A node-centric indirect boundary element method: three-dimensional displacement discontinuities

Vijayakumar, S.; Yacoub, Thamer; Curran, J.H.

doi:10.1016/s0045-7949(99)00078-4

Cited by 11 publications

(7 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…During the loading process, the relative displacement of the rock joint occurs. As shown in (8), we define the displacement discontinuity on the discontinuous plane as displacement difference between the upper plane (seen as +) and the lower plane (seen as -). For the triangular displacement discontinuity element, the distributions of the displacement are obtained as follows.…”

Section: Ddm Theoretical Solutionmentioning

confidence: 99%

See 1 more Smart Citation

Three‐Dimensional Propagation Simulation and Parameter Analysis of Rock Joint with Displacement Discontinuity Method

Jiang

Ding

et al. 2019

Mathematical Problems in Engineering

View full text Add to dashboard Cite

Displacement discontinuities method (DDM) is convenient for and efficient at dealing with discontinuity problems such as fracture and fault. However, the known method of ease iteration is not available for nonlinear joint surface problems. This paper introduces Barton-Bandis nonlinear joint deformation failure criterion, figures out the propagation model of joint through the maximum energy release rate theory of rock fracture mechanics, and establishes three-dimensional nonlinear displacement discontinuity model for rock joint. This paper gives results of the joint propagation pattern and its distribution law under tension and compression with different parameters and side pressure coefficients via compiled program.

show abstract

Section: Ddm Theoretical Solutionmentioning

confidence: 99%

“…Wen independently developed DDM under three-dimensional elastic condition and then applied it to the research on dynamic crack researches [7]. Vijayakumar developed a three-dimensional elasticity triangular DDM and provided an adaptive integral method [8].…”

Section: Introductionmentioning

confidence: 99%

Three‐Dimensional Propagation Simulation and Parameter Analysis of Rock Joint with Displacement Discontinuity Method

Jiang

Ding

et al. 2019

Mathematical Problems in Engineering

View full text Add to dashboard Cite

show abstract

“…Extending their method to a tensor nonuniform mesh, or even to a logically rectangular mesh, might be possible. Vijayakumar et al (2000) describe a method in which slip is piecewise linear on a triangular mesh. They report evaluating tractions at element vertices.…”

Section: Iga and Dc3dmmentioning

confidence: 99%

“…As stress is singular at such locations for piecewise linear slip, I speculate they regularize the integral for the stress at the nodal points of the source element. See Shou et al (1997) and Vijayakumar et al (2000) for a list of other DDMs. In all DDMs to date, elements are flat even if the slip representation is at least locally smooth. On a curved fault, certain components of stress are singular at flat element edges even if the slip field is smooth.…”

Section: Iga and Dc3dmmentioning

confidence: 99%

Software for Efficient Static Dislocation-Traction Calculations in Fault Simulators

