INCLINED LOAD CAPACITY OF SUCTION CAISSON IN CLAY

Transcription

1 INCLINED LOAD CAPACITY OF SUCTION CAISSON IN CLAY by CHAIRAT SUPACHAWAROTE This thesis submitted for the degree of Doctor of Philosophy at The University of Western Australia School of Civil and Resource Engineering December 26

2 -i- Abstract This thesis investigates the capacity and failure mode of suction caissons under inclined loading. Parametric finite element analyses have been carried out to investigate the effects of caisson geometry, loading angle, padeye depth (i.e. load attachment point), soil profile and caisson-soil interface condition. Displacement-controlled analyses were carried out to determine the ultimate limit state of the suction caissons under inclined load and the results presented as interaction diagrams in VH load space. VH failure interaction diagrams are presented for both cases where the caisson-soil interface is fully-bonded and where a crack is allowed to form along the side of the caisson. An elliptical equation is fitted to the normalised VH failure interaction diagram to describe the general trend in the case where the caisson-soil interface is fully-bonded. Parametric study reveals that the failure envelope in the fully-bonded case could be scaled down (contracted failure envelope) to represent the holding capacity when a crack is allowed to form. A stronger effect of crack on the capacity was observed in the lightly overconsolidated soil, compared to the normally consolidated soil. The sensitivity of caisson capacity to the changes in load attachment position or loading angle was quantified based on the load-controlled analyses. It was found that, for caisson length to diameter ratios of up to 5, the optimal centreline loading depth (i.e. where the caisson translates with no rotation) is in the range.65l to.7l in normally consolidated soil, but becomes shallower for the lightly overconsolidated soil profile where the shear strength profile is more uniform. The reduction of holding capacity when the padeye position is shifted from the optimal location was also quantified for normally consolidated and lightly overconsolidated soil profiles at loading angle of 3 Upper bound analyses were carried out to augment the finite element study. Comparison of holding capacity and accompanying failure mechanisms obtained from the finite element and upper bound methods are made. It was found that the upper bound generally overpredicted the inclined load capacity obtained from the finite element analyses especially for the shorter caisson considered in this study. A correction factor is introduced to adjust the upper bound results for the optimal condition. Comparisons of non-optimal capacity were also made and showed that the agreement between the upper bound and finite element analyses are sensitive to the change in the centreline loading depth when the caisson-soil interface is fully bonded, but less so when a crack forms.

3 -ii- Acknowledgement I would like to express a sincere appreciation to my supervisors, Professor Mark Randolph and Dr. Susan Gourvenec to always provide invaluable advices and encouragement during the period of my study. Their supports are very much appreciated. I would also thankful for the financial support provided throughout my study particularly the Postgraduate Scholarship from the Royal Thai Government and Ad-hoc Scholarship from Centre for Offshore Foundation System (COFS). Special thanks extend to colleague, staff and visitors at the University of Western Australia who provide me an enjoyable experience during the period of my study. In addition, I would like to express my sincere gratitude to my previous professors especially at Chulalongkorn University and at the Asian Institute of Technology to guide me throughout the course of civil and geotechnical engineering. Finally I would like to express the most grateful thanks to my family. Their genuine love and understanding help me morally throughout my study. I hereby declare that the contents of this thesis are an original contribution and have not been submitted to any other university. Chairat Supachawarote December 26

4 -iii- Table of Contents Abstract Acknowledgement Table of Contents List of Figures List of Tables Notations i ii iii viii xii xiv Chapter 1 Introduction Overview Historical review of suction caisson Organization of thesis 8 Chapter 2 Background Introduction Method of analyses Limit equilibrium method Upper bound limit analysis Finite element method Vertical loading of suction caissons Reverse end bearing failure Sliding failure Tensile failure Evaluation of parameters α and N c Horizontal loading of suction caissons Development of analytical method 16 Table of contents

5 -iv Optimal load capacity Combined horizontal and vertical loading of suction caisson The effect of crack on the suction caisson capacity Summary 28 Chapter 3 Validation analyses Introduction Analysis description Model geometry and soil properties In situ stress state Soil stress-strain response Caissson-soil interface condition Mesh Loading stages Element type verification Programme of analyses Results of element verification Caisson Load response verification API project summary Programme of analyses Results of caisson load response verification analyses Summary 56 Chapter 4 Parametric study Introduction Model details Model geometry 57 Table of contents

6 -v Soil undrained shear strength and in situ stress state Caisson-soil interface condition Finite element model Programme of analyses Results Limiting load capacity for combined VH loading VH Failure envelopes Effect of variation in shaft interface friction on inclined load capacity Curve fit Effect of variation in load attachment point and loading direction on inclined load capacity Summary of design equations Summary of findings 85 Chapter 5 Effect of crack formation on inclined pullout capacity Introduction Model details Model geometry Soil undrained shear strength and in situ stress state Caisson-soil interface condition Finite element model Programme of analyses Results Limiting load capacity for combined VH loading Normalised pullout capacity Optimal loading point 19 Table of contents

7 -vi- 5.6 The effect of the variation in load attachment point on inclined load capacity Results Conclusions 113 Chapter 6 Upper bound limit analyses of suction caissons Introduction Summary of upper bound limit analyses Plastic work dissipated within conical soil wedge Plastic work dissipated along sliding surfaces Plastic work dissipated along the caisson tip in rotational failure Flow mechanism below wedge failure Reverse end bearing at caisson tip Work against the gravity Validation of upper bound limit analyses Optimal capacity Non-optimal capacity (fully bonded) Non-optimal capacity (crack allowed) Summary of findings 156 Chapter 7 Conclusions and future work Conclusions Parametric study of suction caisson with no crack Parametric study of suction caisson with a crack allowed to form Comparison of the finite element analyses with the upper bound analyses Future work 159 References 16 Table of contents

8 -vii- List of Figures Figure 1.1 Suction caisson during fabrication (Van Splunder workyard, Holland; photo: SPT) 1 Figure 1.2 Suction caissons for the Njord field in the North Sea. (Photo: P. Sparrevik, NGI) 2 Figure 1.3 Suction caisson for Snorre tension-leg platform (Zdravkovic et al. 21) 4 Figure 1.4 Suction caisson for catenary mooring at Nkossa (modified from Colliat, 1996) 5 Figure 1.5 Taut wire mooring at Na Kika (Paton & Wong 24) 5 Figure 1.6 Aspect ratio and diameter of suction caisson utilized for offshore mooring (Data from Table 1.1). 7 Figure 2.1 Failure modes under vertical pullout loading (modified from Senders & Kay 22) 12 Figure 2.2 Flow around failure mechanism; under lateral loading of deeply embedded pile (Randolph & Houlsby 1984) 16 Figure 2.3 Wedge and flow around failure mechanism; under undrained lateral loading of a pile (Murff & Hamilton 1993) 17 Figure 2.4 Wedge, flow around, and rotational flow failure under undrained lateral loading of a caisson (Randolph & House 22) 18 Figure 2.5 Simplified unit lateral pressure N p and rotational flow failure (Aubeny et al. 23) 19 Figure 2.6 Horizontal capacity of suction caissons in soil with uniform strength and strength increasing proportional to depth (Randolph et al. 1998). 2 Figure 2.7 Normalised ultimate capacity under inclined load for caisson load at the top with full skirt adhesion (Zdravkovic et al. 1998) 22 Figure 2.8 Comparison between finite element analyses (Zdravkovic et al. 1998) and upper bound limit analysis (Randolph & House 22) for caisson with L/D = 24/17 under inclined load. 23 List of figures

9 -viii- Figure 2.9 VH failure envelope for caisson with L/D = 2.8 (Senders & Kay 22). 24 Figure 2.1 Comparison of finite element and upper bound results for uniform strength profile (Aubeny et al. 23) 26 Figure 2.11 Upper bound collapse mechanisms with tension crack 28 Figure 3.1 Schematic representation of suction caisson 31 Figure 3.2 Undrained soil strength profiles adopted in validation analyses 32 Figure 3.3 Coulomb friction model adopted in ABAQUS 34 Figure 3.4 Finite element mesh for suction caissons model 36 Figure 3.5 Boundary condition of soil surface at the interface between soil and caisson during geostatic stage 37 Figure 3.6 Schematic diagram of probe load stage 38 Figure 3.7 Location of reference point for caisson rigid body adopted in the analyses 38 Figure 3.8 Load-displacement response for vertical pullout of short caisson in normally consolidated soil (L/D = 1.5) 41 Figure 3.9 Schematic illustration of displacement-controlled swipe and probe tests 46 Figure 3.1 The calculation of optimal level along the centreline z cl (caisson is prevented from rotation) 47 Figure 3.11 Deduced mobilization of end-bearing resistance for all suction caissons 48 Figure 3.12 Comparison of optimal loading point from API project predictors (from Andersen et al. 25) 51 Figure 3.13 Comparison of VH Failure interaction diagram from API project predictors (from Andersen et al. 25) 52 Figure 3.14 Comparison of normalised load F/F opt for caisson load above and below the optimum level from API project predictors (from Andersen et al. 25) 55 Figure 4.1 Schematic representation of suction caisson 58 Figure 4.2 Finite element mesh for caisson with L/D = 3 6 List of figures

10 -ix- Figure 4.3 Schematic of variation in load attachment point and loading angle 62 Figure 4.4 Load-displacement responses for suction caissons with L/D = 1.5, 3, and 5 (constant interface friction ratio of.65) 64 Figure 4.5 Normalised horizontal capacity for caisson with constant interface friction ratio of Figure 4.6 VH failure envelope for caisson with L/D = 1.5, 3, and 5 (constant interface friction ratio of.65) 7 Figure 4.7 Vector summation of the caisson selfweight and mooring loads to account for the effect of caisson selfweight 72 Figure 4.8 Illustration of the effect of caisson selfweight at different loading angles for short and long caissons (L/D = 1.5 and 5). 73 Figure 4.9 VH failure envelopes for different values of interface friction ratio 75 Figure 4.1 Normalised VH failure envelopes for different values of interface friction ratio 76 Figure 4.11 The relationship between normalised horizontal capacity and length to diameter ratio 78 Figure 4.12 Normalised VH failure envelopes for different caisson aspect ratios ( =.65). 79 Figure 4.13 Effect of loading depth on caisson capacity (constant interface friction ratio of.65) 83 Figure 4.14 The influence of loading angle on the capacity of suction caisson. 84 Figure 5.1 Potential caisson movements and the corresponding change in horizontal stress 9 Figure 5.2 Soil profiles adopted in the analyses 91 Figure 5.3 VH failure envelope for L/D = 1.5 (NC) 96 Figure 5.4 VH failure envelope for L/D = 1.5 (LOC1) 97 Figure 5.5 VH failure envelope for L/D = 1.5 (LOC2) 98 List of figures

11 -x- Figure 5.6 VH failure envelope for L/D = 3 (NC) 99 Figure 5.7 VH failure envelope for L/D = 3 (LOC1) 1 Figure 5.8 VH failure envelope for L/D = 3 (LOC2) 11 Figure 5.9 VH failure envelope for L/D = 5 (NC) 12 Figure 5.1 VH failure envelope for L/D = 5 (LOC1) 13 Figure 5.11 VH failure envelope for L/D = 5 (LOC2) 14 Figure 5.12 Comparison of VH failure envelopes from various soil profiles, L/D = Figure 5.13 Comparison of VH failure envelopes from various soil profiles, L/D = 3 15 Figure 5.14 Comparison of VH failure envelopes from various soil profiles, L/D = 5 16 Figure 5.15 Comparison of contracted yield envelope to the original failure envelopes for L/D = 3, LOC1 16 Figure 5.16 Normalised VH interaction diagram for NC soil profile 17 Figure 5.17 Normalised VH interaction diagram for LOC1 soil profile 18 Figure 5.18 Normalised VH interaction diagram for LOC2 soil profile 18 Figure 5.19 The effect of the variation in load attachment point for caisson length to diameter ratio L/D = 3 in lightly overconsolidated soil (LOC1) 112 List of figures

12 -xi- List of Tables Table 1.1 History of suction caisson used for anchoring in the offshore industry (excluding TLP) (Data from: Byrne 2; Colliat 22; Ehlers et al. 24; and Andersen et al. 25) 6 Table 2.1 Reverse end bearing factor from several researchers. 15 Table 3.1 Caisson geometry and soil properties for validation analyses (from Andersen et al. 25) 32 Table 3.2 Summary of methods using by each predictor for inclined load capacity of suction caissons 43 Table 3.3 Programme of analyses 45 Table 3.4 Long caisson (L/D = 5) in normally consolidated soil (Case C1) 49 Table 3.5 Short caisson (L/D = 1.5) in normally consolidated soil (Case C2) 49 Table 3.6 Long caisson (L/D = 5) in lightly overconsolidated soil (Case C3) 5 Table 3.7 Short caisson (L/D = 1.5) in lightly overconsolidated soil (Case C4) 5 Table 3.8 Summary of results from load-controlled analyses (this study, COFS prediction) 53 Table 4.1 Programme of analyses 61 Table 4.2 Limit loads and optimal loading points for α =.65; L/D = Table 4.3 Limit loads and optimal loading points for α =.65; L/D = 3 66 Table 4.4 Limit loads and optimal loading points for α =.65; L/D = 5 67 Table 4.5 The reverse end bearing factors and normalised horizontal capacities (α =.65) 68 Table 4.6 Reverse end bearing factor and normalised horizontal capacity obtained from uniaxial V and H load for interface friction ratio of.5,.65,.8, and 1 77 Table 4.7 Results of load-controlled analyses for α =.65; L/D = Table 4.8 Results of load-controlled analyses for α =.65; L/D = 3 81 Table 4.9 Results of load-controlled analyses for α =.65; L/D = 5 82 List of tables

13 -xii- Table 5.1 Programme of displacement-controlled analyses (rotation prevented) 93 Table 5.2 The reduction of the ultimate horizontal capacity when the crack is allowed to form in different soil profiles and caisson length to diameter ratios. 95 Table 5.3 Optimal loading depth obtained from displacement control analyses (fully bonded) 19 Table 5.4 Optimal loading points obtained from displacement control analyses (crack allowed) 11 Table 6.1 The reduction in ultimate horizontal capacity as the upper bound failure mechanism changes from 2-sided to 1-sided. 126 Table 6.2 Correction factors obtained from the comparison of upper bound and finite element results. 131 Table 6.3 Comparison of resultant loads from finite element load-controlled analyses and AGSPANC upper bound limit analyses in normally consolidated soil (s u /z = 1 kpa/m) loading at 3 from the horizontal. 137 Table 6.4 Comparison of the magnitude of capacity from finite element and upper bound analyses when crack is allowed to form, L/D = 3, LOC1 154 List of tables

14 -xiii- Notations A = cross sectional area of caisson API = American Petroleum Institute A p = external perimeter area of caisson A p,int = internal perimeter area of caisson COFS = Centre for Offshore Foundation Systems CAX4H = Axi-symmetric 1 st order hybrid rectangular element CAX4R = Axi-symmetric 1 st order rectangular element with reduced integration C3D8 = 3-D 1 st order brick elements C3D8H = 3-D 1 st order hybrid brick elements C3D8R = 3-D 1 st order brick elements with reduced integration D = caisson diameter D* = centreline loading depth D = energy dissipation DSS = Direct simple shear D/t =caisson diameter to thickness ratio E = Young's modulus E = unit energy dissipation F = resultant load F opt = optimal resultant load FE, FEA = finite element analysis FEM = finite element method h = depth of the centre of rotation of the caisson along the centreline of the caisson H = horizontal load component k = von Mises parameter Notations

15 -xiv- K = earth pressure coefficient at rest L = caisson length LEA = limit equilibrium analysis LOC = lightly overconsoildated soil LOC1 = the first lightly overconsolidated soil assumed in the analyses (see Figure 5.2) LOC2 = the second lightly overconsolidated soil profile assumed in the analyses (see Figure 5.2) L/D = caisson length to diameter ratio M = resultant moment NC = normal consodated soil (undrained shear strength increases linearly with depth from zero strength at the mudline) NGI = Norwegian Geotechnical Institute N c = reverse end bearing factor N h = normalised horizontal capacity N p = lateral bearing resistance factor OTRC = Offshore Technology Research Centre p lim = limiting pressure on a circular pile loaded laterally q u = unit end bearing q t = unit bottom resistance Q s,ext = external shaft interface friction Q s,int = internal shaft interface friction Q t = bottom resistance r o = caisson radius R = radius of the conical wedge at the mudline assumed in the upper bound analysis SS = Simple shear Notations

16 -xvs u = undrained shear strength of soil s u,ss av = average simple shear undrained shear strength over the caisson length av s u,tip = average soil undrained shear strength at caisson tip (average of triaxial compresson, triaxial extension and simple shear strengths) TLPs = Tension leg platforms UB, UBLA = upper bound limit analysis UWA = University of Western Australia v h = horizontal velocity of the caisson at depth z from the mudline v o = horizontal velocity of the caisson at the centreline loading depth v r = radial velocity (within the conical wedge assumed in the upper bound analysis) v t = slip velocity along sliding surfaces v v = vertical velocity of the caisson v θ = circumferential velocity (within the conical wedge assumed in the upper bound analysis) v z = vertical velocity (within the conical wedge assumed in the upper bound analysis) V = vertical load component V u = net pull-out force at failure W = external work done by the anchor chain W wedge = work done against the gravity (for the conical wedge assumed in the upper bound analysis) W' = submerged weight of suction caisson W plug = submerged weight of the soil plug z cl = optimal centre line loading depth z cl /L = normalised centre line loading depth z o = depth of the conical wedge from the mudline assumed in the upper bound analysis Notations

17 -xviz p = padeye depth Greek α = interface friction ratio (τ f,interface /s u,ss ) α ext = external interface friction ratio α int = internal interface friction ratio β = optimisation parameter representing the component of the vertical velocity δh/δv = ratio of applied horizontal displacement to the vertical displacement ε, ε, ε = radial, circumferential, and vertical strain rates (within the conical wedge rr θθ zz assumed in the upper bound analysis) γ' = submerged unit weight of soil μ = coefficient of friction (Coulomb friction) μ = optimising parameter representing the exponent term defining the rate of decay in radial velocity with the radial distance in the upper bound analysis ν = Poisson ratio θ = loading angle σ vc ' = vertical effective stress σ 1, σ 2, σ 3 = major, intermediate and minor principal stresses τ = shear stress τ c = critical shear stress τ max = limiting shear stress ψ = angle measured from the plane of loading in plan view Notations

18 -1- Chapter 1 Introduction 1.1 Overview Oil and gas exploration has recently moved towards deeper water as the demand for energy keeps rising. In this environment, floating platforms are generally used due to their cost effectiveness over fixed platforms and because of practical limitations for the latter. Floating platforms are maintained in position by a mooring system, the lower end of which is secured by an anchor embedded in the seabed sediments. Suction caissons have become the most widely used type of anchor for various types of mooring systems ranging from catenary chains to light weight taut polyester cables. A suction caisson is a cylindrical shell, which is sealed by a top cap equipped with valves (see Figure 1.1). Typical diameters of suction caissons range between 4 and 8 m. The aspect ratio (length to diameter ratio) is relatively small compared to conventional pile foundations and is normally less than seven as the potential of soil plug failure during installation increases with the increase in aspect ratio. Internal stiffeners are usually incorporated to prevent buckling, since the caisson wall is relatively thin (with caisson diameter to wall thickness D/t in the range 1 to 25) (Andersen et al. 25). Figure 1.1 Suction caisson during fabrication (Van Splunder workyard, Holland; photo: SPT) Various terms have been used to describe this type of foundation, depending on their applications, including suction anchors, bucket foundations, suction piles, suction Chapter 1 Introduction

19 -2- caissons, caisson anchors, skirted foundations, plate foundations, skirt-plated foundations and concrete foundation templates (Deng 21). The term suction caisson is used here, referring to the type of suction-installed foundation used for deep-water anchoring applications focused on in this thesis. During installation water is pumped out from the interior of the suction caisson, creating an internal under pressure relative to the external water pressure thus inducing downward force in addition to its selfweight to drive the caisson into the ground. Once installed, the valve is sealed to maintain passive suctions generated during operational loading conditions. Load is applied to the caisson via a mooring line attached to a padeye located along the caisson shaft below the mudline (see Figure 1.2). In service, any upward movement of the caisson will generate suction pressure (passive suction) induced inside the caisson by reverse end-bearing resistance acting on the soil plug. This suction increases the holding capacity of suction caissons considerably compared with the case where the top lid is vented. Figure 1.2 Suction caissons for the Njord field in the North Sea. (Photo: P. Sparrevik, NGI) The holding capacity of suction caissons can be optimised by locating the padeye such that the caisson translates with minimal rotation. The point where the loading vector intersects the centreline of suction caisson in the optimal condition is known as the Chapter 1 Introduction

20 -3- optimal loading point. The location of the optimal loading point depends primarily on the soil profile considered. When the loading vector passes above or below the optimal loading point, the caisson will rotate forwards or backwards respectively (Andersen et al. 25). 1.2 Historical review of suction caisson The suction caisson concept was first explored by Goodman et al. (1961), who referred to the idea as vacuum anchorage, and carried out a feasibility study on a small model caisson. The experimental results showed that excellent anchorage could be achieved particularly in clay and silt. More detailed investigations with small-scale tests were subsequently carried out (e.g. Brown & Nacci 1971, Helfrich et al. 1976). Suction caissons were introduced to the offshore industry as alternative anchors for mooring a storage tanker at the Gorm field offshore Denmark (Senpere & Auvergne 1982). Since then, but particularly in the 199s and later, suction caissons have been used increasingly throughout the world. Early applications tended to address quasivertical loading, such as for the Snorre tension-leg platform (Figure 1.3), or quasihorizontal loading (maximum of ~2 o from the horizontal) from catenary moorings such as at Nkossa (Figure 1.4). Recently, catenary mooring chains used in moderate water depths have been replaced, particularly in water depth exceeding 1 m, by light weight taut wire or semi-taut wire moorings made from steel wire and synthetic rope; these result in much higher angles of loading (typically 3 to 4 ) such as at Na Kika (Figure 1.5). A chronology of the use of suction caisson foundations for offshore mooring is summarised in Table 1.1. Caisson diameter D is plotted against the length to diameter ratio L/D in Figure 1.6 which shows a range of caissons with typical L/D between 3 and 7. The advent of higher angles of loading has necessitated investigation of interaction effects between vertical and horizontal loading, and a more careful study of the optimal loading depth, the effect of loading angle on the optimal depth, and also the effect of cracking on both vertical and horizontal capacity. This thesis investigates these issues using purely numerical study, based on 3-dimensional finite element analysis, covering the common range of caisson aspect ratios between 1.5 and 5 and soil strength profiles. Chapter 1 Introduction

21 -4- Figure 1.3 Suction caisson for Snorre tension-leg platform (Zdravkovic et al. 21) Chapter 1 Introduction

22 -5- θ max = 15º Figure 1.4 Suction caisson for catenary mooring at Nkossa (modified from Colliat, 1996) Design cases: Mudline chain angles: 2 to 35 degrees Padeye chain angles: 24 to 36 degrees Figure 1.5 Taut wire mooring at Na Kika (Paton & Wong 24) Chapter 1 Introduction

