Simulation of composition of recycled hot-mix asphalt mixture produced in asphalt mixing plant

Construction and Building Materials 214 (2019) 17–27

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Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat

Simulation of composition of recycled hot-mix asphalt mixture produced in asphalt mixing plant Henrikas Sivilevicˇius a,⇑, Ke˛stutis Vislavicˇius b a b

Department of Mobile Machinery and RailwayTransport, Vilnius Gediminas Technical University, Plytine˙s g. 27, LT-10105 Vilnius, Lithuania Department of Applied Mechanics, Vilnius Gediminas Technical University, Saule˙tekio al. 11, LT-10223 Vilnius, Lithuania

h i g h l i g h t s
Homogeneity of reclaimed asphalt are assessing by variation of five indicators 81.
Composition of recycled asphalt mixture determining by the optimization methods 82.
Algorithms permit designing optimal mixture including technological restriction 81.
Numerical example shows that the simulation permit designing best mixture 76.
Designed optimal composition use on recycling mixture in asphalt mixing plant 78.

a r t i c l e

i n f o

Article history: Received 6 November 2018 Received in revised form 4 March 2019 Accepted 30 March 2019

Keywords: Asphalt mixture Recycling Asphalt mixing plant Design of composition Optimization Numerical experiment

a b s t r a c t Recycled hot-mix asphalt (RHMA) mixture is produced from reclaimed asphalt pavement (RAP) by adding an appropriate amount of new mineral materials improving the gradation of RHMA, a lower viscosity bituminous binder and a rejuvenator. The manufactured RHMA mixture must meet the same technical requirements as those for the hot-mix asphalt (HMA) mixture made of new materials only. It is also aimed at reducing its cost to the minimum in order to comply with technical requirements for the RHMA mixture in the asphalt mixing plant (AMP). These goals are ensured in the process of determining the composition of the RHMA mixture applying numerical and experimental methods for selecting an optimal content of old and new materials in the mixture. The article presents a method for determining the composition of the RHMA mixture, which allows calculating the maximum allowable percentage of RAP depending on its homogeneity. Setting the established maximum RAP amount as a constant size, the required content of new mineral materials is estimated thus taking into account bitumen capacities. The price of a single ton of the materials making the RHMA mixture and information on technical requirements for the composition of the RHMA mixture assist in applying certain technological restrictions, which makes it possible to calculate an optimal content of the components. The research findings obtained from the representative sample demonstrated that ready-for-use RAP was not homogeneous, and its five properties used for calculating its maximum allowable amount had different variations. The paper presents the algorithms that are actualized using mathematical programming methods upon the application of which the following objectives were solved: the assessment of technological requirements helped to obtain the RHMA mixtures of the cheapest or densest mineral part, and the mixture having the lowest content of bitumen was received. The article discusses mathematical analogues that can be used for determining whether the RHMA of the right gradation can be produced from the available mineral materials and allows analysing the mixtures that do not meet the established requirements thus identifying the causes of inappropriateness. The introduced algorithms can be applied at the initial stage of designing the RHMA mixture thus reducing the duration and cost of the design process. In order to determine whether the calculated content of old and new materials is appropriate, the standard specimens produced and examined in the laboratory need to be confirmed. Ó 2019 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. E-mail addresses: [email protected] (H. Sivilevicˇius), [email protected] (K. Vislavicˇius). https://doi.org/10.1016/j.conbuildmat.2019.03.330 0950-0618/Ó 2019 Elsevier Ltd. All rights reserved.

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H. Sivilevicˇius, K. Vislavicˇius / Construction and Building Materials 214 (2019) 17–27

1. Introduction The asphalt pavement made of high quality materials and having the optimal composition best resists destructive effects of environmental factors and vehicles. The optimal content of the mineral materials of the asphalt mixture and a bituminous binder (BB) is selected employing calculation and experimental methods. The properties of the designed asphalt mixture must meet the requirements of technical specifications thus reducing its cost [1]. Asphalt mixture consists of BB, coarse and fine aggregate, and a number of additives occasionally used to improve its engineering properties. The purpose of mixture design is to select an optimum BB content for a desired aggregate structure to meet prescribed criteria [2]. Roberts et al. [2] presents a review of the past, present, and future trends in asphalt mixture design as the methods have evolved in an attempt to meet the ever-in-creasing demands of traffic. Since 1940s, most asphalt concrete produced were designed by using the Marshall mix design method. The traditional analysis method that uses six figures of the BB contents versus the test results of unit weight, stability, flow, air void (VTM), void in mineral aggregate (VMA), and void filled with asphalt (VFA) to determinate optimum BB content (OAC) in time-consuming and inefficient [3]. The objective of asphalt mix design is to produce a mixture with optimal mixture properties (stability, durability, flexibility, fatigue resistance, skid resistance, permeability, and workability). Several mix design methods have been proposed over the years to accomplish this task. Until the 1990s, the Hveem and Marshall methods of mix design were the most predominant methods in the United States [4]. The Superior Performance Asphalt Pavements (Superpave) method was to produce mixtures based on volumetric properties, which could directly be correlated to field performance. The method recognizes the role of coarse aggregate angularity, fine aggregate angularity, flat and elongated particles, clay content and gradation in the production of quality mixtures [2,4]. The Superpave design mainly uses volumetric properties for the mix design, similar to the Marshall method. Based on the laboratory results of the temperature study, the performance of the designed asphalt mixes using both the Marshall and Superpave mix design procedures were evaluated and compared [5]. The main conclusions to be drawn are as follows: The BB content determined from the Superpave mix design procedure is lower than that predicted by the Marshall Mix design procedure. An analysis algorithm defined by grey relational-regression analysis (GRRA) method based on grey system theory is conducted to determine optimum BB content (BBC) [3]. To validate and evaluate the method, three different mixture design example data were tested and selected for application. The result show that all of the BBCs are within the range of the specification requirements. The objectives of the work presented in the paper by AwuahOffei and Askari-Nasab [6] are (a) to develop a model to minimize the cost of the designed hot-mix asphalt (HMA) mixture while respecting all the constraints of the Bailey method principles and (b) to developed a numerical solution algorithm to solve such model. First a linear programming (LP) model of the mix design problem was formulated to minimize the cost subject to the constraints imposed by the Bailey method. The algorithm was implemented in MATLAB R2007a. The role of aggregate in HMA performance is well documented in the literature. The aggregate gradation is one most important parametrics in the mechanical properties of HMA. Thus, determining the aggregate gradation is a very significant subject in civil engineering [7]. Typically, aggregate gradation is selected to meet the specifications of Superpave mix design. The porosity of the dominant aggregate size range (DASR), which is the primary structural network of aggregates, has been extensively validated as a tool for evaluating the coarse aggregate structure of laboratory

