Research on Offshore Foundations: Papers at the International Symposium on Frontiers in Offshore Geotechnics Perth, Australia, 2005

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1 Research on Offshore Foundations: Papers at the International Symposium on Frontiers in Offshore Geotechnics Perth, Australia, 5 by G.T. oulsby, C.. artin, B.W. Byrne, R.B. Kelly E.J. azell, L. guyen-sy, F.A. Villalobos and L-B. Ibsen Report o. OUEL 75/5 University of Oxford Department of Engineering Science Parks Road, Oxford, OX PJ, U.K. Tel /8 Fax Civil@eng.ox.ac.uk

2 Research on Offshore Foundations: Papers at the International Symposium on Frontiers in Offshore Geotechnics Perth, Australia, 5 G.T. oulsby, C.. artin, B.W. Byrne, R.B. Kelly E.J. azell, L. guyen-sy, F.A. Villalobos and L-B. Ibsen This report consists of six papers that have been accepted for the International Symposium on Frontiers in Offshore Geotechnics at Perth Australia in September 5. The abstracts of the six papers are: a) Keynote Paper : Suction caissons for wind turbines. Authors: oulsby, G.T., Ibsen, L-B. and Byrne, B.W. Abstract: Suction caissons may be used in the future as the foundations for offshore wind turbines. We review recent research work on the development of design methods for suction caissons for these applications. We give some attention to installation, but concentrate on design for in-service performance. Whilst much can be learned from previous offshore experience, the wind turbine problem poses the particularly challenging combination of a relatively light structure, with large imposed horizontal forces and overturning moments. onopod or tripod/tetrapod foundations result in very different loading regimes on the foundations, and we consider both cases. The results of laboratory studies and field trials are reported. We also outline briefly numerical and theoretical work that is relevant. Extensive references are given to sources of further information. b) Bearing capacity of parallel strip footings on non-homogeneous clay. Authors: artin, C.. and azell, E.J. Abstract: On soft seabed soils, subsea equipment installations are often supported by mudmat foundation systems that can be idealised as parallel strip footings, grillages, or annular (ringshaped) footings. This paper presents some theoretical results for the bearing capacity of (a) two parallel strip footings, otherwise isolated; (b) a long series of parallel strip footings at equal spacings. The soil is idealised as an isotropic Tresca material possessing a linear increase of undrained strength with depth. The bearing capacity analyses are performed using the method of characteristics, and the trends of these (possibly exact) results are verified by a companion series of upper bound calculations based on simple mechanisms. Parameters of interest are the footing spacing, the relative rate of increase of strength with depth, and the footing roughness. An application of the results to the design of perforated mudmats is discussed. c) Investigating six degree-of-freedom loading on shallow foundations. Authors: Byrne, B.W. and oulsby, G.T. Abstract: Previous laboratory studies of the response of shallow foundations have only considered planar loading. This paper describes the development of a loading device capable of applying general loading on model shallow foundations. Loading involving all six degrees of freedom {vertical (V), horizontal (, ), torsion (Q) and overturning moment (, )}, can be applied experimentally to the model foundations. Aspects of the design, including the loading rig configuration, development of a six degree-of-freedom load cell, numerical control algorithms and an accurate displacement measuring system are described. Finally results from initial experiments are presented that provide evidence for the generalisation of existing work-hardening plasticity models from planar loading to the general loading condition.

3 d) The tensile capacity of suction caissons in sand under rapid loading. Authors: oulsby, G.T., Kelly, R.B. and Byrne, B.W. Abstract: We develop here a simplified theory for predicting the capacity of a suction caisson in sand, when it is subected to rapid tensile loading. The capacity is found to be determined principally by the rate of pullout (relative to the permeability of the sand), and by the ambient pore pressure (which determines whether or not the water cavitates beneath the caisson). The calculation procedure depends on first predicting the suction beneath the caisson lid, and then further calculating the tensile load. The method is based on similar principles to a previously published method for suction-assisted caisson installation (oulsby and Byrne, 5). In the analysis a number of different cases are identified, and successful comparisons with experimental data are achieved for cases in which the pore water either does or does not cavitate. e) Theoretical modelling of a suction caisson foundation using hyperplasticity theory. Authors: guyen-sy, L. and oulsby, G.T. Abstract: A theoretical model for the analysis of suction caison foundations, based on a thermodynamic framework (oulsby and Puzrin, ) and the macro-element concept is presented. The elastic-plastic response is first described in terms of a single-yield-surface model, using a non-associated flow rule. To capture hysteresis phenomena, this model is then extended to a multiple yield surface model. The installation of the caisson using suction is also analysed as part of the theoretical model. Some preliminary numerical results are given as demonstrations of the capabilities of the model.. f) oment loading of caissons installed in saturated sand. Authors: Villalobos, F.A., Byrne, B.W. and oulsby, G.T. Abstract: A series of moment capacity tests have been carried out at model scale, to investigate the effects of different installation procedures on the response of suction caisson foundations in sand. Two caissons of different diameters and wall thicknesses, but similar skirt length to diameter ratio, have been tested in water-saturated dense sand. The caissons were installed either by pushing or by using suction. It was found that the moment resistance depends on the method of installation.

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5 Suction Caissons for Wind Turbines Guy T. oulsby, Lars Bo Ibsen & Byron W. Byrne : Department of Engineering Science, Oxford University, U.K. : Department of Civil Engineering, Aalborg University, Denmark ABSTRACT: Suction caissons may be used in the future as the foundations for offshore wind turbines. We review recent research on the development of design methods for suction caissons for these applications. We give some attention to installation, but concentrate on design for in-service performance. Whilst much can be learned from previous offshore experience, the wind turbine problem poses a particularly challenging combination of a relatively light structure, with large imposed horizontal forces and overturning moments. onopod or tripod/tetrapod foundations result in very different loading regimes on the foundations, and we consider both cases. The results of laboratory studies and field trials are reported. We also outline briefly relevant numerical and theoretical work. Extensive references are given to sources of further information.. ITRODUCTIO The purpose of this paper is to review recent research work on the design of suction caisson foundations for offshore wind turbines. ost of the relevant work has been conducted at, or in cooperation with, the universities of Oxford and Aalborg, so we report here mainly the work of our own research groups. Suction caissons have been extensively used as anchors, principally in clays, and have also been used as foundations for a small number of offshore platforms in the orth Sea. They are currently being considered as possible foundations for offshore wind turbines. As discussed by oulsby and Byrne () and by Byrne and oulsby (), it is important to realise that the loading regimes on offshore turbines differ in several respects from those on structures usually encountered in the offshore oil and gas industry. Firstly the structures are likely to be founded in much shallower water: m to m is typical of the early developments, although deeper water applications are already being planned. Typically the structures are relatively light, with a mass of say 6t (vertical deadload 6), but in proportion to the vertical load the horizontal loads and overturning moments are large. For instance the horizontal load under extreme conditions may be about 6% of the vertical load. An important consideration is that, unlike the oil and gas industry where large one-off structures Figure : Offshore tests in Frederikshavn, Denmark. Front: Vestas V9.W turbine. Back: ordex.w turbine. dominate, many relatively small and inexpensive foundations are required for a wind farm development, which might involve anything from to 5 turbines. The dominant device used for large scale wind power generation is a horizontal axis, -bladed

6 turbine with the blades upwind of the tower, as shown in Figure. The details of the generator, rotational speed and blade pitch control vary between designs. ost offshore turbines installed to date generate W rated power, and typically have a rotor about 8m in diameter with a hub about 8m above mean sea level. The size of turbines available is increasing rapidly, and prototypes of 5W turbines already exist. These involve a rotor of about 8m diameter at a hub height of about m. The loads on a typical.5w turbine are shown in Figure, which is intended to give no more than a broad indication of the magnitude of the problem. Figure : Typical loads on a.5w offshore wind turbine ote that in conditions as might be encountered in the orth Sea, the horizontal load from waves (say ) is significantly larger than that from the wind (say ). owever, because the latter acts at a much higher point (say 9m above the foundation) it provides more of the overturning moment than the wave loading, which may only act at say m above the foundation. Using these figures the overturning moment of m would divide as 9m due to wind and m due to waves. Realistic combinations of loads need to be considered. For instance the maximum thrust on the turbine occurs when it is generating at the maximum allowable wind speed for generation (say 5m/s). At higher wind speeds the blades will be feathered and provide much less wind resistance. It is thus unlikely that the maximum storm wave loading would occur at the same time as maximum thrust. Turbine designers must also consider important load cases such as emergency braking. It is important to recognise that the design of a turbine foundation is not usually governed by considerations of ultimate capacity, but is typically dominated by (a) considerations of stiffness of the foundation and (b) performance under fatigue loading. An operational wind turbine is subected to harmonic excitation from the rotor. The rotor's rotational frequency is the first excitation frequency and is commonly referred to as P. The second excitation frequency to consider is the blade passing frequency, often called P (for a three-bladed wind turbine) at three times the P frequency. Figure shows a representative frequency plot of a selection of measured displacements for the Vestas V9.W wind turbine in operational mode. The foundation is a suction caisson. The measured data, monitoring system and Output-Only odal Analysis used to establish the frequency plot are described in Ibsen and Liingaard (5). The first mode of the structure is estimated, and corresponds to the frequency observed from idling conditions. The peak to the left of the first natural frequency is the forced vibration from the rotor at P. To the right of the first natural frequency is the P frequency. It should be noted that the P and P frequencies in general cover frequency bands and not ust two particular values, because the Vestas wind turbine is a variable speed device. To avoid resonances in the structure at the key excitation frequencies (P, P) the structural designer needs to know the stiffness of the foundation with some confidence, this means that problems of deformation and stiffness are as important as capacity. Furthermore, much of the structural design is dictated by considerations of high cycle fatigue (up to about 8 cycles), and the foundation too must be designed for these conditions.. CASES FOR STUDY The two main problems that need to be studied in design of a suction caisson as a foundation are: installation; in service performance. In this review we shall discuss installation methods briefly, but shall concentrate mainly on design for in service performance. The relevant studies involve techniques as diverse as laboratory model testing, centrifuge model testing, field trials at reduced scale, and a full-scale field installation.

7 db. / z P First mode Frequency Domain Decomposition - Peak Picking Average of the ormalized Singular Values of Spectral Density atrices of all Data Sets. P Frequency Figure. Frequency plot of measured displacements for a wind turbine in operational mode. Complementing these experiments are numerical studies using finite element techniques, and the development of plasticity-based models to represent the foundation behaviour. Suction caissons may be installed in a variety of soils, but we shall consider here two somewhat idealised cases: a caisson installed either in clay, which may be treated as undrained, or in sand. For typical sands the combination of permeability value, size of caisson and loading rates leads to partially drained conditions, although much of the testing we shall report is under fully drained conditions. In this paper we report mainly work on sands. We shall consider two significantly different loading regimes, which depend on the nature of the structure supporting the wind turbine. ost offshore wind turbines to date have been supported on a monopile a single large diameter pile, which in effect is a direct extension of the tubular steel tower which supports the turbine. Some turbines have been supported on circular gravity bases. An obvious alternative is to use a single suction caisson to support the turbine, and we shall call this a monopod foundation, Figure 4(a). The monopod resists the overturning moment (usually the most important loading component) directly by its rotational fixity in the seabed. As turbines become larger, monopod designs may become sufficiently large to be uneconomic, and an alternative is a structure founded on three or four smaller foundations: a tripod or tetrapod, Figure 4(b). In either of these configurations the overturning moment on the structure is resisted principally by push-pull action of opposing vertical loads on the upwind and downwind foundations. Alternatives using asymmetric designs of tripod, and those employing acket type substructures are also under consideration. (a) (b) Figure 4: caisson foundations for a wind turbine, (a) monopod, (b) tripod/tetrapod

8 . ORALISATIO PROCEDURES A number of studies have been conducted at different scales and it is necessary to compare the results from these various studies. To do this it is appropriate to normalise all the results so that they can be represented in non-dimensional form. This procedure also allows more confident extrapolation to full scale. The geometry of a caisson is shown in Figure 5. The outside radius is R (diameter D o ), skirt length is L and wall thickness t. In practice caissons may also involve stiffeners on the inside of the caisson, these being necessary to prevent buckling instability during suction installation, but we ignore these in a simplified analysis. Geometric similarity is achieved by requiring similar values of L R and t R. Figure 5: Geometry of a caisson foundation Figure 6: Loading and displacement conventions for a caisson foundation (displacements exaggerated). The sign convention for applied loads and displacements is shown in Figure 6. The rotation of the caisson θ is already dimensionless, and we normalise the displacements simply by dividing by the caisson diameter, to give w R and u R. In sand it is straightforward to show that, for similar values of dimensionless bearing capacity factor, the loads at failure would be proportional to γ and to R. We therefore normalise vertical and horizontal loads as V πr γ and πr γ, where we have included the factor π to give the normalisation factor a simple physical meaning: it is the effective weight of a cylinder of soil of the same diameter of the caisson, and depth equal to the diameter. In a similar way we normalise the overturning moment as 4πR 4 γ. Use of the above normalisation is appropriate for comparing tests in sands with similar angles of friction and dilation. We recognise that these angles both decrease slightly with pressure and increase rapidly with Relative Density (Bolton, 986). This means that comparable tests at smaller scales (and therefore lower stress levels) will need to be at lower Relative Densities to be comparable with field tests. In clay the vertical capacity is proportional to a representative undrained shear strength s u and to R, so we normalise loads as R s u V R s u R π s. π and π, and the moment as u In order to be comparable, tests at different scales will need the profile of undrained strength with depth to be similar. If the strength profile is fitted by a simple straight-line fit su = suo + ρz, then this requires similar values of the factor Rρ suo. Scaling of results using the above methods should give satisfactory results in terms of capacity. For clays it should also lead to satisfactory comparisons in terms of stiffness, provided that the clays being compared have similar values of I r = G su. This condition is usually satisfied if the clays are of similar composition and overconsolidation ratio. For sands, however, an extra consideration needs to be taken into account. The shear modulus of a sand does not increase in proportion to the stress level, but instead can reasonably be expressed by: n G p = g p a p () a where g and n are dimensionless constants, and p a is atmospheric pressure (used as a reference pressure). The value of n is typically about.5, so that the stiffness is proportional roughly to the square root of pressure.

