GEOTECHNICAL CONSIDERATIONS FOR

OFFSHORE GRAVITY TYPE STRUCTURES

WITH EMPHASIS ON FOUNDATION STABILITY

UNDER STORM WAVE LOADING

by

THOMAS C. GAARD

S., The University of California, Davis, 197

A THESIS SUBMITTED IN PARTIAL FULFILMENT OF

THE REQUIREMENTS FOR THE DEGREE OF

MASTER OF APPLIED SCIENCE

in

THE FACULTY OF GRADUATE STUDIES

DEPARTMENT OF CIVIL ENGINEERING

We accept this thesis as conforming

to the required standard

THE UNIVERSITY OF BRITISH COLUMBIA

April, 1982

O Thomas C. Gaard, 1982 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission.

Department of Cl^\ ^^^.,1^

The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3

Date 32/ ^ J z. %

DE-6 (3/81) 11

ABSTRACT

A thorough discussion of offshore gravity type structures

presently being used, or considered for use in the near future

by the oil industry, is presented, along with a brief summary of

the major types of structures now used offshore.

Factors affecting the stability of offshore gravity type

structures are discussed, from the evaluation of a suitable site and the selection of soil parameters, through installation and

short-term foundation safety. A case study of the Ekofisk tank

is included to show how geotechnical concepts are applied offshore. A thorough description of wave loading on offshore gravity structures is presented, including a discussion on how the design storm is used in geotechnical analyses.

Existing stability methods are reviewed. The merits and shortcomings of each method are discussed with respect to their application offshore. Procedures for analyzing the stability of offshore gravity type structures subjected to storm wave loading are developed based on the method of slices. Both Janbu's

(1973) Generalized Procedure of Slices and Sarma's (1973) method are adapted for offshore analyses. The latter method is modified to perform pseudo-three-dimensional analyses. A computer program GRAVSTAB developed for this purpose is described and applied to several example problems. The versatility of the method of analysis is demonstrated and results are compared with existing methods. iii

TABLE OF CONTENTS

ABSTRACT ii

TABLE OF CONTENTS .' iii

LIST OF TABLES vi

LIST OF FIGURES vii

ACKNOWLEDGEMENTS x

NOMENCLATURE xi

CHAPTER 1 : INTRODUCTION 1

CHAPTER 2 : THE OFFSHORE GRAVITY TYPE STRUCTURE 11

2.1 General Characteristics 11

2.2 Platforms For General Offshore Development 14

2.2.1 Concrete Platforms 15

2.2.2 Steel Platforms 18

2.2.3 Hybrid Platforms 23

2.3 Platforms For Arctic Development 25

2.4 Deep Water Platforms And Other Structures 27

2.5 Sources Of New Platform Technology 30

CHAPTER 3 : DESIGN, CONSTRUCTION AND INSTALLATION 31

3.1 Preliminary Considerations 31

3.1.1 Sources Of Loading 31

3.1.1.1 Environmental Loads 31

3.1.1.2 Operational Loads 32

3.1.2 Environmental. Design Parameters 33

3.1.3 Site Selection And Soil Investigations 34

3.1.4 Selection Of Soil Parameters For Design 42

3.2 Platform Design 46 iv

3.2.1 Hydrodynamic Analyses 46

3.2.2 Geotechnical Analyses 47

3.2.3 Structural Requirements And Analyses 55

3.3 Platform Construction 57

3.4 Platform Installation 59

3.5 Platform Instrumentation 63

CHAPTER 4. : THE EKOFISK TANK - A CASE STUDY 67

CHAPTER 5 : CHARACTERISTICS OF WAVE LOADING 93

5.1 Ocean Waves 93

5.1.1 The Wave Climate 93

5.1.2 Wave Theories 94

5.1.3 Results Of Linear Wave Theory 97

5.2 Characterizing The Wave System 97

5.2.1 Obtaining The Design Storm 100

5.2.1.1 Statistical Description 100

5.2.1.2 Geotechnical Equivalent 101

5.2.2 Application Of The Design Storm 102

5.3 Wave Loads On The Foundation System 104

5.3.1 Wave Forces Acting On*The Structure 104

5.3.2 Wave Forces Acting On The Foundation 108

5.4 Effect Of Cyclic Loading On The Foundation System ...109

CHAPTER 6 : PROCEDURES FOR ANALYZING THE STABILITY OF

OFFSHORE GRAVITY TYPE STRUCTURES 115

6.1 Fundamental Considerations 115

6.2 Modelling The Wave-Structure-Soil System 120

6.3 Loading Applied To The Foundation 126

6.4 Available Stability Methods 128

6.4.1 Classical Bearing Capacity Approach 128 V

6.4.2 Other Bearing Capacity Formulations 136

6.4.3 NGI Slip Surface Method 140

6.4.4 Method Of Slices 144

6.4.5 Finite Element Analyses 144

6.4.6 Model Tests 150

6.5 Summary 152

CHAPTER 7 : APPLICATION OF THE METHOD OF SLICES TO

OFFSHORE GRAVITY STRUCTURE FOUNDATIONS 154

7.1 The Method Of Slices 156

7.2 Loading Applied To The Foundation 158

7.3 Treatment Of The Applied Horizontal Force 160

7.4 Modified Janbu Method 161

7.4.1 Assumptions 161

7.4.2 Derivation Of Equilibrium Equations .161

7.4.3 Working Formulas • 164

7.5 Modified Sarma Method 167

7.5.1 Assumptions 169

7.5.2 Derivation Of Equilibrium Equations 170

7.5.3 Working Formulas 173

CHAPTER 8 : EXAMPLES AND APPPLICATION OF ANALYSES 175

8.1 Description Of Computer Procedure 175

8.2 Example 1 - A Multi-layered Cohesive Deposit 177

8.3 Example 2 - A Cohesionless Deposit: Ekofisk Tank ....183

CHAPTER 9 : SUMMARY AND CONCLUSIONS 189

REFERENCES 194 LIST OF TABLES

Table I - Comparison of Fixed Offshore Platforms 16

Table II - North Sea Concrete Gravity Platforms 19

Table III - Gravity Platforms in Other Parts of the World .. 20

Table IV - Environmental Design Criteria for Some Offshore Areas 35

Table V - Geotechnical Concerns for Offshore Gravity Type Platforms 48

Table VI - Example of the Accumulated Effect of a 100-year

Storm 85

Table VII - Some Results of Linear Wave Theory 99

Table VIII - Comparison of Existing Stability Analyses 153

Table IX - Geometry and Loading Data for Example 1 177

Table X - Comparison of Computed Safety Factors for Example 1 179 Table XI - Coefficients for Estimating Undrained Strength from Triaxial Compression Data 182

Table XII - Effect of Shear Zone Representation on

the Safety Factor 184

Table XIII - Geometry and Loading Data for Example 2 185

Table XIV - Effect of A-parameter on the Safety Factor 188 vi i

LIST OF FIGURES

Figure 1.1 - Steel Jacketed Platforms 2

Figure 1.2 - Mobile Platforms 2

Figure 1.3 - The Ekofisk Tank 5

Figure 2.1 - Components of an Offshore Gravity Type Platform 13 Figure 2.2 - North Sea Concrete Gravity Type Offshore

Platforms 18

Figure 2.3 - Tecnomare Steel Gravity Type Offshore Platform 22

Figure 2.4 - Hybrid Gravity Type Offshore Platforms 24

Figure 2.5 - Arctic Platform Designs 27

Figure 2.6 - Proposed Deep-water Platforms 29

Figure 3.1 - Loads Acting on an Offshore Structure 32

Figure 3.2 - Plan of Survey Lines - Grid: Local Transverse , Mercator Spheroid 37 Figure 3.3 - Typical Soil Profile as Identified by Borehole, Cone Pentration Test and Gamma Ray Logging 43

Figure 3.4 - Comparison of Shear Strength Values from Sample Testing and from CPT 45

Figure 3.5 - Possible Failure Modes for an Offshore

Gravity Structure Foundation 50

Figure 3.6 - Possible Modes of Sliding Failure 51

Figure 3.7 - Stability Diagram for a Raft Foundation 53

Figure 3.8 - Installation Sequence for a Gravity Platform .. 60

Figure 3.9 - Detail of CONDEEP Base Structure 61

Figure 3.10 - Maximum Dome Contact Pressures Observed During

Installation of the "Beryl A" CONDEEP 64

Figure 4.1 - Detail of the Ekofisk Tank Bottom 69

Figure 4.2 - Loads on the Ekofisk Tank for the 100-Year Wave 71 vi i i

Figure 4.3 - Design Storm Data for the Ekofisk Field 71

Figure 4.4 - Typical Geotechnical Profile from Ekofisk

Field 72

Figure 4.5 - Shear Strength Data from Ekofisk 72

Figure 4.6 - Predicted Rocking Displacements for the Ekofisk Tank 76 Figure 4.7 - Load-Settlement Curve for Ekofisk Tank 76

Figure 4.8 - Ekofisk Settlement Data Relating Submerged Platform Weight and Storm Wave Data in the Early Months After Installation 79

Figure 4.9 - Settlement Data for Ekofisk Tank During Early Storms 79

Figure 4.10 - Location of Pressure Gauges and Piezometers Beneath Ekofisk Tank 82

Figure 4.11 - Pore Pressures Observed Under Ekofisk Tank During the First Major Storm 82

Figure 4.12 - Pore Pressure Rise per Cycle Observed in Undrained Simple Shear with Cyclic Loading for Samples Prepared with Relative Densities of 80% 85

Figure 4.13 - Theoretical Prediction of the Pore Water Pressure Distribution Beneath the Ekofisk Tank for Relative Densities of 77% and 85% .... 90

Figure 4.14 - Most Critical Failure Surface Found in Stability Analysis of Ekofisk Tank for Wave Loads Applied Under Undrained Conditions 92

Figure 5.1 - Regions of Validity for Various Wave Theories . 98

Figure 5.2 - Profile of an Airy Wave 99

Figure 5.3 - Forces Acting on the Foundation of an Offshore Gravity Structure 105

Figure 5.4 - Typical Design Storm Representation Used in Geotechnical Engineering 107

Figure 5.5 - Stress Path for a Foundation Element with Partial Drainage Subjected to Storm Wave Loading ill

Figure 6.1 - Effective Stresses in Soil for Still Water Conditions (i.e. No Wave Loads) 118 Figure 6.2 - Definition Sketch of Effective Foundation 122

Figure 6.3 - Transformation of Loads, to Foundation Base ....123

Figure 6.4 - Theoretical Rupture Surface Geometry 129

Figure 6.5 - Comparison of Different Proposals for the Value of Nr 132

Figure 6.6 - Geometry of Rupture Surface Used for an

Effective Stress Bearing Capacity Solution ....138

Figure 6.7 - Geometry of Sliding Body Used by NGI ..141

Figure 6.8 - Geometry of Bearing Failure Surface Used in the NGI Slip Surface Method 141 Figure 6.9 - Comparison of Two- and Three-Dimensional Distorted Finite Element Meshes for an Inclined and Eccentric Load 148

Figure 6.10 - Effect of Load Eccentricity on Effective Bearing Area as Evaluated Using the Finite Element 149

Figure 7.1 - Representation of Analysis by the Method of

Slices 155

Figure 7.2 - Geometry and Forces on a (Janbu) Slice 162

Figure 7.3 - Curve Used for Evaluating the Safety Factor ...169

Figure 7.4 - Geometry and Forces on a (Sarma) Slice 171

Figure 7.5 - Typical (Sarma) Slice Showing Side Forces 171

Figure 8.1 - Shear Strength Profile for Example 1 178

Figure 8.2 - Critical Shear Surfaces for Example 1 as Evaluated by Different Stability Methods 180 Figure 8.3 - Zones of Shear on the Potential Failure Surface and Relevant Laboratory Tests 182

Figure 8.4 - Critical Shear Surface for Example 1 Found from Computer Program GRAVSTAB 184

Figure 8.5 - Distribution of Pore Water Pressures in Foundation Soil Used in Example 2 185

Figure 8.6 - Critical Shear Surface for Example 2 188 X

ACKNOWLEDGEMENTS

The author wishes to thank his advisor, Professor W.D. Liam

Finn for his technical guidance and valuable suggestions to improve the presentation of this thesis. Dr. Yogi Vaid's comments throughout the text were also helpful in packaging the final product. He would also like to thank his advisor and

Dr. M. de St. Q. Isaacson for stimulating his interest in many aspects of offshore engineering - a field which the author intends to pursue wholeheartedly. Thanks are also due

Dr. P.M. Byrne for many valuable discussions regarding theoretical aspects of stability analyses among other things.

The program routine in GRAVSTAB used for applying Sarma's method to offshore platforms is an extension of an earlier program

STESL by K.W. Lee and W.D. Liam Finn for the analysis of the stability of underwater slopes. Funding for the computer studies was provided by the National Research Council under grant No.1498 to Professor Finn. This assistance was appreciated. Permission to reproduce many of the figures used in this thesis was kindly granted by numerous people.

To all my friends in Vancouver who made my last two years worth more than an education (and bearable) you are not forgotten. A final thanks to Dr. Isaacson for giving me an interesting job at this university that does not require a suit to be worn (ever) or a shave more than twice a week. xi

NOMENCLATURE

B0 - equivalent foundation width

B - effective foundation width

L0 - equivalent foundation length

A0 - platform base area

D0 - skirt depth below mudline fl' - effective unit weight of soil

PH - horizontal wave load on platform

Pv - vertical platform load at seafloor

APV - vertical wave load on platform

M - moment at seafloor

Ap, - wave pressure on seafloor at tail end of platform

Ap2 - wave pressure on seafloor at nose end of platform

PA - active soil force on nose of foundation

Pp - passive soil force on tail of foundation

Pw - water pressure force on tail of foundation

Ps - shearing resistance on sides of foundation

Pj - shearing resistance on soil-soil interfaces at sides

VBT - vertical load at foundation base

VB ~ VBT Per un^fc width

HBT - horizontal load at foundation base

HB ~ HBT Per unit width

MfeT - moment applied at foundation base h, - moment arm for active or water pressure force

h2 - moment arm for passive soil force xi i

h3 - moment arm for shearing resistance on foundation sides e - eccentricity

HET - horizontal force applied to effective area

HE - HET per unit width

HST - horizontal force applied to sliding surface

Hs - HST per unit width

Fs - maximum shear resistance available from sliding surface per unit width g - load inclination factor a - normal stress o" - effective normal stress tr, - major principal stress

0"3 - minor principal stress u - total pore water pressure

us - static pore water pressure

uc - pore water pressure due to cyclic effects

Au - pore water pressure due to dynamic wave pressure z - depth below mudline

A - pore water pressure parameter

0 - friction angle or mobilized friction angle c - cohesion or mobilized cohesion tan0 - frictional resistance or mobilized friction resistance c' - cohesion in terms of effective stress tan0' - frictional resistance in terms of effective stress

F - factor of safety applied to strength parameters

cu - undrained shear strength

- shear strength

T - shear stress xi i i

Qo - ultimate bearing capacity

q0 - ultimate bearing pressure q' - surcharge

N - bearing capacity factor for friction

N - bearing capacity factor for cohesion

N - bearing capacity factor for surcharge s- - bearing capacity shape influence factors d- - bearing capacity depth influence factors i- - bearing capacity load inclination influence factors

{, - slice number otj - angle made by top of i-th slice with horizontal

^t - angle made by base of i-th slice with horizontal b^ - width of i-th slice xt- - x-coordinate of midpoint of top of i-th slice yt| - y-coordinate of midpoint of top of i-th slice xb^ - x-coordinate of midpoint of base of i-th slice yb^ - y-coordinate of midpoint of base of i-th slice xg^ - x-coordinate of centroid of i-th slice yg^ - y-coordinate of centroid of i-th slice xs- - x-coordinate of point of application of side forces for i-th slice ysc ~ y-coordinate of point of application of side forces for i-th slice h^ - height of i-th slice

- vertical offset of thrust forces for i-th slice

Ah£ - distance between base and line of thrust for i-th slice

FV{, - vertical force on top of i-th slice

FT(. - total vertical load on top of i-th slice

FH: - horizontal force on top of i-th slice xiv

FN-, - normal force on top of i-th slice

FTC - tangential force on top of i-th slice

US^ - pore water force on base of i-th slice

ssL - shear force on one side of i-th slice x 2

- normal force on base of i-th slice

N; - effective normal force on base of i-th slice

Si - shear force on base of i-th slice

E'v - lateral thrust applied to i-th slice

T'v - vertical shear force at x=xj

Q'v - assumed vertical shear force at x=xj v; - vertical resultant on base of i-th slice

H; - horizontal resultant on base of i-th slice

wt - total saturated weight of i-th slice

w;' - effective weight of i-th slice

UH; - resultant water force at x=xj

- pore water pressure at base of i-th slice

- normal stress on base of i-th slice

- shear stress on base of i-th slice

- shear strength at base of i-th slice

- available cohesion on base of i-th slice

tan0 'j - available frictional resistance on base of i -•th slice

- mobilized cohesion on base of i-th slice = 1 tan0'^ - mobilized frictional resistance on base of i - th slice

r t. - factor of safety on interslice face for it-h slice

K - acceleration coefficient as a fraction of gravity

X - vertical shear force multiplier

- K for a given factor of safety V

CHAPTER 1

INTRODUCTION

The increase in global energy consumption and the prevailing geopolitical climate in the world have had disastrous effects on the cost and availability of petroleum to most consumers. This, along with the western world's desire to be energy self-sufficient, has led to the development of energy

resources which were previously considered to be uneconomical.

In an effort to meet the goals of energy self-sufficiency and

(indeed) availability, oil companies have in recent years been

increasing their exploitation of the vast reserves of oil and

gas that exist beneath the continental shelves of the world's

oceans. As consultants to the oil companies, engineers are

required to (1) provide the technical input necessary for the

implementation of hydrocarbon recovery schemes, and (2) to

develop reliable methods for the design, analysis, and

installation of the necessary offshore structures.

Offshore platforms have been in existence since the 1920s

when oil was discovered at Lake Maracaibo, Venezuela. These

structures, usually made of concrete and piled into the soft

nearshore sediments, were crude by today's standards but are

important in that they constituted the beginning of the offshore

oil industry (Bjerrum, 1973). The first "deep-water" fixed

platforms constructed were the steel jacket or template type

structures, similar to those shown in figure 1.1 used in the

Gulf of Mexico, of which some several hundred have been built A) CONVENTIONAL TYPE B) SELF-FLOATER

Figure 1.1 - Steel jacketed offshore platforms (After McPhee and Reeves, 1975) 3

there since the 1960s. These platforms are also familiar sights in other parts of the world, namely: Lake Maracaibo, the

Persian Gulf, the North Sea, the Java Sea, the Gulf of Guinea, offshore California, and to a lesser extent, other locations

(Martin and Shaw, 1974). Semi-submersible and jackup type exploratory drilling rigs such as the ones shown in figure 1.2 are also in widespread use throughout the world.

In 1969, when the Phillips Petroleum Company discovered the first commercial oil field (the Ekofisk field) in the northern

North Sea, engineers were faced with some new and difficult problems when designing the necessary structures for the development of this field. Because of the extreme hostility of the northern North Sea (24 meter high waves at this location) and the lack of nearby harbors (the closest being nearly

320 kilometers away) the need arose for a production platform in close proximity to the drilling platforms (which were to be of the conventional jacket type) which could function as a storage facility in poor weather when tanker loading would-be impossible

(Bjerrum, 1973). From this need came the first offshore gravity type production platform; this is the famed Ekofisk tank designed by the C. G. Doris Company of France. The tank is shown being towed from the Norwegian coast to its home in the northern North Sea in figure 1.3.

Interest in gravity type production platforms has increased steadily since 1973 when the Ekofisk tank was installed, primarily because of the short installation time required for a gravity type structure (no piling necessary in the unpredictable

North Sea) and the successful operation of the Ekofisk tank 4

Figure 1.3 - The Ekofisk tank (See following page) (Reproduced with permission of the Royal Institute of Naval Architects, London.)

6

since installation, including a good performance through a major

storm (90% of the design storm) which occurred six months after

it was installed (Marion, 1974). More than twenty other gravity platforms have been installed to date in the North Sea and other areas of the world (Waagaard, 1977).

The Ekofisk tank was the first offshore gravity type

platform but not the first gravity type structure used offshore.

Gravity type light towers had been used extensively in Sweden

for many years prior to 1973 in shallower, nearshore waters,

usually 20 meters deep or less (Stubbs, 1975). The Royal

Sovereign light tower in the English Channel is perhaps a more

familiar example' of a pre-1973 gravity type structure. These

are relatively small structures which required few new design

concepts, and construction and installation techniques at the

time that they were installed.

The installation of the Ekofisk tank, however, was a

milestone in engineering design and marked a new era for

offshore gravity structures. This tank required many new design

procedures, construction methods, and installation techniques

that had to be developed specifically for these purposes

(Bjerrum, 1973; Gerwick and Hognstad, 1973; Marion, 1974).

In recent years, North American engineers have been playing

an increasing role in the development of offshore gravity

structure technology, although few are formally trained in the

area. With increasing exploration and utilization of oil and

gas resources off the North American coast, the need for

geotechnical engineers with a good working knowledge of offshore

engineering will undoubtedly increase on this continent. 7

The purposes of this thesis are threefold: (1) to introduce the geotechnical engineer to the field of offshore engineering, specifically, to familiarize him with the special problems associated with gravity structures, (2) to present an overview of existing stability methods applicable to offshore gravity type structures, and (3) to develop an alternative procedure for analyzing the stability of an offshore gravity structure subjected to storm wave loading.

This thesis may be divided into two sections. Chapters 2-5 deal with the first consideration, a general background in offshore engineering. The second part of this thesis,

Chapters 6-8, is concerned wholly with the topic of foundation stability under storm wave loading. The preliminary chapters serve a dual purpose. First, they serve to give the reader unfamiliar with offshore engineering a good working knowledge of offshore gravity structures. Secondly, they provide him with an appreciation of the offshore environment and the special design and installation requirements for gravity type structures. This is necessary so that the foundation analyses may be viewed in perspective. The aim of the section on foundation stability under storm wave loading is to present an overview of the stability methods presently available for performing such analyses and to demonstrate the need for and then develop a simple, practical alternative method for effective stress analyses.

Chapter 2 serves as an introduction to offshore gravity type structures. The general characteristics of a gravity 8

structure are described and the major types of platforms are discussed in some detail.

Chapter 3 is concerned with the design, construction, and installation requirements for these structures. First, the sources of loading in the offshore environment are outlined.

Next, the site selection, the offshore site investigation and the selection of geotechnical soil parameters is discussed in depth. Platform design requirements (hydrodynamic, structural, and geotechnical), construction techniques and installation procedures are then delineated. A short section on platform instrumentation finishes off this chapter.

Chapter 4 presents a geotechnical case study of the Ekofisk tank. This chapter serves the purposes of demonstrating how geotechnical analyses are applied offshore and how performance observations may be used as a check on design assumptions and predictions.

Chapter 5, the final chapter in the first part of this thesis, deals with wave loading on gravity platforms. A brief discussion of the wave climate is given and the modelling of ocean waves by wave theories and statistical means is discussed.

The geotechnical equivalent of the statistical design storm, that which is used for cyclic loading studies and to determine the maximum load, is given particular attention. Finally, the characteristics of wave loading on the foundation system are discussed as they pertain to foundation analyses. This chapter also serves as an introduction to the next section.

Chapter 6 presents the quantitative aspects of wave loading on the foundation system. Methods of determining platform 9

stability under storm wave loading are then discussed; the merits and shortcomings of each method when applied to the

offshore gravity structure are emphasized. It becomes clear

that there are two fundamental analytical lines of approach to

the problem: bearing capacity theory and the finite element

method. A simple to use limit equilibrium method for total

stress analyses of clay foundations called the NGI (Norwegian

Geotechnical Institute) slip surface method is described in

detail.

In Chapter 7 an alternative method of analysis based on the

method of slices is presented. This method is along the lines

of the NGI method. It is a pseudo-three-dimensional effective

stress method based on Sarma's (1973) method of slices. Sarma's

method of slices is not well known among practicing engineers

and hence Janbu's (1973) method of slices is also adapted to

perform a gravity structure stability analysis, although only in

two dimensions. This was done so that existing slope stability

programs may be modified to perform some of the analyses and

also to install faith in the use of Sarma's slice method.

In Chapter 8 a computer program GRAVSTAB developed to

perform these analyses is described and several example problems

are worked. The application of the method to both a total

stress analysis and an effective stress analysis is made. The

versatility of the method is shown. This method is of great

practical value for working these types of problems.

The discussion of gravity structures presented herein,

although primarily concerned with platforms, is generally

applicable to all large gravity type offshore structures. The 10

analytical procedures discussed and developed in this thesis are

applicable to any offshore structure with a monolithic gravity

type base, whether it is a platform, light tower, flare

structure or other facility.1

1A flare structure is used for burning off excess gases, primarily methane, produced along with oil from a well. 11

CHAPTER 2

THE OFFSHORE GRAVITY TYPE STRUCTURE

The following discussion of offshore gravity type

structures includes all the major types of gravity structures presently in use and those which are being seriously considered

by the . oil industry for use throughout the world in the near

future.

2.1 General Characteristics

A gravity type structure rests directly on the seabed and

has no subsurface foundation other than shallow skirts and ribs

which portrude through the upper sediments to transfer the

horizontal component of the disturbing force to deeper, stronger

subsoils. In areas where the surficial sediments have adequate

strength to prevent sliding or the raft foundation is excavated,

skirts or ribs may not be present (Huntemann et al, 1979).

Skirts have the added features of providing scour protection

from currents and wave induced water motions and containing

grout which is used during installation. They are therefore

usually necessary unless the foundation has been excavated.

To prevent sliding at the base of the structure or a shear

failure beneath the structure, a vertical force on the

foundation must be maintained in some proportion to the maximum

horizontal load. This is accomplished by using a structure of

ample weight with respect to the horizontal forces expected -

hence the name gravity structure. 12

There are generally three distinct parts of a large gravity

platform: the base caisson, the towers, and the deck. A typical

North Sea concrete gravity platform is shown in figure 2.1.

