physical modelling of the push-over capacity of a jack-up structure on sand in a geotechnical...

Physical modelling of the push-over capacity of ajack-up structure on sand in a geotechnicalcentrifuge

B. Bienen, M.J. Cassidy, and C. Gaudin

Abstract: Offshore jack-up drilling rigs are subjected to loading from wind, waves, and current in addition to their self-weight. This applies combined loading in all six degrees-of-freedom in space on the footings. Although the foundation–soil interaction is crucial to the overall response of a jack-up structure, current state-of-the-art models to predict jack-upfooting behaviour, developed using data from single footing experiments, have not been validated for such multi-footingsystems under general combined loading. This paper introduces the experimental development of a three-legged modeljack-up and loading apparatus designed to investigate the rig’s response — in particular the footing load paths — undercombined loading in three dimensions. Push-over experiments were performed in a geotechnical beam centrifuge on silicasand. Experimental results of two tests on dense sand are discussed, highlighting differences in response and mode of fail-ure depending on the loading direction of the jack-up. The importance of three-dimensional modelling is also stressed byexperimentally demonstrating that the symmetric load case is not necessarily conservative.

Key words: jack-up, physical modelling, centrifuge, structure–soil interaction, three-dimensional.

Resume : Les plates-formes de forages en mer subissent des charges provenant du vent, des vagues et des courants enplus de leur masse. Ceci implique des charges combinees dans les six degres de liberte dans l’espace sur les semelles.Malgre que les interactions fondations–sol soient cruciales dans l’etablissement de la reponse de la plate-forme, les mode-les integrant les connaissances actuelles pour la prediction du comportement des semelles des plates-formes, qui ont etedeveloppes a partir de donnees provenant d’essais a une semelle, n’ont pas ete valides pour des systemes avec semellesmultiples soumis a des charges combinees. Ce papier presente le developpement experimental d’un modele de plate-formea trois pattes et d’un appareil de chargement concu pour investiguer la reponse de la plate-forme - plus particulierement lecheminement de charge de la semelle – soumis a un chargement combine en trois dimensions. Des experiences en deplace-ment lateraux ont ete effectuees dans une centrifuge geotechnique sur du sable de silice. Les resultats experimentaux desdeux essais sur du sable dense sont discutes, demontrant les differences de reponses et de mode de rupture dependammentde la direction de la charge sur la plate-forme. L’importance de la modelisation en trois dimensions est valorisee en de-montrant experimentalement que le scenario de charge symetrique n’est pas necessairement conservateur.

Mots-cles : plate-forme auto-elevatrice, modelisation physique, centrifuge, interaction structure–sol, trois dimensions.

[Traduit par la Redaction]

Introduction

Jack-up drilling rigs are mobile offshore structures typi-cally resting on three shallow foundations called spudcans(Fig. 1). Although the utilization of these rigs in deeperwaters and thus harsher environmental loading conditions isa continuing trend, understanding of the rig’s response andin particular the foundation behaviour remains unsatisfac-tory. This is reflected in reported statistics, as the accidentrate for this type of offshore structure remains higher thanfor fixed platforms (Hunt and Marsh 2004, for instance).

Force-resultant models based on hardening plasticitytheory, representing state-of-the-art foundation modelling

for cases such as jack-ups, have been developed (Schotman1989; Nova and Montrasio 1991; Martin and Houlsby 2001;Byrne and Houlsby 2001; Houlsby and Cassidy 2002; Cas-sidy et al. 2002, 2004; Bienen et al. 2006), where the predic-tion of displacements of the footing under combined loadingis important to predict the overall system response. Resultsfrom single footing tests, performed on a laboratory floor(Martin 1994; Gottardi et al. 1999; Byrne and Houlsby2001; Cassidy and Cheong 2005; Bienen et al. 2006) and ingeotechnical centrifuges (Tan 1990; Murff et al. 1992; Cas-sidy 2007; Bienen et al. 2007) have been used to validatethe footing model features and calibrate its parameters.However, the load paths applied in these experiments weredesigned to aid model development and were not representa-tive of actual jack-up spudcan load paths.

Experiments on model jack-ups have been reported previ-ously. For instance, Vlahos (2004) and Vlahos et al. (2005)describe 1g physical modelling of a 1:250 scale three-leggedjack-up resting on clay. The experiments explored the foot-ing load paths, load redistribution among the footings, hulland footing displacements at failure, and ultimate system ca-

Received 24 May 2007. Accepted 22 October 2008. Publishedon the NRC Research Press Web site at cgj.nrc.ca on12 February 2009.

B. Bienen,1 M. Cassidy, and C. Gaudin. Centre for OffshoreFoundation Systems, The University of Western Australia,35 Stirling Highway, Crawley WA 6009, Australia.

1Corresponding author (e-mail: [email protected]).

190

Can. Geotech. J. 46: 190–207 (2009) doi:10.1139/T08-114 Published by NRC Research Press

pacity. A series of centrifuge tests of a model jack-up hasalso been carried out at Cambridge University on clay(Dean et al. 1996) and sand (Murff et al. 1991; Tsukamoto1994; Dean et al. 1995; Hsu 1998). These studies focussedon footing stiffness (rotational stiffness in particular) underworking loads. However, the model rig was relatively smalland stocky in size, and its dimensions were not representa-tive of present-day field jack-ups, which are rather flexiblestructures with long, relatively slender legs.

In all of these model jack-up experiments, the line of ac-tion of the horizontal load applied at the hull representingenvironmental loading coincided with the system’s axis ofsymmetry (that is, only planar vertical–horizontal–moment(VHM) loading was accounted for). These ‘‘symmetrical’’loading conditions enable simplified two-dimensional (2D)analysis of jack-ups. However, environmental loading fromwind, waves, and current will neither always act along thesystem’s ‘‘axis of symmetry’’ nor necessarily be collinear.This implies combined loading on the jack-up structure,which introduces loading in all six degrees-of-freedom inspace on the shallow footings (Fig. 2). The ‘‘symmetrical’’case may not always be the critical loading direction. There-fore, a better understanding of the behaviour of jack-up rigsunder general combined loading is required to improve mod-els for the prediction of jack-up response in three dimen-sions. To the authors’ knowledge, no experiment on amodel jack-up has been performed where the rig experi-enced general combined loading in three-dimensional (3D)space.

