Bridge Scour Identification and Field Application Based on Ambient

Journal of Marine Science and Engineering

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

Wen Xiong 1,* , C.S. Cai 2, Bo Kong 2, Xuefeng Zhang 3 and Pingbo Tang 4 1 Department of Bridge Engineering, School of Transportation, Southeast University, Nanjing 211189, China 2 Department of Civil and Environmental Engineering, Louisiana State University, Baton Rouge, LA 70803, USA; [email protected] (C.S.C.); [email protected] (B.K.) 3 Research Institute of Highway Ministry of Transport, Beijing 100088, China; [email protected] 4 School of Sustainable Engineering and the Built Environment, Arizona State University, Tempe, AZ 85281, USA; [email protected] * Correspondence: [email protected]

Received: 16 March 2019; Accepted: 18 April 2019; Published: 26 April 2019

Abstract: A scour identification method was developed based on the ambient vibration measurements of superstructures. The Hangzhou Bay Bridge, a cable-stayed bridge with high scour potential, was selected to illustrate the application of this method. Firstly, two ambient vibration measurements were conducted in 2013 and 2016 by installing the acceleration sensors on the girders and pylon. By modal analysis, the natural frequencies of the superstructures were calculated with respect to different mode shapes. Then, by tracing the change of dynamic features between two measurements in 2013 and 2016, the discrepancies of the support boundary conditions, i.e., at the foundation of the Hangzhou Bay Bridge, were detected, which, in turn, qualitatively identified the existence of bridge foundation scour. Secondly, an FE model of the bridge considering soil-pile interaction was established to further quantify the scour depth in two steps. (1) The stiffness of the soil springs representing the support boundary of the bridge was initially identified by the model updating method. In this step, the principle for a successful identification is to make the simulation results best fit the measured natural frequencies of those modes insensitive to the scour. (2) Then, using the updated FE model, the scour depth was identified by updating the depth of supporting soils. In this step, the principle of model updating is to make the simulation results best fit the measured natural frequency changes of those modes sensitive to the scour. Finally, a comparison to the underwater terrain map of the Hangzhou Bay Bridge was carried out to verify the accuracy of the predicted scour depth. Based on the study in this paper, it shows that the proposed method for identifying bridge scour based on the ambient vibration measurements of superstructures is effective and convenient. It is feasible to quickly assess scour conditions for a large number of bridges without underwater devices and operations.

Keywords: bridge scour; identiﬁcation; ambient vibration; ﬁeld application; natural frequency; mode shape; superstructure; cable-stayed bridge

1. Introduction Bridge scour is a significant concern around the world. In the past 40 years, more than 1500 bridges collapsed, and approximately 60% of these failures are related to the scour of foundations in the United States [1,2]. For example, the catastrophic collapse of the Schoharie Creek Bridge in New York in 1987 was caused by the cumulative effects of pier scour [3]. The Los Gatos Creek Bridge over I-5 in the state of California collapsed because of local pier scour during a flood event, and the underlying reason was due to the channel degradation during the 28 years of service [4]. However, the vulnerability of bridges

J. Mar. Sci. Eng. 2019, 7, 121; doi:10.3390/jmse7050121 www.mdpi.com/journal/jmse J. Mar. Sci. Eng. 2019, 7, 121 2 of 24 subject to scouring cannot be predicted by routine hydraulic and geotechnical analyses, because more than 100,000 bridges over water in the United States are identified as “unknown foundations” [4,5]. In China, many cable-supported bridges with super-long spans have been recently constructed over rivers and water channels such as the Yangtze River, Yellow River, Qiantang River, etc. These bridges are enormously vulnerable to the hydrological environments such as the annually typhoon-induced floods. Thus, more serious bridge scour, especially at pylons, occurred very often and developed rapidly. Based on the investigation reports, the scour depths of three typical cable-stayed bridges crossing the Yangtze River in China, i.e., the 2nd Nanjing Yangtze River Bridge, Hangzhou Bay Bridge, and Runyang Yangtze River Bridge, were 20 m, 16 m, and 18 m, respectively [6]. Taking the devastating Typhoon Morakot in the summer of 2009 for a detailed example, as many as 3000 mm of rainfall poured in four days and led to the failures or severe damages of more than 110 bridges [7]. Field investigation indicates that the major cause is foundation scour that removes the bed materials surrounding the piers and abutments. Therefore, it is urgent to develop an effective and economical method to identify bridge scour. An analytical solution or numerical simulation is the common way to predict the bridge scour depth due to its practical conveniences [8–14]. Along with continuous scour experiments, these formulas for calculation are similar to the real situations [15,16]. However, some assumptions may still be applied in the formulas in order to reduce their complexity since the number of the selected parameters is limited. Therefore, these formulas may not be able to reflect the real scouring situations. In the past few decades, many on-site monitoring methods or techniques were proposed to identify or directly measure bridge scour, including the visual inspection by divers [17], and the adoption of fiber Bragg grating (FBG) sensors [18–20], sliding magnetic collars [21], steel rod [21], multi-lens pier scour monitoring [22], microelectro-mechanical system (MEMS) sensors [23], and ultrasonic or radar [24–27]. All of these methods appear quite promising; however, the underwater operability, economic sustainability, or scour refilling process prevent them from further successful and wide application in field monitoring. Bridge scour identification by tracing the changes in dynamic characteristics has attracted a lot of attention in recent years due to its simplicity, efficiency, and low cost. Although the temperature may also induce the change of dynamic characteristics, it has almost no contribution to such difference if compared to the scour influence [28–33]. The temperature effect can be removed by many statistical methods such as NLPCA (Nonlinear Principal Component Analysis), ANN (Artificial Neural Network), SVM (Support Vector Machine), etc. [34–37]. It can also be simply eliminated by selecting the same seasonal period for each dynamic measurement. The frequency change by the internal cracking or corrosion by changing local stiffness can also be simply ignored if compared to the scour effect by changing entire stiffness. Samizo et al. [38] stated that the natural frequencies of bridge piers would be reduced with the increase of scour depths. Foti and Sabia [39] monitored a bridge, which is affected by scouring and subjected to retrofitting, by measuring the traffic-induced vibrations and indicated a great potential for the use of dynamic tests in the scour assessment of bridges. Zarafshan et al. [40] proposed a scour depth detection concept based on measuring the fundamental vibration frequency of a rod embedded in the riverbed using a laboratory test, simulation, and measurements at the bridge site. Prendergast et al. [41] examined the effect that scour has on the frequency response of a driven pile foundation system and proposed a method to predict the scour depth based on a given pile frequency. Elsaid and Seracino [42] experimentally illustrated the use of the horizontally-displaced mode shapes and dynamic flexibility features to identify the scour from the response of the bridge superstructure. Kong and Cai [43] investigated the scour effect on the response of the entire bridge. The results demonstrated that the response changes of the bridge deck and vehicle are significant and can be used for scour damage detection. Prendergast et al. [44] also developed a similar approach to determine the bridge scour condition by using the vehicle-induced vibrations of superstructures and employed a vehicle-bridge-soil interaction (VBSI) model to trace the frequency change induced by the scour. J. Mar. Sci. Eng. 2019, 7, 121 3 of 24

The above studies show the feasibility to establish an effective relationship between the scour effect and the dynamic features obtained from the vibration signals of bridge superstructures. However, most of the previous studies focus on the theoretical significance in the vibration-based method by either analytical solutions or Finite Element (FE) models. More research is still needed in numerous aspects to further improve the reliability and accuracy when applied to the field bridges. For instance, it is usually enormously difficult to accurately quantify the vibration signals of bridges in field environments. The actual condition of the soil surrounding the foundation system is very hard to be obtained, which directly determines the support boundary for the vibration of superstructures. Moreover, the limited number or irrational arrangement of sensors installed on the superstructures may highly reduce the sensitivity of the scour identification when tracing vibrations. It is generally believed that the last mile to the success of such vibration-based methods to identify the scour is the application of studies on real bridges under actual scour and in a field environment. Although Chen et al. [7] has already applied this method to the Kao-Ping-His cable-stayed bridge, more improvements are still needed in many aspects. For example, the information of the bridge condition before the scour is required to be pre-known in Chen et al.’s study [7] and there is no attention paid to the contributions from different vibration modes and structural components. The present study aims to develop a scour identification method for existing bridges based on ambient vibration measurements of superstructures. The Hangzhou Bay Bridge, a 908m cable-stayed bridge, was selected to illustrate the application due to its high scour potential. Firstly, through the acceleration sensors installed on the girder and pylon, two ambient vibration measurements were conducted in 2013 and 2016. By applying the modal analysis on the measurements, the natural frequencies of different orders corresponding to different mode shapes of the superstructure were obtained. Then, by tracing the change of two dynamic features between two measurements, the discrepancies of the support boundary at the foundation of the Hangzhou Bay Bridge were detected, which can qualitatively identified the existence of foundation scour. Secondly, an FE model of the bridge considering soil-pile interactions was established to further quantitatively identify the scour depth in two steps. (1) The stiffness of the soil springs representing the support boundary of the bridge was identified by the model updating method. The principle for a successful identification at this step is to make the simulation results best fit the measured natural frequencies of those modes insensitive to the scour. (2) Then, based on the updated FE model, the scour depth was identified by updating the depth of supporting soils. The principle of model updating at this step is to make the simulation results best fit the measured natural frequency changes of those modes sensitive to the scour. Finally, a comparison with the underwater terrain map of the Hangzhou Bay Bridge was carried out to verify the accuracy of the predicted scour depth. This practical application shows that the proposed method for identifying bridge scour based on the ambient vibration measurements of superstructures is effective and convenient. It is feasible to quickly assess scour conditions for a large number of bridges without underwater devices and operations.