and field asphalt mixtures [8]. The interfacial interaction between BB and several mineral surfaces of different chemical nature as present in asphalt mixtures has been investigated using atomic force microscopy [9]. The functional properties and performance of the constructions – road and pavements – and in particular, their durability depends on the interaction between binder and filler (solid components) and its hence controlled by the properties and strength of the binder-aggregate interface or in other words by the adhesion strength at this interface [9]. Since the aggregate skeleton of asphalt concrete is mainly formed by the coarse aggregates and it has important influences on the creep performance of asphalt concretes [10]. This paper [10] evaluated the property homogeneity of coarse aggregate skeleton on the creep performance of different concretes. Changes in gradation make change of aggregate specific surface and the mixture needs different BB content to coat aggregate particles, to bound them to each other and to make stiff material resistant to rutting. The results from measuring of resistance to permanent deformation show the relation between aggregate specific surface and bitumen film thickness and permanent deformation [11]. For asphalt mixtures of asphalt concrete type with aggregate gradation up to 16 mm with binder content lowered by 0.5% there was always decrease in the average size of strain derived from the fatigue line at 106 load cycles value in the range of 3–19%. There is a strong relationship between this fatigue characteristic and the bitumen film thickness [12]. In general, limestone showed better adhesion to hot-poured binders (crack sealant) than quartzite. Interfacial parameters such as contact angles and surface tensions were successfully used to differentiate between binders [13]. Mixtures made with limestone as a aggregate showed a higher wet/dry ratio in terms of the dynamic modulus than mixtures with granite. This means that mixtures made with limestone aggregates are more resistant to moisture damage [14]. In the study [15], the effect on Marshall Stability (MS) of HMA parameters which are the particle diameters of aggregates, quantity of BB in the HMA. Different environmental temperatures and the exposure times was closely investigated. Based on the numerical analysis for different asphalt concretes, the influences by property homogeneity of aggregate skeleton on the macro creep performance of asphalt concrete and the distribution of micromechanical contacting forces within asphalt concrete were analyzed [10]. Rimša et al. [16] adresses simulation of asphalt on the macroscopic scale, using the Discrete Element Model (DEM). The discrete model presents a 3D network of one-dimensional elements connecting particle’s centres and comprising mutual interaction of particles. The contribution the film layer and the interface thickness for normal stiffness is described analytically and illustrated by simulation results. The developed technique is applied for simulation of Marshall Test, i.e diametric compression cylindrical specimen, widely used for characterization of asphalt mixtures. Ozturk and Kutay [17] presents an artificial neural network (ANN) model to predict the asphalt mixture volumetrics at Superpave gyration levels. The input data-set needed by the algorithm is composed of gradation of the mix, bulk specific gravity aggregates, low- and high-performance grade of the binder, binder content of the mix and the target number of gyration. Asphalt pavements perform in a wide range of temperatures, especially in Eastern European countries, where the daily mean temperature of asphalt layers varies from 18 °C during winter to 47 °C during summer or even higher under more severe climatic conditions [18]. The largest damage to the pavements is caused by the heavy goods vehicles (HGV’s). Due to large axle loads which often assume a dynamic effect, the HGV’s account for almost the total destructive impact on the pavement, though they make about 15% of the total traffic flows on the main roads of Lithuania [19].

H. Sivilevicˇius, K. Vislavicˇius / Construction and Building Materials 214 (2019) 17–27

BB the most damaged in the asphalt pavement. The research [20] studied the effects of ageing on the binder deterioration of long-term pavement performance sites in Southeast Queensland in Australia. The viscosity of the binders shows a rapid rate of increase for the initial 10 years after construction. Therefore, the increase in the viscosity was observed to be gradual and a slower rate of binder deterioration has been reported. Petroleum bitumen used for producing road surfaces slowly reacts with atmospheric oxygen. The reaction eventually leads to the embrittlement of bitumen and failure on the surface under traffic stresses and, for this reason, is of great practical importance. The extent of the reaction is not uniform throughout the surfacing layer but is dependent on the diffusion of oxygen from the surface exposed to the atmosphere [21,22]. Oxygen diffusion and oxidative reaction are two main factors in asphalt oxidative aging discovered by experiment, but the dynamic balance between them could not be easily studied by experimental methods due to its comprehensiveness. A pavement oxidation model was utilized to simulate this process in asphalt: oxygen molecules penetrate into the bitumen film and then react with the bitumen molecules [23]. Due to irreversible processes of oxidation the aged bitumen stiffens, its physiochemical properties, ductility, adhesion and cohesion as well as sectional composition (relative amounts of asphaltenes, oils and resins) change. Bitumen in the old asphalt pavement may be restored to properties approximate to those of the virgin bitumen by adding the following rejuvenators: softening or rejuvenating agents as well as soft bitumen [24]. When HMA pavements reach the end of their usable service lives, the materials in them retain considerable value. In the early 1970s, states and paving contractors began making extensive use of reclaimed asphalt pavement (RAP) as a component in new HMA pavements. Besides possible cost savings, this use of RAP represents an environmentally positive method of recycling. Further, experience has shown that properly designed HMA containing RAP performs as well as HMA prepared exclusively with virgin materials [25]. In recent years the industry focus has been placed on increasing the amount of RAP in mix asphalt production. This is a result of tripled binder costs during the last decade that come at a time of extremely strained funding for road construction and maintenance [26]. RAP is old asphalt pavement that is milled up or ripped off the roadway. This material can be reused in new asphalt mixtures because the components of the mix – the BB and aggregate – still have value. Using RAP in new mixtures can reduce the amount of new material that has to be added, saving money and natural resources. In addition, HMA mixtures with RAP can perform as well as mixtures made with all new material [25]. Reclaimed pavement materials may range from as little as 10 percent to as much as 70 percent of the final mixture. The vast majority of the projects, however, incorporate between 10 and 50 percent RAP in the final mixture [27]. RAP rates between 10% and 30% are commonly used in hot recycled bituminous mixes. Valdés et al. [28] presents an experimental study to characterize the mechanical behavior of bituminous mixtures containing high rates of RAP. Results show that high rates of recycled material can generally be incorporated into bituminous mixes by proper characterization and handling of RAP stockpiles. The applicability of recycled asphalt was tested in laboratory, and asphalt mixes BNHS-22 containing 10%, 15% and 20% of reclaimed asphalt were designed. The results obtained hawe lead to conclusions about the applicability and necessary proportion of recycled asphalt, manufacturing technology, and possible savings in the manufacture of new asphalt mixes [29]. Using increased proportions of RAP in asphalt pavements construction has become a top priority due to significant economic

