c67

Proceedings of OMAE 2001 21st International Conference on Offshore Mechanics and Arctic Engineering

ABSTRA

The leof intense

June 23-28, 2002, Oslo, Norway

OMAE2002-28085R

DETERMINING APPROPRIATE STIFFNESS LEVELS FOR SPUDCAN FOUNDATIONS USING JACK-UP CASE RECORDS

M.J. Cassidy Centre for Offshore Foundation Systems,

The University of Western Australia, Australia

G.T. Houlsby University of Oxford,

United Kingdom

M. Hoyle Noble Denton Europe Ltd., United Kingdom

M.R. Marcom Rowan Companies Inc., United States of America

CT vel of soil stiffness under spudcan footings is an area

records double integrated to determine the displacements. By measuring the wave heights with a downward looking sensor at

Proceedings of OMAE�02 21st International Conference on Offshore Mechanics

and Artic Engineering June 23-28, 2002,Oslo, Norway

OMAE2002-28085

interest and debate, with many practitioners the bow of the jack-up (usually a radar altimeter but on some

believing that current jack-up assessment guidelines are overly conservative. In order to evaluate appropriate stiffness parameters, back-analysis of case records of jack-up platforms in the North Sea has been performed. The records relate to three different rigs at a total of eight locations, which include a variety of soil conditions, water depths and sea-state severity. For each site the horizontal deck displacements and the sea-state conditions under storm loading are available. Numerical simulation of the platforms under storm loading was undertaken with varying levels of foundation stiffness. For each set of stiffness one-hour of numerical simulation was performed, with the most severe recorded environmental loading conditions for that site used. The horizontal deck displacements of the measured data and the numerical simulation results have been compared in both the frequency domain and by the magnitude of response. On the basis of the analyses, recommendations can be made for higher stiffness factors then are currently suggested in the SNAME, 1997 Technical & Research Bulletin 5-5A, Site Specific Assessment of Mobile Jack-up Units (SNAME, 1997).

1.0 INTRODUCTION This paper reports the findings of the back-analysis of case

records of jack-up platforms in the North Sea. The records relate to three different rigs at a total of eight locations, which include a variety of soil conditions, water depths and storm severity and have been previously reported in Temperton et al. (1997) and Nelson et al. (2000).

At each of the locations the record of horizontal deck movement of the jack-up under wave loading was available. Located near the legs on the hull, accelerometers in orthogonal pairs were used to measure deck accelerations and these

1 Copyright © 2002 by ASME

occasions a laser wave gauge), the sea-state records were established. Anemometers located on the top of the derrick and/or legs also monitored wind speeds and directions. These data almost certainly represent the best currently available database of monitored information of full-scale jack-ups under wave and wind loading. Further details of the monitoring program can be found in Nelson et al. (2000).

In order to compare the monitored jack-up units with numerical simulations of the most severe storm events, a suite of random time domain analyses were performed for each site. One hour simulations were performed using a structural dynamic program developed at the University of Oxford and called JAKUP. The motivation behind JAKUP is the development of a balanced approach to the analysis of jack-up units, with the non-linearities in the structural, foundation and wave loading models all taken into account. Key features of the program and aspects important to this study are discussed in section 3, with full details available in Thompson (1996), Williams et al. (1998) and Cassidy (1999).

For each site the stiffness of the foundation model was varied. By changing only this value the natural period of the numerical jack-up model could be adjusted and a comparison with the measured data made. To determine the most appropriate stiffness level the numerical value was adjusted until there was a good correlation with the measured results in both the frequency domain and the magnitude of response.

2.0 THE MEASURED DATA CASE RECORDS A program of monitoring the dynamic behaviour and

environmental conditions of three jack-ups was commissioned by Sante Fe in 1992 and since then eight sites have been subjected to substantial storm conditions (Nelson et al., 2000).

A summary of these sites, which constitute the eight cases analysed, is given in Table 1. All sites were in the Central North Sea and as shown in Table 1 the cases contain a variety of water depths (28.3 to 91.8m) and jack-up orientations. Two of the units (Magellan and Monitor) are Friede and Goldman L780 Mod V units and the other (Galaxy-1) a Friede and Goldman L780 Mod VI. Table 2 outlines details of the soil conditions for all of the sites. These are best estimates from site assessment data, with properties fine-tuned to balance the measured pre-load and penetration levels. More details on this process is given in sections 5.1 and 5.2 for clay and sand respectively. Further details of the site locations and conditions can be found in Nelson et al. (2000).

3.0 ANALYSIS PROGRAM USED IN BACK-ANALYSIS Analytical models for the eight cases were constructed

using the JAKUP program. The key features of this program are: • The program uses the finite element method with dynamics

modelled by time-stepping. In the JAKUP structural model ∆−P , Euler and shear effects are considered and the

Newmark ( 25.0=β 5.0=δ ) solution method used to solve the dynamic equations.

• The structure is modelled as a 2-dimensional “bar stool” model, with the legs and hull represented by elastic finite elements.

• Wave loading is modelled using either regular waves or pseudo-random waves. Extreme events can be modelled using the “NewWave” method (Tromans et al., 1991), and these may be embedded within a pseudo-random background using “Constrained NewWave” (Taylor et al., 1995; Cassidy et al., 2001). Purely random seas, based on the superposition of numerous wavelets and with no NewWave embedment, are also possible and were used in the analyses described here. The wave kinematics are explicitly calculated, and the forces on the rig determined by Morison’s method.

