#
CO_{2}-Optimization of Post-Tensioned Concrete Slab-Bridge Decks Using Surrogate Modeling

^{1}

^{2}

^{*}

## Abstract

**:**

_{2}) emissions using surrogate modeling, whether it is the deck of a post-tensioned cast-in-place concrete slab bridge or any other design structure. The main contribution of this proposal is that it allows optimizing structures methodically and sequentially. The approach presents two sequential phases of optimization, the first one of diversification and the second one of intensification of the search for optimums. Finally, with the amount of CO

_{2}emissions and the differentiating characteristics of each design, a heuristic optimization based on a Kriging metamodel is performed. An optimized solution with lower emissions than the analyzed sample is obtained. If CO

_{2}emissions were to be reduced, design recommendations would be to use slendernesses as high as possible, in the range of 1/30, which implies a more significant amount of passive reinforcement. This increase in passive reinforcement is compensated by reducing the measurement of concrete and active reinforcement. Another important conclusion is that reducing emissions is related to cost savings. Furthermore, it has been corroborated that for a cost increase of less than 1%, decreases in emissions emitted into the atmosphere of more than 2% can be achieved.

## 1. Introduction

_{2}emissions is a relevant factor in the current climate change situation. The need to reduce the carbon footprint affects all human activities, including construction-related ones [1]. Indeed, construction contributes more than 40% of the world’s energy consumption and over one-third of greenhouse gas emissions [2]. It is estimated that the global production of structural concrete accounts for more than 5% of carbon emissions [3]. Therefore, there has been a progressive interest in incorporating environmental sustainability optimization in the construction sector [4].

_{2}emissions has been performed on building structures [9,10,11,12], bridge piers [13], or retaining walls [14,15,16], among other types of structures. In the cases studied, it is found that cost and emissions are related since they decrease as the material used is reduced.

_{2}emissions as an objective function, has been the subject of several works by our research group. Yepes et al. [17] optimized a prefabricated trough girder bridge with a hybrid firefly-based algorithm, showing that a €1 reduction can save up to 1.75 kg of CO

_{2}. García-Segura et al. [18] optimize a post-tensioned box-section footbridge, whose results indicate that the emission reduction is achieved with more significant edges, more active reinforcement cables, and lower concrete characteristic strength. García-Segura and Yepes [19] performed a multi-objective optimization with cost, emissions, and safety for a post-tensioned box-section bridge. Penadés-Plà et al. [20] compared two box-section bridges showing that the emissions in the demolition phase are higher than those in the maintenance and repair phases. It was also shown that, although carbon emissions are an essential indicator of environmental impact, in some cases, it is insufficient, and other environmental impacts should be considered [21]. Yepes et al. [22] applied different metaheuristics to optimize cost and emissions in a single-span mixed concrete and steel footbridge. Martinez-Muñoz et al. [23] perform a recent review of research works related to composite bridges.

_{2}emissions [34] and energy [35].

## 2. Description of the Lightened Slab Bridge Deck

## 3. Methodology

_{2}emissions. A response surface generated by a Kriging metamodel is optimized with these values.

#### 3.1. Sampling Method

#### 3.2. CO_{2} Emissions Assessment

_{2}emissions. In order to compare the designs, the elements relevant to emissions were analyzed, in particular, the type of concrete (strength), the formwork surface used, the amount of steel, and the voids volume. This study analyzes sustainability based on a function of CO

_{2}emissions during construction. To this end, the values for materials were taken from the BEDEC materials database [36]. The data do not reflect transportation emissions, which are highly dependent in all case studies. Note that concrete unit emissions were determined from each mix design. The emissions were evaluated according to the data shown in Table 1.

_{2}. The direct emissions of the materials used are considered since they are the ones that make the difference between the alternatives.

#### 3.3. Response Surface Optimization and Generation Method

_{α}, with α = 1, ..., n. Figure 4 expresses this idea. In this case, the attribute is the emissions produced by the execution of the deck, and the points are the set of solutions extracted by LHS sampling.

_{0}is set following Medina’s method [39], which halves the temperature when the acceptance ratio exceeds 40% and doubles it when the ratio is less than 20%. The temperature is reduced geometrically by the expression T = kT each time it lasts 1000 Markov chains, according to a cooling coefficient k = 0.8. This temperature reduction reduces the probability of accepting a worse solution. Other authors use this algorithm to optimize structures, given its good convergence to the global optimum [40].