This paper introduces the development of a model jack-uprig and loading apparatus. The experiments were performedunder true-scale stresses in a geotechnical beam centrifuge.The aims of the experiments were to show the footing loadpaths of a jack-up on sand for general combined loading in3D space, including load redistribution between the threefootings. This plays an important role as — contrary to asingle-footing system — failure of one spudcan in a multi-footing structure does not necessarily imply failure of thesystem. Further aims include investigation of differences inthe load–displacement response and eventually the failuremodes of the jack-up for different orientations to the appliedload (Fig. 2). The experimental results are intended for eval-uation of the performance of a force-resultant plasticity foot-

ing model for six degrees-of-freedom (Bienen et al. 2006)when used in predicting the response of a three-legged pro-totype jack-up. Unless otherwise stated, all dimensions,loads, and displacements are presented in prototype scale.

Design of a model jack-up for experimentalinvestigation in a beam centrifuge

There are numerous different jack-up designs being usedin the field. As the aim of the tests here was not to focuson one particular rig design, but to investigate jack-up be-haviour in general, a generic prototype was modelled.

Table 1 summarizes key dimensions of several jack-upscurrently operating in the world’s offshore fields. Theseformed the basic considerations for the choice of an averageprototype. However, a number of other design considera-tions also significantly influenced the development.

Design considerations for the model jack-upDesign considerations for the development of the model

jack-up included:

� Creation of a 1:N scale generic model jack-up representa-tive of an average current field jack-up for testing at anacceleration of multiple (N) times Earth’s gravity in thecentrifuge (known as Ng). The experiments were per-formed at an acceleration of 200 g in The University ofWestern Australia (UWA) beam centrifuge (Randolph etal. 1991). The model jack-up was therefore designed as a1:200 scale version of the prototype. Correct scaling ofthe prototype geometry is important to obtain load pathssimilar to those in field jack-ups. This is crucial to therelevance of the experiments. As the model jack-up hadto be accommodated within the space limitations of theUWA beam centrifuge (see Fig. 3), the maximum possi-ble model spudcan diameter (D) was 50 mm. This was toallow leg spacings as described in Table 1 as well as suf-ficient clearance to the testing container boundary. Theremaining model dimensions (Table 2) were then deter-mined using the average field jack-up ratios (Table 1) asguidance. The built design is equivalent to a medium-sizeprototype with a leg length of 89 m and 10 m diameterspudcans (Table 2). The design allows two testing siteson the same soil sample.

Fig. 1. Typical jack-up and spudcan (adapted from Reardon 1986).

Bienen et al. 191

Published by NRC Research Press

� Correct scaling of the structural properties (EA, EI) be-tween model and prototype (Table 3), which is equallyimportant to obtaining load paths relevant to field jack-ups. As the overall system behaviour was of interest inthese experiments rather than stresses in individual mem-bers of the trusswork legs, for instance, the model jack-up is built of equivalent structural members. Cost andtime constraints also supported this design.

� Correct scaling of the mass to apply the correct self-weight. This had to be taken into consideration due tothe chosen experimental set-up for the installation and

preloading phase as well as the horizontal loading phase,and became the deciding factor in selecting fabricationfrom aluminium.The gravitational field in the centrifuge changes with re-

spect to the rotational centre of the centrifuge and thus, itvaries over the model’s height. The experimental prioritywas to scale the soil stress field correctly and therefore, theacceleration level was set at 200 g at the soil surface. It isargued that the measured response of the 1:200 model jack-up is due to the footing reactions at an elevated gravity levelof 200 g, and therefore, the scaling factor of N = 200 is ap-

Fig. 2. Sign convention (after Butterfield et al. 1997) and loading directions.

Table 1. Typical field jack-up dimensions.

RigHulllength (m)

Hullwidth (m)

Hulldepth (m)

Forward leg toaft legs (centre tocentreline) (m)

Aft legs(centre tocentre) (m)

Leg length(m)

Spudcandiameter,D (m)

ENSCO (57, 86, 94)a 54.9–63.2 53.0–53.6 6.1–7.6 36.6–37.8 35.1–37.1 109.7–113.7 12.2–15.2F&G (Alpha 350, JU-2000, Uni-

versal M class)b67.1–70.4 71.8–76.2 8.2–9.5 39.6–47.2 43.3–54.6 140.5–166.9 17.0–18.3

GSF (High Island I, Main Pass I,Rig 103, Rig 127)c

54.9–63.1 51.2–53.6 6.1–7.6 Not known Not known 106.7–126.8 12–14.0

Noble (Carl Norberg, Charles Co-peland, Dick Favor, Ed Noble,George McLeod)d

53.0–63.1 49.4–53.6 5.5–7.6 Not known Not known 76.3–127.1 11.5–14.0

Average, as a proportion of thespudcan diameter D

4.51D 4.18D 0.52D 2.61D 2.71D 8.74D 1.00D

awww.enscous.com.bwww.fng.com.cwww.globalsantafe.com.dwww.noblecorp.com.

192 Can. Geotech. J. Vol. 46, 2009


Fig. 3. Centrifuge constraints, model jack-up, and loading apparatus (schematic, adapted from Byron-Brown 2004).

Table 2. Dimensions of built UWA scaled jack-up, including comparison with Vlahos (1994) and the Cambridge centrifuge model (e.g.Tsukamoto 1994).