• Wind loading is specified by prescribed loads. • The foundation can be modelled as pinned, fixed, elastic

springs, or using one of two advanced work-hardening plasticity models in terms of force resultants on the foundation. This is the most significant aspect of JAKUP for this project.

• Hydrodynamic damping is introduced through Morison’s method, and structural damping is specified using Rayleigh’s method.

The limitation of JAKUP to two-dimensional modelling was not considered significant for the eight cases, as all of the storm directions could be analysed as either two-legs windward one-leg leeward or two-legs leeward one-leg windward (see Table 1 for orientations). The other limitation of the program is that detailed modelling of leg and hull is not possible and no account is taken of nonlinearity at the leg-hull connection. However, an extensive structural calibration process between

the three-dimensional models previously used by Noble Denton Europe Ltd (NDE) (Nelson et al., 2000) and JAKUP confirmed the applicability of JAKUP for these calculations. For each case the structural models of both NDE and JAKUP were subjected to a 10MN impulse load at deck level under four conditions: pinned footings and elastic springs for the jack-up in air (thus excluding hydrodynamic damping) and in water. Comparisons between the models were based upon the following criteria. • The mean (steady state) deck displacement, which gives a

direct measure of the overall stiffness of the system. • The mass distribution was checked by comparing the

natural period of the structure, deduced from the time interval between successive deck displacement peaks.

• The damping factor was determined from the logarithmic decrement for the first six cycles. Since the damping factor depends on mass, stiffness and damping, this represents (having checked mass and stiffness above) a check on the implementation of the damping. In all of the cases the agreement between the NDE

program and JAKUP was extremely good. This correlation gave an assurance of JAKUP’s ability to provide realistic structural modelling of jack-up response and the more advanced foundation capabilities of the JAKUP code could be used with confidence.

4.0 JAKUP MODELS

4.1 Structural models The typical structural configuration used in all of the

numerical JAKUP analyses is shown in Figure 1. The properties used for the three jack-up configurations are also given. As detailed in Table 1, only two spudcan types were used throughout the eight sites. The two shapes and sizes are shown in Figure 2.

4.2 Wave loading For each site the most severe sea-state recorded during the

monitoring period was chosen for numerical simulation. The direction of the sea was assumed to be coincident with the measured wind direction. An equivalent 2-D model was chosen to be as close as possible to this direction. The sea-state was represented by a JONSWAP spectrum, with specified significant wave height, mean crossing period and peak enhancement factor. The sea-state parameters are detailed in Table 2. Wind forces were applied as nodal forces with a summary of conditions given in Table 3.

4.3 Foundation models One of JAKUP's major advantages is the implementation

of “Model B” and “Model C” - strain hardening plasticity models for spudcans on clay and sand respectively. Both models are based on experiments performed at Oxford University and described in Martin and Houlsby (2000) and Gottardi et al. (1999) respectively. In the strain hardening plasticity theory the response of the foundations is expressed


purely in terms of force resultants and is expressed in a way that makes it directly applicable in numerical analysis of structures. The two models are closely related, both having four major components: (1) An empirical expression for the yield surface in three

dimensional vertical, moment and horizontal loading space (V, M/2R, H). A typical yield surface shape is shown in Figure 3 and once the surface is established, any changes of load within this surface will result only in elastic deformation. Plastic deformation can result, however, when the load-state reaches the surface.

(2) An empirical strain-hardening expression to define the variation of the size of the yield surface with the plastic component of vertical displacement. Model B and Model C differ principally in the way this work-hardening is described.

(3) A model for elastic load-displacement behaviour within the yield surface. Finite element work has shown that cross coupling exists between the horizontal and rotational footing displacements (Bell, 1991; Ngo-Tran, 1996), with a linear elastic incremental force-displacement relationship of the form

θ

=

duRddw

KKKK

K

dHRdM

dV

hc

cm

v2

00

002 (1)

where Kv, Km, Kh and Kc represent stiffness values and w , θ and u are the vertical, rotational and horizontal displacements respectively. Figure 4 shows the assumed loading and displacement directions at the foundation. For both Model B and Model C the stiffness factors in Equation 1 are proportional to the shear modulus G.

(4) A suitable flow rule to allow prediction of the ratios between plastic footing displacements during yield. For similar tests the direction of observed plastic displacements differed for clay and sand, making the flow rule another principal variation in the models.

A full description of Model B can be found in Martin (1994) and Martin and Houlsby (2001) and Model C in Cassidy (1999) and Houlsby and Cassidy (2002).

5.0 COMPARISONS WITH CASE HISTORIES For each case, analyses were carried out for one hour of

the measured sea-state, with a variety of different stiffness properties at the foundation. The history of the deck displacement was recorded, and processed in the following way.

