Finite element concept to derive isostatic residual maps — Application to gorda plate and Sierra Nevada regions

A new space-domain operator based on the shape function concept of finite element analysis has been developed to derive the residual maps of the Gorda Plate of western United States. The technique does not require explicit assumptions on isostatic models. Besides delineating the Gorda Plate boundary, the residual maps exhibit a close match both in their anomaly patterns and magnitudes with previously computed residual maps based on the theory of isostasy.     

Seamounts in the Central Indian Ocean Basin: indicators of the Indian plate movement

The study of seamount parameters in the tectonically most-complicated and least-understood Indian Ocean assumes importance since their properties vary as a function of tectonic setting, physics of lithosphere, conduit geometry and chemical composition of magma. More than 100 such seamounts ranging in summit height (h) from 300 to 2870 m, are indentified in the oceanic crust between Indian continent and Mid-Indian Ridge (MIR) and South-East Indian Ridge (SEIR). Most of the minor seamounts (h > 1000) are found in the southern part of the study area. Major seamounts (h < 1000 m) are roughly distributed in two groups—the northern group on Cretaceous Oceanic Crust and southern group on Pliocene-Miocene Oceanic Crust. On an average northern group seamounts (SM 1 to 6) are taller, wider and flatter than those from the southern group. These seamounts appear to be the result of continuous growth from tapped, moving magma chamber while stress depleted magma and inconsistent Indian Plate movement during Mid-Tertiary are attributed to the origin of southern group of smaller seamounts. Distribution and morphology of seamounts as a whole indicate their formation either from Reunion hotspot or from two separate hotspots in the geological past.     

依据恐龙化石恢复印度板块的运行轨迹

越来越多的事实表明,印度板块曾经连续两次撞击了欧亚板块。第一次发生在近200Ma前,通过印度板块将冈 瓦纳大陆上的恐龙动物群带到了亚洲,使中国首次出现了早侏罗世恐龙。确切地说,中国恐龙起源于印度板块的第一 次撞击。侏罗纪之后,印度板块又被引发起顺时针转动,在其东部出现了与泰国之间的断裂,并最终孕育着孟加拉湾 的形成,为第二次撞击拉开了序幕。55Ma前印度板块再次撞向欧亚板块的西藏地区,造就了喜马拉雅山。     

印度板块-古亚洲板块碰撞及亚洲恐龙的出现

印度板块在5500万年前的古近纪撞击了亚洲板块,造就了东西走向的雅鲁藏布江水系和喜马拉雅山系。根据近年来的研究,笔者又提出一个新观点：印度板块在约2亿年前与亚洲板块发生碰撞时,将一个发源于非洲、南美洲的“冈瓦纳恐龙动物群”送上亚洲大陆,在中国西南地区形成以禄丰龙、蜀龙、峨眉龙、马门溪龙为特征的恐龙类动物群。这一事件不仅使亚洲首次出现了恐龙动物,而且板块相撞还造就了南亚地区南北走向的横断山脉和伊洛瓦底江、怒江、澜沧江、金沙江等纵向水系,以及四川盆地的形成。     

印度板块向欧亚板块俯冲碰撞的新模式及其对青藏高原构造演化的影响

青藏高原南部与北部的断裂带走滑方向不同,断裂带在高原东、西两侧的展布规律和构造运动方式也存在极大的差异。通过高原南缘横向地球物理特征的对比,发现该地区东、西两侧深部岩石圈结构存在明显不同,表明印度次大陆向欧亚大陆俯冲碰撞的方式和强度在横向上差异明显。在充分利用高原地质研究最新成果的基础上,提出印度次大陆向欧亚大陆碰撞前地壳增厚及斜向碰撞是造成上述地质现象的根本原因,并由此对青藏高原构造演化的一些特点作了新的解释和探讨。     

印度板块的北缘在哪里?

通过对INDEPTHII在雅鲁藏布江南的2条南北向深地震反射剖面资料的进一步处理,观察到主喜马拉雅逆冲断裂带(MHT)形成的反射向北逐渐倾没于藏南地壳之下。这一反射一直可延伸至康马穹隆北、浪卡子南,在向北延伸的过程中,断裂带向北倾角逐渐加大,可以看到MHT反射最北端的反射同相轴向北倾斜的角度到达27°30'～29°,最深处的双程走时达到22.5s左右。根据深地震反射资料并结合大地电磁(MT)资料,提出印度板块在雅鲁藏布江南30～40km(大约28°50'N)处沿MHT俯冲到了藏南的地壳之下,即在地壳范围内印度板块的最北部边缘位于雅鲁藏布江南30～40km处。     

