# Bridge Scour Identification and Field Application Based on Ambient Vibration Measurements of Superstructures

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. The Hangzhou Bay Cable-Stayed Bridge

#### 2.1. Bridge Information

#### 2.2. Soil Properties

#### 2.3. Potential Scour Development

## 3. Ambient Vibration Measurements

^{2}.

- (1)
- Locations at each wave crest and trough of the mode shapes. These mode shapes are the ones of low order and sensitive to the scour.
- (2)
- Locations at quartile division points between the adjacent crest and trough of the selected mode shape wave. The wave profile can be predicted by the FE method before the measurement.
- (3)
- Locations at the points with a significant change of mode shapes. More than four sensors are suggested to be sequentially installed to determine the curvature of the shape change.
- (4)
- Locations at the scour-sensitive components, such as the pylon and girder near piers.
- (5)
- (6)
- Locations at the components with few local vibrations, such as the web plate or crossbeams of the steel box girder, as shown in Figure 4.
- (7)
- Sensor installation needs to follow the direction of the vibration for each scour-sensitive mode shape. For example, the sensors for measuring the pylon needs to be installed horizontally since the scour-sensitive mode shapes of the pylon mainly vibrate transversely.

## 4. Qualitative Scour Identification by Tracing Dynamic Features

#### 4.1. Identification by the Change of Natural Frequencies

#### 4.2. Identification by the Change of Mode Shapes

## 5. Quantitative Scour Identification by FE Model Updating

#### 5.1. FE Model Establishment

^{2}); ${u}_{z}$ = lateral displacement of the pile at the depth of z (m); and $C$ = foundation coefficient (KN/m

^{3}), which is usually a function of the depth (Equation (3)).

^{4}),; its value can be found in the foundation design specifications of different countries. Considering that the Hangzhou Bay Bridge is located in China, the Chinese code for the design of the ground base and foundation of highway bridges and culverts (JTG D63-2007) was selected in the present study to specify the value of m.

_{j}(j = 1, 2, …, n) and two nodes of the jth element are N

_{j}and N

_{j+1}, as shown in Figure 13.

_{1}and N

_{2}can be derived as:

_{1}and N

_{2}of the 1st element, respectively; and $K({h}_{1})$ = stiffness of soils at the depth h

_{1}based on Equation (4), which is calculated as:

_{0}= width of the pile.

_{j}and N

_{j+1}of the jth element (j > 1) can be derived as:

_{j}and N

_{j+1}of the jth element, respectively; and $K({\displaystyle {\sum}_{i=1}^{j}{h}_{i}})$ and $K({\displaystyle {\sum}_{i=1}^{j+1}{h}_{i}})$ = stiffness of soils at the depths $\sum}_{i=1}^{j}{h}_{i$ and $\sum}_{i=1}^{j+1}{h}_{i$, respectively, which based on Equation (4) are calculated as:

_{1}) should add up to the contributions from both connecting elements (Figure 13). Therefore, the stiffness of all the springs in the FE model can be assigned by the values based on the following equation.

#### 5.2. Identification of Soil Stiffness

_{i}). These K

_{i}values need a further identification based on field measurements to best fit the actual response of the Hangzhou Bay Bridge. Based on Figure 8 and the corresponding discussion, the 6th, 7th, 9th, 10th, and 11th vibration modes have the indicator of $FCR$ less than 5%, which shows that the natural frequencies of these modes are negligibly affected by the scouring between two measurements. In other words, the 6th, 7th, 9th, 10th, and 11th vibration modes are insensitive to the scour. The stiffness of soils/springs (K

_{i}) becomes the last main reason to affect the natural frequencies of these five modes. Therefore, the real values of K

_{i}for all the springs in the FE model can be identified by model updating until the simulated natural frequencies of the scour-insensitive vibration modes match the measurements. The adoption of scour-insensitive vibration modes significantly lowers the scour interference during the model updating of soil stiffness. This mode sensitivity can also be determined by the FE simulation of the bridge if there is not enough information from field measurements. By the parametric study based on the FE model, a scour-sensitive vibration mode still remains sensitive when the scour keeps developing. Considering K

_{i}is a function of the coefficient of m based on Equations (4)–(12); the algorithm for identifying soil/spring stiffness by amending m to update the values of K

_{i}is provided in Figure 14.

