A Numerical Approach to the Non-convex Dynamic Problem of Steel Pile-Soil Interaction under Environmental and Second-Order Geometric Effects

Abstract

The paper deals with a numerical approach for the dynamic soil-pile interaction, considered as an inequality problem of structural engineering. So, the unilateral contact conditions due to tensionless and elastoplastic softening/fracturing behaviour of the soil as well as due to gapping caused by earthquake excitations are taken into account. Moreover, soil-capacity degradation due to environmental effects and second-order geometric effects for the pile behaviour due to preexisting compressive loads are taken into account. The numerical approach is based on a double discretization and on mathematical programming. First, in space the finite element method (FEM) is used for the simulation of the pile and the unilateral contact interface, in combination with the boundary element method (BEM) for the soil simulation. Next, with the aid of Laplace transform, the equality problem conditions are transformed to convolutional ones involving as unknowns the unilateral quantities only. So the number of unknowns is significantly reduced. Then a marching-time approach is applied and finally a nonconvex linear complementarity problem is solved in each time-step.