Movie of Million Block Model of Cavern Response
The details behind the computation responsible for the movie presented below are summarized in two articles that are described below. The first article concentrates on the computer science aspects while the second presents an example of new studies with millions of blocks that are now possible with parallel processing versions of already developed programs. Further questions should be sent to the authors via their Email addresses: email@example.com, firstname.lastname@example.org, email@example.com. Further information concerning computational rock mechanics and mechanics can be found at the authors' web sites by clicking their names below.
OPTIMIZATION OF A DISCRETE ELEMENT PROGRAM FOR PARALLEL PROCESSING
C.H. Dowding, Professor of Civil Engineering
O. Dmytryshyn, Post Doctoral Fellow of Civil Engineering
T.B. Belytschko, Professor of Mechanical Engineering
This paper generalizes the modification of an explicitly computed discrete element code for parallel operation NURBM3D to leverage the experience for similar modification of other such codes. After modification, the code is now capable of analyzing 2,000,000 elements for time varying loading. Modifications included the initial optimization of the primary computational algorithm for serial computation, as well as subsequent modification for SIMD (single instruction multiple data stream) and MIMD (multiple instruction, multiple data stream) parallel computers. Comparative observations are made for pre and post processing issues. This paper has been submitted for publication to the Computers and Geotechnics.
VERY LARGE DISCRETE ELEMENT ASSESSMENT OF 3D CAVERN RESPONSE TO DYNAMIC EXCITATION
T.B. Belytschko,Professor of Mechanical Engineering
O. Dmytryshyn, Post Doctoral Fellow of Civil Engineering
Charles Dowding, Professor of Civil Engineering
Increasing computer speed, which has become possible through the development of massively parallel computers, provided the opportunity to reconfigure NURBM3D to operate in a parallel mode. NURBM3D is a three dimensional distinct element code that is optimized to investigate dynamic response of realistically jointed rock masses. In addition a new Curnier joint response law has been introduced to increase computational efficiency. Model validation was accomplished through comparison of recently measured and computed response of model caverns to large mechanical and explosively-induced over pressures. Finally the new NURBM3DP was employed to calculate response of a 1,200,000 block model of a three dimensional cavern subjected to high frequency earthquake shaking to investigate the importance of end effects and the direction of wave propagation. This paper introduces the new model, substantiates its validation and demonstrates the influence of cavern wall geometry and direction of wave propagation. This paper has been submitted for publication to the Journal of Rock Mechanics and Rock Engineering.
The capability of analyzing rock masses with millions of blocks allowsinvestigation of situations heretofore uncalculatable such as three dimensional(3D) end effects of caverns and behavior with realistic joint spacing.
To demonstrate the computational advances now possible with parallel computation, a 20m wide, 25m high model cavern shown in the movie was shaken with 30Hz high frequency earthquake excitation to compute three dimensional(3D) end response with NURBM3DP. The model volume occupies a prism of blocks 75 by 90 by 45m in the cavern's (z,x,y or vertical, transverse, and longitudinal directions.) Block geometry with a symmetrical 0.7m joint spacing in xz plane and 0.5m joint spacing in y direction can be seen. Varying colors express different magnitudes of relative displacements of blocks during the wave propagation, with the warmest colors representing the largest.
After trimming the overall volume as much as possible, some 1,200,000, 0.7m blocks are necessary to fill the model volume surrounding the excavated cavern. To preserve the significant geometry of the problem and to reduce the burden of post processing graphics, only the blocks bounding the cavern and those on three orthogonal planes are shown. The orthogonal planes define the limits of the model volume. Only one end of the cavern was modeled. Thus in a sense the cavern extends an infinite distance to the left.
This example in the cavern responce article is presented as an illustration of possibilities of parallel computation rather than an exhaustive parameter study. However, it does quantitatively demonstrate 3D end effects not possible with models limited to 2D representations by the small numbers of block. Comparisons of relative displacements at the rounded cavern ends with their analog locations along the cavern sides reflect field experience that rounded excavation slopes endure lower stress concentrations than those with sharp corners. Direction of wave propagation has some influence on the stability value of certain blocks because waves of relatively short rise times "wrap around" the cavern and produce stress concentrations that can be seen in the movie.
Interpreting the response of million block models requires that the response be reported graphically. In fact, graphical interpretation or scientific visualization is such an important consideration that it has become a field unto itself (Williams, 1994, Ph.D. Dissertation, Northwestern University). TecPlot, was found to be sufficient for use in this project and has been employed to produce the black and white graphics as well as the color movies of relative displacement earthquake response.
The movie shows the cavern response to a transverse, polarized 30 Hz shear wave that propagates upward. This motion is continuously repeated. If you have a slow connection or older hardware loading the movie may take a long time. The 800Kb movie file is in a high resolution 16 colors gif89a format. No plug-ins are necessary to view the movie with Netscape 2.0 or newer.
Click here to watch the movie
We would like to acknowledge the support of the National Science Foundationunder Grant MSS 92-16274 and the encouragement of Dr. Priscilla Nelsonof the Geo-mechanics-technical & -environmental Systems G3S Program.We are grateful to Prof. Prithviraj Banerjee for providing access to theNorthwestern University Center for Parallel and Distributed Computing facilitiesalso supported by the National Science Foundation Grant CDA-9703228.