Meshfree method analysis of Biot’s consolidation using the node-based smoothed point interpolation method (NS-PIM)

Abstract

Purpose The purpose of the article is to extend the node-based smoothed point interpolation method (NS-PIM) for soil consolidation analysis based on the Biot’s theory. Design/methodology/approach The shape functions for displacements and pore pressures are constructed using the PIM separately, leading to the Kronecker delta property and easy implementation of essential boundary conditions. Then, a benchmark problem of 2D consolidation under ramp load is solved to investigate the validity of this application. Meanwhile, convergence features of different solutions are studied. Furthermore, the incompressible and impermeable condition under instant load is investigated. The results calculated by the NS-PIM solution with different orders of shape functions are compared. Finally a 2D consolidation problem in construction period is solved. An error estimation method is applied to check the mesh quality. Findings The results of the NS-PIM solution show good agreement with those certified results. Useful convergence features are found when comparing the results of the NS-PIM and the FEM solutions. A simple method is introduced to estimate the errors of the model with rough grids. The convergence features and error estimation method can be applied to check the mesh quality and get accurate results. More stable results can be obtained using the NS-PIM solution with lower order of pore pressure shape functions under the incompressible and impermeable condition. Research limitations/implications It cannot be denied that the calculation of NS-PIM solution takes more time than that of the FEM solution, and more work needs to be carried out to optimize the NS-PIM solution. Also, in further study, the feasibility of more complicated and practical engineering problems can still be probed in the NS-PIM solution. Practical implications This paper introduced a method for the consolidation analysis on the situation of construction loads (“ramp load”) using the NS-PIM which is quite indispensable in many foundation problems. Also, more stable results can be obtained using the NS-PIM solution with lower order of pore pressure shape functions than that with same order of shape functions. Originality/value This study first focuses on the situation of construction loads (“ramp load”) in the NS-PIM consolidation analysis which is quite indispensable in many foundation problems. An error estimation method is introduced to evaluate the mesh quality and get accurate values based on the convergence features of the FEM and NS-PIM solutions. Then, the incompressible and impermeable condition under instant load is investigated, and the analysis show that the NS-PIM with lower order of pore pressure shape functions can get stable results in such conditions.