optimization of padeye position for deepwater suction anchor

Optimization of Padeye Position for Deepwater Suction Anchor under Inclined loading

Zhu Shengqing

American Bureau of Shipping, Singapore E-mail: [email protected]

Abstract: To maximize the load capacity of deepwater suction anchor, padeye position is to be optimized to avoid rotation for a given anchor geometry. This paper presents a robust method to estimate the optimal padeye position of suction anchor in sand using Limit Equilibrium Method. By using this method, a case study which is performed for a typical suction anchor is designed in a typical geotechnical data for sand under inclined loading.

Keywords: Optimization; Deepwater; Suction Anchor; Subsea Engineering. 1. Introduction

Suction anchors, also known as suction pile/suction caisson, are cylindrical structures with upper end closed and lower end open. In the past, it might be used either as a shallow foundation or as a short stubby pile and the shallow foundation option is more common at sandy soil sites. As oil and gas activities proceeding to deepwater, suction anchors with taut mooring system have gradually become important foundations of ships, floating production and storage facilities because of their low cost construction and convenient installation. In taut mooring systems that anchors are responsible of absorbing significant vertical load component as well as horizontal load. After an initial penetration into the seabed by self-weight of suction anchor, an under-pressure will be applied inner the caisson, which push the remainder of the caisson downwards to embed itself, leaving the top flush with the seabed. Compared with conventional driven pile foundations, suction anchors have multiple advantages in deep water:

1) Usable in deepwater and ultra-deepwater 2) Easy to handle 3) Simple installation equipment 4) Load can be instantly applied 5) Tremendous holding power in all directions 6) Better to predict failure loads than with anchors 7) Retrievable 8) Large range of possible use Besides, there is a trend that suction anchor is becoming larger and larger, while its application stretches into

deeper and deeper water. Nowadays, its application is also expanded to fixation of subsea manifold and pipeline [1]. A typical suction anchor is shown in Figure 1.

Figure 1 Typical suction anchor and the top [1]

Journal of Modeling and Optimization

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The design of a suction anchor involves material selection, geometry, and installation analysis, load capacity analysis for in-place condition and long-term analysis. In the stage to determine load capacity for a given suction anchor geometry, the design of payede position is vital for the failure mode and load capacity of suction anchor [1].

This work will focus on the stage that all soil data and geometry of suction anchor are determined while the depth of padeye is to be optimized. The main purpose of this paper is to present design method to optimize the load capacity of suction anchor via seeking the optimal padeye position for a given geometry and the inclined angle.

2. Design Practice

Upon the usage of suction anchor, research on the load capacity and failure mode are widely-documented.

Among them, Limit equilibrium method is the most widely applied theory. Limit equilibrium method solves the problem from the assumption of force and/or moment equilibrium. Duncan states that the factor of safety, F, is defined as the ratio of the shear strength of soil to the shear stress required for equilibrium. At the onset of failure the shear strength along the slip surface is assumed to be fully mobilized and the factor of safety is constant along the length of the entire surface. The factor of safety from the Spencer method will be used for the purposes of this research as it is prone to the least amount of errors and is most suitable to the problem.

Finite Element Analysis is a powerful technique on the load capacity of suction anchor in deepwater. Finite element analysis is a supplement or an alternative to limiting equilibrium analyses, especially for novel geometries or load conditions, and for complex soil profiles. It is found that existing 3-D finite element methods meet the analysis requirements of this code. It was also reported [2] that the plane limit equilibrium method used in the calibration of this code, as well as a quasi 3-D finite element model, where the 3D effects are accounted for by side shear on a 2-D model, generally show good agreement with the 3D finite element analyses. Finite element method sets no prior assumption of failure mechanism, but automatically finds out the critical failure mode for a specific case giving all detailed information about loading and soil characteristics. It owns the advantage of modelling complex conditions like layered soils, irregular geometry, non-optimal load point, and user defined random inclined angle for example. However, the theoretical solution of optimal padeye attachment point needs multiple analyses to obtain.

The plastic limit analysis approach can be applied to soils having anisotropic strength characteristics. Aubeny et al. consider suction caisson lateral load capacity in anisotropic clays under undrained loading conditions. Parametric studies for typical reported ranges of strength anisotropy indicated that isotropic analyses using the direct simple shear strength of the soil provide reasonable agreement (within 10%) with the more rigorous anisotropic analyses. However, data on anisotropic strength characteristics are still relatively limited, particularly with regard to the shearing resistance in a horizontal plane that controls much of the lateral load capacity of suction caissons, so the issue should not be entirely discounted. Aubeny [6] also pointed out that the optimal padeye attachment point should ensure the pure translation for the suction anchor without rotation.

In this work, Plastic Limit Method, FEA technique and other analysis methods with their characteristics are summarized in table 1.

Figure 2 Padeye position for suction anchor

Table 1 Summary of suction anchor analysis methods with their characteristics


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Method Base theory Advantages Limitations Remark

3-D FEA Nonlinear Finite Element Theory

Accommodate all loading/boundary conditions without major assumption

Consuming of Computation resources

Available for all commercial FEA software such as ABSQUS, ANSYS and PLAXIS 3D.

