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Boundary settings for the seismic dynamic response analysis of rock masses using the numerical manifold method 
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下载免费PDF全文 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
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This study focuses on the three‐dimensional (3‐D) characteristics of wave propagation in pipe‐pile using elastodynamic finite integration technique. First, a real 3‐D pile‐soil model in cylindrical coordinate system is presented. Then, the governing equations are established. With the boundary and initial conditions, the numerical solution is obtained. The accuracy and feasibility of the self‐written code are further verified via comparing with the measured data. Velocity histories at different angles of pile top and pile tip are illustrated, and the snapshots reflecting the 3‐D characteristics of wave propagation are given. It shows that the interferences of Rayleigh waves can confuse the result interpretation for pile integrity testing. The increase of hammer contact time can effectively mitigate the interferences, and the interferences of Rayleigh waves are weakest at an angle of 90° from where hammer hits. Besides, surrounding soil can partly mitigate the wave interferences. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
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运用三维数值流形法（3D NMM）进行三维裂纹扩展分析,并采用C++语言编写了相应的程序。充分利用三维数值流形法模拟裂纹扩展的优势,只需要更新裂纹尖端线附近的边界环路和流形单元,不需要使用阶跃函数。根据三维数值流形法计算得到的应力结果,应用非局部求迹方法分析每个裂纹尖端的破坏状态,如果发生破坏则沿垂直于其最大主应力方向扩展。针对裂纹扩展后的不同状况,采用四边形或三角形推进法。裂纹扩展后为了使变形后的面保持平面,必须对新生成的面进行三角化分割。对诸如单边裂纹、平行钱币型裂纹和倾斜钱币型裂纹扩展问题进行数值模拟。计算结果表明,采用三维数值流形法进行裂纹扩展模拟是可行的,文中方法对裂纹尖端线非闭合和闭合的情形均适用,且文中方法对于裂纹尖端线位于单元内部的非平面裂纹扩展也是有效的。 相似文献
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与静态岩石破碎过程相比,冲击作用下岩石的应力改变具有时间效应,应力波传播过程中表现出压、拉变化。基于损伤演化原理和有限元数值模拟方法,针对冲击荷载作用下的压头破岩机制进行了模拟分析。为排除边界上反射波的影响,黏弹性边界被纳入计算中。首先论证了黏弹性边界在均质和非均质介质中的计算精度,然后分析了冲击作用下不同均质度的岩石以及砂砾岩的响应规律,结果显示：在弹性情况下,压头与岩石接触边缘以及自由面附近是拉应力分布区,接触边缘拉应力最大。剪应力最高值并不位于接触面附近,而是离接触面有一定距离。较均质岩石主要呈现拉伸破坏模式,先出现赫兹裂缝,然后是径向裂缝和侧向裂缝,拉应力的产生成为诱发裂缝萌生和扩展的主因。当岩石均质度较低时,岩石的破坏形式呈现多元化,剪切破坏比重加大,表现为复杂的拉剪破坏模式。对于砾石粒径较大、含量较多的砂砾岩,砾石和基质的非均匀性不可忽略,冲击下破坏模式以绕粒环行和穿粒破坏为主。总体说来,对于岩石类准脆性材料,应力波传播过程中产生的拉应力是失稳的诱发和扩展的关键。 相似文献
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Moche Ziv 《国际地质力学数值与分析法杂志》2003,27(3):207-232
The response of an ideal elastic half‐space to a line‐concentrated impulsive vector shear force applied momentarily is obtained by an analytical–numerical computational method based on the theory of characteristics in conjunction with kinematical relations derived across surfaces of strong discontinuities. The shear force is concentrated along an infinite line, drawn on the surface of the half‐space, while being normal to that line as well as to the axis of symmetry of the half‐space. An exact loading model is introduced and built into the computational method for this shear force. With this model, a compatibility exists among the prescribed applied force, the geometric decay of the shear stress component at the precursor shear wave, and the boundary conditions of the half‐space; in this sense, the source configuration is exact. For the transient boundary‐value problem described above, a wave characteristics formulation is presented, where its differential equations are extended to allow for strong discontinuities which occur in the material motion of the half‐space. A numerical integration of these extended differential equations is then carried out in a three‐dimensional spatiotemporal wavegrid formed by the Cartesian bicharacteristic curves of the wave characteristics formulation. This work is devoted to the construction of the computational method and to the concepts involved therein, whereas the interpretation of the resultant transient deformation of the half‐space is presented in a subsequent paper. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
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基于数值流形法（NMM）进行三维裂纹扩展分析研究,编写了相应的C++程序。充分发挥数值流形法在非连续变形分析领域的优势,不需要扩展有限元中的水平集和阶跃函数概念,应用数值流形法计算结果分析裂纹尖端线的破坏状况,对已有的非局部求迹法和三角形推进法进行简化和扩展,提出一种简化算法确定最终的新裂纹扩展面。应用简化算法对水平钱币型裂纹扩展问题进行数值模拟和对比分析研究。计算结果表明,基于数值流形法的三维裂纹扩展算法是可行的,采用简化处理之后,克服原有算法的不足,大大减少了新裂纹尖端线和新裂纹面的数目,降低了计算网格对新裂纹面的影响,提高了计算效率和扩大了应用范围。 相似文献
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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
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数值流形方法（NMM）的最大优势在于可以统一地处理岩土力学中的连续和非连续变形问题。它在求解断裂力学问题时无需强制裂纹与数学网格保持一致,非常适合应用于岩土工程中由连续到非连续的破坏过程模拟。在裂纹扩展过程中,裂纹与数学网格的相对位置将会是任意的,如裂纹尖端可能落在网格内部、网格节点上或网格边上等。因此,对同一条裂纹,通过旋转和移动数学网格构造了它们之间的这种相对位置关系以及一些可能对计算结果产生影响的极端情况,并以应力强度因子作为衡量标准,研究了NMM在处理线弹性断裂力学问题时的网格依赖性。研究表明,NMM即使在处理强奇异性问题时依然有着很好的网格无关性,进一步证实了它在模拟裂纹扩展问题时的鲁棒性。 相似文献
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平面波的传播问题通常可以归结为一维波动方程的定解问题。在非均匀介质中,即使简单的一维波动方程也需要借助于数值方法获得近似解。3层5点古典差分格式是计算偏微分方程一种常用算法,作为一种显式迭代格式,需要满足稳定性条件 ,其中 为波速, 为空间采样间隔, 为时间采样间隔。当 时, ,古典差分格式达到临界稳定状态。在这种情况下,平面波在 时间内的传播距离恰好等于空间采样间隔,差分格式真实地反映了平面波的传播原理,因而可以得到一维波动方程的精确解。但是,由于在非均匀介质中存在不连续的波阻抗界面,此方法不适于计算非均匀介质的波场。为了将临界稳定情况下的古典差分格式推广应用至非均匀层状介质,提出了一种能够处理波阻抗界面的有限差分格式,并应用傅里叶分析法得到其稳定性条件。模型算例验证了此算法的正确性。 相似文献
