Calculation Procedures for Installation of Suction Caissons by G.T. Houlsby and B.W. Byrne
Report No. OUEL 2268/04
University of Oxford Department of Engineering Science Parks Road, Oxford, OX1 3PJ, U.K. Tel. 01865 273162/283300 Fax. 01865 283301 Email
[email protected].
[email protected] uk http://www-civil.eng.ox.ac.uk/
Design procedures for installation installation o f suction caissons in clay and and oth er soils 1
G.T. Houlsby and B.W. Byrne
1
Keywords: clay, foundations, suction caissons, installation
Ab st r act Suction-installed skirted foundations, often referred to as suction caissons, are being increasingly used for a variety of offshore applications. In designing a caisson a geotechnical engineer must consider the installation process as well as the in-place performance. The purpose of this paper is to present calculation procedures for the installation of a caisson in clay. For clay sites, the caisson will often be used as an anchor, with the ratio of the skirt length ( L) to the diameter ( D) as high as 5. Calculation methods are presented for determining the resistance to penetration of open-ended cylindrical caisson foundations with and without the application of suction inside the caisson. Comparisons of between predictions and case records are made. A companion paper (Houlsby and Byrne, 2004) describes the calculation procedure for installation in sand soils. Finally comments are made here about installation in s variety of soils other than homogeneous deposits of clay or sand.
Introduction A suction caisson is a large cylindrical structure, usually made of steel, open at the base and closed at the top. It might be used either as a shallow foundation or as a short stubby pile (often called a suction anchor). The shallow foundation option is more common at sandy soil sites ( e.g. Bye et al., 1995; Hogervost 1980; Tjelta, 1994; Tjelta, 1995; Tjelta et al., 1990) whilst the anchor/pile application is commoner in clay or layered soils ( e.g. Colliat et al., 1996; Colliat et al., 1998; Erbrich and Hefer, 2002; Lacasse, 1999; Solhjell et al., 1998). Figure 1 shows typical diameter and skirt depths for various projects reported in the literature (the figure is taken from Byrne (2000) and with further data from Tjelta (2001)). More recently there is an emerging application of caissons as the foundations for offshore wind turbines (Byrne et al., 2002; Byrne and Houlsby, 2003). This paper addresses installation in clays and other soils whilst a companion paper (Houlsby and Byrne, 2004) considers installation in sand. In the anchor application the caisson will be designed so that the skirt length ( L) is much greater than the diameter ( D) and the ratio L/ D D might be as large as 5 (as shown in Figure 1). As oil and gas exploration heads further offshore and into deeper water, it is likely that anchor applications will become more common. There are particular advantages to using the suction caisson over other anchoring methods ( e.g. drag anchors), in that the caisson can be accurately located, allowing complex mooring line arrangements to be accommodated. The ability to remove a caisson (by simply reversing the installation procedure) allows mooring line arrangements to be altered over the life of a production vessel; and removal at the end of the design life. After an initial penetration into the seabed caused by self weight, a suction (relative to seabed water pressure) is applied within the caisson, which forces the remainder of the caisson to embed itself, leaving the top flush with the seabed. The purpose of this paper is to present design calculations for the installation of the caisson. Separate calculations are of course necessary to assess the capacity of the caisson once installed – either as a shallow foundation or as an anchor. Analyses are presented for the magnitude of the self-weight penetration, the relationship between suction and further 1
Department of Engineering Science, Parks Road, Oxford OX1 3PJ 1
penetration, and the limits to penetration that can be achieved by suction. The analyses are “classical” in the sense that they make simplifying assumptions, borrowing techniques from both pile design and bearing capacity theory. More rigorous analyses, using for instance finite element techniques, could be used for particular installations. The analyses presented here should, however, provide a reasonable approximation for design purposes. Similar methods (although differing in some details) to those described below have been published e.g. by House et al. (1999), but our purpose here is to draw together a comprehensive design method and compare with case records from several sources.
Installation in Clay Figure 2 shows the key variables in the suction caisson problem, so far as the installation is concerned. For the purposes of the installation calculation the strength of the clay is characterised by an undrained strength, which is assumed to increases with depth linearly in the form su = suo + ρ z . The methods described below can readily be adapted to more complex strength variations.
Self-weight penetration The resistance to penetration is calculated as the sum of adhesion on the outside and inside of the caisson, and the end bearing on the annular rim. The adhesion terms are calculated, following usual practice in pile design, by applying a factor α to the value of the undrained strength. The end bearing is calculated, again following standard bearing capacity analyses, as the sum of an N q and an N c term. The result is: V ′
=
hα o su1 (π Do )
adhesion on outside
+
hα i su1 (π Di )
adhesion on inside
+
(γ ′h + su 2 N c )(π Dt ) …(1) end bearing on annulus
where su1 = suo + ρ h 2 is the average undrained shear strength between mudline and depth h, su 2 = suo + ρh is the undrained shear strength at depth h, α o and αi are adhesion factors on the outside and inside of the caisson (as used in undrained pile design) and N c is an appropriate bearing capacity factor for a deep strip footing in clay (typically a value of about 9 might be adopted). For undrained analysis N q = 1 .
Suction-assisted penetration Once the self-weight penetration phase has been completed, so that a seal is formed around the edge of the caisson, it will be possible to commence the suction installation phase. The applied suction in the caisson is s relative to seabed water pressure, i.e. the absolute pressure inside the caisson is p a + γ w hw − s . There are a number of practical limits to the maximum attainable value of s. Amongst these are (a) the absolute pressure at which the water cavitates (usually a small fraction of atmospheric pressure), (b) the minimum absolute pressure that can be achieved by the given pump design, (c) the minimum relative pressure that can be achieved by the pump. The suction causes a pressure differential across the top plate of the caisson, which results effectively in an additional vertical load equal to the suction times the plan area of the caisson. The capacity is again calculated as the sum of the external and internal friction, and end bearing term. Note that the overburden term is reduced in the end bearing calculation by the suction pressure, assuming that the flow of soil under the rim occurs entirely inwards. The result is:
2
(
2
V ′ + s π Di
)
4 = hα o su1 (π Do ) + hα i su1 (π Di ) + (γ ′h − s + su 2 N c )(π Dt )
…(2)
which is readily rearranged to: 2
V ′ + s π Do 4 = hα o su1 (π Do ) + hα i su1 (π Di ) + (γ ′h + su 2 N c )(π Dt )
…(2a)
Note that if the variation of soil strength is not simply linear, all that is necessary is to replace su1 with the average strength from mudline to depth h, and su 2 with the strength at depth h. Equation (2) gives a simple relationship between suction and depth. For constant V ′ and a linear increase of strength with depth (so that su1 and su 2 are linear functions of h), s is a quadratic function of h .
Limits to suction assisted penetration In addition to the limit imposed by the maximum available suction, there is a limit to the depth of penetration that can be achieved by the action of suction. If the difference between the vertical stress inside and outside the caisson, at the level of the caisson tip, exceeds a certain amount, then local plastic failure may occur, and further penetration may not be possible. The mechanism may be thought of as a “reverse” bearing capacity problem, in which the soil flows into the caisson. The average vertical stress (relative to local hydrostatic) inside the caisson at tip level is relatively π Di hα i su1 straightforward to estimate as − s + γ ′h + . The third term in this expression arises from 2 π Di 4
the downward friction inside the caisson, and here it is assumed (for simplicity) that this results in a uniform increase of vertical stress at all radii in the caisson. Note that the assumption of a uniform increase in vertical stress within the caisson is clearly unreasonable at small values of h D , but it will be seen below that this calculation is only needed at h D values greater than about 2, for which the uniform increase is a reasonable approximation. The relevant stress outside the caisson is much harder to estimate, since the downward load from adhesion on the outside of the caisson will enhance the stress in the vicinity of the caisson, but this enhancement is difficult to calculate. However, making the simplifying assumption that the downward load from the adhesion is carried by a constant stress over an annulus with inner and outer diameters Do and Dm , this stress (again relative to local hydrostatic) may be calculated as
γ ′h +
π Do hα o su1
(
2 π Dm
− s + γ ′h +
− Do2
)4
.