2. The Hangzhou Bay Cable-Stayed Bridge

2.1. Bridge Information The Hangzhou Bay Bridge is a large-scale bridge across the Hangzhou Bay in the eastern coastal region of China with a total length of 36 km. It is among the ten longest trans-oceanic bridges in the world. The construction of this bridge was completed on 14 June 2007 and opened to traﬃc on 1 May 2008. It consists of a cable-stayed bridge with the main ship-channel and a large quantity of beam bridges (Figure1). This cable-stayed bridge is selected for the ambient vibration measurement. In the following study, the Hangzhou Bay Bridge only refers to this cable-stayed bridge if not otherwise speciﬁed. J. Mar. Sci. Eng. 2019, 7, x FOR PEER REVIEW 4 of 24 J. Mar. Sci. Eng. 2019, 7, 121 4 of 24 J. Mar.J. Mar. Sci. Sci. Eng. Eng. 2019 2019, 7,, x7 ,FOR x FOR PEER PEER REVIEW REVIEW Beam bridges 4 of 4 of 24 24 Cable-stayed bridge Beam bridgesbridges Cable-stayedCable-stayed bridge bridge

Figure 1. Overview of the cable-stayed bridge and beam bridges. FigureFigure 1. Overview1. Overview of of the the cable-stayedcable-stayed bridge bridge and and beam beam bridges. bridges. Figure 1. Overview of the cable-stayed bridge and beam bridges. The HangzhouThe Hangzhou Bay Bay Bridge Bridge has has one one main main spanspan along with with four four side side spans, spans, each each measuring measuring 70 m, 70 70 m, m, The Hangzhou Bay Bridge has one main span along with four side spans, each measuring 70 m, 160 m,160 448448 m, m, m,448 160160 m, m,160m, andandm, and 7070 m, 70m, m, asas shownas shown shown in in in Figure Figure Figure2a. 2a. The TheThe connection connection connection between between the the thegirder girder girder and and pylonand pylon pylon is 160is m, designed 448 m, 160as a m,semi-floating and 70 m, assystem, shown which in Figure is beneficial 2a. The to connection increasing between the earthquake the girder resistance and pylon at designedis designed as as asemi-ﬂoating a semi-floating system, system, which which is beneﬁcialis beneficial to increasingto increasing the the earthquake earthquake resistance resistance at the at is designedthe limit stage.as a semi-floating The side spans system, are additionally which is supportedbeneficial byto increasingthe auxiliary the piers earthquake in order toresistance improve at limitthe limit stage. stage. The The side side spans spans are ar additionallye additionally supported supported by theby the auxiliary auxiliary piers piers in order in order to improve to improve the thethe limit dynamic stage. behaviorThe side forspans daily ar service.e additionally supported by the auxiliary piers in order to improve the dynamic behavior for daily service. dynamicthe dynamic behavior behavior for daily for daily service. service.

(a) (b)

Figure 2. Layout of the Hangzhou Bay Bridge (Unit: cm). (a) Span arrangement of girder, (b) Pylon. (a) (b)( b)

FigureFigureThe 2. pylon2.Layout Layout of of theof the the Hangzhou Hangzhou Hangzhou Bay BayBay Bridge Bridge is(Unit: designed cm).cm). ( a(as (a)a ))Span Spana Span diamond-shaped arrangement arrangement arrangement of of ofgirder,structure, girder, girder, (b )( bPylon.of) Pylon. which the height is 178.8 m from the base level to the top (Figure 2b) and 138.575 m from the girder. The The pylon of the Hangzhou Bay Bridge is designed as a diamond-shaped structure, of which the ThecableThe pylon systempylon of ofconsists the the Hangzhou Hangzhou of 28 pairs BayBay of BridgeBridge stay cables is designed on each asas sidea a diamond-shaped diamond-shaped of the pylon and structure, structure,is arranged of ofwhich inwhich thedouble-plane height is 178.8 as am semi-fan from the shape. base The level minimum to the top an d(Figure maximum 2b) numberand 138.575 of steel m wiresfrom withinthe girder. a cable The heightthe height is 178.8 is 178.8 m from m from the basethe base level level to the to top the (Figure top (Figure2b) and 2b) 138.575 and 138.575 m from m thefrom girder. the girder. The cable The cableis 109 system and 199, consists respectively. of 28 Thepairs main of girderstay cables is prim onarily each supported side of by the the pyloncable system and is and arranged also sits in systemcable system consists consists of 28 pairs of of28 staypairs cables of stay on each cables side on of theeach pylon side and of isthe arranged pylon and in double-plane is arranged as in a double-planeon a transverse as a semi-fanbeam of theshape. pylon. The The minimum flat steel an boxd maximum is applied number as the girder’s of steel cross-section wires within 3.5 a cable m semi-fandouble-plane shape. as a The semi-fan minimum shape. and The maximum minimum number and maximum of steel number wires within of steel a cablewires iswithin 109 and a cable 199, is 109high and and 199, 37.1 respectively. m wide (Figure The 3).main Inside girder the isbox prim girder,arily thesupported steel crossbeams by the cable are systemadded at and a 3.75 also m sits respectively.is 109 and 199, The respectively. main girder The is primarily main girder supported is primarily by the supported cable system by the and cable also system sits on and a transverse also sits on intervala transverse to improve beam theof girder’sthe pylon. resistance The flat to steelthe torsion. box is applied as the girder’s cross-section 3.5 m beamon a transverse of the pylon. beam The of ﬂatthe steelpylon. box The is appliedflat steel as box the is girder’s applied cross-section as the girder’s 3.5 cross-section m high and 37.1 3.5 m widehigh (Figure and 37.13). Insidem wide the (Figure box girder, 3). Inside the the steel box crossbeams girder, the are steel added crossbeams at a 3.75 are m added interval at toa 3.75 improve m highinterval and 37.1to improve m wide the (Figure girder’s 3). resistance Inside the to boxthe torsion. girder, the steel crossbeams are added at a 3.75 m theinterval girder’s to improve resistance the to girder’s the torsion. resistance to the torsion.

Figure 3. Cross-section of girder (Unit: mm).

Figure 3. Cross-section of girder (Unit: mm). Figure 3. Cross-section of girder (Unit: mm). Figure 3. Cross-section of girder (Unit: mm).

J. Mar. Sci. Eng. 2019, 7, 121 5 of 24

2.2. Soil Properties Based on the boring information at the bridge site, 17 layers of soils numbered from the top to the bottom are categorized as eight types, including the cohesionless sand 1 (Layer 1, elevation: 9.9~ 18.4 m), cohesive clay 1 (Layers 2~5 elevation: 18.4~ 39.9 m), cohesionless sand 2 (Layers 6~8 − − − − elevation: 39.9~ 71.1 m), cohesive clay 2 (Layers 9~10 elevation: 71.1~ 84.0 m), silty fine sand 1 − − − − (Layer 11 elevation: 84.0~ 96.5 m), cohesive clay 3 (Layers 12~15 elevation: 96.5~ 120.8 m), silty − − − − fine sand 2 (Layer 16 elevation: 120.8~ 139.8 m), and rounded gravel (Layer 17 elevation: deeper − − than 139.8 m). The bottom of the piles is located in the 7th category (silty fine sand 2), which is − regarded as a good supporting layer for the foundation [45]. The soil parameters of each layer are tested by the bridge design company and the details are not provided here due to the page limit.

2.3. Potential Scour Development The Hangzhou Bay Bridge is located in the Hangzhou Bay where the sea flow is rapid and turbulent and the tide is intensive. There are many suspended sediments floating with the current, and erosion and deposition occur very often along the seabed. Especially at the foundation of the bridge, the angle between the current direction and piers or pylons is large, resulting in a rapid removal of the soils. In addition, considering the bridge has served for almost ten years, the foundations of the bridge, especially at the pylons, may already have been scoured. In this sense, the Hangzhou Bay Bridge is appropriate as a case study subject to demonstrate the feasibility and convenience of the vibration-based scour identification in engineering practice. The final balanced scour depths of the pylon are predicted by the solutions of different design specifications and water-tank experiments as listed in Table1. It can be observed that the scouring of the Hangzhou Bay Bridge could be very critical during its service time.

Table 1. Predicted results of scour depths (Pylon number: B10/B11).

Riverbed Elevation General Scour Degradational Local Scour Depth Riverbed Elevation before Scour (m) Depth (m) Scour Depth (m) (m) 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 − −

3. Ambient Vibration Measurements Two ambient vibration measurements of the Hangzhou Bay Bridge were conducted in 2013 and 2016 to obtain its dynamic features. The field environmental forces, i.e., earth pulsation, hydrodynamic forces, or random traffic flow, excite the ambient vibration. The measurements covered the interior of the steel box girders at the main and side spans and the pylon structures above the pile cap. The sensors employed in the measurements were the broad-band acceleration-meters INV9828 from COINV (China Orient Institute of Noise & Vibration). The sensitivity of the sensors is 0.17–100 Hz with four gear selections and the resolution response is 0.0004 m/s2. Based on the theory of modal analysis and structural characteristics of the bridge, the following locations were selected to install the sensors and ensure sufficient information measured from the vibration.

(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. J.J. Mar.Mar. Sci.Sci. Eng. 2019, 7, x 121 FOR PEER REVIEW 66 of of 24

(3) Locations at the points with a significant change of mode shapes. More than four sensors are (3)J. Mar.suggestedLocations Sci. Eng. 2019 to at, 7be the, x FORsequentially points PEER withREVIEW installed a significant to determine change of the mode curvature shapes. of Morethe shape than change. four sensors 6 of 24 are (4) Locationssuggested at to the be sequentiallyscour-sensitive installed components, to determine such as the the curvature pylon and of girder the shape near change. piers. (3) Locations at the points with a significant change of mode shapes. More than four sensors are (4)(5) LocationsLocations with at the the scour-sensitive convenience components,of installation such and as measurement. the pylon and For girder example, near piers. all the sensors suggested to be sequentially installed to determine the curvature of the shape change. (5) wereLocations installed with inside the convenience the steel box of girder installation and the and pylon measurement. of the Hangzhou For example, Bay Bridge, all the as sensors shown (4) Locations at the scour-sensitive components, such as the pylon and girder near piers. inwere Figures installed 4 and inside 5. the steel box girder and the pylon of the Hangzhou Bay Bridge, as shown in (5) Locations with the convenience of installation and measurement. For example, all the sensors Figures4 and5. (6) Locationswere installed at the inside components the steel withbox girder few local and thevibrations, pylon of such the Hangzhou as the web Bay plate Bridge, or crossbeams as shown of (6) theLocationsin Figuressteel box at 4 theandgirder, components5. as shown with in Figure few local 4. vibrations, such as the web plate or crossbeams of the (7)(6) SensorsteelLocations box installation girder, at the ascomponents needs shown to in follow with Figure few the4. local direction vibrations, of the such vibration as the forweb each plate scour-sensitive or crossbeams ofmode (7) shape.Sensorthe steel For installation box example, girder,needs as the shown sensors to follow in Figure for the measuring 4. direction ofthe the pylon vibration needs for to each be installed scour-sensitive horizontally mode (7) sinceshape.Sensor the Forinstallation scour-sensitive example, needs the sensors modeto follow shapes for the measuring directionof the pylon theof the pylonmainly vibration needs vibrate for to betransversely.each installed scour-sensitive horizontally mode since the scour-sensitive mode shapes of the pylon mainly vibrate transversely. Theshape. final For arrangements example, the of sensors the sensors for measuring are illustra theted pylonin Figures needs 4 andto be 5 forinstalled the girder horizontally and pylon, since the scour-sensitive mode shapes of the pylon mainly vibrate transversely. respectively.The final The arrangements location of ofeach the sensor sensors is are denoted illustrated with ina capital Figures letter4 and 5to for categorize the girder its and position pylon, at respectively.differentThe structural final The arrangements location regions. of Lof each (L1- the sensorL15)sensors and isare denotedR illustra(R1-R17)ted with in in Figure aFigures capital 4 4 denote letterand 5 tofor the categorize the locations girder and its on position pylon,the girder at respectively. The location of each sensor is denoted with a capital letter to categorize its position at dionff erentthe left structural and right regions. sides of L (L1-L15)the pylon, and respectively; R (R1-R17) inU Figure(U1-U10)4 denote and D the (D1-D7) locations in onFigure the girder 5 denote on different structural regions. L (L1-L15) and R (R1-R17) in Figure 4 denote the locations on the girder thethe leftlocations and right on the sides pylon of the above pylon, and respectively; below the girder, U (U1-U10) respectively. and D M (D1-D7) (M0) in in both Figure Figures5 denote 4 and the 5 on the left and right sides of the pylon, respectively; U (U1-U10) and D (D1-D7) in Figure 5 denote locationsdenote the on intersecting the pylon above location and belowof the thegirder girder, and respectively. pylon. All Mthe (M0) letters in both are Figuresfollowed4 and by5 different denote the locations on the pylon above and below the girder, respectively. M (M0) in both Figures 4 and 5 thenumbers intersecting to indicate location their of relative the girder distances and pylon. to the All pylon the or letters girder. are followed by different numbers to denote the intersecting location of the girder and pylon. All the letters are followed by different indicate their relative distances to the pylon or girder. Installednumbers near to toindicate their relative distances to the pylon or girder. Data acquisition Vertical web plate Longitudinal Installed near to Data acquisition Vertical web plate Longitudinal

