# Development of coupled discontinuous deformation analysis and numerical manifold method (NMMDDA)

Shigeru Miki, Takeshi Sasaki, Tomofumi Koyama, Satoshi Nishiyama, Yozo Ohnish Ohnishi

Research output: Contribution to journalArticle

36 Citations (Scopus)

### Abstract

Discontinuous Deformation Analysis (DDA) and Numerical Manifold Method (NMM) have been widely used for the analyses of discontinuous rock masses. Recently, these discontinuum-based numerical methods have been applied to the simulations for slope failure due to earthquakes, where one of the key issues is the estimation of traveling velocities and distances for the collapsed rock blocks. For the dynamic response analysis of rock slopes, it is necessary to consider the local variation of seismic forces, especially when the slope size is large and/or the slope geometry becomes complicated. In DDA, there is difficulty to consider the local displacements and stress condition of the single block for the basement because of mathematical principle (in DDA, the displacement function is defined at the gravity center of the blocks and the strain in the block is uniform). On the other hand, NMM can simulate both continuous and discontinuous deformation of the block systems. However, the rigid body rotation of blocks cannot be treated properly because NMM does not deal with the rigid body rotation in explicit form. According to the above-mentioned features and drawbacks, it is reasonable to combine DDA and NMM from practical point of view. In this paper, the formulation for the coupled NMM and DDA (NMM-DDA) was presented. For the formulation, NMM and DDA can be easily combined by choosing displacements of the DDA blocks and NMM cover nodes as unknowns, because the processes to establish the equilibrium equations (minimizing total potential energy) and kinematics for block system are same between DDA and NMM. In this paper, some applications of the NMM-DDA to both dynamic and static problems were also presented and the validity and applicability of newly developed DDA-MM were discussed.

Original language English 131-150 20 International Journal of Computational Methods 7 1 https://doi.org/10.1142/S021987621000209X Published - Mar 1 2010 Yes

### Fingerprint

Numerical Manifold Method
Slope
Rocks
Rigid Body
Centre of gravity
Formulation
Potential energy
Earthquake
Dynamic Response
Dynamic response

### Keywords

• Discontinuous deformation analysis (DDA)
• Dynamic response analysis
• Numerical manifold method (NMM)

### ASJC Scopus subject areas

• Computer Science (miscellaneous)
• Computational Mathematics

### Cite this

Development of coupled discontinuous deformation analysis and numerical manifold method (NMMDDA). / Miki, Shigeru; Sasaki, Takeshi; Koyama, Tomofumi; Nishiyama, Satoshi; Ohnishi, Yozo Ohnish.

In: International Journal of Computational Methods, Vol. 7, No. 1, 01.03.2010, p. 131-150.

Research output: Contribution to journalArticle

Miki, Shigeru ; Sasaki, Takeshi ; Koyama, Tomofumi ; Nishiyama, Satoshi ; Ohnishi, Yozo Ohnish. / Development of coupled discontinuous deformation analysis and numerical manifold method (NMMDDA). In: International Journal of Computational Methods. 2010 ; Vol. 7, No. 1. pp. 131-150.
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abstract = "Discontinuous Deformation Analysis (DDA) and Numerical Manifold Method (NMM) have been widely used for the analyses of discontinuous rock masses. Recently, these discontinuum-based numerical methods have been applied to the simulations for slope failure due to earthquakes, where one of the key issues is the estimation of traveling velocities and distances for the collapsed rock blocks. For the dynamic response analysis of rock slopes, it is necessary to consider the local variation of seismic forces, especially when the slope size is large and/or the slope geometry becomes complicated. In DDA, there is difficulty to consider the local displacements and stress condition of the single block for the basement because of mathematical principle (in DDA, the displacement function is defined at the gravity center of the blocks and the strain in the block is uniform). On the other hand, NMM can simulate both continuous and discontinuous deformation of the block systems. However, the rigid body rotation of blocks cannot be treated properly because NMM does not deal with the rigid body rotation in explicit form. According to the above-mentioned features and drawbacks, it is reasonable to combine DDA and NMM from practical point of view. In this paper, the formulation for the coupled NMM and DDA (NMM-DDA) was presented. For the formulation, NMM and DDA can be easily combined by choosing displacements of the DDA blocks and NMM cover nodes as unknowns, because the processes to establish the equilibrium equations (minimizing total potential energy) and kinematics for block system are same between DDA and NMM. In this paper, some applications of the NMM-DDA to both dynamic and static problems were also presented and the validity and applicability of newly developed DDA-MM were discussed.",
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