Other gravity platforms, although somewhat different, have many

of the same features as the one shown.

The deck is used as a work area and often houses living

quarters for the men who service the platform equipment. The

specific equipment on the deck depends on the exact use of the

platform. Facilities for fresh water storage and other platform

requirements are often housed in the towers. The well risers

may also be contained within the legs.2 The base caisson is used

during installation as a buoyancy chamber; the caisson is made

up of a number of cells (either outwardly apparent as with the

platform shown in figure 2.1, or compartmented within the

caisson as with the Ekofisk tank shown in figure 1.3) which are

used to systematically ballast the structure. The skirts are

driven into the foundation soil and the structure is firmly

seated by increasing the ballast. The cells are used as both

ballast tanks and oil storage facilities when the structure is

operational.

These platforms are generally massive structures,

particularly those platforms designed for the North Sea. The

largest of the North Sea giants, a Doris type structure placed

in the U. K.'s Ninian field in 1978, weighed 600,000 tons

2Risers are pipes through which crude oil flows out from the well and up to the platform in to be processed, pumped, or stored. 13

Figure 2.1 - Components of an offshore gravity type platform (Adapted from Klitz, 1980) 14

(Steven, 1981a). This platform is taller than a 50 story building from the base to the deck (not including the deck equipment) and nearly as wide at the base. A Sea Tank type structure also placed in U. K. waters in 1978 holds the depth

record for a gravity platform - 152 meters (Furnes, 1978).

Other gravity platforms in the North Sea are nearly as large, and although the platforms in other offshore areas are appreciably smaller, they are still very large indeed. Clearly

these are enormous structures with unusual design and

construction requirements.

2.2 Platforms for General Offshore Development

Steel jacketed structures and gravity platforms form the

core of structures presently used in offshore hydrocarbon

recovery.3 The jacketed structures are much more numerous.

Generally, the steel jacketed structure, and the gravity

structures discussed in the following subsections, will not be

used in water depths greater than about 250 to 300 meters. In

deeper water, other types of structures will be used.

3 A jacketed structure was successfully placed in 312 meters of water in the Gulf of Mexico in 1980 (Morrison, 1980a). The installation of this type of structure in water of that depth is not seen as a trend for the future. The use of this type of structure was economically justified since the priority was a large number of wells which this platform, with its large base area, was able to provide (Morrison, 1980b). Several other jacketed platforms in similar water depths are planned for use in the Santa Barbara channel. Alternative platform designs such as those discussed in section 2.4 are not fully developed yet. 15

2.2.1 Concrete Platforms

The concrete (reinforced and prestressed) gravity type platform was designed to meet specific requirements for the development of the Ekofisk field in the North Sea. Steel jacketed platforms, the only fixed offshore platforms existing at that time, could not be modified to include the required amount of storage. This requirement for storage was the primary reason that the gravity type platform was developed and remains as an important factor when choosing between steel jacketed and gravity type structures for field development.

It should be remembered that the gravity structure is an alternative to the steel jacketed platform, not a replacement

for it. The two platform types are quite different and generally applicable to different design and production considerations. A brief comparison of the concrete gravity type platform and the steel jacketed platform, the two most common types of (large) fixed offshore structures, is presented in

Table I.

Concrete was the first material used for building gravity type platforms and remains the most common for a variety of

reasons, some being: construction techniques require less

skilled labor than steelwork, the availability of concrete is generally better than that of high grade structural steels, and concrete is more corrosion resistant and has a longer fatigue

life than steel in the marine environment (Stubbs, 1975). The

latter two reasons are very important since maintenance is expensive and repairs are difficult, if even possible, offshore

(Billington, 1979). 16

Table I

Comparison of Fixed Offshore Platforms

STEEL JACKETED PLATFORM CONCRETE GRAVITY PLATFORM

ADVANTAGES ADVANTAGES

-Much industry experience -Requires little specialized labor -Generally cheaper for mild environments -Greater production capacity

-Design less site-specific -Easy to incorporate storage

-More flexible to changes -Short installation time during fabrication -Larger deck -Good for areas with deep soft sediments -Almost complete at tow-out for early production start

-Longer fatigue life

-More corrosion resistant

DISADVANTAGES PISADVANTAGES

-Requires very skilled labor -Inflexible to design/const, changes-very site specific -Long, costly installations -Design more critical to -Hard to provide storage specific water depth

-Relies on the availability -Seabed must be relatively of high-grade steel flat and level

-Difficult to inspect for -Requires good bearing soils damage -Need good knowledge of -Need more deep borings shallow sediments

-Problems with driving large diameter piles

-Shorter fatigue life

-Less corrosion resistant

Adapted from Bell (1974). 17

As of 1981, fourteen concrete gravity type platforms have been installed in the North Sea (Furnes, 1978; Steven, 1981b).

These platforms are of four different types: the Doris, Andoc,

CONDEEP, and Sea Tank designs. The Doris design is that of the

Ekofisk tank (shown in figure 1.3) and looks somewhat different

in general appearance than the other North Sea designs shown in

figure 2.2. Design conditions, analysis techniques, and construction methods are, however, virtually the same for all these platforms. Each platform type was modified somewhat for the specific on-site design criteria: design wave height, water depth, and production requirements (storage capacity and deck

installations). Hence, the size and shape of each platform is distinct. A summary of these platforms is given in Table II along with some of their important features.

Three concrete gravity platforms have been built off the coast of Brazil (Franco, 1976) and one offshore Louisiana

(Huntemann et al, 1979). These platforms are box-shaped and

significantly smaller than the pedestal shaped North Sea giants.

Four steel gravity type platforms off the Congo coast (Lalli,

1977), and a flare offshore Brazil (Burns and D'Amorim, 1977),

are the only other large offshore gravity type structures in the

world outside of the North Sea. A list of these platforms, also

giving some of their important features, is given in Table III.

Gravity platforms made of materials other than concrete are

primarily special designs for particular applications. This is

especially true of the all-steel gravity structure. A) CONDEEP DESIGN B) SEATANK DESIGN C) ANDOC DESIGN

Fig. 2.2 North Sea concrete gravity type offshore platforms (Compiled from Sjoerdsma, 1975a)

00 19

Table II

North Sea Concrete Gravity Platforms

DESIGN FIELD/ WATER DESIGN BASE PURPOSE DATE COUNTRY DEPTH WAVE WIDTH

Doris Ekofisk 70 24.0 93 P-S 1973 (Norway)

CONDEEP Beryl A 120 29.5 100 D-P-S 1975 (U.K.)

CONDEEP Brent B 142 30.5 100 D-P-S 1975 (U.K.)

Doris Frigg CDP1 96 29.0 101 D 1975 (U.K.)

Sea Tank Frigg TP1 104 29.0 72 P 1976 (U.K.)

Doris Frigg MP2 94 29.0 101 B 1976 (U.K.)

CONDEEP Brent D 142 . 30.5 100 D-P-S 1976 (U.K.)

Andoc Dunlin A 152 30.5 104 D-P-S 1977 (U.K./Hoi.)

CONDEEP Statfjord A 149 30.5 1 10 D-P-S 1 977 (Norway)

CONDEEP Frigg TCP2 1 04 29.0 100 T-B-P 1 977 (Norway)

Doris Ninian 139 31.2 140 D-P 1978 (U.K.)

Sea Tank Brent C 142 30.5 100 D-P-S 1 978 (U.K.)

Sea Tank Cormorant A 152 30.5 100 D-P-S 1978 (U.K.)

CONDEEP Statfjord B 144 30.5 152 D-P-S 1981 (Norway)

D=Drilling P=Production S=Storage T=Treatment B=Booster

Note: All dimensions are in meters. Adapted from Furnes (1978). 20

Table III

Gravity Platforms in Other Parts of the World

DESIGNER/ FIELD/ WATER DESIGN BASE PURPOSE DATE CONSTRUCTION COUNTRY DEPTH WAVE SIZE

Tecnomare Loango 89 9.4 3@ 1 81 D 1976 (Steel) (Congo)

Tecnomare Loango 89 9.4 3@ 1 81 D 1976 (Steel) (Congo)

Tecnomare Loango 89 9.4 3@1 81 D 1976 (Steel) (Congo)

Tecnomare Loango 89 9.4 3§18' P 1977 (Steel) (Congo)

Petrobas RGdeNorte 13 ? 46x53 D-P 1978 (Cone-Box) (Brazil)

Petrobas RGdeNorte 13 ? 46x53 D-P 1978 (Cone-Box) (Brazil)

Petrobas RGdeNorte 13 ? 46x53 D-P 1978 (Cone-Box) (Brazil)

ARCO Louisiana 4 ? 23x34 D-P 1978 (Cone-Box) (U.S.A.)

'This design has three base pads (tripod)

Note: D=Drilling P=Production

Note: All dimensions are in meters.

Note: This list may be incomplete. 21

2.2.2 Steel Platforms

Steel gravity platforms similar to the one shown in

figure 2.3 were first installed off the Congo coast in 1976

(Lalli, 1977) and are presently being built for other locations,

including one for the North Sea (Agostoni et al, 1980).* These

platforms have some unique features which were developed to

solve some special foundation problems.

The steel gravity platform was developed for use in the

Loango field off the Congo coast (Lalli, 1977),5 Seabed

conditions there consist of a rocky uneven bottom (McPhee and

Reeves, 1975) which is too hard for piles to be driven into and

too unyieldingly uneven for the base slab of a concrete

structure. The only type of structure that could be placed

economically on the rocky seabed and provide the required amount

of storage was a steel-based gravity platform on base pads.

(Pile driving in these sediments would require all prebored

holes, a lengthy and expensive operation.) The Tecnomare

platform, with its tripod arrangement of legs, may be used in

areas where the seabed is uneven or inclined by jacking up the

legs to compensate for differences in topography (Offshore

"The installation of this platform has been delayed due to numerous problems, including a strike at the construction yard. The platform is not expected to produce before 1983 or 1984 (Steven, 1981c).

5The platform was initially conceived for general offshore areas and later for consideration in the Sicilian channel; however, none of these platforms were ever built. The platform was fully developed for use off the Congo coast where it was first installed. 22

Figure 2.3 - Tecnomare steel gravity type offshore platform (After Lalli, 1975) 23

Europe, 1974). Since no highly skilled labor force was available in the Congo, the platforms had to be built in Europe and towed the 8500 kilometers to the Congo. Towing speed and

stability requirements contributed to the design shape.

A steel gravity platform was chosen for the Maureen field

in the North Sea primarily because of reservoir considerations

(Lalli, 1977). The Maureen field is a so-called marginal field,

that is, one which has very limited potential. Since pipelines

are not economically justified, storage is required. In the

event that the field is not profitable, the structure may be

removed and relocated to a comparable site with a minimum of

structural damage; steel was chosen over concrete for this

reason.

Unfortunately, steel, gravity platforms suffer from many of

the same setbacks as steel jacketed platforms, primarily steel

cost and availability, and the need for a highly skilled labor

force to build them. Hence, they will remain as an alternative

to the concrete structure, not a replacement for it.

2.2.3 Hybrid Platforms

The hybrid gravity platform (Hansen and Ingerslev, 1977;

McPhee and Reeves, 1975) consists of a steel space frame mounted

on a concrete raft. Two different platform designs are shown in

figure 2.4. The hybrid is an attempt to combine the best

features of both the steel jacketed and concrete gravity

structures. It does offer some distinct advantages over its

parents, but it also suffers from some of the same problems,

namely: the need for a highly skilled labor force, the 24

Figure 2.4 - Hybrid gravity type offshore platforms (Compiled from Lalli, 1975, and McPhee and Reeves, 1975) 25

availability of high grade structural steel, and the requirement that the seabed be relatively flat and level with adequate bearing strength.

The design utilizes a gravity base primarily to cut down installation time and cost and a space frame superstructure to attract smaller wave forces. Because the superstructure is lighter and the wave loads smaller than for the all concrete structure, the base may be decreased in size and the overall weight reduced by 65% to 75% (McPhee and Reeves, 1975). If bearing soils are weak, the base size may be increased to avoid overstressing the soil.

Two construction methods add to the platform's flexibility

(Hansen and Ingerslev, 1977). The raft may be towed to the site and installed, then the space frame may be connected and the deck mated, or the components may be built independently and joined upon completion at a protected nearshore location before tow-out. The first construction method allows for a gravity type platform to be used when draft restrictions are critical, that is, when no deep water construction site such as a fjord is located nearby; the raft and tower are floated out separately maintaining towing stability with much less draft. The second construction method may be employed when an early installation date is critical by taking advantage of the modular construction. No hybrid structures have yet been installed.

2.3 Platforms for Arctic Development

Gravity type platforms have also been designed for use in the Arctic. Among these designs are the monocone (Stenning and 26

Schumann, 1979) and multiple-leg structure (Kliewer and Forbes,

1980), both of which are shown in figure 2.5. These structures were designed for shallow ice-infested waters of the Beaufort

Sea. Horizontal ice loads are reduced by the nature of platform geometry. The surface piercing cylindrical leg(s) reduce the area exposed to thinner ice flows, while the conical5 sections

below the surface are designed to fail the thicker ice sheets in

flexure instead of compression, thereby greatly reducing the

lateral loads on the structure.

The multiple-leg structure is made of steel, which is more

resistant to ice scraping and gouging than concrete. The

monocone is constructed of reinforced concrete covered with

steel armor to resist damage from moving ice flows. No

platforms of either design have yet been installed.

Artificial islands are also gravity type structures.

Several types of artificial islands have been proposed for

exploratory drilling structures in the Beaufort Sea, including

the caisson retained structure (de Jong and Bruce, 1978) also

shown in figure 2.5. One of these structures was recently

completed by Dome Petroleum, Ltd. in the Canadian sector. These

structures consist of eight steel wall sections attached via

flexible joints that can move under ice loading to transfer the

large horizontal load to the soil core - which is of sufficient

size to resist shearing failure within the island. Although the

structure's core is built of soil, not concrete or steel, it is

fundamentally a gravity structure, since stability is achieved

by providing a sufficient vertical force on the foundation

(weight) to resist failure from horizontal loading. (a) Multiple Leg Gravity Type (b) Monocone

(c) Caisson Retained Island

Figure 2.5 - Arctic platform designs (Compiled from (a) Kliewer and Forbes, 1980, (b) Bercha and Stenning, 1979, and (c) de Jong and Bruce, 1978) 28

2.4 Deep Water Platforms and Other Structures

For water deeper than about 300 meters, the cost of installing gravity platforms and steel jacketed structures increases very rapidly.6 In these waters, alternative recovery methods are therefore required to make hydrocarbon recovery economically attractive. A number of structures have been proposed for deep water use including the articulated column

(Moinard, 1979), the guyed tower (Finn et al, 1979), and the tension leg platform (Falkner and Franks, 1978), all which are shown in figure 2.6. These structures are likely to be used in water depths of between 300 and 600 meters (Morrison, 1980b).

In deeper water, subsea completion systems (Burkhardt and

Michie, 1979) will probably afford the only economical solution.

The articulated structures, guyed towers, and tension leg platforms are also applicable to areas with small reservoirs of limited potential as well as to purposes other than drilling or production platforms, such as: flare structures, light towers, and tanker loading terminals where traditional designs would be uneconomical. They are designed to be compliant, that is, they move with the disturbing force somewhat instead of trying to act rigidly and prohibit all motion. The forces acting on the

The depth at which these structures become uneconomical is influenced by several factors, namely: the state of current technology, the availability of alternative recovery methods, the nature and severity of environmental loading, and the estimated volume of recoverable hydrocarbons. This depth was chosen based on current publications. The economical depth of monolithic gravity type platforms may be less than this - about 200 meters. 29

(b) Articulated Column (c) Tension-legged Platform (After McPhee and Reeves, 1975)

Figure 2.6 - Proposed deep-water platforms 30

structure are thus reduced and the amount of materials required are therefore significantly less than for traditional designs.

For these structures, the gravity type base may be used as a foundation system (as opposed to the alternative choice, piles) and they are therefore of interest here.

The articulated column is presently being used for flare structures in the North Sea (Sjoerdsma, 1975b) and for tanker loading terminals in both the North Sea (Sjoerdsma, 1975b) and offshore Brazil (Burns and D'Amorim, 1977). However, no drilling or production platforms of this design have been built to date. The North Sea structures are in water depths of between 106 and 150 meters (Moinard, 1979).

2.5 Sources of New Platform Technology

For updating this list, the reader is referred to several of many magazines concerned with offshore oil technology, specifically: Ocean Industry, Offshore, Offshore Engineer, The

Oil and Gas Journal, and the Journal of Petroleum Technology.

Another good source of information are the Proceedings of the

Offshore Technology Conference which is held annually in

Houston, Texas. 31

CHAPTER 3

DESIGN, CONSTRUCTION AND INSTALLATION

3.1 Preliminary Considerations

Before a platform can be designed, some assessment of the sources of loading for the particular area must be made, and the necessary environmental and geotechnical design parameters chosen.

3.1.1 Sources of Loading

The sources of loading in an offshore environment are numerous and of varying degrees of importance at different locations. . Generally, they may be broken into two categories: environmental loads and operational loads. Figure 3.1 shows the primary loads that may act on an offshore structure.

3.1.1.1 Environmental Loads

Environmental loads are defined as loads caused by natural phenomena - those over which man has no control. Environmental loads acting on an offshore structure include (1) the forces caused by interaction between moving fluids and the structure, such as: wind, waves, currents, or flowing soil, (2) forces due to bodies such as ice impacting the structure, (3) stresses induced by thermal gradients, and (4) forces resulting from earthquake induced accelerations in the structure.

Environmental loads transmitted to the foundation are generally inclined, eccentric, and either transient or cyclic in nature. 32

WIND SERVICE

JVA\^WVW EARTHQUAKE

Figure 3.1 - Loads acting on an offshore structure 33

3.1.1.2 Operational Loads

Loads other than environmental are classified as service or operational loads and include those caused by moving equipment and machine vibrations on or within the structure, and those caused by interaction with support vessels, such as: mooring loads, helicopter landings, and possible collisions with either flying or floating vessels. These are usually minor loads necessary only for the design of the deck structure, with the notable exception being collision with a large surface vessel

(tanker) under power.

Additionally, there may be loads imposed on the structure and its foundation by fluctuations in oil storage quantity, density, or temperature. These loads may be significant and must be considered in design; both minimum and maximum values of weight fluctuations must be specified for foundation design.

Minimum values affect stability (overturning) as do maximum values (overstressing).

Eccentric loads may also be imposed on the foundation by varying distributions of deck equipment and oil in the storage tanks. The latter of these may be significant and must either be designed for or prevented.

3.1.2 Environmental Design Parameters

After environmental conditions for the chosen area have been identified, design parameters must be chosen using appropriate and acceptable methods. This is usually outlined by the regulatory agency with jurisdiction in the case who will often have their own standards (Department of Energy (U.K.), 34

1974; Department of the Interior (U.S.A), 1979; Det Norske

Veritas (Norway), 1977; Internationale de la Precontrainte

(France), 1977). In some cases, requirements may also be set

forth by the underwriter (e.g. Lloyd's Register of Shipping) or

the owners, who sometimes use professional society

recommendations such as those of the American Petroleum

Institute (1978).

A partial listing of environmental parameters for some of

the world's offshore areas is given in Table IV. A quick glance

at the table will show that offshore platforms are subjected to

harsh environmental conditions. The results presented in the

table are for specific locations within the offshore areas

listed and may be more or less severe than those at other

locations within the area.

3.1.3 Site Selection and Soil Investigations

Gravity type structures require a fairly level seafloor

free of large boulders and other obstructions that may damage

the base of the structure when it is installed, unless the

foundation may be prepared prior to installation. Foundation

preparation is.limited to water less than about 70 meters deep -

at least on a grand scale (Gerwick, 1974). Recent advances in

underwater equipment and diving technology have probably

extended this depth somewhat. Surface deposits must be somewhat

uniform to prevent excessive differential settlement and, while

necessarily possessing adequate strength for stability, they

must not be so strong as to prevent the penetration of skirts

during installation if skirts are adopted in the design. 35

Table IV

Environmental Design Criteria For Some Offshore Areas

WAVE CURRENT TIDAL WIND ICE GROUND AREA HEIGHT SPEED FLUC. SPEED THICK, ACCEL. (m) (m/s) (m) (m/s) (m) (g's)

Baltimore Canyon 30.0 ? ? - (Ward et al,'77)

Beaufort Sea 12.5 ? 2.81 ? 5.0 ? (Kliewer+Forbes,'80)

Georges Banks 25.2 ? - ? (Ward et al,'77)

Gulf of Alaska (Augustine et al,'78) 40.5 ? ? ? - ? (Bea and Akky,'79) 34.0 ? ? ? 0.41

Gulf of Mexico (Haring+Heideman,'78) 22.8 ? 2.22 ? - ? (Berman et al,'78) 26.5 2'.7 ? ? ?

North Sea 30.5 ? ? 363 - ? (Offshore Europe,'74) 54"

Offshore Brazil 16.0 1 .8 1.9 385 - ? (Burns+D'Amorim,'77)

Offshore Congo 9.4 ? ? ? ? (Lalli,'77)

'Includes a 0.3 meter lunar tide and a 2.5 meter storm surge

2Includes both lunar tide and storm surge

3One hour sustained speed

"Gust (several seconds)

5One minute sustained speed 36

Another site requirement is that the bearing soils have adequate strength to support the structure throughout its operational life; this includes both stability under design loads and the effects of repetitive loading (waves, earthquakes, etc.) on the various subsurface deposits. Additionally, settlement of the structure due to elastic displacements, primary and secondary consolidation, and cyclic compaction, must be within tolerable limits. This is generally a site requirement since little modification may be done to the design of a gravity type structure with regards to settlement. These basic concerns are investigated using information from preliminary surveys, which is usually enough to determine the adequacy of the site.

The selection of a site for an offshore platform is primarily dictated by oil reservoir considerations. There is always, however, some latitude that can be used to optimize foundation conditions (de Ruiter, 1976). The reservoir requirements may usually be met by installing the platform(s) within a fairly large area, on the order of several square kilometers or more. A general survey of the specified area is conducted to determine the most likely sites to place a platform(s). At this time, the type and number of platforms to be placed are often unknown. The survey lines and test holes

for one such survey conducted in the North Sea are illustrated

in figure 3.2.

Geological investigations, both regional and site specific, are made of the proposed area. The regional survey is often 1 1 1 1 1—: lettooo

LEGEND

Soo mtfres » f S\J*.-/& vEUEL-i • BoftCHOuE TrtAtK. WITH TI" PCSITIOWS •* UNI rerJmwnoN TEST *J cXPLeCKTieWWCU. c-

Figure 3.2 - Plan of survey lines - grid: local transverse (After Offshore'Soil Mechanics, 1976) 38

made using only presently available data. The history of the area is investigated, with particular attention paid to factors such as: the location of buried channels, deltaic clays, and tectonic movements. ' Environmental influences are assessed, including: regional and local rates of deposition, proximity to submarine canyons, and permafrost (Garrison and Bea, 1977).

On-site studies are made using specially outfitted survey ships, some of which are over one hundred meters in length. The distribution patterns of minor seafloor features, angles of local slopes, and water depths in the proposed area are found from bathymetry. Geophysical seismic surveys are made at the same time as the bathymetrical studies and from the same ship.

Acoustical profiling is done using electronic transducers which impart an acoustical pulse to the water by either a sound

(Pinger), mechanical (Boomer), or spark (Sparker) disturbance.

The resulting acoustical transmission, after travelling through the water, reaches the seabed and is reflected back by the various subsurface strata. The returning signals are picked up by hydrophone streamers or arrays (Offshore Europe, 1974). High resolution (Pinger or Boomer) surveys are used to gather

information on the upper sediments, those less than about 30 meters deep, and low resolution (Sparker) surveys are conducted to determine the characteristics of deeper strata, although in somewhat less detail.

Some seabed samples are necessary to provide specific geotechnical knowledge of the upper sediments - those most critical to the design of a gravity type structure. Shallow

samples are taken with a gravity corer, vibratory sampler, or 39

other sampling device. Alternatively, cone penetrometers may be used to characterize the surficial sediments, provided some samples are taken for correlation purposes. At least one deep boring (100 to 150 meters) is required to provide information on the sediments within the range of interest for foundation design. The positions of boreholes and the locations of other tests should be known accurately relative to the future structure. This may be accomplished by deploying an array of transponders on the seafloor and locating all boreholes and other test locations with respect to the transponders. The electrical signals emitted by the transponders allow them to be readily located from the surface (McClelland, 1977). A preliminary site selection may be made based on data from the aforementioned tests.

When a site has been chosen for further investigation, a carefully planned field program must be developed (Hitchings et al, 1976). The cost of offshore investigations is extremely high, on the order of tens of thousands of dollars per day for a

large survey ship and crew (Braun, 1974); therefore, the program

of testing must be thoroughly prepared by the geotechnical

consultant before the ship is on-site. All geotechnical testing

is performed by the consultant's geotechnical personnel and

other operations are supervised by his inspectors (de Ruiter,

1976). Engineers on-board monitor the incoming data

continuously to make on-the-spot decisions about the location

and extent of in-situ tests.

The base of the platform should fall within the area

investigated in the final on-site survey. The structure once 40

on-site can be positioned only approximately over the proposed site since it will be constantly in motion under wind, wave, and current excitation. The expected accuracy in positioning must be established and will govern the size of the area to be explored. Error margins in positioning of 50 meters are typical

(McClelland, 1977).

The site investigation is conducted from a ship which is subject to constant motion, as is any drillstring or piece of equipment connected to it. Special equipment has been developed to try to compensate for this motion (Taylor, 1976), however, complete success has not and will not be achieved. Therefore, whenever possible, in-situ testing is done with equipment that rests directly on the seafloor and requires no rigid connection to the surface vessel, only flexible control cables and hydraulic lines.

The site investigation, although well planned, does not follow a strict course. Information gained from early tests is used to determine the need for later tests. This should be kept in mind when reading the following text.

