# Influence of Embedded Charging Units Characteristics on Long-Term Structural Behavior of E-Roads

^{*}

## Abstract

**:**

## 1. Introduction

- Optimization of void CU material, shape, and dimension, considering a 2D Finite Element approach and typical material characteristics from scientific literature;
- Fatigue resistance of e-road_void CU, considering some of the optimized void CU geometries. This part is separated into two steps: the theoretical fatigue assessment, which allows to calculate the critical load repetitions leading to pavement failure, and the case study of Viale Forlanini in Milan, which allows to determine the pavement DI under specific traffic conditions;
- Rutting resistance of e-road_void CU, considering some of the optimized void CU geometries. In line with the previous one, also this part is divided in two steps: the theoretical rutting assessment, which allows to calculate the critical load cycles leading to rut an e-road pavement for a particular Rut Depth (RD) and the case study of Viale Forlanini in Milan, which allows to determine the pavement RD under specific traffic conditions.

_{f}, the bottom-up one is considered. In this case, the fatigue cracking starts at the bottom of the asphalt layer and propagates upwards to the surface [11]. Thus, traffic repetitions N

_{f}—that lead to a bottom-up fatigue cracking—are calculated using Equations (2) to (5), proposed by AASHTO [11].

_{i}= actual number of load repetitions in period i; N

_{fi}= allowable number of axle loads (that leads to failure) in period i.

_{b}= effective binder content by volume (%); V

_{a}= air voids in the Hot Mix Asphalt (HMA) mixture (%); C

_{H}= thickness correction term; H

_{HMA}= total HMA thickness in [in]; ε

_{t}= horizontal tensile strain at the critical location [–]; E = stiffness of HMA measured in [psi].

_{yy}is the vertical compressive strain; n is the actual number of load repetitions; b is a coefficient equal to 0.2 (thickness higher than 0.12 m) or 0.3 (thickness lower than or equal to 0.12 m).

## 2. Materials and Methods

#### 2.1. Optimization of Void CU Material, Shape and Dimension

- Void CU_R1: this is the simplest geometry, showing a rectangular cavity (R1), as studied in previous Author’s research [2];
- Void CU_R2: this geometry has a vertical cavity partition that leads to two rectangular cavities (R2);
- Void CU_C4: this geometry is characterized by four circular cavities (C4) equally distributed along CU horizontal axis;
- Void CU_C6: this geometry is characterized by six circular cavities (C6) equally distributed along CU horizontal axis.

_{ctm}is calculated using Equation (9) from [18].

_{ck}is the characteristic compressive strength of concrete determined by testing cylinders.

^{2}). E-road_void CU_R1_25, studied in previous research [2], is assumed to be the reference cross-sectional geometry. As a first general comment, it is possible to note that an increase in Young’s modulus leads to an increase in cavity area, for the same CU geometry. More in detail, considering rectangular cavities, the cavity area increases by 33% (R1_33), 67% (R1_35), 488% (R2_25), 522% (R2_33), and 555% (R2_35) compared to R1_25. As highlighted, R2_35 is the geometry characterized by the wider cavity area with benefit for electrical device positioning. As regards circular cavities, the CU thickness with Young’s modulus of 33,000 N/mm

^{2}is equal to the thickness with a modulus of 35,000 N/mm

^{2}. This is the result of a design technological choice regarding CU construction, which considers a minimum of 0.02 m for up/down CU thickness. Therefore, the cavity area increases by 179% (C4_25), 319% (C6_25), 336% (C4_33 and C4_35), and 554% (C6_33 and C6_35) with respect to R1_25. Based on these results, it is possible to note that R2_35 has the same cavity area as C6_33/C6_35.

#### 2.2. Methodology

#### 2.2.1. Fatigue

- Theoretical assessment: since the actual traffic is unknown, Miner’s law cannot be applied in a traditional manner. Considering that, theoretically, fatigue cracking appears at DI equal to 1, it is possible to calculate the number of traffic repetitions that leads to that damage value.
- Case study: the actual traffic in Viale Forlanini (Milan) is available, therefore, Miner’s law can be used to calculate pavement DI. Two traffic conditions are examined, as explained in [19]: traffic on one lane—conservative assumption—(5.75 × 10
^{7}ESAL) and traffic equally distributed on two lanes (2.88 × 10^{7}ESAL).

