1. Introduction
Asphalt, a heterogeneous mixture of aggregates, fillers and asphalt binder, is one of the most used infrastructure material. Asphalt’s mechanical properties are influenced by the properties of its constituents, its internal structure and the loading and environmental conditions during its service life. Understanding the degradation of asphalt, such as rutting, ravelling, freezing, strength loss and fatigue cracking, is important for better design, manufacture and maintenance of roads.
One of the major sources of deterioration of asphalt is cracking. The fracture process can be divided into two different stages [
1,
2]: crack initiation and propagation. Crack initiation occurs when the mechanical stress is higher than a given limit, and micro-cracks occur in the mastic [
3]. Under continuous load, these micro-cracks coalesce into macro-cracks, which initiate the propagation phase that ultimately, leads to failure [
1]. The growth of microcracks damages asphalt irreversibly and increases maintenance costs [
4], and this is influenced by different factors such as temperature, loading level and rate, fatigue and mixture composition.
Another cause of asphalt failure in cold regions is thermal cracking (at low temperatures), which may significantly reduce the durability of pavements [
5,
6]. This damage is especially severe when water is present in the asphalt pores due to its comparatively high thermal expansion. Under icing temperatures, the internal pore structure in an asphalt mixture may change following a three-stage process [
7]: (i) water expansion, which causes damage, and expansion of the exiting pores; at −10 °C, for instance, water undergoes 15% volume expansion [
8]; (ii) cracking and merging of the pores and (iii) creation of new voids [
9]. This phenomenon is especially intense in asphalts with a porosity between 6% and 13%, which retain part of the pore water. Asphalts with <6% voids have close pores that prevent water penetration, while asphalts with >13% voids have large pores that do not retain water [
10,
11,
12].
There are many studies, both theoretical and experimental, on asphalt degradation (e.g., [
3,
4,
13,
14,
15,
16]), but only a few experimental works dedicated to low temperatures and freeze-thawcycles [
5,
6,
7,
17,
18,
19]. Furthermore, the experimental tests cannot show the evolution of the damage inside the asphalt’s microstructure, which is critical for understanding the deterioration mechanisms. To the best of our knowledge, there are also no available numerical methods for predicting degradation of asphalt or monitoring the damage progression resulting from freeze-thawactions. The development of such modelling tools, the subject of this paper, allows estimation of asphalt’s service life performance under cold environmental conditions. This is critical for optimising asphalt or developing novel materials with enhanced durability and long-term performance.
Recent advancements in computer technology allow performing realistic simulations of the performance of materials across scales. Novel mesh-free methods are more suited for this purpose as they allow simulation of crack propagation and branching without the need for mesh regeneration. One of the simplest mesh-free methods is the lattice spring model (LSM) that divides solids into computational particles linked together with springs [
20,
21,
22]. Peridynamics (PD) [
23] is a novel mesh-free method developed as an improvement of the LSM [
24] to allow better simulation of the material damage response. The application of PD to the simulation of damage in construction materials is highly innovative and limited, and its asphalt application will be presented in this paper for the first time.
This paper aims to develop a computational tool that allows realistic simulation of the damage of asphalt under mechanical and freeze-thawloads. We present a PD model coupled with discrete multiphysics developed in the LAMMPS molecular dynamics simulation package. This requires developing realistic models considering the aggregates and binder, voids and water, both in liquid and solid forms. Optical and micro-CT images are used to develop models considering the internal microstructure of a range of asphalt materials. PD implemented in LAMMPS also allows considering the plastic [
25] and viscoelastic [
26] response of materials and is therefore suitable for simulation of the response of asphalt materials under higher temperatures. The state-based Peridynamics is used here to evaluate the mechanical response of intact asphalt before and after being subjected to a freeze-thawcycle. The internal damage in the asphalt due to freezing is simulated by coupling Peridynamics with repulsive forces obtained from expansion of liquid phases and their transformation into solid phase using Discrete Multiphysics (DMP) [
27,
28,
29]. The model is then used to discuss the effect of the freezing of the water present in the voids on the asphalt’s mechanical response.