Jack-up rig CommentHulllength

Hullwidth

Hulldepth

Aft legs(centre tocentre)

Fwd. legto aft legs(centre tocentreline) Leg length

Spudcandiameter

Average fieldjack-up

Ratio relating to spudcandiameter D

4.51D 4.18D 0.52D 2.61D 2.71D 8.74D 1.0D

Model jack-upin this paper

Design dimension re-lating to spudcan dia-meter

4.20D 3.90D 0.64D 2.70D 2.50D 8.90D 1.0D

=>Built model basedon 50 mm diameterspudcan

210 mm 195 mm 32 mm 135 mm 125 mm 445 mm 50 mm

Corresponding proto-type (N = 200)

42 m 39 m 6.4 m 27 m 25 m 89 m 10 m

Vlahos (2004) Ratio relating to spudcandiameter

4.33D 3.89D 0.56D 2.83D 2.5D 8.33D 1.0D

Built model (1: 250scale)

324 mm 280 mm 40 mm 216 mm 187 mm 600 mm 72 mm

Corresponding prototype 81 m 70 m 10 m 54 m 46.8 m 150 m 18 m

Cambridgemodel

Ratio relating to spudcandiameter

3.98D 3.29D 1.73D 3.72D 3.22D 4.28D 1.0D

Built model 230 mm 190 mm 106.6 mm 215 mm 186 mm 246.4–250.4 mm

57.8 mm

Corresponding prototype(N = 128)

29.5 m 24.3 m 13.6 m 27.5 m 23.8 m 31.5–32.1 m 6.5 m

Corresponding prototype(N = 256)

58.9 m 48.6 m 27.3 m 55.0 m 47.6 m 63.1–63.33 m 13 m

Note: For consistent modelling of a prototype, a 1:N model is tested at Ng in the centrifuge. Between the model and the prototype, length is scaled by1:N.

Bienen et al. 193


plied when converting the experimental results to prototypeunits according to Table 4. However, scaling by N = 200throughout does not apply to the self-weight. Here, the scal-ing factor varies between N = 145 at the hull to N = 200 atthe spudcans. However, the vertical load acting on the foot-ings is measured throughout the test by strain gauges at thebottom of each of the three legs and therefore, the loads ap-plied to the spudcan footings are known accurately.

HullThe hull of the jack-up, shown in Fig. 4a, takes the shape

of an equilateral triangle of 42 m side length. Similar to theappearance of field jack-ups, the ‘‘triangle corners’’ weretruncated. The hull was required to be significantly stifferthan the legs. However, accurate modelling of the secondmoment of area and the area was sacrificed to correctlyscale the prototype hull mass, which was regarded para-mount. Details, such as ballast tanks or drilling equipment,were not modelled. The model hull was machined from asolid aluminium block. A hole was cut at the centre of grav-ity to accommodate the preloading arrangement.

LegsThe model jack-up legs were made of aluminium pipe

sections representing equivalent structural properties(Table 3). Priority was placed on the accurate modelling ofthe flexural stiffness and self-weight. The chosen cross sec-tion had an outer diameter of 25 mm and a wall thickness of3 mm, equating to a 5 m diameter and 0.6 m wall thicknessin prototype dimensions. The prototype leg length was 89 m.The legs were rigidly attached to the hull, although finitestiffness and nonlinearity of the leg–hull connection (seeSpidsøe and Karunakaran 1996, for example) is recognised.

Spudcan footingsTen metre diameter spudcans were chosen for the model

jack-up. As the spudcan spacing is replicated correctly froma prototype rig, the footing load paths and the load-sharingbetween the footings will be similar to that in the prototype.

The footing elevation and spudcan dimensions are shown inFig. 5. The footing plan is circular. The spudcans arethreaded at the top to screw into the legs. This makes thespudcans interchangeable should it be decided to test the rigwith different diameter or different shaped footings at a laterdate. The footings were machined from aluminium with nospecific treatment applied to the surface, leading to a smoothspudcan–soil interface.

Instrumentation of the model jack-upAlthough it was desirable to record spudcan loads as well

as displacements at the hull and at the spudcans in all sixdegrees-of-freedom (Fig. 2), it was decided not to track foot-ing displacements individually to limit instrumentation.

Load measurementAll three legs were strain-gauged for axial load as well as

bending in both orthogonal axes (Fig. 2). The axial straingauges (EA-13–062UT-350) were located 40 mm above thefootings. Two sets of bending gauges (EA-13–125MK-120)were used, positioned perpendicular to each other at 43 mmfrom the top and 23 mm from the bottom of the legs, re-spectively.

Assuming simple beam theory, the shear forces (H2, H3)and bending moments (M2, M3) in both orthogonal axes canbe derived from the bending gauges. As the vertical load (V)is measured directly, this leaves only the leg torsion, Q, un-known. Although measurement of torsion would be benefi-cial, the torsional component of the footing load wasexpected to be significantly lower than the bending moment,and its absence was not considered a major drawback intracking the footing load paths during the experiment. Itwas omitted in this series of tests because of restrictions inthe maximum number of channels that could be logged onthe UWA beam centrifuge.

Displacement measurementDisplacements in all six degrees-of-freedom were meas-

ured at the hull (hull reference point, Fig. 2). A set of fourlinear displacement transducers was used to record the verti-cal (w) as well as horizontal (u2, u3) displacement alongboth axes. These devices offer very precise displacementmeasurement whilst being compact in size (to enable mount-ing within the space limitations of the centrifuge set-up) andvery lightweight (approximately 13 g at 1g for the smallestand 25.5 g for the largest linear displacement transducer(LDT)), so as to affect the model response as little as possi-ble. The arrangement is shown in Fig. 4b. In addition to the

Table 3. Structural properties of the jack-up model legs and corresponding prototype.

Relationship Built

Property Model Prototype Model Prototype Typical prototype (Vlahos et al. 2005)Eleg — (Not scaled directly) 69 000 (N/mm2) (Not scaled directly) 2.0�108 (kN/m2)Aleg — (Not scaled directly) 207.3 (mm2) (Not scaled directly) 1.0 (m2)Ileg — (Not scaled directly) 12 777.6 (mm4) (Not scaled directly) 7.2 (m4)EA(leg) 1 N2 14.3� 106 (N)* 5.7� 108 (kN)* 2.0� 108 (kN)EI(leg) 1 N4 8.8� 108 (N�mm2) 1.4� 109 (kN�m2) 1.4� 109 (kN�m2)

Note: The model jack-up was built from aluminium, whereas field jack-ups are usually built from steel. Due to the different material and hence,different Young’s modulus, the groups of EA and EI have to be scaled correctly, rather than the properties of E, A, and I individually.