Bradley

2014

Seismological Research Letters

View full text Add to dashboard Cite

Online Material: Software packages with documentation.Quasistatic or quasidynamic rate-state friction (QRSF) simulators are used to study the mechanics of faults (e.g., Shibazaki and Shimamoto, 2007). The displacement discontinuity method (DDM;Crouch and Starfield, 1983) meshes the fault or faults into N elements and constructs a matrix of Green's functions (GFs) relating slip to stress. The simulator evolves strength and slip in time. Usually, the most expensive part of a simulation time step is the matrix-vector product (MVP) of the slip distribution with the DDM matrix; the straightforward implementation performs ON 2 operations. A simulator performs thousands to millions of MVPs with the same DDM matrix.My free and open-source software (FOSS) package hmmvp speeds up simulations by an asymptotic factor of a little less than N faster than the straightforward implementation for both forming an approximation to and performing MVP with the GF matrix.In QRSF simulations, rupture tip length scales as f r ∝ μ ′ d c =bσ for the aging evolution law and f r multiplied by a factor that depends on slip speed and background values for the slip law. In this case, μ ′ μ=1 − ν, μ is the shear modulus, ν is Poisson's ratio, b is the constant multiplying the state term in rate-state friction, σ is the effective normal stress, and d c is the characteristic slip distance for friction evolution (Rubin and Ampuero, 2009). Rupture tips must be well resolved in simulations. If f r is nonuniform on the fault, discretization also can be nonuniform for efficiency. However, not all DDM operators are accurate on nonuniform meshes. My FOSS package dc3dm implements a method, IGA, that is as accurate on a nonuniform mesh as the standard method is on a uniform mesh. dc3dm uses hmmvp to efficiently approximate the IGA operator. H-MATRIXES AND hmmvpA variety of methods can speed up the MVP. Let a rectangular fault be discretized uniformly into N N s N d elements, in which N s is the number of along-strike elements and N d is the number along dip. The straightforward implementation is ON 2 , in which O is big-O notation. In a homogeneous elastic (HE) full-space, the fast Fourier transform (FFT) can be used to calculate stress from slip in ON log N work. In an HE halfspace, the FFTcan be used in the along-strike direction to implement the convolution, resulting in ON 2 d N s log N s time. In general, the FFTcannot be applied to a nonuniformly discretized or nonplanar fault. A class of methods, including fast multipole methods (Greengard and Rokhlin, 1987;Ying et al., 2004), Barnes-Hut (Barnes and Hut, 1986), and hierarchical matrixes (H-matrixes;Hackbusch, 1999), are instead applicable. These methods take advantage of off-diagonal block (for an appropriate permutation) approximate low-rank structure. A block B ≈ UV T , with columnsU ≪ minrowsB; columnsB. For a mesh having N elements, work is close to ON . Among these methods, the H-matrix is best suited to QRSF simulators because it is fastest when the operator is formed infrequently relative to ...

show abstract

“…To evaluate the possible failure mechanism of both events that took place at the level of the seam (±25 m) the 3-D boundary element package EXAMINE 3-D (Rocscience 2008) was employed to estimate stresses between the development tunnels as well as ahead of the double panel. This software is an established numerical tool in the mining industry and is scientifically used to estimate 3-D stresses around underground excavations (Vijayakumar et al 2000;Diederichs et al 2004). The tunnels modelled have dimensions of 700 m × 5 m × 5 m (length × width × height) subjected to an in situ stress field as shown in Fig.…”

Section: Geomechanical Modellingmentioning

confidence: 99%

Rock mechanical analysis of a Ml= 4.0 seismic event induced by mining in the Saar District, Germany

Alber¹,

Fritschen

2011

Geophysical Journal International

View full text Add to dashboard Cite

a 4.0 magnitude seismic event occurred in close proximity to a deep underground longwall coal mine in the German Saar mining district. Preceding this event was a series of smaller seismic events, which can be traced back to geological structures. A seismic network was installed to observe and analyse the seismic events. Underground core drilling was performed to obtain rock samples for rock mechanical testing. Possible causes for the events, failure of rock mass or slip on unknown faults, are evaluated by numerical methods. Failure of rock mass is excluded as a cause since the stresses are well below the strength of the rock mass. Seismic events are of similar fault plane strike and are organized in several clusters, associated with local and regional tectonic elements. It was found from backcalculation that fault planes with friction angles as low as 8 • must have been present. The role of pore pressure on the fault stability is discussed and found to play no role in generating the seismic events. Finally, the question of mining in a rock mass obviously close to failure is addressed and it was concluded that any mining activity would lead to a significant seismic response.

show abstract

A node-centric indirect boundary element method: three-dimensional displacement discontinuities

Cited by 11 publications

References 13 publications

Three‐Dimensional Propagation Simulation and Parameter Analysis of Rock Joint with Displacement Discontinuity Method

Three‐Dimensional Propagation Simulation and Parameter Analysis of Rock Joint with Displacement Discontinuity Method

Software for Efficient Static Dislocation-Traction Calculations in Fault Simulators

Rock mechanical analysis of a Ml= 4.0 seismic event induced by mining in the Saar District, Germany

Contact Info

Product

Resources

About