_{1}= difference between the simulated and measured natural frequencies; ${f}_{sim}^{q}$ and ${f}_{mea}^{q}$ = simulated and measured natural frequencies of the qth vibration mode, respectively; and q = concerned orders, which refer to the orders of the scour-insensitive vibration modes. It is noted that other forms of D

_{1}, i.e., Root-Mean-Squared-Error (RMSE) and the Nash-Sutcliffe Efficiency, can also be used in Equation (13), which should provide the same iteration results.

_{1}is greater than a preset threshold, m for each soil layer needs to be further amended. Meanwhile, the natural frequencies need to be re-simulated based on the FE model with the newly amended m and accordingly a new D

_{1}can also be calculated. This iteration process for updating the value of m (stiffness of springs K

_{i}) is repeated until the value of D

_{1}reaches the threshold.

_{1}. The threshold of terminating the iteration is set as reaching the lowest value of D

_{1}during the updating process. The stiffness of each soil layer keeps being updated by revising the value of m at intervals of 100 kN/m

^{4}per sub-step of the iteration. The values of D

_{1}calculated by Equation (13) at all the sub-steps of the iteration are provided in Figure 15.

_{1}keeps decreasing until the 24th sub-step of the iteration when it increases again. At this sub-step the difference between the simulated and measured natural frequencies of the 6th, 7th, 9th, 10th, and 11th vibration modes reaches its minimum during the entire iteration process. In other words, the pile-soil simulation in the FE model gradually approaches the actual situation of the bridge before this sub-step. Table 6 lists the values of m based on the results at the 24th sub-step of the iteration. Substituting the newly updated m into Equations (4)–(12), the new stiffness of soil springs K

_{i}was subsequently obtained and then correspondingly updated in the FE model of the bridge. The updated values of K

_{i}are listed in Table 7.

#### 5.3. Identification of Scour Depth (Soil Level)

_{2}is proposed in Equation (14) to quantitatively describe the difference between the simulated and measured natural frequency changes of scour-sensitive vibration modes.

_{2}= difference between the simulated and measured natural frequency changes; ${f}_{sim,({h}_{1}+\Delta h)}^{p}$ = simulated natural frequency of the pth vibration mode by the FE model with the scour depth of h

_{1}+ Δh, i.e., h

_{2}; ${f}_{sim,{h}_{1}}^{p}$ = simulated natural frequency of the pth vibration mode by the FE model with the scour depth of h

_{1}; ${f}_{sim,({h}_{1}+\Delta h)}^{p}-{f}_{sim,{h}_{1}}^{p}$ = simulated natural frequency change induced by the increment of scour depth Δh; ${f}_{mea,2016}^{p}$ = measured natural frequency of the pth vibration mode in 2016; ${f}_{mea,2013}^{p}$ = measured natural frequency of the pth vibration mode in 2013; ${f}_{mea,2016}^{p}-{f}_{mea,2013}^{p}$ = measured natural frequency change induced by the increment of scour depth from 2013 to 2016; and p = the orders of the scour-sensitive vibration modes.

_{1}set in the FE model before updating Δh was determined based on the underwater inspection report in 2013. The Δh was amended at intervals of 0.5 m per sub-step of the iteration until the D

_{2}was less than the pre-set threshold. Subsequently, new natural frequencies were simulated based on the FE model with the newly amended Δh and a new D

_{2}was also obtained. The threshold for terminating the iteration is set as reaching the lowest value of D

_{2}. The values of D

_{2}calculated by Equation (14) at all the sub-steps of the iteration are provided in Table 8. Figure 17 plots the variation of D

_{2}along with increasing Δh from 0 m to 7 m.

