From TEKLA model through Final Design ANSYS model and detailed FEMAP/ANSYS models to reality (right).

The 100th anniversary of the Panama Canal was celebrated on Aug. 15, 2014. Meanwhile, the canal expansion project, including construction of a third set of locks, is in full swing. Upon completion of this megaproject, the canal will be able to accommodate passage for vessels with a maximum cargo capacity between 13,000 and 14,000 20-foot equivalent units. Situated approximately 88 feet higher than the two oceans it connects, the canal requires two new lock complexes to achieve this.

In 2009, Autoridad del Canal de Panama (ACP) awarded design and construction of the new locks to the contractors consortium GUPC. CICP, a consortium of engineering companies consisting of two U.S.-based engineering companies — MWH-Global and TetraTech — and the Netherlands-based engineering company Iv-Groep, bore responsibility for most of the engineering and design works. MWH Global is responsible for the overall design project management, hydraulic studies, and design of civil and geotechnical structures as well as the electrical, instrumentation, and controls. TetraTech is responsible for design of the valves required for the locks’ sophisticated filling and emptying system, as well as the water-saving basins and locks-approach structures. Iv-Groep has designed the 16 rolling lock gates and their drive mechanism.

The lock gates for the third set of locks basically consist of two orthotropic steel plates (skins) held apart by truss structures and plates forming the compartmented buoyancy chamber that, when submerged, reduce the operational weight carried by two rolling wagons. These steel structures, as large as 187 by 105 by 33 feet, will be supported by an upper wagon, running on rails situated in the gate recess, and a lower wagon, running on rails situated in the lock chamber. The gates are opened and closed by drive systems consisting of cables, winches, and sheaves.

Lock gate design dealt with many loading criteria, each in an unprecedented scale. The first phase of the design took place during the tender. In this phase, the basic design was determined, adhering to the employer’s requirements. After GUPC was awarded the project, the design was further developed in four phases: Preliminary, Intermediate, Final Design, and Detail Design. These phases comprised a fully engineered design of the lock gates, with dimensions, shaping, and layout of all individual members.

Apart from their enormous dimensions, the amount of ship lockages during the design life led to a design requirement to resist fatigue. On top of that, the area in which the locks are built is sensitive to severe earthquake action, which added another governing load case to the design. In addition, stringent requirements related to availability (99.6 percent), ship collision absorption, and leakage criteria resulted in additional design challenges. Especially so, since, in a multidisciplinary design where individual components are highly interactive, solving an issue at one place affects the design at other places.

Site-specific response spectra for the Pacific Lock Complex.

A collaborative Iv-Groep design team was put in place, with dedicated teams tackling individual design aspects and other teams safeguarding the integral compliance and integrity. The design team consisted of members from several Iv companies — Iv-Infra was responsible for the overall design, while Iv-Consult worked on the detailed design. Because of the tight schedule, this team had to be built up in a short time. In the peak pressure time, it included more than 80 full-time specialists in steel structures, finite element modelling, mechanical design, naval architecture, corrosion protection, and risk analysis. But the challenge was not just the size of project and its tight schedule; the complexity of the boundary conditions and design parameters played a significant role as well.

Real-time computer-aided design processing with TEKLA software functioned as the backbone in the project organization, which was kept up to date to generate the latest revision of drawings and to serve as input to the structural engineers. To optimize the structural weight of each gate type, the design team had to go through various iterations, adjusting the member sizes of the steel structure and analyzing them using ANSYS finite element analysis (FEA) software for the three governing load cases — dry outage, fatigue, and earthquake. Individual design updates were incorporated into the integral design on a continuous basis, allowing for instant checks for consequences and adjustments. The extensive organizational structure of multidisciplinary, yet specialist professionals enabled an integral design that meets all the criteria in an efficient manner.

Earthquake design

The lock gates are designed to meet the requirements of two levels of earthquake: Level I (essentially elastic design, 475-year return period) and Level II (plastic design, 1,000-year return period). The levels correspond to the following performance level criteria:

Level I earthquake:

  • Lock gates will sustain no permanent damage;
  • Damage should be repaired without interruption of operations;
  • Lock gates should operate without interruption after a seismic event; and
  • Displacements of the gates and the lock heads should be limited so no leakage occurs.

Level II earthquake:

  • Lock gates should retain their structural integrity (no collapse);
  • No damage to the structure foundations is allowed; and
  • Lock gates should be able to retract fully into their recess for repair.

One of the most important aspects of the earthquake design is hydrodynamic loading. This is because the gates are submerged structures and the accelerations resulting from earthquakes are multiplied not only by the mass of the structure itself, but also by that of the surrounding and entrapped water. In fact, the added mass of water to be included was about 10 times as much as the weight of a gate itself. The presence of water not only produces hydrodynamic pressures during an earthquake, but also affects the dynamic properties of the structure as it lengthens its period of vibration. Therefore, interaction with water is modeled with lumped added masses, which are applied to the skin plates of the gate.

As it turned out, very little information was available on the hydrodynamic behavior of partially submerged steel structures. The available existing theories, such as the formulas by Westergaard and Housner, were developed for hydrodynamic pressures on concrete dams located adjacent to semi-infinite reservoirs.