## 4. Results

#### 4.1. Diversification Phase

_{2}. The direct emissions of each material are considered since they are the ones that make the difference in the volume of CO

_{2}generated between the alternatives (Table 5).

_{2}. However, optimization on a Kriging model is proposed to obtain a solution with a lower carbon footprint than the sample analyzed. Once the response surface has been optimized with the simulated annealing, the characteristics of the optimum deck would be as shown in Table 6.

#### 4.2. Intensification Phase

## 5. Discussion

^{3}per m

^{2}of the deck. This value is at the lower limit of the recommendations, which advise figures between 0.55 and 0.70 m

^{3}/m

^{2}[41]. Moreover, it coincides with the 25% percentile of the sample [43]. The result confirms that the BOE aims to reduce the measurement of concrete. The amount of active prestressing for the BOE, 16.48 kg/m

^{2}of the slab, although between the suggested limits [41], between 10 and 25 kg/m

^{2}, is below the 25% percentile [43]. This also indicates a tendency to lower the amount of active prestressing used.

^{3}of concrete, which exceeds the suggestions, which advise figures between 70 and 100 kg/m

^{3}[41]. However, the reality indicates that the median is 100.87 kg/m

^{3}[43], implying that the recommendations [41] are below what is executed in real-life bridges. Moreover, the passive reinforcement of the best bridge is lower than the sample’s maximum, which was 187.08 kg/m

^{3}. If we analyze the BOE ratio of 77.00 kg/m

^{2}of the deck, the figure is still high, exceeding the 75% percentile of the sample, although not reaching the maximum of 92.91 kg/m

^{2}. These figures conclude that the lower-emission decks prefer more passive reinforcement to reduce concrete and active prestressing.

^{2}. However, the reality is that only 16.48 kg/m

^{2}was required. Therefore, the BOE uses a smaller amount of active prestressing than is usually used. The design recommendation would be to reduce this amount as much as possible. Likewise, the estimated depth would be 1.13 m, while in BOE, it is 1.10 m, which is sensibly the same. The estimated concrete volume is 0.52 m

^{3}/m

^{2}, similar to the 0.56 m

^{3}/m

^{2}of the BOE. These recommendations are consistent with those obtained by previous works [44] using heuristic optimization techniques, although in that case, with the objective function cost.

^{3}/m

^{2}, are interesting. The measurement of concrete obtained is consistent with the work of Alcalá [36], who, for the economic optimization of this type of bridge, proposes magnitudes of about 0.50 m

^{3}/m

^{2}. The same occurs with the depth/span ratio, around 1/25, with economic decks of larger spans.

_{2}emissions have been analyzed and contrasted [45]. By analyzing the cost of the decks analyzed, it can be seen that BOE costs 181,531 €, while Deck #30, the lowest cost of all, is 179,756 €. Therefore, BOE is 1% more expensive than Deck #30 but emits the least CO

_{2}. However, Deck #30 emits 2% more than the BOE, although it is the cheapest.

^{2}), although within the 95% confidence interval for the mean. The model tells us that, removing the fixed costs of 129.2 €/m

^{2}, for each kg of CO

_{2}/m

^{2}that we reduce in our design, we will save 0.2262 €/m

^{2}.

## 6. Practical Recommendations

_{2}emissions, considering the results obtained during the optimization process. The design recommendations are to use slendernesses as high as possible in the region of 1/30, which implies a more significant amount of passive reinforcement. This increase in passive reinforcement is compensated by reducing the measurement of concrete and active reinforcement. In turn, to reduce the volume of concrete. It is recommended to increase the lightening as much as possible to reduce the volume of concrete.

- -
- Depth/span ratio greater than 1/28.
- -
- Concrete measurements less than 0.60 m
^{3}/m^{2}of the deck. - -
- Amounts of passive reinforcement above 120 kg/m
^{3}of concrete. - -
- Amounts of active prestressing below 17 kg/m
^{2}of the deck. - -
- Concrete grade between C-35 and 40 MPa.
- -
- External lightening between 0.40 and 0.50 m
^{3}/m^{2}of the deck. - -
- Interior lightening below 0.20 m
^{3}/m^{2}of the deck.

