C. Kasbergen

Development and Finite Element Implementation of Stress-Dependent Elastoviscoplastic Constitutive Model with Damage for Asphalt

The development and finite element (FE) implementation of a stress-dependent elastoviscoplastic constitutive model with damage for asphalt is described. The model includes elastic, delayed elastic, and viscoplastic components. The strains (and strain rates) for each component are additive, whereas they share the same stress (i.e., a series model). This formulation was used so that a stress-based nonlinearity and sensitivity to confinement could be introduced into the viscoplastic component without affecting the behavior of the elastic and delayed elastic components. A simple continuum damage mechanics formulation is introduced into the viscoplastic component to account for the effects of cumulative damage on the viscoplastic response of the material. The model is implemented in an incremental formulation into the CAPA-3D FE program developed at Delft University of Technology in the Netherlands. A local strain compatibility condition is utilized such that the incremental stresses are determined explicitly from the incremental strains at each integration point. The model is demonstrated by investigating the response of a semirigid industrial pavement structure subjected to container loading. Results show that the permanent vertical strains in the non-stress-dependent case are significantly lower than the permanent vertical strains in the stress-dependent case. Results also show that in the stress-dependent case, there is a more localized area of high permanent vertical compressive strain directly under the load at approximately halfdepth in the asphalt compared with the non-stress-dependent case, in which the distribution is more even.

Spectral element technique for efficient parameter identification of layered media. I. Forward calculation

Abstract This contribution deals with the use of spectral analysis as a means of analysing the dynamic behaviour of the axially symmetric multi-layered systems as a result of a transient force. The objective of this research work is to develop an accurate and computationally efficient forward tool suitable for solving inverse problems. The spectral element technique is utilized. Details of the mathematical derivation, implementation and verification of newly developed axi-symmetric and half-space spectral elements are presented. It is shown that the suitability of the spectral element method to such a problem encompasses in its ability to model a whole layer without the need for subdivisions. As a consequence, the size of the modelled structure becomes as large as the number of the layers involved. This reduces the computational requirements substantially and hence enables efficient utilization of the method in iterative algorithms for solving inverse problems.

Spectral element technique for efficient parameter identification of layered media: Part II: Inverse calculation

Abstract In Part I of this series of articles a forward model was presented for the simulation of wave propagation in a multi-layer system by means of the spectral element method. In the current article and, on the basis of the forward model, a procedure is presented for inverse calculation of the system parameters. The proposed procedure is based on iterative comparisons of measured versus theoretically determined system transfer functions. The performance of three minimization algorithms; factored Secant update, modified Levenberg–Marquardt and Powell hybrid for solving the resulting system of nonlinear equations is evaluated. For the problem under consideration, the Powell hybrid algorithm exhibits better stability and convergence characteristics. As an application, the inverse procedure is utilized for the determination of pavement layer moduli and thicknesses via the use of the falling weight deflectometer (FWD) test. The calculations show that the developed procedure is accurate and computationally efficient. As a result of these calculations, modifications to the standard practice of FWD measurements and instrumentation are suggested.

Modelling of combined physical–mechanical moisture-induced damage in asphaltic mixes, Part 1: governing processes and formulations

Moisture has for a long time been recognised as a serious contributor to premature degradation of asphaltic pavements. Many studies have been performed to collect, describe and measure the moisture susceptibility of asphaltic mixes. Most of these are aimed at a comparative measure of moisture damage, either via visual observations from field data or laboratory tests or via mechanical tests, which give a so called moisture damage index parameter. The research presented in this paper is part of an ongoing effort at Delft University of Technology, to move away from such comparative or empirical measures of moisture-induced damage and start treating moisture-induced damage in a comprehensive energy based framework. Such a framework would enable realistic predictions and time-assessment of the failure pattern occurring in an asphaltic pavement under the given environmental and traffic loading which could be rutting, cracking, ravelling or any combination or manifestation thereof. The modelling of moisture-induced damage is a complex problem, which involves a coupling between physical and mechanical damage processes. This paper discusses several modes of moisture infiltration into asphaltic mixes and derives the governing equations for their simulations. Moisture diffusion into the mastic film, towards the aggregate–mastic interface and mastic erosion, due to high water pressures caused by the pumping action of traffic loading, are identified as the main moisture-induced damage processes and are implemented in a new finite element program, named RoAM. The paper discusses the necessary model parameters and gives detailed verification of the moisture diffusion and advective transport simulations. In the accompanying paper the developed finite element model is demonstrated via an elaborate parametric study and the fundamental moisture-induced damage parameters are discussed.

