The bearing capacity of a circular footing under 'punch-through' failure By David Edwards, Dave Potts and Lidija Zdravkovic, Department of Civil and Environmental Engineering, Imperial College, London.
Rapid penetrations of offshore jack-up platform footings (spudcans) on layered clays are occurring approximately once a week. These events are due to several factors, one of which is the lack of accurate and robust design approaches for the bearing capacity of a circular footing on layered clays.
Finite element analysis has been used to undertake a parametric study of the bearing capacity of a circular footing on layered clays. By varying the depth of the strong layer and the ratio of the soil strengths, a reliable and safe formula has been proposed that is directly suitable for design.
Punch-through failures in the field Jack-up platforms are the most common type of oil rig in the world, with more than 400 in operation.
The key advantage over other platform types is their mobility and use at any number of different sites at water depths of up to 120m. This versatility has led to their use in a wide range of geographic and geotechnical conditions.
Modern jack-ups generally have three legs, each with a conical footing 15-20m in diameter, referred to as a 'spudcan'.
Upon arrival at a new site, the jack-up's spudcans are individually preloaded to a vertical load that exceeds the maximum predicted in service combined load by using the weight of the rig and sea water ballast tanks.
This load is typically calculated using foundation bearing capacity envelopes as speci. ed by the Society of Naval Architects and Marine Engineers (SNAME) (2002).
In the situation where the seabed consists of a stronger stratum overlying a weaker one, there is the potential for a 'punch-through' failure to occur.
Here the spudcan exerts a suf. ciently high load on the seabed such that the top layer under the footing, punches into the softer stratum.
This normally involves a rapid footing penetration of several metres in a matter of seconds (McClelland et al, 1981, notes one example of a leg penetrating 8.5m in less than 30s).
Osborne and Paisley (2002) classified these sudden settlements into two types: first if a catastrophic loss of the rig or its operability is incurred it is termed a punch-through failure; however, if no significant loss is incurred, it is preferable to refer to it as an 'uncontrolled penetration'.
The frequency of the latter is estimated at one case per week in south east Asia by Osborne & Paisley who also note the large discrepancy between the number of events and the number that are reported in technical papers.
The geotechnical conditions that cause most punch-throughs in south east Asia are described by Castleberry and Prebaharan (1985) as a historically desiccated clay layer overlying soft clay. The upper layer is between 1m and 8m thick and can possess an undrained strength of up to seven times that of the lower layer.
The work presented here is intended to clarify uncertainties involved in the analysis of foundation-bearing capacities in such layered clay stratigraphies that pose a 'punch-through' risk.
Existing design method
The SNAME (2002) design code for jack-up operations recommends the empirical method of Brown and Meyerhof (1969), Equation 1, for the calculation of a spudcan's bearing capacity in layered clays.
The method proposed expressions for 'modified bearing capacity factors', in the case of circular footings, based on 11 model footing tests.
Finite element analysis
Modelling of bearing capacity Spudcans are generally blunt conical footings with a typical cone angle of 150°. Based on the work of Houlsby and Martin (2003), it was considered an acceptable approximation to model the vertical bearing capacity of conical spudcans with a rough, rigid circular footing.
A single finite element mesh was used in all analyses, discretising half the soil domain to take advantage of the axis of rotational symmetry as shown in Figure 2. The remaining elements' dimensions were reduced in the vicinity of the footing to improve soil kinematics at the edge of the footing.
This enabled the bearing capacity factor for a rough circular footing on uniform clay to be determined within 1% of the exact solution, 6.052, of Eason and Shield (1960).
In all analyses the footing's full width or diameter was 20m, while the mesh was split into 12 horizontal layers whose properties could be individually specified to control the thickness of the strong upper layer to between 2m and 50m.
The footing was displaced vertically downwards and the reactions from the soil used to calculate the bearing load. This was continued until a clearly defined failure capacity was reached.
The finite element analyses have been performed with the Imperial College Finite Element Program (ICFEP). Eight noded isoparametric solid elements and six noded, zero thickness interface elements have been used with reduced integration. A modified Newton-Raphson approach with an error controlled sub-stepping stress point algorithm was used to solve the non-linear finite element equations (Potts and Zdravkovic, 1999).
The majority of punch-through failures occur during the installation phase that typically requires a day to complete per spudcan. In the case of a cohesive seabed, this implies the soil behaving in an undrained manner.
The Tresca elastoplastic soil model was thus chosen to represent the geotechnical behaviour of the seabed. More complex constitutive models were not considered due to the difficulties of obtaining the required soil parameters from standard offshore site investigations.
After consideration of punch-through failure case histories (for example, McClelland et al (1981)) and the geotechnical characterisation of south east Asian sea beds by Castleberry and Prebaharan (1985), the lower layer undrained strength was set at 30kPa, while strengths of 30-210kPa were specified for the upper layer. The soil's K o value was set to unity and the undrained Young's Modulus was maintained at 100MPa, with a Poisson's ratio of 0.499.
