Upper-Bound Limit Analysis of Shield Tunnel Stability in Undrained Clays Using Complex Variable Solutions for Different Ground-Loss Scenarios

Continuum upper-bound limit analyses in existing literature are based on empirical formulas or singular analytical solutions for a uniform-convergence type of tunnel boundary condition. This paper presents an upper-bound limit analysis of shield tunnel stability in undrained clays using complex variable displacement fields for four different ground-loss scenarios. The upper-bound theorem was applied on a prescribed perfect plastic Tresca kinematic zone with a slip line boundary to seek the supremum (minimal upper bound) of the tunnel stability number, which should not be exceeded to avoid collapse. For an imposed identical volume of ground loss, the maximum ground surface settlement was found to be the smallest for ground-loss Scenario A (circular convergence), larger for Scenario B (downward oval convergence), and much larger for Scenario C (halved oval convergence), which is slightly smaller than Scenario D (mixed oval convergence); the opposite is true for comparisons of the widths of the settlement troughs. Ground-loss Scenario A presents the worst case in terms of tunnel stability, with the smallest allowable stability number and the widest spread of the least favorable slip line boundary, while Scenario D is the second worst case with the second-smallest allowable stability number. Similar results were found, in sequential order, for Scenarios B and C. The presented approach, because of the complex variable solutions used, may extend upper-bound limit analyses to more complicated tunnel boundary conditions.


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  • Accession Number: 01639571
  • Record Type: Publication
  • Files: TRIS, ASCE
  • Created Date: Jun 1 2017 3:02PM