DNV-RP-E301: Design and Installation of Fluke Anchors … · Methodology for fluke anchor design...

DET NORSKE VERITAS

RECOMMENDED PRACTICERP-E301

DESIGN AND INSTALLATION OFFLUKE ANCHORS IN CLAY

2000

DET NORSKE VERITAS

FOREWORDDET NORSKE VERITAS (DNV) is an autonomous andindependent Foundation with the objectives ofsafeguarding life, property and the environment, at sea andonshore. DNV undertakes classification, certification, andother verification and consultancy services relating toquality of ships, offshore units and installations, andonshore industries world-wide, and carries out research inrelation to these functions.

DNV publishes various documents related to the offshoreindustry, aimed at promoting quality and safety onoffshore units and installations. These documents arepublished within a frame consisting of ServiceSpecifications, Standards and Recommended Practices, seefigure below.

The procedural basis for offshore verification services areprovided in DNV Offshore Service Specifications (OSS-series). The OSS-series of documents are divided into 3parts:

• Classification• Shelf Legislation Compliance Services• Certification and other Services

The technical requirements forming the basis for theverification services are given in DNV Offshore Standards(OS-series) as well as other codes and standards cited byDNV. The DNV OS-series is divided into 6 parts:

A. Quality and Safety MethodologyB. Materials TechnologyC. StructuresD. SystemsE. Special FacilitiesF. Pipelines & Risers

The Recommended Practice publications (RP-series) coverproven technology and solutions which have been foundby DNV to represent good practice, and which representone alternative for satisfying the requirements stipulated inthe DNV Offshore Standards or other codes and standardscited by DNV. The DNV RP-series is divided into 6 parts,identical to OS.

As well as forming the technical basis for DNVverification services, the Offshore Standards andRecommended Practices are offered as DNV’sinterpretation of safe engineering practice for general useby the offshore industry.

ACKNOWLEDGEMENTSThis Recommended Practice is based upon a designprocedure developed within the Joint Industry Project"Design Procedures for Deep Water Anchors" /1/, /2/ and/3/. The following companies sponsored this JIP:

BP Exploration Operating Company Ltd.; BruceAnchor Ltd.; Det Norske Veritas; Health & SafetyExecutive; Minerals Management Service; NorskHydro ASA; Norske Conoco AS; Petrobras; SagaPetroleum ASA; Shell Internationale PetroleumMaatschappij B.V. (Part 1 only); SOFEC Inc. (Part 1only); and Statoil.

DNV is grateful for valuable co-operations and discussionswith these companies. Their individuals are herebyacknowledged for their contribution.

As part of the publication of this RP, a draft copy was sentfor hearing to several companies. Significant, valuable andconcrete comments were provided within the resultingfeedback. The following organisations, which activelyparticipated, are specially acknowledged

Saga Petroleum ASA; Elf Aquitaine; and University ofManchester, School of Engineering

THIS REVISIONThis revision of RP-E301 is made in order to harmonisethe document with other related documents. The mostsignificant revision in this document is the introduction oftwo consequence classes also for the ULS condition andadjustment of the partial safety factors on line tension toconform with results from recent R&D work.

Comments may be sent by e-mail to [email protected] . For subscription orders or information about subscription terms, please use [email protected] .

Comprehensive information regarding DNV services, research and publications can be found at http://www.dnv.com , or can be obtained from DNV,Veritasveien 1, N-1322 Høvik, Norway; Tel +47 67 57 99 00, Fax +47 67 57 99 11.

© 2000 DET NORSKE VERITAS. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, includingphotocopying and recording, without the prior written consent of DET NORSKE VERITAS.

Printed in Norway by Det Norske Veritas AS

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& NOTESDNV RECOMMENDED PRACTICES

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DET NORSKE VERITAS

CONTENTS

1. General ...............................................................................11.1 Introduction........................................................................11.2 Scope and Application......................................................11.3 Structure of the RP............................................................11.4 Definitions ..........................................................................11.5 Abbreviations.....................................................................21.6 Symbols and explanation of terms ..................................22. Fluke Anchor Components ...........................................43. General fluke anchor behaviour..................................44. Methodology for fluke anchor design........................54.1 General.................................................................................54.2 Design charts......................................................................64.3 Analytical tools ..................................................................65. Recommended design procedure.................................65.1 General.................................................................................65.2 Basic nomenclature and contributions to anchor

resistance ............................................................................75.3 Step-by-step description of procedure ...........................95.4 Tentative safety requirements. ........................................95.5 Minimum installation tension. ......................................126. Requirements to Soil Investigation.......................... 137. References....................................................................... 13

0 Recommended Practice RP-E301

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Recommended Practice RP-E301 1

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1. General

1.1 IntroductionThis Recommended Practice features a substantial part ofthe design procedure developed in Part 1 /1/ of the jointindustry project on Design procedures for deep wateranchors, and it was developed further through a pilotreliability analysis in Part 2 /2/. An overview of thisproject is given in /3/.

1.2 Scope and ApplicationThis Recommended Practice applies to the geotechnicaldesign and installation of fluke anchors in clay forcatenary mooring systems

The design procedure outlined is a recipe for how flukeanchors in both deep and shallow waters can be designedto satisfy the requirements by DNV.

According to this recommendation the geotechnicaldesign of fluke anchors shall be based on the limit statemethod of design. For intact systems the design shallsatisfy the Ultimate Limit State (ULS) requirements,whereas one-line failure shall be treated as an AccidentalDamage Limit State (ALS) condition.

For the ULS, the failure event has been defined as theinception of anchor drag. Subsequent drag of any anchoris conservatively assumed to imply mooring systemfailure in the ALS. This avoids the complexity ofincluding uncertain anchor drag lengths in the mooringsystem analysis. Thus, the ALS is formulated to avoidanchor drag, similarly to the ULS.

The line tension model adopted herein splits the tension ina mean and a dynamic component, see background in /4/,which differs from the line tension model adopted in thecurrent DNV Rules for Classification of Mobile OffshoreUnits /5/

Traditionally, fluke anchors have been designed with themandatory requirement that the anchor line has to behorizontal (zero uplift angle) at the seabed level duringinstallation and operation of the anchors. Thisrequirement imposes significant limitations on the use offluke anchors in deeper waters, and an investigation intothe effects of uplift on fluke anchor behaviour, as reportedin /1/, has provided a basis for assessment of anacceptable uplift angle.

Until the design rule presented herein has been calibratedbased on reliability analysis the partial safety factors willbe tentative.

This recommendation is in principle applicable to bothlong term (permanent) and temporary moorings.

1.3 Structure of the RPDefinition of the main components of a fluke anchor isgiven in Chapter 2, followed by a description of thegeneral behaviour of fluke anchors in clay in Chapter 3.

In Chapter 4 a design methodology based on calibratedand validated analytical tools is recommended in lieu ofthe current use of design charts.

The recommended procedure for design and installationof fluke anchors is presented in Chapter 5. The close andimportant relationship between the assumptions for designand the consequential requirements for the installation offluke anchors is emphasized.

General requirements to soil investigations are given inChapter 6.

The intention has been to make the procedure as conciseas possible, but still detailed enough to avoidmisinterpretation or misuse. For transparency detailsrelated to the various design aspects are therefore found inthe appendices.

A number of Guidance notes have been included as anaid in modelling of the anchor line, the anchor and thesoil. The guidance notes have been written on the basis ofthe experience gained through the joint industry project,see /1/ and /2/.

1.4 DefinitionsDip-down point Point where the anchor line starts to

embed.

Fluke Main load bearing component.

Fluke angle Angle between the fluke plane and aline passing through the rear of thefluke and the shackle (arbitrarydefinition).

Forerunner Anchor line segment being embeddedin the soil (preferably wire, but mayalso be a chain).

Inverse catenary The curvature of the embedded partof the forerunner.

Shackle Forerunner attachment point (at thefront end of the shank).

Shank Rigidly attached to the fluke.

Touch-down point Point where the anchor line firsttouches the seabed.


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1.5 Abbreviations

AHV Anchorhandlingvessel

Used to set the anchors

ALS AccidentalDamageLimit State

MBL MinimumBreakingLoad

Breaking load of anchor linesegment

ULS UltimateLimit State

1.6 Symbols and explanation of termsSymbol Term Explanation of term

α Seabed upliftangle

Line angle with the horizontal at thedip-down point

amax Maximumpossible upliftangle

Uplift angle, which makes theanchor drag at constant tensionwithout further penetration at theactual depth

α Anchoradhesionfactor

Accounts for remoulding of the clayin the calculation of the frictionalresistance at the anchor members

αmin Minimumadhesion

Set equal to the inverse of thesensitivity, αmin = 1/St

αsoil Line adhesionfactor

To calculate unit friction in clay ofembedded anchor line

Afluke Anchor flukearea

Based on manufacturer's data sheet.

β Anchorpenetrationdirection

Angle of the fluke plane with thehorizontal

AB Effectivebearing area

Per unit length (related to anchorline segment in the soil)

AS Effectivesurface area

Per unit length (related to anchorline segment in the soil)

cv Coefficient ofconsolidation

See Appendix G

d Nominaldiameter

Diameter of wire, rope or chain

ds Elementlength

Related to embedded anchor line

e Lever arm Between shackle and the line ofaction of the normal resistance atthe fluke

f Unit friction Resistance, both frictional andcohesive, of embedded part ofanchor line

γm Partial safetyfactor onanchorresistance

Accounts for the uncertainty in∆Rcons, ∆Rcy, ∆Rfric, su and su,r

γm,i Partial safetyfactor onseabed

Accounts for the uncertainty in thepredicted seabed friction to be

Symbol Term Explanation of term

friction overcome during anchor installation

γmean Partial safetyfactor onmean linetension

Accounts for the uncertainty inmean line tension

γdyn Partial safetyfactor ondynamic linetension

Accounts for the uncertainty indynamic line tension

kc Empiricalfactor

Used to estimate the cyclicdegradation effect

LF Fluke length Related to fluke area: LF =1.25⋅√Afluke (approximation)

Ls Line lengthon seabed

For the actual mooring lineconfiguration and characteristic linetension TC

Ls,i Line lengthon seabed atanchorinstallation

For the anchor installation lineconfiguration between stern rollerand anchor shackle, and theinstallation tension Tmin

µ Coefficient ofseabedfriction

Average friction coefficient (bothfrictional and cohesive) over linelength Ls or Ls,i

n Exponent Used in empirical formula forloading rate effect

Nc Bearingcapacityfactor for clay

Corrected for relative depth ofembedment, layering, orientation ofrespective anchor members, etc

Neqv Equivalentnumber ofcycles tofailure

The number of cycles at theconstant cyclic shear stress that willgive the same effect as the actualcyclic load history (see AppendixE)

OCR Overconsolidation ratio

Ratio between maximum past andpresent effective vertical stress on asoil element

q Normal stress Related to embedded anchor line

θ Orientation ofanchor lineelement

θ = 0 for a horizontal element

Q1, Q2 Pileresistance

Pile resistance at loading rates v1and v2, respectively

R Anchorresistance

Resistance in the line direction withreference to penetration depth z andincluding the contribution from theembedded anchor line up to the dip-down point.

