# Life Cycle Assessment of Bridges Using Bayesian Networks and Fuzzy Mathematics

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

#### 2.1. Current Situation of Research Results on Environmental Impact of Construction Industry

#### 2.2. Uncertainty of Environmental Impact Factors in Construction Industry

#### 2.3. Environmental Impact Assessment Method of Construction Industry

#### 2.4. Determination of Environmental Impact Assessment Method

## 3. Methodology

#### 3.1. Research Theory (BN and Basic Principles of FMT)

#### 3.2. Theoretical Model Bridge Process

#### 3.3. LCA Research Framework and Parameters

#### 3.4. Research External Conditions

#### 3.5. Impact Factor

#### 3.5.1. Bridge a BN Hierarchical Analysis Model

#### 3.5.2. Establishing Impact Weight Matrix

#### 3.5.3. Hypothesis

**,**there is 1 first-level indicator, 5 second-level indicators, 31 third-level indicators, 68 fourth-level indicators, and 12 fifth-level indicators to derive the conclusion based on Equations (1)–(5).

## 4. Case and Results

#### 4.1. Case Description

#### 4.2. Survey and Design

#### 4.3. Material Manufacturing

#### 4.4. Construction and Installation

#### 4.5. Operation and Maintenance

_{2}concentration, which is set as $\sqrt{{\mathrm{C}}_{0}/0.03}$—CO

_{2}concentration; ${\mathrm{C}}_{{\mathrm{CO}}_{2}}$ is the CO

_{2}concentration (%); ${\mathrm{K}}_{\mathrm{k}1}$ is the location influence coefficient (1.4 or 1.0); ${\mathrm{K}}_{\mathrm{kt}}$ is the $\mathrm{C}$ casting surface influence coefficient, and is set up 1.2; ${\mathrm{K}}_{\mathrm{ks}}$ is the working stress influence coefficient, which is set as 1.0 in the compressive zone and as 1.1 in the tensile zone; $\mathrm{T}$ is the environmental temperature (℃); $\mathrm{RH}$ is the environmental relative humidity; ${\mathrm{K}}_{\mathrm{F}}$ is the substitution coefficient of fly ash; and ${\mathrm{f}}_{\mathrm{cu},\mathrm{e}}$ is the extrapolated value of C compression strength (MPa).

_{2}absorption capacity per unit volume of concrete [64].

_{2}absorption capacity of ordinary Portland cement (mol/m

^{3});$\text{}\mathrm{B}$ is the number of cementitious materials used per unit volume of $\mathrm{C}$ (kg/m

^{3}); and α is the number of mixed materials in ordinary Portland cement (%).

#### 4.6. Disassembly and Recycling

## 5. Discussion

#### 5.1. Case Environmental Impact

#### 5.1.1. BNFC Comprehensive Assessment

#### 5.1.2. Comparative Analysis of the Results of Fuzzy Comprehensive Assessment of LCA and Bayesian

#### 5.1.3. Impact Factor Calibration for SQ and EH

- >>%SQ: z=(4.213e + 05).*x^2−(5.383e + 06).*x + (1.744e + 07).
- >>%EH: z=(3.727e + 05).*x.^2-(4.998e + 06).*x + (1.708e + 07).
- >>clear all; % Curve equation fitting, The first set of calculation programming language;
- >>x = [1 2 3 4 5 6 7 8 9 10 11 12 13];
- >>y = [3175070.133 26344975.58 621212.387 14122.7683 41378.0309 17963.456 5.164350566 20075.328 1057111.776 2554272 5817825 39517468.41 2755301.595];
- >>figure;
- >>plot(x,y,‘bo’);

- >>Clear all;% The second set of calculation programming language;
- >>x = 1:13;
- >>y = 5:3175070;
- >>[x,y] = meshgrid(x,y);
- >>z = (4.213e+05).*x.^2−(5.383e + 06).*x + (1.744e+07);
- >>figure;
- >>surf(x,y,z);
- >>colormap(‘jet’);
- >>shading interp;
- >>light(‘position’,[0.2 0.2 0.8]);
- >>axis square;
- >>xlabel(‘x’);
- >>ylabel(‘y’);
- >>zlabel(‘z’);

#### 5.2. Innovation

#### 5.2.1. Modelling Analysis

**,**the third level of the environmental emissions contribution of cable-stayed bridges can be divided into eight categories and 31 types. The impact factor is considered the variable node $\mathrm{x}$, and the directed edges between nodes represent the interrelationships between nodes; $\mathrm{x}$ corresponds to the probability distribution $\mathrm{P}\left(\mathrm{x}\right)|\mathsf{\pi}\left(\mathrm{x}\right))$. The joint probability distribution for $\mathrm{n}$ nodes (${\mathrm{x}}_{1},{\text{}\mathrm{x}}_{2},\text{}\cdots \cdots ,{\text{}\mathrm{x}}_{\mathrm{n}}$) can be expressed as:

#### 5.2.2. Measures

^{3}; the amounts of waste materials and wastewater generated by EH are 488.38 tonnes and 693.70 m

^{3}. There is a need to install digital automatic control processing equipment for centralized recycling in the mixing plant [75,76,77].

