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Back-Analysis of Tunnel Response from Field Monitoring Using Simulated Annealing

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Abstract

This paper deals with the use of field monitoring data to improve predictions of tunnel response during and after construction from numerical models. Computational models are powerful tools for the performance-based engineering analysis and design of geotechnical structures; however, the main challenge to their use is the paucity of information to establish input data needed to yield reliable predictions that can be used in the design of geotechnical structures. Field monitoring can offer not only the means to verify modeling results but also faster and more reliable ways to determine model parameters and for improving the reliability of model predictions. Back-analysis involves the determination of parameters required in computational models using field-monitored data, and is particularly suited to underground constructions, where more information about ground conditions and response becomes available as the construction progresses. A crucial component of back-analysis is 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, stresses, or tunnel support loads). Methods of back-analysis can be broadly classified as direct and gradient-based optimization techniques. An alternative methodology to carry out the nonlinear optimization involved in back-analyses is the use of heuristic techniques. Heuristic methods refer to experience-based techniques for problem-solving, learning, and discovery that find a solution which is not guaranteed to be fully optimal, but good enough for a given set of goals. This paper focuses on the use of the heuristic simulated annealing (SA) method in the back-analysis of tunnel responses from field-monitored data. SA emulates the metallurgical processing of metals such as steel by annealing, which involves a gradual and sufficiently slow cooling of a metal from the heated phase which leads to a final material with a minimum imperfections and internal dislocations. During cooling, nature follows its own optimization path for the given conditions. Description of SA, its implementation in the computer code FLAC (Itasca Consulting Group in FLAC 5.0 manual. Itasca Consulting Group, Minneapolis, 2008), and use in the back-analysis of the response of a twin tunnel in China are presented.

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Abbreviations

\(\Delta f = f({\mathbf{X}}_{i + 1} ) - f({\mathbf{X}}_{i} )\) :

Objective function

\(\Delta s_{i}\) :

Perturbation step size for parameter x i

ψ:

Dilation angle

ϕ :

Friction angle

γ :

Unit weight of the rock

∆X :

Change in values of the unknown vector of parameters

\(\sigma_{x}\), \(\sigma_{y}\) :

In situ horizontal and vertical stresses

\(x_{i}^{l}\), \(x_{i}^{u}\) :

Lower and upper bound values of parameter x i

c :

Cohesion

CR:

Cooling rate

E :

Energy

E :

Young’s modulus

NI:

Number of iterations

NT:

Number of temperature reductions

RND i :

Random number between 0 and 1

T, T o :

Temperature, initial temperature

v :

Poisson’s ratio

X, X m , X p :

Vectors of unknown, measured, and predicted parameters

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Acknowledgments

The results presented in this paper are part of the AMADEUS (Adaptive real-time geologic Mapping, Analysis and Design of Underground Space) Project funded by the US National Science Foundation under Grant Number CMS 324889. This support is gratefully acknowledged.

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Authors and Affiliations

  1. WSP-Parsons Brinckerhoff, Chicago, IL, 60602, USA

    Sotirios Vardakos

  2. Department of Civil and Environmental Engineering, Colorado School of Mines, Golden, CO, 80401, USA

    Marte Gutierrez

  3. Department of Geotechnical Engineering, Tongji University, Shanghai, 20009, People’s Republic of China

    Caichu Xia

Authors
  1. Sotirios Vardakos
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  2. Marte Gutierrez
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  3. Caichu Xia
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Correspondence to Marte Gutierrez.

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Vardakos, S., Gutierrez, M. & Xia, C. Back-Analysis of Tunnel Response from Field Monitoring Using Simulated Annealing. Rock Mech Rock Eng 49, 4833–4852 (2016). https://doi.org/10.1007/s00603-016-1074-1

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  • DOI: https://doi.org/10.1007/s00603-016-1074-1

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