∆Rcons Consolidationeffect

Added to Ri.

Rcons Consolidatedanchorresistance

Anchor resistance at the dip-downpoint, including effect ofconsolidation (at onset of cyclicloading)

∆Rcy Cyclicloading effect

Added to Rcons.


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Rcy Cyclic anchorresistance

Anchor resistance at the dip-downpoint, including effects ofconsolidation and cyclic loading

RC Characteristicanchorresistance

Anchor resistance at the touch-down point with effects ofconsolidation, cyclic loading andseabed friction included

Rd Designanchorresistance

With specified partial safety factorsincluded

∆Rfric Seabedfriction

Over line length Ls

Ri Installationanchorresistance

Set equal to Ti (if Ti is properlyverified at installation)

RL,α Anchor lineresistance

Resistance of embedded anchor linefor uplift angle α

RL,α=0 Anchor lineresistance

Resistance of embedded anchor linefor uplift angle α=0

Rult Ultimateanchorresistance

The anchor drags without furtherincrease in the resistance duringcontinuous pulling, which alsodefines the ultimate penetrationdepth zult.

Rai Sum of soilresistance atanchorcomponents

Excluding soil resistance at thefluke

RFN Soil normalresistance

At the fluke

RFS Soil slidingresistance

At the fluke

Rmai Momentcontribution

From Rai

RmFS Momentcontribution

From RFS

RmTIP Momentcontribution

From RTIP

RTIP Tip resistance At anchor members

St Soilsensitivity

The ratio between su and su,r, asdetermined e.g. by UU triaxial tests.

su Intactstrength

For fluke anchor analysis, the directsimple shear (DSS) strength or theunconsolidated undrained (UU)triaxial strength is assumed to bethe most representative intactstrength.

su,r Remouldedshear strength

The undrained shear strengthmeasured e.g. in a UU triaxial testafter having remoulded the claycompletely.


τf,cy Cyclic shearstrength

Accounts for both loading rate andcyclic degradation effects on su.

tcons Consolidationtime

Time elapsed from anchorinstallation to time of loading

tcy Time tofailure

Rise time of line tension from meanto peak level during the designstorm (= 1/4 load cycle period)

thold Installationtensionholdingperiod

Period of holding Tmin at the end ofanchor installation

tsu Time tofailure

Time to failure in a laboratory testfor determination of the intactundrained shear strength (typically0.5 − 2 hours)

T Line tension Line tension model followingsuggestion in /4/

Tv, Th Componentsof line tensionat the shackle

Vertical and horizontal componentof the line tension at the anchorshackle for the actual anchor andforerunner

TC Characteristicline tension

Split into a mean and dynamiccomponent

TC-mean Characteristicmean linetension

Due to pretension and the effect ofmean environmental loads in theenvironmental state

TC-dyn Characteristicdynamic linetension

The increase in tension due tooscillatory low-frequency andwave-frequency effects

Td Design linetension

With specified partial safety factorsincluded

Ti Targetinstallationtension

Installation tension at the dip-downpoint.

Tmin Minimuminstallationtension

Installation tension if Ls,i > 0 (forLs,i = 0 Tmin = Ti)

∆Tmin Drop intension

Double amplitude tensionoscillation around Tmin duringperiod thold

Tpre Pretension inmooring line

As specified for the mooringsystem.

Ucons Soilconsolidationfactor

Ucons = (1+∆Rcons/Ri), where ratio∆Rcons/Ri expresses the effect ofconsolidation on Ri

Ucy Cyclicloading factor

Ucy = (1+∆Rcy/Rcons), where ratio∆Rcy/Rcons, expresses the effect ofloading rate and cyclic degradationon Rcons

Ur Loading ratefactor

Ur = (v i/v2)n

v1 Loading rate Loading rate at extreme line tension

v2 Loading rate Loading rate at the end ofinstallation


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Wa' Submergedanchor weight

Taken as 0.87 ⋅ anchor weight in air

Wm Momentcontribution

From anchor weight W

Wl' Submergedweight ofanchor line

Per unit length of actual linesegment

z Anchorpenetrationdepth

Depth below seabed of the fluke tip.

zi Installationpenetrationdepth

For R = Ri.

zult Ultimatepenetrationdepth

For R = Rult.

2. Fluke Anchor ComponentsThe main components of a fluke anchor (Figure 1) are:

− the shank− the fluke− the shackle− the forerunner

Shackle

ForerunnerInverse catenary

Flukeangle

ShankFluke

θ

β

Figure 1 Main components of a fluke anchor.

The fluke angle is the angle arbitrarily defined by thefluke plane and a line passing through the rear of the flukeand the anchor shackle. It is important to have a cleardefinition (although arbitrary) of how the fluke angle isbeing measured.

Normally the fluke angle is fixed within the range 30° to50°, the lower angle used for sand and hard/stiff clay, thehigher for soft normally consolidated clays. Intermediateangles may be more appropriate for certain soil conditions(layered soils, e.g. stiff clay above softer clay). Theadvantage of using the larger angle in soft normallyconsolidated clay is that the anchor penetrates deeper,where the soil strength and the normal component on thefluke is higher, giving an increased resistance.

The forerunner is the line segment attached to the anchorshackle, which will embed together with the anchorduring installation. The anchor penetration path and theultimate depth/resistance of the anchor are significantlyaffected by the type (wire or chain) and size of theforerunner, see Figure 2.

The inverse catenary of the anchor line is the curvature ofthe embedded part of the anchor line, see Figure 2

3. General fluke anchor behaviourThe resistance of an anchor depends on the ability of theanchor to penetrate and to reach the target installationtension (Ti).

The penetration path and ultimate penetration depth is afunction of

• the soil conditions (soil layering, variation in intactand remoulded undrained shear strength)

• the type and size of anchor,• the anchor’s fluke angle,• the type and size of the anchor forerunner (wire or

chain), and• the line uplift angle α at the seabed level.

It should be mentioned that the penetration behaviour, andpredictability, of the new generation fluke anchors ismuch improved compared to older types of anchors.

In a clay without significant layering a fluke anchornormally penetrates along a path, where the ratio betweenincremental penetration and drag decreases with depth,see Figure 2. At the ultimate penetration depth zult theanchor is not penetrating any further. The anchor is“dragging” with a horizontal (or near horizontal) fluke,and the tension in the line is constant. At the ultimatepenetration depth the anchor reaches its ultimateresistance Rult.


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R(z)

Rult=R(zult)

Z

zult

θ

T

Th

Tv

Chain forerunner

with wire

with wire

T(z)

z

α

Pen

etra

tion

dept

h

Drag

Figure 2 Illustration of fluke anchor behaviour, and definition of Rult.

Since reaching the ultimate penetration depth is associatedwith drag lengths in the range 5 to 10 times the penetrationdepth, it is impractical to design an anchor under theassumption that it has to be installed to its ultimatepenetration depth. A more rational approach is to assumethat only a fraction of the ultimate anchor resistance isutilized in the anchor design, as illustrated by theintermediate penetration depth in Figure 2. This will alsolead to more predictable drag, and should drag occur theanchor may have reserve resistance, which can bemobilized through further penetration.

The cutting resistance of a chain forerunner will be greaterthan the resistance of a steel wire, with the result that achain forerunner will have a steeper curvature (inversecatenary) at the anchor shackle than a wire forerunner, i.e.the angle θ at the shackle is larger. This increases theupward vertical component Tv of the line tension T at theshackle with the consequence that a fluke anchor with achain forerunner penetrates less than one with a wireforerunner, and mobilizes less resistance for a given dragdistance.

It has been demonstrated in the JIP on deepwater anchors/1/ that a non-zero uplift angle α at the seabed, see Figure2, can be acceptable under certain conditions as discussedin Appendix F. If the uplift angle becomes excessiveduring installation the ultimate penetration depth may bereduced. The anchor resistance R(z) is defined as themobilized resistance against the anchor plus the resistancealong the embedded part of the anchor forerunner.However, for anchoring systems with a high uplift angle atthe seabed the contribution from the anchor line to theanchor resistance will be greatly reduced, see Eq. (F-1).

4. Methodology for fluke anchor design

4.1 GeneralTraditionally, the methods used for design of fluke anchorshave been highly empirical, using power formulae inwhich the ultimate anchor resistance is related to theanchor weight, but analytical methods are now graduallyreplacing these crude methods. The need for calibratingthe methods used for fluke anchor design against goodanchor test data will, however, be as great as ever.

The data base for fluke anchor tests is quite extensive, butthere are gaps in many data sets, in the sense of missingpieces of information, which makes the back-fittinganalysis and calibration less reliable than it could havebeen. In most cases there are uncertainties attached to thereported installation data, e.g. soil stratigraphy, soilstrengths, anchor installation tension, contribution fromsliding resistance along the anchor line segment on theseabed, depth of anchor penetration, possible effect ofanchor roll during penetration, etc.

It is therefore of a general interest that future fluke anchortesting, and monitoring of commercial anchor installations,be carefully planned and executed, such that the testdatabase gradually improves, see guidance in Appendix C.

Extrapolation from small to medium size anchor tests toprototype size anchors should be made with dueconsideration of possible scale effects.


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In the following the shortcomings with design charts andthe requirements to analytical methods are discussed. It isrecommended herein that the design practice based ondesign charts be replaced with analytical methods, whichutilise recognised theoretical models and geotechnicalprinciples.

4.2 Design chartsThe design curves published by the American PetroleumInstitute in /6/, which are based on work by the Naval CivilEngineering Laboratory (NCEL), give the ultimate anchorresistance Rult of the respective anchors versus anchorweight. These relationships, which plot as straight lines ina log-log diagramme, suffer from the limitations in thedatabase and the inaccuracies involved in simpleextrapolation of the Rult measured in small size anchor teststo larger anchors. The diagrammes assume an exponentialdevelopment in the resistance for each type of anchor andgeneric type of soil based on the so-called Power LawMethod. The anchor resistance resulting from thesediagrammes is for ultimate penetration of the anchor andrepresents a safety factor of 1.0. As mentioned above,anchors are seldom or never installed to their ultimatedepth, which means that the anchor resistance derivedfrom these diagrammes must be corrected for depth ofpenetration, or degree of mobilization. After suchcorrection the resulting anchor resistance may becomparable with the installation anchor resistance Ridefined in this recommendation, although with theimportant difference that it represents only a predictedresistance until it has been verified by measurementsduring anchor installation. As shown in Section 5.2consolidation and cyclic loading effects, and possiblesliding resistance along the length of anchor line on theseabed, can be added to Ri.

Most of the anchor tests in the database, being the basis forthe design charts, are with a chain forerunner. The effect ofusing a wire forerunner therefore needs to be estimatedseparately. Since the clays are divided in stiffness classesfrom very soft to very hard, an anchor penetrating into aclay where the shear strength increases linearly with depth,or is layered, may 'jump' from one stiffness class toanother in terms of resistance, penetration depth and drag.There are many other limitations in the design methodsrelying on the Power Law Method, which justifies using adesign procedure based on geotechnical principles.

