Finite Element Analysis of Screw Piles

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1 1 st Civil and Environmental Engineering Student Conference June 2012 Imperial College London Finite Element Analysis of Screw Piles J. Woodcock ABSTRACT Screw piles are a seldom researched area of geotechnical engineering, despite simple design methods which should see them more commonly utilised. This paper uses finite element analysis to characterise screw pile behaviour when used in softening, undrained clay, concentrating on peak load and displacement. Parameters describing the softening of the clay were varied, as well as certain geometrical parameters of the screw piles themselves. Analyses were run where only one parameter was changed and then compared to a base case. The study found that the shaft stiffness of the pile and brittleness index of the soil have the greatest effect on peak load while soil softening ratio and pile length have only a minor effect. Piles which fail by the cylinder mechanism require the lowest displacement to reach their ultimate load. 1. INTRODUCTION A typical screw pile consists of a hollow or solid shaft to which are attached several helical plates of a chosen size and spacing. They are installed by applying a torque, screwing them down into the ground like an auger, hence the name. Key geometric parameters of a screw pile are labelled in Figure 1: pile length (L), embedment depth (L e ), shaft diameter (D s ), helical plate diameter (D h ), plate spacing (s), plate pitch (p), plate section length (L h ) and heading (h). Other important parameters are the embedment ratio (L e /D h ) and the spacing ratio (s/d h ). piles, assessing the most appropriate design methodology for both tension and compression piles in ideally plastic soil before examining the behaviour of screw piles in strain softening soil which does not appear to have been researched at all. In the interests of space, only the results of the analyses in softening soil are given in detail. The program ICFEP (Imperial College Finite Element Program) (Potts & Zdravković, 1999) has been used for all analyses. Capable of sustaining compression and tension, screw piles are often used to support modest loads and are most often used as a foundation for transmission towers, residential projects, underpins or tie-back anchors for excavations (Perko, 2009). Arup Geotechnics (2005) provides a list of the advantages of using screw piles including quick, spoil-free installation and the possibility of removal/reuse. Screw piles fail by one of two failure mechanisms: either each helical plate fails in individual bearing (with a contribution from shaft friction) or the top and bottom plates enclose a cylinder of soil which resists loading through shear on its sides (alongside shaft friction and some end-bearing) Perko (2009). Well-known bearing capacity and shaft friction expressions can be used to predict the capacity of each. The main reason for studying screw piles is the limited official instruction in their design and use (at least in the UK, where they are barely mentioned in industry standards (BSI, 1986; BSI, 1995)). This project aims to give a definitive answer to contradictory research on the subject of screw 1 Figure 1, Schematic of a screw pile labelling important geometrical parameters. Adapted from Narasimha Rao et al (1991) 2. FINITE ELEMENT MODEL The geometry of the screw pile was approximated as axisymmetric, hence the pitch of the plates was zero. A mesh was designed for a pile of 21m length

2 but was also cropped to allow a 9m pile to be analysed as well. The mesh can be seen in Figure 2. One-dimensional beam elements were used to model the helical plates. Piles with 13, 7, 5, 4, 3, 2 and zero plates were analysed. The other geometrical parameters of the pile were as follows: h=0, D s =0.2m, D h =0.6m, L h =7.2m and L e =13.8/1.8m for the long and short piles respectively. To prevent geotechnical behaviour being limited by structural failure, a linear elastic model (i.e. with no failure criterion) was used for the pile with a Young s Modulus, E, of 200GPa and Poisson s Ratio, μ, of 0.3. In order to model a pile with a tubular shaft, the properties of a tubular pile were smeared across the solid shaft, resulting in a Young s Modulus of 20GPa. The pile-soil interface was modelled as rough. The soil was analysed using the Tresca failure criterion. The constitutive behaviour was initially ideal elastic-plastic but a softening rule was later added for analyses concerning strain-softening soil. The undrained strength of the soil was 100kPa. A strength profile which increased linearly with depth was also analysed but the results were not markedly dissimilar to those presented here. Other soil parameters specified were: unit weight, γ, of 20kN/m 3, coefficient of earth pressure at rest, K 0, of 1 and a Poisson s Ratio, µ s, of (reflecting the undrained nature of the loading). The softening rule for the soil was as follows: peak strength (S u,p ) was reached at the yield and maintained for 2% plastic deviatoric strain before softening linearly, reaching its residual strength (S u,r ) at a strain level (γ r ) which was varied (3, 5, and 10% plastic deviatoric strain). The value of the residual strength was also varied. The left boundary of the mesh in Figure 2 was the axis of rotational symmetry so had to be restrained in the horizontal (r) direction. It was left free to move in the vertical (z) direction. Identical, conditions applied on the right-hand boundary. The bottom boundary was restrained in both the radial and vertical directions. The top boundary was unrestrained. Displacement was applied incrementally to the top of the pile. 150 equal increments of 1mm were applied as standard the exact number was sometimes varied if the pile reached its capacity particularly quickly. 3. SUMMARY OF RESULTS FOR IDEALLY PLASTIC SOIL These analyses were used to find the most appropriate depth and shape factors for predicting the capacity of the screw piles. Over the range of depths investigated, the depth and shape factors of Salgado et al (2004) were found to be best for piles in compression; the uplift factors of Rowe & Davis (1982) and the shape factor of Eason & Shield (1960) were found to be best for piles in uplift. It was also found that shaft friction between the plates had to be accounted for (for piles which failed by the individual bearing mechanism). The most important finding, however, was that the failure mechanism of the pile is governed by the failure mechanism which has the minimum capacity i.e. piles with fewer plates failed in individual bearing. This is contrary to the work of many papers, for example Narasimha Rao et al (1991), who say there is a given spacing ratio (see Section 1) at which the failure mechanism changes. In particular, taking the value of this critical spacing ratio from Narasimha Rao et al (1991) was found to overestimate the capacity by a factor of close to 2 in some cases. Note that the spacing ratio has an indirect effect on capacity as, for constant L h, the spacing ratio determines the number of plates, however, the author feels taking the minimum capacity to be a much more intuitive proposition. Figure 2, The mesh for a long pile analysed by ICFEP 4. RESULTS AND DISCUSSION FOR SOFTENING SOIL 4.1 PREDICTING CAPACITY The methods used for ideally plastic soil cannot account for softening behaviour (Dounias et al, 1988). Reduction factors are available for shaft friction and bearing but clearly there is no reason to think the peak capacity of the screw pile is the sum of the peaks of the two components. Consequently, reduction factors will have to be developed 2