9 Comparing rotational stiffnesses on the basis of a plot of 4πR 4 γ against θ effectively makes the assumption that the shear stiffness is proportional to Rγ, which may be regarded as a representative stress level. Since in fact the stiffness increases at a lower rate with stress level, this comparison will result in larger scale tests giving lower apparent normalised stiffness. This effect can be reduced by multiplying the θ scale by the dimensionless factor n ( p a Rγ ), which compensates for the stiffness variation with stress level. Thus we recommend that to compare both stiffness and capacity data for sands one should plot 4πR 4 γ against θ( p Rγ ). 5 a (assuming n =.5) for moment tests, and V πr γ against ( R)( p Rγ ). 5 w a for vertical loading tests. A fuller description of these normalisation procedures is given by Kelly et al. (5a). 4. ISTALLATIO STUDIES The principal difference between installation of a suction caisson for an offshore wind turbine and for previous applications is that the turbines are likely to be installed in much shallower water. There is a popular misconception that suction caissons can only be installed in deep water, where a very substantial head difference can be established across the lid of the caisson. In shallow water the net suction that can be achieved is indeed much smaller (being limited by the efficiency of the pumps, as the absolute pressure approaches zero), but the suctions that can be achieved are nevertheless sufficient for installation in most circumstances. Only in stiff clays is it likely that some possible caisson designs, which might otherwise be suitable as far as in-service conditions are concerned, could not be installed by suction in shallow water. In Table we list the main instances where caissons have been installed in shallow water, as appropriate to wind turbine installations. The water depths h w are approximate only. In addition to the field tests listed, a large number of small scale model tests of installation have been carried out at Oxford University (on caissons of.m to.4m diameter), the University of Western Australia (UWA), Aalborg and elsewhere. The largest completed installation in shallow water is that of a prototype suction caisson, shown in Figure 7, installed in the offshore research test facility in Frederikshavn, Denmark. The prototype Table : Installations in shallow water h Site Soil w (m) D (m) L (m) Ref. Wilhelmshaven Sand Installation April 5 Frederikshavn Sand.. 6. Frederikshavn Sand Sandy aven Sand Tenby Sand... Burry Port Sand Luce Bay Sand Bothkennar Clay...5 (a) (b).5. Figure 7: Installation of the prototype foundation at the test site in Frederikshavn: (a) during installation, (b) at the end of installation. has a diameter of m and a skirt length of 6m. The operational water depth is 4m, and as the site is in a basin, no wave or ice loads are applied. As seen in Figure 7 the suction caisson was installed in only m of water in the basin. The steel construction has a mass of approximately 4t, and the caisson was placed in late October. The installation period 6

10 was about hours, with the soil penetration time being 6 hours. A computer system was used to control the inclination, suction pressure and penetration rate. Det orske Veritas (DV) has certified the design of the prototype in Frederikshavn to B level. The Vestas V9.W turbine was erected on the foundation in December. The development of the design procedure for the bucket foundation is described in Ibsen and Brincker (4). An even larger installation is currently in progress at Wilhelmshaven, Denmark. There are two main ways of predicting firstly the self-weight penetration of the caisson and secondly the suction required to achieve full installation. The first method (oulsby and Byrne, 5a,b) involves use of adaptations of pile capacity analysis, in which the resistance to penetration is calculated as the sum of an end bearing term on the rim and friction on the inside and outside. In sands the seepage pattern set up by the suction processes alters the effective stress regime in a way that aids installation. The calculation has been implemented in a spreadsheet program SCIP. Figure 8 shows for example a comparison between variation of measured suction in a model test installation with tip penetration of the caisson (Sanham, ), and the SCIP calculation. Penetration, h (mm) Suction, s (Pa) SCIP Results Experimental Result Figure 8: Comparison of SCIP with model test The other approach involves use of CPT data to infer directly the resistance R d to penetration of the caisson. The required suction u req to penetrate the caisson to depth d is calculated as: Rd ( d) G'( d) ureq ( d) = () A suc where G'( d ) is the self-weight of the caisson at penetration depth d (reduced for buoyancy), and Asuc is the area inside the caisson, where the suction is applied. The penetration resistance is calculated from the following expression, which is based on calibration against measured data: d d t tip t out out s d Ain Kin( z) fs ( z) dz R ( d) = K ( d) A q ( d) + A K ( z) f ( z) dz+ () where q t is the corrected cone resistance and f s the sleeve friction at depth z. K t is a coefficient relating q t to the unit tip resistance on the rim. This resistance is adusted for the reduction due to the applied suction by the expression: β t u Kt = ktrt (4) ucrit where k t is an empirical coefficient relating q t to the tip resistance during static penetration of the caisson, r t is the maximum reduction in tip resistance. ucrit is the critical suction resulting in the critical hydraulic gradient i crit = along the skirt. β t is an empirical factor. K out and K in are coefficients relating f s to the unit skin friction on the outside and inside of the skirt. The water flow along the skirt changes the skin friction. For the inside skin friction the coefficient reduces the skin friction when suction is applied, whereas on the outside the skin friction is increased. The coefficients are established as: K K = α + r out out out = α r in in in u u u u crit crit β in β out (5a,b) Where αout andα in are empirical coefficients relating f s to the unit skin friction during static penetration of the caisson. r out and r in are the maximum changes in skirt friction. β out and β in are empirical factors. The required suction u req to penetrate the prototype in Frederikshavn was predicted using equation (). The result of the analysis is shown in Figure 9. The lower line represents u req calculated from the CPT tests. The curved line represents the limiting suction u pip which would cause piping to occur. u max is the theoretical maximum net suction, limited by the possibility of cavitation within the caisson, as the absolute pressure approaches zero, so

11 Penetration, h (mm) Volume, ( - m ) Seepage Volume Volume Displaced Total Volume Figure : Volumes pumped from -cell caisson in sand. Cell Cell Figure 9: Suction required for installation at Frederikshavn Figure : The limiting suction u pip has been achieved and soil failure by piping has occurred. that u max = kpa above water level and increases linearly with the water depth, as shown by Figure 9. u max is used to calculate the accessible net suction, which is limited by the efficiency of the pumps, u pump. As is seen, the suction in shallow water can be limited either by the suction causing piping or by the accessible net suction available from the pumps. The suction u pip causing piping has been studied at the test site in Frederikshavn by installation tests on xm and 4x4m caissons. Figure shows a 4x4m caisson where the limiting suction u pip has been achieved, and soil failure by piping has occurred. The soil outside of the skirt is sucked into the caisson and the penetration of the caisson cannot proceed. If a tripod or tetrapod structure is to be installed, then levelling of the structure can be achieved by separately controlling the suction in each of the caissons. For a monopod structure, however, an alternative strategy has to be adopted. Experience suggests that for installation in either clay or sand, the level of the caisson is rather sensitive to the application of eccentric loads (moments), especially in the early stages of installation. This offers one possibility for controlling the level of the caisson: by use of an eccentric load that can be adusted in position to keep the caisson level. An alternative strategy, which has proven to be highly successful for installation in sand, is to divide the rim into sections and to control the pressures at the skirt tip in each section individually. By applying pressure over one segment of the caisson rim the upward hydraulic gradient within the caisson can be enhanced locally, thus encouraging additional downward movement for that sector. By controlling the pressures at a number of points the caisson may be maintained level. This method would not be applicable in clays. One possibility, as yet untried at large scale, for controlling level in clays would be to use a segmented caisson in which the suctions in the different segments could be controlled independently. Some preliminary small scale tests suggest that this approach might be successful in sand too (Coldicott, 5). Figure shows the volumes of water pumped from the two halves of a 4mm diameter caisson split by a diametral vertical wall. About 6% of the water pumped represents the volume displaced by the descending caisson, whilst about 4% represents seepage beneath the caisson rim. Figure shows that during the installation the suctions developed in the two halves were (as would be expected in a uniform material) almost equal. 5. CAISSO PERFORACE: OOPOD A large number of tests have been devoted to studying the performance of a caisson under moment loading at relatively small vertical loads, as is relevant to the wind turbine design. Some details of the test programmes are given in Table.

12 Penetration, h (mm) Sand: field tests Suction, s (Pa) Cell Cell Figure : Suctions required for installation of -cell caisson in sand. The largest test involves the instrumented Vestas V9.W prototype turbine at Frederikshavn, Denmark. The caisson is installed in a shallow 4m depth lagoon next to the sea, and the turbine is fully operational. The only significant difference between this installation and an offshore one is that the structure is not subected to wave loading. The test program involving the prototype (turbine and caisson) is focusing on long-term deformations, soil structure interaction, stiffness and fatigue. The prototype has been equipped with: an online monitoring system that measures the dynamic deformation modes of the foundation and the wind turbine, a monitoring system that measures the long-time deflection and rotation of the caisson a monitoring system that measures the pore pressure along the inside of the skirt. The online monitoring system that measures the modes of deformation of the foundation and wind turbine involves 5 accelerometers and a real-time data-acquisition system. The accelerometers are placed at three different levels in the turbine tower and at one level in compartments inside the caisson foundation. The positions are shown in Figure, and the locations and measuring directions are defined in Figure4. Output-only odal Analysis has been used to analyze the structural behaviour of the wind turbine during various operational conditions. The modal analysis has shown highly damped mode shapes of the foundation/wind turbine system, which the present aero-elastic codes for wind turbine design cannot model. Further studies are to be carried out with respect to soil-structure interaction. A detailed description of the measuring system and the Output- Only odal Analysis is given by Ibsen and Liingaard (5). Table : oment loading tests D L Site Soil Ref. (m) (m) Frederikshavn Sand Frederikshavn Sand.. - Sandy aven Sand Burry Port Sand.. Luce Bay Sand ,4.5.5,7 Oxford laboratory Sand..,4..5,4,4.5. 4,4.. 4,4,4 Aalborg laboratory Sand Bothkennar Clay Oxford laboratory Clay UWA centrifuge Clay.6. (g).6 Level IV: 89 m Level III: 46 m Level II: m Level I: 6 m Figure : Sensor positions in tower and foundation. The static moment tests referred to in Table at Sandy aven and at Burry Port were relatively straightforward, with very simple instrumentation, but those at Frederikshavn test site and at Luce Bay were detailed investigations. The large scale tests at Frederikshavn is part of a research and development program concerning caisson foundation for offshore wind turbines. The research program is a co-operation between Aalborg -

13 Table. Loading heights in the Aalborg test program Prototype Laboratory odel Field odel p D = m m D =.m.m.4m.m p h [m] m h [m] m h [m] Figure 4: Sensor mountings in the tower and foundation at Frederikshavn. University and BD offshore power (Ibsen et al. ). The large scale tests are complemented by laboratory studies. The laboratory and large scale tests are intended to model the prototype in Frederikshavn directly. In order to design a caisson foundation for offshore wind turbines several load combinations have to be investigated. Each load combination is represented by a height of load h above the foundation and a horizontal force. The moment at the seabed is calculated as = h. Table shows that the resulting loading height varies from m (for a wave force in shallow water) to 4.4m (force from normal production of a W turbine in m of water). Scaling of the tests is achieved by: m m p D h p D h = (6) where D is the diameter of the caisson and index m and p are for model and prototype. The values of the loading height in the test program are shown in Table. The large scale tests at Frederikshavn employ loading by applying a horizontal load at a fixed height, under constant vertical load. A steel caisson with an outer diameter of m and a skirt length of m has been used. The skirt is made of mm thick steel plate. Figure 5 shows the caisson prior to installation, and Figure 6 the overall test setup. Currently experiments have been conducted, but the testing program is ongoing. Each test has three phases: Figure 5: Caisson for large scale test at Frederikshavn tower located on bucket foundation W Vestas windmill on bucket foundation loading wire loading tower Figure 6: Setup for combined loading of xm caisson at Frederikshavn. (Back: prototype W Vestas wind turbine on the x 6m caisson). Installation phase: The caisson is installed by means of suction. CPT tests are performed before and after installation of the caisson.. Loading phase: An old tower from a wind turbine is mounted on top of the caisson. The caisson is loaded by pulling the tower

14 horizontally with a wire. The combined loading (,) is controlled by changing the height of loading.. Dismantling phase. The caisson is removed by applying overpressure inside the bucket. Figure 7 shows the moment rotation curve for a test on the xm caisson at Frederikshavn. The test is performed with h m = 7.4m and a vertical load on the caisson of 7.k. The fluctuations in the curve are caused by wind on the tower. Figure 7: oment-rotation test on xm caisson. Tests at Luce Bay were designed by Oxford University and conducted by Fugro Ltd.. The moment loading tests were of two types. Firstly small amplitude (but relatively high frequency) loading was applied by a Structural Eccentric ass Vibrator (SEV) in which rotating masses are used to apply inertial loads at frequencies up to about z. Secondly larger amplitude, but lower frequency, cycles were applied using a hydraulic ack. A diagram of the loading rig, which allowed both moment and vertical loading tests, is shown in Figure 8. The SEV test involve cycles of moment loading at increasing amplitude as the frequency increases. Figure 9 shows the hysteresis loops obtained from a series of these cycles at different amplitudes. As the cycles become larger the stiffness reduces but hysteresis increases. The tests were interpreted (oulsby et al., 5b) using the theory of Wolf (994), which takes account of the dynamic effects in the soil, and the equivalent secant shear modulus for each amplitude of cycling determined. Figure shows the moment rotation curves for much larger amplitude cycling applied by the hydraulic ack. Again hysteresis increases and secant stiffness decreases as the amplitude increases. The unusual waisted shape of the hysteresis loops at very large amplitude is due to gapping occurring at the sides of the caisson. The secant stiffnesses deduced from both the SEV tests and the hydraulic acking tests are combined in Figure, where they are plotted against the amplitude of cyclic rotation. It is clear that the two groups of tests give a consistent pattern of reduction of shear modulus with strain amplitude, similar to that obtained for instance from laboratory tests. 5. Sand: laboratory tests Turning now to model testing, a large number of tests have been carried out both at Aalborg and at Oxford. Almost all the model tests have involved in plane loading (in which the moment is about an L V V A W A B B L L L L L L R 5 C R C C (a) Figure 8: Field testing equipment, dimensions in mm. Water level and displacement reference frames not shown. (a) arrangement for acking tests on.5m and.m caissons, (b) alternative arrangement during SEV tests. Labels indicate (A) A-frame, (B) concrete block, (C) caissons, () hydraulic acks, (L) load cells, (R) foundations of reaction frame, (V) SEV, (W) weight providing offset load for SEV tests. (b)

15 6z 7z oment (km) 8z 9z Rotation (radians) Figure 9: ysteresis loops from SEV tests on m caisson. 5 4 oment (km) Rotation of caisson centre (R θ) (m) Figure : ysteresis loops from hydraulic acking tests on m caisson. Figure : The caisson test rig at Aalborg University G (Pa) Jacking SEV yperbolic curve fit θ (radians) Figure : Shear modulus against rotation amplitude. axis perpendicular to the horizontal load). owever, a test rig capable of applying full 6 degree-offreedom loading has recently been developed by Byrne and oulsby (5). The model tests at Aalborg are performed by the test rig shown in Figure. The rig consists of a test box and loading frame. The test box consists of a steel frame with an inner width of.6m x.6m and an inner total depth of.65m. The test box is filled with Aalborg University Sand o. After each experiment the sand in the box is prepared in a systematic way to ensure homogeneity within the box, and between the different test boxes. The sand is saturated by the water reservoir shown in Figure. Before each experiment CPT-tests are performed to verify the density and strength of the sand. The caisson is then installed and loaded with a constant vertical load. The vertical load is kept constant through the experiment, while the horizontal force is applied to the tower by the loading device mounted on the loading frame, see Figure. The tower and the loading device are connected by a wire. The combined loading (, ) is controlled by the height of loading h. The loading frame allows the possibility of changing h from.m to 4.m above the sand surface (Table ). The horizontal force is measured by a transducer connected to the wire. The deformation of the foundation and the moment are measured with the measuring cell mounted on the top of the caisson, as shown by Figure. Laboratory tests at Oxford University have used a versatile degree-of-freedom loading rig designed by artin (994) and adapted by Byrne () (see also artin and oulsby () and Gottardi et al. (999)). The rig is shown in Figure 4, and is capable of applying a wide range of combinations of vertical, horizontal and moment loading under either displacement or load control. Typical moment loading tests involve applying a fixed vertical load, and then cycling the rotation at

16 Figure : The measuring cell connecting the caisson and the tower. oment Load, /R () Rotational Displacement, Rθ (mm) Figure 5: oment-rotation test on sand Experiment, /R = Fitted Yield Surface Soil Plug Weight oment Load, /R () Vertical Load, V () Figure 6: Experimentally determined yield surface in V- plane Figure 4: Three degree-of-freedom testing rig at Oxford University increasing amplitude. An example is given in Figure 5. The first interpretation of such tests is to determine the yield surface for a single surface plasticity model (see section 7. below, and also artin and oulsby (), oulsby and Cassidy (), oulsby (), Cassidy et al. (4)). An example of the yield points obtained, plotted in the vertical load-moment plane, is given in Figure 6. Of particular importance is the fact that at very low vertical loads there is a significant moment capacity, and that this extends even into the tensile load range. In these drained tests the ultimate load in tension is a significant fraction of the weight of the soil plug inside the caisson. Sections of the yield surface can also be plotted in - space as shown in Figure 7, where the data here have been assembled from many tests at different stress levels. The flow vectors are also plotted in this figure, and show that in this plane (unlike the V- plane) associated flow is a reasonable approximation to the behaviour. Feld () has observed similar shapes of a yield surface for a caisson in sand. We now consider the possibility of scaling the results of laboratory tests to the field. The test at Frederikshavn shown in Figure 7 was on a caisson with a ratio L R =, at an R value of approximately 8.7, and with a value of V πr γ of about.6. Using the data from the Oxford laboratory on.x.m caissons this requires a vertical load of about 6. In fact a test had been carried out with L R = and V = 5. According to the scaling relationships discussed in section, 4 the moment should be scaled according to R γ (a factor of 65) and the rotational displacement Rθ according to R γ (a factor of 5). Figures 6 and 7 suggest that for a vertical load of 6 rather than

