Numerical manifold method for dynamic nonlinear analysis of saturated porous media

It is well known that the Babuska–Brezzi stability criterion or the Zienkiewicz–Taylor patch test precludes the use of the finite elements with the same low order of interpolation for displacement and pore pressure in the nearly incompressible and undrained cases, unless some stabilization techniques are introduced for dynamic analysis of saturated porous medium where coupling occurs between the displacement of solid skeleton and pore pressure. The numerical manifold method (NMM), where the interpolation of displacement and pressure can be determined independently in an element for the solution of u–p formulation, is derived based on triangular mesh for the requirement of high accurate calculations from practical applications in the dynamic analysis of saturated porous materials. The matrices of equilibrium equations for the second‐order displacement and the first‐order pressure manifold method are given in detail for program coding. By close comparison with widely used finite element method, the NMM presents good stability for the coupling problems, particularly in the nearly incompressible and undrained cases. Numerical examples are given to illustrate the validity and stability of the manifold element developed. Copyright © 2006 John Wiley & Sons, Ltd.     

Restricted Three-Body Problem: An Approximation of its General Solution – Part One – the Manifold of Symmetric Periodic Solutions

This paper gives the results of a programme attempting to exploit ‘la seule bréche’ (Poincaré, 1892, p. 82) of non-integrable systems, namely to develop an approximate general solution for the three out of its four component-solutions of the planar restricted three-body problem. This is accomplished by computing a large number of families of ‘solutions précieuses’ (periodic solutions) covering densely the space of initial conditions of this problem. More specifically, we calculated numerically and only for μ = 0.4, all families of symmetric periodic solutions (1st component of the general solution) existing in the domain D:(x ₀ ∊ [−2,2],C ∊ [−2,5]) of the (x ₀, C) space and consisting of symmetric solutions re-entering after 1 up to 50 revolutions (see graph in Fig. 4). Then we tested the parts of the domain D that is void of such families and established that they belong to the category of escape motions (2nd component of the general solution). The approximation of the 3rd component (asymmetric solutions) we shall present in a future publication. The 4th component of the general solution of the problem, namely the one consisting of the bounded non-periodic solutions, is considered as approximated by those of the 1st or the 2nd component on account of the `Last Geometric Theorem of Poincaré' (Birkhoff, 1913). The results obtained provoked interest to repeat the same work inside the larger closed domain D:(x ₀ ∊ [−6,2], C ∊ [−5,5]) and the results are presented in Fig. 15. A test run of the programme developed led to reproduction of the results presented by Hénon (1965) with better accuracy and many additional families not included in the sited paper. Pointer directions construed from the main body of results led to the definition of useful concepts of the basic family of order n, n = 1, 2,… and the completeness criterion of the solution inside a compact sub-domain of the (x ₀, C) space. The same results inspired the ‘partition theorem’, which conjectures the possibility of partitioning an initial conditions domain D into a finite set of sub-domains D i that fulfill the completeness criterion and allow complete approximation of the general solution of this problem by computing a relatively small number of family curves. The numerical results of this project include a large number of families that were computed in detail covering their natural termination, the morphology, and stability of their member solutions. Zooming into sub-domains of D permitted clear presentation of the families of symmetric solutions contained in them. Such zooming was made for various values of the parameter N, which defines the re-entrance revolutions number, which was selected to be from 50 to 500. The areas generating escape solutions have being investigated. In Appendix A we present families of symmetric solutions terminating at asymptotic solutions, and in Appendix B the morphology of large period symmetric solutions though examples of orbits that re-enter after from 8 to 500 revolutions. The paper concludes that approximations of the general solution of the planar restricted problem is possible and presents such approximations, only for some sub-domains that fulfill the completeness criterion, on the basis of sufficiently large number of families.     

Increasing critical sensitivity of the Load/Unload Response Ratio before large earthquakes with identified stress accumulation pattern

The Load/Unload Response Ratio (LURR) method is proposed for short-to-intermediate-term earthquake prediction [Yin, X.C., Chen, X.Z., Song, Z.P., Yin, C., 1995. A New Approach to Earthquake Prediction — The Load/Unload Response Ratio (LURR) Theory, Pure Appl. Geophys., 145, 701–715]. This method is based on measuring the ratio between Benioff strains released during the time periods of loading and unloading, corresponding to the Coulomb Failure Stress change induced by Earth tides on optimally oriented faults. According to the method, the LURR time series usually climb to an anomalously high peak prior to occurrence of a large earthquake. Previous studies have indicated that the size of critical seismogenic region selected for LURR measurements has great influence on the evaluation of LURR. In this study, we replace the circular region usually adopted in LURR practice with an area within which the tectonic stress change would mostly affect the Coulomb stress on a potential seismogenic fault of a future event. The Coulomb stress change before a hypothetical earthquake is calculated based on a simple back-slip dislocation model of the event. This new algorithm, by combining the LURR method with our choice of identified area with increased Coulomb stress, is devised to improve the sensitivity of LURR to measure criticality of stress accumulation before a large earthquake. Retrospective tests of this algorithm on four large earthquakes occurred in California over the last two decades show remarkable enhancement of the LURR precursory anomalies. For some strong events of lesser magnitudes occurred in the same neighborhoods and during the same time periods, significant anomalies are found if circular areas are used, and are not found if increased Coulomb stress areas are used for LURR data selection. The unique feature of this algorithm may provide stronger constraints on forecasts of the size and location of future large events.     