Firstly the frequency spectrum for the response was obtained for comparison with the measured spectra. The spectrum was obtained by two means: a Fast Fourier Transform (FFT), and by use of Autoregression Coeffiecients. The latter is a more recently developed method, which allows a representation of the spectrum using fewer variables. Details of

the method can be found in Pardey et al. (1996). By comparison with the FFT it gives much smoother spectrum, but otherwise the spectra derived from the two methods are very similar (except for some special cases of mainly theoretical interest). Example spectra derived from the measured deck displacements, resolved to the direction of the storm, for two cases (C1 and S1) are shown in Figure 5. The spectra found were usually characterised by two peaks – one at the dominant wave frequency, and another at the natural period of the structure (which is usually much shorter than the wave period). For the two cases shown in Figure 5 the natural period of the structure is dominating the spectral response with a peak at 0.16Hz for clay case 1 (C1) and at around 0.18Hz for sand case 1 (S1). The main purpose of this study was to match the natural period of the structure.

While the spectra usually give good data on the frequency response, they are poor indicators of the magnitude of response. For this reason a measure of the magnitude of response was also necessary and for both the measured and simulated deck displacements the mean, standard deviation, minimum, maximum and range are compared. The magnitude of the measured results for cases C1 and S1 can be seen in the first lines (highlighted) of Tables 4 and 5 respectively.

5.1 The Clay Cases The strength of the seabed was found by applying vertical

load to the jack-ups of Figure 1 and calibrating the observed penetration with the simulated values for the same pre-load level. At the beginning of the main analysis the vertical preload was applied, then the load reduced to the working load before the wave and wind loads were applied.

On all of the clay sites, initial estimates of the profile of undrained strength with depth were made on the basis of site investigation information. In each case the strength profile was fitted by a linear variation of strength with depth. Most emphasis was placed on data for the depths between the observed penetration and the observed penetration plus one footing radius. None of the sites represented a significant risk of “punch through” conditions.

The load-penetration curve was computed using JAKUP, and the profile of strength then fine tuned to give a match of the observed penetration at preload. Only minor adjustments were necessary at this stage, with the jack-up penetration process effectively used as a very large scale investigation of the strength of the clay. The final penetration curves for the three clay cases are shown in Figure 6(a) and the strength profiles detailed in Table 2.

The significant variable to be found in the back-analyses was the stiffness of the foundations and for all of the clay cases Equation 1 was used as the elastic stiffness matrix in Model B. The shear modulus (G) linearly scales all of the stiffness coefficients in Equation 1 and was determined by

ursIG = (2)


where su is the undrained shear strength measured at 0.15 diameters below the reference point of the spudcan (the first position of maximum diameter above the tip) and Ir the rigidity index.

5.1.1 Example Case C1 The investigation for the stiffness of the spudcan

foundations will be detailed here for clay case C1. The measured spectrum is shown in Figure 5 and the measured response magnitude detailed in the first line of Table 4.

On the basis of laboratory testing the starting point for the estimation of the stiffness value was to assume 80=rI (Martin, 1994). One hour of random sea was simulated through JAKUP and for this level of stiffness the frequency spectrum for the hull displacement response can be seen in Figure 7. Though this case did not reveal two discrete peaks the natural period of the numerical jack-up can be observed at around 0.12Hz (or 8.33s). As some practitioners may have expected this value estimated a natural period lower than that measured. Subsequently rI was increased (stiffening the foundations) and the spectra for values of Ir = 150, 250, 300 and 350 are also shown in Figure 7. To allow comparisons between all stiffness levels the same hour of “random” wave loading, as was used in the 80=rI case, was applied. As the foundation fixity increased the natural period (in seconds) decreased, as did the overall response. The magnitude of displacement for all of these cases are given in Table 4, with the simulated values closest to the measured highlighted. The level of elastic stiffness, for the parameters set out in Equation 1, are also given in Table 4.

There are two upper and lower bound cases to the rotational fixity: pinned and fixed footings. Both assume infinite horizontal and vertical stiffness, but pinned assumes no rotational stiffness whereas fixed assumes infinite. As well as the Model B analysis these two foundation assumptions were also analysed, with their spectra shown in Figure 7 and their displacement magnitudes in Table 4.

On the basis of the measured spectrum it is clear that 250≥rI is required and values of 300 or 350 fit well. As the

fixed case gives only a fractionally different frequency (about 0.16Hz), no upper bound can be placed on the stiffness factor. Examining the range of the displacement magnitudes, and also the standard deviation of the displacement suggests that the higher values of stiffness cannot be justified, with 250 to 300 fitting quite well. Based on this one case a value of 300=rI would be appropriate. The spectrum for this case superimposed on the measure spectrum is shown in Figure 8(a).

5.1.2 Summary of Other Clay Cases Two other clay cases were analysed. They also confirmed

that higher stiffness values may be appropriate. In clay case 2 (C2) an rI of between 300 and 350 was found to fit the data well. On the basis of the measured spectra (position of the peak

response) it first appears that 600≥rI is required. This is shown in Figure 8(b). However, somewhat lower values of rI also give a peak not far from the observed value of about 0.175Hz (5.71s). Examining the range of the displacement magnitudes, and also the standard deviations of the displacements suggests a best fit at an rI value between 200 and 300. Taken together it is considered that the best overall fit for this case is again achieved with 350=rI .

The third clay case (C3) again suggested a high value of stiffness at 600=rI , with the sharp peak of the measured spectrum at 0.21Hz (4.76s) quite well match at this stiffness value. This can be observed in Figure 8(c). The displacement data also suggests that this higher value of stiffness factor can be justified.

A summary of the clay findings is given in Table 6.