Finite element modelling for evaluation of apparent resistivity over complex structures

The paper presents a computational algorithm designed for efficient modelling of apparent resistivity over complex geological structures, using finite element method. The algorithm can be used to study variations of apparent resistivities using any electrode configuration at any point on the earth’s surface, not necessarily regular. A Schlumberger apparent resistivity sounding curve over a buried anticline, is presented here as an example and compared with the corresponding analytical curve, to demonstrate the correctness of the FEM algorithm. The various potential derivatives required for the computation of apparent resistivities evaluated through different electrode configurations have been obtained by calculating the ‘influence coefficients’ using reciprocal theorems, an approach successfully applied in structural engineering. In essence, a set of self balancing nodal currents, obtained from the appropriate derivative(s) of the shape functions of the elements contributing to the point of observation, is applied as the load vector. The resulting quantities corresponding to the potential distribution in traditional finite element method, then, turn out to be the potential derivatives at the point of observation for different positions of the current electrodes. These are known as influence coefficients. The continuum nature of the domain beyond the region of interest has been modelled by using ‘infinite elements’ across which the potential is assumed to decay exponentially.     

多矿物岩石流变性的有限元计算

本文利用有限元计算方法从单矿物的流变关系式来确定其组合而成的岩石整体的流变规律建互了三维不可压缩流体的粘弹性有限元模型，计算模型的骨架矿物橄榄石为立方体，填充矿物尖晶石分别取为立方体、单一球体和多个球体，模拟双矿物在三轴压缩实验条件下的蠕变变形过程。首先，本文验证了使用有限元方法数值模拟双矿物在三轴压缩实验下的蠕变变形的可行性。其次，计算研究了当填充矿物为弱矿物时几何外形对整体流变强度的影响，结果表明，填充矿物的几何外形为立方体时比球体时对整体的流变强度有更大的影响。当填充矿物体积不同时，随着填充矿物体积的增加，填充矿物对整体流变强度的影响也不断加大。最后利用三维模型得到的双矿物整体的流变强度结果，归纳出了填充矿物尖晶石占体积5％，10％，15％，20％时和骨架矿物橄榄石构成的双矿物岩石的蠕变关系式。与Tullis利用平面应变模型归纳出的双矿物经验流变关系式比较，发现Tullis的经验流变公式存在较大的误差，而本文得到的双矿物蠕变公式与理论结果更好地符合、本文结果为研究地幔多矿物岩石流变规律提供了新的途径。     

A numerical sandbox: high-resolution distinct element models of halfgraben formation

Basin-scale tectonics and sedimentation are studied using particle flow code (PFC), a special implementation of the distinct-element method (DEM) using circular elements. Special focus is on the development and application of new techniques, which allow for strain weakening and localisation effects and, thus, the formation of discrete fault patterns in high-resolution DE models.Fundamental modelling assumptions and the procedures necessary to define the microproperties of a DE material from given rock mechanical data are first explained. Recent methodical enhancements, consisting of automatic fault detection (AFD) and intelligent crack management (ICM) algorithms are also discussed. Refined DE modelling techniques are then applied to three scenarios of extensional basin formation, i.e. the evolution of halfgrabens above detachments with simple listric and ramp–flat–ramp geometries, respectively. Numerical modelling results compare favourably with the analogue (‘sandbox’) models widely used in this kind of basin studies. Not only do they reproduce the general basin architecture (e.g. roll-over anticlines and crestal collapse grabens), but also detailed fault structure and the sequence of faulting. In addition, numerical models can describe temporal changes in mechanical material properties to model compaction and diagenesis of syntectonic sediments.     

Metamorphic evolution of the Naga Hills eclogite and blueschist, Northeast India: implications for early subduction of the Indian plate under the Burma microplate