π Di hα i su1
Thus
= γ ′h +
the
“reverse
π Do hα o su1
(
)
bearing
capacity”
failure
would
occur
when
− N c* su 2 , where N c* is a bearing capacity factor
2 π Di2 4 π Dm − Do2 4 appropriate for uplift of a buried circular footing. Substituting the solution for s into equation (2) and simplifying gives: 2 Di + (γ ′h + s N )(π Dt ) = hα o su1 (π Do ) 1 + u2 c 2 2 D − D 4 m o
π Di2 * V ′ + N c su 2
(
)
…(3)
which can be solved for h. Note, however, that although the above equation appears linear in h, in fact su1 and su 2 are themselves linear functions of h, so that the solution again involves solving a quadratic. Furthermore it would be rational to assume that Dm increases with penetration, for instance in the form Dm − Do = 2 f o h , where f o is a constant “loadspread” factor. A further
3
development would be to allow the enhancement of the stress to vary (say linearly) from zero at Dm to a maximum at the caisson surface. It is worth, however, considering some approximate solutions for the maximum penetration. For many cases the final term (the end bearing) is small. We consider also the case where the applied load V ′ is small, and make the approximation Do ≈ D ≈ Di . If we write Dm = mD , then equation (3) leads to the following result for this simplified case: N c* su 2 1 1 − ≈ D 4α o su1 m 2 h
…(4)
The factor N c* 4α o is likely to be in the region of about 3, although it could vary considerably. The factor su 2 su1 would be 1.0 for a homogeneous soil, and 2.0 for the extreme of a soil with a strength increasing linearly with depth from a value of zero at the surface. The final factor varies from 1.0 if m is assumed to be very large, to 0.75 if say m = 2 . The overall result is that the calculated maximum attainable value of h D is likely to be from about 2.5 for stiff clays (with strengths approximately uniform with depth) to 5 for soft normally consolidated clays (with strengths approximately proportional to depth). The effect of accounting for the external load V ′ would be to increase these values. Equation (4), however, provides a useful estimate of the maximum h D ratio of a suction-installed caisson that could be reliably installed in clay. If different assumptions are made about the way the external adhesion load enhances the vertical stress are made, the same broad conclusions arise, although the precise figures will vary. It should be noted that some measured values of installations indicated that higher h D ratios than implied by the above calculation may be achievable. The above may therefore be treated as a conservative calculation. Note also that the end bearing calculation in equations (1) and (2) does not take into account any enhancement of the stress level inside or outside the caisson due to the frictional terms. This follows conventional piling design calculations, in which no such correction is usually included. If this effect was to be taken into account, the factor ′h in equation (1) would be replaced by whichever is the smaller of γ ′h + suction is started,
γ ′h +
π Di hα i su1 π Di2 4
π Do hα o su1
(
)
2 π Dm − Do2 4
or γ ′h +
π Di hα i su1 π Di2 4
(almost invariably the former). Once
′h − s in equation 2 is replaced by the smaller of γ ′h − s +
π Do hα o su1
(
)
2 π Dm − Do2 4
or
(usually the latter except at very small suction). In practice these changes make
very small differences to the calculation.
The effect of internal stiffeners Most suction caissons include some internal structure, usually consisting of either vertical plates or annular plates, to provide strength and stiffness to the cylindrical shell, either to suppress buckling during suction-assisted penetration, or (in the case of a caisson anchor) to reinforce the caisson at the pad-eye connection. The analysis for the case of annular stiffeners is not considered here, but the use of vertical stiffeners results in only a small change in the calculation.
4
In principle stiffeners could be located on the outside of the caisson, but this option does not usually seem to be adopted. The additional resistance offered by the stiffeners can be taken into account by an adhesion term of the form hαsu1l , where l is the perimeter length of the stiffeners (usually approximately twice the plate length for thin plate stiffeners), and an end bearing term of the form (γ ′h + su 2 N c ) A , where A is the end area of the stiffeners. The area on which the suction acts (on the left side of Equation 2) should also be reduced by A, although this correction will usually be tiny. Note that if the stiffeners do not extend the full depth of the caisson, appropriate corrections are required for the value of h used in the contribution from the stiffeners, and in the appropriate su1 and su 2 values. In the calculation of the maximum attainable depth using suction, note that the terms involving adhesion on the inside of the caisson cancel, and have no overall effect on the calculation. The same is true for terms resulting from the resistance from internal (but not external) stiffeners, so for internal stiffeners only Equation (4) can still be used.
Example 1 Consider a suction caisson of outside diameter 12m, wall thickness 45mm and depth 5m. Such a caisson might be considered as a foundation for an offshore structure. The caisson is stiffened by 30 plates 25mm thick and 200mm deep welded as radial fins on the inside of the caisson, and extending for the top 4m of the caisson only. The soil profile is idealised as a layer 2m thick of constant strength 20kPa, with below that a linear increase of strength from 25kPa at 2m at a rate 2.5kPa/m. The buoyant unit weight is taken as 6kN/m 3. The end bearing factor N c is taken as 9, and the adhesion factor α as 0.6 for the outside of the caisson and 0.5 for inside and for the stiffeners. The maximum applied vertical load (including the weight of the caisson and buoyancy effects) is 1000kN and the water depth is 50m. The calculations described above have been implemented in a spreadsheet-based program “SCIP” (Suction Caisson Installation Prediction). Figure 3 shows the calculated loads required to install the caisson in the absence of suction. Figure 4 shows the predictions from SCIP of the variation of suction with depth required for installation, and in this case the maximum suction required is 49kPa.
Example 2: Predicted of installation pressures compared t o centrifuge tests House and Randolph (2001) conducted a series of tests on the centrifuge at the University of Western Australia, investigating the installation of suction caissons in normally consolidated clay. The experiments were carried out at 120g. The strength profile of the clay could be idealised as zero at the surface increasing with depth at a gradient of 144kPa/m to a depth of 67mm then at 204kPa/m (at prototype scale these represent rates of increase of 1.2kPa/m and 1.7kPa/m). The effective unit 3 weight of the soil (accounting for the 120g acceleration) was determined to be 792kN/m . The dimensions of the caisson were 30mm diameter, 0.5mm wall thickness and 120mm skirt length. (Equivalent prototype dimensions 3.6m diameter, 60mm wall thickness, 14.4m skirt length). An effective vertical load of 15.3 N was applied to the caisson. Figure 5 shows the penetration resistance for the caisson without using suction, showing that most of the resistance is in the skirt friction. Figure 6 shows an estimated suction penetration curve, which shows good agreement with the experimental data reported by House and Randolph (2001). The self-weight penetration amounts to 41mm and the maximum suction pressure required is 143.9kPa. An adhesion factor of 0.5 was used for both internal and external walls.
5
Example 3: Prediction of plug failure A series of tests were conducted by House et al. (1999) on the laboratory floor to investigate plug failure during installation of suction caissons in normally consolidated clay. They investigated three caissons with diameters 10.4mm, 15.9mm and 37.2mm. All caissons had a wall thickness of 0.4 mm and an L/ D ratio of 8. In the following a comparison is made for the 15.9mm diameter caisson. The soil strength profile 3 was estimated by House et al. (1999) to be 75kPa/m and the effective unit weight to be 5.9kN/m . The caissons were initially pushed into the clay to a penetration of approximately one diameter before the suction was applied. Assuming a circular end bearing capacit y factor of 8.5 (Houlsby and Martin, 2003), the maximum calculated penetration by SCIP that is possible before a plug failure is expected is 83mm or an h/ D = 5.2. This can be compared to the conclusions drawn by House et al. (1999). They compare the volume of water withdrawn from the caisson cavity during installation to the displaced volume within the caisson (assuming heave has not occurred). When more water is evacuated than can be accounted for by the installed portion of the caisson, they infer that plug heave has occurred. Figure 8 shows, for two installations of the 15.9mm diameter caisson, the excess volume of water removed, plotted against normalised penetration. For the cases shown, House et al. (1999) deduced that plug failure occurs at an L/ D ratio between 4 and 5, which agrees with the prediction given above. Again an adhesion factor of 0.5 was used. Note that although plug failure occurred it was still possible to install the caisson further. Installation continues until all water has been withdrawn from the internal cavity. The consequence of plug failure is that the caisson cannot be installed to its full design depth.