## 7. Conclusions

_{2}emissions. It is also found that the reduction of CO

_{2}is directly related to the cost. Cost optimization would therefore be sufficient to reduce the environmental aspects. In addition, it has been corroborated that a cost increase of less than 1 % leads to a reduction of more than 2 % in the amount of CO

_{2}emissions released into the atmosphere. However, barring a drastic change in technology, the CO

_{2}emissions of individual building units are more stable values than price fluctuations. A clear line of future research to apply this methodology to the entire life cycle analysis and its application to other objective functions such as constructability, safety, energy consumption, or others. In addition, the sensitivity of the parameters to the final results should also be studied.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 5.**Metamodel-based heuristic optimization flowchart [32].

**Figure 8.**Fitted line plot between the emissions and the cost of the calculated bridge decks is referred to as the unit of deck area.

Material | kg CO_{2}/kg | kg CO_{2}/m^{3} | kg CO_{2}/m^{2} |
---|---|---|---|

C-30 concrete | 227.01 | ||

C-35 concrete | 263.96 | ||

C-40 concrete | 298.57 | ||

C-45 concrete | 330.25 | ||

C-50 concrete | 358.97 | ||

Steel reinforcement | 3.03 | ||

Steel prestressed | 5.64 | ||

Formwork | 2.24 | ||

Lightening | 604.42 |

**Table 2.**Ranges of dimensions and their limitations established by regulations [41].

Design Variables | Range | Limitation |
---|---|---|

Concrete grade (f_{ck}) | 30–50 MPa | - |

Depth of the deck (c) | 1.15–1.70 m | >0.90 m |

Base width (b) | 3.00–5.00 m | - |

Cantilever length (v) | Variable | <3.50 m |

Distance between cantilever and nucleus (d) | 0.40 m | - |

Cantilever starting thickness e_{1} (a+b) | 0.35 m | - |

Cantilever edge thickness e_{2} (a) | 0.25 m | >0.20 m |

Minimum void coating | 0.225 m | >0.15 m |

Depth of the Deck (m) | Base Width (m) | Concrete Grade (MPa) | Depth of the Deck (m) | Base Width (m) | Concrete Grade (MPa) |
---|---|---|---|---|---|

0.58 | 0.61 | 0.27 | 0.30 | 0.96 | 0.38 |

0.74 | 0.48 | 0.31 | 0.93 | 0.216 | 0.24 |

0.52 | 0.86 | 0.17 | 0.88 | 0.096 | 0.63 |

0.99 | 0.28 | 0.79 | 0.19 | 0.11 | 0.74 |

0.10 | 0.31 | 0.59 | 0.49 | 0.00 | 0.45 |

0.76 | 0.18 | 0.83 | 0.58 | 0.97 | 0.64 |

0.14 | 0.91 | 0.91 | 0.37 | 0.61 | 0.17 |

0.03 | 0.71 | 0.96 | 0.85 | 0.36 | 0.74 |

0.42 | 0.38 | 0.11 | 0.58 | 0.78 | 0.73 |

0.33 | 0.69 | 0.08 | 0.72 | 0.21 | 0.08 |

0.36 | 0.56 | 0.67 | 0.18 | 0.00 | 0.99 |

0.63 | 0.75 | 0.05 | 0.48 | 0.46 | 0.87 |

0.82 | 0.53 | 0.49 | 0.68 | 0.59 | 0.37 |

0.21 | 0.82 | 0.54 | 0.98 | 0.87 | 0.56 |

0.68 | 0.43 | 0.87 | 0.06 | 0.76 | 0.45 |

Deck | Depth of the Deck (m) | Base Width (m) | Concrete Grade (MPa) | Deck | Depth of the Deck (m) | Base Width (m) | Concrete Grade (MPa) |
---|---|---|---|---|---|---|---|