4.3 Analytical tools

4.3.1 General

The analytical tool should be based on geotechnicalprinciples, be calibrated against high quality anchor tests,and validated.

With an analytical tool the designer should be able tocalculate:

• the relationship between line tension, anchorpenetration depth and drag for the actual anchor andline configuration in the prevailing soil conditions

• how this relationship is affected by changing the typeand/or size of the anchor, the type and/or size of theforerunner, or the soil conditions

• the effect on anchor resistance of soil consolidationfrom the time of anchor installation until theoccurrence of the design event, see guidance inAppendix D

• the effects on the anchor resistance of cyclic loading,i.e. the combined effect of loading rate and cyclicdegradation, see guidance in Appendix E

• the effect on the penetration trajectory and designanchor resistance of changing the uplift angle at theseabed, see guidance in Appendix F

4.3.2 Equilibrium equations for fluke anchor analysis

The analytical tool must satisfy the equilibrium equationsboth for the embedded anchor line and for the flukeanchor.

The inverse catenary of the embedded anchor line isresolved iteratively such that equilibrium is obtainedbetween the applied line tension and the resistance fromthe surrounding soil, see /7/. For the fluke anchor bothforce and moment equilibrium is sought. The equilibriumequations for the anchor line and the anchor as included inan analytical tool developed by DNV are given inAppendix A.

5. Recommended design procedure

5.1 GeneralIn the design of fluke anchors the following issues need tobe addressed:

a) Anchor resistance, penetration and drag vs. installationline tension.

b) Acceptable uplift angle during installation and designextreme line tension.

c) Post-installation effects due to consolidation and cyclicloading.

d) Minimum anchor installation tension and installationprocedures.

The philosophy and strategy for design of fluke anchorsfollowed herein is simple and straightforward. Theassessment of the resistance of an anchor is directly relatedto the ability of the anchor to penetrate and the installationline tension applied, which means that requirements toanchor installation will be closely linked to the anchordesign assumptions. The installation aspects will thereforehave to be considered already at the anchor design stage.


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According to this recommendation the geotechnical designof fluke anchors shall be based on the limit state method ofdesign. For intact systems the design shall satisfy theUltimate Limit State (ULS) requirements, whereas one-line failure shall be treated as an Accidental Limit State(ALS) condition. The line tension model adopted hereinsplits the tension into a mean and a dynamic component,see background in /4/, which differs from the line tensionmodel adopted in the current DNV Rules for Classificationof Mobile Offshore Units /5/. Until the design rule hasbeen calibrated based on reliability analysis the partialsafety factors for the anchor design proposed herein will,however, be tentative.

The recommended procedure for design of fluke anchors isoutlined step-by-step in Section 5.3 The procedure is basedon the limit state method of design, and tentative safetyrequirements are given in Section 5.4. Anchor installationrequirements are presented in Section 5.5, and guidancefor installation and testing of fluke anchors is given inAppendix C.

Guidance for calculation of the effects of consolidationand cyclic loading and for assessment of a safe uplift angleat the seabed are given in Appendix D, Appendix E andAppendix F, respectively. Requirements to soilinvestigations are given in Chapter 6 and Appendix G.

In an actual design situation the designer would benefitfrom having an adequate analytical tool at hand forparametric studies, see Section 4.3 for requirements tosuch analytical tools.

Sound engineering judgement should always be exercisedin the assessment of the characteristic resistance of achosen anchor, giving due consideration to the reliabilityof the analytical tool and the uncertainty in the designparameters provided for the site.

5.2 Basic nomenclature and contributions toanchor resistanceThe basic nomenclature used in the anchor designprocedure proposed herein is shown in Figure 1.

The characteristic anchor resistance RC is the sum of theinstallation anchor resistance Ri and the predicted post-installation effects of consolidation and cyclic loading,∆Rcons and ∆Rcy, see Figure 3. To this resistance in the dip-down point is added the possible seabed friction ∆Rfric asshown in Figure 3b). Eq. (1) below shows the expressionfor RC when Ls > 0.

friccyconsiC RRRRR ∆+∆+∆+= (1)

See guidance for assessment of the consolidation effect∆Rcons in Appendix D, the cyclic loading effect ∆Rcy inAppendix E and the seabed friction contribution ∆Rfric inAppendix A.

Figure 3a) illustrates the anchor installation phase, with thelength of line on the seabed equal to Ls,i. The installationanchor resistance Ri is equal to the target installation linetension Ti assuming that Ti is adequately measured anddocumented. The required characteristic anchor resistanceis then obtained by adding the predicted contributions∆Rcons, ∆Rcy and ∆Rfric to Ri as demonstrated in Eq.(1).

The minimum installation tension Tmin is the requiredinstallation tension in the touch-down point, whichaccounts for the installation seabed friction. The targetinstallation line tension Ti (and by definition Ri) is thenequal to

isli LWTT ,'

min ⋅′⋅−= µ (2)

The installation resistance Ri is thus dependent on a correctassessment of the length Ls,i and the resulting seabedfriction. If Ls,i > Ls, see Figure 3, then the minimuminstallation tension Tmin will have to be increasedcorrespondingly such that the load transferred to the dip-down point is equal to the target installation tension Ti inthat point, see Section 5.5 and Appendix C for guidance.The inevitable uncertainty in the assessment of theinstallation seabed friction requires the introduction of apartial safety factor to account for this, see Section 5.5.

Figure 3 c) and d) illustrate a situation when the anchor isinstalled under an uplift angle αi (angle corresponding tofinal anchor penetration) and an uplift angle α (notnecessarily equal to αi) has been predicted also for thecharacteristic line tension. In this case Eq. (1) simplifies to

cyconsiC RRRR ∆+∆+= (3)

and Ti in Eq. (2) becomes equal to Tmin.

The beneficial effect of soil consolidation and cyclicloading on the anchor resistance may be utilized in thedesign of the fluke anchors, such that the target installationload can be reduced by a factor corresponding to thecalculated increase in the anchor resistance due to thesetwo effects.

This effect may be accounted for by proper adjustment (inthis case increase) of the undrained shear strength based onexperimental data. The effect of repeated cyclic loadingthrough a storm will, however, tend to reduce the shearstrength such that the undrained shear strength for use inthe anchor-soil interaction analyses should account forboth these effects. The most appropriate characteristicstrength would then be to use the cyclic shear strength τf,cy.For normally consolidated and slightly overconsolidatedclays cyclic loading will normally lead to a net increase inthe undrained shear strength, see detailed discussion of thecyclic loading effect in Appendix E.


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Ti

Ri

Tmin

Dip-down Touch-down

a) At installation:(no uplift)

Ls,i

µ W' Ls,i

z = zi

Pen

etra

tion

dept

h

z

Drag

∆Rfric=µ W' Ls

Dip-down Touch-down

b) At operation:(no uplift)

Ri+(∆Rcons+∆Rcy)

Ls

RC = Ri+(∆Rcons+∆Rcy+∆Rfric)

RC TC

TC = TC-mean+TC-dyn

∆Rcons

∆Rcy

Drag

z

z = zi

Ti = Tmin

R i

Dip-down = Touch-down

c) At installation:(uplift angle αι)

αι

Ri = Ti = Tmin

z

Drag

Dip-down = Touch-down

d) At operation:(uplift angle α)

RC = Ri+(∆Rcons+∆Rcy)

RC

TC= TC-mean+TC-dyn

∆Rcons

∆Rcy

αTC

z

Drag

Figure 3 Basic nomenclature.


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If the expected depth of anchor penetration is small, e.g. inlayered soils as discussed in Appendix B, a conservativeapproach will be to disregard completely the effect ofconsolidation. The resistance in the direction of the linetension (break-out) may in these cases be governing for theanchor resistance, and needs to be checked, especially ifthe overlying soft layer is very weak.

The break-out resistance may also be of concern in theassessment of a safe uplift angle at the seabed, when smallanchor penetrations are achieved in layered soils, see moreabout uplift in Appendix F.

5.3 Step-by-step description of procedureThe following main steps should be followed in the designof fluke anchors in clay without significant layering, seeflowchart in Figure 4.

Step-by-step procedure:

1) Select mooring pattern.2) Determine the design line tension Td in the touch-

down point, see Eq.(4).3) Choose an anchor4) Compute the penetration path down to the ultimate

depth zult for this anchor, see Chapter 4 and Figure 2for guidance.

5) Compute the design anchor resistance Rd according toEq. (5) for a number of points along the path,concentrating on the range 50% to 75% of the ultimatedepth.− Check if the design limit state can be satisfied, i.e.

Rd ≥ Td, within this range of penetration.− Return to Step 1 or to Step 2 and select another

mooring pattern and/or anchor if this is not thecase.

6) Compute the minimum installation load Tmin accordingto Eq. (6) for the smallest acceptable depth.− Check if Tmin is feasible with respect to cost and

availability of installation equipment.− The anchor design is acceptable if Tmin is feasible.− Return to Step 1 or Step 3 and consider a different

anchor or mooring pattern,if Tmin is excessive.7) Estimate the anchor drop point based on the computed

drag length for penetration depth z = zi, see Figure 3

Note 1. In case of significant layering reference is made toguidance in Appendix B.

Note 2. The acceptable uplift angle during design loading will bedecided from case to case, see guidance in Appendix F.

Note 3. The uplift angle and the position of the touch-downpoint under design load should be computed by mooring lineanalysis for the design tension, not for the characteristic tension.Hence, these quantities may vary between the ULS and the ALS.

Note 4. The proposed partial safety factors for design of flukeanchors are tentative until the design rule proposed herein hasbeen calibrated based on reliability analysis.

Note 5. Analytical tools used for prediction of anchorperformance during installation and operational conditionsshould be well documented and validated, see guidance inSection 4.3 and Appendix A.

5.4 Tentative safety requirements.

5.4.1 General

Safety requirements for use together with therecommended procedure for (geotechnical) design of flukeanchors are for temporary use until a formal calibration ofthe partial safety factors has been carried out.

The safety requirements are based on the limit statemethod of design, where the anchor is defined as a loadbearing structure. For geotechnical design of the anchorsthis method requires that the following two limit statecategories be satisfied by the design:

• the Ultimate Limit State (ULS) for intact system, and• the Accidental Damage Limit State (ALS) for one-line

failure

The design line tension Td at the touch-down point is thesum of the two calculated characteristic line tensioncomponents TC-mean and TC-dyn at that point multiplied bytheir respective partial safety factors γmean, γdyn, i.e.

dyndynCmeanmeanCd TTT γγ ⋅+⋅= −− (4)

where

TC-mean = the characteristic mean line tension due topretension (T pre) and the effect of meanenvironmental loads in the environmental state

TC-dyn = the characteristic dynamic line tension equal tothe increase in tension due to oscillatory low-frequency and wave-frequency effects

The characteristic tension components may be computedas suggested in /4/.


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Step 4Compute penetration path to zult

See Figure 2

Step 2DetermineTd in touch-down point

for selected mooring patternSee Eq. (4)

Step 3Choose anchor type and size

Step 5Compute Rd for a range of

penetration depths along that pathSee Eq. (5)

Rd >Tdwithin range of

penetrationdepths?