#### 2.2.2. Rutting

- Four e-road cross-sectional geometries are analyzed: R1_35, R2_35, C4_33, and C6_33;
- The characteristics of each material are listed below:
- Three load positions are examined: centered on CU, CU edge, and CU center.

- Theoretical assessment: since the actual traffic is unknown, RD cannot be calculated. Therefore, the aim of this part is the identification of traffic repetition numbers that lead to rut a pavement for a defined depth equal to 1.5 cm [12,13,14]. A spreadsheet solver is developed to calculate those critical cycle numbers.
- Case study: the actual traffic in Viale Forlanini (Milan) is available, therefore, it is possible to calculate the RD. As shown in [19], two traffic conditions are studied: total traffic vehicles on one or two lanes.

## 3. Results and Discussion

#### 3.1. Theoretical Assessment Results

^{2}). By comparing the geometry having a rectangular cavity, it is possible to note an increase of traffic repetition by 37.39% in R1_35 with respect to R1_25. Moreover, considering the same Young’s modulus (35,000 N/mm

^{2}) and a cavity area increase of four times, the R2_35 critical load cycles are higher (26.23%) than the ones in R1_35. Finally, by comparing the smallest and the widest cavity area, an increase in R2_35 by 56.50% is evident with respect to the solid CU_25.

#### 3.2. Case Study Results

- R2_35 rut depth decreases 0.7% (centered on CU) and 6.1% (CU edge) with respect to the circular cavities outcomes;
- R2_35 rut depth increases 37.4% (CU center) with respect to the circular cavities value.

- Fatigue Damage Index: DI
_{Fatigue}= DI, and - Rutting Damage Index: DI
_{Rutting}= RD/1.5 cm

_{Fatigue}= 1 and DI

_{Rutting}= RD/1.5 cm = 1) are indicated in these graphs. Considering fatigue resistance, in both traffic hypotheses, the combination C6_ 33-load along CU edge is higher than the required limit, with DI

_{Fatigue}value from 1.4 to 2.8. On the contrary, all the dots (combinations of CU geometries and load positions) are significantly below the rutting threshold (DI

_{Rutting}= 1) in both traffic conditions.

## 4. Conclusions

- Several CU geometries are suggested to provide the electronic field specialists with different alternatives for satisfying electrical technology needs, while ensuring long-lasting pavement structural performance.
- Among the investigated CU geometries, both rectangular and circular cavities can be used for electrical technologies accommodation; among the others, R2_35 (two rectangular cavities, 295 mm in width and 80 mm in heigh each, 47,200 mm
^{2}of total area) and C6_33 (six circular cavities, 100 mm in diameter each, 47,124 mm^{2}of total area) maximize CU cavity area. - Although R2_35 and C6_33 are characterized by the same cavity area, the obtained results are really different with better outcomes for the rectangular cavities. This means that the CU cavity shape affects the final outcomes. Therefore, both shape and dimension are essential to assess the void CU structural behavior.
- By comparing fatigue and rutting results, it is possible to note that the critical phenomenon is fatigue. In fact, the theoretical assessment demonstrates that the numbers of critical load cycles in fatigue are lower (about three order of magnitude) than the traffic repetitions computed for rutting.
- R2_35 shows different fatigue (the best one) and rutting (the worst one) behaviors when the load is on CU center. Probably, these results can be attributed to the high vertical strains recorded in the wearing course during rutting assessment.
- Load positions affect the theoretical results. In fact, when the load is centered on CU or on CU center, fatigue/rutting results are quite similar under the same CU geometry. The only exception is for rutting of R2_35, which is characterized by high difference between results (that are obtained considering the above load positions). For all geometries and considering both phenomena (except for R2_35-rutting), the most critical load position is load along CU edge.
- For both phenomena, the configuration described by F6_33 and load along CU edge leads to the lower results.
- The case study results corroborate the outcomes of the theoretical part, also in presence of the most conservative assumption of traffic (on one lane).

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Alternative Fuel passenger cars and vans fleet (BEV, PHEV, H2, LPG, CNG, LNG) as % of total passenger cars and vans fleet in EU-27 during 2021; from [1].

**Figure 2.**Alternative Fuel passenger cars and vans (BEV, PHEV, H2, LPG, CNG, LNG) as % of new registrations in the EU-27 during 2021; from [1].

**Figure 3.**Cross-sectional geometry; (

**a**) e-road_void CU_R1; (

**b**) e-road_void CU_R2; (

**c**) e-road_void CU_C4; (

**d**) e-road_void CU_C6.

**Figure 6.**Comparison of the critical load cycles for fatigue and rutting phenomena, according to CU geometries and load positions.

