SS: MODU Anchor- Analytical and Experimental Modeling for Out-of-Plane Loading of Plate Anchors
Authors: Gilbert Robert B. , Lupulescu Cristiana , Lee Chun Ho , Miller Jaime , Kroncke Mark , Yang Ming , Aubeny Charles Paul , Murff James Donald 
Published: July 2009

Abstract
Experiences in recent hurricanes point to the need to better understand how out-of-plane loading can affect the trajectory and ultimate holding capacity of an anchor. To date, there have been limited studies on the behavior of plates and plate anchors under three-dimensional loading conditions. This paper summarizes the results of analytical and experimental studies for out-of-plane loading on plate anchors in normally consolidated clays. A simplified analytical model describing the combination of forces and moments that would cause a square or rectangular bearing plate to move (yield) is developed based on three-dimensional finite element modeling. This model provides an analytical expression of a multi-axial yield interaction surface for the bearing plate that includes all six degrees of freedom. A series of experimental pull-out tests on square and rectangular bearing plates with a variety of different load geometries provides validation to the analytical model. A demonstration is presented at the end of the paper where the behavior of a flat bearing plate attachd to a thin shank is predicted and then tested under normal and out-of-plane loading. This demonstration illustrates how the fundamental work completed thus far can subsequently be used to predict the performance of actual anchors.

Introduction
Mooring systems failures caused 17 deepwater MODU's (mobile offshore drilling units) to go adrift during hurricanes Ivan, Katrina, and Rita. Drifting MODU's can potentially damage other critical elements of the offshore oil and gas infrastructure, e.g., colliding with floating or fixed production systems and transportation hubs, or damaging pipelines by dragging anchors. A critical aspect of this problem is the performance of mooring anchors under conditions of partial failure of the mooring system. Anchors for mooring systems for MODU's are typically designed for anchor line loads that act within the plane of the major axis of the anchor. Under normal loading conditions, this design basis is appropriate. However, if one or more of the mooring lines fail, the remaining anchors will be subjected to out-of-plane anchor line loads. It is important to assess how out-of-plane loading can affect the trajectory and ultimate holding capacity of an anchor. To date, there have been limited studies on the behavior of plate anchors under three-dimensional loading conditions.
This paper summarizes the results of analytical and experimental studies for out-of-plane loading of plates and plate anchors in normally consolidate clays. The phrase " plate anchors?? refers to anchors that develop their capacity primarily from a flat bearing plate attached to a shank, including high holding capacity drag embedment anchors (DEA's), drag embedded vertical load anchors, direct embedded vertical load anchors (VLA's). The phrase " out-of-plane loading?? refers to loads applied out of the plane of the design loading condition. The work was carried out over a two-year period. The analytical work involved conducting finite element analyses of square and rectangular plates under multi-axial loads and developing a simplified analytical predictive model based on the results. The experimental work involved performing load tests on square and rectangular steel bearing plates, nominally 1:30 scale of an actual anchor fluke, in order to validate the analytical model.
The goal of this work was to provide a fundamental basis to better predict the behavior of real-world anchors. Our objective was to develop a simplified analytical model for a square or rectangular bearing plate and to validate it with model tests. This effort provides the basis for extending this model in the future to actual anchors by accounting for the fluke, the shank, the padeye and the anchor line.