Bituminous Composites Research Articles

Investigating aging properties of bitumen modified with polyethylene-terephthalate waste plastic

This paper examines the merits of using recycled polyethylene terephthalate (PET) in bitumen to improve short and long-term aging of bituminous composites used in roadway constructions. A concern with PET is its low compatibility with bitumen leading to its segregation; here, we functionalized PET with waste cooking oil to enhance its compatibility with bitumen. We then studied the efficacy of functionalized PET to delay aging in bituminous composites. To do so, PET particles treated with waste vegetable oil and non-treated PET particles were separately blended into bitumen using a high-shear mixer and aged in the laboratory using a rolling thin film oven (RTFO) and a pressure aging vessel (PAV). The rheological and chemical changes that occurred with aging were captured by a dynamic shear rheometer (DSR) and a Fourier transform infrared (FTIR) spectroscopy. The results showed that binders containing PET had high resistance to aging as measured by their low change in activation energy and healing index after exposure to extended aging. Functionalized PET referred to as “Oil-treated PET” here, has proven efficiency in reducing aging effects, as indicated by lower values of the aging indexes. Oil-treated PET-modified binders lost 15.6% of their healing capacity after long-term aging whereas neat binders lost almost 66%. The outcome of this study exploits the synergy between two waste streams including waste vegetable oil and waste plastics to produce a sustainable modifier for roadway construction to extend their service life while promoting resource conservation and recycling.

Weathering Mechanisms in Bitumen Modified with Polyphosphoric Acid

AbstractThis study examines the effect of weathering on bituminous composites containing polyphosphoric acid (PPA). PPA has been commonly used in bitumen to increase bitumen’s stiffness and elastic...

Experimental and numerical investigation on the rheological behaviour of bituminous composites via DSR testing

Mastic and mortar are two bituminous composites which play a fundamental role in defining bituminous mixes’ properties. Therefore, the main purpose of this paper is to study the behaviour of these materials according to time and frequency with three different approaches: Experimental, analytical, and numerical. To characterise bitumen, mastic, and mortar, a Dynamic Oscillatory Test was carried out on bituminous composites using DSR. Numerically, mortar mechanical properties were assessed by applying a heterogeneous finite element (FE) modelling. Analytical methods such as Generalised self-consistent schemes (GSCS) and Shift-Homothety-Shift and time Shift (SHStS) have succeeded in predicting mastic and mortar properties. Numerical simulation presented a virtual DSR test able to examine stress and strain distribution in the digital model’s microstructure. Since studying the response of the internal structure to an applied stress or strain is complicated using other methods. Thus, aiming to optimise the material formula and improve its mechanical properties.

Protein enriched biowaste: A viable feedstock to make durable bio-binders for bituminous composites

Low resistant to water damage is a major concern in bituminous composites used in roads and roofs. Water damage is attributed to desorption of molecules which are pre-adsorbed to siliceous stone mainly due to the water molecules' higher affinity to active sites of siliceous substrates. This paper shows feasibility of engineering highly water-resistant bio-modifiers from a hybrid biomass feedstock containing a balanced combination of protein and lipid. In the present study, this concept is illustrated by synthesizing a novel bio-modifier referred to as Swilgae from coliquefaction of high-protein algae (A) with high-lipid swine manure (S) for use in bituminous composites. To examine efficacy of Swilgae bio-modifier to enhance bitumen's resistance to water damage, this paper specifically studies adsorption and de-wetting of Swilgae molecules from siliceous substrates as surrogates for quartz and granite stones used in bituminous composites. To do so, we use computational modeling geared toward the use of density functional theory (DFT) combined with laboratory experiments using a moisture-induced shear-thinning test and in-situ Fourier transform infrared (FTIR) spectroscopy. The study results showed that Swilgae bio-modifier is more effective at improving the asphalt resistance to moisture damage than those made from either algae or manure individually, owing to the synergy between lipid-rich swine manure combined with protein-rich algae. This was evidenced in bitumen containing 1A:1S Swilgae showing the least change in the moisture-induced shear thinning among all studied scenarios. This was attributed to the molecular structures of the Swilgae having both lower polarizability and higher adsorption energy per unit area of siliceous surface compared to those made from isolated feedstock. Additionally, Swilgae showed to passivate the active sites of silica and replace water molecules over the silica surface via a competitive adsorption with the water molecules on the hydroxylated silica surface that is consistent with the FTIR results. Therefore, 1A:1S Swilgae molecules build a well-structured bridge between bitumen and siliceous substrates, leading to improved adhesive forces and subsequently enhaced durability in the bituminous composites used in roads and roofs.