Step 6Compute Tmin

for the smallest acceptable depthSee Eq. (6)

Tmin feasible?

Cost OK?

Requiredequipmentavailable?

Step 7Estimate anchor drop point

based on computed drag lengthfor z = zi

See Figure 3

Step 1Select mooring pattern

Anchor design OK!

Yes

Tmin excessive

Return toStep 1 or Step 3

Tmin excessive



Uplift angle OK?See Appendix F

Return to Step 1

No

Yes

No

Yes

No

No

To Step 1

To Step 3To Step 3

To Step 1

Figure 4 Design procedure - flowchart.

Recommended Practice-RP-E301 11

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The design anchor resistance (Rd) is defined as

( ) mfriccyconsid RRRRR γ/∆+∆+∆+= (5)

The purpose of the calculations or testing on which thedesign is to be based, is to maintain the probability ofreaching a limit state below a specified value. In the contextof designing a mooring system the primary objective with theULS design is to ensure that the mooring system stays intact,i.e. to guard against having a one-line failure.

The primary function of an anchor, in an offshore mooringsystem, is to hold the lower end of a mooring line in place,under all environmental conditions. Since extremeenvironmental conditions give rise to the highest mooringline tensions, the designer must focus attention on theseconditions. If the extreme line tension causes the anchor todrag, then the anchor has failed to fulfil its intended function.Limited drag of an anchor need not lead to the completefailure of a mooring system. In fact, it may be a favourableevent, leading to a redistribution of line tensions, andreducing the tension in the most heavily loaded line.However, this is not always the case. If the soil conditionsshow significant differences between anchor locations, then aless heavily loaded anchor may drag first, and lead to anincrease in the tension in the most heavily loaded line, whichmay cause failure in that line. Such a scenario would have toinclude a design analysis that allows anchors to drag,resulting in a much more complicated analysis, and is notrecommended. Instead, the inherent safety margin in theproposed failure event should be taken into considerationwhen setting the target reliability level. Therefore, the eventof inception of drag may be defined as a failure, and is thelimit state definition used in the ULS.

Target reliability levels have to be defined as a part of thecalibration of the design equations and partial safety factors.These levels will be chosen when more experience isavailable from a detailed reliability analysis.

For calibration and quantification of the partial safety factorsfor ULS and ALS design, probabilistic analyses will benecessary. Such studies have been carried out by DNVthrough the Deepmoor Project with respect to both catenaryand taut (synthetic fibre rope) mooring systems /8/. A pilotreliability analysis of fluke anchors, using the extreme linetension distributions from /8/ as a realistic load input, hasbeen performed for one test case as part of the JIP ondeepwater anchors /9/.

Based on the mentioned pilot reliability analysis partialsafety factors have been proposed for design of fluke anchorsin clay. These safety factors, which are considered to beconservative, may be revised when a formal calibration ofthe design rule proposed herein has been performed.

Two consequence classes are considered for the ALS,defined as follows:

1) Failure is unlikely to lead to unacceptable consequencessuch as loss of life, collision with an adjacent platform,uncontrolled outflow of oil or gas, capsize or sinking,

2) Failure may well lead to unacceptable consequences ofthese types.

5.4.2 Partial Safety Factors for the ULS - intact system

For the ULS case, tentative partial safety factors aresuggested in Table 5-1. The factor γm on the predictedcontributions to the anchor resistance are intended to ensureno drag of the anchor for the design line tension.

Ri is known with the same confidence as Ti, and the partialsafety factor is set equal to 1.0 under the assumption that theinstallation tension is measured with sufficient accuracy, e.g.by the DNV Tentune method /10/. If it cannot bedocumented that the installation tension Tmin has beenachieved the partial safety factor on that contribution willhave to be set higher than 1.0.

Table 5-1 Partial safety factors for the ULS.

Consequenceclass

Type ofanalysis

γmean γdyn γm

1 Dynamic 1.10 1.50 1.302 Dynamic 1.40 2.10 1.301 Quasi-static 1.70 1.302 Quasi-static 2.50 1.30

The resistance factor γm shall account also for the uncertaintyin the intact undrained shear strength, as far as it affects thecalculation of the mentioned contributions to RC. It isintended for use in combination with anchor resistancecalculated by geotechnical analysis as described in Section4.3. If the anchor resistance is based on simplified analysis,using design charts as discussed in Section 4.2, thenmodification of the expression for the design resistance Rd inEq. (5) and a change in the partial safety factor γm may beneeded.

5.4.3 Partial Safety Factor for the ALS - one-line failure

The purpose of the accidental damage limit state (ALS) is toensure that the anchors in the mooring system provide anadequate amount of resistance to avoid subsequent mooringsystem failure, if one mooring line should initially fail forreasons outside of the designer's control. Such an initialmooring line failure may also be considered to include thepossibility of anchor drag for that line.

Subsequent drag of any anchor is conservatively assumed toimply mooring system failure in the ALS. This avoids thecomplexity of including uncertain anchor drag lengths in themooring system analysis. Thus, the ALS is formulated toavoid anchor drag, similarly to the ULS.

The target reliability level for consequence class 1 should beset to avoid mooring system failure, but without a high levelof conservatism, since the consequences are notunacceptable. The target reliability level for consequenceclass 2 should be higher in view of the consequences. Itwould seem reasonable to initially adopt the same targetlevels for the anchors as for the mooring lines. However,moderate anchor drag is usually perceived to be less seriousthan line failure, and some relaxation of the target levels maybe possible.


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Detailed analysis of the ALS has not been carried out yet, butsome reduction of the resistance factor γm applied to the ULSseems appropriate for consequence class 1. The partial safetyfactors given in Table 5-2 are tentatively suggested when thecharacteristic anchor resistance is defined as for the ULS, i.e.with the zero drag requirement retained.

Table 5-2 Partial safety factors for the ALS

Consequenceclass

Type ofanalysis

γmean γdyn γm

1 Dynamic 1.0 1.10 1.02 Dynamic 1.00 1.25 1.31 Quasi-static 1.10 1.02 Quasi-static 1.35 1.3

Some drag could possibly be permissible in consequenceclass 2 also, but this would have to be quantified and theresulting offset of the mooring system be checked against theallowable offset of the system. The characteristic resistancewould also have to be redefined for an anchor that isdragging. This case is not covered by the present version ofthis recommended practice.

5.5 Minimum installation tension.The prescribed minimum installation tension Tmin, see Figure3, will to a great extent determine the geotechnical safety ofthe anchor as installed. In the case of no uplift on the seabedduring anchor installation Tmin may be assessed from Eq. (6)below. The line length on the seabed during installation Ls,imay, however, be different from the length Ls assumed in theanchor design calculations, which is accounted for in Eq. (6).

( ) mfriccyconsimisld RRRLWTT γγµ /' ,,min ∆+∆+∆−⋅⋅⋅+= (6)

The uncertainty in the predicted seabed friction from aninstallation resistance point of view is treated differentlyfrom the design situation:

At the stage of anchor installation the prescribed minimuminstallation load Tmin in the touch-down point is intended toensure that the target installation load Ti in the dip-downpoint is reached, accounting for the installation seabedfriction over the length Ls,i. Therefore, the predicted seabedfriction is multiplied by a partial safety factor γm,i.Tentatively this factor is set equal to γm for the predictedanchor resistance, i.e. γm,i = 1.3

When Ti has been verified by measurements during anchorinstallation, the anchor installation resistance Ri is knownwith the same degree of confidence. On this basis the partialsafety factor on Ri is set equal to 1.0 as shown in Eq.(5). Theother contributions, among them the seabed friction ∆Rfric,are predicted and must be divided by a partial safety factorγm, as shown in Eq.(5).

The installation anchor resistance Ri in the dip-down pointbased on the measured installation tension Tmin as given byEq(6) will then become

imislii LWTTR ,,min ' γµ ⋅⋅⋅−== (7)

If the anchor can be installed with an uplift angle and upliftis allowed for also during design loading, the length of lineon the sea bed will be set to zero (i.e. Ls = Ls,i = 0), whichchanges Eq. (6) to

( ) mcyconsd RRTT γ/min ∆+∆−= (8)

In practice, Tmin will have to be calculated through aniterative process following the step-by-step procedureoutlined in Section 5.3. The resulting Tmin will then beevaluated and compared with the installation tension that canbe achieved with the installation scenarios underconsiderations, see also Appendix C.

Eq. (6) and Eq. (8) assume implicitly that the installation linetension is measured with such an accuracy that the partialsafety factor on Ti and thus on Ri can be set equal to 1.0. It istherefore imperative for achieving the intended safety levelthat adequate means for measuring the installation linetension versus time is available on board the installationvessel.


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6. Requirements to Soil InvestigationThe planning and execution of soil investigations for designof fluke anchors should follow established and recognizedoffshore industry practice. As a general guidance to achievethis quality of soil investigation reference is made to theNORSOK standard /11/, which makes extensive referencesto international standards. Some specific recommendationsare given herein for soil investigations for fluke anchors.

For design of fluke anchors the soil investigation shouldprovide information about:

− Seafloor topography and sea bottom features− Soil stratification and soil classification parameters− Soil parameters of importance for all significant layers

within the depth of interest.

The most important soil parameters for design of flukeanchors in clay are the intact undrained shear strength (su),the remoulded undrained shear strength (su,r), the claysensitivity (St), the coefficient of consolidation (cv), and thecyclic shear strength (τf,cy) for each layer of significance.

As a minimum, the soil investigation should provide thebasis for specification of a representative soil profile and theundrained shear strengths (su and su,r) for each significant soillayer between the seabed and the maximum possible depth ofanchor penetration. The number of soil borings/in situ testsrequired to map the soil conditions within the mooring areawill be decided from case to case.

The ultimate depth of penetration of fluke anchors in clayvaries with the size of the anchor and the undrained shearstrength of the clay. It is convenient to account for the sizeof the anchor by expressing the penetration depth in terms offluke lengths. In very soft clay the ultimate penetration maybe up to 8-10 fluke lengths decreasing to only 1-2 flukelengths in strong, overconsolidated clays. However, ananchor is never (or seldom) designed for full utilisation ofthe ultimate anchor resistance Rult, because of the associatedlarge drag distance.

The necessary depth of a soil investigation in a clay withoutsignificant layering will be a function of the size of theanchor, the degree of mobilisation of Rult, and the shearstrength of the clay. The upper few metres of the soil profileare of particular interest for the critical initial penetration ofthe anchor, and for assessment of the penetration resistanceand the inverse catenary of the embedded part of the anchorline.

General requirements to the soil investigation for flukeanchor foundations, in addition to the recommendations in/11/ are provided in Appendix G.

7. References/1/ Dahlberg, R., Eklund, T. and Strøm, P.J. (1996),

Project Summary - Part 1, Joint Industry Project ondesign procedures for deep water anchors, DNVReport No. 96-3673. Høvik.

