A multi-domain decomposition-based Fourier finite element method for the simulation of 3D marine CSEM measurements

We introduce a multi-domain decomposition Fourier finite element (MDDFFE) method for the simulation of three-dimensional (3D) marine controlled source electromagnetic measurement (CSEM). The method combines a 2D finite element (FE) method in two spatial dimensions with a hybrid discretization based on a Fourier FE method along the third dimension. The method employs a secondary field formulation rather than the total field formulation. We apply the MDDFFE method to several synthetic marine CSEM examples exhibiting bathymetry and/or multiple 3D subdomains. Numerical results show that the use of the MDDFFE method reduces the problem size by as much as 87 % in terms of the number of unknowns, without any sacrifice in accuracy.     

GIS地表塌陷计算的有限棱柱法及三维数据模型

具有强大信息管理和可视化功能的GIS已在地下硐室开挖、矿山采掘、边坡等许多工程领域中得到了广泛应用。笔者给出了一种用于地下开挖变形描述和应力分析的方法——有限棱柱法，并就该方法与GIS集成中的数据模型和数据组织方法进行了探讨，建立了基于GIS的虚拟地质体地下开挖变形描述与评价计算的三维可视化系统，并对多语言集成模式和数据可视化方法进行了探讨。同时还给出了该方法的工程应用实例，对该方法的可靠性和有效性进行了验证。     

基于三维有限元法的巷道影响特征

在矿井瞬变电磁法探测中,巷道空间对探测结果存在影响,不利于探测资料的解释。采用三维有限元法,通过建立地质模型模拟了有无巷道时瞬变电磁场的分布情况,绘制了10 us和0.1 ms时刻有无巷道以及巷道不同长度和高度下XOZ平面磁场强度等值线分布图。结果表明：磁场在高阻区扩散速度比低阻区慢;巷道长度的变化对巷道长度方向磁场分布影响较大;巷道高度的变化对巷道上下方磁场分布影响较大。巷道空间在早期对磁场分布影响较大,晚期则影响不大,这为探测资料异常的解释提供了理论依据。     

基于混合网格有限元的直流电阻率法三维正演研究

直流电阻率法因效率高、成本低等特点广泛应用于有色金属、煤田等矿产资源勘探和地质调查行业。但在井–地、地–井电阻率法勘探过程中,钻孔因素(井液电阻率和钻孔孔径)对不同探测模式下视电阻率响应的影响尚未明确,是否影响视电阻率资料的解释是值得探讨的一个问题。因此,提出采用混合网格有限元法实现直流电阻率三维正演。给出异常电位法满足的边值问题及有限元变分问题,应用三棱柱和四面体混合网格实现对计算区域的快速离散,并建立2种网格的线性插值基函数和单元系数矩阵;采用SSOR–PCG迭代算法求解异常电位满足的大型线性方程组,得到各观测点的响应。在保证计算精度的前提下,应用混合网格有效地离散钻孔地电模型,探讨钻孔因素对井–地、地–井观测方式视电阻率数据的影响特征。对于井–地观测方式:钻孔附近视电阻率受钻孔因素影响最大,严重影响视电阻率资料的合理解释,但随着测点收发距的增加,视电阻率响应逐渐趋于围岩电阻率;而且随着发射源深度的增加,钻孔对地表视电阻率响应的影响也逐渐减小。对于地–井观测方式:钻孔因素对浅部数据影响较大,对深部数据影响小,相比于井液电阻率,视电阻率响应更易受钻孔孔径的影响。直流电阻率法混合网格有限元三维正演算法的提出,对实际井–地、地–井电阻率法勘探具有理论指导意义,可结合钻孔信息进行正演模拟分析,选择合适的收发距,有效压制钻孔因素对实测资料的影响。      

A basal slip model for Lagrangian finite element simulations of 3D landslides

A Lagrangian numerical approach for the simulation of rapid landslide runouts is presented and discussed. The simulation approach is based on the so‐called Particle Finite Element Method. The moving soil mass is assumed to obey a rigid‐viscoplastic, non‐dilatant Drucker–Prager constitutive law, which is cast in the form of a regularized, pressure‐sensitive Bingham model. Unlike in classical formulations of computational fluid mechanics, where no‐slip boundary conditions are assumed, basal slip boundary conditions are introduced to account for the specific nature of the landslide‐basal surface interface. The basal slip conditions are formulated in the form of modified Navier boundary conditions, with a pressure‐sensitive threshold. A special mixed Eulerian–Lagrangian formulation is used for the elements on the basal interface to accommodate the new slip conditions into the Particle Finite Element Method framework. To avoid inconsistencies in the presence of complex shapes of the basal surface, the no‐flux condition through the basal surface is relaxed using a penalty approach. The proposed model is validated by simulating both laboratory tests and a real large‐scale problem, and the critical role of the basal slip is elucidated. Copyright © 2016 John Wiley & Sons, Ltd.     