Genetic programming to formulate viscoelastic behavior of modified asphalt binder

The objective of this research was to develop prediction models for complex shear modulus (G*) and phase angle (δ) of bitumens modified with crumb rubber, styrene-butadiene styrene, and polyphosphoric acid at low and moderate temperatures. The experiments consisted of three different dosages of each modifier added to the original bitumen followed by measurement of G* and δ of the original and modified bitumen using the dynamic shear rheometer (DSR) test in frequency sweep mode (21 loading frequencies from 0.1 to 100 Hz) at seven test temperatures: −22, −16, −10, 0, 10, 16 and 22 °C. Having the experimental database, a robust genetic programming (GP) method was used to develop an individual prediction model for each modifier based on temperature, loading frequency, the G* and δ of the original bitumen, and the dosage of the modifier. Results showed that GP successfully developed accurate and meaningful expressions for calculating G* and δ of the modified bitumen as two main constitutive components of the viscoelastic behavior of bituminous composites. Then, a parametric study and sensitivity analysis were performed on the developed models to better understand the effect of variables on the trend of the models. The modifier dosage is the most effective input variable of the model and the amount of G* and δ of the original bitumen accurately reflect the effect of temperature and loading frequency on viscoelastic behavior of the modified bitumen, as they behave linearly at the considered test temperatures.

A heterogeneous micromechanical model for bituminous composites containing rigid and flexible particulates

This paper uses a heterogeneous micromechanical model to evaluate the resistance to thermal cracking in bituminous composites containing granular particulates. Thermal cracking is mainly caused by temperature fluctuations leading to accumulated stress that exceeds the strength of the materials. The presence of various granular particulates significantly affects a material's strength and capacity to release stress. Here, we use a two-dimensional heterogeneous numerical finite element model to evaluate and predict the thermal cracking characteristics of bitumen containing granular particulates such as crumb rubber and taconite. To develop the model, randomly distributed polygons using the Delaunay triangulation method were used to represent taconite and crumb rubber inside a bitumen matrix. The elastic properties of taconite and crumb rubber were assigned to the particulates, and the viscoelastic properties of the bitumen were modeled using a Prony series by implementing a simple fractional viscoelastic model. The study results showed that the flexural creep stiffness and creep rate calculated by the model were in good agreement with the measurements of experiments: the maximum errors were 6.15% for bitumen containing crumb rubber and 13.72% for bitumen containing taconite. Considering that flexural creep stiffness and creep rate are commonly used as indicators of thermal cracking resistance, the newly developed heterogeneous micromechanical model can be used to evaluate the thermal cracking resistance of bituminous matrices containing granular particulates. The model was further used to study the effects of temperature, elasticity, and concentration of particulates on the cracking resistance of the bituminous matrix. For instance, it was found that introducing 16% particulates with an elasticity of 1.02 MPa (representing crumb rubber) to bitumen improves its critical cracking temperature from −25 °C to −29.3 °C. This model provides insights to help the design of bituminous composites with desired cracking resistance properties by incorporating the proper particulates.

Interaction mechanisms of polyphosphoric acid and nano clay in bituminous composites

It has been reported that adding polyphosphoric acid (PPA) to bitumen modified with Montmorillonite clay (MMT) makes the bituminous composite less prone to swelling and more resistant to moisture damage, thus improving two major causes of pavement distress. There has been no in-depth study on the underlying mechanism for such a synergistic effect between MMT and PPA. Here, we used laboratory experiments and computational modeling to study how PPA moderates the intermolecular interactions in bitumen modified with MMT. The results showed that PPA had notable interactions with both MMT and bitumen components (BCs); however, PPA's preferential adsorption to MMT was verified by a significantly higher binding energy (−127.3 kcal/mol) for PPA-sealed MMT than for PPA-BCs (−85.9 kcal/mol). The higher binding energy for PPA-sealed MMT caused PPA to be strongly adsorbed on the MMT surface in the first stage, causing partial intercalation into the clay gallery and blocking subsequent entry of water. PPA's affinity to interact with BCs then allowed PPA to be a bridge between MMT and BCs, leading to more intermolecular interactions and better sealing for MMT. The calculated binding energies for interactions of BC with pre-adsorbed PPA on MMT were higher than those for interactions of BC with PPA alone. In both dry and wet laboratory conditions, bitumen modified with PPA-sealed MMT had higher values of shear thinning and G*/sin(δ) than bitumen modified with MMT.

