Research ArticleNovel Crashworthy Device for Pier Protection from Barge Impact

W. Wang and G. Morgenthal

Modeling and Simulation of Structures, Bauhaus University Weimar, Marienstrasse 13, 99423 Weimar, Germany

Correspondence should be addressed to W. Wang; dwsjzri@gmail.com

Received 22 August 2017; Revised 30 December 2017; Accepted 10 January 2018; Published 2 April 2018

Academic Editor: Chiara Bedon

Copyright © 2018 W. Wang and G. Morgenthal. ,is is an open access article distributed under the Creative CommonsAttribution License, which permits unrestricted use, distribution, and reproduction in anymedium, provided the original work isproperly cited.

Barge impact is a potential hazard for bridge piers located in navigation waterways. Protective structures of different types, forexample, dolphin structures, artificial islands, and guiding structures, have been widely used in bridge designs against bargeimpact. However, such structures often imply high cost and suffer from difficulties in installation as well as maintenancechallenges. ,is paper aims to devise and investigate a new type of crashworthy device which is comprised of vertically supportedimpact cap connected to the bridge pier using a series of steel beams in a frame-type arrangement. ,is sacrificial steel structure isdesigned to form plastic hinges for energy dissipation whilst limiting the force transmitted to the protected pier. ,e dynamicanalysis of the proposed crashworthy device subjected to barge impact is conducted using a simplified impact model previouslydeveloped by the authors. ,e parametric studies in this paper show that the proposed device has a large energy dissipationcapacity and that the magnitude of impact force transmitted to the bridge pier can be dramatically reduced. In addition, anoptimization model is proposed in this paper to achieve the cost-optimized design of the crashworthy device for a given impactscenario with constraints as per the prescribed design requirements.

1. Introduction

Bridge piers located in navigation waterways are oftenthreatened by vessel impact due to the increment of vesseltransportation volume. It was pointed out by Manen andFrandsen [1] and Larsen [2] previously that at least onemajor vessel-bridge collision accident of serious conse-quences occurred each year on average in the past. Bargecollisions upon bridge structures were also frequently re-ported. Such collisions can often lead to catastrophic con-sequences including human casualties and economic losses;thus substantial investigations regarding the quantificationof barge impact loading and dynamic structural responseshave been conducted in recent years [3–8].

Different protection measures are being employed toprotect bridge piers from vessel impact loading or reduce thedamage of bridge piers during impact. As one of theseprotection measures, independent protective structures suchas dolphin structures are frequently used in bridge designs.Such structures were, for example, adopted and installed forlong-span bridges such as the Rosario-Victoria Bridge inArgentina [9], the Rhine Bridge in Kehl, Germany [10], and

the American Sunshine Bridge [11]. ,e advantage of suchindependent protective structures is that they can absorbhigh impact energy and protect bridge piers from directcontact with the vessels. However, such independent pro-tective structures require high cost and suffer from durabilityproblems and challenges regarding installation and main-tenance. In addition, reconstruction of such independentprotective structures after being damaged by vessel impact isoften expensive, if at all possible. Other protective structures,for example, artificial islands [12] or guiding structures [13],are also frequently used. However, these structures sufferfrom problems as those mentioned above.

,e problems related to the above mentioned protectivestructures have led to the investigation of bridge protectionsfrom impact by strengthening the bridge piers themselves,for example, with carbon fibre-reinforced polymers (CFRPs)[6, 14]. Such strengthening techniques can improve the pierresistance; that is, the pier undergoes less damage duringimpact. However, such technique cannot reduce the max-imum impact force; therefore, it is effective for pier pro-tection but not for barge protection [6]. In addition, thestudies by Sha and Hao [6] indicate that the effectiveness of

HindawiAdvances in Civil EngineeringVolume 2018, Article ID 9385643, 15 pageshttps://doi.org/10.1155/2018/9385643

the CFRP strengthening technique is very limited regardingthe maximum pier displacement.

�is paper aims to devise a novel crashworthy devicewhich is comprised of a supported or �oated cap connected tothe pier using steel beams arranged in a frame-type manner.During a high-energy barge impact, many plastic hinges formin the proposed device, enabling it to absorb large amountsof impact energy through plastic deformations. Such crash-worthy device is easy to install, maintain, and restore after animpact event. �rough the choice of con�guration, plasticmoments, and postyield hardening, the maximum forcetransmitted to the main pier can be designed to not exceed anallowable force that is acceptable by the main pier.

To investigate the e�ectiveness of the proposed crash-worthy device for barge impact, the simpli�ed impact modelpreviously developed by the authors is employed in this

paper to conduct dynamic analysis of the device subjected tobarge impact. �e simpli�ed impact model transforms thehighly nonlinear full barge impact model (FBIM) intoa coupled multi-degree-of-freedom model (CMM). �eaccuracy and e�ciency of CMM were thoroughly assessedfor di�erent impact scenarios [8]. �is paper employs suchsimpli�ed impact model to investigate the energy dissipationcapacity of the proposed device and the magnitude of impactforce transmitted to the bridge pier by the steel beams duringimpact for di�erent structural con�gurations. �e para-metric studies in this paper indicate that the proposed devicehas a large energy dissipation capacity for barge impact and cansigni�cantly reduce the maximum impact force transmittedto the bridge pier during impact. To achieve cost-optimizeddesign of such device for a given impact scenario,a mathematical optimization model is proposed in this

5.5

56.1

+8.05 IGM

–53.0 IGM

Structure using steelbeams of I cross section(Figure 2)

Unit: m

Vertical supportby slender pile orfloating element

cap

Figure 1: �e structure connecting the cap and the bridge pier using steel beams of I cross section for a sample bridge pylon foundation.

