Hybrid minimization algorithm applied to tunnel back analysis

Abstract

The paper describes a procedure to perform backanalysis in an automatic manner in the context of a tunnel excavation. The measured displacements are compared with the calculated ones obtained from a Finite Element Analysis, forming the objective function. The parameters that best represent the measured data are those that minimize the objective function and a suitable minimization algorithm is required. In this paper two different minimization algorithms were combined in order to define a hybrid method that makes the most of both. One of the algorithms is a Genetic Algorithm (GA) inspired by Darwin’s theory of evolution and formally proposed by Holland (1975) and initially introduced in the field of geotechnics by Levasseur et al (2008). The other algorithm is based on the gradient method of Gauss-Newton type, described in Ledesma et al (1996). The Finite Element code Plaxis was used as a tool for the direct analysis. The “Hardening soil model” defined by Schanz et al (1999) and subsequently implemented in Plaxis has been the constitutive model selected to simulate the soil behavior. The parameters to identify are the coefficient of lateral earth pressure (K0) and the reference Young’s modulus for unloading and reloading (E ref ur ), to the reference pressure (p ref ). The geometry considered is a synthetic case involving the excavation of a circular tunnel. The paper shows in detail the structure and the different aspects of combining in serial form genetic algorithms with gradient based methods. In particular, a strategy is defined in which the genetic algorithm is used as a first stage to define a smaller search space, located near the minimum, and the gradient method is used as a second stage to finally find the minimum in an efficient manner. The method proposed strives to combine efficiently the advantages of the two types of algorithms and to avoid performing unfruitful gradient searches around local minima.