3 especially for screw piles. This requires use of the results for the ideally plastic soil. The ratio of the peak load of a pile in softening soil to its ultimate load in ideally plastic soil with equal peak strength is the reduction factor, η. The standards expressions mentioned before were found to be accurate in predicting the residual load of the screw piles by treating the soil as ideally plastic with strength equal to the residual strength of the softening soil. 4.2 OBSERVED FAILURE LOADS AND MECHANISMS Figure 3 shows the load displacement curves for 21m, tubular-shafted screw piles in uniform strength softening soil (with γ r =5%, S u,p =100kPa, S u,r =50kPa) with varying number of plates. It can be seen that those with 13, 7, 5 and 4 plates tend to a common residual load. Note also, that their peak loads are all approximately equal and are achieved at similar values of displacement. Vector plots of displacement show that each fails by the cylinder mechanism explaining why they have the same ultimate load. The residual loads for 2- and 3-plate piles each tend to unique values, failing by the individual bearing mechanism explaining why the ultimate loads are different. The actual expression which predicts the failure load and mechanism was found to generally be the one which predicted the lower capacity. 4.3 EFFECT OF PILE STIFFNESS AND SOIL BRITTLENESS INDEX Murff (1980) recognises that the axial stiffness of a straight-shafted pile affects its load-displacement behaviour and its peak load. The results of this investigation show the same is true for screw piles but only for piles which fail by the cylinder mechanism. Figure 4 demonstrates this: the 13- plate pile with a solid-shaft exhibits a substantially larger peak, though this was seen to fall towards the same value as the tubular pile as the number of plates was reduced. The 2-plate pile shows no discernible difference in peak load when shaft stiffness is increased. Values of η can now begin to be calculated. The ultimate capacities of identical piles in ideally plastic soil (analyses whose results are not shown here), can be compared to the peak loads for piles in softening soil. Note that this cannot simply be plotted against the number of piles. To demonstrate why, imagine, say, a 3-plate pile. For large enough L h, the capacity of the cylinder mechanism is greater than that of the individual bearing mechanism, so the failure will be in bearing. If L h is smaller, the cylinder mechanism capacity is also smaller, with the bearing capacity of the individual plates relatively unchanged. Eventually, at a certain value of L h, the failure mechanism will switch. Therefore, the number of plates does not uniquely describe the behaviour of the screw piles. A measure is required that takes into account the full geometry of the piles. The results from the long, tubular pile in soil (with the softening rule as described above) will be the base case against which the effect of other parameters will be measured. Figure 4, Effect of shaft stiffness on load displacement curves of long piles in softening soil. Figure 3, Load-displacement curve (long, tubular pile, uniform strength, softening soil) This is achieved by taking the ratio of the predicted residual capacity of the individual bearing mechanism and the cylinder mechanism. This mechanism capacity ratio (MCR) has a value greater than one for piles which fail by the cylinder mechanism and less than one for piles. This is obviously dependent on the accuracy of the equations, which was generally high enough to correctly predict the failure mechanism. The pile geometry of the screw piles was not greatly varied 3