The seabed topography is mapped in detail using side scan sonar, which is good to about 0.5 meters, and submersibles

(de Ruiter, 1976). Obstacles such as boulders must be accurately located and their significance assessed. If they are too large, the site will not be suitable unless they can be removed. If not,-an alternative site may have to be chosen.

A number of borings are made to varying depths. The number of tests depend on the uniformity of the soil profile.

Generally three to five shallow boreholes (to 30-40 meters) and 41

at least one deep borehole (to 100-200 meters) are sunk

(de Ruiter, 1976). Three corings has been suggested as an

absolute minimum (George, 1976). Samples are usually taken at

intervals of 1.0 to 1.5 meters over the first 15 meters, then

less frequently (McClelland, 1977). The soils can only be

identified with certainty where samples are taken since the

drilling mud and cuttings exit at the seafloor (Low, 1975).

Samples are usually extruded on-board, classified, and

checked for quality. Some samples are selected for on-board

tests, including routine classifications (Atterberg limits,

grain size distribution, etc.) and unconfined compression tests,

while others are prepared for the on-shore laboratories, where

consolidation, triaxial, and other complex tests are carried

out.

Cone penetrometers are used extensively to check the

uniformity of shallow deposits and to estimate the penetration

resistance that will be encountered by the dowels and skirts

during installation.7 They are also used for classification

purposes and for estimating the undrained strength of clays and

relative density of sands. The number of penetration tests

depends on the uniformity of the soil profile with five to

fifteen being typical numbers (de Ruiter, 1976). Additional

acoustical profiling on a fine grid may be necessary if abrupt

'Dowels are cantilever rods which jut out of the base of the platform 5 m or so. They are used to stabilize the structure and prevent it from moving while it is being ballasted and the skirts are being imbedded. 42

changes in stratigraphy are detected (de Ruiter, 1976). A valuable qualitative picture is presented from cone penetration logs that may be used to assess the reliability of boring data.

Down-the-hole penetrometers may be used in deeper boreholes to measure the density and shear strength of deeper sediments.

Gamma ray logging can be done down the boreholes for a minor increase in cost. The gamma ray log provides a continuous picture of the borehole and is useful as a qualitative tool showing stratification and the presence of cohesive soils.

These soils are marked by an increased gamma ray count. Other in-situ tests may be carried out in addition to those mentioned, including vane shear tests which are applicable in areas with soft clays (McClelland, 1977).

3.1.4 Selection of Soil Parameters for Design

Design parameters are chosen based on data from both laboratory and in-situ tests. The borehole profiles are interpreted from cone penetration logs, gamma ray logs, and samples. Samples are used for identifying the deposits and for making site-specific penetrometer correlations. The in-situ tests provide a continuous picture of the profile and are important for identifying interfaces and small scale features, such as thin seams or lenses of varying material in larger seemingly uniform layers, since a continuous record of the drill mud or cuttings is not available. The results of one such borehole interpretation are shown in figure 3.3.

The necessary design parameters are found by using established laboratory tests and in-situ methods properly 43

Soil profII*

Fine to medium umd with diell froamentt (dente)-

Small tilt fraction

Few imotf graved 10- H Grey tilty cloy with teoms of fine land and tilty landdtiff fo very stiff) 15

Fine fa medium land (dense) Seomi of silry clay

Grey illty clay with •£a. teomt of lilt and tilty fine umd(very ttlff) O 25

Silly land layer?

Silly land layer?

35

Silty fine land with of tilty cloy(dente) I—40- Silly clayfoord) Flo.5 TYPICAL SOIL PROFILE AS IDENTIFIED »Y BOREHOLE,CONE PENETRATION TEST AND V RAY LOG

Figure 3.3 - Typical soil profile as identified by borehole, cone pentration test and gamma ray logging (After George, 1976) 44

correlated to the offshore site. Oedometer tests are used to obtain consolidation data. The stress-strain characteristics of the foundation soils and the effective shear strength parameters are found from triaxial tests. Simple shear and direct shear testing may also be done. Relative density and modulus values are best determined from in-situ tests, such as the cone penetrometer with the aid of empirical correlation charts. The modulus value is particularly sensitive to sample disturbance.

When choosing design parameters "one should always be aware of the limitations imposed by the conditions under which investigations at sea have to be carried out," (de Ruiter,

1976).

Obtaining the shear strength parameters presents many difficulties, some being:

- The ability to obtain samples of high quality

- Inherent scatter in laboratory data

- Deciding which type of shear tests are applicable to the problem (Rowe, 1975)

- The natural variability of offshore deposits

When choosing a profile, it must be remembered that an estimate which is too conservative may result in millions of dollars having to be spent to increase the platform size so that a reasonable factor of safety against sliding or bearing failure is obtained, while too liberal an estimate may result in the complete loss of a multi-million dollar investment and many lives.

Results of both in-situ and laboratory shear tests for one particular site are presented in figure 3.4. The interpretation 45

CONE RESISTANCE fkPal— COHESION c (kPa)—•

0 500 WOO 1500 2000 2500 0 40 60 80 100

CD <

I UJ CO

I 1- CL g I

Figure 3.4 - Comparison of shear strength values from sample testing and from CPT (After de Ruiter, 1976) 46

of this profile is certainly subject to personal opinions and prejudices. A thorough knowledge of the types of tests and the

conditions under which they were performed is essential when making such a decision. The cone penetrometer results provide a

useful check on the laboratory data.

3.2 Platform Design

The basic design considerations for a gravity platform are

discussed briefly in this section. Detailed descriptions of

design procedures are beyond the scope of this thesis. The

reader is therefore directed to references if a deeper study is

required.

3.2.1 Hydrodynamic Analyses

Hydrodynamic analyses are performed primarily to provide

the structural engineer with information on the magnitude and

nature of wind, current, and wave loads. The pressure

distributions caused by these loads on the structure, which will

vary both spatially and temporally, are required for the design

of the various components. The total forces acting on the

structure, found from integrating the pressure distributions

with respect to the spatial coordinates, are required for the

design of the foundation. The nature of wave loading on both

the structure and the foundation system is discussed in detail

in Chapter 5.

Wave loads are usually by far the most important fluid

loads encountered. Many analytical procedures have been

developed to calculate the forces due to waves interacting with 47

gravity type structures. In addition to theoretical analyses, model testing is often employed to provide a check on results

(Garrison, 1977), since hydrodynamic theories cannot account for irregular shapes, interference effects, and other such problems that exist with real structures, except by approximate.numerical methods or through the use of empirical coefficients (which are usually based on laboratory tests on small scale models).

Analytical methods are used to calculate the forces on individual members of the structure, since modelling these members individually is impractical.

Scour potential is investigated using model tests since no acceptable analytical theories exist. Even model tests are not very reliable due to scale effects (Maidl and Schiller, 1979) and difficulties in modelling the soil. However, a valuable qualitative picture of the on-site scour potential may be drawn from these tests.

Model tests are invaluable for providing information on towing resistance and motions, floating stability, damage stability, and submergence behavior when touching down (Offshore

Europe, 1974). For these operations, model tests are relied upon heavily and are- always incorporated into the design procedure.

3.2.2 Geotechnical Analyses

After preliminary surveys are completed and a detailed site investigation has been carried out for a possible gravity platform site, comprehensive geotechnical analyses begin. These analyses are summarized in Table V. 48

Table V

Geotechnical Concerns For Offshore Gravity Type Platforms

1) INSTALLATION A) Penetration resistance of dowels and skirts B) Pore pressure dissipation and exit of confined water C) Bearing pressure on cells and slab D) Grouting procedures

2) CONTACT BETWEEN SEAFLOOR AND STRUCTURE A) Scour around or under structure B) Reduced area for bearing or sliding resistance

3) STABILITY UNDER PSEUDOSTATIC LOADS A) Sliding B) Bearing failure C) Overturning

4) SETTLEMENT A) Immediate elastic B) Primary consolidation C) Secondary consolidation D) Cumulative storm and/or earthquake effects 1) Strain softening in clays 2) Densification due shear stress reversals in sand

5) DISPLACEMENTS UNDER PSEUDOSTATIC LOADS A) Horizontal displacements B) Vertical displacements

6) EFFECTS OF CYCLIC LOADING A) Pore pressure rise B) Reduction in shear strength C) Decrease in stiffness D) Associated problems 1) Excessive horizontal displacements 2) Rocking 3) Liquefaction

7) DYNAMIC BEHAVIOUR A) Resonance B) Operational requirements

8) INSTRUMENTATION A) Installation B) Performance monitoring 49

The penetration resistance of dowels and skirts requires a good knowledge of the upper sediments, usually known from extensive cone penetrometer testing. This resistance, which will vary over the site, may be estimated using the standard bearing capacity equations of Meyerhof (1963) or Hansen (1970).

The resistance to dowel or skirt driving is essentially the ultimate bearing capacity of the upper sediments. Penetrometer correlation charts may be used to estimate the bearing capacity factors. The local contact pressures on the base slab may be estimated by elasticity theory, provided that the detailed topography of the seafloor is known (Bjerrum, 1973). Generally, the slab is designed for a specified base pressure, since the topography and distribution of the upper sediments are not precisely known. Other installation problems will be discussed in a subsequent section on platform installation procedures.

Good contact between the seafloor and the slab is necessary to prevent undermining of the foundation from water motions and to insure adequate area for foundation stability. This is achieved by grouting underneath the slab after the platform has been imbedded as far as possible. Proper grouting procedures and composition must be specified.

There are a number of possible failure modes for an offshore gravity structure foundation, including: horizontal sliding, bearing failure, rocking, and liquefaction. These failure modes are shown in figure 3.5.

The stability of the platform is investigated to insure that horizontal sliding or a deep-seated bearing failure does A) SLIDING B) BEARING CAPACITY

Fig. 3.5 Possible failure modes for an offshore gravity structure foundation en (Adapted from Hove and Foss, 1974) o 51

not occur. There are a number of possible mechanisms for a horizontal sliding failure that must be considered in order to find the most critical one. These are shown in figure 3.6.

Bearing failure is investigated using the bearing capacity formulas of Meyerhof (1963) or Hansen (1970), and for clay deposits, a simple limit equilibrium method called the

(Norwegian Geotechnical Institute) slip surface method

(Lauritzsen and Schjetne, 1976). The simple bearing capacity equations give a rough estimate of the bearing strength of foundation soils and are convenient and easy to use. They are not strictly applicable to layered deposits or the ocean wave or earthquake problems where loading conditions are more complicated than the formulae can account for. Therefore, finite element analyses are also performed to provide a more detailed investigation of the bearing stability.

Overturning failure is not a problem if load eccentricity is not too high. This potential problem may be avoided by increasing the base size if necessary. A stability diagram is shown in figure 3.7 to show the basic relationship between vertical and horizontal loads as they relate to foundation stability. The magnitudes of the loads, of course, depend on the foundation size and the strength of the foundation soils.

Calculations for elastic and consolidation settlements are similar to those which are done for any other structure. Of interest here is that the depth of influence, i.e. the size of the stress bulb, is substantially larger for these huge structures than for most projects on land, and therefore, the corresponding settlements are usually greater. In addition to 52

(ol PASSIVE WEDGE FAILURE

(t» DEEP PASSIVE FAILURE

(dl SLIDING FAILURE IN SHALLOW WEAK ZONE WITH WIDELY SPACED SKIRTS

1LIJ11J.IJJ1I.111. ' K ... . . •

(.) SLIDING FAILURE IN SHALLOW WEAK ZONE AVOIDED WITH CLOSELY SPACED SKIRTS

(f) SLIDING FAILURE IN DEEP WEAK ZONE

Figure 3.6 - Possible modes of sliding failure (After Young et al, 1975) 53

Figure 3.7 - Stability diagram for a raft foundation (Adapted from Young et al, 1975)

0 54

these calculations, some assessment of the effect of cumulative storm or earthquake loading on settlement must be made.

Laboratory tests are necessary to determine this influence and appropriate procedures must be used to estimate the amount

(Andersen, 1976; Finn et al, 1977; Lee and Albaisa, 1974).

Cyclic loading and its effects on the foundation soils are investigated in an approximate way. For wave loading, where the period is on the order of several seconds or more, pseudostatic analyses are performed for stability and displacement calculations. Cyclic effects are modelled by changing the soil properties to account for pore water pressure generation. For earthquake loading, full dynamic analyses are required with suitable effective stress computer programs.

Displacements of the structure under pseudostatic wave loads are estimated using the finite element method. These displacements include vertical, horizontal, and rocking motions.

The results are very sensitive to the values chosen for the soil parameters. The effect of cyclic loading may be incorporated here by estimating the pore water pressure rise and decreasing the soil stiffness and shear strength to account for this.

Liquefaction potential is assessed from laboratory test data either directly with cyclic triaxial tests modified to allow for partial drainage (Lee and Focht, 1975a) or indirectly using analytical methods (Rahman et al, 1977). Preliminary studies based on simplified undrained analyses (Bjerrum, 1973) may be useful to assess the need for more advanced investigations, either laboratory or analytical.

Most dynamic analyses are performed by the structural 55

engineer who requires soil parameters to model the stiffness and damping characteristics of the foundation soils. The evaluation

of these soil parameters is the job of the soils engineer.

Seismic considerations have not had a significant influence

on gravity type structures designed to date. However,

earthquake engineering for offshore gravity structures is

receiving increasing attention as structures of this type are

being considered for seismically active areas. A thorough

discussion of this topic is beyond the scope of this thesis and

the reader therefore is referred to several publications that

deal with this subject, namely: Watt et al (1978) and Seines

(1981). Two design codes may also be referenced: those of Det

Norske Veritas (1977) and the American Petroleum Institute

(1978).

A final concern of the geotechnical engineer is the

requirement for monitoring the installation and subsequent

performance of the gravity platform. This is covered in detail

in a later section.

3.2.3 Structural Requirements and Analyses

The final structural analyses and design may proceed when

the environmental loads have been defined and the soil

investigations are complete. An important requirement of

offshore structural design is that the structure be designed for

construction, tow-out, and installation loads, in addition to

the usual procedure of designing for the maximum forces expected

during operational life.

The three main components of the structure: the deck, 56

towers, and base caisson, have distinct design requirements.

The deck, which is usually made of steel, must resist corrosion

(which is higher in the splash zone than elsewhere) and fatigue

failure throughout the platform's life, which is usually between

20 and 30 years. The critical points in the design are, however, not the deck but the towers and base slab (Sjoerdsma,

1975b).

The towers must be designed to prevent implosion under the

large hydrostatic forces due to the structure's deep draft and

the additional wave induced pressure loading. The differential

hydrostatic pressure acting at the base of the towers may be

larger during the construction or tow-out phases, when the cells

are not filled with ballast, than when the platform is on-site

and operational. This must be investigated to determine the

critical design load. The caisson will also have to resist

implosion from large differential hydrostatic pressures if there

are cellular compartments (as with the platforms shown in

figure 2.2). It must also be strong enough to resist damage

from foundation loads. These may be locally high due to contact

pressure with objects such as boulders on the seabed or to the

high resistance of dense sand pockets to deformation during

installation. According to one code (Federation Internationale

de la Precontrainte, 1977), the slab must be designed for 200

t/m2 at all locations to account for uncertainty in soil

investigations and penetration resistance and for higher values

if dense sand is found from soil investigations. This value is

about an order of magnitude higher than the uniform bearing

pressure calculated for the slab. 57

For the base slab, it is readily apparent that the critical design loads are those encountered upon installation. Other critical design conditions are not so obvious. For example, the steel gravity type platforms towed from Europe to the Congo were designed for greater wave loads expected during the tow than they would be subjected to once installed in the relatively calm waters offshore the Congo coast (Lalli, 1977).

The dynamic analyses required for a large gravity type structure are numerous and involved. Since many of the loads acting on the structure (wind, waves, and earthquakes) contain components of many frequencies, spectral analyses are required for both resonance studies and fatigue calculations. In addition to the signal being random, the structure will probably not be symmetrical and different directions of loading will have to be investigated.

For a more thorough presentation of the structural requirements for an offshore gravity structure, the reader is referred to several papers concerned wholly with this topic

(Penzien, 1976; R0ren and Fames, 1976; Waagaard, 1977; Watt,

1979).

3.3 Platform Construction

Of paramount importance in the construction of a large

(concrete) gravity platform is the availability of suitable sites for dry docks, shallow water construction areas, and deep water construction sites.

The base section of the platform is built in an excavated 58

dry dock. When the raft has been completed and the caisson walls raised to a predetermined height, the dry dock is flooded, the cofferdam removed, and the base section floated up and towed out to a shallow water site (usually a nearby or attached bay or

fjord) where it is secured by mooring cables (Clausen, 1976).

Compressed air may be used under the foundation to add buoyancy

if there are problems in floating it out of the dry dock

(Derrington, 1977) or to cut excavation costs (Werenskiold,

1977).

At the shallow water construction site the base caisson is

completed and the towers are erected. When the towers are

completed, the structure is then towed out to a 'deep water

construction area where it partially submerged by flooding

ballast compartments in the base section and towers, and then

moored. It is at this site that the deck is usually mated

(Sjoerdsma, 1975b). The deck, which was built onshore, is

loaded onto two barges (or old tankers). These barges are then

towed out to where the platform is and positioned so that the

deck is over the towers. The platform is then partially

unballasted to raise the deck off the barges and onto the towers

(Clausen, 1976). The structure, virtually complete, is now

ready for tow-out.

The transport of the structure between the various

construction sites and then the tow-out to sea for installation

must be carefully planned before construction begins. There

must be adequate bottom clearance and room to maneuver the

structure throughout all the towing routes. These

considerations are the responsibility of a maritime consultant 59

who is well versed in these practices (Werenskiold, 1977).

3.4 Platform Installation

The platform, being partially submerged for stability, is towed out to location by an array of tugboats. This is an extremely delicate operation that must be very well planned and coordinated by the maritime consultant. The positioning and submerging of the structure is also his responsibility. Weather forecasts are used to choose a sailing time and are constantly monitored and updated to insure calm seas for the tow-out

(Werenskiold, 1977).

The structure once on-site can be placed only approximately on location. Because of the high inertia of such a large structure, even when moving very slowly, there will no doubt be some finite motions at the moment of touchdown, especially if there is a current present (Watt, 1976). The sea must be relatively calm at the time of installation to avoid excessive motions of the structure that may damage the caisson and its appendages. The installation sequence is shown in figure 3.8.

The structure is systematically ballasted once on-site to stay level while sinking. The rate of submergence is carefully monitored so that the structure does not impact the seafloor heavily and damage the bottom slab, skirts or ribs. To aid in placing the structure and minimizing damage to both the structural and soil components of the foundation, steel dowels which portrude several meters below the skirts are provided.

The dowels penetrate the seafloor under the weight of the platform as it sinks and provide resistance to horizontal motion 60

(c) Skirt driving W) Grouting

Figure 3.8 - Installation sequence for a gravity platform (Adapted from Watt, 1976) 61

which could break off the skirts or ribs or gouge out the foundation soils, impairing stability under storm conditions.

The base detail of a CONDEEP type platform installed in the

North Sea is shown in figure 3.9.

As the structure is further submerged, the skirts and ribs penetrate the foundation soil. To keep the structure vertical during skirt penetration into the seabed, which in general will be irregular due to a sloping seafloor and varying soil conditions at the site, large moments may be applied to the foundation by ballasting appropriate cells thereby driving the skirts deeper (Clausen, 1976). Care must be taken to allow ample time for water entrapped within the skirt compartments to flow out from underneath the slab. If the platform is lowered too fast, high current velocities may result and cause channels to be eroded underneath the structure that may lead to more erosion and threaten the stability of the platform (Gerwick,

1974) .

To insure good contact between the base slab of the structure and the foundation soils, the space between them is usually grouted utilizing a built-in piping system in the base provided for this purpose (Callis et al, 1979). Grouting usually begins after a few points on the base have touched down.

The structure must be submerged slowly to allow excess grout to flow out from underneath the structure without damaging the foundation soils or .overstressing the skirts (Watt, 1976).

Submersibles may be used to monitor the success of grouting operations (Callis et al, 1979).

The base of the structure is usually instrumented so that 62

k 50jn j

Figure 3.9 - Detail of CONDEEP base structure (After Clausen, 1976) 63

decisions can be made during installation about the amount of penetration possible. If excessive pressure is exerted on any of the foundation components from either pushing objects such as boulders into the seafloor or increased driving resistance from say a lense of dense sand, the submergence may be halted and grouting to fill the interskirt spaces may commence. For one

CONDEEP structure very high pressures were experienced on the base of one cell during submergence - probably from the high deformation resistance of a lense of dense sand that was

undetected during the soil investigations (Clausen, 1976). The decision to stop driving the platform to prevent structural

damage to the slab was made based on information from

instruments built into the caisson. The data available from the

instrument interpretations is shown in figure 3.10.

After grouting is completed, some form of scour protection

may be placed depending upon local soil conditions and expected

water particle velocities near the structure. Gravel mats

connected to the structure and rolled out after installation is

completed have been used (Offshore Europe, 1974).

3.5 Platform Instrumentation

Platforms are generally well instrumented to (1) aid in

installation, and (2) to provide information on the performance

of the structure during its operational life. Although the cost

of instrumenting the structure is high, the money saved in

construction costs is more than offset by this (McClelland,

1977) since materials and labor are reduced by not having to

increase dimensions to account for uncertainties in installation 64

« 200 Design Maximum Allowable Value

2?

(A

S 100

Expected Maximum Values 0) I E 50

10 15 20 Dome Number

Figure 3.10 Maximum dome contact pressures observed during installation of the "Beryl A" CONDEEP (After Clausen, 1976) 65

loads (soil reactions). Instrumentation for measuring platform response provides data for future design on pore pressure rise, lateral displacements, etc. after the platform is installed.

The following instrumentation has been used to monitor the

installation of platforms now on site (DiBagio et al, 1976):

- Wavedata by means of a buoy anchored near the platform

- Bottom clearance by means of echo-sounders installed under the base of the caisson

- Draft by ,means of pressure transducers mounted near the base

- Ballast water level in cells and towers by means of pressure transducers within these compartments

- Bending moments and axial forces in dowels from strain gauges

- Water pressure in skirt compartments beneath the caisson during penetration and contact grouting by means of differential pressure transducers

- Verticality from a biaxial inclinometer

- Base contact pressures using earth pressure transducers mounted flush on the slab

- Strain in reinforcing steel in base slabs and cell walls by means of strain guages in the reinforcement

- Short term settlement by means of pressure measurements in a closed hydraulic system

Other instrumentation has been used to monitor the performance

of these platforms (DiBagio et al, 1976):

- A complete system for oceanographical/meteorological measurements (wave, tide, current, wind and temperature data)

- Base contact pressures by means of earth pressure transducers mounted flush on the slab

- Structural strain at the base of the towers, giving the moments from wave action transferred to the foundation, from strain gauges

- Linear accelerations and displacements at the base, at mid- 66

height of the towers, and at deck level

- Angular accelerations and displacements at the base and deck levels

- Long-term horizontal and vertical displacements by means of a flexible telescopic casing installed under the caisson

- Pore pressures in the foundation soil by means of piezometers installed beneath the platform

A computer operated digital data acquisition system is used to process data as it is received with the computation of basic statistical data being processed on-line and stored on a magnetic tape (Clausen et al, 1975). 67

CHAPTER 4

THE EKOFISK TANK - A CASE STUDY

The Ekofisk tank has been the subject of numerous papers

(Bjerrum, 1973; Braun, 1974; Clausen et al, 1975; Duncan, 1972;

Gerwick and Hognstad, 1973; Lee, 1976; Lee and Focht, 1975a; Lee and Focht, 1975b; Marion, 1974). Being the first large offshore gravity structure installed, it naturally received a lot of attention in the engineering community. The Ekofisk tank is familiar to almost everyone involved in offshore platform design and construction and has a relatively large body of literature associated with it. With these points in mind, a discussion of the Ekofisk tank would appear to be useful as a means of presenting geotechnical concepts and the application of theories in the offshore environment. A geotechnical case study of the tank is presented herein.

A general description of the Ekofisk tank may be found in several sources (Gerwick and Hognstad, 1973; Marion, 1974;

Offshore Europe, 1974). The details of the design, construction, and installation of this platform are discussed in depth in these papers and will only be highlighted here.

The tank was built near Stavanger, Norway, then towed over

400 kilometers from the Norwegian coast to the Ekofisk field in the middle of the North Sea where it was placed on June 30,

1973. After being positioned, the structure was ballasted with water to imbed it in the foundation soils. Positioning errors were 10 meters off target and 3°50' out of orientation (Marion, 68

1974). The base of the structure, shown in detail in

figure 4.1, is covered with 5 cm high corrugated steel plates

and has 40 cm high skirts along the periphery and 40 cm high

ribs underneath the central structure; these were provided to

obtain full contact with the seafloor soil. After skirt driving

was completed, nylon mats attached just above the skirts were

rolled out by divers and rocks dumped on them to provide

protection against scour (Gerwick and Hognstad, 1973).

Additional sand ballast was added after placement to achieve a

maximum negative buoyancy for the tank. The submerged weight of

the tank after this ballasting was 190,000 metric tons (Clausen

et al, 1975). The final cost of the platform including

installation was in excess of $28 million (Offshore Europe,

1974). 8

The structure is nearly circular in plan, resembling a

square with rounded corners, with an approximate diameter of

93 meters. It is 90 meters high and rests on the seabed in

70 meters of water. One million barrels of crude oil may be

stored in the central reservoir which is roughly 45 meters

square in plan and 70 meters high; this reservoir is composed of

nine lobes for maximum structural strength (Gerwick and

Hognstad, 1973) each with walls nearly one meter thick at the

base (Offshore Europe, 1974). Surrounding the reservoir is a

perforated breakwater designed to reduce wave loads on the tank,

which extends from about 12 meters above the water surface to

"This figure is in 1973 U.S. dollars. 69

Figure 4.1 - Detail of the Ekofisk tank bottom (After Clausen et al, 1975) 70

the base slab where it is rigidly attached. The heavily post- tensioned base slab is 6 meters thick and extends beneath the entire structure forming a huge solid raft foundation covering an area of 7360 m2 (Offshore Europe, 1974).

