Fatima Allou

Prediction of Permanent Deformations of Unbound Granular Materials in Low Traffic Pavements

ABSTRACT Permanent deformations of unbound granular layers and soils, caused by unfavourable moisture conditions, are one of the most common mechanisms of deterioration of low traffic pavements, with unbound granular bases. The paper presents permanent deformation models, developed by LCPC and by the University of Limoges, for the prediction of permanent deformations of unbound granular materials: a simple empirical model and two elastoplasticity based models for cyclic loading: one of them is based on the time independent plasticity with kinematic hardening, and the second one on the shakedown theory. The model parameters have been determined with cyclic triaxial tests performed on a granular base course material, at different moisture contents. An application of the models to finite element calculation of permanent deformations in a pavement structure is presented.

Numerical simulation of local temperature evolution in bituminous materials under cyclic loading

Asphalt concrete is a heterogeneous material containing a viscoelastic bituminous matrix and elastic aggregates. During fatigue testing in the laboratory, the material stiffness decreases as a result of increase in temperature due to self-heating. The objective of this study was to quantify such self-heating, during fatigue testing, as one of the biases affecting the fatigue life estimation of bituminous materials. A heterogeneous approach, which consists of separating the viscoelastic matrix from the elastic aggregates, has been adopted. According to a complex domain approach, a finite element simulation of a cyclic mechanical loading is proposed by taking into account the dissipated energy, internal thermal evolution, temperature dependence of the matrix stiffness and the heat transfer process. In considering a thermomechanical coupling, the numerical simulation results indicate that dissipated energy in the bituminous matrix is influenced by material heterogeneities. A higher dissipated energy can be observed in thin matrix films, where the strain level exceeds that of thicker films. An estimation of temperature evolution using dissipated energy as a heat source is in a good agreement with experimental results. Local temperature variations are dependent on the local heat source, the thermal properties of each phase and aggregate distribution.

Two-dimensional/three-dimensional biphasic modelling of the dynamic modulus of bituminous materials

The main objective of this work is to evaluate the influence of a modelling in two and three dimensions (2D/3D) on the dynamic modulus of bituminous materials based on finite elements method (FEM) under a frequency loading. The dynamic modulus of the matrix and the elastic properties of aggregates were used as input parameters into FEM models qualified by heterogeneous models. The studied bituminous materials are fine mastic and mortar. These two composites are treated as a biphasic composite material, composed of a bituminous binder and an aggregate skeleton. The generalised Maxwell rheological model was used to describe viscoelastic behaviour of the matrix. The aggregate skeleton of composites was generated randomly. The numerical results were compared with the analytical values of the complex modulus obtained by the generalised self-consistent scheme and a satisfactory agreement was obtained. Moreover, the 2D numerical results are situated below the 3D results, and both are placed below the experimental results. The observed gap highlights the weakness of 2D models to describe behaviours, which are highly influenced by heterogeneities in terms of mechanical properties and interlock between aggregates. L’objectif de cet article est d’estimer l’impact du passage d’une modélisation en trois dimensions (3D) à une modélisation en deux dimensions (2D) sur la prédiction du module complexe des matériaux bitumineux par la méthode des éléments finis sous chargement fréquentiel. Les matériaux bitumineux considérés sont le mastic et le mortier. Ces deux composites sont considérés comme des matériaux bi-phasique contenant un liant bitumineux et un squelette granulaire. Le squelette granulaire a été généré aléatoirement. Les résultats du calcul numérique ont été comparés aux résultats issus du modèle analytique GSCS (generalised self-consistent scheme) et une bonne concordance a été observée. Les résultats en 2D sont en deçà de ceux obtenus en 3D et l’ensemble est logiquement situé en dessous des résultats expérimentaux. L’écart observé montre la faiblesse des modèles en 2D pour décrire des comportements largement influencés par l’hétérogénéité des propriétés mécaniques et l’interconnexion des granulats.

3D modelling of tyre-pavement contact pressure

Pavement design assumes uniform contact loading because of bottom-up traditional cracking (far from loading), but nowadays more and more surface damage (top-down cracking and rut) due to new technology in pavement and tyre design is observed. Then, a more realistic tyre–pavement contact modelling has to be considered. In order to go towards more realistic tyre–pavement contact, finite element method consumes a lot of calculation time; so in this article, we propose a semi-analytical model developed for the calculation of ball bearings. The contact is considered as a Hertzian contact, and the surface of the road is flat and that the tyre is smooth. Calculation of contact pressure is compared and validated with experimental data using a device called Stress-In-Motion, which allows contact pressure measurement. Different parameters are assumed in the modelling such as tyre pressure, axle loading and tyre shape. We have now a successful tool to analyse the tyre–pavement contact, more accurate and realistic and especially faster than those used at the moment.

