# Embodied Energy Optimization of Prestressed Concrete Slab Bridge Decks

^{*}

## Abstract

**:**

## 1. Introduction

_{2}emissions and the embodied energy of the structures [4,5,6]. Thus, decreasing costs also reduces both CO

_{2}emissions and energy.

_{2}emissions have been studied for a significant number of structures; however, the reduction of energy in optimized structures has been dealt with much less [6,7,8,9,10,11]. Heuristic algorithms are frequently used in an optimization of single-target (mono-objective). Mainly, the objectives are the cost, the CO

_{2}emissions or the embodied energy [12,13,14,15], while other works perform optimization simultaneously of different objectives (multi-objective) [16,17]. Another way of evaluating the environmental impact is to apply the life-cycle assessment process (LCA). LCA is a highly accepted method for evaluating environmental impacts [18,19,20,21,22,23]. Consequently, the minimization of embodied energy in the constructive process of the structures is not sufficiently studied and is one of the important criteria considered in sustainable constructions.

## 2. The Optimum Design Problem

_{1}and embodied energy f

_{2}, represented by Equations (1) and (2). Both functions must satisfy the structural constraints sc

_{j}of the Equation (3).

_{1}(x

_{1}, x

_{2}, x

_{3}, …, x

_{n})

_{2}(x

_{1}, x

_{2}, x

_{3}, …, x

_{n})

_{j}(x

_{1}, x

_{2}, x

_{3}, …, x

_{n}) ≤ 0,

_{1}, x

_{2}, x

_{3}, …, x

_{n}. The parameters have fixed values, and are the rest of the data required for the calculations of the slab deck. The first objective function considered is the cost of the structure as defined in Equation (4), where p

_{i}are the unit prices and m

_{i}are the measurements of the units used for the construction of the PC slab. The cost function f

_{1}includes the economic valuation of the materials (passive steel, active steel and concrete) and all the inputs necessary to calculate the total cost of the whole deck. To obtain the prices of the work units, the database of the Institute of Construction Technology of Catalonia [35] has been used and is given in Table 1.

_{i}are embodied energy of the PC slab materials and mi the measurements of materials. The values of c

_{i}for concrete, active and passive steel, scaffolding and formwork used in the present study were also taken from the Institute of Construction Technology of Catalonia [35] and are specified in Table 1.

_{j}in Equation (3) are all the Ultimate Limit States (ULS) and the Service Limit States (SLS) that the structure must satisfy, other than the constructability and geometrical constraints of the problem. Solutions that satisfy all the constraints are called feasible solutions. Feasible solutions are processed in this study, and the unfeasible solutions that may appear are eliminated in the optimization process. The structural restrictions imposed on the slab deck are all the obligatory ones for this structure. In conformity with the Spanish Code EHE-08 [36] the checking includes the ULS of flexion, torsion, shear, fatigue, local effects in the flanges, and shear between the flanges and the web; and the SLS of deflections and cracking, considering both the instant and the deferred losses of the active reinforcement. The limit state of decompression and the absence of cracking during prestressing are necessary conditions in structures located in marine environments. In addition, compressed concrete fibers cannot achieve 60% of the characteristic strength. Keep in mind that these factors directly affect the heuristic optimization process. However, to ensure the conditions of durability other specifications should be monitored as the quality of the concrete, the selection of raw materials, proper placement and curing of the concrete. The deflection was limited to 1/14,000th of the length of free span, for instantly and time-dependent deflection with respect to the precamber to the characteristic combination [36] and it was also limited to 1/1000th of the length of free span for the live loads [37]. Other geometrical requirements which are considered for the constructability of the deck are the minimum separation between tendons and reinforcement [36], which determines the minimum thickness of the slab, and the anchorage length of the passive reinforcement. The evaluation of the stresses has been carried out by a beam model formed by 10 linear finite elements per longitudinal span, considering elastic and linear behavior. The model has three degrees of freedom per node typical of the spatial beam plane structures. The effect of the transversal beam over the supports has been considered condensing the degrees of freedom in the stiffness matrix of the structure. The loads considered in the analysis are the ones described in the Spanish Code IAP [37]: self-weight, dead load, live load, thermal effects, and differential settlement of the supports. The algorithm includes a subroutine that verifies all the checking of the deck solution proposed, that in this moment is totally defined.