基于有限单元法的二维／三维大地电磁正演模拟策略

对于二维和三维大地电磁正演问题,有限单元法最后形成了一个线性方程组KX=p。方程组中的K是大型稀疏的带状对称复系数矩阵,其条件数远大于1,为严重病态矩阵,求解其对应方程组会遇到很多困难。不完全LU分解处理的BICGSTAB算法,可用于该线性方程组的求解,并且具有速度快,精度高,稳定性好等优点。为了模拟无穷远边界及满足计算机的内存需求,在保证计算精度的情况下,设计了非均匀网格剖分。在程序编制中,因只存储有限元系数矩阵的非零元素,大大减少了正演计算的时间。通过对二维模型和三维模型电磁响应的计算,验证了该算法的正确性。     

A mixed finite element method for the solution of the magnetostatic problem with highly discontinuous coefficients in 3D

This paper present a new a mixed finite element method for the simulation of magnetostatic problems with highly discontinuous permeability. The method is derived from the well studied mixed formulation for the div-grad system that is known to be accurate for very large discontinuities. The method robustness is demonstrated on a test model problem.     

基于强度折减法的库岸滑坡三维有限元分析

通过现场踏勘调研,根据滑坡的环境地质条件,详细探讨了该库岸滑坡的成因机制和演化过程,并重点分析了滑坡失稳的影响因素。建立滑坡体的三维有限元模型,运用有限元强度折减理论对其稳定性进行了计算分析。结果表明,滑坡体在天然状况下是稳定的,库水位上升至正常蓄水位时将超过滑坡前缘高程,滑坡安全系数降低,不满足规范规定的最小安全系数的要求,在考虑降雨入渗、库水位骤降时,滑坡进一步趋于危险;在考虑蓄水+地震工况时,库岸滑坡有失稳的可能。据此提出了削坡减载治理措施,治理后滑坡在各工况下的安全系数均满足规范的要求,研究成果对滑坡的治理具有较大的参考价值。     

考虑饱和-非饱和渗流场和应力场耦合的三维强度折减有限元程序研制

探索考虑饱和-非饱和渗流场和应力场耦合的三维强度折减有限元技术,并研制成功一个考虑饱和-非饱和渗流场和应力场耦合的三维强度折减有限元程序,通过与传统极限平衡法分析结果对比研究,对抗剪强度折减有限元法分析边坡稳定问题的适用性进行了评价,得出采用三维强度折减有限元法确定考虑饱和-非饱和渗流场的边坡稳定性安全系数是可行的结论.     

钢筋混凝土管桩反射波法的三维有限元分析

对桩-土系统用三维有限元模型和Wilson- 直接积分法计算钢筋混凝土管桩顶面的瞬态动力响应,并由此分析了管桩顶面不同测点的反射波信号特征及其与桩身缺陷的对应规律。计算结果表明：管桩顶部波传播的三维效应对桩身浅部局部缺陷深度的判断有较大的影响,所得结论对由反射波法检测管桩全截面断裂和局部缺陷以及传感器的合理布置有较大的指导作用。     

Site scale modeling of slow-moving landslides,a 3D viscoplastic finite element modeling approach

This paper presents an advanced 3D numerical methodology to reproduce the kinematics of slow active landslides, more precisely, to reproduce the nearly constant strain rate (secondary creep) and the acceleration/deceleration of the moving mass due to hydrological changes. For this purpose, finite element analyses are performed in a large area covering a long time-span (12 years), in order to exhibit different interacting slope movements. First, we perform a stability analysis using the shear strength reduction (SSR) technique with a Mohr-Coulomb failure criteria. It is done in order to compute factors of safety (FS) and to identify two different scenarios, the first one being stable (FS > 1) and the second one being unstable (FS < 1). In the studied test case, the Portalet landslide (Central Spanish Pyrenees), the first scenario corresponds to an initial stable configuration of the slope and the second one to an unstable excavated configuration. Second, taking the first scenario as an initial condition, a time-dependent analysis is performed using a coupled formulation to model solid skeleton and pore fluids interaction, and a simplified ground water model that takes into account daily rainfall intensity. In this case, a viscoplastic constitutive model based on Perzyna’s theory is applied to reproduce soil viscous behavior and the delayed creep deformation due to the excavation. The fluidity parameter is calibrated to reproduce displacements measured by the monitoring systems. Our results demonstrate that 3D analyses are preferable to 2D ones for reproducing in a more realistic way the slide behavior. After calibration, the proposed model is able to simulate successfully short- and medium-term predictions during stages of primary and secondary creep.     

