Implementation and Application of a New Elastoplastic Model Based on a Multiaxial Criterion to Assess the Stress State near Underground Openings

The inelastic MSDPu (for Mises-Schleicher and Drucker-Prager unified) criterion has been developed over the last decade, and has been applied to simple problems for a wide range of geomaterials. This paper presents the approach taken to introduce this multiaxial criterion into a commercially available finite difference code using an elastoplastic framework. The paper begins with a brief review of the MSDPu formulation. Then, the main components of the elastoplastic model and the implementation procedure are described. The ensuing model, called MSDPu -EP (for MSDPu elastoplasticity model), is then validated against some existing and recently developed analytical solutions for the stress state around a circular opening. The newly developed model is further applied to evaluate the stress state near underground openings, using the geometry of a tunnel and of vertical backfilled stopes. A brief discussion follows.

[1]  Poul V. Lade,et al.  Elasto-plastic stress-strain theory for cohesionless soil with curved yield surfaces , 1977 .

[2]  Michel Aubertin,et al.  Numerical Investigation of the Stress State in Inclined Backfilled Stopes , 2009 .

[3]  C. Callari,et al.  Coupled numerical analysis of strain localization induced by shallow tunnels in saturated soils , 2004 .

[4]  Michel Aubertin,et al.  A multiaxial stress criterion for short- and long-term strength of isotropic rock media , 2000 .

[5]  E. T. Brown,et al.  Ground Response Curves for Rock Tunnels , 1983 .

[6]  Hai‐Sui Yu,et al.  Plasticity and geotechnics , 2006 .

[7]  Shailendra K. Sharan,et al.  Elastic–brittle–plastic analysis of circular openings in Hoek–Brown media , 2003 .

[8]  Mohamed A. Meguid,et al.  Stability of D-shaped tunnels in a Mohr-Coulomb material under anisotropic stress conditions , 2006 .

[9]  Charles Wang Wai Ng,et al.  Three-dimensional ground settlements and stress-transfer mechanisms due to open-face tunnelling , 2005 .

[10]  Victor N. Kaliakin,et al.  Soil Constitutive Models: Evaluation, Selection, and Calibration , 2005 .

[11]  F. Dimaggio,et al.  MATERIAL MODEL FOR GRANULAR SOILS , 1971 .

[12]  Chandrakant S. Desai,et al.  Mechanics of Materials and Interfaces: The Disturbed State Concept , 2000 .

[13]  K. Roscoe,et al.  ON THE GENERALIZED STRESS-STRAIN BEHAVIOUR OF WET CLAY , 1968 .

[14]  Shailendra K. Sharan,et al.  Exact and approximate solutions for displacements around circular openings in elastic–brittle–plastic Hoek–Brown rock , 2005 .

[15]  Shailendra K. Sharan,et al.  Analytical solutions for stresses and displacements around a circular opening in a generalized Hoek–Brown rock , 2008 .

[16]  Li Li,et al.  Formulation of a three dimensional analytical solution to evaluate stresses in backfilled vertical narrow openings , 2005 .

[17]  A. Schofield,et al.  On The Yielding of Soils , 1958 .

[18]  Poul V. Lade.  Single Hardening Model for Soils: Parameter Determination and Typical Values , 2005 .

[19]  Michel Aubertin,et al.  An elastoplastic evaluation of the stress state around cylindrical openings based on a closed multiaxial yield surface , 2009 .

[20]  Nagaratnam Sivakugan,et al.  Arching within hydraulic fill stopes , 2007 .

[21]  Michel Aubertin,et al.  A porosity-dependent inelastic criterion for engineering materials , 2004 .

[22]  Georgios Anagnostou,et al.  Significant Parameters in Elastoplastic Analysis of Underground Openings , 1993 .

[23]  Yarlong Wang,et al.  Ground Response of Circular Tunnel in Poorly Consolidated Rock , 1996 .

[24]  J. JeanCharlesRogerSalencon,et al.  CONTRACTION QUASI- STATIQUE D'UNE CAVITE A SYMETRIE SPHERIQUE OU CYLINDRIQUE DANS UN MILIEU ELASTO-PLASTIQUE , 1969 .

[25]  Chandrakant S. Desai,et al.  A general basis for yield, failure and potential functions in plasticity , 1980 .

[26]  Erik Eberhardt,et al.  Numerical modelling of three-dimension stress rotation ahead of an advancing tunnel face , 2001 .

[27]  Lidija Zdravković,et al.  Finite Element Analysis in Geotechnical Engineering: Theory , 1999 .

[28]  P. A. Cundall,et al.  Mixed discretization procedure for accurate modelling of plastic collapse , 1982 .

[29]  Chandrakant S. Desai,et al.  Constitutive laws for engineering materials, with emphasis on geologic materials , 1984 .

[30]  Kyung-Ho Park,et al.  Analytical solution for a circular opening in an elastic-brittle-plastic rock , 2006 .

[31]  Lidija Zdravković,et al.  Finite element analysis in geotechnical engineering , 1999 .

[32]  Richard Brummer,et al.  FLAC and Numerical Modeling in Geomechanics 2003: Proceedings of the 3rd International FLAC Symposium, Sudbury, Canada, 22-24 October 2003 , 2003 .

[33]  R. K. Rowe,et al.  AN ANALYSIS OF THREE-DIMENSIONAL GROUND MOVEMENTS: THE THUNDER BAY TUNNEL , 1991 .

[34]  Michel Aubertin,et al.  Formulation and application of a general inelastic locus for geomaterials with variable porosity , 2005 .

[35]  R. K. Rowe,et al.  Analysis of three-dimensional ground movements: the Thunder Bay tunnel : Can Geotech J V28, N1, Feb 1991, P25–41 , 1991 .

[36]  K. Y. Lo,et al.  Three-dimensional analysis of unlined tunnels in rock subjected to high horizontal stress , 2003 .

[37]  Carlos M Carranza-Torres,et al.  Elasto-plastic solution of tunnel problems using the generalized form of the hoek-brown failure criterion , 2004 .

[38]  George Y. Baladi,et al.  Soil Plasticity: Theory and Implementation , 1985 .