非连续变形分析与现代地壳运动研究

介绍了非连续变形分析(DDA)方法的原理、特点及适用范围,分析了DDA方法较常用的有限元法的优越性,进一步提出把现有平面DDA方程推广到球面DDA方程的基本思路,希望为在大范围内研究地壳运动找到突破口。在此基础上,结合目前我国地学研究的热点,提出了三类最具代表性的实际问题,应用DDA方法可以在此方面进行深入研究

Study on DiscontinuousDeformation Analysis and Modern Crustal Movement

This paper discusses the application of discontinuous deformation analysis (DDA),apowerful numerical method, to the simulation of crustal movement problems. The problems ofcrustal movement contain the movement of large plates to small active faults. Usually, finite element (FE) method is used to the simulation of crustal movement problems, but discontinuousfaults exist in plates and discontinuous medium exist in rocks. So traditional numerical methods(especial for finite element method) are not efficient to simulate crustal movement. DDA methodis better than FE method.　　This paper introduces the principle of DDA method. After DDA method compared with FEmethod,the advantage and limitation of DDA method discussed.　　For efficiently using DDA method in the simulation of crustal movement, the idea of developing DDA method in 2D plane coordinate system to a new DDA method in 2D spherical coordinatesystem is shown for the first time.　　1)Establishing the function equation between displacement and its invariant of any point ofthe blocks on the spherical surface. Based on the basic relation formula of displacement and strainon the spherical coordinate system, the function equation of displacement (u, v) and its invariant( u0, v0, r0, εφ, εθ, γφθ) on the spherical surface can be set up. The linear approximately expres-sion of deformation of blocks will be assumed.　　2) Establishing the relation equation of the blocks on spherical surface depending on the theory of Least Potential Energy. The potential energy expression will be separately resolved,includingthe stiffness stress, initial stress, points loading, volume force, inertial stress,fixed displacement ofpoints etc. By differencing the equation, the coefficient child matrix can be got, and then added tothe relation equation.　　3)Establishing the kinematics equation of block system formed by a lot of blocks on thespherical surface. A mathematic expression must be achieved to describe the relation between thenearby blocks. The invasion is not allowed among the blocks. The problem of no invasion can bewell resolved in high precise through adding rigidity spring on the edge of blocks. The appendingof rigidity spring is judged by distance of invasion on the edge of the nearby blocks.The calculation of distance invasion will be very complex on spherical coordinate system. In order to make thecalculation simple and highly efficient, local plane projection coordinate system is chose and theproblem of spherical surface becomes as easy as the situation of plane coordinate.　　In the fourth part of the paper, focusing on researching region of geosciences, three kinds ofproblem of crustal movement are mentioned, and a working plan is shown. DDA method can playan important part in the areas.