# Study on the Applicability of Elastic Recovery (Resilience) Experiment for Asphalt-Rubber

Authors: Zechen Yao; Renfeng Yang; Jian Kang; Zhigang Zhang
Journal: Advances in Civil Engineering
 (2022)

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## Abstract

In this paper, the applicability of the elastic recovery (resilience) experiment for asphalt-rubber (AR) binders has been quantitatively assessed. The mechanical model, based on the viscoelastic constitutive relation and particle inclusion theory, was developed. The interfacial detachment between crumb rubber (CR) particles and asphalt caused by stress concentration was analyzed with Weibull statistical equations. Based on the road roughness excitation, the vehicle-road coupling vibration model was established to analyze the impact of vehicle loading on road surface deformation. AR binders with different CR particle sizes were assessed using scanning electron microscope (SEM) imaging and prepared for testing the elastic recovery (resilience). The results showed that the greater internal stress caused by the longer stretch length of AR binders in the elastic recovery experiment was ten times higher than that obtained from the resilience experiment, leading to the interfacial detachment between asphalt and the CR particles. Hence, the elastic property of some of the CR particles with high modulus was not reflected, resulting in the test values being lower than actual values. With the reduction of CR particle size, the interfacial detachment was improved in the elastic recovery experiment due to intense material interchange and the enhancement of interfacial bond strength. The millimeter-scale compression deformation of the AR binder in the resilience experiment was closer to the actual deformation of the road surface. The experimental time of resilience (120 min) has been reported less than that for elastic recovery (200 min–230 min). This study shows that the resilience experiment has a significant advantage in assessing the elastic property of the AR binder.


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## Body

## 1. Introduction

The use of modifiers for improving the performance of asphalt pavements has always been the area of interest among researchers [1–3]. Asphalt-rubber (AR) is made by adding Crumb Rubber (CR) into the asphalt. AR can solve the environmental issues arising from the waste tires and improve the road performance of asphalt by using the effective properties of CR particles [4, 5]. Currently, researchers are focusing more on the modification mechanism and production formula of AR [4–9], and there is little research on the evaluation system of AR. Hence, the evaluation system has not been unified for AR around the world. However, the core evaluation indices mainly include needle (cone) penetration, elastic recovery (resilience), viscosity, and softening point [10].Elastic recovery (resilience) is an important index to evaluate the elastic performance for AR binder, and there are some differences between these two evaluation mechanisms. The elastic recovery experiment is primarily used to determine the elastic recovery of the AR binder after a long stretch. In contrast, the resilience experiment is used to evaluate the springback recovery of the AR binder after compression. The elastic recovery at 25°C following SBS modified asphalt evaluation system is mainly used in AR local technical standards in China [11]. However, the United States (ASTM D6114-19 [12], D5329-15 [13]), South Africa, and Italy have selected resilience to evaluate the AR binder [14]. Exploring the applicability of the elastic recovery (resilience) experiment for AR binders is greatly significant in accurately evaluating the elastic property of AR and popularizing its applications.There have been limited studies on elastic recovery (resilience) experiments. Dasek et al. [15] studied the elastic property of CR modified asphalt by two elastic recovery (resilience) experiments, and these test methods were considered to be valid. Yang et al. [10] suggested that the resilience experiment should be used to assess the elastic property of AR binders due to the presence of CR particles. The findings of Liu and Li [16] confirmed that resilience was more suitable for evaluating the elastic property of AR binders, which could better characterize the elastic performance at a small scale. Hao et al. [11] put forward that the elastic recovery experiment reflected the stretch recovery ability for AR binders, whereas the resilience experiment reflected the compression recovery ability for AR binders, which was more effective in characterizing the elastic property of AR mixtures. Wang [14] demonstrated that the experimental results of resilience were not impacted by stress concentration around CR particles, which was more scientifically appropriate and reasonable. Although significant progress has been made in research on the elastic experiment of AR binders, there are still several limitations. Most of these studies have only been carried out using simple elastic recovery (resilience) experiments or qualitative analysis for AR binders. The research studies on the applicability of elastic recovery (resilience) experiments for AR binders from CR modification mechanism and theoretical analysis standpoints are sparse.Combining the CR modification mechanism and detection principle of elastic recovery (resilience) experiment, a mechanical model based on the viscoelastic constitutive relation and particle inclusion theory of composite materials has been developed in this paper. The Weibull statistical equation was used to analyze the interfacial detachment of asphalt and CR particles in the two experiments. Combining SEM observations, the influence model of CR particle size for interfacial detachment was obtained. Based on the road roughness excitation, the applicability of these two evaluation indices was explored from the actual road deformation computed by vehicle-road coupling vibration equation using MATLAB. Elastic recovery (resilience) experiments on AR binders with different CR particle sizes were carried out to verify the correctness of the theoretical analysis. This paper provides a theoretical basis and justification for using resilience to evaluate the AR binders.


