# Potential of Using Waste Materials in Flexible Pavement Structures Identified by Optimization Design Approach

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## Abstract

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_{2}emissions of materials used in pavement construction. In addition, a comparison was made between pavements with and without geosynthetic reinforcement in terms of design, optimum construction cost, and CO

_{2}emissions. The use of geosynthetics is even more effective in pavement structures that contain waste materials in an unbound layer, both in terms of cost and CO

_{2}emissions. The minimum value of the California Bearing Ratio of the subgrade was determined at which the use of geosynthetic reinforcement for pavement structure with and without the inclusion of waste materials is economically and sustainably justified. The use of geosynthetics could result in a 15% reduction in pavement structure cost and a 9% reduction in CO

_{2}emissions due to the reduced thickness of unbound layers. In addition, reducing the CBR of the unbound layer from 100% to 30% due to the inclusion of waste materials implies a cost increase of up to 13%. While the present study is based on an empirical pavement design method in which pavement thickness is limited by the pavement thickness index, the same minimum thicknesses are obtained in the optimization process regardless of whether the objective function is the minimum construction cost or minimum CO

_{2}emissions.

## 1. Introduction

- -
- Reduction in costs associated with disposal.
- -
- Preservation of landfill capacity.
- -
- Conservation of mined natural resources.
- -
- Reduction in environmental and ecological impacts.

_{2}emissions and the cost of using alternative materials for road construction. LCA research of bituminous mixtures containing recycled materials such as crumb rubber found significant environmental impact and energy savings benefits when wet technology was used, but showed almost no benefits when the dry technology was used, which the authors attributed to the lack of data on the maintenance and life cycle of rubber-reinforced asphalt [20]. Practical applications of the use of plastic waste have shown that it is possible to build durable roads from plastic and that the construction of such roads reduces CO

_{2}emissions compared to conventional road pavements [21,22,23]. The research suggests that waste material is an important building stone in pavement design and should be considered when constructing a new pavement. This paper further evaluates the impact of the quality of the waste material and virgin material mixture on the optimal pavement design and its CO

_{2}equivalent.

_{2}emissions in accordance with pavement design guidelines. Genetic algorithms have proven to be very effective because they do not require differentiable functions, which is advantageous for complex nonlinear functions such as those often used in pavement optimization. The main novelty of this work is the optimization model, which allows us to obtain an optimal design of the pavement structure and is able to take into account different material properties affected by the inclusion of waste materials, both in terms of cost and CO

_{2}emissions. Such an approach demonstrates the potential of using waste materials in flexible pavements in terms of cost and CO

_{2}emissions. To represent the effects of the material properties of the asphalt, base layer, sub-base layer, and subgrade, all of which are affected by the inclusion of waste materials, a parametric study was conducted to determine the optimal design of flexible pavement structures using the developed optimization model. Due to the large number of combinations of design parameters (material properties, traffic loads, and geosynthetic reinforcement) involved in the optimization process, manual execution of the algorithm was not possible. Therefore, an optimization model was developed that includes a loop that performs optimizations for each combination. In addition, a sensitivity analysis was performed on the importance of each design parameter based on all optimal solutions.

## 2. The Performance of Asphalt and Unbound Layers Containing Waste Materials

## 3. Optimization Model of Pavement Structure

_{2}emissions generated during construction are evaluated. The optimized pavement structure meets all required standards and specifications based on an empirical pavement design method.

_{as}(m) represents the asphalt surface layer, d

_{ab}(m) represents the binder layer of the asphalt, d

_{b}(m) represents the unbound base layer, and d

_{sb}(m) represents the unbound sub-base layer. Additionally, the construction cost of the pavement structure is defined as COST

_{pav}(EUR). The input data provided are used to represent various parameters and characteristics relevant to the design properties, which are used in the optimization process of the pavement structure. The definitions of the individual input data and the associated values are listed in Table 2. The unit prices (c

_{exe}, c

_{gc}, c

_{fill,sb}, c

_{fill,b}, c

_{as,subs}, c

_{as}, c

_{ab}, and c

_{geo}) of each material used in the pavement structure were assigned, as well as carbon indices (ci

_{exe}, ci

_{fill,sb}, ci

_{fill,b}, ci

_{as,subs}, ci

_{as}, ci

_{ab}, and ci

_{geo}) that allow the calculation of the total CO

_{2}emissions of the materials used in the pavement structure. While the empirical pavement design method is included in the optimization model, where the pavement thickness is limited by the pavement thickness index, it is of utmost importance to determine the equivalence factors a

_{i,as}, a

_{i,ab}, a

_{i,b}, and a

_{i,sb}based on the material properties of the individual pavement layers. In this way, it was possible to take into account the inclusion of waste material affecting the stability according to the Marshall stability test (SM

_{as}and SM

_{ab}) in the asphalt concrete layer and the CBR value (CBR

_{base}and CBR

_{subbase}) for the unbound base and the sub-base layer.

