: progressive damage until failure

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6. Results and Discussion

Using the AC mixture properties (i.e., viscoelastic proper-ties and cohesive zone fracture parameters) and sublayer prop-erties, the pavement sections were then modeled to simulate fatigue cracking in the pavement. For each road type (arterial, collector and local), three different cases of layer materials were studied to compare the damage evolution of surface layer over time. Case 1 is when the AC surface layer with 30% RAP and the base layer without RAP was used, and Case 2 is when the AC surface layer without RAP and the base layer with 30% RAP was used. Case 3 is when both AC surface and base con-tain 30% RAP.

Total 10,000 loading cycles were applied on the pavements and damage status of the surface layer (cohesive elements in critical zone) were obtained. Approximately 10-11 hours were used to run each case using 8 core CPU (each 2.4 GHz clock speed) and 16 GB RAM. Fig. 8 shows horizontal stresses (σxx) induced in the pavement structure due to tire loading. As loading cycles increase, crack initiation occurs mostly due to the tensile stress at the bottom of AC and propagate gradually. The figure clearly shows differences between 1,000 cycles and 4,000 cycles.

Fig. 9 shows model simulation results demonstrating the extent of damage developed in cohesive elements during the loading period for arterial road when the three different RAP usage alternatives were considered. As shown in the figure, when 30% of RAP was used in the surface layer, it can induce much more damage in pavements than cases when RAP was not used in the surface layer. This indicates that pavement per-formance can be affected by the use of RAP in surface mixture

Fig. 8. Horizontal stresses (σxx) and cohesive zone elements induced in the pavement structure due to the increased number of tire loading

Fig. 9. Model simulation results of arterial roads from the three different cases: progressive damage evolution over loading cycles



ers (i.e., AC surface and base) up to 30% in this study can be considered, as it might not significantly mitigate pavement performance due to cracking.

7. Summary and Conclusions

This study presented a mechanistic flexible pavement analy-sis method. The current development of Pavement ME design and other mechanistic approaches are limited to account for AC damage due to cracking. In contrast, this study attempted a purely mechanistic approach that accounts for viscoelastic deformation and nonlinear fracture characteristics of AC materials and pavements. In order to examine the validity and the effectiveness of the method, different pavement configura-tions and traffic loads are considered based on three main functional classes of roads suggested by FHWA i.e., arterial, collector and local. For each road type, three different material combinations for asphalt concrete (AC) and base layers are considered to study damage behavior of pavement.

Overall, it can be concluded that mechanistic pavement modeling attempted in this study could differentiate the per-formance of pavement sections due to variations of design inputs. The promising results, although limited yet to be con-sidered a practical method, infer that a few mixture tests can be integrated with the computational modeling of the mixture tests and subsequent structural modeling of pavements to

when traffic level is high (i.e., arterial roads) due to the mix-ture fracture resistance diminished due to the addition of RAP. However, when RAP was used in base layer, both cases (Case 1 and Case 3) did not show significant differences, which infers that using RAP in base layer might not sensitively affect pavement performance.

Fig. 10 shows model simulation results of collector roads. Compared to the results in Fig. 9, collector roads showed a quite different prediction. Initially, Case 2 (no RAP in surface layer) developed a lower level of damage evolution than two others (with 30% RAP in surface layer); however, overall damage at 10,000 cycles was not very different from others. This indicates that, although it may not be conclusive at this stage, RAP (up to 30% in this study) can be used in both base and surface layers when the level of traffic is relatively low such as collector roads, as the reduced mixture fracture resistance due to RAP addition may not significantly affect pavement performance.

Fig. 11 shows model simulation results when local roads were considered with the three alternatives of RAP use. Results of local roads were similar to the results obtained from collec-tor roads. Initially, Case 2 (no RAP in surface layer) started with a lower level of damage than the cases with RAP in sur-face layer, but its damage evolution rate is similar to others which ultimately resulted in a similar overall amount of dam-age at 10,000 cycles. This reinforces the finding from collector roads. When the level of traffic is low, use of RAP in both lay-

Fig. 10. Model simulation results of collector roads from the three different cases: progressive damage evolution over loading cycles

Fig. 11. Model simulation results of collector roads from the three different cases: progressive damage evolution over loading cycles

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better design mixtures and pavements in a purely mechanistic manner.

To make the mechanistic modeling approach a more practi-cal method, more work needs to be done to make the process in an efficient manner by accounting for a large number of traffic loads while maintaining reasonable computing time and costs. In addition, future advancements including inclusion of degradation models due to moisture damage and aging in asphalt concrete, development of modules for life prediction and cost analysis, consideration of plastic deformation in gran-ular layers to account for rutting. Validation-calibration of the modeling approach with more field performance data are con-sidered as follow-up studies. Toward the validation-calibra-tion, a more realistic modeling in 3D and a larger number of traffic loads can be considered.

Acknowledgements

The authors are grateful for funding provided by the Land and Housing Institute.

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analysis of pavement damage and performance

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