2 Advances in Civil Engineering

paper with constraints as per the prescribed design re-quirements. Examples presented in this paper show that theoptimum con�guration of the device can be obtained fordi�erent impact scenarios using the proposed optimizationmodel.

2. Configuration of the Device

During a barge impact, a portion of the impact energy istransformed into the residual kinetic energy of the bargewhile the rest of the impact energy is dissipated through theplastic deformations of the barge and the impactedstructure. In order to protect both the bridge pier and thebarge, it is necessary to devise a crashworthy device whichis easy to install, maintain and restore and can absorb largeportions of the impact energy through plastic deforma-tions. In this way, the energy absorbed by the barge and thepier during impact would be low, and consequently, boththe barge and the pier can remain in the linear range, thatis, elastic (undamaged), through the limitation of the forcetransmitted.

�e con�guration of the proposed crashworthy device isdepicted in Figure 1 for a sample bridge pylon foundation to

be protected.�e cap structure is designed to collect the localimpact forces and is vertically supported for its self-weightby a structure that does not provide a signi�cant lateralrestraint, for example, a �exible pile system or a �oatingstructure. �e cap is connected to the pylon foundationusing a series of steel beams of I cross section arranged inmultiple frames. �e individual steel beam legs are con-nected bending sti�, for example, through welds, such thata force applied to the cap generates bending moments in thesteel structure. Several planes of beam units can be installedto provide the energy dissipation capacity and the elastic andplastic deformation behavior desired. In Figure 1, threeplanes are shown, which can be braced against each other toavoid out-of-plane stability failure.

For simpli�cation purposes, several assumptions areadopted herein: (1) the lateral resistance of the cap’s sup-porting structure is ignored, (2) the pylon foundation isassumed to be rigid, and (3) the cap is assumed to be rigidand is modeled using a lumped mass. Based on these as-sumptions, the structure shown in Figure 1 can be simpli�edinto the cap steel beam structure, as shown in Figure 2. �ecap can move freely in the horizontal direction whilst itsvertical movement is constrained.

Rigid pier

Steel beam ofI cross section

mc

lsb

Hinge

Cap modeledby rigid mass

l sb

lsb

One beam unit

lsb

(a)

wbi

h bi twi

tfi

(b)

Figure 2: Con�guration of (a) the cap steel beam structure and (b) I cross section of steel beams. Nbu: number of beam units in one plane;lsb: length of each single steel beam; mc: cap mass.

vb

Superstructuremass modeled bya point mass

MSMDiscrete beam elementDiscrete point mass

mb

Pier column modelfixed at bottom

Figure 3: Transformation of FBIM (left) into CMM (right).

Advances in Civil Engineering 3

3. Overview of CMM

�e CMM previously developed by the authors simpli�esthe complex �nite-element barge model into a nonlinear mass-springmodel (MSM) andmodels the pier column using discretemasses and �bre beam elements [8], as shown in Figure 3, wheremb is the lumped barge mass and vb is the impact velocity.

As per previous studies [3, 4, 7], the force-deformationcurve of the barge bow during impact (curve 1) generallyincludes a linear increase of impact force until the forcepeak is followed by an abrupt decrease when the barge bowyields, as shown in Figure 4, where ub is the barge bowdeformation and F is the impact force. �en the impactforce roughly reaches a plateau until the unloading stage.�e shape of curve 1 can be regarded as the superposition oftwo curves—a triangular curve (curve 2) and a bilinearcurve (curve 3), as shown in Figure 4. Two nonlinearsprings which act in parallel are thus introduced to rep-resent the barge bow resistance. �e force-deformationcurves of the two nonlinear springs are taken to be bi-linear and triangular, respectively, as shown in Figure 5,where u1 and u2 are the yielding deformations of two springs,respectively; Fsy is the yielding force of the �rst spring; Fsp isthe peak force of the second spring; and x is the springdeformation. By coupling MSM with the column at theimpact position, the CMM is developed to predict the dy-namic barge impact process e�ciently, as shown in Figure 3.�e MSM parameters are determined by an optimizationmodel which minimizes the integration error of impact forcetime histories determined by CMM and FBIM, respectively.

�e quality of CMM regarding the prediction of impactforce time history and dynamic pier responses was assessedin large detail for di�erent impact scenarios in [8] by usingFBIM as the benchmark model. �e validated CMM is thusused for the studies herein.

4. Simplified Impact Model Based on CMM

In this section, the simpli�ed impact model is developed basedon CMM for dynamic analysis of the proposed crashworthydevice subjected to barge impact. As shown in Figure 6, thesteel beams are modeled using discrete masses and �bre beamelements. �e MSM is coupled with the cap which is expectedto contact with the barge when impact occurs. It is assumed in

this study that the beam elements undergo no shear de-formations or torsional deformations. �e stress-strain curveof the beam steel is bilinear in this study.