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and environmental benefits [30]. The results [31] showed significant reduction in energy consumption and greenhouse gas (GHG) emissions with an increase in RAP content. The recycling of RAP helps road authorities to achieve their gal of a sustainable road transport system by reducing waste production and resources consumption. The environmental and economic benefits of using RAP in HMA applications could be pushed up to the limit, by producing totality recycled HMAs (100% RAP), but the performance of this alternative must be satisfactory [32]. The addition of RAP had a negative effect on the fatigue performance of the base course and positive effect on the binder course. The mixtures containing RAP had lower cumulative strain and strain rate than the mixtures without RAP. It was shown that in spite of the differences in chemical oxidation state and microstructural features, a well-designed mixture containing RAP can perform mechanically as well as that produced with virgin materials in laboratory experiments [33]. Jamshidi et al. [34] characterizes the effects of RAP source on the rheological properties of virgin BB with 15% and 30% recovered binders. The results showed that RAP source significantly influence the binder rheological properties at each aging state and test temperature. RAP homogeneity is accepted as one of the most important quality indicators determining the maximum allowable amount of RAP in RHMA. An increasing variation of RAP gradation and the content and properties of the present old BB result in the reduced potential amount of RAP in RHMA mixture [35–38]. In recent years, recycled or reclaimed asphalt pavement (RAP) has been used increasingly due to its advantages in building sustainable pavement infrastructure. In the meantime, concerns have been raised regarding the performance of mixtures involving RAP. One of the major concerns comes from the material variability because it is believed to possibly result in poor pavement performance, particularly for mixtures with high RAP content [39]. Once concern many agencies have about the use of RAP is the variability of the material. Because RAP is the removed from an old roadway, it may include the original pavement materials, plus patches, ship seals, and other maintenance treatments. Base, intermediate, and surface courses from the old roadway may all be mixed together in the RAP. RAP from several projects may be mixed in a single stockpile. Mixed stockpiles may also include materials from private work that may not have been built to the same original standards [37,40]. Aged asphalt mixture is heavily involved in pavement maintenance and renewed construction because of the development of recycling techniques. The aged BB has partially lost its viscous behavior. Rejuvenators are therefore designed and used in this recycling procedure to enhance the behavior of such aged reclaimed BB [41]. The objective was to produce mixtures with high RAP content that demonstrate similar or better pavement performance than the conventional HMA asphalt [42]. Asphalt rejuvenator partly recovers the RAP binder performance, and the softening effect is very evident; that has a negative effect on the rutting performance of RAP mixes. 100% RHMA lab samples were modified five generic and one proprietary rejuvenators at 12% dose and tested for binder and mixture properties [43]. All products ensured excellent rutting resistance while providing longer fatigue life when compared to virgin mixtures and most lowered critical cracking temperature. Epoxidized soybean oil (ESO) was employed as a nowel penetrant cooperating with a conventional rejuvenator (CR) for the recycling of RAP. The influence of ESO on the diffusibility and the regenerating effects of CR on RAP were investigated [44]. The asphalt industry faces continuing pressure to optimize the use of available resources as material and transport costs both escalate with fuel prices. Use of locally available materials reduces the energy required to move large quantities long distances, and

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the use of RAP reduces both the quantity of aggregate and quantity of asphalt required. However, issues still exist about understanding the effect of RAP on the final asphalt mixture performance [45]. When RAP is added to new asphalt mix, it is important to account for this material in the mix design. RAP and new (virgin) aggregates must meet the mix design criteria when combined at a prescribed ratio. The same is true for RAP and virgin binders. The RAP binder is typically exposed to the elements for a number of years, and it is, therefore, significantly aged. Ageing results in a substantial increase in RAP binder consistency [46]. In study by Sivilevicˇius et al. [36], the principles of asphalt pavement hot recycling are systematized, which allows analysis of the factors of components’ interaction influencing the results of the recycling process. The paper also presents and analyses asphalt recycling technologies in asphalt mixing plant (AMP) and their comparative analysis. Among HMA production process, HMA plants are the most common ones is world. There are about 4000 HMA plants in the Europe and 4500 in the USA [47]. Hot-mix recycled asphalt concrete in plant is one of the available techniques to perform cost and environmental effective pavement recycling. The mix production was made in a batch plant without heating the reclaimed material [48]. The most important conclusion is that it is possible to prepare high modulus mixtures (HMM) with high RAP contents and good mechanical properties similar to those of conventional high modulus mixes. However, preparation in non-adapted plants, where RAP is not previously heated, allows a maximum RAP percentage of approximately 30% only [49]. Miliutenko et al. [50] identified and evaluated potential ways of improving the life cycle environmental performance of asphalt recycling in Sweden. The results showed that hot in-place recycling gave slightly more global warming potential (GWP) and cumulative energy demand (CED) savings than in plant recycling. Two different types of heat transfer techniques are primarily involved in processing RAP in hot mix facilities: conductive heat transfer and convective heat transfer [51]. Ma et al. [52] analyzed the agglomerate characteristics of RAP material and evaluated the influences of the preheating temperature of RAP on the properties of recycled asphalt mixture. The properties of recycled asphalt mixture keep improving with the increase of the preheating temperature of RAP. There is a minimum-temperature limit of RAP preheating to granulate the properties of recycled asphalt mixture. The purpose of paper [53] is to present a physical model dedicated to the evaluation in temperature and moisture of granular solids throughout the drying and heating steps carried out inside a rotary drum. To further investigate the time needed to heat the RAP, the heat transfer between the RAP and superheated virgin aggregates was modeled using finite difference techniques [54]. HMA production is a thermal energy consuming industry. When using the heat provided by the combustions of a fuel, a high-energy efficiency is obtained for the heating and the drying of the components of the mix recipe [55]. Neverthelles, the present study has shown that the exergetic efficiency is very poor. The use milled materials from old porous asphalt (PA) wearing courses in new PA layers promotes an important cycle of re-use that should be encouraged. The experimental study [56] aims to investigate the performance of recycled PA mixtures prepared by partly substituting virgin aggregates with selected coarse reclaimed asphalt (RA) from a milled PA wearing course. Results showed that recycled PA mixtures with 20% and 25% of RA can perform as well as the reference PA mixture in terms of moisture resistance and durability if an accurate mix design is performed. The optimum total binder content was found to increase as the amount RA increases, because of the fact that a prominent part of the aged binder acts as a ‘‘black aggregate” [56]. When RAP is mixed with virgin aggregates and virgin binder, partial blending