_{asb,0}(cm), and the required thickness of the unbound base layer, d

_{b,CBR,mod}(cm), which depend on the CBR of the subgrade, must be determined by a parameterized function. Therefore, the parameters a

_{1}, a

_{2}, c

_{1}, c

_{2}, c

_{3}, c

_{4}, and c

_{5}were determined based on an approximation of the charts included in the technical specifications for roads, which relate to the required thickness and the number of ESALs T

_{n}. Since the main objective of placing the sub-base layer is to improve the CBR value of the subgrade, the thickness of the required unbound sub-base layer d

_{sb,CBR,mod}(cm) is calculated to provide the modified CBR value at the top of the sub-base layer CBR

_{mod}. The correlation between the original CBR value of the subgrade, the thickness of the sub-base, and the modified CBR value at the top of the sub-base is determined by the parameters b

_{1}, b

_{2}, b

_{3}, and b

_{4}. Furthermore, the thickness of the sub-base layer can be reduced by a factor of γ

_{geo,sb}if the geosynthetic reinforcement is installed in the contact between the subgrade and the sub-base layer. Condition 6 ensures that the overall thickness of the pavement is sufficient to be frost resistant. While frost depth depends on geographic location and hydrologic conditions, factors f

_{fr}and h

_{m}are determined using Table 3. Hydrological conditions are favorable if the total thickness of the pavement structure is at least 1.5 m, the water table is constantly below freezing, and drainage is ensured without water inflow within the pavement. Otherwise, the factors for unfavorable conditions must be considered. The last four conditions (conditions 8–11) ensure that the thickness of each pavement layer is of a sufficient minimum thickness according to conventional pavement construction techniques.

## 4. Multi Parametric Optimization

_{2}emissions. An optimization model was used to determine the minimum thickness of each layer that still meets all conditions and consequently ensures sufficient performance over the intended 20-year period. The ESAL is the most important design parameter in pavement design, so a parametric analysis was also performed for this parameter. Therefore, the optimal designs of the pavement structure were determined for 450 combinations of the following parameters:

- -
- Total number of ESALs: T
_{n}(1 × 10^{4}; 1 × 10^{5}; 1 × 10^{6}; 1 × 10^{7}; 1 × 10^{7}). - -
- California Bearing Ratio of subgrade: CBR (3%; 4%; 5%; 6%; 7%).
- -
- Marshall stability of asphalt layers: SM
_{as}= SM_{ab}(2 kN; 4 kN; 6 kN; 8 kN; 10 kN). - -
- California Bearing Ratio of unbound layers: CBR
_{base}= CBR_{subbase}(100%; 60%; 30%).

_{as}= SM

_{ab}). The same applies to the unbound base and the sub-base layer (CBR

_{base}= CBR

_{subbase}).

_{2}emissions. In a parallel coordinate plot, the data points are represented as contiguous lines, and the parallel axes represent the different variables (Marshall stability, CBR of unbound layers, values of optimal pavement cost, and CO

_{2}emissions).

_{2}emissions for different combinations of Marshall stability and CBR of the unbound layers for an ESAL of T

_{n}= 1 × 10

^{6}and for subgrade CBR

_{subgrade}= 3%. While Figure 5b shows the results for pavements with geosynthetics, Figure 5a presents the results without geosynthetic reinforcement. The parallel plot can be read as in Figure 5a (see the blue lines) as follows: For a Marshall stability of SM = 2 kN and a CBR

_{base}= 30%, the optimal construction cost is 95.5 €/m

^{2}and CO

_{2}emissions are 41 kgCO

_{2}/m

^{2}, while for the same SM = 2 kN and a better CBR

_{base}= 100%, the optimal construction cost is 85 €/m

^{2}and CO

_{2}emissions are 39.3 kgCO

_{2}/m

^{2}. In this case, reducing the CBR of the unbound layer from 100% to 30% means an increase of 12% in costs and 4% in CO

_{2}emissions. Similarly, for a pavement structure with geosynthetic reinforcement, and the reduction in the quality of the unbound layers increases the cost by 9% and the CO

_{2}emissions by 3%. It was also found that Marshall stability has the largest impact on both cost and CO

_{2}emissions.