3. Methodology
The real and artificial asphalt mixtures used in this study are presented and discussed in this section. Both imaging of the section and micro-CT scan results are used to generate the initial microstructure of the asphalt models to evaluate the accuracy of the techniques used. The digital microstructures are then modified to represent a range of void % and saturation degree in the asphalt microstructure. The details of the processes followed are also presented in this section.
The numerical models, after validation, were used to simulate compressive tests on asphalt before and after being subjected to a cycle of freeze-thaw. The damage progression under compressive loading and the freeze-thaw was evaluated and discussed with the aim of the numerical results obtained. The details of the numerical analyses and the input parameters used are also presented in this section.
3.1. Mixtures
The asphalt models used in the simulations were derived from samples of four types of asphalts: Dense Asphalt (DA), Porous Asphalt #1 (PA #1), Porous Asphalt #2 (PA #2) and Porous Asphalt #3 (PA #3), with target air voids of 5 10, 13 and 21%, respectively. The physical samples were prepared in the NTEC laboratories at the University of Nottingham, Nottingham, UK. CT-scanned and (as explained later) digitalised in a format readable by the software used to carry out the simulations.
The composition, aggregate gradation and binder contents in the samples are shown in
Table 2. For all mixtures, crushed limestone aggregates with a maximum size of 20 mm and 50/70 pen bitumen were used. The standards BS EN 13043:2013 for DA, BS EN 13108-1 for PA and BS EN 12697–33 were followed to manufacture the materials [
44]. The materials were mixed at 160 °C and roller compacted at 140 °C. Asphalt slabs of 300 × 300 × 50 mm
3 were produced. From the DA slab, a 35 × 35 × 55 mm
3 was cut. From the slabs made of PA #1, PA #2 and PA #3, cores of 100 mm diameter and 50 mm height were extracted.
3.2. DA Model
The DA sample surface was photographed using a digital camera with resolution 1257 × 896 and the pictures converted in a black and white image with MATLAB R2020a (The Math Works, Inc., Natick, MA, USA) and over imposed on a square lattice with side
l = 10
−4 m. Each node of the lattice corresponds to a Peridynamic particle: blue particles were created to represent mastic and red particles to represent aggregates, see
Figure 3. According to the reference [
45], aggregates greater than 1.18 mm can be considered part of the solid skeleton structure. Hence, mastic was defined as a mixture of aggregates ≤ 1.18 mm and bitumen. While we are aware that this is a simplification, we will assume that this value remains constant for the mixtures that we studied.
In DA, voids were not considered due to the difficulty of identifying them using digital photography. DA has 190,000 particles for the mastic and 300,000 for the aggregates.
3.3. PA Models
A Phoenix v|tome|x L 300 micro CT scanner was used to scan PA asphalt samples under dry conditions; the X-ray tube was MXR320HP/11 (3.0 mm Be + 2 mm Al) from GE Sensing and Inspection Technology (Shanghai, China) operating with an acceleration voltage of 290 kV and a current of 1300 mA.
We carried out the X-ray CT scans in the micro-computed tomography Hounsfield facility at the University of Nottingham, Nottingham, UK. We mounted the samples on a rotational table at a distance of 906.84 mm from the X-ray source. The reconstruction of scans was performed using GE Datos|x reconstruction software with 2× resolution to obtain a spatial resolution of 45.2 mm; the scans had an isotropic resolution, meaning that the slice thickness was also 45.2 mm. The raw images were 16-bit images, and the voxel value represented the x-ray attenuation.
Then, ImageJ version 1.49 was used to process the images [
46], convert them to 8-bit grayscale resolution and denoise the images to remove small clusters of voids and grains. The different material components such as aggregates, bitumen and air voids were extracted by segmenting the images based on grayscale thresholding using ImageJ version 1.49 (Rasband, W.S., ImageJ, U. S. National Institutes of Health, Bethesda, MD, USA).
