Formulation of the axisymmetric CPDI with application to pile driving in sand

In foundation engineering practice, pile driving is often used as an efficient method to install piles. While large distortions take place along the pile shaft during the installation, the zone around the pile toe experiences compression. In an attempt to fully understand the build up of resistance when driving piles, it is desirable to model the driving process and the corresponding soil behaviour. The non-linear dynamic analysis of this problem is challenging, given the large deformation that develops together with the associated changes in soil properties. Some numerical methods offer the possibility of handling large material movements by utilising Lagrangian and Eulerian frames of references. However, few of these methods are capable of tracing the material displacement, such as the Material Point Method (MPM). Early implementation of MPM assumes that the mass is concentrated at the material points, which causes noise in the solution. Later implementations assign a spatial domain to the material points to mitigate the grid crossing error. The Convected Particle Domain Interpolation (CPDI) is one such implementation. This paper extends the two-dimensional CPDI formulation for an axisymmetric problem where a pile is driven into sand that is modelled as a hypoplastic model. The extended formulation is tested, validated and compared to that for the case of the two-dimensional plane-strain within the framework of the method of manufactured solution. The hammer blows on the pile are represented by a periodic forcing function. In contrast to earlier studies on pile installation using advanced models, deep penetration is achieved in the present analysis. A non-regular distribution for the particle domains is suggested to avoid unnecessary computation. A frictional contact algorithm is introduced to describe the pile-soil interaction. (C) 2016 Elsevier Ltd. All rights reserved.