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In the bitumen foaming process, the controllable factors, especially the water consumption in foaming, heating temperature of bitumen and bitumen viscosity can directly affect the technical performance of foamed bitumen. To improve the technical performance of foamed bitumen and reveal the influence rule of the controllable factors, the bitumen foaming mechanism is analyzed and the control model of the bitumen foaming behavior is established. After numerical calculation with CFD software, relation degree analysis of experimental data and simulation data was performed by utilizing the Grey relation analysis method. The average density inside the cavity flow field is used as the reference factor of theoretical analysis. Then the influence of the controllable factors on the foamed bitumen technical performance is respectively tested. The results show that the bitumen temperature affects the technical performance most significantly, water consumption of foaming secondly, and the least influentional is bitumen viscosity.
Bitumen foaming, Controllable factor, Foamed bitumen, Average density, Grey relation analysis.
Most highways built early in China are approaching the period of repair or replacement. Road maintenance annually generates up to 160 million tons of waste bitumen pavement material, known as reclaimed asphalt pavement, (RAP) [1]. The practice of not reusing the RAP material in a timely manner will cause significant waste. Reasonable recycling and effective use of waste pavement materials has become a very urgent task. Foamed bitumen which is an environmentally friendly luting cement, is an excellent way to solve this problem [2, 3]. Foamed bitumen can be utilized in a variety of construction technologies, such as foamed bitumen recycling construction technology, foamed bitumen warm mixing technology, foamed bitumen cold mixing technology, etc. However, because of various influencing factors of bitumen foaming, controlling the bitumen foaming process is quite complicated. Thus, producing highquality foamed bitumen is quite difficult. At present, research on bitumen foaming process controlling have mainly focused on the following areas : 1) Determining the test conditions used for obtaining the optimum asphalt foaming effect; 2) exploring the main factors influencing the behavior of bitumen foaming; 3) discussing evaluation index authenticity of foamed bitumen; 4) establishing foamed bitumen recession equation according to different types of bitumen [418]. See Table 1 for references.
Table 1. Study on the influencing factors of asphalt foaming behavior [418]
Years 
Scholars 
Academic viewpoint 
1982 
M.Brennen 
Asphalt163℃ and 2.0% water dosage 
1982 
Ruckel 
Foaming chamber volume 
2003 
HE Guiping 
Asphalt temperature, water dosage, air pressure, water pressure 
2003 
Mofreh F. Saleh 
Soft asphalt foaming effect is better 
2006 
SHI Fangzhi 
Asphalt type, asphalt pressure, foaming water dosage, water pressure additives 
2006 
Yongjoo Kim 
Asphalt temperature170℃, water1.3%, air pressure400KPa, water pressure 500KPa 
All the analysis shows that most of the bitumen foaming mechanism research have used bitumen foaming tests and statistics of relation analysis, regression and fitting to derive a mechanism conclusion. Moreover, similar technical problems often lead to quite different conclusions in some of those research projects. To clarify the influence of the controllable factors during bitumen foaming, CFD software is used for numerical calculation and the Grey relation analysis method is utilized. Finally, the controllable factors' degree of impact is analyzed to provide a theoretical basis for producing foamed bitumen.
Hot bitumen and cold water can change into bitumen droplets and water droplets by nozzle spraying. Cold water droplets directly contact the hightemperature bitumen droplets (160 ℃) when they are sprayed into the foaming cavity at the same time. Then the change of the water occurs and generates a large amount of water vapor. Volume increases immediately lead to increasing pressure in the cavity, which makes the gas pressure into the bitumen continuous phase, forming minute foamed bitumen. Finally the minute foamed bitumen is extruded out of the cavity by the pressure in the cavity. Because the internal pressure is greater than the external pressure of the asphalt film, the minute foamed bitumen after volume expansion form a metastable state of the foam asphalt. Injecting some compressed air with a certain pressure into the cavity supports the bitumen foaming. Figure 1 displays the bitumen foaming mechanism [1922]_{.}