*Priority was placed on scaling the flexural stiffness correctly.

Table 4. Scaling laws.

Model PrototypeLength, displacement 1 NAngle, rotation 1 1Vertical load, V 1 N2

Horizontal load, H 1 N2

Moment, M 1 N3



Fig. 4. Model jack-up and instrumentation: (a) load sensors, (b) displacement and rotation sensors, and (c) schematic. LDT, linear displace-ment transducer.

Bienen et al. 195


three orthogonal displacement components in space (w, u2,u3) measured directly, the twist u can be derived from thepair of LDTs mounted horizontally at the rear of the hull(LDT1 and LDT2, Figs. 4b and 4c).

Rotations in both orthogonal directions (q2, q3) weremeasured using tilt sensors (EZ-VIB-3000–005 Analog Lin-ear Tilt System by Advanced Orientation Systems Inc.).These sensors were found to have a slightly reduced rangeat elevated g levels, which alters the calibration factor. Lin-earity and sensitivity, however, did not seem to be affected.One tilt sensor was mounted on top of the hull along its cen-treline, the other one perpendicular to this at the back of theplatform (Figs. 4b and 4c).

Design of the loading apparatus

The purpose of these experiments was to obtain informa-tion on the footing load paths and the system behaviour ofthe rig during a monotonic push-over. The data is intended tobe used further to validate an existing six degree-of-freedomforce-resultant plasticity footing model (Bienen et al. 2006,2007) at prototype system scale. Therefore, a realistic yet nottoo complex loading situation was sought to be applied to thesystem. Further, this loading needed to be completely auto-mated as the experimental set-up was inaccessible during thetest. The loading distinguishes between an installation andpreloading phase and a horizontal loading (operational)phase.

Installation and preloadingTo produce load paths representative of field jack-ups, it

was important to perform the installation phase of the ex-periments at correctly scaled soil stress levels. Therefore, in-stallation of the model jack-up was to take place in-flight.Further, similar to field procedure, the unit was to be pre-loaded vertically before being unloaded to its self-weight.After the preloading stage, the model jack-up should be freeto move in any direction.

These requirements necessitate the rig to be

(1) suspended above the soil surface during centrifuge spin-up(2) lowered onto the soil in-flight at a controlled rate(3) penetrated into the soil beyond its self-weight to a target

vertical preload, applied through the system’s centre ofgravity

(4) free to sit under its self-weight after the preloadingstage, i.e., with no additional vertical loading and free tomove in any direction.

For the experimental set-up to meet these requirements, arod with top and bottom loading platens was employed forthe installation and preloading phase. This arrangement isrigidly connected to an actuator controlling vertical move-ment as shown in Figs. 3 and 6. The 10 mm diameter rodruns through a 50 mm diameter hole in the hull. The dis-tance between the two platens is 70 mm, whereas the hullthickness is 32 mm, allowing for significant freedom ofmovement of the model jack-up during the operationalphase.

Before installation, the model jack-up rests on the bottomplaten, suspended above the soil surface. The actuator thenlowers the structure onto the soil. In the experiments dis-cussed in this paper, the spudcans were installed at 0.02 m/s.However, this is not believed to be critical as the tests wereperformed on dry sand. The bottom platen is chamferedwhere it faces the hull to ensure the jack-up spudcans‘‘land’’ on the sand at their target positions. Assuming a per-fectly level soil surface and identical density and soil stressfields, each of the three spudcans should penetrate evenlyunder the rig’s self-weight as the loading rod travels throughthe hull. Vertical preload is then applied by the top loadingplaten through the jack-up’s centre of gravity. After reachingthe target preload, the rod is retracted such that the modeljack-up sits freely on the soil sample under its self-weight.

Horizontal loadingEnvironmental loading on a jack-up due to wind, waves,

and current is complex in nature. As a first step, for this ser-ies of tests it was decided to simplify the loading regime toa quasi-static monotonically increasing horizontal load ap-plied at the hull. To study the influence of a variation inloading direction, it was required that the line of action ofthis load to the model jack-up’s axis of symmetry be varied.

Fig. 5. Prototype spudcan elevation and dimensions, load referencepoint.

Fig. 6. Suspension–preloading arrangement.



A pulley system as shown in Figs. 3 and 7 was used toapply the horizontal load. The motor is mounted directlyonto the strongbox. The pulley system can be mountedalong the centreline of the strongbox, which achieves load-ing of the jack-up along its axis of symmetry. For anotherloading direction discussed in this paper, the pulley wasbolted off-centre, which loaded the jack-up along the hori-zontal plane, at an angle of about 228 to its axis of symme-try. The height of the pulley system is adjustable, such thatit can be secured in line with the estimated position of thewire attachment point at the hull after preload. This ensuredhorizontal loading, although a small deflection due to thewire’s self-weight catenary was expected. It was considerednegligible, as the wire was relatively thin and light (at a di-ameter of 1.5 mm) and based on its free length the maxi-mum deflection at the jack-up was less than 28 from thehorizontal.

In the experiments, the horizontal load was applied at the

hull at a velocity of 0.02 m/s. As the tests were performedon dry sand, this rate is not believed to be critical.

Instrumentation of the loading apparatus

Load measurementThe vertical loading rod contains a 10 kN axial load cell,

which monitors the applied preload. It further serves as aback-up measurement, as its reading should coincide withthe sum of the axial leg strain gauges. This was found to bethe case for both experiments. The average difference be-tween the sum of the axial leg loads and the 10 kN axialload was less than 0.5%, with a maximum recorded differ-ence of 0.9%.