The buoyant weight of the tank is now about 190,000 metric

tons and in static water exerts an average pressure of about

25.8 t/m2 on the foundation soils. Under wave loading, there

will be a fluctuating component of the vertical stress which is

on the order of 5% of the static pressure (H0eg, 1976). This

fluctuating vertical load is in phase with the horizontal force

and moment (Schjetne, .1976). For the Ekofisk tank, the

magnitude of the fluctuating vertical force is about 10,000

metric tons for the design wave. Therefore, when analyzing the

foundation for design wave conditions, a vertical force of

200,000 metric tons acting on the foundation is used; this

corresponds to a uniform vertical pressure of about 27.2 t/m2.

For the 100-year design wave, a horizontal force of about

78,600 metric tons will act on the tank (Bjerrum, 1973). Since

this resultant force will act above the seafloor, a moment will

be applied to the foundation. The magnitude of this moment is

approximately 2,800,000 ton-meters (Clausen et al, 1975). The

tank is shown schematically in figure 4.2 with the loads acting

on it corresponding to the 100-year wave. Some design storm

data is shown in figure 4.3.

Foundation conditions at the Ekofisk field are typical of

the North Sea: alternating layers of dense sands and heavily

overconsolidated clays. A typical geotechnical profile from the

Ekofisk field is shown in figure 4.4. The upper 26 meters are 71

^93m-

- S W.L,

Ja^lOpOOt ft = 78,6001 S70m

Pv =19Q000t ^36m

L «X "

Figure 4.2 - Loads on the Ekofisk tank for the 100-year wave

5000 WAVES 15 MRS DURATION

* & 400

20 40 60 60 FT

I I L_ 0 5 <0 IS 20 25 M. WAVE HEIGHT. H

Figure 4.3 - Design storm data for the Ekofisk field (After Lee and Focht, 1975a) 72

« -Mm ,j • —1 20m

7C m

Sand

^^^^^^^^^^^^ Cljy 50 m

Sind

100 m

150 ml-

Figure 4.4 - ^j«^otechnical)Profile fro. EkoHsk Mela

-Om

UNDRAINED SHEAR STRENGTH (t/m') Sea floor jc-70m

Fin* land 11 '° Stiff sandy clay * Fint und i • Si" • < • Hard clay • • 0 IS" > uj uj o in SO 60

• UU triaxial • Unconfintd compression test o Pocket penetrometer

Figure 4.5 - Shear strength data from Ekofisk lArter Clausen et al, 1975) 73

comprised of extremely uniform fine sand with a thin clay seam at about 18 meters below the seafloor; the upper few meters have a relative density on the order of 100% (Bjerrum, 1973). This high density is most probably due to the effect of countless waves that have passed overhead since the sand was deposited

(Bjerrum, 1973). Shear stresses are induced in the soil from passing waves because of the varying pressure distribution they impose on the seafloor (Henkel, 1970). These stresses cycle back and forth and may compact the sand if they are sufficiently large. This is termed "preshearing" (Bjerrum, 1973) and has been demonstrated to be an important source of soil compaction in the laboratory (Lee and Focht, 1975a).

The stiff clay beneath the sand has an undrained shear strength of about 40 t/m2 (Bjerrum, 1973). The clay seam at 18 meters below the mudline is substantially weaker. Some shear strength data is presented in figure 4.5.

Foundation studies for the platform were performed independently by McClelland Engineers, Ltd. and the Norwegian

Geotechnical Institute. The Norwegian Geotechnical Institute represented Det Norske Veritas, the agency responsible for approving the platform safety for the Norwegian government, and was responsible for checking the foundation safety independently of McClelland's findings. There was a great concern about safety since an oil spill of possibly one million barrels would be disastrous (Duncan, 1972). Final approval of the tank required that it could not be used for oil storage for several months after installation; thus, if a failure occurred during this period, no spill could take place (Clausen et al, 1975). 74

Preliminary studies carried out at the Norwegian

Geotechnical Institute (NGI) were reported by Duncan (1972).

Finite element modelling of the foundation, taking into account the nonlinear behaviour of the soils, was done to predict the elastic settlement of the structure and the displacements expected under storm wave loading. Elastic settlement was estimated to be about 30 cm for the tank due to its own weight

(Duncan, 1972). Assuming that the load-settlement curve for elastic settlement is linear, this would imply that the structure would move up and down about 1.5 cm when subjected to the fluctuating vertical force of the design wave.

The horizontal displacements of the tank were estimated to be about 15 cm back and forth for the design wave (Bjerrum,

1973). Concurrent with these linear displacements are rocking motions which result from the cyclic moment. NGI estimates

showed that subject to the design wave, one side of the base

slab would move down 30 cm while the opposite side would move up about 45 cm. Superimposed on the elastic settlement due to the

platform weight, this would mean that one side would lift about

15 cm off the sand (Duncan, 1972) resulting in a possibly

unstable situation. Because the platform would almost

undoubtedly be subjected to numerous storms before the 100-year

design storm would hit, the tank was expected to settle from the

preshearing effect and the sand under the tank to densify and

become stiffer reducing the motions (Duncan, 1972). This

settlement and accompanying increase in stiffness meant that

rocking motions expected for the 100-year wave could be modified 75

from the original estimates. New 'calculations indicated that the base slab would move up about 15 cm on one side and down

15 cm on the other (Bjerrum, 1973). This implied that the base

slab would not be lifted off the soil, and. at all times would exert a positive pressure on the foundation (Bjerrum, 1973).

Results of these studies are shown in figure 4.6.

The NGI finite element studies of displacements included

the effect of the pore water pressure change at the seafloor due

to the passage of waves overhead (Bjerrum, 1973). They did not,

however, include the effects of cyclic loading on the foundation

soils. Rahman et al (1977) have shown that pore water pressure

ratios of about 20% and 8% will occur under the edges and center

of the tank, respectively, when subjected to the 100-year storm.

Their analysis is for a relative density of 85%, which is less

than the relative density in-situ, and includes the effects of

partial drainage in the sand. Although their results are not

strictly correct, they do show that excess pore water pressures

will develop under the tank during design storm loads. This has

been confirmed from observations on-site using piezometers and

pressure gauges installed underneath the structure (Clausen et

al, 1975). Expected rocking displacements would then be greater

than reported by Bjerrum (1973) for the NGI analyses since the

increase in pore water pressure under the tank would decrease

the stiffness of the upper sand layer.

Settlement observatons have been reported by Foss (1974)

and Clausen et al (1975). A load-settlement curve is shown in

figure 4.7 for the installation phase of the tank. After

touchdown, the platform was ballasted to seat it firmly on the 76

Figure 4.6 - Predicted rocking displacements for the Ekofisk tank (After Duncan, 1972)

igure 4.7 - Load-settlement curve for Ekofisk tank (After Clausen et al, 1975) 77

foundation soils. During this time the seabed was being

deformed from both elastic compression and plastic

displacements. The plastic displacements corresponded to the

penetration of short concrete skirts and to the flattening of

the seafloor beneath the structure; since the bearing capacity

of undulations and mounds would be exceeded as the platform

seated, these features were destroyed and the platform settled.

This "bedding settlement" should correspond to the skirt depth

for a flat seafloor, indicating full skirt penetration and base

contact with the seafloor. The load-settlement curve became

nearly linear when the submerged weight reached 50,000 tons.

The penetration of the 40 cm high skirts into the seafloor at

this time was about 35 cm. It is important that the load-

settlement curve became linear. This indicated that

(essentially) full contact between the base of the structure and

the seafloor was achieved (Clausen et al, 1975).

If the linear portion of the load-settlement curve is

extrapolated back to zero submerged weight and forward to

190,000 tons, the elastic settlement of the tank due to its own

weight may be established. This results in an elastic

settlement of about 10 cm, substantially less than the 20 cm

predicted by NGI.9 The discrepancy may be due to the use of

stiffness parameters in the finite element analyses that were

9One should note that Duncan's (1972) reported estimate of 30 cm for elastic settlement of the tank was made before final discrepancies in the value of soil parameters were cleared up (Lee and Focht, 1975a). This estimate was later changed to 20 cm (Braun, 1974). 78

not really representative of the "undisturbed" soil; stiffness parameters were probably chosen much too conservatively as a

consequence of the difficulty and uncertainty associated with

offshore soil testing and sampling - particularly at that time -

a decade ago.

Settlement continued to occur after the platform was

installed. The time history of settlement for the first seven

months after installation is shown in figure 4.8. Most of the

ballast was added to the tank in the first few days after it was

placed. The load-settlement curve previously discussed was

developed for this time interval. Settlement in the early days

of July, 1973, Was due to the elastic response from increased

submerged weight of the platform as it was ballasted.

Settlement in the following months may be attributed to a

variety of factors, namely: increased submerged weight of the

platform (from more ballasting), consolidation in the clay, and

wave action on the tank.

The amount of settlement due to the increased ballast load

can easily be estimated from extrapolating the load-settlement

curve in figure 4.7. The overall elastic settlement would be

about 10 cm and would not increase after the tank was fully

ballasted. At the end of ballasting, settlement was observed to

be about 13 cm (see figure 4.8). Hence, the consolidation and

wave induced settlement was on the order of 3 cm up until the

middle of October (when ballasting was terminated). During this

time the sea was relatively calm as seen from the wave data in

the figure. Note that the wave heights shown are the

significant wave heights (a statistical parameter) not the 79

Figure 4.8 - Ekofisk settlement data relating submerged platfo weight and storm wave data in the early months after installation (After Clausen et al, 1975)

MQ0OO

r itqpoo 5

| tOQOOO

S KtOOO

*1* 1974

Figure 4.9 - Settlement data for Ekofisk tank during early storms (After Clausen et al, 1975) 80

maximum wave heights; these values must be increased by approximately 80% to find the maximum wave heights (Sarpkaya and

Isaacson); the exact increase depends on statistical data which

is not available.

In November, the platform was subjected to several major storms. The first storm hit on 6 November and a settlement of about 2 cm occurred during the next few days (Clausen et al,

1975). On 19 November, the major storm of the year occurred.

When this storm hit, the platform instrumentation was out of service and the wave data was estimated from a nearby weather ship, the "Famita" (Foss, 1974). Estimates put the maximum wave height at about 22 meters, or about 90% of the 100-year design wave - truly a significant storm. The platform settled about

5 cm during the period of 16 November to 20 November (Foss,

1974). Total settlement during November was about 7 cm, of which most probably occurred in the sand. The dense sand consolidated under the action of repeated shear stress reversals

(Clausen et al, 1975). A detailed record of the November

settlements is shown in figure 4.9.

After the storm of 19 November subsided, no detectable additional settlement of the platform occurred for the next two months. From mid-December 1973 to July 1974, the platform was

observed to settle another 1-3 cm (Clausen et al, 1975). This was most likely due to consolidation in the clay. Total

settlement one year after installation was approximately 24 cm.

This was within the 20-40 cm range predicted by NGI (Clausen et

al, 1975). They estimated that the initial settlement would be

20 cm, and that another 15 cm would occur over the life of the 81

structure from storm effects (Braun, 1974). Unfortunately, more

recent data is not available to extend the settlement-time curve

shown in figure 4.8.

Reported differential settlement of the platform after

installation was 13 cm from the northeast (high) to the

southwest (Clausen et al, 1975). (This, however, may not all be

settlement since the seafloor was uneven and perhaps slightly

sloping.) Although seemingly large, this corresponds to the

platform being off vertical by only about one-twentieth of a

degree. In the twelve months after installation, additional

differential settlements of about 2 cm in the east-west and 6 cm

in the north-south directions occurred (Clausen et al, 1975).

Of interest, perhaps, is how the settlement data was

obtained. Sightings were made on a nearby jacketed platform

founded on deep piles. This platform had been placed more than

a year before the Ekofisk tank and was not expected to settle

noticeably during the period under consideration (Foss, 1974).

The development of excess pore water pressure under the

Ekofisk tank has been the subject of several studies.

Fortunately, some pore water pressure data from Ekofisk is

available to compare with theoretical predictions. The platform

base was instrumented with seven pressure gauges and the

underlying soil with twelve piezometers. A description of the

installation of piezometers beneath the tank is given by Clausen

et al (1975). The arrangement of these devices is shown in

figure 4.10.

Data from the storm of 6 November, the first major storm to

hit the platform, is shown in figure 4.11. Several important 82

®: n rtftrt to gauge no.

Figure 4.10 - K^ati?nn.ff^rfSSUre 9au9es and piezometers beneath Ekofisk tank (After Clausen et al, 1975)

75 SO •5 go 95 o 0)(T)

\ i 5 ®_ K —U D O o o < 10 ui in < © 0) in Hydrostatic < ui m (for wattr dtpth • 67.5 m)-\_ z x a. LEGEND: X ui ,® *— a a. Ui 20 _K 4 th Nov. 1322- uBD _ o H 6 th Nov. nSS-uiS. -X— ~ I < ®\ {*)•• n rtftrt to gaugt no. H rtftrt to gaugt no. 25 85 TO 75 W 85 go 1 "5 0 2 ( 6 8 TORE WATER PRESSURE 11/m'l PORE WATER PRESSURE INCREASE It/m') DURING 6. NOV STORM

Figure 4.11 - Pore pressures observed under Ekofisk tank during the first ma-jor storm (After Clausen et al, 1975) 83

observations may be made. First of all, the pore water pressures increased during the storm at all test locations.

Secondly, the maximum pore pressures developed in the sand occurred not at the platform base, but some distance below it.

Thirdly, pore water pressure in the clay seam was substantially higher than in the sand, perhaps indicating that partial drainage occurred in the sand. And finally, the pore water pressures that developed in the sand beneath the clay seam were significantly less than those developed in the sand not far above it. Typical pore water pressure ratios were on the order of 3% to 7% in the sand. Unfortunately, the instruments were not working for the storm of 19 November, which was nearly as large as the design storm. Considerable consolidation had occurred in the sand from previous storms by this time and may have affected the pore pressure response considerably. No other pore water pressure data has been made available, and thus no particular conclusions about the effects of preshearing on pore water pressure response may be made here.

Early theoretical studies of pore water pressure generation

were reported by Bjerrum (1973). He assumed that the sand could

not drain at all over the course of the storm and therefore data

from undrained laboratory shear tests was directly applicable.

The dimensions of the structure are such that full drainage

cannot take place during the storm; the amount of drainage, of

course, depends on the permeability of the soil and length of

the drainage path. Hence, his assumption of no drainage taking

place was not unfounded. The amount of pore water pressure rise

for a single cycle in undrained shear was determined from 84

laboratory tests, the data being shown in figure 4.12. By representing the design storm by the number of waves in specified height bands (i.e. a histogram), the number of shear stress cycles at a particular amplitude may be found since the wave.forces are known. Knowing the number of cycles applied at each shear stress amplitude, the pore water pressure developed under undrained conditions may be estimated by summing up the contribution of all cycles. This is demonstrated in Table VI.

Bjerrum (1973) found for a relative density of about 90%, a pore water pressure ratio of about 31% would be developed beneath the platform, assuming undrained conditions. This analysis, being very simple and conservative, is good for demonstrating whether further analyses are required. It should be noted that no consideration of the distribution of stresses beneath the platform was considered in this analysis.

The results of more advanced analyses are reported by Lee

(1976) and Lee and Focht (1975a). There was some uncertainty with regards to the in-situ relative density (Lee and Focht,

1975a). Preliminary site investigations at the Ekofisk field made by McClelland Engineers, Ltd. suggested that the sand was medium dense to dense with a relative density of about 80%.

Early studies indicated that the sand under the tank might

liquefy under the cyclic storm loads. For this reason, an

extensive program of cyclic testing was carried out on samples

taken from Ekofisk, and further in-situ tests were performed to

better define the relative density of the sand for correlation

with laboratory test results.

The preliminary tests performed to assess the liquefaction 85

UvwrBrassl*vct: T /or' H' vi

Figure 4.12 - Pore water pressure rise per cycle observed in undrained simple shear with cyclic loading for samples prepared with relative densities of 80% (After Bjerrum, 1973)

Table VI

Example of the Accumulated Effect of a 100-year Storm (After Bjerrum, 1973)

Height of Number of waves: m waves, N O TO 4-8 48S 007 0-006 2-9 8-12 471 012 0013 61 12-16 282 017 0030 8-5 16-20 121 0-22 0 065 7-9 20-24 32 0-26 0150 4-8 24-26 3 0-30 0-300 0-9 Total 1394 311 86

potential were standard undrained cyclic triaxial tests used for earthquake studies. Data for samples compacted at three relative densities, 63%, 77%, and 100%, showed that liquefaction

(defined here as when the ratio of the excess pore water pressure to the effective confining pressure is equal to unity) would take place in the tests with relative densities of 63% and

77% when subjected to design storm cyclic shear stresses (Lee and Focht, 1975a). Since the tests used for assessing earthquake liquefaction potential are not really applicable to the ocean wave problem where preshearing will densify the sand before design loads occur and partial drainage will take place, additional tests were performed to reassess the liquefaction potential taking- these factors into account. In this set of tests, samples at different relative densities were sheared in undrained cyclic triaxial tests at low stress levels and then allowed to reconsolidate, simulating the effects of preshearing.

To investigate the beneficial effects of partial drainage, a laboratory test procedure was developed to model this. This laboratory procedure is outlined by Lee and Focht (1975a).

First, the permeability of the sand was established and the time period for 10% consolidation to occur beneath the tank was evaluated based on plane (and radial) flow conditions. This

time period was estimated to be 500 seconds (125 seconds for

radial flow) and was converted to an equivalent number of waves

for the 10% consolidation time period, equalling about 50 (12.5

for radial flow). The samples were then tested undrained for

this number of cycles. The pore water pressure rise was noted,

then the back pressure was increased to 90% of this amount and 87

the drainage line opened to allow the sample to consolidate by

10% of its excess pore water pressure. The drainage line was then closed and the sample was tested undrained for another 50

(12.5) cycles. Testing continued in a similar fashion until the

samples either liquefied or reached equilibrium. From this type of testing, it was found that a sample compacted to 77% relative density would not liquefy.

Shortly after the second stage of laboratory tests had been completed, data from additional cone penetrometer testing at the

site became available. This data indicated that the sand was

extremely dense with a relative density of nearly 100% (Lee and

Focht, 1975a). Additionally, the permeability of the sand was

determined to be much lower than what had been found previously.

A series of new tests were performed on the sand compacted to

100% relative density and tested under conditions of undrained

shear. Tests were performed on samples that were both

unconsolidated and consolidated to simulate the effects of

preshearing. From these test results, it was concluded that the

sand possessed adequate resistance to liquefaction, with the

preshearing of samples adding additional cyclic strength (Lee

and Focht, 1975a).

The problem of pore water pressure generation beneath the

tank was investigated after installation by Rahman et al (1977)

who formulated the problem mathematically. They represented the

soil by finite elements, with linear.stress-strain behaviour,

and considered the distribution of stresses within the soil mass

from both the weight of the tank and the applied wave loads.

Their method is formulated as follows: The zone of directional 88

randomness of the waves is assumed to be sufficiently wide so that loading on any plane passing through the vertical axis of the platform is essentially the same as all the others when time averaged. Hence, the problem can be approximated as being axisymmetric with respect to loading, and therefore, pore water pressure generation and dissipation. The equation for radial and vertical consolidation is then formulated to include a pore water pressure generation term whose parameters are defined by data from undrained cyclic shear tests. The rise in pore water pressure measured in undrained cyclic triaxial tests is found for different cyclic shear stress levels and curves of number of cycles versus pore water pressure are obtained. The coefficients of these curves are used in the pore water pressure generation function. The time history of loading is approximated by a histogram and the loads are applied

incrementally to the platform. The storm is applied by time stepping as follows: a given number of cycles at a certain

stress level (corresponding to an equivalent number of waves of a given height) are applied (through the use of the pore water pressure generation function) and the resulting pore water pressures are then allowed to drain for an amount of time

corresponding to the number of waves. The procedure is

continued until the storm is over, that is, when all the waves

have been represented by the time stepping procedure.

Results of their studies showed that allowing for partial

drainage is extremely important for predicting the correct pore

water pressures developed underneath the Ekofisk platform. They

found that if the foundation sand had a relative density of 77%, 89

liquefaction would not occur; in fact, maximum pore water pressure ratios would be less than about 30% beneath the entire

foundation. A Bjerrum (1973) type of analysis at this relative density would indicate that the sand would have liquefied under

the tank (Rahman et al, 1977). Rahman et al's (1977) type of

analysis can provide information on the distribution of pore

water pressures beneath the tank. The other methods cannot.

Some results of their studies are shown in figure 4.13. It is

of interest to note that maximum pore water pressures are

developed under the edges of the platform, not beneath the

center. This will affect all stress analyses, and is of

particular significance when predicting rocking motions.

Stability analyses were carried out for the tank to insure

safety under storm wave loading. For lack of better methods,

the bearing capacity equations of Hansen (1970) were used.

Several problems were encountered when trying to apply this

well-known bearing capacity formula to the Ekofisk tank

(Bjerrum, 1973). First of all, the bearing capacity factors

used in the equation were determined semi-empirically for model

footings of a very small size. When extrapolating these results

to the Ekofisk tank with a base dimension of about 93 meters,

considerable scale effects were induced. The value of the

bearing capacity factor Nr was decreased to take this into

account (Bjerrum, 1973). The reduction of Nr with footing size

may actually be attributed to a decrease in the friction angle

with an increase in the mean principal stress. Secondly, the

inclined load factor proposed by Hansen (1970) had never been

used on a foundation with such a high ratio of horizontal to 90

1 1 I r

0,-TT*

-i 4 i r>

lb* Himry of CajkMstwit liom

Timt - hra

Dr*85% », »kf •!0'9C*n/MC

Figure 4.13 - Theoretical prediction of the pore water pressure distribution beneath the Ekofisk tank for relative densities of 77% and 85% (After Rahman et al 1977) 91

vertical force (about 38%). A thorough review of model test

results led to the conclusion that the inclination factor of

Hansen (1970) was acceptable for the high ratio of horizontal to vertical load (Bjerrum, 1973). This factor reduced the bearing capacity to one-fifth of its value for vertical loading only.

Finally, the bearing capacity of the tank would be influenced by drainage conditions. Since the wave force would go from zero to

a maximum value in one-quarter of a wave length (about

4 seconds), virtually no drainage could occur. This problem of

(essentially) undrained bearing capacity had never been

investigated before, since complete drainage is usually assumed

for foundations on cohesionless soil (Bjerrum, 1973). To model

this, the undrained friction angle found from triaxial tests,

increased from 34° to 36* to account for assumed plane strain

conditions, was used for stability calculations.

A plasticity solution was carried out to determine the most

critical failure surface for the design loads (Bjerrum, 1973).

This analysis was quite complicated since the pore water

pressure distribution affected the effective stresses which

determined the rupture surface. A lengthy and difficult

iteration procedure was required to find the rupture surface.

The result of this work is shown in figure 4.14. Unfortunately,

no factor of safety was reported. 92

Figure 4.14 93

CHAPTER 5

CHARACTERISTICS OF WAVE LOADING

5.1 Ocean Waves

Ocean waves are generally the most important environmental phenomenon that ocean engineers must deal with when designing

structures for the offshore environment. Although earthquakes or ice loading may apply the largest horizontal forces on a

structure in some areas, wave loading will nonetheless be an

important consideration and must be investigated.

Waves in the ocean come in a variety of forms, including:

wind waves, ship-generated waves, tsunamis, and tides. In the

open ocean where the water is sufficiently deep to prevent

significant tsunami shoaling and tides are not restricted by

narrow passages, wind generated waves will be the most important

of these forms with regards to offshore structure design. These

will be the only ocean waves considered in this thesis.

5.1.1 The Wave Climate

.The generation of wind waves is a complex phenomenon where

energy from the blowing wind is transferred to water particles

at the air-sea interface by pressure gradients and frictional

forces which subsequently set the water into motion (Kinsman,

1965). The amount of energy that can be put into a wave system

depends on the duration, intensity and direction of the wind,

the fetch (the sea distance over which the wind blows), the

frictional resistance of both the seafloor and air-sea 94

interface, and internal energy dissipation. Wind waves may be classified as being either sea or swell. The former are still under the influence of the generating wind, while the latter travel across the ocean surface virtually unaffected by the wind. Empirical charts have been developed to estimate some characteristics of these waves from meteorological data

(e.g. Shore Protection Manual, 1977).

Waves in the ocean are very complex and do not conform to precise mathematical modelling. The sea is characterized by numerous waveforms of varying shape, length, height, speed, and direction, all superimposed on each other in an everchanging arrangement. For this reason, the sea is modelled statistically using spectra to take these factors into account. These spectra are approximations at best, and do not actually define a particular "sea-state" at any time. Very limited data is extrapolated to obtain the statistical properties of the wave system.

For engineering purposes, it is useful to describe the ocean surface by a train of uniform waves of specific height and period travelling in water of constant depth. This is the most

simplistic model of ocean waves and is often adequate for design purposes. Numerous theories have been developed for this

situation.

5.1.2 Wave Theories

All the analytical wave theories make some of the same

basic assumptions (McCormick, 1973). They differ in the way in

which the governing equations and boundary conditions are 95

mathematically formulated. Common to all are the assumptions that the water is incompressible and that flow is irrotational

(no shear stresses at the air-sea interface or at the seafloor).

From potential flow theory, this implies that a velocity potential must exist and satisfy the Laplace equation. This equation is an expression of continuity for irrotational flow and requires a number of boundary conditions to solve it. These are as follows: (1) the bottom is impermeable, nondeformable, and horizontal - a no flow boundary (seabed boundary condition),

(2) the pressure at the air-sea interface is constant (dynamic free surface boundary condition), and (3) the flow at the air- sea interface is in accordance with the geometry and motion of the free surface (kinematic free surface boundary condition).

Additionally, since the velocity potential should be cyclic in nature it is assumed to be periodic with both spatial and temporal variation. Analytical wave theories vary in complexity and accuracy depending on how they approximate the boundary conditions.