Transverse/Lateral

Figure 4. Arrangement of vertical acceleration sensors along the girder. Figure 4. Figure 4. ArrangementArrangement of of vertical vertical accelera accelerationtion sensors sensors along along the the girder. girder.

Installed near to innerInstalled layer near of topylon inner layer of pylon Vertical Vertical Transvers Transvers OrOr Lateral Lateral

LongitudinalLongitudinal

Figure 5. Arrangement of transverse acceleration sensors along the pylon. FigureFigure 5. Arrangement of of transverse transverse accele accelerationration sensors sensors along along the the pylon. pylon.

J. Mar. Sci. Eng. 2019, 7, 121 7 of 24 J. Mar. Sci. Eng. 2019, 7, x FOR PEER REVIEW 7 of 24

All theAll vibrationthe vibration measurements measurements for the for Hangzhou the Hang Bayzhou Bridge Bay were Bridge conducted were conducted under the ambientunder the excitationambient without excitation interrupting without theinterrupting traﬃc. A durationthe traffic. of 20A duration min was adoptedof 20 min for was each adopted time of for recording each time withof a recording sampling with rate ata 100sampling Hz. The rate measurements at 100 Hz. Th insidee measurements the steel box inside girder the were steel targeted box girder to the were identiﬁcationtargeted to of the the identification bending modes of the of the bending girder modes in the vertical of the girder direction. in the Horizontal vertical direction. direction wasHorizontal the targetdirection in the pylonwas the case target for its in transversethe pylon case bending for its modes. transverse It is also bending noteworthy modes. that It is the also measurements noteworthy that needthe to measurements be conducted byneed several to be subsequent conducted stepsby several with thesubsequent common steps or shared withreference the common points, or i.e.,shared M0,reference L1, and R1points, for the i.e., girder M0, L1, and and U6 R1 and for U7 the for girder the pylon, and U6 due and to U7 the for limited the pylon, number due of to available the limited sensors.number Taking of available the reference sensors. point Taking of M0 the as reference an example, point the of acceleration M0 as an example, signals recordedthe acceleration in the time signals domainrecorded from in the the sensor time aredomain provided from inthe Figure sensor6. are provided in Figure 6.

30 )

2 20

10 0

-10 -20 Acceleration (m/s Acceleration -30 Time (20min)

FigureFigure 6. Acceleration 6. Acceleration signals signals at the at referencethe reference point point of M0. of M0.

4. Qualitative Scour Identification by Tracing Dynamic Features 4. Qualitative Scour Identification by Tracing Dynamic Features 4.1. Identification by the Change of Natural Frequencies 4.1. Identification by the Change of Natural Frequencies The very high frequency components of the vibration signals measured in 2013 and 2016 were The very high frequency components of the vibration signals measured in 2013 and 2016 were first removed by the wave filtering (low-pass wave filter) method to eliminate the vehicle-induced first removed by the wave filtering (low-pass wave filter) method to eliminate the vehicle-induced local vibration of the deck. Then, the modal analysis using the subspace iteration method was applied local vibration of the deck. Then, the modal analysis using the subspace iteration method was to the filtered vibration signals. In this way, the natural frequencies of the first eleven orders of the applied to the filtered vibration signals. In this way, the natural frequencies of the first eleven orders Hangzhou Bay Bridge were extracted from the two measurements and are provided in Table2. of the Hangzhou Bay Bridge were extracted from the two measurements and are provided in Table 2. Table 2. Modal analysis results from the measurements in 2013 and 2016.

Table 2. MeasurementModal analysis in results 2013 from the measurements Measurement in 2013 and in 2016 2016. Order FrequencyMeasurement Mode in 2013 Shape Frequency Measurement Modein 2016 Shape Order 1Frequency - 1st Mode LM (girder)Shape Frequency - Mode 1st LM Shape (girder) 21 0.399 - 1st 1st sym-V LM (girder) (girder) 0.342 - 1st 1st LM sym-V (girder) (girder) 32 0.512 0.399 1st anti-Lsym-V (pylon)(girder) 0.342 0.416 1st 1stsym-V anti-L (girder) (pylon) 43 0.578 0.512 1st 1st anti-V anti-L (girder)(pylon) 0.416 0.502 1st 1st anti-L anti-V (pylon) (girder) 5 0.683 1st sym-L (pylon) 0.562 1st sym-L (pylon) 4 0.578 1st anti-V (girder) 0.502 1st anti-V (girder) 6 0.771 2nd sym-V (girder) 0.744 2nd sym-V (girder) 5 0.683 1st sym-L (pylon) 0.562 1st sym-L (pylon) 7 0.952 3rd sym-V (girder) 0.939 3rd sym-V (girder) 6 0.771 2nd sym-V (girder) 0.744 2nd sym-V (girder) 8 1.091 2nd anti-L (pylon) 1.039 2nd anti-L (pylon) 97 1.087 0.952 2nd 3rd anti-Vsym-V (girder)(girder) 0.939 1.071 3rd 2nd sym-V anti-V (girder) (girder) 108 1.341 1.091 4st 2nd sym-V anti-L (girder) (pylon) 1.039 1.334 2nd 4st anti-L sym-V (pylon) (girder) 119 1.588 1.087 3rd 2nd anti-Vanti-V (girder) (girder) 1.071 1.574 2nd 3rd anti-V anti-V (girder) (girder) 10 1.341 4st sym-V (girder) 1.334 4st sym-V (girder) Note: L: lateral bending; V: vertical bending; LM: longitudinal moving; sym-: symmetric; anti-: antisymmetric. There were no sensors11 installed 1.588 along the longitudinal 3rd anti-V direction (girder) of the girder;1.574 therefore, 3rd no resultanti-V is (girder) given in Table2 for theNote: 1st order.L: lateral bending; V: vertical bending; LM: longitudinal moving; sym-: symmetric; anti-: antisymmetric. There were no sensors installed along the longitudinal direction of the girder; Comparingtherefore, the no extractedresult is given natural in Table frequencies 2 for the 1st in theorder. measurements of 2013 and 2016, a significant disparity can be clearly observed in Figure7. In addition, the natural frequencies of almost all the Comparing the extracted natural frequencies in the measurements of 2013 and 2016, a orders decrease in 2016. The global frequency change should be mainly induced by the change of whole significant disparity can be clearly observed in Figure 7. In addition, the natural frequencies of structural stiffness. For bridges, the whole structural stiffness can only be significantly influenced by almost all the orders decrease in 2016. The global frequency change should be mainly induced by the change of whole structural stiffness. For bridges, the whole structural stiffness can only be significantly influenced by the variation of the support boundary which in most cases is caused by

J. Mar. Sci. Eng. 2019, 7, 121 8 of 24 J. Mar. Sci. Eng. 2019, 7, x FOR PEER REVIEW 8 of 24 thethe scour. variation In this of the sense, support the natu boundaryral frequency which change in most of cases the issuperstructure caused by the has scour. a strong In this relationship sense, the withnatural the frequency development change of the of thefoundation superstructure scour. hasThe adecrease strong relationship of the natural with frequencies the development from 2013 of the to 2016foundation shown scour. in Figure The decrease7 clearly of indicates the natural and frequencies qualitatively from identifies 2013 to 2016 the shownscour occurrence in Figure7 clearly at the Hangzhouindicates and Bay qualitatively Bridge. identiﬁes the scour occurrence at the Hangzhou Bay Bridge.

1.6 2013 2016

1.4 )

Hz 1.2 (

1.0

0.8 Frequency range of low orders Girder 0.6

Natrual Frequency Girder 0.4 Pylon Pylon 0.2 2 4 6 8 10 12 Order

Figure 7. Disparity of natural frequencies between two measurements. Figure 7. Disparity of natural frequencies between two measurements. It is also observed from Figure7 that the frequency range of low orders from the 2nd to 5th, especiallyIt is also for theobserved modes offrom the pylon,Figure shows7 that morethe freq distinguishableuency range disparityof low orders between from two the measurements 2nd to 5th, especiallythan other orders.for the This modes observation of the reveals pylon, that show the naturals more frequencies distinguishable of different disparity orders orbetween components two measurementshave different sensitivities than other toorders. the scour This development observation (the reveals variation that ofthe the natural support frequencies boundary). of In different order to ordersdescribe or the components sensitivity, ahave new different parameter sensitivities of the frequency to the change scour ratio,development abbreviated (the to variation “FCR” hereafter, of the supportis proposed boundary). as follows: In order to describe the sensitivity, a new parameter of the frequency change ratio, abbreviated to “ FCR ” hereafter, is proposed as∆ follows:ω FCR = (1) Δωω FCR = ω = the natural frequency; and ∆ω = the change of theω natural frequency (absolute values). (1) Figure8 shows the values of FCR corresponding to different orders of vibration modes based on ω = the natural frequency; and Δω = the change of the natural frequency (absolute values). the two measurements. The values of FCR are generally above the level of 15% for the orders from the Figure 8 shows the values of FCR corresponding to different orders of vibration modes based 2nd to 5th while under the level of 5% for the high orders. This is because the low-order modes of on the two measurements. The values of FCR are generally above the level of 15% for the orders vibration contribute to almost all the measured ambient vibration. Once the vibration is affected by the from the 2nd to 5th while under the level of 5% for the high orders. This is because the low-order scour, the low-order modes should be influenced much more significantly than others. Especially for modes of vibration contribute to almost all the measured ambient vibration. Once the vibration is the low-order modes with the pylon (the 3rd and 5th orders), they have higher values of FCR (20–25%) affected by the scour, the low-order modes should be influenced much more significantly than than those with the girder (15–20%). Although the high-order modes yield the low values of FCR, others. Especially for the low-order modes with the pylon (the 3rd and 5th orders), they have higher a locally higher value of FCR (5%) still can be observed for the 8th mode with the pylon (1st anti-L values of FCR (20–25%) than those with the girder (15–20%). Although the high-order modes yield (girder) + 2nd anti-L (pylon)) than the nearby modes (mostly lower than 1%). This is because the scour, the low values of FCR , a locally higher value of FCR (5%) still can be observed for the 8th mode which directly determines the support boundary of the pylon, has more significant effects on the pylon with the pylon (1st anti-L (girder) + 2nd anti-L (pylon)) than the nearby modes (mostly lower than stiffness than that on the girder. 1%). This is because the scour, which directly determines the support boundary of the pylon, has more significant effects on the pylon stiffness than that on the girder.