�e MATLAB code was written with the �bre method forsolving the numerical model illustrated in Figure 6. �e codewas previously veri�ed by detailed �nite-element simulationresults from LS-DYNA [8]. Geometric nonlinearity of beamelements is analyzed using the corotational approach forproblems of large displacements and small strains. �e basicidea is to decompose the motion of the element into rigid bodypart and pure deformational part. A local coordinate system,which moves and rotates with the element’s overall rigid bodymotion, is de�ned, and the deformational part is measuredunder this local coordinate system [15].

5. Parametric Studies

�e e�ectiveness of the proposed device is investigated inthis section by parametric studies using the simpli�ed im-pact model. �e cap surface which contacts with the barge is�at and is 3.0m in width. �e bridge pier is �at and 6.0m in

ub

F

Figure 4: General shape of barge bow force-deformation curve., curve 1; , curve 2; , curve 3.

u1 lbs x

Fsy

Fsu

Fbs1

(a)

Fsp

x

Fbs2

u1u2

(b)

Figure 5: Bilinear spring model (a) and triangular spring model(b) used in MSM [8].

4 Advances in Civil Engineering

width. �e cap mass (mc) is taken to be 100.0 ton. �e totallength of the beam units in one plane (lcsb) is taken to be15.0m.�e number of planes of beam units (Npl) is taken tobe one in this study. �e information of the prespeci�edparameters regarding the device is tabulated in Table 1.

�ree parameters, that is, beam cross-section dimension,yielding strength of beam steel (fbs

y ), and number of beamunits in one plane (Nbu), are considered for the parametricstudies herein. For comparison purposes, the following baselinesimulation is conducted: beam cross-section dimension asfollows: hbi � 0.75m,wbi � 0.50m, tfi � 0.05m, and twi � 0.03m;beam steel yielding strength of 350.0MPa; and beam unit

number of two in one plane. �e parameter MCbi, whichmeans the ratio of the studied beam cross-section dimensionalparameters, that is, hbi, wbi, tfi, and twi, to the respective beamcross-section dimensional parameters used for the baselinesimulation, is denoted herein.

5.1. Beam Cross-Section Dimension. �ree beam cross-section dimensions corresponding to MCbi of 0.8, 1.0, and1.2, respectively, are considered herein. �e energy absorbedby the device (Wcsb

diss) during impact corresponding to eachbeam cross-section dimension is shown in Figure 7, wherethe total impact energy (Wtotal) and the ratio (rcsbdiss) of energy

Rigid wallPoint mass

mcmb

Hinge

Figure 6: Simpli�ed impact model based on CMM for dynamic analysis of the proposed device subjected to barge impact.

Table 1: Prespeci�ed parameters for parametric studies of the device.

Member Parameter Value

Barge mb � barge mass 1723.7 tonvb � impact velocity 2.0m/s

Cap wc � cap width 3.0mmc � cap mass 100.0 ton

Steel beams

Npl �number of planes of beam units 1lcsb � total length of beam units in one plane 15.0m

ρbs �mass density of beam steel 8020.0 kg/m3

Ebs � elastic modulus of beam steel 200.0GPaEbst � tangent modulus of beam steel 1.5 GPaεbsu � failure strain of beam steel 0.25

Pier wp � pier width 6.0m

0

1

2

3

4

0 1 2 3 4 5t (s)

W (M

Nm

)

(a)

rcsb

(%)

diss

0.8 0.9 1.0 1.1 1.280

85

90

95

100

MCbi (−)

(b)

Figure 7: Time histories of energy absorbed by the device (a) corresponding to di�erent beam cross-section dimensions and the ratio ofenergy absorbed by the device after impact to the total impact energy, respectively, versus MCbi (b). ,Wcsb

diss (MCbi � 0.8); ,Wcsbdiss

(MCbi �1.0); ,Wcsbdiss (MCbi �1.2); ,Wtotal; , the ratio of energy absorbed by the device after impact to the total impact energy.

Advances in Civil Engineering 5

absorbed by the device after impact to the total impactenergy are also presented. Figure 7 shows that a large portionof the impact energy is absorbed by the device and that theincrease of beam cross-section dimension reduces the energyabsorbed by the device due to the decrease of structuredeformation caused by the increase of structure sti�ness, asshown in Figure 8, where the maximum bending momentdiagram of the structure during impact and the structurede�ection after impact corresponding to each beam cross-section dimension are presented.

�e moment-curvature relationship of each beam crosssection and the moment-rotation relationship of a singlesteel beam corresponding to each beam cross-section di-mension are shown in Figure 9, where c is the curvature ofbeam cross section and θb is the relative rotation angle of twoboundary sections of a single steel beam. Figures 8 and 9show that the plastic hinges which form during impactare located at the upper part of the structure, that is, thehorizontal beams at the top and the upper part of thevertical beams, where the maximum bending momentexceeds the corresponding yielding moment of beam crosssection. �e formation of plastic hinges enables the deviceto absorb a large portion of energy during impact, as shownin Figure 7. �e lower part of the structure, that is, thehorizontal beams at the bottom and the lower part of thevertical beams, undergoes only elastic deformations, asFigure 8 shows.

x (m)0 3 6 9 12 15 18

−1

1

3

5

7

9

1.5

3.94.5

1.9 2.0

4.4

3.8

1.5

0

y (m

)

(a)

0 3 6 9 12 15 18−1

1

3

5

7

9

2.5

7.6

8.2

3.4 3.4

8.2 7.4

2.6

0

x (m)

y (m

)

(b)

0 3 6 9 12 15 18−1

1

3

5

7

9

3.5

12.8

13.5

5.0 4.8

13.4

12.7

3.50

x (m)

y (m

)

(c)

Figure 8: Maximum bending moment diagrams of the structuresduring impact and de�ections of the structures after impact corre-sponding to di�erent beam cross-section dimensions (unit: MNm).