23 -6- Table 1.1 History of suction caisson used for anchoring in the offshore industry (excluding TLP) (Data from: Byrne 2; Colliat 22; Ehlers et al. 24; and Andersen et al. 25) Name/Operator Year Location Water Depth (m) No. D (m) L (m) Gorm (Shell) 1981 North Sea Nkossa (Elf) 1995 Gulf of Guinea 2* c YME (Statoil) 1995 North Sea 1* c Harding (BP) 1995 North Sea 11* c Norne (Statoil) 1996 North Sea 35* c Aquila (Agip) 1997 Adriatic 85* c 4.5 (lower) (upper) Njord (Norsk 1997 North Sea 33* c Hydro) Marlim P19 & 1997 Offshore Brazil 77-1* t P26 (Petrobas) Schiehallion (BP) 1997 West of Shetlands 35* c Curlew (Shell) 1997 North Sea 9* c Visund (Norsk 1997 North Sea 35* c Hydro) Njord (Norsk 1997 North Sea 33* c Hydro) Aasgard A 1998 North Sea (Statoil) Laminaria 1998 North West Shelf 4* c (Woodside) Transocean Marianas 1998 Gulf of Mexico 4 2 (Delmar) Marlim P Offshore Brazil 9* t (Petrobras) Aasgard C 1999 North Sea 3 9 NA 15.7 (Statoil) Marlim P Offshore Brazil 81-91* c (Petrobras) Troll C (Norsk 1999 North Sea 33* c Hydro) Kuito (Chevron) 1999 West Africa Hoover-Diana 2 Gulf of Mexico (ExxonMobil) Girassol (TFE) 21 West Africa (Riser) 4.5 (FPSO) 5 (Loading Buoy) 5 (Loading Buoy) Horn Mountain (BP) 22 Gulf of Mexico Na Kika (Shell) 22 Gulf of Mexico 192* t Wen-chang South China Sea (CNOOC) 12.8 Barracuda (Petrobras) 23 Offshore Brazil 825* t Caratinga (Petrobras) 23 Offshore Brazil 13* t (continued on the next page) Chapter 1 Introduction

24 -7- Table 1.1 (Continue) Name/Operator Year Location Bonga (Shell Nigeria) 23 Offshore Nigeria 98 Water Depth (m) No. D (m) L (m) 12 5 (FPSO) 5 Bonga (Shell 3.5 (SPM) Offshore Nigeria Nigeria) Red Hawk (Kerr 23 Gulf of Mexico 16* t McGee) Devils Tower 23 Gulf of Mexico (Dominion) Hostein (BP) 23 Gulf of Mexico Panyu (CNOOC) 23 South China Sea (Semi-FPU) (Manifold) 23.8 Thunder Horse 24 Gulf of Mexico (PLET) 26 (BP) (Water injection) (Water injection) 2 Mad Dog (BP) 24 Gulf of Mexico Atlantis (BP) 24 Gulf of Mexico 12 NA NA * c Catenary mooring * t Taut wire mooring D (m) D Caisson aspect ratio L/ D L 8 Figure 1.6 Aspect ratio and diameter of suction caisson utilized for offshore mooring (Data from Table 1.1). Chapter 1 Introduction

25 Organization of thesis This thesis comprises seven chapters. A brief outline of each chapter is given below: Chapter 2 summarises the background of methods and issues relating to suction caisson analyses and design. The available methods of analysis are outlined followed by a description of the established procedures for calculation of vertical capacity, horizontal capacity, interaction between horizontal and vertical load, and effect of crack formation on the capacity, respectively. Chapter 3 gives details of the 3-dimensional (3-D) finite element analysis used for the research and presents some results from a benchmark problem to verify the accuracy of the 3-D finite element analyses undertaken. Various element types were investigated to find the most appropriate for the analyses in the following chapters. Chapter 4 presents the results of a parametric study of suction caissons in normally consolidated soil where the soil and caisson interface is assumed intact throughout the analyses, with no gap or crack permitted. Several parameters are explored including the caisson aspect ratio, location and direction of the applied load and the interface friction ratio. Maximum caisson capacity is investigated for a range of combined vertical and horizontal loading and the optimum failure envelopes are presented along with a simple expression to describe their shape. The sensitivity of caisson capacity to changes in load attachment position or loading angle is also quantified. Chapter 5 extends the study in Chapter 4 to show the influence of a crack, or gap formation between the soil and caisson at the back of the caisson, on the inclined pullout capacity. Comparison is made between cases where a crack is allowed to form and those where a crack is suppressed, in both normally consolidated and lightly overconsolidated soil. Results are presented as interaction diagrams under combined vertical and horizontal load and are compared with those from upper bound limit analyses. Chapter 6 compares the results of upper bound limit analyses with the finite element results discussed previously, and also comments on the failure mechanisms observed from both approaches. Finally, Chapter 7 summarises the key results from the work and outlines areas for further research. Chapter 1 Introduction

26 -9- Chapter 2 Background 2.1 Introduction Since their first use more than twenty years ago, the performance of suction caissons under operating load conditions has been investigated extensively in order to address design uncertainties. Physical modelling by means of both small-scale 1-g model tests and centrifuge tests have been performed (e.g. Brown & Nacci 1971, Steensen-Bach 1992, Andersen et al. 1993, Watson & Randolph 1997). In addition, several analytical and numerical methods such as limit equilibrium, upper bound limit analysis, and finite element analysis have been used to analyse suction caisson capacity (e.g. Deng 21, Cao et al. 22, Randolph & House 22, Aubeny et al. 23, Cao et al. 25a, 25b). Prediction methods for piles and caissons to evaluate their horizontal capacity and vertical capacity in compression may be considered well established by geotechnical consultants (Dendani 23). However, for caissons used as anchors there are a number uncertainties involving soil behaviour, including such issues as set up or consolidation following installation, different failure mechanisms developed under different loading rates and hence consolidation conditions and response under cyclic loading. In addition, there are several areas of uncertainty even where the soil strength profile is determined, such as the interaction between horizontal and vertical load, optimum location of the load attachment point and how that is affected by the loading angle, and the effect of a crack forming along the caisson wall. Formal design guidelines for suction caisson holding capacity are still under development by the offshore industry, and at present design criteria and computation procedures are normally established on a case-by-case basis. This chapter summarises the background of methods and issues relating to suction caisson analyses and design. First, the available methods of analysis are outlined, followed by a description of the existing procedures for calculation of vertical capacity, horizontal capacity, interaction between horizontal and vertical load, and effect of crack formation on the capacity, respectively. 2.2 Method of analyses Various analytical and numerical methods such as limit equilibrium, upper bound limit analysis, and finite element analysis have been used to analyse the suction caisson Chapter 2 Background

27 -1- holding capacity. Limit equilibrium and upper bound limit analyses are commonly used to obtain a solution for stability problems in soil mechanics, while finite element analysis is more versatile and can be used to solve both stability and pre-failure response. Basic principles regarding these methods are summarised in this section Limit equilibrium method Limit equilibrium is an approximate approach based on a simple static equilibrium. Alternative failure surfaces are constructed from simple shapes such as straight lines, circles, and logspirals and an adequate assumption on the stress distribution along the failure surface must be made so that an equilibrium equation can be written (Chen 1975). The critical position for the failure or slip surface is then identified (usually by trial and error) to minimise the limit equilibrium solution. However, because admissibility of the soil kinematics is not considered the solution is not necessarily an upper bound. This method may give a sensible answer to the problem provided that reasonable assumptions have been made regarding the failure mechanism and limiting stresses acting on the object Upper bound limit analysis In contrast to limit equilibrium, upper bound limit analysis involves identifying kinematically admissible mechanisms. This means that the deformation mode should satisfy both the velocity boundary conditions, and strain and velocity compatibility conditions. The energy expended by the external loads during an increment of displacement and the dissipation of energy within the plastically deformed region defined by the assumed mechanism are then calculated. An expression in terms of variables from the assumed mechanism can then be written from the energy balance between the external work and energy dissipation. The variables are then optimised to give the least upper bound solution for that mechanism. The upper bound method will always give a non-conservative estimate of ultimate limit state, either equal to or greater than the true solution Finite element method In contrast to the analytical methods of limit equilibrium and upper bound limit analysis, the finite element method is a numerical method. The advantage of the finite element method is that there is no need to assume any critical failure mechanism prior Chapter 2 Background

28 -11- to the analyses. A realistic failure mechanism will be found by the method provided that an appropriate constitutive model and appropriately discretised mesh are used. The principle of the finite element method is to divide a continuum into a finite number of discrete elements of finite dimensions, joined by nodes such that there is no physical discontinuity between adjacent elements (Gourvenec 1998). Boundary conditions (e.g. loads, pressure, displacement and body force) are imposed and the assigned primary variable (e.g. nodal displacement) can then be solved for. Secondary variables (e.g. stresses, strains) are then evaluated from the calculated nodal displacements (Potts & Zdravkovic 1999). In the application to geotechnical engineering practise, accuracy when dealing with an almost incompressible material, when simulating undrained soil response, or the convergence of contact analyses, when modelling the interaction between soil and structure, make the analysis more complex. These issues are discussed in Chapter Vertical loading of suction caissons Suction caissons are used to resist quasi-vertical load when used as foundations for tension leg platforms (TLPs). The vertical pullout capacity of suction caissons has been investigated by many investigators either by physical modelling (e.g., Finn & Byrne 1972, Wang et al. 1975, Steensen-Bach 1992, Andersen et al. 1993, Watson & Randolph 1997) or numerical analysis (e.g., Deng 21, Cao et al. 22). Three failure mechanisms: reverse end bearing failure, sliding failure and tensile failure, have been identified as illustrated in Figure 2.1. (a) Reverse end bearing failure (b) Sliding failure (c) Tensile failure Figure 2.1 Failure modes under vertical pullout loading (modified from Senders & Kay 22) Chapter 2 Background

29 Reverse end bearing failure Reverse end bearing failure mechanism occurs for a caisson with a sealed lid when the soil response is undrained, typically when a caisson is subjected to short-term (transient) loading. Passive suction is generated inside the caisson, which prevents the soil plug separating from the caisson top cap resulting in the soil plug being pulled up together with the caisson. The failure mode at the bottom of the caisson was referred to by Finn and Byrne (1972) as a reverse end bearing mechanism (Figure 2.1a). The pullout capacity can be derived from the external skin friction and the reverse end bearing. The unit end bearing q u can be expressed as an end bearing factor N c times the average undrained shear strength from different modes of shearing (i.e. triaxial compression, triaxial extension and simple shear) at the level of the caisson tip. The reverse end bearing failure provides the highest pullout capacity of the three failure mechanisms identified in Figure 2.1. From the above discussion, the vertical pullout capacity under undrained conditions can be written as the sum of the submerged weight of the caisson, W', external shaft interface friction (Q s ) and reverse end bearing (Q b ) as follows: V u = W' + Q s + Q b = W' + α s av u,ss A p + s av u,tip N c A Equation 2.1 where, V u = net pull-out force at failure α = interface friction ratio (τ f,interface /s u,ss ) s u,ss av = average simple shear undrained shear strength over the caisson length A p = perimeter area of caisson s u,tip av = average soil undrained shear strength at caisson tip (average of triaxial compresson, triaxial extension and simple shear strengths) N c = reverse end bearing factor A = cross sectional area of caisson Sliding failure When drained conditions prevail, for example when a suction caisson is subjected to long-term loading or the caisson lid is not sealed (vented), passive suction cannot be generated and the shear failure occurs along the caisson interior and exterior skirt Chapter 2 Background

30 -13- (Figure 2.1b). This is the critical condition where only internal and external friction is to be relied upon beside the caisson self-weight. The pullout capacity can be written as: V u = W' + Q s,int + Q s = W' + α int s av u,ss A p,int + α ext s av u,ss A p Equation 2.2 where, α int, α ext = internal and external interface friction ratio A p,int, A p = internal and external perimeter area of caisson Tensile failure When partially drained conditions prevail, for example when a suction caisson is pulled out at intermediate rates, passive suction may be generated partially. The caisson together with soil plug tends to detach from the soil below the caisson (Steensen-Bach 1992, Deng 21). In this case, the pullout capacity may be calculated as the sum of the submerged weight of the caisson W', external friction, submerged weight of the soil plug W plug and the resistance generated at the bottom of the suction caisson Q t as shown in Figure 2.1c. The bottom resistance (Q t ) depends on the amount of suction generated at the bottom of the caisson as the soil plug is detached. The pullout capacity may be expressed as: V u = W' + Q s,ext + W plug + Q t = W' + α ext s av u,ss A p + W plug + A q t Equation 2.3 where, q t = unit bottom resistance The uncertainty in q t introduces considerable complexity to the problem, which is outside the scope of this thesis. Attempts to address this through physical and numerical modelling have been presented by Clukey et al. (24). 2.4 Evaluation of parameters α and N c In order to predict the vertical pullout capacity accurately, the interface friction ratio α and reverse end bearing factor N c must be selected carefully. A number of experimental (e.g. Fuglsang & Steensen-Bach 1991, Chen & Randolph 25) and numerical investigations on this subject have been carried out (e.g., El-Gharbawy & Olson 1999, Andersen & Jostad 22, 24, Cao et al. 22); however, there is still no resolution of appropriate values of the key design parameters. Chapter 2 Background

31 -14- Suction caissons are installed into the seabed in two steps. First, the caisson is penetrated into the seabed by self-weight. Further penetration is achieved by suction penetration. During installation, the soil undrained shear strength adjacent to the caisson will be reduced to the remoulded shear strength due to disturbance during skirt penetration, and the limiting friction is generally taken as equal to the remoulded shear strength. After penetration, the soil shear strength will increase with time. This strength increase with time following installation is called the set up effect, and arises from a combination of thixotropy and consolidation (Andersen et al. 25). Even after full set up, however, the limiting interface friction usually remains below the pre-installation intact undrained shear strength. It may be expressed conveniently as αs u, with the value of α less than unity. The method of installation has been supposed to affect the caisson shaft capacity. It is customary to assume that the soil displaced by the advancing caisson wall would divide equally inward/outward during self-weight penetration but following a transition stage would flow totally inwards once suction is applied (Andersen & Jostad 22, 24). The flow of soil inwards reduces the increase in total stress outside the caisson by comparison with, say, a driven pile, and thus the final effective stress outside the caisson wall after the excess pore water pressures have dissipated will be lower than assumed in pile design (Andersen & Jostad 22). Andersen and Jostad (22) suggested that the external skin friction may be reduced by up to 35 % compared with the α value of unity usually assumed for piles in normally consolidated soil, because of this suction effect. They proposed a base value of α =.65 for suction caisson design, subject to detailed assessment for given soil properties. The shaft friction may also depend on factors such as the caisson surface roughness, soil type, and overconsolidation ratio. There is still debate regarding the soil flow mechanism during caisson installation, but in order to explore the net effect of the method of installation, comparative experimental studies have been undertaken for jacked and suction-installed caissons. A recent study by Chen and Randolph (25) on the measured radial stress changes and long-term axial capacity from centrifuge tests suggested that the difference between suction and jacked installation is minimal. The reverse end bearing factor is an issue considered further in the present study. Fuglsang and Steensen-Bach (1991) reported centrifuge and laboratory model tests for a Chapter 2 Background

32 -15- caisson with L/D equal to 2 in overconsolidated kaolin clay. The results reflected reverse bearing capacity factors N c between 6.5 and 8.5 which is somewhat less than the theoretical lower bound of 9.2 for a caisson with L/D of 2 (Martin 21). Clukey and Morrison (1993) performed centrifuge tests on a suction caisson with the L/D of 2 in normally consolidated soil and found N c to be 11. In the above modelling, vane shear strengths were used in the interpretation of the relevant parameters, and may have overestimated the average shear strength by a factor of 1.25 (Watson et al. 2). As such, the actual reverse bearing capacity factors may be up to 25 % greater than reported. El-Gharbawy and Olson (1999) proposed solutions for the undrained uplift capacity of caissons, based on the results of laboratory model tests in kaolin clay. They conservatively recommended a reverse bearing capacity factor of 9, irrespective of caisson length-to-diameter ratio. Watson et al. (2) suggested that the uplift resistance is similar to the compression end bearing resistance in terms of magnitude. In spite of measured values of N c that were higher, Randolph and House (22) suggested that the reverse end bearing value of N c be taken as 9 as an appropriately conservative value given the strain-softening nature of the response as the caisson is extracted. Values of the reverse end bearing N c from different laboratory and centrifuge tests are summarised in Table 2.1. The values of N c range from as low as 8.1 to as high as 14.6, although direct comparison is difficult given variations in soil type (overconsolidation ratio, soil strength profiles etc.) and length-to-diameter ratio of the caisson. Table 2.1 Reverse end bearing factor from several researchers. Authors N c L/D Type of test Fuglsang and Steensen-Bach (1991) * 2 1-g and centrifuge Clukey and Morrison (1993) 13.8* 2 centrifuge Randolph and House (22) centrifuge *Shear vane adjusted by multiplying with factor Horizontal loading of suction caissons Suction caissons are commonly used as anchors for catenary mooring lines, where the chain angle at the mudline is close to zero. Allowing for the curvature of the chain within the soil, the loading angle at the caisson padeye will fall within the range 1 to 2 from the horizontal (Randolph & House 22). Chapter 2 Background

33 Development of analytical method The development of an analytical solution for suction caissons under lateral loading was based on the response of pile foundations under lateral loading. Randolph and Houlsby (1984) proposed the limiting lateral resistance of a deeply embedded circular pile in cohesive soil based on upper bound limit analyses. The upper bound solution for the limiting pressure on a circular pile loaded laterally (plane strain conditions) in cohesive soil may be expressed as p lim = N p s u Equation 2.4 where N p is a dimensionless parameter which was found to vary with the interface friction from 9.14 for a fully smooth pile, to for a fully rough pile (see flow mechanisms in Figure 2.2). Although an error was subsequently discovered in the upper bound analysis, recent solutions give a similar range from 9.2 to (Martin & Randolph 26) Smooth, N p = 9.14 Rough, N p = Figure 2.2 Flow around failure mechanism; under lateral loading of deeply embedded pile (Randolph & Houlsby 1984) Murff and Hamilton (1993) investigated the lateral load capacity of piles under undrained conditions based on an upper bound approach. The influence of the free surface is treated by assuming a conical wedge failure mechanism near the surface and flow around failure at depth as suggested by Randolph and Houlsby (1984) as shown in Figure 2.3. Four parameters characterise the kinematics of the failure mechanism which can be optimised to obtain the minimum upper bound limit load. Chapter 2 Background

34 -17- P Wedge failure Flow around failure Figure 2.3 Wedge and flow around failure mechanism; under undrained lateral loading of a pile (Murff & Hamilton 1993) An upper bound solution for suction caissons under lateral load has been proposed by Randolph and House (22) by considering failure in three regions (Figure 2.4a): A passive/active conical wedge region at shallow depth as suggested by Murff and Hamilton (1993). A plane strain flow region below the wedge where the soil flows around the caisson as suggested by Randolph and Houlsby (1984). The net horizontal pressure on the caisson body in this region is taken as the limit pressure for a cylinder moving horizontally through the soil. A rotational flow region which generally forms in a spherical shape with its centre on the caisson axis. Depending on the depth of point of rotation, and hence the load and its angle this region may extend upwards and eliminate the flow region (Figure 2.4b). The least upper bound can be found by optimising six parameters that characterise the failure mechanism. Three parameters give the depth and maximum radial extent of the conical failure wedge and the velocity variation within the wedge. A further three parameters quantify the centre of rotation, ratio of vertical to horizontal velocity and rate of twist. Optimisation can be carried out with a spreadsheet solver (e.g. AGSPANC, Advanced Geomechanics 21). This upper bound solution is not entirely rigorous as it is not kinematically complete since it ignores interaction between the top and the bottom of the plastic 'flow' region (below the conical wedge) and the adjacent soil. Chapter 2 Background

35 -18- However, the upper bound may be made rigorous by forcing the wedge to the base of the caisson, or using an extended base rotational failure. (a) Centre of rotation below the caisson tip (b) External base scoop with high centre of rotation. Figure 2.4 Wedge, flow around, and rotational flow failure under undrained lateral loading of a caisson (Randolph & House 22) Aubeny et al. (23) proposed a limit equilibrium solution as shown in Figure 2.5. An assumed lateral resistance is acting on the caisson surface and spherical failure surface is assumed at the caisson tip. The unit lateral resistance N p is adopted from the parametric studies undertaken by Murff & Hamilton (1993) using their upper bound mechanism, and is given by: Np 1 2 = N N exp( ξ z/d) Equation 2.5 where N 1 is the limiting value of lateral resistance at depth, (N 1 -N 2 ) is the lateral resistance at the free surface, and ξ is a curve fitting factor depending on the characteristics of the soil strength profile. By introducing the simplified variation of N p, the number of optimisation variables can be reduced and therefore the computational efficiency improved. However, the simplification restricts the analysis to uniform and linearly varying profiles of undrained shear strength. Chapter 2 Background

36 -19- Figure 2.5 Simplified unit lateral pressure N p and rotational flow failure (Aubeny et al. 23) Optimal load capacity Unlike pile foundations where the load is generally applied at the top, suction caissons are subjected to load at a padeye located below the mudline in order to minimise the caisson rotation and thus optimise the load capacity. Initial tests on suction caissons subject to horizontal load were conducted with load applied at the mud line (Hogervorst 198). Keaveny el al. (1994) subsequently showed that lowering the load attachment point to mid depth led to almost double the capacity. Randolph et al. (1998) analysed the horizontal capacity of suction caissons based on upper bound limit analyses for cases where the caisson translates with no rotation (fixed head) and where the caisson is free to rotate (free head) in both uniform and normally consolidated soil (undrained shear strength increasing proportionally with depth). As shown in Figure 2.6, the available horizontal capacity increases significantly when the caisson translates with no rotation; the capacity with rotation is as little as 25 to 3 % of the maximum available capacity. Sukumaran et al. (1999) carried out a finite element study on the lateral capacity of suction caissons, modelling properties typical of soft normally consolidated clay soils from the Gulf of Mexico. The suction caisson analyses also indicated that the maximum anchor capacity is obtained when the load attachment point forces the caisson to have a translational mode of failure rather than a rotational mode of failure. Chapter 2 Background

37 -2- Normalised capacity H/LDsu Length-to-diameter ratio L/D Figure 2.6 Horizontal capacity of suction caissons in soil with uniform strength and strength increasing proportional to depth (Randolph et al. 1998). Allersma et al. (1999) performed a series of centrifuge tests and finite element analyses in normally consolidated kaolin clay and concluded that the optimum attachment point is around 2/3 from the top of the caisson. Coffman et al. (24) examined the capacity of suction caissons under horizontal load using a 1-g experimental model and showed that the largest capacity could be achieved when the loading point was between two thirds and three quarters of the caisson embedment. Deng (21) proposed an alternative simplified expression based on finite element study to evaluate the ultimate horizontal capacity of suction caisson in normally consolidated soil as follows: H = N As Equation 2.6 u h u(2l/3) where s u(2l/3) denotes the undrained shear strength at a depth equivalent to 2/3 of the caisson length. He showed that that Nh could be described by an expression of the form: N h α = Equation α z 4 cl zcl + β 6.3 L L Chapter 2 Background

38 -21- The dimensionless parameters α and β are related to the aspect ratio, L/D, and can be expressed as follows:.3785 L α = 7.2 Equation 2.8 D β = 1.58e L.775 D where; z cl = centreline loading depth L = caisson length D = caisson diameter 2.6 Combined horizontal and vertical loading of suction caisson For mudline loading angles which are sufficiently low, as would typically be the case for a catenary type of mooring e.g., less than 2º from the horizontal, Clukey (23) suggests that the interaction effect is insignificant and anchor loading capacity may be taken approximately as the horizontal capacity of the anchor in pure translation divided by the cosine of the loading angle at the padeye. Conversely for high loading angles e.g. less than 2º from the vertical, the vertical capacity will govern and the anchor holding capacities will be the vertical capacity divided by the sine of the loading angle (Clukey 23). Developments in deep water with taut or semi-taut mooring systems often require anchors to sustain loads where the typical mudline loading angle is between 3 and 4º. In this environment, the interaction effect becomes significant therefore the simple calculations given above cannot be applied. Zdravkovic et al. (1998) used finite element analysis to investigate the interaction effect between vertical and horizontal loads for suction caissons in normally consolidated soil for the case where the load is applied at the middle of the caisson top cap. The results were presented in vertical and horizontal load space normalised by the uniaxial vertical load capacity as shown in Figure 2.7. Zdravkovic et al. (1998) proposed a failure envelope in terms of an elliptical function of the following form: 2 ult 2 2 H 2 V ult + = Vmax Equation Chapter 2 Background

