On a nonlinear hybrid method for multiscale analysis of a bearing‐capacity test of a real‐scale segmental tunnel ring

Abstract

Summary A nonlinear hybrid method is developed for multiscale analysis of a bearing‐capacity test of a real‐scale segmental tunnel ring subjected to point loads. The structural analysis consists of two parts. Part I refers to modeling of bending‐induced tensile cracking of the segments, resulting from the external loading. The segments are subdivided into elements, according to the crack spacing. Each element is either intact or contains one central crack band, flanked by lateral undamaged domains. A multiscale model for tensile softening of concrete is used to describe the progressive deterioration of the crack bands. After iterative determination of their state of damage, the effective bending and extensional stiffnesses of the corresponding elements are quantified by means of Voigt‐Reuss‐Hill estimates. The effective stiffnesses are used for linear‐elastic simulations of the segmental tunnel ring. Part II refers to the relative rotation angles at the joints, which are estimated from monitoring data, using the Bernoulli‐Euler hypothesis. Since the validity of this hypothesis is questionable for neck‐like joints, the relative rotation angles are post‐processed such that they refer to rigid body displacements of the segments. The following conclusions are drawn: The presented approach yields good estimates of crack widths. Relative rotation angles at the joints mainly result in rigid body displacements of the segments, governing the convergences. Because realistic interface models are lacking, hybrid analysis based on displacement‐monitoring data allows for performing ultimate‐load analysis of segmental tunnel rings.

Application-oriented fundamental research on concrete and reinforced concrete structures: selected findings from an Austro-Chinese research project

“…Fig. 15 Comparison of the convergences obtained from simulation and measurements: a vertical convergence; b horizontal convergence [10] The simulated convergences agree well with the experimental results, see Fig. 15.…”

“…They assumed that the relative rotation angles at the joints result in rigid-body displacements of the segments. This allows for subdividing the hybrid analysis into two load cases [10].…”

“…Since the validity of this hypothesis is questionable for neck-like joints, the estimated relative rotation angles are post-processed such as to refer to rigid-body displacements of the segments. This includes symmetrization and adding the smallest possible increments such that rigid-body displacements are obtained, see [10] for details. Finally, the two load cases are superimposed.…”

“…Finally, the two load cases are superimposed. This is admissible, even though the analysis of load case I is nonlinear, because superposition of load case II only adds rigid-body displacements, and the equilibrium of the structure is formulated in the undeformed configuration [10]. Fig.…”

“…Bearing capacity tests were analyzed with the help of transfer relations in the form of analytical solutions of the first-order theory of thin circular arches. In the developed hybrid analysis method, transfer relations and measured relative rotations of neighboring segments were combined [9,10]. Herein, the discussion focuses on the convergences, in the vertical and the horizontal direction, governing the serviceability limits, and on the development of plastic hinges at the interfaces, defining the bearing capacity of segmental tunnel rings.…”