Studies on creep and recovery of rheological bodies based upon conventional and fractional formulations and their application on asphalt mixture

Traditionally, the time-dependent behaviour of bituminous mixtures has been modelled using linear visco-elastic theory described by creep and relaxation functions. Research, however, has shown that parameter identification for functions with linear time derivatives becomes problematic when the behaviour of asphalt mixtures needs to be matched for both the loading and unloading responses. The research introduced in this paper explored the possibility of using fractional creep functions for modelling. Furthermore, the possibility of using fractional creep functions for various rheological bodies to investigate the fractional time derivatives for strain is discussed. It is shown that, by means of these creep functions, the time-dependent deformation behaviour of bituminous material in terms of the retarded creep during loading and the relaxation behaviour during unloading may be described more realistically than by using time derivatives of integer order. The fractional creep functions allow for the development of non-linear viscous strain during the creep process and to better match the observed behaviour of asphalt mixtures, compared to the use of conventional linear models. This study specifically investigated the retardation and relaxation times in creep and recovery, and examined how these can be influenced by the choice of the fractional derivatives. The constitutive relationships developed in this paper are implemented in a non-linear computational model based on the finite element method. Modelling of the above-mentioned phenomena is presented and discussed with the help of numerical simulations and determination of model parameters with the help of actual test data.

Spectral element technique for efficient parameter identification of layered media. Part III: viscoelastic aspects

This article addresses the issues of wave propagation in elastic–viscoelastic layered systems and viscous parameter identification from non-destructive dynamic tests. A methodology that combines the spectral element technique, for the simulation of wave propagation, with the differential operator technique, for stress–strain relationship in viscoelastic materials, is adopted. The compatibility between the two techniques stems from the fact that both can be treated in the frequency domain, which enables naturally the adoption of Fourier superposition. The mathematical formulation of spectral elements for Burger’s viscoelastic material model is highlighted. Also, an inverse procedure for the identification of the material’s Young’s moduli and complex moduli for layer systems is described. It is shown that the proposed methodology enables the substitution of an expensive laboratory testing procedure for the determination of material complex moduli with non-destructive dynamic testing. 2002 Elsevier Science Ltd. All rights reserved.

Poroelastic spectral element for wave propagation and parameter identification in multi-layer systems

Abstract This contribution deals with the use of Biots theory of propagation of elastic waves in a fluid-saturated porous solid in conjunction with the computationally efficient spectral element technique as a means for forward analysis of the dynamic behavior of multi-layer systems consisting of both one- and two-phase material layers. Details of the mathematical formulation and verification of an axi-symmetric semi-infinite spectral element for a fully saturated porous medium are presented. The spatial domain of the element in the vertical direction is assumed to extend to infinity. In the radial direction it extends to a finite distance. In the last part of this contribution an example is presented of the use of the developed element for parameter identification of pavement layers via the use of falling weight deflectometer test.

Finite element modelling of field compaction of hot mix asphalt. Part II: Applications

A constitutive model is developed and implemented in the finite element system three-dimensional computer-aided pavement analysis for the simulation of hot mix asphalt field compaction. The details of this model are presented in a companion paper (Masad et al., Finite element modelling of field compaction of hot mix asphalt. Part I: Theory, International Journal of Pavement Engineering, Accepted, 2014). This model is based on nonlinear viscoelasticity theory and can accommodate large deformations that occur during the compaction process. The model was used to study the influence of frequency and amplitude of vibratory compaction rollers on the level of compaction. In addition, it was used to analyse the influence of various methods for compacting longitudinal joints on the percent air voids near these joints. The model was used to simulate the compaction of asphalt pavements with different structures and compacted using various equipment and patterns. The finite element results of the level of compaction and percent air voids were in reasonable agreement with the measurements. The model offers the opportunity to simulate and predict the compaction of asphalt mixtures under various rolling patterns and for different pavement structures.

Development of a thermomechanical tyre–pavement interaction model

Tyre operating temperature is an important concern for both tyre manufacturers and highway agencies which is known to have a major influence on the tyre traction. Most of the past tyre–pavement interaction studies were focused on the performance of the tyre while giving limited importance to the effect of the pavement texture profile. This paper presents a methodology of coupled thermomechanical finite element (FE) model to determine the progressive temperature development in tyre cross section. The model is developed for a test tyre rolling over an FE mesh of an asphalt pavement surface, and the effect of the developed temperature on the hysteretic friction is evaluated. Such a model will enable tyre manufacturers to come up with optimised tyre design; on the other hand, road agencies can design their friction test protocol. In this study, an attempt has been made to examine the developed tyre–temperature in time at different regions of tyre.

Influence of Temperature on Tire–Pavement Friction: Analyses

Past experimental studies show that tire–pavement friction values are related to conditions surrounding the tire such as pavement temperature, ambient temperature, contained air temperature, and surface characteristics of the pavement. For measurements taken in different temperature conditions, road agencies generally apply correction factors. These correction factors are based primarily on experience and previous field test measurements that have very limited transferability under different conditions. This paper studies frictional behavior of test tires under different surrounding temperature conditions using finite element analysis. The scope of this research is to analyze the effect of pavement temperature, ambient temperature, and contained air temperature on frictional measurements. Finite element analysis of fully and partially skidding tires over different asphalt pavement surfaces, namely, porous asphalt, ultrathin surface, and stone mastic asphalt, is considered. Observation showed that a higher pavement temperature, ambient temperature, and contained air temperature resulted in a lower hysteretic friction for a given pavement surface and a given tire slip ratio. In contrast, a lower tire slip ratio and a pavement with higher macrotexture resulted in higher friction. This study highlights that a critical combination of these factors will decrease friction significantly.