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Copyright 1999, Offshore Technology Conference
This paper was prepared for presentation at the 1999 Offshore Technology Conference held inHouston, Texas, 3–6 May 1999.
This paper was selected for presentation by the OTC Program Committee following review ofinformation contained in an abstract submitted by the author(s). Contents of the paper, aspresented, have not been reviewed by the Offshore Technology Conference and are subject tocorrection by the author(s). The material, as presented, does not necessarily reflect anyposition of the Offshore Technology Conference or its officers. Electronic reproduction,distribution, or storage of any part of this paper for commercial purposes without the writtenconsent of the Offshore Technology Conference is prohibited. Permission to reproduce in printis restricted to an abstract of not more than 300 words; illustrations may not be copied. Theabstract must contain conspicuous acknowledgment of where and by whom the paper waspresented.
AbstractAlternatives to piled foundations, such as suction caissons, arebecoming increasingly viable options for fixed platforms,particularly in the development of marginal fields. Whilst piledesign procedures evolved smoothly from onshore experienceand theory, design of shallow foundation systems has had tobe re-examined in light of the intense offshore loadingconditions. This is currently being undertaken throughexperimental investigations, which indicate the possibility ofdefining foundation response using plasticity theory.
This paper reports the response of circular foundations onvery dense sand within the context of plasticity theory. Theload and displacement paths are applied using a sophisticatedthree degree-of-freedom loading rig, designed specifically toexplore plasticity related concepts. The tests are on dry sand toensure drained behaviour. Eight tests are performed on eachsand sample, thus minimising material variations betweentests, which is particularly important at the high peak frictionangles being explored.
The tests were at 1-g, and concentrate on four embedmentratios (0, 0.16, 0.33 and 0.66) on a sand of 95% relativedensity. The research indicates a change in shape of a yieldsurface with increase in embedment ratio. Whilst the testsconcentrate primarily on the plastic deformations, thebehaviour within the yield surface is also examined. Aconceptual model, based on plasticity, is presented.
The findings of the research are particularly relevant to theoffshore industry in the development of shallow and skirtedfoundations for dense sand deposits.
IntroductionHistorically, offshore structures for oil and gas productionhave been anchored to the sea floor by large diameter piles.Recently, a novel foundation type has been used in place of
these piles30, best described as upturned buckets, typically15m diameter and 5m deep, they are usually called suctioncaissons. These foundations are installed by pumping outwater to cause a slight suction to the inside of the caisson,once it has made a sufficient seal within the soil. In the NorthSea, where a large part of the seabed is covered by a layer ofvery dense sand, the suction assists penetration by temporarilyreducing the resistance of the sand as well as increasing the netdownward force on the caisson.
Offshore structures are often exposed to severe loading dueto wave, current and wind forces. Their foundations areexposed to higher horizontal and moment loading than areencountered onshore. Whilst pile design procedures haveevolved from onshore experience and theory, designguidelines for shallow foundation systems, such as suctioncaissons, have yet to be devised for the intense loadingconditions found offshore. In the particular case of suctioncaissons, there are no precedents in onshore experience, and atpresent there is little offshore experience, though this israpidly changing8. This means that there are no acceptedprocedures, such as the API guidelines for piles, nor are therelarge amounts of published data available, as firms tend tokeep any acquired knowledge in-house so as to gaincompetitive advantage.
One of the critical aspects of the design is the ability toresist tension, which may occur under extreme conditions. Theimportant issue is the rate at which the caisson is loaded,compared to the rate of fluid flow within the soil, as the latteraffects the soil response. The typical loading on the foundationwill be random variations about some mean value, whichresults in a complex flow regime within the soil, which in turndominates the response of the foundation. However, it isnecessary to define the long-term drained loading limits ofcaisson response before the effects of loading rate and loadreversal can be explored. This is currently being undertakenthrough experimental investigations in which the foundationresponse is defined within the setting of plasticity theory.Adopting this approach allows a mathematical representationof the foundation, which can be incorporated within typicalnumerical analyses used in the design of offshore structures.
Suction caisson foundations are the focus of much currentresearch, primarily as they offer substantial cost savings inboth materials and installation (both time and money). In thispaper selected results are presented that can be used to
OTC 10994
Drained Behaviour of Suction Caisson Foundations on Very Dense SandB.W. Byrne and G.T. Houlsby, The University of Oxford
2 B.W. BYRNE AND G.T. HOULSBY OTC 10994
establish the long term, or drained, behaviour of foundationswith skirts on very dense sands. These very dense sand layers,with a relative density up to 100%, are typically 10-20m deep,much larger than the probable depths of the caisson skirts, andthus dominate the drained response. The impetus for thisinvestigation is the use of suction caisson technology for thedevelopment of marginal fields, particularly in the North Sea,where small lightweight structures may become feasible.
A Review of Bearing Capacity and Load Interaction.During the passage of wind, waves and current through andpast an offshore structure it is usual to assume that the loadingbecomes unidirectional, particularly during the more extremeenvironmental conditions. Consequently the loading on thefoundations can be represented as the three degree-of-freedomproblem illustrated in Figure 1. Early solutions of this problemdealt with establishing the vertical load that would cause'failure' of the foundation, whilst more recent work is alsoconcerned with describing the load-deformation behaviour.
The problem of the bearing capacity of a foundation undercombined vertical, horizontal and moment loads has receivedconsiderable attention. The generally accepted procedures foruse in the offshore industry are those established byHansen18,19 and Vesic31,32. These deal with the application ofhorizontal load by introducing inclination factors, whichreduce the vertical bearing capacity depending on the ratio ofhorizontal to vertical load. Moment loading is dealt with byexamining a statically equivalent vertical load acting at thecentre of a reduced footing determined by the eccentricity( VMe = ). For a fully combined V:M:H load both processes
are used, that is an inclined load acting on a foundation ofreduced area. Further factors are introduced to account for theeffects of footing embedment. These relationships weredeveloped initially as reduction factors on the allowablevertical load, rather than for the development of interactiondiagrams.
An alternative approach in recent years is to view thecombined load problem in terms of a three-dimensional yieldsurface. Roscoe and Schofield26 first used the concept of ayield surface for this application, and Butterfield and Ticof6
were amongst the first to investigate footing behaviour on sandin this manner, examining strip footings on dense sand. Fromlarge numbers of load controlled ‘probe’ tests, they were ableto map out a yield surface. They suggested that a ‘cigarshaped’ yield surface (Figure 2) would capture the data andsized it by dimensionless peak loads M/BVpeak = 0.1, andH/Vpeak = 0.12, both occurring at V/Vpeak of 0.5. Otherinvestigations have validated the general shape of this surfacein H/Vpeak:V/Vpeak and M/BVpeak:V/Vpeak space, whilst showingthat in M/BVpeak:H/Vpeak space the failure surface can beapproximated by a rotated ellipse5,13,14,16. Dean et al12 point outthat the rotation depends on the position of the load referencepoint.
Tan27 mapped out the behaviour of spudcan footings inV:H space on saturated sand using centrifuge tests. Themajority of tests were ‘sideswipe’ tests, in which the footing
was loaded to a certain level, before being moved horizontallywhilst keeping the vertical displacement locked. Byconsidering the foundation to be elastically incompressibleunder vertical load, then it can be argued that the sideswipepaths are close approximations to paths across the yieldsurface12. Tan suggested that (H/Vo)max occurred at a value of
46.0≈oVV , where Vo was the maximum pure vertical loadexperienced by the foundation. Tan also pointed out that a'parallel point' (analogous to the critical state) existed, at whichstage the plastic displacement increment was purelyhorizontal. Tan conducted investigations into the effect ofembedment, finding that the shape remained similar, with themaximum H/Vo ordinate increasing slightly with increase ofdepth. The influence of cone angle and roughness was alsoexamined.