_{2}emissions by 48% when the Marshal stability of the asphalt layer is reduced from 10 kN to 2 kN. This reduction was calculated for a pavement with geosynthetics and a CBR value of 30% for unbound layers. The use of geosynthetics in most of the cases discussed in the parametric analysis reduces the cost of pavement structure and the amount of CO

_{2}emissions. The largest reduction in COST and CO

_{2}is given in the case where T

_{n}is in the range of 1 × 10

^{4}, CBR = 3%, SM = 10 kN, and the CBR of the base and sub-base layers is 30%. In this case, the use of geosynthetics results in a 15% reduction in COST and a 9% reduction in CO

_{2}due to the reduced thickness of the unbound pavement structure. Figure 6 shows that the use of geosynthetics is economically justified when the CBR of the subgrade is less than 5%, and that the use of geosynthetics is environmentally justified when the CBR

_{subgrade}is less than 6% if the properties of the base and sub-base layer are assumed to be CBR

_{base,subbase}= 100%. If the CBR value of the base and sub-base layer is low (CBR

_{base,subbase}= 30%), the use of geosynthetics is justified from an economic and environmental point of view if the CBR value of subgrade is less than 7%. It was found that the use of geosynthetics is particularly important in the case where the base and subgrade layers partially contain waste materials.

_{2}emissions. It should be noted that for all parameter combinations, the optimal thickness of the asphalt surface layer was calculated as d

_{as}= 4 cm, which corresponds to the minimum value specified. Based on these two tables, it was possible to evaluate the effects of the Marshall stability and the CBR value of the unbound layer on the design of flexible pavements. The thickness of the unbound layers increased from 91 cm to 120 cm when the CBR value of the base and sub-base layers decreased from 100% to 30%. For real-world pavement projects, Table 4 and Table 5 can help engineers and designers select the most appropriate materials, layer thicknesses, and construction methods for pavements where the design is based on the minimum cost and CO

_{2}emissions. The model was developed in a general form that allows an optimal design to be obtained for any input data based on real site conditions, material properties, and traffic loads.

_{n}), the Marshall stability of asphalt layers (SM

_{as}= SM

_{ab}), the California Bearing Ratio of the base and sub-base layer (CBR

_{base}= CBR

_{subbase}), and the subgrade conditions (CBR

_{subgrade}). Through this multiparametric analysis, the primary goal was to employ these key attributes to anticipate other continuous characteristics, including the minimum cost of pavement structure (COST) and the minimum CO

_{2}emissions (CO

_{2}). Prior to employing the predictive model, the dataset was split into a training dataset (odd-indexed samples) and a checking dataset (even-indexed samples). The “exhsrch” function in MATLAB (R2021a) was utilized to exhaustively search among the available inputs and determine the set of inputs that have the greatest impact on the optimal cost of the pavement structure and layer thickness. The “exhsrch” function involved building predictive models for each parameter combination, training them for an epoch, and subsequently reporting their achieved performance. In Figure 7, the leftmost input variable is the most pertinent in terms of the output, as it exhibits the lowest root-mean-square error (RMSE). The RMSE is defined as follows:

_{i}represents the values obtained through the optimization procedure (COST, CO

_{2}). Prediction models often face the challenge of overfitting. However, in this simple prediction model, the training and checking errors are comparable, indicating the absence of overfitting. It is important to note that the primary objective of this prediction model is to identify the inputs that exert the greatest influence on the output, rather than constructing a prediction model with minimal training error. To enhance the accuracy of the prediction model, it is advisable to incorporate more neurons in the neural networks. However, an increase in neurons may potentially lead to overfitting issues. The analysis also examines the combination of two inputs that hold the greatest influence over the output. The results of the parametric analysis unmistakably indicate that the total number of ESALs (T

_{n}) is the most crucial parameter for achieving the optimal cost of a pavement structure. Subsequently, the Marshall stability (SM

_{as}= SM

_{ab}), CBR of the subgrade (CBR

_{subgrade}), and CBR of unbound layers (CBR

_{base}= CBR

_{subbase}) follow suit in terms of their significance.

_{2}emissions for the pavement structure, the bound layers (asphalt layers) are responsible for 96% of the CO

_{2}emissions, while the unbound layers account for the remaining 4%. This distribution of CO

_{2}emissions is valid for T

_{n}= 1 × 10

^{8}, CBR

_{subgrade}= 7%, CBR

_{base}= 100%, and SM

_{as}= 2 kN. The analysis shows that the fraction of CO

_{2}emissions caused by asphalt layers is much more sensitive to design parameters, while the fraction of pavement costs caused by asphalt layers is less sensitive to design parameters.