The simplest theory for ocean waves is the linear theory presented by Airy (1845). He assumed that the periodicity was sinusoidal and that the free surface boundary conditions could be linearized. With these assumptions, the solution of

Laplace's equation subjected to the four boundary conditions results in the velocity potential having only one term, which depends on the wave period and height, the static water depth, and the depth of a reference point below the static water level.

It is sinusoidal and periodic in the direction of propagation with time. From the velocity potential, other equations may be 96

derived for water particle accelerations, velocities and displacements, wave induced pressure on the seafloor, etc. The computed surface waves are known as Airy waves.

Other wave theories commonly used are the higher order

Stoke's (1880) theories, particularly the second and fifth. The free surface boundary conditions in these theories are estimated to higher orders by a perturbation process. The resulting velocity potential has the same number of terms as the order of the theory, and is a series approximation. The individual terms are sinusoidal; however, the waveform, being comprised of different sinusoidal forms superimposed on each other, is not.

These waves are characterized by steeper crests and shallower troughs than linear (sinusoidal) waves.

For shallow water, where the bottom significantly affects the travelling surface gravity wave, the waveform may be approximated by the Jacobian elliptical cosine (cn) function

(Korteweg and De Vries, 1895) to any order desired. These are the cnoidal wave theories. They compare well with wave tank tests in shallow water, but are complicated and difficult to use

(Shore Protection Manual, 1977).

Numerical wave theories have also been developed. Dean's

(1965) theory, which is the best known, is based on stream functions instead of velocity potentials and requires the use of a computer to solve the equations for any given set of wave parameters. Its use is limited in engineering applications because the method, due to its complexity, cannot be used in most wave force theories.

The regions of validity for the best known wave theories 97

are shown in figure 5.1. Clearly no one theory can be regarded as being the best for all applications.

5.1.3 Results of Linear Wave Theory

Linear wave theory, besides being the simplest to use, is more reliable than the other analytical theories over a greater range of conditions. It does not suffer from numerical instability as most of the other theories do when applied in regions beyond their (calculated) range of validity (Sarpkaya and Isaacson, 1981). For these reasons, it is the most widely used wave theory by practicing engineers. Additionally, most wave force theories assume that the waves may be represented by linear theory, although the wave length used in the resulting wave force equations may be computed using another wave theory, usually Stoke's fifth order theory. Linear theory is used extensively in spectral wave force calculations (Bea and Lai,

1978).

The profile of a linear wave is shown in figure 5.2, and some results of linear wave theory are presented in Table VII.

Note that only the wave height, water depth, and either wave length or period are needed to define a linear wave. This is also the case for other wave theories. The wave length and period are related by the dispersion relation, which is derived from the velocity potential.

5.2 Characterizing the Wave System

Since wind waves are random in nature, they are best described statistically. Approximations may then be made to 98

005• | i i 1 1 r

0.00005' o.OOl 0.002 0.005 0.01 0.02 005 0.1 0.2

d

Figure 5.1 Regions of validity for various wave theories (After Sarpkaya and Isaacson, 1981) 99

Wove speed,c

L 5 B z • d Wove period, L/c T = d k = 2JT-/L Surface elevation shown ot t = 0 6 - kx-a)t

Figure 5.2 - Profile of an Airy Wave (After Isaacson, 1980)

Table VII

Some Results of Linear Wave Theory (After Sarpkaya and Isaacson, 1981)

irH cosh (ks) Velocity potential A *= — sin 6 kTsinh(kd) EH cosh (ks) . m — • sin e 2u> cosh (kd) Dispersion relation c2 = -y- = f - tanh (kd) k2 k H Surface elevation T| • — COS e H cosh (ks) . Horizontal particle displacement tB • sin 6 ' 2sinh(kd) H sinh (ks) Vertical particle displacement t • i COS 6 * 2sinh(kd) nH cosh (ks) Horizontal particle velocity u • cos 6 T sinh (kd) irH sinh (ks) . Vertical particle velocity w * — . . „ sin 6 T sinh (kd) 8u 2ir2H cosh (ks) Horizontal particle acceleration — c —. sin 8 8t T2 sinhftd) aw 2w2H sinh (ks) Vertical particle acceleration — * x cos S at T2 »inh(kd) 1 „ cosh (ks) Pressure p •= -pgz + -pgH—___cose 2 cosh (kd) Group velocity - 1 Ii 2kd 1 00 2 [ iinh (2kd)JC Average energy density E^ipgH2 100

characterize the wave system in simpler terms for the purposes of foundation design.

5.2.1 Obtaining the Design Storm

The design storm is usually found by extrapolating data

from wave records. This data is often rather sparse and must be

representative of storm wave conditions to use the statistical methods developed for defining the design storm.

5.2.1.1 Statistical Description

The distribution of wave heights for a particular sea-state

may be characterized by a Rayleigh distribution, assuming that

the free surface is Gaussian for a specific recording interval,

usually 6 hours. The assumption that the free surface variation

for a particular sea-state may be represented by a Gaussian

distribution corresponds well with observations. Data from the

recording interval is assumed to be described by a 10 minute

sample which is representative of the 6 hour recording interval.

To describe the variation of sea-states over the long-term

(years), it is convenient to represent each recording interval

by one statistical parameter, the significant wave height,

denoted Hs. This is defined as the average height of the one-

third highest waves in the wave record, i.e. the recording

interval. For any recording interval the significant wave

height may be computed without much difficulty . (usually by a

digital computer).

A probability distribution may be fitted to the significant

wave heights from numerous records to estimate the significant 101

wave height for some remote event (e.g. the design storm). This is usually done using the extreme value statistics of Gumbel

(1958). The probability of a rare event occurring may be found for a specified recurrence interval (e.g. 100 years). Thus, the significant wave height for the design storm may be estimated from wave records. The distribution of wave heights within the design storm may be found using short-term statistics - the

Rayleigh distribution. The whole procedure may be repeated to find the distribution of wave periods for the design storm.

The duration of a storm may be days, however, for practical purposes some time limit must be chosen. A design storm of twelve hours is often used (Isaacson, 1981). The storm is assumed to buildup, peak, and decay during this time. The duration of the design storm will affect the wave statistics.

5.2.1.2 Geotechnical Equivalent

For geotechnical purposes, this type of representation is not very useful in practice. Therefore, for a specified design storm, it is useful to transform the statistical distributions of wave heights and periods into a histogram relating wave heights to frequency of occurrence (i.e. number of waves of some height) and a curve defining the wave height - wave period relationship. This, in geotechnical literature, is known as the

"design storm".

Because the distribution of wave heights during a storm is represented by a Rayleigh distribution, the number of waves in any particular band of heights will be known. This is easily transformed into a histogram. The histogram could have as many 102

bands as there are waves in the storm. This, needless to say, would be impractical. Generally five to fifteen divisions is acceptable, depending on the type of analysis to be performed and the accuracy desired. Six (Bjerrum, 1973) to sixteen (Lee and Focht, 1975a) divisions have been used for pore water pressure generation studies.

The duration of the design storm is also of interest, since the amount of pore water pressure dissipation occurring in granular deposits will be sensitive to this. Bjerrum (1973) suggests that the storm may be assumed to buildup over six to nine hours, maintain full-storm conditions for three to nine hours, then subside in another six to nine hours. He used the worst six hours of the design storm to analyze the pore water pressure buildup under the Ekofisk tank. These 6 hours of storm contained 1394 waves. Lee and Focht (1975a) used a group of

5000 waves to characterize a thirteen hour storm for the Ekofisk tank. Such a large group of waves appears to be excessive since the smaller waves will have little effect on pore water pressure generation. This is confirmed by Rahman et al (1977) who used a six hour storm to analyze the same problem. They found that equilibrium pore water pressure ratios of a few percent at most were quickly achieved and maintained at the lower cyclic stress ratios produced from the numerous smaller waves.

5.2.2 Application of the Design Storm

Using the actual time history of the storm is impractical.

Therefore, the geotechnical design storm approximation may be used. Of primary interest here is when to apply the maximum 103

wave during the design storm to find the most critical condition for stability. Bjerrum (1973) assumed that it is conservative to apply the maximum wave at the end of the design storm when pore water pressures would be the highest. Based on an undrained analysis of the sand during the storm, the pore water pressures would indeed be the highest at the end of the storm.

His reasoning with regard to maximum pore water pressures corresponding to the critical time to apply the maximum wave is sound, however, the end of the design storm is not necessarily the most critical with respect to stability. For cohesionless soils, some drainage will take place during the storm and the maximum pore water pressures under the foundation will probably occur at the height of the storm or just thereafter. Rahman et al (1977) assumed that the storm is characterized by smaller waves increasing in height to a maximum (the design wave), then decreasing in a similar fashion, as Bjerrum did (1973) and they applied the waves to the foundation system with this order in mind - representing the time history of loading in an approximate way. They found that for the Ekofisk tank (founded on fine sand), the maximum pore water pressures would occur just after the peak of the storm. For this type of analysis, the critical application of the maximum wave would be just after the peak of the storm. Intuitively, this seems correct for foundations on sand. For foundations on clay, where no substantial drainage can take place during the storm, the usual procedure is to apply the design wave to the structure at the end of the storm (Schjetne, 1976). This approach is conservative, but not unduly so, at least for stiff clays 104

(Andersen et al, 1976).

5.3 Wave Loads on the Foundation System

Wave loads on the foundation system consist of the forces exerted on the structure and transferred to the soil by the raft and the pressure on the exposed seabed due to travelling surface gravity waves. Both must be considered when designing the foundation. Because the period of wind waves is on the order of two to twenty seconds, forces on the foundation may be considered to act pseudostatically for stress analysis. The effects of cyclic loading on the soil should be modelled appropriately.

The loads acting on the foundation of a gravity structure subjected to wave action and the resulting soil reactions are shown in figure 5.3.

5.3.1 Wave Forces Acting on the Structure

Wave loads acting on the structure are found using formulas derived from potential flow theory with empirical coefficients.

There are two basic methods for finding wave forces on structures: the design wave method and the spectral analysis method. In the spectral method, forces are defined statistically, whereas in the design wave method, forces are treated deterministically.

When waves propagate past a structure, forces are exerted on it from both frictional and inertial effects caused by the moving fluid. The former component is highly nonlinear while the latter is not (Morison, 1950). If the lateral dimension of Figure 5.3 Forces acting on the foundation of an offshore gravity structure 106

a structure is significant compared to the wave length (20% or more), the water particle motions and waveform are greatly disturbed by the presence of the body as the wave passes; this must be taken into account when predicting the wave loads acting on the body (MacCamy and Fuchs, 1954). Diffraction theory was developed for this purpose (MacCamy and Fuchs, 1954) and may now be applied to large volume structures of arbitrary shape such as gravity platforms (Garrison, 1979; Hogben et al, 1977). Linear diffraction theory (developed for Airy waves) is presently used

for both deterministic and probabilistic wave force calculations

for gravity platforms (Isaacson, 1980). In the diffraction

regime, the drag component is small and may be neglected,

leaving only the inertial component. The inertial force on a vertical surface piercing cylinder computed from linear diffraction theory is represented by a single term for a given wave and varies sinusoidally in time (MacCamy and Fuchs, 1954).

For the geotechnical engineer, the significance of this is

that the overall wave forces on a gravity structure will vary

nearly sinusoidally in time. Although the wave forces will

differ for different waves in the storm, individual wave forces

may be defined completely by a magnitude, oscillatory period,

phase angle, and frequency of occurrence. For geotechnical

purposes, the phase angle is unimportant except when finding the

design pressure on the seabed corresponding to the maximum wave.

The design storm may then be transformed from a wave height—

frequency of occurrence histogram, for the given wave height—

wave period curve, to one of force--frequency of occurrence.

This representation is shown in figure 5.4. The variation of O 5 10 15 20 25 30 0 12 3 4 5 6

Wave Height (m) Time (hrs)

(c) Horizontal force--wave parameter relationship (d) Time history of wave forces

Figure 5.4 - Typical design storm representation used In geotechnical engineering o -j 108

cyclic "shear stresses during the storm may be be found in the same way once the horizontal forces are defined.

5.3.2 Wave Forces Acting on the Foundation

For any given wave, the resultant vertical and horizontal forces may be computed from diffraction theory. The wave forces acting on the foundation are the same as the wave forces acting on the structure, however, a moment must be applied to the foundation to account for the resultant horizontal force acting some height above the seabed.

The forces acting on that part of the seabed not under the raft are due to the weight of the overlying body of water and the influence of passing waves. The pressure at any location on the seafloor is composed of a steady and a fluctuating component. The steady component is uniform over the seafloor

(assuming that the water depth does not change) and is nothing more than the normal hydrostatic pressure. The fluctuating component is the dynamic pressure due to particle accelerations in the wave and at the seafloor is very nearly equal to the hydrostatic pressure due to the weight of a column of water displaced from the static water level as the wave passes. Any appropriate wave theory may be used to find the seabed pressure distribution; the fluctuating component will be of nearly the same form as the free surface. Linear theory is commonly used and the resulting seafloor (cyclic) pressure distribution is sinusoidal.

The steady component is uniform everywhere, and therefore is of no significance since it affects neither the effective 109

stresses or the stress gradients in the soil. The fluctuating component is of interest for two reasons, namely: (1) it does

not act uniformly over the seafloor at any given time and must

therefore be considered as an external load, and (2) it induces

stress gradients which produce cyclic shear stresses in the

soil.

When finding the pressure distribution corresponding to the

design wave, the phasing of the wave forces must be considered.

The seafloor pressures near the platform will be less than the

pressure amplitude. The maximum forces acting on a platform

usually occur when the nodal points of the waveform are near the

platform's vertical axis, i.e. when the waveform passes through

the still water level near the platform's vertical axis. For

long (large) waves, this means that the pressure curve has a

node somewhere over the raft and that the maximum pressures on

the seabed due to the wave will be some distance from the edge

of the platform (approximately one-quarter of a wavelength away

from the vertical axis of the platform).

5.4 Effect of Cyclic Loading on the Foundation System

The effects of cyclic loading on the soil must be taken

into account for all stress analyses. Such effects influence

the safety of the platform with respect to failure (sliding,

bearing, rocking, liquefaction or otherwise), as well as the

platform motions during storm loading and long-term effects such

as settlement.

Using a storm histogram similar to the one shown in

figure 5.4(d) to represent the time history of loading, the 110

stress path for an element beneath a sand foundation may look like that which is shown (unidirectionally) in figure 5.5. This representation is idealized for the purposes of illustration.

The figure may be interpreted as follows. The first histogram band represents some number of cycles at one stress amplitude.

This amplitude is the distance from point "a" to the effective stress axis. The resulting residual pore water pressure decreases the effective normal stress. Hence, movement from point "a" to "b". The next set of stress cycles are at a magnitude represented by the distance from point "c" to the horizontal axis. Pore water pressure reduces the effective normal stress to point "d". The stress path shown in the figure does not show the full path, i.e. the return to the horizontal axis (zero shear stress) for each set of cycles is not shown.

This was left out to clearly illustrate the effects of cyclic loading on a foundation element. Similarly, the path continues as the cyclic stress amplitude increases to a maximum corresponding to the design wave, then decreases. Note that excess pore water pressures exist in the foundation element throughout the storm.

Much data is available for sand tested under undrained conditions. This is due to the interest in earthquake induced liquefaction which has attracted scores of researchers.

Partially drained sand behaviour has not been well studied, and little information is available on the subject. Partial drainage for cohesionless soils has not been directly modelled in laboratory shear tests. Instead, modified undrained cyclic triaxial .tests are used (Lee and Focht, 1 975a). 111

EFFECTIVE NORMAL STRESS, U'

Figure 5.5 1 12

Pore water pressure generation in undrained shear depends on the characteristics of the sand, the magnitude of the static shear stress in the soil before testing, and the magnitude and time history of the applied cyclic shear stresses. The amount of pore water pressure generation in undrained shear may be estimated from laboratory tests that appropriately model the ocean wave loading problem (Lee and Focht, 1975b).

Estimation of the pore water pressures developed under an offshore gravity type structure may be made using (1) laboratory

tests such as those described by Lee and Focht (1975a) which model partial drainage and preshearing using modified cyclic

triaxial tests, or (2) from numerical methods that model the

soil by finite elements and solve the equations of radial and

vertical consolidation (Rahman et al, 1977). Undrained analyses

in sand (Bjerrum, 1973) are too conservative and are not

appropriate for advanced studies.

Cyclic loading of clay has recently been a subject of

intensive study (Andersen et al, 1976; van Eekelen and Potts,

1978) as some of the gravity platforms in the North Sea are

underlain by substantial clay deposits. The results of an

extensive study on clay behaviour under cyclic loading were

reported by Andersen et al (1976), and demonstrated several

important concepts. First of all, shear strain may be used

instead of pore pressure development as a parameter for

describing response to cyclic loading. Cyclic shear strains are

uniquely related to the effective stress and independent of the

overconsolidation ratio or number of cycles. Secondly, the 113

effective strength parameters c' and tan0' are virtually

unaffected by cyclic loading, but the undrained strength cw is.

Thirdly, the undrained strength is a function of cyclic shear strain and the number of stress cycles applied. And finally, the higher the overconsolidation ratio for a given cyclic stress ratio, the fewer number of cycles are necessary to bring the sample to failure. Andersen (1976) developed a method based on the accumulation of cyclic shear strains to predict failure from excessive displacements.

It has been found for insensitive clays that if the applied shear stress level is below some critical value, a state of non- failure equilibrium will be reached where the stress-strain curves follow closed hysteresis loops with no further increase in pore water pressure (Sangrey et al, 1969). If this critical value is exceeded, each loading cycle will cause a cumulative increase in pore water pressure and displacements which ultimately results in a shear failure. This failure will occur at a reduced undrained strength which is about two-thirds of the value for static loading. This critical cyclic shear stress level should be determined experimentally for each cohesive deposit (Bjerrum, 1973).

Consolidation history is important when assessing the effects of cyclic loading on clay. For normally consolidated and slightly overconsolidated deposits, drainage after cyclic

loading implies consolidation and an increase in the un.dirained

strength. For heavily overconsolidated clays, swelling may

occur after loading is terminated, with a corresponding

reduction in strength (Schjetne, 1976). The effect of this on 114

platform safety is as follows: For foundations on highly overconsolidated deposits, the safety of the platform will decrease with subsequent cyclic loading. The safety of platforms on normally consolidated or slightly overconsolidated soil will increase in time. However, these deposits are usually unsuited for a gravity platform since displacements may be excessive under storm wave loading. 115

CHAPTER 6

PROCEDURES FOR ANALYZING THE STABILITY OF

OFFSHORE GRAVITY TYPE STRUCTURES

6.1 Fundamental Considerations

The purpose of a stability analysis is to assess the margin of safety against an ultimate foundation failure. This margin of safety may be expressed in one of two ways: by a load safety

factor or a material factor. The load safety factor is defined as the ratio of the load required to cause an ultimate failure to the design load, when the design strength of the soil is used. The material safety factor is the amount by which the

strength parameters must be reduced to bring the soil to a state of limiting equilibrium under the design loads. The degree of

strength mobilization in the soil is often how this latter

result is expressed. The two safety factors will in general be

di f ferent.

Onshore, a safety factor of about three is commonly used to

take into account uncertainties associated with the values of

strength parameters, ground water conditions, loading

conditions, and the reliability of analytical methods.

Offshore, a much lower safety factor is used and a considerable

amount of effort is spent in trying to better define the problem

than is commonly done for most onshore projects. The use of

more rigorous analyses is justified economically, since the

degree of uncertainty will be less, and therefore, the factor of

safety may be reduced. For this reason, bearing capacity theory 116

is generally used only for a preliminary estimate of the adequacy of a site for a gravity type structure. Limit equilibrium methods based on slip surfaces and the finite element method are usually employed.

Evaluation of the safety factor requires three things: an estimation of the shear strength of the soil, estimation of the shear stresses in the soil, and the postulation of a failure mechanism. The shear strength of the soil may be defined by the

Mohr-Coulomb failure criteria, which is

Tr. = c + a tan0 (6.1) where c and tan0 are the shear strength parameters and C is the normal stress on the shear surface. In terms of effective stress, this equation is

Tf= c'+ a'tan0' (6.2) where c' and tan0' are the effective shear strength parameters and 6" is the effective normal stress, defined as

cr =

One should remember that each half wave cycle the direction of loading reverses. There are, therefore, both shear stress

reversals and pulsating vertical stresses in the soil. Both will affect the magnitude of the pore water pressure at any time during the storm.

It is convenient to discuss the pore water pressure in the

soil in terms of its various components. The total pore water

pressure, u, at any location is given by

u = us + ue+ Au (6.4)

where us is the hydrostatic component, uc is the residual pore 117

water pressure due to cyclic loading at any time during the storm, and Au is that part due to the changes in the principal stresses.

The hydrostatic pore water pressure in the soil is simply

us = ^d + Ywz (6.5a)

where )(w is the unit weight of seawater, d is the still water depth, and z is the depth below the mudline. Note that this term includes the pressure due to the static body of water above the mudline. The effective stresses in the soil are, however, not influenced by the presence of an overlying body of water.

This is illustrated in figure 6.1. This may be taken as

us = V„z ' (6.5b) if the weight of the overlying body of water is omitted from all calculations.

The component of pore water pressure in the soil due to changes in the principal stresses may be determined from

(Skempton, 1954)

Au = B[AO"3 + A (AC, - AC3 ) ] (6.6)

where cr, is the major principal stress, o~3 is the minor principal stress, and A and B are dimensionless pore pressure parameters measured in the laboratory. This component will be a maximum or minimum (for dilation) for the design wave. The B- parameter may be taken as unity for offshore foundation analyses. For an elastic isotropic soil, the A-parameter is equal to one-third. This implies that the rise in pore water pressure is equal to the total stress increment. For other values of this parameter, the pore water pressure rise is not equal to the total hydrostatic stress increment. 118

d unnnij * I / Z / 1 (i) (2)

Us

* - Xwd + Hz

u « l«(d • D0) u « *w(d • x)

6' - q • ).Do cr' - Y'z

(2)

Figure 6.1 - Effective stresses in soil for still water conditions (i.e. no wave loads) 119

Pore water pressures within the soil mass due to cyclic loading may be estimated using (1) data from cyclic shear tests with a numerical model such as Rahman et al's (1977) to account for consolidation, (2) data from modified cyclic triaxial tests such as those described by Lee and Focht (1975a) correlated with the in-situ stresses, or (3) from experience gained through observations of platforms instrumented for performance. A combination of these methods may be used. In addition to the pore water pressures generated as a consequence of cycling loads on the structure, excess pore water pressures will also be developed in the soil not under (or influenced by the presence of) the raft. Stress gradients are induced in the seabed from the pressure variations caused by passing waves (Henkel, 1970).

If the waves are large enough and loading is sustained, liquefaction may occur (Finn and Lee, 1978).

A stability analysis for a clay foundation may often be performed using a total stress analysis. The pore water pressure rise in a foundation element will be nearly equal to the total spherical stress increment for overconsolidated clay.

The A-parameter is close to one-third for these clays (Skempton and Bjerrum, 1957). An effective stress analysis may also be performed. This method presents two difficulties, namely: the pore water pressures must be estimated and the effective shear strength parameters have to be evaluated. These parameters must be found from laboratory shear tests which require good quality samples. These are often unattainable. A total stress analysis may be performed without estimates of the pore water pressures 120

or laboratory shear test data. The undrained strength determined from in-situ tests such as the cone penetrometer or vane may be used directly, reduced appropriately for the estimated effect of cyclic loading (i.e. strain softening).

This has been the case for most North Sea gravity structures founded on clay (Schjetne, 1976).

It should be noted that for cohesive soils the pore water- pressures developed within the soil mass due to the weight of the platform may not have dissipated substantially by the time that a major storm hits the field. In this case, an effective stress analysis is required and loads less than the design wave loads may be used. A total stress analysis for the design storm loading, which may be assumed to hit the platform at a later date, may also be performed. Some sort of risk analysis will be required.

For the stability analysis of a foundation on cohesionless soil an effective stress analysis is performed. This requires estimates of the pore water pressures within the soil mass. Any appropriate method may be used to estimate these pore water pressures. The friction angle must be determined from laboratory shear tests. Cone penetration resistance can help to establish the relative density which is needed for interpreting the tests.

6.2 Modelling the Wave-Structure-Soil System

Since gravity platforms never approximate strip footings and rarely rest on the seabed without some sort of subsurface

foundation, i.e. skirts and ribs, some assumptions regarding 121

geometry must be made so that analytical techniques may be used.

The platform is usually modelled by an "equivalent rectangular foundation", that is, one with the same area as the actual platform base. The "effective foundation" is usually assumed to be at skirt-tip level (Lauritzsen and Schjetne, 1976). This assumption is good if failure does not extend up into the skirt compartments. The skirts should be spaced closely enough together to prevent failures of the kinds shown in figures

3.6(a), 3.6(b), and 3.6(d). A definition sketch of the effective foundation is shown in figure 6.2(a) for a two- dimensional representation and in 6.2(b) for a three-dimensional one.

When modelling the foundation system, it is important to include all the forces which act on both the structure and the seabed adjacent to it. The points of application of the resultant forces, or the distribution of pressures, must be either known or assumed. The loads acting at the foundation base are required for a stability analysis. The wave loads, which are specified at the seafloor, must be transmitted to the foundation base by including the forces acting between the seafloor and the skirt tips in the resultant load. Figure

6.3(a) shows the forces acting on the foundation system, and figure 6.3(b) shows the resultant loads which are used in a stability analysis. These forces are defined qualitatively in the following paragraphs.

The vertical load applied to the effective foundation, VBT,

will consist of the buoyant weight of the platform Pv , the

fluctuating vertical force due to the wave APV (which will be 122

(b) Three-dimensional representation

Figure 6.2 - Definition sketch of effective foundation 123

AP(X) APlX) 1" nrrrr W»V« I I I I I l * R

(a) Loads acting on the platform

APOO AP(X) rrrrrr IffNt/l 1 T 1 ' ' 1 r » OIMBT

(b) Loads transferred to the foundation base

Figure 6.3 - Transformation of loads to foundation base 124

downward for design conditions), and the added load from soil contained within the skirt compartments. Vertical shear forces acting on the periphery of the imbedded foundation may usually be ignored. The distribution of vertical stress beneath the raft will be nonuniform since loading is inclined and eccentric.