Extensive use of swipe testing was made by Martin22, whomapped out the behaviour of spudcan footings on a clay withincreasing strength with depth. Martin found that the shape ofyield surface could be normalised with respect to the verticalload capacity at any depth, and obtained a similar shape to thatof Butterfield and Ticof6. Martin used a mathematical functionto describe the yield surface, defined by the maximumordinates of H/Vo (M = 0) and M/2RVo (H = 0), as well as thecurvature at high and low load, and the eccentricity of theellipse. Martin developed a three-dimensional work hardeningplasticity theory based on the experimental results. He usedtheoretical stiffness coefficients for elastic behaviour, andtheoretical lower bound bearing capacity solutions to definethe vertical bearing capacity with penetration. Martinincorporated this plasticity model in a structural analysis of ajack-up. Thompson29 used this model for dynamic analyses ofa jack-up rig.
Recent experimental work by Gottardi and Houlsby17
followed a programme designed to develop a three-dimensional plasticity model for circular footings on densesand. A numerical model, ‘Model C’, has since been createdbased on these results and shown to provide accuratesimulations of selected test results10. This model assumes thatthe yield surface does not change shape as Vo changes. Thetests were conducted from a high ratio of vertical load to thepeak bearing capacity sustainable by the soil. An empiricallyderived hardening law was used. The surface was againsimilar in shape to that found by previous researchers, and isshown in Figure 2. The peak value of H/Vo was 0.116 and ofM/2RVo was 0.086. This model is being used as part of acomplex dynamic analysis package using state-of-the-art waveloading techniques to represent extreme events10.
Experimental ApparatusTo test the plasticity model it is essential to establish:
(i) The shape of a yield surface.(ii) The mechanism of hardening of the surface.(iii) A flow rule or plastic potential.(iv) The elastic behaviour within the surface.Studies of this kind normally use eccentric inclined loads16,
or examine the two-dimensional cases (V, H), and (V, M/2R)25.
OTC 10994 DRAINED BEHAVIOUR OF SUCTION CAISSON FOUNDATIONS ON VERY DENSE SAND 3
At the University of Oxford a loading rig was developed,initially to explore the behaviour of spudcan footings onclay22. It has undergone several modifications, and it isadaptable to any soil. The unique feature of this apparatus isthat any combination of displacement paths can be applied tothe model footing using computer controlled stepper motors.The response of the footing is determined by measuring theresultant loads using a 'Cambridge' load cell, whilst accuratefoundation displacements are measured using a system ofLVDTs. A primary advantage of using this displacementcontrolled apparatus is the ability to explore work softeningbehaviour. Figure 3 shows the loading rig, further mechanicaldetails of which are given by Martin22 and Gottardi andHoulsby15. The footing behaviour was assumed to be rateindependent in the dry sand. However, the rates used neverexceeded 0.01mm/s or 0.01°/s such that, if any existed, theeffects of rate should be negligible. The co-ordinate systems,sign conventions and notations for the loads and displacementsare shown in Figure 2, following Butterfield et al7. The loadreference point was at the base of the footing (i.e. mudline),consistent with previous work conducted on flat footings atOxford University.
Extensive modification has also been undertaken on thedata acquisition and control side of the apparatus. Whilst theprime motivation for upgrading the electronics was the needfor better control and acquisition during transient and cyclictesting on saturated samples, the increased performanceallowed for rather sophisticated testing on dry samples ofsand.
The control program allows the control of each of the threestepper motors independently. The motors can either be movedthrough specified amounts at specified speeds, or a PID11
control loop can be used in which the velocity and direction ofthe stepper motor is used as the control signal. Using thismethod it is possible to provide independent force ordisplacement control on all three axes.
The displacements of the footing are measured via threesmall LVDTs (individual ranges of 10 mm), from which thecomponents of movement (δw, δu, 2Rδθ) can be determinedtrigonometrically. It is possible to resolve the movements ofthe footing to ±1µm. The loads are processed depending onthe rotation of the footing, and are resolved to ±0.5 N.
Four footings were used to explore the effects of skirtpenetration. The footing diameter was 100mm. It is useful todefine the non-dimensional embedment ratio (y), as the skirtlength (L) divided by the diameter (D);
y = L/D..................................................................................(1)
to compare different suction caissons. The two platforms thathave used the suction caissons on dense sand both usedcaissons with an embedment ratio of 0.33. Previous testing atOxford and NGI aimed at resolving design aspects of thesecond of these platforms (Sleipner Vest) and therefore alsoused this ratio (the results of the tests are confidential). It isnecessary to be able to compare the results with a variety ofdifferent skirt depths so ratios of 0, 0.166, 0.33 and 0.66 were
used. The results from an embedment ratio of 0 can becompared to other data on flat footings, particularly the seriesof tests by Gottardi and Houlsby15.
The sand used throughout the testing was produced using acyclone separation system. The choice of sand was dictated bythe proposed use of the same sand for modelling rate effectswhen saturated. It will be saturated by silicone oil, to modeldrainage times appropriate to the loading of offshorefoundations. Figure 4 shows the grading curve of the sand andothers that have been used for 1-g modelling of footings. Alsoshown are the grading curve boundaries of the sands at thesites of the Europipe and Sleipner Vest platforms. Table 1gives the typical properties of the sand.
The sand was contained in tanks of internal diameter1100mm, and depth 250mm, to provide a single sample largeenough to accommodate multiple tests. The samples wereprepared by loosely placing sand within the container. Asmooth wooden lid was placed upon the very loose sand,surcharged with a very small weight (to apply a slightconfining pressure), and the sample was vibrated until nofurther downward movement of the lid was observed. Thismethod, also used by Lau21, was able to produce very densesamples with typical characteristics shown in Table 2.
Typical ResultsThe tests are shown schematically in Figure 5. Initial testingindicated that the behaviour depends on the ratio of themaximum vertical load previously experienced by the footingto the peak bearing capacity sustainable by the soil (Vo/Vpeak).The programme was therefore designed to explore this effectas well as other aspects of the plasticity model. The testsincluded:
(a) Characterisation Tests: Characterisation of the sampleswas essential so that a comparison across different sampletanks could be made. The initial characterisation was made interms of relative density, of which a mean of 97.8% and astandard deviation of 1.81% was obtained. A more importantcharacterisation was made by determining a bearing capacityfactor (and hence friction angle) of the sample by conducting avertical loading test in the centre of the sample, used a 50mmdiameter footing, which was loaded to a displacement of about10mm. On several samples multiple bearing capacity testswere conducted at other locations to examine the consistencyof the samples. If the peak vertical bearing capacity of a flatfooting is defined as:
πγ= γ 4'
21 2
* DDNVpeak ...................................................(2)
then it is possible to determine a value for the bearing capacityfactor, Nγ
∗. Similarly, by following the procedures of Bolton3 itis possible to deduce a value for the angle of friction (eithertriaxial or plane strain) based on the relative density of thesand. The triaxial angle of friction has been plotted against Nγ
∗
in Figure 6, and compared to a theoretical curve determined byBolton and Lau4 using the method of characteristics. There is a
4 B.W. BYRNE AND G.T. HOULSBY OTC 10994
reasonable correlation between the experimental andtheoretical results. The scatter within the experimental resultscan be explained by the fact that the bearing capacity factorcan vary significantly for small changes in the relative density,particularly at the high friction angles being explored.
(b) Swipe Tests: The majority of the tests were swipe tests.Each test involves loading the footing to a given load oV , andthen rotating it or displacing it horizontally (or anycombination of these two) whilst keeping the verticaldisplacement constant. Tan27 and Martin22 argue that the loadpath traced under these displacement paths gives a directindication of the shape of the yield surface - assuming that theratio of vertical elastic stiffness to vertical plastic stiffness islarge. A correction can be made for the expansion of the yieldsurface in other cases. Since the stiffness of the rig is finite, acorrection must usually be made for the expansion of the yieldsurface as a result of the increased penetration of the footingassociated with the relaxation of the rig as the vertical loadlevel falls. In these tests this correction was avoided by usingfeedback to control the vertical displacement. By conductingswipe tests at different starting ratios of oVV , the behaviourwithin the yield surface could also be examined. Swipe tests atvery low oVV ratios give an indication of the yield surface atlow vertical load.
(c) Constant Load Tests: The expansion of the yieldsurface (that is the hardening behaviour) can be examined byconducting tests similar to swipe tests, but at constant verticalload rather than constant vertical displacement.
