A layer equation method for 1-D consolidation under time-dependent reloading

Most of available meshless methods for time-dependent settlement problems depend on deriving an algebraic equation for each layer, in which, the derived equation has an infinite number of series functions with an infinite number of coefficients. In this paper, a Layer Equation Method (LEM) is adapted for analyzing time-dependent settlement problems. The technique of LEM is a semi-analytical solution that deals with a limited number of algebraic equations instead of solving numerically the partial differential equations. Consequently, it leads to a significant reduction in variables of the problem. This method can take into account any variable initial stress along the clay layers. It is also applicable for stress coefficient technique, in which the vertical stress in any node at coordinate (x, y, z) may be considered. An application for the method on reloading time-dependent settlement of clay is presented in which a deep excavation is necessary for buildings with basements. In this case, the soil stress reduces due to excavation, and the reloading of the soil should be taken into account.