Tectonic slices and lenses of eclogite within mafic and ultramafic rocks of the Early Cretaceous–Eocene Naga Hills ophiolite were studied to constrain the physical conditions of eastward subduction of the Indian plate under the Burma microplate and convergence rate prior to the India–Eurasia collision. Some of the lenses are composed of eclogite, garnet-blueschist, glaucophanite and greenschist from core to margin, representing a retrograde hydrothermal alteration sequence. Barroisite, garnet, omphacite and epidote with minor chlorite, phengite, rutile and quartz constitute the peak metamorphic assemblage. In eclogite and garnet-blueschist, garnet shows an increase in Mg and Fe and decrease in Mn from core to rim. In chlorite in eclogite, Mg increases from core to rim. Inclusions of epidote, glaucophane, omphacite and quartz in garnet represent the pre-peak assemblage. Glaucophane also occurs profusely at the rims of barroisite. The matrix glaucophane and epidote represent the post-peak assemblage. The Fe³⁺ content of garnet-hosted omphacite is higher than that of matrix omphacite, and Fe³⁺ increases from core to rim in matrix glaucophane. Albite occurs in late stage veins. P – T pseudosection analysis indicates that the Naga Hills eclogites followed a clockwise P – T path with prograde metamorphism beginning at ∼1.3 GPa/525 °C and peaking at 1.7–2.0 GPa/580–610 °C, and subsequent retrogression to ∼1.1 GPa/540 °C. A comparison of these P – T conditions with numerical thermal models of plate subduction indicates that the Naga Hills eclogites probably formed near the top of the subducting crust with convergence rates of ∼ 55–100 km Myr⁻¹, consistent with high pre-collision convergence rates between India and Eurasia.     

Three-dimensional numerical analysis of the keying of vertically installed plate anchors in clay

Plate anchors, such as suction embedded plate anchors and vertically driven plate anchors, offer economically attractive anchoring solutions for deep/ultra-deep water offshore developments. The rotation/keying processes of plate anchors will cause embedment losses, which lead to decreases of the uplift resistances of the anchors in normally consolidated soil. In the present paper, the keying processes of vertically installed strip and square plate anchors are simulated using the 3-D large deformation finite element method. The effects of loading eccentricity and pullout angle on the embedment loss during keying are investigated. Both the development of the uplift resistance and the soil flow mechanisms are presented. The numerical results show that the loading eccentricity e/B has a much larger effect on the embedment loss than the pullout angle does. The anchor shape has a minimal effect on the loss in anchor embedment. The shape factors (square/strip) are 1.05–1.09 for loss of embedment and 1.10–1.19 for capacity.     

刚性桩复合地基抗震性能的有限元分析

近年来刚性桩复合地基在工程中的应用日益广泛,但是,对该种复合地基在动力荷载下,尤其在是地震作用下的动力响应性状却研究很少。考虑地震作用下土-桩-上部结构之间的相互作用,采用三维有限元方法,对刚性桩单桩复合地基的地震响应进行时域内的模拟计算与分析研究,分析了这种复合地基与桩基础地震响应的差异,并对影响刚性桩复合地基抗震性能的一些因素进行了研究,得出了一些对刚性桩复合地基的抗震设计有参考价值的结论。     

Finite element analysis of a pilot gas storage in rock cavern under high pressure

A three-dimensional finite element analysis was performed to simulate field tests at a pilot gas storage project. The storage was a shallow rock cavern lined with a 6 mm thick steel liner. During the tests, high internal pressure up to 52 MPa was applied and deformation of both rock mass and the steel liner was recorded. The maximum rock displacements of less than 6 mm was numerically predicted and fits the measurement very well. The three-dimensional nonlinear finite element modeling has confirmed the overall stability of the structure and revealed the functioning of each structural component, including the rock mass, concrete lining and the steel liner.     

Finite element modelling of thick plates on two‐parameter elastic foundation

This paper is intended to give some information about how to build a model necessary for bending analysis of rectangular and circular plates resting on a two‐parameter elastic foundation, subjected to combined loading and permitting various types of boundary conditions. The formulation of the problem takes into account the shear deformation of the plate and the surrounding interaction effect outside the plate. The numerical model based on an 18‐node zero‐thickness isoparametric interface element interacting with a thick Reissner–Mindlin plate element with three degrees of freedom at each of the nine nodes, which enforce C⁰ continuity requirements for the displacements and rotations of the midsurface, is proposed. Stiffness matrices of a special interface element are superimposed on the global stiffness matrix to represent the stiffening elastic foundation under and beyond the plate. Some numerical examples are given to illustrate the advantages of the method presented. Copyright © 2001 John Wiley & Sons, Ltd.     

移动荷载作用下Winkler地基板的等参元分析

采用基于Mindlin板理论的8节点等参单元和Newmark逐步积分法,对Winkler地基上的弹性薄板和厚板在移动荷载作用下的动力响应进行了分析,并与已有的薄板有限条法分析结果进行了对比。考察了荷载移动速度、地基基床系数、系统阻尼比对地基板动力响应的影响。分析结果表明,系统存在固有的共振速度,地基基床系数是确定共振速度的最重要因素,薄板与厚板的挠度响应模态有很大差异。结果证明了该方法的有效性和准确性,对实际工程有重要的应用价值。     

Finite element simulations of seismic effects on retaining walls with liquefiable backfills