This is usually taken into account by considering only that area of " the foundation base which is symmetrical with respect to the resultant vertical load. The resultant vertical load is then applied centrally on this "effective area" (Hansen, 1961). The

effectve area is represented by BL0 in figure 6.2(b). It may be determined once the load eccentricity at the base is established. This eccentricity is initially unknown since the moment at the base of the structure depends on the soil forces acting between the mudline and skirt-tip level; these forces must be determined from an iteration procedure. However, the moment at base level may be approximated by choosing reasonable values for the soil forces. The effective area may then be established. The effective area will usually not be influenced

significantly by the soil forces, particularly for shallow

foundations. For one-dimensional eccentricity, that is, when

loading is parallel to one side of the equivalent rectangular

base, only one dimension of the equivalent foundation is

reduced. This is normally the case for gravity structures since

they are usually of similar width and length (i.e. they are

approximately radially symmetric). Meyerhof's (1953) "effective

width" principle is then used.

The horizontal force which acts on the effective

foundation, HRT, is somewhat more difficult to assess. This 125

force is equal to the resultant of the horizontal wave load PH and the horizontal components of all the forces acting between

the mudline and skirt-tip level: the active soil force PA on the

tail end of the foundation, the passive soil force Pp on the

nose of the foundation, and shear forces Ps on the sides of the

imbedded base. These forces must be estimated. Generally, the

active and passive soil forces are assumed to act only

horizontally. For structures with significant penetration into

the seafloor, this assumption may not be reasonable. When the

active soil force is negative, as for clay foundations, a

tension crack is assumed to exist at the tail end of the

platform. A water force, Pw, due to the dynamic wave pressure

(which is not in equilibrium with the soil pore water pressures)

acts in any crack. The shear forces acting on the sides of the

foundation, Ps, reduce the horizontal force applied to the

foundation base. This resistance is not included for a plane

strain analysis. The distribution of horizontal force over the

foundation base is assumed differently in various stability

theories.

The dynamic wave pressure acting on the seabed, Ap(x),

varies roughly sinusoidally; the estimated variation depends on

the wave theory used to calculate it. For the purpose of a

gravity structure stability analysis, it is often adequate to

apply the pressure uniformly on either end of the raft, taking

magnitude and phasing into consideration, since the variation of

this pressure over a short distance is usually minimal. The

dynamic wave pressure will affect the magnitudes of soil forces

acting on the structure above skirt-tip level. 126

The effects of cyclic loading on the foundation soils must be adequately taken into account in accordance with sections 5.4 and 6.1. The effect of consolidation history on clay and preshearing in sand, must be considered when choosing strength parameters appropriate for design storm analyses.

6.3 Loading Applied to the Foundation

The vertical load at the effective foundation level, V61,

is equal to the sum of the vertical load at the seafloor and the

submerged weight of soil within the skirt compartments. This may be written as

VBT= Pv + APV + (A0D0)i" (6.7)

where Pv is the vertical platform load in the absence of environmental loading (the buoyant weight of the platform, which

is not constant over the life of the structure), APV is the

vertical load due to environmental loading, A0 is the area of

the equivalent base, D0 is the depth of the effective

foundation, and H' is the effective unit weight of soil.

The horizontal load acting on the foundation base, HBT, is

the resultant of the applied environmental load PH and all the

horizontal forces acting on the platform between the seafloor

and skirt-tip level. This may be expressed as

H = *T PH + (P* or Pj - Pp (6.8)

where the active soil force is defined by

2 2 PA = [ (0.5rDo +Ap,Do)tan (45'-0/2)-2cDotan(45'-0/2) ]L0 (6.9)

Here, Apf is the dynamic wave pressure acting on the seabed at

the tail end of the platform, 0 is the mobilized friction angle, 127

c is the mobilized cohesion, and L0 is the equivalent platform

length. If PA is negative, a water pressure force Pw replaces it, given by

Pw= Ap,D0L0 (6.10)

The passive soil force is defined as

2 2 o Pp= [(0.5o'Do +Ap2Do)tan (45 +0/2)+2cDotan(45°+0/2)]L0 (6.11)

where Ap2 is the dynamic wave pressure acting on the seabed near

the nose of the platform. Note that Ap2 is a negative quantity.

The preceding equations may be used to define plane strain loading. This is done by dividing each equation by the

equivalent platform length L0 to find the force per unit length.

For a three-dimensional analysis, the aforementioned equations may also be used, with one exception: shearing resistance on the sides of the foundation must be included. In this case,

Equation (6.8) may be written as

+ HBT = P« (PA or Pw) - Pf - Ps (6.12)

where the shearing resistance on the sides of the foundation Ps is defined by

Ps = 2D0B0(c + O.5tf'Dotan0) (6.13)

The moment applied at the foundation base, MB1, is the resultant of the moment at the seafloor M, and the moments due to all the forces acting between the seafloor and the foundation base. This may be expressed as

MfeT= M + PHD0 + (PA or Pw)hi - Pfh2 - Psh3 (6.14)

where h,, h2, and h3 are moment arms for the appropriate forces.

These may be found from earth pressure theory.

The effective width B may be found once the eccentricity is known. This may be written as 128

B = B0(1 ~ 2e) (6.15)

where B0 is the equivalent foundation width and the eccentri• city e is given by

e = (MB7Afc-r)/B0 (6.16)

6.4 Available Stability Methods

Presently, there are a number of analytical or numerical methods which may be used to assess the foundation stability of a gravity platform. These are: the bearing capacity methods, the NGI slip surface method, and the finite element method.

Centrifuge tests may also be performed to investigate foundation stability. These methods are discussed in depth in the following sections. The problems encountered when applying them to offshore gravity structures are emphasized. In the following chapters, an alternative procedure based on the method of slices

is presented.

6.4.1 Classical Bearing Capacity Approach

The stability of shallow foundations is often investigated using bearing capacity theory. Computation of the ultimate load

Q0, or ultimate bearing pressure q0, is based on a simplified

model of an infinitely long rigid strip footing of width B0

resting in a homogeneous deposit of effective unit weight

cohesion c, and friction angle 0, at a depth D0. The footing is

loaded with a central vertical load Q which is assumed to produce a uniform pressure q. The adjacent soil is loaded with a uniform surcharge q'. This representation is shown in

figure 6.4. 129

Qo=q0B0

Figure 6.4 - Theoretical rupture surface geometry 130

The bearing capacity problem is represented mathematically by a rather cumbersome set of partial differential equations. A closed form analytical solution has not yet been found, although for special cases of this problem, solutions are available

(e.g. Prandtl, 1921).

The most widely recognized solution is that of Terzaghi

(1943). He proposed that the ultimate bearing capacity be evaluated from

q0 = -„'BNY+ cNc+ q'N. (6.17) 2 * * where the N-values are known as bearing capacity factors. These coefficients arise from the plasticity solution. Since

Nt and N% are calculated for one rupture surface and Ny for another, this equation is an approximation (Hansen, 1970). The location of the theoretical rupture surface is different for each combination of c, 0, and q'. The equation is, however, conservative and errors are generally less than 20% (Lundgren and Mortensen, 1953).

The Terzaghi (1943) solution is generally accepted, but the numerical values of the bearing capacity factors to be used in the equation are not. The bearing capacity factors arise from

the plasticity solution and depend only on the friction angle -

for a particular shape of the assumed rupture surface. It is

this dependence on the shape of the assumed rupture surface that

gives rise to the many different interpretations of these

factors. The variations in the Nc- and N^-values for different

solutions may be on the order of a factor of two, and the 131

differences in the N^-values may be even more. This discrepancy

is of particular interest for gravity structures founded on

cohesionless soil where the frictional (first) term in

Equation (6.17) is predominant. Values of Ny as a function of

the friction angle have been compiled by Andersen (1972) from

the published results of several authors. His findings are

shown graphically in figure 6.5. It is clear that there is

considerable variability in the value of Ny for a given value of

the friction angle depending upon whose results are used.

Equation (6.17) is an approximate theoretical solution for

a; very idealized foundation. Real foundations are never

infinite in length and loading is often inclined Or eccentric or

both. For gravity structures, loading is always inclined and

eccentric. Eccentricities of 10% and inclined load factors of

0.2 to 0.4 are common.10 Since an analytical solution is not

possible except for the simplest of cases, empirical factors

have been employed to improve results.

To extend Terzaghi's (1943) solution to include the effects

of the shearing resistance of the soil above the foundation

base, inclined loading, and different foundation shapes,

Equation (6.17) is rewritten as (Hansen, 1961):

q0 = — V BNy sy dr iy + cNeScd^i,. + q'N^d^i^ (6.18)

where the s-, d-, and i-parameters are empirical coefficients

10The inclined load factor, denoted by &, is the ratio of the horizontal to vertical load. 132

Figure 6.5 - Comparison of different proposals for the value of Ny (After Andersen, 1972) 133

which represent the effects of foundation shape, imbedment depth, and load inclination, respectively. These empirical coefficients were found using plate loading tests by varying one parameter (set) at a time and corrrelating the results to

Equation (6.18). Curves were fitted to the data to determine approximate analytical expressions. Equation (6.18) is the general formula for the bearing capacity of a rigid horizontal

footing resting in a homogeneous horizontal deposit and is the basis of the two most widely used bearing capacity theories,

those of Meyerhof (1963) and Hansen (1970). The two theories differ in their estimation of these coefficients and the N- values.

Hansen's (1970) formulation is the method preferred

offshore. This is due to several factors. The most obvious one

is that gravity structure technology developed in Europe where

engineers used Hansen's (1961,1970) theory for bearing capacity

problems. A thorough study of this method, for application to

cohesionless deposits, was made prior to installation of the

Ekofisk tank (Bjerrum, 1973). The conclusion drawn from this

study was that Hansen's (1970) method will provide acceptable

results, even for large load inclinations, when used for the

purposes it was developed for. (i.e. for total stress analyses

of homogeneous deposits.)

Eccentric loading is not treated by using empirical

coefficients. The effective area approach proposed by Meyerhof

(1953) is used instead. A concentric load is applied to the

footing on a reduced area. The dimensions of this centrally

loaded "effective area" are then used in the general bearing 134

capacity equation, Equation (6.18). Overall moment equilibrium is satisfied when using this technique. The horizontal force is also assumed to act only over the effective area. This method of treating eccentric loads is found to be conservative (Hansen,

1970).

For total stress analyses of clay foundations, substantial sliding resistance may be mobilized on that part of the foundation base outside of the effective area. This resistance will reduce the horizontal force acting on the effective area; that force used in the bearing capacity calculation. Since the horizontal force is critical in reducing the ultimate bearing capacity, consideration of any amount of resistance that may be mobilized outside of the effective area is extremely important if undue conservatism is to be avoided. Bearing capacity theory may be modified to take this into account (Lauritzsen and

Schjetne, 1976). The horizontal load taken on the foundation base outside of the effective area is subtracted from the total load. This force may be found using the procedure outlined in the following section.

The bearing capacity solutions mentioned above assumed that the soil was homogeneous, with constant values of the cohesion, friction angle, and effective unit weight. This is, of course, a great simplification, since real soil deposits are never homogeneous. Offshore deposits in particular tend to be nonhomogeneous. They are usually layered and often consist of clay interbedded with sand, or vice versa. This is due to the nature of the depositional environment. Meyerhof (1963) proposed that when the aforementioned soil properties vary 135

within the deposit, average values should be used. This is reasonable if the variations are small. Since bearing capacity theory is based on the assumption that critical shear zones develop within the soil mass, average values within the potential failure body should be used instead of average values along the potential failure surface (Lauritzsen and Schjetne,

1976). The evaluation of suitable soil parameters to use in the analysis is quite subjective since the location of the rupture surface is often unknown. This problem becomes more critical as load inclination increases and the foundation soils become less homogeneous.

For layered foundations, further assumptions regarding the location of the shear zones may be made. This problem was addressed by Terzaghi and Peck (1948) who developed a crude but useful procedure for treating this type of problem. More recent solutions have been presented by Button (1953) for a two-layer cohesive deposit, by Meyerhof (1974) for the case of a sand layer over clay, and by Davis and Booker (1973) for the case where the undrained strength increases linearly with depth. The case where a soft layer is sandwiched between two stronger materials was investigated by Yamaguchi and Terashi (1971).

Other approximate techniques for dealing with multiple layer systems have been presented by .Brown and Meyerhof (1969) and

Reddy and Srinivasan (1967), among others. These solutions are extensions of Terzaghi's (1943) theory. The extension of bearing capacity theory to layered foundations is quite

subjective and approximate..

Fully drained conditions are usually assumed for a bearing 136

capacity analysis of sand. This is not the case for a large offshore gravity structure on this type of deposit which is subjected to storm wave loading. To be at all useful, the bearing capacity formula should take into account the pore water pressures developed in the soil.

6.4.2 Other Bearing Capacity Formulations

The first bearing capacity method formulated to consider wave induced pore water pressures was that developed by Hansen

(Bjerrum, 1973). This method was used to assess the stability of the Ekofisk tank and was reported in detail at a later date by Hansen (1976). The theory was developed based on the assumuptions that the soil is homogeneous and that a rotational type of failure about a point "o" below the foundation base will occur (see figure 4.14). A rigid-plastic failure mechanism was assumed and the the pore water pressures induced by the dilatancy of the sand were included (Hansen, 1976). In general, the solution to this problem is very difficult to obtain because the rupture surface, which is found based on the effective stress distribution, must first be computed from an estimated pore water pressure distribution. The computed displacement field then gives a corrected distribution of pore water pressures. This leads to an extremely complicated iterative solution. Residual pore water pressures due to cyclic loading are not considered. This method is not easy to use and has no advantages over other effective stress bearing capacity solutions (e.g. the following method).

Janbu et al (1976) developed a two-dimensional bearing 137

capacity solution for a weightless soil with zero pore water pressure. They extended this solution to include soil weight and excess pore water pressures in an approximate way; the force equilibrium equations derived for the Generalized Procedure of

Slices (GPS) method (Janbu, 1973) were numerically integrated; the integration was performed over a bearing capacity rupture surface similar to the one shown in figure 6.6. The stress distribution on the assumed rupture surface is found by employing the GPS method. Both the vertical and horizontal loads are assumed to act on the effective foundation area. This treatment is adequate for cohesionless soils.

Their result is expressed by a modified bearing capacity equation. This is

T= r(o;+ a - uw)tan0 (6.19)

o~v+ a = BNy + (q'+ a)N^- ukNw (6.20) where T is the average horizontal shear along the base, r is the relative degree of horizontal shear mobilization, tan0 is

the mobilized frictional resistance, o~v is the average vertical

soil reaction over the base, a is the attraction (c/tan0), ufc is

the average pore water pressure along the base, and NH is a dimensionless bearing capacity factor. An iterative solution is required to determine the safety factor since the soil forces are expressed in terms of the degree of strength mobilization.

Curves were developed for the bearing capacity factors which may be used to speed up the solution procedure.

A pore water pressure distribution in the soil corresponding to the maximum wave is assumed based on changes in 138

Figure 6.6 - Geometry of rupture surface used for an effective stress bearing capacity solution 139

the principal stresses over one loading cycle. The maximum pore water pressure at any location is found from Equation (6.6).

Cumulative pore water pressures from cyclic loading are incorporated into the analysis by using a simple pore water pressure generation model. This is given by

Afo", - o-3) (6.21) where n is the number of bands in the design storm histogram, m is a dimensionless pore pressure parameter obtained from cyclic load tests, and N is the number of cycles at any stress level. Since the concern is with relatively small pore water pressure ratios, not liquefaction, this type of pore water pressure model is used. A pore water pressure model such as

Seed et al's (1976) arcsine formula is unnecessary. The pore water pressures on the assumed failure surface must be found by using an iteration technique, since the stresses and pore pressure parameters depend on the degree of strength mobilization in the soil.

Another bearing capacity formulation was developed by Murff and Miller (1977) to analyze the foundation stability of a gravity platform. They approximated the set of partial differential equations derived for classical bearing capacity plasticity solution. This set of partial differential equations

is solved numerically and allows more complex boundary conditions to be specified. Hence, factors such as inclined

loading and irregular base geometry may be dealt with directly,

instead of by using empirical coefficients as other bearing

capacity theories do. Results are comparable to classical 140

theory and are somewhat conservative.

Since the solution is found numerically, soil properties may vary with depth. The shape of the failure surface is

necessarily defined mathematically to solve the equations, and

therefore, it is constrained to a functional representation such

as a logarithmic spiral. This constraint on shape limits the

usefulness of this method for layered foundations.

6.4.3 NGI Slip Surface Method

A slip surface method was developed at the Norwegian

Geotechnical Institute to investigate the stability of offshore

gravity platforms founded on clay. Details of this method have

been reported by Lauritzsen and Schjetne (1976) and Schjetne

(1976). An alternative approach to the bearing capacity

formulation was desired that was simple to use, reliable, and

applicable to offshore gravity structures founded on layered

deposits.

The NGI slip surface method offers some distinct advantages

over bearing capacity theory, namely: complex loading can be

accomodated somewhat more easily, the horizontal force is

applied on both the effective area and non-effective area so

that undue conservatism is avoided, and layered foundations may

be analyzed directly since the soil properties may vary along

the potential failure surface. This method is based on an

assumed failure mechanism with the geometrical model of the

"sliding body" shown in figure 6.7. The body has a constant

cross section over the platform length and is cut off by

vertical planes at the sides. Figure 6.7 - Geometry of sliding body used by NGI

Figure 6.8 _ Geometry of bearing failure surface used in the NGI slip surface method (After Lauritzsen and Schjetne, 1976) 142

The surface of the sliding body is broken up into four sections as shown in figure 6.8: an active section "ab", a flat section "be", an inclined section "cd", and a passive section "de". The inclined section "cd" is directly beneath the effective area. The resistance to sliding for each of these sections is evaluated under force equilibrium conditions. The factor of safety is found from overall horizontal force equilibrium. Only the magnitudes of forces are considered, not the distribution, since moment equilibrium is not applied to the

sliding body.

Inherent in this method, is the assumption that the

shearing resistance at the soil-soil interfaces on the side areas will reduce the horizontal force acting on the base. This

resistance is assumed to act horizontally. Hence, Equation

(6.12) may be rewritten to include this resistance:

H P + P B, = H < A or Pw) - Pp - P& - Pt (6.22)

where Px is defined as

P3 = 0.4(2cAs) (6.23)

Here, c is the average cohesion and As is one side area (shown

in figure 6.8 as "cefd"). The coefficient is used to account

for the fact that the postulated failure mechanism is not the

correct one. If the soil did indeed fail, there would be

significant differences between the assumed vertical plane

surfaces on the foundation sides and the actual failure

geometry. A plane strain analysis is essentially being modified

to do a pseudo-three-dimensional one. The 0.4 value was chosen

to make the factor of safety agree with Hansen's (1970) 143

formulation for a homogeneous deposit, which was modified to

reduce the horizontal force acting on the effective area.

The horizontal force taken along the flat or sliding

section "be" of the foundation base is found from

H„ = c(B0-B)L0 (6.24)

This is a mobilized force with the factor (B0-B)L0 being nothing more than the area of the sliding surface. The horizontal force

applied to the effective area may then be found from

HE, = HftT - HST (6.25)

The NGI slip surface method is relatively simple to use.

To find the critical slip surface, the angle °c is incremented in

steps and the minimum factor of safety is established. ' The

analysis may be done by hand, although use of a small computer

program will speed up the analysis considerably, especially when

there are a number of layers. For layered foundations, the NGI

slip surface method usually predicts a lower safety factor than

the bearing capacity formulas. This safety factor should be

used in preference to the bearing capacity result.

The geometry of the slip surface is fixed, only the angle

changes; the passive zone is always at 45° with respect to the

horizontal. The slip surface is constrained to the shape shown

in figure 6.8. The slip surface used in calculations really has

a sharp corner where the passive wedge starts. This is not

shown in the figure. For layered foundations, average soil

properties along the slip surface are used. A thin seam of weak

material will therefore be represented only by a slight decrease

in the average cohesion computed on the potential failure

surface. This will have a minimal effect on the computed factor 144

of safety and discretion must be used when interpreting results.

The possibility of a deep sliding type of failure, such as that shown in figure 3.6(f), occurring, cannot be properly assessed.

The NGI slip surface method may only be used for total stress analyses of clay foundations. A direct extension of this method to an effective stress analysis is not possible. Since the distribution of shear and normal stresses along a potential failure surface is not considered within any of the four shear zones, the inclusion of stress dependent frictional resistance and pore water pressures would be exceedingly crude. The method of slices could be used for extending the NGI slip surface approach to treat these types of problems.

6.4.4 Method of Slices

This technique has been mentioned for offshore gravity

structure stability analyses (Eide, 1974; H0eg, 1976; Lauritzsen and Schjetne, 1976; Young et al, 1975), although no compre•

hensive treatment has yet been reported. None of the available

slice methods are directly applicable to offshore gravity

structures in their present forms. This technique will be

adapted so that it may be used for offshore stability analyses

in the following chapter.

6.4.5 Finite Element Analyses

The finite element method may be used to assess foundation

stability (Broughton, 1975; Prev0st et al, 1981a; Vaughan et al,

1976; Zienkiewicz et al, 1979), although it is used primarily

for displacement calculations. This is a powerful technique 145

that can easily deal with complex loading and variable soil properties. A stress-strain model is used, which is more realistic than the rigid, perfectly plastic representation used in the bearing capacity and limit equilibrium methods to better model true soil behaviour. The stress-strain models used in finite element analyses vary widely.

The finite element method is basically an extension of matrix structural analysis techniques which solve the equations of equilibrium for a set of structural members. The soil is discretized into "elements" and the force-displacement equations are written for the set of soil elements. The nonlinear, anisotropic, elastoplastic, path-dependent stress-strain properties of the soil may be modelled in finite element analyses by using appropriate constitutive relations

(Prev0st et al, 1981a). Cyclic loading is treated by using a quasi-static approach. The results of finite element analyses

are very dependent on the assumed constitutive relations used as

input. Because soil stiffness parameters are required to

perform the analyses, finite element studies are generally done

only after the detailed site investigation has been carried out.

A high degree of uncertainty is always associated with the in-

situ stiffness parameters measured for offshore deposits.

In the finite element method, the applied loads are

incremented to stepwise approximate the stress-strain curve. If

loading is carried out far enough, some soil elements will reach

stress levels high enough to "fail", that is, they can no longer

support an increased load. Since they are confined by other

elements that have not reached a critical failure stress level, 146

large displacements of the failed elements cannot occur; failure

is localized. A progressive failure will occur as more elements fail under an increasing load. Eventually, no more load can be added without excessive displacements (and load transfer) within much of the soil mass; this corresponds to a total failure.

The ultimate bearing capacity, or applied vertical load at

failure, is well defined for dense sands and insensitive clays, but for loose sands and sensitive clays it is not (Vesic, 1975).

Fortunately, offshore gravity structures are usually founded on the former type of deposits where finite element analyses can generally distinguish a total bearing failure. Excessive displacements may occur rather suddenly upon application of the critical load increment. The ratio of the failure load to the design load will define the load safety factor since the design

soil strength is used in the analysis. Considerable experience

is required to interpret results from finite element analyses.

Prev0st et al (1981a) performed an extensive series of

finite element analyses. They compared their results with centrifuge test data for a model footing on plastic silt

(Prev0st et al, 1981b) where the load was increased monotonically to failure. Both two- and three-dimensional

analyses were performed; the former assumed plane strain

conditions, while the latter modelled the foundation as a

circular footing with three-dimensional constitutive relations.

The three-dimensional analysis was found to adequately predict

displacements at the failure state and loads observed in the model test. The two-dimensional results were found to be

consistent with the experimental data. The (exaggerated) 147

distorted meshes for both two- and three-dimensional analyses at similar load inclinations and eccentricities are shown in figure 6.9. Note that the displacement patterns are similar.

Prev0st et al (1981a) concluded that although two-dimensional finite element studies cannot "provide exact quantitative information about the behaviour of the soil-structure system, they would still provide useful answers regarding relative magnitudes of loads and displacements." This would imply that the plane strain assumption for foundation analysis may be adequate in many cases.

The effect of load eccentricity was studied using the two- dimensional model. Some results are shown in figure 6.10. It is clearly evident that the effective bearing area reduces with

increasing eccentricity. In fact, the effective bearing area appears to be very nearly equal to the effective area defined by

Equation (6.15) for plane strain loading.

Two-dimensional finite element methods cannot be adapted to perform a pseudo-three-dimensional analysis like, the NGI slip

surface method. That is, shearing resistance at the soil-soil

interfaces on the sides of the potential failure body cannot be

included in the element equilibrium equations. A complete

three-dimensional analysis can model this, but is exceedingly expensive to perform.

Since many soil parameters are stress dependent, iteration

techniques must be used to achieve stress compatability. This

requirement for many iterations with a large set of simultaneous

equations means that use of a computer with a large memory is mandatory. It also leads to the high cost of running these 148

(a) Two-dimensional

— It s y

wilF

_ ' ' ' / I I \ \ S _ .

(b) Three-dimensional

Figure 6.9 Comparison of two- and three-dimensional distorted finite element meshes for an inclined and eccentric load (After Prevost et al, 1981a) 149

Figure 6.10 Effect of load eccentricity on effective bearing area as evaluated using the finite element method (After Prevost et al, 1981a) 150

types of computer programs. For a multimillion dollar platform, this may be of little significance. However, for smaller structures, computer costs can be an important consideration.

Many engineers are unwilling to base their decisions solely on finite element analyses. This may be due to a distrust of the constitutive relations used to model soil behaviour or the numerical techniques employed in solving the equations. A high degree of uncertainty associated with the estimation of stiffness parameters is also an important factor.