Pseud 3-D FEA

Nonlinear Finite Element Theory & Fourier Series

Computing resource is reduced

Accuracy depending on precise perdition of failure modes

Limit equilibrium method

Elastic equilibrium theory

Easy to apply for elastic analysis and engineering design

Detailed stress distribution is absent

plastic limit analysis [7]

Plastic Limit theory

Upper bound, without lower bound of load capacity can be predicted

Upper bound may not be used for engineering design for load capacity

P-Y method

L/D>1.5

3. Optimization of Padeye position It is widely recognized that to maximize the load capacity of suction anchor, the padeye should be in the

point that the suction anchor will translate with rotation under inclined load [2-7]. It is estimated that this status corresponds to a special location of load attachment point- optimal load point, which is found to be around 70 percent of the caisson embedment depth [7] as shown in Fig.3.

Figure 3 Failure modes under lateral load and inclined load [8]

For a suction anchor with embed length L and outer diameter D for a given inclined angle , the optimal

padeye depth is pL . The final objective will be the optimal ratio of L

Lp .

In 1993, Murff and Hamilton pioneered an accurate model based on the velocity in Figure 4 with the upper bound method of plasticity. They assume a 3D failure mechanism in Figure 5. In 2005, Aubeny developed the theory using Plastic Limit Analysis and gave a mature methodology for load capacity of suction anchor [7].


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Figure 4 Suction Caisson rigid body motions under inclined loading.

Figure 5 Soil collapse mechanism by a) Murff and Hamilton, b) Aubeny et al. [7]

Figure 6 Failure Mechanism at Bottom of caisson [7]


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Figure 7 Illustration of the geometry for suction anchor with padeye

The failure mechanism of suction anchor is illustrated in Figure 6 and a simplified dimensionless expression for moment capacity boM can be formulated [7]:

uavg

bo

SR

M325.0

= R

R

12 + e¯ R

RS 12

(1)

Where

R is the outer radius of suction anchor and R = D/2

uavgS is the average strength of soil over suction anchor tip

1R is the radius of rotation from the tip level of the suction anchor

2I is a constant, which is 2I = 1.118 [7].

To maximize the capacity, we differentiate Eq. (1) with respect to 1R and make it to be zero, which gives:

R

R1 =2

2

2ln

I

I

(2)

Substituting R=D/2 and 2I = 1.118 into Eq. (2), we get the solution for 1R :

D

R1 = 0.252 (3)

As shown in Figure 7, the following equation can be drawn as per Fig. 7:

pL = L － 1R － 3R (4)

and

3R = tan2

D (5)

Substituting Eq. (3) and (5) into Eq. (4), pL is given by

pL = L － (2

tan+ 0.252)D (6)

It is shown in Eq. (6) that the depth of padeye is dependent on the geometry of suction anchor, as well as the

inclined angle over padeye. To seek the ratio of L

Lp , Eq. (6) can be deformed as


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L

Lp = 1 －(2

tan+ 0.252)

L

D (7)

Eq. (7) is plotted in Figure 8.

Figure 8 Variation of optimal padeye position with aspect ratio of suction anchor for different inclined

angle

As can be seen in Figure 8, the ratio L

Lp increases with the aspect ratio L/D increasing and it increases when

the inclined angle decreasing.

4. Conclusions

The optimal padeye position is sought for suction anchor via Plastic limit Method and the load capacity of a given suction anchor is maximized with an explicit formula in this paper. The optimal padeye depth increases with the aspect ratio L/D increasing and it increases when the inclined angle decreasing. Furthermore, the optimal padeye position is around 70% of the length of suction anchor in soil. 5. Acknowledgement

The authors are also grateful for the technical discussion with Professor Charles Aubeny of Texas A&M University on the load capacity of suction anchor. 6. References [1] Yong Bai, Qiang Bai. Subsea Engineering Handbook. 1st Edition, 2012 [2] API RP 2A, Recommended Practice for Planning, Designing and Constructing Fixed Offshore Platform Working Stress Design, 21st Edition. Washington, D.C. American Petroleum Institute, 2005. [3] API RP 2SK, Design And Analysis Of Station-keeping Systems for Floating Structures, 2005. [4] ABS FPI Guide, For Building and Classing Floating Production Installations, 2007. [5] DNV- RP-E303. Geotechnical design and installation of suction anchors in clay. DNV Recommended Practice, 2005. [6] Charles Aubeny, J. Donald Murff. Simplified limit solutions for the capacity of suction anchors under undrained conditions. Ocean Engineering 32, 2005, 864–877. [7] Aubeny, C.P., Han, S.W., Murff, J.D. Inclined load capacity of suction caissons. International Journal for Numerical and Analytical Methods in Geomechanics 27, 2003, 1235–1254.


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optimization of padeye position for deepwater suction anchor

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