DynamicResponseAnalysisofLateralImpactForceofFrame …downloads.hindawi.com/journals/ace/2019/6918376.pdf · 2019. 12. 6. · the pile body, rock mass modulus, the position of the

Research ArticleDynamic Response Analysis of Lateral Impact Force of FrameWharf with Rock-Socketed Piles in Inland River Steel Sheath

Xiaolong Zhang,1,2 Bingchuan Duan,2 Chengzhi Wang ,1 and Duoyin Wang 1,2

1National Engineering Research Center for Inland Waterway Regulation, Chongqing Jiaotong University,Chongqing 400074, China2Key Laboratory of Hydraulic and Waterway Engineering of Ministry of Education, Chongqing Jiaotong University,Chongqing 400074, China

Correspondence should be addressed to Duoyin Wang; [email protected]

Received 19 August 2019; Accepted 14 November 2019; Published 6 December 2019

Academic Editor: Hugo Rodrigues

Copyright © 2019 Xiaolong Zhang et al. .is is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work isproperly cited.

In this study, a three-dimensional finite element model was established to simulate the dynamic response of a large-scale steel-reinforced concrete composite high-pile wharf with a rock-socketed steel sheath. .e model is based on the second phase of theChongqing Orchard Harbor structure project in conjunction with the project “Research on the mechanism of interface damageand energy dissipation of the structure of the large-scale steel-reinforced concrete composite high-pile wharf in inland waters.”.e stiffness of frame wharf is studied from the perspective of modal and transient dynamic analysis of structural dynamics. .edistribution of the low-order modal frequency is more uniform. With the increase of the order, the modal frequency of thestructure shows a periodical jump. .e overall stiffness of the frame structure is larger with the steel sheath, and the longitudinalstiffness is less than the transverse stiffness. Under the action of transverse impact load, the members and joints of the steel-concrete structure exhibit synchronous mechanical response characteristics in the time domain. .e peak values of displacementand stress of the structural joints occur 0.05 s after the peak value of the load-time history, and the peak value of reverse response offorce occurs at 2.3 s, which is markedly smaller than the peak value of the response of load direction. Reducing the local positionalstiffness of the load point is beneficial to improve the stress of the entire structure. .e weak links of the frame structure appear atthe joints of the members. Because of the hoop action of the steel sheath, the stress of the reinforced concrete pile core is moreuniform. .e peak value of the equivalent stress of the steel sheath member is generally larger than that of the reinforced concretepile core, and the stress is highly concentrated at the joints of the steel tube longitudinal and transverse braces.

1. Introduction

As a result of the normal operation plan of the.ree GorgesReservoir, which has a maximumwater level of 175.00m, thewharf upstream of the dam in the reservoir area will ex-perience a long period of deep water, as well as a flood periodin which the water level will steeply rise and fall. However,the construction period, during which the water level is low,is very short. Furthermore, the geological condition of thereservoir bank at the wharf construction site is bare rock orbedrock covered with a very thin soil layer, which ischaracterized by large vertical and horizontal fluctuations ofbedrock, interlaced sandstone, and mudstone, a large

topographic height difference, and a large volume of soil androck in the port land area. .e traditional wharf structurecannot meet many aspects of the demand, including con-struction and use after completion.

.erefore, the steel shell rock-socketed pile frame wharfhas been widely used. To date, some preliminary researchresults have been obtained on the static load mechanicalproperties of structures. .e steel pipe made of a rib-steelplate was first used in Dazhi Bridge in Japan [1], and the ribsallowed the steel pipe and the reinforced concrete in the pipeto achieve the overall stress effect. .e pipe with the rib-steelplate was appraised by the construction center of Japan in1984. Compared with a concrete-filled steel tube composite

HindawiAdvances in Civil EngineeringVolume 2019, Article ID 6918376, 15 pageshttps://doi.org/10.1155/2019/6918376

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pile without the rib, it had better economic performance.Using steel tubes to restrain concrete can effectively preventthe development of concrete cracks so that the steelsheeting has higher bearing capacity, better plasticity, andimproved toughness compared with the traditional con-crete-filled steel tube structure, and it improves the com-pressive strength and strain capacity of concrete. Large-scale tests, elastic-plastic dynamic analysis, and parametricmoment and curvature analysis have found that the failurelimit state of hyperbolic bending is mainly controlled by thetensile strain of longitudinal reinforcement at the tophinge. When subjected to single curvature bending, theultimate state is controlled by the tensile strain in the tubeat the underground hinge. However, for steel pipes withsingle curvature and relatively large thickness, the structuremay remain elastic during an earthquake [2, 3]..e bearingcapacity of a rock-socketed pile with a steel shell is affectedby factors such as the pile diameter, the embedded depth ofthe pile body, rock mass modulus, the position of theoperation point, and the width of flaps. .e effect of thesteel tube reduces the displacement of the pile top by atleast 50%, and the steel tube bears nearly 60% of thebending moment, while the tube at the maximum point ofthe antibending moment only bears about 28% of thebending moment [4–6]. Under the action of lateral load,the large-diameter rock-socketed concrete-filled steel tubepile bears most of the lateral load, so the stress concen-tration effect near the bottom of the steel tube should beconsidered in the design. Both the steel tube and backfillsand can effectively limit the displacement of the pile underthe action of working load [7]. .e use of a wharf structurefor the frame structure has received little research atten-tion. To date, comparisons with field load test validationand many changes in the parameters of numerical analysishave revealed that the joint shear force of vertical andhorizontal braces with steel liners is bigger and the frontrow pile structure is larger. At the steel liner and reinforcedconcrete junction, steel liners form a vertical and horizontalbrace connection for a structure with weak links [8, 9].