## 2. Experiments

### 2.1. Materials

The asphalt in this study was a pure asphalt binder with 70 penetration grade obtained from the LuZheng company in China. Ambient grinding CR of #20, #30, #40, #60, and #80 mesh produced by HuaYi company in China were used to prepare AR binders. The main technical parameters are given in Tables1 and 2.Table 1
Main technical indexes of base asphalt.
Experiment itemUnitQuality indexTest methodResults25°C needle penetration0.1 mm60∼80T060469.2Penetration index—−1.5∼+1.0T0604−1.22Softening point°C≥46T060647.2415°C force ductilitycm≥100T0605100+Solubility%≥99T060799.56Flash-point°C≥260T061130115°C densityg/cm3——1.034Table 2
Main technical indexes of CR.
Density (g/cm3)Water (%)Ash (%)Rubber content (%)Fiber content (%)Burning residual (%)1.120.64.5510.537.5


### 2.2. Preparation of AR Binders

The wet process was used to prepare the AR binders. The #20, #30, #40, #60, and #80 mesh CR (20% by the weight of asphalt) was mixed with the base asphalt to prepare AR binders. The AR binders were obtained by adding CR to base asphalt, which was melted at 80–90°C previously. Manual stirring for 5 minutes was done to disperse CR in the base asphalt efficiently and then blended using a high-speed mixer (at about 1000 rpm) at 180°C (±5°C) for 45 minutes, in accordance with ASTM D6114-19 [12].


### 2.3. Experimental Methods

To analyze the impact of finer CR particles on the interfacial detachment, the AR binders with #40, #60, and #80 mesh CR were observed using FEI Quanta FEG 250 FESEM following GB/T 16594–08 [17]. The AR binders were tested for elastic recovery and resilience at 25°C using a bitumen ductility meter (SYD-4508G-1) and a digital penetration meter (SYD-2801L) conforming to NB/SH/T 0737–14 [18] and ASTM D5329-15 [13], respectively.


## 2.1. Materials

The asphalt in this study was a pure asphalt binder with 70 penetration grade obtained from the LuZheng company in China. Ambient grinding CR of #20, #30, #40, #60, and #80 mesh produced by HuaYi company in China were used to prepare AR binders. The main technical parameters are given in Tables1 and 2.Table 1
Main technical indexes of base asphalt.
Experiment itemUnitQuality indexTest methodResults25°C needle penetration0.1 mm60∼80T060469.2Penetration index—−1.5∼+1.0T0604−1.22Softening point°C≥46T060647.2415°C force ductilitycm≥100T0605100+Solubility%≥99T060799.56Flash-point°C≥260T061130115°C densityg/cm3——1.034Table 2
Main technical indexes of CR.
Density (g/cm3)Water (%)Ash (%)Rubber content (%)Fiber content (%)Burning residual (%)1.120.64.5510.537.5


## 2.2. Preparation of AR Binders

The wet process was used to prepare the AR binders. The #20, #30, #40, #60, and #80 mesh CR (20% by the weight of asphalt) was mixed with the base asphalt to prepare AR binders. The AR binders were obtained by adding CR to base asphalt, which was melted at 80–90°C previously. Manual stirring for 5 minutes was done to disperse CR in the base asphalt efficiently and then blended using a high-speed mixer (at about 1000 rpm) at 180°C (±5°C) for 45 minutes, in accordance with ASTM D6114-19 [12].


## 2.3. Experimental Methods

To analyze the impact of finer CR particles on the interfacial detachment, the AR binders with #40, #60, and #80 mesh CR were observed using FEI Quanta FEG 250 FESEM following GB/T 16594–08 [17]. The AR binders were tested for elastic recovery and resilience at 25°C using a bitumen ductility meter (SYD-4508G-1) and a digital penetration meter (SYD-2801L) conforming to NB/SH/T 0737–14 [18] and ASTM D5329-15 [13], respectively.


