Marek Klimczak

Numerical modeling of asphalt concrete and other asphalt mixes used in road engineering is an actively developed research field. In this study, a framework combining the following aspects is presented: (1) reliable reconstruction of the real samples; (2) using realistic material models of the microstructure constituents; and (3) providing high numerical efficiency. Asphalt concrete microstructure was reconstructed using image processing. The Burgers material model was applied to the subdomains identified as the mastic, and the linear elastic model was used for the aggregate particles. In order to increase the numerical efficiency, the developed homogenization method was used to accelerate the finite element analysis. The main novelty of this study is the integration of the Burgers material model with the numerical homogenization in the small strains range. A homogenization error measured in the maximum norm was smaller than 7% in the presented numerical examples (6.8% for the elasticity and 6.9% for the viscoelasticity problem, respectively). Simultaneously, the observed reduction in the number of degrees of freedom was larger than 510 times. The obtained results confirmed the applicability of the developed methodology to the analysis of the viscoelastic materials in the range of the small strains.

The overall response of asphalt concrete under a subjected load is governed not only by the properties of its constituents but also by the interactions among them. In this paper, we focus on the numerical analysis of aggregate debonding, which is typically a phenomenon that precedes crack initiation. The interfacial transition zone plays a crucial role in the macroscopic performance of this material. Using image processing to reconstruct a specific sample microstructure, we carried out several finite element analyses to assess the impact of the debonding phenomenon on the general performance of asphalt concrete. Image segmentation algorithms were employed to accurately detect aggregate boundaries, followed by vectorization to describe their geometries. After applying a series of error-controlled geometry simplification procedures, the final microstructure was exported to the ABAQUS/Standard 2023 environment. A linear elastic solution for the reconstructed asphalt concrete sample was used as the reference solution. It was compared with linear viscoelastic solutions with a perfect bonding between constituents and, in the next step, with debonding allowed at aggregate–matrix interfaces. The latter phenomenon was analyzed by enforcing respective contact conditions between the aggregate and the bituminous matrix. It was found that introducing the viscoelastic material model for mastic resulted in a 142.72% increase in the vertical extreme displacement relative to the purely elastic solution. When debonding effects were additionally considered, this increase rose to 188.44%. The results confirm the necessity of debonding conditions to be introduced in reliable finite element analyses of asphalt concrete.

The semi-circular bending method (SCB) is a useful test for evaluating the cracking resistance of asphalt mixtures with added reclaimed asphalt shingles. A mixture of the asphalt concrete AC 16 with 50/70 paving bitumen was used for the binder course test as a reference mix. The purpose of the paper is to evaluate two aging conditions (short-term and long-term) of the above-mentioned asphalt mixtures in relation to their fracture properties. Laboratory experiments are enhanced with the application of image processing techniques (digital image correlation and image segmentation) that account for the asphalt mixture heterogeneity. Consequently, they can provide a more detailed description of the specimen performance. Statistical analyses of the laboratory results indicate that the best sensitivity in terms of differentiating the tested mixtures, especially taking into account the aging conditions of the mixtures, was observed for the post-peak parameters such as the flexibility index (FI), toughness index (TI), and, above all, cracking resistance index (CRI), for which the average coefficient of the result variability is approximately 10%, while for the FI and TI parameters it is approximately 30%. Digital image correlation analyses provided a confirmative illustration of the aforementioned observation.

In the finite element analysis of asphalt concrete (AC), it is nowadays common to incorporate the information from the underlying scales to study the overall response of this material. Heterogeneity observed at the asphalt mixture scale is analyzed in this paper. Reliable finite element analysis (FEA) of asphalt concrete comprises a set of complex issues. The two main aspects of the asphalt concrete FEA discussed in this study are: (1) digital reconstruction of the asphalt pavement microstructure using processing of the high-quality images; and (2) FEA of the asphalt concrete idealized samples accounting for the viscoelastic material model. Reconstruction of the asphalt concrete microstructure is performed using a sequence of image processing operations (binarization, removing holes, filtering, segmentation and boundaries detection). Geometry of the inclusions (aggregate) are additionally simplified in a controlled mode to reduce the numerical cost of the analysis. As is demonstrated in the study, the introduced geometry simplifications are justified. Computational cost reduction exceeds of several orders of magnitude additional modeling error occurring due to the applied simplification technique. Viscoelastic finite element analysis of the AC identified microstructure is performed using the Burgers material model. The analysis algorithm is briefly described with a particular focus on the computational efficiency aspects. In order to illustrate the proposed approach, a set of 2D problems is solved. Numerical results confirm both the effectiveness of the self-developed code and the applicability of the Burgers model to the analyzed class of AC analysis problems. Further research directions are also described to highlight the potential benefits of the developed approach to numerical modeling of asphalt concrete.

