Wave Load Analysis for Offshore Structures

Understanding Wave Load Analysis: A Critical Component of Offshore Structural Design

Offshore structures operating in the North Atlantic face some of the most challenging marine environments on Earth. From fixed platforms supporting wind turbines to floating production facilities and subsea infrastructure, these engineering marvels must withstand tremendous forces generated by ocean waves. Wave load analysis forms the cornerstone of safe, reliable offshore structural design, ensuring that these installations can survive extreme weather events while maintaining operational integrity throughout their design life.

For engineering projects along the Atlantic Canadian coastline, understanding wave mechanics and their interaction with marine structures is particularly crucial. The waters off Nova Scotia, New Brunswick, and Newfoundland experience significant wave heights that can exceed 15 metres during severe storms, with wave periods ranging from 8 to 18 seconds. These conditions demand rigorous analytical approaches and sophisticated modelling techniques to accurately predict structural responses.

Fundamental Principles of Wave Mechanics in Offshore Engineering

Wave load analysis begins with a thorough understanding of ocean wave behaviour. Engineers must consider multiple wave theories depending on water depth, wave height, and wave period. The selection of an appropriate wave theory directly influences the accuracy of load predictions and, consequently, the safety and economy of the final design.

Linear Wave Theory (Airy Theory)

Linear wave theory, also known as Airy theory, serves as the foundation for most wave load calculations. This theory assumes small wave amplitudes relative to wavelength and water depth, producing sinusoidal wave profiles. While it provides acceptable results for many design scenarios, linear theory tends to underestimate peak forces in shallow water conditions and during extreme wave events.

The key parameters derived from linear wave theory include:

• Wave celerity: The speed at which the wave form travels, calculated as C = gT/2π in deep water conditions

• Wavelength: The horizontal distance between successive wave crests, approximately 1.56T² metres in deep water

• Particle velocities: Horizontal and vertical water particle velocities that decay exponentially with depth

• Dynamic pressure: The fluctuating pressure component acting on submerged surfaces

Nonlinear Wave Theories

For more accurate representation of wave behaviour in extreme conditions, engineers employ nonlinear wave theories. Stokes wave theory, available in second through fifth order formulations, better captures the asymmetric wave profiles with sharper crests and flatter troughs characteristic of real ocean waves. In shallow water environments common to many Maritime installations, cnoidal wave theory or stream function theory may be more appropriate.

The choice between wave theories often depends on the ratio of water depth (d) to wavelength (L) and wave height (H) to wavelength. For typical North Atlantic conditions with water depths of 30 to 100 metres, Stokes fifth-order theory is frequently employed for design wave analysis.

Hydrodynamic Force Calculation Methods

Converting wave kinematics into structural forces requires application of established hydrodynamic principles. The methodology varies significantly based on structural dimensions relative to wavelength, a relationship characterised by the diffraction parameter D/L, where D represents the characteristic structural dimension.

Morison Equation for Slender Members

The Morison equation remains the primary tool for calculating wave forces on slender cylindrical members such as jacket legs, braces, and risers. This semi-empirical formulation combines inertia and drag force components:

F = ρCₘV(∂u/∂t) + ½ρCdA|u|u

Where ρ is seawater density (approximately 1,025 kg/m³), Cₘ is the inertia coefficient, Cd is the drag coefficient, V is the displaced volume, A is the projected area, and u represents water particle velocity.

Selecting appropriate hydrodynamic coefficients is critical to accurate force prediction. For smooth circular cylinders, typical values range from Cd = 0.65-1.05 and Cₘ = 1.6-2.0, depending on surface roughness, Reynolds number, and Keulegan-Carpenter number. Marine growth accumulation, particularly prevalent in nutrient-rich Atlantic Canadian waters, can significantly increase drag coefficients, sometimes by 50% or more for heavily fouled members.

Diffraction Analysis for Large Volume Structures

When structural dimensions approach or exceed 20% of the wavelength, diffraction effects become significant and the Morison equation no longer applies. Large volume structures such as gravity-based platforms, floating production units, and monopile foundations for offshore wind turbines require diffraction analysis based on potential flow theory.

Modern diffraction analysis employs boundary element methods (BEM) or finite element methods (FEM) to solve the velocity potential around the structure. Software packages commonly used in Canadian offshore engineering practice include WAMIT, ANSYS AQWA, and DNV SESAM, which can handle complex geometries and compute first and second-order wave forces, added mass, and radiation damping coefficients.

Design Wave Approaches and Spectral Analysis

Offshore structural analysis typically employs two complementary approaches: deterministic design wave analysis and stochastic spectral analysis. Both methodologies serve important roles in comprehensive wave load assessment.

Deterministic Design Wave Method

The design wave approach applies a single extreme wave, typically representing the 100-year return period event, to evaluate maximum structural responses. For Atlantic Canadian waters, design wave parameters are derived from hindcast databases covering several decades of storm events. Characteristic values for the Scotian Shelf region include:

• 100-year significant wave height (Hs): 12-15 metres depending on specific location

• Associated peak spectral period (Tp): 14-18 seconds

• Maximum individual wave height (Hmax): Typically 1.86 × Hs, yielding values of 22-28 metres

• Associated wave period: 0.9-1.0 × Tp

Design wave analysis provides clear maximum force and moment values for structural sizing but cannot capture the dynamic amplification effects that may occur when wave frequencies approach structural natural frequencies.