of RAP binder occurs in the HMA. Agencies limit the amount of RAP because the degree of blending between the RAP and the virgin materials is not known [57]. The methodology provides a systematic approach for determining the degree of partial blending in the RAP mixture. The ability to accurately determine the degree of partial blending will help in determining the virgin binder content to be added in the mixture. Longer RAP/virgin aggregate mixing times could result in recycled hot asphalt mixtures with higher stiffness modulus and better homogeneity. In addition, RAP size seriously affects the level of blending hence the stiffness variation of recycled mixtures [58]. The objective of study by Yan et al. [59] were to evaluate recycled mixture’s performance with different RAP contents and recycling agents (RA). Optimum RA contents were determined according to asphalt blending charts based on penetration index. The performance of recycled mixtures and control virgin asphalt mixture was evaluated based on retained stability, Tensile Strength Ratio (TSR), dynamic stability (DS), failure strain, and fatigue life. Zaumanis and Mallick [60] summarises the state-of-the-art approaches for increasing the amount of RAP in asphalt mixture above 40%. The production challenges and common pavement distresses of very high RAP content mixtures are identified and methods to optimize the mix design as well as production technology in order to allow manufacturing of such sustainable mixtures are described. The best practices for RAP management and economic benefits of high RAP use are also discussed. Baptista et al. [61] describes a mix design procedure and a case study carried out for hot-mix recycled based on the mechanical performance of several blends, which are applicable to common practice in Portugal. The study designed a typical 0/25 bituminous mixture for the base layer, with incorporates up to 40% of reclaimed bituminous material, introduced into the plant mixer without previous heating. Vislavicˇius and Sivilevicˇius [38] presents the algorithm for predicting the composition of material constituent of RHMA, taking into consideration the variation of gradation of all mineral materials and RAP, in the absence of random batching errors. When simulating the gradation of the RAP and mineral materials are selected by using a random number generator. The mathematical model and algorithm produced in the article [1] were used to design a comprehensive HMA mixture produced exclusively from virgin materials. This principle and methodology can be applied for designing the optimal composition of RHMA including RAP as an additional separate material in which the old BB must be improved by adding new low-viscosity bitumen. The maximum allowable amount of RAP subject to the homogeneity of RAP is determined in RHMA mixture. The paper is aimed at providing algorithms, mathematical models and numerical examples for determining the composition of recycled HMA mixture meeting technical and technological requirements. Such composition should be the cheapest, the densest one and have the lowest content of bitumen.

2. Mythology of determination optimal composition of RHMA 2.1. Determination of maximum allowable RAP content The maximum allowable amount of RAP in newly recycled HMA is determined taking into account the homogeneity of RAP [35,62,63]. To assess homogeneity, a sample from the prepared 500 t RAP was taken. However, at least five samples from each individual stockpile must be considered and examined. Thus, the following properties are defined: the softening point °C of old BB, the binder content, by percent, the content of the particles less than 0.063 mm (mineral filler) by percent, the content of fine aggregate, i.e. the particles from 0.063 mm to 2 mm (usually only

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wearing and binder layer of pavement) and coarse aggregate content, i.e. particles >2 mm. As a result, the possible (maximum allowable) amount ofRAPK i (Max. RAP %), subject to RAP homogeneity, is determined by evaluating the intervals of property indicators, ranges ai and general admissible deviation N adm;i according to [63]. The amount ofRAPK i is calculated in relation to formulas (1) or (2). In the case of a mixture of the asphalt base layer and asphalt base-wearing course used in a single layer of pavement, formula (1) applies to all properties. In the case of the mixture of binder course and the asphalt surface, formula (1) is applied for the property of old bitumen softening point, whereas other properties take formula (2):

Ki ¼

0:50Nadm;i 100 ai

ð1Þ

0:33Nadm;i 100; ai

ð2Þ

or

Ki ¼

where K i – possible to add (maximum allowable) amount of RAP in recycled HMA mixture, mass %, ai – the range of the property indicators for RAP (sample compile of at least 5 sepatate samples); ai ¼ xmax;i  xmin;i ; Nadm;i – general admissible deviation subject to the property of RAP and a type of recycled HMA mixture i.e. used in the layer of the pavement (Table 1); i – the i-th property of RAP (i = 1,. . .,5). Amount K i is calculated according to each of the five specified properties, and the minimum value of possible to add RAP content must be selected. 2.2. Mathematical analogues Mathematical analogue for simulation composition of recycled hot–mix asphalt (RHMA) mixtures mineral part assumes be following expression:

9  xj ! min; ðaÞ > > > > Pm > pL;i  j¼1 aij  xj  pU;i ; i ¼ 1; 2; . . . ; n; ðbÞ > > = Pm ðc Þ j¼1 dv j  xj  hv ; v ¼ 1; 2; . . . ; s; > > Pm > ðdÞ > > j¼1 xj ¼ 1; > > ; xj  0; ðeÞ Pm

j¼1 cj

ð3Þ

where cj is the weight multiplier of mineral material j, xj is the quantity of mineral material j of an asphalt mixture in parts of the unit, m is the number of mineral materials, aij is the quantity of mineral material j in percent passing through sieve i; pL;i ; pU;i are quantity limits on the percent passing of all mineral materials through sieve i, dv j is the coefficient of additional inequality v corresponding to mineral material j; hv is the limit value of additional Table 1 General admissible deviation N adm;i for the BB softening point, its content and gradation of aggregate skeleton of RAP [63]. RAP properties

^C Softening point T sp ; A Binder content, weight % % particles passing 0.063 sieve (mineral filler) % particles 0.063–2 mm (fine aggregate) % particles retained 2 mm sieve (coarse aggregate)

For recycled HMA mixture using in pavement of wearing, base and wearing-base courses

of road base

8.0

8.0

1.0 6.0

1.2 10.0

16.0

16.0

16.0

18.0

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inequality v, s is number of additional inequalities. It is imported to know that the inequalities (3, c) mathematically express technological limitations (there may be none of them). The last conditions (3 d and 3 e) ensures the reality of the problem. The mathematical analogue for simulation content of the required bitumen is as follows:

9 > ðaÞ > > > > j¼1 k¼1 > > > > m r P P > > pL;i  ajk;i  xjk  pU;i ; i ¼ 1; 2; . . . ; n; ðbÞ > > > > j¼1 k¼1 > > > ðc Þ = xj1 ¼ xj2 ¼ . . . ¼ xjk ¼ . . . ¼ xjr ; m P > > dv j  xj  hv ; v ¼ 1; 2; . . . ; s; ðdÞ > > > > j¼1 > > > > m P > > xj1 ¼ 1; ðeÞ > > > > j¼1 > > ; ðf Þ xj  0; m P r P

bjk  ajk  xjk ! min;

ð4Þ

The object function of the problem conveys the required BB of all mineral materials. In this expression coefficient bjk is bitumen capacity of the k-th narrow fraction of the j-th mineral material (j = 1, 2, . . ., m, k = 1, 2, . . ., r, where m is the number of mineral materials; r is the number of the narrow fractions of a mineral material), coefficient ajk indicates the content of the k-th narrow fraction (%) in the j-th mineral material and variable xjk is content of required BB corresponding the k-th narrow fraction of the j-th mineral material. Inequalities (4b) satisfy quantity limits on the percent passing of all mineral materials through sieves, where ajk;i is the content of k-th narrow fraction (%) in the j-th mineral material that passes through the i-th sieve. Coefficients pL;i ; pU;i are quantity limits on the percent passing of all mineral materials through sieve i. Therefore, the contents of all narrow fractions of certain mineral materials must be the same, i.e. the contents of narrow fractions must satisfy the condition (4 c). This means that the number of variables is not j r but j. They are expressed by the parts of the unit, and therefore have to meet the condition (4 c). The last three conditions mean the same like in mathematical analogues (3).

3. Algorithms of determination optimal RHMA mixture 3.1. Materials The asphalt mixing plant (AMP) stockpiles and silos are used for storing cold mineral materials before the season of producing the mixture. To perform a numerical examples seven materials, including RAP, and non-activated dolomite imported filler (IF), natural quartz sand (NS), granite sifting (GS), crushed granite 4/8 (CG 4/8), crushed granite 8/11 (CG 8/11) and crushed granite 11/16 (CG 11/16) were selected. The produced asphalt mixture of the mix group Asphalt Conrete AC 16 VS will contain recycled (old and new) road bitumen at grade 70/100 the content of which in the RHMA mixture should make not less than Bmin = 5.2%. The required viscosity of new BB is not specified, since it depends on the content of old BB present in the mixture of RAP viscosity and the total content of BB in RHMA mixture. The HMA mixture of the mix group asphalt concrete AC 16 VS of the surface layer of the pavement should be designed. Data describing the gradation of mineral materials and limits pL ðlowerÞ andpU (upper) on designed asphalt mixture gradation are presented in Table 2. Table 2 provides the averages of percent passing calculated from sufficiently large representative samples taken from the

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Table 2 The gradation of stockpile mineral materials and gradation limits of the asphalt mixture AC 16 VS. Sieve size (mm)

Gradation of the RAP and stockpile virgin mineral materials (percent passing) RAP

IF

0.063 11.5 83.8 0.125 14.8 93.4 0.25 21.1 97.9 0.5 30.0 99.5 1 39.8 99.8 2 51.5 100 5.6 73.3 100 8 84.3 100 11.2 94.1 100 16 98.8 100 22.4 100 100 Bintuminous binder – road bitumen at grade 70/100.

Limits on asphalt mixture gradation

NS

GS

CG4/8

4.2 10.1 21.8 39.6 52.9 64.2 87.4 96.1 100 100 100

11.3 16.7 27.5 35.2 45.7 53.2 91.8 100 100 100 100

2.6 2.1 1.8 5 2.9 2.3 2.0 7 3.4 2.5 2.3 14 4.0 2.9 2.7 20 4.7 3.4 3.1 26 8.8 4.1 3.8 35 16.7 6.9 5.4 54 90.1 12.2 9.2 62 99.3 94.3 14.7 70 100 99.1 89.0 90 100 100 99.1 100 In AC 16 VS mixture minimum binder content Bmin  5.2% [63]

stockpile of each aggregate, an IF closed silos and a RAP covering stockpile. At the initial stage of solving the problem, the maximum allowable percentage of dosed RAP subject to the included amount of components and variations in the properties of the old BB is determined. For that purpose, the mean, standard deviation and range content of BB, mineral filler, fine aggregate and coarse aggregate present in 43 separate RAP samples were calculated (Table 3). To define data distribution complying with normal distribution, skewness and kurtosis were applied. Range values were used for calculating maximum RAP amount. The homogeneity of new mineral materials is not significant for selecting the appropriate amount in the RHMA mixture, and therefore the indicators of their gradation variation were not calculated. The maximum percentage of RAP is also determined estimating the range [63] of the softening point T sp of the old BB according to Eq. (1) or variation. The properties of the old BB present in RAP were found in 25 of 43 samples. As for some RAP samples, the amount of old BB obtained following extraction was too small to

CG8/11

CG11/16

pL,

pU,

i

i

9 17 24 30 36 45 66 76 85 100 100

determine all its properties. The statistical indicators of the most important properties of BB present in RAP demonstrate significant variation and a large deviation from normal distribution (Table 4, Fig. 1). Dynamic viscosity (coefficient of variation, CoV = 65.1%) has the greatest variation in RAP, where a softening point (CoV = 8.8%) – the lowest one. The value of CoV from a not very small sample from normal general entirety (population) should not exceed 33%. When the modules |sk| and |ku| of skewness and kurtosis obtained from 25 samples are smaller than the values of their standard deviations ssk and sku respectively and multiplied by 3 and 5 correspondingly, it is reasonable to assume that experimental data are distributed according to the normal (Gaussian) distribution. The values of standard deviations ssk and sku are only subject to the sample size and calculated according to the formulas given in the article [36]. The sample consisting of 25 separate samples can be expressed as 3ssk ¼ 1:39 and 5sku ¼ 4:51. Only the penetration of old BB|sk| = 1.563 is larger than the critical value of standard deviation 3ssk , which indicates that its (pen) separate values (single

Table 3 Statistical data on the amount of the recovered soluble old BB and mineral components present in the processed RAP (sample size n = 43). Statistical indicator