5.2 Example Case on Sand When using Model C for analysing spudcans on sand the

penetration depends almost entirely on the chosen angle of friction, with a minor influence of the effective unit weight (which was fixed on the basis of site investigation). For all of the sand sites, the angle of friction was adjusted until the observed penetration was matched. The resulting values are quite low (in the range of 27° to 30.5°), but are quite credible for silty material. Note that, since the measured penetration was only resolved to the nearest 0.3m, this process is rather approximate, and too much credibility should not be given to the friction values. The final penetration curves are shown for the relevant five sand cases in Figure 6(b). The subsequent behaviour of Model C depends principally on the ratio of vertical load to preload and not to the angle of friction itself.

In the sand analyses presented here the shear modulus was calculated using the formula recommended by Wroth and Houlsby (1985) and detailed for Model C in Cassidy (1999) and Cassidy and Houlsby (1999). It uses a non-dimensionalised shear modulus factor g to scale the shear modulus by

aa p

RgpG γ ′= 2 (3)

where ap is atmospheric pressure, R the maximum embedded spudcan radius and γ ′ the submerged unit weight of the soil. Equation 3 is derived from the empirical observation that the shear modulus depends approximately on the square root of the stress level, with γ ′R2 a representative estimate of the mean stress (Wroth and Houlsby, 1985).

5.2.1 Example Case S1 The results of an example sand case analysis are shown in

Figure 9. The elastic stiffness values used in Model C and corresponding to the parameters of Equation 1 are listed in Table 5. The starting point for the analysis was a shear modulus


factor in Equation 3 of 4000=g . However, this was found to be too stiff as reflected in an estimated natural period of 0.25Hz (4.0s). There is a sharply defined measured peak in the spectrum at about 0.18Hz (as shown in Figure 5), with this being well matched by the simulations using 300=g . The displacement data also suggests that 300=g is appropriate, as highlighted in Table 5.

5.2.2 Summary of Other Sand Cases Four other sand cases were analysed and comparisons of

their measure response and interpreted best numerical fit are shown in Figure 10. A summary of the results and stiffness values thought appropriate is given in Table 7. Unfortunately not all of the sand cases gave conclusive evidence as to a match between the measured and analysed data.

It was on the basis of laboratory tests that the estimated initial value of the dimensionless stiffness factor g was assumed to be 4000. The three case histories, which give a clear indication of a suitable value of g for the field (cases S1, S2 and S3), give values of about 500, 400 and 300, i.e. a factor of about 10 lower on average. Two cases (S4 and S5) are inconclusive, but not entirely inconsistent with a value of 400. The reasons for the discrepancy between laboratory and field results are thought to be due to difficulties recording very small displacements in the experiments and also scaling effects between the experimental and field results. The values of stiffness implied by g = 400 are, however, higher than those obtained using the SNAME (1997) procedures.

6.0 CONCLUSIONS In the testing program eight case records of jack-ups in the

North Sea were back analysed to fit soil stiffness parameters. On the basis of these records, it is possible to recommend higher stiffness factors than are currently suggested in the practice for Site Assessment of Mobile Jack-Up Units (SNAME, 1997). Such higher stiffness factors had been expected to be appropriate by some practitioners, but the case records studied here provide a firmer basis than had hitherto been available for recommending higher stiffness factors. A publication on recommendations arising from this back analysis and also outlining a calculation method for spudcan stiffness levels, within the context of current practices in the SNAME guidelines, will be forthcoming.

Although the present project has gone some way to clarifying the uncertainties about the appropriate stiffness for analysis of jack-ups, there remain a number of issues to be resolved, and further work in this area would be beneficial. The case data recorded were all for relatively mild environmental conditions and a study using harsher environmental conditions would be most valuable. Further monitoring and back analysis is therefore recommended. Any field monitoring should concentrate on gathering high-quality site-investigation data so that the soils can be properly characterised. Other direct

indications of stiffness such as the measurement of soil rebound as the preload is dumped, would also be a valuable check.

Whilst validation against field records is of primary importance, a greater coverage of different cases (especially extreme events) can be achieved by validation against further model tests, and this should be pursued.

Models B and C are probably the most advanced foundation models for the analysis of jack-ups currently available, but they are inadequate as far as the modelling of cyclic behaviour is concerned. The development of models that provides realistic modelling of behaviour during cycling, including a gradual degradation of stiffness with strain amplitude, is required (and is currently being investigated at Oxford University and the University of Western Australia).

ACKNOWLEDGMENTS This work was supported by the International Association

of Drilling Contractors (IADC) and the authors thank them for permission to publish this paper.

The Centre for Offshore Foundation Systems was established and is funded under the Australian Governments Special Research Centres Program.

REFERENCES Bell, R.W. (1991). The analysis of offshore foundations subjected

to combined loading. M.Sc. Thesis, University of Oxford. Butterfield, R., Houlsby, G.T. and Gottardi, G. (1997).

Standardized sign conventions and notation for generally loaded foundations, Géotechnique, Vol. 47, No. 5, pp1051-1054.

Cassidy, M.J. (1999). Non-linear analysis of jack-up structures subjected to random waves, DPhil Thesis, University of Oxford, United Kingdom.

Cassidy, M.J. and Houlsby, G.T. (1999). On the modelling of foundations for jack-up units on sand, Proc. 31st Offshore Technology Conference, Houston, OTC 10995.

Cassidy, M.J., Eatock Taylor, R., Houlsby, G.T. (2001). Analysis of jack-up units using a Constrained NewWave methodology. Applied Ocean Research, Vol. 23, pp. 221-234.

