塔中地区构造应力场数值模拟研究

构造应力场研究对于油气运聚分析及储层特征描述具有重要的理论和实际意义。本文根据塔中隆起断裂特征及其演化史,结合钻井资料,选择中下奥陶统碳酸盐岩为主要研究对象,应用大型有限元分析软件ANSYS,在处理断层问题时运用非连续的接触算法,模拟了中奥陶世末、中泥盆世末、三叠纪末、新近纪末的构造应力场,研究了该区不同时期的古应力分布特征。研究表明,最大主压应力受东部车尔臣-星星峡走滑断裂影响显著,在隆起区沿断裂带呈条带状低值分布,在不同时期塔中Ⅰ号断裂带无一例外地位于最大主压应力的最低区,反映了塔中断裂带尤其是塔中Ⅰ号断裂带是油气运移的有利指向区。最小主压应力沿断裂带呈条带状高值分布,在断裂的上盘、断裂走向发生变化和断裂的倾末端是张应力高值区,为张裂缝发育的重要构造部位。最小主压应力和最大剪应力受车尔臣-星星峡走滑断裂的影响明显减弱。     

多重散射问题的改进算法以及双排非连续弹性屏障对水平向剪切波的隔离研究

与Aviles等学者的多重散射隔振理论相比较,采用更为完整的Fourier-Bessel函数系的级数展开表达式来研究弹性波入射下的多重散射问题。引入Graf加法定理,并结合位移和应力边界条件,推导了无限均匀弹性介质中任意分布的多个弹性圆柱体对于平面水平向剪切波(SH波)入射时散射系数的理论解析解。随后,取圆柱体分布于两条相互平行的直线上,则问题演变为双排弹性桩屏障对于弹性波的隔离问题。引入无量纲位移(屏障后土体总的位移与仅由入射平面水平向剪切波引起的位移的比值)和透射系数(屏障宽度范围内无量纲位移的几何平均值)的概念来研究屏障的隔振效果。重点讨论了双排桩间距h以及桩土的剪切模量比ξ对于屏障整体隔振效果的影响,阐述了双排桩屏障的隔振性状。特别地,当h=0时,该问题退化为常见的单排非连续屏障的隔振问题。     

公路隧道局部塌方洞段的围岩稳定性评价

结合某公路隧道工程,以现场地质调查和监测资料为基础,在结构面发育且可能发生大规模塌方的围岩洞段,根据现场实际统计的优势结构面产状,采用关键块体理论、非连续变形方法（DDA）首先确定围岩主要的失稳破坏模式,然后运用连续介质分析程序FLAC,在DDA方法确定的围岩实际变形破坏塌方形态的基础上进行计算分析,评价围岩的整体稳定性及加固措施的有效性。分析表明,围岩破坏的主要模式为受结构面控制的局部块体的失稳,工程开挖后围岩不会发生大变形,这与实际情况基本一致,为安全施工提供了保证。采用非连续变形方法和连续介质计算相结合的分析方法对隧道工程塌方稳定性进行研究,取得了较好的效果,研究方法和经验可为类似工程参考并借鉴。     

Part II. Discontinuous Galerkin method applied to a single phase flow in porous media

Discontinuous Galerkin numerical simulations of single phase flow problem are described in this paper. The simulations show the advantages of using discontinuous approximation spaces. hp convergence results are obtained for smooth solutions. Unstructured meshes and unsmooth solutions are also considered.     

模拟摩擦接触问题的新型无网格数值方法

针对摩擦接触问题,给出一种新型的无网格数值方法。该方法基于单位分解思想,在标准无网格Galerkin法的位移模式中嵌入不连续函数和裂尖奇异函数,分别反映接触面的不连续性和接触面端点的奇异性;结合接触摩擦定律,继而构造出求解摩擦接触问题的无网格线性互补模型。在该方法中,接触面方程使用接触点对离散,全局离散系统方程则转化为标准的线性互补问题,可以很方便地使用Lemke算法求解。算例分析证明,本文方法的正确性和有效性。     

基于尺度律的裂隙网络生成及其对地下厂房稳定性的影响分析

以锦屏二级为工程背景,通过对猫猫滩闸址区域内断层的统计,得到断层数量与尺度的幂律关系,并通过分段线性拟合的方法估算了断层系统的尺度-数量分维发现,当断层迹长 0.1 km时,分维 0.487 5;当断层迹长 0.1 km时,分维 1.496 1。通过该尺度律关系,结合蒙特卡洛法,推演了更小规模的节理的空间分布。运用DDA数值计算程序,分析并模拟了大水沟地下厂房的开挖过程,获得了高度节理化的由开挖引起的应力、位移变化图。     

Highly efficient iterative methods for solving linear equations of three-dimensional sphere discontinuous deformation analysis

The efficiency of solving equations plays an important role in implicit-scheme discontinuous deformation analysis (DDA). A systematic investigation of six iterative methods, namely, symmetric successive over relaxation (SSOR), Jacobi (J), conjugate gradient (CG), and three preconditioned CG methods (ie, J-PCG, block J-PCG [BJ-PCG], and SSOR-PCG), for solving equations in three-dimensional sphere DDA (SDDA) is conducted in this paper. Firstly, simultaneous equations of the SDDA and iterative formats of the six solvers are presented. Secondly, serial and OpenMP-based parallel computing numerical tests are done on a 16-core PC, the result of which shows that (a) for serial computing, the efficiency of the solvers is in this order: SSOR-PCG > BJ-PCG > J-PCG > SSOR>J > CG, while for parallel computing, BJ-PCG is the best solver; and (b) CG is not only the most sensitive to the ill-condition of the equations but also the most time consuming under both serial and parallel computing. Thirdly, to estimate the effects of equation solvers acting on SDDA computations, an application example with 10 000 spheres and 200 000 calculation steps is simulated on this 16-core PC using serial and parallel computing. The result shows that SSOR-PCG is about six times faster than CG for serial computing, while BJ-PCG is about four times faster than CG for parallel computing. On the other hand, the whole computation time using BJ-PCG for parallel computing is 3.37 hours (ie, 0.061 s per step), which is about 36 times faster than CG for serial computing. Finally, some suggestions are given based on this investigation result.     

Unified displacement boundary constraint formulation for discontinuous deformation analysis (DDA)

Displacement boundary constraints in discontinuous deformation analysis (DDA) are applied using stiff penalty springs. A co‐ordinate‐free formulation for displacement boundary constraints is presented here for DDA, which unifies previous derivations for points of fixity, and for points constrained to induce or prohibit block motion in specified directions as a function of location or time. Examples for each type of constraint are used to illustrate the behaviour of the algorithm and provide a link with previous formulations for each case. The new, unified formulation has five benefits: (1) simple to express algorithmically; (2) easy to program and verify; (3) penalty values in different directions may be chosen to allow fixed points, lines, curves or planes; (4) formulation works for 2D and 3D; (5) displacement constraint may be a function of time or location or both. Feedback in the algorithm may induce internal resonance in homogeneously deformable discrete elements used in DDA, and resonance in block‐to‐block contact interactions. Consequently, high mass problems with insufficient damping may suffer from excessive ‘vibrational hammering’, inducing physically implausible behaviour such as elastic rebound. Copyright © 2005 John Wiley & Sons, Ltd.     

非连续变形分析与现代地壳运动研究

介绍了非连续变表分析（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。     

球面坐标系非连续变形分析折数学模型

从球面坐标系的弹性力学基础方程出发，推导出球面上块体的位移与6个位移不变量之间的数学关系，进一步建立了联立方程式的球面坐标形式，为大范围现代地壳运动的非连续形变形下了数学基础。