(d) Vertical Loading Tests: These tests involve loading thefooting vertically, usually to 2400N (the limit of the rig), andunload/reload loops at 1000N and 2000N. At the very simplestlevel the hardening of the yield surface is linked solely to thevertical plastic displacement, thus these tests give a measure ofthe hardening relationship.
(e) Elasticity Tests: Whilst the prime objective of thetesting was to obtain information about the plastic response ofthe footing, several tests were undertaken to evaluate theelastic behaviour within the yield surface. The results fromthese can be compared to finite element results2. In these testsone load on the footing was typically cycled while keepingother loads constant. The cyclic amplitude was increased toexamine the boundary between elastic and plastic behaviour.
(f) Loop Events: These events consist of completing acircle in θRu 2: space by control of all three displacements.The vertical load is kept constant by a feedback system. Theresulting load path gives an indication of the shape of the yieldsurface in RMH 2: space.
(g) Radial Loading Tests: These involve applying a linearpath in load space to the footing and examining the resultingpath in displacement space. Typically the horizontal and/ormoment load is specified as a fraction of the vertical load.These tests give further information about the hardeningrelationship for the yield surface.
Overall ten sample tanks were prepared with sand in a verydense state, enabling 80 test sites, and 250 individual test
events to be completed. The interpretation of these results willenable the construction of a plasticity model for skirted andflat footings on dense sand. Selected data will be used in thefollowing sections to illustrate behaviour.
Analysis of ResultsThis section includes some re-interpretation of previouslypublished data specifically relating to flat footings, as well asanalysis of the new data on skirted footings.
Vertical Loading Behaviour and Interpretation ofHardening Law. An explicit indication of the hardening ofthe yield surface can be observed in the vertical loading tests,in which the horizontal and moment loads are kept to aminimum whilst the vertical load is increased. For the testsanalysed in this paper a relatively simple representation of thehardening law can be used. The tests in question probed onlyvery low values of the ratio V/Vpeak, at which stage the verticalloading relationship is essentially linear. The verticaldisplacement, δw, is defined as the sum of elastic and plasticdisplacements;
pe www δ + δ = δ ...................................................................(3)
where δwe is the elastic vertical displacement and δwp is theplastic vertical displacement. Any vertical loading behaviourinside the yield surface can be represented by:
V = kewe ................................................................................(4)
where ke is the elastic stiffness of the foundation on the sand.The hardening of the surface can then be linked to the plasticvertical displacements such that the apex of the yield surface,Vo, is defined as:
Vo = kpwp...............................................................................(5)
where kp is the plastic stiffness of the foundation on the sand.Adopting this idealisation proves to be most convenient wheninterpreting the swipe tests. During the swipe test the verticalpenetration remains constant while the vertical load reduces.The elastic vertical displacement is negative, and is balancedby an equal positive plastic vertical displacement. This impliesan increase in Vo, which must be taken into account insubsequent analysis. The modified value VoN can be calculatedas:
pe
peoIoN kk
VkkVV
−
−= ............................................................(6)
where VoI is the value for Vo at the start of the swipe and V isthe instantaneous value of vertical load. Figure 7 shows anaccumulation of vertical loading tests, for various footings,taken up to a vertical load of 2400N, the limit of the loadingrig. During these tests two unload-reload loops wereundertaken to determine the vertical elastic stiffness. Anaccumulation of unload-reload loops is also shown in Figure 7,showing good repeatability between sample tanks, and littleeffect of footing skirt depth. In general there is little to
OTC 10994 DRAINED BEHAVIOUR OF SUCTION CAISSON FOUNDATIONS ON VERY DENSE SAND 5
distinguish between the vertical loading tests for the differentskirt depths. It appears that the effect of the overburden on thefoundation response is not significant at these low values ofV/Vpeak. It is also likely that the slight disturbance to thesample immediately around the skirt, caused during thepenetration, may mean that the skirt itself contributes little tovertical capacity at small penetrations. From the elasticunloading/loading results it is clear that, whilst there is somehysteresis evident, 3000N/mm would be a representativeelastic stiffness. A value of 600N/mm is representative of theplastic stiffness, in the range of loads from 500N to 2000N.
Throughout the following analysis Vpeak refers to the peakvertical bearing capacity of a flat surface footing (unlessotherwise specified by the subscript peak(skirted)). In placesthe skirted footings are referenced to a bearing capacity of askirted footing, so as to account for overburden effects. Thisvalue could be estimated by:
( )( )DKL
DN
DDLNV qskirtedpeak
πδγ+
πγ+
πγ= γ
tan2'
42'
4'
2
2*
2*
)(
.............(7)
using values for the bearing capacity factors taken from Boltonand Lau4. The frictional component is typically small for theshort skirt depths being studied, but the overburden effect canadd significantly to the bearing capacity. The value for Nq
* canbe obtained by interpolating between values from Bolton andLau4, based on Nγ
∗ determined from the bearing capacity tests.A typical value for Ktanδ is 0.25, and it is recognised thatVpeak(skirted) is insensitive to slight changes in this value. Fromabove it is clear that:
δ++=
γ
tan22
1 **
)(
)(K
D
LN
ND
L
V
Vq
flatpeak
skirtedpeak................(8)
Equation 8 can be approximated for the values of L/Dbeing explored in this study, combined with the appropriatebearing capacity factors, by the following linear relationship:
D
L
V
V
flatpeak
skirtedpeak89.01
)(
)( += .................................................(9)
If the peak bearing capacity for the flat footing is scaleddirectly from the results of the 50mm diameter footing bearingcapacity test used for characterisation, then it isstraightforward to estimate the value for the skirted footingbearing capacity. Unfortunately, none of the skirted footingswas taken to bearing capacity failure, so the values for Ktanδand Nq
* were not verified. However, it is clear that the capacityincreases significantly with skirt depth.
Swipe Testing of Flat Footings. Before examining thebehaviour of skirted footings it is necessary to explore fullythe response of a flat footing, as that provides the baseline forexamining the skirted footing performance. The results from
the study by Gottardi and Houlsby15, interpreted by Gottardi etal.17, provide a convenient starting point.A Conceptual Understanding of Results. Gottardi et al.17
assumed that the yield surface remained constant in shape,while expanding according to the work-hardening rule. Theyield surface was based on the results of the main group ofswipe tests conducted from Vo = 1600N, at a ratio of Vo/Vpeak
of 0.78. Several additional swipe tests (in tests GG09, GG24,GG13 and GG27) started from different vertical loads.Examining firstly the behaviour of the footing in the V:Hplane, Figure 8(a) shows a series of tests, all starting from
1/ ≈oVV , with forces normalised by the oV value. Figure
8(b) shows the same tests but with forces normalised by
peakV . It is clear that the shape of the yield surface changes in
a consistent way with the ratio peako VV / . It appears that
Tan's27 'parallel point' (analogous to a critical state) is close tothe origin, as the load on the foundation does not tend to afinite limiting value, as would be expected if the parallel pointexisted at some distance from the origin. This observation isconfirmed by Gottardi and Houlsby’s horizontal swipe test ona sample starting at low oVV / .
This last observation conflicts with those of Tan27, whonoted that a parallel point for horizontal movement occurred atV/Vo of 0.152. It is quite probable that his swipe tests involveda slight moment loading, which was not measured during thetesting. It may well be that the parallel point movessignificantly away from the origin, towards the location forpure moment loading (as detailed below), for quite smallmoments (as may have been applied in Tan's tests).
Examining the behaviour in the V:M/2R plane, a slightlydifferent behaviour appears. Again a dependence of the shapeof the yield surface on the ratio of Vo/Vpeak is indicated, asshown in Figures 9(a) and 9(b). The parallel point appears inthis case to be located at some distance from the origin. It canbe defined more consistently in the plot normalised withrespect to peakV , and occurs at about V/Vpeak of 0.26 and
M/2RVpeak of 0.061. Using these values it is clear that the valuefor M/2RV tends to about 0.25 for large rotations. By simplerearrangement this leads to a maximum load eccentricity, e, ofR/2, given that M = Ve.