## 3. Mechanical Model in Elastic Recovery (Resilience) Experiment

In this section, the mechanical model was developed to explore the applicability of the elastic recovery (resilience) experiment for AR binder. Figure1 shows the schematic illustrations of the detection mechanism for the elastic recovery (resilience) experiment. The yellow particles in the diagrams show CR particles. The elastic recovery experiment is mainly used to evaluate the elastic recovery of the AR binder after a longer stretch deformation (10 cm), whereas the resilience experiment is employed for evaluating the springback recovery of the AR binder after compression deformation (about 1 cm).Figure 1
Schematic diagrams of detection mechanism for elastic recovery (resilience) experiment. (a) Elastic recovery experiment; (b) resilience experiment.
(a)(b)AR binder is a solid-liquid two-phase material, in which the base asphalt is a kind of typical viscoelastic body. However, due to the potential of CR particles in absorbing the light component of asphalt in the reaction process, it is no longer a pure elastomer. To simplify the analysis, CR is regarded as a viscoelastic body whose modulus is higher than that of base asphalt. Since the experimental process of elastic recovery is carried out at constant speed [18], the strain inside the specimen is considered to increase linearly. Using the Kelvin model to analyze the loading process, the elastic modulus and the damping of CR particles and base asphalt are represented as L1, η1, L0, η0, respectively, as shown in Figure 2(a). The stress-strain relationship is, σ=Lε+ηε˙, as shown in Figure 2(b).Figure 2
Loading process analysis.
(a)(b)According toEshebly’s inclusion theory [19] and Mori-Tanaka’s homogenization theory [20, 21],(1)σ¯1=σ¯+σ^+σpt=L1ε0+ε^+εpt+A1=L0ε0+ε^+εpt−ε∗+A1,(2)σ¯0=σ¯+σ^,(3)εpt=Sε∗,(4)σ¯=c1σ¯1+c0σ¯0,where σ¯1 is the stress of CR particles; σ¯0 is the stress of base asphalt; σ¯ is the external stress; ε0 is the external strain; σ^ is the difference between σ¯0 and σ¯; ε^ is the difference between the strain of base asphalt and ε0; σpt is the difference between σ¯0 and σ¯1; εpt is the difference between the strain of base asphalt and the strain of CR particles; ε∗ is Eigenstrain; c1 and c0 are the volume content of CR particles and base asphalt, respectively; S is Eshelby tensor related to the property of matrix material and particle shape; and Ai represents a constant.According to equation (1) through equation (4),(5)ε^=−c1S−Iε∗+A2.According to (1) and (5),(6)ε∗=−L1−L0S+I−Sc1+A3+L0−1L1−L0ε0+A4.According to (6),(7)σ¯1=L0I+Gε0+GA4ΔL+A1,where G=c0L1−L0S+I−Sc1+A3+L0−1L1−L0I−S and(8)ΔL=L1−L0.The aforementioned analysis is aimed at specimen deformation in multiple directions in space. As the experimental progress of elastic recovery (resilience) is unidirectional tension, the parameters in a single direction are only considered to simplify the analysis further. Letε0=Δx/x0, where Δx is the stretch length and x0 is the original length of the specimen. Then, (7) can be converted into(9)σ¯1=L0I+GΔxx0+GA4ΔL+A1.WhenΔL is constant, it can be seen that stress in particles increases linearly with the stretch length Δx. Meanwhile, this equation can also be used to analyze the compression progression of the resilience experiment. As the deformation of elongation and compression is about 10 cm and 1 cm, respectively, according to (9), the stress in CR particles in the elastic recovery experiment is about ten times that of the resilience experiment. Therefore, compared with the resilience experiment, more severe stress concentration may occur in the elastic recovery experiment, which may cause interfacial detachment of the CR particles and base asphalt. The Weibull statistical model can be used to describe the accumulation probability of interface detachment [21]:(10)Pσ¯1=1−e−σ¯1/S0m,where σ¯1 is CR particle stress and S0 and m are scale and shape parameters, respectively. As it is tough to determine the accurate values of S0 and m, Figure 3 shows the detachment probability curve with common values [21] calculated by MATLAB. It is observed that when the difference of particle stress is ten times, it is easy to appear detachment ultimately (the probability reaches 1) between CR particles and base asphalt in elastic recovery experiments, whereas rarely detachment occurs in resilience experiments.Figure 3
Prediction of detachment possibility with common values.
(a)(b)Figure4 intuitively illustrates the detachment process of CR particles and base asphalt in the elastic recovery experiment. As shown in Figure 4(a), the CR particles and base asphalt bear stress simultaneously at the beginning of the stretch, and no detachment occurs in the specimen. As shown in Figure 4(b), due to the difference in elasticity modulus, adhesive failure occurs with the increase of stretch length, and the corresponding stress transferred by CR particles is reduced. It is also evident from Figure 4(c) that when the specimens show complete detachment, CR particles have already lost the capacity of transfer stress in the experiment, which was replaced by adjacent base asphalt. In other words, the high elasticity of some of the CR particles cannot be detected due to detachment, resulting in the values of experimental results being lower than the actual values. Hence, the elastic recovery experiment may not accurately determine the elastic property of AR binders compared with the resilience experiment.Figure 4
Detachment process of CR particles and base asphalt in elastic recovery experiment. (a) No detachment, (b) partial detachment, and (c) completely detachment.
(a)(b)(c)Figures5(a) and 5(b) show the schematic diagrams of AR specimens with different CR particle sizes (same content). It can be clearly seen that the contact area between CR particles and asphalt increases with the reduction of CR particle size. On one hand, the increase in contact area intensifies the reaction between the CR particles and asphalt, thereby improving the material interface and reducing the difference of elastic modulus between asphalt and CR, which reduces stress concentration. In addition, the increase of contact area improves the bonding area between CR particles and asphalt, meaning that the interfacial bond strength is improved. Therefore, with the reduction of CR particle size, the interfacial detachment between CR particles and asphalt is improved in the elastic recovery experiment.Figure 5
AR specimens with different CR particle sizes. (a) AR specimen with coarse CR particles and (b) AR specimen with fine CR particles.
(a)(b)


