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Modelling the flow of asphalt under simulated compaction using discrete element
Construction and Building Materials 227 (2019) 116432
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Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Modelling the flow of asphalt under simulated compaction using discrete element Ehsan Ghafoori Roozbahany a,b, Manfred N. Partl b, Denis Jelagin b a b
VTI Swedish National road and transport research institute, Olaus Magnus väg 35, Linköping 583 30, Sweden Department of Civil and Built Environment, KTH Royal Institute of Technology, Brinellvägen 23, Stockholm 10044, Sweden
h i g h l i g h t s Possible impacts of the design of the compaction Flow test (CFT) on its results were examined. CFT mold length of 150 mm is suitable for mixtures with NMASs up to 11 mm at wearing course thicknesses. Using the current rectangular loading strip in CFT is suitable for simulating the flow under large drum sizes. The loading rate of 15 mm/min seems suitable for the CFT as it allows mixtures to relax under loading at low viscosities.
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Article history: Received 20 December 2017 Received in revised form 17 May 2019 Accepted 17 July 2019
Keywords: Discrete element Asphalt compaction Compaction flow test Boundaries
a b s t r a c t The flow differences between the particles of asphalt mixtures compacted in the laboratory and in the field have been identified as one of the reasons for the discrepancies between laboratory and field results. In previous studies, the authors developed a simplified test method, the so-called compaction flow test (CFT), for roughly simulating the flow of particles in asphalt mixtures under compacting loads in laboratory. The CFT was used in different studies to examine its capability of revealing the differences between the flow behavior of different asphalt mixtures under various loading modes. The promising results encouraged further development of the CFT by investigating the possible impacts of simplifications and boundary conditions on the results of this test. For this reason, discrete element method (DEM) was utilized to investigate possible impacts of the mold size, geometry of the loading strip as well as the loading rate on the results of the CFT. The results of the simulation indicate that in case of wearing course layers with nominal maximum aggregate size of 11 mm, the length of the CFT mold can be increased from 150 mm to 200–250 mm for reducing flow disturbances from the mold walls. However, since the majority of the flow of asphalt mixture particles is expected to take place within the first 100–150 mm length of the mold, reasonable results can still be obtained even without changing the size of the CFT mold. Moreover, comparing results with different loading strip geometries and loading rates indicates that the current CFT setup still appears to provide consistent results. Ó 2019 Elsevier Ltd. All rights reserved.
1. Background Asphalt compaction is one of the most complex phases of the road construction. This complexity challenges the choice of the right compaction method for asphalt mixture with different characteristics. The suitability of the chosen compaction method is mostly assessed by means of the achieved density which is regarded as one of the most important factors that can reflect the strength and resistance of the compacted asphalt layer against the traffic and environmental loads. However, relying on the density as quality parameter may result in over-compaction and E-mail addresses: [email protected], [email protected] (E.G. Roozbahany) https://doi.org/10.1016/j.conbuildmat.2019.07.158 0950-0618/Ó 2019 Elsevier Ltd. All rights reserved.
crashing of aggregates in the mixture, thus lowering the mechanical functions of the layer. Therefore, the term ‘‘compactability” has been used to reflect the required effort for compacting an asphalt mixture until it reaches its expected density. The compactability on a laboratory level was determined with modified compaction simulators, such as gyratory compactors, that allowed measuring the required compaction energy for reaching a certain density of the mixtures [1]. This method appeared to be suitable for comparing mixtures with different characteristics. However, the setups of the gyratory and similar laboratory compactors have raised questions about how laboratory scale compactions can be related to real field situations. Literature [2], field observations and earlier studies by the authors [3] suggest that the material flow of asphalt
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mixtures under compacting loads in the field is not only vertical but also a combination of vertical and lateral movements, thus playing a prominent role in creating differences between laboratory and field compaction. Hence, information on the flow behavior of asphalt mixtures was found to be one key for avoiding overcompaction and for evaluating the compaction characteristics of different asphalt mixtures. Therefore, in an earlier study [4], the authors developed a simplified laboratory scale test method, the so called compaction flow test (CFT), for simulating the flow behavior of asphalt mixtures under the compacting loads. The test consists of a rectangular aluminum mold with bottom area 150 100 mm2 and an adjustable height for different lift thicknesses that is filled with a fresh asphalt mixture and is loaded from one side of the mold with a 50 mm wide loading strip, as shown in Fig. 1. This configuration allows the asphalt mixture to flow both vertically and laterally similar to what can possibly happen in the field not only in front but also at the edges of the roller compactor drum during the breakdown stage of compaction. In another study [5], the CFT was used for investigating the impact of mixture characteristics on the flow behavior and in several follow up studies [6–8] the CFT was used for investigating other important parameters such as lift thickness, static or dynamic compaction regime as well as roughness of the bottom surface. For studying the internal movements in the mixtures during the CFT, X-ray imaging was used. Trial CFT tests conducted on reference model materials [4] indicated that the internal movements in a mixture during the test strongly influence the uplifts appearing on the load free surface of the specimen. These uplifts were measured with an ultrasonic sensor alternatively to the X-ray imaging [5]. Analyzing the X-ray images from the CFT showed that coupling the uplift measurements and the results of the required compaction effort can help to distinguish the mixtures in a reasonable way. Comparing the results from all these studies showed that the CFT was able to rank the parameters with highest to lowest influence on the flow behavior of asphalt mixtures under compaction. Such findings suggested that the CFT may have the potential to become a simple but still effective on-site tool for assessing compactability of the mixtures right after production in an asphalt plant or before placing the mixture on the road. In this way, CFT measurements in the field may reveal the current condition of the mixture to the construction crew and help them make adjustments for achieving better compaction results. However, before using the CFT as an on-site tool, it is vital to understand its boundaries and the effect of its design on the results. Hence, the intention of this study is to examine the possible impacts of the CFT design and boundaries on its results. Using modeling tools for simulating the extreme cases seems to be the most efficient way in this regard since it allows studying the different influential factors independently without being biased by experimental side effects.
Since the main focus of the CFT is on the flow of particles in the asphalt mixture, discrete element method (DEM) appears most suitable as it enables generating idealized asphalt mixtures composed of individual particles, thus providing enough flexibility to simulate various conditions with a minimum of effort. The particle flow code, PFC [9], is a commercially available DEM software that uses the Newton’s force-displacement law. It has been widely applied for simulating rock mechanical as well as asphalt pavement problems in both 2D and 3D. In this study, pfc3DÒ version 4 is used for conducting a parametric study on the possible impacts on the CFT results due to changing parameters such as mold size, and loading strip geometry and rate. 2. Methodology In this section, assumptions, variations and input values for generating the idealized model specimens of this study are described in detail. 2.1. Mixture gradation All earlier studies [4–8] confirmed that gradation has the highest impact on the flow behavior of the mixtures under compacting loads. In the same studies, it was demonstrated that under a certain imposed displacement, mixtures with coarse structures show high flow and require high compaction efforts. Therefore, a coarse graded mixture consisting of spherical particles was generated for studying an extreme situation that could produce maximum possible flow in the CFT. Since the CFT has mostly been used for testing asphalt mixtures with nominal maximum aggregate size (NMAS) of 11 mm, it was decided to consider the coarsest possible case passing from the sieve size number 16 and remaining on number 4. The size distribution of the generated particles is shown in Fig. 2. The size distribution in this study was chosen based on the relative portion ratios among the coarse aggregate sizes in a typical stone mastic asphalt (SMA) with the NMAS of 11 mm in Sweden. 2.2. Particles interaction The interaction among particles was simulated using two contact models, i.e. elastic and viscoelastic, as briefly described below. 2.2.1. Elastic contact model The linear elastic contact model uses normal (kn) and shear (ks) spring stiffness assigned to each particle, Fig. 3, as inputs for calculating the contact stiffness between two contacting particles. Assuming the particles to act in series, Eqs. (1) and (2) then used for obtaining the contact normal (Kn) and shear (Ks) stiffness. The slipping behavior between two contacting particles at the contact points was also defined by a friction coefficient l [9]. A
B
A
B
ð1Þ
A
B
A
B
ð2Þ
K n ¼ ðkn kn Þ=ðkn þ kn Þ K s ¼ ðks ks Þ=ðks þ ks Þ
Obviously, this assumption is a very rough approximation for simulating the mixture behavior. However, as shown in earlier studies [10,11], it enables a qualitative representation of the flow behavior of the mixtures. The required input values, i.e. normal kn and shear ks stiffness for generated particles was calculated using the suggested equations in the literature [12], as shown in Eqs. (3) and (4). Where E and G were the Young’s and Shear moduli of the aggregate, and ‘‘R” was the radius of the generated particle.