Whilst a model with a fixed shape of the yield surfacecaptures approximately the behaviour of the foundation, amore subtle modelling is necessary to capture the featuresmentioned above. This is particularly important given that thetypical ratios of Vo/Vpeak applicable to the design of offshorestructures would often be below about 0.25. Figure 10 shows anew understanding of the yield surface, in which the shapedepends on the Vo/Vpeak. ratio. Precise mathematical formshave not yet been derived for the component parts of this newyield surface. In the following the surface through Vpeak will bereferred to as the outer surface, and those through lower Vo
values the inner surfaces (of variable shape). The innersurfaces each appear to intersect the outer surface, so that atlow V/Vo all yield points fall on the outer surface.
6 B.W. BYRNE AND G.T. HOULSBY OTC 10994
Behaviour of Flat Footings in the H:V Plane and theM/2R:V Plane (DM2 and DM3). The first two series of testson very dense sand were used to further the understanding ofthe flat footing behaviour as illustrated in the Gottardi andHoulsby tests. Under horizontal loading, four swipe tests werecarried out from 1/ =oVV , but at different ratios of Vo/Vpeak,
including values much lower than those examined by Gottardiand Houlsby. Figures 11(a) and (b) show the resultsnormalised with respect to Vo and Vpeak. For the tests at verylow stresses there is a significant change in the shape of theyield surface. After an initial reduction of V, the vertical loadincreases again as the footing slides at approximately constantH/V. This is indicative of dilatant behaviour for the tests atlower stress levels. At large displacements sliding failurecontinues with a reduction of V again occurring. The testsconfirm that the 'parallel point' for horizontal loading is eitherat or very close to the origin. Two further tests (shown as thinlines on Figure 11) are for swipe tests starting at 1/ <oVV .The filled square points indicate approximately the transitionfrom 'elastic' to 'plastic' behaviour for these tests. The teststarting from 5.0/ =oVV , shows significant elastic behaviouruntil the load point encounters the yield surface, as shown forthe test from V/Vpeak = Vo/Vpeak = 0.22 (the corresponding testat 1/ =oVV ). The other test, at a significantly lower oVV / ,suggests that a transition is reached slightly within the outeryield surface (sliding line). Both tests reach the sliding lineand move towards the ‘parallel point’ at or close to the origin.
A further example of the location of the boundary betweenelastic and plastic behaviour can be seen in Figure 12. Thisshows the load and displacement paths for three tests. The firsttest (A) is a swipe test from 1/ =oVV and Vo/Vpeak = 0.16. Itshows slightly dilatant behaviour as the sliding failure line isreached, after which the load point moves towards the origin.The point at which the sliding line is reached is given by asolid square point on both plots. As expected there issignificant plastic horizontal displacement during the swipetest. The second test (B) is a constant vertical load test, fromV/Vpeak = 0.1, with again a value Vo/Vpeak = 0.16. Test (A)would be expected to give an indication of the position of theyield surface that existed prior to the constant V test. The opensquare on the graphs indicates the location of the boundarybetween 'elastic' and 'plastic' behaviour, whilst the solid squareindicates when the sliding line is reached.
It is clear that there is minimal displacement until after theyield surface is intersected, after which there are largecombined displacements, which continue after the sliding lineis reached. There is substantial vertical penetration during theplastic displacement, which is consistent with the continualloss of vertical load during the horizontal swipe. The third test(C) shown on Figure 12 is a radial loading test, which againwas preloaded to Vo/Vpeak of 0.16. A similar range of 'elastic'behaviour, in load space, compared to the constant load swipetest can be observed.
Under rotational loading it is clear that a ‘parallel point’may exist, as observed in the Gottardi et al15 results. However,
the location of this point was beyond the limits of the loadingrig. Seven swipe tests from 1/ =oVV were performed asshown in Figure 13, showing clearly that the load paths followa yield surface before moving upward to a parallel point.Figure 13(a) shows that the shape of the yield surface remainsapproximately constant, except for the tests performed at verylow values of Vo/Vpeak. Also shown on Figure 13 are five tests(shown as thin lines) from 1/ <oVV . One test (D) showssome ‘elastic’ behaviour before following the appropriateyield surface to the rotational boundary. Upon reaching therotational boundary the load path moves towards the 'parallel'point. The other swipe tests all move towards the 'parallel'point directly, but show only small horizontal displacementsuntil close to the sliding line.
Three tests similar to those shown in Figure 12 wereperformed to assess the elastic boundary for moment loading,and are presented in Figure 14 in the same format as Figure12. The closed square symbol shows where the swipe testencountered the rotational boundary, and a change of load pathfollows. The second test (B) is the constant load test, whichwas preloaded similarly swipe test (preloaded to Vo/Vpeak of0.16). The open square symbol on both plots shows thetransition from 'elastic' behaviour to 'plastic' behaviour, whichoccurs at some distance from the yield surface anticipatedfrom the swipe test. Upon reaching the rotational boundarysignificant heave is apparent as the soil beneath the foundationdilates strongly. This is consistent with the movement towardsthe parallel point in the swipe test. The third test (C) is a radialloading test, again on a foundation which has been preloadedto Vo/Vpeak of 0.16. The elastic/plastic transition point ismarked by an open square symbol, and the position isconsistent with the constant V test.
Current Results and Conventional Bearing Capacity Theory.Conventional theories of bearing capacity, such as thatproposed by Meyerhof24 and Hansen18 are usually as regardedas conservative when compared to experimental evidence20.These theories use reduction factors on the vertical bearingcapacity to account for shape, load inclination and loadeccentricity amongst other effects. These factors are largelyderived from empirical observations, together with sometheoretical input. By manipulation of the reduction factorexpressions it is quite simple to derive an interaction envelopefor say H:V or H:M or even V:M:H space. For example thevertical bearing capacity of a surface strip footing is:
( )γγ= BNAV peak '5.0 ........................................................(10)
If an inclined load is applied then the sustainable verticalload is reduced by a factor iγ such that;
( )γγγ= iBNAV '5.0 .........................................................(11)
where Meyerhof24 suggests:
OTC 10994 DRAINED BEHAVIOUR OF SUCTION CAISSON FOUNDATIONS ON VERY DENSE SAND 7
2
1
φΩ−=γi and
=Ω
VH
arctan ............................... (12)
By simple rearrangement it is possible to obtain:
φ
−=
5.0
1tanpeakpeakpeak VV
VV
VH
........................ (13)
which is an expression of interaction between H and V. Analternative expression for iγ as suggested by Hansen18 is;
4
1
−=γ V
Hi ................................................................... (14)
which leads to an interaction solution of:
−=
25.0
1peakpeakpeak V
V
V
V
V
H.................................. (15)
Surprisingly the Hansen solution makes no use of the angleof internal friction of the soil, which intuitively needs to beincluded if horizontal sliding of the foundation is incorporatedat low ratios of V/Vpeak. These relationships can be comparedwith the outer yield surface suggested in Figure 10.
A similar relationship can be obtained for the interactionbetween moment load and vertical load. Meyerhof24 suggestedthat a footing under moment loading be considered as thestatically equivalent vertical load acting at an eccentricity efrom the centre of the footing. The footing then has reducedwidth, called an effective width, of ( )eB 2− , and theappropriate interaction relationship can be derived:
−=
5.0
121
PeakPeakPeak VV
VV
BVM
............................. (16)
Hansen (1961) also adopts this approach. A similarapproach can be found in the procedures recommended by theAmerican Petroleum Institute1 for the drained design ofshallow foundations. Care should be taken when using theseexpressions to interpret the results of experimentalinvestigations. Typically it is suggested that the expressionsprovide a conservative estimate to the capacity interaction, butthey also provide quite a close approximation to theexperimentally observed outer yield surfaces. This can be seenin Figures 15 and 16 which show the appropriate curves withthe experimental data reported here as well as that obtained byGottardi and Houlsby15. Clearly the conventional theorieswould provide a conservative estimate if they were to be usedin terms of Vo instead of Vpeak and then applied to results fromtests conducted at ratios of Vo/Vpeak < 1.