## 4. Experimental Results

### 4.1. Observations of AR Binders

Figure6 shows the AR binders with different CR particle sizes. Noticeable CR particles can be observed in AR binders with #20 and #30 CR. Tiny CR particles distributed within the AR binders with #40, #60 CR can also be observed. However, CR particles cannot be observed in AR binders with #80 CR macroscopically. The SEM images of AR binders with #40, #60, and #80 CR are shown in Figure 7. The gray particles shown in the images are the CR particles. Figure 7(a) shows that the AR binder with #40 CR has many noticeable gray particles indicating distinct solid-liquid two-phase features. With the reduction of CR particle size, this solid-liquid two-phase feature gradually weakens. In Figure 7(c), the two-phase continuous blending structure system constituted by asphalt and CR is formed due to severe reactions, indicating the intense material interchange occurred, and CR particles are no longer independent in base asphalt, which is consistent with the previously published findings in the literature [22]. Therefore, the interfacial detachment between CR particles and asphalt can be improved by reducing CR particle size. This corroborates the theoretical analysis in Section 3.Figure 6
AR binders with different CR particle sizes. (a) AR with #20 CR, (b) AR with #30 CR, (c) AR with #40 CR, (d) AR with #60 CR, and (e) AR with #80 CR.
(a)(b)(c)(d)(e)Figure 7
SEM images of AR binders with different CR particle sizes. (a) AR with #40 CR, (b) AR with #60 CR, and (c) AR with #80 CR.
(a)(b)(c)


### 4.2. Experimental Results for Elastic Recovery (Resilience)

Figures8 and 9 show the AR binders with #20–80 CR in the experimental process for elastic recovery (resilience) at 180 °C. It can be seen that the AR binders with #20, #30, #40, and #60 CR have obvious holes (silver holes shown in white circle) in the stretching process of elastic recovery experiments, whereas only some cracks occur in the AR binders with #80 CR. As shown in Figure 9, there are no apparent holes and cracks in AR binders in resilience experiments. It can be seen intuitively that the detachment phenomenon in elastic recovery experiments is much severe than that in resilience experiments. It shows that under the condition of longer stretch length in elastic recovery experiment, AR binders with coarser CR are more likely to exhibit stress concentration, leading to the interfacial detachment of CR particles and asphalt easily, with the subsequent appearance of the holes. There are no apparent holes, and cracks appeared in AR binders in resilience experiments. The experimental results are consistent with the theoretical analysis in Section 3. It is worth mentioning that only holes and cracks on the surface of the specimen can be observed, and it is reasonable to speculate that many invisible cracks and holes are generated inside specimens in elastic recovery experiments.Figure 8
AR binders with #20–80 CR in the experimental procedure for elastic recovery at 180°C. (a) AR with #20 CR, (b) AR with #30 CR, (c) AR with #40 CR, (d) AR with #60 CR, and (e) AR with #80 CR.
(a)(b)(c)(d)(e)Figure 9
AR binders with #20–80 CR in the experimental procedure for resilience at 180°C. (a) AR with #20 CR, (b) AR with #30 CR, (c) AR with #40 CR, (d) AR with #60 CR, and (e) AR with #80 CR.
(a)(b)(c)(d)(e)To intuitively analyze the experimental progress of elastic recovery (resilience) for AR binders, the schematic diagrams of AR binders before and after stretching (compressing) are shown in Figure10. Figure 10(a) shows that the CR particles are uniformly distributed in asphalt before stretching, and the interface is well bonded. With the stretching of the AR binder, the stress concentration occurs in the specimen due to the difference in elasticity modulus. When internal stress is higher than the interfacial bond strength between asphalt and CR particles, the interfacial detachment starts, and cracks and holes appear in the specimens. When the holes are generated in the AR binders, the CR particles (red particles in Figure 10(b)) located within the hole region can no longer transfer stress. The bearing capacity is eventually lost. Hence, the nearby asphalt bears the stretching deformation and subsequent elastic recovery, as shown in Figure 10(b). This indicates that the elastic property of some CR particles with high modulus cannot be tested in the experiments (red particles in Figure 10(b)), leading to the test values being lower than actual values. In other words, this experimental method cannot accurately reflect the elastic properties of both CR and asphalt. The compressive deformation is small in the resilience experiment, so it is challenging to ascertain interfacial detachment caused by stress concentration in AR binders, and the elastic property of both asphalt and CR can be reflected. Hence, the resilience experiment may be more suitable for evaluating AR binders, particularly for AR binders with coarser CR particles. Due to the difference between these two detection mechanisms, it is of little significance to compare the results of elastic recovery experiments and resilience experiments [23]. Therefore, it is not analyzed in this paper.Figure 10
Schematic diagrams of AR specimens (a) before stretching (compressing) and (b) after stretching (compressing).
(a)(b)It is worth noting that the experimental time of resilience (120 min) is significantly less than that of elastic recovery (200 min–230 min) according to the stipulations in ASTM D5329-15 [13] and NB/SH/T 0737–14 [18], which shows the usefulness of the resilience experiment in terms of saving experimental time.