kn ¼ 4 E R
Fig. 1. Schema of the compaction flow test (CFT).
ð3Þ
3
E. Ghafoori Roozbahany et al. / Construction and Building Materials 227 (2019) 116432 Table 1 Burger’s model parameters for mastic at 150 °C [16]. E1 (MPa)
g1 (MPas)
E2 (MPa)
g2 (MPas)
15.996
652.714
10.891
1.898
Fig. 2. Size distribution of the generated particles.
Fig. 5. Micro behaviors of two contacting particles in (a) normal and (b) shear directions.
Fig. 3. Schema of the linear elastic model in (a) normal and (b) shear directions.
ks ¼ 4 G R
ð4Þ
Because granite is widely used for asphalt mixtures in Sweden, simulations in this study were performed with the shear modulus G and tg Poisson’s ratio of the particles of 27GPa and 0.25 respectively. Hence, the input value for Young’s modulus was calculated using Eq. (5).
E ¼ 2 G ð1 þ tg Þ
ð5Þ
In order to lower the computational time, the calculated normal and shear stiffness were lowered by a factor of 1000. 2.2.2. Viscoelastic contact model In many studies, e.g. [13–15], the Burger’s model has been used to simulate the viscoelastic behavior of mastics in asphalt mixtures. Since simulating the mastics would substantially increase the simulation time, the authors used the Burger’s model for introducing viscoelasticity among the contact points of the generated particles in the previous section. The Burger’s contact model consists of Maxwell and Kelvin parts as shown in Fig. 4; where E1 and g1 are modulus of immediate elasticity and coefficient of viscosity respectively; and E2 and g 2 are modulus of delayed elasticity and coefficient of elastic delay viscosity respectively. Normally, from the laboratory tests the macro scale behavior of the mastics can be obtained. For example, Chen et al. in 2011 [16] calculated the viscoelastic input values for mastics with maximum aggregate size of 2.36 mm that were also used in this study as input values (Table 1). As suggested in the literature [17], Eqs. (6)–(9) used for converting the macro scale results of the mastics to the micro scale input parameters (Fig. 5) in both normal and shear directions that can be used among the contacting particles.
Kmn ¼ E1 L;
Kms ¼ E1 L=ð1 þ tt Þ
ð6Þ
gmn ¼ g1 L; gms ¼ g1 L=ð1 þ tt Þ
ð7Þ
Kks ¼ E2 L=ð1 þ tt Þ
ð8Þ
gkn ¼ g2 L; gks ¼ g2 L=ð1 þ tt Þ
ð9Þ
Kkn ¼ E2 L;
The parameters with initial index of m belong to the Maxwell section and those with the initial index of k belong to the Kelvin part. The second index stands for the direction of the element, i.e. n means normal and s shear. tt is the Poisson’s ratio of the mastics that was assumed in one case incompressible, hence, chosen to be 0.5 [18]. The ‘‘L” was assumed 1 mm, implying a fictitious constant film thickness of mastic acting among all contacting particles. Obviously, the assumptions made for this study are not pretending to represent the exact behavior of asphalt mixtures but are expected to help simulating flow patterns similar to those observed in the earlier experiments. 2.3. Mold size The X-ray image analysis on real CFT specimens [4], confirmed that the movements in the XY plane, Fig. 1, were minor as compared with those in the XZ plane. Hence, in order to lower the computation time in this study, the width of the fictitious mold for the simulation was reduced from 100 mm in the real tests to 80 mm which still is large enough, i.e. 5 times larger than the largest generated particle size. Since the CFT must also be suitable for investigating the flow behavior of wearing course layers, the minimum and optimum lift thicknesses recommended for wearing course layers, i.e. 2.5 and 4 times the NMAS, were chosen for generating the height of the fictitious specimens for the simulation. In addition, a 25% higher lift was considered for the loose specimen before compaction. Hence, molds with heights of 35 mm and 55 mm were generated as shown in Fig. 6. Moreover, it is necessary to investigate whether the mold size affects the flow behavior of mixtures tested with the CFT. Therefore, in addition to the original length of the CFT mold, i.e. 150 mm, another mold with double length (300 mm) was generated (Fig. 7). The generated walls of the mold were given higher stiffness input values than the generated particles. Therefore, the normal and shear stiffness of the walls were assumed 20 GPa and 8 GPa respectively. 2.4. Loading strip geometries
Fig. 4. The schema of the Burger’s model (macro scale behavior).
When developing the CFT, a rectangular loading strip was chosen since this configuration was expected to represent the situation at the edges of a roller compactor drum passing on a newly placed asphalt layer. It was also assumed that this could roughly simulate the compaction in front of a large roller compactor drum with the contact surface length as large as one third of the total specimen length. However, since there are numerous roller compactors with different wheel sizes, in this study, the influence of curvature of the roller drum on the CFT results was evaluated by changing the geometry of the loading strip. In order to account for an extreme case, the rectangular loading strip (Fig. 8a) was compared with an angular one (Fig. 8b) with an inclination of 6°, accounting for a fictitious roller drum with a relatively small diameter of 500 mm (Fig. 8).
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Fig. 6. Generated CFT molds for lift thicknesses of 2.5 and 4 times the NMAS.
Fig. 7. The CFT mold with 300 m of length for measuring the effective length where most of the flow in the XZ plane takes place.
Fig. 8. (a) Rectangular loading strip; (b) angular loading strip.
In this study, the inputs for the loading walls were assumed the same as the ones chosen for the generated mold walls.