The horizontal load applied to the hull is measured by a1 kN axial load cell inserted into the pulley wire just beforeits attachment point at the hull (Figs. 4a and 4c). Thismounting position was chosen so that no deductions had to

Fig. 7. Pulley system (schematic): (a) top view; (b) side view.

Bienen et al. 197


be made due to (minor) frictional losses at the pulleys. Apin joint is located between the bolt that screws into thejack-up hull and the load cell, allowing it to swivel depend-ing on the vertical position of the rig to the pulley system.

Displacement measurementThe vertical displacement of the rod as well as the wire

movement as measured through the motor encoders were re-corded in the experimental data files. The vertical actuatordisplacement can also be used as a check of the platform’svertical displacement during the installation and preloadingphase.

Centrifuge testingThe experiments were performed at 200 g in the UWA

beam centrifuge, details of which can be found in Randolphet al. (1991). It is a 1.8 m radius centrifuge with a maximumpayload of 200 kg at 200 g. Details of tests 1 and 2 are pro-vided in Table 5.

Test set-upThe test set-up is schematically shown in Fig. 3. A

385 mm tall and 300 mm wide frame bolted onto the strong-box provides the mounting for the vertical actuator, fromwhich the model jack-up is suspended, as well as for thefixed ends of all LDTs and the pulley. The tilt sensors aremounted directly on the jack-up hull. The pulley motor isbolted onto the strongbox outside the frame.

The model jack-up legs are labelled A, B, and C as indi-cated in Figs. 2, 4, and 7.

Further, as the experimental set-up extends considerablyabove the top of the strongbox, the frame is clad with per-spex and aluminium sheets serving as a windshield againstthe drag forces exerted by the air in-flight. The aluminiumsheets also add stiffness to the frame.

The test is confined to one-half of the strongbox, enablingtwo tests to be performed on the same soil sample (the twotests discussed in this paper were performed on the samesample). To avoid boundary effects, a minimum clearanceof two footing diameters between the edge of the footingsand the strongbox walls was maintained. This is consistentwith the minimum values required to eliminate boundary ef-fects proposed by Tsukamoto (1994).

Soil characteristicsThe tests were carried out on commercially available

superfine silica sand, characterized by d50 = 0.190 mm anda critical state friction angle fcv = 34.98. The maximum andminimum dry densities were 14.88 and 17.95 kN/m3, respec-tively (Cheong 2002). The sample was prepared by carefullypouring the sand into the strongbox in five successive layersof 30 mm, each of them vibrated for 20 s on a vibrating ta-ble. This process has been used for several years at UWAand has demonstrated very good repeatability and samplehomogeneity. The sample was prepared and vibrated dry toachieve a relative density Dr & 84%. The calculation of rel-ative density was based on the overall weight of the soilsample and its measured volume.

A sample height of 150 mm ( = 3D) was chosen to avoidboundary effects, but also to minimize the overall set-up

height. The expected penetration was limited to approxi-mately 0.3D.

The stress relief due to unloading to 1 g between tests 1and 2 was erased during spin-up back to 200 g. For bothtests the sample was normally consolidated.

Discussion of resultsThe response is discussed in terms of displacements at the

hull reference point {w, u2, u3, u, q2, q3} as well as footingloads {V, H2, H3, Q, M2, M3} and the load applied throughthe pulley system. The sign convention adopted here isshown in Fig. 2. Zero vertical displacements are assumedwhen the spudcan tips are just touching the soil surface.The footing loads are inferred from the leg strain gauges forthe footing load reference point (LRP) (Fig. 5).

Where resultant displacements, rotations, horizontal loadsor moments are shown, the components in the 2 and 3 direc-tions have been resolved to one resultant value. That meansthat the resultant horizontal displacement u ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiu2

2 þ u23

p, for

instance, indicates the displacement magnitude in the hori-zontal plane but not the directionality.

The term ‘‘failure’’ in this paper is defined as foundationfailure. The jack-up cannot resist any additional externalload and displacements become excessive. Eventually, thiswill lead to the rig overturning and thus, losing load ca-pacity.

Installation and preloading phaseThe model jack-up, suspended above the soil surface dur-

ing spin-up of the centrifuge, was lowered onto the soil afterthe centrifuge had reached the target acceleration (N = 200 g).In all centrifuge tests, spudcan A touched down first, fol-lowed by spudcan C and then B (Figs. 8a and 9a). This isthought to be due to minimal differences in weight distribu-tion on the model jack-up (due to cable routing, the pulleywire, etc.), which resulted in slight positive rotation in the q2direction (by about 0.58 to 0.638, measured by tilt sensor 1)and about 0.618 to 0.758 in the negative q3 direction (meas-ured by tilt sensor 2). Further, the suspension platen that themodel jack-up was resting on (until the spudcans began tocarry the self-weight) may not have been perfectly parallel tothe soil surface. This may have contributed to the rotations inthe q2 and q3 directions.

After the self-weight penetration of the spudcans (Fig. 8a,test 1; Fig. 9a, test 2), spudcans A and C experienced someloss of vertical load, whereas spudcan B gradually gainedsome vertical load. This can be explained by the self-righting of the jack-up as the tapered suspension platenwithdrew from the inside of the hull, leaving the jack-upfree to move, which resulted in all rotations as well as themovements measured in the u2 and u3 directions duringspin-up to be released.

Upon contact of the preloading platen with the top of thehull, the vertical load on all three footings rapidly increased.After reaching the target preload (the load loss upon haltingthe preloading process is due to relaxation of the sand), theplaten was withdrawn such that once again the jack-up satfreely under its self-weight. Table 6 summarizes the verticalspudcan loads after the preloading phase.

When plotted as vertical load versus penetration (Fig. 10),the curves of test 1 and test 2 are almost identical. This in-



dicates not only a very high degree of uniformity throughoutthe sand sample, but it also proves that the test set-up andprocedure are reliable and provide very good repeatabilityof the experiments. Furthermore, the consistency of theload–penetration curves indicates that the distance between

the test sites ensures that failure mechanisms generated bytest 1 do not affect the results of test 2.