Example 4: Nkossa Field Installation This calculation involves some modification to the basic procedures described above to account for the geometry of the caissons used in the Nkossa field off the coast of West Africa (Colliat et al., 1996; Colliat et al., 1998). Two different anchor sizes were used depending on the loading conditions. We will only consider the installation of the smaller of the two, defined by Colliat et al. (1998) as a Type I anchor. The geometry of the caissons is unusual, as they have a step change in diameter part way down the caisson. The bottom section is 4m in diameter and extends for 4.8m whilst the top section is 4.5m in diameter and is 7.5m long. The anchor chain lug is located at the change in caisson diameter. The wall thickness for the pipe sections was 15mm and the design penetration was 11.8m. The larger top section was to accommodate any soil heave that occurred during installation. Internal stiffening plates are also believed to have been used. However, these are omitted in the calculation here, as there is insufficient information about the detailed geometry of the stiffeners. The weight (in air) of the caisson is given as “41 tons” which converts to a submerged weight of approximately 350kN. Colliat et al. (1998) give a summary of the soil conditions, which includes average shear strengths as well as upper and lower bound strength envelopes. For the purpose of this calculation, the average strength is taken, and is 5kPa at the surface increasing at 1.0kPa/m for the first 5m, below 3 which the gradient changes to 1.67kPa/m. The effective unit weight of the soil is taken as 6kN/m . Whilst Colliat et al. (1998) suggest an adhesion factor of 0.3 based on model scale field tests, but the calculations here show an excellent agreement with the measurements if an adhesion factor of 0.45 (which seems quite reasonable) is used. To account for the effect of the increase in diameter of the top section of the caisson, the internal adhesion factor was set to zero for the top section. End bearing is also taken into account at the step between the two diameters. Figure 7 shows the suction pressures required compared to the average and range measured during the field installation (on the basis of data presented by Colliat et al., 1998). The slight underestimation of the required suction may be because the stiffeners are not taken into account.
6
In the three example calculations where it is possible to compare with data, it is clear that a good relation exists between predicted and observed behaviour, using reasonable estimates of soil parameters. Obviously the key parameter that is required for predictions of caissons in clay is the undrained strength profile, and an estimation of the adhesion factor α.
Installation in other materials Layered materials Figure 1 shows that a number of installations have occurred in layered materials. We describe briefly the issues that must be considered during the design for these sites. Sand over Clay The sequence of sand over clay probably would not cause problems for installation - typically the installation would proceed through the sand (using the calculations given by Houlsby and Byrne (2004)), and once into the clay the resistance would in most cases be lower, and could be calculated using the same principles as for clay alone (although with a modification to the calculation of the friction). Clay over Sand Clay over sand is likely to be more problematical. The caisson penetrates through sand when the applied suction creates gradients in the sand which degrades the tip resistance to almost zero. The pressure differential also provides a net downward force on the caisson, but this contributes less significantly to the installation. Without the flow field in the soil it might be impossible to install the caisson, due to the high bearing resistance of the sand (especially if it is very dense). During installation in clay it is the net downward force caused by the pressure differential which causes the caisson to be forced into the soil. When the installation occurs in a layered soil there are questions as to whether the caisson will penetrate through a sand layer after it has passed through a clay layer, as it will not be possible to develop the flow regime which degrades the skirt tip resistance to near zero.
There are several field case studies which provide evidence that installation under these conditions may, however, still be possible. The most notable is the large scale deepwater penetration test which was conducted during the investigations for the Gullfaks C platform (Tjelta and Hermstad, 1986). The soil profile consists of a number of layers of medium to dense sand and clay. The cone tip resistances reach 20-24MPa in the denser sand layers, 4-10MPa in the medium sand layers and 12MPa in the clay layers. The foundation consists of two 6.5m diameter cylinders joined by a concrete beam, the structure being 22m in depth. A maximum suction of about 480kPa (linearly increasing with depth) was required to install the caisson to its full depth. A water jetting system at the caisson tip was used during the penetration of the initial sand layer, thus reducing the tip resistance. Removal was also possible, requiring approximately 250kPa of overpressure (linearly decreasing) at the maximum depth. Further references to suction anchor installation in layered material can be found in Senpere and Auvergne (1982) and Tjelta (2001). The former describe the installation in the Gorm field, where soil plug failure occurred in all caissons. The installation was nonetheless successful as a jetting procedure was used to remove material from within the caisson. Tjelta (2001) describes in issues related to the Curlew, YME and Harding fields but does not give specific details. Finely interbedded materials There is no particular reason to suppose that finely interbedded materials would pose problems, unless the composition of the beds differed in some extreme way. There are, however, no recorded cases in such materials.
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Stiff (possibly fissured) clay There is a concern that it might not be possible to install suction caissons in stiff clays. The principal reason is that, given that such materials are often fissured, or are prone to fissuring, it may not be possible to form the necessary seal around the rim of the caisson for penetration to proceed. One possibility is that fracturing may occur, with water simply flowing through the fissures. This problem may be exacerbated by the fact that the penetration resistance in very stiff clays would be high. Information for this case is relatively scarce. In most cases where stiff clays have been encountered (i.e. in the Visund, Njord and Aquila fields as discussed by Solhjell et al., 1998) the soil conditions consisted of a layer of soft clay overlying much stiffer clay. In these cases it appears that the soft clay layer is deep enough so that a seal could be created. Whilst there is no evidence to support whether or not installation in stiff fissured clay is possible or not, it should be noted that the condition where a stif f clay exists at mudline might be a rather scarce occurrence.
Coarse materials For obvious reasons, extremely heterogeneous materials would be likely to cause problems for installation of a suction caisson. Materials with a significant fraction of coarse gravel or larger sizes would almost certainly present an obstacle to installation. Certain (but not all) glacial tills would therefore be problematical. Very open gravels, even if not particularly coarse, would present problems in that flows during pumping would be very high.
Silts It is difficult to do calculations for silts, because it is difficult to determine whether drained and undrained behaviour would be appropriate, and partially drained calculations for caisson penetration have not been formulated. However, given that penetration in clays and sands is relatively straightforward, it would be expected that reasonably homogeneous silts would not pose difficulties.
Carbonate soils Erbrich and Hefer (2002) present the case history of the installation of suction anchors at the Laminaria site in the Timor Sea. Whilst the installation of the 9 anchors was successful, the suction pressures measured were significantly lower than those predicted in the original design calculations. Erbrich and Hefer (2002) report very low values for the adhesion factor (of the order of 0.1 – 0.2) that arise from the back-analysis of the field data. It is clear that for extremely fine-grained carbonate soils (as at the Laminaria case) the clay calculation is appropriate, while for the coarser materials the sand calculation is appropriate. Because of the crushability of carbonate materials, very low values of K tan δ would probably be appropriate in the friction calculation.
Rocks It is unlikely that suction caissons could be installed into any but the very softest of “rocks”.
Special conditions The influence of special conditions ( e.g. shallow gas deposits within the depth of the caisson, organic material etc.) is almost unknown and would have to be dealt with on an ad hoc basis.