#### 5.3. Transportation

#### 5.3.1. Modelling in Operation and Maintenance Phase

#### 5.3.2. Calculations in the Operation and Maintenance Phase

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

BN | Bayesian networks |

LCA | Life cycle assessment |

FMT | Fuzzy mathematics theory |

BNFC | Bayesian network fuzzy number comprehensive evaluation |

GWP | Global warming parameters |

AP | Acidification parameters |

FEP | Freshwater eutrophication parameters |

PMFP | Particulate matter formation parameters |

WP | Solid waste parameters |

SQ | Su Qian bridge |

EH | Gong He cable-stayed bridge |

C | Concrete |

Km | Kilometers |

kwh | Kilowatt-hour |

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**Figure 5.**Schematic diagram of tree-shaped BN of environmental impact contribution of cable-stayed bridge.

**Figure 7.**Comparison diagram of research and analysis conclusions of SQ’s contribution to the environment.

**Figure 8.**Comparison diagram of research and analysis conclusions of EH environmental impact contribution.

**Figure 9.**Comparison of the conclusions of using two methods to study the environmental impact contribution of SQ and EH.

**Figure 10.**The matching degree of the contribution of SQ and EH to the environmental impact is fit to the numerical curve.

**Figure 11.**The influencing factors obtained by the three evaluation methods are compared and fitted with the analysis of mean difference.

**Figure 13.**SQ and EH maintenance and operation stage environmental impact fitting and future change trend interpolation analysis.

**Figure 15.**A schematic diagram of the numerical comparison of the environmental impact contribution types of SQ and EH.

**Figure 16.**A Summary table of vehicle assessment data during operation and maintenance for SQ and EH.

**Figure 17.**Five-stage contribution of transportation vehicles and operation and maintenance vehicle assessment chart for SQ and EH.

Bridge Name | Design Institute and Project Site | Design Time | Survey and Design Time (Days) | Project Staff (Person) | Number of Drilling Holes | Drilling Depth | Drilling Working Hours | ||
---|---|---|---|---|---|---|---|---|---|

(km) | (Days) | Survey | Design | Survey | Design | (Piece) | (m) | (Hours) | |

SQ | 6 | 360 | 120 | 240 | 12 | 16 | 26 | 1456 | 11 |

EH | 389 | 821 | 173 | 648 | 14 | 20 | 34 | 2210 | 16 |

Bridge Name | Duration of the Hanging Basket (Days) | Total Construction Period (Days) | Main Tower Lifting Equipment | Working Power (kwh) | Equipment Weight (Tonnes) | Managed Personnel (Persons) | Construction Worker (Persons) |
---|---|---|---|---|---|---|---|

SQ | 255 | 729 | Tower crane | 90 | 78.54 | 24 | 260~320 |

EH | 495 | 601 | Tower crane | 82.4 | 72.15 | 28 | 280~340 |

SQ, EH Maintenance and Repair Cycle | ||
---|---|---|

Material | Damage Mechanism | Cycle |

Steel | Aging; carbonization; rust; chloride salt corrosion; freeze–thaw environment; sulfate corrosion; alkali aggregation reaction | Maintenance/1 Year |

Inspection and repair/2 Years | ||

Maintenance and repair/70 Years | ||

Expansion joint; Waterproof level; Bridge deck pavement | Wear; aging; chloride salt corrosion; freeze–thaw environment; sulfate corrosion; destruction | Maintenance/1 Year |

Inspection and repair/2 Years | ||

Replacement/10Years | ||

Main beam; Anti-collision guardrail; Bridge deck drainage; Lighting | Shock; vibration; overload; uneven settlement; chloride salt corrosion; freeze–thaw environment; sulfate corrosion; alkaline material reaction | Maintenance/1 Year |

Inspection and repair/5 Years | ||

Replacement/50Years | ||

Paint for caps; Piers and beams | Chemical attack; abrasion; erosion; aging; chloride salt attack; freeze–thaw environment; sulfate attack | Maintenance/1 Year |