3. Results and discussions The presented results for each case are mean values of simulations with 3 randomly generated particle configurations. Below, the results from elastic and viscoelastic simulations are presented separately.
parameters for generating a reasonably comparable flow of particles in the simulation. In order to compare the obtained results from the experiments with those in the generated models, the embedded 10 mm screws, used in the experiments in Fig. 9, were represented by spherical particles with the diameter of 10 mm in the generated models, Fig. 10. The idea was to find proper friction coefficients for the generated particles and mold walls which would result in forming a flow pattern larger than those observed in the experiments. Hence, a mold size of 150 80 50 mm3 was generated and filled with the particle size distribution mentioned in Section 2.1 with using different friction coefficients and porosities; then, the generated models were loaded with loading rate of 15 mm/min similar to the CFT setup. The loading surface was assigned the same input values as the generated mold walls. After examining a large number of try and errors, the friction coefficients of 1 and 0.05 were chosen for the particles and the mold walls respectively. In addition, the chosen porosity of the generated model was 42%. As a result, the detected flow of the chosen particles in the model, Fig. 10, surpassed the movements of the screws in the experiments, suggesting to be a suitable choice for examining the boundaries of the CFT setup, see Fig. 11. Since the size distribution as well as the chosen input parameters appeared to provide a more critical behavior than the real wearing course mixtures, the same parameters were used in this study for investigating the possible impact of the changes of the mold size as well as the loading geometry and rate on the expected flow in CFT. In the following, the results for the impact of the mold size and the change of loading strip geometry on the flow of particles under linear elastic conditions are presented.
3.1. Elastic simulation 3.1.1. Determining complementary input parameters In order to check the boundaries of the CFT setup, input parameters had to be found that can provide a flow higher than those obtained in earlier CFT studies. In a previous study [7], the authors filled a CFT mold of 150x100x50mm3 with SMA11 and for investigating flow at different regions of the specimens used steel screws as shown in Fig. 9. The results of the flow measurements obtained from that study were taken as a reference for obtaining the input
3.1.2. Mold size As described in the methodology part, the mold sizes of 300 80 55 mm3 and 300 80 35 mm3 were generated and filled with similar particle size distribution and porosity used in the previous section. However, the imposed displacement was increased from 25% to 30% of the mold total height for making the flow even more extreme. Fig. 12 shows examples of the simulations on the larger size molds with different heights. Each spec-
Fig. 9. An example of the obtained X-ray images before (left) and after (right) the CFT.
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Fig. 10. Using 10 mm spherical particles at different locations of generated CFT models for flow comparisons with the experiments.
Fig. 11. Comparison between the movements of the experiments and the generated model (units in mm).
imen was vertically loaded by means of a rectangular loading strip with a loading surface 50 80 mm2 and the speed of 15 mm/min, as also shown in Fig. 7. For each height, three random replicates were generated and an average among the movements of the chosen particles were obtained for each region. As the results indicate in Fig. 13, the highest movements of the particles were recorded within the first 150 mm of the mold from the loading side; however, in the second half of the mold the movements are limited. In order to have a better understanding of the overall flow within the generated CFT specimens with a larger mold size, the total movements of the generated particles in horizontal (X) and vertical (Z) directions for each region were obtained as shown in Fig. 14. The results of the simulation, shown in Fig. 14, show that most of the horizontal flow towards the load free side of the CFT molds occurred within the first half of the mold (0–150 mm) and substantially decreased in the second half (150–300 mm). This also holds for vertical movements of the thinner specimen. However,
the maximum share of the total vertical movements for the thicker specimen is still considerable within the first 20 mm. This also confirms the earlier experimental results [6], which indicated that thin lift thicknesses reduce the size of the shear planes in the specimen. Considering the fact that the loading condition was extreme and higher than the 25% additional height initially assumed for the generated models, it is expected that the impact of the CFT on the flow in normal loading conditions would be lower than the observed results in this simulation. In order to examine the validity of the obtained results, a limited number of CFT was carried out in the laboratory using a rectangular mold of 275 180 60 mm3. The mold was filled with a SMA11 mixture and loaded with a loading rate of 15 mm/min until reaching 30% of its total height. The results, shown in Fig. 15, indicates that in spite of the large displacement imposed to the specimens, the horizontal flow of particles are high in the first 150 mm of the mold and then starts to decrease gradually until it dramatically drops after 205 mm. The shear plane from the tracks on the side walls of the CFT mold showed that the vertical movements under the extreme loading conditions can reach between 200 and 210 mm of the mold in its larger dimension. Hence, the experimental results indicated that despite of the simplicity of the generated models, the obtained results from the simulations provided extreme conditions comparable to the reality. Based on the simulation and experimental results, it could be concluded that increasing the mold length from 150 mm to 200– 250 mm may help avoiding the disturbance of the flow of the asphalt mixtures with NMAS of 11 mm in the CFT. However, using the 150 mm size mold under the normal CFT loading conditions can still be reasonable as it does not seem to compromise the results significantly and makes the preparation and handling of the specimens faster, more efficient and easier.
Fig. 12. Examples of the generated assemblies for examining the impact of the mold size on the CFT flow in extreme cases.
Fig. 13. Averages of movements of the chosen particles in different regions of the generated specimens.
E. Ghafoori Roozbahany et al. / Construction and Building Materials 227 (2019) 116432
100-150 (mm)
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300mm Fig. 14. Expected shares of total vertical and horizontal movements (the summation of the absolute movements of all particles in horizontal and vertical directions) in the XZ plane in different zones of the two mold sizes 300 80 55 mm3 (top) and 300 80 35 mm3 (bottom); the presented results were obtained from calculating the mean value of 3 replicates.
3.1.3. Effect of loading strip geometry Two loading strip geometries were simulated in this study as explained and demonstrated earlier in Fig. 8. Fig. 16 shows that the change of the loading strip from rectangular to the angular one appears to decrease the total horizontal and vertical flow of the generated particles in the simulated CFT specimens. For the thicker specimens, the total horizontal and vertical movements under the angular loading strip were lower than those under the rectangular loading strip as much as 22% and 23% respectively. These reductions appeared to be more significant in the thinner specimens as the total horizontal and vertical movements under the angular loading strip were reduced as much as 38% and 35% respectively comparing to those under the rectangular one. The most significant differences between the results of these two loading strip geometries were recorded in the 100–150 mm region. This suggests that the rollers with larger drums provide more significant flow than those with smaller drums ahead of the compacting load location. The comparison between the directions and intensity of the movements of the embedded particles in different regions of the simulated CFT molds, Fig. 17, also indicated the impact of the angular loading strip on the overall flow. Such results indicate the effectiveness and reliability of using embedded particles in CFT specimens when carrying out in-depth studies on the overall flow behavior of asphalt mixtures with the X-ray CT or other flow tracking methods [19].
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Fig. 16. Impact of changing the loading strip geometry on the horizontal and vertical flow of particles (each value was obtained from an average among 3 replicates.)
3.2. Viscoelastic simulation 3.2.1. Mold size As expected, adding the chosen viscoelastic properties among the particle contacts lowered the lateral flow of particles since it lowered the stiffness at the contact points among the particles. The results of the simulation summarized in Fig. 18 also prove that the overall flow of particles was reduced when using viscoelastic inputs as compared with the elastic ones. This suggests that the given input values lowered the shear plane size of the flow, limiting the length of lateral particle rearrangements. Such results were also qualitatively observed in an earlier study [4] when the flow of an aggregate assembly with and without bitumen was compared using the CFT. Hence, since the elastic simulation led to more extreme conditions relevant for the mold size optimization, the calculations for the mold size were not carried out in the viscoelastic simulation. 3.2.2. Effect of loading strip geometry Similar to the elastic simulation, the calculation of the flow was also carried out with the viscoelastic contact properties. Fig. 19 shows the results of the vertical and horizontal movements of particles in the XZ plane when compacted with the two chosen loading strips. Similar to the elastic simulation, the overall horizontal and vertical movements were higher when loading with the rectangular loading strip for both specimen thicknesses. The difference of total horizontal movements for the thicker specimens under the two loading strip geometries was 24% and it was 30% in the case of the thinner generated specimens. The results also indicate that the total vertical movements in thicker simulated specimens loaded with the rectangular loading strip was 28% higher than those loaded with the angular loading strip. Similar comparison for the thinner simulated specimens also shows this increment as much as 38%. It can be noticed that the change of the contact models did not have a significant impact on the recorded differences
Fig. 15. Left: the footprint of the asphalt mixture particles in the horizontal direction on the large CFT mold walls; right: the shear plane formed on the sidewall of the large CFT mold.