/2/ Dahlberg, R, Strøm, P.J., Ronold, K.O., Cramer, E.Mathisen, J., Hørte, T. and Eklund, T. (1998), ProjectSummary - Part 2, Joint Industry Project on designprocedures for deep water anchors, DNV Report No.98-3591. Høvik.

/3/ Dahlberg, R. (1998), Design Procedures forDeepwater Anchors in Clay, Offshore TechnologyConference, Paper OTC 8837, pp. 559-567. Houston.

/4/ Egeberg, B., Mathisen, J., Hørte, T. and Lie H.(1998), Modifications to DNV Mooring Code(POSMOOR) and their Consequences, Conferenceon Offshore Mechanics and Arctic Engineering(OMAE), Paper 1460. Lisbon.

/5/ DNV Rules for Classification of Mobile OffshoreUnits (1996), Position Mooring (POSMOOR), Pt.6Ch.2, January 1996.

/6/ API Recommended Practice 2SK (1996),Recommended Practice for Design and Analysis ofStationkeeping Systems for Floating Structures , 2ndEdition, effective from March 1997.

/7/ Vivitrat, V., Valent, P.J., and Ponteiro, A.A (1982),The Influence of Chain Friction on Anchor PileBehaviour, Offshore Technology Conference, PaperOTC 4178. Houston.

/8/ Hørte, T., Lie, H. and Mathisen, J. (1998),Calibration of an Ultimate Limit State for MooringLines, Conference on Offshore Mechanics and ArcticEngineering (OMAE), Paper 1457. Lisbon.

/9/ Cramer, E.H., Strøm, P.J., Mathisen, J., Ronold,K.O. and Dahlberg, R. (1998), Pilot ReliabilityAnalysis of Fluke Anchors, Joint Industry Project ondesign procedures for deep water anchors, DNVReport No. 98-3034. Høvik.

/10/ Handal, E. and Veland, N. (1998), Determination oftension in anchor lines , 7th European Conference onNon-Destructive Testing, Copenhagen, 26-29 May,1998.

/11/ NORSOK standard (1996), Common RequirementsMarine Soil Investigations, G-CR-001, Rev. 1, datedMay 1996.


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Appendix A:Analysis tool for fluke anchor design

A1 GeneralAn analytical tool for fluke anchor design should be ableto calculate anchor line catenary in soil as well as the flukeanchor equilibrium itself. Further, the analytical toolshould be able to assess the effect of consolidation asbeing an important design issue in soft clay. Thefollowing section describes in brief the principles for suchan analytical tool developed by DNV /A-1/.

A2 Anchor line seabed frictionThe resistance due to seabed friction ∆Rfric in Eq. (1) isexpressed as follows:

slsfric LWLfR ⋅⋅=⋅=∆ 'µ (A-1)

where

f = unit friction (also of cohesive nature)

Ls = line length on seabed for thecharacteristic line tension TC

µ = coefficient of seabed friction

Wl' = submerged weight of the anchor line perunit length

Guidance NoteBased on the back-fitting analysis of data from measurementson chain segments reported in /A-2/ and estimated values forwire, the following coefficients of seabed friction arerecommended for clay1):

Table A-1 Coefficient of seabed fricti on

Wire Lower bound Default value Upper bound

µ 0.1 0.2 0.3

Chain Lower bound Default value Upper bound

µ 0.6 0.7 0.81) The unit friction f along the embedded part of the anchor line

as required for calculation of anchor line contribution to theanchor resistance R i is given by Eq. (A-5).

--- End of Guidance Note ---

A3 Equilibrium equations of embeddedanchor lineThe equilibrium of the embedded part of the anchor linecan be solved approximately by closed form equations orexactly in any soil strength profiles by iterations /7/. Thenormal stress q and the unit soil friction f, which act on ananchor line element in the soil are shown schematically inFigure A-1.

q

f

θW l'

ds

dθT

Figure A-1. Soil stresses at an anchor line segment insoil

The loss in line tension dT over one element length ds iscalculated from the following formula:

)sin(' θ⋅−⋅−= lWASfdsdT (A-2)

where

T = anchor line tension

? = orientation of anchor line element (θ = 0for a horizontal element)

AS = effective surface of anchor line per unitlength of line

ds = element length

The angular advance from one anchor line element to thenext is then solved by iterations from the followingformula:

TWABq

dsd l )cos(' θθ ⋅−⋅

=(A-3)

where

q = normal stress

AB = effective bearing area of anchor line perunit length of line

Guidance NoteThe following default values are suggested for the effectivesurface area AS and the effective bearing area AB:

Table A-2 Effective surface and bearing area

Type of forerunner AS AB

Chain 11.3⋅d 2.5⋅d

Wire or rope π⋅d d

where


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d = nominal diameter of the chain and actualdiameter of the wire or rope.


The normal stress q on the anchor line is calculated fromthe following equation:

uc sNq ⋅= (A-4)

where

Nc = bearing capacity factor

su = undrained shear strength (direct simpleshear strength suD is recommended)

Effect of embedment on the bearing capacity factor shouldbe included.

Guidance NoteBased on the back-fitting analysis reported in /A-2/, thefollowing bearing capacity factors are recommended for theembedded part of the anchor line in clay1):

Table A-3 Bearing capacity factor for wire/chain 1)

Wire / Chain Lowerbound

Defaultvalue

Upperbound

Nc 9 11.5 14

1) See Guidance Note above for values of the effective bearingarea AB, which is a pre-requisite for use of the bearingcapacity factors given here.


The unit friction f along the anchor line can be calculatedfrom the following formula:

usoil sf ⋅= α (A-5)

where

αsoil = adhesion factor for anchor line

Guidance NoteBased on the back-fitting analysis of data from measurementson chain segments reported in /A-2/, and estimated values forwire, the following coefficients of seabed friction arerecommended for the embedded part of the anchor line clay1):

Table A-4 Adhesion factor for wire and chain 1)

Wire Lower bound Default value Upper bound

αsoil 0.2 0.3 0.4

Chain Lower bound Default value Upper bound

αsoil 0.4 0.5 0.6

1) See Guidance Note above for values of the effectivesurface area AS, which is a pre-requisite for use of theadhesion factor given here


A4 Equilibrium equations for fluke anchorMoment equilibrium and force equilibrium can be solvedfor the fluke anchor for two different failure modes. Onemode leading to further anchor penetration in a directionclose to the fluke penetration direction, and a second modeleading to reduced or no further penetration. In principle,the soil resistance contributions are the same for the twofailure modes, but in the first failure mode the soilresistance normal to the fluke may not take on the ultimatevalue. Using the symbols shown in Figure A-2 thenecessary equilibrium equations are defined and explainedin the following.

RFS

Penetration direction

RFN

Rai

T

θ

Wa'

e

βRTIP

Figure A-2. Principal soil reaction forces on a fluke(anchor penetration direction coincides with flukepenetration direction).

For the range of possible penetration directions, thehorizontal and vertical equilibrium should satisfy thefollowing equations:

Horizontal equilibrium:

+⋅+⋅=⋅ ∑=

)cos()cos()cos(1

ββθ FS

N

iai RRT

)sin()cos( ββ ⋅+⋅ FNTIP RR

(A-6)

Vertical equilibrium

−+⋅=⋅ ')cos()sin( aFN WRT βθ

⋅+⋅+⋅∑

=

)sin()sin()sin(1

βββ TIPFS

N

iai RRR

(A-7)

where

T, θ = tension and corresponding orientation ofanchor line at the shackle

RFN = soil normal resistance at the fluke

RFS = soil sliding resistance at the fluke

RTIP = tip resistance at the fluke

Rai = soil resistance at the remainingcomponents of the anchor (separatedthrough anchor geometry)

Wa' = submerged anchor weight

β = penetration direction of fluke


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The normal resistance will be the normal stress times thebearing area of the anchor part being considered, and mayneed to be decomposed in the three orthogonal directionsdefined (one vertical and two horizontal). The normalstress can be calculated from the following formula:

uc sNq ⋅= (A-8)

where

Nc = bearing capacity factor

Sliding resistance will be the unit friction times theadhesion area of the anchor part being considered. The unitfriction f along the anchor part can be calculated from thefollowing formula:

usf ⋅= α (A-9)

where

α = adhesion factor for anchor

The bearing and adhesion areas should in this case bemodelled with due consideration of the actual geometry ofthe anchor.

Guidance NoteBased on the back-fitting analysis reported in /A-2/ thefollowing values are tentatively recommended for theresistance towards the various anchor members in clay:

Table A-5 Bearing capacity and adhesion factor

Bearing capacity factor 1)

(Nc ) for:Adhesion factor

(α) for:

RFN Rai RTIP RTIP RFS

12.5 2) 12.5 12.5 1 / St 1 / St

1) Effect of shape, orientation and embedment of the variousresistance members on the anchor should be included asrelevant.

2) Actual degree of mobilisation of this value as required tosatisfy moment equilibrium.


Due consideration should be given to the difference inadhesion for continuous penetration and inception ofanchor drag (failure event). For the latter, an adhesionfactor compatible with time available for consolidationshould be assessed, see Appendix D.

Horizontal and vertical equilibrium for a certain flukepenetration direction can now be achieved for a number offluke orientations and line tensions at the shackle. In orderto determine the correct penetration direction and thecorresponding line tension, moment equilibrium must besatisfied (here taken with respect to the shackle point):

( ) 01

=⋅+−++∑=

eRWmRmRmRm FNTIPFS

N

iai

(A-10)

where

RmFS = moment contribution from soil slidingresistance at the fluk e

RmTIP = moment contribution from tipresistance at the fluke

Wm = moment contribution from anchorweight

RFN = soil normal resistance at the fluke

e = lever arm between shackle and the lineof action of the normal resistance at thefluke

Rmai = moment contribution from soilresistance at the remaining componentsof the anchor (separated through anchorgeometry)

When the anchor penetrates in the same direction as thefluke, any possible lever arm (e) and normal resistance thatcan be replaced by a realistic stress distribution at the flukeshould be considered. When the anchor penetrates inanother direction than the fluke, the centre of normalresistance on the fluke should act in the centre of the flukearea.

A5 References/A-1/ Eklund T and Strøm, P.J. (1998), DIGIN

Users’s Manual ver. 5.3 , DNV Report No.96-3637, Rev. 03, dated 20 April 1998.Høvik

/A-2/ Eklund T and Strøm, P.J. (1998), Back-fitting Analysis of Fluke Anchor Tests inClay, DNV Report No. 96-3385, Rev. 03,dated 16 September 1997. Høvik


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Appendix B:Anchors in layered clay

B1 GeneralThe general anchor behaviour addressed in Chapter 0 andFigure 2 is for fluke anchors in clay without significantlayering. Guidance for assessment of the penetrationability of fluke anchors in layered clay is given in thefollowing. Layering is understood herein as a soil layersequence comprising a soft layer overlain and/or underlainby a relatively stiffer clay (or sand) layer.