As the spudcan tips penetrated (0–1.45 m, Fig. 10), verylittle axial load was picked up due to the small bearingarea. However, as the spudcans penetrated further, the shal-

Fig. 8. Time history, test 1: (a) vertical load, (b) displacement, (c) rotation, and (d ) horizontal load components; (e) moment componentsduring the horizontal loading phase.

Table 5. Details of experiments.

Test properties Installation–preloading phase Operational phase

Testname

Gravitylevel

Horizontalloading direction,a (Fig. 2)

Sand relativedensity, Dr

Vself-weight perspudcan (MN)

Vpreload perspudcan (MN)

Vself-weight/Vpre-load

sself-weight/gR

Max Happlied

(total at hull)(MN)

Test 1 200 g 0 Dense (84%) 49.7–58.5 106.4–145.5 0.40–0.51 7.29–8.58 22.0Test 2 200 g 22 Dense (84%) 47.6–56.8 116.9–158.4 0.36–0.49 6.98–8.33 17.9

Bienen et al. 199


lower angled part of the footing underside (1.45–2.35 m,Fig. 10) proceeded to make contact with the soil, which cre-ated a much more rapid increase in bearing area and thus invertical load as well. At point P1, the spudcans were bearing

the entire self-weight of the jack-up. Also visible in this fig-ure is the relaxation and the load re-distribution between thefootings due to the self-righting of the rig as discussedabove. The response upon reloading (on commencement of

Fig. 9. Time history, test 2: (a) vertical load, (b) displacement, (c) rotation, and (d ) horizontal load components; (e) moment componentsduring the horizontal loading phase.

Table 6. Vertical load on spudcans.

Test Load type Spudcan A Spudcan B Spudcan CTest 1, a = 08 Preload (MN) 145.5 106.4 123.5

Self-weight (MN) 58.5 54.5 49.7Self-weight/preload 0.402 0.512 0.402

Test 2, a = 228 Preload (MN) 158.4 116.9 129.2Self-weight (MN) 56.8 56.7 47.6Self-weight/preload 0.359 0.485 0.368



preloading) was very stiff with the curves re-joining the vir-gin penetration line once the footings carried more than theirprevious highest vertical load. Full spudcan penetration (i.e.,maximum bearing area) was achieved at w = 2.35 m and theentire footing undersides were in contact with the soil (asmarked in Fig. 10).

However, it needs to be borne in mind that the displace-ment recorded in the experiments was measured at the hullreference point, not at the individual spudcans. Visual infor-mation at this point indicated that spudcan A had indeedfully penetrated, but spudcans B and C were seated slightlyhigher in the soil. This was observed in both experiments.

After the target preload (point P2) was applied, the jack-up was unloaded to its self-weight. The vertical load on thefootings dropped accordingly. The horizontal loading phasecommenced at point P3. During this stage, which is dis-cussed in the following sections, the forward footing A wasmore heavily loaded vertically than footings B and C.

Horizontal loading (operational) phaseResults for the horizontal loading phase of the experi-

ments are shown in Figs. 8 and 9 as well as Figs. 11 to 13.The experiments were terminated when the displacementsincreased significantly with virtually no increase in externalload, which indicates imminent failure.

Test 1: horizontal loading along the axis ofsymmetry

In test 1, the horizontal load was applied along the axis ofsymmetry (along the 3 axis, Fig. 2). The maximum appliedload measured in the experiments was 22.0 MN, at whichstage the jack-up horizontal hull displacement was 2.39 m(see also Fig. 11 with further discussion following). Whenthe experiment was terminated, 3.63 m of horizontal dis-placement in the u3 direction, 0.688 of rotation in this plane(q2), and 0.028 m of additional vertical penetration (0.0028spudcan diameters) were recorded, all measured at the hullreference point (Figs. 8b and 8c). The horizontal displace-ment at hull level is due to horizontal spudcan displacementas well as rotation at spudcan level being projected over the

large leg length (Fig. 14 shows rotation but only a minimalamount of horizontal displacement of the forward spudcanA, while the aft spudcans B and C experienced larger hori-zontal displacement as well as rotation). Displacements androtations out of plane were negligible as expected in thissymmetric loading case: a change of 0.13 m in the u2 direc-tion was measured while the rotation out of plane (in the q3direction) remained approximately zero until shortly beforethe test was terminated (Figs. 8b and 8c). Although sometwist was developed during the early stages of the horizontalloading phase (with the maximum twist u being 0.298), itreduced to about zero twist as the applied load increased, aswould be expected during a symmetrical pull. Only shortlybefore the test was terminated, when q3 picked up, did u in-crease again slightly.

The horizontal pull at hull level changed the vertical load-ing on the footings as the overturning motion resulted in apush–pull mechanism between the forward and the aft legs,respectively, whilst also introducing H3 and M2 loading onthe spudcans (Fig. 8). The M2 moment loading was large inmagnitude due to the large leg length (i.e., lever arm withrespect to the footings). The H2 and M3 reaction componentswere small in comparison due to the symmetric nature of theloading. Generally speaking, the two aft spudcans B and Cbehaved very similarly, as would be expected under thesesymmetrical loading conditions. The minor differences re-sulted from slightly different embedment (Fig. 14a photo-graphic evidence, not measured) and a slight splaying of thelegs.

The reason for the curves of spudcan A terminating ear-lier than those for spudcans B and C in all plots of test 1(see Figs. 8a and 8d, for instance) is that leg A exceededthe capacity of the bending gauges. However, as the bendingmoments remained well below the structural capacity of themodel jack-up legs, the test proceeded.

Figure 8e shows that initially moment (M2) loading issimilar on all three spudcans. However, from as early asM2 & 20 MNm, the response exhibited by spudcan A isslightly stiffer than that of the other two footings. Further, itis very interesting that the forward spudcan A continued toattract overturning moment throughout the entire test (albeit

Fig. 10. Vertical spudcan load versus penetration. HRP, hull reference point; P1, P2, and P3 refer to the self-weight penetration, penetrationunder preload, and commencement of the horizontal loading phase, respectively.