J. Mar. Sci. Eng. 2019, 7, x FOR PEER REVIEW 9 of 24

J. Mar. Sci. Eng. 2019, 7, 121 9 of 24 J. Mar. Sci. Eng. 2019, 7, x FOR PEER REVIEW 9 of 24 25 Frequency range of low orders

Pylon 25 Frequency range of low orders 20 Pylon 20 Girder 15

Girder 15 FCR (%) 10

FCR (%) 10 Frequency range of high orders 5 Frequency range of high orders 5 0 24681012 Order 0 24681012 FCR Order Figure 8. Values of corresponding to different orders of the vibration mode. Figure 8. Values of FCR corresponding to different orders of the vibration mode. 4.2. IdentificationFigure by 8. the Values Change of ofF CRMode corresponding Shapes to different orders of the vibration mode. 4.2. Identification by the Change of Mode Shapes 4.2. IdentificationThe mode shapes by the Changeof the first of Mode eleven Shapes orders of the Hangzhou Bay Bridge were obtained using the subspaceThemode iteration shapes method of the based first eleven on the orders ambient of thevibration Hangzhou measurements. Bay Bridge wereFigure obtained 9 compares using four the subspacepairsThe of mode iterationmode shapes shapes method of theof based firstthe elevengirder on the orderswhich ambient of have th vibratione Hangzhou the same measurements. Bay order Bridge when were Figure extracted obtained9 compares usingfrom four thethe subspacepairsmeasurements of mode iteration shapes of method2013 of theand based girder 2016 on which (the the haveshapeambient the scale samevibration was order determined measurements. when extracted by theFigure from same the 9 compares measurementsnormalization four pairsofprocessing). 2013 of and mode 2016 shapes (the shape of scalethe girder was determined which have by thethe same same normalization order when processing). extracted from the measurements of 2013 and 2016 (the shape scale was determined by the same normalization 2.5 processing).Change of mode shapes Change of mode shapes 2013 1.0 2.0 2016 2.5 Change of mode shapes Change of mode shapes 2013 1.0 0.5 1.5 2.0 2016

1.0 0.5 1.5 0.0 Mode ShapeMode Mode shapeMode 0.5 1.0 0.0 -0.5

0.0 ShapeMode Mode shapeMode 0.5 2013 -0.5 2016 -0.5 -1.0 0.0 2013 0 100 200 300 400 500 600 700 800 900 0 100 2016 200 300 400 500 600 700 800 900 -0.5 -1.0 Bridge length (m) Bridge length (m) 0 100 200 300 400(a) 500 600 700 800 900 0 100 200 300( 400b) 500 600 700 800 900 Change of mode Bridgeshapes length (m) Bridge length (m) 2013 2013 1.0 1.0 (a) 2016 (b) 2016 Change of mode shapes 2013 2013 1.00.5 1.0 2016 0.5 2016

0.50.0 0.5 Mode shape Mode Mode shapesMode 0.0 0.0-0.5 Change of mode shapes Mode shape Mode Mode shapesMode 0.0 -0.5-1.0 -0.5 Change of mode shapes Change of mode shapes -1.0-1.5 0 100 200 300 400 500 600 700 800 900 -0.5 0 100 200 300 400 500 600 700 800 900 Bridge lengthChange (m) of mode shapes Bridge length (m) -1.5 0 100 200 300 400(c) 500 600 700 800 900 0 100 200 300( 400d) 500 600 700 800 900 Bridge length (m) Bridge length (m) Figure 9. The change(c of) the mode shapes of the girder. (a) The 1st vertical bending(d) mode (symmetric), (b) The 1st vertical bending mode (antisymmetric), (c) The 2nd vertical bending mode (symmetric) (d) The 3rd vertical bending mode (symmetric).

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Figure 9. The change of the mode shapes of the girder. (a) The 1st vertical bending mode J. Mar.(symmetric), Sci. Eng. 2019, (7b, 121) The 1st vertical bending mode (antisymmetric), (c) The 2nd vertical bending mode10 of 24 (symmetric) (d) The 3rd vertical bending mode (symmetric).

TheThe significantsignificant changeschanges ofof thesethese modemode shapesshapes afterafter threethree yearsyears areare highlightedhighlighted inin FigureFigure9 9 in in the the rectangle.rectangle. MostMost changeschanges ofof thethe modemode shapesshapes occuroccur locallylocally atat thethe vibrationvibration crestscrests andand troughstroughs ofof thethe girdergirder especiallyespecially in in the the main main span span close close to theto the span span center center and pylon.and pylon. Such Such shape shape changes changes become become more distinguishablemore distinguishable if the order if the of order the mode of the decreases. mode decr Foreases. example, For example, the 1st mode the in1st Figure mode9 ain presents Figure 9a a muchpresents more a distinguishablemuch more distinguishable shape change thanshape the change 3rd mode than in Figurethe 3rd9d. mode It is alsoin Figure noticed 9d. that It besides is also thenoticed significant that besides local changes, the significant the mode local shapes changes, also the vary mode along shapes the whole also vary bridge along length the (908whole m). bridge This globallength di(908fference m). This in the global mode difference shapes can in be the mainly mode attributed shapes can to di befferent mainly supporting attributed boundaries to different of thesupporting bridge. It boundaries has been widely of the believed bridge. thatIt has the been bridge widely scour believed is the most that probable the bridge and scour usually is the physical most explanationprobable and for usually the variation physical of the explanation supporting for boundary. the variation In this of sense, the thesupporting change of boundary. the mode shapesIn this ofsense, the girder, the change especially of the at theirmode local shapes crests of and the troughs, girder, becomesespecially another at their convincing local crests indicator and troughs, for the scouringbecomes ofanother the Hangzhou convincing Bay indicator Bridge. for the scouring of the Hangzhou Bay Bridge. SimilarSimilar shapeshape changeschanges cancan alsoalso bebe foundfound byby comparingcomparing modemode shapesshapes ofof thethe pylonpylon whichwhich havehave thethe samesame orderorder whenwhen extractedextracted fromfrom thethe measurementsmeasurements ofof 20132013 andand 2016.2016. TheThe comparativecomparative resultsresults ofof thethe laterallateral bending modes of of the the pylon pylon are are provided provided in in Figure Figure 10 10 (the (the shape shape scale scale was was determined determined by bythe the same same normalization normalization processing), processing), where where the the left left figure figure is is based based on on the the mode that twotwo pylonspylons vibratevibrate antisymmetricallyantisymmetrically andand thethe rightright oneone isis basedbased onon thethe symmetricsymmetric mode.mode. TheThe unsmoothunsmooth modemode shapesshapes inin thethe figurefigure areare duedue toto thethe limitedlimited numbernumber ofof thethe sensorssensors installedinstalled inin thisthis case.case. ItIt cancan bebe seenseen fromfrom bothboth modesmodes thatthat thethe upperupper sectionsection ofof thethe pylonpylon presentspresents aa muchmuch moremore significantsignificant shapeshape changechange thanthan thethe bottombottom part.part. TheThe lowerlower thethe orderorder ofof thethe modemode is,is, thethe moremore distinguishabledistinguishable thethe shapeshape changechange betweenbetween twotwo measurementsmeasurements is. If If comparing comparing the the results results of of Figure Figure 10 10 to to Figure Figure 9,9, the the pylon pylon presents presents a amore more visible visible change change of of mode mode shapes shapes between between two two me measurementsasurements than than the the girder. girder. This This is because is because the thepylon pylon vibrates vibrates as a as rigid a rigid rotation rotation around around the thefoun foundationdation and and the thescour scour depth depth directly directly determines determines the theunsupported unsupported height height of ofthe the pylon. pylon. Therefore, Therefore, by by tracing tracing the the change change of of mode mode shapes shapes of of the pylon,pylon, especiallyespecially onon thethe toptop sections,sections, thethe changechange validatesvalidates againagain thethe previousprevious identificationidentification resultsresults forfor thethe scourscour ofof HangzhouHangzhou BayBay Bridge.Bridge.

2013 2013 140 2016 140 2016

120 120

100 100

80 80 Change of Change of mode shapes mode shapes 60 60 Pylon height (m) height Pylon Pylon height (m) height Pylon

40 40

20 20 01 01 Mode shape (Lateral direction) Mode shape (Lateral direction) (a) (b)

FigureFigure 10.10. TheThe changechange ofof thethe modemode shapesshapes ofof thethe pylonpylon (only(only oneone pylonpylon isis shown).shown). ((aa)) TheThe 1st1st laterallateral bendingbending modemode (antisymmetric)(antisymmetric) ((bb)) TheThe 1st1st laterallateral bending bending mode mode (symmetric). (symmetric).

BasedBased onon the the analysis analysis above, above, it can it becan concluded be concluded that: (1) that: the scour(1) the development scour development of the Hangzhou of the BayHangzhou Bridge canBay be Bridge qualitatively can be identiﬁed qualitatively by tracing identified the change by tracing of either the natural change frequencies of either or natural mode shapesfrequencies between or mode the measurements shapes between of the 2013 measurements and 2016; (2) theof 2013 dynamic and 2016; features (2) the of low dynamic orders features are more of sensitivelow orders to theare scourmore thansensitive those to of the high scour orders; than (3) those the pylonof high presents orders;more (3) the sensitive pylon presents change of more the dynamicsensitive featureschange of to the the dynamic scour than features the girder to the does, scou evenr than for the the girder high orders.does, even for the high orders.

