# Influence of Superstructure Pouring Concrete Volume Deviation on Bridge Performance: A Case Study

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Analysis of Influence of PCVD on Performance of CRCR Bridge

#### 2.1. General

#### 2.2. Model Method

#### 2.2.1. Geometric Form

#### 2.2.2. Material Models

#### 2.2.3. Loading and Boundary Conditions

^{2}. The bridge has 4 traffic lanes and the loading form of vehicle loads, according to the Chinese design specification [28], in each lane is shown in Figure 4. The purpose of referring to the specification is to ensure that the bridge produces a live-load response that is as close to the actual situation as possible, so the relevant safety factors are not considered. In order to maximize the mid-span deflection, a concentrated load ${P}_{k}$ = 360 kN is applied to the mid-span on all 4 lanes, and a uniform load ${q}_{k}=$10.5 kN/m is distributed over the entire lane.

#### 2.2.4. Element Selection and Mesh

#### 2.2.5. Comparison Model Settings

#### 2.2.6. Operating Condition Setting

#### 2.3. Model Calculation Result

## 3. Case Study

#### 3.1. Engineering Background

#### 3.2. Measuring Approach

#### 3.3. The Status of PCVD of the Whole Cross Section

#### 3.4. The Status of PCVD of Each Part in Cross-Section

#### 3.5. Absolute Quantity Analysis of PCVD of Each Part

#### 3.6. Coefficient of Variation of Dead Load Due to Casting Size Deviation

## 4. Analysis of the Influence of PCVD on Stiffness

^{−19}< 0.01, in general, the pouring deviation ratio of all parts had a strong correlation with the stiffness-deviation coefficient, indicating a strong significance.

## 5. Conclusions

- The influence of volume deviation at different positions within the cross-section on the cross-sectional stiffness varies. The structural stiffness is more sensitive to the thickness of the top slab and the flange. The combined effect of dead-load variation and cross-sectional stiffness variation on structural performance is uncertain and may be beneficial or detrimental to structural performance. Specific analysis of the actual research object is required.
- The section deviation rate is in the range of 6.33~10.75% at the 95% confidence interval, and the deviation rate of different sectional parts is in the range of 5.05~12.97%, which indicates that the cast-in-place concrete bridge with cantilever generally has PCVD. The maximum standard deviation is 12.26%, which indicates that the amount of deviation is random and scattered.
- The weighted mean deviation value of each part was calculated, and the results showed that the near pier bottom slab, mid-span bottom slab and top slab have larger deviation values, which may have a more pronounced effect on the dead load. Among them, the near pier bottom slab is most likely to a produce larger deviation value and should be the part of primary concern when studying dead-load variation.
- In this paper, the dead-load deviation coefficient c
_{W}and the stiffness deviation coefficient c have been proposed for the assessment procedure of the influence of PCVD on existing bridges’ performance. This case study can serve as a benchmark for guiding the internal-force calculation and service state analysis of bridges of the same type.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Newly built and total number of continuous reinforced concrete rigid-frame (CRCR) bridges in China [1].

**Figure 7.**Cross-section inspection status. (The gray block represents the checked section. The number on the beam represents the segment number. The span (∙)# is the span number). (

**a**) Bridge A, (

**b**) Bridge B.

**Figure 8.**Cross-sectional measurement position layout. (

**a**) Layout of thickness measurement position, (

**b**) schematic of thickness measurement position on site, (

**c**) layout of outline measurement position, (

**d**) schematic of outline measurement position.

**Figure 9.**Measurement tools and usage. (

**a**) Thickness measurement method, (

**b**) Measurement method of outline dimension.

**Figure 12.**Frequency histogram of ${K}_{i}$ of each cross-section of bridge A and bridge B, (

**a**) bridge A, (

**b**) bridge B.

Model No. | Description | Increase Method | Legend: Red Is the Outline of the Increasing Area |
---|---|---|---|