, original shape of the device; , deformed shape of the device.(a) MCbi � 0.8; (b) MCbi � 1.0; (c) MCbi � 1.2.

0.0 0.1 0.2 0.30

5

10

15

20

γ (m−1)

M (M

Nm

)

(a)

0.0 0.2 0.4 0.6 0.8 1.00

5

10

15

20

M (M

Nm

)

b (rad)θ

(b)

Figure 9: Moment-curvature relationships of the I cross sections(a) and moment-rotation relationships of single steel beams(b) corresponding to di�erent beam cross-section dimensions.

, MCbi � 0.8; , MCbi � 1.0; , MCbi � 1.2.

6 Advances in Civil Engineering

�e time histories of impact force on the pier with thedevice corresponding to each beam cross-section dimensionand without the device, respectively, together with the re-duction ratio (rf ) of maximum impact force when the deviceis used, are shown in Figure 10, which shows that themaximum impact force can be signi�cantly reduced whenthe device is used. �e increase of beam cross section wouldincrease the magnitude of impact force due to the increase ofcross-section �bres.

5.2. Yielding Strength of Beam Steel. �ree steel yieldingstrengths of 250.0MPa, 350.0MPa, and 450.0MPa, re-spectively, are considered herein. �e energy absorbed bythe device (Wcsb

diss) during impact corresponding to each steelyielding strength is shown in Figure 11, where the totalimpact energy (Wtotal) and the ratio (rcsbdiss) of energyabsorbed by the device after impact to the total impactenergy are also presented. Figure 11 shows that the increaseof steel yielding strength reduces the energy absorbed by thedevice during impact.�is is because the structure resistanceincreases with the increase of steel yielding strength andconsequently the structure undergoes smaller deformations,as shown in Figure 12.

�e time histories of impact force on the bridge pier withthe device corresponding to each steel yielding strength andwithout the device, respectively, together with the reductionratio of maximum impact force when the device is used, areshown in Figure 13, which shows that the increase of steelyielding strength would increase the magnitude of impactforce on the pier due to the increase of structure resistance.

5.3. Number of Beam Units. �e devices of one beam unit,two beam units, and three beam units, respectively, areconsidered herein.�e energy absorbed by the device (Wcsb

diss)during impact corresponding to each beam unit number isshown in Figure 14, where the total impact energy (Wtotal) andthe ratio (rcsbdiss) of energy absorbed by the device after impactto the total impact energy are also presented. Figure 14 showsthat the increase of beam unit number slightly reduces theenergy absorbed by the device. �is is because the structurebecomes sti�er when more beam units are used, as indicatedin Figures 15 and 16 which show that the structure undergoessmaller de�ections and smaller deformations during impactwhen more beam unit number is used.

�e time histories of impact force on the pier with thedevice corresponding to each beam unit number andwithout the device, respectively, together with the reductionratio (rf ) of maximum impact force when the device is used,are shown in Figure 17, which shows that the magnitude ofimpact force on the pier increases when beam unit numberincreases due to the increase of structure sti�ness.

6. Cost-Optimized Design of the Device

�e studies in the previous section have shown the greatpotentiality of the proposed crashworthy device for pier pro-tection from barge impact due to its large energy dissipationcapacity during impact. In order to achieve cost-optimized

0 1 2 3 4 50

10

20

30

40

t (s)

F (M

N)

(a)

0.00 0.02 0.04 0.06 0.08 0.100

10

20

30

40

t (s)

F (M

N)

(b)

0.8 0.9 1.0 1.1 1.280

85

90

95

100

MCbi (−)

r f (%

)

(c)

Figure 10: Impact force time histories on the bridge pier for the wholeimpact process (a), for the �rst 0.10 s of impact process (b) corre-sponding to di�erent beam cross-section dimensions, and the reductionratio of maximum impact force versus MCbi (c). , without thedevice; , MCbi � 0.8; , MCbi � 1.0; , MCbi � 1.2.

Advances in Civil Engineering 7

design of such device for a given impact scenario, a mathe-matical optimization model is proposed in this section withconstraints as per the prescribed design requirements.

6.1. Mathematical Optimization Model. For a given bargemass (mb) and impact velocity (vb), when the number ofplanes of beam units (Npl), the yielding strength of beamsteel (fbs

y ), and the maximum allowable impact force Fallowmax

on the bridge pier are speci�ed, the device can be designed insuch a way that the design requirements are satis�ed and therequired cost is minimized by using minimum amount ofsteel. �e design of the device can thus be transformed intoan optimization problem where the number of beam units inone plane (Nbu), the four dimensional parameters of the Icross section, that is, hbi,wbi, tfi, and twi, and the length of each

single steel beam lsb are optimized. For simpli�cation pur-poses, the four dimensional parameters of the I cross sectionare assumed to satisfy the relationships as tabulated in Table 2.