J. Mar. Sci. Eng. 2019, 7, x FOR PEER REVIEW 11 of 24 J. Mar. Sci. Eng. 2019, 7, 121 11 of 24 5. Quantitative Scour Identification by FE Model Updating 5. QuantitativeThe change Scour of pile-soil Identification stiffness by affects FE Model vibration Updating modes by changing the restriction capacity provided by soils (such as fixed or joint connections). The change of scour depth affects vibration The change of pile-soil stiffness affects vibration modes by changing the restriction capacity modes by changing the component length of foundations (pile, pier, or pylon). Considering the provided by soils (such as fixed or joint connections). The change of scour depth affects vibration modes above different influential sources, all the vibration modes of bridges can be classified into two by changing the component length of foundations (pile, pier, or pylon). Considering the above different groups: scour-sensitive modes and scour-insensitive modes. Then, the quantitative scour influential sources, all the vibration modes of bridges can be classified into two groups: scour-sensitive identification was conducted in the following three steps: (1) First, an FE model was established as modes and scour-insensitive modes. Then, the quantitative scour identification was conducted in the the object for the model updating; (2) Second, the soil stiffness (stiffness of soil-pile springs) was following three steps: (1) First, an FE model was established as the object for the model updating; identified by model updating until the simulation results best fit the measurements of the (2) Second, the soil stiffness (stiffness of soil-pile springs) was identified by model updating until scour-insensitive vibration modes. (3) Using the soil-updated model, the scour development was the simulation results best fit the measurements of the scour-insensitive vibration modes. (3) Using finally identified by model updating until the simulation results best fit the variation between two the soil-updated model, the scour development was finally identified by model updating until the measurements of the scour-sensitive vibration modes. In the second step, the scour-insensitive simulation results best fit the variation between two measurements of the scour-sensitive vibration vibration modes were used to update the values of soil stiffness. This is because all the global modes. In the second step, the scour-insensitive vibration modes were used to update the values of soil vibration modes of bridges should be influenced by different soil stiffness no matter if they are stiffness. This is because all the global vibration modes of bridges should be influenced by different soil scour-sensitive or scour-insensitive. A similar phenomenon can also be found in the Kao-Ping-His stiffness no matter if they are scour-sensitive or scour-insensitive. A similar phenomenon can also be cable-stayed bridge [7] and Jintang cable-stayed bridge whose frequencies of the scour-insensitive found in the Kao-Ping-His cable-stayed bridge [7] and Jintang cable-stayed bridge whose frequencies modes have 5% to 10% changes when the pile-soil stiffness increases by 75%. of the scour-insensitive modes have 5% to 10% changes when the pile-soil stiffness increases by 75%.

5.1.5.1. FEFE ModelModel EstablishmentEstablishment BasedBased onon the the engineering engineering drawings drawings of theof the Hangzhou Hangzhou Bay Bridge,Bay Bridge, a 3D Finitea 3D ElementFinite Element (FE) model (FE) wasmodel created was created using the using ANSYS the ANSYS program. program. A fish-bone A fish- structuralbone structural system system was selectedwas selected to model to model the superstructurethe superstructure which which can can accurately accurately simulate simulate the the sti ffstiffnessness of of cable-stayed cable-stayed bridges bridges by by using usingbeam beam elementselements (Figure(Figure 11 11))[47 [47].]. In In the the model, model, the the main main girder girder was simulatedwas simulated by a longitudinalby a longitudinal single beam,single i.e.,beam, Beam188 i.e., Beam188 element, element, with all thewith material all the propertiesmaterial properties referring to referring the detailed to the design detailed parameters. design parameters. The Beam188 element has three translational and three rotational degrees-of-freedom The Beam188 element has three translational and three rotational degrees-of-freedom (DOFs) for each (DOFs) for each node. The crossbeams intersected with the main girder were modeled by transverse node. The crossbeams intersected with the main girder were modeled by transverse beams using the beams using the same Beam188 element. The torsional moments of inertia of crossbeams were same Beam188 element. The torsional moments of inertia of crossbeams were considered by the Mass21 considered by the Mass21 element. All the stayed cables connected to the ends of crossbeams were element. All the stayed cables connected to the ends of crossbeams were modeled by the Link8 element modeled by the Link8 element with the consideration of the existing cable forces. The Link8 element with the consideration of the existing cable forces. The Link8 element has two translational DOFs for has two translational DOFs for each node. The pylons were also modeled using the Beam188 each node. The pylons were also modeled using the Beam188 element to reduce the computation effort. element to reduce the computation effort. The cross sectional configurations and material properties The cross sectional configurations and material properties for each component of the FE model are for each component of the FE model are listed in Tables 3 and 4, respectively. The densities of the listed in Tables3 and4, respectively. The densities of the girder and cross beams were re-calculated girder and cross beams were re-calculated after accounting for all the stiffening and non-structural after accounting for all the stiffening and non-structural components. components. Y

Z X Pier B13 Pier B12 Coordinate system

Pylon B11

Pier B9 Pylon B10 Pier B8 Pylon B10/B11

(a) (b)

FigureFigure 11.11. FE model usingusing aa ﬁsh-bonefish-bone structuralstructural system.system. (a)) AxonometricAxonometric view,view, ((bb)) VerticalVertical view. view.

J.J. Mar. Mar. Sci. Sci. Eng. Eng.2019 2019, 7, ,7 121, x FOR PEER REVIEW 12 12 of of 24 24

Table 3. Configurations for cross-sections of girder. Table 3. Conﬁgurations for cross-sections of girder. Principal Bending Secondary Torsional Width Height 2 Principal Secondary Torsional Components Area (m ) Moment of Inertia Bending Moment Moment ofWidth Height Components Area (m2) Bending Moment Bending Moment Moment of (m) (m) (m4) of Inertia (m4) Inertia (m4) (m) (m) of Inertia (m4) of Inertia (m4) Inertia (m4) Girder 1.54 182.37 2.80 7.00 37.10 3.50 PylonGirder 9.02–55.02 1.54 8.56–157.60 182.37 52.18–1171. 2.8040 7.004.11–578.98 37.103.5–7.5 3.50 6.0–9.7 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 CrossbeamCrossbeam 21.46 21.46 108.30 108.30 203.70 203.70 228.20 228.20 - - - - 0.00327– StayStay cables cables 0.00327–0.009275 ------0.009275 Table 4. Material properties for diﬀerent components. Table 4. Material properties for different components. Properties Density Elasticity Modulus Poisson’s Properties Density3 Elasticity Modulus Poisson’s Components (kg/m ) (MPa) Ratio Components (kg/m³) (MPa) Ratio Girder 10.288 103 2.10 105 0.3 × 3 ×5 CrossbeamGirder 10.288 10.288 × 103 2.102.10 × 10 10 5 0.3 0.3 × 3 ×5 Stay cablesCrossbeam 10.2888.450 ×10 103 2.101.90 × 10 10 5 0.3 0.3 × 3 ×5 PylonStay cables 2.600 8.450 × 103 1.903.50 × 10 10 4 0.3 0.2 × 3 ×4 PiersPylon 2.600 2.600 × 103 3.503.30 × 10 10 4 0.2 0.2 Piers 2.600 ×× 103 3.30 × 10×4 0.2

The key issue to establish the FE model of a scoured bridge is the pile-soil interaction and the The key issue to establish the FE model of a scoured bridge is the pile-soil interaction and the correspondingcorresponding e ffeffectiveective area. area. Soil Soil behavior behavior is is highly highly nonlinear nonlinear and and in in particular particular its its sti stiffnessffness changes changes nonlinearlynonlinearly with with the the strain. strain. The responseThe response of the pile-soilof the pile-soil system issystem heavily is dependent heavily dependent on the magnitude on the andmagnitude type of externaland type loads. of external However, loads. in However, the service in the stage service of bridges, stage of the bridges, external the loads external over loads the bridgeover the will bridge only leadwill only to a verylead to small a very lateral small strain lateral being strain imparted being imparted into the into soil the surround soil surround the piles. the Therefore,piles. Therefore, for the casefor the of thecase Hangzhou of the Hangzhou Bay Bridge, Bay itBridge, is assumed it is assumed that the soilthat strainsthe soil remain strains within remain thewithin “small-strain” the “small-strain” linear-elastic linear-elastic region of region the soil of response the soil response curve. curve. InIn the the present present study, study, the the pile-soil pile-soil interaction interaction was was represented represented by the by stitheffness stiffness of soils. of soils. All the All soil the layerssoil layers in the FEin modelthe FE weremodel simulated were simulated by the discrete by the and discrete closed spacedand closed spring spaced elements spring (Combin14) elements at(Combin14) intervals of at 0.5 intervals m along of the 0.5 piles m along (Figure the 12piles). The (Figure spring 12). element The spring of the element Combin14 of the with Combin14 a null masswith matrix a null has mass two translationalmatrix has DOFs two (degreestranslational of freedom) DOFs and(degrees allows one-dimensionalof freedom) and uniaxial allows movementone-dimensional along the uniaxial axis of movement the spring. along Each nodethe axis of theof the pile spring. connects Each two node spring of the elements pile connects along thetwo longitudinalspring elements and lateral along directionsthe longitudinal of the bridge. and lateral For the directions purpose of dynamicthe bridge. interaction For the modeling,purpose of thedynamic springs interaction are assumed modeling, to provide the dynamic springs impedanceare assumed only to provide and inertial dynamic effects impedance are ignored. only Then, and aninertial appropriate effects determination are ignored. ofThen, the element an appropriate stiffness ofdetermination the springs becomes of the theelement next pursuit,stiffness which of the playssprings a very becomes important the next role pursuit, in the soil which behavior plays simulation. a very important role in the soil behavior simulation.

At intervals of 0.5m Lateral direction of the bridge Along the piles

Longitudinal direction of the bridge

FigureFigure 12. 12.Simulation Simulation of of the the pile-soil pile-soil interaction. interaction.