## 4.1. Observations of AR Binders

Figure6 shows the AR binders with different CR particle sizes. Noticeable CR particles can be observed in AR binders with #20 and #30 CR. Tiny CR particles distributed within the AR binders with #40, #60 CR can also be observed. However, CR particles cannot be observed in AR binders with #80 CR macroscopically. The SEM images of AR binders with #40, #60, and #80 CR are shown in Figure 7. The gray particles shown in the images are the CR particles. Figure 7(a) shows that the AR binder with #40 CR has many noticeable gray particles indicating distinct solid-liquid two-phase features. With the reduction of CR particle size, this solid-liquid two-phase feature gradually weakens. In Figure 7(c), the two-phase continuous blending structure system constituted by asphalt and CR is formed due to severe reactions, indicating the intense material interchange occurred, and CR particles are no longer independent in base asphalt, which is consistent with the previously published findings in the literature [22]. Therefore, the interfacial detachment between CR particles and asphalt can be improved by reducing CR particle size. This corroborates the theoretical analysis in Section 3.Figure 6
AR binders with different CR particle sizes. (a) AR with #20 CR, (b) AR with #30 CR, (c) AR with #40 CR, (d) AR with #60 CR, and (e) AR with #80 CR.
(a)(b)(c)(d)(e)Figure 7
SEM images of AR binders with different CR particle sizes. (a) AR with #40 CR, (b) AR with #60 CR, and (c) AR with #80 CR.
(a)(b)(c)