In 1987, aiming to study the dynamic response ofstructures under impact dynamic loads, Eibl et al. conductedtheoretical analysis and experimental research on thestructural design of concrete beams and columns that wereresistant to accidental impact [10]. In 1992, Louw comparedthe dynamic response and static characteristics of 28 con-crete cantilever columns when they were impacted by lateralloads [11, 12]. Zhang et al. found that the vibration period ofthe full vertical pile wharf under the cyclic load is longer thanthat of the high pile wharf near the shore and closer to thevibration period under the wave load. Under the wavedynamic load, the dynamic amplification of the full verticalpile wharf structure is obvious, and the dynamic amplifi-cation system of the displacement of the full vertical pilewharf under the wave cyclic load and the ship impact loadnumber were calculated [13, 14]. .e unstructured framesand pipes at the top of the wharf connect the adjacentsections together, which has an important influence on thedynamic characteristics of the wharf, especially the longi-tudinal dynamic characteristics [15].

In recent years, many domestic and internationalscholars have studied the dynamic characteristics of concreteunder impact by using numerical simulation and damagetheory [16]. At present, there have been many studies on theimpact of reinforced concrete. However, because of therelatively late use of the concrete-filled steel tube, which ischaracterized by beams, columns, and rods, little research onits impact has been carried out, although some qualitativeanalysis results have indicated the good impact resistance ofthe concrete-filled steel tube [17]. In 1998, the first study ofthe lateral impact failure of the hollow steel tube wascompleted by Dr. Tieguang Zhang in Cambridge University.He tested and theoretically analyzed a variety of elasticimpact hollow steel tubes and reported various failure modesof a steel tube under lateral impact. He concluded that steeltubes have good impact resistance [18].

Modal analysis is also a part of structural dynamicanalysis. Modal analysis is an important method to de-termine the stiffness distribution of a wharf structure andlearn the stiffness strength of each part of the system. Ad-ditionally, it is an important method for the dynamic designand fault diagnosis of a wharf structure [19]..ere have beenfew modal analysis studies on the structure of the domesticwharf. Gu [20] was the first to apply the modal test to wharfstructure analysis. In the study, by analyzing the modal testunder the three constraints of the large cylinder model, thefirst three-order mode shapes of the large cylinder wharfstructure are obtained, and the modal changes in the wharfstructure were analyzed after adding a superstructure.Huang et al. [21] established a spatial model by the finiteelement method, studied the natural vibration frequencyand mode distribution of an overhead vertical wharfstructure, and discussed the dynamic characteristics of thewharf structure. Song [22] used the finite element method toestablish a simply supported beam-slab model to analyze themodality of the overhead ramp structure of the automobiledownhill dock. Structural dynamic characteristics were usedto find the dangerous area during structural vibration, whichprovided a basis for the design of the wharf. Xu [23] aimed tostudy the shaking phenomenon of a high-pile wharfstructure during the operation period. .e dynamic finiteelement numerical analysis method was used to analyze thenatural vibration frequency of the wharf structure, and thenatural vibration frequencies of the different treatmentmeasures were compared. Finally, the wharf shakingproblem was effectively solved. Zhou et al. [24] used thefinite element method to establish a finite element model of apier structure for modal analysis. .ey obtained the modalcharacteristics of the pier structure and evaluated its safetyby combining the basic working conditions of the pier.

Harmonic response analysis [25] is used to determinethe law of the maximum value of the steady-state dynamicresponse of the linear structure with the load frequency tocontinuous load changes according to sinusoidal law overtime. Spectral analysis is an analytical method that combinesthe structure of modal analysis with the known spectrum tocalculate the maximum dynamic response of the structure. Itis mainly used to determine the dynamic response of thestructure to random loads or load variation over time.

2 Advances in Civil Engineering

Transient dynamic analysis, also known as time historyanalysis, is used to calculate the dynamic response of astructure under loads (such as sudden load, impact load, andfast-moving load) that change with time. .e aim of tran-sient dynamic analysis is to determine displacement, stress,strain, and other changes over time under dynamic load..erelationship between them is shown in Figure 1.

In this study, the Solid65 solid element was used tosimulate the pile body between the steel casing and the pilefoundation in order to accurately and reasonably reflect thenonlinear contact between the steel casing and the rein-forced concrete pile foundation when the steel casing isinvolved in the pile body force. .e contact situation wasselected by using the Targe 170 target unit and the Conta173contact unit to form a contact pair. Modal analysis andtransient dynamic analysis are proposed for analyzing thesteel-filled rock-socketed pile frame wharf.