AccordingAccording to to the the one-parameter one-parameter Winkler Winkler soil soil model model for piles,for piles, the lateralthe lateral resistance resistance of soils of soils on the on pilethe at pile a certain at a certain depth depth is linearly is linearly varied varied with thewith increase the increase of the of lateral the lateral displacement displacement of the pile.of the This pile. linearThis elasticlinear elastic expression expression is provided is provided by the by following the following mathematical mathematical equation. equation. σ = Cu σz =z Cuz z (2)(2)

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σ 2 where z = lateral resistance of soils on the pile at the depth of z (kN/m ); u z = lateral 2 wheredisplacementσz = lateral of the resistance pile at the of soils depth on of the z pile(m); at and the depthC = foundation of z (kN/m coefficient); uz = lateral (KN/m displacement3), which ofis 3 theusually pile ata function the depth of ofthe z (m);depth and (EquationC = foundation (3)). coefficient (KN/m ), which is usually a function of the depth (Equation (3)). = n CCkz= kzn (3)(3) k where k = =coe coefficientfficient related related to to the the soil soil types, types, mechanical mechanical parameters, parameters, material material properties, properties, depth, depth, etc.; zetc.;= soil z = depth;soil depth; and nand= exponent n = exponent of z. Furtherof z. Further assigning assigningn a value n a value of 1.0 of in the1.0 presentin the present study yieldsstudy Equationyields Equation (4), a simplified (4), a simplified Winkler-based Winkler-based relationship relationship between betweenC and z C. and z. Cmz=× (4) C = m z (4) where m = coefficient (kN/m4),; its value can be found× in the foundation design specifications of wheredifferentm countries.= coefficient Considering (kN/m4),; that its valuethe Hangzhou can be found Bay Bridge in the is foundation located in China, design the specifications Chinese code of diforff erentthe design countries. of the Considering ground base that and the foundation Hangzhou of Bay highway Bridge bridges is located and in China,culverts the (JTG Chinese D63-2007) code forwas the selected design in of the the present ground study base and to specify foundation the value of highway of m. bridges and culverts (JTG D63-2007) was selectedSince in the presentspring studyelements to specifywere modeled the value discrete of m. ly at intervals of 0.5 m, Equation (4) as a continuousSincethe relationship spring elements between wereC and modeled z cannot be discretely directly atapplied intervals to determine of 0.5 m, the Equation stiffness (4) of each as a continuousspring. Therefore, relationship the betweenlateral resistanceC and z cannot of so beils directly between applied two toclose-by determine springs the sti ffneedsness ofto each be spring.equivalently Therefore, converted the lateral into two resistance nodal forces of soils at between the nodes two of close-bythe springs. springs Such needs equivalence to be equivalently between a convertedcontinuous into soil two force nodal and forces two atdiscrete the nodes nodal of thespring springs. forces Such was equivalence achieved by between keeping a continuousthe lateral soilrestrain force and and bending two discrete moment nodal of spring the pile forces the was same achieved. The byspecific keeping conversion the lateral process restrain of and the bending lateral momentforces on of the the pile pile involves the same. the The following specific conversionsteps and the process result of is the applicable lateral forces to both on the pilelongitudinal involves theand following lateral springs. steps and the result is applicable to both the longitudinal and lateral springs. Step (1): The The pile pile embedded embedded in inthe the soil soil is divided is divided into into n elements n elements from from the top the to top bottom. to bottom. The Thelength length of each of each pile pileelement element is h isj (jh j= (1,j = 2,1, …, 2, ...n) ,andn) and two two nodes nodes of the of thejth jelementth element are are Nj Nandj and Nj+1 N,j +as1, asshown shown in inFigure Figure 13. 13 .

e 1 1 1,1 N K = K x(y)

1 longitudinal(lateral) h

2 e e

N K 2 = K 2,1 + K2,2 2 h e e 3 3 3,2 3,3 N K = K + K

S t i f s h f p n r e Pile i s n s g s o f

e e n

N K n =K n,n-1 +Kn,n n h e Kn+1 =Kn+1,n n+1 N z Figure 13. Schematic presentation of the equivalence.

Step (2): Based on Equation (4), the stistiffnessffness distribution of soils along the pile forms a triangle shape startingstarting from from the the top top of theof pilethe embeddedpile embedded in soils. in Then,soils. accordingThen, according to the equivalence to the equivalence principle specified earlier, the stiffness of discrete springs at the nodes N and N can be derived as: principle specified earlier, the stiffness of discrete springs at the1 nodes2 N1 and N2 can be derived as: (K())hh××1 Khh ()( ) e e K=×=h1 11h1111 K h1 h1 K =K1,1 × = × (5)(5) 1,1 2 23× 3 66

K(h1) ××h1 2 K(h1) h1 e e K()hh11112 Khh () K2,1 =K =×=× = × (6)(6) 2,1 2 23× 3 33

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e e where K1,1 and K2,1 = stiﬀness of springs at the nodes N1 and N2 of the 1st element, respectively; and K(h1) = stiﬀness of soils at the depth h1 based on Equation (4), which is calculated as:

K(h ) = b m h (7) 1 0 × × 1 where b0 = width of the pile. Similarly, the stiﬀness of springs at the nodes Nj and Nj+1 of the jth element (j > 1) can be derived as:

Pj Pj+1 Pj K( = hi) hj [K( = hi) K( = hi)] hj Ke = i 1 × + i 1 − i 1 × (8) j,j 2 6

Pj Pj+1 Pj K( = hi) hj [K( = hi) K( = hi)] hj Ke = i 1 × + i 1 − i 1 × (9) j+1,j 2 3 e e where Kj,j and Kj,j+1 = stiﬀness of springs at the nodes Nj and Nj+1 of the jth element, respectively; (Pj ) (Pj+1 ) Pj Pj+1 and K i=1 hi and K i=1 hi = stiﬀness of soils at the depths i=1 hi and i=1 hi, respectively, which based on Equation (4) are calculated as:

Xj Xj K( hi) = b0 m hi (10) i=1 × × i=1

Xj+1 Xj+1 K( hi) = b0 m hi (11) i=1 × × i=1 Step (3): Since one node connects two elements, the stiﬀness of the spring at each node (Dexcept node N1) 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.

= e K1 K1,1 = e + e K2 K2,1 K2,2 . . (12) = e + e Kn Kn,n 1 Kn,n = e− Kn+1 Kn+1,n

5.2. Identification of Soil Stiffness The above theoretical derivation provides the preliminary values for the stiffness of soils/springs (Ki). These Ki values need a further identification based on field measurements to best fit the actual response of the Hangzhou Bay Bridge. Based on Figure8 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 (Ki) becomes the last main reason to affect the natural frequencies of these five modes. Therefore, the real values of Ki 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 Ki 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 Ki is provided in Figure 14. J. Mar. Sci. Eng. 2019, 7, 121 15 of 24 J. Mar. Sci. Eng. 2019, 7, x FOR PEER REVIEW 15 of 24

Figure 14. Algorithm for identifying soil stiffness. Figure 14. Algorithm for identifying soil stiffness. Following the algorithm, the foundation soils of the Hangzhou Bay Bridge were first divided into elevenFollowing diff erentthe algorithm, layers according the foundation to the geological soils of the survey Hangzhou results. Bay Since Bridge the bridge were first is located divided in intoChina, eleven all the different soil layers layers were according assigned to with the initialgeological values survey of m basedresults. on Since the Chinesethe bridge code is forlocated design in China,of ground all the base soil and layers foundation were assigned of highway with bridgesinitial values and culverts of m based (JTG on D63-2007), the Chinese as listedcode for in Tabledesign5. ofThe ground stiffness base of soiland springsfoundation in the of FEhighway model bridges with these and initial culverts values (JTG of D63-2007), m was accordingly as listed in calculated Table 5. Theby Equations stiffness of (4)–(12). soil springs By using in the this FE FE model model, with the these simulated initial naturalvalues of frequencies m was accordingly of different calculated orders of bythe Equations bridge were (4)–(12). numerically By using obtained. this FE model, the simulated natural frequencies of different orders of the bridge were numerically obtained. Table 5. Soil layers and initial values of m. Table 5. Soil layers and initial values of m. Layer Number Soil Material Thickness (m) Depth (m) m (kN/m4) Layer Number Soil Material Thickness (m) Depth (m) m (kN/m4) 1 O ① MuddyMuddy mild mild clay clay 14.0114.01 14.01 14.01 2000 2000 O2 Muddy clay 5.41 19.42 2000 ② Muddy clay 5.41 19.42 2000 O3 Clay 4.96 24.38 3000 ③ Clay 4.96 24.38 3000 O4 Mild clay 5.62 30 3500 ④ O5 ClayeyMild silt clay 31 5.62 30 61 3500 4000 O6 ⑤ ClayClayey silt 9.17 31 70.17 61 4000 3000 O7 ⑥ Mild clayClay 3.919.17 70.17 74.08 3000 3000 O8 ⑦ SiltyMild sand clay 12.49 3.91 74.08 86.57 3000 5000 O9 ⑧ MildSilty clay sand 7.1412.49 86.57 93.71 5000 3500 O10 ⑨ ClayMild clay 4.98 7.14 93.71 98.69 3500 3000 O11 ⑩ Silty sandClay 17.184.98 98.69 115.87 3000 5000 ⑪ Silty sand 17.18 115.87 5000 In order to quantitatively describe the difference between the simulated and measured natural In order to quantitatively describe the difference between the simulated and measured natural frequencies, a new parameter is proposed in Equation (13). frequencies, a new parameter is proposed in Equation (13). X qqq q 2 2 D1Df== ()(ff − f ) (13) 1  simsim − meamea (13) qq

q q where D1 = difference between the simulated and measured natural frequencies; fsim and fmea = 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

J. Mar. Sci. Eng. 2019, 7, 121 16 of 24

q q where D1 = difference between the simulated and measured natural frequencies; fsim and fmea = simulated and measured natural frequencies of the qth vibration mode, respectively; and q = concerned J. Mar. Sci. Eng. 2019, 7, x FOR PEER REVIEW 16 of 24 orders, which refer to the orders of the scour-insensitive vibration modes. It is noted that other forms of D1, i.e., Root-Mean-Squared-Error (RMSE) and the Nash-Sutcliffe Efficiency, can also be used in other forms of D1, i.e., Root-Mean-Squared-Error (RMSE) and the Nash-Sutcliffe Efficiency, can also Equationbe used in (13), Equation which (13), should which provide should the provide same iteration the same results. iteration results. If D is greater than a preset threshold, m for each soil layer needs to be further amended. If D11 is greater than a preset threshold, m for each soil layer needs to be further amended. Meanwhile,Meanwhile, thethe naturalnatural frequenciesfrequencies needneed toto bebe re-simulatedre-simulated based on the FE model with the newly amended m and accordingly a new D can also be calculated. This iteration process for updating the amended m and accordingly a new D11 can also be calculated. This iteration process for updating the value of m (stiffness of springs K ) is repeated until the value of D reaches the threshold. value of m (stiffness of springs Ki i) is repeated until the value of D11 reaches the threshold. ForFor the the Hangzhou Hangzhou Bay Bay Bridge, Bridge, the the orders orders of of the the scour-insensitive scour-insensitive vibration vibration modes modes are are the 6th,the 6th, 7th, 9th,7th, 10th, 9th, and10th, 11th. and Considering11th. Considering the soil the sti soilffness stif barelyfness barely changes, changes, either theeither measurements the measurements in 2013 orin 2016 can be selected as the data of modal analysis to calculate D . The threshold of terminating the 2013 or 2016 can be selected as the data of modal analysis 1to calculate D1. The threshold of iteration is set as reaching the lowest value of D during the updating process. The sti ness of each terminating the iteration is set as reaching the lowest1 value of D1 during the updatingff process. The 4 soilstiffness layer keepsof each being soil la updatedyer keeps by being revising updated the value by revising of m at intervals the value of of 100 m kNat /intervalsm per sub-step of 100 kN/m of the4 iteration.per sub-step The valuesof the iteration. of D1 calculated The values by Equation of D1 calculated (13) at all by the Equation sub-steps (13) of at the all iteration the sub-steps are provided of the initeration Figure 15are. provided in Figure 15.