Polyphosphoric Acid's synergy with bio-modified bituminous composites

Polyphosphoric acid (PPA) is among the most common modifiers used to increase bitumen's elasticity, improve bitumen's performance grade, and widen bitumen's operative temperature range. Recently, attention has been directed toward significant variations in PPA effectiveness when used in different bituminous composites. In other words, the same exact dosage of PPA affects various bitumens differently. The latter has been attributed to unexpected synergitic or antagonistic interplay between PPA and bitumen components. Considering the increasing use of bio-modifiers in asphalt industry, understanding such interplay is critical in design and engineering of bituminous composites. Here, we use the laboratory experiments and computational modeling, using density functional theory (DFT), to examine and compare the synergistic effects between PPA and each of five bio-modifiers (derived from wood pellet, miscanthus, castor oil, corn stover, or waste vegetable oil) to promote the durability and sustainability of bituminous composites while enhancing resource conservation and biowaste valorization. Based on the results, the bio-modifier made from wood pellets has the highest synergy with PPA (leading to the best dosage efficiency for PPA), followed by bio-modifiers made from miscanthus, castor oil, and corn stover. The bio-modifier made from waste vegetable oil shows the least synergy with PPA. The DFT results show the strong non-covalent interactions between PPA oligomers and the lignin units of the wood-based bio-modifier. In addition, due to the higher polarity of the wood-based bio-modifier compared to the bio-modifier from waste vegetable oil, a higher phosphorylation is expected to occur in the wood-based bio-modifier when exposed to PPA.

Enhancing Biomass Value Chain by Utilizing Biochar as A Free Radical Scavenger to Delay Ultraviolet Aging of Bituminous Composites Used in Outdoor Construction

This study examines the merits of using biochar to delay aging in construction while promoting the economic viability of biofuel production and enhancing the biomass value chain. Biochar residue from pyrolysis of biomass to biofuel was introduced to neat asphalt and rubberized asphalt binders. The study results showed biochar can delay oxidation and UV-induced aging at binder and mixture level as evidenced by lowering rheological and chemical aging indexes. The rheological aging index was measured based on the change in crossover modulus due to aging, and the chemical aging index was measured based on the change in carbonyl and sulfoxide functional groups due to aging. Four types of aging were examined including oxidation and UV aging at the binder level as well as aging and weathering at the mixture level. In terms of oxidation aging, biochar was more effective for rubberized asphalt, while in the case of UV aging, neat asphalt appeared to benefit more than rubberized asphalt from the presence of biochar. The latter can be attributed to the role of biochar as a UV-light blockage and free radical scavenger. Rubberized asphalt inherently contains carbon black which enhances the internal resistance against UV aging, hence the role of biochar was not as significant in rubberized asphalt compared to that of the neat asphalt. However, in the case of oxidation aging, biochar noticeably improved the rubberized asphalt compared to neat asphalt. The study outcomes provide a simultaneous solution to promote resource conservation and enhance aging resistance of bituminous composites. Biochar, carbonaceous particles, made from biowaste can be used as a free radical scavenger to delay ultraviolet aging of bituminous composites. Therefore, this study promotes sustainability by creating applications for biochar while increasing pavement durability by delaying asphalt aging.

Transesterification of Waste Cooking Oil to Produce A Sustainable Rejuvenator for Aged Asphalt