2. Numerical Modeling

2.1. Engineering Structure Overview. A structural section ofthe second phase of Chongqing Orchard Port was used as theprototype. .e structural section includes five rows ofshelves, each of which is three-span four-pile. .e span andspacing are 0.8m, the diameter of the front steel cylinder is2.2m, and the diameter of the rear three rows of the steelcylinder is 2m..e frame structure is shown in Figure 2..elongitudinal and transverse braces of the lower part of theframe structure are hollow steel tubes, the longitudinal andtransverse braces of the upper structure are reinforcedconcrete beams, and the upper part of the steel barrel isconnected with the longitudinal and transverse bracingjoints of the reinforced concrete..e upper part of the framestructure is the longitudinal and transverse beams of thewharf, and the upper part of the beam is the two-way slab.

2.2. Numerical Model

2.2.1. Unit Selection. According to the characteristics of theoverhead vertical wharf structure with steel casing in the pilebody, six types of units were selected for numerical simu-lation, namely, Beam188 unit, Solid65 unit, Shell63 unit,Shell181 unit, Tar170 unit, and Conta173 unit. .e Beam188unit—a three-dimensional linear finite strain beam ele-ment—was used to simulate the beam, track beam, column,transverse contact beam, and longitudinal contact beam inthe frame pier structure. .e Solid65 solid element was usedto simulate the pile body and the contact between the steelcasing and the pile foundation in order to realistically andreasonably reflect the nonlinear contact between the steelcasing and the reinforced concrete pile foundation when thesteel casing is involved in the pile body force. In this case, theTarge 170 target unit and the Conta173 contact unit wereused to form a contact pair for simulation, and the Shell63shell unit was used to simulate the panel. In addition, all thesteel members in the structure, such as the steel casing, steelcross bracing, steel longitudinal bracing, steel front bracing,and steel shipbuilding members, were simulated by theShell181 shell unit..e finite element calculationmodel used

in this study has a large scale, with 445,768 units and a totalof 379,841 nodes. .e finite element calculation model isshown in Figure 3.

2.2.2. Material Parameter Selection. In the finite elementanalysis of the reinforced concrete pile base in the wharfstructure, reinforced concrete is composed of two com-pletely different materials. If the characteristics of the two aretaken into account separately, the modeling is more com-plex, which substantially increases the freedom of structuraldisplacement and is not conducive to solving the problem.Generally, when we carry out structural analysis, we equatereinforced concrete to homogeneous materials by usingequivalent material characteristics, such as elastic modulusand weight. .e material parameters set by finite elementanalysis in this chapter are shown in Table 1.

2.2.3. Determination of Boundary Conditions and ImpactLoads. In the numerical model, the embedded point of pilefoundation is set as consolidation, and the consolidationposition is at the bottom of pile, where the displacement inall directions is zero.

.is paper focuses on the structural dynamic response ofthe terminal structure: it considers the steel guard effectunder the dynamic effect of a simulated ship impact force, soit does not consider load effects such as load and cableingress on the dynamic characteristics of the terminalstructure; it only examines the dynamic response of theterminal itself. .e load encompasses only the impact loadthat the structure bears under self-weight and the impactload change curve over time: that is, the impact force-loadtime curve is related to the performance curve of the guardand the stiffness of the structure itself, and it needs to bedetermined by appropriate tests. .e dynamic load chosenin this study is a simplified half-sine pulse load with a loadduration of 2 s, and its peak value was determined from thepeak value of the sine wave load in the experiment. .eimpact force should be determined according to the ship’seffective impact energy, the performance curve of the rubberfender, and the stiffness of the berthing member. .e impactforce acts on two fenders in the prototype structure; given asingle fender reaction force of 516 kN, the ship’s impact forceis 1032 kN. In a dock structure test, the reverse force of thewharf structure was 10.32 kN using a similar ratio. .eimpact load is shown in Figure 4.

Structuraldynamicsanalysis

Modal analysis

Harmonic response analysis

Transient dynamic analysis

Spectrum analysis

Figure 1: Classification of structural dynamic analysis.

Advances in Civil Engineering 3

2.2.4. Contact Parameter Setting between Steel Casing andPile Foundation. .e contact relationship between steel pilecasing and reinforced concrete pile core of pile foundationincludes normal relationship and tangent relationship.

(1) Normal Relation. In the normal relationship, thetransmission of contact force should be satisfied, and thereis no penetration between the two contact surfaces. For the

Conta173 contact unit selected in the calculation model inthis paper, the contact stiffness is defined by the realconstant FKN, which is set to 0.1. .e steel casing and thepile foundation are defined as hard contact, and no pen-etration occurs between the two contact surfaces to reflectthe limitation of the lateral compression stress of the steelcasing on the reinforced concrete pile under the dynamicload.

Figure 3: Finite element model of the steel shell cast-in-place pile with a rock-embedded structure.