Mean Standard deviation xi;max xi;min Range (ai Þ Skewness (sk) Kurtosis (ku) CoV, %

Old BB content (%)

4.86 0.35 7.57 3.66 3.91 0.851 1.922 7.2

Mineral component composed of aggregate skeleton of the RAP, (%) Mineral filler (<0.063 mm)

Fine aggregate (0.063–2 mm)

Coarse aggregate (>2 mm)

11.5 1.27 14.2 8.4 5.8 0.121 0.288 11.0

40.0 5.65 52.1 19.1 33.0 1.156 3.589 14.1

48.5 6.76 70.9 33.7 37.2 0.795 2.078 13.9

Table 4 Statistical indicators of properties of old BB in processed RAP (sample size n = 25). Statistical indicator

Aged BB property Penetration at 25 °C 101 mm (pen),



Mean (x) Standard deviation (SD) Maximum (xi;max ) Minimum (xi;min ) Skewness (sk) Kurtosis (ku) CoV; %

Penetration index (PI)

Softening point °C (T sp )

Frass breaking point °C (T F )

Dynamic viscosity at °C Pa  s (gÞ

Kinematic viscosity

49.52

55.22

13.80

1075.6

727.8

0.1846

19.47 98.0 27.0 1.563 1.551 39.3

4.85 62.2 44.9 0.958 0.273 8.8

2.550 9.0 18.0 0.282 0.752 –

700.7 2614 144 0.630 0.381 65.1

240.8 1175 305 0.048 0.359 33.1

0.421 0.79 1.02 0.102 0.320 –

at 135 °C,

mm2 s

ðmÞ

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23

Fig. 1. Variation of properties of soluble old BB in processed RAP.

test results) are not normally distributed. According to skewness, the distribution of other indicators for BB quality agrees with normal distribution. According to kurtosis, the distribution of six analyzed quality indicators for old BB satisfies normal distribution, since their |ku| is less than 5sku . With reference to Eqs. (1) and (2), the calculated maximum allowable dosage of RAP shows that the maximum content (34.84%) can be proportioned according to the content of the mineral filler (particles less 0.063 mm) in RAP while the minimum content (8.43%) – according to that of the BB (Table 5). Therefore, the allowable content of the RAP defined according its homogeneity in the RHMA mixture equals 8.43%. This content of RAP is taken as a constant size when selecting the content of new materials in the RHMA mixture. Taking into account five indicators, the maximum allowable amount of RAP equal to 8.43% is calculated, which does not exceed

10% provided in [64] for mixtures of the mix group Asphalt Concrete. 3.2. Determining minimum cost of mineral part of RHMA mixture The problem of determining the minimal cost of mineral materials contained in the RHMA mixture was solved using the mathematical analogue (3). The following average costs of 1 ton of mineral materials were fixed: RAP – 12.00 €, non-activated dolomite imported filler – 30,00 €, natural quartz sand –1.50 €, granite sifting – 14.50 € and all fractions of crushed granite – 21.00 €. It is important to note that the price of RAP consists of two components: the price of the mineral part and the price of BB. Extracting from RAP BB, it turned out that it is 4.86%. We will use BB with the price of 1 tone of 220 €. Thus, the price of one ton of the mineral part in the RAP is 2.41 € like the price of BB is 9.59 €. These prices

Table 5 Variations in the properties of 25 separate samples taken from the RAP stockpile and the maximum allowable amount of a possible addition in RHM mixture. RAP properties

Old BB sofftening point T sp , °C BB content in RAP, % Mineral filler (<0.063 mm) content, % Fine aggregate (0.063 mm – 2 mm) content, % Coarse aggregate (>2.0 mm) content, %

Experimentally determined value xi;max

xi;min

62.2 7,57 14.2 52.1 70.9

44.9 3.66 8.4 19.1 33.7

Range ai

N adm;i

Estimated maximum (%) of RAP mass K i in recycled HMA mixture group of asphalt concrete AC16VS used in wearing course of pavement

17.3 3.91 5.8 33.0 37.2

8.0 1.0 6.0 16.0 16.0

23.12 (Eq.1) 8.43 (Eq.2) 34.84 (Eq.2) 16.00. (Eq.2) 14.19 (Eq.2)

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of materials are considered only for illustrating a numerical example and should not be used as permanent ones by all companies producing the asphalt mixture in any country. To show possibilities of mathematical analogue (3) three variants of designed RHMA mixture are presented in Table 6. In the first line of the Table 6, there are results obtained without any technological restrictions. Of course, the price of designed RHMA mixture is minimum. The second line contains the results obtained under accepted technological restriction and suggesting that the RHMA mixture should include 8.43% of RAP (Table 5). The third line contains the results obtained under accepted both technological restrictions and suggesting that the RHMA mixture should include 8.43% of RAP and technological restrictions indicating that the RHMA mixture should include four times more granite sifting (GS) than quartz natural sand (NS), ensuring fine aggregate of the required angular particles. It is evident that technological restrictions can be included subject to the goal of a designer (Table 6). It is clear, that under stronger technological restrictions, the cost of mineral materials of RHMA mixture increased.

Table 8 The limits on asphalt mixture AC 16 VS gradation accordingly the first and the last step of simulation. Sieve size (mm)

pL, 0.063 0.125 0.25 0.5 1 2 5.6 8 11.2 16 22.4

Limits on asphalt mixture gradation (sixth step)

Limits on asphalt mixture gradation (first step) PU,

i

5 7 14 20 26 35 54 62 70 90 100

pL,

i

9 17 24 30 36 45 66 76 85 100 100

PU,

i

6 9.5 16.5 22.50 28.50 37.50 56.75 65.5 73.75 92.50 92.50

i

8 14.5 21.5 27.5 33.50 42.5 63.25 72.50 81.25 100 100

fraction; b) bitumen capacities of the fine aggregate fractions from 0.063 mm to 2.00 mm have to be the same as NS; c) bitumen capacities and the fractions from 2.00 mm to 22.4 mm have to be the same as GS. The results of calculating minimal BB content using the mathematical analogue (4) are displayed in Table 11. The first line contains the solution when no technological restriction were introduced. The second line contains the results obtained under accepted technological restrictions and suggesting that the RHMA mixture should include 8.43% of RAP. The third line contains the results obtained under accepted both technological restrictions and suggesting that the RHMA mixture should include 8.43% RAP and technological restrictions indicating that the RHMA mixture should include four times more granite sifting (GS) than quartz natural sand (NS). It is evident that the technological restrictions can be included subject to goal of designer. It is clear, that under stronger technological restrictions, the content of bitumen in RHMA mixtures increased. It is possible for all recycled HMA mixture designed to obtain the cost of all mineral materials and the content of BB. In the Table 12. there are presented summary results obtained under accepted both technological restrictions and suggesting that the RHMA mixture should include 8.43% of RAP and technological restrictions indicating that the RHMA mixture should include four times more granite sifting (GS) than quartz natural sand (NS).