This study examines the merits of esterification of waste cooking oil to reduce its acidic content for use as a rejuvenator for aged asphalt. It further examines how acidic compounds in bitumen increases the moisture susceptibility of bituminous composites made from siliceous stones and bitumen. While some acidic compounds are inherent in bitumen, the recent widespread use of bio-modifiers such as waste cooking (vegetable) oil has further increased the acidic compounds in bio-modified bitumen. Acidic compounds adsorb well to siliceous stones, but they are easily replaced by water molecules, giving rise to moisture damage. It was found that a reduction or removal of the acidic compounds of waste cooking oil via transesterification significantly enhances its resistance to moisture damage. The study results showed that treated waste cooking oil is not only a promising rejuvenator to be used with aged bitumen, but also quite resistant to moisture damage. It was also found that transesterification reduces the acid value of bitumen from 12 to 0.27 (mg KOH/g). This turned a moisture-susceptible bitumen to nearly a moisture-resistant bitumen as evidenced by nearly no change in moisture-induced shear thinning after 24hr water conditioning. The outcome of the study shows significant role of acidic compounds in moisture damage, and the importance of accounting for the acidity of rejuvenators to ensure their durability. The study results confirm the feasibility of tuning waste cooking oil to a sustainable asphalt rejuvenator to promote both resource conservation and asphalt recycling.

Effect of bio-oil on rheological and calorimetric properties of RTFOT aged bituminous compositions

In the current research rejuvenation of aged bitumen by the oxidation product of rapeseed oil biodiesel (F) is considered thu s contributing to the solution of global warming. Aging of bitumen was performed by rolling thin film oven test (RTFOT). In the first stage RTFOT bitumen was modified with F at various weight contents (2, 5, 10 wt.%). Subsequently, 2 wt.% of F was introduced into different modified bituminous compositions with total polymer content of 3 wt.%. In comparison to the traditionally used styrene-butadiene copolymer (SBS), ethylene-octene copolymer with α-octene group content of 38% (EOC) were applied as F rejuvenated RTFOT modifiers. Structure as well as rheological properties of thus modified bituminous systems were characterised using dynamic shear rheometer (DSR), Fourier-transform infrared spectrometer (FTIR), and temperature-modulated differential scanning calorimeter (MDSC). It has been demonstrated that F rejuvenated polymer modified RTFOT demonstrates improved low-temperature properties, as well as increased rutting resistance and fatigue resistance.

Radiation Resistance of Bituminous Waterproofing Materials

The features of gas formation and changes in the molecular structure and performance properties of BN grade waterproofing asphalt under gamma-irradiation at an absorbed dose to 200 kGy have been studied. The radiation-chemical yield of total gases did not exceed 0.46 molecule/100 eV, showing high resistance to gas evolution. Changes in the molecular structure confirm the occurrence of destructive processes in the polyaromatic moiety. The penetration and ductility of the irradiated samples increase by factors of 8 and 10, respectively, and the softening and flash points are 40°C lower than those in unirradiated samples. The mechanism of action of ionizing radiation on bituminous compositions has been discussed in terms of competition between destruction and polycondensation processes in high-molecular-weight heterogeneous systems, such as waterproofing asphalt.

Surface Morphology and Chemical Mapping of UV-Aged Thin Films of Bitumen

This study decouples effects of ultraviolet (UV) exposure on the surface and bulk properties of bituminous composites. UV exposure accelerates oxidative aging of bitumen, but its effects are concen...

Microbiological corrosion of building materials

The research results in the field of microbiological corrosion of building materials of domestic and foreign experts are presented. It is shown that microorganisms cause corrosion of concrete on cement and other binding metal and other materials. Metals in the order of decreasing the rate of biocorrosion are arranged in the following row: aluminum, mild steel, zinc, brass, copper, stainless steel. Concrete, due to its high surface activity, is capable of adsorbing a wide variety of substances, including microorganisms: bacteria and mycelial fungi. Among bacteria, nitrifying agents, thionic, iron and silicate bacteria and others participate in the corrosion of cement concrete (mainly due to their acid secretions). According to the data of a number of authors, on the surface of stone building materials mycelial fungi of the genera Penicillium, Aspergillus, Trichoderma, Cephalosporium prevail. Biodeterioration in this case mainly comes down to the disruption of cohesion of constituent components as a result of exposure to mineral or organic acids, as well as enzymes and due to chemical reactions between the cement stone of solutions and concretes and the waste products of microorganisms. The compositions of bituminous composites at various ratios of the materials used without inclusion in the composition of fungicides showed non-fungal resistance and non-fungicide. Comparison of concrete on gypsum and phosphogypsum binders showed that samples on a phosphogypsum binder overgrow microorganisms somewhat more, wood materials are subject to significant biodeterioration at high humidity. Biodegradation of wood occurs mainly due to the use of mushrooms as food sources of cellulose, lignin and other components. Synthetic polymers and materials based on them are significantly superior to natural polymers in biostability. However, under certain operating conditions, they are damaged by biological agents. Biological damage to plastics, as well as other materials, occurs simultaneously with their aging under the influence of external physical and chemical factors (ultraviolet radiation, water, temperature changes, etc.). Additives that are usually always present in polymer compositions (fillers, plasticizers, stabilizers, antioxidants, modifiers, pigments, etc.) significantly affect the biostability of polymeric materials. One of the effective ways to increase the biostability of composite building materials is the introduction of fungicidal additives in their composition. It is also shown that of great importance in increasing the durability and increasing the life of some building structures (metal products, communications, underground pipelines and some others) is their protection by paint and varnish coatings.