1.50

2.36

2.91

3.46

4.56

4.01

5.18

1.80

Longitudinal beam

0.30

D C B A

0.80 0.80 0.803.00

0.30

Rail Bollard

Reinforced concretelongitudinal braceReinforced concretetransverse braceSteel tubelongitudinal braceSteel tubetransverse brace

Transverse beam

(a)

0.150.15 1.60

1 2 3 4 5

[email protected] = 3.201.60 0.15

0.15

(b)

Figure 2: Experimental model (unit: m). (a) Section. (b) Elevation.

Table 1: Steel casing and concrete material parameters.

Materials Elastic modulus (MPa) Poisson’s ratio Density (kg·m− 3) Minimum yield stress (MPa)Steel 2.1× 105 0.3 7800.0 418Concrete 2.4×104 0.2 2200


(2) Tangential Relation. In the tangential relationship be-tween the steel casing and reinforced concretepiles—assuming that there is only a relative sliding trendbetween the steel casing and reinforced concrete pilefoundation under external loads, but no relative slidingoccurs—the static friction coefficient between the twocontact surfaces is defined as 0.25 [26], which reflects theaxial friction effect of the steel casing on reinforced concretepiles under dynamic load.

2.2.5. Load Conditions. Comparison of the results of thedynamic response test of the wharf structure was facilitatedby applying the impact force to the P1 framed bend of thewhole structure under five conditions corresponding to thedynamic response test (Figure 4).

2.3. Experimental Verification. A structural section of thesecond phase of Chongqing Orchard Port was used as aprototype, and a physical model with a geometric scale of 1 :10 was produced. See Figure 5 for details.

.e position and number of strain gauges for eachsection of the member are shown in Figure 6.

In working conditions 3 and 5, the transient strains attwo points above the steel sheath were collected, and theexperimental data and numerical calculation data werecompared. See Figures 7 and 8 for details. .e results showthat the numerical model can better reflect the dynamicresponse of the structure under lateral impact load.

3. Numerical Analysis

3.1. Computational Model Analysis of the Overhead VerticalWharf with Rock-Socketed Cast-In-Place Piles with a SteelRetaining Barrel. In the actual calculation, it is important toconsider the modes that contribute to the satisfaction of theactual project needs, thereby considerably reducing theworkload required to solve the problem. .erefore, the

natural frequencies and natural periods corresponding to thefirst 30 modes of the experimental model structure of theorchard wharf were analyzed by using finite element soft-ware and are listed in Table 2. Figure 9 shows the frequency-modal order curve of the model structure, which is drawnwith the data obtained from the modal analysis.

(1) .e frequencies from the first to the third order ofthe structure are 11.889–13.764Hz, and the corre-sponding modes of the first and third orders of thestructure are of horizontal motion in the planewithout vertical motion. .e natural frequencies ofthe wharf model structure first appear in the regionof lower stiffness. .e transverse members (such asthe cross beam, reinforced concrete cross brace, andsteel cross brace) in the structure give the framedbend better integrity and greater stiffness. Longitu-dinal members (such as longitudinal beams, rein-forced concrete longitudinal braces, and steellongitudinal braces) provide weaker stiffness thantransverse members. .erefore, the transverse stiff-ness of the structure is larger than the longitudinalstiffness. From the first mode of vibration, thestiffness of the longitudinal component should bestrengthened in the design.

Impact forcecondition 1Impact forcecondition 2Impact forcecondition 3Impact forcecondition 4Impact forcecondition 5

(a)

10.32

F (k

N)

t (s)0 1 2

(b)

Figure 4: Impact load. (a) Impact force calculation conditions. (b) Semisinusoidal impact load-time history curve.

Figure 5: Physical test model.


(2) As shown in Table 2, the natural frequency of thewharf model structure presents a piecewise cen-tralized distribution, and the first three naturalfrequencies of the structure do not change much inthe frequency range of 11–13Hz, which indicatesthat the stiffness of the structure is relatively

uniform. In the first three modes with low fre-quencies, the structure is more easily excited byexternal loads. When the structure is subjected tohorizontal loads, such as impact force, the vibrationresponse of the first three modes may predominate..e frequencies of the third and fourth modes, the

Spac

ing

605

100

100

100

315

440

150

8585

925

P1-Z4-7

P1-Z4-6

P1-Z4-5

Rive

r sid

e

Shor

e sid

eP1-Z4-4

P1-Z4-3

P1-Z4-2

P1-Z4-1

402

P1-Z4-8

P1-Z4-9

P1-Z4-10

145

115

160

(a)

605

615

325

8524

068

529

486

100

100

Rive

r sid

e

Shor

er si

de

P1-Z1-2

P1-Z1-1

P1-Z1-3

P1-Z1-4373

P1-Z1-5

P1-Z1-6

P1-Z1-7

P1-Z1-8

P1-Z1-9

P1-Z1-10

(b)

Figure 6: .e position and number of strain gauges for each section of the member. (a) Pile Z4. (b) Pile Z1.