Gottardi, G., Houlsby, G.T. and Butterfield, R. (1999). The plastic response of circular footings on sand under general planar loading, Géotechnique, Vol. 49, No. 4, pp 453-470.

Houlsby, G.T. and Cassidy, M.J. (2002). A plasticity model for the behaviour of footings on sand under combined loading. Géotechnique, Vol. 52, No. 2, pp.117-129.

Martin, C.M. (1994). Physical and numerical modelling of offshore foundations under combined loads. D.Phil. Thesis, University of Oxford, United Kingdom.

Martin, C.M. and Houlsby, G.T. (2000). Combined loading of spudcan foundations on clay: laboratory tests. Géotechnique, Vol. 50, No. 4, pp 325-338.

Martin, C.M. and Houlsby, G.T. (2001). Combined loading of spudcan foundations on clay: numerical modelling. Géotechnique, Vol. 51, No. 8, pp 687-700.

Nelson, K., Smith, P., Hoyle, M., Stoner, R. and Versavel, T. (2000). Jack-up response measurements and the underprediction of spud-can fixity by SNAME 5-5A. Proc. 32nd Offshore Technology Conference, Houston, OTC 12074.


Ngo-Tran, C.L. (1996). The analysis of offshore foundations subjected to combined loading. D.Phil. Thesis, University of Oxford.

Pardey, J., Roberts, S. and Tarassenko, L. (1996). A review of parametric modeling techniques for EEG analysis. Med. Eng. Phys. Vol. 18, No. 1, pp. 2-11.

SNAME T&R 5-5A (1997). Site specific assessment of mobile jack-up units. 1st Edition – Rev 1. Society of Naval Architects and Marine Engineers, New Jersey.

Taylor, P.H., Jonathan, P. and Harland, L.A. (1995). Time domain simulation of jack-up dynamics with the extremes of a Gaussian process. Proc. 14th Int. Conf. on Offshore Mechanic and Arctic Engineering (OMAE), Vol. 1-A, pp. 313-319.

Temperton, I., Stoner, R.W.P. and Springett, C.N. (1997). Measured jack-up fixity: analysis of instrumentation data from three North Sea jack-up units and correlation to site assessment procedures.

Proc. of 6th Int. Conf. Jack-Up Platform Design, Construction and Operation, City University, London.

Thompson, R.S.G. (1996). Development of non-linear numerical models appropriate for the analysis of jack-up units. D.Phil. Thesis, University of Oxford.

Tromans, P.S., Anaturk, A.R. and Hagemeijer, P. (1991). A new model for the kinematics of large ocean waves -applications as a design wave-. Proc. 1st Int. Offshore and Polar Engng Conf. , Edinburgh, Vol. 3, pp. 64-71.

Williams M.S., Thompson R.S.G., Houlsby G.T. (1998). Non-linear dynamic analysis of offshore jack-up units. Computers and Structures, 69(2), pp. 171-180.

Wroth, C.P. and Houlsby, G.T. (1985). Soil mechanics – property characterization and analysis procedures. Proc. 11th Int. Conf. on Soil Mech. and Fndn Engng, San Francisco, Vol. 1, pp. 1-55.

Table 1 - Summary of the eight site conditions

Rig Water depth (m)

Spudcan penetration (m)

Leg length (to hull) (m)

Still water load (MN)

Pre-load ratio*

Spudcan type (see Figure 2)

Orientation

C1 Magellan 91.8 2.4 117.7 157.3 1.89 1 2 windward – 1 leeward C2 Magellan 88.5 3.0 110.5 157.5 1.62 1 1 windward – 2 leeward C3 Galaxy-1 89.4 6.7 115.3 231.5 1.66 2 2 windward – 1 leeward S1 Galaxy-1 74.5 1.2 95.8 229.1 1.68 2 2 windward – 1 leeward S2 Magellan 77.0 0.9 98.9 161.1 1.54 1 1 windward – 2 leeward S3 Monitor 83.5 0.9 104.2 147.6 1.65 1 1 windward – 2 leeward S4 Monitor 28.3 0.6 47.5 151.1 1.65 1 1 windward – 2 leeward S5 Galaxy-1 91.8 1.5 113.1 227.7 1.69 2 1 windward – 2 leeward

*Pre-load ratio is defined as the preload divided by the total still water load (vertical operating load). Table 2 - Summary of soil conditions at each site and sea-state parameters used for JONSWAP spectrum

Notes on soil conditions

Preload per leg (MN)

Undrained strength at mudline

(kPa)

Strength increase with

depth ρ (kPa/m)

Submerged unit weight

(kN/m3)

Friction angle φ′

(°)

Hs (m) TZ (s) Peak enhancement

factor (γ)

C1 OCR 15-60 99.0 33 20 - - 5.84 8.87 1.15 C2 OCR 5-15 85.0 41 4 - - 8.03 8.84 1.4 C3 OCR 10-20 128.0 42 2 - - 6.8 7.96 2.8 S1 128.0 - - 9.3 30.4 4.1 6.89 2.2 S2 82.5 - - 9.1 27.15 9.85 8.78 2.35 S3 81.1 - - 9.0 27.1 5.09 7.35 1.9 S4 83.0 - - 9.1 29.0 5.97 7.53 2.4 S5 128.0 - - 9.5 27.6 4.64 7.65 1.1