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Fig. 17. The XZ plane movements of the embedded spheres under different loading strip geometries; black arrows show the rectangular and the gray ones represent the angular loading geometries. (Units are in mm.)
50-100 mm
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11%
18%
59%
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10%
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compaction which can increase the repeatability of the test. Therefore, it still seems reasonable to keep the CFT setup as simple as it is with the rectangular loading strip.
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Fig. 19. The impact of the loading strip geometry change on the horizontal and vertical flows of particles (Each value was obtained from an average among 3 replicates.)
Total vertical movements (mm)
between the simulated flow under the rectangular and angular loading strips. The obtained results from the elastic and viscoelastic simulations revealed the possible differences between the flow behavior of asphalt mixtures loaded with the rectangular and angular loading strips. However, it is important to understand that the chosen drum diameter of 500 mm was an extremely small size and the compactor drum sizes used for medium and large scale road projects normally have less than 2° initial inclination when touching the newly laid asphalt layer. In addition, using a rectangular loading strip in the CFT setup allows a more regular and uniform
5000 4000 3000 2000 1000 0
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Fig. 18. The percentages of decrease in the overall particle flow in the viscoelastic simulations comparing with the results of the elastic simulations in the XZ plane.
3.2.3. Change of loading rate In order to examine the sensitivity of the CFT results to the loading rate, in addition to the selected CFT loading rate 15 mm/min, other loading rates were also used in the simulations, increasing the loading rate by factors of 5 and 10. All simulations were carried out on the mold size of 150 80 55 m3. The impact of the change in loading rate was studied by calculating the sum of the movements of all the particles in vertical direction as well as the vertical movements of all particles overflowing the top edge of the load free side of the mold during the simulation of the test. The results from changing the loading rate show that increasing the rate of 15 mm/min up to about 10 times also increases the total vertical flow of the DEM generated particles (Fig. 20a). In addition, the results of vertical movements rising above the top edge of the mold on the load free side of the simulated specimens, Fig. 20b, also indicate that the uplift movements become very close at high loading rates as compared to slower loading rates. Hence, the chosen loading rate of 15 mm/min seems to be reasonable for the CFT as it allows the material to relax during the test for the assemblies with rather low viscosities, thus roughly representing conditions of asphalt mixtures at high temperatures. Obviously, lowering the loading rate even below 15 mm/min can allow more relaxation of the material during the CFT; however, it may also allow the mixture to cool down during the test, thus increasing the viscosity of the mixture during the test more significantly than when tested with 15 mm/min. Besides, rapid loading can result in crashing the aggregates under the loading that can significantly affect the CFT results. Hence, the loading rate of 15 mm/min was still considered appropriate for performing CFT. It is important to note that the crashing of the aggregates during the loading was not experimentally examined in this study and is
500 419
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50 100 150 Loading rate (mm/min)
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b
Fig. 20. (a) Total vertical movements and (b) vertical movements higher than the mold edge on the load free side of the simulated CFT for the specimen size of 150 80 55 m3.
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intended to be explored in detail in upcoming studies by the authors. 4. Conclusions The results of the discrete element simulation of the CFT with pfc3D in this study with respect of the different influence parameters relevant for the optimization of the CFT are as follows: – The simulation showed that, no matter how large the length of the CFT mold would be, the majority of the flow for the extremely coarse assembly of large spherical particles with the NMAS of 11 mm and with the lift thicknesses of the wearing course occurs within the first 150 mm of the mold, close to the loading strip. This shows that the current CFT mold length is suitable for testing standard mixtures with NMASs up to 11 mm. However, for mixtures with larger NMAS, similar parameter studies would have to be carried out. – The results of this study show that the current rectangular loading strip used in the CFT setup may require adjustments for a better simulation of the flow under small roller drums. However, it still seems reasonable to use the rectangular loading strip in the CFT setup for simulating the flow under larger drum sizes, normally used for medium and large size road constructions, as it simplifies the test setup for the further use in the field without compromising the results dramatically. – Changing the loading rate appears to have a substantial impact on the CFT results. The DEM simulation suggests that the current loading rate of the CFT, i.e. 15 mm/min, seems to be a suitable choice as it is slow enough to allow the specimens to relax under the loading at low viscosities. However, it is still fast enough to avoid high temperature loss during the test.
Declaration of Competing Interest There is no conflict of interest in this paper. Acknowledgment The authors would like to acknowledge the financial support provided by Swedish road administration (Trafikverket) and also Swedish Research Council Formas for this study.
References [1] H. Bahia, T. Friemel, P. Peterson, J. Russell, Optimization of constructibility and resistance to traffic: a new design approach for HMA using the superpave compactor, J. Assoc. Asphalt Paving Technol. 67 (1998) 189–232. [2] K. Mollenhauer, M.P. Wistuba, Influence of asphalt compaction procedure on 3D deformation properties, Int. J. Pavement Eng. 17 (1) (2016) 5–12. [3] E. Ghafoori Roozbahany, M.N. Partl, P.J. Witkiewicz, Fracture testing for the evaluation of asphalt pavement joints, Road Mater. Pavement Des. 14 (4) (2013) 764–791. [4] E. Ghafoori Roozbahany, M.N. Partl, A. Guarin, Particle flow during compaction of asphalt model materials, Constr. Build. Mater. 100 (2015) 273–284. [5] E. Ghafoori Roozbahany, M.N. Partl, A new test to study the flow of mixtures at early stages of compaction, Mater. Struct. 49 (9) (2016) 3547–3558. [6] E. Ghafoori Roozbahany, M.N. Partl, A. Guarin, Influence of layer thickness on the flow of asphalt under simulated compaction, in: 10th International Conference on the Bearing Capacity of Roads, Railways and Airfields, Athens, Greece, June 28–30, 2017. [7] E. Ghafoori Roozbahany, A. Guarin, M.N. Partl, Influence of static and vibratory compaction on the flow behavior of asphalt surface courses, in: 71st RILEM Week and International Conference on Advances in Construction Materials and Systems, Chennai, India, September 3–8, 2017. [8] E. Ghafoori Roozbahany, M.N. Partl, A. Guarin, Monitoring the flow of asphalt mixtures compacted on two different rough surfaces, in: 4th Conference on Smart Monitoring, Assessment and Rehabilitation of Civil Structures, Zurich, Switzerland, September 13–15, 2017. [9] Itasca Consulting Group Inc. PFC2D/3D (Particle Flow Code in 2/3 Dimensions), Version 2.0. Minneapolis, MN: ICG, 1999. [10] A. Abbas, E. Masad, T. Papagiannakis, A. Shenoy, Modelling asphalt mastic stiffness using discrete element analysis and micromechanics-based models, Int. J. Pavement Eng. 6 (2) (2005) 137–146. [11] Q.L. Dai, Z. You, Prediction of creep stiffness of asphalt mixture with micromechanical finite element and discrete element models, J. Eng. Mech. 133 (2) (2007) 163–173, https://doi.org/10.1061/(ASCE)0733-9399(2007) 133:2(163). [12] S. Adhikari, Z. You, 3D discrete element models of the hollow cylindrical asphalt concrete specimens subject to the internal pressure, Int. J. Pavement Eng. 11 (5) (2010) 429–439. [13] G. Chang, J. Meegoda, Micromechanical model for temperature effects of hotmix asphalt concrete, Transp. Res. Rec.: J. Transp. Res. Board 1687 (1999) 95– 103. [14] A.C. Collop, G.R. McDowell, Y. Lee, Use of the distinct element method to model the deformation behavior of an idealized asphalt mixture, Int. J. Pavement Eng. 5 (1) (2004) 1–7. [15] H. Kim, W.G. Buttlar, Micro mechanical fracture modelling of asphalt mixture using the discrete element method, in: C.W. Schwartz, E. Utumluer, L. Tashman (Eds.), GSP 130: Advances in Pavement Engineering, Proc., Sessions of the Geo-Frontiers 2005 Congress, ASCE, Reston, Va., 2005, pp. 209–223. [16] J. Chen, B. Huang, X. Shu, Air-void distribution analysis of asphalt mixture using discrete element method, J. Mater. Civ. Eng. 25 (10) (2012) 1375–1385. [17] Y. Liu, Q. Dai, Z. You, Viscoelastic model for discrete element simulation of asphalt mixtures, J. Eng. Mech. 135 (4) (2009) 324–333. [18] D.W. Christensen, Jr., D.A. Anderson, Interpretation of dynamic mechanical test data for paving grade asphalt, Charleston, S.C., 1992, pp. 67–116. [19] E. Ghafoori Roozbahany, M.N. Partl, A. Guarin, Introducing a new method for studying the field compaction, Road Mater. Pavement Des. (2017) 1–13.
