混合多位移模式的非连续变形分析法研究

传统的非连续变形分析法（DDA）法采用简单的线性位移模式计算效率高,描述大块体的高阶多项式位移模式在一定程度保留了该特点,并提高了计算精度。近年来流行的耦合有限元、自然单元的DDA法实质上是引入相应的插值形函数构成块体位移函数,计算相对低效,但具有计算更精细、更容易施加边界条件等优点。为结合传统DDA法与DDA耦合法各自的优点,建立了一种同时利用传统DDA法线性位移模式与耦合型DDA法非线性位移模式的混合法。该方法非线性模式主要针对大块体,采用了自然单元插值,缘于其具有一定无网格特征,且效率比有限元高。建立了混合模式下的整体矩阵并推导出接触等因素刚度子矩阵和荷载子向量的具体表达式。该方法建模更加方便合理,计算精度、效率介于线性模式的传统DDA法和非线性位移模式的耦合法之间。通过基本算例验证了混合法的有效性,并给出了节理围岩-隧道衬砌整体分析模型的计算结果,体现了新方法的优越性。     

非连续变形分析中块体大转动问题研究

原有非连续变形分析（DDA）采用一阶近似后的位移增量表达式更新块体构形,推导相关子矩阵,且对不同时步计算出的应变增量直接叠加,当模拟的块体发生大转动时往往会产生较大误差。为考虑块体转动与变形的耦合作用,引入先变形、后转动的块体位移增量表达式。重新推导了惯性力子矩阵,将块体转动时的离心力与科氏力加到荷载矩阵中。计算时对应变分量及其相关变量进行坐标变换与修正,并采用新引入的位移增量表达式计算块体顶点位移,进行后接触修正与更新块体构形。数值算例表明,改进后的程序能够消除转动带来的误差,自动考虑了块体转动时离心力和科氏力引起的变形,应变计算精度更高。改进方法克服了块体体积自由膨胀、应变场畸变等问题,给出了合理的块体应变。     

黄土沉积过程及微结构模型的非连续变形分析

黄土是一种具有特殊结构的多孔隙、弱胶结的松散沉积物,存在典型的微观架空结构,其力学行为是微观结构变形与破坏的宏观体现。从本质上揭示黄土的力学行为,需从黄土微结构出发,而黄土的物质组成和微结构特征受其特殊的风积成因所控制,基于此本文提出了一种模拟黄土沉积过程并构建其初始结构模型的方法。为了生成黄土沉积后所形成的微结构模型,并对其进行变形模拟,首先在确定黄土颗粒形态的基础上利用Monte Carlo法生成沉积前的黄土颗粒群,然后引入非连续变形分析方法(DDA)模拟颗粒的下落,该方法能够模拟颗粒下落过程中的相互碰撞及摩擦,由此建立与实际比较接近的黄土初始结构模型。从模型中可以识别出大、中、小3类孔隙结构和台阶(staircase)、重叠(stack)、点接触(point contact)、T型4种接触形式。对所生成的黄土结构模型进行不同压力下的压缩试验,选择不同部位的颗粒作出了径向分布函数,从微观角度说明了黄土在压缩过程中大孔隙和架空结构会首先被破坏。设计了与数值模拟相同条件下的物理模型试验,将两者试验结果进行对比,结果表明数值模拟与物理模型试验的e-lgp压缩曲线的趋势大致相同,表明所提出方法是可行的。该方法为进一步开展黄土力学行为的微观分析提供了基础。     

自然邻点插值算法及其在二维不规则数据网格化中的应用

由于观测数据的不足,对不规则散点数据的二维插值在地球物理中应用非常广泛。这里研究并实现了自然邻点二维插值算法,并以一个大地电磁测深反演数据为例,验证了该方法的可行性与效果。实际资料试算与成图结果表明,该方法具有精度高、插值效果好、速度快以及便于模拟地形数据等优点。     

非连续变形分析方法中的阻尼问题研究

定量研究了非连续变形分析(DDA)方法中的黏性阻尼与数值阻尼。首先,基于Newmark直接积分法,推导了块体系统的运动方程。其次,通过动力学中的黏性阻尼理论建立了DDA中动力系数、时间步长与黏性阻尼比的关系式,探讨了DDA中的常加速度积分方案的数值阻尼分区及阻尼比计算方法,进而得到两种阻尼共同作用时的阻尼比表达式,并分析了频域内阻尼比的分布情况。最后,以谐振激励下的块体振动为例,通过对比不同阻尼作用下块体位移的DDA计算值与理论解,验证了本文提出的阻尼比计算公式的正确性。研究表明：黏性阻尼对低频的衰减作用明显,数值阻尼则可以很快地消除高频干扰,而二者共同作用下可降低阻尼的频率相关性。该研究成果为DDA的振动、波动等动力计算的阻尼取值提供了理论依据。     