Table 3 – Wind loads applied as nodal point forces

Hull Force (MN)

Equivalent location above

seabed (m)

Windward leg force

above hull (MN)


seabed (m)

Windward leg force

below hull (MN)


seabed (m)

Leeward leg force

above hull (MN)


seabed (m)

Leeward leg force

below hull (MN)


seabed (m) C1 0.163 126.72 0.079 144.7 0.096 114.6 0.040 144.7 0.042 14. C2 1.581 129.5 0.062 137.9 0.031 101.9 0.124 137.9 0.055 102.7 C3 0.837 133.9 0.138 151.1 0.041 106.1 0.074 151.1 0.035 102.1 S1 0.476 116.9 0.106 143.8 0.025 87.1 0.052 143.8 0.016 84.4 S2 2.099 118.9 0.125 133.3 0.053 89.3 0.250 133.3 0.072 92.4 S3 0.327 120.2 0.022 135.6 0.013 92.5 0.044 135.6 0.017 96.3 S4 1.068 63.4 0.197 108.7 0.033 37.3 0.394 108.7 0.042 40.9 S5 0.967 134.4 0.070 152.0 0.023 104.6 0.137 152.0 0.059 102.3


Table 4 - Stiffness values used and the deck displacement response magnitudes for Clay Case 1 (C1)

Stiffness Values Used in Analyses Deck displacement response magnitudes Kv Km Kh Kc mean Range of displacement Range Standard deviation (MN/m) (MNm/rad) (MN/m) (MN/m) (mm) lower (mm) upper (mm) (mm) (mm) Observed N.A. N.A. N.A. N.A. N.A. -63.1 56.2 119.3 13.9 Pinned infinity 0 infinity N.A. 27.2 -308.9 333.5 642.4 97.7 Ir = 80 514.1 28708.8 353.3 -24.4 -25.9 -93.9 113.1 207.0 25.1 Ir = 150 964.0 53829.0 662.5 -45.8 -10.3 -57.9 74.2 132.1 14.9 Ir = 250 1606.7 89714.9 1104.1 -76.3 -4.3 -49.4 81.1 130.5 12.0 Ir = 300 1928.0 107657.9 1325.0 -91.6 -2.9 -56.4 83.3 139.7 12.2 Ir = 350 2249.4 125600.9 1545.8 -106.8 -1.8 -46.1 66.4 112.5 11.1 Fully Fixed infinity infinity infinity N.A. 3.0 -35.4 43.1 78.5 8.9 Table 5 - Stiffness values used and the deck displacement response magnitudes for Sand Case 1 (S1)

Stiffness Values Used in Analyses Deck displacement response magnitudes Kv Km Kh Kc mean Range of displacement Range Standard deviation (MN/m) (MNm/rad) (MN/m) (MN/m) (mm) lower (mm) upper (mm) (mm) (mm) Observed N.A. -43.7 40.2 83.9 7.0 Pinned infinity 0 infinity N.A. 57.5 -57.5 63.3 120.8 10.6 g = 100 408.0 13100.9 354.1 -293.2 64.0 -64.0 53.5 117.5 11.0 g = 200 816.0 26201.9 708.2 -586.3 48.2 -48.2 41.5 89.7 8.8 g = 300 1224.0 39302.8 1062.3 -879.5 41.5 -41.6 48.8 90.4 7.4 g = 400 1632.0 52403.7 1416.4 -1172.6 37.7 -37.8 39.1 76.9 6.3 g = 500 2039.9 65504.6 1770.5 -1465.8 30.5 -35.0 31.8 66.8 5.1 g = 1000 4079.9 131009.3 3541.0 -2931.6 28.6 -28.5 20.2 48.7 3.2 g = 2000 8159.8 262018.5 7082.1 -5863.2 24.6 -24.7 21.9 46.6 2.7 g = 3000 12239.7 393027.8 10623.1 -8794.7 23.1 -23.1 18.5 41.6 2.4 g = 4000 16319.6 524037.0 14164.1 -11726.3 22.3 -22.3 18.1 40.4 2.1 Fully Fixed infinity infinity infinity N.A. 16.8 -16.9 13.7 30.6 1.6 Table 6 - Summary of results for clay

Test Estimated best fit (Ir) Comments C1 300 Value fits both frequency and magnitude tests C2 350 Compromise between higher value or frequency and lower value for magnitude and standard deviation. C3 600 Both frequency and magnitude of displacements suggested this value. However, this test may-be a possible

outlier. Table 7 - Summary of results for sand

Test Estimated best fit (g) Comments S1 300 Value fits both frequency and magnitude tests (see section 6.2.1 for analysis) S2 (500) The measured data of Case S2 showed no clear peak in response other than near the dominant wave

frequency. The calculated response only showed this behaviour for very low stiffness values (around g = 100). However, the weak peak at about 0.18Hz (5.56s) can be well fitted with g of 500 or 1000. The magnitude of the displacements for the low stiffness values are significantly too large and these are best fit by stiffness in the range g = 500 to 4000. No firm conclusion can therefore be drawn, but a value of 500 could be justified.

S3 400 A value of g = 300 best fits the measured peak, but on the basis of measured displacement 400 and 500 fit equally well. On balance a value of g = 400 is deemed appropriate.