Figure 1. Bitumen foaming mechanism schematic
Bitumen foaming is a physical change between multiphase flows. There is a strong coupling turbulent flow field between each phase fluid because each different phase has different velocity. Therefore, appropriately using the mixture model for the fluent is very important. Control equations of bitumen foaming behavior are as follows:
Mass conservation equation:
$\frac{\partial \rho}{\partial \tau}+\frac{\partial\left(\rho u_{x}\right)}{\partial x}+\frac{\partial\left(\rho u_{y}\right)}{\partial y}+\frac{\partial\left(\rho u_{z}\right)}{\partial z}=0$(1)
Momentum conservation equation:
$\rho \frac{d u}{d \tau}=\rho F_{b}\nabla P+\mu \nabla^{2} u+\frac{1}{3} \mu \nabla(\nabla \bullet u)$(2)
Energy conservation equation:
$\frac{d e}{d \tau}=\frac{q}{\rho}+\frac{k}{\rho} \nabla^{2} t\frac{p}{\rho}(\nabla \bullet u)+\frac{\mu \varphi}{\rho}$(3)
Turbulent kinetic energy K equation:
$\rho \frac{d k}{d t}=\frac{\partial}{\partial x_{i}}\left[\left(\mu+\frac{\mu_{t}}{\sigma_{k}}\right) \frac{\partial_{k}}{\partial x_{i}}\right]+G k+G b\rho \varepsilonY_{M}$(4)
Dissipation rate equation:
$\rho \frac{d \varepsilon}{d t}=\frac{\partial}{\partial x_{i}}\left[\left(\mu+\frac{\mu_{t}}{\sigma_{\varepsilon}}\right) \frac{\partial \varepsilon}{\partial x_{i}}\right]+C_{1 \varepsilon} \frac{\varepsilon}{k}\left(G_{k}+C_{3 \varepsilon} G_{b}\right)C_{2 \varepsilon} \rho \frac{\varepsilon^{2}}{k}$(5)
In the formulas: the ρ represents the density, $u_{\mathrm{x}}, u_{\mathrm{y}}, u_{\mathrm{z}}$ are respectively the velocity component at x, y, z direction; τ is time and $F_{b}$ is the mass force per unit; p is the stress, e is the internal fluid energy per unit, q is the energy generated by heat exchange, $G_{\mathrm{k}}$ is the turbulence energy made by average velocity gradient; $G_{\mathrm{b}}$ is the turbulence energy made by buoyancy, $Y_{M}$ is the influence made by compressible flow turbulence expansion on the total dissipation; $\sigma_{\mathrm{k}}$ is turbulent Prandtal constant; $\sigma_{\varepsilon}$ is the dissipation ration Prandtl constant; k is turbulent energy; ε is the dissipation ratio.
In numerically simulating of bitumen foaming, the bitumen nozzle, water nozzle and air nozzle are referred to as”Velocityinlet”, and the foamed bitumen nozzle is”Outflow” [23]. The wall satisfies the noslip condition, using the standard wall function method to set the nearwall region. The mixed flow field inside the cavity is characterized as gasliquid multiphase mixture unsteady flow, where the main phase is compressed air phase, and the others are bitumen phase, water phase and water vapor phase.
The numerical simulation of bitumen foaming can result in many physical flows distribution, such as pressure, speed, temperature, density, etc. A case of foaming water consumption, with 1%, 2%, 3%, 4%, 5% are shown in the stress diagram (Figure 2), velocity diagram (Figure 3), temperature diagram (Figure 4), density diagram (Figure 5).
As Figure 2 shows, when the dosage of foaming water changes, the internal cavity flow field will undergo a corresponding change. After being numerically calculated, the pressure, density, velocity and density averages are shown in Table 2. To date, foamed bitumen is principally measured according to two main parameters: the expansion ratio (ER), which measures the increase of bitumen in volume after being sprayed, and the halflife (HL), which evaluates the durability and stability of the foamedstate before collapsing [2426]. This paper takes the expansion and halflife as the Grey relation degree reference factors, using HR Yang’s experimental data (Table 3) to exchange and analyze. The expansion ratio and halflife test curve with different dosages of foaming water can be drawn. After the pressure, velocity, temperature and average density are numerically calculated under the same condition, the corresponding simulated curve is given (Figure 6). When the dosage of water changes, the expansion ratio, halflife, pressure, density, velocity and average density all change. It is difficult to note the degree of association among the expansion, halflife and numerical simulation of the flow field, as shown in Figure 6. Therefore, the Grey relation analysis method is adopted in order to determine which physical quantity of numerical simulation flow field has the largest relation to the expansion ratio and halflife. The physical quantity with the largest relation will be used as a theoretical evaluation factor.