Results Strip footings
Before proceeding to analyse circular footings on layered clays, the back-analysed bearing capacity factors for strip footings were . rst validated against the upper and lower bounds of Meri. eld & Sloan (1999). In their work, results were presented as modi. ed bearing capacity factors as de. ned in Equation 3.
For each of the upper-layer thicknesses and ratios of layer strengths investigated, the N mc values obtained from the . nite element analyses were found to lie approximately midway between the upper and lower bounds of Meri. eld and Sloan, as illustrated for the case of H/B=0.5 in Figure 3.
This con. rms the validity of the approach undertaken and suggests that identical analyses with an axi-symmetric geometry will yield results of a similar accuracy and con. dence.
The predictions using Equation 1 of Brown and Meyerhof are also shown in Figure 3 for comparison. It is clear that at strength ratios greater than 1.7, this solution lies below the lower bound and is hence overly conservative.
From the results presented for circular footings in Figure 4, it can be seen that as the upper layer thickness increases, the ultimate bearing capacity increases to a maximum, limiting value. This upper limit of bearing capacity corresponds to the ultimate bearing capacity of the footing if there was no weaker sub-layer present. The bearing capacities are also proportional to the upper to lower layer strength ratio, S uu /S ul .The suite of bearing capacity curves in Figure 4 appear geometrically similar, and hence should reduce to one, fundamental curve when normalised. The (H/D) values are normalised with respect to the (H/D) Limit , which is characterised as the (H/D) value at which the lower, weaker clay does not in. uence the bearing capacity of the footing at the surface.
The (H/D) Limit values were calculated by locating the precise intersection of each curve with the corresponding maximum value of Q f and are found to vary with the ratio of clay layer strengths, as demonstrated in Figure 5, with a quadratic curve of best . t de. ned by Equation 4.
The bearing capacity values can similarly be normalised to 'r' values, as in Equation 5. Here 'r' relates the bearing capacity value in layered soils, Q f, to the capacity on a uniform soil of the upper clay strength and of the lower clay strength.
Thus if a footing was located on a very thin, strong layer, its bearing capacity would be approximately equal to a footing on the lower, weaker clay, hence r would approach zero. Conversely, if the footing was located on a layer of in. nite thickness, its bearing capacity would equal that of the upper layer only, and r would equal unity.
Figure 6 con. rms that the data points presented in Figure 4 lie on a wellde. ned line, which can be approximated by Equation 8.
By equating Equations 5 and 8, one can deduce a relationship for Qf as in Equation 9 below, that can be used in design.
The results of a parametric study of the bearing capacity of circular footings on layered clays where there is a risk of punch-through failure have been presented.
The data generated have shown existing methods of analysis to predict overly conservative foundation capacities.
This opportunity for improved ef' ciency in foundation design has led to the formulation of a new design approach, based on careful numerical analyses, for circular footings relevant to spudcans. The errors in the bearingcapacity predictions using the method proposed here have been shown to be signi'cantly less than the existing design code.
The work presented here, however, does not account for the high number of uncontrolled leg penetrations that are occurring in practice.
The conservatism of the current design codes would suggest that the major cause of these incidents in layered clays, may be the lack of a suitable site investigation before jack-up installation.
Brown J and Meyerhof G (1969). Experimental study of bearing capacity in layered clays, Proc. of the 7th int conf on soil mech and foundation eng 2.
Castleberry J and Prebaharan N (1985). Clay crusts of the Sunda Shelf - a hazard to jack-up operations, 8th South east Asia geotechnical conf.
Eason G and Shield R (1960) The plastic indentation of a semi-in' nite solid by a perfectly rough circular punch, Journal of Applied Mathematics and Physics (ZAMP), Vol. 11 Houlsby G and Martin C (2003). Undrained bearing capacity factors for conical footings on clay, Géotechnique, 53(5) McClelland B, Young A and Remmes B (1981). Avoiding jack-up rig foundation failures, Proc. of the symp. on geotechnical aspects of coastal and offshore structures, Bangkok.
Merifield R, Sloan S and Yu H (1999). Rigorous plasticity solutions for the bearing capacity of twolayered clays, Géotechnique, 49 5 471-490 Osborne J and Paisley J (2002). South east Asia jack-up punch-throughs: the way forward- , Proc of the conf on offshore site investigation and geotechnics - sustainability and diversity, London.
Potts DM and Zdravkovic L (1999). Finite element analysis in geotechnical engineering. London:
Skempton A (1951). The bearing capacity of clays, Building Research Congress, London 1 SNAME (2002). Guidelines for site specific assessment of mobile jack-up units - SNAME 5-5A - Revision 2