Contents lists available at ScienceDirect
Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Modelling the flow of asphalt under simulated compaction using discrete element Ehsan Ghafoori Roozbahany a,b, Manfred N. Partl b, Denis Jelagin b a b
VTI Swedish National road and transport research institute, Olaus Magnus väg 35, Linköping 583 30, Sweden Department of Civil and Built Environment, KTH Royal Institute of Technology, Brinellvägen 23, Stockholm 10044, Sweden
h i g h l i g h t s Possible impacts of the design of the compaction Flow test (CFT) on its results were examined. CFT mold length of 150 mm is suitable for mixtures with NMASs up to 11 mm at wearing course thicknesses. Using the current rectangular loading strip in CFT is suitable for simulating the flow under large drum sizes. The loading rate of 15 mm/min seems suitable for the CFT as it allows mixtures to relax under loading at low viscosities.
a r t i c l e
i n f o
Article history: Received 20 December 2017 Received in revised form 17 May 2019 Accepted 17 July 2019
Keywords: Discrete element Asphalt compaction Compaction flow test Boundaries
a b s t r a c t The flow differences between the particles of asphalt mixtures compacted in the laboratory and in the field have been identified as one of the reasons for the discrepancies between laboratory and field results. In previous studies, the authors developed a simplified test method, the so-called compaction flow test (CFT), for roughly simulating the flow of particles in asphalt mixtures under compacting loads in laboratory. The CFT was used in different studies to examine its capability of revealing the differences between the flow behavior of different asphalt mixtures under various loading modes. The promising results encouraged further development of the CFT by investigating the possible impacts of simplifications and boundary conditions on the results of this test. For this reason, discrete element method (DEM) was utilized to investigate possible impacts of the mold size, geometry of the loading strip as well as the loading rate on the results of the CFT. The results of the simulation indicate that in case of wearing course layers with nominal maximum aggregate size of 11 mm, the length of the CFT mold can be increased from 150 mm to 200–250 mm for reducing flow disturbances from the mold walls. However, since the majority of the flow of asphalt mixture particles is expected to take place within the first 100–150 mm length of the mold, reasonable results can still be obtained even without changing the size of the CFT mold. Moreover, comparing results with different loading strip geometries and loading rates indicates that the current CFT setup still appears to provide consistent results. Ó 2019 Elsevier Ltd. All rights reserved.
1. Background Asphalt compaction is one of the most complex phases of the road construction. This complexity challenges the choice of the right compaction method for asphalt mixture with different characteristics. The suitability of the chosen compaction method is mostly assessed by means of the achieved density which is regarded as one of the most important factors that can reflect the strength and resistance of the compacted asphalt layer against the traffic and environmental loads. However, relying on the density as quality parameter may result in over-compaction and E-mail addresses: [email protected], [email protected] (E.G. Roozbahany) https://doi.org/10.1016/j.conbuildmat.2019.07.158 0950-0618/Ó 2019 Elsevier Ltd. All rights reserved.
crashing of aggregates in the mixture, thus lowering the mechanical functions of the layer. Therefore, the term ‘‘compactability” has been used to reflect the required effort for compacting an asphalt mixture until it reaches its expected density. The compactability on a laboratory level was determined with modified compaction simulators, such as gyratory compactors, that allowed measuring the required compaction energy for reaching a certain density of the mixtures [1]. This method appeared to be suitable for comparing mixtures with different characteristics. However, the setups of the gyratory and similar laboratory compactors have raised questions about how laboratory scale compactions can be related to real field situations. Literature [2], field observations and earlier studies by the authors [3] suggest that the material flow of asphalt
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mixtures under compacting loads in the field is not only vertical but also a combination of vertical and lateral movements, thus playing a prominent role in creating differences between laboratory and field compaction. Hence, information on the flow behavior of asphalt mixtures was found to be one key for avoiding overcompaction and for evaluating the compaction characteristics of different asphalt mixtures. Therefore, in an earlier study [4], the authors developed a simplified laboratory scale test method, the so called compaction flow test (CFT), for simulating the flow behavior of asphalt mixtures under the compacting loads. The test consists of a rectangular aluminum mold with bottom area 150 100 mm2 and an adjustable height for different lift thicknesses that is filled with a fresh asphalt mixture and is loaded from one side of the mold with a 50 mm wide loading strip, as shown in Fig. 1. This configuration allows the asphalt mixture to flow both vertically and laterally similar to what can possibly happen in the field not only in front but also at the edges of the roller compactor drum during the breakdown stage of compaction. In another study [5], the CFT was used for investigating the impact of mixture characteristics on the flow behavior and in several follow up studies [6–8] the CFT was used for investigating other important parameters such as lift thickness, static or dynamic compaction regime as well as roughness of the bottom surface. For studying the internal movements in the mixtures during the CFT, X-ray imaging was used. Trial CFT tests conducted on reference model materials [4] indicated that the internal movements in a mixture during the test strongly influence the uplifts appearing on the load free surface of the specimen. These uplifts were measured with an ultrasonic sensor alternatively to the X-ray imaging [5]. Analyzing the X-ray images from the CFT showed that coupling the uplift measurements and the results of the required compaction effort can help to distinguish the mixtures in a reasonable way. Comparing the results from all these studies showed that the CFT was able to rank the parameters with highest to lowest influence on the flow behavior of asphalt mixtures under compaction. Such findings suggested that the CFT may have the potential to become a simple but still effective on-site tool for assessing compactability of the mixtures right after production in an asphalt plant or before placing the mixture on the road. In this way, CFT measurements in the field may reveal the current condition of the mixture to the construction crew and help them make adjustments for achieving better compaction results. However, before using the CFT as an on-site tool, it is vital to understand its boundaries and the effect of its design on the results. Hence, the intention of this study is to examine the possible impacts of the CFT design and boundaries on its results. Using modeling tools for simulating the extreme cases seems to be the most efficient way in this regard since it allows studying the different influential factors independently without being biased by experimental side effects.