Figure 2. Pressure diagram with different dosages of foaming water
Figure 3.Velocity diagram with different dosages of foaming water
Figure 4. Temperature diagram with different dosages of foaming water
Figure 5. Density diagram with different dosages of foaming water
Table 2. Simulation results of different dosages of foaming water
Dosages Of Foaming Water 
1% 
2% 
3% 
4% 
5% 
Emperature(K) 
404 
396 
387 
382 
378 
Velocity(Cm/S) 
539 
561 
565 
568 
586 
Density(Kg/M^{3}) 
595 
585 
594 
625 
630 
Pressure(Pa) 
12007 
9140 
8567 
8188 
7919 
Table 3. Experimental results of different dosages of foaming water
Dosages Of Foaming Water 
1% 
2% 
3% 
4% 
5% 
Expansion Ratio 
8.4 
15.7 
20.5 
21.7 
24.5 
HalfLife(S) 
14.1 
5.3 
4.7 
5.3 
4.9 
(a) Experimental results
(b) Simulation results
Figure 6. Result of experiment and numerical simulation
The Grey relation analysis method analyzes the effect of all factors on the system by comparing the Grey relation degree [2729]. The greater the Gray relation degree is, the greater the impact of the factors on the system will be. The Grey relation analysis method can refine the main factors and features that affect the system among many factors, as well as analyze the differences of effects of each factor on the system. This paper uses the Grey relation analysis method twice. First, relation degree analysis of experimental data and simulation data was performed to determine the evaluation reference factors used for theoretical analysis, which clearly characterized the association degree between the numerical results of the flow field distribution and experimental results of asphalt foaming. Second, the relation degree between the controllable factors and the reference factors was determined on the basis of evaluating reference factors used for theoretical analysis. The calculation process is as follows. Firstly, the reference sequence and compared sequence are determined. The reference sequence is a data sequence that reflects the characteristics of system behavior. The compared sequence is a data sequence composed of factors affecting the system behavior. The reference sequences are recorded as $\left\{X_{0}\right\}$ and compared sequences are recorded as $\left\{X_{i}\right\}$ .They are selected as follows:
$X_{0} : X_{0}=\left[x_{0}(1), x_{0}(2), x_{0}(3) \cdots \cdots x_{0}(k)\right]$
$(i=1,2,3, \cdots, n)$(6)
$\left\{\begin{aligned} X_{1} &=\left[x_{1}(1), x_{1}(2), x_{1}(3), \cdots \cdots, x_{1}(k)\right] \\ X_{2} &=\left[x_{2}(1), x_{2}(2), x_{2}(3), \cdots \cdots, x_{2}(k)\right] \\ X_{n} &=\left[x_{n}(1), x_{n}(2), x_{n}(3), \cdots \cdots x_{n}(k)\right] \end{aligned}\right.$
$(i=1,2,3, \cdots, n)$(7)
Then, the reference sequence and compared sequence were dealt with using the dimensionless (initialization) method. There is no comparability due to the different units of the original factors. Therefore, sequences were dealt with to eliminate the influence of dimension to form a new sequence with the same starting point, as expressed in Eq. (8):
$Y_{i}=X_{i} / x_{i}(1)=\left[y_{i}(1), y_{i}(2), y_{i}(3), \cdots \cdots, y_{i}(n)\right](i=1,2,3, \cdots, n)$(8)
Then, the relation coefficient of each sequence is solved according to the calculation of Eq.(9) .
$\eta_{i}(K)=\frac{\min \min \leftY_{0}(k)Y_{i}(k)\right+\rho \max \max \leftY_{0}(k)Y_{i}(k)\right}{\leftY_{0}(k)Y_{i}(k)\right+\rho \max \max \leftY_{0}(k)Y_{i}(k)\right}$(9)
where, $(i=1,2,3, \cdots, k), \rho$ is resolution factor, $\rho \in(0,1), \rho=0.5 \mathrm{s}, \frac{\min \min }{\mathrm{k}}\leftY_{0}(k)Y_{i}(K)\right$ is the minimum difference between two levels; $\max _{k} \max _{k}\leftY_{0}(k)Y_{i}(k)\right$ is the maximum difference between two levels. To more conveniently compare, take the average value of each sequence as the relation degree of the reference sequence and compared sequence and then calculate the relation degree according to Eq. (10).
$\gamma_{i}=\frac{1}{n} \sum_{k=1}^{n} \eta(k)$(10)
5.1 Determination of foamed bitumen reference factors used for theoretical evaluation
As Table 4 shows, the expansion ratio (ER) and halflife (HL) are regarded as the reference sequence in the bitumen foaming test, the average temperature, average pressure, average velocity and average density of the internal flow field of the foam cavity after the numerical calculation are seen as comparison reference.
Table 4. Bitumen foaming behavior data
Factors 
Data sequence(k) 