## 4.2. Experimental Results for Elastic Recovery (Resilience)

Figures8 and 9 show the AR binders with #20–80 CR in the experimental process for elastic recovery (resilience) at 180 °C. It can be seen that the AR binders with #20, #30, #40, and #60 CR have obvious holes (silver holes shown in white circle) in the stretching process of elastic recovery experiments, whereas only some cracks occur in the AR binders with #80 CR. As shown in Figure 9, there are no apparent holes and cracks in AR binders in resilience experiments. It can be seen intuitively that the detachment phenomenon in elastic recovery experiments is much severe than that in resilience experiments. It shows that under the condition of longer stretch length in elastic recovery experiment, AR binders with coarser CR are more likely to exhibit stress concentration, leading to the interfacial detachment of CR particles and asphalt easily, with the subsequent appearance of the holes. There are no apparent holes, and cracks appeared in AR binders in resilience experiments. The experimental results are consistent with the theoretical analysis in Section 3. It is worth mentioning that only holes and cracks on the surface of the specimen can be observed, and it is reasonable to speculate that many invisible cracks and holes are generated inside specimens in elastic recovery experiments.Figure 8
AR binders with #20–80 CR in the experimental procedure for elastic recovery at 180°C. (a) AR with #20 CR, (b) AR with #30 CR, (c) AR with #40 CR, (d) AR with #60 CR, and (e) AR with #80 CR.
(a)(b)(c)(d)(e)Figure 9
AR binders with #20–80 CR in the experimental procedure for resilience at 180°C. (a) AR with #20 CR, (b) AR with #30 CR, (c) AR with #40 CR, (d) AR with #60 CR, and (e) AR with #80 CR.
(a)(b)(c)(d)(e)To intuitively analyze the experimental progress of elastic recovery (resilience) for AR binders, the schematic diagrams of AR binders before and after stretching (compressing) are shown in Figure10. Figure 10(a) shows that the CR particles are uniformly distributed in asphalt before stretching, and the interface is well bonded. With the stretching of the AR binder, the stress concentration occurs in the specimen due to the difference in elasticity modulus. When internal stress is higher than the interfacial bond strength between asphalt and CR particles, the interfacial detachment starts, and cracks and holes appear in the specimens. When the holes are generated in the AR binders, the CR particles (red particles in Figure 10(b)) located within the hole region can no longer transfer stress. The bearing capacity is eventually lost. Hence, the nearby asphalt bears the stretching deformation and subsequent elastic recovery, as shown in Figure 10(b). This indicates that the elastic property of some CR particles with high modulus cannot be tested in the experiments (red particles in Figure 10(b)), leading to the test values being lower than actual values. In other words, this experimental method cannot accurately reflect the elastic properties of both CR and asphalt. The compressive deformation is small in the resilience experiment, so it is challenging to ascertain interfacial detachment caused by stress concentration in AR binders, and the elastic property of both asphalt and CR can be reflected. Hence, the resilience experiment may be more suitable for evaluating AR binders, particularly for AR binders with coarser CR particles. Due to the difference between these two detection mechanisms, it is of little significance to compare the results of elastic recovery experiments and resilience experiments [23]. Therefore, it is not analyzed in this paper.Figure 10
Schematic diagrams of AR specimens (a) before stretching (compressing) and (b) after stretching (compressing).
(a)(b)It is worth noting that the experimental time of resilience (120 min) is significantly less than that of elastic recovery (200 min–230 min) according to the stipulations in ASTM D5329-15 [13] and NB/SH/T 0737–14 [18], which shows the usefulness of the resilience experiment in terms of saving experimental time.


## 5. Impact of Vehicle Loading on Road Surface Deformation

The purpose of the elastic recovery (resilience) experiment is to evaluate the elastic property of the AR binder. Good elastic property can effectively reduce the residual deformation of road materials and improve the cracking resistance [14, 24]. However, in the actual service process of asphalt pavement, it is worth determining whether it is necessary to use such a long stretch length (10 cm) in an elastic recovery experiment to evaluate the elastic property of the AR binder. In this section, based on the road roughness excitation, the road surface deformation caused by vehicles with different overload conditions under various pavement grades was computed by the vehicle-road coupling vibration model and finite element model to evaluate the applicability of elastic recovery (resilience) experiment for AR binders.


### 5.1. Vehicle-Road Coupling Vibration Model

Extensive experiments and analysis by the automobile industry show that the quarter vehicle model is quite successful in predicting the vertical vibration acceleration of vehicles, and there is no need to build a multidegree of freedom model [25]. The model is shown in Figures 11 and 12.Figure 11
Vehicle-road contacting diagram.Figure 12
Vehicle-road coupling vibration model.The dynamic equation of the vibration system is as follows:(11)msy¨s+csy˙s−y˙t+ksys−yt=0,(12)mty¨t+cty˙t−y˙r+ktyt−yr−csy˙s−y˙t−ksys−yt=0,where ms is suspension system mass; mt is nonsuspension system mass; ks is suspension system stiffness; kt is nonsuspension system stiffness; ys and yt are the vertical displacements of the suspension system and nonsuspension system, respectively; and yr is vertical displacement excitation of road surface roughness. The additional random dynamic load of vehicle on the road surface is as follows:(13)Ft=cty˙t−y˙r+ktyt−yr.The dynamic load factor is as follows:(14)D=P0+FtmaxP0=FtmaxP0+1,where P0 = (ms + mt)g and F(t)max is maximum additional dynamic load.


