Dynamic Parallel Analysis Of 3D-DDA Based On Meta-Contact Search Method

As an important engineering material and engineering environment,the research of rock mass is one of the important topics for human beings.Due to the discontinuous characteristics of rock masses,discontinuous deformation analysis(DDA)is indispensable in the research of various large deformation and dynamic problems of rock masses.However,there are still some problems to be solved in DDA,such as(1)the lack of three-dimensional boundary integration;(2)high cost of contact detection;(3)the classical direct search algorithm is difficult to deal with irregular blocks and large penetration;(4)uncertainty of contact surface;(5)the error of contact force calculation and(6)the inefficient overall calculation of DDA.To solve the above problems,the major work of this paper is as follows:(1)DDA simultaneous equations are derived based on the principle of virtual work,and threedimensional boundary integration is introduced;(2)Based on the approximate cover of2 D polygon edges or 3D polyhedron surfaces(collectively referred to as meta-cover in this paper,see page 54),the rough search based on meta-cover is developed,which notably improves the efficiency;(3)Based on Contact Theory(Shi 2015),the global search for vertex-edge contact between 2D polygons or vertex-face and cross edge-edge contact between 3D polyhedrons(collectively referred to as meta-contact in this paper,see page 77)is carried out,and a Global meta contact Direct Search(GDS)algorithm is proposed to enable it to deal with irregular blocks and large penetration;(4)Last Entrance Meta contact(LEM)is proposed,and the contact face of the first contact point is selected by calculating the entrance order of element contact;(5)The implicit contact force or explicit contact force is proposed to improve the accuracy of contact force,and(6)hardware is used to accelerate DDA calculation.In this paper,the above(2),(3)and(4)are collectively referred to as meta contact search,which is applicable to any numerical method that needs to deal with the contact between polygons or polyhedrons,such as DDA,NMM(Numerical Manifold Method),DEM(Distinct Element Method)and FEM(Final Element Method).(1)DDA governing equation based on virtual work principle and three-dimensional boundary integralBased on the principle of virtual work,the governing equation of DDA is derived,and the submatrix derivation of each load or constraint is given,which lays a foundation for the better application of DDA to multi-field and complex constitutive problems;By projecting the three-dimensional block boundary(surface)to the coordinate surface,the analytical solution of the polynomial integral on the boundary(surface)is obtained using the two-dimensional simplex integral,which provides a basis for the imposition of surface constraints.(2)Meta contact search--rough search based on meta cover The rough search is divided into global rough search for adjacent blocks and local rough search for adjacent geometric elements.The grid search algorithm for non-uniform blocks is introduced into DDA,which expands the concept of judgment cell;A rough search algorithm of meta cover is proposed,which updates the judgment criteria of adjacent blocks,and improves the judgment efficiency of adjacent blocks in global rough search.Meta cover and its intersection provide separate approximate cover for geometric elements at the block boundary,and improve the local rough search efficiency of adjacent geometric elements.(3)Meta contact search-global meta contact direct search algorithmThe direct search algorithm used in DDA uses locality assumption and contact type assumption,so it can not deal with irregular blocks and large penetration well,and it is easy to cause false contact problems and vanishing contact problems,which will lead to calculation failure.It is difficult to relax no-overlapping condition if only the entrance block and reference point in contact theory are used for contact judgment.Therefore,the Global Direct meta-contact Search(GDS)algorithm is developed.The GDS algorithm does not use the local or contact type assumption,and the contact theory can easily prove that the GDS algorithm theoretically can completely avoid the false contact problem and vanishing contact problem,and can consider the relaxed no-overlapping condition.(4)A criterion for entrance order of meta contact searchIn order to solve the problem of indeterminate contact face,the entrance order criterion of meta contact is proposed,that is,the Last Entrance Meta-contact criterion(LEM).It is pointed out that "for the contact between two polygons/polyhedrons,the first entrance point occurs on the contact surface defined by the last entrance meta contact(definition 4.1,see page 71)".The the Last Entrance Meta-contact algorithm based on this criterion can consider the location and moving trend of the block to select appropriate meta contact,which provides a unified solution for the uncertainty problem of two-dimensional and three-dimensional block contact faces.(5)Implicit(augmented open-closed iteration)and explicit schemes for three dimensional frictionIn order to solve the problem of contact force calculation error,two ideas are proposed to improve the friction force calculation accuracy.The first is to use the implicit sliding friction force based on the enhanced open-close iteration,and propose four enhanced modifications to obtain the controllable accuracy.The second scheme uses explicit friction and other interactions to improve the accuracy with a small time step,and decomposes the overall large equation solution into small equations for each block to solve independently.This method will greatly reduce the difficulty of parallelizing DDA.(6)Map/Reduce based cloud parallel EDDA/DDEMTo improve computing efficiency and apply it to different hardware acceleration schemes.The classical program is modified according to two main cycles according to the data reading and writing mode,and the grid search function is added.In order to isolate the work of code design from hardware parallel acceleration,the code is reconstructed according to the pattern of Map/Reduce,which is based on block coarse grain parallel and has the advantage of modularization;The data structure is designed according to the principle of enhancing locality and improving cache hit rate.The parallel mode of Map/Reduce is implemented in parallel on multi-core CPUs and GPUs using Open MP and CUDA.For the first time,EDDA/DDEM is used to simulate the movement of more than one million blocks,and its speed is comparable to some popular parallel DEM algorithms.Based on the aforementioned work,they were applied to landslide analysis,wave propagation through rock mass,rock wall failure simulation of 2016 Kumamoto earthquake,and goaf collapse analysis containing millions of blocks,providing strong support for solving large deformation and dynamic problems of rock mass.