17 oment Load, /R() Incremental Rotation, Rdtheta (mm) orizontal Load, () Incremental orizontal Displacement, du (mm) 5 a moment capacity say 5% higher might be expected, and that for the higher value of R a further increase of say 5% is appropriate. We therefore apply a factor of 75 to the moments and 5 to the rotational displacements. The result is shown in Figure 8. It can be seen that after scaling the moment at a Rθ value of.4 m is about km, compared to about 8km measured in the field. Although there is a factor of about between these values, it must be borne in mind that there are a number of possible causes of difference between the tests (e.g. the sand in the field test may be much denser), and also that a factor of 75 has already been applied: a factor of is relatively small by comparison. 5. Clay: field and laboratory tests V = -5 V = V = 5 Figure 7: Yield surfaces and flow vectors in - space. oment, (km) Rotational Displacement, Rtheta (m) Figure 8: Laboratory moment test scaled to field conditions for comparison with Figure 7 Less work has been carried out on clay than on sand. The large scale trials at Bothkennar (oulsby et al. 5b) are complemented by laboratory studies intended to model these trials directly, and therefore add confidence to the scaling of the results to prototype size caissons (Kelly et al., 5a). /[s u (R) ] /[s u (R) ] At Bothkennar, moment loads were applied to a m x.5m caisson by two means. Small amplitude, but relatively high frequency (z) loading was applied by means of the SEV device described above, and larger amplitude cycles, but at much lower frequency, were applied using a hydraulic ack. In both cases the loading was 4m above the caisson, so that h load D =.. The most important observation from these tests was the gradual reduction of secant stiffness (and increase in hysteresis) as the amplitude of the load cycles increases. The laboratory tests, specifically modelling the field tests, involved ust relatively low frequency loading. After the scaling relationships described in section were applied, there was a satisfactory agreement between laboratory and field data, especially at relatively small amplitudes of movement. As an example, Figure 9(a) shows the results (in dimensionless form) for rotation of the.m diameter caisson in the field, and Figure 9(b) the equivalent results, also in dimensionless form, from the small scale model test. The pattern of behaviour is remarkably similar in the two tests. This sort of comparison is vital to establish θ (a) field test (b) model test Figure 9: oment-rotation results presented in nondimensional form for laboratory and field tests. θ

18 confidence in the use of model testing to develop design guidelines. 6. CAISSO PERFORACE: TETRAPOD OR TRIPOD In the following, in which we consider multiple footing designs to support the wind turbine, we shall refer principally to a tetrapod (four footings) rather than a tripod. As a tripod is perhaps the most obvious multiple footing design to use, and has the obvious advantage of simplicity, our preference for the tetrapod deserves some explanation. As is discussed below, prudent design of a multiple footing structure will avoid tension being applied to any of the foundations (except under the most extreme of circumstances). This in effect dictates the separation of the foundations for a given overturning moment and weight of structure. Approximate calculations indicate that the tetrapod structure is usually a more favourable configuration to avoid tension, as it requires somewhat less material. The differences are not large, and a tripod may be preferred in some circumstances, but we shall refer to a tetrapod, as this will probably be more efficient. The important mechanism is the same in both cases: the overturning moment is resisted by opposing push-pull action on the foundations. In Table 4 we list the tests that have been carried out on vertical loading of caissons relevant to the wind turbine problem. In addition to these studies there are a number of other relevant studies which have been directed towards vertical loading of caissons for structures in the oil and gas industry or for use as anchors. 6. Sand: field and laboratory tests The simplest tests on vertical loading of caissons in sand, which are relevant both to installation and to subsequent performance, simply involve pushing caissons vertically into sand to determine the vertical load-displacement response. Figure shows the results of a set of such tests on caissons of different L/D ratios, Byrne et al. (). It is clear from the figure that there is a well-established pattern. While the caisson skirt is penetrating the sand there is relatively low vertical capacity, but as soon as the top plate makes contact with the sand there is a sudden increase in capacity. The envelope of the ultimate capacities of footings of different initial L/D ratios also forms a single consistent line. Of most importance, however, is the performance of the caissons under cyclic vertical loading. Figure Table 4: Vertical loading tests D L Site Soil Ref. (m) (m) Luce Bay Sand ,5 Oxford.5.5,5 Sand laboratory ,,,5 Bothkennar Clay.5. 6 UWA centrifuge (g) Vertical Load, V () Clay ormalised Vertical Displacement, w/d Vertical Displacement, w (mm) Figure : Vertical load-penetration curves for caissons of different L/D ratios Vertical Stress (kpa) Vertical Displacement (mm) Figure : Cyclic vertical loading of model caisson. shows the results of tests on a mm diameter caisson subected to rapid cyclic loading. Smallamplitude cycles show a stiff response, with larger cycles showing both more hysteresis and more accumulated displacement per cycle. The most important observation is that as soon as the cycles go into tension, a much softer response is observed, and the hysteresis loops acquire a characteristic banana shape. Clearly the soft response on achieving tension should be avoided in design. Closer examination of the curves reveals that the softening in fact occurs

19 Vertical Stress (kpa) Vertical Displacement (mm) Direction of movement 5mm/s, kpa mm/s, kpa mm/s, kpa Figure : Tensile capacity of model caisson pulled at different rates and at different ambient pressures. V/[γ'(R) ] 5 4.5m Field.5m Suction.m Pushed.5m Pushed [w/(r)][p a /(Rγ')] / Figure : ysteresis loops from tests at different scales and rates. once the drained frictional capacity of the skirts has been exceeded, rather than simply the transition into tension. Paradoxically, although additional accumulated displacement is observed once tension is reached, this accumulated displacement is downwards (not upwards as one might expect because of the tensile loading). The above observations mean that tension must be avoided in a prudent design of a tripod or tetrapod foundation for a wind turbine. owever, in all but the shallowest of water, avoiding this tension means that either the foundation must have a large spacing between the footings, or that ballasting must be used. The latter may in fact be a cost effective measure in deep water. Some designers may wish to reduce conservatism by allowing for the possibility of tension under extreme circumstances. It is therefore useful to examine the ultimate tensile capacity under rapid loading. Figure shows the result of three such tests. The slowest test (at 5mm/s) is almost drained, and a very low capacity in tension is indicated. The capacity in this case is simply the friction on the skirts. The test at mm/s (but zero ambient water pressure) shows a larger capacity, and it is straightforward to show that this is controlled by cavitation beneath the foundation. This means that at elevated water pressures (as in the third test) the capacity rises approximately in step with to the ambient water pressure, as correspondingly larger pressure changes are required to cause cavitation. This problem is studied in more detail by oulsby et al. (5a). It is important to note, however, that although ambient water pressure increases the ultimate capacity, it has negligible influence on the tensile load at which a flexible response begins to occur. Comparison of cyclic loading tests at different scales and at different speeds shows that it is difficult to scale reliably the accumulated displacements, which reduce with larger tests and higher loading rates. owever, when the scaling rules described earlier are applied, the shapes of individual hysteresis loops at different scales and at different rates become remarkably similar. Figure shows a comparison, for instance, of loops at three different load amplitudes from four different tests. At each particular load amplitude the loops from the different tests are very similar. The accumulation of displacement after very large numbers of cycles is difficult to predict, and so far few data are available. Rushton (5) has carried out vertical loading tests to about cycles on a model caisson in sand, using a simple loading rig which employs a rotating mass and a series of pulleys to apply a cyclic load. A typical result is shown in Figure 4, on a caisson mm diameter and mm deep, with cycling between ± 6. The caisson is therefore subected (at the minimum vertical load) to a small tension, but less than the frictional capacity of the skirts. The dimensionless accumulated vertical displacement is seen in Figure 4 to increase approximately with the logarithm of the number of cycles of loading (after about cycles). ote that even in this case where there is a tensile loading in part of the cycle, the net movement is downwards. The displacement is of course very sensitive also to the amplitude of the cycling. 6. Clay: field and laboratory tests Very few vertical loading tests relevant to the wind turbine problem have been completed on caissons in clay, although there have been a number of studies directed towards suction caissons used as tension

20 [w/(r)][p a /(Rγ )] / anchors, e.g. El-Gharbawy (998), Watson (999), ouse (). At Bothkennar tests were carried out in which inclined (but near vertical) loading was applied to a.5m diameter caisson (oulsby et al., 5b). Difficulties were encountered with the control of the loads using a hydraulic system, and the resulting load paths are therefore rather complex, leading to difficulties in interpretation. Further work on vertical loading in clay is required before definitive conclusions can be drawn, and in particular the issue of tensile loading in clay needs attention. Some preliminary results (Byrne and Cassidy, ), shown in Figure 5, show that the tensile response may be sensitive to prior compressive loading. Footings loaded in tension immediately after installation showed a stiff tensile response, whilst those loaded after first applying a compressive load to failure showed a more flexible tensile response. Vertical Stress, V/A (kpa) in ax umber of Cycles Figure 4: Accumulated displacement during long term cyclic vertical loading on sand Test : Post Bearing Capacity Test : Pre Bearing Capacity ormalised Displacement, (w + L)/D Figure 5: Tension tests on caisson foundations in clay 7. UERICAL STUDIES 7.. Finite element studies A number of analyses of suction caissons for offshore wind farms have been carried out as part of commercial investigations for possible proects. A more detailed research proect was carried out by Feld (). Finite element analysis is particularly appropriate for establishing the effects of design parameters on the elastic behaviour of caissons, and has been used by Doherty et al. (4a,b) to determine elastic stiffness coefficients for caisson design which take into account the flexibility of the caisson wall as well as coupling effects between horizontal and moment loading. 7. Plasticity models An important tool for the analysis of soil-structure interaction problems, particularly those involving dynamically sensitive structures are force resultant models. In these the behaviour of the foundation is represented purely through the force resultants acting upon it, and the resulting displacements (see Figure 4). Details of stresses and deformations within the soil are ignored. The models are usually framed within the context of work-hardening plasticity theory. Examples include models for foundations on clay (artin and oulsby, ) and on sand (oulsby and Cassidy, ). Overviews of the development of these models are given by oulsby () and Cassidy et al. (4) These models have been further developed specifically for the offshore wind turbine application. The developments include: Generalisation to full three-dimensional loading conditions, Inclusion of special features to represent the caisson geometry, Expression of the models within the continuous hyperplasticity framework to allow realistic description of hysteretic response during cyclic loading. A model with all these features is described by Lam and oulsby (5). The fitting of cyclic data to a continuous hyperplastic model is discussed by Byrne et al (a). 8. OTER COSIDERATIOS We have concentrated here on the design of caisson foundations as far as capacity and stiffness are concerned for in-service conditions. owever, there a number of other issues which need to be addressed in a caisson design, and we mention them here briefly. 8. Scour Scour is more important for caissons, since they are relatively shallow, than for piles. The size of caissons, and the fact that part of the caisson

21 inevitably protrudes above mudline level, creates rather aggressive conditions for scour. The fact that the caissons may be installed in mobile shallowwater environments means that proper consideration of this problem is essential, especially in sands. If the scour depth can be determined with sufficient confidence (e.g. from comprehensive model testing) then it may be possible to permit the scour to occur, and simply allow for this in the design by ensuring that the caisson is deep enough. It is more likely, however, that scour protection measures such as rock-dumping will need to be employed. Practical experience suggests that such protection must be placed very soon after caisson installation, as scour can occur very rapidly. In highly mobile environments, significant scour can, for instance, occur due to the currents in a single tide. odel testing indicates, however, that scour protection measures can be effective in preventing further erosion (R. Whitehouse: private communication). For in-service conditions regular monitoring for the possibility of scour would be prudent. 8. Liquefaction The transient pore pressures induced in the seabed can induce liquefaction, especially if the seabed is partially saturated due to the presence of gas (as can occur in shallow seabeds, largely due to decay of organic matter). The problem is a complex one, but typically, at one stage in the wave cycle, the pore pressure in the seabed can become equal to the overburden stress, and the effective stress falls to zero. This problem is further complicated by the presence of a structure, which clearly modifies the pore pressure pattern that would occur in the far field. Although some progress has been made, the interactions are complex, and theoretical modelling of the problem is not straightforward. 8. Wave-induced forces A quite different problem from liquefaction is also related to the fact that the principal forces on the structure are wave induced. As a wave passes the column of the structure it exerts large horizontal forces (of the order of a few meganewtons for a large wave), which also cause overturning moments. owever, at the same time the wave causes a transient pressure on the seabed, and on the lid of the caisson. Because the caissons are in shallow water these pressures are quite large. The pore water pressure within the caisson is unlikely to change as rapidly as the pressure on the lid, so there will be pressure differentials across the lid of the caisson which result in net vertical forces, and overturning moments on the caisson. The relative phase of the different sources of loading is important. As the crest of the wave ust reaches the structure, the wave kinematics are such that the horizontal forces are likely to be largest. At this stage the pressure on the upwave side of the caisson is likely to be larger than on the downwave side. The net result is that the moment caused by the pressures on the caisson lid opposes that caused by the horizontal loading, so this effect is likely to be beneficial to the performance of the caisson. Little work has, however, yet been completed on the magnitudes of these effects. The problem is complicated by the fact that the kinematics of large (highly non-linear) shallow water waves is still a matter of research, as is their interaction with structures. 8. COCLUSIOS In this paper we have provided an overview of the extensive amount of work that has been carried out on the design of suction caisson foundations for offshore wind turbines. Further verification of the results presented here is still required, and in due course it is hoped that this will come from instrumented caisson foundations offshore. Our broad conclusions at present are: Suction caissons could be used as foundations for offshore wind turbines, either in monopod or tripod/tetrapod layout. The combination of low vertical load and high horizontal load and moment is a particular feature of the wind turbine problem. Stiffness and fatigue are as important for turbine design as ultimate capacity. onopod foundation design is dominated by moment loading. Tripod/tetrapod foundation design is dominated by considerations of tensile loading. The moment-rotation response of caissons in sand has been extensively investigated by model tests and field trials, and modelled theoretically by finite element analyses and force resultant (yield surface) models. As amplitude of moment loading increases, stiffness reduces and hysteresis increases. oment loading in clay has been less extensively investigated in the laboratory and field. Vertical loading in sand has been extensively investigated in the laboratory and field.