Shakedown Approaches to Rut Depth Prediction in Low-Volume Roads

Rutting, due to permanent deformations of unbound materials, is one of the principal damage modes of low traffic pavements. Flexible pavement design methods remain empirical; they do not take into account the inelastic behavior of pavement materials and do not predict the rutting under cyclic loading. A finite-element program, based on the concept of the shakedown theory developed by Zarka for metallic structures under cyclic loadings, has been used to estimate the permanent deformations of unbound granular materials subjected to traffic loading. Based on repeated load triaxial tests, a general procedure has been developed for the determination of the material parameters of the constitutive model. Finally, the results of a finite-element modeling of the long-term behavior of a flexible pavement with the simplified method are presented and compared to the results of a full-scale flexible pavement experiment performed by Laboratoire Central des Ponts et Chaussees. Finally, the calculation of the rut depth evolution with time is carried out.

Modelling self-heating and thixotropy phenomena under the cyclic loading of asphalt

Asphalt concrete is a heterogeneous material containing a viscoelastic bituminous matrix and elastic aggregates. When testing asphalt materials under cyclic loading, various phenomena (so-called biasing effects) can decrease the modulus. This effect has been explained by an increase in the temperature of materials due to energy dissipation (self-heating), thixotropy and damage. The aim of this study is to analyse a uniaxial cyclic tension-compression test performed on bitumen and asphalt mixes, in modelling self-heating as one of the biasing effects. To quantify the self-heating and dissipated energy (as a heat source), a heterogeneous thermomechanical approach is introduced by separating the viscoelastic bituminous matrix from the elastic aggregates. According to this approach, various processes such as energy dissipation in the matrix due to viscoelastic properties, the thermal sensitivity of the matrix as well as its capacity to develop a heat source and diffuse heat through aggregates can all be studied. Local temperature variations are calculated by considering the heterogeneous dissipated energy field as a heat source. The complex modulus variation can then be calculated by taking into account both the temperature field and thermal sensitivity of the material. Simulation results show that as opposed to bitumen, in which 100% of complex modulus variations observed during a strain sweep test are due to self-heating, the results on asphalt mixes indicate that thixotropy varies with mechanical properties to a greater extent than self-heating. This fact is probably correlated with a higher strain level in thin bituminous matrix films, a higher load velocity in thin matrix films, material heterogeneity, and the 3D characteristic of matrix loading during the tension-compression test on asphalt mixes.

Top-down and bottom-up fatigue cracking of bituminous pavements subjected to tangential moving loads

A model allowing for the determination of bituminous pavement degradation on traffic circle is presented. The development work has relied on the viscoelastic modeling of bituminous pavements subjected to multiple-axle traffic loads, using the following variables: pavement structure, load speed (or frequency), load configuration, and bituminous materials temperature. The method derived has successfully simulated the phenomenon under investigation. Results obtained indicate that the design concept based on bending fatigue in bituminous layers is not sufficient to realistically predict the degradation of a bituminous pavement structure. The phenomenon of shear at bituminous interface must also be taken into account, as revealed by the simulation results for the degradation of two pavement structures from the French design code [10] (i.e. flexible pavement and thick asphalt pavement).

Micromechanical modelling of bituminous materials’ complex modulus at different length scales

Abstract The aim of this work is to establish a multi-scale modelling technique usable in the study of the complex viscoelastic properties of asphalt mixes. This technique is based on a biphasic approach. At each scale, the heterogeneous media is considered as a two-phase material composed of granular inclusions with linear elastic properties and a matrix of bituminous materials exhibiting linear viscoelastic behaviour at small strain values. In this approach, the homogeneous equivalent properties of biphasic composites are transferred from one scale of observation to the next, higher scale of observation. The viscoelastic properties of the matrix and the elastic properties of the aggregates serve as the input parameters for the numerical models. The generalised Maxwell rheological model is used to describe the viscoelastic behaviour of the matrix. Thanks to the rheological properties of bitumen and the elastic properties of the aggregates, the viscoelastic properties of mastic, mortar and hot mix asphalt (HMA) as bituminous composites can be, respectively, estimated using a micromechanical finite element model. Random inclusions of varying sizes and shapes are generated in order to construct the granular skeleton. A cyclic loading was imposed on the top layer of the digital model. The dynamic modulus of the pre-cited bituminous composites, obtained from the presented multi-scale modelling process while passing from the bitumen to the HMA scale, is validated by comparison with experimental measurements when possible. Concerning our results, we have found that at low temperature (−10 °C), the predicted dynamic modulus is satisfactorily comparable to the experimental measurements. On the other hand, an acceptable gap between predicted numerical results and experimental data takes place when the temperature increases.

Investigation on Mechanical Properties of Bituminous Materials through 2D/3D Finite Element Numerical Simulations

The main objective of this work is to evaluate the influence of a modeling in two and three dimensions (2D, 3D) on the dynamic modulus of bituminous materials based on finite elements method (FEM). The dynamic modulus of the matrix and the elastic properties of aggregates were used as input parameters into the FEM model. The aggregate skeleton of composites was generated randomly. In order to construct numerical master curve of bituminous material this model was subjected to various frequencies loading.