–3.00E – 05

–2.50E – 05

–2.00E – 05

–1.50E – 05

–1.00E – 05

–5.00E – 06

0.00E + 000 0.5 1 1.5 2 2.5

Loading time (s)

Stra

in v

alue

(ε)

Calculated valueTest value

(a)

–6.00E – 06

–5.00E – 06

–4.00E – 06

–3.00E – 06

–2.00E – 06

–1.00E – 06

0.00E + 000 0.5 1 1.5 2 2.5

Stra

in v

alue

(ε)

Loading time (s)


(b)

Figure 7: Strain-time history curve of the no. 373 measuring point on the river side of Z1GH. (a) Working condition 3. (b) Workingcondition 5.


seventh and eighth modes, and the tenth and fif-teenth modes are close to each other, and the fre-quencies jump in stages, reflecting the dramaticchange in the corresponding stiffness from simplemodes to complex modes. .erefore, the excitation

sources in these ranges should be avoided as much aspossible when the wharf structure test is carried out.

3.2. Transient Dynamic Analysis of the Wharf Test ModelStructure

3.2.1. Deformation of Structure. .e semisinusoidal waveload used to simulate the impact force was applied to thestructure, and the displacement response of the wharfstructure under this load was calculated. In the finite elementcalculation of the wharf, the displacement of the wharf topnode is the focus of scientific research and engineeringdesign. .e peak displacement of the structure’s top nodeand the impacted node under five working conditions areshown in Table 3. .e displacement-time histories andstructural deformation diagrams of key points under fiveworking conditions are given. Among the data shown, thestructural deformation diagram corresponds to the time at

–5.00E – 06

0.00E + 00

5.00E – 06

1.00E – 05

1.50E – 05

2.00E – 05

0 0.5 1 1.5 2 2.5

Stra

in v

alue

(ε)

Loading time (s)


(a)

Loading time (s)


0.00E + 00

5.00E – 07

1.00E – 06

1.50E – 06

2.00E – 06

2.50E – 06

3.00E – 06

0 0.5 1 1.5 2 2.5

Stra

in v

alue

(ε)

(b)

Figure 8: Strain-time history curve of the no. 402 measuring point on the shore side of Z4GHT. (a) Working condition 3. (b) Workingcondition 5.

Table 2: Frequency and period of each order mode.

Order number Period (s) Frequency (Hz) Order number Period (s) Frequency (Hz)1 0.0841 11.889 16 0.0095 105.252 0.0832 12.026 17 0.0088 113.713 0.0727 13.764 18 0.0080 125.194 0.0234 42.794 19 0.0079 126.445 0.0218 45.921 20 0.0077 130.66 0.0195 51.25 21 0.0075 133.067 0.0173 57.89 22 0.0075 133.858 0.0142 70.406 23 0.0075 134.09 0.0122 82.049 24 0.0074 134.8810 0.0109 91.53 25 0.0073 136.7411 0.0107 93.662 26 0.0072 139.3412 0.0104 95.723 27 0.0072 139.4813 0.0100 99.779 28 0.0071 141.0714 0.0098 101.95 29 0.0071 141.1315 0.0096 104.3 30 0.0070 141.94

10 20 30 400Modal order

020406080

100120140160

Freq

uenc

y (H

z)

Figure 9: Frequency-modal order relationship curve.


0.50

3E –

05

–0.8

08E

– 03

–0.9

10E

– 03

–0.7

07E

– 03

–0.5

03E

– 03

–0.3

00E

– 03

–0.6

05E

– 3

–0.4

02E

– 03

–0.1

98E

– 03

–0.9

67E

– 04

MX

MN

Nodal solutionTime = 1.05UX (avg)RSYS = 0DMX = 0.001002SMN = –0.910E – 03SMX = 0.503E – 05

Z

X

Y

(a)

Nodal solutionTime = 1.05UX (avg)RSYS = 0DMX = 0.001739SMN = –0.001586SMX = 0.972E – 05

MX

MN

0.97

2E –

05

–0.0

0140

9

–0.0

0158

6

–0.0

0123

2

–0.8

77E

– 03

–0.5

22E

– 03

–0.0

0105

4

–0.7

00E

– 03

–0.3

45E

– 03

–0.1

68E

– 03

Z

X

Y

(b)Nodal solutionTime = 1.05UX (avg)RSYS = 0DMX = 0.002762SMN = –0.002701SMX = 0.497E – 05

MXMN

0.49

7E –

05

–0.0

024

–0.0

0270

1

–0.0

0209

9

–0.0

0149

8

–0.8

97E

– 03

–0.0

0119

8

–0.2

96E

– 03

–0.0

0179

9

–0.5

96E

– 03

Z

X

Y

(c)

MN

MX


0.46

8E –

05

–0.0

0248

3

–0.0

0297

4

–0.0

0217

2

–0.0

0155

–0.9

28E

– 03

–0.0

0123

9

–0.3

06E

– 03

–0.0

0186

1

–0.6

17E

– 03

Z

X

Y

(d)

MX

0.81

4E –

05

–0.0

0265

7

–0.0

0299

1

–0.0

0232

4

–0.0

0165

8

–0.0

0199

1

–0.0

0132

5

–0.6

58E

– 03

–0.3

25E

– 03

–0.9

91E

– 03


MN

Z

X

Y

(e)

Figure 10: X-directional displacement nephogram of structural integral (unit: m). (a) Working condition 1. (b) Working condition 2. (c)Working condition 3. (d) Working condition 4. (e) Working condition 5.


which the maximum response of the structure occurs undereach working condition, DMX is the maximum sum ofdisplacement vectors in all directions in the structural de-formation diagram, and SMN and SMX are the minimumdisplacement and maximum displacement of the nodescorresponding to the maximum response time of the currentquery, respectively.