S4 (500-2000)

A significantly higher natural frequency of 0.32Hz was measured in the much shallower water at this site. The calculated spectrum did not fit this well, but g values in the range 500 to 2000 do provide some indication of a small peak in broadly the same frequency range. However, the displacement data is inconclusive with the extremes of the range best fitted with high stiffness, whilst the standard deviation fitted well with a low stiffness. Unfortunately, no conclusions could be drawn at this site.

S5 (400) The measured data show only a weak peak at about 0.18Hz, with the frequency being quite well matched by the calculations with g = 400. However, the displacements are best fitted by the pinned footing case. Overall the analysis does not fit the pattern of the measured data well enough for any firm conclusions to be drawn


Figure 1 – Typical structural configuration used (refer to Table 1 for case number) Figure 2 – Spudcan shapes and sizes (refer to Table 2 for case number)
u

w

θ

Reference position

Current positionM

V

H

2R

Figure 4 - Loads and displacements at the foundation level (after Butterfield et al., 1997)

V

Yield surface in (V, M/2R, H) load space

M/2R H

1.83m

C.L.

2.435m 3.665m 2.995m

1.4m

0.44m

C.L.

2.44m 6.65m

Spudcan Shape 1 Spudcan Shape 2

Structural Properties Used Magellan Monitor Galaxy-1 Hull length (m) 42.19 45.72 47.86 For each leg I (m4) 10.462 10.462 28.84 A (m2) 0.444 0.444 0.744 As (m2) 0.038 0.038 0.0592 Hull I (h1) (m4) 19.58 19.58 24.84 I (h2) (m4) 39.17 39.17 49.68

structural node

Hull length

upwave leg(s)

downwave leg(s)

h1 h2

Mean water depth 90 m

Figure 3 – Model C yield surface shape for three degrees of freedom (V:M/2R:H)


0.0E+00

1.0E-03

2.0E-03

3.0E-03

4.0E-03

5.0E-03

6.0E-03

7.0E-03

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Frequency (Hz)

Pow

er S

pect

rum

(m2 /H

z)

Figure 5 – Measured deck displacement spectra for clay case 1 (C1) and sand case 1 (S1)

(a) Clay Case 1 (C1) (b) Sand Case 1 (S1)

0.0E+00

2.0E-04

4.0E-04

6.0E-04

8.0E-04

1.0E-03

1.2E-03

1.4E-03

1.6E-03

1.8E-03

2.0E-03

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Frequency (Hz)

Pow

er S

pect

rum

(m2 /H

z)

0

1

2

3

4

5

6

7

8

0 50 100 150Vertical pre-load per spudcan (MN)

pene

tratio

n fr

om ti

p (m

)

C1C2C3

0

0.5

1

1.5

2

0 20 40 60 80 100 120 140

Vertical pre-load per spudcan (MN)

pene

tratio

n fr

om ti

p (m

)

S1 S2

S3 S4

S5

Figure 6 - Vertical preloading of the spudcan footings

(a) clay cases (b) sand cases


Case C1 IR = 80 (first approx.)

0.0E+00

1.0E-03

2.0E-03

3.0E-03

4.0E-03

5.0E-03

6.0E-03

7.0E-03

8.0E-03

9.0E-03

1.0E-02

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Frequency (Hz)

Pow

er S

pect

rum

(m2 /H

z)

ar 11 coef.FFT N = 512

Case C1 IR = 150

0.0E+00

2.0E-04

4.0E-04

6.0E-04

8.0E-04

1.0E-03

1.2E-03

1.4E-03

1.6E-03

1.8E-03

2.0E-03

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Frequency (Hz)

Pow

er S

pect

rum

(m2 /H

z)


Case C1 IR = 250

0.0E+00

2.0E-04

4.0E-04

6.0E-04

8.0E-04

1.0E-03

1.2E-03

1.4E-03

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Frequency (Hz)

Pow

er S

pect

rum

(m2 /H

z)


Case C1 IR = 300

0.0E+00

2.0E-04

4.0E-04

6.0E-04

8.0E-04

1.0E-03

1.2E-03

1.4E-03

1.6E-03

1.8E-03

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Frequency (Hz)

Pow

er S

pect

rum

(m2 /H

z)


Case C1 IR = 350

0.0E+00

2.0E-04

4.0E-04

6.0E-04

8.0E-04

1.0E-03

1.2E-03

1.4E-03

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Frequency (Hz)

Pow

er S

pect

rum

(m2 /H

z)ar 11 coef.FFT N = 512

Case C1 Pinned Footings

0.0E+00

5.0E-02

1.0E-01

1.5E-01

2.0E-01

2.5E-01

3.0E-01

3.5E-01

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Frequency (Hz)

Pow

er S

pect

rum

(m2 /H

z)


Case C1 Fully Fixed Footings

0.0E+00

2.0E-04

4.0E-04

6.0E-04

8.0E-04

1.0E-03

1.2E-03

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Frequency (Hz)

Pow

er S

pect

rum

(m2 /H

z)


Figure 7 – Frequency spectra for clay case 1 (C1)

0.0E+00

1.0E-03

2.0E-03

3.0E-03

4.0E-03

5.0E-03

6.0E-03

7.0E-03

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Frequency (Hz)

Pow

er S

pect

rum

(m2 /H

z)

storm.IR = 350

Figure 8 – Comparison of measured and simulated frequency spectra for all clay cases

0.0E+00

1.0E-03

2.0E-03

3.0E-03

4.0E-03

5.0E-03

6.0E-03

7.0E-03

8.0E-03

9.0E-03

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Frequency (Hz)

Pow

er S

pect

rum

(m2 /H

z)

stormIR = 600

0.0E+00

5.0E-04

1.0E-03

1.5E-03

2.0E-03

2.5E-03

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Frequency (Hz)

Pow

er S

pect

rum

(m2 /H

z)

stormIR = 600

(a) Clay Case 1 (C1) (b) Clay Case 2 (C2) (c) Clay Case 3 (C3)


Case S1 g = 4000 (first approx.)