## 5. Conclusions

_{2}emissions. The inclusion of waste materials was accounted for via equivalence factors used in the empirical pavement design method. The geosynthetic reinforced and unreinforced pavement design was optimized for different traffic loads and material properties. The proportion of costs and CO

_{2}emissions of the asphalt layers were also calculated. The main conclusions are the following:

- -
- For the most unfavorable design parameters examined in the parametric analysis, the thickness of the unbound layers increased from 91 cm to 120 cm (32% increase in thickness) when the CBR value of the base and sub-base layers decreased from 100% to 30%.
- -
- For the most unfavorable design parameters examined in the parametric analysis, the thickness of the asphalt layer increased from 36 cm to 58 cm (61% increase in thickness) when the Marshall stability value of the asphalt layer decreased from 10 kN to 2 kN.
- -
- The analysis shows that the proportion of CO
_{2}emissions caused by asphalt layers can vary from 30% to 96% depending on the design parameters, while the proportion of costs caused by asphalt layers only ranges from 67% to 79% for the same design parameters. This is due to the fact that the ratio of CO_{2}emissions between the asphalt layer and the unbound layer is higher than the ratio of prices. - -
- The results of the parametric analysis show that the total number of ESALs (T
_{n}) is the most important parameter for achieving the optimal cost of a pavement structure. This is followed by the Marshall stability (SM), the CBR value of the subgrade (CBR_{subgrade}), and the CBR value of the unbound layers (CBR_{base}= CBR_{subbase}) in terms of their importance. - -
- The use of geosynthetics could result in a 15% reduction in pavement structure cost and a 9% reduction in CO
_{2}emissions due to the reduced thickness of unbound layers. However, the use of geosynthetics could also result in an increase in road pavement structure cost and CO_{2}emissions under favorable site conditions (e.g., with a CBR subgrade of 7%). - -
- The empirical design method for pavements limits the Marshall stability to approximately 10 kN, although the stability of asphalt concrete could be higher. Therefore, the mechanical-empirical design method could further improve the optimization model by considering even larger Marshall stability values.

_{2}emissions while achieving a reduction in waste deposition. Since this optimization model and, consequently, the results presented are based on an empirical pavement design method, further investigations could be investigated by semi-empirical pavement design methods or methods based on finite element modeling.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Equivalence factors for given values of (

**a**) Marshall stability of asphalt and (

**b**) CBR of base and sub-base material.

**Figure 3.**Various test results of SM for different waste materials and their content in the bituminous mix.

**Figure 5.**Parallel coordinate plot of optimal pavement cost and CO

_{2}emissions for different Marshall stability of asphalt layer and CBR of unbound layers: (

**a**) without geosynthetic reinforcement and (

**b**) with geosynthetic reinforcement.

**Figure 6.**Costs and CO

_{2}emissions of road pavements depend on the quality of the subgrade and the use of geosynthetics.

**Figure 7.**Influence of each input variable on the optimal cost of a pavement structure and the CO

_{2}emissions (training data in blue line, test data in red line).

Objective function | $COS{T}_{pav}={C}_{exc}+{C}_{gc}+{C}_{fill,b}+{C}_{as,subs}+{C}_{fill,sb}+{C}_{as}+{C}_{ab}+{C}_{geo}$ |

${C}_{exc}={c}_{exc}\xb7{h}_{total}\xb7\left({B}_{ve}+{B}_{as}\right)\xb7L$ | |

${C}_{gc}={c}_{gc}\xb7\left({B}_{ve}+{B}_{as}\right)\xb7L$ | |

${C}_{fill,b}={c}_{fill,b}\xb7\left({B}_{ve}+{B}_{as}\right)\xb7{d}_{b}\xb7L$ | |

${C}_{as,subs}={c}_{as,subs}\xb7{B}_{as}\xb7L$ | |

${C}_{fill,sb}={c}_{fill,sb}\xb7\left({B}_{ve}+{B}_{as}\right)\xb7{d}_{sb}\xb7L$ | |

${C}_{as}={c}_{as}\xb7{B}_{as}\xb7{d}_{as}\xb7L$ | |

${C}_{ab}={c}_{ab}\xb7{B}_{as}\xb7{d}_{ab}\xb7L$ | |

${C}_{geo}={c}_{geo}\xb7\left({B}_{ve}+{B}_{as}\right)\xb7L$ | |

CO_{2} emissions | $C{O}_{2,total}=C{O}_{2,exc}+C{O}_{2,fill,b}+C{O}_{2,as,subs}+C{O}_{2,fill,sb}+C{O}_{2,as}+C{O}_{2,ab}+C{O}_{2,geo}$ |

$C{O}_{2,exc}=c{i}_{exc}\xb7{h}_{total}\xb7\left({B}_{ve}+{B}_{as}\right)\xb7L$ | |

$C{O}_{2,fill,b}=c{i}_{fill,b}\xb7\left({B}_{ve}+{B}_{as}\right)\xb7{d}_{b}\xb7L\xb7{\rho}_{base}$ | |