�e optimization model and the corresponding con-straints are described as follows:

minimize:

msb � 4Nbu + 1( )lsbAINplρbs, (1)

0 1 2 3 4 50

1

2

3

4

t (s)

W (M

Nm

)

(a)

80

85

90

95

100

250 300 350 400 450f bs (MPa)y

rcsb

(%)

diss

(b)

Figure 11: Time histories of energy absorbed by the device (a)corresponding to di�erent yielding strengths of beam steel andthe ratio of energy absorbed by the device after impact to thetotal impact energy, respectively, versus yielding strength ofbeam steel fbs

y (b). , Wcsbdiss (fbs

y � 250.0MPa); , Wcsbdiss

(fbsy � 350.0MPa); ,Wcsb

diss (fbsy � 450.0MPa); ,Wtotal; ,

the ratio of energy absorbed by the device after impact to thetotal impact energy.

0 3 6 9 12 15 18−1

1

3

5

7

9

2.5

5.7

6.3

3.0 3.0

6.3 5.6

2.1

0

x (m)

y (m

)

(a)

0 3 6 9 12 15 18−1

1

3

5

7

9

2.5

7.68.2

3.4 3.4

8.2 7.4

2.60

x (m)

y (m

)

(b)

0 3 6 9 12 15 18−1

1

3

5

7

9

2.5

9.410.2

3.4 3.2

10.1 9.3

2.50

x (m)

y (m

)

(c)

Figure 12: Maximum bending moment diagrams of the structuresduring impact and de�ections of the structures after impact cor-responding to di�erent yielding strengths of beam steel (unit:MNm). , original shape of the device; , deformed shapeof the device. (a) fbs

y � 250.0MPa; (b) fbsy � 350.0MPa;

(c) fbsy � 450.0MPa.

8 Advances in Civil Engineering

subject to:

5hbi ≤ lsb, (2)

Nlbu ≤Nbu ≤N

ubu, (3)

hlbi ≤ hbi ≤ hubi, (4)

llsb ≤ lsb ≤ lusb, (5)

Fmax ≤Fallowmax , (6)

Dmaxcap ≤D

allowmax � Nbulsb, (7)

wheremsb is the total mass of steel beams (ton),AI is the areaof the I cross section (m2), ρbs is the mass density of beamsteel (ton/m3),Nl

bu and Nubu are the lower bound and upper

bound of the number of beam units in one plane (–), re-spectively, hlbi and h

ubi are the lower bound and upper bound

of the depth of the I cross section (m), respectively, llsb and lusb

are the lower bound and upper bound of beam length (m),respectively, Fmax is the maximum impact force on thebridge pier during impact (MN), Dmax

cap is the maximum capdisplacement during impact (m), andDallow

max is the maximumallowable cap displacement (m). �e value of Dallow

max is takento be Nbulsb to avoid the contact of adjacent vertical beamsduring impact.

0 1 2 3 4 50

10

20

30

40

t (s)

F (M

N)

(a)

0.00 0.02 0.04 0.06 0.08 0.100

10

20

30

40

t (s)

F (M

N)

(b)

250 350 45080

85

90

95

100

r f (%

)

f bs (MPa)y

(c)

Figure 13: Impact force time histories on the bridge pier for the whole impact process (a), for the �rst 0.10 s of impact process (b)corresponding to di�erent yielding strengths of beam steel and the reduction ratio of maximum impact force versus yielding strength ofbeam steel fbs

y (c). , without the device; , fbsy � 250.0MPa; , fbs

y � 350.0MPa; , fbsy � 450.0MPa.

0 1 2 3 4 50

1

2

3

4

t (s)

W (M

Nm

)

(a)

1 2 380

85

90

95

100

Nbu (−)

rcsb

(%)

diss

(b)

Figure 14: Time histories of energy absorbed by the device (a) corresponding to di�erent beam unit numbers and the ratio of energyabsorbed by the device after impact to the total impact energy, respectively, versus beam unit number in one plane Nbu (b). ,Wcsb

diss (Nbu �1); ,Wcsbdiss (Nbu � 2); ,Wcsb

diss (Nbu � 3); ,Wtotal; , the ratio of energy absorbed by the device after impact tothe total impact energy.

Advances in Civil Engineering 9

�ree variables, that is, Nbu, hbi, and lsb, are included inthe optimization process. �e sequential quadratic pro-gramming (SQP) [16] is used for solving the proposedconstrained optimization problem.