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基于对非饱和多孔介质的研究成果,考虑孔隙中液相和气相的相互影响,研究了非饱和土地基中Rayleigh波的传播特性。通过非饱和土中固相、液相和气相的质量平衡方程、动量平衡方程和非饱和土有效应力原理,建立了问题的弹性波动方程。通过引入势函数及考虑自由透水（透气）的边界条件,经过理论推导给出了非饱和土中Rayleigh波的弥散特征方程。通过数值算例分析了Rayleigh波的波速和衰减系数随饱和度、频率和固有渗透系数等因素的变化规律。结果表明：不同饱和度下波速随频率和固有渗透系数的变化均是先不变,然后小幅下降,再急剧增加,最后趋于一致;衰减系数在不同饱和度下随频率的增大而增大,随固有渗透系数的增大而先增大后减小。 相似文献
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In this paper, a numerical model is developed for the fully coupled hydro‐mechanical analysis of deformable, progressively fracturing porous media interacting with the flow of two immiscible, compressible wetting and non‐wetting pore fluids, in which the coupling between various processes is taken into account. The governing equations involving the coupled solid skeleton deformation and two‐phase fluid flow in partially saturated porous media including cohesive cracks are derived within the framework of the generalized Biot theory. The fluid flow within the crack is simulated using the Darcy law in which the permeability variation with porosity because of the cracking of the solid skeleton is accounted. The cohesive crack model is integrated into the numerical modeling by means of which the nonlinear fracture processes occurring along the fracture process zone are simulated. The solid phase displacement, the wetting phase pressure and the capillary pressure are taken as the primary variables of the three‐phase formulation. The other variables are incorporated into the model via the experimentally determined functions, which specify the relationship between the hydraulic properties of the fracturing porous medium, that is saturation, permeability and capillary pressure. The spatial discretization is implemented by employing the extended finite element method, and the time domain discretization is performed using the generalized Newmark scheme to derive the final system of fully coupled nonlinear equations of the hydro‐mechanical problem. It is illustrated that by allowing for the interaction between various processes, that is the solid skeleton deformation, the wetting and the non‐wetting pore fluid flow and the cohesive crack propagation, the effect of the presence of the geomechanical discontinuity can be completely captured. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
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A validation study of the distinct lattice spring model (DLSM) for wave propagation problems is performed. DLSM is a microstructure-based numerical model, which is meshless and has advantages in modelling dynamic problems where stress wave propagation is important. To verify the applicability of DLSM to modelling wave propagation through a discontinuous medium, the virtual wave source (VWS) method is used to obtain analytical solutions for wave propagation across a jointed rock mass. Numerical modelling results of the commercial code UDEC are selected as the reference. The effects of particle size and lattice rotation angle on wave propagation are first studied. Then, the results of wave transmission across a single joint with a different joint stiffness and across multiple parallel joints with different joint spacings are derived with DLSM, UDEC and VWS. These results are in good agreement with each other. Therefore, the capability of DLSM to model P-wave propagation across jointed rock mass is verified, which provides confidence for the further application of DLSM to modelling more complex problems. 相似文献
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A new finite element scheme is proposed, in this paper, for solving two-dimensional wave propagation problems in multilayered soils resting on a rigid base. The multilayered soils are treated as multiple horizontal layers of lateral infinite extension in geometry. Since these horizontal layers can be truncated by two artificially truncated vertical boundaries, two high-order artificial boundary conditions are applied for propagating the incoming waves from the interior domain into the far field of the system. Both the semi-analytical method and the truncated boundary migration procedure are used to derive the high-order artificial boundary conditions, which are comprised of a physically meaningful dashpot and a generalized energy absorber. The main advantage of using the proposed finite element scheme is that the derived artificial boundary condition can be straightforwardly implemented in the finite element analysis, without violating the band/sparse structure of the conventional finite element equation. The related numerical examples have demonstrated that the proposed finite element scheme is of high accuracy in dealing with wave propagation problems in multiple horizontal layers. 相似文献