**Figure 7.**Comparison between DI

_{Fatigue}and DI

_{Rutting}values according to CU geometries and load positions considering (

**a**) traffic on one lane; (

**b**) traffic on two lanes.

Concrete Characteristics | |||||
---|---|---|---|---|---|

Bulk Density [N/m ^{3}] | Young’s Modulus [N/mm^{2}] | Poisson’s Ratio [-] | Failure Tensile Stress [N/mm^{2}] | ||

Compressive strength classes of concrete | C20/25 | 23,000 | 25,000 | 0.20 | 2.21 |

C30/37 | 33,000 | 2.90 | |||

C40/45 | 35,000 | 3.51 |

Concrete Young’s modulus [N/mm^{2}] | ||||||

25,000 | 33,000 | 35,000 | ||||

CU geometry | Thickness [mm] | Up | 70 | 60 | 50 | |

Down | 40 | 40 | 40 | |||

Lateral | 280 | 280 | 280 | |||

Cavity dimension [mm] | 240 × 30 | 240 × 40 | 240 × 50 | |||

Cavity area [mm^{2}] | 7200 | 9600 | 12,000 | |||

ID | R1_25 | R1_33 | R1_35 | |||

Thickness [mm] | Up | 20 | 20 | 20 | ||

Down | 40 | 40 | 40 | |||

Lateral | 90 | 80 | 70 | |||

Cavity dimension [mm] | 265 × 80 | 280 × 80 | 295 × 80 | |||

Cavity area [mm^{2}] | 42,400 | 44,800 | 47,200 | |||

ID | R2_25 | R2_33 | R2_35 | |||

Thickness [mm] | Up | 30 | 20 | 20 | ||

Down | 30 | 20 | 20 | |||

Lateral | 96 | 80 | 80 | |||

Cavity dimension [mm] | 80 × 80 | 100 × 100 | 100 × 100 | |||

Cavity area [mm^{2}] | 20,106 | 31,416 | 31,416 | |||

ID | C4_25 | C4_33 | C4_35 | |||

Thickness [mm] | Up | 30 | 20 | 20 | ||

Down | 30 | 20 | 20 | |||

Lateral | 46 | 29 | 29 | |||

Cavity dimension [mm] | 80 × 80 | 100 × 100 | 100 × 100 | |||

Cavity area [mm^{2}] | 30,159 | 47,124 | 47,124 | |||

ID | C6_25 | C6_33 | C6_35 |

**Table 3.**Distribution of vertical/horizontal stresses σ

_{yy}/σ

_{xx}[N/m

^{2}] at different cross-sectional geometries of e-road and different load positions.

Cross-Sectional Geometries | |||||
---|---|---|---|---|---|

Void CU_R1_35 | Void CU_R2_35 | Void CU_C4_33 | Void CU_C6_33 | ||

Load centered on CU | σ_{yy} | ||||

σ_{xx} | |||||

Load on CU edge | σ_{yy} | ||||

σ_{xx} | |||||

Load on CU center | σ_{yy} | ||||

σ_{xx} |

Bulk Density [N/mm ^{3}] | Young’s Modulus [N/mm^{2}] | |||||||
---|---|---|---|---|---|---|---|---|

Winter | Spring/Autumn | Summer | ||||||

Theoretical | Case Study | Theoretical E + 50% | Case Study 8 °C | Theoretical | Case Study 21 °C | Theoretical E − 50% | Case Study 34 °C | |

Wearing Course | 24,000 | 24,240 | 8250 | 17,502 | 5500 | 8092 | 2750 | 2822 |

Binder Course | 23,500 | 23,970 | 5250 | 17,242 | 3500 | 8610 | 1750 | 3363 |

Theoretical | Case Study | |
---|---|---|

Maximum horizontal tensile strains ε_{t} [-] | According to geometries, load positions and temperatures | |

Asphalt concrete Young’s modulus E [N/mm^{2}] | According to Table 4 | |

Binder content V_{b} [%] | 5.00 | 4.80 |

Air void content V_{a} [%] | 4.00 | 3.85 |

HMA total thickness H_{HMA} [m] | 0.19 | 0.19 |

n [ESAL] Corresponding to DI = 1 | CU Geometries | ||||
---|---|---|---|---|---|

R1_35 | R2_35 | C4_33 | C6_33 | ||

Load positions | Centered on CU | 3.83 × 10^{8} | 4.19 × 10^{8} | 4.45 × 10^{8} | 4.11 × 10^{8} |