The picture was over imposed on a square lattice with side
l = 4 × 10
−4 m using Matlab 2020a. As in the case of DA, each node of the lattice corresponds to a peridynamic particle: blue particles are assigned to mastic, and red particles are used to represent aggregates, see
Figure 3. No computational particle was created in areas corresponding to the voids. Since the void fraction and aggregate size differed in the three samples, the number of particles was not the same. Sample PA #1 had 341,000 particles for the mortar and 367,000 for the aggregates; PA #2 148,000 particles for the mortar and 538,500 for the aggregates; PA #3 172,000 particles for the mortar and 455,000 particles for the aggregates.
3.4. Additional Asphalt Geometries
To generate new geometries of asphalt mixtures with a range of air void properties, using ImageJ, we assumed that the mixtures from
Figure 4 were the reference. From each of these specimens, we produced five different materials. (i) Without air voids; (ii) with the 25% smallest air voids; (iii) with the 50% smallest air voids; (iv) with 75% of the smallest air voids and (v) with 100% of the air voids (equivalent to the reference sample). See an example in
Figure 5. The air voids’ geometries, including the average void area, diameter, perimeter, circularity and aspect ratio, were measured using the Particle Analysis function in ImageJ [
45]. Finally, a suffix indicating the final void fraction was assigned to each generated sample. For example, PA #1/2.5% means that we started from PA #1 and filled all the voids so that the final void fraction was 2.5%. The aggregate gradation and binder contents are shown in
Table 3. Increasing the amount of mastic, we add bitumen and dust smaller than 1.18 mm, keeping the skeleton structure constant.
Table 4 shows the topological properties of air voids in asphalt mixtures produced in this section. Similar results were presented in [
12]. These results will be used below to evaluate the influence of freezing on the degradation of pavements.
3.5. Freeze-Thaw Simulation
We only used PA #2, which has a 13% air void content, to evaluate the effect of freeze-thaw on mechanical properties. For this purpose, we artificially filled some of the voids with ice, presented as yellow particles in
Figure 6. To distinguish among samples, a suffix indicating the final ice content was assigned to each generated sample. For example, PA #2/0.65% means that we started from PA #2 and filled all the voids so that the final ice content was 0.65%.
Figure 6 shows how this process was carried out. We started with the real PA #2 sample whose void fraction was 13%. Then, we gradually covered some of the voids (chosen randomly) with ice (yellow particles) until the ice content was 0.65%,
Figure 6a, 1.3%,
Figure 6b, 3.25%,
Figure 6c, 6.5%,
Figure 6d, 9.75%,
Figure 6e and finally 13%,
Figure 6f. The freeze-thaw simulation was performed following these steps:
Water expands in the voids simulating ice formation, leading to cracking.
After the water expansion is completed, the simulation is carried out for additional 106 time steps to relax the system with no external load.
Water shrinks in the void, simulating ice melting.
Water is removed.
After the water is removed, the simulation is carried out for additional 106 time steps to relax the system with no external load.
Finally, the sample is tested under simulated compression to assess mechanical response changes after the sample is subjected to a freeze-thawcycle.
3.6. Numerical Modelling Details and Input Parameters
The intrinsic properties of the mastic and aggregate were the same for all simulations. In this study, we focused on temperatures below −10 °C and, therefore, we used the Peridynamic model for brittle materials discussed before. The mechanical properties used in the simulations of bitumen and asphalt mixtures are reported in
Table 5; they were obtained from [
47] and [
48]. The peridynamic parameters of the asphalt binder used for the simulations are listed in
Table 6.
The calculation of the temperature profile inside the sample would require a non-isothermal model (the reader can refer to [
37] for modelling heat transfer and phase transition with particle methods). During solidification, water remains at 0 °C because of the latent heat. The scenario we have in mind is when the water has permeated into the asphalt and freezes. We assume that the external temperature is sufficiently low; as a first approximation, the average temperature of the asphalt sample is close to −10 °C.
To simulate a uniaxial compressive test, each sample is placed into the simulation box between two rigid walls (boundary conditions). The simulations are carried out under plane stress conditions. For the model, this implies that we take a parallel slice with a thickness larger than the horizon and impose the stress along the z direction equal to zero. The physical parameters at the interface were set to the physical parameters of the mastic. The upper wall moves downward at a controlled velocity, and the lower wall is fixed. Uniaxial compression test simulation is carried out along the y-direction at a compression rate of 0.001 m/s; (we verified that quasi-static conditions were achieved at 0.001 m/s), the other directions were set to be free to expand or shrink. The time step used in all simulations was 10−8 s.