0.0E+00

5.0E-06

1.0E-05

1.5E-05

2.0E-05

2.5E-05

3.0E-05

3.5E-05

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Frequency (Hz)

Pow

er S

pect

rum

(m2 /H

z)


Case S1 g = 3000

0.0E+00

5.0E-06

1.0E-05

1.5E-05

2.0E-05

2.5E-05

3.0E-05

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Frequency (Hz)

Pow

er S

pect

rum

(m2 /H

z)


Case S1 g = 500

0.0E+00

5.0E-05

1.0E-04

1.5E-04

2.0E-04

2.5E-04

3.0E-04

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Frequency (Hz)

Pow

er S

pect

rum

(m2 /H

z)ar 11 coef.FFT N = 512

Case S1 g = 400

0.0E+00

1.0E-04

2.0E-04

3.0E-04

4.0E-04

5.0E-04

6.0E-04

7.0E-04

8.0E-04

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Frequency (Hz)

Pow

er S

pect

rum

(m2 /H

z)


Case S1 g = 300

0.0E+00

2.0E-04

4.0E-04

6.0E-04

8.0E-04

1.0E-03

1.2E-03

1.4E-03

1.6E-03

1.8E-03

2.0E-03

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Frequency (Hz)

Pow

er S

pect

rum

(m2 /H

z)


Case S1 g = 200

0.0E+00

2.0E-04

4.0E-04

6.0E-04

8.0E-04

1.0E-03

1.2E-03

1.4E-03

1.6E-03

1.8E-03

2.0E-03

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Frequency (Hz)

Pow

er S

pect

rum

(m2 /H

z)


Case S1 g = 100

0.0E+00

2.0E-04

4.0E-04

6.0E-04

8.0E-04

1.0E-03

1.2E-03

1.4E-03

1.6E-03

1.8E-03

2.0E-03

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Frequency (Hz)

Pow

er S

pect

rum

(m2 /H

z)


Case S1 Pinned Footings

0.0E+00

2.0E-04

4.0E-04

6.0E-04

8.0E-04

1.0E-03

1.2E-03

1.4E-03

1.6E-03

1.8E-03

2.0E-03

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Frequency (Hz)

Pow

er S

pect

rum

(m2 /H

z)


Case S1 Fully Fixed Footings

0.0E+00

2.0E-06

4.0E-06

6.0E-06

8.0E-06

1.0E-05

1.2E-05

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Frequency (Hz)

Pow

er S

pect

rum

(m2 /H

z)


Case S1 g = 1000

0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

7.0E-05

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Frequency (Hz)

Pow

er S

pect

rum

(m2 /H

z)


Figure 9 – Frequency spectra for sand case 1 (S1)

Case S1 g = 2000

0.0E+00

5.0E-06

1.0E-05

1.5E-05

2.0E-05

2.5E-05

3.0E-05

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Frequency (Hz)

Pow

er S

pect

rum

(m2 /H

z)



0.0E+00

2.0E-04

4.0E-04

6.0E-04

8.0E-04

1.0E-03

1.2E-03

1.4E-03

1.6E-03

1.8E-03

2.0E-03

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Frequency (Hz)

Pow

er S

pect

rum

(m2 /H

z)

stormg = 300

Figure 10 – Comparison of measured and simulated frequency spectra for all sand cases

0.0E+00

1.0E-03

2.0E-03

3.0E-03

4.0E-03

5.0E-03

6.0E-03

7.0E-03

8.0E-03

9.0E-03

1.0E-02

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Frequency (Hz)

Pow

er S

pect

rum

(m2 /H

z)

stormg = 500g = 1000

0.0E+00

1.0E-03

2.0E-03

3.0E-03

4.0E-03

5.0E-03

6.0E-03

7.0E-03

8.0E-03

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Frequency (Hz)

Pow

er S

pect

rum

(m2 /H

z)

stormg = 300g = 400

(a) Sand Case 1 (S1) (b) Sand Case 2 (S2) (c) Sand Case 3 (S3)

0.0E+00

2.0E-05

4.0E-05

6.0E-05

8.0E-05

1.0E-04

1.2E-04

1.4E-04

1.6E-04

1.8E-04

2.0E-04

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Frequency (Hz)

Pow

er S

pect

rum

(m2 /H

z)

stormg = 2000g = 500

(d) Sand Case 4 (S4) (b) Sand Case 5 (S5)

0.0E+00

2.0E-03

4.0E-03

6.0E-03

8.0E-03

1.0E-02

1.2E-02

1.4E-02

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Frequency (Hz)

Pow

er S

pect

rum

(m2 /H

z)stormg = 400


c67

Documents