渗透系数对渗流速度影响的热-水-应力耦合二维有限元分析

使用建立的饱和-非饱和介质中热-水-应力耦合弹塑性模型,取一组真实的缓冲材料、岩体及贮存容器（用加热器代替）的物理力学指标作为基本计算条件,以一个假想的核废料处置库为模拟对象,就高、中、低3种渗透系数进行了二维有限元数值分析,考察了近场的渗流速度大小及方向的变化,认识到：在其他计算参数相同的条件下,缓冲材料的渗透系数越高,近场的渗流速度越大,缓冲层达到饱和状态也越快;当缓冲层达到饱和状态后,如果玻璃固化体继续放热,有可能使得近场的温度梯度的作用强于水力梯度的作用,导致渗流速度方向发生逆转,即水分由内向外迁移;依渗透系数不同,其渗流速度的大小、方向有显著差异,这也势必引起放射性核素随地下水流动扩散的复杂多变。     

澜沧江某电站左岸地下洞室群围岩稳定性的三维数值模拟

在岩体结构模型概化的基础上 ,采用三维有限元数值分析方法 ,系统研究了澜沧江某大型水电站大跨度、高边墙地下洞室群开挖完成后围岩的二次应力场、变形场和塑性破坏区的变化特征。总结了地下洞室群围岩应力、变形和破坏区的分布特征和变化规律 ,为洞室群稳定性评价和工程施工设计提供了基础资料和参考依据。     

An extension of the Saltykov method to quantify 3D grain size distributions in mylonites

The estimation of 3D grain size distributions (GSDs) in mylonites is key to understanding the rheological properties of crystalline aggregates and to constraining dynamic recrystallization models. This paper investigates whether a common stereological method, the Saltykov method, is appropriate for the study of GSDs in mylonites. In addition, we present a new stereological method, named the two-step method, which estimates a lognormal probability density function describing the 3D GSD. Both methods are tested for reproducibility and accuracy using natural and synthetic data sets. The main conclusion is that both methods are accurate and simple enough to be systematically used in recrystallized aggregates with near-equant grains. The Saltykov method is particularly suitable for estimating the volume percentage of particular grain-size fractions with an absolute uncertainty of ±5 in the estimates. The two-step method is suitable for quantifying the shape of the actual 3D GSD in recrystallized rocks using a single value, the multiplicative standard deviation (MSD) parameter, and providing a precision in the estimate typically better than 5%. The novel method provides a MSD value in recrystallized quartz that differs from previous estimates based on apparent 2D GSDs, highlighting the inconvenience of using apparent GSDs for such tasks.     

On the use of enriched finite element method to model subsurface features in porous media flow problems

In this paper, a new enrichment scheme is proposed to model fractures and other conduits in porous media flow problems. Inserting this scheme into a partition of unity based method results in a new numerical method that does not require the mesh to honor the specific geometry of these subsurface features. The new scheme involves a specially designed integration procedure and enrichment functions, which can capture effects of local heterogeneity introduced by subsurface features on the pressure solution. The new method is also capable of modeling fractures with low as well as high conductivity. Another feature of the proposed scheme is that, even though two enrichment functions are used to model the permeability change at the two rock/fracture interfaces of a fracture, only one element partition is made for numerical integration. To demonstrate the accuracy and effectiveness of the proposed approach, production problems for wells that were stimulated or completed by longitudinal fracture, transverse fractures, and perforations are studied.     

Study on the mechanical behavior of sands using 3D discrete element method with realistic particle models

Presented is a study on the geometrical characteristics of sand particles and the mechanical behavior of sand material under external loading. Based on computed tomography technique, a reconstruction method of granular particles was developed and used to build a database of 3D geometrical models for sand particles. The studied sand particles showed good regularities in morphological characteristics and thus were suitable to be used for the random generation of numerical samples. DEM tests using realistically shaped particles were proven to better simulate the mechanical behavior of the sample during elastoplastic loading stage, which was an issue for the simplified spherical particles. The generation, extension, and breakage of the force chains controlled the strain softening behavior of sands. Anisotropy analysis using the spherical harmonic series showed that the evolution of anisotropy directions and parameters corresponded well with the macroscopic mechanical behavior of the material. Pore volume computation based on Voronoi diagram was performed to illustrate the formation and evolution of localized shear zone. The mesoscopic analysis showed that particle shape significantly influences the mechanical behavior of sands and thus should be properly modeled in numerical simulations.