3.3. Designing the densest RHMA mixture For illustrating an algorithm for simulating the densest gradation of mineral part contained in the recycled HMA mixture, a problem of the minimal cost was selected. Also the technological restriction that the asphalt mixture should include 8.43% of RAP was accepted. It was assumed that following the usual step of calculation, the interval between the specific points pL;i andpU;i of gradation limit curves RHMA mixture was narrowed by 10%. Calculation results are presented in Table 7. When the seventh step was executed no result were obtained. The values of limits pL;i andpU;i corresponding first and sixth step are presented in Table 8. 3.4. Calculating minimum recycled BB content The percentage of the narrow fractions compounding the mineral materials and RAP of the designed RHMA mixture is presented in Table 9. Bitumen capacities (%) of the narrow fractions of mineral materials and RAP are presented in the Table 10. The bitumen capacities of the narrow fractions of the RAP was determined by assuming such assumptions: a) the bitumen capacity of the first narrow fraction (0–0.063 mm) is the same as that of IF of the same

Table 6 The minimal cost of the mineral part of designed asphalt mixture. Technological limitation

Content of mineral materials, %

No limitation RAP = 8.43% RAP = 8.43%, GS/NS = 4

Cost, EUR/ton

RAP

IF

NS

GS

CG4/8

CG8/11

CG11/16

0 8.43 8.43

2.02 1.11 0

62.03 57.50 12.81

0 0 51.37

0 0 0

19.68 17.05 0

16.27 15.90 27.38

5.43 8.33 13.60

Table 7 The results of calculating the densest gradation of the mineral part RHMA mixture. Technological limitation

Step No

RAP = 8.43%, GS/NS = 4

1 2 3 4 5 6

Content of mineral materials, %

Cost of the mineral part (EUR)

RAP

IF

NS

GS

CG4/8

CG8/11

GS 11/16

8.43 8.43 8.43 8.43 8.43 8.43

0 0 0 0 0 0

12.81 12.58 12.54 12.41 12.29 12.16

51.37 50.81 50.29 49.77 49.26 48.74

0 0 0 0 0 0

0 0 0 0 0 0.47

27.38 28.04 28.69 29.34 29.98 30.16

13.60 13.65 13.72 13.77 13.83 13.89

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Table 9 The percentage of the narrow fractions compounding the RAP and mineral materials of the RHMA mixture calculated using percent passing values (Table 2). Sieve size, mm (size fractions) passing 0.063 0.063–0.125 0.125–0.25 0.25–0.5 0.5–1 1–2 2–5.6 5.6–8 8.0–11.2 11.2–16 16–22.4 22.4–31.5 Total

Content of the narrow fraction, % RAP

IF

NS

GS

CG4/8

CG8/11

CG11/16

11.5 3.3 6.3 8.9 9.8 11.7 21.8 11.0 9.8 4.7 1.2 0 100

83.8 9.6 4.5 1.6 0.3 0.2 0 0 0 0 0 0 100

4.2 5.9 11.7 17.8 13.3 11.3 23.2 8.7 3.9 0 0 0 100

11.3 5.4 10.8 7.7 10.5 7.5 38.6 8.2 0 0 0 0 100

2.6 0.3 0.5 0.6 0.7 4.1 7.9 73.4 9.2 0.7 0 0 100

2.1 0.2 0.2 0.4 0.5 0.7 2.8 5.3 82.1 4.8 0.9 0 100

1.8 0.2 0.3 0.4 0.4 0.7 1.6 3.8 5.5 74.3 10.1 0.9 100

Table 10 Bitumen capacities (%) of the narrow fractions of mineral materials calculated from regression equations [1]. Size of the narrow fraction. (mm)

Average size (mm)

Less than 0.063 0.063–0.125 0.125–0.25 0.25–0.5 0.5–1 1–2 2–5.6 5.6–8 8–11.2 11.2–16 16–22.4 22.4–31.5

Bitumen capacity of the narrow fraction of the mineral material

0.02971 0.09049 0.18034 0.3607 0.7214 1.4427 3.4965 6.7289 9.5106 13.4578 19.0211 26.6923

RAP

IF

NS

GS

CG4/8

CG8/11

CG11/16

15.37 8.52 7.04 5.82 4.81 3.97 5.46 4.88 4.60 4.34 4.09 4.09

15.37 11.31 9.35 7.72 6.38 5.27 4.12 3.44 3.13 2.84 2.58 2.58

11.59 8.52 7.04 5.82 4.81 3.97 3.11 2.59 2.36 2.14 1.95 1.95

12.27 10.16 9.03 8.03 7.14 6.34 5.46 4.88 4.60 4.34 4.09 4.09

12.27 10.16 9.03 8.03 7.14 6.34 5.46 4.88 4.60 4.34 4.09 4.09

12.27 10.16 9.03 8.03 7.14 6.34 5.46 4.88 4.60 4.34 4.09 4.09

12.27 10.16 9.03 8.03 7.14 6.34 5.46 4.88 4.60 4.34 4.09 4.09

Table 11 The results of simulating minimum of BB content in the RHMA mixture. Technological limitation

No limitation RAP = 8.43% RAP = 8.43%. GS/NS = 4

Content of the stockpile mineral material %

Bitumen content, %

RAP

IF

NS

GS

CG4/8

CG8/11

CG11/16

0 8.43 8.43

2.08 1.42 0

62.1 55.80 10.52

0 0 42.08

0 0 0

0.786 0 4.82

35.12 34.49 34.17

5.00 5.05 5.89

Table 12 The results of simulating mineral materials and BB cost in the RHMA mixture. Criteria of optimization

Minimal cost of mineral part of RHMA mixture Maximal densest of RHMA mixture gradtion Minimal bitumen content