1 
2 
3 
4 
5 

ER X01 
8.4 
15.7 
20.5 
21.7 
24.5 

HL X02 
14.1 
5.3 
4.7 
5.3 
4.9 

Temperature X1 
407 
399 
391 
382 
383 

Pressure X2 
87 887 
90 853 
91 205 
91 652 
91 776 

Velocity X3 
6.25 
6.52 
6.63 
6.71 
6.84 

Density X4 
567 
573 
576 
593 
599 
After calculation, the Grey relation degree between the average values of temperature, pressure, velocity, density and the expansion rate and the halflife are obtained and listed in Table 5. r1, r2, r3, r4 represent respectively the Grey relation degree of expansion ratio with the average temperature, pressure, velocity, and density. r5, r6, r7, r8 represent respectively the Grey relation degree of halflife with the average temperature, pressure, velocity, and density.
Table 5. The degree of relation between numerical calculation physical field and foamed bitumen performance indicators
Factors 
Relation Coefficient 
Relation Degree 

ER 
$\eta_{1}$ 
1 
0.35 
0.34 
0.37 
0.35 
r1=0.5275 
$\eta_{2}$ 
1 
0.33 
0.32 
0.33 
0.32 
r2=0.5386 

$\eta_{3}$ 
1 
0.33 
0.31 
0.32 
0.30 
r3=0.5422 

$\eta_{4}$ 
1 
0.34 
0.32 
0.33 
0.31 
r4=0.5369 

HL 
$\eta_{5}$ 
1 
0.53 
0.40 
0.38 
0.33 
r5=0.4822 
$\eta_{6}$ 
1 
0.54 
0.41 
0.39 
0.35 
r6=0.4584 

$\eta_{7}$ 
1 
0.55 
0.42 
0.40 
0.35 
r7=0.4515 

$\eta_{8}$ 
1 
0.54 
0.41 
0.39 
0.35 
r8=0.4604 
Table 6. Relation degree average and dispersion

Pressure 
Density 
ER 
0.5386 
0.5369 
HL 
0.4584 
0.4604 
Average 
0.4985 
0.4987 
Dispersion 
0.0567 
0.0541 
5.2 The relational degree analysis of controllable factors in bitumen foaming
The average value of the density field inside the cavity is invoked as the reference sequence. The dosage of foaming water, bitumen temperature and bitumen viscosity are considered as comparison sequence, as shown in Table 7. The Grey relation analysis method was used again to estimate the relation degree of controllable factors. Results are displayed in Table 8.
Table 7. Numerical calculation result
Controllable Parameters 
Result 

Water(%) 
Temperature (℃) 
Viscosity (Pa•S) 
Density (kg/m3) 