6.2. Application Example. In this section, the optimumcon�gurations of the devices corresponding to several dif-ferent impact scenarios are obtained using the proposedoptimization model. �e combinations of three barge

0 1 2 3 4 50.0

0.5

1.0

1.5

2.0

2.5

t (s)

Dca

p (m

)

(a)

1 2 31.0

1.3

1.6

1.9

2.2

2.5

Nbu (−)

Dm

ax (m

)ca

p

(b)

Figure 15: Time histories of cap displacement corresponding to di�erent beam unit numbers (a) and maximum cap displacement Dmaxcap

versus beam unit number in one plane Nbu (b). , Nbu � 1; , Nbu � 2; , Nbu � 3.

x (m)0 3 6 9 12 15 18

−1

1

3

5

7

9

3.1

8.0 8.1

2.9

0

y (m

)

(a)

0 3 6 9 12 15 18−1

1

3

5

7

9

2.5

7.6 8.2

3.4 3.4

8.2

7.4

2.60

x (m)

y (m

)

(b)

0 3 6 9 12 15 18−1

1

3

5

7

9

1.7

7.17.6

3.2

3.6

8.4 8.4

3.5 3.0

7.67.2

1.70

x (m)

y (m

)

(c)

Figure 16: Maximum bending moment diagrams of the structures during impact and de�ections of the structures after impact corre-sponding to di�erent beam unit numbers (unit: MNm). , original shape of the device; , deformed shape of the device. (a)Nbu � 1;(b) Nbu � 2; (c) Nbu � 3.

10 Advances in Civil Engineering

masses, that is, 181.4 ton (empty barge), 952.6 ton (halfloaded barge), and 1723.7 ton (fully loaded barge), and threeimpact velocities, that is, 1.0m/s, 3.0m/s, and 5.0m/s, areconsidered herein. Each impact scenario is labeled as ISij,where i denotes the number index of barge mass varyingfrom 1 to 3 and j denotes the number index of impactvelocity varying from 1 to 3, as tabulated in Table 3. �e capsurface which contacts with the barge is �at and is 3.0m inwidth. �e cap mass (mc) is taken to be 100.0 ton. �enumber of planes of beam units (Npl) is taken to be two.�eyielding strength of beam steel (fbs

y ) is taken to be350.0MPa, and themaximum allowable impact force (Fallow

max )on the bridge pier is taken to be 5.0MN. �e information ofthe prespeci�ed parameters regarding the structure is tab-ulated in Table 4.

�e optimum parameters generated by the proposedoptimization model, the total masses of beam steel, and thecon�gurations of optimum devices corresponding to di�erentimpact scenarios are tabulated in Table 5.�e total number ofbeam units (Ntotal

bu �Nbu ×Npl) and the total mass of beamsteel (msb) used by the optimum device plotted against totalbarge impact energy (Wtotal) are shown in Figure 18, whichshows that Ntotal

bu increases to four, corresponding to twobeam units in one plane, when Wtotal reaches around5.0MNm. �is is because the maximum cap displacement(Dmax

cap ) increases with the increase of Wtotal, as shown inFigure 19. When Wtotal reaches around 5.0MNm, Dmax

cap in-creases to such a level that two beam units in one plane areneeded to increase the maximum allowable cap displacement

(Dallowmax ) based on (7), enablingDmax

cap to be lower thanDallowmax to

satisfy the design requirement. It is also shown in Figure 18that msb approximately shows linear dependency on Wtotal,indicating that msb is approximately directly proportional tobarge mass while an increase of impact velocity could lead toa roughly quadratic increase of msb.

�e maximum cap displacements (Dmaxcap ) and maxi-

mum impact forces (Fmax) on the pier corresponding todi�erent impact scenarios are tabulated in Table 6, whichshows that for each impact scenario, Dmax

cap is smaller thanDallow

max and Fmax is smaller than Fallowmax (5.0MN); thus thedesign requirements can be satis�ed for all impact sce-narios.�emaximum impact forces (Funprot

max ) on the pier fordi�erent impact scenarios without using the optimumdevices are also tabulated in Table 6 along with the re-duction ratio (rf ) of maximum impact forces when theoptimum devices are used. It is shown in Table 6 that theoptimum device can signi�cantly reduce the maximumimpact force on the pier by more than 90.0% for di�erentimpact scenarios. Table 6 indicates that for a given impactvelocity, Funprot

max is not strongly in�uenced by barge mass.�is phenomenon has been explained in detail in [8]. It isalso indicated from Table 6 that Dmax

cap is often close to or

0 1 2 3 4 50

10

20

30

40

t (s)

F (M

N)

(a)

0.00 0.02 0.04 0.06 0.08 0.100

10

20

30

40

t (s)

F (M

N)

(b)

1 2 380

85

90

95

100

Nbu (−)

r f (%

)

(c)

Figure 17: Impact force time histories on the bridge pier for the whole impact process (a), for the �rst 0.10 s of impact process(b) corresponding to di�erent beam unit numbers, and the reduction ratio of maximum impact force versus beam unit number Nbu (c).

, without the device; , Nbu � 1; , Nbu � 2; , Nbu � 3.

Table 2: Relationships of I cross-section dimensional parameters.

Ratio Value (–)wbi/hbi 1.0tfi/hbi 0.05twi/hbi 0.03

Table 3: Impact scenarios considered for structure optimization.

Impact scenario mb (ton) vb (m/s)IS11 181.4 1.0IS12 181.4 3.0IS13 181.4 5.0IS21 952.6 1.0IS22 952.6 3.0IS23 952.6 5.0IS31 1723.7 1.0IS32 1723.7 3.0IS33 1723.7 5.0

Advances in Civil Engineering 11

equal to Dallowmax . ,is is because for a given impact scenario,

decreasing the amount of beam steel would reduce thestructure stiffness and consequently lead to the increase ofDmax

cap until the point where Dmaxcap approximately reaches

Dallowmax and the optimum solution is attained.,emaximum bendingmoment diagrams and deflections of

the optimumdevices corresponding to impact scenarios IS31, IS32,and IS33 are shown in Figure 20, which shows that the horizontalbeams at the top and two vertical beams in themiddle experienceapparent plastic deformations after impact, enabling the devices toabsorb high energy during impact, as shown in Figure 21.