$C{O}_{2,as,subs}=c{i}_{as,subs}\xb7{B}_{as}\xb7L$ | |

$C{O}_{2,fill,sb}=c{i}_{fill,sb}\xb7\left({B}_{ve}+{B}_{as}\right)\xb7{d}_{sb}\xb7L\xb7{\rho}_{sub-base}$ | |

$C{O}_{2,as}=c{i}_{as}\xb7{B}_{as}\xb7{d}_{as}\xb7L\xb7{\rho}_{as}$ | |

$C{O}_{2,ab}=c{i}_{ab}\xb7{B}_{as}\xb7{d}_{ab}\xb7L\xb7{\rho}_{ab}$ | |

$C{O}_{2,geo}=c{i}_{geo}\xb7\left({B}_{ve}+{B}_{as}\right)\xb7L$ | |

Condition 1 | ${D}_{total}\ge {D}_{req}$ |

${D}_{total}={d}_{as}\xb7{a}_{i,as}+{d}_{ab}\xb7{a}_{i,ab}+{d}_{b}\xb7{a}_{i,b}$ | |

${D}_{req}={d}_{asb,0}\xb70.38+{d}_{b,CB{R}_{mod}}\xb70.14$ | |

${d}_{asb,0}={a}_{1}\xb7{T}_{n}{}^{{a}_{2}}$ | |

${d}_{b,CB{R}_{mod}}=\left(\left({c}_{1}-{c}_{2}\xb7CB{R}_{mod}\right)\xb7\mathrm{ln}\left({T}_{n}\right)-{c}_{3}+{e}^{\left({c}_{4}\xb7CB{R}_{mod}\right)\xb7{c}_{5}}\right)/{\gamma}_{geo,b}$ | |

Condition 2 | ${D}_{total,AC}\ge {D}_{req,AC}$ |

${D}_{total,AC}={d}_{as}\xb7{a}_{i,as}+{d}_{ab}\xb7{a}_{i,ab}$ | |

${D}_{req,AC}={d}_{asb,0}\xb70.38$ | |

Condition 3 | ${D}_{total,base}\ge {D}_{req,base}$ |

${D}_{total,base}={d}_{b}\xb7{a}_{i,b}$ | |

${D}_{req,base}={d}_{b,CB{R}_{mod}}\xb70.14$ | |

Condition 4 | ${d}_{prov}\ge {d}_{asb,0}$ |

${d}_{prov}={d}_{as}+{d}_{ab}$ | |

Condition 5 | ${d}_{b}\ge {d}_{b,req}$ |

${d}_{b,req}={d}_{b,CB{R}_{mod}}$ | |

Condition 6 | ${h}_{total}\ge {h}_{req}$ |

${h}_{total}={d}_{as}+{d}_{ab}+{d}_{b}+{d}_{sb}$ | |

${h}_{req}={h}_{m}\xb7{f}_{fr}$ | |

Condition 7 | ${d}_{sb}\ge {d}_{sb,CB{R}_{mod}}$ |

${d}_{sb,CB{R}_{mod}}=\left({b}_{1}\xb7\left(\frac{{b}_{2}\xb7\left(CB{R}_{mod}-CBR\right)}{{b}_{3}-CBR}+{b}_{4}\right)\xb7\left(\frac{0.14}{{a}_{i,sb}}\right)\right)/{\gamma}_{geo,sb}$ | |