Pre-Peak V:M:H Flat Footing Behaviour (DM9). Furthertesting was carried out to determine the shape of the yieldsurface at different ratios of Vo/Vpeak and 2RH/M for a flat
footing. During the testing, in tank DM9, the footing wasmoved not more than 0.75mm, such that the outer yieldsurface was not intercepted. By conducting the testing in thismanner it was possible to carry out multiple tests on individualsites, to build a complete three-dimensional picture of theshape of the yield surface. Swipe tests were conducted atseveral ratios of 2RH/M, to provide sufficient data for a simplesurface fitting exercise to be carried out. By assuming that theinner yield surfaces can be described by a three-dimensionalshape, it is possible to determine parameters with which toassess the development of the yield surfaces with the increaseof Vo/Vpeak. The simplest mathematical form of such a shape (arotated parabolic ellipsoid) is:
0116
2
2
2
22
2
22
=
−
−
−
+
oo
ooooooo
V
V
V
V
RVmh
aHM
RVm
M
Vh
H
..................(17)
where the values of mo, ho and a can be determined from aleast squares analysis of the data. A simpler assessment of thedata can be obtained by normalising individual data points (H,M/2R) using the expression;
2
22
2
2
2 ooooooo RVmh
aHM
RVm
M
Vh
Hq −
+
= .............(18)
which collapses the data onto a single plane in q:V/Vo space.In this space the yield surface becomes the parabola
( ) 014 =−− vvq , where v = V/Vo. Figure 17 shows such anormalisation for the data from Vo/Vpeak = 0.28, showingswipes conducted from V=1800N.
Accumulation of Test Results for Flat Footings. Theaccumulation of test results reported here and those byGottardi and Houlsby is shown in Figure 18. In both instancesthe footing diameter was 100mm, bearing on dense to verydense sand. The ho and mo values are mainly derived bymodelling individual swipe tests with a simple parabola. Thereis a strong correlation in the data with trend lines given by:
−=
peak
oopeako V
Vhh ln36.01 ....................................(19)
−=
peak
oopeako V
Vmm ln36.01 ..................................(20)
where hopeak = 0.11 and mopeak = 0.08, corresponding to theyield surface at the peak bearing capacity. These expressionsare validated only for Vo/Vpeak greater than 0.025. The peakvalues compare well with the interaction loci that Meyerhof24
suggests for φ = 43°, where hopeak = 0.113 and mopeak = 0.074(occuring at V/Vpeak = 0.44).
8 B.W. BYRNE AND G.T. HOULSBY OTC 10994
Swipe Testing of Skirted Footings. A large proportion of thetesting was to study the effect of a skirt on the drainedbehaviour of the foundation. Broadly speaking the behaviourof a flat footing will give indications of the general behaviourof the skirted foundation. The effects of different ratios ofVo/Vpeak(skirted) was not therefore examined in detail for theskirted footings. The testing at individual test sites wasrestricted to not more than two swipes, since the site was thensufficiently disturbed to affect the results.
Behaviour of Footings in the H:V Plane and the M/2R:VPlane for Different Ratios of L/D (DM4 and DM5). Severaltests were conducted in which the only parameter varied wasthe embedment ratio, y = L/D. Swipe tests were performed atsimilar ratios of Vo/Vpeak for different footings to ascertain theeffect of the skirt depth. For each set of tests the value for2RH/M was fixed. In tank DM4 the value for H was set tozero, whilst in DM5 the value for M/2R was set to zero. Figure19 shows the results from tank DM5, the horizontal swipe testsat V/Vo = 1 were conducted from starting values of Vo/Vpeak of0.08 and 0.21. The flat footing tests show behaviour typical ofswipe tests, in which the load path traces around a yieldsurface, before tracking down the sliding line, towards theorigin. At the low stress level the strongly dilatant sand causesa slight increase in capacity as it expands, before allowing thefooting to follow the sliding line as the soil beneath the footingbegins to contract. Looking at displacement paths, it is clearthat, if associated flow is assumed in the H:M/2R plane, theyield surface for the flat footing is almost perpendicular to theH axis. A very slightly different displacement path is followedonce the sliding line is reached.
Three skirted footings were used during these tests, with yratios of 0.16, 0.33 and 0.66. There are minimal differences inthe load paths tracked by these three footings, though it isclear that there is a significant difference between theshallowest of the skirted foundations and the flat footing. In allthree cases strongly dilatant behaviour is observed as the loadpaths track slightly up the sliding line. If the tests had beentaken to larger displacements it is expected that contractantbehaviour would have been observed, as for the flat footing.There are, however, significant differences in the behaviour indisplacement space, but for the deeper embedment depthsthese differences become progressively smaller. For theembedment ratio of 0.16 the yield surface crosses thehorizontal axis at an angle of approximately 67° to thehorizontal axis (assuming associated flow). At the embedmentratios of 0.33 and 0.66 it crosses at approximately 47° and 43°respectively. Clearly, for the skirted footings, the displacementpath is such that both horizontal load and moment load aredeveloped as the footing is displaced horizontally. To reducethe negative moment load developed the footing would have torotate positively. The larger the skirt depth the larger are thepositive rotations required to keep the moment to zero.
Similar observations can be made about the results of tankDM4, in which rotational swipes at 1/ =oVV were carried outwith horizontal loading set to zero (shown in Figure 20). There
is no significant difference in the load paths traversed by thefooting, but in displacement space there is a significantdifference. This is to be expected because as the footingrotates positively to create positive moments, a negativehorizontal load is induced on the skirted footing. To reducethis horizontal load to zero, the footing must experiencepositive horizontal displacements, the magnitude of whichdepends on the skirt depth of the footing. There is a well-defined relationship between the skirt depth and the ratios ofrotational to horizontal footing movement in this case. Againassuming normality of flow in this plane it is clear that theyield surface crosses the moment axis at approximately 9°( 0=y ), 14° (y = 0.16), 22° (y = 0.33) and 34° (y = 0.66).
The surprising aspect of these tests is that the drainedcapacity for pure moment loading is not significantlyenhanced by the skirt. It is clear though that as the skirt depthincreases that the size of the yield surface in the horizontalloading direction becomes larger. This ties in with thevariation of ho with Vo/Vpeak (evident in flat footing tests),given that Vo was constant for all tests, but Vpeak(skirted) increasesfor the skirted footings.
Swipe Testing at Different Ratios of 2RH/M for L/D = 0.33(DM6 and DM7). To evaluate the changes of shape of theyield surface, two sets of testing were carried out at differentratios of Vo/Vpeak(skirted), and consisted of swipe tests from
1/ =oVV at different ratios of 2RH/M. Test series DM6consisted of 16 swipes at Vo/Vpeak(skirted) = 0.16, whilst DM7consisted of seven swipe tests at Vo/Vpeak(skirted) = 0.1. Both setsof tests used a footing of diameter 100mm and embedmentratio of 0.33.
Examining only test series DM6 (as DM7 shows similartrends). Figure 21 shows the load paths in the H:M/2R plane.The solid squares on the graph indicate the estimated transitionpoints from inner yield surfaces to the outer envelope. Theyserve as an indication of the shape of the outer yield surface.The open symbols on the graph are points at selected values ofV/Vo, and indicate possible shapes of the inner yield surface. Itappears that both inner and outer surfaces can be approximatedas ellipses. Also included on Figure 21 is an indication of theyield surface shape, determined during a loop event at aconstant load of 800N and V/Vo of 0.33.
An assumption made previously was that normality appliedin the deviator plane (that is H:M/2R) of load space, this hasbeen indicated by other studies (for example Gottardi et al17).It is possible to check whether this is true for these tests byplotting the force ratios against the plastic displacement ratiosas in Figure 22. If normality holds then plasticity theory givesthe plastic strain rate ratio as:
RHam
hM
aMh
mRH
R
u
o
o
o
o
p
p
2
2
2 −
−=
δθ
δ...............................................(21)
This relationship has been plotted on Figure 22 using
OTC 10994 DRAINED BEHAVIOUR OF SUCTION CAISSON FOUNDATIONS ON VERY DENSE SAND 9
parameters derived from least squares fitting of theexperimental yield surface shape. The data support anassociated flow rule, although there is some scatter,particularly in the negative quadrant in which the curvature ofthe yield surface is greatest.
