三维多值走时地震波场重建及格林函数计算   总被引：7，自引：0，他引：7       下载免费PDF全文

张钋  杨长春  李幼铭 《地球物理学报》2000,43(2):241-250

针对三维复杂介质地震波传播数值计算中出现的多值走时情况,阐述了地震波场重建及格林函数计算中的困难,提出一种在相空间拉格朗日流形上的波场重建及格林函数计算方法．本文算法应用于三维叠前深度偏移处理流程时,可高效地获得均匀网格点上地震波多值走时及振幅的数值计算结果．文中还阐明两类数值计算过程判据,以在多值走时区域及计算的全区域中,控制射线追踪过程中的射线密度及格林函数计算精度．算例验证了本文方法的有效性．  相似文献   

涡旋流自发辐射惯性重力波的初步解析研究   总被引：2，自引：1，他引：1       下载免费PDF全文

赵南  甘璐  沈新勇 《应用气象学报》2010,21(1):83-88

平衡流(或粗略地说涡旋流)调整目前被认为是惯性重力波产生的一种新的机制并被称为自发辐射问题。基于f平面上正压模式,该文对涡旋流自发辐射惯性重力波这一问题进行了初步解析研究。首先,通过该模式讨论了慢流形和平衡流的概念并强调了平衡流的涡旋运动特征。假定Froude数F《1且Rossby数ε=O(1)(即近似为平衡流的涡旋流包括了梯度风和其他非地转成分),于是基本方程可以写为有关惯性重力波的非齐次波动方程,其非齐次项与涡旋流的非平衡性质有关,而对于严格平衡的涡旋流,非齐次项消失,故涡旋流的非平衡性实际上提供了惯性重力波的强迫源,通过找出该方程的格林函数给出了反映自发辐射的非齐次解。在远离波源的区域,该非齐次解可以展开为远场形式,包括单极、偶极和四极辐射,另一方面,在波源区域以内及其附近,解的近场形式可以看作是慢流形的近似表达式。结果表明:与涡旋流相伴随的辐合/辐散运动主要由两部分组成,即由它自发辐射出的惯性重力波以及从属于平衡流的缓慢变化的辐合/辐散运动。与Ford的匹配渐近展开方法相比较,尽管不能给出更高阶近似,但格林函数法得到的非齐次解形式,在描写自发辐射方面更具物理直观性。  相似文献   

数值流形方法对岩土工程开挖卸荷问题的模拟   总被引：9，自引：0，他引：9  

朱爱军  邓安福  曾祥勇 《岩土力学》2006,27(2):179-183

基于数值流形方法数学覆盖与物理网格的相对独立性,考虑任一时刻体系中真实存在的各平衡力项对体系平衡的作用,提出用数值流形方法模拟岩土工程开挖卸荷的方法。相对于传统数值方法,数值流形方法在模拟开挖时不用计算开挖面上的释放荷载,不用为卸除的材料部分准备专门的单元,简单的数学网格可以适应任意的开挖过程,使其对开挖的模拟更加简便和有效,同时高阶的流形方法对开挖问题具有较高的求解精度。  相似文献   

节理岩体冲击破坏的数值流形方法模拟     

刘红岩  王贵和 《岩土力学》2009,30(11):3523-3527

节理的存在是岩体明显区别于岩石的一个重要特征,也是导致岩体具有非均质性及各向异性的一个重要因素。节理岩体在爆炸冲击荷载作用下的破坏特征不仅是岩体力学研究的一个热点问题,也是岩石爆破领域经常遇到的一个工程问题。目前,常用的有限元和离散元等数值方法都不能很客观地反映岩体中节理分布的实际规律,而最新出现的数值流形方法则完全能够按照岩体中节理的实际分布规律进行建模,并能够很好地模拟岩体在外力作用下新裂纹的产生及已有节理的开裂。对3种不同节理岩体,即无节理岩体、均布水平节理岩体、均布垂直节理岩体等在均布垂直于圆周方向上的冲击荷载作用下的破坏过程进行了模拟。由模拟结果可以明显看出,节理的存在对岩体的破坏型式起到了关键性的控制作用。对于完整岩体,其破坏型式呈现出了很好的对称性;而对于水平及垂直节理岩体,其破坏型式在很大程度上受到节理分布的控制。研究结果对岩石爆破工程设计具有一定的指导意义。  相似文献   

基于改进数值流形法的接触裂纹问题研究     

杨石扣  张继勋  任旭华 《岩土力学》2019,40(5):2016-2021

接触裂纹问题在工程结构中较为常见。结合数值流形法在裂纹处理上的优势,分析了压剪荷载作用下的接触裂纹问题,模拟了压剪裂纹渐进扩展过程。为了减少由于裂纹尖端位置不同而产生的误差,对裂纹尖端附近一定范围内的每一个物理覆盖附加奇异覆盖函数项,并根据裂纹尖端位置和单元含奇异物理覆盖的数目进行分区积分。选取一个压剪破坏算例,分析了法向接触力对应力强度因子计算结果的影响,并模拟了其渐进破坏过程。计算结果表明,所提方法在压剪裂纹问题方面的可行性,与未细化和覆盖细化方法得到的结果相比,更能准确地描述裂纹扩展路径。法向接触力对II型应力强度因子的贡献为0,对I型应力强度因子的影响较大,相对误差随网格密度变化明显,且法向接触力对I型应力强度因子的影响要比直接施加内压时的影响大。  相似文献   