有限覆盖径向点插值法及其在土工问题中的应用

将有限覆盖技术与径向点插值方法相结合发展了有限覆盖径向点插值无网格方法,从而综合了数值流形方法与点插值方法的各自优点,能够有效地处理连续与非连续性问题。用该方法构造的形函数具有Kronecker ? -函数属性,方便了位移边界条件的处理。在简要阐述了这种方法基本原理的基础上,将该方法用用于地基附加应力计算分析,结果证明本文方法精度高,方法简单有效。     

水电站地下洞室群分步开挖的非连续变形分析

利用大岗山水电站的地质勘探资料建立不同贯穿节理组合下地下洞室群的DDA模型,分析了洞室群开挖的破坏模式,并简单阐述其破坏机制。基于Monte-Carlo方法模拟节理的随机分布,结合大岗山水电站的开挖设计方案,对地下洞室群在分步开挖过程中的位移及应力演化进行研究。研究表明：洞室群开挖完成后,洞周块体的位移均指向洞内,尾调室上下游与主厂房上游的变形较大;洞周块体的大主应力均平行于洞室边界线,尾调室的应力释放比较明显,其边墙块体发生了滑移;洞室群在开挖过程中互相影响,其中主变室受主厂房和尾调室的影响比较明显。研究结果指出了洞室群开挖过程中需要关注和加固的具体部位,为工程支护措施的优化提供了依据。     

基于线性互补的非连续变形分析

非连续变形分析(DDA)方法是一种新的用来分析块体系统运动和变形的非连续介质数值计算方法。研究的核心工作是致力于对现有DDA接触问题处理方法的改进。DDA主要采用罚函数法和Lagrange乘子法处理接触问题,合理设定罚参数很困难,此外,因开闭迭代而引起的刚度矩阵的不连续变化也会导致收敛方面的困难。为避免引入罚参数及传统意义上的开闭迭代,用混合线性互补模型(LCDDA)对DDA方法进行了重新描述。在此基础上,综合基于非光滑分析的Newton法的局部平方收敛和最速下降法的全局线性收敛的优势,提出求解LCDDA模型的有效算法。根据上述思想及理论研究成果编制了完整的计算程序,算例计算结果证明了方法的精度及可行性。     

非连续变形分析的精度改进方法及研究趋势

由石根华提出的非连续变形分析(DDA)方法理论严密且计算较为高效,在模拟块体滑移、转动和张开等大变形、大位移问题方面具备独特优势,因而在岩土工程领域得到了广泛运用。然而DDA方法在提出初期不可避免地存在一些精度问题,对此石根华及国内外学者就问题产生原因和改进方法开展了大量研究工作。基于部分相关成果的研究学习,对改进原始DDA计算精度的各类方法进行归纳探讨,主要包括:(1)DDA块体内部应力位移场的精度控制;(2)块体接触问题处理方法的改进;(3)人为参数的合理选取;(4)能量耗散机制的考虑;(5)人工边界的改进等方面。对以上方法的改进效果和计算效率进行了简要分析和讨论,在此基础上对DDA的研究热点和发展趋势进行了概述,为该方法的进一步发展和完善提供思路。     

非连续变形分析中时间步及弹簧刚度取值研究

非连续变形分析（DDA）是一种隐式求解的动力学计算方法,且采用在块体界面加减刚硬弹簧的方式来满足块体界面无张拉和无嵌入的接触准则,其中时间步长和弹簧刚度两个物理量的取值直接影响DDA的计算结果。基于对DDA时间步和弹簧刚度在程序运行过程中的调整策略和块体接触的简化力学概念模型,研究了惯性力在DDA收敛求解中的作用过程。采用数值模拟试验对自由落体和斜面单滑块模型在3种力学状态下的相关力学问题进行了数值模拟研究,通过对自由落体运动的模拟,研究了时间步长单一因素对计算结果的影响规律,并初步确定了时间步长的合理取值区间。在此基础上,采用斜面单滑块模型,研究了时间步长和弹簧刚度对计算结果的共同影响,确定了不同时间步长条件下弹簧刚度的合理取值区间。研究成果表明,合适的时间步长和弹簧刚度的取值组合构成一个单连通参数取值域,当时间步和弹簧刚度的取值组合位于此“域”范围内时,DDA的计算结果是合理的。     