In this paper, we present an enhanced version of the two-scale numerical homogenization with application to asphalt concrete modeling in the elastic range. We modified the method of effective material parameters tensor assessment for analysis based on the representative volume element (RVE). As...

Bitumen binder is a component of asphalt mixtures that are commonly used as the materials constituting the upper layers of a pavement’s structure. Its main role is to cover all the remaining constituents (aggregate, filler and other possible additives) and create a stable matrix, in which they are embedded due to the adhesion forces. The long-term performance of bitumen binder is crucial to the holistic behavior of the layer made of the asphalt mixture. In this study, we use the respective methodology to identify the parameters of the well-established Bodner–Partom material model. For the purposes of its parameters identification, we carry out a number of the uniaxial tensile tests with different strain rates. The whole process is enhanced with a digital image correlation (DIC) to capture the material response in a reliable way and to provide deeper insight into the experiment results. The obtained model parameters were used to compute numerically the material response using the Bodner–Partom model. Good agreement between the experimental and numerical results was observed. The maximum error for the elongation rates equal to 6 mm/min and 50 mm/min is of order of 10%. The novel aspects of this paper are as follows: the application of the Bodner–Partom model to the bitumen binder analysis and the DIC-enhancement of the laboratory experiment.

In this paper, we deal with the issue of asphalt concrete microstructure recognition for further numerical analysis. An efficient reconstruction of the underlying microstructure makes the composite analysis more reliable. We propose for this purpose a methodology based on the image processing and focus on a two-dimensional case (it can be easily used as a part of the 3D geometry reconstruction, however). Initially obtained geometry of the inclusions is further simplified to reduce the cost of the finite element mesh generation. Three straightforward geometry simplification algorithms are used to perform this process in a controlled way. Subsequently, we present the solutions of two problems, i.e., heat flow and elasticity (plane strain), in order to illustrate the effectiveness of the whole elaborated methodology. The numerical results were obtained using the finite element method. Consequently, an error analysis is demonstrated in order to refer the overkill mesh solutions to the ones presented in this study. The main finding of this paper is the efficient methodology dedicated to a digital reconstruction of the asphalt concrete microstructure by the image processing. It can be also extended to other materials exhibiting similar microstructure.

In this paper, we present a new approach to model the steady-state heat transfer in heterogeneous materials. The multiscale finite element method (MsFEM) is improved and used to solve this problem. MsFEM is a fast and flexible method for upscaling. Its numerical efficiency is based on the natural parallelization of the main computations and their further simplifications due to the numerical nature of the problem. The approach does not require the distinct separation of scales, which makes its applicability to the numerical modeling of the composites very broad. Our novelty relies on modifications to the standard higher-order shape functions, which are then applied to the steady-state heat transfer problem. To the best of our knowledge, MsFEM (based on the special shape function assessment) has not been previously used for an approximation order higher than p = 2, with the hierarchical shape functions applied and non-periodic domains, in this problem. Some numerical results are presented and compared with the standard direct finite-element solutions. The first test shows the performance of higher-order MsFEM for the asphalt concrete sample which is subject to heating. The second test is the challenging problem of metal foam analysis. The thermal conductivity of air and aluminum differ by several orders of magnitude, which is typically very difficult for the upscaling methods. A very good agreement between our upscaled and reference results was observed, together with a significant reduction in the number of degrees of freedom. The error analysis and the p-convergence of the method are also presented. The latter is studied in terms of both the number of degrees of freedom and the computational time.

In this paper, we present an enhanced framework for the synthetic asphalt concrete (AC) microstructure generation for the numerical analysis purposes. It is based on the Voronoi tessellation concept with some necessary extensions that allow for the reliable generation of the aggregate particles of the given size distribution. The synthetic microstructure generation allows for faster numerical modeling of the novel materials. It can partially replace the X-ray computed tomography approach, which is frequently used in such analysis. Our framework is a kind of compilation of the known techniques with the enhancements applied to expedite the microstructure modeling process. Therefore, the generated microstructure is used in the numerical upscaling to model the macroscale asphalt concrete properties. We restrict ourselves (in this paper only) to the 2D elastic computations. We also assume the perfect bonding between these two materials and the static load for the sake of simplicity. The upscaling is performed by the multiscale finite element method (MsFEM). A short recapitulation of the MsFEM foundations as well as the numerical test comparing the overkill mesh solution with the upscaled one is provided in the paper. The test results confirm that the whole presented methodology can serve as a fast and reliable tool for the tests on novel asphalt mixtures and other heterogeneous materials. It can reduce the cost of the design process substituting some of the laboratory experiments, giving the opportunity to test the developed constitutive models and expedite the numerical analysis itself.