Determination of Shape of Outer Yield Surface (DM8). It isclear that there is a significant change in the yield surfaceshape with increasing skirt depth. The most noticeable changesoccur in the -H:+M and the +H:-M quadrants, which are nottypically encountered in normal loading regimes. The yieldsurface shape in the positive quadrant becomes flatter withincreasing embedment.
To determine the shape of both yield surfaces, inner andouter, would require a large number of swipe tests. It ispossible to determine the shape of the outer yield surface atlow vertical loads by performing loop events at constant load.These are performed by imposing a circular displacement pathin deviator displacement space whilst keeping the vertical loadconstant. If the footing is undergoing plastic deformations theload path traced should be across the yield surface. If thefooting is at low peakVV / then small deformations will be
required to achieve plastic deformations.By using constant load loop events it is possible to map out
the probable yield surface shape for different embedmentdepths on the same sample of sand. This is important, as itsimplifies interpretation by minimising the possible effects ofsample differences. Each site on the sample was subjected toseveral loop events at different levels of vertical load. Anaccumulation of these results, normalised by the parametersdefined below, is shown in Figure 23. The normalisedvariables are defined as:
( ) 21)( 1 ββ −
=vCvhV
Hh
oskirtedpeak
.................................. (22)
( ) 21
)( 12 ββ −=
vCvmRV
Mm
oskirtedpeak
.......................... (23)
where v = V/Vpeak(skirted) and C is defined as:
( )( )
22
11
2121
ββ
β+β
ββ
β+β=C ....................................................... (24)
The constants used in the normalisation are separately definedby least squares fitting of the yield surface for each skirt depth.It is clear that as the skirt depth increases the shape of theellipse, as indicated in normalised deviator load space by thepronounced elongation of the surface.
Implications for the Offshore Design EngineerThe results presented in this paper have provided informationthat enables an improved understanding of the behaviour ofskirted footings under combined loading, particularly on verydense sand. These results are particularly relevant to thedesign of small shallow foundations for offshore structures, in
which the drained behaviour will be the limiting design case.The drained behaviour also provides a lower bound to thepartially drained performance of foundations, and as such theresults must also be considered in the design of much largerfoundations.
Effects of Scale. The objective of this research was toestablish the general behaviour of a foundation subjected tocombined loading. The effects of scale are not significant, asthe generic behaviour of the foundation at model scale is notexpected to differ significantly from one at prototype scale.However, it is worthwhile making some comments on thescaling of results, as the numerical values of parameters maychange with scale. It is assumed that the model and prototypesands are the same, and deposited at the same density. Thevertical capacity is a function of the loaded area and the soilstrength. If N is a geometric scaling factor then:
Areaprototype = N2Areamodel...................................................(25)
Soil strength is a function of the stress level in the soil, andthese stress levels will factor by N. Soil strength does not scalelinearly, because at the low stress levels (in the model) thepeak friction angle and dilation rate of the sand are higher thanat the high stress levels at prototype scale. Thus soil strengthwill scale only with approximate order of magnitude N.Combining the two leads to all forces (that is V:M/2R:H)scaling with approximate order N3. Bolton3 gives an indicationof the dependence of strength of a granular material on thestress level, acknowledging the non-linearities involved. Toexamine further how these parameters may differ with scalingto prototype dimensions it would be necessary to perform keyone gravity tests at either field scale or in a geotechnicalcentrifuge.
Positive Quadrant Negligibly Affected by Change in SkirtDepth. One surprising aspect of the results, as discussedabove, is that the yield surface in the quadrant of positiveloading is relatively unaffected by the depth of the skirt. Theloading that would typically be applied to an offshorefoundation under normal service conditions falls in thisquadrant. Whilst the overall shape of the positive quadrantremains similar, it is clear that for the same diameter footingsa skirted footing will have a larger compressive verticalcapacity. Given that the non-dimensional sizes of the yieldsurface are similar, the maximum horizontal and rotationalcapacities will factor approximately with with the increase inVpeak(skirted) due to the increased embedment. By adopting adeeper skirt it might be possible to reduce the diameter of thefoundation and still achieve suitable performance. The depthof the skirt is limited by the ability to install the foundation bysuction and dead weight.
The Concept of Safety Factors. The research indicates thattwo possible approaches can be made for defining safetyfactors for a footing on sand. It is possible to define a safetyfactor against significant or plastic movements, as would berequired for serviceability requirements. Load combinations
10 B.W. BYRNE AND G.T. HOULSBY OTC 10994
crossing the internal yield surfaces can be sustained by thesand, but at the expense of some limited plastic footingdisplacements. If load combinations are such that the outeryield surface is reached then more substantial footingdisplacements, and foundation 'failure', will be observed.These outer yield surfaces, such as those defined byMeyerhof24 and Hansen18 in their early studies, indicate themaximum combinations of load that can be sustained by thesand, regardless of displacements. Safety factors couldalternatively be defined in terms of these outer surfaces. Formaximum performance of the foundation it would bepreferable to preload to a large percentage of the bearingcapacity, before reducing to a working load of 0.5 ≈peakV/V
(which should lead to the largest safety factors against failurefor typical loading patterns). In most situations it may not bepossible to apply preload to the foundations, however, it maystill be preferable to design the footing for operation at
0.5 ≈peakV/V .
Development of Numerical Models for Use in StructuralAnalyses Packages. Numerical models based on workhardening plasticity theory can be used to model skirtedfoundations on dense sand as 'macro' elements withinstructural analyses packages. The behaviour of the soil-foundation combination is highly complex, as illustrated inthis paper, and needs to be appropriately represented withinsuch analyses so that realistic results can be obtained. This isgradually being undertaken, though primarily at a researchlevel, rather than as part of a typical analysis of an offshorestructure. This is in part due to the lack of data available forthe derivation of parameters to define the numerical model,although this is being addressed23,15,9. The model developmenthas so far been focussed on the drained behaviour of granularsoil, in response to loading on the foundation. It is clear fromthis paper that the understanding of the drained response hasimproved significantly over the past few years, and it is nowappropriate to consider the partially drained behaviour offoundations on granular materials.
ConclusionsIn this paper we present the results of a series of loading testsof model footings on very dense sand. A sophisticated loadingrig was used to complete over 250 individual tests todetermine the behaviour of footings with different skirt depthsunder a variety of conditions. These footings are representativeof a novel offshore foundation, called a 'suction caisson',which has become a viable alternative in the development ofmarginal offshore resource fields. The results represent thelong-term (drained) response to general loading regimes. Thetests were specifically designed to allow derivation of modelsof foundation behaviour based on work-hardening plasticitytheory. This investigation should be of interest to the oil andgas industry as the understanding of load-transfer mechanismsfor these foundations are still in their infancy.
Previous studies have indicated that plasticity theory maybe able to provide a rational framework for understanding this
complex non-linear geotechnical problem. This paper hasshown that the response of a skirted footing can besuccessfully described within a plasticity context. The yieldsurfaces in V:M/2R:H space are shown to be well describedby parabolic ellipsoids, as indicated by several previousstudies16,22,17,9. The study indicated that the shape of theseyield surfaces, during pre-peak bearing capacity behaviour,was a function of the ratio Vo/Vpeak. The study also indicatedthe change in shape of the yield surface with increasingembedment ratio. In all cases the use of an associated flowrule in the deviatoric (M/2R:H) plane was supported by thetests.
The results will provide the basis for the development ofsimple numerical solutions to various aspects of the combinedloading problem. They provide evidence of trends andrelationships, which were previously not quantified. Thedevelopment of numerical solutions is important as they makethe design process simpler for the engineer, particularly duringthe conceptual stages of a project. The results also provide thebasis for the development of more detailed models, whichwould be used during the design stage of a project.
AcknowledgementsThe first author would like to acknowledge the generous
support of the Rhodes Trust during the course of the research.The support and funding from the EPSRC (GR/L/64478entitled "model tests of suction caissons in dense sand") forthe experimental equipment and technician time is alsogratefully acknowledged.
