The Optimization Algorithm for Large-Scale In Situ Stress Field

Abstract

In situ stress state is a predominant factor for the design and safe construction of geotechnical engineering. For a real construction site, the amount of calculation using a finite element method for in situ stress field increases dramatically with the increase of the calculation freedom due to large-scale uncertainties. In order to reduce the computing cost without losing the accuracy of the calculation, an optimization algorithm combined with a reduced order model, which is realized by the proper orthogonal decomposition algorithm (POD) for large-scale in situ stress field, is put forward in this paper. The POD algorithm produces a set of orthogonal bases through the extraction of the field variables, combining with the Galerkin finite element method to create a reduced order numerical model. The reduced order model is then calculated with a global optimization algorithm to inversely find the solution for the actual in situ stress field. In order to verify the accuracy and efficiency of the method, two examples are presented to simulate the inverse calculation of the in situ stress field. They showed that the computation time of the POD method could reach 1/10 of the ordinary computation time. Also, the results showed good accuracy with a minimum computational expense, which can provide a reference for inverse calculation of large-scale in situ stress field.