22 The as the amplitude of vertical loading increases, stiffness reduces and hysteresis increases. Once tension is reached there is a sudden reduction of stiffness. Whilst high ultimate tensile capacities are possible (especially in deep water) this is at the expense of large movements. Application of scaling procedures for tests in both sand and clay allows model and field tests to be compared successfully as far as stiffness and the shapes of hysteresis loops is concerned. Cumulative displacements after very many cycles are harder to model. The design of caisson foundations also needs to take into consideration issues such as scour and liquefaction. It is hoped that the conclusions above lead in due course to application of suction caissons as foundations for offshore wind turbines, thereby making an important renewable energy source more economically viable. ACKOWLEDGEETS The work at Oxford University has been supported by the Department of Trade and Industry, the Engineering and Physical Sciences Research Council and a consortium of companies: SLP Engineering Ltd, Aerolaminates (now Vestas), Fugro Ltd, Garrad assan, GE Wind and Shell Renewables. An outline of the proect is given by Byrne et al. (b). The work of Richard Kelly, guyen-sy Lam and Felipe Villalobos on this proect is gratefully acknowledged. REFERECES. Bolton,.D. (986) The strength and Dilatancy of Sand, Geotechnique, Vol. 6, o., pp Byrne, B.W. () "Investigations of Suction Caissons in Dense Sand", D.Phil. Thesis, Oxford University. Byrne, B.W. and Cassidy,.J. () Investigating the response of offshore foundations in soft clay soils, Proc. OAE, Oslo, Paper OAE Byrne, B.W. and oulsby, G.T. (999) "Drained Behaviour of Suction Caisson Foundations on Very Dense Sand", Offshore Technology Conference, -6 ay, ouston, Paper Byrne, B.W. and oulsby, G.T. 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Doherty, J.P., Deeks, A.J. and oulsby, G.T. (4a) "Evaluation of Foundation Stiffness Using the Scaled Boundary ethod", Proc. 6th World Congress on Computational echanics, Beiing, 5- Sept., in press 6. Doherty, J.P., oulsby, G.T. and Deeks, A.J. (4b) "Stiffness of Flexible Caisson Foundations Embedded in on-omogeneous Elastic Soil", Submitted to Proc. ASCE, Jour. Structural Engineering Division 7. El-Gharbawy, S.L. (998) The Pullout Capacity of Suction Caisson Foundations, PhD Thesis, University of Texas at Austin 8. Feld T. () Suction Buckets, a ew Innovative Foundation Concept, applied to offshore Wind Turbines Ph.D. Thesis, Aalborg University Geotechnical Engineering Group, Feb.. 9. Gottardi, G., oulsby, G.T. and Butterfield, R. (999) "The Plastic Response of Circular Footings on Sand under General Planar Loading", Géotechnique, Vol. 49, o. 4, pp oulsby, G.T. () "odelling of Shallow Foundations for Offshore Structures", Proc. Int. Conf. on Foundations, Dundee, -5 Sept., Thomas Telford, pp -6. oulsby, G.T. and Byrne, B.W. () Suction Caisson Foundations for Offshore Wind Turbines and Anemometer asts, Wind Engineering, Vol. 4, o. 4, pp oulsby, G.T. and Byrne, B.W. (5a) Design Procedures for Installation of Suction Caissons in Clay and Other aterials, Proc. ICE, Geotechnical Eng., Vol. 58 o. GE, pp oulsby, G.T. and Byrne, B.W. (5b) Design Procedures for Installation of Suction Caissons in Sand, Proceedings ICE, Geotechnical Eng., in press 4. oulsby, G.T. and Cassidy,.J. () "A Plasticity odel for the Behaviour of Footings on Sand under Combined Loading", Géotechnique, Vol. 5, o., ar., oulsby, G.T., Kelly, R.B. and Byrne, B.W. (5a) "The Tensile Capacity of Suction Caissons in Sand under Rapid

23 Loading", Proc. Int. Symp. on Frontiers in Offshore Geotechnics, Perth, Australia, September, in press 6. oulsby, G.T., Kelly, R.B., uxtable, J. and Byrne, B.W. (5b) Field Trials of Suction Caissons in Clay for Offshore Wind Turbine Foundations, Géotechnique, in press 7. oulsby, G.T., Kelly, R.B., uxtable, J. and Byrne, B.W. (5c) Field Trials of Suction Caissons in Sand for Offshore Wind Turbine Foundations, submitted to Géotechnique 8. ouse, A. () Suction Caisson Foundations for Buoyant Offshore Facilities, PhD Thesis, the University of Western Australia 9. Ibsen, L.B., Schakenda, B., ielsen, S.A. () Development of bucket foundation for offshore wind turbines, a novel principle. Proc. USA Wind Boston.. Ibsen, L.B. and Brincker, R. (4) Design of ew Foundation for Offshore Wind Turbines, Proceedings of The nd International odal Analysis Conference (IAC), Detroit, ichigan, 4.. Ibsen L.B., Liingaard. (5) Output-Only odal Analysis Used on ew Foundation Concept for Offshore Wind Turbine, in preparation. Kelly, R.B., Byrne, B.W., oulsby, G.T. and artin, C.. () "Pressure Chamber Testing of odel Caisson Foundations in Sand", Proc. Int. Conf. on Foundations, Dundee, -5 Sept., Thomas Telford, pp 4-4. Kelly, R.B., Byrne, B.W., oulsby, G.T. and artin, C.., 4. Tensile loading of model caisson foundations for structures on sand, Proc. ISOPE, Toulon, Vol., Kelly, R.B., oulsby, G.T. and Byrne, B.W. (5a) "A Comparison of Field and Laboratory Tests of Caisson Foundations in Sand and Clay" submitted to Géotechnique 5. Kelly, R.B., oulsby, G.T. and Byrne, B.W. (5b) "Transient Vertical Loading of odel Suction Caissons in a Pressure Chamber", submitted to Géotechnique 6. Lam,.-S. and oulsby, G.T. (5) "The Theoretical odelling of a Suction Caisson Foundation using yperplasticity Theory", Proc. Int. Symp. on Frontiers in Offshore Geotechnics, Perth, Australia, Sept., in press 7. artin, C.. (994) "Physical and umerical odelling of Offshore Foundations Under Combined Loads", D.Phil. Thesis, Oxford University 8. artin, C.. and oulsby, G.T. () "Combined Loading of Spudcan Foundations on Clay: Laboratory Tests", Géotechnique, Vol. 5, o. 4, pp artin, C.. and oulsby, G.T. () Combined Loading of Spudcan Foundations on Clay: umerical odelling, Géotechnique, Vol. 5, o. 8, Oct., Rushton, C. (5) Cyclic testing of model foundations for an offshore wind turbine, 4 th year proect report, Dept. of Engineering Science, Oxford University 4. Sanham, S.C. () Investigations into the installation of suction assisted caisson foundations, 4 th year proect report, Dept. of Engineering Science, Oxford University 4. Villalobos, F.A., Byrne, B.W. and oulsby, G.T. (5) "oment loading of caissons installed in saturated sand", Proc. Int. Symp. on Frontiers in Offshore Geotechnics, Perth, Australia, Sept., in press 4. Villalobos, F., oulsby, G.T. and Byrne, B.W. (4) "Suction Caisson Foundations for Offshore Wind Turbines", Proc. 5th Chilean Conference of Geotechnics (Congreso Chileno de Geotecnia), Santiago, 4-6 ovember 44. Watson, P.G. (999) Performance of Skirted Foundations for Offshore Structures, PhD Thesis, the University of Western Australia 45. Wolf, J.P. (994) Foundation Vibration Analysis Using Simple Physical odels, Prentice all, ew Jersey

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25 Bearing capacity of parallel strip footings on non-homogeneous clay C.. artin & E.C.J. azell Department of Engineering Science, University of Oxford, UK ABSTRACT: On soft seabed soils, subsea equipment installations are often supported by mudmat foundation systems that can be idealised as parallel strip footings, grillages, or annular (ring-shaped) footings. This paper presents some theoretical results for the bearing capacity of (a) two parallel strip footings, otherwise isolated; (b) a long series of parallel strip footings at equal spacings. The soil is idealised as an isotropic Tresca material possessing a linear increase of undrained strength with depth. The bearing capacity analyses are performed using the method of characteristics, and the trends of these (possibly exact) results are verified by a companion series of upper bound calculations based on simple mechanisms. Parameters of interest are the footing spacing, the relative rate of increase of strength with depth, and the footing roughness. An application of the results to the design of perforated mudmats is discussed. ITRODUCTIO Shallow foundations are usually designed on the assumption that they act in isolation. When two footings (or a group of footings) are closely spaced, however, there is a beneficial interaction that can be quantified in terms of the efficiency, i.e. the ratio of the overall (group) bearing capacity to the sum of the individual (isolated) bearing capacities. The literature on this topic has been surveyed by azell (4). For footings on sand, numerous theoretical and experimental studies have shown that the effect of interaction becomes highly significant for friction angles greater than about and spacings less than about one footing width B. In contrast, the undrained bearing capacity of closely spaced footings on clay has received very little attention, perhaps because the early theoretical work of andel (96) showed that the beneficial effect of interaction was insignificant, even for fully rough footings. This was confirmed experimentally by azell (4), though only a few of his tests were conducted on clay. When considering the relevance of these findings to the design of grillages or closely spaced footings on soft offshore soils, it is important to note that the theoretical studies by andel (96) were confined to homogeneous soil, and although in the experiments of azell (4) there was a marked increase of undrained strength with depth, the dimensionless ratio kb/s u was no more than. for the small model footings tested (s u = mudline strength intercept, k = rate of increase of strength with depth). In water depths greater than a few hundred metres, the undrained strength at seabed level can be as low as to kpa, increasing with depth at to kpa/m (Randolph 4). A typical offshore mudmat might be 5 m wide, and if supported by a single strip footing (without perforations) this would imply typical values of the ratio kb/s u in the range.5 to 5. When calculating the bearing capacity of an isolated footing at the upper end of this range, the influence of non-homogeneity on the bearing capacity would certainly be accounted for, either by adopting appropriate plasticity solutions (Davis & Booker 97, oulsby & Wroth 98), or by selecting a representative strength s u > s u. It is therefore of interest to investigate the undrained bearing capacity of closely spaced footings for a similar range of kb/s u, and to assess the effect of using a mudmat with perforations in place of a continuous foundation (this is sometimes done to save weight, and to make the structure easier to remove). For a small degree of perforation it might be envisaged that there will be arching over the gap(s), such that there is no loss of bearing capacity, and even if some soil is squeezed through, there may still be a beneficial interaction effect. ere we investigate these issues using plasticity analyses. BEARIG CAPACITY AALYSES. Isolated footings The bearing capacity of an isolated strip footing on non-homogeneous clay was first studied by Davis &

26 Booker (97). They showed that for any value of kb/s u (zero to infinity) the stress and velocity fields computed using the method of characteristics furnished lower and upper bounds that were coincident. Davis & Booker s analyses have since been verified by several authors, and they can also be replicated using the free computer program ABC (artin 4). Figure a shows the variation of the bearing capacity factor c as a function of kb/s u. ote that c is defined with respect to the mudline strength, i.e. as Q u /Bs u where Q u is the ultimate bearing capacity (per unit run). Figure b shows, for the same range of kb/s u, the extent of the zone of plastic deformation adacent to each side of the footing. This distance is important because it also corresponds to the critical spacing at which parallel strip footings first begin to interact and give an overall bearing capacity that is greater than the sum of the individual capacities. As kb/s u increases, the zone of plastic deformation becomes smaller, so the footings need to be closer for any interaction to occur. Also shown in Figure are the results of upper bound calculations performed using the generalised ill- and Prandtl-type mechanisms of Kusakabe et al. (986), which were originally developed for circular footings on non-homogeneous clay. There is close agreement with the exact curves when kb/s u is small, but this deteriorates somewhat with increasing non-homogeneity, especially for the rough footing.. Interacting footings methodology In principle, bearing capacity analyses can be performed for an arbitrary number of parallel strip footings at arbitrary spacings, but the calculations can become tedious, particularly when using the method of characteristics. Figure shows the two problems considered here, both of which allow a favourable exploitation of symmetry: a pair of parallel strips, and an infinite number of parallel strips at equal spacings. Although impossible to realise in practice, the latter case is relevant to the interior members of a grillage containing many bearing elements. ote that in this paper S refers to the edge-to-edge spacing, not the centre-to-centre spacing as preferred by some authors. ote also that the footings are assumed to be rigidly connected, such that they move down together without any horizontal displacement or rotation (for a pair of closely spaced footings there is a tendency for separation and tilting to occur). The main bearing capacity analyses for interacting footings were performed using the method of characteristics. A modified version of the the atlab program InterBC, developed by azell (4) for interacting footings on a homogeneous c-φ-γ soil, was used. For a pair of footings, the program considers the right-hand footing and builds two meshes of characteristics, one commencing from the exterior soil surface, and one from the gap between the footing and the axis of symmetry (see Fig. ). An iterative adustment process is used to ensure that the two meshes are fully compatible at their common point C (same coordinates, same stresses). aving calculated the stress field, the program works back through the mesh and constructs the associated velocity field. These calculations are more complicated than those for an isolated footing, since the inward-flowing soil crosses a velocity discontinuity AD. ote that for non-homogeneous soil, the velocities outside AOD are not always parallel to the characteristics. Two separate calculations of the bearing capacity are performed: one by integrating the stresses along ACB (deducting the self-weight of the false head if applicable), and the other by equating the internal and external work rates of the collapse mechanism. In all of the analyses for this study it was found that, as the mesh of characteristics was refined, the two calculations of the bearing capacity converged to identical values. While this indicates that there are no regions of negative plastic work, it does not necessarily mean that the calculated bearing capacity is the exact collapse load, since it has not been demonstrated that the stress field can be extended throughout the soil. Construction of such an extension is straightforward for isolated footings (see e.g. Davis & Booker 97, artin 5), but for interacting footings it would be necessary to incorporate a nonplastic zone to allow the maor principal compression to flip from horizontal to vertical at some point on the z axis. This is not easy, and suggests that the method of characteristics cannot readily be used to obtain strict lower bounds for interacting footings (finite element limit analysis could be used). For a pair of smooth footings, the squeezing type failure of Figure a is always critical (except on homogeneous soil, where there is no interaction effect, and an infinite number of one- and two-sided mechanisms giving c = + π can be devised). For a pair of rough footings that are very closely spaced, overall failure as a single footing of width B + S may be more critical than the squeezing failure of Figure b. When determining the variation of bearing capacity with spacing, it is always necessary to check this alternative mechanism, for which the bearing capacity can be determined using ABC. Figure 4 shows some typical solutions for the case of infinitely many, equally spaced footings on non-homogeneous clay. ere the double symmetry means that it is only necessary to analyse half of one footing, so analysis using the method of characteristics is relatively straightforward. A single mesh is constructed, starting from the soil surface and bouncing characteristics off the centerline of the gap as before. The mesh is adusted until point C lies directly beneath the centre of the footing, with the maor principal compression aligned vertically. Calculation of the associated velocity field again incorporating a discontinuity along AD can then be

27 performed. As in the two-footing case, it was always found that the stress- and velocity-based calculations of the bearing capacity converged to the same value as the mesh was refined. This converged value represents a rigorous upper bound, but not a rigorous lower bound since the stress field is incomplete. If the number of footings is truly infinite then there is no alternative overall failure mechanism squeezing failure is the only option, and the bearing capacity must approach infinity as the spacing tends to zero. As well as the analyses performed using InterBC, some simple ill- and Prandtl-type upper bound mechanisms were devised for the problems shown in Figure. These were based on the mechanisms of Kusakabe et al. (986), but modified to allow a rigid wedge of soil to be extruded vertically between the interacting footings. In Figures and 4 the outlines of the optimal upper bound mechanisms are superimposed on the method of characteristics solutions, and there is a fairly close correspondence between the two. ote that for rough footings, the Prandtltype mechanism shown in Figures b and 4b is only critical when kb/s u is small; otherwise a ill-type mechanism (similar to Figs a, 4a) governs.. Interacting footings results Concentrating first on the pair of interacting footings, Figure 5 shows the variation of efficiency (as defined at the start of the paper) with the normalised spacing S/B. For a spacing of zero, the two footings behave as a single footing of width B. Although this has no net effect when the soil is homogeneous, there is a beneficial interaction when the strength increases with depth since the influence of nonhomogeneity is enhanced (kb/s u is greater than kb/s u, so the operative c is greater in Fig. a). For smooth footings the efficiency immediately begins to drop as soon as a gap is introduced, while for rough footings there is a brief increase in efficiency prior to the transition between overall and squeezing failure (see Section.). In all cases there is a gradual decline towards unit efficiency as the critical spacing plotted in Figure b is approached. The results for homogeneous soil (Fig. 5a) agree with those of andel (96): there is no gain in efficiency for a pair of smooth footings, and a peak of ust.7 (at S/B =.5) for a pair of rough footings. When the strength increases with depth, the potential gains in efficiency are rather greater, but the spacing needs to be small (<.B), and the benefit from interaction is almost all attributable to the effective augmentation of kb/s u rather than a genuine arching effect. In fact, the rough footing curves in Figure 5 clearly show that the influence of arching diminishes rapidly as non-homogeneity becomes more significant; when kb/s u there is an almost immediate transition from overall failure to squeezing failure as the spacing is increased from zero. The predictions from the method of characteristics are consistent with those from the simple upper bound analyses, shown as dotted lines in Figure 5. The efficiency curve for a pair of rough footings on homogeneous clay (Fig. 5a) also agrees remarkably well with that obtained by Galloway (4) using the finite element program ABAQUS. This suggests that the results obtained here from the method of characteristics may well be exact, though it is not immediately clear why the squeezing stress field should suddenly cease to become extensible at the same moment that overall failure becomes critical. It is noteworthy and surely no coincidence that Galloway s analyses also predict a peak efficiency of.7 at a spacing of S/B =.5, coinciding with an abrupt transition from overall to squeezing failure. Corresponding results for an infinite number of equally spaced footings are shown in Figure 6. The higher the value of kb/s u, the closer the footings need to be before there is any significant gain in efficiency (> say %). For a given spacing, the increase in efficiency is greatest for the homogeneous soil, and considerably higher (by a factor of up to ) for rough footings than for smooth footings. The critical spacings at which the curves in Figure 6 reach unit efficiency are the same as those in Figure 5. The dotted lines in Figure 6 show that the upper bound calculations give the same general trend, but they overpredict the efficiency factor quite seriously as the spacing becomes small. This is because the simple collapse mechanisms (consisting only of fan zones and rigid blocks) are unsuitable for modelling the increasingly complex velocity field as S/B. APPLICATIO: PERFORATED UDATS A common situation involving closely spaced footings is the design of a mudmat with perforations. In practice such structures would usually have square or circular geometry, with the bearing elements taking the form of a bidirectional grillage, or perhaps created by making a series of regularly spaced holes in an initially solid base. Although the actual failure mechanisms in these cases are complex (requiring D analysis), it is nevertheless instructive to perform some simplified calculations for plane strain conditions, to examine the general effect of introducing perforations. For brevity, only the two extreme cases shown in Figure 7 are considered. The notation adopted is the same as that used in the paper by White et al. elsewhere in these proceedings: W is the overall width of the mudmat, B* is the width of the individual bearing elements, and R is the perforation ratio (i.e. the fraction of W that has been removed). In Figure 7a, the ratios S/B* and kb*/s u both change constantly as R is increased from zero (the former increases and the latter decreases). In Figure 7b, S/B* again increases as R is increased, but the ratio