### 5.2. Simulation Model

Currently, the researchers usually use Power Spectral Density (PSD) to represent the road surface roughness [25]. ISO/TC 108/SCN67 (Draft method for representation of road surface roughness) [26] and GB 7031 (vehicle vibration–describing method for road surface irregularity) [27] propose the classifications of road surface roughness according to PSD. Table 3 shows the geometric average of roughness coefficient G0 with different road surface grades [28].Table 3
Classification standard of road surface roughness in ISO/TC 108/SCN67.
Road surface gradesG0 × 10−6(m2.c.m−1)Lower limitUpper limitGeometric averageA83216B3212864C128512256D51220481024E204881924096F81923276816384G3276865536131072H131072262144524288Due to the uncertainty in road surface roughness, it is difficult to use an analytical formula to calculate the road loading. Hence, it is an excellent method to use a software to generate the excitation functions according to different grades of the road surface. The simulation of white noise excitation based on linear filtering is currently one of the most widely used methods. The mathematical model in the time domain is as follows:(15)y˙rt=−2πf0yrt+2πn0G0uwt,where f0 = 0.0628 Hz is lower cut-off frequency [29]; n0 = 0.1 m−1 is reference space frequency; G0 is roughness coefficient; u is driving speed; and w(t) is random white noise.According to equations (10) through (14), the system was simulated by Simulink in MATLAB, and the model is shown in Figure 13. According to the model, the road surface loading caused by vehicles with different overload conditions under different road surface grades can be computed. The medium-sized vehicle is taken as the analysis object, and the structural parameters are shown in Table 4 [30].Figure 13
Vehicle-road coupling vibration simulation model based on the random excitation of road surface roughness.Table 4
Medium-sized vehicle parameters.
ParameterMass (kg)Stiffness (Kn.m−1)Damping (Kn.s.m−1)Suspension system450050015Nonsuspension system50015005


### 5.3. Simulation Results

Figure14 shows the simulation results of road surface loading (F(t)max + P0) caused by the medium-sized vehicle, with different overload conditions (0–80%), at the speed of 30 m/s under different road surface grades (A-H). It can be observed that road surface loading gradually increases with the decrease of road grade and the aggravation of overload conditions.Figure 14
Impact of vehicle overload condition on road surface loading (A∼H).According to the simulation results of road surface loading, the road surface deformation caused by vehicles is analyzed using Abaqus software. The contact area between the tires and the road surface is 0.0672 m2 [31], with the total number of tires being four. The results of road surface loading are imported into Abaqus software to compute the road surface deformation. To simplify the model, the road surface is set as elastomer with elastic modulus E = 1400 Mpa and density ρ = 2400 kg m−3 [32]. The pressure is set on the contacting surface between the tires and the road surface, while the bottom of the road surface is considered fully constrained. The model is verified by grid independence. The computed results are shown in Figures 15 and 16.Figure 15
Impact of vehicle overload condition on road surface stress (A∼H).Figure 16
Impact of vehicle overload condition on road surface deformation (A∼H).As shown in Figures15 and 16, the road surface stress and road deformation increases significantly with the decrease of road grade and the aggravation of vehicle overload. However, even in the worst-case scenario (80% overloading and H grade road surface), the road surface deformation is about 0.3 mm. This is consistent with the results in reference [31, 33, 34]. Hence, compared with a longer stretch length (10 cm) in the elastic recovery experiment, the detection mechanism of millimeter-scale compression springback recovery of resilience experiment is closer to the actual loading condition of the road surface.


## 5.1. Vehicle-Road Coupling Vibration Model

Extensive experiments and analysis by the automobile industry show that the quarter vehicle model is quite successful in predicting the vertical vibration acceleration of vehicles, and there is no need to build a multidegree of freedom model [25]. The model is shown in Figures 11 and 12.Figure 11
Vehicle-road contacting diagram.Figure 12
Vehicle-road coupling vibration model.The dynamic equation of the vibration system is as follows:(11)msy¨s+csy˙s−y˙t+ksys−yt=0,(12)mty¨t+cty˙t−y˙r+ktyt−yr−csy˙s−y˙t−ksys−yt=0,where ms is suspension system mass; mt is nonsuspension system mass; ks is suspension system stiffness; kt is nonsuspension system stiffness; ys and yt are the vertical displacements of the suspension system and nonsuspension system, respectively; and yr is vertical displacement excitation of road surface roughness. The additional random dynamic load of vehicle on the road surface is as follows:(13)Ft=cty˙t−y˙r+ktyt−yr.The dynamic load factor is as follows:(14)D=P0+FtmaxP0=FtmaxP0+1,where P0 = (ms + mt)g and F(t)max is maximum additional dynamic load.