0.010 0.010

0.009 0.009 1 1 0.008 Selected zoom area 0.008

0.007 0.007 Value of D Value of D of Value

0.006 0.006 with scour-insensitive modes with scour-insensitive modes 0.005 0.005 10 12 14 16 18 20 22 24 26 28 30 10 12 14 16 18 20 22 24 26 28 30 Sub-step of iteration for updating m (Ki) Sub-step of iteration for updating m (Ki) (a) (b)

Figure 15. Values of D1 versus sub-steps of iteration. (a) Iteration results at all the 35 sub-step,

Figure(b) 15. Iteration Values results of D1 versus in a selected sub-steps range of iteration. (10th–30th). (a) Iteration results at all the 35 sub-step, (b) Iteration results in a selected range (10th–30th). Based on Figure 15, and especially the selected results in Figure 15b, the value of D1 keeps decreasing until the 24th sub-step of the iteration when it increases again. At this sub-step the diﬀerence Based on Figure 15, and especially the selected results in Figure 15b, the value of D1 keeps betweendecreasing the until simulated the 24th and measuredsub-step of natural the iteration frequencies when of theit increases 6th, 7th, 9th,again. 10th, At andthis 11th sub-step vibration the modesdifference reaches between its minimum the simulated during theand entire measured iteration natu process.ral frequencies In other words,of the 6t theh, pile-soil7th, 9th, simulation10th, and in11th the vibration FE model modes gradually reaches approaches its minimum the actual during situation the entire of the iteration bridge process. before this In sub-step.other words, Table the6 listspile-soil the values simulation of m basedin the onFE themodel results gradually at the 24thapproaches sub-step the of theactual iteration. situation Substituting of the bridge the before newly updatedthis sub-step. m into Table Equations 6 lists (4)–(12), the values the of new m stibasedﬀness on of the soil results springs at Kthei was 24th subsequently sub-step of obtainedthe iteration. and thenSubstituting correspondingly the newly updated updated in m the into FE modelEquation ofs the (4)–(12), bridge. the The new updated stiffness values of soil of springsKi are listed Ki was in Tablesubsequently7. obtained and then correspondingly updated in the FE model of the bridge. The updated values of Ki are listed in Table 7.

Table 6. Updated values of m after the iteration.

Layer Number Soil Material m (kN/m4) 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

J. Mar. Sci. Eng. 2019, 7, 121 17 of 24

Table 6. Updated values of m after the iteration.

Layer Number Soil Material m (kN/m4) Node Numbers of Single Pile O1 Muddy mild clay 4400 0–28 O2 Muddy clay 4400 29–39 O3 Clay 5400 40–49 O4 Mild clay 5900 50–60 O5 Clayey silt 6400 61–122 O6 Clay 5400 123–140 O7 Mild clay 5400 141–148 O8 Silty sand 7400 149–173 O9 Mild clay 5900 174–187 O10 Clay 5400 188–197 O11 Silty sand 7400 198–232

Table 7. Updated stiﬀness of soil springs after the iteration (Partially).

Node Numbers of K (103 Node Numbers of K (103 Node Numbers of K (103 Single Pile kN/m) Single Pile kN/m) Single Pile kN/m) 0 0.4578 60 240.5908 ...... Layer O8 1 4.1201 61 247.7074 173 647.3823 Layer O1 ...... Layer O5 62 251.7026 174 624.7812 28 79.6559 ...... 175 628.3514 Layer O9 29 82.4027 122 414.2214 ...... 30 85.1494 123 405.1850 187 671.1936 Layer O2 ...... 124 408.4526 188 674.7637 Layer O6 39 130.7830 ...... 189 678.3339 Layer O10 40 138.2117 140 496.3355 ...... 41 141.5827 141 506.9653 197 856.8126 Layer O3 ...... 142 510.5355 198 891.0923 Layer O7 49 181.6084 ...... 199 895.5702 50 187.8406 148 644.8105 Layer O11 ...... Layer O4 51 191.5237 149 671.6777 Layer O8 232 520.9233 ...... 150 676.1555

So far, the soil stiffness (stiffness of soil-pile springs) of the Hangzhou Bay Bridge was identified by best fitting the scour-insensitive vibration modes and accordingly updating the FE model. This updated FE model will be used in the following study as a reference model to further quantitatively identify the scour depth. It should also be noted that even if the soil stiffness is not identified accurately enough, the scour depth increasing is still the most significant reason for the change of vibration modes since the soil property hardly changes during the bridge service.

5.3. Identification of Scour Depth (Soil Level) Considering there is no significant damage reported by the routine inspections on the superstructures of the Hangzhou Bay Bridge, the scour development should be the only reason for the variation of the dynamic features of the bridge. Therefore, in this case the scour depth was identified by updating the previous soil-updated FE model to best fit the measured natural frequency change from 2013 to 2016. Different from the soil updating, the scour-sensitive vibration modes were selected as the best fitting objects to update the scour depth. Using the scour-sensitive vibration modes can include the most scour effects on the variation of natural frequencies. In this way, the interference of other factors can be lowered to the maximum extent during the model updating of the scour depth. The algorithm for identifying the scour depth by model updating is provided in Figure 16. J. Mar. Sci. Eng. 2019, 7, 121 18 of 24 J. Mar. Sci. Eng. 2019, 7, x FOR PEER REVIEW 18 of 24

Figure 16. Algorithm for identifying scour depth.

Another parameter D2 isis proposed in Equation (14) to quantitatively describe the didifferencefference between the simulated and measured natural frequencyfrequency changeschanges ofof scour-sensitivescour-sensitive vibrationvibration modes.modes. X= pppp−− − 2 Dff2p[(ffsim ,( h+Δ h ) simp , h)( meap ,2016 mea ,2013p )] 2 D2 = [(f 11f ) ( f f )] (14)(14) p sim,(h1+∆h) sim,h1 mea,2016 mea,2013 p − − − p where D2 = difference between the simulated and measured natural frequency changes; f +Δ = sim,( h1 h ) where D2 = difference between the simulated and measured natural frequency changes; p simulatedf natural= simulated frequency natural of the frequency pth vibration of the modepth by vibration the FE model mode with by the the FE scour model depth with of h the1 + sim,(h +∆h) p Δh, i.e.,1 h2; f = simulated natural frequency of the pth vibration mode by the FE model with the sim, h1 p scour depth of h1 + ∆h, i.e., h2; f = simulated natural frequency of the pth vibration mode by the FE ppsim,h1 scour depth of h1; ff+Δ − =p simulated naturalp frequency change induced by the increment sim,( h11 h ) sim , h model with the scour depth of h1; f ( + ) fsim h = simulated natural frequency change induced p sim, h1 ∆h − , 1 p of scour depth Δh; fmea,2016 = measuredp natural frequency of the pth vibration mode in 2016; fmea,2013 by the increment of scour depth ∆h; fmea,2016 = measured natural frequency of the pth vibration mode p ffpp− p p in= measured 2016; f natural= measured frequency natural of the frequency pth vibration of the p thmode vibration in 2013; mode inmea,2016 2013; f mea ,2013 = measuredf = mea,2013 mea,2016 − mea,2013 measurednatural frequency natural change frequency induced change by inducedthe increment by the of increment scour depth of scour from depth2013 to from 2016; 2013 and top = 2016; the andordersp = ofthe the orders scour-sensitive of the scour-sensitive vibration modes. vibration modes. For the Hangzhou Bay Bridge, the scour-sensitive vibration modes are the 2nd, 3rd, 4th, and 5th modes with more than 15% FCRFCRbased based on on Figure Figure8. 8. The The initial initial value value of of scour scour depth depth hh11 setset in the FE model beforebefore updatingupdating∆ Δhhwas was determined determined based based on on the the underwater underwater inspection inspection report report in 2013.in 2013. The The∆h wasΔh was amended amended at intervals at intervals of 0.5 of m 0.5 per m sub-step per sub-step of the of iteration the iteration until the untilD2 thewas D less2 was than less the than pre-set the threshold.pre-set threshold. Subsequently, Subsequently, new natural new frequenciesnatural frequencie were simulateds were simulated based on based the FE on model the FE with model the newlywith the amended newly ∆amendedh and a newΔh andD2 was a new also D obtained.2 was also The obtained. threshold The for threshold terminating for the terminating iteration is the set asiteration reaching is set the as lowest reaching value the of lowestD2. The value values of ofD2D. The2 calculated values of by D Equation2 calculated (14) by at Equation all the sub-steps (14) at all of the iterationsub-steps are of providedthe iteration in Table are provided8. Figure 17in plotsTable the 8. Figure variation 17 ofplotsD2 thealong variation with increasing of D2 along∆h fromwith 0increasing m to 7 m. Δh from 0 m to 7 m. As can be seen from Figure 17, the D2 decreases with the progressive scouring until the ∆h reaches Table 8. Values of D2 for different Δh. the increment of 4.5 m. Thereafter, the D2 turns to increase as the ∆h continues going deeper. In other words, the lowest valueContribution of D2 is obtainedContribution at the 10thContribution sub-step of theContribution iteration when the ∆h is 4.5 m. At this moment,Δh (m) theof di thefference 2nd betweenof the the 3rd simulated of andthe 4th measured of natural the 5th frequencyD2changes of the 2nd, 3rd, 4th, andorder 5th vibration(Hz) modesorder (Hz) reaches itsorder minimum (Hz) value.order Therefore, (Hz) the scouring of the Hangzhou0 Bay Bridge0.010290 from 2013 to 2016−0.00965 was successfully−0.000916 identified − as0.032545 the increment 0.001259 of 4.5 m. It is clearly observed0.5 from0.010844 Table9 that after−0.00858 model updating−0.000283 the frequency − changes0.031154 by adding0.001162 4.5 m scour depth in the1 FE model,0.011381 which is very close−0.00754 to the measured0.000338 changes. The−0.029802 proposed scour0.001075 identification method worked1.5 very0.011662 well in the present−0.00703 case study. 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

J. Mar. Sci. Eng. 2019, 7, 121 19 of 24

Table 8. Values of D2 for diﬀerent ∆h.