39 -22- θ = º 2 º 45º 7º 8º 9º L/D = 12/17 L/D = 8/17 L/D = 17/17 L/D = 24/17 θ Hult/Vmax L/D = 1 Elliptical function D L V ult /V max Figure 2.7 Normalised ultimate capacity under inclined load for caisson load at the top with full skirt adhesion (Zdravkovic et al. 1998) Randolph and House (22) described upper bound limit analyses with AGSPANC (Advanced Geomechanics 21). The finite element results from Zdravkovic et al. (1998) were used to validate the upper bound solution as shown in Figure 2.8 for a caisson with length to diameter ratio L/D of 24/7. Results from AGSPANC lie outside the envelope predicted by the finite element analyses by up to 2%. Randolph and House (22) commented that the elliptical yield surface is surprising in view of yield envelopes for surface foundations, which show reductions in vertical capacity of only 5-7% due to the action of lateral loading. Chapter 2 Background

40 -23- D Figure 2.8 Comparison between finite element analyses (Zdravkovic et al. 1998) and upper bound limit analysis (Randolph & House 22) for caisson with L/D = 24/17 under inclined load. Senders & Kay (22) carried out finite element analyses of suction caissons in normally consolidated soil under the optimal condition where the caisson is constrained against any rotation. In contrast to Zdravkovic et al. (1998), Senders & Kay (22) normalised the vertical and horizontal load by the maximum vertical and maximum horizontal load, respectively and suggest the elliptical failure envelope of the form: V V ult max a H + H ult max b = 1 Equation 2.1 with a = b = 3 recommended for preliminary design of suction caissons. The interaction diagram for L/D = 2.8, showing limiting combinations of vertical and horizontal load obtained from displacement application at several angles of loading, is shown together with the suggested equation in Figure 2.9. Senders and Kay (22) also found that the optimal centreline loading point, which is the centreline intercept of the loading vector, was located at 2/3 of the caisson length below the mudline. Chapter 2 Background

41 V V ult max 3 + H H ult max 3 1 Vertical load (MN) 8 6 Probe paths Horizontal load (MN) Figure 2.9 VH failure envelope for caisson with L/D = 2.8 (Senders & Kay 22). Aubeny et al. (23) modified the previous limit equilibrium solution for lateral loading to incorporate the vertical movement of the caisson. Finite element analysis was carried out for caissons with length to diameter ratio L/D equal to 2, 6, and 1. Results were compared with their limit equilibrium solution for loads applied at the top and at mid depth of the caisson. The analyses were carried out in both uniform and linearly varying undrained strength profiles. The results for uniform strength profile are shown in Figure 2.1. The results agree well for the long caissons with L/D equal to 6 and 1; however, for the shorter caisson with L/D = 2, the discrepancy is larger especially when considering loads with a large vertical component. This observation is similar to that reported by Randolph and House (22) described earlier. Aubeny et al. (23) suggested the differences between limit equilibrium and finite element analyses for the shorter caisson may be attributed to the simplified limit analysis model where the Chapter 2 Background

42 -25- external friction is assumed to be equal to the full shear strength of soil over the entire length of caisson with no reduction to account for stress interactions occurring near the bottom of the caisson, which appear to be more important for short caissons. Clukey et al. (23) compared centrifuge tests results for caissons with L/D slightly less than 5 with the limit equilibrium solutions given by Aubeny et al. (23) for caissons with L/D = 6 and reported that the capacities measured in the centrifuge tests were slightly lower for loading angles less than 4º. For loading angle higher than 4º, both centrifuge test and upper bound analyses showed no interaction between vertical and horizontal capacity (i.e., the vertical uplift capacity controlled the response). From above discussion, a discrepancy appears in the prediction of ultimate limit state under combined VH loading of short caissons (i.e. L/D less than 2) from upper bound, limit equilibrium and finite element analyses and from experimental investigations. This topic is discussed further in this thesis. This thesis will also consider non-optimal loading, which has received little attention before. The study will explore how the padeye (or centreline intersection) depth and loading angle affects the failure mode and capacity. Chapter 2 Background

43 -26- L/D = 2 Top load Mid depth Normalised vertical load V/s u DL Top load Mid depth L/D = 6 L/D = 1 Top load Mid depth Normalised horizontal load H/s u DL Figure 2.1 Comparison of finite element and upper bound results for uniform strength profile (Aubeny et al. 23) Chapter 2 Background

44 The effect of crack on the suction caisson capacity When a suction caisson moves laterally, the stress increases on the front and reduces on the back side of the caisson. Theoretically, when the reduction in stress is higher than the original horizontal earth pressure, a gap may form. If suction can be mobilised the gap may be suppressed, depending on the extent to which suctions generated on the active side of the caisson can be maintained. When a suction caisson is subjected to inclined loading it is even more difficult to predict whether a crack would form and the consequential effect on the capacity. Randolph et al. (1998) reported centrifuge model tests of suction caissons under lateral undrained loading in normally consolidated silty clay and observed that a crack formed only at large displacements (around 36% of the caisson diameter). Following formation of a crack, the capacity rapidly dropped by about 18% of the peak value. A companion test in lightly overconsolidated soil showed crack formation immediately, with a clear vertical scarp face behind the caisson. In the upper bound limit analyses reported by Randolph and House (22), a crack is assumed to open in the upper part where the wedge failure mechanism occurs. When the rotation point lies above the caisson tip, an external scoop mechanism is formed as shown in Figure 2.11a. In contrast, an internal scoop mechanism is formed when the rotation point lies below the caisson tip (Figure 2.11b). In either case, the wedge mechanism is assumed either 1-sided (if a crack opens up) or 2-sided (with no crack). In the former case, work has to be done against the self-weight of the soil in the wedge on the passive side of the caisson. Andersen and Jostad (1999) suggested that for undrained analyses the caisson capacity should be calculated both with and without a crack, and the lowest capacity used in design. They also suggested that the padeye depth should be chosen such that small backward rotation of the caisson occurs during failure, in order to inhibit a gap forming behind the caisson. In the case where the centre of rotation for the caisson remains above the seabed surface, backward rotation may still not prevent formation of a crack throughout the caisson depth, since all points on the caisson move forward. Recent experimental studies of caissons under inclined load in normally consolidated clay (Clukey et al. 23, Coffman 24) showed no trace of cracking even at large displacements. Thus, while it appears that a crack is more likely to form in Chapter 2 Background

45 -28- overconsolidated soil, a quantitative study of the effect of cracking on caisson capacity has not been reported to date. Tension crack Wedge Tension crack Wedge Soil flow Soil flow External scoop mechanism Internal scoop mechanism (a) Rotation point above caisson tip (b) Rotation point below caisson tip Figure 2.11 Upper bound collapse mechanisms with tension crack 2.8 Summary Several methods have been used in the evaluation of suction caisson capacity i.e. limit equilibrium method, upper bound limit analyses, and finite element analyses. The accuracy of the prediction depends very much on the assessment of parameters such as N c and α. Vertical, horizontal, and combined load capacity have been investigated by several researchers as described in this chapter. The evaluation of the horizontal and vertical compression capacity might be considered well established by the geotechnical consultant whereas there is still no established method to evaluate the inclined load capacity. This research investigates the inclined load capacity through a programme of parametric study. The potential of crack to form at the active side of the caisson is also another important issue to consider in this thesis which is not yet fully investigated in the literature. In the next chapter, the analysis procedures using in the 3-dimensional finite element model adopted in this thesis to evaluate the inclined pull out capacity of suction caissons are described. The validation of appropriate element type and other analysis conditions are also discussed. Chapter 2 Background

46 -29- Chapter 3 Validation Analyses 3.1 Introduction In this chapter, finite element analysis procedures adopted throughout the research presented in this thesis are described, followed by the results from validation analyses undertaken to establish an appropriate element type and other analysis conditions. The accuracy of finite element analyses for simulation of the undrained soil response has been found to be unfavourable using customary displacement-based elements but may be improved by adopting special finite element techniques such as reduce integration or hybrid element formulations (Sukumaran et al. 1999). Experience with this project has also shown that the interaction modelling between soil and structure, such as in the present case between soil and the caisson, adds complexity to the problem and can be detrimental to the convergence of the solutions. To verify the element type for the analyses in this study, the vertical pullout of a short caisson with a length to diameter ratio L/D of 1.5 was considered. Axi-symmetric and 3-D models were used in the analyses. Pullout was achieved either by imposing a vertical upward displacement (displacement-controlled analysis) or a directly applied force (load-controlled analysis) to the top of the caisson along its central axis. The suitability of reduced integration and the hybrid element was investigated by this means. Verification of the finite element analysis for general loading conditions was undertaken by analysing the inclined loading capacity of caissons of two different geometries in two different soil profiles: normally consolidated and lightly overconsolidated. Verification was based on results from a recent study on deepwater anchor design practice sponsored by the American Petroleum Institute (API project), which considered inclined pullout of suction caisson (Andersen et al. 25). The API project was undertaken to evaluate currently available design methods in order to establish a basis for a design code for suction caissons. Predictions were carried out by several organisations including the Norwegian Geotechnical Institute (NGI), the Offshore Technology Research Centre (OTRC), and the Centre for Offshore Foundation Systems (COFS). The research presented in this thesis formed the results referred to as the COFS finite element predictions in the API project (Randolph & Supachawarote 23). Suction caissons with length to diameter ratios L/D of 1.5 and 5 in normally consolidated and Chapter 3 Validation Analyses

47 -3- lightly overconsolidated soil profiles were considered. The validity of the finite element approach adopted in the research and presented in this thesis can be assessed by comparison with results from the other predictors. The API project is introduced later and a comparison of the load response computed is made with the other API project predictors as validation of the finite element technique adopted. 3.2 Analysis description The finite element software package, ABAQUS, was used for the analyses carried out for the research presented in this thesis. The software is described by Hibbitt, Karlsson & Sorenson, Inc. (HKS 23). The package contains an extensive library of 2-D and 3-D elements and has the capability to model contact interaction i.e. separation and slip. This section describes the model details and analysis procedure adopted in this study Model geometry and soil properties A schematic representation of the suction caisson and nomenclature used in this research is presented in Figure 3.1. Each caisson is defined by its diameter D, shaft length L and wall thickness t. The caisson diameter has been taken as 5 m and the length varied to give different desired length to diameter ratios L/D = 1.5 and 5. A nominal wall thickness of 5 mm (or D/1) has been used in all cases, although as the caisson is modelled as a thin-walled rigid body the actual wall thickness has no effect on the results. The caisson is embedded with the top cap flush with the surrounding ground level. Loads are applied at an angle θ from the horizontal. The load attachment point, or padeye, is located at a depth z p along the caisson shaft and the depth to the point of intersection of the line of action of the load with the centreline of the caisson is denoted by z cl. Chapter 3 Validation Analyses

48 -31- D z cl F z p L θ t Figure 3.1 Schematic representation of suction caisson Caisson capacity and mode of failure depends on various factors such as the soil profile, the loading angle and the depth of the load attachment point (i.e. the padeye depth). The critical factor in determining whether the caisson translates without rotation (representing the optimum capacity) or rotates forwards or backwards is the centreline loading point; i.e. the point of intersection of the loading vector with the centreline of the caisson at the depth z cl. When load vector lies above a certain depth at the centreline, the caisson rotates forwards while the caisson rotates backwards when the load vector lies below that depth. The depth at the centreline where caisson translates with no rotation is defined as the optimal loading depth z cl. Two soil profiles were considered, normally consolidated and lightly overconsolidated profiles (see Figure 3.2). Details of the two caisson geometries and soil properties used in the analyses reported in this chapter are summarised in Table 3.1. Vertical pullout of case C2 was used for element type verification while inclined loading of cases C1 to C4 was used for the caisson-load response verification. Chapter 3 Validation Analyses

49 -32- z 5 m s u = 1 kpa s u = 1.25 z kpa s u = 2 z kpa (a) Normally consolidated (b) Lightly overconsolidated Figure 3.2 Undrained soil strength profiles adopted in validation analyses Table 3.1 Caisson geometry and soil properties for validation analyses (from Andersen et al. 25) CASE: C1 C2 C3 C4 Geometry Outside diameter D (m) Penetration depth L (m) Length/Diameter ratio L/D Structural model Rigid cylinder Submerged weight (kn) Soil data s u (kpa) 1.25z 1 for z < 5 m, 2z for z 5 m Interface friction ratio α.65 Vertical effective stress σ vc ' (kpa) 6z 7.2z Coefficient of earth pressure at rest K (z < 5 m) and.65 (z 5 m) In situ stress state The in situ stress state or the initial stress state was specified at the beginning of each analysis. The geostatic effective stresses in the soil were determined according to submerged unit weights, γ', of 6 kn/m 3 for the normally consolidated soil and 7.2 kn/m 3 Chapter 3 Validation Analyses

50 -33- for the lightly overconsolidated soil. The earth pressure coefficient at rest, K, was taken as uniform and equal to.55 for the normally consolidated soil, and 1 in the upper 5 m reducing to.65 below that depth for the lightly overconsolidated soil (see Table 3.1) Soil stress-strain response The undrained stress-strain response of the soil was modelled using a linear elastic perfectly plastic model, with a von Mises failure criterion. The elastic response of the soil was defined by the Young s modulus E and Poisson s ratio ν. The Young s modulus of the soil was taken proportional to the local shear strength, with E/s u = 5, and Poisson s ratio was taken as.49 to model the incompressible nature of soil. The von Mises criterion can be expressed in term of principal stresses as: (σ 1 = 6k σ2) + (σ2 σ3) + (σ3 σ1) Equation 3.1 where σ 1, σ 2, σ 3 = major, intermediate and minor principal stresses respectively k = von Mises parameter The von Mises parameter k is taken as the undrained shear strength s u. The parameter k equates to the shear strength in plane strain shearing, where the intermediate principal stress σ 2 equals the average of the major and minor principal stresses σ1 + σ = 2 3 σ2. The shear strength under triaxial conditions, where the intermediate principal stress is equal to either the major or the minor principal stress, would be.866 times the plane strain shear strength. Therefore, the von Mises model leads to an average shear strength (averaged over triaxial compression, simple shear and triaxial extension) of.91 times the von Mises parameter k Caisson-soil interface condition The shear strength at the interface between the caisson shaft and the soil is described by the interface friction ratio α. The value of α is generally assumed to lie in the range.5 to 1, and to be lower than adopted for driven piles in similar soil because of the thinwalled nature of suction caissons and their method of installation. In this study, the interface friction ratio α was assumed to be.65 for most of the analyses. This is believed to be a reasonably conservative value as discussed in Section 2.4, although will Chapter 3 Validation Analyses

51 -34- vary depending on the particular soil conditions. The main results in the thesis are presented in a normalised form where adjustments for different values of α may be made without difficulty. The default interface friction in the current version of ABAQUS (HKS 23) is based on a Coulomb friction model. The interface can carry shear stresses up to a critical value before sliding begins to occur. The critical shear stress τ c is proportional to the contact pressure p between two surfaces (τ c = μp) where μ is the coefficient of friction. The user has an option to limit the shear stress to a limiting shear stress τ max as shown in Figure 3.3. Interface shear stress τ max μ Stick region Contact pressure p Figure 3.3 Coulomb friction model adopted in ABAQUS To represent a reduced shear strength at the interface of the caisson shaft as a function of soil undrained shear strength, a thin band of soil elements (1 % of the caisson diameter) adjacent to the external cylindrical surfaces of the caisson was assigned shear strength values of.65 times the value in the remaining soil at that depth, thus reducing the interface limiting friction. For analyses where a crack was allowed to occur, an artificially high coefficient of friction μ of 1 was adopted, but with the standard ABAQUS condition of zero friction for non-compressive normal stress. The high friction coefficient ensured that, where the crack did not open, the limiting friction was dictated by the thin band of reduced strength soil elements just outside the interface. The internal soil was assumed to be fully bonded to the caisson beneath the top cap, assuming contact is maintained with the soil by means of suction. The internal interface Chapter 3 Validation Analyses

52 -35- was not assigned any strength reduction, for convenience in model preparation as it does not affect the solution in this case Mesh The finite element meshes used in the validation analyses are shown in Figure 3.4 (the soil inside the caissons has been coloured for visual clarity). A similar mesh discretisation was selected for both geometries. The mesh extends to a total width of 75 m and 15 m, and a total height of 25 m and 75 m for the short caisson (L/D = 1.5) and the long caisson (L/D = 5) respectively. The total number of degrees of freedom was approximately 26, and 23, for these two cases. Only half of the model was used with the plane of symmetry cut across the xz plane. Displacement in the y- direction was constrained along the plane of symmetry. The lateral boundary of each mesh was constrained against horizontal displacement (both x- and y- directions), while the base of the meshes was constrained against horizontal and vertical displacements (x-, y- and z- directions). Chapter 3 Validation Analyses

53 -36- C L 75 m 7.5 m 25 m (a) L/D = 1.5 C L 15 m 25 m 75 m (b) L/D = 5 z y x Figure 3.4 Finite element mesh for suction caissons model Chapter 3 Validation Analyses

54 Loading stages The analyses were carried out in 3 loading stages to facilitate obtaining a converged solution: geostatic, soil-caisson contact, and loading stages. The external boundary condition as described in section is applied to the model throughout the analyses. Stage 1: Geostatic Geostatic equilibrium is ensured in this stage i.e. the specified initial stress is established in equilibrium with the soil unit weight specified. The caisson is assumed to have no interaction with the soil and is constrained against any movement at this stage. The caisson is assumed to be wished in place. At this stage, the displacements of soil along the contact surface between caisson and soil are constrained against any movement normal to the contact surfaces as shown in Figure 3.5. Figure 3.5 Boundary condition of soil surface at the interface between soil and caisson during geostatic stage Stage 2: Caisson-soil contact The caisson and the soil surfaces constraints are released allowing contact between the caisson and the soil to be established. The contact interaction described in Section is applied to the model. The caisson weight is transferred to the soil. If the caisson unit weight is equal to the unit weight of soil, the model is in equilibrium with initial displacements and loads of zero. However, the caisson unit weight is normally higher than the soil which will cause the soil to displace. In this case, an initial displacement is recorded and the initial load is set to zero. Chapter 3 Validation Analyses

55 -38- W Contact established Figure 3.6 Schematic diagram of probe load stage Stage 3: Loading Load is applied to the caisson at the reference point by either imposing a displacement or a directly applied force to simulate the inclined pullout. When a directly applied force is imposed, the reference point of caisson rigid body is chosen to be at the location of padeye. In contrast, the reference point is assumed to be at the centre of caisson top cap in cases where displacement is imposed on the caisson (see Figure 3.7). The rotation of the caisson body could be restrained by setting the rotation degree of freedom of the reference point to zero. Reference point under applied displacement δ F Reference point under applied force Figure 3.7 Location of reference point for caisson rigid body adopted in the analyses Chapter 3 Validation Analyses

56 -39- Under displacement control, the direction of the applied displacement is defined by the ratio between the magnitude of imposed horizontal and the vertical displacement components δh/δv. The displacement is increased in increments until the incremental increase in the calculated reaction force is zero i.e. continued deformation at constant load. If a constant load is not achieved, the failure load is taken at a displacement of 2 % of the caisson diameter. Under load control, the direction of applied load is defined by the loading angle θ. The load is increased incrementally until the displacement becomes too large and the solution diverges. Failure load was then taken at a displacement of 2% of the caisson diameter by interpolation between two closest available output states obtained from automatic iteration. 3.3 Element type verification In this validation only case C2 in Table 3.1 is considered, i.e. a short caisson, with a length to diameter ratio L/D of 1.5, in a deposit with a normally consolidated strength profile. The soil undrained shear strength was assumed to increase proportionally with depth as shown in Figure 3.2a. The vertical pullout was carried out to assess the performance of various element types for future use in this thesis. Sukumaran et al. (1999) applied the finite element technique using ABAQUS to analyse suction caisson capacity and recommended the use of standard displacement elements with reduced integration to improve analysis performance for nearly incompressible material. In contrast, mixed formulation of force and displacement hybrid elements are recommended over standard displacement formulated elements for modelling the response of nearly incompressible materials by ABAQUS (HKS 23). To address this ambiguity, a comparison of the two different types of elements was carried out Programme of analyses Two different kinds of elements were trialled in both axi-symmetric and 3-D conditions: standard 1 st order elements based on a displacement formulation with reduced integration (fewer integration points being used than theoretically required) (Both CAX4R and C3D8R with 1 integration point) and 1 st order hybrid elements based on a mixed formulation of force and displacement with full integration (CAX4H with 4 integration points and C3D8H with 8 integration points). Only 1 st order or linear elements were considered, as 2 nd order or quadratic elements are not recommended for Chapter 3 Validation Analyses

57 -4- contact problems as oscillations and spikes in the contact pressure may occur (HKS 23). In all analyses, a conventional small displacement formulation was adopted, with no updating of the geometry during the analyses. Analyses were carried out using displacement control to impose an upward vertical motion on the caisson top cap. A vertical displacement was applied to the reference point of the caisson rigid body, equivalent to 2% of the caisson diameter (.2D). One load control analysis was carried out for the 3-D finite element model using hybrid elements Results of element verification The results of the element verification in terms of load-displacement curves are presented in Figure 3.8. Close agreement is observed between displacement and hybrid elements, regardless of whether the geometry was modelled as axisymmetric or as a full 3-D domain. In addition, the load-controlled analysis agrees well with the displacement-controlled analyses. The expected magnitude of the base resistance can be estimated by subtracting the theoretical shaft resistance from the total load obtained from the vertical pullout analyses using the 3-D hybrid element allowing for displacements of.5 to 1 % of the caisson diameter to mobilise the shaft resistance. The end bearing factor N c can then be calculated according to: L N c = q/s u = V u /As u, tip αsuda p /su,tip Equation 3.2 z= where; V u = pullout force at failure (taken as force at the displacement of.2d) q = average base end bearing pressure A = cross sectional area of caisson s u = soil undrained shear strength α = interface friction ratio A p = perimeter area of caisson L = caisson length D = caisson diameter Chapter 3 Validation Analyses

58 -41- In the special case where the soil undrained shear strength increases linearly with depth with zero undrained shear strength at the mudline N c = V u /As u, tip L 2α Equation 3.3 D The analyses using the displacement elements did not give a clear limiting load, while those using the hybrid elements achieved a plateau with essentially zero gradient. Previous study by Hu and Randolph (22) suggested the failure mode for relatively shallow caissons of this type in normally consolidated soil involves a full flow mechanism extending to the surface, therefore these analyses would be expected to achieve a well-defined failure load. As such, the hybrid elements were preferred and were adopted for all other analyses carried out for this research. An end bearing factor N c of 1. is obtained from the limit load at 253 kn which is comparable to a value of compression end bearing factor of 1.4 deduced from the finite element results tabulated by Hu and Randolph (22) for caissons in normally consolidated soil. 25 Vertical load (kn) D, displacement element 1 3-D, hybrid element Axi-sym, displacement element 5 Axi-sym, hybrid element 3-D, hybrid element, load control Normalised displacement, δ/d Figure 3.8 Load-displacement response for vertical pullout of short caisson in normally consolidated soil (L/D = 1.5) Chapter 3 Validation Analyses