6.4.6 Model Tests

Model testing for stability problems is done using centrifuge tests (Andersen et al, 1979; Heijnen, 1981; Prev0st et al, 1981b; Rowe, 1975; Rowe et al, 1976). A small model

foundation is placed on a carefully constructed soil profile in a bucket which is then mounted on an arm connected to a central

shaft and spun. The deadweight bearing pressure is derived from

the resulting centrifugal forces. A horizontal load may be applied to the model by means of a jack or cyclic loads may be

imposed on the model by using a displacement-controlled servo-

hydraulic actuator (Andersen et al, 1979). For tests with

cyclic loading, water can be put on the soil surface to apply a

back pressure; this may be necessary to prevent cavitation which

will not occur in the field under high hydrostatic pressures.

Irregular platform geometry is easily accounted for in

centrifuge tests since a structural model of any shape may be

made. Centrifuge tests do not suffer from one of the major

problems that other model tests do: the inability to simulate 151

high stresses resulting from gravitational loads in the prototype. These tests are an attempt to predict foundation

behaviour without much of the subjectiveness of numerical

techniques. They do require field and laboratory test data to

define the in-situ soil properties.

Variable soil properties are modelled by building a soil

profile with different layers using soil from the test site to

control factors such as particle size and fabric. Clays are

remolded and consolidated to the specified overconsolidation

ratio. The more nonuniform the soil profile is in-situ, the

harder it is to model. Generally, a few layers at most are

used. Not only do the soil profile and loading history have to

be representative of the prototype, so do the pore water

pressures. For cohesionless soils where substantial drainage

may take place in the model, in-situ consolidation is modelled

by scaling the time factor. This is usually done by using pore

fluids much more viscous than water.

If similarity requirements between the model and prototype

are satisfied, then the various factors influencing the test do

not have to be distinguished separately (Heijnen, 1981). For

example, the stresses within the soil mass do not have to be

determined, since they are not used in setting up the test. In

numerical studies, stresses are computed using parameters

obtained from laboratory shear tests. The stresses existing in

the centrifuge model soil are similar to those in the prototype

soil if the soil profiles and loading are the same. Centrifuge

tests, like finite element studies, find the load safety factor

and provide information on displacement and failure modes. 152

Centrifuge tests have been used to investigate the foundation stability of existing platforms (Rowe, 1975) and for theoretical studies (Andersen et al, 1979; Prev0st et al,

1981b), but they have not yet been used in design. This will likely change in the future as testing procedures improve

(Heijnen, 1981). The major drawback of - centrifuge testing is that it is time consuming, expensive, and can be conducted at a limited number of facilities.

6.5 Summary

A summary of the existing stability methods applicable to offshore gravity structures is given in Table VIII. It is quite evident that there are two distinct classes of analyses: the relatively simple bearing capacity formulations and the NGI slip surface method, and the more sophisticated analyses which consider more realistic stress-strain behaviour. There is presently no analytical alternative to the crude bearing capacity approach or the NGI slip surface method except the finite element method. A simple effective stress method is needed which can adequately treat both layered foundations and complex loading. In the following chapters, such a technique, based on the method of slices, is presented. Table VIII - Comparison of Existing Stability Methods

DISADVANTAGES METHOD ADVANTAGES -DOES NOT CONSIDER STRESS-STRAIN BEHAVIOUR -SIMPLE TO USE

-SUITABLE FOR HAND CALCULATIONS -BASED ON FIXED GEOMETRY OF RUPTURE SURFACE -CANNOT TREAT COMPLEX LOADING CONDITIONS .. AR1NG CAPACITY THEORY -EASY TO PERFORM PARAMETER STUDIES (CLASSICAL) -LIMITED TO TOTAL STRESS ANALYSES

-NOT GOOD FOR LAYERED FOUNDATIONS

-SUBJECTIVITY OF BEARING CAPACITY FACTORS

-RELATIVELY EASY TO USE -DOES NOT CONSIDER STRESS-STRAIN BEHAVIOUR

-SUITABLE FOR HAND CALCULATIONS -BASED ON FIXED GEOMETRY OF FAILURE SURFACE -ONLY FOR TOTAL STRESS ANALYSES OF CLAY NGI SLIP SURFACE METHOD -APPLICABLE TO LAYERED FOUNDATIONS -EASY TO PERFORM PARAMETER STUDIES -DOES NOT CONSIDER DISTRIBUTION OF LOADS -PROBLEMS WITH THIN SEAMS

-CONSIDERS STRESS-STRAIN BEHAVIOUR -CANNOT STUDY THREE-DIMENSIONAL EFFECTS

-CAN ACCOMODATE IRREGULAR GEOMETRY -REQUIRES MANY SOIL PARAMETERS AS INPUT -MUCH DATA PREPARATION REQUIRED FINITE ELEMENT METHOD -APPLICABLE TO LAYERED FOUNDATIONS (TWO-DIMENSIONAL) -CAN STUDY SOIL-STRUCTURE INTERACTION -EXPENSIVE ANALYSES

-POSSIBLE TO STUDY PROGRESSIVE FAILURE -REQUIRES THE USE OF A LARGE COMPUTER

-PROVIDES INFORMATION ON FAILURE MODES

-MODELS STRESS-STRAIN BEHAVIOUR -EXTENSIVE PREPARATION REQUIRED

-CAN ACCOMODATE IRREGULAR GEOMETRY -REQUIRES SPECIALLY TRAINED PERSONNEL -REQUIRES SOIL FROM FIELD SITE CENTRIFUGE MODEL TESTING -APPLICABLE TO LAYERED FOUNDATIONS -TRUE THREE-DIMENSIONAL ANALYSIS -EXPENSIVE ANALYSES

-PROVIDES INFORMATION ON FAILURE MODES -LIMITED TO FACILITIES WITH CENTRIFUGES Ul 150

types of computer programs. For a multimillion dollar platform, this may be of little significance. However, for smaller structures, computer costs can be an important consideration.

Many engineers are unwilling to base their decisions solely on finite element analyses. This may be due to a distrust of the constitutive relations used to model soil behaviour or the numerical techniques employed in solving the equations. A high degree of uncertainty associated with the estimation of stiffness parameters is also an important factor.

6.4.6 Model Tests

Model testing for stability problems is done using centrifuge tests (Andersen et al, 1979; Heijnen, 1981; Prev0st et al, 1981b; Rowe, 1975; Rowe et al, 1976). A small model foundation is placed on a carefully constructed soil profile in a bucket which is then mounted on an arm connected to a central shaft and spun. The deadweight bearing pressure is derived from the resulting centrifugal forces. A horizontal load may be applied to the model by means of a jack or cyclic loads may be imposed on the model by using a displacement-controlled servo- hydraulic actuator (Andersen et al, 1979). For tests with cyclic loading, water can be put on the soil surface to apply a back pressure; this may be necessary to prevent cavitation which will not occur in the field under high hydrostatic pressures.

Irregular platform geometry is easily accounted for in centrifuge tests since a structural model of any shape may be made. Centrifuge tests do not suffer from one of the major problems that other model tests do: the inability to simulate 151

high stresses resulting from gravitational loads in the prototype. These tests are an attempt to predict foundation

behaviour without much of the subjectiveness of numerical

techniques. They do require field and laboratory test data to define the in-situ soil properties.

Variable soil properties are modelled by building a soil

profile with different layers using soil from the test site to

control factors such as particle size and fabric. Clays are

remolded and consolidated to the specified overconsolidation

ratio. The more nonuniform the soil profile is in-situ, the

harder it is to model. Generally, a few layers at most are

used. Not only do the soil profile and loading history have to

be representative of the prototype, so do the pore water

pressures. For cohesionless soils where substantial drainage may take place in the model, in-situ consolidation is modelled

by scaling the time factor. This is usually done by using pore

fluids much more viscous than water.

If similarity requirements between the model and prototype

are satisfied, then the various factors influencing the test do

not have to be distinguished separately (Heijnen, 1981). For

example, the stresses within the soil mass do not have to be

determined, since they are not used in setting up the test. In

numerical studies, stresses are computed using parameters

obtained from laboratory shear tests. The stresses existing in

the centrifuge model soil are similar to those in the prototype

soil if the soil profiles and loading are the same. Centrifuge

tests, like finite element studies, find the load safety factor

and provide information on displacement and failure modes. 152

Centrifuge tests have been used to investigate the foundation stability of existing platforms (Rowe, 1975) and for theoretical studies (Andersen et al, 1979; Prev0st et al,

1981b), but they have not yet been used in design. This will likely change in the future as testing procedures improve

(Heijnen, 1981). The major drawback of - centrifuge testing is that it is time consuming, expensive, and can be conducted at a limited number of facilities.

6.5 Summary

A summary of the existing stability methods applicable to offshore gravity structures is given in Table VIII. It is quite evident that there are two distinct classes of analyses: the relatively simple bearing capacity formulations and the NGI slip surface method, and the more sophisticated analyses which consider more realistic stress-strain behaviour. There is presently no analytical alternative to the crude bearing capacity approach or the NGI slip surface method except the finite element method. A simple effective stress method is needed which can adequately treat both layered foundations and complex loading. In the following chapters, such a technique, based on the method of slices, is presented. Table VIII - Comparison of Existing Stability Methods

DISADVANTAGES METHOD ADVANTAGES

-SIMPLE TO USE -DOES NOT CONSIDER STRESS-STRAIN BEHAVIOUR

-SUITABLE FOR HAND CALCULATIONS -BASED ON FIXED GEOMETRY OF RUPTURE SURFACE -CANNOT TREAT COMPLEX LOADING CONDITIONS ....AR1NG CAPACITY THEORY -EASY TO PERFORM PARAMETER STUDIES (CLASSICAL) -LIMITED TO TOTAL STRESS ANALYSES

-NOT GOOD FOR LAYERED FOUNDATIONS

-SUBJECTIVITY OF BEARING CAPACITY FACTORS

-RELATIVELY EASY TO USE -DOES NOT CONSIDER STRESS-STRAIN BEHAVIOUR

-SUITABLE FOR HAND CALCULATIONS -BASED ON FIXED GEOMETRY OF FAILURE SURFACE -ONLY FOR TOTAL STRESS ANALYSES OF CLAY NGI SLIP SURFACE METHOD -APPLICABLE TO LAYERED FOUNDATIONS -EASY TO PERFORM PARAMETER STUDIES -DDES NOT CONSIDER DISTRIBUTION OF LOADS -PROBLEMS WITH THIN SEAMS

-CONSIDERS STRESS-STRAIN BEHAVIOUR -CANNOT STUDY THREE-DIMENSIONAL EFFECTS

-CAN ACCOMODATE IRREGULAR GEOMETRY -REQUIRES MANY SOIL PARAMETERS AS INPUT -MUCH DATA PREPARATION REQUIRED FINITE ELEMENT METHOD -APPLICABLE TO LAYERED FOUNDATIONS (TWO-DIMENSIONAL) -CAN STUDY SOIL-STRUCTURE INTERACTION -EXPENSIVE ANALYSES

-POSSIBLE TO STUDY PROGRESSIVE FAILURE -REQUIRES THE USE OF A LARGE COMPUTER

-PROVIDES INFORMATION ON FAILURE MODES

-MODELS STRESS-STRAIN BEHAVIOUR -EXTENSIVE PREPARATION REQUIRED

-CAN ACCOMODATE IRREGULAR GEOMETRY -REQUIRES SPECIALLY TRAINED PERSONNEL -REQUIRES SOIL FROM FIELD SITE CENTRIFUGE MODEL TESTING -APPLICABLE TO LAYERED FOUNDATIONS -TRUE THREE-DIMENSIONAL ANALYSIS -EXPENSIVE ANALYSES

-PROVIDES INFORMATION ON FAILURE MODES -LIMITED TO FACILITIES WITH CENTRIFUGES 154

CHAPTER 7

APPLICATION OF THE METHOD OF SLICES TO

OFFSHORE GRAVITY STRUCTURE FOUNDATIONS

In this chapter the method of slices equations are modified so that they may be used to analyze the foundation stability of an offshore gravity structure subjected to storm wave loading.

A pseudo-three-dimensional technique not unlike that used in the

NGI slip surface method is included in the analysis. A pore water pressure model based on changes in the principal stresses is used to account for wave induced pore water pressures. Use of this model with the method of slices is described in the following chapter. The method developed herein is also useful for analyzing clay foundations for a deep sliding type of failure. In these cases bearing capacity theory and the NGI slip surface method are inapplicable. The method derived from

Sarma's (1973) method of slices is not difficult to understand or complex to use and is of significant practical value.

A typical representation of the problem by the method of slices is shown in figure 7.1. The failure model used is similar to the one used by NGI, that which was shown in,

figure 6.7. The only difference is that the shear surface may take on a different shape (i.e. it is not constrained to shape

shown in figure 6.8 - straight lines defining the inclined and passive sections.) It is convenient to label the two parts on the structure base; the flat section "ab" will be referred to as

the sliding section, while the portion "be" will be termed the 154

CHAPTER 7

APPLICATION OF THE METHOD OF SLICES TO

OFFSHORE GRAVITY STRUCTURE FOUNDATIONS

In this chapter the method of slices equations are modified so that they may be used to analyze the foundation stability of an offshore gravity structure subjected to storm wave loading.

A pseudo-three-dimensional technique not unlike that used in the

NGI slip surface method is included in the analysis. A pore water pressure model based on changes in the principal stresses is used to account for wave induced pore water pressures. Use of this model with the method of slices is described in the following chapter. The method developed herein is also useful for analyzing clay foundations for a deep sliding type of failure. In these cases bearing capacity theory and the NGI slip surface method are inapplicable. The method derived from

Sarma's (1973) method of slices is not difficult to understand or complex to use and is of significant practical value.

A typical representation of the problem by the method of slices is shown in figure 7.1. The failure model used is similar to the one used by NGI, that which was shown in figure 6.7. The only difference is that the shear surface may take on a different shape (i.e. it is not constrained to shape shown in figure 6.8 - straight lines defining the inclined and passive sections.) It is convenient to label the two parts on the structure base; the flat section "ab" will be referred to as the sliding section, while the portion "be" will be termed the Figure7.1 Representation of stability analysis by the method of slices 01 01 156

effective area.

Two different procedures are developed. The first method is an adaptation of Janbu's (1973) Generalized Procedure of

Slices. This method was chosen because it is applicable to slip surfaces of arbitrary shape and because it is familiar to most foundation engineers. Adaptation of this method to a pseudo- three-dimensional is not easily made due to the way in which the equations are derived. An alternative method based on Sarma's

(1973) formulation is presented. This method is easily adapted to perform a pseudo-three-dimensional analysis. Sarma's (1973) method of slices is not well known among practicing engineers.

At a first glance, the method may appear to be an awkward approach to the stability problem. However, a more thorough study will show that the method is in fact quite logical and extremely versatile.

The slice equations are derived in general form, that is, they are independent of the assumptions regarding external loading. When specific problems are analyzed, further assumptions are made, regarding for instance: the load distribution on the foundation base, the pore water pressures in the soil, the distribution of soil parameters with both depth and horizontal position, and the shape of a potential failure surface. These factors will vary with the type of problem to be analyzed, and hence, versatility is maintained.

7.1 The Method of Slices

The method of slices is a limit equilibrium analysis which treats the soil as a rigid plastic material. The degree of 157

safety against an ultimate foundation failure is expressed as

F = T|/T (7.1) where F = the factor of safety,

the shear strength along some shear surface, and

^ = the shear stress along the same shear surface.

The purpose of a stability analysis is to find the minimum value of F corresponding to the most critical stability condition.

The determination of the factor of safety against an ultimate foundation failure requires estimates of (1) the shear strength of the soil along the most critical shear surface, (2) the shear stress along this surface, and (3) the location of this surface.

The following sections will concern themselves with finding the shear stresses on a shear surface and deriving expressions for the factor of safety.

Since the shear strength and shear stress will vary along the shear surface, the soil is broken up into slices. The shear strength may vary from slice to slice as will the shear stress on the base of each slice. If the factor of safety is assumed to be constant along the entire shear surface, then Equation

(7.1) will be a weighted average for the factor of safety, or

F = - l^(a; ) (7.2) n L-i

where the a-t's are weighting parameters that depend on slice geometry and loading and n is the number of slices. The individual ratios of shear strength to shear stress may be examined to see if the ratio anywhere exceeds unity. This is not valid since the shear stress cannot exceed the available strength. Local overstressing within the potential failure body 158

may be examined by comparing the shear strengths to shear stresses along the slice interfaces. Equations will be developed to check if the failure condition is violated within the potential failure body.

The shear strength may be defined by the Mohr-Coulomb failure criteria, which in terms of effective stress is

(Equation 6.2)

*tj= c'+ C7'tan0' (7.3)

Equation (7.1) essentially defines a state of limit equilibrium. This equation may be rearranged to define the average shear stress in terms of the shear strength. This is simply

*t = ^(1/F) • (7.4) where 1/F is the degree of strength mobilized in the soil. This is constant for any shear surface. Introducing Equation (7.3) into (7.4) yields the mobilized or equilibrium shear stress on the shear surface for each slice. This is

~CL = C'+ 6Jtan0; (7.5) where c^= c'/F, and (7.6a)

tan0i= tan0'-/F (7.6b)

These are the mobilized strength parameters.

7.2 Loading Applied to the Foundation

The vertical load at the seafloor is increased by the effective weight of soil within the skirt compartments when applied at the foundation base. This may be written as

• Vtvr= Pv + APv + (BoDoLo)*' (7.7)

The vertical load applied to the foundation base per unit width 159

as used in the method of slices is simply

v* = V^/Lo (7.8)

The horizontal load acting on the foundation base is the

resultant of the applied environmental load PH and all the soil

forces acting on the platform between the seafloor and skirt-tip

level. This may be expressed as (Equation 6.12)

HM= PH + (PA or Pw) - Pf - Ps (7.9)

where PA , Pw, Pf , and Pt are defined by equations (6.9), (6.10),

(6.11) and (6.13), respectively. These equations are summarized here for reference purposes.

2 2 , PA= [ (O.5^'Do +Ap1Do)tan (45'-0/2)-2cDotan(45 -0/2) ]L0 (7.10)

Pw= Ap^oLo (7.11)

2 2 PP= [(0.5*'Do +Ap2Do)tan (45°+0/2)+2cDotan(45'+0/2)]L0 (7.12)

Ps= 2D0B0(c + O.5-i-'Dotan0) (7.13)

The horizontal force per unit width applied to the foundation

base is

Hft = HaT/L0 (7.14)

The moment applied at the foundation base is the resultant

of the moment at the seafloor and the moments due to all the

forces acting between the seafloor and the foundation base.

This may be expressed as (Equation 6.14)

MaT= M + PHD0 + (PA or Pw)h, - Pph2 - Psh3 (7.15)

It is useful to use the concept of effective area when

treating the distribution of the horizontal force on the

foundation base. Since there is only single eccentricity on the

equivalent foundation base, the effective width is all that is

required. This is defined as (Equation 6.15)

B = B0(1 - 2e) (7.16) 160

with the eccentricity being given by (Equation 6.16)

e = (7.17) Bo

7.3 Treatment of the Applied Horizontal Force

The horizontal force applied at the foundation base may be separated into two parts: that which acts on the sliding surface "ab" and that which acts over the effective area "be".

This may be written simply as

HBT= HST+ HET (7.18)

where HS1 is the force taken by the sliding surface "ab", and

Hnis the force taken by the effective area "be".

Equation (7.18) may be written as

HB = Hs + HE (7.19) per unit width. The horizontal force taken by the sliding surface per unit width is given by

Hs = \(c + o"tan0)dx (7.20)

The horizontal force taken by the effective area per unit width may be found by inserting Equation (7.20) into (7.19) and rearranging. This yields f h

HE = Hft - \(c + O"tan0)dx (7.21)

The horizontal force taken by any slice may be found from

FHL= He(bt/B) (7.22)

where bt is the width of a slice. Combining equations (7.21) and

(7.22) yields

FH-t = [HB-\(c + o"'tan0)dx] (b:/B) (7.23) 161

7.4 Modified Janbu Method

The application of Janbu's (1973) Generalized Procedure of

Slices (GPS) method to the analysis of offshore gravity structure foundations requires some modifications. Basically, what is required is the inclusion of horizontal forces acting on the tops of the slices (everywhere in the equations) and the determination of the magnitudes of these forces. They are initially unknown since the force taken outside the effective area on the sliding surface "ab" is expressed in terms of the degree of strength mobilized in the soil. An iteration procedure must be used to establish the horizontal force applied to the effective area, and hence to the slices.

The derivation presented below follows that given by Janbu

(1973) as closely as is possible so that a comparison between the two sets of equations may be made and so that existing slope stability programs can be easily modified.

7.4.1 Assumptions

Janbu's (1973) Generalized Procedure of Slices is founded on the following assumptions:

A - Plane strain conditions apply.

B - The position of the line of thrust for the normal interslice forces is assumed to be known.

C - The normal force on the base is assumed to act where the the total resultant vertical force intersects the base.

7.4.2 Derivation of Equilibrium Equations

The following equations include all the forces acting on the slice shown in figure 7.2. The geometrical variables and FV, * S.W.L.

FH,

Figure 7.2 - Geometry and forces on a (Janbu) slice 163

forces for any slice are defined in the figure. These equations were developed for the loading defined in sections 7.2 and 7.3 and for the model shown in figure 7.1.

The equations for the vertical and horizontal equilibrium of a slice are

FT-fc + AT- = N-cosoi + SLsinc,; (7.24)

AEi - FHi = N^sinc; - S-cosc;, (7.25)

where FTL = FVt + W, (7.26)

AT; = T(t+1)-T(i) (7.27)

AE-, = E(L + 1 )-E(L)„ (7.28)

Moment equilibrium about the assumed point of application of N-

(mid-base) yields

E-Ay; " AE-Ah; + T; b; + FH-.h; = 6 (7.29)

Note that T-'bi-and E^-Ay,; are couples and that terms of second order have been neglected. This equation may be rearranged to find the interslice shear force T-, namely,

T- = -E'tan6c + Ah i (AE - /b ^ ) - h-^FH^b-J (7.30)

where tan6; = Ayc/bt (7.31)

For overall vertical equilibrium, the total vertical resultant on the shear surface must be equal to the weight of the body plus the boundary loads applied to the soil mass. If •

v-t is the total vertical resultant on the base of a slice, then

E[Vt] = Z[FT;] (7.32)

From equation (7.24) note that

V-L = NjCOSo-t + Sjsina; = FTZ + AT; (7.33)

Introducing this equation into (7.32) yields

l[ATr] = 0 (7.34)

Overall horizontal equilibrium requires that the total 164

horizontal resultant on the shear surface be in equilibrium with

the horizontal boundary forces. If is the total horizontal

resultant on the base of a slice, then

E[H-j = He (7.35)

From equation (7.25) it may be written that

H; = N-sinc; - S^OSc^ = AE z - FH-t (7.36)

Introducing this equation into (7.35) yields

I[AE-J = 0 (7.37)

noting from Equation (7.22) that E[FHr] = He

7.4.3 Working Formulas

The complete set of basic equations which must be satisfied

for each slice is

Ti = c; + (crL-u-t )tan0,; (7.38)

o-t = PPC + TTi - "Cjtanoi (7.39)

2 AE = FH; + (PP; +TT- Jb-^tano; - T; b: ( 1 +tan at ) (7.40)

T; = -E-ttan6! + Ahc (dEc/dbc ) - h;(dFH£/dbj) (7.41)

where is the shear stress, c; the cohesion, 6"; the normal

stress, Ui the pore water pressure, and tan0j the frictional

resistance on the base of a slice. Additionally,

PP-,, = FT-t /b-t , and (7.42)

TTt = AT; /b; (7.43)

Note that Equation (7.38) defines the state of limit

equilibrium, that (7.39) is the equation for vertical

equilibrium of a slice, and that (7.40) is one equation for both

vertical and horizontal slice equilibrium. Moment equilibrium

for a slice of infinitesimal width is defined by Equation

(7.41 ). 165

The requirement for overall horizontal equilibrium, from

Equations (7.19) and (7.37) may be written as

I[AE;;] = H6 - Hs - Ht (7.44)

This may also be written as

E[AEr] = Hs + E[FHj] - He (7.45)

Inserting Equation (7.40) into (7.45) and rearranging, yields

2 l[FHl + (PPi +TTL )b;tancx ] - E[*t;bf ( 1+tan ar) ] = HB- Hs- E[FH- ]

(7.46)

The maximum horizontal resistance available from the sliding surface per unit width may be expressed as

Fs = \(c' + cr'tan0')dx = (HS)F (7.47)

Introducing = ~C$:/F and (7.47) into (7.46) and solving for F yields

2 E[ tr.b;( 1+tan a;) ] + F. F = - (7.48)

E[ (PP-t+TT-)brtano-t ] + HB

Introducing Equation (7.39) into (7.38) gives a general expression for the shear strength, which is

v T4.= c'- + (PPr+TTc -u£- X-tanor)tan0V (7.49)

Introducing = ^;/F into the above expression and solving for T^; yields

c ',- + (PP- +TT- -u-L) tan0 '-

T4.= -^ i ' ' (7.50)

1 + (1/F)tan0'; tanoc

The average factor of safety for the general case is found by

using Equation (7.48) with T4;. defined by Equation (7.50). For

simplicity, several abbreviated terms, are used to define ' the

factor of safety. For each slice the following abbreviations will be used: 166

BZ = (PPj+TTC)bitana- (7.51)

2 AX = T$:b.( 1+tan o-t) (7.52)

By inserting Equations (7.51) and (7.52) into (7.48), the formula for the average factor of. safety is reduced to

E[AX] + F. F = (7.53)

E[Br] + Hs

By introducing Equation (7.50) into (7.52) the Az term for each slice can be calculated in three steps as follows:

A;' = [cL +(PPJ+TTJ-ur)tan0i ]b- (7.54)

1 + (1/F)tan0't- tano^ NA = (7.55)

2 1 + tan at

A = A '/NA (7.56)

The A and B values depend on the interslice shear force which in turn depends on the factor of safety. Hence, the need for an iteration technique arises.