Replacement/5Years | ||

Abutment | Chemical attack; wear; impact; aging | Maintenance/1 Year |

Inspection and repair/5 Years | ||

Replacement/25Years | ||

Main Galasso | Chemical corrosion; vehicle overload and insufficient maintenance | Maintenance/1 Year |

Inspection and repair/5 Years | ||

Replacement/30Years |

**Table 4.**Summary table of five-stage modelling formulas [11].

Stage | Modelling Formula | Explanation |
---|---|---|

SD | ${\mathrm{EC}}_{\mathrm{SD}}$$={\mathrm{E}}_{\mathrm{m}}$+${\text{}\mathrm{M}}_{\mathrm{m}}$+${\mathrm{P}}_{\mathrm{m}}$+${\mathrm{W}}_{\mathrm{m}}$+${\text{}\mathrm{M}\text{}}_{\mathrm{p}}$+${\mathrm{S}}_{\mathrm{m}}$ | ${\mathrm{E}}_{\mathrm{m}}\text{}\mathrm{is}\text{}\mathrm{TVEC}$(kg);${\text{}\mathrm{M}}_{\mathrm{m}}$ is EEC (kg);${\text{}\mathrm{P}}_{\mathrm{m}}$ is the worker EC (kg) |

MM | ${\mathrm{EC}}_{\mathrm{MM}\text{}}$$={\mathrm{E}}_{\mathrm{m}}$+${\mathrm{M}}_{\mathrm{m}}$+${\text{}\mathrm{P}}_{\mathrm{m}}$+${\text{}\mathrm{M}}_{\mathrm{p}}$+ ${\text{}\mathrm{R}}_{\mathrm{m}}$ | ${\mathrm{M}}_{\mathrm{p}}$ is PGGDSEC (kg);${\text{}\mathrm{R}}_{\mathrm{m}}$ is the material EC (kg) |

CI | ${\mathrm{EC}}_{\mathrm{CI}}$$={\mathrm{M}}_{\mathrm{m}}$+${\mathrm{P}}_{\mathrm{m}}$+${\text{}\mathrm{M}}_{\mathrm{p}}$$+{\text{}\mathrm{R}}_{\mathrm{m}}$$+{\text{}\mathrm{L}}_{\mathrm{m}}$ | ${\mathrm{L}}_{\mathrm{m}}$ is the EC of power and fuel consumption during construction (kg) |

MO | ${\mathrm{EC}}_{\mathrm{MO}}$=${\text{}\mathrm{C}}_{\mathrm{m}}$+${\mathrm{S}}_{\mathrm{m}}$+(8) + (9) + (10) +${\text{}\mathrm{E}}_{\mathrm{MM}}$$+{\mathrm{E}}_{\mathrm{CI}}$ | ${\mathrm{C}}_{\mathrm{m}}$ is TVEC (kg);${\text{}\mathrm{S}}_{\mathrm{m}}$ is the EC number (kg) |

DR | ${\mathrm{EC}}_{\mathrm{DR}}$$={\text{}\mathrm{E}}_{\mathrm{m}}$+${\text{}\mathrm{M}}_{\mathrm{m}}$+${\mathrm{P}}_{\mathrm{m}}$+${\text{}\mathrm{M}}_{\mathrm{p}}$$+{\text{}\mathrm{R}}_{\mathrm{m}}$ | ${\mathrm{W}}_{\mathrm{m}}$ is OFEC (kg) |

**Table 5.**Summary table of bridge environmental impact contributions (Table 4 formula calculation).

Environmental Contribution Stage | Bridge Name | GWP (kg) | AP (kg) | FEP (kg) | PMFP (kg) | WP (kg) | Transportation Contribution (kg) | The Proportion |
---|---|---|---|---|---|---|---|---|

Survey and design | SQ | 322,603.10 | 0.29 | 1444.66 | 14.12 | 5609.22 | 4525.62 | 1.37% |

EH | 6,075,65.23 | 0.52 | 2781.15 | 27.12 | 10,798.15 | 12,504.05 | 2.01% | |

Material manufacturing | SQ | 35,783,970.10 | 338,386.32 | 218,677.39 | 1,027,034.48 | 1,911,752.52 | 551,965.85 | 1.41% |

EH | 32,607,070.35 | 297,990.71 | 193,603.27 | 915,282.34 | 1,679,151.52 | 554,608.67 | 1.55% | |

Construction and installation | SQ | 21,604,311.50 | 334.85 | 22,516.66 | 1212.05 | 86,335.68 | 98,670.19 | 0.45% |

EH | 23,954,772.44 | 337.00 | 29,475.12 | 1389.47 | 113,471.60 | 89,074.70 | 0.37% | |

Maintenance and operation | SQ | 79,173,042.18 | 155,891.23 | 514,843.27 | 702,336.77 | 1,390,668.18 | 1,057,111.78 | 1.29% |