Since the main focus of the CFT is on the flow of particles in the asphalt mixture, discrete element method (DEM) appears most suitable as it enables generating idealized asphalt mixtures composed of individual particles, thus providing enough flexibility to simulate various conditions with a minimum of effort. The particle flow code, PFC [9], is a commercially available DEM software that uses the Newton’s force-displacement law. It has been widely applied for simulating rock mechanical as well as asphalt pavement problems in both 2D and 3D. In this study, pfc3DÒ version 4 is used for conducting a parametric study on the possible impacts on the CFT results due to changing parameters such as mold size, and loading strip geometry and rate. 2. Methodology In this section, assumptions, variations and input values for generating the idealized model specimens of this study are described in detail. 2.1. Mixture gradation All earlier studies [4–8] confirmed that gradation has the highest impact on the flow behavior of the mixtures under compacting loads. In the same studies, it was demonstrated that under a certain imposed displacement, mixtures with coarse structures show high flow and require high compaction efforts. Therefore, a coarse graded mixture consisting of spherical particles was generated for studying an extreme situation that could produce maximum possible flow in the CFT. Since the CFT has mostly been used for testing asphalt mixtures with nominal maximum aggregate size (NMAS) of 11 mm, it was decided to consider the coarsest possible case passing from the sieve size number 16 and remaining on number 4. The size distribution of the generated particles is shown in Fig. 2. The size distribution in this study was chosen based on the relative portion ratios among the coarse aggregate sizes in a typical stone mastic asphalt (SMA) with the NMAS of 11 mm in Sweden. 2.2. Particles interaction The interaction among particles was simulated using two contact models, i.e. elastic and viscoelastic, as briefly described below. 2.2.1. Elastic contact model The linear elastic contact model uses normal (kn) and shear (ks) spring stiffness assigned to each particle, Fig. 3, as inputs for calculating the contact stiffness between two contacting particles. Assuming the particles to act in series, Eqs. (1) and (2) then used for obtaining the contact normal (Kn) and shear (Ks) stiffness. The slipping behavior between two contacting particles at the contact points was also defined by a friction coefficient l [9]. A
B
A
B
ð1Þ
A
B
A
B
ð2Þ
K n ¼ ðkn kn Þ=ðkn þ kn Þ K s ¼ ðks ks Þ=ðks þ ks Þ
Obviously, this assumption is a very rough approximation for simulating the mixture behavior. However, as shown in earlier studies [10,11], it enables a qualitative representation of the flow behavior of the mixtures. The required input values, i.e. normal kn and shear ks stiffness for generated particles was calculated using the suggested equations in the literature [12], as shown in Eqs. (3) and (4). Where E and G were the Young’s and Shear moduli of the aggregate, and ‘‘R” was the radius of the generated particle.
kn ¼ 4 E R
Fig. 1. Schema of the compaction flow test (CFT).
ð3Þ
3
E. Ghafoori Roozbahany et al. / Construction and Building Materials 227 (2019) 116432 Table 1 Burger’s model parameters for mastic at 150 °C [16]. E1 (MPa)
g1 (MPas)
E2 (MPa)
g2 (MPas)
15.996
652.714
10.891
1.898
Fig. 2. Size distribution of the generated particles.
Fig. 5. Micro behaviors of two contacting particles in (a) normal and (b) shear directions.
Fig. 3. Schema of the linear elastic model in (a) normal and (b) shear directions.
ks ¼ 4 G R
ð4Þ
Because granite is widely used for asphalt mixtures in Sweden, simulations in this study were performed with the shear modulus G and tg Poisson’s ratio of the particles of 27GPa and 0.25 respectively. Hence, the input value for Young’s modulus was calculated using Eq. (5).
E ¼ 2 G ð1 þ tg Þ
ð5Þ
In order to lower the computational time, the calculated normal and shear stiffness were lowered by a factor of 1000. 2.2.2. Viscoelastic contact model In many studies, e.g. [13–15], the Burger’s model has been used to simulate the viscoelastic behavior of mastics in asphalt mixtures. Since simulating the mastics would substantially increase the simulation time, the authors used the Burger’s model for introducing viscoelasticity among the contact points of the generated particles in the previous section. The Burger’s contact model consists of Maxwell and Kelvin parts as shown in Fig. 4; where E1 and g1 are modulus of immediate elasticity and coefficient of viscosity respectively; and E2 and g 2 are modulus of delayed elasticity and coefficient of elastic delay viscosity respectively. Normally, from the laboratory tests the macro scale behavior of the mastics can be obtained. For example, Chen et al. in 2011 [16] calculated the viscoelastic input values for mastics with maximum aggregate size of 2.36 mm that were also used in this study as input values (Table 1). As suggested in the literature [17], Eqs. (6)–(9) used for converting the macro scale results of the mastics to the micro scale input parameters (Fig. 5) in both normal and shear directions that can be used among the contacting particles.
Kmn ¼ E1 L;
Kms ¼ E1 L=ð1 þ tt Þ
ð6Þ
gmn ¼ g1 L; gms ¼ g1 L=ð1 þ tt Þ
ð7Þ
Kks ¼ E2 L=ð1 þ tt Þ
ð8Þ
gkn ¼ g2 L; gks ¼ g2 L=ð1 þ tt Þ
ð9Þ
Kkn ¼ E2 L;
The parameters with initial index of m belong to the Maxwell section and those with the initial index of k belong to the Kelvin part. The second index stands for the direction of the element, i.e. n means normal and s shear. tt is the Poisson’s ratio of the mastics that was assumed in one case incompressible, hence, chosen to be 0.5 [18]. The ‘‘L” was assumed 1 mm, implying a fictitious constant film thickness of mastic acting among all contacting particles. Obviously, the assumptions made for this study are not pretending to represent the exact behavior of asphalt mixtures but are expected to help simulating flow patterns similar to those observed in the earlier experiments. 2.3. Mold size The X-ray image analysis on real CFT specimens [4], confirmed that the movements in the XY plane, Fig. 1, were minor as compared with those in the XZ plane. Hence, in order to lower the computation time in this study, the width of the fictitious mold for the simulation was reduced from 100 mm in the real tests to 80 mm which still is large enough, i.e. 5 times larger than the largest generated particle size. Since the CFT must also be suitable for investigating the flow behavior of wearing course layers, the minimum and optimum lift thicknesses recommended for wearing course layers, i.e. 2.5 and 4 times the NMAS, were chosen for generating the height of the fictitious specimens for the simulation. In addition, a 25% higher lift was considered for the loose specimen before compaction. Hence, molds with heights of 35 mm and 55 mm were generated as shown in Fig. 6. Moreover, it is necessary to investigate whether the mold size affects the flow behavior of mixtures tested with the CFT. Therefore, in addition to the original length of the CFT mold, i.e. 150 mm, another mold with double length (300 mm) was generated (Fig. 7). The generated walls of the mold were given higher stiffness input values than the generated particles. Therefore, the normal and shear stiffness of the walls were assumed 20 GPa and 8 GPa respectively. 2.4. Loading strip geometries
Fig. 4. The schema of the Burger’s model (macro scale behavior).
