Modeling and Development of Impact Loads on Marine Structures Due to Vessel Collision

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The collapse of the Francis Scott Key Bridge in Baltimore in March 2024 renewed focus on one of structural engineering’s most demanding challenges: developing and modeling impact loads on marine infrastructure due to vessel collision. While the probability of ship impact has been reduced over time with advances in navigation systems, AIS (automatic identification system) tracking, and vessel traffic management, it has not been eliminated. Marine structures, including bridge piers, dolphins (man-made structures of wood, steel, or concrete installed to protect substructures), offshore platforms, and port facilities, are often located in heavily trafficked waterways. These structures are exposed to vessels that can range from smalls crafts to large container ships exceeding 400 meters in length. While collision events are relatively rare, their consequences can be severe involving progressive structural failure, loss of life, and major economic disruption. Because these low probability events carry high load demand, a highly rigorous, mechanics-based approach to impact load development and structural modeling may be necessary.

Unlike standard loads such as gravity loads, vessel impact is fundamentally an energy dissipation problem. It is highly transient, nonlinear, and event driven by force interaction between deformable bodies. The impact load emerges from the dynamic exchange of energy and momentum between the vessel, structure, and foundation system and the stiffness of the structure and the vessel. Vessel collision should therefore be treated as an energy dissipation problem rather than a static force application. The total kinetic energy during the collision event depends on the displacement mass of the vessel, the additional mass due to hydrodynamic effects, and the impact velocity. The additional mass from hydrodynamic effects accounts for the immense volume of water traveling with the ship around the hull, which significantly amplifies the total effective mass of the vessel.

During impact, kinetic energy of the vessel is dissipated and absorbed simultaneously through several distinct mechanisms. A large portion of the energy is absorbed by the deformation of the structure and the vessel bow crushing. The vessel bow undergoes progressive plastic crushing through the sequential collapse of its hull and internal framing. The stationary structure absorbs energy through localized deformation and damage and, in severe events, global lateral displacement. A fraction of the energy is absorbed by the lateral compression of the surrounding soil, rearrangement of soil particle grains under lateral demand, and compaction of soil beneath the foundation units as axial loads redistribute during impact. Partial uplift of the vessel hull against the water surface further dissipates a portion of the collision energy. Because it is difficult to quantify every dissipation mechanism accurately, models should be simplified by purposefully neglecting non-governing mechanisms.

To perform an impact analysis, one or more design vessels must be determined and agreed upon by all stakeholders, including the owner of the structure and governing agencies. The magnitude and character of the impact load are directly governed by the design vessel. Impact energy scales linearly with mass and the square of velocity, meaning a smaller, faster powered vessel may produce a more demanding load than a larger, slowly drifting one.

If the protection is sized for largest possible impact, it might result in a massive and cost-prohibited protection system, especially for waterways used by large vessels. Therefore, the design vessel is selected using a probability-based analysis procedure in which the predicted annual frequency of collapse is compared to an acceptance criterion. The AASHTO LRFD Bridge Design Specifications (10th edition, 2024) and the AASHTO Guide Specifications for Vessel Collision Design of Highway Bridges (2010) provide three frameworks—Method I (Deterministic Analysis), Method II (Probabilistic Analysis), and Method III (Risk Based, Economic Analysis) for vessel selection based on waterway traffic composition and acceptable risk thresholds.

Per AASHTO Method II analysis, the acceptable Annual Frequency of Collapse (AF) is <0.0001 for Critical/Essential Bridges and <0.001 for Typical Bridges (The operational importance classification should be decided by the bridge’s owner). The AF is estimated as:

AF = (N) (PA) (PG) (PC) (PF)
Where:
N = Annual Number of Vessels
PA = Probability of Vessel Aberrancy
PG = Geometric Probability
PC = Probability of Collapse
PF = Protection Factor

This framework directly informs the severity of the impact load to be developed, linking structural demand to pre-determined quantified risk rather than arbitrary worst-case assumptions.
Past research has attempted to translate complex collision scenarios into quantified impact loads that can be used for design. Minorsky (Minorsky, V.U.: “An Analysis of Ship Collision with Reference to Protection of Nuclear Power Plants,” Journal of Ship Research, Vol. 3, 1959) relates the volume of structural material destroyed to absorbed kinetic energy, establishing the foundational energy-based framework for impact assessment. Pedersen and Zhang (Pedersen, P.T.; Zhang, S. “On Impact Mechanics in Ship Collisions,” Mar. Struct. 1998, 11, 429–449.) advanced this by accounting for bow geometry, deformation mechanics, and energy partitioning between vessel and structure—a more physically complete model validated against documented collision events.