Spectral Analysis and Fatigue Assessment

Spectral analysis characterises the sea state as a superposition of regular wave components with varying heights, periods, and directions. Standard wave spectra used in North Atlantic design include the JONSWAP spectrum, particularly appropriate for fetch-limited conditions, and the Pierson-Moskowitz spectrum for fully developed seas.

The JONSWAP spectrum, with its characteristic peak enhancement factor (γ) of 1.0 to 7.0 (typically 3.3 for North Sea and Atlantic conditions), better represents the sharper spectral peaks observed in real ocean measurements. Directional spreading functions account for the three-dimensional nature of wave energy distribution.

Time-domain or frequency-domain spectral analysis enables accurate fatigue damage assessment, crucial for structures expected to operate for 25 to 50 years in the demanding Atlantic environment. Accumulated fatigue damage is typically evaluated using Miner's rule, with appropriate S-N curves selected based on joint classification and cathodic protection systems.

Special Considerations for Atlantic Canadian Offshore Projects

Engineering offshore structures for deployment in Maritime waters requires attention to several region-specific factors that can significantly influence wave load analysis and structural design.

Combined Wave-Current Loading

The interaction between waves and currents affects both wave kinematics and hydrodynamic forces. Tidal currents in the Bay of Fundy reach velocities exceeding 4 metres per second, while persistent ocean currents along the Scotian Shelf typically range from 0.5 to 1.5 m/s. Current superposition on wave particle velocities increases drag forces nonlinearly and must be properly accounted for in design calculations.

Canadian Standards Association guidelines (CSA S474) and relevant offshore codes recommend specific methods for wave-current combination, including appropriate blockage factors and current profile specifications.

Ice and Wave Combined Loading

Structures operating in the Gulf of St. Lawrence or on the Grand Banks must consider the combined effects of wave loading and ice forces. While these phenomena rarely occur simultaneously at maximum intensity, transition periods when deteriorating ice fields coincide with storm events require careful analysis. Ice management strategies and structural design provisions must complement wave load resistance capabilities.

Seabed Conditions and Foundation Response

Wave-induced loads transfer through the structure to foundations, which must adequately resist both static and cyclic loading. Soil conditions along the Atlantic Canadian continental shelf vary considerably, from dense glacial tills to soft marine clays. Cyclic degradation of soil strength under repeated wave loading can reduce foundation capacity over time, particularly relevant for monopile and suction caisson foundations supporting offshore wind installations.

Advanced Analysis Techniques and Emerging Technologies

The offshore engineering industry continues to develop more sophisticated tools for wave load prediction, driven by demands for greater accuracy, efficiency, and the ability to analyse novel structural concepts.

Computational Fluid Dynamics (CFD)

CFD analysis using Reynolds-Averaged Navier-Stokes (RANS) solvers or more advanced techniques such as Large Eddy Simulation (LES) enables detailed resolution of wave-structure interaction phenomena that simplified theories cannot capture. Applications include:

• Wave run-up and green water loading on platform topsides

• Slamming loads on hull structures and ship-shaped vessels

• Vortex-induced vibrations in cross-flow conditions

• Validation of Morison coefficients for non-cylindrical members

While computationally intensive, CFD analysis provides invaluable insights for critical design scenarios and helps calibrate simplified models used in routine engineering practice.

Model Testing and Validation

Physical model testing in wave basins remains an essential validation tool, particularly for floating structures and complex fixed installations. Canadian facilities, including the National Research Council's offshore engineering basin in St. John's, Newfoundland, provide world-class capabilities for testing scale models in simulated Atlantic storm conditions. Model test results inform numerical model calibration and provide confidence in design methodologies for novel concepts.

Regulatory Framework and Industry Standards

Wave load analysis for offshore structures must comply with applicable Canadian regulations and international standards. Key reference documents include:

• CSA S474: Canadian standard for offshore structures, incorporating provisions specific to Canadian environmental conditions

• ISO 19901-1: Metocean design and operating considerations

• API RP 2A-WSD/LRFD: Recommended practice for fixed offshore platforms

• DNV-ST-0119 and DNV-RP-C205: Environmental conditions and environmental loads standards

• Canada-Nova Scotia Offshore Petroleum Board (CNSOPB) guidelines: Regional regulatory requirements

Engineers must demonstrate compliance with these standards through detailed design documentation, independent verification, and appropriate quality assurance procedures.

Partner with Experienced Marine Engineering Professionals

Wave load analysis demands specialised expertise combining oceanographic knowledge, hydrodynamic theory, structural engineering principles, and practical offshore experience. The consequences of inadequate analysis can include structural failure, environmental damage, and loss of life, making competent engineering support essential for any offshore project.

Sangster Engineering Ltd. provides comprehensive marine and structural engineering services from our base in Amherst, Nova Scotia. Our team understands the unique challenges of Atlantic Canadian offshore environments and applies rigorous analytical methods to deliver safe, efficient structural designs. Whether you are developing offshore renewable energy installations, marine infrastructure, or coastal protection systems, we offer the technical capabilities and regional expertise your project requires.

Contact Sangster Engineering Ltd. today to discuss your wave load analysis requirements and discover how our professional engineering services can support your offshore development objectives throughout Atlantic Canada and beyond.

Partner with Sangster Engineering

At Sangster Engineering Ltd. in Amherst, Nova Scotia, we bring decades of engineering experience to every project. Serving clients across Atlantic Canada and beyond.

Contact us today to discuss your engineering needs.