Experience has shown that a fluke anchor will oftenpenetrate through a surface layer of sand or relativelystiffer clay into an underlying softer clay layer, providedthat the thickness of this surface layer is less than 30 to 50% of the fluke length of the actual anchor. Although thiscannot be taken as a guarantee, it can be used as guidancewhen various anchor alternatives are being evaluated. Theprevailing soil conditions and possible past experiencewith fluke anchor installation in the actual area should beevaluated before the choice of anchor is made.

In a soft-stiff layer sequence the ability of an anchor topick up the resistance of the underlying stiffer layerdepends on the difference in soil strength between the twolayers, the depth to the stiffer layer and the angle of thefluke plane when it meets the stiffer layer. If this 'attack'angle is too small the anchor will drag on top of the stifflayer at constant load. If it is too large the anchor mayrotate and break out of the soil rather than continue alongthe initial penetration path. In both these cases the targetinstallation load will not be reached. Changing the flukeangle or choosing another type and/or size of anchor mayimprove the situation.

A stiff-soft-stiff layer sequence involves the extracomplication that penetration through the upper stiff layermay require a smaller fluke angle than desirable forpenetration through the locked-in soft layer down to andinto the second stiff layer. Again, the anchor should meetthe deeper stiff layer at an angle, which ensures a grip andpenetration also into that layer. If the thickness of the twofirst layers is such that the anchor approaches the deeperlayer at an angle, which is too small, the anchor will justdrag along the surface of that layer. This may bevisualised by the fact that the drag becomes excessive, ornon-tolerable, and the target installation load is neverreached. In most cases, predictions may show that thepenetration path improves in that respect, and becomessteeper for a given depth and a given fluke angle, if theanchor is increased in size. It may also be possible to findmore optimal, non-standard, combinations between anchorsize and fluke angle, which account both for the overlyingand the underlying stiff layer.

From the above it is evident that layer thickness, depth toboundaries between layers, and soil strength need to bedocumented for proper design of a fluke anchor foundationand to avoid unexpected behaviour of the anchor duringthe installation phase, see Chapter 6 and Appendix G forrequirements to soil investigation.


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Appendix C: Installation and testing of fluke anchors

C1 GeneralFluke anchor design is by tradition empirical as illustratedby the design charts published by the American PetroleumInstitute /6/. The anchor tests being the basis for suchdesign charts are of variable quality, and typically there aregaps in the test data, which makes it difficult to fullyunderstand and rely on the test results. All reasonableefforts should therefore be made to ensure that themeasurements are reliable and include the most crucial testdata for maximum usefulness of the results andimprovement of the database. This should be fullyappreciated when installing both test anchors andprototype anchors.

C2 Minimum installation tensionThe anchor installation should follow procedures, whichhave been presented and agreed to by all parties well aheadof the installation. By prescribing a minimum installationtension Tmin, see Section 5, the intention is to ensure thatthe design assumptions are fulfilled during anchorinstallation. In other words, if the anchor is installed toTmin the design anchor resistance Rd has implicitly alsobeen verified. This tension level should be held for aspecified holding period, which period may be soildependent. Any relaxation (drag) during this periodshould be compensated for, such that the required linetension is maintained as constant as possible. The anchorinstallation and testing log should document the events andthe measurements taken from start to end of theinstallation.

C3 Monitoring of fluke anchor installations

C3.1 GeneralWhen installation of prototype, or test anchors, is beingplanned it is essential that the most essential boundaryconditions for the installation be taken into consideration.Well ahead of the installation such backgroundinformation should be compiled and documented.

If practical (e.g. if ROV assistance is available duringanchor installation) it is recommended to check theposition and orientation of the anchor, as well as thealignment, straightness and length on the seabed of the aslaid anchor line, before start of tensioning. Significantmisalignment of the installation anchor line will requireextra line tension to reach the specified target installationtension Ti, which has to be estimated and accounted for.

During the anchor installation a number of parametersneed to be measured to serve as a documentation of theinstallation. The more information that is recorded beyondthe minimum documentation requirements, the moreuseful the installation data will become in the end.

Monitoring of the anchor installation should, as aminimum, provide data on

− line tension− line (pitch) angle at the stern roller− anchor drag

These items should be measured as a function of time fromstart to end of the installation using the clock on the PC asa reference time. A calibrated transducer, being a segmentof the installation line, should preferably be used tomeasure the line tension.

If manual measurements are taken intermittently, seechecklist below, they should be stored into the PC log atthe time of the event.

The final installation measurements should at leastdocument that the minimum installation tension Tmin has beachieved and maintained during the specified holding time.

The checklist below indicates the type of information thatshould be focussed on before and during the installationand testing of fluke anchors. This checklist can be used asa guidance both for installation of both prototype and testanchors.

C3.2 Checklist1) Before the installation.a) Assessment of the most likely soil stratigraphy at the

anchor location and the soil strength of significantlayers (from soil investigation report), see Chapter 6for guidance.

b) Specification of the anchor and the installation lineconfiguration.

c) Specification of the fluke angle(s) to be used, and howthis angle is defined, see Section 2 and Figure 1 forguidance.

d) Estimate of friction resistance at the stern roller.e) Equipment and procedures for anchor installation, e.g.

type and tensioning system of the vessel, method oflaying and tensioning the anchors, availability of ROV,etc.

f) Type of measurements to be undertaken, andprocedures to be applied, from check list below.


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2) During the installation.a) Line tension (horizontal component measured at deck

level)1

b) Drag (method of measurement, reference point)c) Penetration depth (method of measurement, at least the

final depth)d) Line angle with the horizontal outside the stern roller

(at least for the final line tension)e) Pull-in speed (vessel speed, drag and line angle at stern

roller versus time)

3) Final installation measurementsa) Maintaining Tmin (during specified holding time

thold = 15 to 30 minutes)b) Measure tension vs time during holding time (mean

tension ≥ Tmin)c) Drag (corresponding to final penetration depth)d) Penetration depth (best estimate of final depth)

The database for fluke anchors loaded to their ultimateresistance Rult is unfortunately limited to rather smallanchors. The largest anchors tested in connection withoffshore projects have normally not reached the Rult, butfor the future it would be fruitful for the industry if themost significant parameters (line tension, drag and finalpenetration depth) are recorded during all installations, atleast in a few locations out of many.

In this connection it is important that all reasonable effortsare made to make the recorded data as reliable as possible,since the assessment of the safety of the anchoring systemdepends on such installation data.

1 It is recommended to measure the installation tension by meansof the DNV Tentune method /10/.

C4 Anchor installation vesselsThe bollard pull of the most powerful new generationanchor handling vessels is in the range 2 to 2.5 MN.Depending on the required minimum installation tensionTmin at the touch-down point, one or two AHV's may berequired. As an alternative to using AHV's the anchortensioning can be done from a special tensioningvessel/barge or from the floater itself. If two oppositeanchors are tensioned simultaneously line tensions up to 5to 6 MN or even 10 MN can be reached.

The chosen scenario for anchor installation shall ensurethat the specified minimum installation tension Tmin can bereached. The bollard pull, winch capacity and minimumbreaking load (MBL) of the installation wire on the actualvessel(s) will have to be assessed on this basis. If Tmincannot be reached due to pulling limitations set by thevessel(s), the design anchor resistance Rd according toEq.(5), and thus the intended safety level of the anchors,will not be achieved.

It is essential that all parties involved in the decisionsrelated to the anchor design appreciate the relationshipbetween anchor resistance and installation tension. In deepwaters, unless lightweight anchor lines are used, theweight and sea bed friction of the anchor lines limits thenet line tension that can be used for anchor penetration,which must be considered when the requirements for theinstallation vessel are specified.


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Appendix D: Effect of consolidation

D1 GeneralDuring continuous penetration of the anchor, the frictionresistance will be governed by the remoulded shearstrength, sur, in a narrow zone close to the anchor. In ananalytical model this may be accounted for through theadhesion factor, α, which will depend on the soilsensitivity, St, i.e. the ratio between the intact (in situ)undrained shear strength, su, and su,r

St = su / su,r (D-1)

The minimum α-value is tentatively set equal to theinverse of the sensitivity, i.e.

αmin= 1 / St (D-2)

After an anchor has been installed to a certain installationtension (and depth), the remoulded soil will graduallyreconsolidate and regain its intact shear strength. As aresult the resistance against further penetration willincrease. This effect is in the literature referred to assoaking, set-up or consolidation of the anchor and theanchor line.

D2 Assessment of the effect of consolidation

The effect of soil consolidation is that the installationanchor resistance Ri will increase as a function of thetime elapsed since installation tcons to a maximum value,which depends on the soil sensitivity St. For a particularanchor and depth of penetration this increase may bedescribed through the consolidation factor Ucons, i.e.

Ucons = f(tcons, St, and geometry, depth andorientation of the anchor)

(D-3)

From a geotechnical point of view there should be nomajor difference between fluke anchors and e.g. piles orthe skirts of a gravity base structure, when the effects ofinstallation and subsequent reconsolidation on the clayundrained shear strength are considered. Theconsolidated resistance Rcons is the installation resistancewith superimposed consolidation effect as shown in Eq.(D-4).

( )iconsiconscons RRRURR /1 ∆+⋅= =i (D-4)

The degree of consolidation that can be applied to thefrictional part of the resistance can be assessed bylooking at the drainage characteristics in a zone adjacentto the anchor, which is influenced (remoulded) due to theanchor penetration. The length of this zone depends onthe anchor geometry and the actual soil characteristics.Guidance for modelling and calculation of theconsolidation effect can be obtained using the experiencefrom e.g. tests on piles.

The consolidation factor Ucons related to the total anchorresistance will be much smaller than reflected by thesensitivity of the clay, since the frictional resistance onlycontributes to part of the total resistance. The relationbetween the consolidation factor Ucons and the increase inthe frictional resistance depends on the geometry of theanchor, and its final depth of penetration into the soilduring the installation phase. A reliable quantification ofthis effect can only be obtained by site-specific relevantfull-scale tests or by adequate analytical tools. Theanalytical tools should be able to predict both thepenetration part and the subsequent consolidatedcondition. It is essential that the analytical tool accountsfor full force and moment equilibrium that is compatiblewith the failure modes in question, see Appendix A.

Caution is recommended in the assessment of thepossible consolidation effect when the likely failuremode, following upon such consolidation, may eitherreduce or prevent further penetration. Overloading willin this case initiate anchor movement in the direction ofthe line tension, before the full effect from consolidationis utilised. When such movement has been initiated, thesoil closer to the flukes will loose the effect fromconsolidation, and the anchor will continue to drag inremoulded soil conditions. This can in particular beexpected close to the seabed, where the resistance in thedirection of the line tension is limited, but may also berelevant at larger depths, if the anchor has penetratedwith a very large fluke angle, or in layered soil if thefluke tip has penetrated partly into a stiffer layerunderlying a soft layer.

In practice, the consolidation factor Ucons must beassessed on a case by case basis.

