ABSTRACT

Back-analysis is a systematic procedure to determine model parameters using measured response. The use of back-analysis is particularly appropriate for tunnel constructions where more information on the ground characteristics and response become available as the construction progresses. Back-analysis requires an algorithm to find a set of input parameters that will minimize the difference between predicted and measured performance. This paper presents one such algorithm based on Simulated Annealing (SA). The specific method belongs to a general class of heuristic based methodologies for locating global solutions for non-linear optimization problems. SA presents certain advantages when dealing with highly non-linear ground response and subsequent non-linear behavior of a multi-variable error function to be minimized. The SA-based back-analysis procedure is implemented in the commercially available computer code FLAC. The performance of the proposed method is illustrated by its application to the modeling of the Heshang Tunnel in China.

1 INTRODUCTION

Computational models for geotechnical applications have undergone major improvements in the past several decades. Computational models can be used in a performance-based engineering design and evaluation of geotechnical structures by providing detailed evaluation of damage and estimated consequences. However, determination of model parameters remains to be the "Achilles heel" of computational modeling (Brown et al. 2002). This is particularly true due to significant uncertainties in material properties and loads encountered in geotechnical engineering. Geological, geophysical, in situ and laboratory investigations needed in analysis and design are time consuming and expensive, and are carried out extensively only for very important projects.

Direct measurements of field response can provide faster and more economical means of determining model parameters and for improving the reliability of model predictions. The determination of parameters required in computational models using measured response is referred to by different terms, including back-analysis, parameter or system identification, inverse analysis and model updating.

In contrast to forward analysis where response is predicted given the required input data (e.g., material parameters and loads), back-analysis involves determining the input parameters given the response (i.e., from field measurements). Back-analysis requires an algorithm to find a set of input parameters that will minimize the difference between predicted and measured performance (e.g., in terms of deformations or stresses). Back-analysis is particularly suited for underground constructions such as tunneling where more information on the ground characteristics and response become available as the construction progresses.

Back-analysis requires an algorithm to handle the minimization of the difference between predicted and measured response, which is expressed in terms of an error or objective function. Methods of back-analysis can be broadly classified as direct and gradient based optimization techniques. Direct optimization methods exploit the vector relation between two successive solutions, and perform linear combinations of sequential solutions and attempts to find the local optimum. In gradient-based methods, the infinitesimal change of the solution path and the corresponding gradient are used to control the solution processes. Usually such methods may offer higher solution precision at the expense of the calculation run time required for the estimation of the first or second order derivatives

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