When developing the CFT, a rectangular loading strip was chosen since this configuration was expected to represent the situation at the edges of a roller compactor drum passing on a newly placed asphalt layer. It was also assumed that this could roughly simulate the compaction in front of a large roller compactor drum with the contact surface length as large as one third of the total specimen length. However, since there are numerous roller compactors with different wheel sizes, in this study, the influence of curvature of the roller drum on the CFT results was evaluated by changing the geometry of the loading strip. In order to account for an extreme case, the rectangular loading strip (Fig. 8a) was compared with an angular one (Fig. 8b) with an inclination of 6°, accounting for a fictitious roller drum with a relatively small diameter of 500 mm (Fig. 8).
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Fig. 6. Generated CFT molds for lift thicknesses of 2.5 and 4 times the NMAS.
Fig. 7. The CFT mold with 300 m of length for measuring the effective length where most of the flow in the XZ plane takes place.
Fig. 8. (a) Rectangular loading strip; (b) angular loading strip.
In this study, the inputs for the loading walls were assumed the same as the ones chosen for the generated mold walls.
3. Results and discussions The presented results for each case are mean values of simulations with 3 randomly generated particle configurations. Below, the results from elastic and viscoelastic simulations are presented separately.
parameters for generating a reasonably comparable flow of particles in the simulation. In order to compare the obtained results from the experiments with those in the generated models, the embedded 10 mm screws, used in the experiments in Fig. 9, were represented by spherical particles with the diameter of 10 mm in the generated models, Fig. 10. The idea was to find proper friction coefficients for the generated particles and mold walls which would result in forming a flow pattern larger than those observed in the experiments. Hence, a mold size of 150 80 50 mm3 was generated and filled with the particle size distribution mentioned in Section 2.1 with using different friction coefficients and porosities; then, the generated models were loaded with loading rate of 15 mm/min similar to the CFT setup. The loading surface was assigned the same input values as the generated mold walls. After examining a large number of try and errors, the friction coefficients of 1 and 0.05 were chosen for the particles and the mold walls respectively. In addition, the chosen porosity of the generated model was 42%. As a result, the detected flow of the chosen particles in the model, Fig. 10, surpassed the movements of the screws in the experiments, suggesting to be a suitable choice for examining the boundaries of the CFT setup, see Fig. 11. Since the size distribution as well as the chosen input parameters appeared to provide a more critical behavior than the real wearing course mixtures, the same parameters were used in this study for investigating the possible impact of the changes of the mold size as well as the loading geometry and rate on the expected flow in CFT. In the following, the results for the impact of the mold size and the change of loading strip geometry on the flow of particles under linear elastic conditions are presented.
3.1. Elastic simulation 3.1.1. Determining complementary input parameters In order to check the boundaries of the CFT setup, input parameters had to be found that can provide a flow higher than those obtained in earlier CFT studies. In a previous study [7], the authors filled a CFT mold of 150x100x50mm3 with SMA11 and for investigating flow at different regions of the specimens used steel screws as shown in Fig. 9. The results of the flow measurements obtained from that study were taken as a reference for obtaining the input
3.1.2. Mold size As described in the methodology part, the mold sizes of 300 80 55 mm3 and 300 80 35 mm3 were generated and filled with similar particle size distribution and porosity used in the previous section. However, the imposed displacement was increased from 25% to 30% of the mold total height for making the flow even more extreme. Fig. 12 shows examples of the simulations on the larger size molds with different heights. Each spec-
Fig. 9. An example of the obtained X-ray images before (left) and after (right) the CFT.
E. Ghafoori Roozbahany et al. / Construction and Building Materials 227 (2019) 116432
5
Fig. 10. Using 10 mm spherical particles at different locations of generated CFT models for flow comparisons with the experiments.
Fig. 11. Comparison between the movements of the experiments and the generated model (units in mm).
imen was vertically loaded by means of a rectangular loading strip with a loading surface 50 80 mm2 and the speed of 15 mm/min, as also shown in Fig. 7. For each height, three random replicates were generated and an average among the movements of the chosen particles were obtained for each region. As the results indicate in Fig. 13, the highest movements of the particles were recorded within the first 150 mm of the mold from the loading side; however, in the second half of the mold the movements are limited. In order to have a better understanding of the overall flow within the generated CFT specimens with a larger mold size, the total movements of the generated particles in horizontal (X) and vertical (Z) directions for each region were obtained as shown in Fig. 14. The results of the simulation, shown in Fig. 14, show that most of the horizontal flow towards the load free side of the CFT molds occurred within the first half of the mold (0–150 mm) and substantially decreased in the second half (150–300 mm). This also holds for vertical movements of the thinner specimen. However,
the maximum share of the total vertical movements for the thicker specimen is still considerable within the first 20 mm. This also confirms the earlier experimental results [6], which indicated that thin lift thicknesses reduce the size of the shear planes in the specimen. Considering the fact that the loading condition was extreme and higher than the 25% additional height initially assumed for the generated models, it is expected that the impact of the CFT on the flow in normal loading conditions would be lower than the observed results in this simulation. In order to examine the validity of the obtained results, a limited number of CFT was carried out in the laboratory using a rectangular mold of 275 180 60 mm3. The mold was filled with a SMA11 mixture and loaded with a loading rate of 15 mm/min until reaching 30% of its total height. The results, shown in Fig. 15, indicates that in spite of the large displacement imposed to the specimens, the horizontal flow of particles are high in the first 150 mm of the mold and then starts to decrease gradually until it dramatically drops after 205 mm. The shear plane from the tracks on the side walls of the CFT mold showed that the vertical movements under the extreme loading conditions can reach between 200 and 210 mm of the mold in its larger dimension. Hence, the experimental results indicated that despite of the simplicity of the generated models, the obtained results from the simulations provided extreme conditions comparable to the reality. Based on the simulation and experimental results, it could be concluded that increasing the mold length from 150 mm to 200– 250 mm may help avoiding the disturbance of the flow of the asphalt mixtures with NMAS of 11 mm in the CFT. However, using the 150 mm size mold under the normal CFT loading conditions can still be reasonable as it does not seem to compromise the results significantly and makes the preparation and handling of the specimens faster, more efficient and easier.
Fig. 12. Examples of the generated assemblies for examining the impact of the mold size on the CFT flow in extreme cases.
Fig. 13. Averages of movements of the chosen particles in different regions of the generated specimens.
E. Ghafoori Roozbahany et al. / Construction and Building Materials 227 (2019) 116432
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300mm Fig. 14. Expected shares of total vertical and horizontal movements (the summation of the absolute movements of all particles in horizontal and vertical directions) in the XZ plane in different zones of the two mold sizes 300 80 55 mm3 (top) and 300 80 35 mm3 (bottom); the presented results were obtained from calculating the mean value of 3 replicates.