1.5 
140 
0.25 
498 

2 
150 
0.16 
499 

2.5 
160 
0.11 
520 

3 
170 
0.08 
528 
Table 8. Grey relation degree of the Controllable parameters
Coefficient 
1 
2 
3 
4 
Degree(r) 
$\eta_{9}$ 
1 
0.75 
0.60 
0.51 
0.79 
$\eta_{10}$ 
1 
0.99 
1 
0.98 
0.88 
$\eta_{11}$ 
1 
0.60 
0.43 
0.33 
0.60 
As Table 8 shows, the Grey relation degree of controllable factors and the internal density field of the cavity are r9=0.79, r10=0.88, r11=0.60. Among them, r9, r10, r11 are the relation degree of dosage of foaming water, bitumen temperature and viscosity of bitumen. All the analysis demonstrates that the dosage of foaming water, viscosity of bitumen and bitumen heating temperature will affect the bitumen foaming behavior. The degree of influence sorted in descending order is bitumen heating temperature, dosage of foaming water and bitumen viscosity. The viscosity of bitumen declines with the increase in the bitumen heating temperature. From the analysis results, within a certain temperature range the impact of bitumen viscosity changing in the bitumen foaming process is lower than that of the bitumen heating temperature. Therefore, when using the method of Grey relation analysis, selection of the range of the comparison sequence is essential. The bitumen foaming process has strong fuzziness and strong coupling characteristics. The Grey relation analysis method can provide a useful way to quantitatively analyze the bitumen foaming behavior.
(1) After the numerical calculation of bitumen foaming, among the velocity field, pressure field, temperature field and density field, the relation between the average value of the density field and the performance of the foamed bitumen is better.
(2) Taking the average density of the inner flow field as the reference standard, by utilizing the Grey relation analysis method, it was determined that that Grey relation degree of bitumen heating temperature, dosage of foaming water, bitumen viscosity respectively was 0.79, 0.88, 0.60. The results show that the dosage of foaming water, the heating temperature of bitumen and the viscosity of bitumen all affect the process of bitumen foaming, and the influence of bitumen heating temperature is greatest. The second greatest influence is the dosage of foaming water, and the influence of bitumen viscosity on the bitumen foaming process is the least influential in the three contrast sequence.
This project is supported by National Natural Science Foundation of China (Grant No.51265033) and Natural Science Foundation of Inner Mongolia (Grant No.2012MS0702).
ρ 
Density 
$u_{\mathrm{x}}, u_{\mathrm{y}}, u_{\mathrm{z}}$ 
Velocity component at x, y, z direction 
τ 
Time 
$F_{b}$ 
Mass force per unit 
p 
Stress 
e 
Internal fluid energy per unit 
q 
Energy generated by heat exchange 
$G_{\mathrm{k}}$ 
Turbulence energy made by average velocity gradient 
$G_{\mathrm{b}}$ 
Turbulence energy made by buoyancy 
$Y_{M}$ 
Influence made by compressible flow turbulence expansion on the total dissipation 
$\sigma_{\mathrm{k}}$ 
Turbulent Prandtal constant 
$\sigma_{\varepsilon}$ 
Dissipation ration Prandtl constant 
k 
Turbulent energy 
ε 
Dissipation ratio 
$\left\{X_{0}\right\}$ 
Reference sequences 
$\left\{X_{i}\right\}$ 
Compare sequences 
$\rho$ 
Resolution factor 
ER 
Expansion ratio 
HL 
Halflife 
[1] Jia Peng, “Research of recycling pavement structure and material for common stem road,” Ph.D. thesis, Beijing Jiao tong University, 2014.
[2] Cheng Haiying and Wang AnLin, “Research for foam asphalt technology and equipment,” Construction Machinery and Equipment, vol. 41, no. 3, pp. 1822, 2010.
[3] Cheng HaiYing, Zhang Yu, Wang AnLin et al., “Foaming chamber design and evaluation based on the analysis of bitumen foaming essential characteristics,” Chinese Journal of Mechanical Engineering, vol. 48, pp. 13, 2012. DOI: 10.3901/JME.2012.13.152.
[4] M. F. C. Van de Ven, et al., “Development of (half) warm foamed bitumen mixes: state of the art,” International Journal of Pavement Engineering, vol. 8, pp. 163175, 2007. DOI: 10.1080/10298430601149635.
[5] Brennen M., Tia M., Altschaeffl A. G., et al., “Laboratory investigation of the use of foamed asphalt for recycled bituminous pavements,” Transportation Research Record, pp. 8087, 1983.
[6] Mofreh F. Saleh, “Effect of Rheology on the bitumen foam ability and mechanical properties of foam bitumen stabilised mixes,” International Journal of Pavement Engineering, vol. 8, no. 2, pp. 99110, 2007. DOI: 10.1080/10298430601149650.
