# S Wang Beca Consultants, Wellington, NZ (formerly University of Auckland, NZ)

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2 springs, while t-z springs act in simulating shaft friction. Additionally, the pile tip response is represented using a q-z spring. These springs are linked to slave nodes which are subsequently constrained to pile nodes via equal constraints. Forces or displacements can be imposed upon either the pile or fixed soil nodes emulating a range of loading scenarios. p-y spring t-z spring Equal DOF Slave soil node Pile node Fixed soil node Pile element q-z spring Figure 1. Definition of FE model implemented within OpenSees. The various components of the model, which is based on the work by McGann et al. (2011), are outlined in Figure 1. Full details of the modelling and relevant equations are available in Wang and Orense (2013). 2.1 Modelling of p-y springs p-y curves form the basis in simulating the horizontal response of the soil. OpenSees requires definition of both the ultimate lateral resistance ( ) and the displacement at which 50% of the ultimate lateral resistance is mobilized in monotonic loading ( ) Definition of backbone resistance curve The backbone curve is modelled on formulae established by Hansen and Christensen (1961). The resultant pressure (passive minus active pressure) per front area of the pile governing the ultimate lateral resistance in terms of depth is generalized as: (1) where is the effective overburden pressure and the cohesion. and are parameters relating to pressure at an arbitrary depth and are dependent solely on the angle of internal friction ( ). The distribution of initial stiffness ( ) is necessary to compute the displacement. For sands, this stiffness is dependent upon and on location of the soil with respect to the water table. The curves specified by the American Petroleum Institute (API, 1987) are used for this purpose. The continuous function of the p-y relation in the form of a hyperbolic tangent proposed by McGann et al. (2012) is employed Modification for influence of liquefaction Although dramatic reductions in initial stiffness and ultimate lateral resistance occur within liquefied layers, McGann et al. (2012) has shown that non-liquefied soil at the layer interface will also experience significant reductions in shear strength. Therefore, the reduction in and for these regions must also be accounted for. This is achieved through modifying the p-y relationship through ratios which are functions of depth. These ratios when applied to or values in their homogenous state will capture its liquefied profile.

4 The experiment was simulated for pile head loads of 116kN and 251kN within OpenSees. The soil was assumed a submerged unit weight of 10kN/m 3 with an angle of internal friction of 30 o. Figure 2 shows theoretical results produced from OpenSees. It can be seen that the overall shape of the bending moment curve is adequately captured in both cases with the location of the maximum negative moment being represented fairly accurately via the FE model. Moment magnitudes produced theoretically for the 116kN case are also consistent with that of its experimental counterpart. However, the model slightly overestimated the maximum negative moment for the 251kN case. Figure 2. Bending moment distribution for (a) lateral load of 116kN (26kip); and (b) 251 kn (56.5 kip) computed via OpenSees. The experimental results were extracted from Liu and Dobry (1995). 3.2 Vertical pile subject to lateral spreading The 1995 Kobe earthquake resulted in an oil storage tank supported by 69 concrete piles experiencing permanent displacements due to lateral spreading of the ground of up to 55cm. The piles measure 45cm in diameter and extend 23 meters into the ground. One such pile in particular located on the rim was displaced by 40cm of which was extensively studied by Ishihara and Cubrinovski (2004). Additionally, the pile response for a free-field displacement of 30cm has also been investigated. An equivalent linear analysis procedure was adopted by Ishihara and Cubrinovski (2004) in investigation of the pile giving displacements and bending moments along its depth for both ground displacement cases (Figure 3). The soil profile consists of a 2.5m surface layer overlaying a deposit of liquefiable sand 11m thick. The response of the liquefied soil is characterized via an equivalent linear function subject to a degradation factor, of 0.01 and This pressure displacement relationship is held constant throughout the liquefied layer. The distribution of lateral spreading is held constant within the unliquefiable crust while following that of a cosine curve throughout the liquefied layer. The concrete pile section was represented via a tri-linear M-Φ relationship typical to that of a pre-stressed high-strength concrete pile.