Condition 8 | ${d}_{as}\ge {d}_{as,min}$ |

Condition 9 | ${d}_{ab}\ge {d}_{ab,min}$ |

Condition 10 | ${d}_{b}\ge {d}_{b,min}$ |

Condition 11 | ${d}_{sb}\ge {d}_{sb,min}$ |

Symbol | Value | Description |
---|---|---|

c_{exe} (€/m^{3}) | 9 | unit price of the ground excavation |

c_{gc} (€/m^{2}) | 2.5 | unit price of the ground compaction |

c_{fill,sb} (€/m^{3}) | 24 | unit price of the unbound sub-base fill |

c_{fill,b} (€/m^{3}) | 36 | unit price for unbound base fill |

c_{as,subs} (€/m^{2}) | 1.5 | unit price of the asphalt substrate |

c_{as} (€/m^{3}) | 300 | unit price of the asphalt surface layer |

c_{ab} (€/m^{3}) | 200 | unit price of the asphalt binder layer |

c_{geo} (€/m^{2}) | 3.2 | unit price of the geosynthetics |

B_{ve} (m) | 1 | width of the verge |

B_{as} (m) | 8 | width of the asphalt surface |

L (m) | 1000 | length of pavement sections |

ci_{exe} (kgCO_{2}/m^{3}) | 1.38 | carbon index for the ground excavation |

ci_{fill,b} (kgCO_{2}/kg) | 0.00248 | carbon index for unbound sub-base fill |

ci_{as,subs} (kgCO_{2}/m^{2}) | 0.35 | carbon index for unbound base fill |

ci_{fill,sb} (kgCO_{2}/kg) | 0.00248 | carbon index for asphalt substrate |

ci_{as} (kgCO_{2}/kg) | 0.08278 | carbon index for asphalt surface layer |

ci_{ab} (kgCO_{2}/kg) | 0.08278 | carbon index for asphalt binder layer |

ci_{geo}(kgCO_{2}/m^{2}) | 0.396 | carbon index for geosynthetics |

ρ_{base} (kg/m^{3}) | 1800 | density of the unbound base fill |

ρ_{sub-base} (kg/m^{3}) | 1800 | density of the unbound sub-base fill |

ρ_{as} (kg/m^{3}) | 2400 | density of the asphalt surface layer |

ρ_{ab} (kg/m^{3}) | 2400 | density of the asphalt binder layer |

t_{1}= t_{3} (-) | 0.182104767 | parameter for a_{i,as} and a_{i,ab} determination |

t_{2}= t_{4} (-) | 0.389702035 | parameter for a_{i,as} and a_{i,ab} determination |

t_{5}= t_{7} (-) | 0.049219606 | parameter for a_{i,b} and a_{i,sb} determination |

t_{6}= t_{8} (-) | 0.227144669 | parameter for a_{i,b} and a_{i,sb} determination |

a_{1} (-) | 0.6567 | parameter for required thickness of the asphalt |

a_{2} (-) | 0.2175 | parameter for required thickness of the asphalt |

b_{1} (-) | 8.382 | parameter for required thickness of sub-base |

b_{2} (-) | −0.791 | parameter for required thickness of sub-base |

b_{3} (-) | 1.975 | parameter for required thickness of sub-base |

b_{4} (-) | 1.912 | parameter for required thickness of sub-base |

c_{1} (-) | 6.239 | parameter for required thickness of base layer |

c_{2} (-) | 0.376 | parameter for required thickness of base layer |

c_{3} (-) | 26.64 | parameter for required thickness of base layer |

c_{4} (-) | 0.141 | parameter for required thickness of base layer |

c_{5} (-) | 4.882 | parameter for required thickness of base layer |

CBR_{mod} (%) | 15.0 | modified CBR value at the top of the sub-base layer |

γ_{geo,sb}(-) | 2.0 | reduction factor for the consideration of the geosynthetic |

h_{m} (cm) | 80 | depth of frost penetration |

f_{fr} (-) | 0.8 | Factor for the conditions of the material at the site |

d_{as,min} (m) | 0.04 | minimum thickness of the asphalt surface layer |

d_{ab,min} (m) | 0.06 | minimum thickness of the asphalt binder layer |

d_{b,min} (m) | 0.25 | minimum thickness of the unbound base layer |

d_{sb,min} (m) | 0.20 | minimum thickness of the unbound sub-base layer |

Resistance of the Material under the Pavement Structure against the Effects of Freezing and Thawing | Hydrological Conditions | Minimum Thickness of Pavement Structure h _{req} = (f_{fr})∙h_{m}h _{m} Is Depth of Frost Penetration | |
---|---|---|---|

to an Altitude of 600 m | from an Altitude of 600 m | ||

resistant | favorable | (0.6)∙h_{m} | (0.7)∙h_{m} |

unfavorable | (0.7)∙h_{m} | (0.8)∙h_{m} | |

not resistant | favorable | (0.7)∙h_{m} | (0.8)∙h_{m} |

unfavorable | (0.8)∙h_{m} | (0.9)∙h_{m} |

CBR_{base} = CBR_{subbase} = 100% | CBR_{base} = CBR_{subbase} = 30% | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

T_{n} (ESAL) | SM | d_{as} + d_{ab} | d_{b} | d_{sb} | COST | CO_{2} | d_{as} + d_{ab} | d_{b} | d_{sb} | COST | CO_{2} |

(-) | (kN) | (cm) | (cm) | (cm) | (€/m^{2}) | (kgCO_{2}/m^{2}) | (cm) | (cm) | (cm) | (€/m^{2}) | (kgCO_{2}/m^{2}) |

