Keywords: axisymmetric, non-linear analysis, pile, uplift, sand.

The behaviour of single straight-shafted piles subject to uplift in cohesionless soil is investigated numerically by finite element analysis and by physical modelling in a geotechnical centrifuge.The prototype piles modelled in the centrifuge were 0.5 and 1m in diameter and up to 9m in length, embedded in nominally dense and loose sand strata. The uplift behaviour of 1m diameter piles up to 11m in length in loose and dense sand was investigated theoretically using an axisymmetric non-linear finite element program SOSTAX.

The constitutive soil model utilised in the numerical modelling was the well-established variable elastic hyperbolic model from the work of Duncan and Chang [1]. The model parameters relating to first time loading, and unloading/reloading were determined from triaxial compression tests on the sand involved. The mesh comprised 19 medium elements in the horizontal direction while the number in the vertical direction ranged up to 21 depending on the length of the pile. The pile was enclosed by a vertical column of friction elements of zero width linking the soil to the pile. For continuity of mesh these elements extended from the soil surface to the lower boundary of the mesh. They were made stiff in tangential and normal directions in regions below the pile, so that they effectively joined together the soil elements on either side. The behaviour of the friction interface elements was determined by assuming hyperbolic relationships between shear stress and relative displacement based on the work of Clough and Duncan [2] and Goodman et al. [3]. All nodes on the lower boundary of the mesh were restrained in the vertical direction and allowed to slide horizontally, while nodes on the side boundary were restrained horizontally with vertical movement being permitted.

Uplift loads were applied in a number of increments with relatively large increments at lower stress levels and small increments at higher stress levels. Two analyses were carried out for each increment, initially using the parameters assigned after the previous increment and a second time using the parameters based on the average stresses appropriate to first time loading, unloading or reloading in each element. The criterion for distinguishing first time loading from unloading or reloading was the reciprocal factor of safety RFOS [4] defined by the ratio between current and maximum shear stress for a particular element. The elastic unloading-reloading modulus was used for calculating the stress-strain matrices when RFOS was less than the previous maximum value. Piles exhibited a rapid increase in resistance with vertical displacement followed by a clearly defined `yield' point after which considerably larger displacements occurred with further increase in load. Pile length/diameter ratio, sand packing and initial stress state were all found to influence the pullout response significantly.

In the centrifuge tests piles embedded in dense sand also mobilised their maximum uplift capacities after a small movement of between 0.5mm and 1mm. In all cases further movement produced a steady reduction in uplift resistance. The reduction in the case of the shortest piles was considerable and could be attributed to the collapse of sand into the gap formed below the pile as the test proceeded. Uplift resistances, expressed dimensionlessly as breakout factors, increased markedly with length/diameter ratio and sand packing. Breakout factors for 0.5m diameter prototype piles were slightly higher than those for 1m diameter piles indicating a relatively minor influence of size. Failure displacements normalised to pile diameter generally increased with pile embedment ratio and pile diameter.

Good agreement was found between uplift capacities from the SOSTAX finite element and the centrifuge predictions for 1m diameter prototype piles. Also data from field tests on drilled piers in dense sand matched experimental results well. The experimental results showed a significant post-peak reduction in uplift resistance. This was not obtained in the theoretical predictions due to the inability of the soil model to reproduce this post-peak softening behaviour. This region of the uplift load/displacement response is not however of great interest since the piles have then failed. Failure displacements were considerably smaller in the finite element analyses than predicted by centrifuge tests and further investigation is in progress on this point.

1

J.M. Duncan, C.Y. Chang, "Non-linear analysis of stress and strain in soils", Journal of Soil Mechanics and Foundations Division, ASCE, 96, 1629- 1653,1970.

2

R.W. Clough, J.M. Duncan, "Finite element analysis of retaining wall behaviour", Journal of Soil Mechanics and Foundations Division, ASCE,97,1657-1673,1971.

3

R.E. Goodman, R.L. Taylor, T.L. Brekke, "A model for the mechanics of jointed rock", Journal of Soil Mechanics and Foundations Division, ASCE, 94,637- 659,1968.

4

E.A. Dickin, G.J.W. King, "Numerical modelling of the load-displacement of anchor walls", Computers and Structures, 63(4), 849-858, 1997. doi:10.1016/S0045-7949(96)00066-1

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