Homogenizing spatially variable Young modulus using pseudo incremental energy method

摘要

Homogenization is the process of representing a spatially variable property by an equivalent (or effective) homogenous property. The second and fifth authors proposed the pseudo incremental energy (PIE) method to represent a spatially variable Young's modulus by an effective Young's modulus for a rigid footing problem, the overall Young's modulus actually "felt" by the footing. The effective Young's modulus is based on a non-uniform geometric average with weights provided by PIE. It performs better than the conventional uniform geometric average at a cost of computing PIE weights from one deterministic finite element analysis. The current paper extends the previous work on PIE in four respects. First, a new PIE procedure is developed to address a known issue in the previous PIE. Second, the applicability of the new PIE is verified for a wide variety of two-dimensional (2D) and three-dimensional (3D) geotechnical problems, including 2D retaining wall, 2D & 3D axially loaded pile, 2D & 3D laterally loaded pile, and 2D & 3D base heave. Third, the new PIE is extended to problems with layered soils, where each layer is modeled by a separate random field. Finally, the new PIE is implemented to a real case study of a 3D rigid footing. The new PIE method can approximately match the results from a random finite element analysis (RFEA) at the realization level (not ensemble statistics level) at an acceptable cost of one deterministic finite element analysis. It is much cheaper than RFEA that requires hundreds of thousands of deterministic analyses. It is slightly more costly than the original PIE.