Bienen et al. 201


with softening stiffness) whilst the moment load on the twoaft spudcans reduced to residual values of about 21 MN�m(spudcan B) and 14 MN�m (spudcan C), respectively, afterpeaking at M2 & 58–61 MN�m. Experimental evidence of asingle footing on dense sand under increasing rotation atconstant vertical penetration (Gottardi et al. 1999, for in-stance) showed peak resistance after a small rotation. Thisappears to hold for spudcans B and C. However, in contrastto the single footing tests, the aft spudcans here were notforced to remain at a constant vertical penetration. Photo-graphs taken in-flight (Fig. 14) showed upward movement,which would have contributed to the loss of moment reac-tion due to the reduction in bearing area. At the same time,the forward leg penetrated further under increased combinedloading, which appears to be the reason why the moment ca-pacity kept increasing. Note that this does not contradict therecorded vertical displacement remaining almost constant, asthis measurement refers to the hull reference point where thevertical displacements of the forward and aft legs appear tohave cancelled out.

The loss of load on the aft spudcans B and C and the con-sequential shedding of load onto spudcan A exhausted thecombined load capacity of the footing system. The jack-upwas unable to withstand any higher applied load and dis-

placements became excessive (see also Fig. 11), indicatingthat the system had failed. The jack-up in this loading direc-tion is expected to eventually overturn through lift-off of theaft spudcans B and C. Note that a single-footing systemwould have failed much earlier as loads cannot be redistrib-uted to other footings in the system.

Test 2: horizontal loading at a = 228 to theaxis of symmetry

Test 2 was terminated at an applied resultant load of17.9 MN, with the components in the 3 and 2 directions cal-culated as being 16.6 and 6.7 MN, respectively. At thispoint, the measured displacement components at the hullreference point were u3 = 1.90 m and u2 = 0.75 m (Figs. 9band 11), yielding a resultant horizontal displacement of2.04 m. In comparison, the resultant horizontal displacementrecorded for the symmetrical loading case at the same ap-plied load was significantly less, only 1.36 m (Fig. 11).

Horizontal loading applied at an angle to the jack-up’saxis of symmetry introduced combined loading in all sixdegrees-of-freedom in space on the spudcan footings. Thatis, although the general system and footing behaviour maybe similar to the symmetrical loading case, H2, M3 and Q

Fig. 11. Comparison of hull displacement response between tests: (a) horizontal displacement; (b) rotation.



(though not measured here) reaction components claimedpart of the combined load capacity in this test. Further, theresponses on spudcans B and C were different. However,the majority of the out-of-plane loading was carried by theforward spudcan A (Figs. 9d and 9e). While H2 increased to7.1 MN, loading in this degree-of-freedom on spudcan B re-

mained negligible and spudcan C only registered loading ofup to about 1.3 MN in magnitude. Similarly, spudcan A car-ried more than 570% of M3 moment load compared with ei-ther footings B or C.

In this loading direction, only spudcan B shows a peakedresponse in the M2 direction (Fig. 9e). The magnitude of

Fig. 12. Comparison of response: (a) change of vertical load, (b) resultant horizontal load, and (c) resultant moment.

Bienen et al. 203


about 60 MN�m is very similar to the same footing in thesymmetrical loading case. Also, the forward footing A at-tracts increasing moment load. However, spudcan C exhibits

different behaviour than under symmetrical load. It, too, car-ries increasingly more moment loading. However, this re-sponse is much softer than on spudcan A.

Fig. 13. Load distribution between the spudcans: (a) resultant horizontal load and (b) resultant moment.

Fig. 14. Photographs of the spudcans taken in-flight during test 1.



The peak and subsequent loss of H3 on spudcan B coin-cides with a marked change in response visible in all curves(Fig. 9). This coincides with heave measured at the hullreference point (which was not observed in the symmetricalloading direction) and a sudden increase in rotation q3,which was approximately 08 until then.

It was visually observed that during the horizontal pullphase of the experiment, the jack-up pivoted around spudcanC while tilting in the direction of the pull. This resulted inthe forward footing A penetrating further while spudcan Bshowed upward displacement (Fig. 15). This is also indicatedin the vertical load on spudcan B tending towards 0 MN(Fig. 9a). Further, the horizontal displacement as well as therotations increased at an increasing rate (Fig. 11), with thecurves tending towards asymptotic behaviour (i.e., increasingdisplacements at no additional applied load). This is indica-tive of imminent failure. Therefore, the jack-up is not ex-pected to be able to withstand significantly higher externalload before overturning through lift-off of spudcan B.

Comparison of the results obtained from thetwo different loading directions

The experimental results can best be compared by plottingload and displacement response against the applied horizon-tal load (Figs. 11 and 12) or by plotting the reactions of therespective spudcans against each other (Fig. 13).

Interestingly, the jack-up shows very similar resultant dis-placement magnitudes for both loading directions until ap-proaching failure (Fig. 11a). However, the response of thejack-up loaded at an angle to its axis of symmetry softenssignificantly at an applied load of about 16.8 MN(Fig. 11a). Eventually, the rig incurred a large increase indisplacement with little additional applied load. The sym-metrical load case shows a similar response (Fig. 11b), indi-cative of imminent failure, at only about a 20% higherapplied load. Hull rotation is also nearly identical for bothloading directions until approaching failure (Fig. 11b). Asexpected, twist is much larger in the unsymmetrical loadingcase. Its magnitude far outstripps both other rotational direc-tions. Again, a further, more rapid increase at little addi-

tional applied load was observed immediately before thetest was stopped.

The results of the symmetrical load case show a suddenloss of some applied load, which is only partially regained,towards the end of the test. This is most visible in Fig. 11a(where it is circled). The cause of this was sudden failure ofthe sand in front of the heavily loaded spudcan A, resultingin sudden irreversible displacement. This was visually ob-served.