8
Pumping r equirements The flow capacity of pumps for installation in clay needs only to be that necessary (with a suitable 2
Di
margin) to remove the water from the caisson as penetration proceeds, that is q = π
v , where q 4 is the required flow rate and v is the vertical penetration velocity. In sands the capacity must also be sufficient to cope with the seepage beneath the foundation. This can be assessed by conventional 2
Di
seepage calculations, giving a total required flow rate of q = π
4
v + F
skD
γ w
, where F is a
dimensionless factor that depends on h D and k is the sand permeability (Houlsby and Byrne, 2004).
Conclusions In this paper we present the calculation procedures that are required for suction caisson installation in clay. Calculations include those for self-weight penetration, penetration under suction and the limits to the suction assisted penetration. The calculation procedures are compared to case records, showing good agreement with the measured responses. The paper concludes with discussion of potential issues when installing suction caissons in a variety of other soils.
Ac kn ow led gem ent s B.W.B. acknowledges generous support from Magdalen College, Oxford. The authors are grateful to Dr Andrew House for provision of original data for use in examples 2 and 3.
Nomenclature D f h hw K L l m
caisson diameter load spread factor for vertical stress enhancement installed depth of caisson height of water above mudline factor relating vertical stress to horizontal stress caisson skirt depth perimeter length of stiffeners within caisson multiple of the diameter that the vertical stress is enhanced (i.e. Dm = mDo )
N q N c pa s su 0
bearing capacity factor (overburden) bearing capacity factor (cohesion) atmospheric pressure suction within the caisson with respect to the ambient seabed water pressure shear strength at mudline
su1
average shear strength over depth of skirt
su 2
shear strength at caisson skirt tip
t V , V’ z
α δ γ , γ ’ γ w ρ
wall thickness vertical load, effective vertical load vertical coordinate below the mudline adhesion factor interface friction angle unit weight of soil, effective unit weight of soil unit weight of water rate of change of shear strength with depth 9
σv, σv’
vertical stress, effective vertical stress
subscripts i o
inside caisson outside caisson
References Bye, A., Erbrich, C.T., Rognlien, B. and Tjelta, T.I. (1995) “Geotechnical design of bucket foundations” Paper OTC 7793, Offshore Technology Conference , Houston, Texas Byrne, B.W. (2000) “Investigation of suction caissons in dense sand” DPhil Thesis, Oxford University Byrne, B.W. and Houlsby, G.T. (2003) “Foundations for offshore wind turbines” Phil. Trans. Roy. Soc. of London, Series A, 361, December, pp 2909-2930 Byrne, B.W., Houlsby, G.T., Martin, C.M. and Fish, P. (2002) “Suction caisson foundations for o offshore wind turbines” Wind Engineering 26, N 3 Colliat, J-L., Boisard, P., Gramet, J-C. and Sparrevik, P. (1996) “Design and installation of suction anchor piles at a soft clay site in the Gulf of Guinea” Paper OTC 8150, Offshore Technology Conference , Houston, Texas Colliat, J-L., Boisard, P., Sparrevik, P. and Gramet, J-C. (1998) “Design and installation of suction anchor piles at a soft clay site” Proc ASCE Jour. of Waterway, Port, Coastal and Ocean Eng. 124, No 4, pp 179–188 Erbrich, C.T. and Hefer, P.A. (2002) “Installation of the Laminaria suction piles – a case history” Paper OTC 14240, Offshore Technology Conference , Houston, Texas Houlsby, G.T. and Byrne, B.W. (2004) “Design procedures for installation of suction caissons in sand” Submitted to Geotechnical Engineering Houlsby, G.T and Martin, C.M. (2003) "Undrained Bearing Capacity Factors for Conical Footings on Clay", Géotechnique , Vol. 53, No. 5, June, pp 513-520 House, A.R., Randolph, M.F. and Borbas, M.E. (1999) “Limiting aspect ratio for suction caisson installation in clay” Proc. 9th Int. Symp. on Offshore and Polar Eng. , Brest, France House, A.R. and Randolph, M.F. (2001) “Installation and pull-out capacity of stiffened suction caissons in cohesive sediments” Proc. 11th Int. Symp. on Offshore and Polar Eng. , Stavangar, Norway Hogervost, J.R. (1980) “Field trials with large diameter suction piles” Paper OTC 3817, Offshore Technology Conference , Houston, Texas Lacasse, S. (1999) “Ninth OTRC Honors Lecture: Geotechnical contributions to offshore development.” Paper OTC 10822, Offshore Technology Conference , Houston, Texas Senpere, D. and Auvergne, G.A. (1982) “Suction anchor piles – a proven alternative to driving or drilling” Paper OTC 4206, Offshore Technology Conference , Houston, Texas Solhjell, E., Sparrevik, P., Haldorsen, K. and Karlsen, V. (1998) “Comparison and back calculation of penetration resistance from suction anchor installation in soft to stiff clay at the Njord and Visund Fields in the North Sea” Proc SUT Conf. on Offshore Site Investigation and Foundation Behaviour , London, UK Tjelta, T.I. and Hermstad, J. (1986) “Large-scale penetration test at a deepwater site” Paper OTC 5103, Offshore Technology Conference , Houston, Texas Tjelta, T.I. (1994) “Geotechnical aspects of bucket foundations replacing piles for the Europipe 16/11-E Jacket” Paper OTC 7379, Offshore Technology Conference , Houston, Texas Tjelta, T.I. (1995) “Geotechnical experience from the installation of the Europipe Jacket with bucket foundations” Paper OTC 7795, Offshore Technology Conference , Houston, Texas. Tjelta, T.I., Aas, P.M., Hermstad, J. and Andenaes, E. (1990) “The skirt piled Gullfaks C Platform installation” Paper OTC 6473, Offshore Technology Conference , Houston, Texas
10
th
Tjelta, T.I. (2001) “Suction piles: their position and application today” Proc. 11 Int. Symp. on Offshore and Polar Eng. , Stavangar, Norway
Figures Diameter (m) 0
5
10
15
20
0
5 Sleipner T
YME Jack-up
Draupner E Shallow Foundations
10 Snorre TLP ) 15 m ( h t p e D
20 Gullfaks C
25
Trials Laminaria Project - Clay
Anchor Foundations
Project - Layered Project - Sand
30
L/D = 1 35
Figure 1: summary of uses of caisson foundations (from Byrne (2000) with further data from Tjelta (2001))
V'
Mudline
hc z
t
h
Di
Do
Figure 2: outline of suction caisson
11
Load without suction (kN) 0
1000
2000
3000
4000
5000
6000
7000
0 0.5
Adhesion End be aring Total
1 1.5 ) m ( z h t p e D
2 2.5 3 3.5 4 4.5 5
Figure 3: calculated loads on caisson for Example 1 in the absence of suction
Required suction s (kPa) 0
5
10
15
20
25
30
35
0 0.5 1 1.5 ) 2 m ( z h2.5 t p e D
3
3.5 4 4.5 5
Figure 4: calculated suction for Example 1
12
40
45
50
Load without suction (kN) 0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0 Adhesio n End be aring Total
0.02
0.04 ) m ( z h t p e D
0.06
0.08
0.1
0.12
Figure 5: calculated loads for Example 2 in the absence of suction
0
20
40
60
Required suction s (kPa) 80 100 120
140
0
Calculated Experiment
0.02
0.04 ) m ( z h0.06 t p e D
0.08
0.1
0.12
Figure 6: calculated suction for Example 2
13
160
180
Required suction s (kPa) 0
20
40
60
80
100
120
140
160
180
0
Calculated
0.02
Experimental 0.04 ) m0.06 ( z h t p e D0.08
0.1
0.12
0.14
Figure 7: comparison of calculated and experimental suction pressures for House and Randolph (2001) NC-IP2 experiment, Example 3
Excess Volume of Fluid Removed (ml) -2
-1
0
1
2
3
4
5
6
7
0 Installation 2
1
Installation 4 Predicted level of plug failure
/ h : n o i t a r t e n e p d e s i l a m r o N
2 3 4 5 6 7 8
Figure 8: variation with depth of excess volume of water removed for Example 3
14
Required suction s (kPa)
0
20
40
60
80
100
120
140
160
0
2
4 ) m ( z h t p e D
6
8
10
12
14
Figure 9: Comparison between calculated and observed suction pressures at the Nkossa installation, Example 4
15
Design procedures for installation o f suction caissons in sand 1
G.T. Houlsby and B.W. Byrne
1
Keywords: sand, foundations, suction caissons, installation
Ab st ract Suction installed caisson foundations are being used or considered for a wide variety of offshore applications ranging from anchors for floating facilities to shallow foundations for offshore wind turbines. In the design of the caissons the installation procedure must be considered as well as the in-place performance. The scope of this paper is to consider the calculations appropriate for the installation of caissons in sands. Calculation methods are presented for determining the resistance to penetration of open-ended cylindrical caisson foundations both with and without the application of suction inside the caisson. Comparisons are made with case records. A companion paper (Houlsby and Byrne, 2004) addresses the calculation procedure for installation in clays as well as other soils.