[7] He, Gui Ping and W. G. Wong, “Effects Of moisture on strength and permanent deformation of foamed asphalt mix incorporating RAP materials,” Construction & Building Materials, vol. 22, no. 1, pp. 3040, 2008. DOI: 10.1016/j.conbuildmat.2006.06.033.
[8] Ozturk, Hande I., and M. E. Kutay, “Novel testing procedure for assessment of quality of foamed warm mix asphalt binders,” Journal of Materials in Civil Engineering, vol. 26, pp. 839844, 2014. DOI: 10.1061/(ASCE)MT.19435533.0000924.
[9] He, Gui Ping and W. G. Wong, “Laboratory study on permanent deformation of foamed asphalt mix incorporating reclaimed asphalt pavement materials,” Construction & Building Materials, vol. 21, pp. 18091819, 2007. DOI: 10.1016/j.conbuildmat.2006.05.024.
[10] Kim, Yongjoo, et al., “Development of mix design procedure for cold inplace recycling with foamed asphalt,” Journal of Materials in Civil Engineering, vol. 18, pp. 116124, 2006. DOI: 10.1061/(ASCE)08991561(2006)18:1(116).
[11] Wang AnLin, Zan PengYu, Lin Fei et al., “An engineering method for parameter sensitivity analysis of asphalt foaming,” Journal of Building Materials, vol. 15, no. 2, pp. 218221, 2012. DOI: 10.3969/j.issn.10079629.2012.02.013.
[12] Roberts, F. L., et al., “Hot mix asphalt materials, mixture design, and construction,” National Asphalt Pavement Association, 1991.
[13] Feng L. I., Huang S. and Jian X. U., “Foamed bitumen decay equation and bitumen foaming characteristics evaluation,” Journal of Tongji University, vol. 7, pp. 10311035, 2011. DOI: 10.3969/j.issn.0253374x.2011.07.016.
[14] Yang HuRong, He GuiPing, Han HaiFeng, “Effect of bitumen viscosity on foamability,” Highway, vol. 6, pp. 106112, 2004.
[15] Nataatmadja, Andreas, “Some characteristics of foamed bitumen mixes,” Transportation Research Record Journal of the Transportation Research Board, vol. 1767, pp. 120125, 2001. DOI: 10.3141/176715.
[16] Hailesilassie, Biruk W., M. Hugener and M. N. Partl, “Influence of foaming water content on foam asphalt mixtures,” Construction & Building Materials, vol. 85, pp. 6577, 2015. DOI: 10.1016/j.conbuildmat.2015.03.071.
[17] Iwański, Marek and A. ChomiczKowalska, “Laboratory study on mechanical parameters of foamed bitumen mixtures in the cold recycling technology,” Procedia Engineering, vol. 57, pp. 433442, 2013. DOI: 10.1016/j.proeng.2013.04.056.
[18] Crispino, Maurizio, et al., “Effects of foam agents on foaming processes and physical and rheological properties of bitumen,” Sustainability, Ecoefficiency, and Conservation in Transportation Infrastructure Asset Management, 2014. DOI: 10.1201/b1673023.
[19] Yu Liang, Lu Hai –Bing and Shi FangZhi, “Research on evaluation indexes of the foaming feature of asphalt,” Construction Technology, vol. 8, pp. 8285, 2009. DOI: 10.13824/j.cnki.cmtm.2009.08.011.
[20] Shi F. Z., He Z. H., Lu W. M., et al., “Principle and study of bitumen foaming,” Journal of Building Materials, vol. 2, pp. 183187, 2004. DOI: 10.3969/j.issn.10079629.2004.02.011.
[21] Cheng HaiYing, Hu Zhiyong and Chen Wenyan, “The flow control method of foamed bitumen,” International Journal Of Heat And Technology, vol. 33, no. 3, pp. 145150, 2015. DOI: 10.18280/ijht.330322.
[22] Hailesilassie, Biruk W., M. Hugener, and M. N. Partl, “Influence of foaming water content on foam asphalt mixtures,” Construction & Building Materials, vol. 85, pp. 6577, 2015. DOI: 10.1016/j.conbuildmat.2015.03.071.
[23] Cheng HaiYing, Hu Zhiyong and Jia Lei, “Response surface methodology of foamed bitumen expansion ratio,” International Journal of Heat and Technology, vol. 33, no.3, pp. 3542, 2015. DOI: 10.18280/ijht.330305.
[24] MartinezArguelles, Gilberto, et al., “Investigating physical and rheological properties of foamed bitumen,” Construction & Building Materials, vol. 72, pp. 423433, 2014.
[25] Windhagen, Wirtgen GmbH, Cold Recycling Manual, 1st ed, Germany, 2012.
[26] A guideline for the design and construction of bitumen emulsion and foamed bitumen stabilised material (Interim Technical Guideline, TG2). 2nd ed. Pretoria, South Africa: CSIR Transportek, Asphalt Academy; 2009.
[27] Liu SiFeng, “Emergence and development of grey system theory and its forward trends,” Journal of Nanjing University of Aeronautics & Astronautics, vol. 2, pp. 266272, 2004. DOI: 10.16356/j.10052615. 2004.02.027.
[28] Lu, Meng and K. Wevers, “Grey system theory and applications: A way forward,” Journal of Grey System, vol. 10, pp. 4753, 2007.
[29] Trivedi, H. V. and J. K. Singh, “Application of Grey system theory in the development of a runoff prediction model,” Biosystems Engineering, vol. 92, pp. 521526, 2005. DOI: 10.1016/j.biosystemseng.2005.09.005.