An important result is that a lower applied load can bewithstood before the jack-up approaches failure in the un-symmetrical loading case.

Comparison of spudcan load pathsAlthough the jack-up showed seemingly very similar

overall behaviour in both loading configurations (apart fromthe obvious difference in twist), the load histories of the re-spective spudcans are different (Fig. 12).

The vertical load history on the forward leg A is similar inboth tests until approaching failure (Fig. 12a). The relativelysmall change in vertical load on spudcan C (test 2) indicatesthat this footing did not play a significant role in the push–pull mechanism to withstand the overturning moment, butrather acted as a pivot point. Further, the fact that spudcanB shed vertical load at a faster rate in test 2 than in test 1hints that this footing experienced more negative verticalmovement (heave), which is also evident in the photos takenin-flight. The corresponding larger reduction in bearing areaaccelerates the moment loss at larger applied loads(Fig. 12c). Spudcan C (test 2) is able to accommodate addi-tional moment load even if its vertical reaction drops slightly(Figs. 9, 12). As the overall vertical displacement at the hullreference point remains virtually unchanged and is very sim-ilar to the symmetrical loading case (Figs. 8 and 9), it is as-sumed that spudcan A penetrates more in test 2 than in test 1to compensate for the larger heave on spudcan B.

Further clues as to how the loads are shared between thespudcans are contained in Fig. 13. Horizontal and momentloads are shared evenly between the three spudcans only atthe very onset of applied horizontal load at the hull (withthe dashed line indicating even load distribution). However,

Fig. 15. Photographs of the spudcans taken in-flight during test 2.

Bienen et al. 205


already very early in the horizontal load phase, moment loadis shed from spudcans B and C onto A (Fig. 13b). In thesymmetric loading case, this load transferral is very similaron both aft footings, as expected. This process accelerates asthe bearing area on footings B and C reduces due to de-creasing vertical penetration (i.e., heaving). When loadingthe jack-up at an angle to its axis of symmetry, however, inthe later stage of the push-over, slightly more moment is at-tracted by spudcan C (but not as much as on spudcan A),while spudcan B sheds moment load at an increasing rate.Horizontal load is also increasingly resisted by spudcan A.While in test 1 this load is shed similarly from the two aftspudcans B and C, in test 2, spudcan B carries proportion-ally slightly more and spudcan C carries correspondinglyless horizontal load. Increasingly rapid re-distribution ofhorizontal and moment loads between the three spudcans isevident, especially in test 2 as the rig approaches failure(Figs. 12b, 12c, and 13).

Therefore, although the behaviour of the jack-up when ex-pressed as overall displacements and rotations seemed rathersimilar until the rig neared failure (apart from the hulltwist), the individual footing load histories differ signifi-cantly. This indicates that the jack-up approaches failure atsignificantly less external load when the load acts at an an-gle to its axis of symmetry. This highlights that the symmet-ric loading direction may not always be critical, andanalysing a jack-up’s capacity in this loading directionalone, which allows for simplification to plane frame analy-sis, may not be conservative.

Conclusion

This paper has detailed the development of a genericmodel jack-up and loading apparatus for experimentation ina geotechnical centrifuge, such that the unit can be tested atstress levels corresponding to those experienced by the pro-totype. This is particularly important for experiments onsand due to its stress-dependent behaviour. Emphasis wasplaced on detailing the scaling law considerations arisingthrough the size of the model. The experimental set-up al-lowed horizontal loading to be applied not only along therig’s axis of symmetry, but also at an angle to it, enablingstudies of jack-up behaviour under general combined load-ing in space. The results will be used to validate a force-resultant plasticity footing model for load paths relevant tojack-up footings.

In this paper, the results of two tests of different orienta-tions of the model jack-up to the applied horizontal loadwere discussed. In one of the experiments, the jack-up washorizontally loaded along its axis of symmetry, whereas inthe other experiment the load was applied at an angle to it.Although the overall vertical displacements as well as the re-sultant horizontal displacements and rotations were very sim-ilar for both loading directions (until the jack-up approachedfoundation failure), the load paths of the individual footingswere shown to differ significantly. This is expected on thebasis of static theory. However, this eventually led to differ-ent modes of failure, which highlights the importance of afooting model capable of predicting the load–displacementpath of each of the footings for the prediction of the overallsystem response.

The different footing load paths led to the jack-up failingat lower external load in the unsymmetrical orientation thanwhen loaded symmetrically. This suggests that the symmet-ric orientation does not always represent the critical caseand plane frame (2D) analysis may not be conservative.This is believed to be the first physical observation of suchbehaviour; however, it has been previously shown to be pos-sible numerically (Bienen and Cassidy 2006). This empha-sises the importance of three-dimensional modelling.

AcknowledgementsThe first author gratefully acknowledges the support of an

International Postgraduate Research Scholarship of Aus-tralia. Helpful advice from Professor Mark Randolph isgratefully acknowledged. Further, support from the technicalstaff (Shane De Catania, John Breen, Tuarn Brown, DonHerley, Philip Hortin, David Jones, Neil McIntosh, Gary Da-vies) is acknowledged. The authors acknowledge the contri-bution Julian Byron-Brown made to the development of theexperimental equipment during his Honours thesis at TheUniversity of Western Australia in 2004. Support from theAustralian Research Council (ARC) through the ARC Dis-covery grant scheme (DP0345424) is gratefully acknowl-edged.

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List of symbols

A cross-sectional areaD spudcan diameter

Dr relative densityd50 grain size

E Young’s modulusH, H2, H3 horizontal load

Hmax maximum horizontal loadI second moment of area

M, M2, M3 moment loadQ torsional loadR radius

u, u2, u3 horizontal displacementV vertical loadw vertical displacementa loading directiong unit weight

q2, q3 rotationss vertical stress

4cv critical state friction angleu twist

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physical modelling of the push-over capacity of a jack-up structure on sand in a geotechnical...

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