59 Caisson Load response verification Inclined pullout analyses for all cases listed in Table 3.1 (cases C1 to C4) were carried out to validate the caisson-load response. Suction caissons with length to diameter ratios L/D of 1.5 and 5 in normally consolidated and lightly overconsolidated soil were considered. The 3-D 1 st order hybrid brick elements (C3D8H) were used to model the soil for all cases. The caisson-soil interfaces were assumed to be fully bonded i.e. no crack was allowed to form. In reality a crack might form at the back side of the caisson as discussed in more detail in Chapter 2. Analyses in which a crack is allowed to form are presented in Chapter 5. The results are referred to here as COFS finite element prediction. The results are compared with results from other predictors who participated in the API project API project summary The API project was undertaken to evaluate the variability in design methods in order to establish a basis for a design code for suction caissons. Predictions of inclined pullout capacity were carried out by several organisations including the Norwegian Geotechnical Institute (NGI), the Offshore Technology Research Centre (OTRC), and the Centre for Offshore Foundation Systems (COFS) based on the caisson geometry and soil properties described in Table 3.1. Four predictions used analytical methods such as upper bound limit analysis and limit equilibrium and three predictions used finite element analyses. Full details of the API project are available from Andersen et al. (25). A summary of methods used by each of the predictors participating in the API project is given in Table 3.2. The predictions P1 to P4 are analytical predictions based on methods presently available for suction caisson analyses. The finite element predictions were independently performed by COFS, OTRC, and NGI. Chapter 3 Validation Analyses

60 -43- Table 3.2 Summary of methods using by each predictor for inclined load capacity of suction caissons Predictor Method/Software Description P1 LEA (Fall15) Simplified limit equilbrium method based on linear strength profiles. P2 UBLA (AGSPANC) Upper bound method based on procedure described in Section P3 LEA (HVCap) Plane strain limiting equilibrium model P4 UBLA (AGSPANC) Earlier version of AGSPANC COFS (this study) 3-D FEM (ABAQUS) 1 st order hybrid brick element with full integration, von Mises criterion OTRC 3-D FEM (ABAQUS) 1 st order hybrid brick element with full integration, von Mises criterion NGI 3-D FEM (BIFURC-3-D) 2 nd order displacement brick element with reduced integration, Tresca criterion limit equilibrium analysis upper bound limit analysis Predictor P1 used a limit equilibrium analysis (Fall15). The soil was modelled by a simple rigid-plastic, undrained cohesive soil model (Tresca criterion). The lateral and end bearing capacity factors N p and N c were calculated using an empirical equation based on a parametric study using the complete upper bound failure mechanism (Murff & Hamilton 1993, Han 22). The end bearing resistance was calculated with an N c value of 6 at the mudline increasing to 1 at three diameters depth, with the shear strength taken at the tip of the caisson. The method is restricted to linear strength profiles. The calculation for cases C3 and C4 i.e. LOC cases were therefore carried out by assuming the strength profile for cases C3 and C4 as follows: Case C3: along caisson s u = z kpa; at the tip s u = (z 25) kpa Case C4: along caisson s u = z kpa; at the tip s u = (z 7.5) kpa Chapter 3 Validation Analyses

61 -44- Predictor P2 used an upper bound limit analysis (AGSPANC, Advanced Geomechanics 22). Forward and backward rotation of the caisson, any profile of soil strength, and anisotropic shear strength can be analysed from this program. An end bearing capacity factor N c of 9 was used for all the caisson geometries in this prediction. Predictor P3 used a plane 2-D limiting equilibrium model (HVCap, Andersen & Jostad 1999). The capacities of caissons with a specified load attachment point were calculated by a finite element program, BIFURC-2-D (part of HVMCap, NGI, 2). The 3-D effect in the upper part with active and passive earth pressures is modelled by side shear factors calibrated from full 3-D finite element analyses. Side shear factors of.5 between soil and structure and.6 in the soil were used in the calculations. In the deeper part, where the soil flows around the caisson, the 3-D effect was modelled by coupling between vertical shear stress and roughness found from 3-D finite element analyses. Predictor P4 used an earlier version of the program AGSPANC for all load inclination except the uplift case. To estimate the external skin friction along the caisson shaft the specified shear strength profile was used along with the specified α coefficient of.65. The reverse end bearing capacity factor N c was estimated to be 1 for long (L/D = 5) and 8 for short caissons (L/D = 1.5). This factor was used along with the simple shear strength at the tip of the caisson to determine the reverse end bearing in uplift. The soil anisotropy factor used to make the predictions for the lateral passive pressure was 8 % of the SS shear strength. For Case C1 the capacity in the interaction region was defined from the results of centrifuge model tests and a plasticity based solution calibrated to finite element results (Clukey et al. 23). Finite element analyses were carried out by COFS, NGI, and OTRC. COFS used the analyses procedure described in Section 3.2. NGI modelled the caisson as stiff elastic elements (with a shear modulus of about 5 times the elastic shear modulus of the surrounding soil). Isoparametric (16 node) zero thickness interface elements with a shear strength of.65 of the undrained SS strength were used. The Tresca yield criterion and anisotropic undrained shear strength were adopted. OTRC modelled the caisson as a solid rigid cylinder. The reduced soil strength along the skirt wall was modelled by a narrow (approximately.2 m thick) zone of elements adjacent to the caisson wall having strength equal to.65 times the undrained SS strength. The von Mises failure criterion with the von Mises parameter taken as the undrained simple shear strength was adopted. Chapter 3 Validation Analyses

62 Programme of analyses In this study (COFS finite element prediction) eight different analyses, both displacement and load-controlled, were carried out for each case as summarised in Table 3.3. Table 3.3 Programme of analyses Test Control type Details Rotation A1 Swipe: V then H A2 Reverse swipe: H then V A3 Displacement Displacement probe: δh/δv =.25 A4 Displacement probe: δh/δv = 1 A5 A6 A7 A8 Load Displacement probe: δh/δv = 4 Angle θ: 3, optimum level Angle θ: 3, loading point above optimum level (z p = 2.5 m for L/D = 1.5 and z p = 12.5 m for L/D = 5) Angle θ: 3, loading point below optimum level (z p = 6 m for L/D = 1.5 and z p = 2 m for L/D = 5) restricted permitted Displacement-controlled analyses were continued to total caisson displacement of 1 m (2 % of the caisson diameter). Rotation of the caisson was restricted in all the displacement-controlled analyses (Analyses A1-A5). Displacement-controlled swipe paths (Tan 199), with the caisson displaced to failure vertically first and then displaced horizontally (VH) as shown in Figure 3.9a, or the reverse (HV), were carried out. The displacement was applied to the reference point of the caisson located at the centre of top cap with the rotation degree of freedom of caisson rigid body fixed at zero to restricted caisson from rotation. The benefit of swipe tests for certain foundation geometries is that the complete failure envelope can be identified in a single analysis. Additionally, ultimate limit states at discrete points were identified by fixed displacement ratio probe tests as illustrated in Figure 3.9b. The displacement ratio (δh/δv) was kept constant throughout the analysis with values of.25, 1 and 4 considered. Chapter 3 Validation Analyses

63 -46- mudline δv V H δh (a) Swipe VH - applied dv, then dh, rotation constrained mudline δv δh (b) Probe constant δh δv Initial position of caisson reference point Final position of caisson reference point, rotation constrained Figure 3.9 Schematic illustration of displacement-controlled swipe and probe tests The optimal loading depth along the centreline z cl can be obtained from moment equilibrium as the caisson moves without rotation. The reference point can be shifted to a depth where the moment reaction is zero as illustrated in Figure 3.1. The optimal level in this case is the reaction moment at the caisson reference point divided by the total horizontal force. Load-controlled analyses were carried out with loading angle θ of 3 with a directly applied concentrated force at the padeye. Load was applied to the caisson reference point at the padeye located along the caisson shaft. Rotation of the caisson rigid body was restricted in analysis A6 and permitted in analyses A7 and A8. Attachment points z p of 12.5 m and 2 m for the caisson with L/D = 5 and 2.5 m and 6 m for caisson with L/D = 1.5 were chosen for comparison. Chapter 3 Validation Analyses

64 -47- C L V M H C L V H C L reference point M V H z cl = M/H Figure 3.1 The calculation of optimal level along the centreline z cl (caisson is prevented from rotation) Results of caisson load response verification analyses The results from this study (COFS FEA) are presented in this section. The reverse end bearing resistance was verified for all cases (C1 to C4 in Table 3.1). The results of inclined load resistance are then presented. Verification has been made by comparison among the predictors participating in the API project Reverse end bearing Base resistance has been estimated from the vertical pullout load obtained from the analyses using Equation 3.2 for all the cases listed in Table 3.1. The base resistance values are normalised by the soil undrained shear strength at the caisson tip and plotted against the normalised displacement as shown in Figure The normalised terminal base resistance represents the end-bearing factor (N c = q u /s u ). As expected, both short caissons (C2 and C4) achieved a terminal base resistance exhibiting an end-bearing factor, N c of 1. (C2) to 1.7 (C4), while the long caissons showed a gradually increasing base resistance, consistent with deep bearing failure, and mobilised endbearing factors of 1.1 (C1) to 1.2 (C3) at a displacement of.2d. Chapter 3 Validation Analyses

65 Case L/D Soil profile Normalised base pressure, q/su range of N c value from all predictors Case C1 Case C2 Case C3 Case C4 C1 5 C2 1.5 C3 5 C4 1.5 NC LOC Normalised displacement, δ/d Figure 3.11 Deduced mobilization of end-bearing resistance for all suction caissons The N c values obtained are reasonable when compared with the end-bearing factors observed by other researchers (Fuglsand & Steensen-Bach 1991, Clukey & Morrison 1993, Randolph & House 22, see Table 2.1) Inclined loading resistance Limiting horizontal and vertical loads, together with the corresponding loading angles, displacement directions at failure and optimal centreline loading point are given in Table The loading angle for displacement control analyses were obtained at failure. The optimal centreline loading depths are essentially independent of the loading direction, although with a slight tendency to decrease with increasing loading angle. The normalised centreline loading depth, z cl /L, gives the most useful indication of the failure mode of the caisson, and the proximity to optimal conditions. In the normally consolidated profile the optimum loading depth z cl /L is.7, while for the lightly overconsolidated profile it reduces from.68 for the long caisson to.59 for the short caisson, reflecting differences in the depth of the shear strength centroid. Chapter 3 Validation Analyses

66 -49- Table 3.4 Long caisson (L/D = 5) in normally consolidated soil (Case C1) H horizontal load component V vertical load component F resultant load θ loading angle δh/δv ratio of applied displacement z cl /L normalised centre line loading depth H (MN) V (MN) F (MN) θ (deg) δh/δv z cl /L Table 3.5 Short caisson (L/D = 1.5) in normally consolidated soil (Case C2) H (MN) V (MN) F (MN) θ (deg) δh/δv z cl /L Chapter 3 Validation Analyses

67 -5- Table 3.6 Long caisson (L/D = 5) in lightly overconsolidated soil (Case C3) H (MN) V (MN) F (MN) θ (deg) δh/δv z cl /L Table 3.7 Short caisson (L/D = 1.5) in lightly overconsolidated soil (Case C4) H (MN) V (MN) F (MN) θ (deg) δh/δv z cl /L The comparison of loading angle at failure and optimal attachment point by predictors who participated in the API project is shown in Figure The data identified by COFS 3D FE indicates the predictions carried out from this research project. It can be seen that the finite element results from all the predictors are in good agreement. The finite element results also agree well with the analytical solutions, particularly when the Chapter 3 Validation Analyses

68 -51- range of inclination angles commonly used for mooring applications ( 45 from the horizontal), although the results diverge at the higher load inclination. z cl /L z cl /L Loading angle at failure (deg) Loading angle at failure (deg) (a) Case C1 NC, L/D = 5 (b) Case C2 NC, L/D = 1.5 z cl /L z cl /L Loading angle at failure (deg) Loading angle at failure (deg) (c) Case C3 LOC, L/D = 5 (d) Case C4 LOC, L/D = 1.5 Figure 3.12 Comparison of optimal loading point from API project predictors (from Andersen et al. 25) Chapter 3 Validation Analyses

69 Failure interaction diagrams Failure interaction diagrams in horizontal-vertical loading space are shown in Figure Results are generally in an excellent agreement among predictors, with most discrepancies arising from errors in prediction of the uniaxial vertical or horizontal capacities. The difference in capacity is generally less than 3%. Results from COFS (this study) have a tendency to be more conservative than from the NGI. However, OTRC obtained 11% higher vertical capacity than COFS and NGI in case C3. (a) Case C1 NC, L/D = 5 (b) Case C2 NC, L/D = 1.5 (c) Case C3 LOC, L/D = 5 (d) Case C4 LOC, L/D = 1.5 Figure 3.13 Comparison of VH Failure interaction diagram from API project predictors (from Andersen et al. 25) Chapter 3 Validation Analyses

70 Capacity under load control Under load control, the inclined pullout capacity (and mode of failure) depends on the loading angle and the depth of the load attachment point. As noted earlier, the intersection of the loading vector with the centreline of the anchor is the most critical factor in determining whether the anchor translates without rotation (representing the optimum capacity) or rotates forwards or backwards. The load attachment point was varied above and below the optimum level while keeping the loading angle θ constant at 3º. Results from this study (COFS prediction) are tabulated in Table 3.8. Table 3.8 Summary of results from load-controlled analyses (this study, COFS prediction) (a) Forward Rotation Case Depth (m) z a /L z cl /L Capacity (MN) C C C C (b) Optimal Attachment Depth Case Depth (m) z a /L z cl /L Capacity (MN) C C C C (c) Backward Rotation Case Depth (m) z a /L z cl /L Capacity (MN) C C C C Chapter 3 Validation Analyses

71 -54- In the normally consolidated profile the optimum loading depth is.7l, while for the lightly overconsolidated profile the optimal loading depth reduces from.68l for the long caisson to.59l for the short caisson, reflecting differences in the depth of the shear strength centroid. The inclined pullout capacity is normalised by the optimal load capacity and plotted against the normalised centreline loading depth as shown in Figure 3.14 together with results from other predictors. Good agreement may be observed among predictors using finite element analysis. The calculations based on Murff & Hamilton (1993) using the fitted function for the lateral bearing capacity factor, N p (P1) also give good agreement with the finite element results, although with a tendency to overpredict capacities (underpredicting the reduction due to forward rotation of the caisson). Rigorous use of the upper bound approach for the shallow anchor in normally consolidated soil (P2) tended to underestimate the reduction in capacity for loading below the optimum point, and in the worst case gave a significant (33%) overprediction of capacity. The calculations with a plane-strain finite element model where 3D effects are taken into account by side shear factors (P3), gave capacities in reasonably good agreement with the 3D finite element capacities (within less than 1%). Chapter 3 Validation Analyses

72 -55- F/F opt F/F opt z cl /L z cl /L (a) Case C1 NC, L/D = 5 (b) Case C2 NC, L/D = 1.5 F/F opt F/F opt z cl /L z cl /L (c) Case C3 LOC, L/D = 5 (d) Case C4 LOC, L/D = 1.5 Figure 3.14 Comparison of normalised load F/F opt for caisson load above and below the optimum level from API project predictors (from Andersen et al. 25) Chapter 3 Validation Analyses

73 Summary From the validation analyses presented in this chapter, the reverse end bearing factors obtained from finite element analyses were in line with the previous study. The hybrid element was verified for use in the inclined loading analyses by comparing prediction for a selection of soil condition and caisson geometry with other finite element and analytical predictions by other researchers. These predictions form part of the API Deepstar project as introduced in Section 3.1. The element type and analysis procedures outlined in this chapter have been validated by this comparative study and are therefore adopted for the remaining research in the following chapters. The inclined load capacity of suction caisson for a wider selection of soil undrained strength condition, caisson geometry and caisson interface condition are investigated and reported. Chapter 3 Validation Analyses

74 -57- Chapter 4 Parametric Study 4.1 Introduction This chapter presents results from a parametric study of the capacity of suction caissons carried out using 3-D finite element analyses. Several parameters including caisson length to diameter ratio, location and direction of load application and interface friction ratio were studied to generalise the load response of suction caissons in normally consolidated soil under inclined loading. The analysis procedures validated in Chapter 3 are adopted in this chapter. The 1 st order, fully integrated, hybrid brick elements were used in all analyses and a series of displacement and load-controlled analyses were carried out. Displacement-controlled swipe and probe tests were used to identify the optimal caisson capacity over a range of combined vertical and horizontal loading. Results are presented in terms of the interaction diagrams between limiting vertical and limiting horizontal load (VH failure envelope). The VH failure envelopes in normalised load space were also considered to identify a general trend of the load response of the suction caissons. Load-controlled analyses were carried out to identify the sensitivity of caisson capacity to changes in load attachment position and loading angle. It was assumed that full bonding along the caisson-soil interface was maintained during loading. The influence of a crack forming along the caisson-soil interface is described in detail in Chapter 5. In this chapter, the model is described, then results of VH interaction are presented for caissons with a constant interface friction ratio of.65 and then compared with results for different interface friction ratios. The results are presented in VH and normalised VH space. An elliptical equation is fitted to the normalised VH failure envelope to describe the general trend. The impact on the inclined load capacity of variation in loading attachment point and loading angle, from the optimal condition where the caisson translates with no rotation, is then assessed. Finally, a suggested design procedure based on the analysis results is presented. Chapter 4 Parametric study

75 Model details Model geometry A schematic representation of the caisson geometry is shown in Figure 4.1 (repeated from Fig 3.2). The caissons are assumed to be wished in place. Each caisson is defined by its diameter D, shaft length L and wall thickness t. Caissons with length to diameter ratios L/D of 1.5, 3, and 5 were investigated covering a range of caisson dimensions used for practical applications. The caisson diameter was kept constant at 5 m and the length varied to give the prescribed length to diameter ratio. The caisson is assumed to be a thin-walled rigid body with a wall thickness of 5 mm (or D/1) used in all cases. The load attachment point, or padeye is located, at a depth z p along the caisson shaft and the depth to the point of intersection of the line of action of the load with the centre line of the caisson is denoted by z cl. Loads are applied to the caisson at an angle θ from the horizontal. D z cl F zp L θ t Figure 4.1 Schematic representation of suction caisson Soil undrained shear strength and in situ stress state The analyses intended to replicate the undrained response of a soft normally consolidated soil with an undrained shear strength increasing proportionally with depth, z according to s u = 1z kpa. While this strength gradient is lower than in many natural deposits, it allows easy scaling of the results to higher strength gradients. The soil Chapter 4 Parametric study

76 -59- stress-strain response was taken as elastic perfectly plastic with a von Mises failure criterion. A constant stiffness to strength ratio E/s u of 5 and Poisson s ratio of.49 were adopted. The geostatic effective stresses in the soil were determined according to submerged unit weight, γ', of 6 kn/m 3. The earth pressure coefficient at rest, K, was taken as uniform with depth and equal to Caisson-soil interface condition The validation analysis presented in chapter 3 assumed a reasonably conservative value of shaft interface friction of.65, as recommended by Andersen and Jostad (22). The sensitivity of suction caisson capacity to different values of interface friction ratio is evaluated in this chapter. The interface friction ratio was assumed to be.65 in the first series of analyses. The shaft interface friction was represented by a narrow band of soil elements with a width equal to the caisson wall thickness, on the external surface of the caisson prescribed a reduced undrained shear strength s u of.65 of the shear strength in the remaining soil at that depth to model the interface friction. The internal soil was assumed to be fully bonded to the caisson beneath the top cap and internal caisson wall, assuming contact is maintained with the soil by means of suction. Separation of soil from the caisson-soil interface was suppressed in all cases. The sensitivity of suction caisson capacity to the change in interface friction ratio was investigated by varying the interface friction ratio from.65 to.5,.8 and 1, thus covering a range for the interface friction from half the in situ undrained shear strength to the full value. 4.3 Finite element model The first order 8-node fully integrated hybrid brick elements (C3D8H) were used to model the soil. The unit weight of the caisson was assumed to be equal to that of soil to provide a geostatic equilibrium state at the beginning of the analysis. The corresponding submerged weights of the caissons used in the analyses are 4.6 kn for L/D = 1.5 and kn for L/D = 5, respectively. In reality a steel caisson would weigh up to 9 times of this value. The additional weight will enhance the available pullout capacity. The enhancement of capacity due to the actual caisson weight can be considered by simple Chapter 4 Parametric study

77 -6- superposition of the additional caisson weight to the calculated caisson capacity. The actual caisson weight does not affect the horizontal capacity under pure translation (i.e. H ult ). In between this i.e. loading angle of 3 or 45, the appropriate adjustment is discussed in the context of the interaction diagrams presented in Section The finite element mesh previously used in the validation analyses is adopted in this study for the case of L/D = 1.5 and 5 (see Figure 3.4). The finite element meshes for caissons with length to diameter ratios of 3 is shown in Figure 4.2. The soil inside the caisson is shaded for visual clarity. Only half of the model is used as symmetry exists in the plane of loading. External boundary conditions ensure horizontal displacement normal to the plane of symmetry is prevented. Horizontal displacement is constrained along the external boundary and all displacements are constrained across the base of the mesh. CL 9 m 15 m 45 m Figure 4.2 Finite element mesh for caisson with L/D = Programme of analyses Displacement-controlled swipe tests, fixed displacement ratio probe tests and analyses with directly applied loading were carried out. For each caisson geometry and interface friction ratio, ten different analyses were carried out as summarized in Table 4.1. The displacement was applied to the reference point of the caisson rigid body located at the centre of top cap with the rotation degree of freedom fixed at zero to restricted caisson Chapter 4 Parametric study

78 -61- from rotation for all displacement-controlled analyses (Analysis A1 A5) while load was applied to the reference point of the caisson rigid body located along the caisson shaft in load-controlled analyses (Analysis A6 to A8). Table 4.1 Programme of analyses No. Control type Details Rotation A1 Swipe: V then H A2 Reverse swipe: H then V A3 Displacement Displacement probe: δh/δv =.25 A4 Displacement probe: δh/δv = 1 restricted A5 Displacement probe: δh/δv = 4 A6 Angle 3 ; padeye at optimal depth A7 A8 Load Angle 3 ; padeye above optimal depth (z p /L =.333 for L/D = 1.5; z p /L =.5 for L/D = 3, 5) Angle 3 ; padeye below optimal depth (z p /L =.8) permitted A9 Angle 25 ; padeye at 3 optimal depth A1 Angle 35 ; padeye at 3 optimal depth Displacement-controlled swipe paths in vertical and horizontal load space (VH) and the reverse swipe (HV) (analysis A1 and A2) were carried out to identify the complete failure envelope in a single analysis. For the VH swipe, the caisson was first brought to failure vertically by imposing a displacement of.2d; then the caisson was displaced horizontally by a displacement of.2d with no further vertical motion allowed. For the HV (reverse) swipe, the caisson was first failed horizontally before being displaced vertically with no further horizontal motion. Additionally, ultimate limit states at discrete points on the failure envelope were identified by fixed displacement ratio probe tests, with displacement ratios (δh/δv) of.25, 1 and 4 (analysis A3 A5). Vertical and horizontal displacement was imposed simultaneously while keeping the constant displacement ratios. The schematic for swipe and probe tests was illustrated in Figure 3.6. Variation in load attachment point and loading angle is illustrated in Figure 4.3. Three load-controlled analyses were undertaken with a loading angle θ of 3 (analysis A6 Chapter 4 Parametric study