EH | 69,602,711.16 | 238,252.02 | 466,229.79 | 850,705.27 | 1,325,559.61 | 1,345,777.99 | 1.86% | |

Disassembly and recycling | SQ | 4,184,764.66 | 43.94 | 234.27 | 31.98 | 891.24 | 1,985,014.96 | 47.42% |

EH | 2,412,687.90 | 12.23 | 316.02 | 11.24 | 1222.36 | 194,206.26 | 8.04% |

Types of EC | Bridge Name | Analysis Value (kg) | V1 | V2 | V3 | V4 | V5 |
---|---|---|---|---|---|---|---|

GWP | SQ | 141,068,691.53 | 0.23% | 25.37% | 15.31% | 56.12% | 2.97% |

EH | 129,184,807.08 | 0.47% | 25.24% | 18.54% | 53.88% | 1.87% | |

AP | SQ | 494,656.64 | 0.00% | 68.41% | 0.07% | 31.52% | 0.01% |

EH | 536,917.19 | 0.00% | 55.50% | 0.06% | 44.43% | 0.00% | |

FEP | SQ | 757,716.26 | 0.19% | 28.86% | 2.97% | 67.95% | 0.03% |

EH | 693,040.75 | 0.40% | 27.94% | 4.25% | 67.36% | 0.05% | |

PMFP | SQ | 1,730,629.40 | 0.00% | 59.34% | 0.07% | 40.58% | 0.00% |

EH | 1,768,574.83 | 0.00% | 51.75% | 0.08% | 48.17% | 0.00% | |

WP | SQ | 3,395,256.84 | 0.17% | 51.75% | 0.08% | 48.17% | 0.00% |

EH | 3,132,009.78 | 0.34% | 53.61% | 3.62% | 42.38% | 0.04% |

Impact Factor | Bridge Name | GWP | AP | FEP | PMFP | WP |
---|---|---|---|---|---|---|

${a}_{i}$ | SQ | 0.96% | 0.00% | 0.01% | 0.01% | 0.02% |

EH | 0.95% | 0.00% | 0.01% | 0.01% | 0.02% | |

${V}_{i}$ | SQ | 20.00% | 20.00% | 20.00% | 20.00% | 20.00% |

EH | 20.00% | 20.00% | 20.00% | 20.00% | 20.00% | |

${K}_{j}$ | SQ | 0.0478% | 0.0002% | 0.0003% | 0.0006% | 0.0012% |

EH | 0.0477% | 0.0002% | 0.0003% | 0.0007% | 0.0012% | |

${K}_{j}^{\prime}$ | SQ | 0.9567% | 0.0034% | 0.0051% | 0.0117% | 0.0230% |

EH | 0.9547% | 0.0040% | 0.0051% | 0.0131% | 0.0231% |

Bridge Name | Car Type | Emission Coefficient (g/km) | 2002~2011 Year | 2011~2020 Year | 2021~2110 Year |
---|---|---|---|---|---|

Number of Passing Vehicles (Units) | |||||

SQ | Passenger car | 305.4g/km | 0.00 | 250,608.00 | 2,243,160.00 |

Commercial vehicle | 271.8g/km | 0.00 | 82,896.00 | 735,480.00 | |

New energy vehicle | 292.5g/km | 0.00 | 387.00 | 3010.00 | |

EH | Passenger car | 305.4g/km | 212,700.00 | 243,156.00 | 1,982,869.33 |

Commercial vehicle | 271.8g/km | 110,400.00 | 125,592.00 | 1,023,578.67 | |

New energy vehicle | 292.5g/km | 0.00 | 36.00 | 255.11 |

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**MDPI and ACS Style**

Zhou, Z.-W.; Alcalá, J.; Kripka, M.; Yepes, V.
Life Cycle Assessment of Bridges Using Bayesian Networks and Fuzzy Mathematics. *Appl. Sci.* **2021**, *11*, 4916.
https://doi.org/10.3390/app11114916

**AMA Style**

Zhou Z-W, Alcalá J, Kripka M, Yepes V.
Life Cycle Assessment of Bridges Using Bayesian Networks and Fuzzy Mathematics. *Applied Sciences*. 2021; 11(11):4916.
https://doi.org/10.3390/app11114916

**Chicago/Turabian Style**

Zhou, Zhi-Wu, Julián Alcalá, Moacir Kripka, and Víctor Yepes.
2021. "Life Cycle Assessment of Bridges Using Bayesian Networks and Fuzzy Mathematics" *Applied Sciences* 11, no. 11: 4916.
https://doi.org/10.3390/app11114916