28 kb*/s u is effectively zero from the outset (since the number of perforations is very large, the width B* of each individual bearing element is very small). In both cases, as R is increased there eventually comes a point where there is no longer any interaction between adacent bearing elements of the mudmat. Results for the single perforation scenario of Figure 7a are shown in Figure 8. If the overall width W is taken as given, it is appropriate to characterise the non-homogeneity by kw/s u, and to define a gross bearing capacity factor with respect to W, i.e. c = Q u /Ws u. Using this convention, c for a smooth, singly-perforated mudmat on homogeneous soil decreases linearly from + π to as R increases from to. The other curves in Figure 8a show that breaking W into two smaller widths causes most of the benefit derived from the increase of strength with depth to be lost quite quickly, followed by a more gradual decline once R passes about.. The corresponding curves for rough-based mudmats with a single central perforation (Fig. 8b) have an initial plateau where overall failure is more critical than squeezing failure. owever the beneficial effect of this arching across the perforation is only significant when kw/s u is small. Figure 9 presents results for the other scenario of a mudmat with numerous perforations (Fig. 7b). In this case both the smooth and rough curves exhibit plateaus corresponding to overall failure, but once squeezing failure becomes critical the bearing capacity starts to decline (somewhat more rapidly than in Fig. 8). Regardless of the value of kw/s u, the appropriate squeezing curve is always that for homogenous soil, for the reason mentioned above: the ratio kb*/s u is effectively zero because B* << W. (The curved envelopes in Figs 9a, b are simply alternative presentations of the data for kb/s u = in Figs 6a, b.) Perhaps the most interesting prediction in Figure 9 is that for a rough mudmat on homogeneous soil, a perforation ratio in excess of 5% can be tolerated without any reduction in capacity. Unfortunately this is clearly not the case when kw/s u >. 4 COCLUSIOS This paper has presented theoretical solutions for the vertical bearing capacity of rigidly connected, parallel strip footings on clay exhibiting a linear increase of undrained strength with depth. Both a pair of footings and a large group of equally spaced footings have been considered. Results have been obtained using the method of characteristics, and confirmed by independent upper bound calculations based on simple mechanisms. The former results are believed to represent exact solutions, though they have only been established as upper bounds at this stage. A practical application to the design of perforated mudmats on soft offshore soil has been explored. REFERECES Davis, E.. & Booker, J.R. 97. The effect of increasing strength with depth on the bearing capacity of clays. Géotechnique (4): Galloway,. 4. Interaction between adacent footings in offshore foundation systems. Final year proect report, Department of Engineering Science, University of Oxford. azell, E.C.J. 4. Interaction of closely spaced strip footings. Final year proect report, Department of Engineering Science, University of Oxford. oulsby, G.T. & Wroth, C.P. 98. Calculation of stresses on shallow penetrometers and footings. OUEL Report o. 5/8, Department of Engineering Science, University of Oxford. Kusakabe, O., Suzuki,. & akase, A An upper-bound calculation on bearing capacity of a circular footing on a non-homogeneous clay. Soils and Found. 6(): andel, J. 96. Interférence plastique de fondations superficielles. Proc. Int. Conf. on Soil ech., Budapest: artin, C.. 4. ABC Analysis of Bearing Capacity. Software and documentation available for download from www-civil.eng.ox.ac.uk/people/cmm/software/abc. artin, C.. 5. Exact bearing capacity calculations using the method of characteristics. Issues lecture, Proc. th Int. Conf. of IACAG, Turin, to appear. Randolph,.F. 4. Characterisation of soft sediments for offshore applications. Keynote lecture, Proc. nd Int. Conf. on Site Investigation, Porto. (a) (b) c = Q u /Bs u Critical S/B Smooth Rough kb/s u.5 Smooth Rough 4 5 kb/s u Figure. Isolated strip footing on non-homogeneous clay: (a) bearing capacity (b) critical edge-to-edge spacing for interaction between parallel footings. Results from simple UB calculations (after Kusakabe et al. 986) shown dotted.

29 (a) (a) kb/s u = B S B. (b) etc. z s u = s u + kz φ u = S B S B S B S B S z s u = s u + kz φ u = Figure. Parallel strip footings on non-homogeneous clay: (a) pair of footings (b) many footings, equally spaced. etc. x x Efficiency.. Smooth Rough Smooth effic. = for all S/B S/B (b) kb/s u =. (a) Smooth A O C B Efficiency.. Smooth Rough D S/B (b) Rough (c) kb/s u = O A B. D C Efficiency.. Smooth Rough Figure. Pair of parallel strip footings on non-homogeneous clay (kb/s u =, S/B =.5): characteristics and velocity vectors, with mechanism outlines from simple UB calculations S/B (d) kb/s u = 5 (a) Smooth. O D A C ote: half of one footing shown Efficiency.. Smooth Rough (b) Rough O D A C ote: half of one footing shown Figure 4. any parallel strip footings on non-homogeneous clay (kb/s u =, S/B =.5): characteristics and velocity vectors, with mechanism outlines from simple UB calculations S/B Figure 5. Pair of parallel strip footings: variation of efficiency with edge-to-edge spacing. Efficiency = ratio of overall (group) capacity to sum of individual (isolated) capacities. Results from simple UB calculations shown dotted.

30 (a) Smooth Efficiency (b) Rough Efficiency kb/s u =,,, S/B kb/s u =,,, S/B Figure 6. any parallel strip footings: variation of efficiency with edge-to-edge spacing. Efficiency = ratio of overall (group) capacity to sum of individual (isolated) capacities. Results from simple UB calculations shown dotted. (a) (b) W B* S B* B* S Perforation ratio R = W S W..... Perforation ratio R S = B * + S Figure 7. udmat with (a) single central perforation (b) many identical perforations. Perforation ratio R = fraction of overall width W that has been removed. (a) Smooth c = Q u /Ws u (b) Rough c = Q u /Ws u kw/s u =,,, R = S/W kw/s u =,,, R = S/W Figure 8. udmat with single central perforation: variation of bearing capacity with perforation ratio. Initial plateaus in (b) correspond to overall failure of mudmat. (a) Smooth c = Q u /Ws u (b) Rough c = Q u /Ws u kw/s kb/s u =,,, 5 envelope continues linearly to (, ) R = S/(B*+S) kw/s kb/s u =,,, 5 envelope continues linearly to (, ) R = S/(B*+S) Figure 9. udmat with many identical perforations: variation of bearing capacity with perforation ratio. Initial plateaus correspond to overall failure of mudmat.

31

32 Investigating 6 degree-of-freedom loading on shallow foundations B.W. Byrne & G.T. oulsby Department of Engineering Science, University of Oxford, United Kingdom ABSTRACT: Previous laboratory studies of the response of shallow foundations have only considered planar loading. This paper describes the development of a loading device capable of applying general loading on model shallow foundations. Loading involving all six degrees of freedom {vertical (V), horizontal (, ), torsion (Q) and overturning moment (, )}, can be applied experimentally to the model foundations. Aspects of the design, including the loading rig configuration, development of a six degree-of-freedom load cell, numerical control algorithms and an accurate displacement measuring system are described. Finally results from initial experiments are presented that provide evidence for the generalisation of existing workhardening plasticity models from planar loading to the general loading condition. ITRODUCTIO. otivation The response of shallow foundations subected to general loading is an important area of civil engineering, particularly in the offshore industry, where foundations must be designed for loadings due to harsh environmental conditions. These conditions may lead to large vertical (V), horizontal () and moment () loads on the foundations. Whilst earlier studies considered overall stability, more recent studies have attempted to model the displacements, using model tests to calibrate work hardening plasticity theories (oulsby et al., 999; artin and oulsby,, ; Byrne and oulsby, ; Cassidy et al. ; oulsby and Cassidy, ). Recently, this work has focussed on suction caisson foundations (Byrne et al., ; Byrne and oulsby, ). With geometry rather like an upturned bucket, the caisson is simply installed by sucking the water out, and thus forcing the skirts into the seabed. This type of foundation has potential applications in the developing offshore wind energy industry. In this application the loading consists of very high moment and horizontal loads, but low vertical loads. This is a very different pattern of loading from that experienced by heavier structures in the oil and gas sector. In addition, the wind and wave directions may not coincide, so the base shear and moment are not in the same direction. Considerable uncertainty surrounds how these foundations may perform under these loading conditions (Byrne and oulsby, ).. Background Theory Figure shows a shallow foundation under three degree-of-freedom loading as defined by Butterfield et al. (997). This problem has received much attention over the past twenty years, and the load displacement behaviour of the foundation can be captured well by work-hardening plasticity theories (as shown by the papers cited above). A key component of the plasticity theories is the definition of a suitable yield surface. Figure shows the shape of a yield surface that has been defined experimentally, for shallow foundations under three degree-of-freedom loading. This shape can be expressed mathematically as equation. f = m h m + a m h m () o o o o h h β v β ( v) = β V where v =, m =, h =, h o is the V o RV o V o normalised horizontal load capacity, m o is the normalised moment capacity, a is the eccentricity of the ellipse in the h:m plane, ( ) ( β ) + β β β + β = and β β β and β are shaping β β

33 R Reference position r w u parameters for the section in the vertical load plane. umerous studies have identified the parameter values for the yield surface for a variety of footing types and for different soils - for example see oulsby et al. (999) for shallow circular foundations on sand, or artin and oulsby () for spudcans on clay. A natural extension of the these theories is to six degrees-of-freedom and artin (994) proposed an expression for this case: h h m m q f = ho ho mo mo qo () hm hm β ( ) β β a v v = homo where h =, h =, m =, V o V o RV o Q m = and q =. Figure shows the RV o RV o definitions of the loads from Butterfield et al. (997). The displacements work-conugate to the V,,, Q, are loads (, ) ( w, u, u, ω, θ θ ), V Current position Figure : Sign conventions for degree-of-freedom loading (Butterfield et al., 997).. There has been no systematic study of footing response to full six degree-offreedom loading to verify the extension of the planar loading theories to the general case. In the following the development of a loading device capable of applying the general loading is discussed, and some /R Yield surface Figure : Yield surface for shallow foundations. θ V Q V Figure : 6dof loading on a circular foundation. initial experimental results are presented that can be used to verify equation. DESIG OF A 6 D-O-F LOADIG RIG. The loading system Previous experimental work at Oxford has used a three degree-of-freedom (dof) loading device designed by artin (994). This planar loading device achieves vertical and horizontal motion by using a system of sliding plates, and rotational movement by rotating the loading arm relative to these plates. All motions are independent of each other, and are each driven by a stepper motor these features are useful for implementing load and displacement control systems. owever, this type of system would become too cumbersome for six degree-of-freedom (6dof) motions, and so an alternative approach is required. Typically, in robotics applications, the Stewart Platform (Stewart, 965) is considered to be the most elegant approach to achieving 6dof movement of a platform. There are numerous applications of this system in robotics, but the authors do not believe the system has been used for the testing of civil engineering structures, and in particular testing of foundations The arrangement described in this paper is a variant of the Stewart platform, and similar arrangements are used, for instance, in the automobile industry for dynamic testing of vehicles. The system uses six actuators which, at one end, are connected to the loading platform, and at the other are connected to a stiff reaction frame. Provided that six properly arranged actuators are used, and are pinned at both ends, then it is possible to achieve 6dof motion of the loading platform by changing the lengths of the actuators in a coordinated fashion. By careful selection of the actuator geometry, it is possible to ensure that the control problem is well-conditioned, so that calculations proceed in a straightforward fashion. The disadvantage with the Stewart Platform is that the simple motions are not linearly or independently related to the motion of any individual actuator, unlike the dof system of artin (994).

34 Actuator Lengths A A A A4 A5 A6 Forward Kinematics Inverse Kinematics Platform Pose w u u ω θ θ Figure 4: Photos of the 6dof loading rig including a close-up of the small LVDT measurement system. Therefore, quite complex control routines are required to ensure that all actuators move in concert to achieve the desired motion. Figure 4 shows the loading rig as constructed, showing three actuators approximately vertical and three actuators approximately horizontal. This arrangement ensures that the problem is well conditioned, as the main motions can be directly related to the motions of a sub-set of the actuators. For example, to achieve vertical movement the three vertical actuators must move the same distance, while only a slight adustment of the horizontal actuators is required. The actuators, supplied by Ultra otion, are linear actuators each powered by an Animatics Smartotor. This brushless DC servo-motor incorporates an integrated control system featuring a motion controller, encoder and amplifier. The actuators have a maximum extension of mm and can move at rates of up to 5mm/s. Commands to the actuators can specify relative motions, position, velocity or acceleration. The actuators are daisychained together and commands can be sent to individual actuators and then executed simultaneously with a global command. ore importantly, a number of moves can be downloaded to on-board memory on the motors, and then executed according to a synchronised clock system common to all actuators. This makes it possible to execute complicated platform motions provided one can determine, in advance, a time history of the individual actuator motions required.. The control program A program has been written in Visual Basic to control the loading system. The program allows input of a sequence of moves in terms of the motions ( w, u, u, ω, θ, θ ) of the platform, known as the pose. These motions can be described in terms of a rotation and translation matrix (i.e. a transformation matrix). This matrix can be applied to the coordinates of the pinned connections of the actuators with the loading platform to produce a new set of coordinates for the platform in its new position. If the Figure 5: Calculation procedures used in computer program. co-ordinates of the other (fixed) ends of the actuators are known, then it is possible to determine the required lengths of each actuator. To move the platform to the new position simply requires extending/retracting each actuator to its required length. This calculation procedure is known as the inverse kinematics problem and is a simple analytical calculation. The opposite calculation, called the forward kinematics problem, is not so straightforward, and requires a numerical solution. If the lengths of each actuator are known, then it is possible to calculate the new pose of the platform. Within the actuators are linear potentiometers that allow the user to determine the current length of the actuator, and therefore the pose of the platform. Both inverse and forward kinematics procedures are used within the software as shown in Figure 5. A typical test proceeds by determining the initial platform pose using the forward procedure. The user then specifies a sequence of moves in terms of platform pose. These moves are broken into a series of small moves so that the non-linearity of motion of each actuator can be captured. The inverse procedure is used to calculate for each of the moves the required length of each actuator. A file of actuator lengths with time (position-time data) is recorded. The relevant data from this file are sent to each actuator, and each movement is executed simultaneously. An on-board buffering system allows moves to be downloaded to each actuator. The actuators themselves use sophisticated control processes to determine the velocity and accelerations required, so that the actuator reaches each position at the time required, thereby ensuring a smooth motion. While the moves are being performed the control program logs the data. In particular the actuator lengths are recorded and the platform pose is calculated and displayed.. The load cell The load cell was constructed using a thin walled cylinder of radius r = 7.5mm, wall thickness t =.475mm and length 7mm. It was fabricated from Aluminium alloy with a Young s odulus of 7 GPa and a shear modulus of 7. GPa. The thin