## 5.2. Simulation Model

Currently, the researchers usually use Power Spectral Density (PSD) to represent the road surface roughness [25]. ISO/TC 108/SCN67 (Draft method for representation of road surface roughness) [26] and GB 7031 (vehicle vibration–describing method for road surface irregularity) [27] propose the classifications of road surface roughness according to PSD. Table 3 shows the geometric average of roughness coefficient G0 with different road surface grades [28].Table 3
Classification standard of road surface roughness in ISO/TC 108/SCN67.
Road surface gradesG0 × 10−6(m2.c.m−1)Lower limitUpper limitGeometric averageA83216B3212864C128512256D51220481024E204881924096F81923276816384G3276865536131072H131072262144524288Due to the uncertainty in road surface roughness, it is difficult to use an analytical formula to calculate the road loading. Hence, it is an excellent method to use a software to generate the excitation functions according to different grades of the road surface. The simulation of white noise excitation based on linear filtering is currently one of the most widely used methods. The mathematical model in the time domain is as follows:(15)y˙rt=−2πf0yrt+2πn0G0uwt,where f0 = 0.0628 Hz is lower cut-off frequency [29]; n0 = 0.1 m−1 is reference space frequency; G0 is roughness coefficient; u is driving speed; and w(t) is random white noise.According to equations (10) through (14), the system was simulated by Simulink in MATLAB, and the model is shown in Figure 13. According to the model, the road surface loading caused by vehicles with different overload conditions under different road surface grades can be computed. The medium-sized vehicle is taken as the analysis object, and the structural parameters are shown in Table 4 [30].Figure 13
Vehicle-road coupling vibration simulation model based on the random excitation of road surface roughness.Table 4
Medium-sized vehicle parameters.
ParameterMass (kg)Stiffness (Kn.m−1)Damping (Kn.s.m−1)Suspension system450050015Nonsuspension system50015005


## 5.3. Simulation Results

Figure14 shows the simulation results of road surface loading (F(t)max + P0) caused by the medium-sized vehicle, with different overload conditions (0–80%), at the speed of 30 m/s under different road surface grades (A-H). It can be observed that road surface loading gradually increases with the decrease of road grade and the aggravation of overload conditions.Figure 14
Impact of vehicle overload condition on road surface loading (A∼H).According to the simulation results of road surface loading, the road surface deformation caused by vehicles is analyzed using Abaqus software. The contact area between the tires and the road surface is 0.0672 m2 [31], with the total number of tires being four. The results of road surface loading are imported into Abaqus software to compute the road surface deformation. To simplify the model, the road surface is set as elastomer with elastic modulus E = 1400 Mpa and density ρ = 2400 kg m−3 [32]. The pressure is set on the contacting surface between the tires and the road surface, while the bottom of the road surface is considered fully constrained. The model is verified by grid independence. The computed results are shown in Figures 15 and 16.Figure 15
Impact of vehicle overload condition on road surface stress (A∼H).Figure 16
Impact of vehicle overload condition on road surface deformation (A∼H).As shown in Figures15 and 16, the road surface stress and road deformation increases significantly with the decrease of road grade and the aggravation of vehicle overload. However, even in the worst-case scenario (80% overloading and H grade road surface), the road surface deformation is about 0.3 mm. This is consistent with the results in reference [31, 33, 34]. Hence, compared with a longer stretch length (10 cm) in the elastic recovery experiment, the detection mechanism of millimeter-scale compression springback recovery of resilience experiment is closer to the actual loading condition of the road surface.


## 6. Summary and Conclusion

In this paper, the particle inclusion theory andKelvin model were used to analyze the detachment process of AR binder in elastic recovery (resilience) experiment, and the vehicle-road coupling vibration model and FEM were used to obtain the road surface deformation. Relevant experiments were carried out to verify the theoretical analysis. It is concluded that resilience has a significant advantage in evaluating the elastic property of AR binders. The key findings are summarized, and the conclusions drawn are given as follows:(1)
The longer stretch length of AR binders in the elastic recovery experiment easily generates greater internal stress in specimens, which is ten times higher than that obtained in the resilience experiment, resulting in severe stress concentration. The interfacial detachment between CR particles and asphalt occurs and generates holes in the specimens, destroying the continuity of the AR binder. Hence, some CR particles with high modulus cannot be tested during the elastic recovery experiment, resulting in lower experimental results than the actual values. The millimeter-scale compression deformation of AR binders in the resilience experiment is hardly influenced by the CR particles, indicating the real elastic property of AR binder containing asphalt and CR accurately.(2)
With the increase of CR mesh number, the difference of elastic modulus between asphalt and CR is reduced, which is caused by the enhancement of material interface, and the contacting area between asphalt and CR is improved. This results in the reduction of stress concentration and the enhancement of interfacial bond strength, respectively, and as such, the interfacial detachment is improved in the elastic recovery experiment. Hence, it is only applicable to the evaluation of materials that are approximated to a single-phase body.(3)
Even in the worst-case scenario (80% overloading andH grade road surface), the actual compressive deformation of the road surface is below 1 mm, which is closer to the force state of AR binders tested by the resilience experiment.(4)
The experimental time of resilience (120 min) is far less than that of elastic recovery (200 min-230 min), which helps save time and reduce complexity.



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*Source: 2286794-2022-01-04.xml*