Slope stability analysis using smoothed particle hydrodynamics (SPH) method

Abstract In conventional deformation analysis of geomaterials, the infinitesimal and the finite deformation theories have been widely used. These theories have been successfully implemented in several numerical methods, such as finite element method (FEM). As a result, it is now possible to predict a wide variety of deformation behaviors of geomaterials. However, when dealing with large deformation problems using the framework of the FEM, excess distortion of the FEM mesh may lead to instability of the calculation. In this study, in order to solve large deformation problem of geomaterials, the smoothed particle hydrodynamics (SPH) method is used. The method is a kind of particle method based on the mesh-free Lagrangian scheme, and is one of the promising numerical methods in the field of geotechnical engineering. The method can solve large deformation problems without mesh distortion. Moreover, it can handle the governing equations and existing constitutive models for geomaterials based on a continuum mechanics. Therefore, this method can represent the entire deformation process of a geomaterial from the small strain region to the large deformation region. In this paper, first, basic theory and formulation of the SPH method based on solid mechanics are summarized. Then, the result of a simple calculation is shown to verify the accuracy of the spatial derivatives based on the theory of the SPH method. Also, simulations of simple shear tests of both an elastic and elasto-plastic material are carried out and the obtained results are compared with theoretical solutions. Based on the obtained results, calculation accuracy of the method is discussed. Finally, a series of slope stability analyses are carried out. The numerical results obtained from the SPH method and the safety factors obtained from the Fellenius method are compared. The results indicated that the SPH method is able to express the same tendencies of safety factor obtained from the conventional circular slippage calculations. Moreover, the SPH method can evaluate both the deformation and stability simultaneously. Based on the series of validations and simulations, the effectiveness of the SPH method is discussed from the point of view of geotechnical engineering.

[1]  A. Schofield,et al.  Yielding of Clays in States Wetter than Critical , 1963 .

[2]  J. Monaghan,et al.  SPH elastic dynamics , 2001 .

[3]  J. Monaghan.  SPH without a Tensile Instability , 2000 .

[4]  Kenichi Maeda,et al.  Development of seepage failure analysis procedure of granular ground with Smoothed Particle Hydrodynamics (SPH) method , 2004 .

[5]  M. Pastor,et al.  A depth‐integrated, coupled SPH model for flow‐like landslides and related phenomena , 2009 .

[6]  Guirong Liu,et al.  Smoothed Particle Hydrodynamics: A Meshfree Particle Method , 2003 .

[7]  L. Lucy.  A numerical approach to the testing of the fission hypothesis. , 1977 .

[8]  Atsushi Yashima,et al.  Numerical simulation of flow failure of geomaterials based on fluid dynamics , 2005 .

[9]  Frédéric Dufour,et al.  Large deformation FEMLIP drained analysis of a vertical cut , 2012 .

[10]  R. P. Ingel,et al.  An approach for tension instability in smoothed particle hydrodynamics (SPH) , 1995 .

[11]  J. Monaghan,et al.  Smoothed particle hydrodynamics: Theory and application to non-spherical stars , 1977 .

[12]  R. P. Ingel,et al.  STRESS POINTS FOR TENSION INSTABILITY IN SPH , 1997 .

[13]  D. Balsara.  von Neumann stability analysis of smoothed particle hydrodynamics—suggestions for optimal algorithms , 1995 .

[14]  Mario Gallati,et al.  SPH Simulation of Sediment Flushing Induced by a Rapid Water Flow , 2012 .

[15]  M. Gotoh.  An inquiry into the spin of a deforming body. , 1986 .

[16]  Yosuke Higo,et al.  A COUPLED MPM-FDM ANALYSIS METHOD FOR MULTI-PHASE ELASTO-PLASTIC SOILS , 2010 .

[17]  Wai-Fah Chen,et al.  Nonlinear analysis in soil mechanics : theory and implementation , 1990 .

[18]  森口 周二.  CIP-based numerical analysis for large deformation of geomaterials , 2005 .

[19]  S. Attaway,et al.  Smoothed particle hydrodynamics stability analysis , 1995 .

[20]  J. Wells,et al.  Slope stability analysis and discontinuous slope failure simulation by elasto-plastic smoothed particle hydrodynamics (SPH) , 2011 .

[21]  D. Sulsky.  Erratum: Application of a particle-in-cell method to solid mechanics , 1995 .

[22]  Eduardo Alonso,et al.  Progressive failure of Aznalcóllar dam using the material point method , 2011 .

[23]  Lagrangian mesh-free particle method (SPH) for large deformation and post-failure of geomaterial using elasto-plastic constitutive models , 2007 .

[24]  Manuel Pastor,et al.  A SPH Depth Integrated Model for Popocatepetl 2001 Lahar. , 2009 .

[25]  Martin W. Heinstein,et al.  An analysis of smoothed particle hydrodynamics , 1994 .

[26]  P. Cundall,et al.  A discrete numerical model for granular assemblies , 1979 .

[27]  Hirotaka Sakai,et al.  DEVELOPMENT OF SEEPAGE FAILURE ANALYSIS METHOD OF GROUND WITH SMOOTHED PARTICLE HYDRODYNAMICS , 2006 .

[28]  Shaofan Li,et al.  “Smoothed particle hydrodynamics — a meshfree method” , 2004 .

[29]  D. C. Drucker,et al.  Soil mechanics and plastic analysis or limit design , 1952 .

[30]  J. Monaghan,et al.  Shock simulation by the particle method SPH , 1983 .

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