35 Figure 6: The 6 degree-of-freedom load cell. walled section was machined from a larger block, leaving heavy end flanges. The transition from thinwalled section to flange was smoothed at an appropriate radius to minimise stress concentrations. A total of strain gauges are fixed to the outer surface of the cylinder to measure the appropriate strains. Figure 6 shows the completed cell. The strain gauges were arranged in six Wheatstone bridge circuits, each corresponding to the measurement of a particular load component. Each circuit was fully compensated for temperature. Eight gauges were used for the vertical and torque circuits, and four gauges for the moment and horizontal load circuits. The cell was calibrated by applying known loads and measuring the output from all six circuits. By varying the loads one at a time, it is possible to determine components of the matrix X relating loads to voltages in the equation C = XF where C is the circuit output vector and F is the load vector. Figure 7 shows the results from the six circuits for changes in the vertical load. The slopes for these six curves represent the components of the part of the matrix relating to vertical load (i.e. the first column of the matrix X). Inverting X produces a six by six calibration matrix that can be incorporated into the control program, so that loads are calculated during the experiment. ote that the design of the circuits is such that the off-diagonal terms are small. This is indicated in Figure 7 where only one circuit is responsive to the change in applied load..4 Small LVDT system One determination of the platform pose is by using the linear potentiometers within the actuators. This, however, provides only a coarse measurement of the platform pose. In particular there are issues of electrical noise and rig stiffness which have a significant impact on both the resolution and accuracy of this measurement. To achieve a more accurate determination of the foundation movement a system of small LVDTs (mm range) are used. These are placed in a similar configuration to the actuators, but supported on a separate frame as shown in Figure 4. The program carries out the forward kinematics calculation to determine the pose of the platform, given the measured lengths of the LVDTs. This allows very fine resolution of the foundation movement to the order of a few microns (Williams, 5). EXPERIETAL RESULTS Some preliminary experimental results on a 5mm diameter flat circular footing using only displacement control are presented here. At the time of writing load control routines were being developed and are anticipated to be implemented in the near future. The experiments were carried out on Leighton Buzzard 4/5 silica sand. This is a uniform sand with particle sizes ranging from.6mm to.8m. The maximum and minimum void ratios are.79 and.49 respectively. The sand was prepared in a loose state with a relative density estimated as %. Fuller details of the experimental work are reported by ap Gwilym (4), Stiles (4) and Williams (5). The experiments were designed to determine the shape of the yield surface in the six dimensions. A number of swipe tests were performed with various combinations of translations and rotations at a constant vertical displacement. The swipe test has been used extensively to determine the shape of yield surfaces, see artin (994), Gottardi et al. (999), artin and oulsby (), Byrne and oulsby (). Circuit Output (V) C C C C4 C5 C6 Vertical Load () Vertical Load () Figure 7: Calibration curves for the loadcell under vertical loading Vertical Displacement (mm) Figure 8: Typical vertical loading results.

36 . Vertical loading Prior to carrying out the swipe tests it was necessary to perform vertical loading tests, as these give information for the hardening law. Five experiments are shown in Figure 8, showing good repeatability of the results. ote that the measurement of the displacement is coarse, as in these experiments the small LVDT system was not used. /V o, /RV o, Q /V o orizontal Swipes Rotational Swipes. Swipe tests A number of swipe tests were performed to investigate the suitability of equation. A typical experimental result for a swipe test is shown in Figure 9. In this test the footing was displaced vertically to a pre-specified distance at which point the vertical load reached approximately 5. At this load the footing was translated horizontally. The figure shows that as the footing translates horizontally the relevant horizontal load traces a path around a yield surface. In this particular test the translation was u so the only horizontal load developed was. It is instructive to observe that the other load components are all relatively unaffected by the translation, as was expected. It is also possible to carry out tests involving translations u, u, -u and -u. The results of these translations are shown in Figure where the load paths for and are plotted. ote that each of the tests starts at a different vertical load. owever, it is clear that the magnitudes and the shapes of the load paths are Loads,, /R, Q /R () orizontal Loads,, () Vertical Load, V () Figure 9: A horizontal swipe result Vertical Load, V () Figure : orizontal swipe results. /R /R Q/R. Twisting Swipes V /Vo Figure : Results normalised by V o. similar for the different translations. This confirms the expectation that similar load paths will be traced out regardless of the translation direction. Similar experiments were carried out for rotations and twists with the same results (i.e. the results were independent of direction). The data, such as shown in Figure, can be easily compared by normalising all the loads by V o as suggested in equation. Results are plotted in Figure for all possible pure horizontal, rotational and twisting swipes with the negative swipes reflected about the vertical load axis. It is clear that the results depend on the mode (i.e. translation/ twisting/rotation) of the swipe test but not on the direction. Equation can be fitted to the above results to give the parameter values in Table, which are compared to data for footings on sand under planar loading. Table : Parameter values for work-hardening model Parameter This study Gottardi et al., 999 Byrne and oulsby, h o...54 m o q o. /A /A β β a In determining these parameters it was also necessary to use results for combined swipes, that is swipes involving simultaneous rotation and translation and other combinations of movements. For instance Figure shows the results from a test where a translation of u and rotation of -θ were applied simultaneously to the foundation. A number of these tests (twenty included in the above analysis) were performed as they are necessary in determining the fit, and in particular determining the parameter a which gives the rotation of the ellipse in the h:m plane. The test shown in Figure could not have been performed using the previous dof loading rig as it involves non co-planar loads. Equally Figure shows a test unique to the 6dof device in that during the swipe test the footing was first rotated by θ and

37 ormalised Loads, /Vo, /RVo then rotated by θ. (i.e. orthogonal and consecutive rotations). Initially under the rotation θ the load path for tracks around a yield surface. When θ stops and θ starts the response for drops off and the response for picks up and eventually tracks around the same yield surface that tracked. 4 COCLUSIOS In this paper the description of a unique loading device capable of applying six degree-of-freedom motion to a model foundation is presented. The resulting loads on the foundation are measured using a six degree-of-freedom load cell. A number of experiments, mainly displacement controlled swipe tests, are presented and interpreted to provide verification of the extension of a three degree-offreedom plasticity model to six degrees-of-freedom. Further experimental work is required to verify the model fully. V/Vo /R Figure : on co-planar loading applied to the foundation. /RV o /R /R V /V o Figure : A swipe test where consecutive rotations are performed. in constructing the 6dof load cell and Chris Waddup who made the actuator frame and LVDT support frame. We also acknowledge the work carried out by final year undergraduate proect students: Llywelyn ap Gwilym, Ed Stiles and Rachel Williams. The experimental work described here was conducted by these students under the direction of BWB. 6 REFERECES ap Gwilym, T.Ll. ab E. (4). Control of a six degree of freedom loading rig. Fourth year proect report, Department of Engineering Science, University of Oxford. Butterfield, R., oulsby, G.T. and Gottardi, G. (997). Standardised sign conventions and notation for generally loaded foundations. Géotechnique 47, o 5, pp 5-54; corrigendum Géotechnique 48, o, p 57. Byrne, B.W. and oulsby, G.T. (). Observations of footing behaviour on loose carbonate sands. Géotechnique 5, o 5, pp Byrne, B.W. and oulsby, G.T. (). Foundations for offshore wind turbines. Phil. Trans. Roy. Soc. A 6, Dec., pp Byrne, B.W., oulsby, G.T., artin, C.. and Fish, P.. (). Suction caisson foundations for offshore wind turbines. Wind Engineering 6, o. Cassidy,.J., Byrne, B.W. and oulsby, G.T. (). odelling the behaviour of a circular footing under combined loading on loose carbonate sand. Géotechnique 5, o, pp Gottardi, G., oulsby, G.T. and Butterfield, R. (999). The plastic response of circular footings on sand under general planar loading. Géotechnique 49, o 4, pp oulsby, G.T. and Cassidy,.J. (). A plasticity model for the behaviour of footings on sand under combined loading. Géotechnique 5, o, pp 7-9. artin, C.. (994). Physical and numerical modelling of offshore foundations under combined loads. DPhil Thesis, University of Oxford. artin, C.. and oulsby, G.T. (). Combined loading of spudcan foundations on clay: laboratory tests. Géotechnique 5, o 4, pp 5-8. artin, C.. and oulsby, G.T. (). Combined loading of spudcan foundations on clay: numerical modelling. Géotechnique 5, o 8, pp Stewart, D. (965) A platform with six degrees of freedom. The Institution of echanical Engineers 8, o 5, pp7-84. Stiles, E. (4). Experiments using a six degree of freedom loading rig. Fourth year proect report, Department of Engineering Science, University of Oxford. Williams, R. (5). Six degree of freedom loading tests on sand and clay. Fourth year proect report, Department of Engineering Science, University of Oxford, in preparation. 5 ACKOWLEDGEETS The authors acknowledge the funding from the Lubbock Trustees (pilot proect grant), the Royal Society (equipment grant), the Department of Engineering Science at Oxford University and EPSRC. We acknowledge the work of Clive Baker

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39 The tensile capacity of suction caissons in sand under rapid loading Guy T. oulsby, Richard B. Kelly & Byron W. Byrne Department of Engineering Science, Oxford University ABSTRACT: We develop here a simplified theory for predicting the capacity of a suction caisson in sand, when it is subected to rapid tensile loading. The capacity is found to be determined principally by the rate of pullout (relative to the permeability of the sand), and by the ambient pore pressure (which determines whether or not the water cavitates beneath the caisson). The calculation procedure depends on first predicting the suction beneath the caisson lid, and then further calculating the tensile load. The method is based on similar principles to a previously published method for suction-assisted caisson installation (oulsby and Byrne, 5). In the analysis a number of different cases are identified, and successful comparisons with experimental data are achieved for cases in which the pore water either does or does not cavitate.. ITRODUCTIO Suction caissons are an option for the foundations for offshore structures. Under large environmental loads the upwind foundations of a multiple-caisson foundation might be subected to tensile loads. Recent research indicates that serviceability requirements will often dictate that, under working and frequently encountered storm loads, tensile loads on caissons should be avoided, as they are accompanied by large displacements. owever, it may be appropriate to design structures so that under certain extreme conditions the caissons are allowed to undergo tension. It is therefore necessary to have a means of estimating the tensile capacity of a caisson foundation, whilst recognising that large displacements may be necessary to mobilise this capacity. The calculations are also relevant to the holding capacity of caisson anchors subected to pure vertical load, and to calculation of forces necessary to extract a caisson rapidly (for whatever reason). Under rapid tensile loading, a suction caisson in sand will exhibit a limiting load which will typically consist of a suction developed within the caisson, and friction on the outer wall. owever, a number of different possible modes of failure exist. The purpose of this paper note is to set out simple calculations for capacities under various failure modes, and to compare these with experimental results.. TESILE CAPACITY CALCULATIOS. Drained capacity If the tensile load is applied very slowly, then pore pressures will be small, and a fully drained calculation is applicable for calculating the capacity. For the purposes of calculation an idealised case of a foundation on a homogeneous deposit of sand is considered here. The resistance on the caisson is calculated as the sum of friction on the outside and the inside of the skirt. The effective stresses on the annular rim are likely to be sufficiently small that they can be neglected, and it is assumed that the soil breaks contact with the lid of the caisson. The frictional terms are calculated in the same way as for the installation calculation (oulsby and Byrne, 5), by calculating the vertical effective stress adacent to the caisson, then assuming that horizontal effective stress is a factor K times the vertical effective stress. Assuming that the mobilised angle of friction between the caisson wall and the soil is δ then we obtain the result that the shear stress acting on the caisson is σ v K tan δ. ote that in the subsequent analysis the values of K and δ never appear separately, but only in the combination K tan δ, so it is not possible to separate out the effects of these two variables. Allowance is made, however, for the possibility of different values of K tan δ acting on the outside and inside of the caisson. A difference

40 between this analysis and conventional pile design is that the contribution of friction in reducing the vertical stress further down the caisson is taken into account. If, as a preliminary, no account is taken of the reduction of vertical stress close to the caisson due to the frictional forces further up the caisson, then the tensile vertical load on the caisson for penetration to depth h is given by: γ h γ h V = o o tan ( K tan δ) ( πd ) ( K δ) ( πd ) i i () friction on outside friction on inside where the dimensions are as in Figure, and γ is the effective weight of the soil. V is the buoyant weight of the caisson and structure. A check should always be made that the friction calculated inside the caisson does not exceed the weight of the trapped soil plug γ hπd i 4. Ignoring the reduction of the stress in this case proves unconservative (i.e. it overestimates the force that can be developed), so we develop here a theory which takes this effect into account. Consider first the soil within the caisson. Assuming that the vertical effective stress is constant across the section of the caisson, the vertical equilibrium equation for a disc of soil within the caisson (Figure ) leads to: ( K tan δ) ( πd ) 4σ ( K δ) d σ v σ v i i v = γ = γ tan dz πd D i 4 i Writing D i ( ( K tan δ) ) = Zi i () 4 i, Eq. () becomes dσ v σ + v = γ, which has the solution dz Zi σ v = γ Zi ( exp( z Zi )) for σ v = at z =. The total frictional terms depend on the integral of the vertical effective stress with depth, and we can also h v i i obtain σ dz = γ Z ( exp( h Z ) + ( h Z )) i. For small h Zi the integral simplifies to γ h as in Eq. (). For brevity in the following we shall write y x = exp x + x, so that in the the function ( ) ( ( ) ) h v i i. above σ dz = γ Z y( h Z ) A similar analysis follows for the stress on the outside of the caisson. We assume that (a) there is a zone between diameters D o and D m = mdo in which the vertical stress is reduced through the action of the upward friction from the caisson, (b) within this zone the vertical stress does not vary with radial coordinate and (c) there is no shear stress on vertical planes at diameter D m. We then obtain the same results as for the inside of the caisson, but with Z replaced by Z = D ( m ) 4( K tan δ) ( ) i o o o. Alternative assumptions could be made for the variation of D m with depth, but at present there is little evidence to ustify any more sophisticated approach. If D m is taken as a variable, then the differential equation for vertical stress will usually need to be integrated numerically. Accounting for the effects of stress enhancement, Eq. () becomes modified to: h V = σ vodz h σ vidz ( K tan δ) ( πd ) ( K tan δ) ( πd ) i o i o + () In the special case where m is taken as a constant and uniform stress is assumed within the caisson this becomes: h V = γ Zo y Z o h γ Zi y Z i ( K tan δ) ( πd ) ( K tan δ) ( πd ) i o i o (4) V' udline σ' v πd i /4 z h γ'(πd i /4)dz σ' v (Ktanδ) i πd i dz Figure : Caisson geometry D i D o (σ' v + dσ' v )πd i /4 Figure : Vertical equilibrium of a slice of soil within the caisson