Finite element simulations of two centrifuge tests on the same cantilever retaining wall model holding liquefiable backfill were conducted using the Biot formulation‐based program DIANA–SWANDYNE II. To demonstrate the effects due to different pore fluids in seismic centrifuge experiments, water was used as the pore fluid in one experiment whereas a substitute pore fluid was used in the second experiment. The cantilever wall model parameters were determined by comparing simulations with measurements from free‐vibration tests performed on the model wall without backfill. The initial stress conditions for dynamic analysis for the soil backfill were obtained by simulating static loads on the retaining wall from the soil backfill. Level‐ground centrifuge model results were used to select the parameters of the Pastor–Zienkiewicz mark III constitutive model used in the dynamic simulations of the soil. The effects due to different pore fluids were captured well by the simulations. The magnitudes of excess pore pressures in the soil, lateral thrust and its line of action on the wall, and wall bending strains, deflections, and accelerations were predicted well. Predictions of settlements and accelerations in the backfill were less satisfactory. Relatively high levels of Rayleigh damping were needed to be used in the retaining wall simulations in order to obtain numerically stable results, which is one of the shortcomings of the model. The procedure may be used for engineering purpose dealing with seismic analysis of flexible retaining walls where lateral pressures, bending strains and deflections in the wall are typically of importance. Copyright © 2008 John Wiley & Sons, Ltd.     

Numerical study on finite element implementation of hypoplastic models

A comprehensive numerical study on finite element implementation of hypoplastic models is presented. Two crucial aspects, local integration of the constitutive equations (the local problem) and forming tangent operators for Newton–Raphson iteration (the global problem), are investigated. For solving the local problem, different integration algorithms, including explicit and implicit methods, are examined using tri-axial compression tests and incremental stress response envelopes, as well as typical boundary value problems. For solving global problems, three different ways of generating the tangent operator are compared. The numerical evidences indicate that, in terms of accuracy, efficiency and robustness, explicit methods with substepping and error control are the best choices for constitutive integration of hypoplastic models while the so-called continuum tangent operators have certain advantages over two other types of numerically-generated consistent tangent operators.     

Refinement of thrust faulting models for the Central New Madrid seismic zone

We present the results of the joint relocation of events recorded during 1989–1992 by the PANDA network in the central New Madrid seismic zone. The near-surface material in the study area is a gently-dipping layer of poorly consolidated sediments with low P-wave velocity and high V_p/V_s (estimated values: 1.8 km s⁻¹ and 3). The sediments are underlain by high-velocity Paleozoic rocks. Under the network the difference in sediment thickness is only 0.6 km, but because of the low velocities the location of the events using layered models is affected by errors. Application of the joint hypocentral determination (JHD) technique to a subset of 580 events shows that the single-event locations may be in error by as much as 1 km in depth, depending on where the events are located. Analysis of synthetic data generated for a realistic 3-D velocity model supports the JHD results. The analysis of synthetic data also suggests that a V_p/V_s≤ 2.3 is more appropriate for the post-Paleozoic Mississippi embayment sediments. Based on the JHD locations we present a new interpretation of the seismicity, with two en-echelon SW-dipping thrust faults connected by a west-dipping thrust fault. These faults appear associated with the Reelfoot scarp and its northern extension, the Kentucky bend scarp.     

A quasistatic analysis of a plate on consolidating layered soils by analytical layer‐element/finite element method coupling

In this paper, a coupling method between finite element and analytical layer‐elements is utilized to analyze the time‐dependent behavior of a plate of any shape and finite rigidity resting on layered saturated soils. Based on the integral transform techniques together with the aid of an order reduction method, an analytical layer‐element solution is derived from the governing equations for three‐dimensional Biot consolidation with respect to a Cartesian coordinate system and then extended to be the fundamental solution for the layered saturated soil under a point load. The Mindlin plate is modeled by eight‐noded isoparametric elements. The governing equations of the interaction between soil and plate in the Laplace‐Fourier transformed domain are deduced by referring to the coupling theory of FEM/BEM, and the final solution is obtained by applying numerical inversion. Numerical examples concerned with the time‐dependent response of a plate are performed to demonstrate the influence of soil and plate properties on the interaction process. Copyright © 2014 John Wiley & Sons, Ltd.     

有限元法在滑坡稳定性分析中的应用

对比了滑坡稳定性分析的极限平衡法、数值分析法、概率法。而后,介绍了有限元法滑坡稳定性分析基本原理,并应用有限元法对中里滑坡进行了稳定性分析,得出了中里滑坡的主应力图和稳定系数,并将稳定系数与其他方法的结果进行了比较,得出有限元法是一种可靠的分析方法,其结果可应用于后期治理设计。