1 | 1.45 | 4.35 | 35 | 16 | 1.30 | 4.90 | 40 |

2 | 1.55 | 4.10 | 35 | 17 | 1.65 | 3.65 | 35 |

3 | 1.45 | 4.75 | 35 | 18 | 1.65 | 3.45 | 45 |

4 | 1.70 | 3.80 | 45 | 19 | 1.25 | 3.50 | 45 |

5 | 1.20 | 3.85 | 40 | 20 | 1.40 | 3.30 | 40 |

6 | 1.55 | 3.60 | 45 | 21 | 1.45 | 3.90 | 45 |

7 | 1.20 | 4.85 | 50 | 22 | 1.35 | 3.60 | 35 |

8 | 1.15 | 4.50 | 50 | 23 | 1.50 | 3.35 | 45 |

9 | 1.35 | 3.95 | 30 | 24 | 1.50 | 4.50 | 45 |

10 | 1.30 | 4.45 | 30 | 25 | 1.55 | 3.20 | 30 |

11 | 1.35 | 4.25 | 45 | 26 | 1.25 | 3.00 | 50 |

12 | 1.50 | 4.55 | 30 | 27 | 1.40 | 3.45 | 45 |

13 | 1.60 | 4.20 | 40 | 28 | 1.50 | 3.55 | 35 |

14 | 1.25 | 4.70 | 40 | 29 | 1.70 | 3.85 | 40 |

15 | 1.50 | 4.05 | 45 | 30 | 1.15 | 3.70 | 40 |

CO_{2} (kg) | Deck | CO_{2} (kg) | Deck | CO_{2} (kg) |
---|---|---|---|---|

439,416 | 11 | 455,374 | 21 | 464,536 |

460,393 | 12 | 434,674 | 22 | 416,584 |

455,722 | 13 | 503,797 | 23 | 455,442 |

484,897 | 14 | 462,915 | 24 | 490,669 |

407,988 | 15 | 482,659 | 25 | 403,972 |

456,668 | 16 | 477,491 | 26 | 423,112 |

472,401 | 17 | 444,714 | 27 | 470,008 |

471,362 | 18 | 464,051 | 28 | 418,839 |

406,654 | 19 | 420,514 | 29 | 468,898 |

436,703 | 20 | 443,840 | 30 | 394,616 |

Depth of the Deck (m) | Base Width (m) | Concrete Grade (MPa) | CO_{2} (kg) |
---|---|---|---|

1.15 | 3.55 | 40 | 391,370.00 |

Deck | Depth of the Deck (m) | Base Width (m) | Concrete Grade (MPa) | CO_{2} (kg) |
---|---|---|---|---|

31 | 1.15 | 3.40 | 35 | 411,077.14 |

32 | 1.25 | 3.35 | 35 | 398,614.42 |

33 | 1.15 | 3.65 | 45 | 422,934.14 |

34 | 1.15 | 3.35 | 40 | 395,465.24 |

35 | 1.15 | 3.25 | 40 | 397,153.86 |

Depth of the Deck (m) | Base Width (m) | Concrete Grade (MPa) | CO_{2} (kg) |
---|---|---|---|

1.10 | 3.40 | 35 | 386,514.57 |

**Table 9.**Unit prices of materials [36].

Material | €/kg | €/m^{3} | €/m^{2} |
---|---|---|---|

C-30 concrete | 99.81 | ||

C-35 concrete | 104.57 | ||

C-40 concrete | 109.33 | ||

C-45 concrete | 114.10 | ||

C-50 concrete | 118.87 | ||

Steel reinforcement | 1.16 | ||

Steel prestressed | 3.40 | ||

Formwork | 33.81 | ||

Lightweighting | 99.81 |

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**MDPI and ACS Style**

Yepes-Bellver, L.; Brun-Izquierdo, A.; Alcalá, J.; Yepes, V.
CO_{2}-Optimization of Post-Tensioned Concrete Slab-Bridge Decks Using Surrogate Modeling. *Materials* **2022**, *15*, 4776.
https://doi.org/10.3390/ma15144776

**AMA Style**

Yepes-Bellver L, Brun-Izquierdo A, Alcalá J, Yepes V.
CO_{2}-Optimization of Post-Tensioned Concrete Slab-Bridge Decks Using Surrogate Modeling. *Materials*. 2022; 15(14):4776.
https://doi.org/10.3390/ma15144776

**Chicago/Turabian Style**

Yepes-Bellver, Lorena, Alejandro Brun-Izquierdo, Julián Alcalá, and Víctor Yepes.
2022. "CO_{2}-Optimization of Post-Tensioned Concrete Slab-Bridge Decks Using Surrogate Modeling" *Materials* 15, no. 14: 4776.
https://doi.org/10.3390/ma15144776