I | Benchmark model | No increase. | |

II | 10% overall increase | Weighted distribution of each and every part of the top slab, web and bottom slab. | |

III | 10% top slab increase | Increase the same thickness from both sides of the horizontal axis through the centroid of the top slab. | |

IV | 10% web increase | Increase the same thickness from both sides of the vertical axis through the centroid of the web. | |

V | 10% bottom slab increase | Increase the same thickness from both sides of the horizontal axis through the centroid of the bottom slab. |

Working Conditions | Deflection γ (mm) | % Ratio of Comparative Model Deflection to Benchmark Model | |||||||
---|---|---|---|---|---|---|---|---|---|

${\mathsf{\gamma}}_{\mathrm{I}}$ | ${\mathsf{\gamma}}_{\mathrm{II}}$ | ${\mathsf{\gamma}}_{\mathrm{III}}$ | ${\mathsf{\gamma}}_{\mathrm{IV}}$ | ${\mathsf{\gamma}}_{\mathrm{V}}$ | $\raisebox{1ex}{${\mathsf{\gamma}}_{\mathrm{II}}$}\!\left/ \!\raisebox{-1ex}{${\mathsf{\gamma}}_{\mathrm{I}}$}\right.$ | $\raisebox{1ex}{${\mathsf{\gamma}}_{\mathrm{III}}$}\!\left/ \!\raisebox{-1ex}{${\mathsf{\gamma}}_{\mathrm{I}}$}\right.$ | $\raisebox{1ex}{${\mathsf{\gamma}}_{\mathrm{IV}}$}\!\left/ \!\raisebox{-1ex}{${\mathsf{\gamma}}_{\mathrm{I}}$}\right.$ | $\raisebox{1ex}{${\mathsf{\gamma}}_{\mathrm{V}}$}\!\left/ \!\raisebox{-1ex}{${\gamma}_{\mathrm{I}}$}\right.$ | |

Dead load | −136.7 | −126.7 | −108.9 | −123.5 | −137.6 | 92.7% | 79.7% | 90.3% | 100.7% |

Live load | −40.7 | −33.0 | −24.3 | −36.4 | −39.9 | 81.2% | 59.8% | 89.4% | 98.1% |

Combined | −177.3 | −159.7 | −133.2 | −159.8 | −177.5 | 90.1% | 75.1% | 90.1% | 100.1% |

Web | Top Slab | ||
---|---|---|---|

W1 | Height of left web | T1 | Thickness of left top slab near slabs with haunched ribs |

W2 | Height of right web | T2 | Thickness at the inflection point of left top slab |

W3 | Thickness of top of left web | T3 | Thickness at the inflection point of right top slab |

W4 | Thickness of bottom of left web | T4 | Thickness of right top slab near slabs with haunched ribs |

W5 | Thickness of top of right web | T5 | Width between the inflection point of top slab |

W6 | Thickness of bottom of right web | ||

Flange | Bottom slab | ||

F1 | Thickness at the edge of left flange | B1 | Thickness of left bottom slab near slabs with haunched ribs |

F2 | Thickness of left flange near slabs with haunched ribs | B2 | Thickness of middle of bottom slab |

F3 | Thickness of right flange near slabs with haunched ribs | B3 | Thickness of right bottom slab near slabs with haunched ribs |

F4 | Thickness at the edge of right flange | B4 | Width between the inflection point of bottom slab |

F5 | width of top slab | B5 | Width of bottom slabs outline |

Bridge | Symbol | Sample Size | Average | Lower 95% | Upper 95% | Standard Deviation | Min | Median | Max |
---|---|---|---|---|---|---|---|---|---|