Introduction Suction caissons are large cylindrical structures, usually made of steel, open at the base and closed at the top. After an initial penetration into the seabed caused by self weight, a suction (relative to seabed water pressure) is applied within the caisson, which forces the remainder of the caisson to embed itself, leaving the top flush with the seabed. The purpose of this paper is to present design calculations for the installation of caissons in sand. When the suction is applied the pressure differential on the lid of the caisson effectively increases the downward force on the foundation. However, in sand the applied suction also generates flow within the soil. The pore pressure gradients are beneficial to the installation process and must be accounted for in the design calculation. Separate calculations are of course necessary to assess the capacity of the caisson once installed – whether used as a shallow foundation or anchor. Some of the issues that need to be addressed for the in-service performance of suction caissons in sand are discussed by Byrne and Houlsby (2002, 2003, 2004). The first major structure installed in dense sand using suction caissons was Statoil’s Draupner E riser platform (formerly Europipe 16/11 E) in the North Sea. This was installed successfully during 1994 in 70 m water depth. The caisson foundations were 12m in diameter and the skirts were 6m long, and designed to be installed with suction. The design for the installation was based on a combination of field testing, laboratory testing and finite element modelling (as described by Tjelta, 1994; Bye et al., 1995; Tjelta, 1995). Statoil installed a second caisson founded structure in the North Sea in 1996 (Sleipner T). During the detailed design of this structure Erbrich and Tjelta (1999) developed a design methodology using design charts based on finite element calculations. The analyses presented in this paper differ from the finite element approach in that they are “classical” in the sense that they employ simplifying assumptions, borrowing techniques from both pile design and bearing capacity theory. More rigorous analyses, using for instance finite element techniques (as for instance outlined by Erbrich and Tjelta (1999)), could be used for particular installations. The analyses presented here should, however, provide a reasonable approximation for design purposes.
1
Department of Engineering Science, Parks Road, Oxford OX1 3PJ 1
An alys is We will consider a circular caisson of outside diameter Do and wall thickness t , so that the inside diameter is Di = Do − 2t . It is useful also to define the mean diameter D = ( Do + Di ) 2 . For most cases t << D , so that Do ≈ D ≈ Di . The water depth is hw , and the vertical coordinate, measured as a depth below mudline, is z. The current embedment of the caisson is h and the height of the caisson is hc , see Figure 1. The unit weight of water is γ w and of the soil is γ . The buoyant unit weight of the soil is γ ′ = γ − γ w . Atmospheric pressure is p a . It is assumed that the net downward vertical load on the caisson, when it is submerged in water, is V ′ . This is the weight of the caisson, less any buoyant effects and any part of the weight supported by craneage, plus any applied downward loading e.g. from the weight of an attached structure. Note that V ′ will vary with the penetration of the caisson in some way that is unrelated to the following calculations, as more of the attached structure becomes submerged, and as the load taken by a crane is reduced. The caisson is assumed to be a simple cylinder, although in practice a number of complicating features are often employed such as: (a) vertical stiffeners attached to the inside of the caisson, (b) annular stiffeners attached to the inside of the caisson, (c) more complex designs such as stepped caissons.
Installation Calculations for Sand The installation process can be broken into two components; (a) self-weight penetration and (b) suction installation. The self-weight penetration in the absence of suction is important, as a seal is necessary at the edge of the foundation in order for the suction component to be performed adequately. The designer will need to understand the interaction between the soil density (and therefore peak friction angle), the skirt wall thickness and the effective vertical load (V’) acting on the foundation so that a sufficient penetration into the sand can be obtained. Once a seal can be assured the suction phase can be completed. The designer will need to predict the required suction as a function of depth of penetration. This information can be used to assess pump capacity, and the rate at which suction needs to be applied. The installation contractor will need to appreciate the implications of variations in applied suction, so that effective control of installation is achieved. If the suction is applied too quickly, then localised piping may occur. This could prevent full installation of the foundation. Finally the designer needs to be aware of any limitations to the design, such as the maximum aspect ratio that can be installed with suction whilst avoiding the possibility of liquefaction of the internal plug of soil. For the purposes calculation an idealised case of a foundation on a homogeneous deposit of sand (assumed drained) will be considered in this paper.
Self-weight penetration The resistance on the caisson is calculated as the sum of friction on outside and inside, and the end bearing on the annulus. The frictional terms are calculated in a similar way as in pile design, by calculating the vertical effective stress adjacent 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 . Note 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 2
K tan δ acting on the outside and inside of the caisson. The difference in the following analysis from conventional pile design is that the contribution of friction in enhancing the vertical stress further down the caisson is taken into account. The end bearing is taken as the sum of N q and N γ terms in the conventional way, and it is assumed that solutions for a strip footing of width t are appropriate for the caisson rim. If (following conventional pile design practice) no account is taken of the enhancement of vertical stress close to the pile due to the frictional forces further up the caisson, then the result for the vertical load on the caisson for penetration to depth h, in the absence of suction, is given by:
γ ′h 2 γ ′h 2 V ′ = (K tan δ )o (π Do ) + ( K tan δ)i (π Di ) 2 2 friction on outside
t + γ ′hN q + γ ′ N γ ( π Dt ) …(1) 2
friction on inside
end bearing on annulus
However, ignoring the enhancement of the stress in this case proves unconservative ( i.e. it would underestimate the force and suction required for full penetration), so we develop here a theory which takes this effect into account. Consider first the soil within the caisson. If we assume that the vertical effective stress is constant across the section of the caisson, then the vertical equilibrium equation for a disc of soil within the caisson (see Figure 2) leads to the equation: d σ ′v
= γ ′ +
dz
σ′v (K tan δ)i (π Di ) π Di2
= γ ′ +
4σ′v ( K tan δ)i Di
4
Writing Di (4(K tan δ )i ) = Z i this equation becomes
d σ′v dz
−
σ′v
…(2)
= γ ′ , which has the solution
Z i
′ i (exp( z Z i ) − 1) for σ′v = 0 at z = 0 . The total frictional terms in fact depend on the σ′v = γ Z integral h
of
the
vertical
effective
stress
with
′ i (exp(h Z i ) − 1 − (h Z i )) . For small h Z i ∫ σ′v dz = γ Z 2
depth,
and
we
can
also
obtain
the integral simplifies to γ ′h 2 2 .