Mechanical experiment evaluation of the microvascular self-healing capability of bitumen using hollow fibers containing oily rejuvenator

Smart microvascular self-healing bituminous composites are considered a promising approach to prolong pavement service life. The objective of this work was to investigate the microvascular self-healing capability of bituminous material by using hollow fibers with oily rejuvenator through a direct-tension mechanical experiment. The hollow fibers with oily rejuvenator were prepared using a wet-spinning approach by applying polyvinylidene fluoride material. The fixed-length hollow fibers with sealed ends were mixed in bitumen to form composite samples. Through a repetitive tensile method, the tension strength data were used to calculate the self-healing efficiency autonomously by considering crack closure and healing at various healing temperatures and times. The scanning-electron-microscope morphology showed that the polyvinylidene fluoride hollow fibers had a tight interfacial structure with bituminous material without debonding. X-ray computed tomography results indicated that the fibers were distributed homogeneously in bitumen. The fiber content and fiber orientation affected the self-healing capability of bituminous samples at 0 °C. To simplify the influence of the above two factors of the fibers, only one fiber was placed in bitumen samples parallel to the tension direction. With an increase in temperature from 0 to 30 °C, the self-healing capability of the bitumen samples increased dramatically. This phenomenon is attributed to the accelerated penetration speed of rejuvenator in the bitumen. An increase in time increased the self-healing capability of the bitumen samples. The rejuvenator may have sufficient time to leak from the hollow fibers and penetrate the bitumen. The results provide a guide to the microstructural design of the vascular fibers and the application of hollow fibers in self-healing asphalt pavement.

BITUMINOUS COMPOSITE COMPRISING AMORPHOUS SILICA FROM RICE HUSKS

The composites were prepared with a ratio of bitumen to silica of 1:0, 1:1.5, 1:1.6, 1: 1.7, 1:1.8, 1:1.9 and 1:2 by weight, and calcined at the temperature of 150 °C for 6 hours. The structural and microstructural characteristics of the bituminous composites were examined by X-ray diffraction (XRD), Fourier Transform Infrared (FTIR), Differential Thermal Analysis (DTA/TGA), and Scanning Electron Microscopy/Energy-Dispersive X-ray (SEM/EDX). Further evaluation was made by comparing the characteristics of the modified bituminous composites including the density, porosity, compressive strength, swelling thickness, and water absorption. The XRD study revealed that the major phases were silica and carbon amorphous, which were associated with the Si–OH, Si–O-Si and C–H functional groups according to the FTIR analysis. The DTA/TGA analysis resulted in an increase in the temperature decomposition by adding silica which was 230 to 315 °C. In addition, an increased silica addition was followed by an increase in the density, compressive strength, swelling thickness, and water absorption, while the opposite was true for the porosity. Based on these characteristics, rice husk silica has a positive effect on improving the mixture of high and low temperature performance, water stability, for use as a substitute in lightweight steel roof devices Keywords: Rice husk, Silica, Asphalt, Microstructure, Structure

Multi-Scale Numerical Viscoelastic Simulation of Fatigue Behavior of Asphalt Mixtures Modified with Polyphosphoric Acid