1.0 × 10^{4} | 10 | 10 | 25 | 66 | 61.9 | 22.0 | 10 | 33 | 87 | 72.5 | 23.7 |

1.0 × 10^{5} | 10 | 10 | 25 | 66 | 61.9 | 22.0 | 10 | 33 | 87 | 72.5 | 23.7 |

1.0 × 10^{6} | 10 | 13 | 25 | 66 | 68.2 | 26.7 | 13 | 33 | 87 | 78.7 | 28.4 |

1.0 × 10^{7} | 10 | 22 | 25 | 66 | 87.0 | 40.9 | 22 | 33 | 87 | 97.5 | 42.6 |

1.0 × 10^{8} | 10 | 36 | 25 | 66 | 116.3 | 62.9 | 36 | 33 | 87 | 126.8 | 64.6 |

1.0 × 10^{4} | 8 | 10 | 25 | 66 | 61.9 | 22.0 | 10 | 33 | 87 | 72.5 | 23.7 |

1.0 × 10^{5} | 8 | 10 | 25 | 66 | 61.9 | 22.0 | 10 | 33 | 87 | 72.5 | 23.7 |

1.0 × 10^{6} | 8 | 13 | 25 | 66 | 68.2 | 26.7 | 13 | 33 | 87 | 78.7 | 28.4 |

1.0 × 10^{7} | 8 | 22 | 25 | 66 | 87.0 | 40.9 | 22 | 33 | 87 | 97.5 | 42.6 |

1.0 × 10^{8} | 8 | 36 | 25 | 66 | 116.3 | 62.9 | 36 | 33 | 87 | 126.8 | 64.6 |

1.0 × 10^{4} | 6 | 10 | 25 | 66 | 61.9 | 22.0 | 10 | 33 | 87 | 72.5 | 23.7 |

1.0 × 10^{5} | 6 | 10 | 25 | 66 | 61.9 | 22.0 | 10 | 33 | 87 | 72.5 | 23.7 |

1.0 × 10^{6} | 6 | 14 | 25 | 66 | 70.3 | 28.3 | 14 | 33 | 87 | 80.8 | 30.0 |

1.0 × 10^{7} | 6 | 23 | 25 | 66 | 89.1 | 42.4 | 23 | 33 | 87 | 99.6 | 44.1 |

1.0 × 10^{8} | 6 | 38 | 25 | 66 | 120.5 | 66.0 | 38 | 33 | 87 | 131.0 | 67.7 |

1.0 × 10^{4} | 4 | 10 | 25 | 66 | 61.9 | 22.0 | 10 | 33 | 87 | 72.5 | 23.7 |

1.0 × 10^{5} | 4 | 10 | 25 | 66 | 61.9 | 22.0 | 10 | 33 | 87 | 72.5 | 23.7 |

1.0 × 10^{6} | 4 | 16 | 25 | 66 | 74.5 | 31.4 | 16 | 33 | 87 | 85.0 | 33.1 |

1.0 × 10^{7} | 4 | 27 | 25 | 66 | 97.5 | 48.7 | 27 | 33 | 87 | 108.0 | 50.4 |

1.0 × 10^{8} | 4 | 44 | 25 | 66 | 133.0 | 75.4 | 44 | 33 | 87 | 143.5 | 77.1 |

1.0 × 10^{4} | 2 | 13 | 25 | 66 | 68.2 | 26.7 | 13 | 33 | 87 | 78.7 | 28.4 |

1.0 × 10^{5} | 2 | 13 | 25 | 66 | 68.2 | 26.7 | 13 | 33 | 87 | 78.7 | 28.4 |

1.0 × 10^{6} | 2 | 21 | 25 | 66 | 84.9 | 39.3 | 21 | 33 | 87 | 95.5 | 41.0 |

1.0 × 10^{7} | 2 | 36 | 25 | 66 | 116.3 | 62.9 | 36 | 33 | 87 | 126.8 | 64.6 |

1.0 × 10^{8} | 2 | 58 | 25 | 66 | 162.3 | 97.4 | 58 | 33 | 87 | 172.8 | 99.1 |

CBR_{base} = CBR_{subbase} = 100% | CBR_{base} = CBR_{subbase} = 30% | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

T_{n} (ESAL) | SM | d_{as} + d_{ab} | d_{b} | d_{sb} | COST | CO_{2} | d_{as} + d_{ab} | d_{b} | d_{sb} | COST | CO_{2} |

(-) | (kN) | (cm) | (cm) | (cm) | (€/m^{2}) | (kgCO_{2}/m^{2}) | (cm) | (cm) | (cm) | (€/m^{2}) | (kgCO_{2}/m^{2}) |