3.1.3. Effect of loading strip geometry Two loading strip geometries were simulated in this study as explained and demonstrated earlier in Fig. 8. Fig. 16 shows that the change of the loading strip from rectangular to the angular one appears to decrease the total horizontal and vertical flow of the generated particles in the simulated CFT specimens. For the thicker specimens, the total horizontal and vertical movements under the angular loading strip were lower than those under the rectangular loading strip as much as 22% and 23% respectively. These reductions appeared to be more significant in the thinner specimens as the total horizontal and vertical movements under the angular loading strip were reduced as much as 38% and 35% respectively comparing to those under the rectangular one. The most significant differences between the results of these two loading strip geometries were recorded in the 100–150 mm region. This suggests that the rollers with larger drums provide more significant flow than those with smaller drums ahead of the compacting load location. The comparison between the directions and intensity of the movements of the embedded particles in different regions of the simulated CFT molds, Fig. 17, also indicated the impact of the angular loading strip on the overall flow. Such results indicate the effectiveness and reliability of using embedded particles in CFT specimens when carrying out in-depth studies on the overall flow behavior of asphalt mixtures with the X-ray CT or other flow tracking methods [19].
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Fig. 16. Impact of changing the loading strip geometry on the horizontal and vertical flow of particles (each value was obtained from an average among 3 replicates.)
3.2. Viscoelastic simulation 3.2.1. Mold size As expected, adding the chosen viscoelastic properties among the particle contacts lowered the lateral flow of particles since it lowered the stiffness at the contact points among the particles. The results of the simulation summarized in Fig. 18 also prove that the overall flow of particles was reduced when using viscoelastic inputs as compared with the elastic ones. This suggests that the given input values lowered the shear plane size of the flow, limiting the length of lateral particle rearrangements. Such results were also qualitatively observed in an earlier study [4] when the flow of an aggregate assembly with and without bitumen was compared using the CFT. Hence, since the elastic simulation led to more extreme conditions relevant for the mold size optimization, the calculations for the mold size were not carried out in the viscoelastic simulation. 3.2.2. Effect of loading strip geometry Similar to the elastic simulation, the calculation of the flow was also carried out with the viscoelastic contact properties. Fig. 19 shows the results of the vertical and horizontal movements of particles in the XZ plane when compacted with the two chosen loading strips. Similar to the elastic simulation, the overall horizontal and vertical movements were higher when loading with the rectangular loading strip for both specimen thicknesses. The difference of total horizontal movements for the thicker specimens under the two loading strip geometries was 24% and it was 30% in the case of the thinner generated specimens. The results also indicate that the total vertical movements in thicker simulated specimens loaded with the rectangular loading strip was 28% higher than those loaded with the angular loading strip. Similar comparison for the thinner simulated specimens also shows this increment as much as 38%. It can be noticed that the change of the contact models did not have a significant impact on the recorded differences
Fig. 15. Left: the footprint of the asphalt mixture particles in the horizontal direction on the large CFT mold walls; right: the shear plane formed on the sidewall of the large CFT mold.
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Fig. 17. The XZ plane movements of the embedded spheres under different loading strip geometries; black arrows show the rectangular and the gray ones represent the angular loading geometries. (Units are in mm.)
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compaction which can increase the repeatability of the test. Therefore, it still seems reasonable to keep the CFT setup as simple as it is with the rectangular loading strip.
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1349mm
3322mm
1168mm
Z
0-50 mm 456mm
50-100 mm 294mm
100-150 mm 326mm
0-50 mm 622mm
50-100 mm 560mm
100-150 mm 551mm
X
859mm
1432mm
522mm
910mm
2316mm
812mm
Fig. 19. The impact of the loading strip geometry change on the horizontal and vertical flows of particles (Each value was obtained from an average among 3 replicates.)
Total vertical movements (mm)
between the simulated flow under the rectangular and angular loading strips. The obtained results from the elastic and viscoelastic simulations revealed the possible differences between the flow behavior of asphalt mixtures loaded with the rectangular and angular loading strips. However, it is important to understand that the chosen drum diameter of 500 mm was an extremely small size and the compactor drum sizes used for medium and large scale road projects normally have less than 2° initial inclination when touching the newly laid asphalt layer. In addition, using a rectangular loading strip in the CFT setup allows a more regular and uniform
5000 4000 3000 2000 1000 0
3694
0
3828
3952
50 100 150 Loading rate (mm/min)
a
200
Movements upper than mold edge (mm)
50-100 mm
35mm
0-50 mm
55mm
Fig. 18. The percentages of decrease in the overall particle flow in the viscoelastic simulations comparing with the results of the elastic simulations in the XZ plane.
3.2.3. Change of loading rate In order to examine the sensitivity of the CFT results to the loading rate, in addition to the selected CFT loading rate 15 mm/min, other loading rates were also used in the simulations, increasing the loading rate by factors of 5 and 10. All simulations were carried out on the mold size of 150 80 55 m3. The impact of the change in loading rate was studied by calculating the sum of the movements of all the particles in vertical direction as well as the vertical movements of all particles overflowing the top edge of the load free side of the mold during the simulation of the test. The results from changing the loading rate show that increasing the rate of 15 mm/min up to about 10 times also increases the total vertical flow of the DEM generated particles (Fig. 20a). In addition, the results of vertical movements rising above the top edge of the mold on the load free side of the simulated specimens, Fig. 20b, also indicate that the uplift movements become very close at high loading rates as compared to slower loading rates. Hence, the chosen loading rate of 15 mm/min seems to be reasonable for the CFT as it allows the material to relax during the test for the assemblies with rather low viscosities, thus roughly representing conditions of asphalt mixtures at high temperatures. Obviously, lowering the loading rate even below 15 mm/min can allow more relaxation of the material during the CFT; however, it may also allow the mixture to cool down during the test, thus increasing the viscosity of the mixture during the test more significantly than when tested with 15 mm/min. Besides, rapid loading can result in crashing the aggregates under the loading that can significantly affect the CFT results. Hence, the loading rate of 15 mm/min was still considered appropriate for performing CFT. It is important to note that the crashing of the aggregates during the loading was not experimentally examined in this study and is
500 419
400
422
350
300 200 100 0 0
50 100 150 Loading rate (mm/min)
200
b
Fig. 20. (a) Total vertical movements and (b) vertical movements higher than the mold edge on the load free side of the simulated CFT for the specimen size of 150 80 55 m3.
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E. Ghafoori Roozbahany et al. / Construction and Building Materials 227 (2019) 116432
intended to be explored in detail in upcoming studies by the authors. 4. Conclusions The results of the discrete element simulation of the CFT with pfc3D in this study with respect of the different influence parameters relevant for the optimization of the CFT are as follows: – The simulation showed that, no matter how large the length of the CFT mold would be, the majority of the flow for the extremely coarse assembly of large spherical particles with the NMAS of 11 mm and with the lift thicknesses of the wearing course occurs within the first 150 mm of the mold, close to the loading strip. This shows that the current CFT mold length is suitable for testing standard mixtures with NMASs up to 11 mm. However, for mixtures with larger NMAS, similar parameter studies would have to be carried out. – The results of this study show that the current rectangular loading strip used in the CFT setup may require adjustments for a better simulation of the flow under small roller drums. However, it still seems reasonable to use the rectangular loading strip in the CFT setup for simulating the flow under larger drum sizes, normally used for medium and large size road constructions, as it simplifies the test setup for the further use in the field without compromising the results dramatically. – Changing the loading rate appears to have a substantial impact on the CFT results. The DEM simulation suggests that the current loading rate of the CFT, i.e. 15 mm/min, seems to be a suitable choice as it is slow enough to allow the specimens to relax under the loading at low viscosities. However, it is still fast enough to avoid high temperature loss during the test.
Declaration of Competing Interest There is no conflict of interest in this paper. Acknowledgment The authors would like to acknowledge the financial support provided by Swedish road administration (Trafikverket) and also Swedish Research Council Formas for this study.
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