Content of the stockpile mineral material % RAP

IF

NS

GS

CG4/8

CG8/11

CG11/16

8.43 8.43 8.43

0 0 0

12.81 12.16 10.52

51.37 48.74 42.08

0 0 0

0 0.47 4.82

27.38 30.16 34.17

4. Conclusions 1. The amount of reclaimed asphalt pavement (RAP) added to the recycled hot-mix asphalt (RHMA) mixture decreases with an increase in the variation of the content of components and the properties of old BB present in RAP. RAP homogeneity is the most important quality indicator determining the maximum allowable dosage of RAP in the asphalt mixing plant (AMP) for producing the RHMA mixture. The maximum amount of RAP is calculated applying the principle of homogeneous using different formulae presented in normative documents and research papers. As for this work, the maximum amount

Cost of mineral materials, €/t

BB content, %

13.60 13.89 14.65

6.16 6.08 5.89

of RAP has been calculated considering five indicators having the greatest variation and investigated in the course of the experiment, i.e. BB content. The range of this indicator demonstrates that when asphalt mixture of the mix group Asphalt Concrete AC 16 VS of the RHMA mixture is used in the surface course of the pavement, the dosage of RAP cannot exceed 8.43%, which corresponds to 10% of RAP provided by European Standard EN 13108–1: 2006. 2. In comparison with the currently used techniques, the employed methodology for determining the composition of the mineral part and the total amount (old and new) of BB of the RHMA mixture has a number of advantages, which allows:

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(a) immediately determining whether an RHMA mixture of the desired gradation can be obtained from the available mineral materials; b) producing the RHMA mixture of the cheapest mineral part; c) obtaining the densest RHMA mixture; d) assessing technological etc. requirements; e) receiving and analysing solutions non-conforming to the Standard; f) defining the required amount of BB. 3. The presented methodology and algorithms for optimizing old and new materials can be applied at the initial stage of designing the recycled HMA mixture, which allows reducing the duration and cost of the entire design process. At the final stage of designing the RHMA mixture, in order to verify whether the considered amount of the total materials is appropriate, it is necessary to produce and test the specimens of the RHMA mixture under laboratory conditions applying Marshall, Superpave, Wheel tracking or other method. Conflict of interest There is no Conflict of interest. References  nas, Technological and economic design [1] H. Sivilevicˇius, K. Vislavicˇius, J. Brazˇiu of asphalt mixture composition based on optimization methods, Technol. Econ. Develop. Econ. 23 (4) (2017) 627–648, https://doi.org/10.3846/ 20294913.2017.1312631. [2] F.L. Roberts, L.N. Mohammad, L.B. Wang, History of hot-mix asphlt mixture design in the United States, J. Mater. Civ. Eng. 14 (4) (2002) 279–293, https:// doi.org/10.1061/(ASCE)0899-1561(2002) 14:4(279). [3] J.-C. Du, M.-F. Kuo, Grey relational-regression analysis for hot mix asphalt design, Constr. Build. Mater. 25 (5) (2011) 2627–2634, https://doi.org/10.1016/ j.conbuildmat.2010.12.011. [4] E.R. Brown, P.S. Kandhall, F.L. Roberts, Y.R. Kim, D.-Y. Lee, T.W. Kennedy, Hot Mix Asphalt Materials, Mixture Design, and Construction, third ed., NAPA Research and Education Foundation, Lanham, Maryland, 2009, p. 720. [5] P. Jitsangiam, P. Chindaprasirt, H. Nikraz, An evaluation of the suitability of SUPERPAVE and Marshall asphalt mix designs as they relate to Thailand’s climatic conditions, Constr. Build. Mater. 40 (2013) 961–970, https://doi.org/ 10.1016/j.conbuildmat.2012.11.011. [6] K. Awuah-Offei, H. Askari-Nasab, Asphalt mix design optimization for efficient plant management, Transp. Res. Rec. 2098 (2009) 105–112, https://doi.org/ 10.3141/2098-11. [7] M. Vadood, M.S. Johari, A.R. Rahaei, Introduction a simple method to determine aggregate gradation of hot mix asphalt using image processing, Int. J. Pavement Eng. 15 (1–2) (2014) 142–150, https://doi.org/10.1080/ 10298436.2013.786076. [8] A. Gaurin, R. Rique, S. Kim, O. Sirin, Disruption factor of asphalt mixtures, Int. J. Pavement Eng. 14 (5–6) (2013) 472–485. http://10.1080/10298436.2012. 727992. [9] H.R. Fischer, E.C. Dillingh, C.G.M. Hermse, On the interfacial interaction between bituminous binders and mineral surfaces as present in asphalt mixtures, Appl. Surf. Sci. 265 (2013) 495–499, https://doi.org/10.1016/j. apsusc.2012.11.034. [10] X. Ding, T. Ma, W. Zhang, D. Zhang, T. Yin, Effects by property homogeneity of aggregate skeleton on creep performance of asphalt concrete, Constr. Build. Mater. 171 (2018) 205–213, https://doi.org/10.1016/ j.conbuildmat.2018.03.150. [11] E. Remišová, Effect of film thickness on resistance to permanent deformation in asphalt mixtures, Balt. J. Road Bridge Eng. 10 (4) (2015) 333–339, https:// doi.org/10.3846/bjrbe.2015.42. [12] P. Hy´zl, O. Dašek, M. Varaus, D. Stehlik, P. Coufalik, J. Daškova, I. Krcˇmova, P. Nekulova, The effect of compaction degree and binder content on performance properties of asphalt mixtures, Balt. J. Road Bridge Eng. 11 (3) (2016) 222–232, https://doi.org/10.3846/bjrbe.2016.26. [13] E.H. Fini, I.L. Al-Qadi, T. Abu-Lebdeh, J.-F. Masson, Use of surface energy to evaluate adhesion of bituminous crack sealants to aggregates, Am. J. Eng. Appl. Sci. 4 (2) (2011) 244–251. [14] M. Arabani, G.H. Hamedi, Using the surface free energy method to evaluate the effects of liquid antistrip additives on moisture sensitivity in hot mix asphalt, Int. J. Pavement Eng. 15 (1–2) (2014) 66–78, https://doi.org/10.1080/ 10298436.2013.778410. [15] E. Özgan, S. Serin, T. Kap, Multi-faceted investigation into the effects of hotmix asphalt parameters on Marshall Stability, Constr. Build. Mater. 40 (2013) 419–425, https://doi.org/10.1016/j.conbuildmat.2012.11.002. [16] V. Rimša, R. Kacˇianauskas, H. Sivilevicˇius, Numerical analysis of asphalt mixture and comparison with physical Marshall test, J. Civ. Eng. Manage. 20 (4) (2014) 570–580, https://doi.org/10.3846/13923730.2014.920413.

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