## 3. Experimental

_{0}, geometrically decreasing during the process (T = kT) through a cooling coefficient k. Several iterations, called a Markov chain, are allowed at each step of temperature. The SA method is capable of surpassing local optima at high-medium temperatures and gradually converges as the temperature falls to zero. The process generates an initial solution of the values of the variables by a random choice between the upper and lower limits. The procedure continues until a feasible solution is found. The initial feasible solution is continuously modified by small movements that are performed by the variation of 7 of the 33 variables. Each modified discrete variable changes one position in the table. The initial temperature was adjusted following the method proposed by Medina [39]. The cooling coefficient and the length of the Markov Chains are obtained by a previous calibration work with values of 0.85 and 20,000, respectively. When the temperature is less than 0.2% of the initial value, or two chains run without improvement, the process stops. Computer runs were performed fifty times to obtain minimum, mean, and standard deviation of the random results. The algorithm described has been applied to a deck of three spans of 20–36–20 m of length, and 11.0 m width, considering the parameters described in Table 2. This bridge deck is a typical road overpass on highways [40]. The structural check and the algorithm were encoded in Fortran 95 language, with a compiler Compacq 6.6.0. The process ran on a personal computer with an INTEL Q6600 processor of 2.4 GHz.

## 4. Results and Discussion

## 5. Conclusions

_{2}emission), the consideration of other algorithms, and a sensitivity analysis of the parameters. In addition, different structures are to be considered.

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

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**Table 1.**Embodied energy and cost [31].

Unit | Description | Embodied Energy (kW·h) | Cost (€) |
---|---|---|---|

m^{3} | scaffolding | 4.11 | 10.12 |

m^{2} | slab formwork | 32.13 | 41.93 |

m^{2} | lightening | 82.38 | 110.14 |

kg | steel B-500-S | 9.72 | 0.59 |

kg | steel Y-1860-S7 | 20.55 | 5.89 |

m^{3} | slab concrete HP 35 | 419.40 | 110.14 |

m^{3} | slab concrete HP 40 | 447.13 | 119.32 |

m^{3} | slab concrete HP 45 | 471.87 | 131.25 |

m^{3} | slab concrete HP 50 | 546.10 | 146.77 |

Parameter | Value |
---|---|

Number of spans | 3 |

Lengths | 20.0–36.0–20.0 m |

Pavement thickness | 0.1 m |

Guard rail weights | 2 × 5 kN/m |

Vertical thermal gradient | 10 °C |

Differential settlement between supports | 0.5 cm |

EHE ambient exposure | IIb |

Minimum Cost | Minimum Embodied Energy | |||
---|---|---|---|---|

Cost (Euros) | Embodied Energy (kW·h) | Cost (Euros) | Embodied Energy (kW·h) | |

Mean value | 271,759.70 | 1,049,609.81 | 288,357.54 | 974,196.41 |

Standard deviation | 2354.26 | 24,717.23 | 10,463.24 | 14,770.64 |

Minimum value | 267,443.44 | 1,002,850.06 | 296,191.13 | 944,517.94 |

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**MDPI and ACS Style**

Alcalá, J.; González-Vidosa, F.; Yepes, V.; Martí, J.V. Embodied Energy Optimization of Prestressed Concrete Slab Bridge Decks. *Technologies* **2018**, *6*, 43.
https://doi.org/10.3390/technologies6020043

**AMA Style**

Alcalá J, González-Vidosa F, Yepes V, Martí JV. Embodied Energy Optimization of Prestressed Concrete Slab Bridge Decks. *Technologies*. 2018; 6(2):43.
https://doi.org/10.3390/technologies6020043

**Chicago/Turabian Style**

Alcalá, Julián, Fernando González-Vidosa, Víctor Yepes, and José V. Martí. 2018. "Embodied Energy Optimization of Prestressed Concrete Slab Bridge Decks" *Technologies* 6, no. 2: 43.
https://doi.org/10.3390/technologies6020043