The stresses on the shear surface may be calculated as follows:

T; = — = (7.57)

2 F F-{(1+tan o:)bc] and

V; = PP: + TTt - Tttanac . (7.58) in accordance with Equation (7.39). The interslice forces may be found as follows: Introduce Equations (7.51) and (7.52) into

(7.40) to find

AEi = FHj.+ B : - Ar/F (7.59)

Summing the AE values for each slice gives rise to

EC = E[AE:] (7.60)

The vertical shear force T-t, is given by (Equation 7.41) 167

Tt = -E-ttan6-t + Ah-t (dE^/dbj) - h- (dFH[/db\) (7.61)

All of the preceding equations must be satisfied simultaneously by an iteration procedure.

The average factor of safety on a slice interface is found from

c'jh; + (E;-UHc)tan0'c = (7.62) Tt

where UH-t is the water pressure force on the slice interface in question. For a theoretically correct solution, F'~ must be greater than F. Note that average soil properties are used here.

7.5 Modified Sarma Method

Sarma's (1973) approach to deriving a slice method differs substantially from the other slice methods applicable to slip surfaces of arbitrary shape: those of Janbu (1973), and

Morgenstern and Price (1965). These methods solve the slice equilibrium equations and find the factor of safety by changing the value of the forces on the shear surface until slice equilibrium is satisfied. Since these forces are expressed in terms of the factor of safety, which is initially unknown, an iteration procedure is required.

Sarma (1973) also solves the slice equilibrium equations, but in a different way. A destabilizing force is introduced into the equilibrium equations for each slice. This force is equal to the product of the acceleration coefficient K and the slice weight - a pseudo-earthquake force. A factor of safety is assumed and the forces which depend on the degree of strength 168

mobilization in the soil are expressed in terms of the limit equilibrium parameters. The analysis is performed for several values of the factor of safety. Since the solution requires no numerical iterations for the factor of safety, only distinct calculations, there is no possibility of numerical instability.

This factor can be invaluable at times when the other slice methods provide no reasonable answer. The solution for any particular shear surface is found when the acceleration coefficient is equal to zero for some value of the factor of safety. A curve of F vs. K may be drawn as shown in figure 7.3.

The "static" factor of safety may then be picked off the curve.

In the case of an earthquake stability analysis, the solution is found when the acceleration coefficient is equal to some specified value. A distribution of the destabilizing force within the soil mass may be assumed for this type of work.

Sarma's (1973) approach has been adopted for offshore stability analyses at the University of British Columbia. Finn and Lee (1978) modified this method to analyze the stability^ of underwater slopes subjected to seismic loading. A pore water pressure generation model was included in the analysis and the number of cycles to failure was found for undrained loading.

Further work in this area is presently (1982) being done.

Sarma's (1973) method is derived in such a way that many modifications may easily be made. A pseudo-three-dimensional analysis may be made by including the forces acting on the side areas (see figure 6.2(b)) in the slice equilibrium equations. 169

* 0-7

Si*of/c factor of safety 8

•12 t*o 0

2

Factor of safety , F

Figure 7.3 - Curve used for evaluating the safety factor (After Finn and Lee, 1978) 170

7.5.1 Assumptions

The fundamental assumptions on which this slice method is based are:

A - Plane strain conditions apply.

B - The point of application of the normal force acting on the base of each slice is assumed to be known.

C - The relative magnitudes of the interslice shear forces are assumed to be known.

Additionally, for a pseudo-three-dimensional analysis

D - The magnitudes and positions of the side forces on each slice are assumed to be known.

7.5.2 Derivation of Equilibrium Equations

The following equations include all the forces acting on the slice shown in figures 7.4 and 7.5. The geometrical variables and forces for any slice are defined in figure 7.4.

The forces acting on the side areas are included in the slice equilibrium equations as mobilized forces acting parallel to the base. For any slice this force may be defined as

SS-L = [2(bE)(ytl-yb:)(c + cr'tan0)]/Lo (7.63)

Note that this force is expressed in terms of its equivalent magnitude per unit length. The effective normal stress may be computed from earth pressure theory. For vertical and horizontal equilibrium of a slice

NjCOSG;: + StSinc-t = W; - AT; + FN-COS0;

+ FSjsinp; - SScsino; (7.64)

S;;COScc - Njisino; = KWC + AEX - FN;sin0r

+ FS;COSPj - SScCOSO; (7.65)

The limiting equilibrium condition may be defined by 171

Figure 7.5 - Typical (Sarma) slice showing side forces 172

Sz = (N'c tan0'- + c'-t b-tsecc; )/F (7.66)

This equation may be written as

Sc = N'£ tan0-t + Cibisecai (7.67) by using the mobilized strength parameters. The effective normal force can be calculated as

N'-t = N- - US: (7.68)

where US-L is the force due to pore water pressure on the base of any slice due to pore water pressure. This is simply

USt = Uxbcseccj (7.69)

Equations (7.64) and (7.65) can be used to solve for N-t and Tj, namely,

N; = (Wt-AT:)coscc " (KW;+AEC)sinoj

+ FNfcos(«i-pt) - FS;sin(o;-»K ) (7.70)

S-t = (W;-AT;;) sina; + (KW t + AE r ) c OS a :

+ FN-tsin(o-t-pj ) + FSrcos(o£-0r ) - SS: (7.71)

These equations together with (7.68) can be substituted into

(7.67) to obtain

AT-tan(0-t-oj ) + AE- = BBC - KW- (7.72) where

BB;; = (W£-USj )tan(0--a j) + [cr b£ secat-cos0i+FNcsin(0--a.+pI )

-FS;COs(0j-o;+*j )+SSjCOS0£ ]sec(0£-a-) (7.73)

Equation (7.72) is simplified by summing both sides of the equation. Note that

E[AEt] = E(n+1) - E(1) = 0 (7.74) since both E(n+1) and E(1) equal zero. Hence,

[ (ATt)tan(0;-o-t) ] = E[BB-J - E[KWC] (7.75)

Equation (7.75) is therefore one equation which satisfies both vertical and horizontal equilibrium for all slices. A second 173

equation is obtained if moment equilibrium of the whole sliding body about the origin is considered.

[ (Nj;Coso;+Sjsincc)xbc ] - E[ (-N£ sinctj+St coso- )ybt- ]

- E[(W:)xg:] + E[(KWt-)yg-J - E[FNE (xtccos*c +ytt- sin*. ) ]

- E[FS; (xt: sinp£ -yt-cos$r) ] + E[SSj (xst sincc -ys-tcosa£) ] = 0

(7.76)

This equation may be combined with Equations (7.64), (7.65), and

(7.72) to eliminate N-t, Sj , and AEj, resulting in

I [Wftxbj-xgj)] + E[KWrygT] - E[BB;ybt-] + E [ FNj sin*- (ybc -yt£ ) ]

+ EtSSiCOSo^yb.-ys^) ] - E[FSt-cos<»t (yb£-yt- ) ]

= [ (ATj; {xbi-ybctan(0i-oi;)} ] (7.77)

7.5.3 Working Formulas

The distribution of the interslice shear forces is assumed so that

Tc = X-Qj or AT; = X.-DQj; (7.78)

The Q-t values may be found as follows:

, Q. = [(Et-UHt;)tan0 £ +c'ch^]f(x) (7.79) where f(x) is a distribution parameter. This may be taken as unity since it gives acceptable results (Sarma, 1973). E^ may be expressed as

2 Et = K;(0.5 ht + QSjh-) (7.80) where QS; is the average surcharge above any slice interface,

is given by Sarma (1973) as

, 1 - sin(2ol-0'f )[ (1-2Rtt)sin0 'u/ h-)cos0V ]

K-t = (7.81)

1 + sin(2o;-0'^ )sin0';

R* is the ratio of excess pore water pressure to vertical stress and is taken as an average value. The strength parameters may 174

also be taken as average values. Sarma (1973) discusses in detail how to obtain the Q- values.

Upon substituting Equation (7.78) into (7.75) and (7.77) the following equations are obtained-

S1 • X + S2-K = S3 (7 .82)

S4- X - S5-K = S6 (7 .83)

jre S1 thru S6 are defined as follows:

SI = E[DQttan(0i-o'l)] (7 .84)

S2 = E[W-J (7 .85)

S3 = I[BB t] (7 .86)

S4 = E[DQt{xbi;-yb:tan(0t-c {)} ] (7 .87)

S5 = l[Wiybf] (7 .88)

S6 = E[FN;(yb£-ytc )sin* ,] - E[FSt- (yb--ytc Jcos*;; ]

+ E[SS;(ybt-ys-t)cosac] - EtBB-.yg;;] (7 .89)

The interslice forces and the forces acting on the base can be found using the equilibrium equations derived in the preceding section once K and > are known.

The average factor of safety on a slice interface is found

from

c'c hj + (Ei-UHc )tan0V F\ = (7.90) 175

CHAPTER 8

EXAMPLES AND APPPLICATION OF ANALYSES

8.1 Description of Computer Procedure

A computer program GRAVSTAB was developed to perform the analyses described in the preceding chapter. A thorough description of the program may be found in the program documentation which is available through the Soil Dynamics Group

at the University of British Columbia. A brief description of

the program will be given here. The routine for the modified

Sarma analysis was taken from the program STESL (Lee and Finn,

1978) and modified for a gravity structure stability analysis.

The routine used to perform a modified Janbu analysis was

written by the author; the equations derived in the preceding

chapter were used. This routine (and the Sarma routine as well)

was tested with numerous example problems, including those given

in the papers by Janbu (1973) and Finn and Lee (1978) to

eliminate any programming errors.

The two slice methods agree very closely for slope analyses

and for foundation analyses of cohesive deposits. This is not

the case for foundation analyses of cohesionless deposits. It

was found that the stresses computed at the base of each slice

from Janbu's (1973) method did not form a smooth curve over the

slip surface. There is some instability associated with this.

In fact, Janbu's (1973) method often did not provide an answer

for these problems. The solution was very unstable and

divergent. 176

The loads used in an analysis are found from the equations in sections 7.2 and 7.3. These loads, which are expressed in terms of the mobilized strength, are found iteratively. As a first approximation the effective foundation width is assumed to be constant in any analysis. Although the effective width is initially unknown, it may be estimated by assuming a reasonable factor of safety which when used in the appropriate equations yields a numerical value for the effective width. The variation of the effective foundation width with the safety factor is minimal and in most cases may be ignored.

The soil data may be input in one of two ways: layer by

layer, or slice by slice. The former method requires less data

input and lends itself well to investigating different potential

slip surfaces in multi-layered deposits since the strength parameters will be automatically calculated for each slice every

time a new slip surface is chosen. To aid in finding the

critical shear surface, a simple rerun control option may be

used (as many times as desired). The slice coordinates on the

shear surface (between the two end coordinates "b" and "d" shown

in figure 7.1) may be incremented by a given percentage of their

current values to vary the position of the slip surface. Hence,

the depth coordinates for any shape of shear surface need to be

input only once since they may be moved up and down between the

two end values to locate the critical position of the shear

surface for that particular shape. The critical shear surface

may thus be found approximately with a minimum amount of effort

since only a few shapes (that is, shear surface coordinate sets) 177

need to be specified.

Pore water pressures may be taken as being hydrostatic or they may be input individually for each slice. The latter method is used for an effective stress analysis; only the excess pore water pressures need to be input. For a three-dimensional analysis, the pore water pressures on the sides of the slices are also required. It is often adequate to use the hydrostatic pore water pressures here since this type of analysis is quite approximate.

The stresses computed on the base of each slice are standard output for GRAVSTAB. They may be examined to see if overstressing occurs anywhere. These stresses may also be used

in an effective stress analysis to estimate the instantaneous pore water pressures assuming that the pore water pressure distribution due to the short-term (i.e. undrained) wave loading may be found based on Equation (6.6). This is demonstrated for

Example 2.

8.2 Example 1 - A Multi-layered Cohesive Deposit

The first example problem to be analyzed is a CONDEEP type

structure founded on a nonhomogeneous cohesive deposit. This

problem was taken from Lauritzsen and Schjetne (1976) and

represents, an • actual offshore platform in the North Sea. The

required geometry and loading data is given in Table IX. The

actual platform base is nearly circular with a diameter of

approximately 100 meters. The shear strength profile is shown

in figure 8.1. One profile is that given by Lauritzsen and

Schjetne (1976). The other is an approximation of this profile Table IX Geometry and Loading Data for Example 4

Equivalent Platform Length, L0 68.3 m

Equivalent Platform Width, B0 68.3 m

Effective Foundation Depth, D0 3.5 m

Total Vertical Load, Pv + APW 187,000 t

Horizontal Wave Load, PH 49,100 t Moment at Seafloor, M 2,240,000 t-m

Dynamic Wave Pressure, Ap, 3.5 t/mJ

Dynamic Wave Pressure, Ap2 -3.5 t/m*

Unit Weight of Soil, V 2.0 t/m3

Figure 8.1 - Shear strength profile for Example 1 179

using layers with different undrained strengths. The latter profile was used for the slice analyses discussed below.

The procedure used to search for the most critical shear

surface is as follows: A first estimate of the critical shear

surface is made using the NGI slip surface method. A computer program SLIPSURF was written for this purpose. The critical

slip surface found in this way is then rounded off at the sharp

corner and the shape is altered several times. As described

before, each shear surface shape which is input is moved up and

down to find the minimum value of the factor of safety. By

using just a few different geometries for the shear surface, the

general shape of the critical shear surface may be estimated.

More iterations based on information provided by the early runs

may be done if greater accuracy is desired. The critical shear

surfaces evaluated by a number of methods are shown in

figure 8.2. The corresponding safety factors are given in

Table X. The angle which the bearing capacity rupture surface

makes with the horizontal may be determined approximately

(Lauritzsen and Schjetne, 1976). For this example problem the

safety factors determined by the NGI slip surface method and the

procedures developed in this thesis agree quite well. The slice

methods predict a slightly lower factor of safety. This is in

part due to the position of the critical slip surface determined

by the two methods; the critical slip surface determined by the

method of slices passes through more of the weak zone. For most

total stress analyses of cohesive foundations, the NGI slip

method is adequate. However, if a thin layer of very weak

material exists within the strata, then the NGI method is of 180

Table X

Comparison of Computed Safety Factors for Example 1

CALCULATED SAFETY FACTOR

METHOD OF ANALYSIS Plane Strain Actual Case B/L = 0 B/L = 1

Hansen's (1970) Formula, modified 2 . 1 51 2.351

Meyerhof's (1963) Formula, modified 2. 171 2.491

NGI Slip Surface Method 2.001 2 . 1 51

Modified Janbu Method of Slices 1 .92 -

Modified Sarma Method of Slices 1 .93 2.06

'From Lauritzsen and Schjetne (1976)

Method of SI Ices

NGI Slip Surface Method

Hansen Bearing Capacity Theory

Figure 8.2 - Critical shear surfaces for Example 1 as evaluated by different stability methods 181

little use in assessing the platform stability. It is also important to note that the increase in the safety factor for the pseudo-three-dimensional analyses is nearly identical for both the NGI method and the procedure developed in this thesis based on Sarma's method.

In the foregoing analyses, the undrained strength was assumed to be constant with horizontal position. Since the stress conditions will vary considerably along a potential failure surface, the use of laboratory shear test results which reflect the different states of stress may be appropriate.

There are four distinct states of stress existing within the soil mass. These are shown in figure 8.3.

The undrained shear strength may be found by using the stress path method (Lambe, 1967). Laboratory samples are subjected to the estimated in-situ and total stresses that they will be subjected to in the field. The resulting undrained shear strengths determined in this way may then be used directly in a stability analysis. Since there is often a lack or absence of good quality samples, all the tests shown in figure 8.3 may not always be performed. In these cases, the undrained strength estimated from in-situ tests may be related to the standard or triaxial compression value. The other shear strengths may be taken as various percentages of this value. Some possible values for these coefficients are given in Table XI.

The shear strength profile must then be represented by both depth and horizontal variations. Assuming that a layered profile may be used, the strength variation with horizontal position may easily be incorporated into the numerical technique 182

Table XI

Coefficients for Estimating Undrained Strength from Triaxial Compression Data

SHEAR TEST x C,,

Direct Shear 0.75

Triaxial Extension 0.50

Triaxial Compression 1 .00

1 \ 11

ACTIVE - ZONE PASSIVE -T| TRIAXIAL f -

Figure 8.3 - Zones of shear on the potential failure surface and relevant laboratory tests (Adapted from Kjekstad and Lunne, 1979) 183

by using the triaxial compression values multiplied by the appropriate coefficients in the various shear zones. Another stability analysis was performed using these new values for the undrained strength. The critical shear surface found using this new profile was almost identical to the one found for the original profile. Results of this study are reported in Table

XII. The use of the shear zone concept for specifying the strength along the failure surface is a matter which has not yet been resolved. It is important to note that reducing the safety

factor by such a substantial amount has a tremendous effect on the cost of the platform since the base size must be increased to reduce the average bearing pressure. This cost increase may be on the order of many millions of dollars.

The critical shear surface found for the aforementioned analyses is shown in figure 8.4. This type of plot is standard output of GRAVSTAB and is useful for examining the location of this surface with respect to different strata. (It is also useful for locating this surface.) Note the length of that part of the surface which runs through the weaker layers.

8.3 Example 2 - A Cohesionless Deposit; Ekofisk Tank

The second example problem to be analyzed is the Ekofisk tank. The required geometry and loading data is given in

Table XIII. The distribution of residual pore water pressures due to cyclic loading is given in figure 8.5. This distribution was developed based on observations reported by Clausen et al

(1975); these pore water pressures were shown in figure 4.11.

The contours drawn on the figure are based on Rahman et al's Table XII

Effect of Shear Zone Representation on the Safety Factor

STRENGTH PROFILE USED COMPUTED SAFETY FACTOR

Regular Strengths 1 .93

Shear Zone Strengths 1 .62

WflHPLf 1 - COUDfFP STRUCTURE 03.30 Q N. FEB. 02. 1062 2-0 ANALYSIS »PLANE STRAIN)

PLATFORN BRSE

I 0

Figure 8.4 - Critical shear surface for Example 1 found from computer program GRAVSTAB Table XIII

Geometry and Loading Data for Example 2

Equivalent Platform Length, L0 85.8 m

Equivalent Platform Width, B0 85.8 m

Effective Foundation Depth, D0 0.4 m

Bouyant Platform Weight, Pv 190,000 t

Vertical Wave Load, APW 10,000 t

Horizontal Wave Load, PH 78,600 t

Moment at Seafloor, M 2,800,000 t-m

Dynamic Wave Pressure, Ap,« 3.0 t/m2

2 Dynamic Wave Pressure, Ap2 -3.0 t/m

Unit Weight of Soil, K 2.0 t/m»

Figure 8.5 - Distribution of pore water pressures in foundation soil used in Example 2 186

(1977) work.

The most difficult part of this analysis is estimating the instantaneous pore water pressures due to the cycling loads.

These were found based on Equation (6.6), which is

AU = A0"3 + A (ACT, - ACT3) (9.1)

The method of slices may be used to find the changes in the principal stresses. The procedure used to determine the principal stresses is as follows: A slip surface is analyzed and the factor of safety corresponding to Au=0 is found. The same slip surface is then analyzed without the wave loads, i.e. the vertical platform load only. This load is now assumed to act over the total foundation area. The "no load" factor of safety is then established. The stresses at the base of each slice are then determined from the equilibrium equations derived in the previous chapter. This procedure has been set up in GRAVSTAB.

Only the A-parameter is required as input for any slip surface.

The principal stresses and pore water pressure changes for the

instantaneous wave loads are then computed and the new safety

factor is determined. The principal stresses may be evaluated

from

cr, = cr+ [(1 - cos2*)/sin<*] (9.2)

o3 = 6- [(1 + cos2*)/sin*] (9.3) where * is defined by

ot = 45°+ 0/2 (9.4)

Here 0 is the mobilized friction angle. This will be different

for each case. For the no-load analysis this value will be very

low.

The critical slip surface found for the tank is shown in 187

figure 8.6. Only the residual pore water pressures due to cyclic loading were used and pore water pressures associated with total stress increments were neglected (i.e. Au=0). This is felt to be conservative since the dense Ekofisk sand would probably dilate and create negative pore water pressures in much of the soil mass during loading. The value of the A-parameter has a marked effect on the computed factor of safety. For the slip surface shown in the figure, four values of the A-parameter were chosen between 0.0 and -0.33. The latter value corresponds to a dense sand at failure. The safety factors computed with these different values are shown in Table IX.

For this problem, the increase in the safety factor due to added resistance from the side areas was minimal. For sand foundations with shallow failure mechanisms this will generally be the case. For deeper failure mechanisms which occur in cohesive foundations, the added resistance can increase the safety factor substantially. This was shown in the total stress analysis in Example 1 and would also show up in an effective stress analysis of the same foundation. 188

Table XIV

Effect of A-parameter on the Safety Factor

VALUE OF A-PARAMETER COMPUTED SAFETY FACTOR

-0.33 1.77 -0.20 1.61

Au-0 1.51

-0.10 1.49 0.00 1.37 i DMU 1 - «C •na PA. m m « urn

nr..'auJJJJJJJll V

'1* i. i. Ah.k.^HcjM.^ iu JM iu

Figure 8.6 - Critical shear surface for Example 2 found from computer program GRAVSTAB 189

CHAPTER 9

SUMMARY AND CONCLUSIONS

Offshore gravity structures have a bright future in offshore development schemes. They offer the advantage of being nearly complete at tow-out, thereby minimizing installation time. This is particularly important in hostile environments such as the northern North Sea where conventional steel jacketed structures present a substantial risk in terms of short-term safety. It also allows for an earlier production start. By nature of their design, these structures incorporate storage and provide a large deck area which is necessary for production equipment. This is a significant advantage for marginal field recovery or for locations offshore where pipelines are not economically justified.

Offshore engineering presents many challenges for the geotechnical specialist. Although offshore engineering has existed for many years, only recently has hydrocarbon exploration moved into deeper waters where the design of major structures has consistently required an advancement of the state of the art in not only geotechnical engineering but also in structural, hydrodynamic, and oceanographical engineering. The development of new techniques and design philosophies in all of these fields requires that the geotechnical engineer be familiar with them since he must play a key role in gravity structure design.

Instrumentation has :' provided some useful data for 190

predicting the magnitudes of settlements expected for a large gravity structure. However, the availability of this data is limited and most engineers will have to design future structures based on what is "publically known". Published data for the

Ekofisk tank demonstrates that platform settlement is difficult to assess. More recent data is available for other platforms which confirms this result. Since settlement due to cyclic effects is an important consideration, some assessment must be made. Presently, the evaluation of cyclic settlements for offshore gravity type structures is made using very simplistic models. Cyclic settlement analysis for offshore gravity type structures is an area which requires a considerable amount of research. Cooperation among those individuals and corporations involved in this research would greatly accelerate progress in this area.

Stability is the other principal problem that geotechnical engineers must deal with. This is a complex problem which must be viewed in perspective. The procedures discussed and developed within this thesis may only be used if certain criteria are met. For example, full contact is usually assumed; this critical assumption must be verified by instrument data.

Instrumentation is used to provide information on the stress distribution over the slab and also the distribution of pore water pressures within the soil mass. The evaluation of residual pore water pressures due to cyclic loading by theoretical methods is by no means reliable. In fact,

substantial discrepancies exist between theoretical estimates and on-site observations. 191

Estimation of the stability of a gravity type structure is presently assessed by using bearing capacity theory, the finite element method, or the NGI slip surface method for clay foundations. Bearing capacity theory is of limited value for use in offshore analyses primarily because of the inability to

(1) treat adequately complex loading, (2) analyze layered foundations, and (3) perform effective stress analyses.

Extensions of classical theory have been proposed to deal with the latter problem, however, these theories are of limited value. The NGI slip surface method is an improvement over bearing capacity theory, however, this method is only applicable to total stress analyses of cohesive deposits. The finite element method may also be used to assess platform stability.

The most serious problems associated with this method are that the soil stiffness parameters need to be known accurately and

the assumed constitutive relations be reasonable for the soil analyzed. Both of these factors must be considered in the light

of the reliability of offshore soil investigations.

An alternative approach to the bearing capacity and finite

element methods was presented. This procedure is based on the method of slices. Two methods were derived. Janbu's (1973) method, which is well known to most foundation engineers, was

extended to treat gravity structure problems in two dimensions.

A pseudo-three-dimensional analysis procedure was not developed

within this framework. An alternative technique, based on

Sarma's (1973) method of slices was developed. Three-

dimensional effects were easily incorporated into Sarma's (1973) 192

method. This method is also numerically stable which makes a

solution possible for any problem by using the method of slices.

The analysis procedures developed in this thesis were

applied to two example problems - one on a layered cohesive

deposit and one on cohesionless soil. The first example

illustrated how a total stress analysis could be performed.

Results were compared with existing methods and shown to be

good. The pseudo-three-dimensional analysis suggests that the

safety factor can be increased by about six percent due to the

added resistance from the side areas. This result agrees well

with the NGI slip surface method. The NGI method provides

reasonable results for cohesive foundations without thin weak

seams. For the problem analyzed, the method of slices is shown

to give a lower factor of safety, although not substantially

lower for this profile. For other profiles the difference may

be greater. The values of the undrained strength chosen along

the slip surface have a pronounced effect on the computed safety

factor. The use of the shear zone concept reduces the safety

factor considerably.

An effective stress analysis was also performed. The

critical part of this analysis was the determination of the

instantaneous pore water pressures due to the wave loads. The

method of slices was used to predict these pore water pressures

based on changes in the principal stresses. This procedure was

incorporated' into the computer program GRAVSTAB. The value of

the A-parameter has a significant effect on the pore water

pressures developed and hence the factor of safety computed.

For a dense sand, such as Ekofisk sand, where dilation will 193

occur, the stability will increase since the pore water pressures on the slip surface will be less.

The procedures developed in this thesis were shown to provide reasonable answers to offshore gravity structure stability problems. The procedure based on Sarma's (1973) method of slices is preferred since it can provide information on three-dimensional effects and does not suffer from numerical instability. This method, which is easy to use and applicable to a wide range of problems, is suggested as a means of estimating offshore gravity structure stability under storm wave loading.

$SIGNOFF 194

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