The AASHTO LRFD Bridge Design Specifications (10th edition, 2024) provides an equivalent static force as a function of vessel deadweight tonnage and impact velocity. (A3.14.8) Force resulting from a barge collision is also included in the Specification. Additional factors including structural type and shape of the ship’s bow, amount of ballast carried in the bow, size and velocity of the ship, geometry of the collision, and geometry and strength characteristics of the pier or protection system, are assumed and not included as variables in these equations. While practical for preliminary design, it simplifies a complex dynamic event into a single static value, failing to capture time-dependent load development, structural flexibility effects, or impulse characteristics governing dynamic response. AASHTO LRFD allows for a more rigorous analysis procedure to be used in lieu of the static analysis procedure.

A detailed model requires defining the ship bow force–deformation relationship. As the ship strikes the structure, its bow acts as a crumple zone. As the bow contacts and crushes against the structure, resistance builds progressively, reflecting the sequential collapse of bow framing. This nonlinear curve, when integrated with deformation, equals the energy absorbed by the vessel—directly linking load development to energy balance and serving as the primary input for dynamic structural analysis. Exact specifications and details of the design vessel are required to perform this modeling effort. Any information about the design vessel, if it is even available, would only represent the specific design vessel at the time of modeling. Other vessels using the channel would perform differently. Additionally, any changes in vessel traffic during the life of the structure would not be accounted for. Probable vessel traffic changes should be accounted for during the design of any protection structure.

The impact load must be expressed as a force–time history for dynamic analysis. This is derived by coupling the nonlinear bow force–deformation relationship with the vessel equation of motion, producing a time-varying contact force that rises rapidly to a peak and decays as the vessel decelerates. The shape of this profile is governed by the relative stiffness of the bow and the impacted structure.

Peak force depends critically on system stiffness. Stiffer structures generate higher peak forces over shorter contact durations, while flexible systems extend contact duration and reduce peak demand. This relationship has direct implications for both load development and structural design. The impulse of the force–time history must equal the change in vessel momentum. This momentum balance is a fundamental mechanical constraint and an essential validation check. Force histories violating this condition are physically inconsistent and must be rejected regardless of how they were derived.

The geometry of the bow as it contacts the structure governs the spatial load distribution. Sharp bows form concentrate loads over small contact areas, producing intense local stresses, while blunt geometries distribute pressure more broadly. Adequate mesh refinement at the contact interface is therefore essential in finite element models, as coarse discretization misrepresents pressure localization and distorts both peak force magnitude and distribution. Similar to other conditions, this requires detailed information of the design vessel.

In the case of Vessel Collision analysis, software that specializes in soil-structure interaction can be instrumental in determining the reaction of the structure. A soil specific software, such as FB-MultiPier (Bridge Software Institute), provides detailed nonlinear characterization of the pile foundation system. This governs both the transmission of impact loads into the ground and the energy dissipated through soil–structure interaction. By calculating p–y curves to represent lateral soil resistance along pile depth, the full range of foundation behavior can be captured, incorporating soil grain disturbance, lateral compression around pile shafts, and compaction beneath pile tips.

The resulting lateral stiffness characteristics and nonlinear response curves are transferred into a structural modeling software, such as LUSAS Infrastructure design software (finite element analysis). The structural software is used to appropriately represent the complex structural response. The p-y curves are included in the structural software to ensure that the foundation flexibility and soil energy absorption are physically consistent with the global structural analysis. The structural model provides an advanced finite element environment in which derived force–time histories are applied through transient dynamic analysis, capturing inertial effects, dynamic amplification, and structural wave propagation that static methods cannot represent. Material nonlinearity, geometric nonlinearity, and soil–structure interaction are all accommodated. Fender systems are represented as nonlinear springs within LUSAS, capturing their progressive force–deformation behavior and energy absorption directly within the structural model.

For a vessel collision model to most accurately represent the actual conditions, the balance of energy must be satisfied. The vessel’s initial kinetic energy should account for all possible dissipation mechanisms—bow crushing, structural deformation, soil grain disturbance, pile tip compaction, vessel hull uplift, etc. Models that inadequately represent any of these pathways risk misallocating energy, either inflating or underestimating the peak structural forces transmitted to the structure. However, accounting for all possible mechanisms is seldom possible, and conservative assumptions should be made to account for any uncertainty. Any results should be cross-checked against momentum balance and energy partitioning to produce physically credible impact load predictions for marine structure design.

In the design environment, not all information can be known with enough accuracy to create a detailed model. One example of this includes the use of a design vessel that conservatively represents the vessel traffic. As this is not intended to be an actual vessel, a detailed vessel model cannot be created. In these cases, conservative and accepted assumptions should be made, such as the equations for length of bow damage included in the AASHTO LRFD Specification, for the design of the marine structure. ■

Adrienne Crider, PE, is a senior project manager with Modjeski and Masters, Inc. with more than 20 years of experience in the design, rehabilitation, and analysis of movable and fixed bridges. She has led and contributed to the structural design, analysis, and rating of numerous bridge projects across the U.S.