NomenclatureVo = Maximum vertical load previously applied to the
footing (equal to the apex of yield surface)Vpeak = Peak vertical bearing capacity of a flat footing
Nγ = Bearing capacity factor for strip footing (friction)Nq = Bearing capacity factor for strip footing
(overburder)Nc = Bearing capacity factor for strip footing (cohesion)
Nγ* = Bearing capacity factor for circular footing
(friction)iγ = Inclination factorV = Vertical load on footingH = Horizontal load on footingM = Moment load on footing
v, h, m = Non-dimensional load parameterse = Eccentricity of vertical load causing momentR = Radius of footingD = Diameter of footingB = Width of strip footingL = Skirt depth of footingy = Embedment ratiow = Vertical displacementu = Horizontal displacement
2Rθ = Rotational displacementk = Vertical stiffness coefficientγ' = Effective unit weight of soil
OTC 10994 DRAINED BEHAVIOUR OF SUCTION CAISSON FOUNDATIONS ON VERY DENSE SAND 11
RD = Relative density of soilφ = Angle of friction of soil
ho = Horizontal dimension of yield surfacemo = Moment dimension of yield surface
a = Eccentricity of yield surface ellipse
References1. American Petroleum Institute. 1993. Recommended practice
for planning, designing and constructing fixed offshoreplatforms - load and resistance factor design. RP 2A-LRFD,1st Ed., Washington DC.
2. Bell, R.W. 1991. The analysis of offshore foundationssubjected to combined loading. M.Sc. Thesis, University ofOxford.
3. Bolton, M.D. 1986. "The strength and dilatancy of sands".Geotechnique 36, No 1, pp. 65-78.
4. Bolton, M.D. and Lau, C.K. 1993. "Vertical BearingCapacity Factors for Circular and Strip Footings on Mohr-Coulomb Soil". Canadian Geotechnical Journal. Volume30, pp 1024 - 1033.
5. Butterfield, R. 1981. "Another look at gravity platformfoundations". CISM Course, Soil Mech Fndn Engng inOffshore Technology, Udine.
6. Butterfield, R. and Ticof, J. 1979. "Design parameters forgranular soils (discussion contribution)". Proc 7th Int ConfSoil Mech Fndn Engng, Brighton, 4, pp. 259-261.
7. Butterfield, R., Houlsby, G.T. and Gottardi, G. 1997."Standardised Sign Conventions and Notation for GenerallyLoaded Foundations". Geotechnique 47, No 4, UK.
8. Bye, A., Erbrich, C., Rognlien, B., and Tjelta, T.I. (1995)."Geotechnical design of bucket foundations". Proc. ofOffshore Technology Conference, OTC 7793.
9. Byrne, B.W. and Houlsby, G.T. 1998. "Model Testing ofCircular Flat Footings on Loose Uncemented CarbonateSand: Experimental Data". OUEL Report No 2192/98.Department of Engineering Science. Oxford University.
10. Cassidy, M.J. and Houlsby, G.T. 1999. "On the modelling offoundations for jack-up units on sand". Paper No OTC10995. Proceedings of the Offshore Technology Conference,Houston, USA.
11. Clarke, D.W. 1984. "PID Algorithms and their ComputerImplementation". Trans Inst M C, Vol. 6, No 6, pp 305 -316.
12. Dean, E.T.R., James, R.G., Schofield, A.N., Tan, F.S.C, andTsukamoto, Y. 1992. "The bearing capacity of conicalfootings on sand in relation to the behaviour of spudcanfootings of jack-ups". Proc Wroth Memorial Symposium,Predictive Soil Mechanics, Oxford, pp. 230-253. ThomasTelford, London.
13. Georgiadis, M and Butterfield, R. 1988. "Displacements offootings on sand under eccentric and inclined loads".Canadian Geotechnical Journal 25, pp. 199-212.
14. Georgiadis, M. 1993. "Settlement and rotation of footingsembedded in sand". Soils and Foundations 33, No 1, pp.169-175.
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2071/95, Oxford University Engineering Laboratory.16. Gottardi, G. and Butterfield, R. 1993. "On the bearing
capacity of surface footings on sand under general planarloads". Soils and Foundations 33, No 3, pp 68-79.
17. Gottardi, G., Houlsby, G.T. and Butterfield, R. 1997. "ThePlastic Response of Circular Footings on Sand UnderGeneral Planar Loading". Report No OUEL 2143/97. OxfordUniversity Engineering Laboratory.
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19. Hansen, J.B. 1970. "A revised and extended formula forbearing capacity". Bulletin No 28, Danish GeotechnicalInstitute, Copenhagen, pp. 5-11.
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21. Lau, C.K. (1988). Scale Effects in tests on footings. PhDThesis, University of Cambridge.
22. Martin, C.M. 1994. Physical and numerical modelling ofoffshore foundations under combined loads. DPhil Thesis,University of Oxford.
23. Martin, C.M. and Houlsby, G.T. 1994. "Combined LoadingTests of Scale Model Spudcan Footings on Soft Clay:Experimental Data". Report No OUEL 2029/94. OxfordUniversity Engineering Laboratory.
24. Meyerhof, G.G. 1953. "The bearing capacity of foundationsunder eccentric and inclined loads". Proc 3rd Int Conf SoilMech Fndn Engng, 1, pp. 440-445.
25. Nova, R and Montrasio, L. 1991. "Settlements of ShallowFoundations on Sand". Geotechnique 41, No 2, pp 243 - 256.
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12 B.W. BYRNE AND G.T. HOULSBY OTC 10994
Coefficient of Uniformity, Cu 3.64Specific Gravity, Gs 2.69
Minimum density, γmin 12.72 kN/m3
Maximum density, γmax 16.85 kN/m3
Critical state friction angle, φcs 32.5°Permeability (80% Rd with water), k 7 x 10-6 m/s
Table 1 - Properties of the Baskarp Cyclone Sand used throughout the testing
Sample Test γγkN/m3
RD Vmax(50)
kNqfail
kPaNγγ
∗∗ φ φ deducedfrom RD
(Bolton3)
φφ deducedfrom Nγγ
∗∗
(Boltonand Lau4)
Trial Trial1_2 16.77 98.60 900 458.37 1093.07 44.29 46.12Trial Trial2_1 16.77 98.60 902.93 459.86 1096.62 44.29 46.13Trial Trial4_2 1 16.77 98.60 918.99 468.04 1116.13 44.29 46.19Trial Trial7_1 16.77 98.60 940.53 479.01 1142.30 44.29 46.27Trial Trial8_1 16.77 98.60 895.37 456.01 1087.44 44.29 46.11DM1 DM1-BC 16.56 94.63 1019.88 519.42 1254.53 43.70 46.61DM1 DM1-6 16.56 94.63 1098.38 559.40 1351.09 43.70 46.90DM2 DM2-BC 16.69 97.14 928.09 472.67 1132.49 44.07 46.24DM3 DM3-BC 16.71 97.34 846.26 431.00 1031.96 44.10 45.92DM4 DM4-1 16.75 98.25 937.78 477.61 1140.23 44.24 46.27DM4 DM4-2 16.75 98.25 924.51 470.85 1124.09 44.24 46.22DM5 DM5-BC 16.79 98.96 808.14 411.58 980.37 44.34 45.71DM6 DM6-BC 16.74 97.93 703.68 358.38 856.48 44.19 45.21DM7 DM7-BC 16.81 99.26 1107.23 563.91 1341.89 44.39 46.87DM8 DM8-BC 16.56 94.60 884.16 450.30 1087.71 43.69 46.11DM9 DM9-BC 16.67 96.74 785.06 399.83 959.20 44.01 45.63DM10 DM10-BC 16.54 94.26 622.00 316.78 766.02 43.64 44.34
Standard Deviation 0.10 1.81 136.17 69.35 166.16 0.27 0.67Average 16.69 97.08 892.93 454.77 1089.70 44.06 46.03
Table 2 - Summary of Bearing Capacity Tests carried out during testing series
u
w
θ
Reference position
Current positionM
V
H
2R
V
H
M/2R
Yield surface
Fig.1 - Sign convention and notation Fig. 2 - Cigar shaped yield surface in V:M/2R:H space
DRAINED BEHAVIOUR OF SUCTION CAISSON FOUNDATIONS ON VERY DENSE SAND
0
10
20
30
40
50
60
70
80
90
100
0.0001 0.001 0.01 0.1 1 10Particle Size (mm)
Per
cent
age
Pas
sing
(%
)
Lau (1986) Sand
Sleipner &Europipe SandBaskarp 15 Sand
Lau (1986) Silt
Silica Flour 300s
Baskarp CycloneSand
10
100
1000
10000
30 35 40 45 50Angle of Friction, φφtr
Bea
ring
Cap
acit
y F
acto
r, N
γγ RD = 20% RD = 100%
Fig. 3 - Combined loading rig at Oxford. Fig. 4 - Particle size distribution for experimental sand.