Guidance NoteRange of values for Ucons vs. typical soil sensitivity St

Table D-1 Consolidation factor, Ucons

Ucons

Soil sensitivity,St

Lowerbound

Defaultvalue

Upperbound

2 1.25 1.30 1.35

2.5 1.35 1.45 1.55



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Appendix E: Effect of cyclic loading

E1 BackgroundIn order to understand how cyclic loading may affect theresistance of fluke anchors a parallel may be drawnbetween piles and fluke anchors. Important work on theeffect of loading rate on axial pile capacity has beenpublished by Bea and Audibert /E-1/, followed by Kraft etal /E-2/, and later by Briaud and Garland /E-3/.Fundamental work on the effects of cyclic loading on theundrained shear strength of clay and the cyclic response ofgravity base foundations has been published by Andersenand Lauritzen /E-4/.

Cyclic loading affects the static undrained shear strength(su) in two ways:

During a storm, the rise time from mean to peak load maybe about 3 - 5 seconds (1/4 of a wave frequency loadcycle), as compared to 0.5 to 2 hours in a staticconsolidated undrained triaxial test, and this higher loadingrate leads to an increase in the undrained shear strength

As a result of repeated cyclic loading during a storm, theundrained shear strength will decrease, the degradationeffect increasing with the overconsolidation ratio (OCR) ofthe clay.

The following relationship is suggested in /E-3/ fordescription of the effect of the loading rate, v , on pilecapacity, Q

(Q1/Q2) = (v1/v2)n (E-1)

where Q1 and Q2 represent the pile capacity at loading ratesv1 and v2, respectively.

E2 Application to fluke anchor designThe rate of loading experienced by the anchor (and theclay surrounding the anchor) is normally higher duringwave loading than during anchor installation, and theanchor resistance increases relative to the increase in rateof loading. Using the experience from pile testing asexpressed by Eq. (E-1) a loading rate factor Ur may beintroduced, which expresses the loading rate effect on theanchor resistance, i.e.

Ur = (v1/v2)n (E-2)

One practical problem with Eq. (E-2) is to determinerepresentative values for the loading rates v1 and v2.Another problem is to assess the value of exponent n in theequation for Ur. In addition, Eq. (E-2) does not accountfor the strength degradation due to cyclic loading.

The most direct, and preferred, approach to account forboth the loading rate effect and the cyclic degradationeffect is to determine the cyclic shear strength τf,cy of theclay, following the strain accumulation proceduredescribed in

The strain accumulation method utilises so-called strain-contour diagrammes to describe the response of clay tovarious types, intensities and duration of cyclic loading:

Given a clay specimen with a certain su and OCR, which issubjected to a load history defined in terms of a sea stateand a storm duration, the intensity of that storm isgradually increased until calculations according to thestrain accumulation method show that the soil fails incyclic loading.

In a catenary mooring system the loads transmitted to theanchors through the anchor lines will always be in tension(one-way), which has a less degrading effect on the shearstrength than two-way cyclic loading (stress reversal). Thefailure criterion for one-way cyclic loading is developmentof excessive accumulated permanent strains. Themaximum shear stress the soil can sustain at that state offailure is equal to the cyclic shear strength τf,cy.

The load history for use in the calculations should accountfor the combination of wave-frequency load cyclessuperimposed on low-frequency, slowly varying, loadcycles, particularly the amplitude of cyclic loads relative tothe average (or mean) load level.

If cyclic soil data, applicable for the actual site, areavailable, the cyclic strength τf,cy may be determinedaccording to the procedure outlined in /E-4/. The cyclicstrength τf,cy as defined in /E-4/ incorporates effects of bothloading rate and cyclic degradation, provided that thecyclic load period is representative for the variation in linetension with time at the anchoring point. This would leadto a combined loading rate and cyclic degradation factor,or simply a cyclic loading factor Ucy as shown in Eq. (E-3)below.

Ucy = τf,cy/su = f [tsu/tcy, soil data, loadhistory, etc]

(E-3)

where

τf,cy = cyclic shear strength with time to failure

tcy = (1/4)⋅(load period)

su = static undrained shear strength with time tofailure

tsu = 1 hour


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If a fluke anchor has been subjected to consolidation for acertain period of time after the installation took place thereference anchor resistance for assessment of the cyclicloading effects will be the consolidated anchor resistanceRcons in Eq. (D-4). This leads to the following expressionfor the cyclic anchor resistance Rcy.

cysconicyconsicy R?RRUURR ∆++=⋅⋅= )( (E-4)

The expression for Ucy then becomes:

( )conscycy RRU /1 ∆+= (E-5)

If no relevant cyclic soil data exist for the site, andexperience from better documented sites with similar soilconditions cannot be drawn upon, a conservativeassessment of τf,cy may be made based on Eq. (E-2)corrected for the effect of cyclic strength degradation. Inorder to account for the possible strength degradation dueto one-way cyclic loading, the net effect of loading rate (Ur- 1) should therefore be multiplied by a cyclic degradationfactor k c. The expression for Ucy is then changes to:

Ucy = 1 + k c⋅(Ur - 1) = 1 + k c⋅{(v1/v2)n -1} (E-6)

k c is a function of the line tension load history through astorm and the characteristics of the clay. The load historyvaries with water depth, type of rig and mooring lineconfiguration. Therefore the value of k c should beassessed from case to case.

Guidance for assessment of both the loading rate factor Urand the cyclic loading factor Ucy can be found in thepublished information about cyclic behaviour of clay, e.g.tests on Drammen clay in /E-4/, on Troll clay /E-5/ and onMarlin clay in /E-6/. It is noted based on the test resultspresented for the Marlin clay that carbonate content maysignificantly affect the cyclic response of clay. Caution istherefore warranted in the use of experience from testingof non-carbonate clay, if the actual clay contains more than10 % carbonate.

Guidance NoteBasis for an approximate assessment of the effect of cyclicloading is provided in the following.

Loading rate factor Ur

As outlined above the effect of cyclic loading is two-fold, theloading rate effect and the cyclic degradation effect.In a cyclic laboratory test on clay the cycle period is often setto 10 seconds, which means that the load rise time tcy frommean level to the first peak load is 2.5 seconds (= tcy). If thecycle amplitude is high enough to fail the clay specimen duringthat first quarter of the first load cycle (Neqv = 1), thecorresponding cyclic strength τf,cy of the clay divided by thestatic undrained shear strength suD is a measure of the loadingrate factor Ur for the actual clay, i.e.

Ur = τf,cy/su,D (for Neqv = 1).

Figure E-1 presents excerpts of published results from cyclicdirect simple shear tests on the Drammen clay /E-4/, on theTroll clay /E-5/ and on the Marlin clay /E-6/.Figure E-1a) shows the loading rate factor Ur as a function ofthe average shear stress level τa/suD during the test. It is worthnoting that the loading rate effect is most pronounced for τa/suDin the range 0.5 to 0.7, and that for higher shear stress levelsthe effect reduces at an accelerating rate, particularly for thecarbonate type Marlin clay (Unit IIb), which has a carbonatecontent of 15 - 20 % according to /E-6/.Based on the mooring analysis it will be possible to define themean, low-frequency and wave-frequency components of thecharacteristic line tension, such that a basis is obtained forassessment of a likely range for the parameter ? a/suD.Typically the line tension in a catenary mooring system maygenerate an average shear stress level τa/suD in the range 0.6 to0.8. For this range Ur = 1.4 - 1.75 for four of the examplesshown in Figure E-1a), but may be as low as 1.2 (or lower) asindicated by the curve for the Marlin carbonate clay.

Cyclic loading factor Ucy

Following the strain accumulation procedure as described indetail in /E-4/, and briefly summarised in this Appendix, thecyclic test data may be used for prediction of the cyclic loadingfactor Ucy.In Figure E-1b) and c) the Ucy-factor is plotted for Neqv = 3 andNeqv = 10. In the latter case this means that if the calculationsleads to failure in cyclic loading for a given cyclic load historythe same effect will be achieved if 10 cycles of the extremeload amplitude in the same load history is applied to the clay.Experience has shown that the cyclic shear strength will oftenbe found for Neqv = 5 - 10, but unless site specific tests havebeen performed it is recommended to make conservativeassumptions about the cyclic loading effect. By conservativeis meant that the strength and plasticity properties of the clayshould evaluated and compared with the data base, that thestress history of the soil profile is assessed, that possiblecarbonate content is accounted for, etc. When looking at rangeof Ur and Ucy reported for the different clays in Figure E-1 it isevident that experience from testing of one clay will notnecessarily be representative of the behaviour of another clayin another geological environment. Unless a site specificcyclic testing programme has been designed and executed, theempirical data like those shown in the figure and elsewhere inthe literature should therefore be used with caution.As a further background for the results shown in Figure E-1Table E-3 gives some characteristics of the tested clay.

Other effectsThe cyclic laboratory tests behind Figure E-1 were carried outon normally consolidated clay (OCR = 1-1.5), but the effect ofOCR on the cyclic bahaviour for so-called one-way cyclicloading (no shear stress reversal), which is a relevantassumption when mooring line tension is considered, ismoderate. Typically Ur and Ucy will be reduced by up to 5 %when OCR increases from 1 to 4, by up to 15 % when OCRincrease from 1 to 7 and by 20 % when OCR increases from 1to 10.The cyclic response will also be affected by the frequency ofloading, e.g. low-frequency versus wave-frequency tensioncomponents. The low-frequency component has typically aperiod, which is about 10 times longer than the wave-frequency component represented in the test results plotted inFigure E-1. Recognising the effect of loading rate an increasein the load rise time tcy from 2.5 seconds to 25 seconds, i.e.one log-cycle change, will give a reduction in the net cyclicloading effect by about 10 %, e.g. a reduction from Ucy = 1.3 toUcy = 1.27.


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Loading rate factor U r (for Neqv=1)

0.8

1

1.2

1.4

1.6

1.8

0.5 0.6 0.7 0.8 0.9 1

Average shear stress level τa/suD

Lo

adin

g r

ate

fact

or

U r

Drammen clayTroll clay (Unit 1)Troll clay (Unit 2)Marlin clay (Unit IIa)Marlin clay (Unit IIb)

Neqv = 1

(a)

Cyclic loading factor Ucy (for N eqv=3)

0.8

1

1.2

1.4

1.6

1.8

0.5 0.6 0.7 0.8 0.9 1

Average shear stress level τa/suD

Cyc

lic lo

adin

g fa

cto

r U c

y


Neqv = 3

(b)

Cyclic loading factor Ucy (for Neqv=10)

0.8

1

1.2

1.4

1.6

1.8

0.5 0.6 0.7 0.8 0.9 1

Average shear stress level τa/su D

Cyc

lic lo

adin

g fa

cto

r U c

y


Neqv = 10

(c)

Figure E-1. Example of cyclic direct simple shear test data (from /E-4/, /E-5/ and /E-6/).

Table E-1 Characteristics of tested clay (ref. Figure E-1)

Parameter Drammen Troll (Unit 1) Troll (Unit 2) Marlin (Unit IIa) Marlin (Unit IIb)

suD [kPa] 8.6 ≈20 ≈90 ≈10 ≈30

OCR [-] 1 1.45 1.45 1 1

w [%] 52 47-70 18-26 60-90 40-65

PI [%] 27 37 20 35-60 30-42



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E3 References/E-1/ Bea, R.G. and Audibert, J.M.E. (1979),

Performance of dynamically loaded pilefoundations, Proceedings from BOSS’79,Paper No. 68, pp. 728-745. London.