六面体有限覆盖的三维数值流形方法的非线性分析     

周小义  邓安福 《岩土力学》2010,31(7):2276-2282

对三维问题的分析是数值流形方法发展的必然,在数值流形方法覆盖位移函数的基础上构造了一种六面体有限覆盖的三维流形单元,推导了相应的应变矩阵、刚度矩阵及平衡方程等表达式。同时,由于目前数值流形方法的模拟分析主要是采用线弹性模型,而对于非线性模型分析研究很少;根据数值流形方法的特点和岩土体的本构模型,给出了适用于数值流形方法进行非线性分析的算法。该方法利用中点增量法进行求解,以改变 模型和 模型中弹性模量的方式来反映非线性,其实质是用分段线性来取代非线性。通过地基沉降计算算例表明,数值流形方法在三维岩土体中进行非线性分析中是有效的。  相似文献   

接触处理Munjiza方法在数值流形法中的应用     

徐栋栋  孙冠华  郑宏 《岩土力学》2013,34(2):526-534

数值流形法（NMM）在接触处理过程包括：接触方式判断,包括点-点和点-线接触;开-闭迭代,确定块体系统的约束状态;以及接触传递,将有效的接触对传递到下一个时步。过程稍显繁琐和耗时,且与真实的物理接触状态有异。由Munjiza所提出的NBS（no binary search）接触检测算法,将单元映射到规则格子中,以链表结构将其有效地连接在一起,只在单元所在格子以及周围格子内部进行接触判断,接触检测效率大为提高,计算量仅随单元数线性增长,内存需求也很低。在计算接触力时以所定义的势为媒介,用重叠面积来衡量接触力的大小,属于分布式接触力,更接近于实际,避免了原NMM接触处理过程的繁琐。因此,将其作为一种平行的接触处理方法引入到NMM中,并以算例验证,证实了算法的可行性。  相似文献   

A coupled time integration algorithm for discontinuous deformation analysis using the numerical manifold method     

Xiaolei Qu  Guowei Ma  Chengzhi Qi  Arcady V. Dyskin  Chen Xia 《国际地质力学数值与分析法杂志》2020,44(8):1145-1169

To improve the computational efficiency of the numerical manifold method for discontinuous deformation simulations, a spatial-domain coupled explicit-implicit time integration algorithm is proposed. A subdomain partition algorithm based on a super manifold element is developed for the numerical manifold method to simulate dynamic motions of blocky rock mass. In different subdomains, explicit or implicit time integration method is employed respectively based on its contact and motion status. These subdomains interact through assembling the corresponding explicit or implicit time integration-based matrices of different rock blocks. The computational efficiency of the discontinuity system under dynamic loading is improved by partially diagonalizing the global matrices. Two verification examples of a sliding block along an inclined plane under a horizontal acceleration excitation and a multiblock system acted on by dynamic forces are studied to examine the accuracy of the proposed numerical method, respectively. A highly fractured rock mass situated on an inclined slope subjected to seismic excitations is then studied to show the computational efficiency of the developed algorithm. The simulated results are in good agreement with those from the versions using purely implicit or explicit time integration algorithm for the numerical manifold method. The computational efficiency is shown to be higher using the proposed algorithm, which demonstrates its potential for application in dynamic analysis of highly fractured rock masses.  相似文献   

Boundary settings for the seismic dynamic response analysis of rock masses using the numerical manifold method          下载免费PDF全文

Yongtao Yang  Hongwei Guo  Xiaodong Fu  Hong Zheng 《国际地质力学数值与分析法杂志》2018,42(9):1095-1122

Aiming to accurately simulate seismic dynamic response of rock masses using the numerical manifold method (NMM), boundary settings must be treated carefully. In this paper, 4 issues in boundary settings are investigated to improve the performance of NMM: (1) Nonreflecting boundaries including the viscous boundary and viscoelastic boundary are considered; (2) A free‐field boundary is incorporated into NMM to accurately simulate external source wave motion; (3) A seismic input boundary is considered, and the force input method is introduced; and (4) A static‐dynamic unified boundary is incorporated for the convenience of transforming displacement boundary into other types of boundaries, such as nonreflecting boundaries and seismic input boundary. Several benchmark problems are solved to validate the improved NMM. Simulation results agree well with analytical ones, indicating that the improved NMM is able to simulate seismic dynamic response of rock masses reliably and correctly.  相似文献   

Energy‐work‐based numerical manifold seepage analysis with an efficient scheme to locate the phreatic surface     

Yuan Wang  Mengsu Hu  Quanlin Zhou  Jonny Rutqvist 《国际地质力学数值与分析法杂志》2014,38(15):1633-1650

A major challenge in seepage analysis is to locate the phreatic surface in an unconfined aquifer. The phreatic surface is unknown and assumed as a discontinuity separating the seepage domain into dry and wet parts, thus should be determined iteratively with special schemes. In this study, we systematically developed a new numerical manifold method (NMM) model for unconfined seepage analysis. The NMM is a general numerical method for modeling continuous and discontinuous deformation in a unified mathematical form. The novelty of our NMM model is rooted in the NMM two‐cover‐mesh system: the mathematical covers are fixed and the physical covers are adjusted with iterations to account for the discontinuity feature of the phreatic surface. We developed an energy‐work seepage model, which accommodates flexible approaches for boundary conditions and provides a form consistent with that in mechanical analysis with clarified physical meaning of the potential energy. In the framework of this energy‐work seepage model, we proposed a physical concept model (a pipe model) for constructing the penalty function used in the penalty method to uniformly deal with Dirichlet, Neumann, and material boundaries. The new NMM model was applied to study four example problems of unconfined seepage with varying geometric shape, boundary conditions, and material domains. The comparison of our simulation results to those of existing numerical models for these examples indicates that our NMM model can achieve a high accuracy and faster convergence speed with relatively coarse meshes. This NMM seepage model will be a key component of our future coupled hydro‐mechanical NMM model. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献