A Model of Point-to-Face Contact for Three-Dimensional Discontinuous Deformation Analysis

Jiang, Qinghui; Yeung, M.R.

doi:10.1007/s00603-003-0008-x

Cited by 135 publications

(72 citation statements)

References 23 publications

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“…Numerical inaccuracies introduced in matrix multiplication may also lead to non-orthonormal matrices after several updates, whereas Equations (1) and (16) always yield an orthonormal matrix.…”

Section: S(a) · C = C · S(a)mentioning

confidence: 98%

“…For example, 3DEC [39,40] uses normal and tangential springs at the intersection point between a discontinuity face and a block's vertex. BSM3D [41][42][43] and 3D-DDA [15,16,44,45] use similar springs located at the vertices of the contact area. In general, these contact points change from one iteration to the next.…”

Section: F Tononmentioning

confidence: 99%

“…Pioneered by Wittke [10,11], the study of rotational failure modes (b) and (c) in Figure 2 was also pursued using analytical methods by Chan and Einstein [12], Mauldon and Goodman [13], and Tonon [14]. These analytical methods cannot handle general simultaneous sliding and rotation; Yeung and co-workers [15][16][17] thus used a numerical method, such as the discontinuous deformation analysis (DDA), to overcome the problem.…”

Section: Introductionmentioning

confidence: 97%

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Analysis of single rock blocks for general failure modes under conservative and non‐conservative forces

Tonon

2007

Num Anal Meth Geomechanics

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SUMMARYAfter describing the kinematics of a generic rigid block subjected to large rotations and displacements, the Udwadia's General Principle of Mechanics is applied to the dynamics of a rigid block with frictional constraints to show that the reaction forces and moments are indeterminate. Thus, the paper presents an incremental-iterative algorithm for analysing general failure modes of rock blocks subject to generic forces, including non-conservative forces such as water forces. Consistent stiffness matrices have been developed that fully exploit the quadratic convergence of the adopted Newton-Raphson iterative scheme. The algorithm takes into account large block displacements and rotations, which together with nonconservative forces make the stiffness matrix non-symmetric. Also included in the algorithm are in situ stress and fracture dilatancy, which introduces non-symmetric rank-one modifications to the stiffness matrix. Progressive failure is captured by the algorithm, which has proven capable of detecting numerically challenging failure modes, such as rotations about only one point. Failure modes may originate from a limit point or from dynamic instability (divergence or flutter); equilibrium paths emanating from bifurcation points are followed by the algorithm. The algorithm identifies both static and dynamic failure modes. The calculation of the factor of safety comes with no overhead. Examples show that the equilibrium path of a rock block that undergoes slumping failure must first pass through a bifurcation point, unless the block is laterally constrained. Rock blocks subjected to water forces (or other non-conservative forces) may undergo flutter failure before reaching a limit point.

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Section: S(a) · C = C · S(a)mentioning

confidence: 98%

Section: F Tononmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

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Analysis of single rock blocks for general failure modes under conservative and non‐conservative forces

Tonon

2007

Num Anal Meth Geomechanics

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“…The key to any discontinuity-based numerical method is a rigorous contact theory that can describe the interactions of multiple three-dimensional (3D) blocks [16]. Developing such a theory is a difficult task because contacts may exist between any combination of vertices, edges and faces, and contacts between blocks must be identified and updated continuously throughout the computation process [17].…”

Section: Introductionmentioning

confidence: 99%

“…Wu et al [29] presented an algorithm that found vertex-to-face contacts as the first step toward a more comprehensive 3D analysis. Yeung et al [30] and Jiang and Yeung [16] developed a pointto-face model, which formed part of a contact method to be used in 3D DDA. Wu [31] presented a new edge-to-edge contact calculation algorithm in which edge-to-edge contacts were transformed into vertex-to-face contacts.…”

Section: Introductionmentioning

confidence: 99%

A shrunken edge algorithm for contact detection between convex polyhedral blocks

Wang

Feng

2015

Computers and Geotechnics

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High‐order three‐dimensional discontinuous deformation analysis (3‐D DDA)

Beyabanaki

Jafari

Yeung

2009

Numer Methods Biomed Eng

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Three-dimensional discontinuous deformation analysis (3-D DDA) with high-order displacement functions has been derived for the requirement of highly accurate stress and strain calculations. The high-order displacement function allows nonlinear distributions of stresses and strains within a discrete block, which significantly enhances 3-D DDA as an analysis technique. Formulations of stiffness and force matrices in second-and third-order 3-D DDA due to elastic stress, initial stress, body force, point load, fixed point, inertial force, normal and shear contact forces and friction force are presented. The VC++ codes for the second-and third-order cases have been developed, and they have been applied to examples of 3-D beams, bending under various loading conditions applied at the end and to an example of discontinuous problem. Results of modeling, are well in agreement with theoretical solutions. In contrast, the results calculated for the same model, using original first-order 3-D DDA are far from the theoretical solutions.blocks [13,14]. The NMM, still retaining most of the DDA's attractive features, can be considered a generalized finite element and DDA method. Additionally, Chen et al. developed the high-order version of the manifold method [15] and Cheng et al. [16] showed that the use of more advanced Wilson non-conforming element in NMM can be useful in obtaining more accurate results for simple covers. Cheng and Zhang [17] presented three-dimensional NMM based on tetrahedron and hexahedron elements.An alternative approach is to include more polynomial terms in the displacement function. Unlike the sub-blocking method, it is possible to obtain good results using high-order displacement functions without discretizing the blocks. In the sub-blocking method, constraints between subblocks may not be satisfied accurately, which may lead to some errors in results, but this source of error is avoided in higher-order methods. The number of unknowns of analysis for one block using third-order displacement function is equal to the unknowns of analysis for a block divided into five sub-blocks. Using the sub-blocking method, to obtain good results comparable those from using a third-order displacement function, it is usually necessary to divide a block to many sub-blocks; however, the accuracy is problem dependent. Chern et al. [18] and Koo et al. [19] implemented a second-order displacement function in 2-D DDA. Ma et al. [20] and Koo and Chern [21] implemented a third-order displacement function in 2-D DDA method. Hsuing [22] developed a more general formulation for 2-D DDA. These studies showed that complicated stress and strain fields can be modeled using high-order displacement functions. MacLaughlin and Doolin [23] provided a review of more than 100 published and unpublished validation studies on the DDA approach. Previous DDA studies focused on solving problems in two dimensions, but in many engineering problems, three-dimensional effects have to be considered. Up to now, relatively little work on DDA development ...

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A Model of Point-to-Face Contact for Three-Dimensional Discontinuous Deformation Analysis

Cited by 135 publications

References 23 publications

Analysis of single rock blocks for general failure modes under conservative and non‐conservative forces

Analysis of single rock blocks for general failure modes under conservative and non‐conservative forces

A shrunken edge algorithm for contact detection between convex polyhedral blocks

High‐order three‐dimensional discontinuous deformation analysis (3‐D DDA)

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