79 -62- A8), applied at the optimal depth to avoid rotation of the caisson (deduced from the displacement-controlled analyses) and at padeye depths at the caisson wall z p of.5 and.8 times the embedment for the intermediate and long caisson (L/D = 3 and 5), and.333 and.8 times the embedment for the short caisson (L/D = 1.5) (see Figure 4.3a). The effect of loading angle was also investigated by varying the loading angle from 3 to 25 and 35 (analysis A9 A1) while keeping the load attachment point at the optimal padeye depth corresponding to a loading angle of 3 from analysis A6 (see Figure 4.3b). z p θ (a) Variation in load attachment depth z p (b) Variation in loading angle θ Figure 4.3 Schematic of variation in load attachment point and loading angle 4.5 Results First, the results of the analyses of the suction caissons with a constant interface friction ratio of.65 are presented in forms of the limit loads plotted in VH load space. The results for caissons with interface friction ratio varied to.5,.8 and 1 are then presented. The general trend was found by normalising the results, which were fitted by a simple elliptical expression. Finally, the effects of the variation in load attachment point and loading angle on the inclined load capacity are quantified Limiting load capacity for combined VH loading The analysis results for suction caissons with a constant interface friction α =.65 are presented in this section. The load-displacement responses obtained from the displacement-controlled analyses (analyses A1 A5) are shown in Figure 4.4. The resultant load F was obtained from the horizontal and vertical reaction forces according Chapter 4 Parametric study

80 -63- to 2 F = V + H 2. It may be seen that steady ultimate resultant loads F are reached by a caisson displacement of 2 % of the diameter in almost all cases except for the vertical loading response of the long caissons, which show a small positive gradient due to the continuing mobilization of the deep end bearing failure. The load-displacement plotted in Figure 4.4 also show the significant increase in load capacity with increasing length to diameter ratio; for example, the ultimate horizontal capacity (H u ) increases 1 fold as L/D increases from 1.5 to 5. The apparent enhance capacity is largely due to the soil strength increasing with depth and if the comparison is made in terms of normalised ultimate horizontal capacity (H u/ldsu, av), the equivalent increase in capacity is less than 2%. The limiting horizontal and vertical loads (H and V), resultant load F, normalised resultant load F/s u,av LD, loading angle θ, ratio of applied displacement δh/δv, and normalised centre line loading depth z cl /L are summarized in Tables 4.2 for caisson with length to diameter ratio of 1.5 under optimal loading conditions in which the caisson translates with no rotation (analyses A1 A6). Limiting horizontal and vertical loads (H and V) were taken at a total displacement of 2% of the caisson diameter, which was justified by the load-displacement response shown in Figure 4.4. Loading angle θ was obtained from the limit loads at failure according to θ = tan -1 (V/H). The optimal loading depth measured along the centre line of the caisson (z cl ) was determined from moment equilibrium by dividing the reaction moment at the reference point of the rigid body representing the caisson by the corresponding horizontal reaction force (see Figure 3.7). Chapter 4 Parametric study

81 -64-2 Resultant load (kn) L/D = 1.5 Horizontal Probe, dh/dv = 4 Probe, dh/dv = 1 Probe, dh/dv =.25 Vertical Normalised displacement, δ /D Resultant load (kn) L/D = Normalised displacement, δ /D 2 Resultant load (kn) L/D = Normalised displacement, δ /D Figure 4.4 Load-displacement responses for suction caissons with L/D = 1.5, 3, and 5 (constant interface friction ratio α of.65) Chapter 4 Parametric study

82 -65- The uniaxial horizontal and vertical limit loads are shown in cases 1 and 8, respectively. The terminal points obtained from swipe and reversed swipe tests are given in cases 2 and 7, respectively. The limit loads from probe tests are shown in cases 4 6. Loadcontrolled results for caisson under load acting at 3 with no rotation are shown in case 3. Similar information for caissons with length to diameter ratios of 3 and 5 are shown in Table 4.3 and 4.4, respectively. It is observed that the maximum capacity of the shorter caisson (L/D = 1.5) is mobilised under loads with a higher vertical component, while the longer caissons (L/D = 3 and 5) exhibit maximum capacity under loads with higher lateral components. As the short caisson has a greater vertical pullout resistance than lateral resistance, the inclined pullout resistance reduces as the loading angle tends towards the horizontal. The reverse is true for the longer caissons. It is also observed that the normalised resultant load F/s u,av LD increases with loading angle for short caisson (L/D = 1.5) but reduces with loading angle for the intermediate and long caisson (L/D = 3 and 5). The optimal centre line loading depth (z cl ) is essentially independent of the loading direction, and is approximately.7l regardless of caisson length to diameter ratio. There is a slight tendency for shallower optimal loading depths as the vertical component of the loading angle increases, but for those cases the optimal loading depth becomes irrelevant as the caisson fails essentially by vertical motion. Chapter 4 Parametric study

83 -66- Table 4.2 Limit loads and optimal loading points for α =.65; L/D = 1.5. H horizontal load component V vertical load component F resultant load θ loading angle δh/δv ratio of applied displacement z cl /L normalised centre line loading depth No. H (MN) V (MN) F (MN) F/su,avLD θ (deg) δh/δv z cl/l Analysis no A6 4 A A A A A1 A2 A1 Table 4.3 Limit loads and optimal loading points for α =.65; L/D = 3 No. H (MN) V (MN) F (MN) F/s u,av LD θ (deg) δh/δv z /L cl Analysis no A6 4 A A A A A1 A2 A1 Chapter 4 Parametric study

84 -67- Table 4.4 Limit loads and optimal loading points for α =.65; L/D = 5 No. H (MN) V (MN) F (MN) F/su,avLD θ (deg) δh/δv z cl/l Analysis no. 1 A A A6 4 A A A A A1 The limit loads under uniaxial V and H may be expressed in terms of the reverse end bearing factor N c and normalised lateral bearing factor capacity N h, respectively. The reverse end bearing factor N c is the unit base resistance obtained by subtracting the theoretical shaft resistance from the ultimate uniaxial vertical load V u. The general expression to calculate N c was given in Equation 3.2. A simplified expression for the special case where the soil undrained shear strength increases proportionally with depth was given by Equation 3.3 and is repeated here in Equation 4.1. Similarly, the normalised horizontal capacity N h is the unit lateral pressure obtained by subtracting the base shear resistance from the ultimate uniaxial horizontal load H u. An expression to calculate N h is given by Equation 4.2. N c = V u /As u, tip L 2α Equation 4.1 D N h =(H u -A s u,tip )/LDs u,av. Equation 4.2 where; V u = ultimate uniaxial vertical load H u = ultimate uniaxial horizontal load L = caisson length D = caisson diameter A = cross sectional area of the caisson Chapter 4 Parametric study

85 -68- A p = perimeter area of the caisson s u,tip = soil undrained shear strength at caisson tip s u,av = average soil undrained shear strength long the length of the caisson α = interface friction ratio The reverse end bearing factor N c and normalised horizontal capacity N h for caissons with length to diameter ratio of 1.5, 3 and 5 are tabulated in Table 4.5. The reverse end bearing factor N c does not change very much with the change in the length to diameter ratio and ranges between 1.2 and By contrast, the normalised horizontal capacity increases with the increase in the length to diameter ratio. The normalised horizontal capacity is expected to converge with increasing length to diameter ratio to the limit pressure for a long cylinder moving laterally through the soil. The normalised horizontal capacity is plotted with the caisson length to diameter ratio as shown in Figure 4.5. As the length to diameter ratio increases, the rate of increase of normalised horizontal capacity reduces and is expected to reach the value representing an infinitely long pile. The limit pressure of for an infinitely long circular pile with interface friction ratio of.65 (Randolph & Houlsby 1984) is comparable to the normalised horizontal capacity of 11.1 for the caisson with length to diameter ratio of 5. Since the limit pressure given by Randolph and Houlsby (1984) is a function of the interface friction ratio, the normalised horizontal capacity is also expected to be dependent on the interface friction ratio. The effects of interface friction ratio on the reverse end bearing factor and normalised horizontal capacity are investigated in Section Table 4.5 The reverse end bearing factors and normalised horizontal capacities (α =.65) L/D N c N h Chapter 4 Parametric study

86 -69- Normalised horizontal capacity N h limit lateral pressure for long cylinder = (Randolph and Houlsby 1984) Length to diameter ratio L/D Figure 4.5 Normalised horizontal capacity for caisson with constant interface friction ratio of VH Failure envelopes Failure envelopes in vertical (V) and horizontal (H) load space are plotted in Figure 4.6. Failure envelopes from the swipe and reverse swipe analyses, load paths in the fixed displacement ratio probe tests and interpolated failure envelopes along with the failure states from the load-controlled analyses are shown. Bounding envelopes interpolated through the terminating points of the fixed displacement ratio probe tests are shown by the dashed lines. The interaction diagrams are plotted on equal V and H scales to show the variation in shape of the envelopes with caisson length to diameter ratio. Chapter 4 Parametric study

87 (a) L/D = 1.5 Swipe Reverse swipe Probe dh/dv =.25 Probe dh/dv = 1 Probe dh/dv = 4 Load control, θ = 3 o Failure envelope Displacement vector Vertical Load (kn) 4 2 (b) L/D = (c) L/D = Horizontal Load (kn) Figure 4.6 VH failure envelope for caisson with L/D = 1.5, 3, and 5 (constant interface friction ratio α of.65) Chapter 4 Parametric study

88 -71- Studies of surface footings (e.g. Gourvenec and Randolph 23) have shown that the load path from swipe analyses (based on the sideswipe tests introduced by Tan 199) tracks very close to the true failure envelopes in the VH plane, indicated by good agreement between failure envelopes predicted by fixed displacement ratio probe tests and swipe analyses. Comparison of the failure envelopes from the fixed displacement ratio analyses with those predicted by the swipe analyses in Figure 4.6 show that the swipe path cuts significantly inside the true failure envelope, with the latter identified by the fixed displacement ratio probe tests and load-controlled analysis. The principle of the swipe test is that by forcing plastic deformation in one direction, but preventing any deformation in the other direction, the path stays close to the failure envelope (in order to ensure plastic deformation occurs in the swipe direction), with elastic and plastic deformations compensating in the fixed direction. However, for embedded foundations in this study, significant plasticity occurs in the soil around the foundation at load states well below failure, so that the resulting load paths cut inside the failure envelope. The fixed displacement ratio analyses follow a load path initially at an angle governed by the elastic stiffness but with the gradient changing due to internal plastic yielding as the paths approach the failure envelope. Once this is reached, each load path travels around the failure envelope until it reaches a point where the normal to the envelope matches the prescribed displacement ratio. In Figure 4.6 incremental displacement vectors at failure are superimposed at the end of the displacement driven probe paths, confirming normality was observed in all cases. As discussed in section 4.3, the incorporation of the actual caisson selfweight could be considered in a context of interaction diagrams. The additional caisson selfweight W * might be treated as vertical load acting on the caisson and the resultant loads F could be obtained by the vector summation with the load from the mooring line F as shown in Figure 4.7a. As a result, the interaction diagram would shift in the vertical direction by the magnitude of the additional caisson selfweight as shown in Figure 4.7b. Chapter 4 Parametric study

89 -72- W * F F F W * θ F W * (a) Vector summation of selfweight and the mooring load Altered interaction diagram Vertical load W * F Original interaction diagram W * F Horizontal load (b) The altered interaction diagram incorporating the effect of caisson selfweight Figure 4.7 Vector summation of the caisson selfweight and mooring loads to account for the effect of caisson selfweight For example, the selfweights of 33 kn and 11 kn adopted in the API Deepstar project introduced in Section 3.1 for the caissons with L/D = 1.5 and L/D = 5 respectively would enhance the vertical pullout capacity by 16 % and 12 % respectively. The effect of selfweight on the inclined load capacity depends not only on the load inclination but also the caisson dimensions considered. The effect of the caisson selfweight for L/D = 1.5 and L/D = 5 is illustrated in Figure 4.8. It can be seen that when the load inclination is large, e.g. θ = 6, the caisson selfweight enhances the capacity of both short and long caissons by the corresponding magnitude in the vertical Chapter 4 Parametric study

90 -73- direction. However, at small load inclination, e.g. θ = 1, the caisson weight would not affect the capacity at all. At moderate load inclinations, e.g. θ = 3, the caisson weight would only enhance the capacity for long caissons but does not alter the capacity for short caissons. Vertical Load (kn) 2 θ = 6 Altered interaction diagram 15 Original interaction diagram 1 θ = 3 5 θ = Horizontal Load (kn) (a) Short caisson L/D = 1.5 (b) Long caisson L/D = 5 2 Vertical Load (kn) Altered interaction diagram θ = 6 θ = 3 Original interaction diagram Horizontal Load (kn) θ = 1 (b) Long caisson L/D = 5 Figure 4.8 Illustration of the effect of caisson selfweight at different loading angles for short and long caissons (L/D = 1.5 and 5). Chapter 4 Parametric study

91 Effect of variation in shaft interface friction on inclined load capacity The effect of interface friction ratio on inclined load capacity is investigated in this section. The interface friction ratio is varied from.65 to.5,.8, and 1. Fixed displacement ratio probe tests were carried out to identify a true failure envelope. The resulting envelopes are plotted in Figure 4.9 (the data markers indicate the end points of the analyses). As expected the greatest load capacity is obtained when the caisson is fully bonded to undisturbed soil (i.e. α = 1) with the caisson capacity decreasing as the shaft friction ratio reduces. The reduction of maximum horizontal load capacity is about 8-11% as the interface strength reduces from α = 1 to.5 regardless of caisson length to diameter ratio. The influence of the reduction of interface strength on the maximum vertical load capacity is greater for the longer caisson as the capacity reduces by 13% for L/D = 1.5 and reduces by 25% for L/D = 5, as the interface strength reduces from α = 1 to.5. While the size of the failure envelope is clearly affected by the interface friction ratio the shapes of the envelopes are similar. This is confirmed by re-plotting the data in terms of normalised loads, as in Figure 4.1, which leads to a unique failure envelope for each of the caisson length to diameter ratios, regardless of the value of α. Chapter 4 Parametric study

92 (a) L/D = Vertical load (kn) (b) L/D = α =.5 α =.65 α =.8 α = 1 5 (c) L/D = Horizontal load (kn) Figure 4.9 VH failure envelopes for different values of interface friction ratio α Chapter 4 Parametric study

93 (a) L/D = Normalised vertical load V/Vult (b) L/D = (c) L/D = 5 α =.5 α =.65 α =.8 α = 1 curve fit Normalised horizontal load H/H ult Figure 4.1 Normalised VH failure envelopes for different values of interface friction ratio α Chapter 4 Parametric study

94 -77- The reverse end bearing factor N c and the normalised horizontal capacity N h is again calculated from the uniaxial V and H based on Equations 4.1 and 4.2 for all the caisson geometry and interface friction ratio investigated in this Chapter. The calculation results and the limit pressure for infinitely long cylinder under lateral load given by Randolph and Houlsby (1984) are shown in the Table 4.6 and plotted in Figure The reverse end bearing N c varies in a small range between 1.14 to 1.51 while the normalised horizontal capacity increases with the caisson length to diameter ratio and interface friction ratio and appears to converge to the limit pressure given by Randolph and Houlsby (1984). Table 4.6 Reverse end bearing factor and normalised horizontal capacity obtained from uniaxial V and H load for interface friction ratio of.5,.65,.8, and 1 L/D N c N h α =.5 α =.65 α =.8 α = 1 α =.5 α =.65 α =.8 α = long cylinder Chapter 4 Parametric study

95 -78- Normalised horizontal capacity N h α =.5 α =.65 α =.8 α = Length to diameter ratio L/D Figure 4.11 The relationship between normalised horizontal capacity and length to diameter ratio Curve fit The normalised failure envelopes in VH load space shown in Figure 4.1 can be described by an elliptical function expressed as H H ult a + V V ult b = 1 Equation 4.3 The coefficients a and b for a best fit are given as functions of caisson geometry according to: a =.5 + L / D b = 4.5 L / 3D Equation 4.4 Envelopes from the curve fit (lines) are indicated on the plots in Figure 4.12 and show that very good agreement is achieved with the finite element results (discrete points). This curve fit yields a unique expression to describe the failure envelopes for caisson length to diameter ratios between 1.5 and 5. Note that the previous study by Senders and Chapter 4 Parametric study

96 -79- Kay (22) suggested that the coefficient a and b should be taken as 3 for preliminary design regardless of caisson dimension. Normalised vertical load V/V ult L/D = 1.5 L/D = 3 L/D = Normalised horizontal load H/H ult Figure 4.12 Normalised VH failure envelopes for different caisson aspect ratios (α =.65). It should be noted that the load paths predicted by the numerical analyses terminate at V > (as observed in the VH swipe result) with the plastic displacement ratio parallel to the H axis. By contrast, with the elliptical expression a plastic potential parallel with the H loading direction is only achieved when V =. However, this is unlikely to give significant errors in practice. The normalised failure envelopes for caissons of different length to diameter ratio are plotted together as shown in Figure It is observed that the failure envelope for shorter caissons lie within the failure envelope of longer caissons. Therefore, the failure envelopes for caissons with lower length to diameter ratios could be conservatively employed to represent the caissons with higher length to diameter ratios Effect of variation in load attachment point and loading direction on inclined load capacity As discussed earlier, the point of intersection of the loading vector with the centre line of the caisson or centre line loading point is the critical factor in determining whether the caisson translates without rotation (representing the optimal capacity) or rotates forwards or backwards (resulting in reduction in load capacity). Varying the load attachment point or loading direction would affect the capacity and mode of failure as Chapter 4 Parametric study

97 -8- the loading vector shifts from the optimal location. The optimal loading point was identified by displacement-controlled analyses in Section to be approximately.7l regardless of loading angle and caisson length to diameter ratio which allows the optimal padeye depth (measured along the caisson shaft) to be calculated for any given loading angle by elementary trigonometry (i.e. for a caisson with diameter D and loading angle θ, the padeye position would be at a depth of.7l -.5D tanθ). The effect of variation in load attachment point and loading direction on inclined load capacity is examined in this section according to the results from analyses A6 A1 listed in Table 4.1. Extra analyses with the load attachment point varied from the original programme were also carried out to assess the sensitivity of the inclined load capacity to the change in load attachment point. A constant interface friction ratio of.65 was adopted for all analyses. Table 4.7 shows the results for caisson length to diameter ratio of 1.5 including the padeye depth z p, loading angle θ, normalised padeye depth z p /L, normalised centre line loading depth z cl /L, resultant force F, and percentage of the resultant load to the optimal load (θ = 3 ) respectively. Case 1 presents an optimal condition for loading point at 3 in which the centre line loading depth is equal to.7l. The attachment depths are varied in Cases 2-5 (shaded) with constant loading angle of 3. Load is applied at the optimal padeye depth for loading angle of 3º (z p = 3.8 m) in Cases 6 and 7 with loading angle varied to 25º and 35º respectively. Similar presentations for caissons with length to diameter ratios of 3 and 5 are shown in Table 4.8 and 4.9, respectively. The caissons rotate forward when the centre line loading depth is less than.7l and rotate backwards when the loading depth exceeds.7l. It is also observed that the inclined load capacity reduces as the load attachment depth shift from the optimal depth while keeping the loading angle constant. However, the inclined load capacity increases in some cases with the change in loading angle (e.g. case 7 with L/D = 1.5, and case 8 with L/D = 5). The discussion on the effect of variation the load attachment depth and loading angle is continued in more detail in Sections and respectively. Chapter 4 Parametric study

98 -81- Table 4.7 Results of load-controlled analyses for α =.65; L/D = 1.5. z p z cl padeye depth centre line loading depth θ loading angle L caisson length F resultant load % opt percentage of the resultant load to the optimal load (θ = 3 ) No. z p (m) θ (deg) z p /L z cl /L F (MN) % opt. Rotation Forward Forward Backward Backward Forward Backward Table 4.8 Results of load-controlled analyses for α =.65; L/D = 3 No. z p (m) θ (deg) z p /L z cl /L F (MN) % opt. Rotation Forward Forward Forward Backward Backward Backward Backward Forward Backward Chapter 4 Parametric study

99 -82- Table 4.9 Results of load-controlled analyses for α =.65; L/D = 5 No. z p (m) θ (deg) z p /L z cl /L F (MN) % opt. Rotation Forward Forward Backward Backward Backward Backward Forward Backward Load attachment point Translation of the load attachment point above or below the optimal padeye depth can have a significant detrimental effect on load capacity of the caisson. For example, for the caisson with L/D of 3, a shift in the load attachment point by 1% of the caisson length above the optimal load attachment point leads to a 2% reduction in the capacity. Alternatively, moving the padeye 1% of the caisson length below the optimal load attachment point causes a reduction in load capacity of 35% for the short caisson (L/D = 1.5), and 25% and 15% for the intermediate and long caissons respectively (L/D = 3 and 5). The effect of the shift in the padeye below the optimal depth is more significant for the shorter caisson since the line of action of the load becomes very close to the base of the caisson. Figure 4.13 represents graphically the variation in ultimate capacity with the centre line loading depth. Capacity is expressed normalised as a percentage of the optimal value for a loading angle of 3 from the horizontal, and the load attachment point is expressed as a depth measured along the centre line of the caisson z cl (as opposed to the padeye depth measured along the shaft wall z p ). Figure 4.13 shows the optimal centreline loading depth of approximately.7l irrespective of the caisson length to diameter ratio (as indicated by the displacement-controlled analyses, see Table 4.2). For small vertical shifts in the line of action of the load, within ±.5L from the Chapter 4 Parametric study

100 -83- optimal position, only a small reduction (less than 5%) in ultimate capacity is observed. As the position of load attachment moves further from the optimal position load capacity reduces at an increasing rate following a similarly linear profile for either forward or backward rotation for the short and long caissons. Interestingly, while the reduction in capacity for the intermediate caisson (L/D = 3) follows the same trend for backward rotation as for the other caissons, for forward rotation (i.e. when the load attachment point is shallower than optimal) the caisson experiences a more rapid loss of load capacity. The change in kinematic failure mechanisms are considered in detail in Chapter 6, where they are compared with results from upper bound analyses. 1 8 Normalised capacity (% of the optimum) 6 4 L/D = 1.5 L L/D = 3 2 L/D = 5 Trend line Normalised centre line depth, z cl /L z cl 3º Figure 4.13 Effect of loading depth on caisson capacity (constant interface friction ratio α of.65) Loading direction The effect of a change in the angle of loading, applied at the optimal padeye depth for when θ = 3º, is more complex than the effect of translation of the load attachment point. While a change in the loading angle causes a shift in the line of action of the load, causing the caisson to rotate and therefore reduce its load carrying capacity, this is coupled with the effect of the interaction of the vertical and lateral load. The percentage of the resultant load to the optimal load is plotted against the loading angle as shown in Figure The results show that the capacity increases for the short caisson (L/D = 1.5) but reduces for the long caisson (L/D = 5) as the loading angle becomes more Chapter 4 Parametric study