A | ${K}_{A}$ | 116 | 7.24% | 6.33% | 8.16% | 4.95% | −3.38% | 7.92% | 17.87% |

B | ${K}_{B}$ | 75 | 8.89% | 7.04% | 10.75% | 8.06% | −3.98% | 7.27% | 37.88% |

Symbol | Skewness | Kurtosis |
---|---|---|

${K}_{A}$ | −0.02537 | −1.04462 |

${K}_{B}$ | 0.16332 | 1.69674 |

Symbol | Average | Standard Deviation | Lower 95% | Upper 95% | Min | Median | Max | |
---|---|---|---|---|---|---|---|---|

Flange | ${K}_{AF}$ | 7.83% | 10.35% | 5.93% | 9.73% | −15.71% | 5.64% | 32.10% |

Top | ${K}_{AT}$ | 7.68% | 8.84% | 6.05% | 9.31% | −15.47% | 5.27% | 35.89% |

Web | ${K}_{AW}$ | 6.38% | 7.20% | 5.05% | 7.70% | −5.82% | 5.10% | 35.82% |

Bottom | ${K}_{AB}$ | 7.70% | 7.78% | 6.27% | 9.13% | −16.06% | 7.14% | 28.65% |

Symbol | Average | Standard Deviation | Lower 95% | Upper 95% | Min | Median | Max | |
---|---|---|---|---|---|---|---|---|

Top | ${K}_{BT}$ | 10.15% | 12.26% | 7.33% | 12.97% | −10.58% | 8.67% | 56.46% |

Web | ${K}_{BW}$ | 5.70% | 9.30% | 3.55% | 7.86% | −17.45% | 4.74% | 36.28% |

Bottom | ${K}_{BB}$ | 10.20% | 11.85% | 7.48% | 12.93% | −9.54% | 8.52% | 58.27% |

Symbol | Skewness | Kurtosis | |
---|---|---|---|

Bridge A | ${K}_{AF}$ | 0.3826 | −0.84707 |

${K}_{AT}$ | 0.70596 | 0.64497 | |

${K}_{AW}$ | 2.24166 | 5.53851 | |

${K}_{AB}$ | 0.2462 | 0.38215 | |

Bridge B | ${K}_{BT}$ | 1.28908 | 3.40778 |

${K}_{BW}$ | 0.82647 | 2.63577 | |

${K}_{BB}$ | 1.37295 | 2.96537 |

Sample Size | Average | Standard Deviation | Skewness | Kurtosis | Median | Lower 95% | Upper 95% |
---|---|---|---|---|---|---|---|

116 | 0.1338 | 0.0819 | −0.2876 | 0.5849 | 0.1367 | 0.1187 | 0.1488 |

Coefficients | Standard Error | T Stat | p-Value | |
---|---|---|---|---|

C | 0.058 | 0.010 | 5.882 | 4.36 × 10^{-8} |

${\beta}_{1}$ | 0.130 | 0.059 | 2.192 | 0.030 |

${\beta}_{2}$ | −0.002 | 0.070 | −0.035 | 0.972 |

${\beta}_{3}$ | 0.110 | 0.073 | 1.517 | 0.132 |

${\beta}_{4}$ | 0.759 | 0.068 | 11.163 | 7.44 × 10^{-20} |

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**MDPI and ACS Style**

Yu, J.; Zhang, J.; Li, P.; Han, X. Influence of Superstructure Pouring Concrete Volume Deviation on Bridge Performance: A Case Study. *Buildings* **2023**, *13*, 887.
https://doi.org/10.3390/buildings13040887

**AMA Style**

Yu J, Zhang J, Li P, Han X. Influence of Superstructure Pouring Concrete Volume Deviation on Bridge Performance: A Case Study. *Buildings*. 2023; 13(4):887.
https://doi.org/10.3390/buildings13040887

**Chicago/Turabian Style**

Yu, Jintian, Jinquan Zhang, Pengfei Li, and Xu Han. 2023. "Influence of Superstructure Pouring Concrete Volume Deviation on Bridge Performance: A Case Study" *Buildings* 13, no. 4: 887.
https://doi.org/10.3390/buildings13040887