7. Summary

,is paper devised a novel crashworthy device for pierprotection from barge impact and conducted parametricstudies to investigate the effectiveness of the proposeddevice using the simplified impact model. A mathematicaloptimization model was developed with constraints as perthe prescribed design requirements to achieve cost-optimized design of the device for a given impact scenario.

,e studies indicate that the proposed crashworthydevice has a large energy dissipation capacity due to the

Table 5: Optimum parameters, total masses of beam steel, and configurations of optimum devices corresponding to different impactscenarios.

Impactscenario Nbu (–) hbi (m) lsb (m) msb (ton) Optimum structure

configurationIS11 1 0.20 1.00 0.41IS12 1 0.25 1.26 0.82

IS13 1 0.35 1.76 2.22

IS21 1 0.23 1.16 0.64

IS22 2 0.41 2.04 6.23

IS23 2 0.57 2.83 16.62

IS31 1 0.29 1.43 1.19

IS32 2 0.50 2.51 11.60

IS33 2 0.70 3.48 30.77

Table 4: Prespecified parameters for structure optimization.

Member Parameter Value

Barge mb � barge mass 181.4 ton ∼ 1723.7 tonvb � impact velocity 1.0m/s ∼ 5.0m/s

Cap wc � cap width 3.0mmc � cap mass 100.0 ton

Steel beams

Npl � number of planes of beam units 2ρbs �mass density of beam steel 8020.0 kg/m3

Ebs � elastic modulus of beam steel 200.0GPaEbst � tangent modulus of beam steel 1.5GPa

fbsy � yielding strength of beam steel 350.0MPaεbsu � failure strain of beam steel 0.25

Design requirements

Nlbu � lower bound of Nbu 1

Nubu � upper bound of Nbu 10

hlbi � lower bound of hbi 0.2m

hubi � upper bound of hbi 1.0m

llsb � lower bound of lsb 1.0mlusb � upper bound of lsb 5.0m

Fallowmax �maximum allowable force on pier 5.0MN

12 Advances in Civil Engineering

0 5 10 15 20 250

1

2

3

4

5

Wtotal (MNm)

From le� to right: IS11; IS21; IS12; IS31

IS13

IS22 IS32 IS23 IS33

Nto

tal (−

)bu

(a)

0 5 10 15 20 250

5

10

15

20

25

30

35

Wtotal (MNm)

msb

(ton

)

From le� to right: IS11; IS21; IS12; IS31IS13

IS22

IS32

IS23

IS33

(b)

Figure 18: �e total number of beam unitsNtotalbu and the total mass of

beam steelmsb used by the optimum device versus barge impact energyWtotal (Npl � 2).

0 5 10 15 20 250

2

4

6

8

Wtotal (MNm)

IS11

From le� to right: IS21; IS12; IS31; IS13

IS22

IS32

IS23

IS33

Dm

ax (m

)ca

p

(a)

0 5 10 15 20 250

1

2

3

4

5

Wtotal (MNm)

F max

(MN

)

From le� to right: IS11; IS21; IS12; IS31

IS13

IS22

IS32

IS23

IS33

(b)

Figure 19: Maximum cap displacement Dmaxcap (a) and maximum

impact force on the bridge pier Fmax (b) versus barge impact energyWtotal using the optimum device.

Table 6: Maximum cap displacements and maximum impact forces on the pier using or without using optimum devices corresponding todi�erent impact scenarios.

Impact scenario Dmaxcap (m) Dallow

max (m) Fmax (MN) Funprotmax (MN) rf � 100 × (Funprotmax −Fmax)/F

unprotmax (%)

IS11 0.23 1.00 0.30 16.24 98.15IS12 1.26 1.26 0.50 39.90 98.75IS13 1.75 1.76 1.03 47.57 97.83IS21 1.16 1.16 0.41 27.24 98.50IS22 4.07 4.08 1.52 39.68 96.17IS23 5.64 5.66 2.99 48.53 93.84IS31 1.43 1.43 0.63 27.18 97.68IS32 5.01 5.02 2.41 39.45 93.89IS33 6.95 6.95 4.56 48.63 90.62

Advances in Civil Engineering 13

formation of plastic hinges in the structure during impact.�ese number and location of plastic hinges, and con-sequently the energy that can be absorbed, is determinedby the design of the frame-like steel beam arrangement.�e studies show that the magnitude of the impact forcetransmitted to the main bridge pier can be dramaticallyreduced when the device is properly designed and installedand that the maximum force transmitted can be chosen aspart of the device design. Amathematical optimization modelproposed in this paper can be used for obtaining the optimum

0 4 8 12 16 20−1

1

3

5

7

9

0.17

0.55 0.55

0.17

x (m)

y (m

)

(a)

0 4 8 12 16 20−1

1

3

5

7

9

1.08

2.51

3.17

1.54 1.51

3.14

2.49

1.04

x (m)

y (m

)

(b)

0 4 8 12 16 20−1

1

3

5

7

9

2.73

6.56

8.36

3.99 4.05

8.43

6.56

2.80

x (m)

y (m

)

(c)

Figure 20: Maximum bending moment diagrams of the optimumdevices during impact and de�ections of the structures after theimpact corresponding to the impact scenarios (a) IS31, (b) IS32, and(c) IS33 (unit: MNm). , original shape of the device; ,deformed shape of the device.