_{2}decreases with the progressive scouring until the Δh reaches the increment of 4.5 m. Thereafter, the D

_{2}turns to increase as the Δh continues going deeper. In other words, the lowest value of D

_{2}is obtained at the 10th sub-step of the iteration when the Δh is 4.5 m. At this moment, the difference between the simulated and measured natural frequency changes of the 2nd, 3rd, 4th, and 5th vibration modes reaches its minimum value. Therefore, the scouring of the Hangzhou Bay Bridge from 2013 to 2016 was successfully identified as the increment of 4.5 m. It is clearly observed from Table 9 that after model updating the frequency changes by adding 4.5 m scour depth in the FE model, which is very close to the measured changes. The proposed scour identification method worked very well in the present case study.

## 6. Verification by Results from Underwater Terrain Map

## 7. Concluding Remarks

- (1)
- Methodology improvements: In this study, the variation of mode shapes is incorporated to qualitatively detect the existence of bridge foundation scour, and a new two-step scour identification method was also proposed. By this method the scour is quantitatively identified by best fitting the scour-sensitive vibration modes (the 2nd step) using an FE model whose soil stiffness is pre-updated by best fitting the scour-insensitive modes (the 1st step).
- (2)
- Application improvements: The Hangzhou Bay Bridge, a 908 m cable-stayed bridge, was selected as a case study to comprehensively illustrate the application of this method. Another successful field application is important for this vibration-based scour identification method, which presently happens to significantly lack application for real bridges.

- (1)
- The high-order vibration modes are insensitive to the scour. The low-order vibration modes, especially for the modes of pylon, are very sensitive to the scour. Therefore, the natural frequencies of high and low vibration modes can be used as the tracing targets for updating the soil stiffness and scour depth.
- (2)
- The documented results from the underwater terrain map verify the accuracy of the proposed scour identification based on the ambient vibration measurements.
- (3)
- The proposed qualitative identification method can also be used to narrow down the number of bridges in need of further evaluation, e.g., the quantitative identification. It is noted that the quantitative identification needs enough bridge information to conduct the model updating. Both the qualitative and quantitative identification methods were suggested to be applied accordingly.
- (4)
- Once applied in practice, this vibration-based scour identification does not require any underwater devices and operations and could be easily integrated to a routine assessment task for bridges.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 9.**The change of the mode shapes of the girder. (

**a**) The 1st vertical bending mode (symmetric), (

**b**) The 1st vertical bending mode (antisymmetric), (

**c**) The 2nd vertical bending mode (symmetric) (

**d**) The 3rd vertical bending mode (symmetric).

**Figure 10.**The change of the mode shapes of the pylon (only one pylon is shown). (

**a**) The 1st lateral bending mode (antisymmetric) (

**b**) The 1st lateral bending mode (symmetric).

**Figure 15.**Values of D

_{1}versus sub-steps of iteration. (

**a**) Iteration results at all the 35 sub-step, (

**b**) Iteration results in a selected range (10th–30th).

Riverbed Elevation before Scour (m) | General Scour Depth (m) | Degradational Scour Depth (m) | Local Scour Depth (m) | Riverbed Elevation after Scour (m) |
---|---|---|---|---|

Solution 1: Amended Formula 65-1, 65-2 [46] | ||||

−12.3 | 7 | 10.8 | −30.1 | |

Solution 2: Formula HEC-18 [9] | ||||

−12.3 | 0.9 | 7 | 14.9 | −35.1 |

Solution 3: Scour experiment in a water-tank | ||||

−12.3 | 21.8 | −34.1 |

Order | Measurement in 2013 | Measurement in 2016 | ||
---|---|---|---|---|

Frequency | Mode Shape | Frequency | Mode Shape | |

1 | - | 1st LM (girder) | - | 1st LM (girder) |

2 | 0.399 | 1st sym-V (girder) | 0.342 | 1st sym-V (girder) |

3 | 0.512 | 1st anti-L (pylon) | 0.416 | 1st anti-L (pylon) |

4 | 0.578 | 1st anti-V (girder) | 0.502 | 1st anti-V (girder) |

5 | 0.683 | 1st sym-L (pylon) | 0.562 | 1st sym-L (pylon) |

6 | 0.771 | 2nd sym-V (girder) | 0.744 | 2nd sym-V (girder) |

7 | 0.952 | 3rd sym-V (girder) | 0.939 | 3rd sym-V (girder) |

8 | 1.091 | 2nd anti-L (pylon) | 1.039 | 2nd anti-L (pylon) |

9 | 1.087 | 2nd anti-V (girder) | 1.071 | 2nd anti-V (girder) |

10 | 1.341 | 4st sym-V (girder) | 1.334 | 4st sym-V (girder) |

11 | 1.588 | 3rd anti-V (girder) | 1.574 | 3rd anti-V (girder) |

Components | Area (m^{2}) | Principal Bending Moment of Inertia (m^{4}) | Secondary Bending Moment of Inertia (m^{4}) | Torsional Moment of Inertia (m^{4}) | Width (m) | Height (m) |
---|---|---|---|---|---|---|