Applying disk-based discontinuous deformation analysis (DDA) to simulate Donghekou landslide triggered by the Wenchuan earthquake

In this paper, for the first time, disk-based discontinuous deformation analysis (DDA) is applied to simulate a real landslide triggered by an earthquake. For this purpose, the kinematic behaviour of the Donghekou landslide triggered by the Wenchuan earthquake is simulated and the results obtained using disk-based DDA are compared with actual data. The comparisons show that there is a good agreement between the results obtained using disk-based DDA and observed data. The simulation results provided an understanding of the failure behaviour and temporal evolution of the landslide. This study shows that disk-based DDA is a practical numerical tool that can be used to simulate the post-failure behaviour of landslides triggered by an earthquake.     

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.     

节理岩质边坡变形的DDA模拟

对原非连续变形分析方法（DDA方法）中边界约束方法进行了推广，将其应用于节理岩质边坡变形规律的数值模拟，并利用模型实验结果验证了推广方法的正确性。     

Neighborhood discontinuities in bivariate interpolation of scattered observations

Because of the need for computational efficiency, bivariate interpolation methods applied to scattered observations often involve two stages. Initially the variable is estimated at regular grid nodes using a running subset of data (usually of fixed number). This, however, will produce discontinuities in the interpolated surface. Thus a second stage, curvilinear interpolation technique, is applied to estimated values to smooth out the effect of discontinuities. Such problems can be overcome efficiently in processing large data sets by interpolating over natural neighbor subsets. Interpolation procedures that generate discontinuities in the interpolated surface are inappropriate for geological applications, where dislocations due to structural complications may be present.     

Application of discontinuous deformation analysis on stability analysis of slopes and underground power houses

Continuous computation and limit equilibrium computation are the two independent computations for practical rock engineering. For global stability analysis, limit equilibrium is still the fundamental method. For any numerical method, reaching limit equilibrium requires large displacements, discontinuous contacts, precise friction law, multistep computation and stabilised time-step dynamic computation. Therefore three convergences are unavoidable: convergence of equilibrium equations, convergence of open-close iterations for contacts and convergence of the contact forces of dynamic computations. This paper utilises mainly two dimensional discontinuous deformation analysis (DDA) and an available simple version of three dimensional DDA. The applications show DDA has the ability to reach the limit equilibrium of block systems.     

Considerations of the discontinuous deformation analysis on wave propagation problems

In rock engineering, the damage criteria of the rock mass under dynamic loads are generally governed by the threshold values of wave amplitudes, such as the peak particle velocity and the peak particle acceleration. Therefore, the prediction of wave attenuation across fractured rock mass is important on assessing the stability and damage of rock mass under dynamic loads. This paper aims to investigate the applications of the discontinuous deformation analysis (DDA) for modeling wave propagation problems in rock mass. Parametric studies are carried out to obtain an insight into the influencing factors on the accuracy of wave propagations, in terms of the block size, the boundary condition and the incident wave frequency. The reflected and transmitted waves from the interface between two materials are also numerically simulated. To study the tensile failure induced by the reflected wave, the spalling phenomena are modeled under various loading frequencies. The numerical results show that the DDA is capable of modeling the wave propagation in jointed rock mass with a good accuracy. Copyright © 2009 John Wiley & Sons, Ltd.     

Modeling the interaction between fluid flow and particle movement with discontinuous deformation analysis (DDA) method

Coupled hydro‐mechanical processes in granular media represent the interaction between solid particles movement and fluid flow during external and/or internal loading. The processes attract attention in geotechnical engineering since they cause many disasters such as landslide, slope collapse, boiling/quicksand and soil liquefaction, etc. This study presents a numerical method combining discontinuous deformation analysis (DDA) for mechanical calculation and finite element method for fluid flow simulation to model the interaction between solid particles' movement and fluid flow from microscopic point of view. The term of hydraulic pressure was newly formulated and introduced to the original DDA. The simplified examples are given to verify the new method, and the computational results correlate well with the theoretical calculations, further development is also considered. Copyright © 2010 John Wiley & Sons, Ltd.