0
A similar analysis follows for the stress on the outside of the caisson. If we make the assumption that the enhanced stress is constant between diameters Do and Dm = mDo , and further assume that there is no shear stress on vertical planes at diameter Dm , then we obtain the same results as for
(
)
inside the caisson, but with Z i replaced by Z o = Do m 2 − 1 (4(K tan δ )o ) . If
the
more
realistic 2
assumption
Z o = Do (1 + (2 f o z Do )) − 1 (4(K tan δ )o ) ,
d σ′v dz
−
σ′v Z o
and
Dm = Do + 2 f o z
an
analytical
is
solution
made to
the
then equation
= γ ′ cannot be obtained (or at the very least is not straightforward). The equation can,
however, readily be integrated numerically to give the variation of vertical stress with depth. If this approach is adopted then it would be consistent to assume that within the caisson at small z D the stress is only enhanced in an annulus between Dn and Di , where Dn = Di − 2 f i z . This leads to 2
Z i = Di 1 − (1 − (2 f i z Di ))
(4(K tan δ)i ) , and the differential equation for the vertical stress must 3
again be solved numerically. The resulting solution applies down to a value z = Di 2 f i , at which Dn = 0 . Below this the original expression for Z i is appropriate. In Equation (1) the end bearing term accounts for a triangular assumed stress distribution across the tip of the caisson, see Figure 3(a). Now that the stress inside and outside the caisson may be different, the assumed stress distribution across the tip of the caisson is as in Figure 3(b). The mean stress on the tip is calculated as follows. First determine σ′vo and σ′vi . For all likely combinations of parameters σ′vo < σ′vi ; because there is greater enhancement of the stress within the caisson 2tN γ rather than outside. If σ′vi − σ′vo < then the stress distribution is as shown in Figure 3(b) and N q
2 x 2 t (σ′vo − σ′vi ) N q N where x = + . σ′end = σ′vo N q + γ ′ t − γ ′ t 2 4 N γ γ If σ′vi − σ′vo ≥
2tN γ N q
then all the flow occurs outwards, x = 0 and σ′end = σ′vo N q + ′tN γ .
Accounting for these effects of stress enhancement, Equation (1) becomes modified to: h
h
∫
∫
V ′ = σ′vo dz (K tan δ)o (π Do ) + σ ′vi dz ( K tan δ)i ( π Di ) + σ′end ( π Dt ) 0
…(3)
0
In the special case where m is taken as a constant and uniform stress is assumed within the caisson this can be expressed as:
h h − 1 − (K tan δ)o (π Do ) ′ o2 exp V ′ = γ Z Z Z
o o h h ′ i2 exp − 1 − (K tan δ )i (π Di ) + σ′end (π Dt ) + γ Z Z i Z i
…(4)
Suction-assisted penetration 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 p a + γ w hw − s , then it is assumed that the excess pore pressure at the tip of the caisson is as , i.e. the absolute pressure is p a + γ w (hw + h) − as . There is therefore an average downward hydraulic gradient of as γ w h on the outside of the caisson and upward hydraulic gradient of (1 − a )s γ w h on the inside. Because the flow is more restricted inside the caisson than outside, a is expected to be a factor somewhat less than 0.5. Calculations for a are presented later in this paper. We assume that the distribution of pore pressure on the inside and outside of the caisson is linear with depth. 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 ′ − (1 − a ) s h inside the caisson. We further assume that the internal vertical effective stress is reduced sufficiently so that the failure mechanism involves movement of soil entirely inwards ( x = t in Figure 3(b)). The capacity, accounting for the pressure differential across the top of the caisson, is again calculated as the sum of the external and internal frictional terms, and the end bearing terms:
4
V ′ +
(
2 s π Di
h
) ∫
4 = σ′vo dz ( K tan δ )o (π Do ) 0
h
…(5)
+ ∫ σ′vi dz (K tan δ)i (π Di ) + (σ′vi N q + γ ′tN γ )(π Dt ) 0
Where in general the external and internal vertical stresses are determined by numerical integration using the modified values of the effective unit weight on the outside and inside of the caisson. In the special case where m is taken as a constant and uniform stress is assumed within the caisson this can be expressed as:
(
)
2 V ′ + s π Di 4 = γ ′ +
h as 2 h − 1 − (K tan δ)o (π Do ) Z o exp h Z o Z o
h h (1 − a )s 2 + γ ′ − Z i exp − 1 − (K tan δ)i (π Di ) h Z i Z i
…(6)
h (1 − a )s ′ + γ ′ − − + γ exp 1 Z N tN i γ (π Dt ) q h Z i Equations (5) and (6) are each linear equation in s, and can be used to solve for the suction required to achieve a penetration h. Note that because of the assumption of pure inward failure, Equation (6) does not reduce to exactly Equation (3) in the absence of suction. The difference, which is very small, can be resolved as
follows. Noting that σ ′vo = γ ′ + for σ′vo − σ′vi ≥
2tN γ N q
h h as (1 − a )s − 1 and σ′vi = − 1 , γ ′ − Z i exp Z o exp h h Z o Z i
then x = t and Equation (6) applies. For σ′vi − σ′v0 ≥
2tN γ N q
then x = 0 and
pure outward flow occurs, and the final term in Equation (6) should be replaced by
h γ ′ + as Z o exp − 1 N q + γ ′tN γ (π Dt ) . For intermediate cases the last term is replaced by h Z o 2 x 2 (σ′ − σ′vi ) N q N γ and x = t + vo σ′end (π Dt ) , where σ′end = σ′vo N q + γ ′ t − . ′ γ γ 2 4 t N It can be verified that there are smooth transitions between each of these conditions. In each case there is an equation that can be solved for s (for the intermediate case it is a quadratic, in the other cases linear). It can, however, easily be verified that that for most cases the outward flow and intermediate solutions only apply for a very small range of penetration at the beginning of the suction process, during which there is a transition in the flow direction of the sand. For practical purposes the transition phase can be ignored. If the sand is not homogeneous, but consists of a number of layers with different design values of γ ′ , φ′ and K tan δ , then the above calculation can be adapted in a reasonably straightforward way, although the integrals for the vertical stress solution become even more cumbersome. Of more significance could be changes of permeability with depth, since this might affect the pore pressure factor a. Caution should therefore be exercised in this case. 5
Limits to suction-assisted penetration As the suction is increased, the upward hydraulic gradient on the inside of the caisson approaches the value at which a piping failure might be induced. At this stage the vertical effective stress inside the caisson at the caisson tip (and in fact throughout the depth of the caisson) falls to zero. It is anticipated that if attempts were made to increase the suction further, local piping failures would be induced, possibly with a major inflow of water into the caisson, but without significant further penetration. This condition will occur when γ ′h − (1 − a )s = 0 , i.e. s = γ ′h (1 − a ) . Substituting this into the penetration equation (6) (for the simplified vertical stress distribution) and simplifying we obtain: 2 h h γ ′h π Di γ ′ − 1 − (K tan δ )o (π Do ) + (γ ′tN γ )(π Dt ) V ′ + Z o2 exp = Z (1 − a ) 4 (1 − a ) Z o o
…(7)
Solving the above equation for h leads to the maximum depth of penetration that can be achieved using suction. Note because the equation is transcendental in h, and the factor a is a function of h D , the equation needs to be solved iteratively. We can observe, however, that the last term is typically small. For small applied vertical loads V ′ , and taking Di ≈ D ≈ Do , the above leads to the simple solution 2 4(K tan δ)o Z o h h exp . If we ignore the effect of stress enhancement, i.e. for h= 1 − − D Z o Z o
h h h 2 D ≈ 1 h − − ≈ small h Z o , then exp and we obtain . This can be used Z 2 Z 2 K tan ( ) δ 2 Z o o o o to provide an initial estimate of the maximum achievable penetration with suction. Since K tan δ is often approximately 0.5, we conclude that in sand the limit on suction assisted penetration is likely to be of similar magnitude to the diameter. Note that this limit is much smaller than for installation in clays (Byrne and Houlsby, 2004). In fact a slightly more stringent limit on suction-assisted penetration can be established on the same basis as the “reverse bearing capacity” solution used for clays (Byrne and Houlsby, 2004). Again a plastic failure could occur with flow of soil into the caisson and without further penetration. This condition will occur when σ′vo = N q σ′vi . That is (for the simplified vertical stress distribution):
h h (1 − a )s ′ as γ + Z i exp − 1 = N q γ ′ − Z i exp − 1 h Z i h Z i
…(8)
Although Equation (12) provides a more conservative estimate of the limit of suction-assisted penetration, since N q is usually a large number (typically more than 30), in fact it differs very little from the condition γ ′h − (1 − a )s = 0 discussed above.