0 2 4 6 8 100.0

0.2

0.4

0.6

0.8

1.0

t (s)

W (M

Nm

)

(a)

0 2 4 6 8 100

2

4

6

8

t (s)

W (M

Nm

)

(b)

0 2 4 6 8 100

5

10

15

20

25

t (s)

W (M

Nm

)

(c)

Figure 21: Energy absorbed by the optimum device ( ) and thetotal impact energy ( ) during impact corresponding to theimpact scenarios (a) IS31, (b) IS32, and (c) IS33.

14 Advances in Civil Engineering

configuration of the device which satisfies the design require-ments for a given impact scenario.

,e concept proposed here can be extended further toother configurations, for example, symmetrical or entwinedarrangements which avoid vertical displacements or reducethe device’s overall dimensions, respectively.

,e device concept presented and the analysis modeladopted have the potential to rationalize ship impact pro-tection and thus to provide cost-effective future protectionsolutions.

Conflicts of Interest

,e authors declare that there are no conflicts of interestregarding the publication of this paper.

Acknowledgments

,e authors wish to thank the China Scholarship Councilfor providing scholarship to W. Wang for conducting thestudy.

References

[1] S. E. Manen and A. G. Frandsen, “Ship collision with bridges,review of accidents,” in Ship Collision Analysis, H. Gluver andD. Olsen, Eds., pp. 3–11, Balkema, Rotterdam, Netherlands,1998.

[2] O. D. Larsen, Ship Collision with Bridges, the Interactionbetween Vessel Traffic and Bridge Structures, IABSE, Zuerich,Switzerland, 1993.

[3] P. Yuan, Modeling, Simulation, and Analysis of Multi-BargeFlotillas Impacting Bridge Piers, Ph.D. thesis, Department ofCivil Engineering, University of Kentucky, Lexington, Ken-tucky, 2005.

[4] C. H. Cao, Simplified Static and Dynamic Analysis for Barge-Bridge Collision, M.S. thesis, Department of Bridge Engineering,Tongji University, Shanghai, China, 2010, in Chinese.

[5] Y. Y. Sha and H. Hao, “Laboratory tests and numericalsimulations of barge impact on circular reinforced con-crete piers,” Engineering Structures, vol. 46, pp. 593–605,2013.

[6] Y. Y. Sha and H. Hao, “Laboratory tests and numericalsimulations of CFRP strengthened RC pier subjected to bargeimpact load,” International Journal of Structural Stability andDynamics, vol. 15, no. 2, p. 1450037, 2015.

[7] Y. Y. Sha and H. Hao, “Nonlinear finite element analysis ofbarge collision with a single bridge pier,” Engineering Struc-tures, vol. 41, pp. 63–76, 2012.

[8] W. Wang and G. Morgenthal, “Dynamic analyses of squareRC pier column subjected to barge impact using efficientmodels,” Engineering Structures, vol. 151, pp. 20–32, 2017.

[9] R. Saul, K. Humpf, and A. Patsch, “,e Rosario-Victoriacable-stayed bridge across the river Paraná in Argentinaand its ship impact protection system,” in Proceedings of theFirst International Conference on Steel and Composite Struc-tures, pp. 1011–1018, Pusan, South Korea, June 2001.

[10] G. Morgenthal and R. Saul, “Die Geh- und RadwegbrueckeKehl–Strasbourg,” Stahlbau, vol. 74, no. 2, pp. 121–125, 2005,in German.

[11] M. Knott, “Pier protection system for the sunshine skywaybridge replacement,” in Proceedings at 3rd Annual In-ternational Bridge, pp. 56–61, Pittsburghn, PA, USA, 1986.

[12] B. C. Simonsen andN. Ottesen-Hansen, “Protection of marinestructures by artificial islands,” in Proceedings of the In-ternational Symposium on Advances in Ship Collision Analysis,Balkema Publishers, pp. 201–215, Copenhagen, Denmark,May 1998.

[13] H. Svensson, “Protection of bridge piers against ship colli-sion,” Steel Construction, vol. 2, no. 1, pp. 21–32, 2009.

[14] R. Pinzelli and K. Chang, “Reinforcement of bridge piers withFRP sheets to resist vehicle impact: tests on large concretecolumns reinforced with aramid sheets,” in Proceedings of theInternational Conference on FRP Composites in Civil Engi-neering, pp. 12–15, Hong Kong, China, December 2001.

[15] T. N. Le, J. M. Battini, and M. Hjiaj, “Corotational dynamicformulation for 2d beams,” in ECCOMAS ;ematic Confer-ence on Computational Methods in Structural Dynamics andEarthquake Engineering, Corfu, Greece, May 2011.

[16] W. Hock and K. Schittkowski, “A comparative performanceevaluation of 27 nonlinear programming codes,” Computing,vol. 30, no. 4, pp. 335–358, 1983.

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