Contribution Contribution Contribution Contribution ∆h (m) of the 2nd of the 3rd of the 4th of the 5th D2 order (Hz) order (Hz) order (Hz) order (Hz) 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 − − J. Mar. Sci. Eng.2 2019, 7, x FOR 0.011941 PEER REVIEW 0.00653 0.000982 0.028489 0.000998 19 of 24 − − 2.5 0.012232 0.00603 0.001316 0.027839 0.000963 − − 3.53 0.0125530.012931 −0.005060.00554 0.002121 0.001684 −0.0265780.027202 0.000904 0.000931 − − 3.54 0.0129310.013432 −0.004580.00506 0.002696 0.002121 −0.0259510.026578 0.000882 0.000904 − − 4.54 0.0134320.014141 −0.004110.00458 0.003513 0.002696 −0.0253380.025951 0.000871 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 0.015081 0.00364 0.004593 0.024732 0.000873 5.5 0.016170 −−0.00319 0.005847 −−0.024145 0.000889 5.5 0.016170 0.00319 0.005847 0.024145 0.000889 6 0.017323 −−0.00273 0.007169 −−0.023549 0.000913 6 0.017323 0.00273 0.007169 0.023549 0.000913 6.5 0.018492 −−0.00228 0.008515 −−0.022964 0.000947 6.5 0.018492 0.00228 0.008515 0.022964 0.000947 7 0.019654 −−0.00184 0.009849 −−0.022392 0.000988 7 0.019654 0.00184 0.009849 0.022392 0.000988 − −

0.00130

0.00125

0.00120

0.00115

0.00110

2 0.00105 D

0.00100

0.00095

0.00090

0.00085

0 1 2 3 456 7 Δh (m)

Figure 17. Variation of D2 along with the increasing ∆h. Figure 17. Variation of D2 along with the increasing Δh. Table 9. Comparison between measured and simulated frequency changes. As can be seen from Figure 17, the D2 decreases with the progressive scouring until the Δh Measured Frequency Simulate Frequency Change/Difference by reachesOrder the increment of 4.5 m. Thereafter, the D2 turns to increase as the Δh continues going deeper. Change/Difference from 2013 to 2016 Adding 4.5 m Scour Depth In other words, the lowest value of D2 is obtained at the 10th sub-step of the iteration when the Δh is 4.5 m. At2 this moment, the difference 0.057 between the simulated and 0.071measured natural frequency 3 0.096 0.092 changes 4of the 2nd, 3rd, 4th, 0.076and 5th vibration modes reaches its minimum 0.079 value. Therefore, the scouring5 of the Hangzhou Bay 0.121 Bridge from 2013 to 2016 was successfully 0.121 identified as the increment of 4.5 m. It is clearly observed from Table 9 that after model updating the frequency changes by 6.adding Verification 4.5 m byscour Results depth from in Underwaterthe FE model, Terrain which Map is very close to the measured changes. The proposed scour identification method worked very well in the present case study. In this section, the documented results from the underwater terrain map were used to verify the accuracyTable of 9. theComparison scour identification between measured by theand proposedsimulated frequency method changes. based on the ambient vibration measurements. Measured Frequency Change/Difference from Simulate Frequency Change/Difference by OrderSince a 6 m-deep local scour hole was observed at the Hangzhou Bay Bridge, an underwater 2013 to 2016 Adding 4.5 m Scour Depth terrain scanning measurement was conducted every year. A multiple-wave depth survey system called 2 0.057 0.071 “Atlas3 FanSweep20 (FS20)” was0.096 applied for the scanning, which included 0.092 the depth measurement meter,4 global navigation satellite0.076 system (GNSS) receiver, sound velocity meter, 0.079 differential global positioning5 system (DGPS) device,0.121 acoustic doppler current profiler (ADCP), 0.121 electronic total station, and survey boat. Each scanning can draw a digitized underwater terrain map for the region around the 6. Verification by Results from Underwater Terrain Map In this section, the documented results from the underwater terrain map were used to verify the accuracy of the scour identification by the proposed method based on the ambient vibration measurements. Since a 6 m-deep local scour hole was observed at the Hangzhou Bay Bridge, an underwater terrain scanning measurement was conducted every year. A multiple-wave depth survey system called “Atlas FanSweep20 (FS20)” was applied for the scanning, which included the depth measurement meter, global navigation satellite system (GNSS) receiver, sound velocity meter, differential global positioning system (DGPS) device, acoustic doppler current profiler (ADCP), electronic total station, and survey boat. Each scanning can draw a digitized underwater terrain map

J. Mar. Sci. Eng. 2019, 7, 121 20 of 24 J. Mar. Sci. Eng. 2019, 7, x FOR PEER REVIEW 20 of 24

Hangzhoufor the region Bay around Bridge, the as shownHangzhou in Figure Bay Bridge, 18. The as scour shown developments in Figure 18. can The be scour quantitatively developments obtained can bybe comparingquantitatively the obtained scanning by results comparing between the di ﬀscannierentng years. results By doingbetween this, different Table 10 years. lists the By incrementsdoing this, ofTable the scour10 lists depths the increments from 2013 toof 2016the scour at the depths side pier from (B9) 2013 and to pylon 2016 (B10) at the [6 ].side It shouldpier (B9) be notedand pylon that all(B10) the [6]. elevation It should values be noted in Table that 10 all were the elevatio measuredn values in the in deepest Table positions10 were measured of the local in scourthe deepest holes. Topositions make sure of the the local underwater scour holes. scan resultsTo make and sure the the vibration-based underwater scan identiﬁcation results and results the vibration-based are comparable, theidentification months of conductingresults are comparable, the vibration the measurements months of conducting in 2013 and the 2016 vibration were selected measurements according in to 2013 the timeand 2016 of the were underwater selected scan.according to the time of the underwater scan.

FigureFigure 18.18. Underwater terrain map of the Hangzhou BayBay Bridge.Bridge. Table 10. Scour depth developments based on underwater terrain map. Table 10. Scour depth developments based on underwater terrain map. Terrain Elevation in Terrain Elevation in Scour Depth Foundation Terrain Elevation Terrain Elevation Scour Depth Foundation 2013 (m) 2016 (m) Developments (m) in 2013 (m) in 2016 (m) Developments (m) Pier B9 Pier B9 19.4 23.4 4 (North side pier) −−19.4 −23.4− 4 (NorthPylon B10side pier) Pylon B10 20.2 25.4 5.2 (North pylon) −−20.2 −25.4− 5.2 (North pylon)

An obvious scour development can be observed from Table 10 at either the side pier or pylon An obvious scour development can be observed from Table 10 at either the side pier or pylon during the time from 2013 to 2016. The maximum increment was 5.2 m, locally located at the pylon during the time from 2013 to 2016. The maximum increment was 5.2 m, locally located at the pylon B10, which was very similar to the above identified scouring of 4.5 m. The disparity between the B10, which was very similar to the above identified scouring of 4.5 m. The disparity between the identification by the superstructure vibrations and the result by the direct underwater measurements identification by the superstructure vibrations and the result by the direct underwater is only 13%. If considering the scouring of 5.2 m could include the interference of sediment refilling in measurements is only 13%. If considering the scouring of 5.2 m could include the interference of scour holes, the real scour development at the pylon should be less than 5.2 m. Moreover, the scour may sediment refilling in scour holes, the real scour development at the pylon should be less than 5.2 m. quickly vary in a very short-term period even though the underwater scan and vibration measurements Moreover, the scour may quickly vary in a very short-term period even though the underwater scan were conducted in the same season. That is also one of the possible reasons for the disparity (4.5 m and vibration measurements were conducted in the same season. That is also one of the possible versus 5.2 m). Therefore, it was verified that the proposed method by the ambient vibrations of the reasons for the disparity (4.5 m versus 5.2 m). Therefore, it was verified that the proposed method by superstructure can assure an accurate and quantitative result for the practical scour identification. the ambient vibrations of the superstructure can assure an accurate and quantitative result for the Although the dynamic nature of live bed scour condition (erosion and refilling) would continuously practical scour identification. change the underwater scanning results of scour over time, it is actually not significant compared to Although the dynamic nature of live bed scour condition (erosion and refilling) would the final scour depths and total lengths of piles. Such a measuring difference from real scour depths continuously change the underwater scanning results of scour over time, it is actually not significant should only result in slight influence on the assessment of bridge safety and stability. Moreover, only compared to the final scour depths and total lengths of piles. Such a measuring difference from real the underwater terrain measurements were conducted as the yearly routine scour inspection for the scour depths should only result in slight influence on the assessment of bridge safety and stability. Hangzhou Bay Bridge. Therefore, using the data from the underwater terrain measurements becomes Moreover, only the underwater terrain measurements were conducted as the yearly routine scour the best choice at present to verify the accuracy of the proposed method. inspection for the Hangzhou Bay Bridge. Therefore, using the data from the underwater terrain In addition to the good accuracy, the proposed method only needs to trace the vibration signals of measurements becomes the best choice at present to verify the accuracy of the proposed method. the superstructure without any underwater operations or devices. The acceleration sensors on the In addition to the good accuracy, the proposed method only needs to trace the vibration signals of the superstructure without any underwater operations or devices. The acceleration sensors on the

J. Mar. Sci. Eng. 2019, 7, 121 21 of 24 superstructure and their signal receiver are the only instruments installed during the identification. By doing this, the common issues of traditional scour inspections can be well avoided or solved, such as the high expense of operations, high maintenance of devices, and difficulty of long-term and high-frequency assessments. Therefore, this vibration-based scour identification could be easily integrated to a routine and long-term assessment task for bridges.

7. Concluding Remarks This study shows the great potential for the use of the ambient vibration of the superstructure in identifying the bridge scour. The improvements in the present study compared to other existing studies are concluded from following two aspects.

(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.

The following conclusions can also be drawn.

(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.

While the current research led to several new and interesting conclusions regarding the application of identifying bridge scour based on the ambient vibrations of the superstructure, additional research would also be beneficial. For example, the reliability in the practice of this method needs more validations, especially when other local damages besides the foundation scour pre-exist in the superstructure. Since the measurements of vibration modes (e.g., scour-sensitive and -insensitive) significantly affect the accuracy of the identification, an investigation on effective arrangement of sensors is also needed. More applications on different types of bridges are still required to fully confirm the applicability of the proposed vibration-based method.

Author Contributions: W.X. managed the whole research plan, took care all the data analysis, and did the manuscript writing. C.S.C. did the quantitative scour identiﬁcation and model updating. B.K. did part of the simulation and the corresponding data analysis. X.Z. provided some of the original data. P.T. did the qualitative scour identiﬁcation analysis. Funding: This research was funded by the Natural Science Foundation of Jiangsu Province of China (grant number BK20161417), Fundamental Research Funds for the Central Universities (grant number 2242016R30023), and Highway Science and Technology Project of Zhejiang Province of China (grant number 2018H10). J. Mar. Sci. Eng. 2019, 7, 121 22 of 24

Acknowledgments: The financial support for this work from the Natural Science Foundation of Jiangsu Province of China (Project No. BK20161417), Fundamental Research Funds for the Central Universities (2242016R30023), and Highway Science and Technology Project of Zhejiang Province of China (2018H10) is gratefully acknowledged. The opinions and statements do not necessarily represent those of the sponsors. Conflicts of Interest: The authors declare no conflict of interest.

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