/E-2/ Kraft, L.M., Cox, W.R. and Verner, E.A.(1981), Pile load tests: Cyclic loads atvarying load rates, American Society ofCivil Engineers, Vol. 107, No. GT1,January 1981, pp. 1-19.

/E-3/ Briaud, J-L and Garland, E. (1983), Loadingrate method for pile response in clay,American Society of Civil Engineers, Vol.111, No. 3, March 1985, pp. 319-335.

/E-4/ Andersen, K. H. and Lauritzen, R. (1988),Bearing capacity for foundations with cyclicloads, ASCE Journal of GeotechnicalEngineering, Vol. 114, No. 5, May, 1988,pp. 540-555.

/E-5/ By, T. and Skomedal, E. (1992), Soilparameters for foundation design, Trollplatform, Behaviour of Offshore StructuresBOSS'92, pp. 909-920.

/E-6/ Jeanjean. P, Andersen K.H. and Kalsnes B.(1998), Soil parameters for design ofsuction caissons for Gulf of Mexicodeepwater clays, Offshore TechnologyConference , Paper OTC 8830, pp. 505-519.Houston.


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Appendix F: Uplift angle at the seabed

F1 GeneralThe anchor line in a mooring system may be split intothree parts, one part embedded in the soil, a secondpart resting on the seabed, and a third part suspendedin water.

The length of anchor line lying on the seabed at anytime during anchor installation will be a function ofat least the following factors

− the configuration of the anchor line− the actual length of line between the anchor

shackle and the pulling source (stern roller)− the actual line tension− the anchor line catenary (suspended part)− the inverse catenary of the line (embedded part)− the penetration trajectory of the anchor (position

of the shackle)At some point the length of the seabed part becomeszero and a further increase in the line tension ordecrease in distance will result in a situation wherethe anchor line intersects the seabed under an upliftangle (α), see Figure F-1. The characteristic anchorresistance is then given by Eq. (1) for Ls = 0.

Figure F-1 illustrates two situations after hook-up tothe floater. If the seabed uplift angle during designloading approaches the angle θ at the anchor shackleestablished during installation (extreme uplift), theanchor force and moment equilibrium from theinstallation stage may be affected, which may reducethe anchor resistance. This situation must beavoided. Line 2 illustrates a situation, where theuplift angle after hook-up affects the inverse catenaryonly down to Point A, such that the anchor is not atall affected. An acceptable uplift angle after hook-upshould give a seabed uplift angle, which issignificantly less than the angle θ at the anchorshackle. This would affect the installation shape(inverse catenary) of the line only to a limited depthbelow the seabed, indicated by Point A in Figure F-1.Guidance is given below for assessment of anacceptable seabed uplift angle.

Z

θ

T

Th

Tv

T(z)

z

α

Pen

etra

tion

dept

h

Drag

Extremeuplift

Acceptableuplift

Point A- Depth of uplift effect(referred to line installation shape)

Installationuplift angle

α=θ

Figure F-1 Non-zero uplift angles in the dip-down point.


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Historically both installation and operation of flukeanchors have been based on the requirement of zero upliftangle of the line at the seabed. Likely reasons for thistraditional practice are listed below.

− Fluke anchors have traditionally been associated withmoorings for ships and mobile drilling rigs, whichoften are equipped with anchors for a wide range ofsoil conditions, leading to minimum, or no,requirements for site specific soil investigations.

− In the mooring analyses the anchoring point has beenmodelled as a fixed point somewhere at the seabed,neglecting the fact that the fluke anchor embeds intothe soil.

− The design approach for such anchors has been rathercrude, reflecting the uncertainties in the boundaryconditions, e.g. the soil data.

− Fluke anchors have been installed based on previousexperience and empirical data, often extrapolated fromsmall-scale tests.

− Only a few of the experimental data from installationshave included uplift of the anchor line.

Accordingly, it has been difficult to take the step to allowfor uplift, although it has been a recognised understandingfor some time that fluke anchors can accept a certaindegree of vertical loading. It has, however, not beenpossible to quantify the effect of uplift on the anchorbehaviour.

Both with respect to anchor installation and later operationof a mooring system, there will be a potential forsignificant cost savings if a safe uplift angle can bedocumented and agreed upon. In the following, guidlinesare given for assessment of a safe uplift angle in normallyconsolidated to slightly overconsolidated clay.

F2 Assessment of a safe uplift angleThere are two situations to consider with respect toassessment of a safe uplift angle, firstly during anchorinstallation and secondly during extreme environmentalloading after hook-up of the anchors to the floater. Non-zero uplift angles during installation typically occur whenanchors are installed using a short scope of wire either bybollard pull (and blocked line) or by winch pull (from astationary vessel).

An anchor should under no circumstances be set with ananchor line giving an initial non-zero uplift angle fromstart of the installation. This would reduce the possibilityfor the anchor to enter the soil. As a minimum, theembedment of the fluke should be 2.5 fluke lengths (LF)before uplift is applied. This will also limit the possiblemaximum uplift angle for all practical means consideringthe path reaching an ultimate depth. An uplift angleexceeding 10° should not be expected during installationof a fluke anchor according to this procedure, even if theanchor approaches its ultimate depth.

The penetration path is only slightly affected by the upliftangles following upon the adoption of the installationprocedure described above. If the anchor was to beinstalled to the ultimate depth using this procedure, theultimate depth reached would be reduced only by a fewpercent as a result of the increased uplift angle at theseabed. Considering that the anchor resistance is mainly afunction of the penetration depth, this means that thechange in anchor resistance for most installation cases isnegligible.

The anchor line may have either a wire or a chainforerunner, and the effect of using one type of line or theother affects the behaviour of the anchor. An anchorpenetrated with a wire will reach a larger ultimate depththan an anchor with a chain, since the soil cuttingresistance is less for a wire than for a chain, see sketch inFigure 2. The maximum acceptable uplift angle for ananchor installed to the ultimate depth with a wireforerunner therefore becomes larger than with a chainforerunner.

Uplift angles for the permanently moored installation maybe larger than those reached during anchor installation,since the installation vessel uses either long lines or atensioner to maintain a zero, or small, uplift angle at theseabed. The scope used during hook-up to the permanentinstallation is often less than during anchor installationleading to higher uplift angles during storm loading thanthe anchor has experienced during installation. Providedthat the uplift angle (α) at the seabed is significantly lessthan the line angle (θ) at the anchor shackle afterinstallation the anchor resistance will not be adverselyaffected by this increase in uplift angle. The reason is thatthe shape (inverse catenary) of the forerunner below Pointin Figure F-1 will not be changed for the situationillustrated.

Line tension exceeding the available anchor resistance atany time after anchor installation will be experienced bythe anchor as a sudden change in uplift angle at the anchorshackle. If the load is high enough to set the anchor inmotion, the anchor resistance will drop to Ri plus theloading rate effect representative of the actual overloadingsituation. The anchor will then, due to the higher upliftangle, follow a more shallow penetration path than duringanchor installation. The penetration path becomesshallower the higher the uplift angle at the seabed is afterhook-up to the floater. The maximum possible uplift angle(αmax) is the angle, which makes the anchor drag at aconstant depth, and gradually pulls the anchor out of thesoil for higher angles. Tentatively, a safe α-angle may beset to 50% of αmax, although limited to α = 10°. Inpractice, this can be achieved by limiting the uplift angleto 50% of the angle θ at the anchor shackle.

The effect on the anchor resistance of increasing the upliftangle after installation from 0°to θ/2 may be assumed tovary linearly according to the following simple expression


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)/21(0,, θααα −= =LL RR

(valid for α<θ/2 and α<10°)

(F-1)

where RL is the contribution to the anchor resistance Rifrom the embedded part of the anchor line.

The design of a fluke anchor foundation, including hook-up considerations, should always ensure that extremeloads, which possibly may exceed the installation load willlead to a failure mode, which penetrates the anchor furtherdown into the soil.


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Appendix G: General requirements to soil investigation

G1 Geophysical surveysThe depth of sub-bottom profiling should correspond tothe depth of rock or the expected depth of fluke anchorpenetration. The seismic profiles should preferably be tiedin to geotechnical borings within the mooring area, whichwill improve the basis for interpretation of the results fromthe geophysical survey.

Guidance noteIt is recommended to survey at least 1.5 times the expectedfluke penetration depth.


G2 Geotechnical surveysThe soil investigation should be planned and executed insuch a way that the soil stratigraphy can be described insufficient detail for both the anchor and the anchor lineanalysis. The required depth coverage will vary from caseto case, see Chapter 6.

The extent of the soil investigation, sampling frequencyand depth of sampling/testing, will depend on a number ofproject specific factors, e.g. the number of anchorlocations, soil stratigraphy and variability in soilconditions with depth and between the potential anchoringpoints, as highlighted by the results of the geophysicalsurvey, water depth, sea floor bathymetry, etc.

Piezocone penetration testing (PCPT) normally bringsvaluable and useful information about soil stratigraphy, butthe undrained shear strength derived from such tests willbe uncertain if the PCPT results are not calibrated againstlaboratory strength tests on recovered soil samples. Ifgenerally adopted correlation factors are used theundrained shear strength derived will be affected by theuncertainty in this correlation factor.

If soil layering is such that the layer sequence and thevariation of thickness and layer boundaries will become animportant anchor design and installation consideration, itmay be necessary to document the soil layer sequence ateach anchor location. The thickness of all significantlayers, and the thickness variation between the anchoringlocations, should be known with reasonable accuracy priorto the design of the anchor foundation.

For the anchor design, most weight should be given to theundrained shear strength derived from direct simple shear(DSS) and unconsolidated undrained (UU) triaxial tests.These types of test are considered to give the mostrepresentative estimates of the intact undrained shearstrength of the clay. Clay sensitivity (St) is also asignificant soil parameter in the anchor design, whichrequires companion determinations (on the same soilspecimen) of intact and remoulded shear strengths, eitherby UU triaxial tests or by fall-cone tests.

For assessment of the post-installation effect due to soilreconsolidation, the consolidation characteristics of theclay, particularly the coefficient of consolidation (cv)should be gathered as part of the soil investigation.

For calculation of the effect of cyclic loading on the longterm anchor resistance, it is recommended to carry outstatic and cyclic undrained DSS tests. These tests shouldbe carried out on representative soil samples of highquality, which shall be subjected to stress conditions,which simulate the in situ conditions as closely as possible.A combined static/cyclic test programme should allowdetermination of the strength of the soil under the range ofloading conditions to be covered by the anchor design, e.g.cyclic tests with a representative combination of averageand cyclic shear stresses. The test programme should allowthe construction of a strain contour diagramme, as requiredfor calculation of the cyclic shear strength (τf,cy), see /E-4/and Appendix E for details. If site specific soil data arenot provided for assessment of the cyclic loading effect, aconservative assessment of this effect is warranted.

DNV-RP-E301: Design and Installation of Fluke Anchors … · Methodology for fluke anchor design...

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