Open Access

ARTICLE

Shell-specific Interpolation of Measured 3D Displacements, for Micromechanics-Based Rapid Safety Assessment of Shotcrete Tunnels

S. Ullah¹, B. Pichler¹, S. Scheiner^1,2, C. Hellmich^1,3

1 Institute for Mechanics of Materials and Structures, Vienna University of Technology, Karlsplatz 13/202, A-1040 Vienna, Austria
2 Current address: School of Computer Science and Software Engineering, The University of Western Australia, 35 Stirling Highway, Crawley WA 6009, Australia
3 Corresponding author, Associate Professor, Institute for Mechanics of Materials and Structures, Vienna University of Technology, Karlsplatz 13/202, A-1040, Vienna, Austria. Tel.: +43-1-58801-20220; Fax: +43-1-58801-20299; E-mail: Christian.Hellmich@tuwien.ac.at

Computer Modeling in Engineering & Sciences 2010, 57(3), 279-316. https://doi.org/10.3970/cmes.2010.057.279

Abstract

Point-wise optical measurements of 3D displacement vectors over time are a key input for monitoring shotcrete tunnel shells during construction according to the New Austrian Tunnelling Method (NATM). Aiming at estimation of the stresses prevailing in the highly loaded, hydrating material, we here deal with two different interpolation strategies for reconstructing, from measured displacement vectors, the 3D displacement field histories of the inner surface of the tunnel shell. The first approach considers spatial interpolation of displacement components in a fixed Cartesian base frame, while the second (new) approach refers to displacement components in a moving base frame consisting of vectors tangent to the cylindrical coordinate curves along the tunnel shell. Subsequently, thin shell kinematics allow for (analytical) conversion of the aforementioned displacement field histories into strain field histories throughout the entire tunnel shell. Finally, thermochemomechanical constitutive modeling (including extension of a recently developed, experimentally validated micro-viscoelasticity model for hydrating shotcrete, towards the nonlinear regime) allows for conversion of the aforementioned strain fields into stress fields. The latter differ qualitatively, depending on the chosen interpolation strategy. Thereby, the moving base frame-related interpolation scheme results in more realistic estimations of the actual load carrying behavior of an NATM tunnel.

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