As an early work in this area, Salas and Belzunce (1965) presented theoretical solutions based on Elastic theory which assumes that the soil behavior can be characterized by a Boussinesq half-space. The effect of pile compressibility was not taken into account in the approach.
The analyses presented by Poulos and Mattes (1969), Poulos and Davis (1972, 1975), Kuwabara and Poulos (1989) could be classified under the simplified boundary
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element approach. In this technique, the pile is discretized into small segments using the finite element method or finite difference technique while treating the soil as an elastic continuum which is only discretized at the pile-soil interface. The load- displacement relationship of the system is formulated by considering the equilibrium of the pile-soil interaction forces and the compatibility of the pile and soil displacements. The continuum approach adopted by Poulos and his co-workers is restricted to end-bearing piles based on “mirror-image” technique using the Mindlin’s equation (Mindlin, 1936). The role of this “mirror-image” technique is to enforce zero vertical displacement at the pile base thus satisfying the boundary condition of a rigid bearing stratum since Mindlin’s solution is only strictly valid for a homogeneous, isotropic elastic half-space. Similar imaging technique to enforce zero pile toe settlement was adopted by Teh and Wong (1995) in their proposed simplified elastic interaction procedure for the analysis of the variations of downdrag forces in pile groups. The governing equations which take into account pile-soil slip are derived explicitly. It was demonstrated that the number of iterations required to achieve a solution is small and is not dependent on the magnitude of the soil settlement. Hence, the approach can be more economical than the various incremental methods.
Ng et al. (1976) used the solutions of Chan et al. (1974) for a point force in a two- layer system to consider the compressibility influence of underlying layer on piles subjected to negative skin friction but the pile was terminated at the interface of the two layers in the study. In the analysis proposed by Lee et al. (1985) and Kog et al.
(1986), a single pile was considered to penetrate into the bearing layer, which extended the work of Ng et al. (1976). Chow et al. (1990) proposed a numerical procedure for the downdrag analysis of group piles which penetrate a consolidating upper soil layer and socket into a firm bearing stratum of finite stiffness. It was found that the pile-soil-
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pile interaction has a beneficial effect of reducing the downdrag forces and settlements of the group piles when compared to the corresponding single pile values, provided that the soil settlements are not so large as to cause full slippage at the interface in all the piles. Lee (1993) described a simplified load-transfer approach for analyzing the response of pile groups under negative skin friction. The interaction between piles bearing on a stiffer stratum was determined from a modified form of Mindlin’s solution for a vertical point load in a homogeneous, isotropic elastic half-space by employing the Steinbrenner’s approximation.
More recently, other numerical approaches to analyze NSF on piles have been proposed. These numerical approaches differ from each other mainly in the way the soil was modeled. For example, Lim et al. (1993) presented a simple discrete element approach using subgrade reaction method to analyze NSF on single piles. Wong and Teh (1995) presented a simplified numerical procedure for the analysis of negative skin friction on piles in a stratified soil deposit. The pile-soil interface behavior is modelled by hyperbolic soil springs in a manner similar to the load transfer method. A framework for determining the hyperbolic parameters from conventional soil tests was established to enable a rational analysis to be carried out using the proposed numerical method. Chow et al. (1996) presented a simplified method for the analysis of socketed pile group subject to NSF. The soil behaviour is modeled using a hybrid approach in which the soil response at the individual piles is modeled using the subgrade reaction method while pile-soil-pile interaction is determined using elastic theory.
NSF on piles, especially on pile groups is practically three-dimensional in nature.
Some researchers have recently utilized 3D finite element method (FEM) to analyze the problem. For example, Indraratna and Balasubramaniam (1993) used finite element code CRISP to obtain predictions on the basis of purely undrained model and Biot-
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coupled consolidation model. The modified Cam-clay model was used to represent the consolidation behavior of the soft clay. The behavior at the soil-pile boundary was investigated by employing a finite thickness solid element with different material properties. In the analysis, a limiting relative displacement of 3 mm was considered as sufficient for the mobilization of the maximum skin friction. It was found that the shear stress distribution acting along the pile shat was directly dictated by the behavior of the thin layer elements used for modeling the soil-pile interface. Jeong and Kim (1998) used ABAQUS to analyze the group effect which causes different downdrag distribution in individual pile within the group. Major parameters such as group spacing, the total number of piles, and the relative position of piles within the group were studied. However, the behavior of slip at the pile-soil interface was neglected in the analysis. Lee et al. (2002) conducted 3D numerical analysis of NSF on piles using ABAQUS. The soil slip at the pile-soil interface has been found to be the most important factor in governing the development of dragload and the resulting group effect. The group effect depends not only on the configuration of the pile group, but also on soil slip along the pile-soil interface, governed mainly by their interface friction coefficient and the soil settlement. The same numerical approach using ABAQUS was also used to analyze the development of downdrag settlement of piles constructed in consolidating soil (Lee and Ng, 2004). It was again demonstrated that the downdrag settlement computed from the no-slip elastic analysis was about 8-14 time larger than that computed from the elasto-plastic slip analysis. It was found that relative reduction in downdrag settlement is more sensitive to the total number of piles than to the pile spacing within a pile group. Comodromos and Bareka (2005) used FLAC3D, a 3D geotechnical software using finite difference method, to study the effects of construction sequence on the development of NSF on pile groups. It was
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demonstrated that for fixed-head friction pile groups the dragload group effect is significantly greater than in the case of free-head end-bearing pile groups. It has also been demonstrated that when the construction of an embankment precedes the application of the foundation working load, the effect of negative skin friction is considerably smaller than in the reverse case.