The Peridynamic stress was calculated from the total force per volume, acting through the first layer of particles in contact with the upper wall. The resultant force was obtained by multiplying the particle’s volume and the average force density of the top layer. The simulations were carried out with the Peridynamics package [
49] in LAMMPS/stable_7Aug2019-foss-2019a (
http://lammps.sandia.gov) [
50].
4. Model Validation
We modelled the tensile strength of bitumen beams tested in [
45] to validate the accuracy of the modelling strategy and its parameters. For this purpose, we produced 3D and thin plate (i.e., pseudo 2D with the thickness slightly larger than the horizon simulated under the plane stress condition) models of the bitumen with different resolutions (number of particles used for development of the model) and checked the sensitivity of the results to these parameters.
The 3D specimen had dimensions of 1.0 × 5.0 × 0.5 cm
3 simulated with four lattice resolutions in the range
l = 10
−3 – 10
−4 m; see
Figure 7a–c. In addition, the thin plate specimen had dimensions of 1.0 × 5.0 cm
2 and a resolution of
l = 10
−3 – 10
−4 m, see
Figure 7d.
The number of particles in the 3D samples was 3366, 23,331, 332,826 and 2,580,641, for l 10−3, 5 × 10−4, 2 × 10−4 and 10−4 m, respectively. The number of particles in the thin plates was 3927, 14,847, 76,806 and 303,606, for l 10−3, 5 × 10−4, 2 × 10−4 and 10−4 m, respectively. The simulations were conducted at the two strain rates, 30 and 140 mm × min−1. The Peridynamic stress was calculated from the total force per volume, acting through the first layer of particles in contact with the upper wall.
Figure 8 shows the bitumen’s beam’s failure in a 3D simulation showing that breakage is visually comparable with an equivalent experiment from the literature [
45].
Figure 9a shows the tensile results of the 3D beam. Results are independent of the loading rate, and when the particle resolution is
l < 2 × 10
−4 m, simulations are very close to the experimental data.
Figure 9b shows the 2D (thin plate) results. For
l < 2 × 10
−4 m, the results are independent of the particle resolution. However, contrary to the 3D results, they do not converge to the experimental data. In 2D, the greatest difference between the experiment and simulation is 10%. However, the 3D simulation at
l = 10
−4 m has eight times as many particles as the 2D simulation at the same resolution, which makes the simulation 16 times slower. Therefore, we decided to accept the error and run the simulations for thin plates at lattice
l = 10
−4 m.
6. Conclusions
In this article, we have demonstrated the use of Peridynamics combined with Discrete Multiphysics to model crack formation and propagation in asphalt at low temperatures taking into account air voids and ice formation. Find below some of the conclusions:
This paper demonstrates a way to understand how microcracks are formed in the asphalt under freezing conditions, a phenomenon that is extremely difficult to observe in experiments.
The simulations show the model’s reliability in obtaining a mechanical response comparable with experimental tension and compression tests of bitumen and asphalt, respectively.
As expected, the higher the void fraction, the higher the loss of compressive strength of an asphalt mixture. Further, the size and shape of the voids affect the strength of the asphalt. Larger voids are more detrimental than smaller voids, especially if they have a high aspect ratio and low circularity.
Using this model, we observed that the amount of mastic in densely packed mixtures does not have a strong influence on the compressive strength of asphalt. However, less densely packed mixtures, such as porous asphalt, are more sensitive to the amount of mastic in the asphalt.
The model can also assess the effect of ice formation on the asphalt structure. Water particles are created in the voids, and their volume is increased with time to simulate solidification. The simulations show the formation of cracks produced by water expansion during solidification and the consequent loss in mechanical strength. To the best of our knowledge, water expansion in cavities has not been simulated to date.
This methodological study provides researchers in the field with a powerful new tool for understanding the behaviour of asphalt under scenarios that, so far, have not been accessible to computer simulation. The systematic study of asphalt mechanical properties changes due to the size, number and distribution of ice-filled voids will be done in future research.