.e expanded analysis of the whole deformation of thestructure and the displacement-time history curve of thejoints are detailed below:

(1) .e analysis in Figure 10 shows that when thestructure fully responds to the impact load, the pointwith larger vector displacement appears far from theaction point, indicating that the structure showsgreater overall stiffness under the impact dynamicload. .e time at which the maximum impact force

reaches 10.3 kN is 1.0 s, but the maximum dis-placement occurs at more than 1.05 s. .is is becausethe energy transfer of the impact force takes a certainamount of time in the structure, and the response ofthe structure has a lag effect. .e one-way full re-sponse lag time of the structure is 0.05 s, which alsoshows that the frame structure has better overallrigidity.

(2) Table 3 shows that the maximum displacement of thetop node of the structure under working condition 2is the largest and that the displacement of the loadingpoint under working conditions 3–5 is the largestand tends to decrease..is is because, under workingcondition 2, the lateral stiffness of the structure at theloading point is larger and the local deformation andenergy absorption of the loading point are less.

–1.125–1

–0.875–0.75

–0.625–0.5

–0.375

–0.125–0.25

00.125

0 0.8 1.6 2.4 3.2 4 4.8 5.6 6.4 7.2 8

Valu

e

Time

(×10–3)

(a)

(×10–3)

–1.6

–1.1

–0.6

–0.1

0.4

0 0.8 1.6 2.4 3.2 4 4.8 5.6 6.4 7.2 8

Valu

e

Time

(b)

(×10–4)

–7.2–6.4–5.6–4.8

–4–3.2–2.4–1.6–0.8

00.8

0 0.8 1.6 2.4 3.2 4 4.8 5.6 6.4 7.2 8

Valu

e

Time

(c)

Time

(×10–4)

–6.4–5.6–4.8

-4–3.2–2.4–1.6–0.8

00.81.6

0 0.8 1.6 2.4 3.2 4 4.8 5.6 6.4 7.2 8

Valu

e

(d)

(×10–4)

–4.5–4

–3.5–3

–2.5–2

–1.5–1

–0.50

0.5

0 0.8 1.6 2.4 3.2 4 4.8 5.6 6.4 7.2 8

Valu

e

Time

(e)

Figure 11: X-directional displacement-time history curves of the top joints of structures (unit: m). (a) Working condition 1. (b) Workingcondition 2. (c) Working condition 3. (d) Working condition 4. (e) Working condition 5.


Conversely, the stiffness of the structure is thesmallest at the action point of working conditions3–5, and the local deformation and energy absorp-tion of the action point are larger.

(3) From the analysis of the displacement-time historycurve of the joint shown in Figure 11, it can be seenthat the displacement-time history curve is ap-proximately half sinusoidal waveform during the

action time of the impact load of 2 seconds, which isconsistent with the impact load-time history curvewaveform. .e displacement value of the observednode increases sharply in the first 1.0 second anddecreases in the last 1.0 second. Since 6S after thetime history curve is the monitoring of the structuralvibration after loading, at this time, because of thenatural vibration of the structure, the node of the

Nodal solutionTime = 1.05SEQV (avg)DMX = 0.001002SMN = –0.646698SMX = 21650

2165

0

2406

0.64

6698

4812

9623

7217

1202

8

1683

9

1924

5

1443

4

MX

MN

Z

X

Y

(a)

Nodal solutionTime = 1.05SEQV (avg)DMX = 0.00739SMN = 0.773669SMX = 42850

4762

0.77

3669

9523

1904

5

1428

4

2380

6

3332

8

3808

9

2856

7

2485

0

MX

MN

Z

X

Y

(b)Nodal solutionTime = 1.05SEQV (avg)DMX = 0.002762SMN = 0.406741SMX = 0.166E + 07

1842

03

0.40

6741

3684

05

7368

10

5526

08

9210

12

0.12

9E +

07

0.14

7E +

07

0.11

1E +

07

0.16

6 +

07MX

MN

Z

X

Y

(c)

MN

MX

Nodal solutionTime = 1.05SEQV (avg)DMX = 0.002864SMN = 0.194818SMX = 0.171E + 07

1895

74

0.19

4818

3791

48

7582

97

5687

23

9478

71

0.13

3E +

07

0.15

2E +

07

0.11

4E +

07

0.17

1E +

07

Z

X

Y

(d)Nodal solutionTime = 1.05SEQV (avg)DMX = 0.003074SMN = 0.5667766SMX = 0.177E + 07

1965

49

0.56

6776

3930

97

7861

93

5896

45

9827

42

0.13

8E +

07

0.15

7E +

07

0.11

8E +

07

0.17

7E +

07

MX

MN

Z

X

Y

(e)

Figure 12: Stress distribution diagram of the structure at maximum response time (unit: kPa). (a) Working condition 1. (b) Workingcondition 2. (c) Working condition 3. (d) Working condition 4. (e) Working condition 5.


structure has obvious displacement that is oppositeto the loading direction at 2.3 s, and the maximumdisplacement does not exceed 1/13 of the loadingdirection displacement. Under the condition of theimpact dynamic load and the consolidation of thepile bottom, the structure shows positive and neg-ative back-and-forth vibration of the load action, but

the vibration in the direction of the load phase is verysmall and can be neglected.

