Performance of Embedded Anchor Chains and Consequences for Anchor Design
Authors: Neubecker S.R. , Randolph M.F. 
Published: October 2008

ABSTRACT
With the growth in popularity of floating systems for offshore oil production, there has been an increased focus on the design of permanent mooting systems. It is widely acknowledged that the anchor chain plays an important part in the total mooting system by developing functional load and introducing an inclination of the load at the subseabedanchorage.
By making a simple and valid assumption, the force equilibrium equations of the chain are simplified to produce closed form expressions for both the force distribution and the geometric profile of the anchor chain. This paper thenshows how these equations can be applied to simplify the design of anchor piles and drag anchors.

INTRODUCTION
While gravity anchors have been employed as moorings for some installations, the most common forms of anchor for permanent moorings are pile anchors and drag anchors. Both of these anchoring methods result in the attachment point for the chain being embedded at some depth below the mudline.
When the anchor chain connection is below the mudline, horizontal tensioning will result in cutting and sliding of the chain through the soil, which in turn results in large soil. resistive forces acting on form an inverse catenary anchorage (Figure 1).
Analysis of embedded the chain. The chain will thenshape from the mudline to theanchor chains is therefore important for two reasons. Firstly, frictional loaddeveloped along the chain means that the chain tension will be smaller at the anchorage than at the mudline, allowing optimisation of the anchor size.
Secondly, the inverse catenary shape of the chain results in a component of uplift being applied to the anchor. This information is critical to the anchor design since it will determine the failure mode for anchor piles, and the embedment performance of drag anchors.
Previously, the only available method for predicting the resulting anchor chain profile and load development involved numerical integration of the governing differential equations, together with iteration of one of the unknown boundary conditions in order to match the known boundary conditions, This method was initially performed using small circular elements of chain, as presented by Reese (1973) and Gault & Cox (1974). Vivatrat et al (1982) simplified the method by assuming small curvi-linear chain segments.
The main complication in the governing differential equations arises from the self-weight, w, of the chain. However, the self-weight is generally only significant at shallow embedment depths, and may be allowed for by a simple adjustment of the profile of bearing resistance. This allows an analogical solution to be developed, as described by Neubecker and Randolph (1994). Theadvantages of the analytical solution are twofold. Firstly the solution obviates the need for unwieldy numerical computations (which occupy the bulk of computational time for programs that model drag anchor embedment). Secondly, the solutions give direct insight into the keyvariables that dictate chain performance, and provide a theoretical basis for the design of anchor piles, drag anchors and other embedded anchoring systems. This paper summarises analytical solutions for the profile.