41 The calculation accounting for stress reduction obviates the need to check that the internal friction does not exceed the soil plug weight, as the capacity asymptotically approaches that value at large h.. Tensile capacity in the presence of suction If the caisson is extracted more rapidly, then transient excess pore pressures will occur, and the suction within the caisson will need to be taken into account. We return later to the calculation of the relationship between the rate of movement and the suction, but first address the calculation of load in terms of the suction. If the pressure in the caisson is s with respect to the ambient seabed water pressure, i.e. the absolute pressure in the caisson is pa + γ whw s (where p a is atmospheric pressure, γ w is the unit weight of water and h w the water depth), then we at first assume that the excess pore pressure at the tip of the caisson is as, i.e. the absolute pressure is pa + γ w( hw + h) as. There is therefore an average downward hydraulic gradient of as γ wh on the outside of the caisson and upward hydraulic gradient of ( a) s γ h w on the inside. We assume that the distribution of pore pressure on the inside and outside of the caisson is linear with depth. A detailed flow net analysis shows that this approximation is reasonable. The solutions for the vertical stresses inside and outside the caisson are exactly as before, except that γ is replaced by γ + as h outside the caisson and by γ ( a) s h inside the caisson. The capacity, accounting for the pressure differential across the top of the caisson and pore pressure on the rim (only relevant for a thick caisson), is again calculated as the sum of the external and internal frictional terms: D i ( Do Di ) V s π as π + + = 4 4 (5) h σ vodz h ( K tan δ) o ( πdo ) + σ vidz ( K tan δ) i ( πdi ) In the special case of m constant and a uniform stress assumed within the caisson, this gives: D i V s π as π as h γ + Zo y h Z o γ ( a) h ( D D ) o 4 s h Zi y Z i i ( K tan δ) ( πd ) o = ( K tan δ) ( πd ) i o i (6) We can often make a further simplifying assumption, that the suction is sufficiently large that the soil within the caisson liquefies and therefore ( a) s γ =. For a large suction this means that h a and almost all of the suction appears at the caisson tip. The above rearranges to give as s γ + =, and equation (6) can be simplified to: h h D i V s π as π s h Zo y h Z o ( D D ) o 4 ( K tan δ) ( πd ) o i o = (7) In the case either that the thickness of the caisson is small, or that a this simplifies to the following (writing the outer diameter as D, and the caisson area πd 4 = A ): s h V = Z y h Z 4Z = sa + y Dh ( K tan δ)( πd) h Z sa ( K tan δ) where Z = D( m ) ( 4K tan δ) (8). eglecting the effects of stress reduction would give: h V = sa + ( K tan δ) (9) D which means that the capacity is simply calculated by applying a linearly varying factor to the suction force beneath the lid.. Undrained failure A further condition should be considered: that of undrained failure of the sand. In any dilative sand, however, the pore pressures developed under undrained conditions are potentially so large that invariable (except in very deep water) the cavitation mechanism would intervene first. Since the undrained strength of sand is in any case very difficult to determine, we do not pursue this case here.. RELATIOSIP BETWEE SUCTIO AD DISPLACEET RATE At low displacement rates, the rate of influx of water q to the caisson can be calculated by Darcy s law, and equated to the rate of displacement times the

42 area of the caisson. Flow calculations were presented by oulsby and Byrne (5), and yield: kods πdi dh q = F = () γ w 4 dt where F is a dimensionless factor as determined by the procedures in oulsby and Byrne (5), which may be fitted approximately by the equation F =.6 ( + 5h D) for. h D. 8. If the displacement rate is increased, the above condition is interrupted by one of two conditions (a) the suction becomes large enough for liquefaction of the sand within the caisson to occur or (b) cavitation occurs within the caisson. When liquefaction occurs, the permeability of the liquefied sand increases to a large value, with the result that the a factor in the calculation of the load changes (as noted above) to near unity. The displacement rate may still be estimated from a flow calculation, but the appropriate boundary condition now becomes one of the suction applied at the base rather than top of the caisson. odified values of F (termed F L for this case) are given in Figure, and may be fitted approximately by the equation F = exp( 5h D) for. h D.. When cavitation occurs, either before or after liquefaction, the displacement rate becomes unlimited and (assuming that cavitation occurs at an absolute pressure fp a where f is a constant), the suction will be constant and determined by p a + γ whw s = fpa, or s = pa ( f ) + γ whw. In practice it appears that the factor f is near zero. 4. SUARY OF AALYSIS CASES The following summary presents equations for the above cases, for a thin-walled caisson. To simplify the equations we neglecting here the stress reduction effect, although this should be included in more Dimensionless flow factor F L Aspect ratio h/d Figure : Dimensionless flow factor for liquefaction case accurate calculations: (a) Small dh dt π Dγ dh s = w (from Eq. ()) and: 4 F ko dt V = sa ( a) as s πdh γ + ( K tan δ) o + γ ( K tan δ) i h h (for dh dt =, s = and these reduce to the equations for the fully drained case). (b) Liquefaction without cavitation γ h Onset of liquefaction occurs at s =, after that ( a) π Dγ w dh s = and: 4 FL ko dt h V = sa + ( K tan δ) o D ote that this will imply a sudden ump in s and V at the onset of liquefaction. (c) Cavitation without liquefaction Onset of cavitation occurs at s = pa ( f ) + γ whw. After that dh dt is unbounded, s is constant and: V = sa as γ + h as in case(a). ( K tan δ) o + γ ( a) h s ( K tan δ) i πdh (d) Cavitation with liquefaction Since s is constant once cavitation occurs, this condition can only occur when liquefaction occurs before cavitation. Onset of cavitation is at s = pa ( f ) + γ whw, after which dh dt is unbounded, s is constant and: h V = sa + ( K tan δ) o as in case (b). D ote that the above cases only occur in order (a), (b), (d) or (a), (c). When several possibilities exist for calculating load capacity it is often true that the correct case is simply found by calculating all cases and then taking the lowest value. ote in this analysis that this simple approach cannot be adopted as the onset of some states can preclude other cases occurring, and the calculated load is not necessarily the lowest of the cases. 5. COPARISOS WIT DATA We present here a number of pullout tests conducted two sands and at different pullout rates. The tests

43 pressure (kpa) Experiment Theory were conducted in a pressure chamber: some tests at an ambient (mudline) water pressure equal to atmospheric, and some at atmospheric plus kpa. The model caisson was 8mm diameter, 8mm skirt length. In the following the loads presented include the caisson weight. The first test reported here (Test 9) was conducted on Redhill Sand, at a pullout rate of mm/s and atmospheric pressure. Figure 4 shows the record of suction developed beneath the lid of the caisson against time, and Figure 5 shows the corresponding vertical load. It can be seen that (with a minor initial fluctuation) the suction rapidly approaches kpa, at which stage cavitation occurs. At around 44.5s there is a sudden loss of both suction and vertical load, but this is of little practical t (s) Figure 4: Pressure v. time for Test 9 V (k) Experiment Theory t (s) Figure 5: Vertical load v. time for Test 9. interest since by then the displacements are enormous and about three-quarters of the caisson had been pulled out of the soil. Figure 6 shows the ratio V / sa, showing that this ratio remains approximately constant during most of the pullout. It can readily be shown that the suction in this case rapidly increased to sufficient value to cause liquefaction (which would occur at a suction of only about kpa), and that the relevant case for analysis here is case (d). The predicted values from the theory described above (including stress reduction) are also shown on each of Figures 4 to 6, and it is clear that the theory (whilst not capturing some of the detail at the beginning of the pullout) predicts the broad trends of the test correctly. Figures 7 and 8 show corresponding results for Test (at the same pullout rate) but at an ambient pressure of atmospheric plus kpa. The suctions developed at this rate of loading are insufficient to cause cavitation, which would occur at -kpa relative to ambient. It can be seen that again the theory predicts the overall pattern of behaviour well. This time it is case (b) that applies. The fluctuations in predicted suction (and hence load) are due to minor variations in the calculated velocity of extraction. Figures 9 and show the results from Test, which is directly comparable to Test 9, but this time pressure (kpa) Experiment Theory t (s) Figure 7: Pressure v. time for Test 5. V / sa.5..5 Experiment Theory V (k) Experiment Theory t (s) Figure 6: V/sA v. time for Test t (s) Figure 8: Vertical load v. time for Test

44 at a pullout rate of only 5mm/s. Although the suctions are sufficient to cause liquefaction, the pullout rate is such that the suction is sufficiently small so that cavitation does not occur, and the vertical loads are correspondingly lower too. The predicted suction and load are also shown on the Figures. The match to the data could be improved by adusting the permeability, but the value used in the predictions were deliberately kept the same for all three tests discussed. The permeability value used was k =.5 m/s, which is somewhat higher than estimated previously for this sand (Kelly et al. 4). The other parameters used are K tan δ =. 7 and m =. 5. Finally, Figures and present equivalent data for a test on P5 sand, which is much finer that Redhill Sand, and has an estimated permeability of 4 k =. m/s. The extraction rate was 5mm/s, and in this case, although the extraction rate is lower, the pore pressures are sufficient to cause cavitation even with the ambient pressure of atmospheric plus kpa. The predicted and measured values of maximum tensile load for the three tests on Redhill sand and one on P5 are shown in Table. The order of magnitude of the tensile load is correctly predicted in all cases, even though the actual capacity of the caisson varies greatly in the different tests. pressure (kpa) Table : Predicted and measured tensile loads Test ax. tensile load (k) Predicted easured Test (5mm/s, kpa)..4 Test 9 (mm/s, kpa).. Test (mm/s, kpa) P5 sand: Test (5mm/s, kpa) COCLUSIOS In this paper we develop a simplified theory for predicting the maximum tensile capacity of a caisson foundation in sand. The calculated capacity depends critically on the rate of pullout (in relation to the permeability) and the ambient water pressure (which determines whether cavitation occurs). The theory is used successfully to explain widely differing experimental results for caissons pulled out under different conditions. REFERECES oulsby, G.T. and Byrne, B.W., 5. Design procedures for installation of suction caissons in sand, Proc. ICE, Geotechnical Engineering, in press. Kelly, R.B., Byrne, B.W., oulsby, G.T. and artin, C.., 4. Tensile loading of model caisson foundations for structures on sand, Proc. ISOPE, Toulon, Vol., pressure (kpa) Experiment Theory -5 - t (s) Figure 9: Pressure v. time for Test. Experiment Theory t (s) Figure : Pressure v. time for Test V (k) t (s) Experiment Theory Figure : Vertical load v. time for Test V (k) t (s) Figure : Vertical load v. time for Test Experiment Theory

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46 The theoretical modelling of a suction caisson foundation using hyperplasticity theory Lam guyen-sy & Guy T. oulsby Department of Engineering Science, Oxford University ABSTRACT: A theoretical model for the analysis of suction caison foundations, based on a thermodynamic framework (oulsby and Puzrin, ) and the macro-element concept is presented. The elastic-plastic response is first described in terms of a single-yield-surface model, using a non-associated flow rule. To capture hysteresis phenomena, this model is then extended to a multiple yield surface model. The installation of the caisson using suction is also analysed as part of the theoretical model. Some preliminary numerical results are given as demonstrations of the capabilities of the model.. ITRODUCTIO In developments of offshore wind turbines, the foundations account for a significant fraction of the overall installed cost, approximately 5% to 4% of the total cost (oulsby and Byrne, ). To satisfy the increasing need for renewable energy, there are a number of offshore wind farms to be constructed off the coast of the UK within the next few years. The possible use of caisson foundations for these turbines is therefore an important economical issue. From previous research, there are elastic-plastic theoretical models available for analysis of shallow offshore foundations, such as odel B for a ackup footing on clay (artin, 994) and odel C for footings on sand (Cassidy, 999). These models are based on the idea of a macro-element, representing the foundation behaviour. The loading on the footing is represented by force resultants at a chosen reference point on the footing, and the movement by the corresponding displacements of this point. In this paper, a macro-element model for a caisson is presented in outline. The main goal of this work is to establish a theoretical framework to model correctly the cyclic behaviour of a caisson foundation, and this necessitates extension of previous modelling concepts to use of multiple yield surfaces.. CAISSO FOUDATIOS A caisson foundation consists essentially of two parts: a circular top plate and a perimeter skirt, see Figure. The whole foundation is installed by the combination of gravity and suction within the caisson. In Figure, d is the distance between the Load Reference Point (LRP) and an idealised soil surface position ust as installation begins. The position of the LRP is arbitrary, but is conveniently taken at the oint between the caisson and the support structure. The conventions for forces are shown in Figure. The forces V R, R, R, Q R, R, and R are applied at the LRP. In the analysis, however, it is often convenient to use the force system, σ i = ( V,,, Q,, ) at the idealised soil surface level. The relationships between these two systems are: V = V R ; = R ; = R ; Q = Q R ; = R + d R ; = R d R The displacement vector at soil surface level is ε i = ( w, u, u, ω, θ, θ ). The corresponding displacements at the LRP are given w = w R ; u = u R + dθ R ; u = u R - dθ R ; ω = ω R ; θ = θ R ; θ = θ R.. RATE-IDEPEDET SIGLE YIELD SURFACE YPERPLASTICITY ODEL Based on the hyperplasticity framework (oulsby and Puzrin, ), a mechanical model can be derived from two scalar functions: the Gibbs free energy g, and either the dissipation function d or yield function y. The yield function is used here, since it can be identified directly from test results. The macro-element model is expressed in terms of the force vector σ i and displacement vector ε i. It is also necessary to introduce the generalized force vector χ i = ( χv, χ, χ, χq, χ, χ ) and finally the plastic displacement (or internal variable)

47 vector α = ( α, α, α, α, α α ) i V Q, R R V R V R LRP mudline d Soil surface level Figure. Geometry of caisson footing. In general, for a model without elastic-plastic coupling, the free energy g and yield function y can be expressed as: g ( σ ) σ α + g ( α ) = g i i i i () ( σ, χ, α ) = y () = y i i i. The Gibbs free energy function g In Eq. (), g represents the elastic response of the foundation and is independent of plastic displacements. For linear elasticity it takes the following form: g V = K K D d Q R Q K D K D R V R V K D K + 4 D R Q K K 5 4 R RR D () in which: K = GRk ; K = GR k 8GR k 4 d + GRd k ; K = GRk ; K 4 = 4GR k 4 GRk d; K 5 = 8GR k 5 and D = K K K 4. G is the shear modulus of the soil, and the factors k k 5 are dimensionless stiffness coefficients as proposed by Doherty et al. (4), who give elastic solutions for a caisson Figure. Conventions for forces foundation, in which the elastic stiffness of the caisson itself is taken into account. The g term, which is the work of the plastic displacements, specifies the kinematic hardening of the model. A simple linear hardening relationship is achieved if g is a quadratic function of the plastic strains, and this form will later be used here as the basis for the multiple-surface model: * * * * αv α α 5αQ g = * * α α * ( α α α α ) (4) * where * 5 are hardening parameters which can conveniently be expressed in terms of the elastic stiffness factors K K 5. Details of these functions are discussed later. For the time being, however, we simply take g = for the single surface model since the yield surface in this case does not undergo kinematic hardening.. The yield function y In the hyperplasticity framework (oulsby and Puzrin, ), the yield function has been regconised as the singular Legendre transform of the dissipation function d in case of rate-independent materials. The yield surface is therefore expressed as a function of the generalised forces χ i. Furthermore, the appearance of force components, (analogous to the true stresses σ i in continuum plasticity models), in the form of the yield function leads automatically to non-associated flow rules (Collins and oulsby, 997), which are known as the appropriate to describe soil behaviour. Consequently, association factors which play an interpolation role between true and generalised forces are proposed in the yield function. artin (994) and Cassidy (999) have establised the yield functions in elastic-plastic models (odel B and odel C for ack-up and circular footings of offshore structures on clay and sand). Based on these results, a yield function for a caisson footing is proposed with certain modifications to include aspects such as the nonassociated flow rule: β β = y = t Sβ v + t v (5) in which: [( v + t )( v )] S = sgn, further definitions follow below: β β + β + t β+β = β ( ) β β ( ) β and

