Proceedings of the Thirty-second (2022) International Ocean and Polar Engineering Conference
Shanghai, China, June 5–10, 2022
Copyright © 2022 by the International Society of Offshore and Polar Engineers (ISOPE)
ISBN 978-1-880653-81-4; ISSN 1098-6189

www.isope.org

Equivalent calculation method of impact force for ship-bridge collision using simplified model
Tao Wanga , Jin Pana , Ming Cai Xub,ca Department of Naval Architecture, Ocean and Structural Engineering, School of Naval Architecture, Ocean and Energy Power Engineering,Wuhan University of Technology, Wuhan, Hubei, China;b School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, Wuhan, Hubei, China
c Wuhan Lituo Bridge Protection Technology CO., LTD, Wuhan, Hubei, China

collapse of two side spans. During the above ship-bridge collisions,significant lateral loads imparted to pier structures leads to its collapse.
Therefore, engineers must account for lateral ship impact forces when
designing bridge structures over navigable waterways.
After decades of years’ research on ship-bridge impact accidents,
principle methods to calculate ship impact force are empirical formula
method and numerical analyses method. However, vessel impacts arefundamentally dynamic in nature, and the former, which is a static
analysis procedure, may not be adequate in designing bridge
substructures to resist vessel impacts, although it is very simple andpractical for bridge engineers. Numerical analyses methods are used toanalyze the impact force history under ship collisions, respectively: (1)explicit finite-element techniques generated by LSTC (2007); and (2)simplified analytical model of ship-bridge collision. Explicit finiteelement techniques can provide more accurate results and a visualfailure procedure of the ship and bridge. However, a large amount ofeffort to make models and time for calculation make this methodinconvenient and kind of unapproachable. Thus, a simplified model ofship-bridge collision was proposed to calculate the interaction force
between ship and pier quickly. The influence of dynamic crush stiffnessof ship bow, which depends on different impact velocities, was notconsidered in computing impact force histories since the static crush
curves of ship bows or specific impact-depth curves were used toanalyze the dynamic responses of pier. Thus, the reasons for its
inaccuracy to the results should be further discussed.
In recent years, impact force histories obtained from explicit finiteelement method and simplified model have been studied by manyscholars. Fan (2011) presented an alternative simplified interaction
model based on the results of explicit finite-element method to evaluate
the dynamic demand of bridge structure under vessel impact efficiently.
Consolazio (2005) proposed simplified model that leverages thecapabilities of existing nonlinear dynamic pier analysis programs bycoupling nonlinear barge and pier responses together in acomputationally efficient and modular manner. Yuan (2008) introduced
an elastoplastic spring-mass model for the analysis of multi-barge
flotillas colliding with bridge piers at zero angle of attack, which
accounted for the essential factors pertaining to ship impact, such aspier geometry and stiffness, and dynamic interaction between barges.
Song (2019) proposed a simplified analytical model for predicting thetime-history of ship impact loading on bridges and evaluated its
efficiency of the proposed model by a case study involving two bridge

ABSTRACTThe pier of a bridge crossing the river is susceptible to vessel impactthat may lead to bridge failure. To reliably assess pier dynamic
response during the collision accident and design the bridge piers toresist such impact efficiently, the impact force histories should beaccurately defined. In this paper, a 5,000DWT bulk carrier is modeledby explicit nonlinear software LS-DYNA. Meanwhile, a FE model ofship-rigid wall collision is developed and its impact force histories aswell as impact force-displacement curves are analyzed in detail. Aquasi-static method is employed to obtain the nonlinear static
relationships between crush force and depth of ship-bow. In
combination with static and dynamic deformation energy under various
impact velocities, the dynamic crush stiffness is taken account into
ship-bow stiffness during the collisions. In addition, a 2-DOF
simplified interaction model is presented to calculate ship impact
efficiently, which includes two mass points and two spring elements.
Based on the finite element software Midas civil, the dynamic
responses of a specific pier obtained from explicit finite-element
method (LS-DYNA) and the simplified model are compared,respectively. According to the analysis result, the range of application
for the simplified model is discussed.

KEY WORDS: Ship, Pier, Impact force, Dynamic response,Simplified model.

INTRODUCTION
Accidental ship collision is an important consideration in designing
bridge structures across navigable waterways. The high kinetic energyof passing ships will pose a serious threat to bridge structures. It wasnoted (Cowan, 2007) that many waterways have relatively shallow
channels, and therefore are unable to accommodate large-draft vessels.
It has been noted in the literature (Larsen, 1993) that, on average, atleast one serious ship collision occurs per year. For example, Michael(2018) pointed out that an empty 35,000 DWT bulk carrier collided
with one of the support piers of the Sunshine Skyway Bridge in theUSA in 1980, which lead to the collapse of bridge and 35 people losing
their lives. Sha (2012) indicated that in 2007, a cargo vessel ploughed
into the Jiujiang cable-stayed bridge in Guangdong, China, causing the3250