1.0 × 10^{4} | 10 | 10 | 25 | 33 | 54.6 | 20.5 | 10 | 33 | 44 | 61.9 | 21.6 |

1.0 × 10^{5} | 10 | 10 | 25 | 33 | 54.6 | 20.5 | 10 | 33 | 44 | 61.9 | 21.6 |

1.0 × 10^{6} | 10 | 13 | 25 | 33 | 60.9 | 25.2 | 13 | 33 | 44 | 68.1 | 26.3 |

1.0 × 10^{7} | 10 | 22 | 25 | 33 | 79.7 | 39.3 | 22 | 33 | 44 | 87.0 | 40.4 |

1.0 × 10^{8} | 10 | 36 | 25 | 33 | 109.0 | 61.3 | 36 | 33 | 44 | 116.2 | 62.4 |

1.0 × 10^{4} | 8 | 10 | 25 | 33 | 54.6 | 20.5 | 10 | 33 | 44 | 61.9 | 21.6 |

1.0 × 10^{5} | 8 | 10 | 25 | 33 | 54.6 | 20.5 | 10 | 33 | 44 | 61.9 | 21.6 |

1.0 × 10^{6} | 8 | 13 | 25 | 33 | 60.9 | 25.2 | 13 | 33 | 44 | 68.1 | 26.3 |

1.0 × 10^{7} | 8 | 22 | 25 | 33 | 79.7 | 39.3 | 22 | 33 | 44 | 87.0 | 40.4 |

1.0 × 10^{8} | 8 | 36 | 25 | 33 | 109.0 | 61.3 | 36 | 33 | 44 | 116.2 | 62.4 |

1.0 × 10^{4} | 6 | 10 | 25 | 33 | 54.6 | 20.5 | 10 | 33 | 44 | 61.9 | 21.6 |

1.0 × 10^{5} | 6 | 10 | 25 | 33 | 54.6 | 20.5 | 10 | 33 | 44 | 61.9 | 21.6 |

1.0 × 10^{6} | 6 | 14 | 25 | 33 | 63.0 | 26.8 | 14 | 33 | 44 | 70.2 | 27.9 |

1.0 × 10^{7} | 6 | 23 | 25 | 33 | 81.8 | 40.9 | 23 | 33 | 44 | 89.0 | 42.0 |

1.0 × 10^{8} | 6 | 38 | 25 | 33 | 113.2 | 64.5 | 38 | 33 | 44 | 120.4 | 65.6 |

1.0 × 10^{4} | 4 | 10 | 25 | 33 | 54.6 | 20.5 | 10 | 33 | 44 | 61.9 | 21.6 |

1.0 × 10^{5} | 4 | 10 | 25 | 33 | 54.6 | 20.5 | 10 | 33 | 44 | 61.9 | 21.6 |

1.0 × 10^{6} | 4 | 16 | 25 | 33 | 67.2 | 29.9 | 16 | 33 | 44 | 74.4 | 31.0 |

1.0 × 10^{7} | 4 | 27 | 25 | 33 | 90.2 | 47.2 | 27 | 33 | 44 | 97.4 | 48.3 |

1.0 × 10^{8} | 4 | 44 | 25 | 33 | 125.7 | 73.9 | 44 | 33 | 44 | 132.9 | 75.0 |

1.0 × 10^{4} | 2 | 13 | 25 | 33 | 60.9 | 25.2 | 13 | 33 | 44 | 68.1 | 26.3 |

1.0 × 10^{5} | 2 | 13 | 25 | 33 | 60.9 | 25.2 | 13 | 33 | 44 | 68.1 | 26.3 |

1.0 × 10^{6} | 2 | 21 | 25 | 33 | 77.6 | 37.8 | 21 | 33 | 44 | 84.9 | 38.9 |

1.0 × 10^{7} | 2 | 36 | 25 | 33 | 109.0 | 61.3 | 36 | 33 | 44 | 116.2 | 62.4 |

1.0 × 10^{8} | 2 | 58 | 25 | 33 | 155.0 | 95.9 | 58 | 33 | 44 | 162.2 | 97.0 |

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## Share and Cite

**MDPI and ACS Style**

Jelušič, P.; Gücek, S.; Žlender, B.; Gürer, C.; Varga, R.; Bračko, T.; Taciroğlu, M.V.; Korkmaz, B.E.; Yarcı, Ş.; Macuh, B.
Potential of Using Waste Materials in Flexible Pavement Structures Identified by Optimization Design Approach. *Sustainability* **2023**, *15*, 13141.
https://doi.org/10.3390/su151713141

**AMA Style**

Jelušič P, Gücek S, Žlender B, Gürer C, Varga R, Bračko T, Taciroğlu MV, Korkmaz BE, Yarcı Ş, Macuh B.
Potential of Using Waste Materials in Flexible Pavement Structures Identified by Optimization Design Approach. *Sustainability*. 2023; 15(17):13141.
https://doi.org/10.3390/su151713141

**Chicago/Turabian Style**

Jelušič, Primož, Süleyman Gücek, Bojan Žlender, Cahit Gürer, Rok Varga, Tamara Bračko, Murat V. Taciroğlu, Burak E. Korkmaz, Şule Yarcı, and Borut Macuh.
2023. "Potential of Using Waste Materials in Flexible Pavement Structures Identified by Optimization Design Approach" *Sustainability* 15, no. 17: 13141.
https://doi.org/10.3390/su151713141