The effect of internal stiffeners The resistance of internal axial stiffening plates can be taken into account by adding resistance terms accounting for the friction and the end bearing on each plate. For the simplified vertical stress
h h ′ i2 exp − 1 − (K tan δ )s l , where l distribution the frictional terms will be of the form γ Z Z Z
i
i
is the perimeter length of the stiffeners, and the end bearing terms will be of the form 6
h t γ Z ′ i exp − 1 N q + γ ′ s N γ A , where t s is the stiffener thickness and A is the end area of 2 Z i the stiffener. Once suction is applied the friction term is modified by replacing γ ′ by ′ (1 − a )s and the end bearing expression becomes γ − , h t h γ ′ − (1 − a )s Z i exp − 1 N q + γ ′ s N γ A . Note the factor t s 2 in this expression rather 2 h Z i than t for the caisson wall: this is because the soil flows to either side of the stiffener. Furthermore Z i =
the
influence
π Di2
of
4(π Di (K tan δ )i + l ( K tan δ)s )
the
stiffeners
alters
the
expression
for
Z i
to
.
If the stiffeners do not extend to the base of the caisson then again corrections need to be made to the above expressions to account for this. It should be noted though that the calculations for the vertical effective stress at any level in the caisson then may involve rather cumbersome integrations. External stiffeners in sand would almost certainly cause problems during installation, as their tips would not be in the region where the effective stress is reduced. As a result they would attract a very large tip resistance. Annular stiffeners, which are often used for caissons in clay, would almost certainly prevent installation in sand.
Pressure factor a and flow calculations The factor a should be 0.5 for very shallow penetration in a soil of uniform permeability, and would be a function of h D . As suction is applied there is the possibility that the sand within the caisson becomes loosened and thus exhibits a higher permeability. For simplicity one can consider a permeability k o for the soil outside the caisson and k i > k o inside the caisson. The ratio k f = k i k o will affect the value of a .
Finite element analyses have been used to calculate the value of a in a soil of uniform permeability for a thin-walled caisson for values of h D up to 0.8 and for values of k f of 1, 2 and 5. The results of two separate studies (using slightly different mesh details, Aldwinkle (1994), Junaideen (2004))) are shown in Figure 4. An approximate fit for k f = 1 given by:
h a = a1 = c0 − c1 1 − exp − c2 D
…(9)
with the values c0 = 0.45 , c1 = 0.36 , c2 = 0.48 . This equation captures the trend of the calculations reasonably well, although for h D = 0 the value should theoretically be 0.5 and for very large h D the factor would be expected to tend to zero. The effects of different k f values can be accounted for by a simple calculation in which the head loss within the caisson is reduced in inverse proportion to the permeability. This results in:
7
a=
a1k f
(1 − a1 ) + ak f
…(10)
where a1 is the value from Equation 9. Figure 4 shows a comparison between calculated factors using Equations 9 and 10 and numerically calculated factors using finite element analysis. The flow beneath the caisson due to the suction can be determined using Darcy’s law as: k Ds q= o F
γ w
…(11)
where F is a dimensionless factor that depends on the ratios h D and k f . Calculated values of F using finite element analysis (Junaideen, 2004) are presented in Figure 5. If it is assumed that the excess pressure across the base of the caisson is uniform and of value − s (1 − a ) , then F can be estimated from the expression F = (1 − a )πk f
(4h D) . The faint lines in Figure 5 show the
computed F values from this expression with a determined by equations 9 and 10. It can be seen that at large h / D the results from the finite element analysis approach this value. This is because the assumption of uniform pressure across the base of the caisson is reasonable in this case, whilst at shallow depths there is a higher pressure towards the centre of the caisson, resulting in much higher flows. As an example of the flow calculation, for a caisson of diameter 6m penetrated 4m into a soil with a uniform permeability of 2 × 10 −4 m s , and with an applied suction of 58kPa the estimated flow would be
2 × 10 −4 × 6 × 58
× 0.85 = 0.006 m 3 s . If the caisson was installed to this depth in a period
10 of 2 hours, then the pumping rate simply to remove the water from the caisson would be
π × 32 × 4 = 0.016 m 3 s . Such a calculation can be used to assess the relative contributions of the 2 × 3600 two flow terms to the net required pumping capacity. The calculations described in the preceding sections have been implemented in a spreadsheet-based program “SCIP” (Suction Caisson Installation Prediction). This is used for the calculations in the examples below. In all these examples the diameter over which the vertical stress is enhanced varies linearly with depth ( i.e. the “loadspread” factors are f o = f i = 1 ).
Example 1: trial installations at Tenby and Sandy Haven Results are reported here of two trial installations of caissons made by Offshore Data Ltd at Tenby and Sandy Haven, on the south coast of Wales. At Tenby (Example 1a) a 2m diameter, 2m high caisson was installed in dense sand. Figure 6 shows a comparison between the calculated suction and the measured data. The data used for the computations in this and subsequent examples are given in Table 1. It can be seen that the observed suction against penetration response is fitted well, and that the limit to suction-assisted penetration of 1.4m is also fitted: at this depth no further penetration was observed in spite of an increase in suction. The second case (Example 1b) is a 4m diameter caisson, 2.5m high and with a wall thickness of 20mm, which was installed at Sandy Haven. Figure 7 presents the output from the SCIP program and compares it to the measured suction against penetration of the caisson. The suction increased approximately linearly with depth up to the full penetration of 2.5m.
8
The results from the SCIP program have been obtained by choosing parameters to fit the data best. The suction against depth curve (which is in fact almost a straight line) depends principally on the values of K tan δ and k f , and very little on other quantities. Clearly the above figures match very closely the observations at these sites, and all the figures in Table 1 are entirely plausible. Note that for the purposes of the installation a conservative calculation (somewhat unusually) will require higher estimates of the strength parameters than might be used for a capacity calculation.
Example 2: Draupner E As described in the introduction, this structure was installed by Statoil in 1994 and was the first jacket structure to be installed using suction caissons for the foundation. The soil conditions consist of a very dense sand, and a friction angle of 44 ° is estimated. As described by Tjelta (1994, 1995) the foundations consist of 12m diameter caissons of skirt length 6m. The wall thickness is taken to be 45mm. Tjelta (1995) describes the installation procedure and states that the self weight penetration was achieved by flooding the jacket legs, thereby increasing the submerged “weight” of the structure from 1350t to 2700t ( i.e. 6622kN per foundation). Internal stiffeners have been neglected as no information is available about the geometry. Figure 8 shows the predictions as given by the spreadsheet program SCIP compared to the range of field measurements as obtained on site for the four caissons and reported by Tjelta (1995). The permeability factor was taken as 3.0 to provide a good correlation between the case record and the calculated suction pressures.
Example 3: Sleipner T The Sleipner T structure was the second jacket to be installed by Statoil in the North Sea. The foundations are 15m in diameter and the skirt depth is 5m (Bye et al., 1995; Lacasse, 1999). The wall thickness is taken to be 45mm and again the internal stiffeners are neglected as there is insufficient information available on this detail. The soil conditions consist of a very dense sand, and a friction angle of 45 ° is used in the calculations. Lacasse (1999) presents measured data from the installation, which show that the self weight penetration is about 1.95m. It is possible to use this information to back-calculate the effective vertical load applied to each foundation as this is not given in the literature. An effective vertical load per foundation of 12MN gives the appropriate selfweight penetration, and this corresponds to a weight of the jacket of about 48MN, which is reasonable. Using the parameter values in Table 1 provides a good fit to the range of data on observed suction as reported by Lacasse (1999), as shown in Figure 9.
