Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Fast parallel algorithms for short-range molecular dynamics

The validity of the cubic law for laminar flow of fluids through open fractures consisting of parallel planar plates has been established by others over a wide range of conditions with apertures ranging down to a minimum of 0.2 µm. The law may be given in simplified form by Q/Δh = C(2b)3, where Q is the flow rate, Δh is the difference in hydraulic head, C is a constant that depends on the flow geometry and fluid properties, and 2b is the fracture aperture. The validity of this law for flow in a closed fracture where the surfaces are in contact and the aperture is being decreased under stress has been investigated at room temperature by using homogeneous samples of granite, basalt, and marble. Tension fractures were artificially induced, and the laboratory setup used radial as well as straight flow geometries. Apertures ranged from 250 down to 4µm, which was the minimum size that could be attained under a normal stress of 20 MPa. The cubic law was found to be valid whether the fracture surfaces were held open or were being closed under stress, and the results are not dependent on rock type. Permeability was uniquely defined by fracture aperture and was independent of the stress history used in these investigations. The effects of deviations from the ideal parallel plate concept only cause an apparent reduction in flow and may be incorporated into the cubic law by replacing C by C/ƒ. The factor ƒ varied from 1.04 to 1.65 in these investigations. The model of a fracture that is being closed under normal stress is visualized as being controlled by the strength of the asperities that are in contact. These contact areas are able to withstand significant stresses while maintaining space for fluids to continue to flow as the fracture aperture decreases. The controlling factor is the magnitude of the aperture, and since flow depends on (2b)3, a slight change in aperture evidently can easily dominate any other change in the geometry of the flow field. Thus one does not see any noticeable shift in the correlations of our experimental results in passing from a condition where the fracture surfaces were held open to one where the surfaces were being closed under stress.

/pdf/validity-of-cubic-law-for-fluid-flow-in-a-deformable-rock-2ynq4id3hq.pdf

VALIDITY OF CUBIC LAW FOR FLUID FLOW IN A DEFORMABLE ROCK FRACTURE - eScholarship

Abstract Knowledge of the spacing and size of discontinuities in a rock mass is of considerable importance for the prediction of rock behaviour. The characteristics of discontinuities can be estimated using scanline surveys but the precision of the estimates must be obtained and the bias caused by linear sampling must be eliminated before they can validly be used. Initially, an expression is presented which gives the degree of confidence that can be assigned to the measured mean discontinuity spacing. A reduced form of this expression is obtained for cases where the discontinuity spacings follow the negative exponential distribution. The precision of discontinuity frequency and RQD estimates is also explained. The distribution of trace lengths produced by the intersection of planar discontinuities with a planar rock face is used to determine the distribution of trace lengths, the distribution of semi-trace lengths and the distribution of censored semi-trace lengths intersected by a randomly located scanline. Comparison of the actual and sampled distributions demonstrates the bias introduced by scanline sampling of trace lengths. Relations between the distributions can be used to produce analytical or graphical methods of estimating mean trace length from censored measurements at exposures of limited extent.

Estimation discontinuity spacing and trace length using scanline surveys

http://uu.diva-portal.org/smash/get/diva2:1153724/FULLTEXT01

The use of discrete fracture networks for modelling coupled geomechanical and hydrological behaviour of fractured rocks

Numerical investigation of the effect of joint geometrical parameters on the mechanical properties of a non-persistent jointed rock mass under uniaxial compression

A discrete numerical approach for modeling face stability in slurry shield tunnelling in soft soils

Pile and pile group response to tunnelling using a large diameter slurry shield – Case study in Shanghai

Physical model test and numerical analysis on the behavior of stratified rock masses during underground excavation

This study explores the link between the monotonic and cyclic undrained behaviour of sands using the discrete element method (DEM). It is shown that DEM can effectively capture the flow deformation of sands sheared under both monotonic and cyclic undrained loading conditions. When subjected to cyclic shearing, flow-type failure is observed for a loose sample, while cyclic mobility is observed for a dense sample. A strong correlation between the monotonic and cyclic loading behaviour that has been revealed experimentally is also confirmed in DEM simulations: (a) flow deformation occurs in the compressive loading direction when the cyclic stress path intersects the monotonic compression stress path prior to the monotonic extension stress path, and vice versa; (b) the onset of flow deformation in q–
 $$p^{\prime }$$
 space is located in the zone bounded by the critical state line and the instability line determined from monotonic simulations. Hill’s condition of instability is shown to be effective to describe the onset of flow failure. Micro-mechanical analyses reveal that flow deformation is initiated when the index of redundancy excluding floating particles drops to below 1.0 under both monotonic and cyclic loading conditions. Flow deformation induced by either monotonic or cyclic loading is characterized by an abrupt change of structural fabric which is highly anisotropic. The reason why the dense sample dilated during monotonic loading but showed cyclic mobility (temporary liquefaction) during cyclic loading is attributed to the repeating reversal of loading direction, which leads to the periodic change of microstructure.

/pdf/dem-analysis-of-the-onset-of-flow-deformation-of-sands-4c8yxgk7gh.pdf

Zixin Zhang

Papers

A discrete numerical approach for modeling face stability in slurry shield tunnelling in soft soils

Pile and pile group response to tunnelling using a large diameter slurry shield – Case study in Shanghai

Physical model test and numerical analysis on the behavior of stratified rock masses during underground excavation

DEM analysis of the onset of flow deformation of sands: linking monotonic and cyclic undrained behaviours

The role of TBM asymmetric tail-grouting on surface settlement in coarse-grained soils of urban area: Field tests and FEA modelling