Multi-Objective Optimization of Large Diameter Hollow Sandwich Steel Pipe Concrete Combined Single Pile Foundation Section for Offshore Wind Power

Literature Overview

This paper addresses the cross-sectional dimensional optimization of large-diameter hollow sandwich steel pipe concrete combined single pile foundations used in offshore wind power installations. As offshore wind turbines grow larger with taller towers and heavier nacelles, the foundation systems must withstand significantly increased wind and wave loads while maintaining economic feasibility. The sandwich steel pipe concrete (SSPC) concept involves a large-diameter steel pipe filled with concrete, sometimes with an internal steel tube or core, creating a hybrid structural system that combines the ductility of steel with the compressive strength of concrete.

The optimization problem is inherently multi-objective because engineers must simultaneously minimize material cost, maximize structural stiffness, ensure adequate fatigue life, and satisfy geometric constraints imposed by manufacturing and installation logistics. The cross-sectional dimensions that serve as design variables typically include the outer diameter of the steel pipe, the wall thickness of the steel pipe, the diameter of the internal core, and the concrete fill ratio.

Core Technical Framework

The multi-objective optimization is typically formulated using evolutionary algorithms such as NSGA-II or MOGA, where the objective functions include:

The design variables are constrained by manufacturing limits, such as the maximum rollable diameter for seamless or spiral-welded pipe production, and installation limits, such as the maximum crane capacity and vessel deck width. The Pareto front obtained from the optimization provides a set of non-dominated solutions that represent the trade-off between cost and performance.

Structural Behavior and Load Analysis

The SSPC single pile foundation experiences complex loading conditions including axial compression from the tower weight, lateral bending from wind and wave forces, and torsional moments from asymmetric wind loading. The steel pipe and concrete work together in a composite action, where the steel provides tensile capacity and the concrete provides compressive capacity. The bond between the steel pipe inner surface and the concrete is critical for composite action, and this bond is typically enhanced by surface roughening of the pipe interior or the use of shear connectors.

The section properties of the SSPC pile are calculated using the transformed section method, where the concrete is converted to an equivalent steel area using a modular ratio of approximately 6–8 for typical concrete grades and structural steel. The moment of inertia and section modulus of the composite section are significantly higher than those of a hollow steel pipe of the same outer diameter, which is the primary advantage of the SSPC concept.

Optimization Results and Design Guidelines

The optimization study typically reveals several important design trends. First, there exists an optimal wall thickness range beyond which additional steel provides diminishing returns in terms of stiffness improvement relative to cost increase. For a typical 6–8 meter diameter SSPC pile, the optimal wall thickness is in the range of 30–50 mm, depending on the load case and soil conditions. Second, the concrete fill ratio has a significant effect on the section's torsional stiffness but a relatively minor effect on the lateral stiffness, which is dominated by the steel pipe's contribution.

The optimization also highlights the importance of the transition zone between the pile head and the transition piece. This region experiences high stress concentrations due to the change in section geometry and the application of eccentric loads. The design should include generous fillet radii and consider the fatigue implications of the weld details in this critical zone.

Engineering Practice Integration

In practice, the optimization results must be validated through finite element analysis that accounts for non-linear material behavior, soil-structure interaction, and fatigue damage accumulation. The API RP 2A and DNV-ST-0119 standards provide the framework for load analysis and design verification. The manufacturing of large-diameter SSPC piles typically involves the use of spiral-welded or UOE-form-and-weld pipe, with wall thicknesses up to 50–60 mm achievable through multi-pass submerged arc welding.

Key manufacturing considerations include:

• Pipe straightness tolerance must be within 1 in 1000 of length to ensure proper concrete placement.
• The internal surface of the steel pipe should be cleaned to remove mill scale and rust to ensure adequate bond with the concrete.
• The concrete mix design should include fibers or micro-silica to reduce shrinkage cracking and improve durability in the marine environment.
• The welding of the internal core to the outer pipe, if present, should use full-penetration butt welds with 100% radiographic inspection.

Study Insights and Implications

The multi-objective optimization of SSPC single pile foundations demonstrates that significant cost savings can be achieved through rational design rather than conventional trial-and-error approaches. The Pareto-optimal solutions provide engineers with a menu of design options that can be selected based on the specific project requirements and risk appetite. The key insight is that the SSPC concept offers a versatile and economically attractive solution for large offshore wind foundations, provided that the cross-sectional dimensions are carefully optimized to balance cost, performance, and manufacturability. Future work should focus on the long-term fatigue performance of SSPC piles under realistic offshore loading spectra and the development of standardized design procedures that incorporate the optimization results.