101 -84- vertical. The results also show that the capacity increases for the long caisson (L/D = 5) but reduces for the short caisson as the loading angle becomes flatter. This is supported by the fact that the short caisson exhibits a greater vertical pull-out resistance than lateral resistance as shown previously (Tables , Figure 4.6). Conversely the long caissons mobilise a greater lateral resistance than vertical pull-out and consequently suffer a reduction in capacity as the loading angle tends towards vertical. By contrast, the intermediate caisson (L/D = 3) suffers a reduction in capacity whether the loading angle increases or decreases, as the interaction effect is not strong enough to cancel out the negative effect from caisson rotation. However, the intermediate caisson seems less sensitive to the loading angle as the capacity reduces only up to 2 % when the loading angle changes by ±5º while the capacity can reduce by up to 7 % for the long caisson (L/D = 5) when the loading angle changes within the same range. % opt * L/D=1.5 L/D=3 L/D= Loading angle (degrees) * % opt = percentage of the resultant load to the optimal load (θ = 3 ) Figure 4.14 The influence of loading angle on the capacity of suction caisson. 4.6 Summary of design equations The parametric study presented in this chapter has led to a simple design equation for the normalised VH failure envelope. This design equation is applicable for normally consolidated soil with strength increasing proportionally with depth according to s u = kz. The failure envelope is presented as an elliptical equation as: H H ult a + V V ult b = 1 In order to apply this equation, the following steps are suggested: Chapter 4 Parametric study

102 -85- Select the caisson length to diameter ratio L/D and interface friction ratio α. The exponent a and b can be obtained from the best fit found from finite element analysis as follows: a =.5 + L / D b = 4.5 L / 3D The ultimate horizontal and vertical capacity (H ult and V ult ) can then be assessed from the expressions: H ult = s u,av LD N h + (πd 2 /4)su,tip V ult = s u,tip N c (πd 2 /4) + s απdl) u,av where: LD = projected horizontal area of the caisson πd 2 /4 = cross-sectional area of suction caisson πdl = external circumference of suction caisson s u,tip = undrained shear strength at the caisson tip s = average undrained shear strength of soil along the caisson length u,av N = normalised horizontal capacity h N c = reverse end bearing factor The analysis results from this study show that the reverse end bearing ranges between 1.1 and 1.5. However, the reverse end bearing value of N c is customarily taken as 9, an appropriately conservative value given the strain-softening nature of the response as the caisson is extracted (Randolph & House, 22). Similarly the normalised horizontal capacity N h was found in this study to be ranging from 8.1 to 11.9 depending on the length to diameter ratio and interface friction ratio. Data in Table 4.6 and Figure 4.11 may be used to interpolate the normalised horizontal capacity. 4.7 Summary of findings This chapter has presented results of a parametric study and the findings are summarised as follows: Chapter 4 Parametric study

103 -86- Suction caissons show considerable increase in load carrying capacity as the length to diameter ratio of the caisson is increased. In this study a 1 fold increase in horizontal capacity was found for an increase in length from 1.5D to 5D. The increase in capacity is mainly due to the effect of the soil undrained shear strength increasing with depth. The optimal centre line loading depth z cl is largely independent of the direction of loading. In this study z cl was approximately.7l. Displacement-controlled swipe tests cut significantly inside the true failure envelopes for the caissons contrary to their accepted use for surface footings. Load capacity is strongly dependent on the external interface friction between caisson and soil. In this study limit loads were reduced by up to 25 % as the interface friction ratio reduced from α = 1 to.5. The effect of shaft friction on caisson capacity can be represented by scaling failure envelopes by the uniaxial limit loads. Failure envelopes for caissons under inclined loading for varying length to diameter ratio and interface friction are described by a simple elliptical curve fit defined by coefficients as a function of caisson length to diameter ratio. A shift of the location of padeye as little as 1 % of the caisson length can cause a reduction in capacity of up to 2 %. A change in loading angle without adjustment of the padeye location could have either a positive or a negative effect on the resultant load capacity depending on the VH interaction for any given caisson length to diameter ratio. Chapter 4 Parametric study

104 -87- Chapter 5 Effect of Crack Formation on Inclined Pullout Capacity 5.1 Introduction This chapter presents a parametric study, extending the work in Chapter 4 by considering the potential for a crack to form when suction caissons are subject to inclined pullout load, and the effect of the crack on the capacity. A series of finite element analyses were carried out to quantify the effect of a crack forming in a normally consolidated and two lightly overconsolidated soil profiles. Suction caissons with length to diameter ratios of 1.5, 3 and 5 were considered, covering typical caisson dimensions used in the field. Previous numerical and analytical studies on suction caisson capacity have usually assumed perfect interface bonding between the caisson shaft and the soil, although the interface friction has been varied (e.g. Sukumaran et al. 1999, Deng & Carter 2, McCarron & Sukumaran 2, Senders & Kay 22, Cho & Bang 22). This assumption may be adequate in normally consolidated soil according to observations made in experimental studies (see Section 2.7). However, while it appears that a crack is more likely to form in overconsolidated soil, a detailed quantitative study of the effect of a crack forming on the caisson capacity has not as yet been presented in the literature. This chapter investigates the effect of a crack on the inclined pull-out capacity of suction caissons through a series of 3-D parametric finite element analyses. Comparisons are made between cases where a crack is allowed to form and those where crack formation is suppressed. Normally consolidated and lightly overconsolidated soil profiles are considered. Results are presented as interaction diagrams under combined vertical and horizontal load. In addition load control analyses were performed to confirm the location of the optimal padeye position and the reduction in the capacity as position of the padeye is adjusted. 5.2 Model details Model geometry A schematic representation of the caisson geometry was shown in Figure 4.1. The caisson diameter D is 5 m and the length L varied to give aspect ratios, L/D of 1.5, 3, Chapter 5 Effect of crack formation on inclined pullout capacity

105 -88- and 5 respectively. A wall thickness t of 5 mm (or D/1) was used in all cases. The caisson is embedded with the top cap flush with the surrounding ground level and the load attachment (or padeye) point, at a depth z p along the caisson shaft. Under inclined load, a caisson might rotate forward, backward or translate horizontally with no rotation depending on whether the line of action of resultant force passes above, below or through the optimal loading point. The form of deformation affects the potential for a crack to form, and so the different deformation modes are discussed in detail here. Figure 5.1 illustrates the potential modes of the caisson movement and corresponding change in horizontal stress when subject to an upward inclined load. The displaced caisson is shown by the dashed outline. The soil surface is assumed to be at the same level as the caisson top cap. The optimal condition is represented by Mode 1 when the caisson translates with no rotation. When the loading point is much higher than the optimal loading point, the caisson movement is dominated by forward rotational movement (Mode 2). When the loading point is shifted to slightly above the optimal loading point, the caisson translates with some forward rotation (Mode 3). The caisson mainly translates, but with slight backward rotation, if the centreline loading point lies just below the optimal loading point (Mode 4). The caisson movement is dominated by backward rotation if the loading point lies far below the optimal loading point (Mode 5). The change in horizontal stresses, either increases or decreases, are also indicated for each mode of failure in Figure 5.1. The centre of rotation of the caisson is lying within the caisson length in Modes 2 and 5 while the centre of rotation is located below and above the caissons in Modes 3 and 4 respectively. The potential for a crack to form depends on many factors. Theoretically, when the reduction in horizontal stress is higher than the in situ effective lateral earth pressure acting on the caisson surface, a crack might form. However, if suction can be mobilised, any crack may be suppressed. The potential for a crack to form when a suction caisson is subjected to an inclined load is difficult to predict because it depends on whether negative pore pressure generated at the active side will dissipate or not. Andersen and Jostad (1999) suggested that the padeye depth should be chosen such that small backward rotation of the caisson occurs during failure, in order to inhibit a crack forming behind the caisson. However, there is a possibility that a crack could form at the back of the caisson even with backward rotation, as illustrated in Figure 5.1 (Mode Chapter 5 Effect of crack formation on inclined pullout capacity

106 -89-4) if the negative change in horizontal stress exceeds the in situ effective lateral earth pressure. As indicated in Figure 5.1, the crack might form up to the full length of the caisson in Modes 3 and 4. However, as the change in horizontal stresses in Modes 2 and 5 as shown in Figure 5.1 that the negative change of horizontal stress cover the whole length of the caisson. However, the maximum crack depth for Modes 2 and 5 is limited to the depth of the centre of rotation of the caisson as the change in horizontal stress become positive. Chapter 5 Effect of crack formation on inclined pullout capacity

107 -9- Δσ h +Δσ h Δσ h +Δσ h Mode 1: Optimal loading Δσ h +Δσ h Δσ h +Δσ h +Δσ h Δσ h Δσ h +Δσ h Mode 2: Forward rotation Mode 4: Backward rotation and translation Δσ h +Δσ h +Δσ h Δσ h Δσ h +Δσ h Δσ h +Δσ h Mode 3: Forward rotation and translation Mode 5: Backward rotation Figure 5.1 Potential caisson movements and the corresponding change in horizontal stress Chapter 5 Effect of crack formation on inclined pullout capacity

108 Soil undrained shear strength and in situ stress state Finite element analyses were carried out for suction caissons in a typical normally consolidated (NC) and two lightly overconsolidated (LOC1 and LOC2) soil profiles as shown in Figure 5.2. Mudline level NC s u = 1.5z kpa K =.55 σ v = 6z (kpa) LOC1 s u = max(1, 2.z) kpa K = 1. (z < 5) =.65 (z 5) σ v = 7.2z (kpa) LOC2 s u = z kpa K =.65 σ v = 7.2z (kpa) Figure 5.2 Soil profiles adopted in the analyses The normally consolidated soil is assumed to have undrained shear strength s u equal to zero at the mudline, increasing linearly with depth z at a rate of 1.5 kpa/m. The strength gradient of 1 kpa/m was used in Chapter 4 to represent a soil profile with strength increasing proportionally with depth, which allowed easy scaling of the results to higher strength gradients. However, in the modelling of crack formation in this chapter, the key dimensionless group is the strength ratios s u /γ z (or k/γ' for normally consolidated conditions), since stress changes are a function of the shear strength, s u, while the in situ effective horizontal stress is given by K γ'z. If a crack does form the failure mechanism may change from two-sided to one-sided, although in the latter case additional work must then be done against the weight of soil in the (upward moving) wedge on the passive side of the caisson (Murff & Hamilton 1993). The change in mechanism following crack formation is expected to affect the inclined pullout capacity of the suction caisson significantly. In this study, a more realistic strength gradient of 1.5 was therefore adopted for the normally consolidated soil profile (NC). The first lightly Chapter 5 Effect of crack formation on inclined pullout capacity

109 -92- overconsolidated soil profile (LOC1) was assumed to have an undrained shear strength of 1 kpa down to 5 m depth, increasing linearly with depth below that level at a rate of 2 kpa/m. The second overconsolidated profile (LOC2) was assumed to have the undrained shear strength equal to 1 kpa at the surface and increasing linearly with depth at a rate of 1.5 kpa/m. The soil parameters including soil undrained shear strength, coefficient of earth pressure at rest K, and initial effective vertical stress σ v are also given in Figure 5.2. The geostatic effective stresses in the soil were determined according to submerged unit weights, γ of 6 or 7.2 kn/m 3. A constant stiffness to strength ratio E/s u of 5 and Poisson s ratio of.49 were adopted. Soil response was taken as elastic perfectly plastic using a von Mises failure criterion as described in Section Caisson-soil interface condition The interface friction αs u between the external caisson wall and soil was assumed to be.65 times the intact shear strength of soil at that depth. A thin band of elements just outside the interface with a strength of.65 times that of the soil mass at the equivalent depth was introduced, as for the previous analyses where no crack was considered (Section 4.2.3). The potential for a crack to form on the active side of the caisson was investigated by introducing a contact surface between the caisson and the soil. The contact surface was assigned Mohr-Coulomb properties with an artificially high friction coefficient of 1 (see Section 3.2.4), but with the standard ABAQUS condition of zero friction for non-compressive normal stress. The high friction coefficient ensured that, where a crack did not open, the limiting friction was dictated by the thin band of reduced strength soil elements just outside the interface. It should be noted that the analyses were still total stress analyses, with no attempt to deduce pore pressure and effective stress changes. Thus, the contact surface would open, ensuring zero frictional transfer or further normal stress transfer, once the total normal stress reduced to zero (from an initial value equal to the geostatic effective horizontal stress at that level). 5.3 Finite element model First order 8-noded fully integrated hybrid brick elements (C3D8H) were used to model the soil. The unit weight of the caisson was assumed to be equal to that of the soil to provide geostatic equilibrium at the beginning of the analysis. The finite element meshes for the caissons with length to diameter ratios of 1.5, 3, and 5 were identical to Chapter 5 Effect of crack formation on inclined pullout capacity

110 -93- those shown previously in Chapters 3 and 4, and as used for the parametric study in Chapter 4. Identical boundary conditions were adopted as previous so that the only significant difference in the analyses was the introduction of the contact surface around the shaft of the caisson. 5.4 Programme of analyses For each caisson geometry considered five different standard analyses were undertaken, using displacement control with the caisson rotation prevented, as summarized in Table 5.1. Displacement-controlled swipe paths (Tan, 199), with the caisson brought to failure vertically first and then displaced horizontally at constant embedment (VH), or the reverse (HV) (Analyses A1 and A2), were undertaken. The analysis results from Chapter 4 showed that the swipe paths track inside the failure envelope, and thus are of limited use in defining it, but they are provided here for information. Ultimate limit states for combined VH loads were identified at discrete points on the failure envelope by fixed displacement ratio probes δh/δv of.25, 1 and 4 (Analyses A3-A5). The displacement was applied to the reference point of the caisson rigid body located at the centre of top cap with the rotation degree of freedom fixed at zero to restricted caisson from rotation. Additional analyses with different displacement ratios were carried out in some cases to enable better definition of the failure envelope. Table 5.1 Programme of displacement-controlled analyses (rotation prevented) No. Details A1 Swipe: V then H A2 Reverse swipe: H then V A3 Displacement probe: δh/δv =.25 A4 Displacement probe: δh/δv = 1 A5 Displacement probe: δh/δv = Results First, the VH failure envelopes are presented for all caisson dimensions and soil profiles. The results show a comparison between the cases where a crack is allowed to form and where the crack is suppressed. Normalised failure envelopes are then presented to show the general trends. Finally, the optimal padeye depths obtained from the analyses are presented. Chapter 5 Effect of crack formation on inclined pullout capacity

111 Limiting load capacity for combined VH loading Failure envelopes in vertical (V) and horizontal (H) load space for the caisson aspect ratios L/D = 1.5, 3, and 5 are shown for each of the soil profiles in Figures The envelopes derived when no crack is allowed to form are also shown for comparison (taken from Section 4.5.1). A continuous bounding failure envelope inferred from the fixed ratio displacement probes is indicated in each of the plots by dashed lines. The fixed displacement ratio analyses follow a load path initially at an angle governed by the elastic stiffnesses but with the gradient changing due to internal plastic yielding as the paths approach the failure envelope. Once this is reached, each load path travels around the failure envelope until it reaches a point where the normal to the envelope matches the prescribed displacement ratio. The displacement increment vectors shown at the end of each displacement probes seem to satisfy the normality condition quite well in most cases, although slight deviation occurs in the cases where a crack forms, particularly at high ratios of H/V. The swipe paths cut inside the true failure envelopes as commented in Chapter 4 due to significant plasticity occurring in the soil around the foundation at load states well below failure. The swipe paths end up on the failure envelope when no crack is allowed but can terminate inside the envelope when a crack is allowed (reverse swipe, H followed by V only). Note that the end-points of the swipe (and reverse swipe) paths indicate load combinations where purely horizontal or vertical motion of the caisson occurs, and thus the displacement increment vector is parallel to the vertical or horizontal load axis. The reason that the reverse swipe paths can end up inside the failure envelope defined by other loading paths (where a crack is allowed to form) is because in the reverse swipe paths a crack is formed first during failure under horizontal displacement, and remains open during the subsequent vertical displacement. However, other loading paths at high δv/δh do not cause a crack to form, and thus lead to higher capacity. The load-path dependence of crack formation is an important consideration in design. The VH failure envelopes from different soil profiles are plotted in Figure 5.12 to In normally consolidated (NC) soil, the failure envelopes are virtually the same for the short caisson with L/D = 1.5 whether a crack is allowed to form or not. Capacity is reduced for longer caissons (e.g. horizontal capacity reduces by up to 11 % for L/D = 5, see Table 5.2). This suggests that no crack would form for short caissons in normally consolidated soil but the potential for a crack to form increases with higher caisson Chapter 5 Effect of crack formation on inclined pullout capacity

112 -95- length to diameter ratio L/D. The potential for crack formation also depends on the ratio s u /γ z. An initial study adopted a smaller s u /γ z (2/3 of the value used in this study) and no crack formed for any of the caisson dimensions considered, but effects become more pronounced with a higher s u /γ z. In the lightly overconsolidated soils, a significant effect of the crack on the load capacity has been observed. The reduction in the ultimate horizontal capacity observed in the two lightly overconsolidated soil profiles is between 14 % and 27 % (see Table 5.2). The reduction in capacity generally reduced as the L/D increases. Table 5.2 The reduction of the ultimate horizontal capacity when the crack is allowed to form in different soil profiles and caisson length to diameter ratios. L/D % Reduction in the ultimate horizontal capacity NC LOC1 LOC From a design perspective it may be appropriate to make a conservative assumption by contracting the yield envelopes for all V, H combinations by the ratio H ult,crack /H ult,fully bonded. An example of the contracting yield envelope for L/D = 3 in lightly overconsolidated soil (LOC1) along with the original failure envelopes is shown in Figure This assumption is conservative for condition of high V/H. In this case, it is interestingly to note that the envelope coincides with the end point of the reverse swipe at high V/H. The change in kinematic mechanisms accompanying failure of suction caissons, with and without crack formation, are considered in detail in Chapter 6, where they are compared with results from upper bound analyses. Chapter 5 Effect of crack formation on inclined pullout capacity

113 -96-3 Vertical Load (kn) Horizontal Load (kn) (a) fully bonded Incremental displacement vector at failure Swipe Reverse swipe Probe dh/dv =.25 Probe dh/dv = 1 Probe dh/dv = 4 Envelope Vertical Load (kn) Swipe Reverse swipe Probe dh/dv =.25 Probe dh/dv = 1 Probe dh/dv = 4 Envelope No crack envelope Horizontal Load (kn) (b) crack allowed Figure 5.3 VH failure envelope for L/D = 1.5 (NC) Chapter 5 Effect of crack formation on inclined pullout capacity

114 Vertical Load (kn) Swipe Reverse swipe Probe dh/dv =.25 Probe dh/dv = 1 Probe dh/dv = 4 Envelope Horizontal Load (kn) 5 (a) fully bonded Vertical Load (kn) Swipe Reverse swipe Probe dh/dv =.25 Probe dh/dv = Horizontal Load (kn) Probe dh/dv = 4 (b) crack allowed Figure 5.4 VH failure envelope for L/D = 1.5 (LOC1) Chapter 5 Effect of crack formation on inclined pullout capacity

115 -98-6 Vertical load (kn) Swipe Reverse swipe Probe dh/dv =.25 Probe dh/dv = 1 Probe dh/dv = 4 Envelope Horizontal Load (kn) (a) fully bonded 6 Vertical load (kn) Horizontal Load (kn) (b) crack allowed Swipe Reverse swipe Probe dh/dv =.25 Probe dh/dv = 1 Probe dh/dv = 4 Probe dh/dv =.1 Probe dh/dv =.5 Probe dh/dv =.125 Envelope No crack envelope Figure 5.5 VH failure envelope for L/D = 1.5 (LOC2) Chapter 5 Effect of crack formation on inclined pullout capacity

116 Vertical Load (kn) Swipe Reverse swipe Probe dh/dv =.25 Probe dh/dv = 1 Probe dh/dv = 4 Envelope Horizontal Load (kn) (a) fully bonded 1 Vertical Load (kn) Horizontal Load (kn) (b) crack allowed Swipe Reverse swipe Probe dh/dv =.25 Probe dh/dv = 1 Probe dh/dv = 4 Envelope No crack envelope Figure 5.6 VH failure envelope for L/D = 3 (NC) Chapter 5 Effect of crack formation on inclined pullout capacity

117 -1-15 Vertical Load (kn) Horizontal Load (kn) (a) fully bonded 15 Swipe Reverse swipe Probe dh/dv =.25 Probe dh/dv = 1 Probe dh/dv = 4 Envelope Vertical Load (kn) Horizontal Load (kn) (b) crack allowed Swipe Reverse swipe Probe dh/dv =.25 Probe dh/dv = 1 Probe dh/dv = 4 Probe dh/dv =.1 Probe dh/dv =.5 Probe dh/dv =.125 Envelope No crack envelope Figure 5.7 VH failure envelope for L/D = 3 (LOC1) Chapter 5 Effect of crack formation on inclined pullout capacity

118 Vertical load (kn) Swipe Reverse swipe Probe dh/dv =.25 Probe dh/dv = 1 Probe dh/dv = 4 Envelope Horizontal Load (kn) (a) fully bonded 15 Vertical Load (kn) Swipe Reverse swipe Probe dh/dv =.25 Probe dh/dv = 1 Probe dh/dv = 4 Probe dh/dv =.1 Probe dh/dv =.5 Probe dh/dv =.125 Envelope No crack envelope Horizontal Load (kn) (b) crack allowed Figure 5.8 VH failure envelope for L/D = 3 (LOC2) Chapter 5 Effect of crack formation on inclined pullout capacity

119 -12-3 Vertical Load (kn) Swipe Reverse swipe Probe dh/dv =.25 Probe dh/dv = 1 Probe dh/dv = 4 Envelope Horizontal Load (kn) (a) fully bonded 3 Vertical Load (kn) Swipe Reverse swipe Probe dh/dv =.5 Probe dh/dv =.25 Probe dh/dv = 1 Probe dh/dv = 4 Envelope No crack envelope Horizontal Load (kn) (b) crack allowed Figure 5.9 VH failure envelope for L/D = 5 (NC) Chapter 5 Effect of crack formation on inclined pullout capacity

120 Vertical Load (kn) Swipe Reverse swipe Probe dh/dv =.25 Probe dh/dv = 1 Probe dh/dv = 4 Envelope Horizontal Load (kn) 4 (a) fully bonded Vertical Load (kn) Horizontal Load (kn) (b) crack allowed Swipe Reverse swipe Probe dh/dv =.1 Probe dh/dv =.5 Probe dh/dv =.125 Probe dh/dv =.25 Probe dh/dv = 1 Probe dh/dv = 4 Envelope No crack envelope Figure 5.1 VH failure envelope for L/D = 5 (LOC1) Chapter 5 Effect of crack formation on inclined pullout capacity

121 -14-4 Vertical Load (kn) Swipe Reverse swipe Probe dh/dv =.25 Probe dh/dv = 1 Probe dh/dv = 4 Envelope Horizontal Load (kn) (a) fully bonded 4 Vertical Load (kn) Horizontal Load (kn) (b) crack allowed Swipe Reverse swipe Probe dh/dv =.1 Probe dh/dv =.5 Probe dh/dv =.125 Probe dh/dv =.25 Probe dh/dv = 1 Probe dh/dv = 4 Envelope No crack envelope Figure 5.11 VH failure envelope for L/D = 5 (LOC2) Chapter 5 Effect of crack formation on inclined pullout capacity

122 -15- Vertical Load (kn) NC (fully bonded) LOC1 (fully bonded) LOC2 (fully bonded) NC (crack allowed) LOC1 (crack allowed) LOC2 (crack allowed) Horizontal Load (kn) Figure 5.12 Comparison of VH failure envelopes from various soil profiles, L/D = 1.5 Vertical Load (kn) NC (fully bonded) LOC1 (fully bonded) LOC2 (fully bonded) NC (crack allowed) LOC1 (crack allowed) LOC2 (crack allowed) Horizontal Load (kn) Figure 5.13 Comparison of VH failure envelopes from various soil profiles, L/D = 3 Chapter 5 The effect of crack on inclined loading capacity