Fatigue cracking is one of the main distresses affects the service life of asphalt mixture. Recently, polyphosphoric acid (PPA) widely used as a modifier to improve mechanical and rheological characteristics of asphalt binders and mixtures especially at high and low service temperatures. While there are several studies devoted to investigate high and low service temperature of PPA modified asphalt binder and mixture, its fatigue behaviour needs to be studied in more detail. The main objective of this paper is to develop a multiscale heterogeneous numerical finite element (FE) model as well as experimental program to investigate the effect of PPA modification on fatigue behaviour of different bituminous composites from neat asphalt binder to asphalt mixture. The experimental program includes frequency sweep test at test temperature of 25°C by implementing dynamic shear rheometer (DSR) for neat and PPA modified asphalt binder and also indirect tensile fatigue (ITF) at frequency of 1 Hz (0.1 s loading time and 0.9 s rest time) under constant stress of 300 kPa at test temperature of 25°C by using a UTM-25kN. Three different contents of PPA is used for modifying neat asphalt binder including 0.5, 1 and 1.5 wt.% of neat binder to consider the variation of modifier extent on fatigue behaviour of neat asphalt binder and mixture. The mixture specimens were prepared with granite aggregate and asphalt binder of 85/100 penetration grade. The asphalt mixture is modeled as a biphasic medium composed of granular inclusions with linear elastic properties and bituminous matrix exhibiting linear viscoelastic behavior at small strain values. The generalized Maxwell rheological model was used to simulate viscoelastic behavior of the asphalt binder and PPA modified asphalt binder. In order to create the aggregate skeleton of the bituminous composites, a custom software (called “MOA”, French acronym for Random Object Modeler) developed in University of Limoges, has been used to generate random inclusions of various sizes and shapes. The experimental results of asphalt binder and mixture indicated that modification with PPA has a significant effect on improving asphalt mixture’s fatigue life especially in dosage of 1%. On the other hand, results of numerical simulation have shown a good agreement with experimental results.

Gasification of Brazilian coal-chars with CO2: effect of samples’ properties on reactivity and kinetic modeling

The gasification of coals obtained from important coalfields in Brazil was investigated in 1.0 bar of CO2 using a thermogravimetric analyzer. Tests were carried out in two sequential steps: pyrolysis under N2 at 1213 K and isothermal gasification under CO2 in the temperature range of 1113–1213 K. The kinetic study was performed in the kinetically controlled regime and three gas-solid models were fitted to the experimental data. According to the results, subbituminous coal-chars presented higher reactivities than bituminous types, with maceral and ash compositions playing a key role in the overall process. The reaction rates increased with increasing temperature, with maximum values found in the conversion range of 10–60%. The random pore model that predicts a maximum point of reactivity over the reaction course suitably described the gasification kinetics. Values of activation energy between 146.63(±0.03) kJ/mol and 215.09(±0.05) kJ/mol were found, which are consistent to literature data of coals gasified worldwide. Despite the relatively high ash content (32–45%), the Brazilian coals appeared to be sufficiently reactive to be gasified, thus indicating the significance of this study to the development of gasification process in Brazil.

Effect of shale adhesion agents on the physicochemical properties and performance characteristics of bitumen emulsions

A method for the preparation of bitumen emulsions with the addition of shale adhesion agents is proposed. Upon the introduction of shale adhesion agents into a matrix of bituminous compositions, an improvement in the physicochemical properties and performance characteristics of emulsions, such as relative viscosity and adhesion, was observed in comparison with the properties of traditional bitumen emulsions.

Initial strain energy-based thermo-elastoviscoplastic two-parameter damage self-healing model for bituminous composites—Part II: Computational aspects

This paper describes the implementation of the initial strain energy-based thermo-elastoviscoplastic two-parameter damage self-healing models for bituminous materials to compare the model predictions with experimental measurements. Computational algorithms based on the two-step operator splitting methodology are proposed and employed for numerical results. The elastic two-parameter damage self-healing predictor and the viscoplastic corrector are coupled with the Arrhenius-type temperature term via the net stress concept in conjunction with the hypothesis of strain equivalence and then systematically used for numerical implementation of the models. Four numerical examples of three-dimensional problems are first demonstrated for the effect of temperature and rest period for healing phenomenon. Second, experimental validation of the proposed model against monotonic constant-strain test at different temperatures and controlled-strain cyclic tension test is presented. It is observed that numerical simulations by the two-parameter model agree well with experimental results. In particular, the softening responses of the bituminous composites are well predicted for monotonic constant-strain rate test and the viscous damage behavior can be reasonably predicted by the proposed two-parameter damage models. It is noted that the two-parameter model can better predict the thermo-mechanical behavior of asphalt and is more versatile than the one-parameter isotropic damage self-healing model.