Modeling the degradation of old subway galleries using a continuum approach

Abstract The underground transit system of the Paris metro was built in the early 20th century. Many tunnels and galleries of this underground system were constructed with old masonry whose properties have changed with time and increasing use, and its strength may have deteriorated under the impact of several weathering factors. Therefore, research has been initiated to diagnose structural deterioration of the tunnels and galleries used by the Paris metro system. This paper outlines the current state of the metro galleries in which cracks have developed in the tunnel lining caused by degradation of the abutment materials. The initial state of the stresses applied to the structure immediately after the construction is also analyzed through a double comparison (analytical–numerical and numerical 2D–3D). Then the damage of the galleries is modeled by taking into account the effect of the tunnel linings’ reduced strength. By means of an equivalent homogeneous model and a strain-softening approach, deformations associated with crack appearance can be located. The numerical results show that the state of different components of the underground structure during the lifetime of the galleries can be assessed.

[1]  Vincent Labiouse,et al.  Analysis of the evolution of road tunnels equilibrium conditions with a convergence–confinement approach , 2010 .

[2]  L. J. Sluys,et al.  Viscoplasticity for instabilities due to strain softening and strain‐rate softening , 1997 .

[3]  C. González-Nicieza,et al.  Influence of the depth and shape of a tunnel in the application of the convergence-confinement method , 2008 .

[4]  D. E. Gill,et al.  Design of tunnel linings in a creeping rock , 1988 .

[5]  P. Lourenço.  Computational strategies for masonry structures : Proefschrift , 1996 .

[6]  Farid Benboudjema,et al.  Coupling between leaching and creep of concrete , 2008 .

[7]  Franz-Josef Ulm,et al.  Chemoporoplasticity of Calcium Leaching in Concrete , 1999 .

[8]  K. Terzaghi.  Theoretical Soil Mechanics , 1943 .

[9]  Ted Belytschko,et al.  Continuum Theory for Strain‐Softening , 1984 .

[10]  Z. T. Bieniawski,et al.  Time-dependent behaviour of fractured rock , 1970 .

[11]  Mgd Marc Geers,et al.  Viscous regularization of strain localisation for softening materials , 1993 .

[12]  Yuanqiang Cai,et al.  Continuum Damage Mechanics and Numerical Applications , 2011 .

[13]  Nobuaki Otsuki,et al.  Long-term forecast of Ca leaching from mortar and associated degeneration , 2002 .

[14]  Z. Bažant,et al.  Nonlocal damage theory , 1987 .

[15]  Shunde Yin,et al.  Strain‐softening analysis of a spherical cavity , 2012 .

[16]  Abdul Shakoor,et al.  An investigation of the relationship between uniaxial compressive strength and degradation for selected rock types , 1996 .

[17]  Yoshiaki Fujii,et al.  Circumferential strain behavior during creep tests of brittle rocks , 1999 .

[18]  L. J. Sluys,et al.  A new method for modelling cohesive cracks using finite elements , 2001 .

[19]  P. K. Kaiser,et al.  Hoek-Brown parameters for predicting the depth of brittle failure around tunnels , 1999 .

[20]  C. Le Govic,et al.  Wood viscoelastic compliance determination with special attention to measurement problems , 1993 .

[21]  J. Tissaoui,et al.  Effects of Long-Term Creep on the Integrity of Modern Wood Structures , 1996 .

[22]  Jean Salençon,et al.  Introduction to the yield design theory and its applications to soil mechanics , 1990 .

[23]  B. Damjanac,et al.  Mechanical degradation of emplacement drifts at Yucca Mountain—A modeling case study , 2007 .

[24]  M. Cervera,et al.  Continuum damage model for orthotropic materials: Application to masonry , 2011 .

[25]  Thierry Verdel,et al.  Numerical modelling and mechanical behaviour analysis of ancient tunnel masonry structures , 2008 .

[26]  Roberto Nova,et al.  Mechanical effects of chemical degradation of bonded geomaterials in boundary value problems , 2002 .

[27]  Thierry Verdel,et al.  Numerical modelling of masonry joints degradation in built tunnels , 2009 .

[28]  Qi-Zhi Zhu,et al.  Modeling of creep in rock materials in terms of material degradation , 2003 .

[29]  Claude Bacconnet,et al.  Characterization of the masonry lining of an underground structure by geoendoscopy , 2013 .

[30]  Jian-Fu Shao,et al.  Influences of chemical degradation on mechanical behaviour of a limestone , 2011 .

[31]  René de Borst,et al.  Gradient-dependent plasticity: formulation and algorithmic aspects , 1992 .

[32]  Mark S. Diederichs,et al.  Manuel Rocha Medal Recipient Rock Fracture and Collapse Under Low Confinement Conditions , 2003 .

[33]  Roberto Nova,et al.  Coupling transport of chemical species and damage of bonded geomaterials , 2007 .

[34]  Marwan Al-Heib.  Distinct Element Method Applied on Old Masonry Structures , 2012 .

[35]  M. Elices,et al.  Nonlinear fracture of cohesive materials , 1991, International Journal of Fracture.

[36]  B. Damjanac,et al.  Mechanical Degradation of Emplacement Drifts at Yucca Mountain-A Modeling Case Study-Part I: Nonlithophysal Rock , 2007 .

[37]  Sandhya Samarasinghe Gamalath.  Long-term creep modeling of wood using time temperature superposition principle , 1991 .

[38]  D. F. Malan,et al.  Manuel Rocha Medal Recipient Simulating the Time-dependent Behaviour of Excavations in Hard Rock , 2002 .

[39]  Marc G. D. Geers,et al.  Nonlocal implicit gradient-enhanced elasto-plasticity for the modelling of softening behaviour , 2003 .

[40]  Raoul François,et al.  Leaching of both calcium hydroxide and C-S-H from cement paste: Modeling the mechanical behavior , 1996 .

[41]  A. Needleman.  Material rate dependence and mesh sensitivity in localization problems , 1988 .