Variability in Early Amazonian Tharsis stress state based on wrinkle ridges and strike-slip faulting

We present evidence for a decrease in the magnitude of Tharsis-circumferential compressive stress during the Late Hesperian to the Middle Amazonian based on chronologic changes in the predominant style of faulting in southern Amazonis Planitia. Using high-resolution MOLA topography, we identify a population of strike-slip faults that exhibit Middle Amazonian-aged displacements of regional chrono-stratigraphic units. These strike-slip faults are adjacent to an older population of previously documented Late Hesperian-aged thrust faults (wrinkle ridges). Along-strike orientations of these thrust and strike-slip faults reveal the Tharsis-radial stress to be the area's most compressive remote principal stress and that this stress orientation and magnitude persisted throughout the Late Hesperian to the Middle Amazonian. We show that the change in the predominant style of faulting from thrust faulting to strike-slip faulting during this time requires a decrease of the Tharsis-circumferential compressive stress to a magnitude less than lithostatic load, with negligible change in stress orientation.     

湖北省巴东县黄土坡滑坡深部变形防治方案探讨

文章根据几年来从事黄土坡滑坡区的勘查、可研及现场工程管理的认识，从滑坡分布特征、物质构成、稳定研究、变形特征等方面对滑坡进行研究。针对该滑坡厚度巨大，滑体强度高，近期深部变形较明显的实情，作者以库仑定律为基础，提出采用岩土加固治理滑坡区深部滑移的初步治理方案。     

A response‐based decoupling criterion for multiply‐supported secondary systems

It is often infeasible to carry out coupled analyses of multiply‐supported secondary systems for earthquake excitations. ‘Approximate’ decoupled analyses are then resorted to, unless the response errors due to those are significantly high. This study proposes a decoupling criterion to identify such cases where these errors are likely to be larger than an acceptable level. The proposed criterion is based on the errors in the primary system response due to decoupling and has been obtained by assuming (i) the input excitation to be an ideal white noise process, (ii) cross‐modal correlation to be negligible, and (iii) the combined system to be classically damped. It uses the modal properties of the undamped combined system, and therefore, a perturbation approach has been formulated to determine the combined system properties in case of light to moderately heavy secondary systems. A numerical study has been carried out to illustrate the accuracy achieved with the proposed perturbation formulation. The proposed decoupling criterion has been validated with the help of two example primary‐secondary systems and four example excitation processes. Copyright © 2002 John Wiley & Sons, Ltd.     

Nonlinear earthquake response analysis and energy calculation for seismic slit shear wall structures

Based on the concept of structural passive control, a new type of slit shear wall, with improved seismic performance when compared to an ordinary solid shear wall, was proposed by the authors in 1996. The idea has been verified by a series of pseudo-static and dynamic tests. In this paper a macro numerical model is developed for the wall element and the energy dissipation device. Then, nonlinear time history analysis is carried out for a 10-story slit shear wall model tested on a shaking table. Furthermore, the seismic input energy and the individual energy dissipated by the components are calculated by a method based on Newmark-β assumptions for this shear wall model, and the advantages of this shear wall are further demonstrated by the calculation results from the viewpoint of energy. Finally, according to the seismic damage criterion on the basis of plastic accumulative energy and maximum response, the optimal analysis is carried out to select design parameters for the energy dissipation device.     

玛尼7.9级地震对昆仑山口西8.1级地震的触发作用及动力背景初探

根据库仑静应力变化的概念，对青藏块体中部地区1997年11月8日玛尼7．9级地震及2001年11月14日昆仑山口西8．1级地震的应力触发作用进行了初步研究。不同震源机制解计算结果表明，玛尼地震造成了昆仑地震断层面上10^-3MPa量级的库仑应力增量，该变化仅使得昆仑地震的发生提前了最长10年左右，表明当前地壳应变能水平可能并不很低。对照20世纪初以来全球7级以上强震频度和强度演化特征与地球自转变化的关系，认为地球自转幅度衰减、变化频率升高是近期强震活动的重要控制因素。昆仑山口西8．1级地震的发生，可能是地球自转持续加速阶段后期，青藏块体内部区域应力场逐渐强化，及玛尼地震应力触发的结果。     

小浪底工程岩体力学参数研究

本文系统研究了小浪底工程的岩体的强度特征,采用了室内试验,野外结构面统计,工程地质类比法、模型试验法和Hoek Brown的经验法,估算了工程岩体的力学指标,指出了上述各种方法中所存在的不足,认为在工程实践中,应尽可能使用多种估计方法,交叉校核所得参数,以提高参数的可靠性,保证工程的安全,节约投资。