     

2D inversion of the magnetotelluric data from Mahallat geothermal field in Iran using finite element approach

The natural-field magnetotelluric (MT) method has proven very useful for mapping the geothermal fields as resistivity sections. The depth of investigation of the MT method is sufficiently large to penetrate deep into the upper crust. MT soundings along two transects across Mahallat geothermal field in Iran were carried out to determine the crustal structure in the region. The selected MT profiles in the region cross over the hydrothermally altered zones and different geological structures. Data were acquired along two profiles crossing the Mahallat hot springs with a total of 28 MT stations in a frequency range of 8,000 to 0.008 Hz. Spacing between stations was kept 500 m for a good resolution. We have used the code MT2DInvMATLAB for inversion using the method of finite elements for forward modeling. Apparent resistivity and phase data of transverse electric (TE), transverse magnetic (TM), and TE + TM modes along each profile were modeled. The geothermal fluid reservoir is resolved at 1,000 to 3,000 m depth and the geothermal resource is estimated to be located at 7,000 m or deeper.     

结合有限单元法运用三次样条技术求解达西速度

求解含水层中溶质和热量的运移时,连续的达西速度场十分重要。传统有限单元法能够精确求解水头,但其水头一阶导数在节点上不连续,求解通过截面流量时,流入量和流出量不相等。将有限单元法与三次样条技术结合,利用三次样条函数逼近水头,保证水头一阶导数的连续性,从而利用达西公式求解出连续的达西速度场,保证流量的连续性。通过对均质和非均质介质下的二维稳定流的数值模拟,发现这种结合三次样条技术的有限单元法能够精确求解水头、达西速度与流量。     

Modelling of rutting of two flexible pavements with the shakedown theory and the finite element method

This paper presents a finite element program, for the modelling of rutting of flexible pavements. In its present version, the program incorporates a permanent deformation model for unbound granular materials based on the concept of the shakedown theory developed by Zarka for metallic structures under cyclic loadings and has been used to estimate the permanent deformations of unbound granular materials (UGM) subjected to traffic loading. The calculation is performed in two steps: the first step consists in modelling the resilient behaviour of the pavement in 3D, using non-linear elastic models, to determine the stress field in the pavement. Then stress paths are derived and used to calculate the permanent deformations and the displacements, using a Drucker–Prager yield surface. An application to the prediction of the permanent deformations of experimental pavements with an unbound granular base, tested on the LCPC pavement testing facility is presented.     

Sedimentation rate and subsidence history of the southeastern Karoo Basin,South Africa,using 1D backstripping method

Backstripping analysis has been carried out on five boreholes and one outcrop section of the Ecca Group in the Main Karoo Basin of South Africa to determine the sedimentation rate and subsidence history of the basin. The result shows that the rate of sedimentation in the Prince Albert, Whitehill, Collingham, Ripon and Fort Brown Formations range between 0.003–0.03, 0.02–0.05, 0.01–0.05, 0.03–0.22, and 0.15–0.025 mm year^?1, respectively. The backstripped subsidence curves that are constructed by removing the effects of decompaction to the water column and sediment loads show subsidence rates decreasing with time, resembling the typical thermal subsidence curves of passive continental margins. Three major subsidence episodes characterized the Ecca Group, namely, (1) rapid subsidence in an extensional regime, (2) slow subsidence in the middle of basin development and (3) another rapid subsidence in a compressional regime. The aforementioned subsidence episodes show that the southeastern Karoo Basin was located on a passive continental margin, suggesting that the subsidence was initiated and mainly controlled by mechanical (gravitational loading) or tectonic events, with little contribution of thermal events. The average rate of tectonic subsidence in the Prince Albert, Whitehill, Collingham, Ripon and Fort Brown Formations are 63, 28, 25, 215 and 180 m Ma^?1, respectively. It is also inferred that the southeastern Karoo Basin evolved from a passive continental margin into an Andean-type continental foreland basin; thus, portraying a completely evolved post-rift setting along the southeastern Gondwana margin.