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A Boundary Element based Discontinuous Deformation Analysis (BE‐DDA) method is developed by implementing the improved dual reciprocity boundary element method into the open close iterations based DDA. This newly developed BE‐DDA is capable of simulating both the deformation and movement of blocks in a blocky system. Based on geometry updating, it adopts an incremental dynamic formulation taking into consideration initial stresses and dealing with external concentrated and contact forces conveniently. The boundaries of each block in the discrete blocky system are discretized with boundary elements while the domain of each block is divided into internal cells only for the integration of the domain integral of the initial stress term. The contact forces among blocks are treated as concentrated forces and the open–close iterations are applied to ensure the computational accuracy of block interactions. In the current method, an implicit time integration scheme is adopted for numerical stability. Three examples are used to show the effectiveness of the algorithm in simulating block movement, sliding, deformation and interaction of blocks. At last, block toppling and tunnel stability examples are conducted to demonstrate that the BE‐DDA is applicable for simulation of blocky systems. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
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The method of fundamental solution for 3‐D wave scattering in a fluid‐saturated poroelastic infinite domain 下载免费PDF全文
下载免费PDF全文 Zhongxian Liu Zhikun Wang Alexander H.D. Cheng Jianwen Liang Chuchu Wang 《国际地质力学数值与分析法杂志》2018,42(15):1866-1889
By using a complete set of poroelastodynamic spherical wave potentials (SWPs) representing a fast compressional wave PI, a slow compressional wave PII, and a shear wave S with 3 vectorial potentials (not all are independent), a solution scheme based on the method of fundamental solution (MFS) is devised to solve 3‐D wave scattering and dynamic stress concentration problems due to inhomogeneous inclusions and cavities embedded in an infinite poroelastic domain. The method is verified by comparing the result with the elastic analytical solution, which is a degenerated case, as well as with poroelastic solution obtained using other numerical methods. The accuracy and stability of the SWP‐MFS are also demonstrated. The displacement, hoop stress, and fluid pore pressure around spherical cavity and poroelastic inclusion with permeable and impermeable boundary are investigated for incident plane PI and SV waves. The scattering characteristics are examined for a range of material properties, such as porosity and shear modulus contrast, over a range of frequency. Compared with other boundary‐based numerical strategy, such as the boundary element method and the indirect boundary integral equation method, the current SWP‐MFS is a meshless method that does not need elements to approximate the geometry and is free from the treatment of singularities. The SWP‐MFS is a highly accurate and efficient solution methodology for wave scattering problems of arbitrary geometry, particularly when a part of the domain extends to infinity. 相似文献
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Daniel T. C. Yao Waldyr Lopes de Oliveira‐Filho Xiao‐Chuan Cai Dobroslav Znidarcic 《国际地质力学数值与分析法杂志》2002,26(2):139-161
The consolidation and desiccation behaviour of soft soils can be described by two time‐dependent non‐linear partial differential equations using the finite strain theory. Analytical solutions do not exist for these governing equations. In this paper, we develop efficient numerical methods and software for finding the numerical solutions. We introduce a semi‐implicit time integration scheme, and show numerically that our method converges. In addition, the numerical solution matches well with the experimental result. A boundary refinement method is also developed to improve the convergence and stability for the case of Neumann type boundary conditions. Interface governing equations are derived to maintain the continuity of consolidation and desiccation processes. This is useful because the soil column can undergo desiccation on top and consolidation on the bottom simultaneously. The numerical algorithms has been implemented into a computer program and the results have been verified with centrifuge test results conducted in our laboratory. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
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李信富 《中国地质大学学报(英文版)》2011,(3)
The perfectly matched layer(PML) was first introduced by Berenger as an absorbing boundary condition for electromagnetic wave propagation.In this article,a method is developed to ex-tend the PML to simulating seismic wave propagation in fluid-saturated porous medium.This non-physical boundary is used at the computational edge of a Forsyte polynomial convolutional differenti-ator(FPCD) algorithm as an absorbing boundary condition to truncate unbounded media.The incor-poration of PML in Biot's equations is gi... 相似文献