CU edge | 3.05 × 10^{8} | 3.85 × 10^{8} | 5.02 × 10^{7} | 1.58 × 10^{7} | |

CU center | 4.38 × 10^{8} | 4.46 × 10^{8} | 4.23 × 10^{8} | 3.88 × 10^{8} |

**Table 7.**Critical numbers of traffic repetition, according to different e-road cross-sectional geometries.

Critical Load Cycles n [ESAL] | Cavity Area [m^{2}] | ||
---|---|---|---|

Cross-sectional geometry | e-road_solid CU_25 | 2.46 × 10^{8} | 0.0 |

e-road_ void CU_R1_25 | 2.22 × 10^{8} | 7.2 × 10^{−3} | |

e-road_void CU_R1_35 | 3.05 × 10^{8} | 12.0 × 10^{−3} | |

e-road_ void CU_R2_35 | 3.85 × 10^{8} | 47.2 × 10^{−3} | |

e-road_ void CU_C4_33 | 5.02 × 10^{7} | 31.4 × 10^{−3} | |

e-road_ void CU_C6_33 | 1.58 × 10^{7} | 47.1 × 10^{−3} |

n [ESAL] Leading to RD = 1.5 cm | CU Geometries | ||||
---|---|---|---|---|---|

R1_35 | R2_35 | C4_33 | C6_33 | ||

Load positions | Centered on CU | 1.22 × 10^{11} | 1.31 × 10^{11} | 1.30 × 10^{11} | 1.28 × 10^{11} |

CU edge | 1.07 × 10^{11} | 5.92 × 10^{10} | 4.84 × 10^{10} | 2.91 × 10^{10} | |

CU center | 1.28 × 10^{11} | 3.56 × 10^{10} | 1.26 × 10^{11} | 1.09 × 10^{11} |

Damage Index [-] | CU Geometries | |||||
---|---|---|---|---|---|---|

R1_35 | R2_35 | C4_33 | C6_33 | |||

Load positions and traffic conditions | Centered on CU | One lane | 0.34 | 0.31 | 0.29 | 0.31 |

Two lanes | 0.17 | 0.16 | 0.14 | 0.15 | ||

CU edge | One lane | 0.40 | 0.35 | 0.86 | 2.79 | |

Two lanes | 0.20 | 0.17 | 0.43 | 1.39 | ||

CU center | One lane | 0.29 | 0.29 | 0.31 | 0.34 | |

Two lanes | 0.14 | 0.15 | 0.15 | 0.17 |

Rut Depth [cm] | CU Geometries | |||||
---|---|---|---|---|---|---|

R1_35 | R2_35 | C4_33 | C6_33 | |||

Load positions and traffic conditions | Centered on CU | One lane | 0.145 | 0.142 | 0.143 | 0.143 |

Two lanes | 0.123 | 0.120 | 0.121 | 0.121 | ||

CU edge | One lane | 0.151 | 0.183 | 0.169 | 0.195 | |

Two lanes | 0.127 | 0.154 | 0.143 | 0.165 | ||

CU center | One lane | 0.142 | 0.224 | 0.154 | 0.163 | |

Two lanes | 0.121 | 0.190 | 0.131 | 0.138 |

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## Share and Cite

**MDPI and ACS Style**

Nodari, C.; Ketabdari, M.; Crispino, M.; Toraldo, E.
Influence of Embedded Charging Units Characteristics on Long-Term Structural Behavior of E-Roads. *Smart Cities* **2022**, *5*, 756-770.
https://doi.org/10.3390/smartcities5030039

**AMA Style**

Nodari C, Ketabdari M, Crispino M, Toraldo E.
Influence of Embedded Charging Units Characteristics on Long-Term Structural Behavior of E-Roads. *Smart Cities*. 2022; 5(3):756-770.
https://doi.org/10.3390/smartcities5030039

**Chicago/Turabian Style**

Nodari, Claudia, Misagh Ketabdari, Maurizio Crispino, and Emanuele Toraldo.
2022. "Influence of Embedded Charging Units Characteristics on Long-Term Structural Behavior of E-Roads" *Smart Cities* 5, no. 3: 756-770.
https://doi.org/10.3390/smartcities5030039