Example 4: Laboratory Tests This final example, shown in Figure 10, reports laboratory scale tests by Sanham (2003). The caisson foundation is 150mm in diameter with a skirt length of 200mm (so that, unlike the previous cases, the L/ D ratio is greater than 1). The applied vertical load in three tests reported here was 45N, 85N and 165N giving a self-weight penetration of approximately 28mm, 49mm and 79mm. In this particular case, due to the combination of the different variables, it is possible for the foundation to be installed, even though the L/ D ratio is greater than 1.0. Figure 10 shows the three suction against penetration curves, compared to the theoretical calculations. The SCIP calculation captures the trend of variation between the curves as a function of the applied load. The examples show that, with plausible choice of input parameters, the presented method of analysis fits case records of installation in sand well. It is appreciated that there are, of course a number of parameters on which the calculation depends, so that to a large extent this match can be 9
achieved by careful choice of parameters. For use as a predictive tool, experience needs to be gained on appropriate parameter selection.
Conclusions In this paper we present a series of design calculations that can used to assess the installation of skirted foundations installed into sand using suction. The calculations cover self-weight penetration, suction assisted penetration and an assessment of the limitations to the suction installation process. These calculations have been implemented in spreadsheet program to enable predictions of installation to be made. In the final part of the paper we compare the predictions with four case records, and a good agreement is found with the measured data .
Ac kn ow led gem ent s B.W.B. acknowledges generous support from Magdalen College, Oxford. The authors are grateful to Zeena Junaideen, who carried out the finite element calculations reported in Figures 4 and 5, and to Rob Ellis of Offshore Data Ltd for supplying the data used in Examples 1a and 1b.
Nomenclature
δ φ γ , γ ’ γ w σv, σv’
ratio of excess pore pressure at tip of caisson skirt to beneath the base caisson diameter rate of change of diameter that the vertical stress is enhanced installed depth of caisson height of water above mudline factor relating vertical stress to horizontal stress ratio of permeability within caisson to outside caisson (i.e. k f = k i/k o) caisson skirt depth perimeter length of stiffeners within caisson multiple of the diameter that the vertical stress is enhanced (i.e. Dm = mDo) bearing capacity factor (overburden) bearing capacity factor (self-weight) atmospheric pressure suction within the caisson with respect to the ambient seabed water pressure wall thickness vertical load, effective vertical load vertical coordinate below the mudline interface friction angle angle of friction of the soil unit weight of soil, effective unit weight of soil unit weight of water vertical stress, effective vertical stress
subscripts i o
inside caisson outside caisson
a D f h hw K k f L l m N q N γ pa s t V , V’ z
References Aldwinkle, C.G. (1994) “ The installation of offshore plated foundations for oil rig. ” Final Year Project Report, Department of Engineering Science, Oxford University Bye, A., Erbrich, C.T., Rognlien, B. and Tjelta, T.I. (1995) “Geotechnical design of bucket foundations” Paper OTC 7793, Offshore Technology Conference , Houston, Texas 10
Byrne, B.W. and Houlsby, G.T. (2002) “Experimental investigations of the response of suction caissons to transient vertical loading” Proc. ASCE, Journal of Geotechnical Engineering o 128, N 11, November, pp 926-939 Byrne, B.W. and Houlsby, G.T. (2003) “Foundations for offshore wind turbines” Philosophical Transactions of the Royal Society of London, Series A 361, December, pp 2909-2930 Byrne, B.W. and Houlsby, G.T. (2004) “Experimental investigations of the response of suction caissons to transient combined loading” Proc. ASCE, Journal of Geotechnical and o Geoenvironmental Engineering 130, N 3, March, pp 240-253 Erbrich, C.T. and Tjelta, T.I. (1999) “Installation of bucket foundations and suction caissons in sand – Geotechnical performance” Paper OTC 10990, Offshore Technology Conference , Houston, Texas Houlsby, G.T. and Byrne, B.W. (2004) “Design procedures for installation of suction caissons in clay and other materials” Submitted to Geotechnical Engineering Junaideen, Z. (2004) Private communication Lacasse, S. (1999) “Ninth OTRC Honors Lecture: Geotechnical contributions to offshore development” Paper OTC 10822, Offshore Technology Conference , Houston, Texas Sanham, S.C. (2003) “ Investigations into the installation of suction assisted caisson foundation. ” Final Year Project Report, Department of Engineering Science, Oxford University Tjelta, T.I. (1994) “Geotechnical aspects of bucket foundations replacing piles for the Europipe 16/11-E Jacket” Paper OTC 7379, Offshore Technology Conference , Houston, Texas Tjelta, T.I. (1995) “Geotechnical experience from the installation of the Europipe Jacket with bucket foundations” OTC 7795, Offshore Technology Conference , Houston, Texas
Table Exampl e
Location
D (m)
L (m)
t (mm)
1a Tenby 2.0 2.0 8 1b Sandy Haven 4.0 2.5 20 2 Draupner E 12.0 6.0 45 3 Sleipner T 15.0 5.0 45 4 Laboratory tests 0.15 0.2 1.65 Table 1: Data used for SCIP calculations
11
V ' (kN)
10 100 6622 12000 variable
φ′
′ 3
o
40 o 40 44 o o 45 o 45
(kN/m ) 8.5 8.5 8.5 8.5 8.5
K tan δ k i k o
0.48 0.48 0.63 0.8 0.45
3.0 2.0 3.0 3.0 2.5
Figures
V'
Mudline
hc
t
h
z
Di
Do
Figure 1: outline of suction caisson
σ'vπDi2/4 σ'v(Ktanδ)iπDidz γ '(πDi2/4)dz (σ'v + dσ'v)πDi2/4 Figure 2: equilibrium of slice of soil within caisson
t
σ'v
σ'v
σ'vo
t x
σ'vNq
σ'voNq
2γ 'Nγ
2γ 'Nγ 1
(a)
1 (b) Figure 3: stress distribution across tip of caisson
12
σ'vi
σ'viNq
0.9
Junaideen kf = 1 Junaideen kf = 2
0.8
Junaideen kf = 5 Aldwinkle kf = 1 Aldwinkle kf = 2
0.7
Aldwinkle kf = 5 Equation 9
a r o t c a f e r u s s e r p e r o P
Equations 9, 10 (kf = 2)
0.6
Equations 9, 10 (kf = 5)
0.5 0.4 0.3 0.2 0.1 0 0
0.2
0.4
0.6
0.8
1
Pentration h/D
Figure 4: variation of pore pressure parameter a with h D and k f
5 kf = 1
4.5
kf = 2 4
kf = 5
3.5 F r o t c a f
w o l f s s e l n o i s n e m i D
3 2.5 2 1.5 1 0.5 0 0
0.2
0.4
0.6
0.8
Penetration h/D
Figure 5: variation of dimensionless flow parameter F
13
1
Required suction s (kPa) 0
5
10
15
20
25
30
0 Suction
0.2
Maximum penetration 0.4
Tenby installation
0.6 ) 0.8 m ( z h 1 t p e D 1.2
1.4 1.6 1.8 2
Figure 6: Calculated suction and case record for Tenby installation, Example 1a
Required suction s (kPa) 0
10
20
30
40
50
0 Predicted suction 0.5
Sandy Haven installation
1 ) m ( z h t 1.5 p e D
2
2.5
3
Figure 7: Calculated suction and case record for Sandy Haven installation, Example 1b
14
Required suction s (kPa) 0
20
40
60
80
100
0
1 Predicted suction Range of measured suction 2 ) m ( h
3 h t p e D 4
5
6
Figure 8: Calculated and measured suction at Draupner E, Example 2
Required suction s (kPa) 0
20
40
60
80
100
0
1 Predicted suction Range of measured suction 2 ) m ( h
h 3 t p e D
4
5
6
Figure 9: Calculated and measured suction at Sleipner T, Example 3
15