Girder | 1.54 | 182.37 | 2.80 | 7.00 | 37.10 | 3.50 |

Pylon | 9.02–55.02 | 8.56–157.60 | 52.18–1171.40 | 4.11–578.98 | 3.5–7.5 | 6.0–9.7 |

Crossbeam | 21.46 | 108.30 | 203.70 | 228.20 | - | - |

Stay cables | 0.00327–0.009275 | - | - | - | - | - |

Properties | Density (kg/m ^{3}) | Elasticity Modulus (MPa) | Poisson’s Ratio | |
---|---|---|---|---|

Components | ||||

Girder | 10.288 × 10^{3} | 2.10 × 10^{5} | 0.3 | |

Crossbeam | 10.288 × 10^{3} | 2.10 × 10^{5} | 0.3 | |

Stay cables | 8.450 × 10^{3} | 1.90 × 10^{5} | 0.3 | |

Pylon | 2.600 × 10^{3} | 3.50 × 10^{4} | 0.2 | |

Piers | 2.600 × 10^{3} | 3.30 × 10^{4} | 0.2 |

Layer Number | Soil Material | Thickness (m) | Depth (m) | m (kN/m^{4}) |
---|---|---|---|---|

① | Muddy mild clay | 14.01 | 14.01 | 2000 |

② | Muddy clay | 5.41 | 19.42 | 2000 |

③ | Clay | 4.96 | 24.38 | 3000 |

④ | Mild clay | 5.62 | 30 | 3500 |

⑤ | Clayey silt | 31 | 61 | 4000 |

⑥ | Clay | 9.17 | 70.17 | 3000 |

⑦ | Mild clay | 3.91 | 74.08 | 3000 |

⑧ | Silty sand | 12.49 | 86.57 | 5000 |

⑨ | Mild clay | 7.14 | 93.71 | 3500 |

⑩ | Clay | 4.98 | 98.69 | 3000 |

⑪ | Silty sand | 17.18 | 115.87 | 5000 |

Layer Number | Soil Material | m (kN/m^{4}) | Node Numbers of Single Pile |
---|---|---|---|

① | Muddy mild clay | 4400 | 0–28 |

② | Muddy clay | 4400 | 29–39 |

③ | Clay | 5400 | 40–49 |

④ | Mild clay | 5900 | 50–60 |

⑤ | Clayey silt | 6400 | 61–122 |

⑥ | Clay | 5400 | 123–140 |

⑦ | Mild clay | 5400 | 141–148 |

⑧ | Silty sand | 7400 | 149–173 |

⑨ | Mild clay | 5900 | 174–187 |

⑩ | Clay | 5400 | 188–197 |

⑪ | Silty sand | 7400 | 198–232 |

Node Numbers of Single Pile | K (10^{3} kN/m) | Node Numbers of Single Pile | K (10^{3} kN/m) | Node Numbers of Single Pile | K (10^{3} kN/m) | |||
---|---|---|---|---|---|---|---|---|