3.2.2. Stress of the Structure. e peak stress of the pilefoundation structure and its location under ve workingconditions are shown in Table 4. Table 5 lists the stress peak

(×10)

0250500750

1000125015001750200022502500

Valu

e0.8 1.6 2.4 3.2 4 4.8 5.6 6.4 7.2 80

Time

(a)

(×10)

0

1000

2000

3000

4000

5000

Valu

e

0.8 1.6 2.4 3.2 4 4.8 5.6 6.4 7.2 80Time

(b)

(×103)

0200400600800

100012001400160018002000

Valu

e

0.8 1.6 2.4 3.2 4 4.8 5.6 6.4 7.2 80Time

(c)

(×103)

0200400600800

100012001400160018002000

Valu

e

0.8 1.6 2.4 3.2 4 4.8 5.6 6.4 7.2 80Time

(d)(×10)

0.8 1.6 2.4 3.2 4 4.8 5.6 6.4 7.2 80Time

0250500750

1000125015001750200022502500

Valu

e

(e)

Figure 13: vonMises stress-time curve of maximum stress node (unit: kPa). (a)Working condition 1. (b)Working condition 2. (c)Workingcondition 3. (d) Working condition 4. (e) Working condition 5.

Nodal solutionTime = 1.05SEQV (avg)DMX = 0.826E – 3SMN = 33.85SMX = 21650

2436

33.8

5

4837

9641

7239

1204

3

1684

7

1924

8

1444

5

2165

0

(a)

MX

MN


2436

33.8

5

4837

9641

7239

1204

3

1684

7

1924

8

1444

5

2165

0

(b)

Figure 14: Equivalent stress diagram of Z1 steel casing on the shore side under working condition 1 (unit: kPa). (a) Shore side. (b) River side.


values of the main components of the lower structure of thetest model under various working conditions. In addition,the stress distribution diagram of the whole structure underdifferent working conditions at the maximum response timeis given, and the nodes that produce the maximum stressresponse are taken as the key points. .e stress-time historydiagram is also shown.

(1) As can be seen from Table 4 and Figures 12 and 13,the maximum stress response time of the wharfmodel structure under a low-speed impact load is1.05 s, and the stress waveform and load remainconstant. .e peak value is 0.05 s later than the peakvalue of the impact load. At the end of impactloading, different degrees of stress vibration

Z

Y

X

MN

MX

26.8

73

231.

8

641.

652

436.

726

846.

578

1256

1461

1052

1666


1871

(a)


26.8

73

231.

8

641.

652

436.

726

846.

578

1256

1461

1052

1666

1871

MN

MXZ

Y

X

(b)

Figure 15: Equivalent stress diagram of Z1 reinforced concrete pile on the shore side under working condition 1 (unit: kPa). (a) Shore side.(b) River side.

Table 3: Maximum lateral displacement and response time of key points of structures.

Name Workingcondition 1Working

condition 2Working

condition 3Working

condition 4Working

condition 5

Maximum out-of-river displacementof top joints of structures

Size(×10− 3m) 0.910 1.577 0.713 0.591 0.440

Responsetime (s) 1.05s 1.05s 1.05s 1.05s 1.05s

Maximum river-orienteddisplacement of top joints ofstructures

Size(×10− 3m) 0.0528 0.0811 0.0446 0.0395 0.0331


Maximum offshore displacement ofimpacted joints

Size(×10− 3m) 0.897 1.555 2.700 2.794 2.991


Maximum riverward displacement ofimpacted joints

Size(×10− 3m) 0.0442 0.0751 0.113 0.115 0.118


Table 4: Maximum von Mises equivalent stress table for the whole structure.

Name Working condition 1 Working condition 2 Workingcondition 3Working

condition 4Working

condition 5Maximum stress value(kPa) 21650 42580 1.66×10

6 1.70×106 1.77×106

Maximum stressresponse time (s) 1.05 1.05 1.05 1.05 1.05

Location of maximumstress occurrence

.e lower side of theconnection between the firstrow of steel barrels and steel

braces

.e lower side of theconnection between the firstrow of steel barrels and steel

braces

Impact point ofsteel pillar




appeared in various working conditions. In workingcondition 1 and working condition 2, the maximumstress appears on the lower side of the joint betweenthe first row of the steel casing and the steel crossbracing, that is, the welding place of the two steelmembers of the steel casing and the steel crossbracing. .e maximum stress in working conditions3–5 occurs near the impact force acting on the steeldocking column. .us, when the structure is sub-jected to a horizontal dynamic load, the maximumstress appears in the weakest part of the structure.From the point of view of the equivalent force peakin the whole structure, the stress peak value of thecomponents in working conditions 3–5 is 102 timeslarger than that in working conditions 1-2. .is isbecause of the hollow steel tube of the dockingcolumn at the loading points of the latter threeworking conditions; the transverse stiffness is lessthan the longitudinal stiffness of the steel tube at thejunction of the steel transverse brace and the steelcasing, and the steel casing is wrapped by a rein-forced concrete core.

