# Comparison of Prediction Methods for Axial Strength of Ground Connections with Shear Keys
## 1 Introduction  
A grouted connection is a lap connection between two steel tubes of different diameters. The cement-based high-strength grouting material is poured into the annular space formed between two steel tubes. The grouted connection transfers internal forces through shear and friction between the pipe wall and the grouting body. In the marine environment, implementation of the project is affected not only by wind, surge, humidity, strong corrosion, and other environmental factors, but also by the construction technology. Especially when the connection between the pile foundation structure and the superstructure is required to be completed under water, it is very difficult to implement the connection. Based on the practice of different connection modes, grouted connections are widely used in offshore engineering because of their advantages of good integrity, convenient construction, and lower cost. More and more offshore platforms and structures are being connected in this way, such as oil production platforms, cross-sea bridges, offshore wind power structures, etc. With the development of offshore wind power, grouted connections have gradually been applied to foundation structures for offshore wind turbine power infrastructure. According to the statistics of offshore wind turbines built in Europe, 60% of foundations have adopted grouted connections [1]. Although groutedconnection has been actively applied in marine engineering, its development is not acceptable when compared with land engineering counterparts, so the relevant research output is relatively limited, and there is an urgent need for more research work to be carried out. With and without a shear key installed are the two major types of grouted connection. The shear key can significantly increase the axial strength of the grouted connection. In recent years, slip settlement of offshore wind turbine tower foundations without shear key grouted connections has been spotted in Europe. Subsequently, grouted connections with shear keys or conical joints became a concern and some codes stipulated that grouted connections transferring axial force should not use connections without shear keys. The current regulations concerning the design for grouted connections with shear keys mainly include a document on pile/sleeve connections by the British Health and Safety Executive (HSE, 2002) [2]; the Recommended Practice for Planning, Designing, and Constructing Fixed Offshore Platforms by the American Petroleum Institute (API, 2007) [3]; the standard on petroleum and natural gas industries: fixed steel offshore structures by the International Organization for Standardization (ISO, 2007) [4]; the standard on the design of steel structures by the Norwegian Oil and Gas Association (NORSOK, 2013) [5]; and standards on support structures for wind turbines and design of offshore wind turbine structures by Det Norske Veritas and Germanischer Lloyd (DNV GL, 2016; DNV, 2013) [6; 7]. Research on grouted connections started in the early 1970s, and many scholars have conducted significant studies of related research during the last few decades. Through experiments, [PERSON] et al. [8; 9] proposed a formula for calculating the shear strength of a grouting connection section and the corresponding parameter relationship, which was adopted by HSE. [PERSON] et al. [10] also obtained the calculation formula of carrying capacity through the test data, which was embedded in the API's standards. These early studies mainly focused on specific projects, resulting in single rather than systematic study output, so limitations on the calculation formulas were unavoidable. In order to get more accurate calculation methods, further studies have been conducted. In combination with practical engineering, [PERSON] et al. [11] revealed that the axial bearing performance of a grouted connection was much more affected by the diameter and surface manufacturing error of the connection segment than that described in the specification. [PERSON] et al.