Layer ① | 0 | 0.4578 | Layer ⑤ | 60 | 240.5908 | Layer ⑧ | … | … |

1 | 4.1201 | 61 | 247.7074 | 173 | 647.3823 | |||

… | … | 62 | 251.7026 | Layer ⑨ | 174 | 624.7812 | ||

28 | 79.6559 | … | … | 175 | 628.3514 | |||

Layer ② | 29 | 82.4027 | 122 | 414.2214 | … | … | ||

30 | 85.1494 | Layer ⑥ | 123 | 405.1850 | 187 | 671.1936 | ||

… | … | 124 | 408.4526 | Layer ⑩ | 188 | 674.7637 | ||

39 | 130.7830 | … | … | 189 | 678.3339 | |||

Layer ③ | 40 | 138.2117 | 140 | 496.3355 | … | … | ||

41 | 141.5827 | Layer ⑦ | 141 | 506.9653 | 197 | 856.8126 | ||

… | … | 142 | 510.5355 | Layer ⑪ | 198 | 891.0923 | ||

49 | 181.6084 | … | … | 199 | 895.5702 | |||

Layer ④ | 50 | 187.8406 | 148 | 644.8105 | … | … | ||

51 | 191.5237 | Layer ⑧ | 149 | 671.6777 | 232 | 520.9233 | ||

… | … | 150 | 676.1555 |

Δh (m) | Contribution of the 2nd order (Hz) | Contribution of the 3rd order (Hz) | Contribution of the 4th order (Hz) | Contribution of the 5th order (Hz) | D_{2} |
---|---|---|---|---|---|

0 | 0.010290 | −0.00965 | −0.000916 | −0.032545 | 0.001259 |

0.5 | 0.010844 | −0.00858 | −0.000283 | −0.031154 | 0.001162 |

1 | 0.011381 | −0.00754 | 0.000338 | −0.029802 | 0.001075 |

1.5 | 0.011662 | −0.00703 | 0.000660 | −0.029139 | 0.001035 |

2 | 0.011941 | −0.00653 | 0.000982 | −0.028489 | 0.000998 |

2.5 | 0.012232 | −0.00603 | 0.001316 | −0.027839 | 0.000963 |

3 | 0.012553 | −0.00554 | 0.001684 | −0.027202 | 0.000931 |

3.5 | 0.012931 | −0.00506 | 0.002121 | −0.026578 | 0.000904 |

4 | 0.013432 | −0.00458 | 0.002696 | −0.025951 | 0.000882 |

4.5 | 0.014141 | −0.00411 | 0.003513 | −0.025338 | 0.000871 |

5 | 0.015081 | −0.00364 | 0.004593 | −0.024732 | 0.000873 |

5.5 | 0.016170 | −0.00319 | 0.005847 | −0.024145 | 0.000889 |

6 | 0.017323 | −0.00273 | 0.007169 | −0.023549 | 0.000913 |

6.5 | 0.018492 | −0.00228 | 0.008515 | −0.022964 | 0.000947 |

7 | 0.019654 | −0.00184 | 0.009849 | −0.022392 | 0.000988 |

Order | Measured Frequency Change/Difference from 2013 to 2016 | Simulate Frequency Change/Difference by Adding 4.5 m Scour Depth |
---|---|---|

2 | 0.057 | 0.071 |

3 | 0.096 | 0.092 |

4 | 0.076 | 0.079 |

5 | 0.121 | 0.121 |

Foundation | Terrain Elevation in 2013 (m) | Terrain Elevation in 2016 (m) | Scour Depth Developments (m) |
---|---|---|---|

Pier B9 (North side pier) | −19.4 | −23.4 | 4 |

Pylon B10 (North pylon) | −20.2 | −25.4 | 5.2 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Xiong, W.; Cai, C.S.; Kong, B.; Zhang, X.; Tang, P.
Bridge Scour Identification and Field Application Based on Ambient Vibration Measurements of Superstructures. *J. Mar. Sci. Eng.* **2019**, *7*, 121.
https://doi.org/10.3390/jmse7050121

**AMA Style**

Xiong W, Cai CS, Kong B, Zhang X, Tang P.
Bridge Scour Identification and Field Application Based on Ambient Vibration Measurements of Superstructures. *Journal of Marine Science and Engineering*. 2019; 7(5):121.
https://doi.org/10.3390/jmse7050121

**Chicago/Turabian Style**

Xiong, Wen, C.S. Cai, Bo Kong, Xuefeng Zhang, and Pingbo Tang.
2019. "Bridge Scour Identification and Field Application Based on Ambient Vibration Measurements of Superstructures" *Journal of Marine Science and Engineering* 7, no. 5: 121.
https://doi.org/10.3390/jmse7050121