Implementation of the finite element method in the three‐dimensional discontinuous deformation analysis (3D‐DDA)

Grayeli, Roozbeh; Hatami, Kianoosh

doi:10.1002/nag.704

Cited by 30 publications

(14 citation statements)

References 16 publications

(34 reference statements)

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“…Only a limited number of attempts to check the validity and accuracy of 3D‐DDA have recently been published 27–33 perhaps due to the difficulty in developing a complete contact theory that governs the interaction of many 3D blocks 34. Considering 3D validations, Shi 25 reports very high accuracy for two examples of block sliding modelled with 3D‐DDA, subjected to gravitational load only.…”

Section: Introductionmentioning

confidence: 99%

Dynamic sliding of tetrahedral wedge: The role of interface friction

Bakun-Mazor

Hatzor

Glaser

2011

Num Anal Meth Geomechanics

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SUMMARYThe role of interface friction is studied by slow direct shear tests and rapid shaking table experiments in the context of dynamic slope stability analysis in three dimensions. We propose an analytical solution for dynamic, single and double face sliding and use it to validate 3D-DDA. Single face results are compared with Newmark's solution and double face results are compared with shaking table experiments performed on a concrete tetrahedral wedge model, the interface friction of which is determined by constant velocity and velocity stepping, direct shear tests.A very good agreement between Newmark's method on one hand and our 3D analytical solution and 3D-DDA on the other is observed for single plane sliding with 3D-DDA exhibiting high sensitivity to the choice of numerical penalty value.The results of constant and variable velocity direct shear tests reveal that the tested concrete interface exhibits velocity weakening. This is confirmed by shaking table experiments where friction degradation upon multiple cycles of shaking culminated in wedge run out. The measured shaking table results are fitted with our 3D analytical solution to obtain a remarkable linear logarithmic relationship between friction coefficient and sliding velocity that remains valid for five orders of magnitude of sliding velocity. We conclude that the velocity-dependent friction across rock discontinuities should be integrated into dynamic rock slope analysis to obtain realistic results when strong ground motions are considered.

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Section: Introductionmentioning

confidence: 99%

Dynamic sliding of tetrahedral wedge: The role of interface friction

Bakun-Mazor

Hatzor

Glaser

2011

Num Anal Meth Geomechanics

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“…Since the introduction of 3D-DDA by Shi (2001) a limited number of verification and validation studies has been published thus far (e.g. Yeung et al 2003, Jiang and Yeung 2004, Liu et al 2004, Moosavi et al 2005, Wu et al 2005, Wang et al 2006, Grayeli and Hatami 2008, Keneti et al 2008 perhaps due to the difficulty in developing a complete contact theory that governs the interaction of many 3D blocks (Yeung et al 2007). Shi (2001) reports very high accuracy for two examples of block sliding * Corresponding author.…”

Section: Introductionmentioning

confidence: 97%

Modelling dynamic deformation in natural rock slopes and underground openings with DDA: review of recent results

Hatzor

Bakun-Mazor

2011

Geomechanics and Geoengineering

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We present validations and applications of the numerical Discontinuous Deformation Analysis method (DDA) for different cases of dynamic loading in the context of rock mass deformation. Following a review of 2D and 3D-DDA validations against analytical solutions for single and double face sliding, we present dynamic DDA applications in natural rock slopes and underground openings. Modelling dynamic rock slope deformation is demonstrated using the case of Masada rock slopes, with some new findings on the dynamic deformation of overhanging cliffs in general. Modelling underground deformation is demonstrated using the case of an active open pit mine in Israel developed in a rock mass containing multiple karstic caverns. The DDA method is shown here to be a powerful numerical tool for modelling dynamic rock mass deformation when the interaction between multiple discrete elements dictates the expected global deformation.

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“…Grayeli and Mortazavi (2006) as well as Grayeli and Hatami (2008) present the finite element derivations for the implementation of FEM/DEM in DDA. In this formulation, the blocks are discretised internally using linear elastic, quadratic (i.e.…”

Section: Introductionmentioning

confidence: 99%

Elastic–plastic discontinuous deformation analysis using Mohr–Coulomb model

Mikola

Hatami

Doolin³

2011

Mining Technology

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The original (i.e. first order) discontinuous deformation analysis (DDA) formulation has two main shortcomings. First, a linear function is used to represent the displacement field in the blocks. This formulation implies that the state of stress (and strain) within each block is constant. Second, the material within each block is assumed as linear elastic. These two major limitations can often render the original DDA analysis method unrealistic and significantly inaccurate. In the modified DDA approach introduced in this study, these two limitations have been addressed. The authors have used the finite element method (FEM) to discretise each block in the DDA formulation using an automatic mesh generation algorithm to determine the distributions of stress and strain within each block to a desired accuracy. In addition, the Mohr-Coulomb elastic-plastic yield criterion is incorporated within the modified DDA analysis method using a time marching algorithm to account for the possibility of material failure. This allows the plastic behaviour (i.e. yielding) of the material within each block be included in the analysis, which is a significant improvement over the original DDA method. The numerical implementation of the Mohr-Coulomb criterion involves trials using initial elastic stress increment and comparisons with the yield criterion within each element. The proposed DDA formulation including the Mohr-Coulomb failure criterion (termed here as the MC-DDA method) is validated against selected analytical solutions, numerical solutions from FLAC verification problems and field measurements.

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Implementation of the finite element method in the three‐dimensional discontinuous deformation analysis (3D‐DDA)

Cited by 30 publications

References 16 publications

Dynamic sliding of tetrahedral wedge: The role of interface friction

Dynamic sliding of tetrahedral wedge: The role of interface friction

Modelling dynamic deformation in natural rock slopes and underground openings with DDA: review of recent results

Elastic–plastic discontinuous deformation analysis using Mohr–Coulomb model

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