123 -16- Vertical Load (kn) NC (fully bonded) LOC1 (fully bonded) LOC2 (fully bonded) NC (crack allowed) LOC1 (crack allowed) LOC2 (crack allowed) Horizontal Load (kn) Figure 5.14 Comparison of VH failure envelopes from various soil profiles, L/D = 5 15 Vertical Load (kn) 1 5 Failure envelope (crack allowed) Contracted envelope Reverse swipe Failure envelope (fully bonded ) Horizontal Load (kn) Figure 5.15 Comparison of contracted yield envelope to the original failure envelopes for L/D = 3, LOC1 Chapter 5 The effect of crack on inclined loading capacity

124 Normalised pullout capacity Normalised VH failure envelopes, with H and V divided by the maximum values for uniaxial loading (pure V or pure H), are shown in Figures for all soil profiles considered. When the crack was not allowed to form, longer caissons give higher normalised capacity. The general trend of the normalised capacity when the crack is not allowed to form was discussed in Section and a general expression was presented. When the crack is allowed to form, the normalised capacity reduces significantly, especially in lightly overconsolidated soil. Interestingly, for each soil profile the normalised failure envelopes when a crack is allowed to form lie very close to each other regardless of the caisson length to diameter ratio. For the normally consolidated soil (NC), the normalised envelopes when the crack is allowed to form track very close to the normalised envelope for short caisson with no cracking. For the lightly overconsolidated soil (LOC1 and LOC2), the normalised envelopes when the crack is allowed to form lie inside the enveloped when no crack forms. When the degree of the interaction is high i.e., at the normalised horizontal load H/H ult =.7, the normalised vertical load V/V ult when crack is allowed is approximately 11% and 14% lower than that of short caissons with no cracking for LOC1 and LOC2 respectively. 1.8 V/Vult L/D = 1.5 (fully bonded) L/D = 3 (fully bonded) L/D = 5 (fully bonded) L/D = 1.5 (crack allowed) L/D = 3 (crack allowed) L/D = 5 (crack allowed) H/H ult Figure 5.16 Normalised VH interaction diagram for NC soil profile Chapter 5 The effect of crack on inclined loading capacity

125 V/Vult L/D = 1.5 (fully bonded) L/D = 3 (fully bonded) L/D = 5 (fully bonded) L/D = 1.5 (crack allowed) L/D = 3 (crack allowed) L/D = 5 (crack allowed) H/H ult Figure 5.17 Normalised VH interaction diagram for LOC1 soil profile 1.8 V/Vult L/D = 1.5 (fully bonded) L/D = 3 (fully bonded) L/D = 5 (fully bonded) L/D = 1.5 (crack allowed) L/D = 3 (crack allowed) L/D = 5 (crack allowed) H/H ult Figure 5.18 Normalised VH interaction diagram for LOC2 soil profile Chapter 5 The effect of crack on inclined loading capacity

126 Optimal loading point The study presented in Chapter 4 concluded that the optimal centre line loading depth z cl when no crack is allowed to form is virtually the same for any loading angle and caisson geometry, with a value of approximately.7l in normally consolidated soil. The optimal loading depths derived from the results of the displacement-controlled analyses where a crack is allowed, using moment equilibrium as described in Section (Figure 3.1), are summarised in Tables 5.3 and 5.4. The normalised optimum loading depth is given for all caisson dimensions and soil profiles considered in this study at displacement ratios δh/δv =.25, 1, 4, and (pure horizontal translation). The calculated optimal loading depths range from.58l to.72l. The optimal loading depth in normally consolidated soil when a crack is allowed to form is similar, at around.7l, to the previous study where the caisson-soil interface is fully bonded. For lightly overconsolidated soil, the optimal loading depth shifts upwards compared to the normally consolidated (NC) case, both for the fully bonded and crack allowed cases. This effect is particularly noticeable for the shorter caissons where the centroid of the shear strength profile is higher as the soil strength is more uniform. The optimal loading depth is also deeper when a crack is allowed to form compared to the fully bonded case. Table 5.3 Optimal loading depth obtained from displacement control analyses (fully bonded) z cl /L Soil Profile L/D δh/δv =.25 δh/δv = 1 δh/δv = 4 δh/δv = NC LOC LOC Chapter 5 The effect of crack on inclined loading capacity

127 -11- Table 5.4 Optimal loading points obtained from displacement control analyses (crack allowed) z cl /L Soil Profile L/D δh/δv =.25 δh/δv = 1 δh/δv = 4 δh/δv = NC LOC LOC The effect of the variation in load attachment point on inclined load capacity Previous section showed the reduction in caisson capacity if a crack forms and reveals that the optimal loading point is lower when a crack is allowed to form. Andersen and Jostad (1999) suggest that the padeye depth should be chosen such that small backward rotation of the caisson occurs during failure, in order to inhibit a crack forming behind the caisson. As shown in Tables 5.3 and 5.4, the optimal loading depth when a crack is allowed to form is generally higher than when the caisson-soil interface is assumed to be fully bonded. In order to generate backward rotation sufficient to suppress a crack (Mode 5 in Figure 5.1), the padeye needs to be placed much lower than the optimal padeye depth recommended for the case with no crack. It should also be considered that by lowering the padeye depth, a crack might still form (with a Mode 4 or 5 failure mechanism as shown in Figure 5.1). In order to illustrate the effect of crack forming on the capacity as discussed here, a hypothetical case study is considered for the caisson length to diameter ration L/D = 3 in the lightly overconsolidated soil (LOC1). Finite element load control analyses were carried out varying the padeye depth while maintaining a constant loading angle of 3. Chapter 5 The effect of crack on inclined loading capacity

128 Results The results from the finite element load control analyses are shown in Table 5.5. The padeye depth, centreline loading depth, resultant loads, and mode of failure obtained from the analyses are presented. The resultant loads were generally taken at the padeye displacement of 2 % of the caisson diameter (.2D). However, in the case where the analyses fail to converge before the displacement of.2d is reached, the limit load is taken at the last increment of the analyses. The analyses were carried in both when the caisson-soil is fully bonded and when crack is allowed to form. Table 5.5 Resultant load varying the padeye depth for L/D = 3, θ = 3 (a) fully bonded z p (m) z cl /L F (kn) Rotation Mode of failure * Forward Forward Backward Backward Backward 5 (b) crack allowed z p (m) z cl /L F (kn) Rotation Mode of failure * Forward Forward Forward Backward Backward Backward 5 * see Figure 5.1 When cracking is permitted, a crack does form in each case. Capacity is consistently lower, for a given normalised centreline loading depth, when a crack is presented Chapter 5 The effect of crack on inclined loading capacity

129 -112- compared to the fully bonded case, and the optimal loading point is deeper for the cracked case. As expected, caisson rotates forward when the centreline loading point is higher than the optimal loading point and rotate backward when the loading point is lower than the optimal loading point (as obtained from the displacement control analysis). The resultant loads are plotted against the centreline loading point in Figure Locating the padeye so that the caisson rotates backward as suggested by Andersen and Jostad (1999), is accompanied by a decrease in capacity from the optimal case where the caisson translates with no rotation as the crack is still formed. Failure mode 4 (Figure 5.1) in which the centre of rotation is below the caisson tip is observed even at the distance of.22l lower than the optimal loading point (z p = 1 m). In order for the caisson to rotate backward enough to generate mode 5 failure as in Figure 5.1, the centreline loading point has to be located much lower, z cl =.896 as in Table 5.5b. Although a crack does not form in the active zone near the mudline, a crack has been shown to form at depth as the caisson displacement is relatively large and suction pressures are unable to suppress the crack. Resultant load (kn) Foreward rotation Backward rotation fully bonded crack allowed Optimal loading 3 Failure modes depth 5 (see Figure 5.1) z cl /L Figure 5.19 The effect of the variation in load attachment point for caisson length to diameter ratio L/D = 3 in lightly overconsolidated soil (LOC1) The results from the load-controlled finite element analyses also show that the capacity is relatively insensitive to the change in the padeye point when the centreline loading point is located around the optimal loading depth e.g. changing the z cl from.663l to Chapter 5 The effect of crack on inclined loading capacity

130 L when a crack is allowed to form would only change in capacity of only.5%. In order to optimise the capacity, it is recommended to place the padeye so that the centreline loading point is located between the optimal loading point for fully bonded conditions and with a crack forms. In this case, the caisson would rotate slightly backward before a crack would form but rotate slightly forward after crack has formed. By placing the padeye outside this range, the capacity in either cases (fully bonded or with a crack) would decrease more from the optimal capacity e.g. when z cl is.763l the capacity reduces by 6.5% and 8% from the optimal condition when the crack formed and when the caisson-soil interface is fully bonded respectively. 5.7 Conclusions The following conclusions can be drawn from the finite element results: In normally consolidated soil, a crack did not form along the side of the short caisson (L/D = 1.5) under any combination of VH loading. The potential for crack formation increased with caisson length and with higher strength ratios s u /γ z. The effect of a crack on the inclined pullout capacity of caissons in normally consolidated soil is relatively low (up to 11%). In lightly overconsolidated soils the reduction in load capacity is up to 27%. Vertical capacity is only marginally affected by crack formation while the horizontal capacity is considerably affected. The finite element results showed that the crack does not form when the vertical component of load is large. The contracted envelope discussed in Section is suggested for design unless specific measures are incorporated to prevent crack formation. The optimal centreline loading depth varies slightly with the loading angle for different soil properties, reducing from around.7l in normally consolidated soil to around.6l for short caissons in lightly overconsolidated soil, where the strength variation over the length of the caisson is small. In general, unless specific design considerations dictate otherwise, it is recommended to place the padeye so that the centreline loading point, for the extreme loading case, is located between the optimal loading point for the fully bonded conditions and that with a crack allowed. This will closely optimise the capacity, and tend to give slightly backward rotation initially, thus helping to avoid formation of the crack. Chapter 5 The effect of crack on inclined loading capacity

131 -114- Chapter 6 Upper Bound Limit Analyses of Suction Caissons 6.1 Introduction This chapter presents a study based on upper bound limit analysis of suction caissons in clay. The analyses were carried out using AGSPANC (Advanced Geomechanics 21). The accuracy of the upper bound analyses in predicting the optimal capacities (i.e. with no caisson rotation) was validated by comparing the upper bound results with the previous finite element results presented in Chapters 4 and 5. Ultimate limit states of suction caissons with dimensions L/D = 1.5, 3, and 5 in normally consolidated and lightly overconsolidated soil were compared. Both cases where the caisson and soil is fully bonded and where a crack is allowed to form down the active side of the caisson were considered. Comparison of the VH failure envelopes, resultant loads at failure and failure mechanisms between two methods are presented. Similar comparisons between upper bound and finite element results for non-optimal capacity, varying the padeye position along the caisson shaft, are also presented. In this chapter, the upper bound method is first described. Results of the comparison between the upper bound analyses and the previous finite element results are then presented. Both the magnitude of capacity and the failure mechanisms are investigated. 6.2 Summary of upper bound limit analyses Upper bound solutions for suction caissons were introduced by Randolph et al. (1998) and subsequently incorporated into AGSPANC (Advanced Geomechanics 21) which is used throughout this chapter. The development of the upper bound method was summarised in Section This section summarises the procedures and assumptions adopted in the upper bound limit analyses reported in this chapter. The failure mechanisms proposed by Randolph et al. (1998) (as shown in Figure 2.4) comprise three main regions: a conical wedge region at shallow depth, a flow around region below the wedge region, and a rotational flow region around the bottom of the caisson, which generally forms a spherical shape with its centre on the caisson axis. The adoption of the flow around region removes the rigour of the upper bound solution since it overlooks interaction between the top and the bottom of the flow around region and the adjacent soil and hence the solutions obtained could be lower than the true upper bound (Advanced Geomechanics 21). By forcing the wedge to extend to the bottom of the caisson or forcing the rotational flow region to extend to the wedge Chapter 6 Upper bound limit analyses of suction caissons

132 -115- region, a rigorous solution can be obtained (although not necessarily the minimum upper bound solution). In the simulation of a crack forming along the active side of the caisson, the same failure mechanism is assumed but with the wedge in the conical wedge region restricted to the front half of the caisson. The crack is always assumed to propagate from the surface to the bottom of the wedge region and is therefore always in the upper part where the wedge failure mechanism governs. Unlike, the case where the caisson-soil interface is fully-bonded, the potential energy change due to vertical movement of the soil in the wedge region does not cancel out and therefore needs to be considered. A schematic representation of the notations used to describe the failure mechanism assumed in the upper bound analyses is presented in Figure 6.1. The conical wedge is assumed to have a radius R at the mudline, extending vertically down to the depth z o where the radius reduces to the caisson radius r o. The centre of rotation of the caisson is assumed to be at a depth h along the centreline of the suction caisson. The horizontal velocity of the caisson at the centreline loading depth D* (previously referred to as z cl ) is denoted v o. The horizontal velocity of the caisson at depth z from the mudline may then be written as: h z v h = v o Equation 6.1 h D * The vertical velocity of the caisson v v is assumed to be proportional to the horizontal velocity of the caisson at the centreline loading depth v o given by: v v = - βv o Equation 6.2 where β is the optimisation parameter representing the component of vertical velocity (β ). Chapter 6 Upper bound limit analyses of suction caissons

133 -116- r o R D L D * θ F z o h Centre of rotation Figure 6.1 Schematic representation showing the notations used to describe the failure mechanism assumed in the upper bound analyses. The external work done by the anchor chain may be written as: W = Fv o cosθ + Fv v sin θ = Fv o (cos θ + βsin θ) Equation 6.3 The external work done by the anchor chain equates to the sum of internal plastic work and potential energy dissipated in each of the following failure mechanisms: Plastic work dissipated within the conical soil wedge Interface shearing on the conical wedge Interface shearing on the caisson-soil contact Caisson tip rotational failure (scoop mechanism) Flow mechanism below the wedge failure Work against gravity (1-sided failure only). The total energy dissipation may be written in terms of optimisation parameters (R, μ, h, z o and β). An equation may be written based on a balance of external work and the energy dissipation. The minimum collapse load could be obtained by optimisation of the parameters (R, μ, h, z o and β). Chapter 6 Upper bound limit analyses of suction caissons

134 -117- Complete expressions for internal plastic work and potential energy dissipation were summarised in the thesis by House (22). Selected expressions are provided in the following section Plastic work dissipated within conical soil wedge The radial velocity within the conical wedge is assumed to decrease with distance r from the caisson face and angle ψ measured from the plane of loading in plan view as given by: v r μ ro h z = v o cosψ Equation 6.4 r h D* where μ is an optimising parameter representing the exponent term defining the rate of decay in radial velocity with the radial distance. The circumferential velocity v θ is assumed to be zero v θ = Equation 6.5 As deformation of the material is assumed to take place undrained, the constant volume condition can be written as: ε + ε + ε Equation 6.6 rr θθ zz = where the radial, circumferential, and vertical strain rates are given by partial differential equations: v r ε rr = Equation 6.7 r 1 v θ v r v r ε θθ = = Equation 6.8 r θ r r v z ε zz = Equation 6.9 z By substituting the radial velocity v r from Equation 6.4 into Equation 6.6, the vertical velocity v z can be obtained as: v z z o = vr Equation 6.1 R ro The incremental shear strain can be obtained from the following expression: Chapter 6 Upper bound limit analyses of suction caissons

135 -118- vr vz γ rz = + Equation 6.11 z r 1 vr γ rθ = Equation 6.12 r θ 1 vz γ zθ = Equation 6.13 r θ The unit energy dissipation for the von Mises yield criterion is defined by: E = s 2ε ε Equation 6.14 u ij ij where 2 2 2ε ε = 2(ε + ε + ε ij ij rr θθ 2 zz ) represents an equivalent octahedral shear strain rate. The unit energy is integrated over the volume of the conical wedges to obtain the internal energy dissipation Plastic work dissipated along sliding surfaces The energy dissipation on sliding surfaces such as interface shearing along the conical wedge and interface shearing along the caisson-soil contact surfaces is evaluated by the surface integral of τ v t where vt is the slip velocity, which can be derived from the basic assumptions given in Equations 6.2 and 6.4, and τ is the limiting shear stress, which is taken as s u within the body of the soil, and αs u on the caisson-soil interface Plastic work dissipated along the caisson tip in rotational failure Various failure mechanisms at the caisson tip are shown in Figure 6.2. The rotational failure mechanism at the caisson tip depends on whether the centre of rotation lies above or below the tip of the caisson. When the centre of rotation is located below the caisson tip, the shearing dissipation in the scoop mechanism is given by: sin 3 2π v r D 2 o = su cos ω sin ωsin φ sinω dω dφ h + Equation 6.15 φ= 1 ro r ω= where r 1 is the vertical distance between the centre of rotation to the caisson tip given by: r 1 = L h Equation 6.16 r 2 is the radius of the scoop given by: Chapter 6 Upper bound limit analyses of suction caissons

136 ro r1 r = + Equation 6.17 ω = angle from the vertical of the radial line to the circular failure surface z = depth from the mudline to the circular failure surface given by: z 2 = h + r cosω Equation 6.18 A similar expression can be obtained for the case where the centre of rotation is below the skirt tip by substituting z given in Equation 6.18 by: z 2 = h r cosω Equation 6.19 Figure 6.2 Failure mechanisms at the caisson tip (Randolph et al. 1998) Flow mechanism below wedge failure In the flow region, the plastic work per unit projected area of the caisson is taken as the product of the horizontal velocity v h defined by Equation 6.1 and the limiting net soil pressure, expressed as: E = p v lim h = N p s u v h Equation 6.2 where N p is the lateral bearing resistance factor which varies with the interface friction from 9.14 for a fully smooth caisson, to for a fully rough caisson according to the plasticity solutions of Randolph and Houlsby (1984). As noted in Section 2.5.1, although an error was subsequently discovered in the original formulation for N p, recent solutions give a similar range from 9.2 to (Martin & Randolph 26). In this study, a slightly different lateral bearing resistance factor N p, as adopted by House (22), which gives N p = 9.16 for fully smooth caisson and N p = for fully rough caisson is used as given by: Chapter 6 Upper bound limit analyses of suction caissons

137 -12- N p = α 1.35α 2 Equation 6.21 The unit energy dissipation is defined by: E = 2r s N v Equation 6.22 o u p h The unit energy is integrated along the length of flow region to obtain the total energy dissipation Reverse end bearing at caisson tip The reverse end bearing at the caisson tip may also contribute to the energy dissipation as given by: D = βπr N s Equation o c u,tip The study on the end bearing capacity was summarised in Section 2.4 which indicated from various experiments that the end bearing factors vary from 8.1 to In order to compare the upper bound results with the finite element results, the end bearing factors deduced from the finite element results were adopted in this chapter Work against the gravity The work against the gravity is only concerned in the 1-sided failure mechanism as the work against gravity for both wedges cancels out in the 2-sided mechanism. The work done against the gravity may be written as: R r= ro R r z o R ro π 2 W = 2 v γ rdθdzdr Equation 6.24 wedge z z= θ= 6.3 Validation of upper bound limit analyses The upper bound limit analysis program AGSPANC (Advanced Geomechanics 21) was validated with the previous finite element results. First, the optimal capacities (i.e. with no caisson rotation) were investigated by adopting the caisson dimensions and soil profiles used in Chapter 5. Upper bound analyses were then carried out to identify the non-optimal capacities by varying the location of the padeye along the caisson shaft. Alternative interface conditions, where the caisson-soil interface is fully bonded and where the crack is allowed to form, were considered. The results were compared with the finite element load-controlled analyses obtained from Chapter 4 for the cases where the caisson-soil interface is fully bonded and from Chapter 5 for the cases where a crack Chapter 6 Upper bound limit analyses of suction caissons

138 -121- is allowed to form. Comparisons of both the magnitude of capacities and the failure mechanisms are presented Optimal capacity The upper bound analyses prescribed the caissons to translate with no rotation to identify the optimal capacity of the suction caissons. Suction caisson dimensions, soil profiles and interface friction ratio used in the finite element analyses presented in Chapter 5 were adopted (L/D = 1.5, 3, 5, soil profiles as shown in Figure 5.2, and interface friction ratio α =.65). Both 1-sided and 2-sided mechanisms were considered to represent cases where a crack forms at the back (active side) of the caisson and cases where the soil is fully bonded to the caisson surface. Loading angles of, 15, 3, 45, 6, 75, and 9 degrees were considered. The vertical pullout capacities were taken as those obtained from the finite element analyses by adopting the reversed end bearing factors N c obtained from the finite element results presented in Chapter VH Failure envelopes The VH failure envelopes obtained from the upper bound analyses and previous finite element analyses are shown in Figures Comparisons between the failure envelopes obtained from both methods are presented for different soil profiles (see Figure 5.2) and caisson length to diameter ratios (L/D = 1.5, 3, and 5). The solid lines represent the results where the caisson-soil interface is fully bonded (2-sided mechanism in the upper bound analyses) and the dashed lines represent the results where the crack is allowed to form (1-sided mechanism in the upper bound analyses). Note that the upper bound analyses assume that the crack always forms in the wedge region while the crack will not form in the finite element analyses if the reduction in the horizontal stress is less than the horizontal effective earth pressure acting on the caisson-soil interface. Chapter 6 Upper bound limit analyses of suction caissons

139 FEA fully bonded Vertical Load (kn) 2 1 (a) NC FEA crack allowed UB 2-sided UB 1-sided Horizontal Load (kn) 5 Contracted failure envelope Vertical Load (kn) (b) LOC Horizontal Load (kn) 8 Vertical Load (kn) Contracted failure envelope (c) LOC Horizontal Load (kn) Figure 6.3 Comparison of VH failure envelopes obtained from the finite element analyses and upper bound limit analyses (L/D = 1.5) Chapter 6 Upper bound limit analyses of suction caissons

140 FEA fully bonded Vertical Load (kn) 8 4 (a) NC FEA crack allowed UB 2-sided UB 1-sided Horizontal Load (kn) 15 Vertical Load (kn) 1 5 Contracted failure envelope (b) LOC Horizontal Load (kn) 2 Vertical Load (kn) Contracted failure envelope (c) LOC Horizontal Load (kn) Figure 6.4 Comparison of VH failure envelopes obtained from the finite element analyses and upper bound limit analyses (L/D = 3) Chapter 6 Upper bound limit analyses of suction caissons

141 -124- Vertical Load (kn) (a) NC Horizontal Load (kn) 4 FEA fully bonded FEA crack allowed UB 2-sided UB 1-sided Vertical Load (kn) Vertical Load (kn) Contracted failure envelope (b) LOC Horizontal Load (kn) Contracted failure envelope (c) LOC Horizontal Load (kn) Figure 6.5 Comparison of VH failure envelopes obtained from the finite element analyses and upper bound limit analyses (L/D = 5) Chapter 6 Upper bound limit analyses of suction caissons

142 -125- When the caisson-soil interface is fully bonded, the upper bound analyses generally overpredict the capacities obtained from the finite element analyses. For the short caisson (L/D = 1.5), the upper bound overpredicts the finite element results in all soil profiles. The agreement between both methods improves as the length to diameter ratio L/D increases. The failure envelopes obtained from both methods are virtually the same for the long caisson (L/D = 5) in all soil profiles. The magnitude of overprediction by the upper bound is quantified in the next section. The 1-sided upper bound results slightly overpredict the finite element results (crack allowed to form) in all soil profiles, although the reduction in capacity was maintained even at high load inclinations where the finite element results indicated that a crack would not form. As a result, the upper bound analyses underpredict the finite element results at a high load inclination. However, from a design perspective it may be appropriate to assume conservatively that a crack forms prior to loading. In this case, at a high load inclination, the upper bound results would be preferred over the finite element results. Alternatively, the contracted failure envelope as suggested in Section might be adopted. The contracted failure envelopes, as shown in Figures , track very close to the upper bound envelopes at high load inclination and the finite element envelopes at low load inclination particularly for the intermediate and long caissons. When a crack forms, the capacity reduces as the failure mechanism changes from the 2- sided failure to 1-sided failure. In lightly overconsolidated soil (LOC1 and LOC2), the upper bound results show a stronger effect of a crack compared to the results in the normally consolidated soil (NC) as shown in Table 6.1. However, the effect of a crack also depends on the ratio s u /γ z as discussed in Chapter 5. The reduction in the ultimate horizontal capacity observed in normally consolidated soil is between 4 % and 9 % and in the two lightly overconsolidated soil profiles is between 12 % and 32 %. The reduction in capacity generally reduces as the L/D increases. Similar reduction in the ultimate horizontal capacity was indicated by the finite element results as shown in Table 5.2. Chapter 6 Upper bound limit analyses of suction caissons