Extensive study was required to verify if these theories could be applied on steel structures, which are relatively flexible. Meetings were organized with a panel of experts from all over the world to summarize and compare methods applied worldwide; several tests, both in-laboratory and full-scale, on existing hydraulic structures were carried out; and results of dynamic analysis with the Westergaard added masses were compared with results of Computational Fluid Dynamics Analysis with Arbitrary Euler Lagrange elements to discretely model the fluid continuum. The conclusion from these studies was that application of the Westergaard formula is reasonable and conservative enough for design purposes.

Response Spectrum Analysis (RSA) and Non-linear Time History Analysis (THA) were used for dynamic analysis of the lock gates. For the RSA, the provided site-specific (Atlantic and Pacific locks) response spectra have been used. The spectral ordinates are high compared with design spectra of commonly used codes and engineering manuals (e.g., the peak ground acceleration at the rock base for the Pacific Complex and Level I earthquake is 0.52g), revealing the stringent requirements and design challenge. For Level I earthquake, the RSA is carried out using the same FEA model used for static and fatigue design.

Welds to be checked for each node.

However, the dynamic behavior of the lock gate also is affected by interaction with the concrete lock walls, the non-elastic behavior of the bearings, ground conditions, and soil-structure interaction. Therefore, THA is also carried out with a model where the lock head and the foundation are combined. Seven time histories from around the world scaled to fit the site-specific spectra were provided by the ACP and used for the THA. For Level II earthquake, a Push-Over Analysis was carried out to examine the plasticity of the gate.

On several occasions, the unprecedented design requirements pushed the team to introduce mechanical applications from other fields, applying the following for the first time in lock gate design:

  • Seismic loading (vertical), accidental flooding, and the presence of heavy vehicles on gates provided with bridgeways, combined with the already large variation in water levels, initially caused heavy loading on the supporting wagons required to move the gate. To limit the required dimensions of these wagons, a load-limiting device (LLD) was designed. During overload, the LLD limits the maximum load on the wagons, allowing the more robust structural frame of the lock gate to bring the load directly to the concrete lock floor.
  • Stringent leakage criteria imposed a delicate challenge to the design. To protect Panama’s fresh water supply, leakage was limited to 5 liters/meter sealing/minute on average. An innovative sealing/guiding system was designed, allowing for smooth horizontal guiding and a quick and correct installation of the sealing/guiding panels, while meeting the stringent sealing requirements.
  • Due to the large differential head between adjacent chambers, buoyancy chambers required to reduce the operating weight had to be situated at the bottom of the gates. A special floating mechanism consisting of removable bulkheads and temporary solid ballast has been designed to allow replacement of the gates efficiently and safely, floating by themselves in a stable and upright manner.
  • The required level of availability called for the ability to perform quick and efficient maintenance. Special features allow replacement of the rolling wagons within four hours, as per the employer’s requirements.

These examples, combined with other discipline-specific design challenges, necessitated an integral, holistic approach to gate design.

Detail and final design

The step from design to construction requires workshop drawings of each detail. In the Detail Design stage, the objective was to finalize layout of the connection details. These had to be presented to the gate fabricator to enable production of the workshop drawings. During Final Design, all connections between bracing, stiffeners, and columns had been grouped in a certain minimum notch class. During Detailed Design, all nodes had to be designed and analyzed in detail to verify compliance with the fatigue requirements as set up during the Final Design.

The first step to achieve this was to determine the stresses using detailed FEA models prepared in the FEA software products, FEMAP and/or ANSYS. However, to limit the amount of FEA runs, the approximately 400 nodes per gate were divided into 50 blocks of similar geometry and loading conditions. Each of these 50 unique nodes was then modeled in detail and incorporated into the existing, less-refined, global model of the gate. As such, the correct interaction between the node and the rest of the gate was maintained. Subsequently, several copies of the global model were made with a limited number of detailed node models in each of them, to take maximum advantage of the available computer resources.

After that, the most time-consuming part of the process started. Each weld or other fatigue detail had to be classified into a certain notch group. The calculated stresses were translated to stresses in the weld and verified against the allowable stresses for the corresponding fatigue detail according the appropriate code. With an average of 100 welds to be checked per node, 50 unique nodes per gate, and six gate types, this resulted in a total of 30,000 welds to be verified.

To speed up this repetitive process and to avoid mistakes, several steps were automated. A program was written to automatically recognize the connections between the various plates in the FEA model. This program then transferred these to dedicated spreadsheets, together with the different stress components, information about type of connection (crux, tee, or angled), and a picture of the connection. After entering the weld size, type, and notch class for each of the welds, these spreadsheets were then used to determine the expected cumulative damage (fatigue) at the end of the design life.

The design of the 16 lock gates for the new Panama Canal has been completed. The lock gates are currently being fabricated in Italy and transported to Panama. They are able to withstand all the appropriate load combinations and are compliant with the employer’s requirements. This was accomplished by an extensive project team consisting of experts in their field who together produced an integral design.

Jeremy Augustijn, senior project manager at Iv-Infra bv, is specialized in multidisciplinary projects with an emphasis on complex steel structures. As CICP design engineer, he was responsible for the design of the lock gates, including the gate drive system and appurtenances. Charalampos Bouras, senior structural engineer at Iv-Infra bv, is specialized in steel structures design, finite element modelling, and dynamic analysis of structures. Andries Kaptijn, senior structural engineer at Iv-Consult bv, has more than 11 years of experience, mainly in design and calculation of structures and equipment where fatigue governs the design.