Fig. 6 - Bearing capacity test results.
OTC 10994 13
Fig. 5 - Typical tests required to explore plasticity concepts.
V
M/2
R
M/2
R
H
Expanding yieldsurfaces
Constant V test
Elasticity test
Constant w test
Radial loading test
Loop test
Tests at fixed2RH/M
0
500
1000
1500
2000
2500
3000
-2 -1 0 1 2 3 4 5 6δδw (mm)
V (
N)
Skirted footings
Flat footings 0
200
400
600
800
1000
1200
-0.3 -0.2 -0.1 0 0.1
Fig. 7 - Assembly of vertical loading curves for different footings (unload-reload loops are shown inset).
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.0 0.2 0.4 0.6 0.8 1.0
V /V peak
H/ V
peak
(b)
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.0 0.2 0.4 0.6 0.8 1.0
V /V o
H/ V
o
(a)
-0.04
-0.02
0.00
0.02
0.04
0.06
0.08
0.10
0.0 0.2 0.4 0.6 0.8 1.0
V /V peak
M/ 2
RV
peak
(b)
-0.10
-0.05
0.00
0.05
0.10
0.15
0.20
0.0 0.2 0.4 0.6 0.8 1.0
V /V o
M/ 2
RV
o
(a)
Fig. 8 - V :H results from Gottardi and Houlsby normalised by (a) V peak , and, (b) V o .
Fig. 9 - V :M /2R results from Gottardi and Houlsby normalised by (a) V peak , and, (b) V o .
B.W. BYRNE AND G.T. HOULSBY14 OTC 10994
Fig. 10 - New framework for understanding of yield surfaces for combined loading response of foundations.
0
0.01
0.02
0.03
0.04
0.05
0.06
0 0.05 0.1 0.15 0.2 0.25 0.3
V /V peak
H/ V
peak
(a)
0
0.1
0.2
0.3
0.4
0.5
0 0.2 0.4 0.6 0.8 1V /V o
H/ V
o(b)
0
0.01
0.02
0.03
0.04
0.05
0.06
0 0.05 0.1 0.15 0.2 0.25
V /V peak
H/ V
peak
B
A
C
elastic/plastic transition
(a)
-0.01
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
-0.005 0 0.005 0.01 0.015 0.02 0.025
δδw /2R
δδu/2
R
B
C
A sliding line intersection
(b)
Fig. 11 - V :H results from current study for flat footings normalised by (a) V peak , and, (b) V o .
Fig. 12 - Different loading tests under horizontal loading shown in (a) load space, and (b) displacement space.
DRAINED BEHAVIOUR OF SUCTION CAISSON FOUNDATIONS ON VERY DENSE SANDOTC 10994 15
V/Vpeak
H/V
peak
or
M/2
RV
peak
0 1
Outer yield surfacecorresponding to peak bearingcapacity
Inner yieldsurfaces
Parallel point formoment tests
Parallelpoint forhorizontaltests
Moment test
Horizontal test
Region of interest in this study
0
0.02
0.04
0.06
0 0.05 0.1 0.15 0.2 0.25 0.3V/V Peak
M/2
RV
peak
D
(a)
0
0.1
0.2
0.3
0.4
0.5
0.6
0 0.5 1 1.5V /V o
M/2
RV
o
D
(b)
Fig. 13 - V :M /2R results from current study for flat footings shown normalised by (a) V peak , and (b) V o .
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0 0.05 0.1 0.15 0.2 0.25 0.3
V /V peak
M/2
RV
peak
C
A
Belastic/plastic
transition
(a)
0
0.01
0.02
0.03
0.04
0.05
0.06
-0.005 0 0.005 0.01 0.015 0.02 0.025
δδw /2R
δθδθ (
Rad
ians
) C
A
B
(b)
0
0.02
0.04
0.06
0.08
0.1
0.12
0 0.2 0.4 0.6 0.8 1V /V peak
H/ V
peak
Meyerhof locus (φ = 36o and 43o)
Gottardi and Houlsby results
This study
Sliding line : H/V = tan δ where δ = 29o
Hansenlocus
0
0.02
0.04
0.06
0.08
0.1
0 0.2 0.4 0.6 0.8 1
V /V peak
M/2
RV
peak
Meyerhof and Hansen interaction locus
Gottardi and Houlsby results
This study
Fig. 15 - Conventional theory for horizontal loading compared to recent results.
Fig. 14 - Different tests under moment loading shown in (a) load space, and (b) displacement space.
Fig. 16 - Conventional theory for moment loading compared to recent results.
B.W. BYRNE AND G.T. HOULSBY16 OTC 10994
0
0.2
0.4
0.6
0.8
1
1.2
0 0.2 0.4 0.6 0.8 1
V /V o
q
Simple parabola
0
0.05
0.1
0.15
0.2
0.25
0.3
0 0.2 0.4 0.6 0.8 1V o /V peak
ho
, mo
Byrne - ho (DM9) Byrne - mo (DM9)Byrne - ho (DM2) Byrne - mo (DM3)Gottardi - ho Gottardi - moModel C - ho Model C - moMeyerhof - ho (phi=43) Meyerhof - mo
-0.01
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0 0.02 0.04 0.06 0.08
δδu /2R
δθδθ (
radi
ans)
(b)
Increase in L /D
ratio
0
0.01
0.02
0.03
0.04
0.05
0.06
0 0.05 0.1 0.15 0.2 0.25 0.3V /V peak
M/2
RV
peak
(a)
0
0.01
0.02
0.03
0.04
0.05
0.06
0 0.005 0.01 0.015 0.02 0.025 0.03
δδu /2R
δθδθ (
Rad
ians
)
(b)Increase in L /D ratio
Fig. 19 - Results from horizontal swipe tests (DM5) showing test paths in (a) load space, and, (b) displacement space.
Fig. 20 - Results from moment swipe tests (DM4) showing test paths in (a) load space, and, (b) displacement space.
Fig. 17 - Data from test series DM9 normalised and plotted in q :V/V o space.
Fig. 18 - Accumulation of results from various studies of flat footings showing dependence of parameters on V o /V peak .
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0 0.05 0.1 0.15 0.2 0.25
V /V peak
H/ V
peak
L/D = 0
L/D = 0.16
L/D = 0.33
L/D = 0.66
(a)
DRAINED BEHAVIOUR OF SUCTION CAISSON FOUNDATIONS ON VERY DENSE SANDOTC 10994 17
-400
-300
-200
-100
0
100
200
300
400
500
-600 -400 -200 0 200 400 600H (N)
M/2
R (
N)
Transition Points
-90
-60
-30
0
30
60
90
-90 -60 -30 0 30 60 90
atan(δδu /2R δθδθ) (degrees)
atan
(2R
H/ M
) (d
egre
es) Theoretical
relationship
Experimental Values
-4
-3
-2
-1
0
1
2
3
4
-4 -2 0 2 4
Normalised Horizontal Load
Nor
mal
ised
Mom
ent
Loa
d
Increase in L /D ratio
Fig. 23 - Accumulation of results of loop events for different skirt depths.
Fig. 22 - Assessment of associated flow rule in the deviatoric plane for series DM6.
Fig. 21 - Accumulation of swipe tests from V /V o = 1 for series DM6 (y = 0.33).
B.W. BYRNE AND G.T. HOULSBY18 OTC 10994