7 and modified API procedure also observes an increase in the ultimate lateral resistance with depth. As this relation is effectively constant for the method adopted by Ishihara and Cubrinovski (2004) in any given soil layer, minor discrepancies between the two analyses are expected. Use of a bi-linear M-Φ relation representing only up to the yield point of the concrete pile proved adequate for this case. This is most likely due to the fact that the moments experienced by the pile did not greatly exceed the yield range. Hence, it was not critical to define the third linear gradient leading to the ultimate moment. However, if free-field displacements of greater magnitude were to be analysed, the FE model would likely overestimate the bending moment as the pile curvature extends past its point of yielding; this case would indicate pile breakage. 4.2 Extension to raked piles After full-validation, the model developed has been extended to analyse the response of inclined/raked piles. Analysis of centrifuge tests involving single inclined piles and actual case histories such as the Landing Road Bridge response during the 1987 Edgecumbe earthquake (Wang and Orense, 2013) successfully demonstrated excellent performance of the model. 4.3 Limitations Several limitations surround the proposed FE model in evaluating the performance of pile foundations. Firstly, the validity of vertical springs has not been fully justified through tests involving purely axial loads. 5 CONCLUDING REMARKS A 2D BNWF finite element model to be implemented via OpenSees has been created. This allows for the simulation of pile foundations subject to the effects of liquefaction. The model has been compared against experimental data and with an alternative equivalent linear analysis procedure. The model can be used to analyse different scenarios involving piles subjected to laterally spreading soils. The Brinch Hansen curve combined with the modified API distribution for proved capable in simulating the behaviour of non-liquefied soil. The effects of lateral spreading due to soil liquefaction can be adequately incorporated using stiffness and resistance reduction factors. The free field soil deflection profile selected for the liquefied layer greatly affects the distribution of pile displacement and bending moment. Use of a linear profile produces lower deflections along the depth of the pile while giving larger moments at the pile head. 6 REFERENCES American Petroleum Institute, A.P.I. (1987). Recommended Practice for Planning, Designing and Constructing Fixed Offshore Platforms. API Recommended Practice 2A (RP-2A). Washington D.C. Bowen, H. J. & Cubrinovski, M. (2008). Pseudo-static analysis of piles in liquefiable soils: Parametric evaluation of liquefied layer properties. Bulletin of the New Zealand Society for Earthquake Engineering, 41. Finn, W. D. L. & Fujita, N. (2002). Piles in liquefiable soils: Seismic analysis and design issues. Soil Dynamics and Earthquake Engineering, 22, Hansen, J. B. & Christensen, N. H. (1961). The ultimate resistance of rigid piles against transversal forces. Bulletin No. 12. Geoteknisk Institute, Copenhagen.

8 Ishihara, K. & Cubrinovski, M. (2004). Case studies of pile foundations undergoing lateral spreading in liquefied deposits. Fifth International Conference on Case Histories in Geotechnical Engineering. New York, NY. Kulhawy, F. H. (1991). Drilled Shaft Foundations. In: FANG, H.-Y. (ed.) Foundation Engineering Handbook, 2nd Edition. Van Nostrand Reinhold, New York. Liu, L. & Dobry, R. (1995). Effect of liquefaction on lateral response of piles by centrifuge model tests. NCEER Bulletin, January Mazzoni, S., McKenna, F., & Fenves, G. L. (2011). OpenSees getting started manual. McGann, C. R., Arduino, P. & Mackenzie-Helnwein, P. (2011). Applicability of conventional p-y relations to the analysis of piles in laterally spreading soil. Journal of Geotechnical and Geoenvironmental Engineering, 137, McGann, C. R., Arduino, P. & Mackenzie-Helnwein, P. (2012). Simplified procedure to account for a weaker soil layer in lateral load analysis of single piles. Journal of Geotechnical and Geoenvironmental Engineering, 138, Meyerhof, G. G. (1976). Bearing capacity and settlement of pile foundations. Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 102, Mosher, R. L. & Dawkins, W. P. (2000). Theoretical Manual for Pile Foundations. Washington D.C.: US Army Corps of Engineers, Engineer Research and Development Center. Tokimatsu, K. (2007). Earthquake Resistant Bases and Foundations, Chap 4. In: Horikawa, K. (ed.) Civil Engineering, Vol 1. Encyclopedia of Life Support Systems (EOLSS). Vijayvergiya, V. N. (1977). Load-movement characteristics of piles. Proc., Ports 77 Conference. New York Wang, S. & Orense, R.P. (2013). Modelling of raked pile foundations in liquefiable ground. Soil Dynamics and Earthquake Engineering (submitted).

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