143 -126- Table 6.1 The reduction in ultimate horizontal capacity as the upper bound failure mechanism changes from 2-sided to 1-sided. L/D % Reduction in the ultimate horizontal capacity NC LOC1 LOC The results also show a tendency for the interaction effects between vertical and horizontal loading in the upper bound analyses to be underpredicted for the shorter caissons, manifesting as a more rectangular-shaped failure locus than those observed in the finite element analyses Magnitude of capacities The magnitude of resultant loads obtained from upper bound analyses and previous finite element analyses for each caisson dimensions and soil profiles considered are plotted against the loading angles at failure (i.e. tan -1 (V/H)) in Figures The solid lines represent the results where the caisson-soil interface is fully bonded (2-sided) and dashed lines represent the results where a crack is allowed to form (1-sided). The differences in the results obtained from both methods were quantified by correction factors, which are the ratios of the finite element results to the upper bound results. The correction factors obtained at different loading angles are presented in Table 6.2. When the caisson-soil interface is fully bonded, the upper bound analyses (2-sided) overpredict the capacity for both the short and intermediate caissons (L/D = 1.5 and 3) while giving excellent agreement with the finite element results for the long caisson (L/D = 5). The differences in both results are highest at a loading angle of around 4 to 5 for the short caisson and 3 to 35 for the intermediate caisson with overprediction of finite element results by up to 16 %. When a crack is allowed to form, the upper bound results (1-sided) agree reasonably well with the finite element results for all caisson geometries. However, as the load inclination increases toward the vertical, the upper bound analyses begin to underpredict the finite element results as the upper bound assumes that the crack would always form in the wedge region in the upper bound analyses. As noted earlier, this is not the case Chapter 6 Upper bound limit analyses of suction caissons

144 -127- for the finite element where the results show that no crack forms. Correction factors higher than 1, as shaded in Table 6.1b, represent these cases. In design, a conservative correction factor of 1 (i.e. adopting the upper bound results) is suggested to be used in these cases as a crack might form prior to loading and the capacity could reduce significantly. The correction factors are generally lower in the shorter caissons. However, there are generally no significant differences between the correction factors for a given caisson dimension in different soil profiles. Chapter 6 Upper bound limit analyses of suction caissons

145 -128- Resultant Load F (kn) (a) NC FEA fully bonded FEA crack allowed UB 2-sided UB 1-sided Loading angle (deg) 6 Resultant Load F (kn) (b) LOC Loading angle (deg) Resultant Load F (kn) (c) LOC Loading angle (deg) Figure 6.6 Magnitude of resultant loads at different loading angles, L/D = 1.5 Chapter 6 Upper bound limit analyses of suction caissons

146 -129- Resultant Load F (kn) (a) NC FEA fully bonded FEA crack allowed UB 2-sided UB 1-sided Loading angle (deg) Resultant Load F (kn) (b) LOC Loading angle (deg) Resultant Load F (kn) (c) LOC Loading angle (deg) Figure 6.7 Magnitude of resultant loads at different loading angles, L/D = 3 Chapter 6 Upper bound limit analyses of suction caissons

147 -13- Resultant Load F (kn) (a) NC FEA fully bonded FEA crack allowed UB 2-sided UB 1-sided Loading angle at failure (deg) Resultant Load F (kn) (b) LOC Loading angle at failure (deg) Resultant Load F (kn) (c) LOC Loading angle at failure (deg) Figure 6.8 Magnitude of resultant loads at different loading angles, L/D = 5 Chapter 6 Upper bound limit analyses of suction caissons

148 -131- Table 6.2 Correction factors obtained from the comparison of upper bound and finite element results. (a) fully bonded angle ( ) L/D = 1.5 L/D = 3 L/D = 5 NC LOC1 LOC2 NC LOC1 LOC2 NC LOC1 LOC (b) crack allowed angle L/D = 1.5 L/D = 3 L/D = 5 ( ) NC LOC1 LOC2 NC LOC1 LOC2 NC LOC1 LOC Chapter 6 Upper bound limit analyses of suction caissons

149 Failure mechanisms Previous finite element analyses carried out in Chapter 5 adopted displacementcontrolled analyses where the ratio of horizontal to vertical displacement was kept constant while the load paths would vary at different stages of loading. The failure mechanism for pure horizontal translation of suction caisson in lightly overconsolidated soil (LOC1), where the load path is the same as the displacement path, allowing the finite element and upper bound results to be compared directly, is presented in this section. The failure mechanisms under the optimal condition obtained from both the upper bound and finite element analyses, both for cases where the caisson-soil interface is fully bonded and where the crack is allowed to form, are presented in Figures It may be observed from the results in Figures that the failure wedges obtained from the finite element analyses stretch to the bottom of the caissons in all cases. However, the gradient of the wedge varied with the depth (i.e. curve-edge wedge). It was also observed that the shape of the failure wedges for the cases where the crack is allowed to form are similar to those obtained from the fully bonded cases (but only with single wedge). In contrast, the failure mechanisms obtained from the upper bound 2-sided failure shows that the wedges stretch to a similar depth (around 4 m) for all the caisson geometries. This is as expected because when the caissons translate with no rotation, all the boundary conditions around the wedge are the same (i.e. the horizontal displacement along the depth of the caisson-soil interface is constant). Upper bound analyses do not (strictly) yield horizontal stresses, just optimal geometry for the different region of the mechanism. Therefore the transition depth, from the wedge region to the flow around region with limiting bearing factor of N p, will be the same for any caisson lengths. However, the depth of the wedge failures is deeper relative to the caisson length in the shorter caissons; thus, e.g. the failure wedges extend to around a half of the caisson length for the short caisson (L/D = 1.5) but extend only to around one-sixth of the caisson length for the long caisson (L/D = 5). Consequently, the failure of the caisson is increasingly dominated by the flow around mechanism as the length to diameter ratio increases. By contrast, the upper bound 1-sided failure mechanisms stretch to the bottom of the caisson for all caisson geometries with no flow around region observed. Chapter 6 Upper bound limit analyses of suction caissons

150 -133- As noted in the previous section, the upper bound results agree better with the finite element results for the longer caisson when the caisson-soil interface is fully bonded. The failure mechanisms obtained in this section suggest that the upper bound results might give a better agreement to the finite element results when the failure mechanisms are dominated by the flow around failure. This observation is investigated further in the next section on the non-optimal capacity. Finite element analysis Upper bound analysis Radius (m) Depth (m) (a) fully bonded 1 Radius (m) Depth (m) (b) crack allowed Figure 6.9 Failure mechanisms obtained from finite element and upper bound analyses for suction caisson with L/D = 1.5 under pure horizontal translation in lightly overconsolidated soil (LOC1) Chapter 6 Upper bound limit analyses of suction caissons

151 -134- Finite element analysis Upper bound analysis Radius (m) (a) fully bonded Depth (m) Radius (m) (b) crack allowed Depth (m) Figure 6.1 Failure mechanisms obtained from finite element and upper bound analyses for suction caisson with L/D = 3 under pure horizontal translation in lightly overconsolidated soil (LOC1) Chapter 6 Upper bound limit analyses of suction caissons

152 -135- Finite element analysis Upper bound analysis Radius (m) Depth (m) (a) fully bonded Radius (m) Depth (m) (b) crack allowed Figure 6.11 Failure mechanisms obtained from finite element and upper bound analyses for suction caisson with L/D = 5 under pure horizontal translation in lightly overconsolidated soil (LOC1) Chapter 6 Upper bound limit analyses of suction caissons

153 Non-optimal capacity (fully bonded) The upper bound analyses varying the padeye depth along the caisson shaft were carried out to identify the inclined load capacity of suction caissons when the caissons are free to rotate (non-optimal capacity). The 2-sided failure mechanism was assumed in the upper bound analyses, to model the fully bonded caisson-soil interface condition assumed in the finite element load-controlled analyses in the normally consolidated soil (s u /z = 1 kpa/m) carried out in Chapter 4. The same caisson geometries, interface friction ratio, and loading angle at failure as in the finite element analyses were considered (L/D = 1.5, 3, 5, α =.65, θ = 3 ). Both the magnitude of capacity and failure mechanisms obtained from the two methods were investigated Magnitude of capacity Comparisons of the magnitude of capacity obtained from the upper bound and the previous finite element analyses (see Section 4.5.5) are presented in Tables The padeye depth z p, normalised centreline loading depth z cl /L, normalised resultant loads F/LDs u,avg and the differences between the resultant loads obtained from both methods are tabulated (notify that a positive sign is for the case where the upper bound overpredicts finite element results). Note that additional finite element analyses were carried out at the different padeye depths to investigate more fully the sensitivity of the inclined load response to the change in padeye depths. The normalised resultant loads are plotted against the centreline loading depth in Figure The optimal loading points for all the caisson geometries obtained from both methods varied in a narrow range around a depth of.7l. Note that, for loading depths close to the optimal loading depth, the upper bound results sometimes indicate a different direction of rotation of the caisson compared to the finite element results, due to the slight difference in the optimal loading depth. Chapter 6 Upper bound limit analyses of suction caissons

154 -137- Table 6.3 Comparison of resultant loads from finite element load-controlled analyses and AGSPANC upper bound limit analyses in normally consolidated soil (s u /z = 1 kpa/m) loading at 3 from the horizontal. (a) L/D = 1.5 No. z p (m) z cl /L F/LDs u,avg FE UB % Difference (b) L/D = 3 No. z p (m) z cl /L F/LDs u,avg FE UB % Difference Chapter 6 Upper bound limit analyses of suction caissons

155 -138- (c) L/D = 5 No. z p (m) z cl /L F/LDs u,av FE UB % Difference z cl z cl /L L/D = 1.5 (FE) L/D = 1.5 (UB) L/D = 3 (FE) L/D = 3 (UB) L/D = 5 (FE) L/D = 5 (UB) F/Lds u,avg Figure 6.12 Normalised resultant loads comparison between finite element and upper bound analyses for caissons in normally consolidated soil (s u /z = 1 kpa/m) Chapter 6 Upper bound limit analyses of suction caissons

156 -139- The differences between the resultant loads obtained from the upper bound and finite element analyses are plotted against the centreline loading depth in Figure The upper bound generally overpredicts the finite element results with the only exception being the long caisson with backward rotation where the upper bound slightly underpredicts the finite element results. For the short caisson (L/D = 1.5), the overprediction by the upper bound peaks when the caisson rotates slightly backward with the centreline loading depth z cl =.83L, where the upper bound overpredicts the finite element results by as much as 15.5 %. In the intermediate and long caissons (L/D = 3 and 5), the overprediction by the upper bound peaks when the caisson rotates forward with overpredictions up to 16 % for L/D = 3 at z cl =.66L and 15 % for L/D = 5 at z cl =.46L. zcl zcl/l..1 FE > UB UB > FE L/D = 1.5 L/D = 3.2 L/D = Optimal loading depth Forward rotation Backward.9 rotation % Difference between finite element and upper bound analyses Figure 6.13 Differences between the inclined load capacities obtained from the finite element and upper bound analyses in normally consolidated soil (s u /z = 1 kpa/m). While the overprediction by the upper bound analyses can be substantial at a certain centreline loading depth, the agreement between both results improves significantly with the shift of the centreline loading depth as shown in Figure When the centreline loading point shifts downward, the upper bound results converge to within 5 % from the finite element results in all caisson geometries. When the centreline loading point moves higher, the difference in both results reduces to around 1 % for the intermediate and long caissons while the upper bound results converge to the finite element results for the short caisson. Chapter 6 Upper bound limit analyses of suction caissons

157 Failure mechanisms The failure mechanisms obtained from both the upper bound and finite element analyses in normally consolidated soil (s u /z = 1 kpa/m) are presented in Figures for all caisson geometries. The load and displacement vectors at the centreline loading point obtained from the upper bound are also shown (the displacement vector is the vector acting at the centreline loading point and the load vector is shown as acting at the padeye located along the caisson wall and is dashed within the caisson). The resultant displacement, horizontal and vertical displacement contour plots are also presented in Figures for the cases where the differences between the results obtained from both methods are high as highlighted in Table 6.3. When the centreline loading point is located high enough, the caissons rotate forward and combinations of wedge-flow around and full circular rotational failure were observed. The centre of rotation in these cases was located near the tip of the caisson in all caisson geometries (see Figures 6.14a, 6.15a, and 6.16a). For the short caisson (L/D = 1.5), only wedge and rotational flow mechanisms are observed from both methods without the flow around region. In this case, the upper bound results agree very well with finite element results. For the longer caisson, the flow around region increasingly dominated and the upper bound increasingly overpredicts the finite element results. This is similar to the observation for the optimal condition. The depths of the centre of rotation of the caissons obtained from both methods agree very well in most cases except for the short caisson (L/D = 1.5) with centreline loading point located slightly below the optimal loading point. For that case the centre of rotation obtained from the upper bound is slightly below that obtained from the finite element analysis and the upper bound overpredicts the capacity obtained from the finite element results significantly (15.5 % overprediction). The rotational flow failure extends to the mudline as shown in Figure 6.14f. However, as the centreline loading point moves deeper, the full circular rotational failure eventually moves below the soil surface as shown in Figures 6.14g and 6.14h. In this case the capacity obtained from the upper bound agrees very well with the finite element results. For longer caissons (L/D = 3 and 5) with backward rotation, the circular rotational flow failure from the upper bound results is only observed below the tip of the caissons. The full circular rotational flow failure was not observed in the upper bound results even if the centreline loading points were as deep as the tip of the caissons. Instead Chapter 6 Upper bound limit analyses of suction caissons

158 -141- combinations of the wedge and flow around mechanisms were observed within the caisson length as shown in Figures 6.15e 6.15i and Figures 6.16e 6.16h. While the failure mechanisms obtained from both methods appear to be different in these cases, the upper bound results agree very well with the finite element results particularly for the long caisson. For the intermediate caisson, the upper bound results also converge to the finite element results provided that the centreline loading depth is deep enough. The typical failure patterns obtained from the upper bound are summarised in Figure The failure patterns shown shaded in Figure 6.26 are those where the upper bound overpredictions are higher than 8 %. Chapter 6 Upper bound limit analyses of suction caissons

159 (a) z p = m 1.18 % difference Finite element analysis Upper bound analysis Radius (m) Depth (m) (b) z p = 2 m 5.83 % difference Radius (m) Depth (m) (c) z p = 2.5 m 4.86 % difference 1 Radius (m) Depth (m) (d) z p = 3.2 m 3.83 % difference Radius (m) Depth (m) Figure 6.14 Comparison of displacement vector plot obtained from the finite element analyses and failure mechanisms obtained from upper bound analyses, L/D = 1.5 (to be continued) Chapter 6 Upper bound limit analyses of suction caissons

160 (e) z p = 3.8 m % difference Finite element analysis Upper bound analysis Radius (m) Depth (m) (f) z p = 4.8 m 15.5 % difference Radius (m) Depth (m) (g) z p = 5.5 m 8.34 % difference Radius (m) Depth (m) (h) z p = 6 m 3.86 % difference Radius (m) Depth (m) Figure 6.14 Comparison of displacement vector plot obtained from the finite element analyses and failure mechanisms obtained from upper bound analyses, L/D = 1.5 Chapter 6 Upper bound limit analyses of suction caissons

161 -144- Finite element analysis Upper bound analysis (a) z p = 2.5 m Diff = 9.86 % (b) z p = 5 m Diff = 1.5 % Depth (m) Depth (m) Radius (m) Radius (m) (c) z p = 7.5 m Diff = % (d) z p = 8.5 m Diff = 16.4 % (e) z p = 9 m Diff = % Depth (m) Depth (m) Depth (m) Radius (m) Radius (m) Radius (m) Figure 6.15 Comparison of displacement vector plot obtained from the finite element analyses and failure mechanisms obtained from upper bound limit analyses, L/D = 3 (to be continued) Chapter 6 Upper bound limit analyses of suction caissons

162 -145- Finite element analysis Upper bound analysis (f) z p = 9.75 m Diff = 7.74 % Depth (m) Radius (m) (g) z p = 1.5 m Diff = 3.97 % Radius (m) Depth (m) (h) z p = 11.1 m Diff = 3.2 % Radius (m) Depth (m) (i) z p = 12 m Diff = 3.71 % Radius (m) Depth (m) Figure 6.15 Comparison of displacement vector plot obtained from the finite element analyses and failure mechanisms obtained from upper bound limit analyses, L/D = 3 Chapter 6 Upper bound limit analyses of suction caissons

163 (a) z p = 5 m Diff = 1.79 % Finite element analysis Upper bound analysis Radius (m) Depth (m) (b) z p = 8 m Diff = 1.3 % Radius (m) Depth (m) (c) z p = 1 m Diff = % Radius (m) Depth (m) (d) z p = 12.5 m Diff = 9.29 % Radius (m) Depth (m) Figure 6.16 Comparison of displacement vector plot obtained from the finite element analyses and failure mechanisms obtained from upper bound limit analyses, L/D = 5 (to be continued) Chapter 6 Upper bound limit analyses of suction caissons

164 -147- Finite element analysis Upper bound analysis (e) z p = 15 m Diff = 3.3 % Radius (m) Depth (m) (f) z p = 17 m Diff = % Radius (m) Depth (m) (g) z p = 18 m Diff = -2.6 % Radius (m) Depth (m) (h) z p = 2 m Diff = % Radius (m) Depth (m) Figure 6.16 Comparison of displacement vector plot obtained from the finite element analyses and failure mechanisms obtained from upper bound limit analyses, L/D = 5 Chapter 6 Upper bound limit analyses of suction caissons

165 Displacement contour from finite element Displacement contour from finite element (without soil plug) Horizontal displacement contour from finite element Vertical displacement contour from finite element (Upper bound overprediction = 11. %) Figure 6.17 Displacement contours obtained from the finite element analyses for L/D = 1.5, z p = 3.8 m Displacement contour from finite element Displacement contour from finite element (without soil plug) Horizontal displacement contour from finite element Vertical displacement contour from finite element (Upper bound overprediction = 15.7 %) Figure 6.18 Displacement contours obtained from the finite element analyses for L/D = 1.5, z p = 4.8 m Chapter 6 Upper bound limit analyses of suction caissons

166 Displacement contour from finite element Displacement contour from finite element (without soil plug) Horizontal displacement contour from finite element Vertical displacement contour from finite element (Upper bound overprediction = 13.9 %) Figure 6.19 Displacement contours obtained from the finite element analyses for L/D = 3, z p = 7.5 m Displacement contour from finite element Displacement contour from finite element (without soil plug) Horizontal displacement contour from finite element Vertical displacement contour from finite element (Upper bound overprediction = 17.9 %) Figure 6.2 Displacement contours obtained from the finite element analyses for L/D = 3, z p = 8.5 m Chapter 6 Upper bound limit analyses of suction caissons

167 Displacement contour from finite element Displacement contour from finite element (without soil plug) Horizontal displacement contour from finite element Vertical displacement contour from finite element (Upper bound overprediction = 11.8 %) Figure 6.21 Displacement contours obtained from the finite element analyses for L/D = 3, z p = 9 m Chapter 6 Upper bound limit analyses of suction caissons

168 Displacement contour from finite element Displacement contour from finite element (without soil plug) Horizontal displacement contour from finite element Vertical displacement contour from finite element (Upper bound overprediction = 1.8 %) Figure 6.22 Displacement contours obtained from the finite element analyses for L/D = 5, z p = 5 m Displacement contour from finite element Displacement contour from finite element (without soil plug) Horizontal displacement contour from finite element Vertical displacement contour from finite element (Upper bound overprediction = 1.3 %) Figure 6.23 Displacement contours obtained from the finite element analyses for L/D = 5, z p = 8 m Chapter 6 Upper bound limit analyses of suction caissons

169 Displacement contour from finite element Displacement contour from finite element (without soil plug) Horizontal displacement contour from finite element Vertical displacement contour from finite element (Upper bound overprediction = 14.8 %) Figure 6.24 Displacement contours obtained from the finite element analyses for L/D = 5, z p = 1 m Displacement contour from finite element Displacement contour from finite element (without soil plug) Horizontal displacement contour from finite element Vertical displacement contour from finite element (Upper bound overprediction = 9.3 %) Figure 6.25 Displacement contours obtained from the finite element analyses for L/D = 5, z p = 12.5 m Chapter 6 Upper bound limit analyses of suction caissons

170 -153- Typical failure patterns Short caisson Intermediate caisson Long caisson Depth (m) Radius (m) Depth (m) Radius (m) Depth (m) Radius (m) Forward rotation Depth (m) Radius (m) Depth (m) Radius (m) Depth (m) Radius (m) Depth (m) Radius (m) Depth (m) Radius (m) Depth (m) Radius (m) Backward rotation Depth (m) Radius (m) Depth (m) Radius (m) Depth (m) Radius (m) Depth (m) Radius (m) Depth (m) Radius (m) Depth (m) Radius (m) Depth (m) Radius (m) Depth (m) Radius (m) Figure 6.26 Typical failure patterns obtained from the upper bound analyses in normally consolidated soil Chapter 6 Upper bound limit analyses of suction caissons

171 Non-optimal capacity (crack allowed) Upper bound analyses (1-sided failure mechanism) were carried out to investigate the non-optimal capacity of suction caissons when a crack is allowed to form. The results are compared here with the finite element load-controlled analyses presented in Chapter 5. The caisson with length to diameter ratio L/D of 3 in lightly overconsolidated soil (LOC1) was adopted. The interface friction ratio was assumed to be.65. A comparison of the magnitude of capacities and failure mechanisms is presented Magnitude of capacity The capacities obtained from both methods (finite element results from Section 5.6) are shown in Table 6.3. The upper bound consistently overpredict the finite element results by % for all the centreline loading depths. The optimal loading depths obtained from both methods are roughly the same at around.66l. Table 6.4 Comparison of the magnitude of capacity from finite element and upper bound analyses when crack is allowed to form, L/D = 3, LOC1 No. z p (m) z cl /L FE F/LDs u,av UB % Difference Failure mechanism The failure mechanisms in the cases shaded in Table 6.5 are shown in Figure It can be seen that the upper bound failure mechanisms obtained from all cases are very similar (the wedge extending to the bottom of the caisson). Therefore, it is quite reasonable that the upper bound overpredicts the finite element results by a similar amount with the change in the padeye depth. Chapter 6 Upper bound limit analyses of suction caissons

172 -155- Finite element analysis Upper bound analysis Depth (m) Radius (m) (a) z p = 7 m Depth (m) Radius (m) (b) z p = 8.5 m Depth (m) Radius (m) (c) z p = 12 m Figure 6.27 Comparison of displacement vector plot obtained from the finite element analyses and failure mechanisms obtained from upper bound limit analyses, L/D = 3 Chapter 6 Upper bound limit analyses of suction caissons