An explicit time integration scheme of numerical manifold method

X. L. Qu, G. Y. Fu, G. W. Ma

Research output: Contribution to journalArticleResearchpeer-review

24 Citations (Scopus)


The traditional numerical manifold method (NMM) has the advantage of simulating a continuum and a discontinuum in a unified framework based on a dual cover system. However, since an implicit time integration algorithm is used, the computational efficiency of the original NMM is very low, especially when more contacts are involved. The present study proposes an explicit version of the NMM. Since a lumped mass matrix is used for the manifold element, the accelerations by the corresponding physical covers can be solved explicitly without forming a global stiffness matrix. The open-close iteration is still applied to ensure computational accuracy. The developed method is first validated by two examples, and a highly fractured rock slope is subsequently simulated. Results show that the computational efficiency of the proposed explicit NMM has been significantly improved without losing the accuracy. The explicit NMM is more suitable for large-scale rock mass stability analysis and it deserves to be further developed for engineering computations in rock engineering.

Original languageEnglish
Pages (from-to)53-62
Number of pages10
JournalEngineering Analysis with Boundary Elements
Publication statusPublished - 1 Nov 2014
Externally publishedYes


  • Computational accuracy
  • Computational efficiency
  • Explicit version
  • Numerical manifold method

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