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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 852875, 13 pages
Research Article

Factors Influencing Quasistatic Modeling of Deformation and Failure in Rock-Like Solids by the Smoothed Particle Hydrodynamics Method

1State Key Laboratory of Subtropical Building Science, School of Civil Engineering and Transportation, South China University of Technology, Guangzhou 510640, China
2State Key Laboratory of Hydroscience and Engineering, Department of Hydraulic Engineering, Tsinghua University, Beijing 100084, China

Received 26 November 2012; Accepted 25 December 2012

Academic Editor: Fei Kang

Copyright © 2013 X. W. Tang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


As a Lagrangian mesh-free numerical method, the Smoothed Particle Hydrodynamics (SPH) method has been traditionally applied for modeling astrophysics, fluid flows and thermal problems, and there has been a growing interest in applying SPH to solid deformation problems. However, the potential of this method for quasistatic analysis of rock-like brittle materials has not been clearly explored. The major aim of this paper is to investigate the effects of key factors in SPH on the load-deformation response of rock-like solids, including variations in the particle approximation theory, the magnitude of the smoothing length and its variable method. Simple uniaxial compression (UC) loading conditions were chosen, and a series of numerical studies were carried out sequentially on an idealized elastic case and an actual test of marble material. Typical results of the axial stress-strain response from infinitesimal to finite deformation as well as the progressive failure process for the marble tests are given and the influences of various factors are discussed. It is found that only provided proper choices of particle momentum equation and the smoothing length parameter, the SPH method is capable for favorably reproducing the deformation and progressive failure evolution in rock-like materials under quasistatic compression loads.