(2) FromTable 5, it can be seen that the peak stress values ofthe steel casing members under the same workingcondition are generally larger than those of reinforcedconcrete pile foundations. .is indicates that the steelcasing absorbs more impact energy during structuraltransmission under impact force and the mechanicalproperties of the reinforced concrete piles are not fully

developed. Figures 14 and 15 show that the stressconcentration of the steel casing is extensive at the jointsof the longitudinal and transverse braces, while the stressdistribution of the reinforced concrete pile core in thesteel casing is relatively uniform because of the hoopaction of the steel sheath. .e maximum stress of thepile foundation appears in the embedded section of thefoundation because the lateral loads on the super-structure are ultimately borne by the embedded sectionof the pile foundation, and there are no lower stiffnesscomponents in the embedded section of the pile toabsorb the energy resulting from the impact load.

4. Conclusion

.e dynamic response analysis of the first structural sectionof the second-phase wharf of Chongqing Orchard Portunder lateral impact load reveals several phenomena:

(1) .e rigidity of the model structure of the rock-socketed cast-in-place pile wharf with steel casingwas strengthened by the reinforcement of the lon-gitudinal and transverse braces of reinforced con-crete and the frame structure of the steel longitudinaland transverse braces..e integrality is good, but thelongitudinal rigidity of the structure needs to bestrengthened..e modal frequencies of the structureare concentrated in segments, and the stiffness valuesof the same group of modes of the model structureare close to each other. .is shows that the stiffness

Table 5: von Mises equivalent stress peak table of pile foundation structure.

Structural computing componentsComputational results

Workingcondition 1

Workingcondition 2

Workingcondition 3

Workingcondition 4

Workingcondition 5

P1Z4 steel casing (kPa)River side 19642 39168 19157 14079 53400Shoreside 3969.2 9461.6 3944.8 4155 24936

P1Z4 concrete pile foundation(kPa)

River side 1355.3 2978.2 1420.1 1121.3 2286.5Shoreside 1823.1 3492.9 1813.5 1446.4 1888.4

P1Z1 steel casing (kPa)River side 12984 29236 34110 51611 1557Shoreside 21650 42685 24966 14556 24966

P1Z1 concrete pile foundation(kPa)

River side 1471.1 3211.7 1557 2574.5 1911.6Shoreside 1806.2 3464.4 1911.6 2950.8 1557

P1 bent steel cross brace (kPa)

Upperside 10661 20965 11750 6887 11242

Underside 11526 23172 12485 11385 13264

P1 bent steel berthing column(kPa)

River side 5698.8 27785 1657800 1706200 1768900Shoreside 11819 27120 60117 72759 58926

P1 bent steel front brace (kPa)

Upperside 7841.6 17685 11293 29258 19368

Underside 9385.1 20980 12358 39896 24458

P1 is the first framed bend, and Z1 is the first row of the steel barrel socketed piles from the river side to the bank side.


distribution of the structure is uniform, and thefrequency jumps between different frequency bands,which is necessary to avoid the excitation loads neareach dense frequency band.

(2) .e displacement response of the frame structure totransverse impact dynamic load is consistent fordifferent load action points. It is necessary to avoidthe transverse load action in the position at which thelocal stiffness of the frame structure is larger in orderto avoid the back-and-forth vibration caused byexcessive displacement of the whole structure.

(3) .e stress response-time history of the structure isconsistent with the load waveform. At the end of the2S load, stress vibration occurs. .e overall stiffnessof the frame structure is better, but the stress con-centration occurs in the longitudinal/transversebraces, the steel casing, and their connections. .estress distribution of the reinforced concrete pilecore is relatively uniform because of the hoop actionof the steel casing, and the stress at the bottom of theembedded section of the foundation is larger. In thedesign, other longitudinal/transverse braces withhigher stiffness should be considered, and newstructural forms should be used to reinforce ordistribute stress in places connected with steel casing.Steel-concrete cooperative structural forms made ofsteel casing and reinforced concrete pile cores withimproved mechanical properties should be adopted.

(4) .is paper reports the dynamic response analysis ofthe overhead vertical wharf with rock-socketed steelsheath piles. .e influence of welding effects, such asthe influence of the steel longitudinal/transversebrace and steel sheath on the structural dynamicresponse, was not considered, and the dynamiccoupling response of the single-foundation embed-ded in the pile foundation was not considered.Further research should be carried out in combi-nation with the theory of steel-concrete structurecoupling and pile-foundation coupling.

Data Availability

.e data used to support the findings of this study areavailable from the corresponding author upon request.

Conflicts of Interest

.e authors declare that they have no conflicts of interest.

Acknowledgments

.e authors would like to acknowledge the financial supportfrom the National Natural Science Foundation of Chinaunder contract no. 51579021.

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