4 so extra research would be prudent to assess the generality of this measure. The same was done for piles in soil where the brittleness index (as defined by Bishop (1967) and cited in Bishop (1971)) was varied, by increasing the residual strength from 50 to 75kPa (giving values of brittleness index, I B, of 100% and 33.33% respectively). The results of these variations can be seen individually compared to the base case (long, tubular pile in soil with residual strength of 50kPa) in Figures 5 and EFFECT OF PILE LENGTH AND SOFTENING RATIO The definition of softening ratio adopted here is that of Kalteziotis et al (1984): the ratio of the Young s Modulus of the Soil to the gradient of the stress strain curve as it drops from peak to residual strength. Therefore, smaller values of γ r yield a steeper gradient and a lower softening ratio, S R. The variation of γ r gives softening ratios of 3, 8.7 and 23. A higher softening ratio was found, however, to increase η by only a small amount. It was still found to be constant with MCR. Similarly, the shorter piles tested had only marginally higher peaks than the longer piles. 4.5 PILE SERVICEABILITY It is useful to know at what displacement screw piles achieve their peak loads so that the serviceability limit of the pile can be ascertained. Figure 5, Comparison of η against MCR for base case and pile with stiffer shaft Figure 7 shows the displacement at which screw piles reached their peak loads plotted against MCR. It is clear that piles which fail by the cylinder mechanism achieve their peak load at a significantly smaller displacement; therefore they are less likely to have their load limited by settlement criteria. The stiffness of the pile shaft also has a significant effect on the displacement required to mobilise the peak load but this effect is actually dependent on the length of the pile (notice how the close together the points for short tubular and short solid shafts are). Figure 6, Comparison of η against MCR for tubular piles in soil with varying residual strength The most striking features of these Figures are: η is constant at around 0.6 for the tubular pile when I B is 100% and 0.8 when I B is 33.33%; pile stiffness makes no difference to the peak load when MCR<1; η for the solid-shaft pile may be levelling off at a value close to 0.8 though more data points are required to verify this. Note that installation of the pile was not modelled so the pile-soil interface stress followed the full stress-strain curve (i.e. stress increased to a peak and then softened). In reality, the installation of the pile would reduce the strength of the interface to residual. This could be achieved in future analyses by using zero-thickness interface elements which would limit the stress to a certain proportion of the residual strength. Figure 7, Displacement at peak load for piles in softening soil with variety of lengths and shaft stiffness 5. CONCLUSIONS To summarise the findings of this paper, there is a great variety of variables in the analysis of screw piles in softening soil: the softening parameters of the soil itself as well as the large array of geometrical parameters detailed in Figure 1. Of the parameters which were investigated, the ones 4

5 which affected the screw pile capacity the most were the pile shaft stiffness and brittleness index. However, the effects of these were examined independently the effect of altering combinations of parameters was not investigated. Additionally, not all parameters were varied; the geometry of the piles was largely kept the same and the strain at which softening began was not changed. The biggest factors in the pile displacement at peak load were the failure mechanism, shaft stiffness and length. Piles which failed by the cylinder mechanism reached their peak at considerably lower displacements than those which failed by the individual bearing mechanism (with all other parameters equal). Perko, H.A. (2009), Helical Piles: A Practical Guide to Design and Installation, New Jersey, John Wiley & Sons Potts, D.M. & Zdravković, L., (1999), Finite Element Analysis in Geotechnical Engineering - Theory, London, Thomas Telford Ltd. Rowe, R.K. & Davis, E.H. (1982) The behaviour of anchor plates in clay, Géotechnique, 32 (1) 9 23 Salgado, R., Lyamin, A. V., Sloan, S. W. & Yu, H. S. (2004) Two- and three- dimensional bearing capacity of foundations in clay, Géotechnique 54 (5) The Mechanism Capacity Ratio is suggested as a non-dimensional measure of screw pile geometry and failure mechanism though more analyses are recommended in which the pile geometry is varied. 6. ACKNOWLEDGEMENTS The author thanks Dr. Lidija Zdravković for her considerable help throughout this project. 7. REFERENCES Arup Geotechnics (2005) Screwfast Foundations Ltd. Design of Screw Piles: Assessment of Design Methodology, Ove Arup & Partners Ltd. Bishop, A.W. (1971) The influence of progressive failure on the choice of the method of stability analysis, Géotechnique, 21 (2) British Standards Institution (1986) BS 8004:1986, Code of Practice for Foundations, London, BSI. British Standards Institution (1995) DD ENV :1995, Eurocode 7: Geotechnical Design. Part 1: General Rules (together with United Kingdom National Application Document), London, BSI. Eason, G. & Shield, R.T. (1960) The Plastic Indentation of a Semi-Infinite Solid by a Perfectly Rough Circular Punch, Zeitschrift für angewandte Mathematik und Physik, 11 (1) Kalteziotis, N.A., Menzies, B.K. & Tarzi, A.I. (1984) A bearing capacity correction for strain-softening, saturated clays, Ground Engineering, 17 (5) Murff, J.D. (1980) Pile capacity in a softening soil, International Journal for Numerical and Analytical Methods in Geomechanics, 4 (2) Narasimha Rao, S., Prasad, Y.S.V.N. & Dinakara Shetty, M. (1991) The behaviour of model screw piles in cohesive soils, Soils and Foundations, 31 (2)