48 ( h m h ) + h + m + m + q + a m avχv + ( av )( V ρv ) V t = h (6) v = (7) ( χ + ρ ) + ( a ) av V V V V ρv v = (8) V a ( χ + ρ ) + ( a ) ρ h = (9) hv a ( χ + ρ ) + ( a ) ρ h = () hv aq ( χq + ρq ) + ( aq ) Q ρq q = () RqV ( ( )) m a χ + ρ + d χ + ρ = RmV + ( a )( + d ) ( ρ + dρ ) () ( ( )) m a χ + ρ d χ + ρ = RmV + ( a )( d ) ( ρ dρ ) () It is convenient to note that the vertical load at which the maximum dimension of the yield surface is achieved V β is βt β t + α = α =, leading to =. V β + β β α V is the vertical bearing capacity of the foundation (the intercept of the yield surface on the positive V-axis). Appropriate values of the parameters specifying the yield surface shape for a typical fully embedded caisson are β = β =.99; t =.88. The parameters m, h and q are factors which determine the sizes of the yield surface in the moment, horizontal and torsion directions: typical values are.5,.7 and. respectively. The parameters a V, a V, a, a, a Q are the association factors ; ρ V, ρ, ρ, ρ Q, ρ and ρ are the back stresses which are the difference between true force and generalised force, and are in turn expressed as functions of the internal variable α. i 4. RATE-IDEPEDET COTIUOUS YPERPLASTICITY ODEL The main reason for the introduction of continuous hyperplasticity, which is in effect models an infinite number of yield surfaces, is to simulate a smooth transition between elastic and plastic behaviour, and capture with reasonable precision the hysteretic response of a foundation under cyclic loading. Such behaviour can not be described by a conventional single yield surface model. 4. The Gibbs free energy function g Starting from the form of Gibbs free energy function for a single yield surface model as in Eq. (), further developments for a continuous hyperplasticity model can be made. The Gibbs free energy function now becomes a functional as follows: gˆ = g σiαˆ idη + * * α * ˆ αˆ ˆ ˆ ˆ αˆ V + dη + dη + (4) * ˆ α * α * 5 ˆ ˆ ˆ Q ˆ αˆ + dη + dη + dη * + ˆ 4 ( αˆ αˆ αˆ αˆ ) dη where η is a dimensionless parameter which varies from to and expresses the relative sizes of the yield surfaces. When η =, no plastic behaviour occurs. Once η =, fully plastic behaviour occurs. The hat notation is used to denote any function of η. The hardening parameters in Eq. (4) now become functions of η. These functions determine the shapes of the force-displacement curves. yperbolic curves may conveniently be used and for this case the hardening functions have the form: n ˆ * i ( η) = Ai Ki ( bi η) i (5) where A i, b i and n i are parameters defining the shape of the curves. 4. The yield function y For a certain value of η, the yield function can be expressed as follows: ˆ β ˆ β y ˆ = t ηsβ vˆ + t vˆ = (6) where tˆ = hˆ + hˆ + mˆ + mˆ + qˆ + a( hˆ ˆ mˆ hmˆ ) (7) All the definitions of variables in Eqs. (6) and (7) are as for single-yield model, but these variables are determined for the yield surface corresponding to η. 5. ULTIPLE-YIELD SURFACE YPERPLASTICITY ODEL The concept of an infinite number of yield surfaces can model very well the response of a foundation under cyclic loading. owever, to implement the model in a numerical analysis, it is necessary to discretise the continuous plasticity model to a multiple-yield-surface model. Firstly, the integrals in the Gibbs free energy become summations. Secondly, the continuously varying functions of η are replaced by discrete variables.

49 5. The Gibbs free energy function g The hat notation as in Eq. (4) is now abandoned to express the fact that the variables are no longer functions, but a series of discrete values. is the number of yield surfaces chosen to simulate the continuous yield surface. We replace η by the factor / where is the number of the yield surface which is being considered. In the summation, the increment dη in the integral becomes: d = = η (8) The free energy function is therefore: ( ) = = = = = = = = α α α α + α + α + α + α + α + α + + σ α = Q V i i g g * 4 * * * 5 * * * (9) The above is appropriate provided that the value chosen is large enough to result in a small dη i to achieve a reasonable approximation to the integral by use of a summation. Eq. (5) now becomes: ( ) ( ) i n i i i i b A K = * () 5. The yield function y Using the same style of yield function as in Eq. (6), the th yield surface can be expressed as: = + β = β β v t v S t y () Where equations exactly similar to (6) to () apply, but with each definition applying for the th surface, thus Eq. (7) becomes for example: ( ) ( ) ( ) V V a a v V V V V V ρ + + ρ χ = () The factors, S, β, β, β and t, have the same values as in the single yield surface model. The definitions of the generalised forces can be expressed as follows: V n V V V V V b K A V g α = α = χ () n n b K A b K A g 4 α + α = α = χ (4) n n b K A b K A g 4 α α = α = χ (5) Q n Q Q Q Q Q b K A Q g α = α = χ 5 (6) n n b K A b K A g 4 α α = α = χ (7) n n b K A b K A g 4 α + α = α = χ (8) The coordinates of center of th yield surface in stress space can be defined as: V V χ V = ρ (9) and likewise for the other variables. Figure 4 shows the form of yield surfaces after a purely vertical loading. The size of the smallest yield surface in the vertical load direction is set as a certain fraction of the size of the outer yield surface. Between the inner and outer surfaces a uniform distribution of sizes of yield surfaces is used. The purpose of using a non-zero size of the first yield surface on the V-axis is to control the development of vertical plastic displacement on vertical unloading. 5. Incremental response In the multiple-yield-surface model, using rateindependent behaviour, the loading point must always be within or on each yield surface. This condition requires that the y-values for all active yield surfaces must be identically zero. The imposition of these consistency conditions is not straightforward in numerical analyses. The use of rate-dependent behaviour has been proposed as a means to simplify the numerical difficulties by oulsby and Puzrin () and Puzrin and oulsby (). The dissipation function d is in this case separated into two functions; force potential function z and flow potential w. oulsby and Puzrin () note that w can take alternative forms, depending on

50 the form of the viscosity assumed. In this paper, linear viscosity is used and the flow potential functions can be defined as: t ( σ, α, χ ) y i i i w ( σi, αi, χi ) = () µ Where µ is the viscosity; y is the th yield function which no longer needs to be identically zero. ote that w is only zero when the rates of change of plastic displacements are all zero. The incremental changes of plastic displacements caused by the th yield surface can be defined as: 46.5mm; the length of the perimeter skirt = 46.5mm. The caisson is installed to the full penetration position and then the horizontal and moment loads are applied. The vertical load V increases to the value of V = 945 during the penetration process and decreases to the value of V = 5 before the lateral loads are applied. During the Vertical loads (k) Vertical penetration w ithout suction Vertical penetration w ith suction assistance t. v = V/V.5.5 Vertical penetrations (m) Figure 5. Installation processes with and without suction Initial fraction =.8 Figure 4. ultiple yield surfaces w y y dα i = dt = dt () χi µ χi The total displacement increments are now calculated as: dεi g g = σk σi σk σ α = i i y µ y χi dt () 6. UERICAL ILLUSTRATIOS Firstly, a result modelling the suction assisted penetration process using the concepts of oulsby and Byrne (5) is shown in Figure 5. Secondly, a numerical example is given to illustrate test results which are obtained from laboratory testing of model caissons. In this example, A V =.; A = A = A Q = A = A =.5; b V = b = b = b Q = b = b =.; n V = n = n = n Q = n = n =.. Twenty yield surfaces are used. The values of yield function parameters are: a m = a h =.7; a V =.97; a V =.; t =.88; m =.5; h =.7; the shear modulus of the soil is G =.7Pa, self-weight γ = 5.74k/m, Poisson ratio ν =.; initial fraction for the first yield function =.8. The radius of caisson R = (m) () test results -5 theoretical results - theta (rad) Figure 6. Rotation under cyclic loading 6 test results 4 Theoretical results u (m) Figure 7. orizontal displacement under cyclic loading

51 w (m) application of the cyclic loads, the vertical load is kept constant at 5. The resulting moment-rotation behaviour is shown in Figure 6, and horizontal loaddisplacement in Figure 7. Finally the vertical movements during the cycling are presented in Figure 8. In each case the analyses are compared to test results, and it can be seen that a satisfactory agreement is achieved. 7. DISCUSSIO test results theoretical theta (rad) Figure 8. Vertical movements under cyclic loading There are four main points that must be addressed in this model: the choice of the hardening functions, the values of the association factors, the effects of suction pressures and the use of the rate dependent solution. Firstly, the hardening functions, i *, determine the distributions of plastic displacements which are caused by each yield surface. Therefore, the solutions can become stiffer or softer by increasing or decreasing the factors A i, b i or n i. It is very important to determine the appropriate value of the shear modulus G. Since the hardening functions depend on the elastic stiffness factors, which include the shear modulus, the value of G strongly affects the solutions. Secondly, the association factors play the role of determining the direction of the flow vectors of the plastic strains. To choose suitable values for these factors, it is necessary to consider some special aspects of the yield yield functions, such as the positions of the parallel points where the vertical plastic displacement incerments are zero. The directions of the flow vectors in the (V, ) plane, (, ) plane or (V, ) plane can be obtained from tests. Furthermore, during the application of lateral loads, the upward or downward movements of the footing are also depend on the position of the parallel point and the value of the vertical load. owever, the details of these expressions are beyond the scope of this paper. Thirdly, as shown in Figure 5, by using suction, the vertical load which must be applied for installation is rather small compared with that for installation using purely vertical load. This feature is very useful because it is impossible to apply a large value of vertical load to install the caisson in practice. Consequently, by using suction assisted penetration, this obstacle can be overcome. Lastly, in order to avoid numerical difficulties, the rate-dependent solution has been proposed. The most important aspect of using the rate-dependent solution is the relationship among the viscosity µ, the time step dt and the load step. Suitable values must be chosen to maintain accuracy and stability for the numerical solution. There are as yet no precise procedures for selecting for these parameters. owever, by using some trials, one can determine suitable values for µ, dt and load step. 8. COCLUSIOS This paper presents a multiple yield surface hyperplasticity model for caisson foundations. Preliminary choices for the parameters are made. The model captures reasonably well the behaviour of a caisson foundation under cyclic loading, and could be incorporated in numerical analyses of caisson/structure systems. REFERECES Cassidy,.J., 999. on-linear analysis of Jack-Up structures subected to random waves. DPhil thesis, University of Oxford. Collins, I.F. and oulsby, G.T., 997. Application of Thermomechanical Principles to the odelling of Geotechnical aterials. Proc. Royal Society of London, Series A, Vol. 45, pp 975- Doherty, J.P., Deeks, A.J. and oulsby, G.T., 4. Evaluation of Foundation Stiffness Using the Scaled Boundary ethod. Proc. 6 th World Cong. on Comp. ech., Beiing, 5- Sept. oulsby, G.T. and Byrne, B.W.,. Suction caisson foundations for offshore wind turbines and anemometer masts. Wind Engineering, Vol. 4, o. 4, pp oulsby, G.T. and Byrne, B.W., 5. Design Procedures for Installation of Suction Caissons in Sand, Proc. ICE, Geotechnical Engineering, in press. oulsby, G.T and Cassidy,.J.,. A plasticity model for the behaviour of footings on sand under combined loading. Géotechnique, 5, o, pp. 7-9 oulsby, G.T. and Puzrin, A..,. A Thermomechanical Framework for Constitutive odels for Rate-Independent Dissipative aterials. Int. J. of Plasticity, Vol. 6, o. 9, pp oulsby, G.T. and Puzrin, A..,. Rate-Dependent Plasticity odels Derived from Potential Functions. J. of Rheology, Vol. 46, o., Jan./Feb., pp -6. artin, C.., 994. Physical and numerical modelling of offshore foundations under combined loads. DPhil thesis, University of Oxford. Puzrin, A.. and oulsby, G.T.,. Rate Dependent yperplasticity with Internal Functions, Proc. ASCE, J. Eng. ech. Div., Vol. 9, o., arch, pp 5-6

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53 oment loading of caissons installed in saturated sand Felipe A. Villalobos, Byron W. Byrne & Guy T. oulsby Department of Engineering Science, Oxford University ABSTRACT: A series of moment capacity tests have been carried out at model scale, to investigate the effects of different installation procedures on the response of suction caisson foundations in sand. Two caissons of different diameters and wall thicknesses, but similar skirt length to diameter ratio, have been tested in water-saturated dense sand. The caissons were installed either by pushing or by using suction. It was found that the moment resistance depends on the method of installation.. ITRODUCTIO Suction caisson foundations are increasingly being used in offshore applications. They have been used for fixed structure applications, as described by Bye et al. (995), and also for floating facilities (ouse, ). ore recently they are being considered as foundations for offshore wind turbines (Byrne and oulsby, ). The wind turbine structures may be founded on single or multiple caissons. The multiple caisson problem is addressed by Kelly et al. (4), so in this paper we concentrate on the single caisson problem. Typical dimensions and loads for this problem are shown in Figure. Byrne and oulsby () describe this problem in detail, but the main differences in loads on the foundations for offshore wind turbines as compared to typical oil and gas structures are that: (a) the vertical load is much smaller, (b) the horizontal and moment loads are proportionately larger. ew design methods must be developed to allow safe designs to be engineered for this regime of loading. As a result Byrne et al. () describe a research proect aimed at developing such design guidelines. This paper outlines the results from a part of that proect. Initial studies of the moment capacity of caisson foundations in the laboratory were carried out in drained sand. Preliminary results from these experiments are described by Byrne et al. (). As the sand used during the tests was dry, the caissons were installed into the prepared sand bed by applying a vertical load. The advantage of using dry sand is that the test bed can be prepared quickly, and a large number of tests can be carried out at specified densities. To mitigate the effects of scale, Figure : Dimensions and magnitude of loads for a.5w turbine structure founded on a monopod suction (adapted from Byrne and oulsby, ) the tests beds were chosen to be relatively loose. Clearly using installation by applying vertical loads is different from the procedure that has to be used in the field i.e. the suction installation process. The different installation techniques may impose different stress paths on elements of soil around the caisson, which in turn may affect the response of the caisson to the applied loads. Therefore it is necessary to carry out experiments similar to those

54 in the dry sand, but on caissons installed by suction, to observe if there are any fundamental differences in behaviour. Combined vertical, moment and horizontal loading tests have been conducted on caissons installed by suction and by vertical load in a watersaturated, dense sand. Load-displacement data are presented and interpreted for installation and for moment loading tests.. EQUIPET AD ATERIALS. Sand samples The sand used during the experiments was a commercially produced sand called Redhill. The properties of this sand are given in Table. Table : Redhill properties (Kelly et al., 4).6,.96 D, D, D 5, D 6 (mm).8,.,.,. Coefficients of uniformity, C u and curvature C c Specific gravity, G s.65 inimum dry density, γ min (k/m ).76 aximum dry density, γ max (k/m ) 6.8 Critical state friction angle, φ cs 6º The sand samples were saturated with water inside a tank of diameter mm and depth 4mm. Preparation of the test bed involved an initial phase of fluidisation by an upward hydraulic gradient induced in the sand bed. The sample was then densified by vibration under a small confining stress. The density was determined by measuring the weight and the volume of the sample. The preparation process was halted once a target density was reached. The peak triaxial angle of friction was estimated as 44. o to 45. o from the correlation of Bolton (986), for the range of relative densities tested (see Table ).. Testing procedure Tests were performed using a three degree-offreedom loading rig (DOF) designed by artin (994). This rig, shown in Figure, can apply any combination of vertical, rotational and horizontal displacement (w, Rθ, u) to a footing by means of computer-controlled stepper motors (R is the radius of the footing). Byrne () has installed a software control program, so that any combination of vertical, moment or horizontal load (V, /R, ) can also be applied to the footing. All displacements and loads are monitored and recorded using appropriate dataacquisition routines as well as being used within feedback control routines. It is possible to apply Figure : DOF-loading rig Figure : Suction device loads and displacements to the footing which represent the offshore environment loads of gravity, wind, waves and currents. The geometry of the model suction caissons used in the experiments is given in Table. The model caissons were fabricated from aluminium alloy, with a relatively smooth (but not polished) surface. Table : Geometry of the model caissons tested Diameter, R (mm) 9 Length of skirt, L (mm) 46.5 Thickness of the skirt wall, t (mm).4. Aspect ratio, L/R.5.5 Thickness ratio, R/t 86 The loading apparatus was modified to allow the footings to be suction installed. Previous experiments had only used caissons forced into the ground by vertical load. To enable the suction installation phase to be carried out, the equipment was modified as shown in Figure. The suction caisson, attached to the DOF loading rig, was pushed into the ground about mm with the air valve open. This allowed the pressure inside the