Bivariate Gaussian mixture–based equivalent linearization method for stochastic seismic analysis of nonlinear structures

To address challenges in stochastic seismic analysis of nonlinear structures, this paper further develops a recently proposed Gaussian mixture–based equivalent linearization method (GM‐ELM). The GM‐ELM uses a Gaussian mixture distribution model to approximate the probabilistic distribution of a nonlinear system response. Using properties of the Gaussian mixture model, GM‐ELM can decompose the non‐Gaussian response of a nonlinear system into multiple Gaussian responses of linear single–degree of freedom oscillators. With the set of the equivalent linear systems identified by GM‐ELM, response statistics as crossing rate and first‐passage probability can be computed conveniently using theories of linear random vibration analysis. However, the original version of GM‐ELM may lead to an inaccurate estimate because of the heuristic parameters of the linear system introduced to supplement insufficient information. To overcome this limitation and define unique equivalent linear systems, this paper proposes a further developed version of GM‐ELM, which uses a mixture of bivariate Gaussian densities instead of univariate models. Moreover, to facilitate the use of elastic response spectra for estimating the mean peak responses of a nonlinear structure, a new response spectrum combination rule is proposed for GM‐ELM. Two numerical examples of hysteretic structural systems are presented in this paper to illustrate the application of the bivariate GM‐ELM to nonlinear stochastic seismic analysis. The analysis results obtained by the bivariate GM‐ELM are compared with those obtained by the univariate GM‐ELM, the conventional equivalent linearization method, the tail equivalent linearization method, and Monte Carlo simulation. The supporting source code and data are available for download at https://github.com/yisangri/GitHub‐bGM‐ELM‐code.git     

Evaluation of wind effects on a supertall building based on full‐scale measurements

This paper describes the results obtained from the full‐scale measurements of wind effects on a 70‐storey building in Hong Kong. The building which has a height of approximately 370 m is the second tallest structure in Hong Kong. The field data such as wind speed, wind direction and wind‐induced acceleration responses have been measured since 1995 including the close passage of two typhoons; typhoon Sally and typhoon Kent. Detailed analysis of the field data is conducted. The full‐scale measurements are compared with the wind tunnel results obtained in the Boundary Layer Wind Tunnel Laboratory at Western Ontario University. The amplitude‐dependent characteristics of damping and natural frequency that were obtained by using the random decrement technique are investigated. Copyright © 2000 John Wiley & Sons, Ltd.     

中国大地测量数据处理60年重要进展 第二部分:大地测量参数估计理论与方法的主要进展

大地测量参数估计原理是大地测量数据处理的重要基础。中国学者经过60年不懈努力,在自由网平差、拟稳平差、半参数估计、不适定问题解算方法、抗差估计、自适应滤波等领域做出了重要贡献,建立了许多新的理论、模型和方法,推进了大地测量数据处理理论的进展。这一部分重点介绍建国60年来中国学者在大地测量数据处理原理、方法方面取得的成就。     

利用卫星轨道资料获取降水云团尺度的新方案

提出一种新的统计方案,以目标面积比为核心度量指标,并参照连续圆形目标定义目标面积比意义上的等效半径,实现对目标宏观尺度大小的量化估计。此方法能有效减轻轨道截断效应所造成的目标尺度低估,可对通过计数类方法得到的目标空间尺度做出有效修正。     

A continuum model of layered rock masses with non-associative joint plasticity

Layered rock masses can be modelled either as standard, orthotropic continua if the layer bending can be neglected or as Cosserat continua if the influence of layer bending is essential. This paper presents a finite element smeared joint model based on the Cosserat theory. The layers are assumed to be elastic with equal thickness and equal mechanical properties. All the cosserat parameters are expressed through the elastic properties of layers, layer thickness and joint stiffness. Plastic-slip as well as tensile-opening of layer interface (joint) are accounted for in a manner similar to the conventional non-associative plasticity theory. As an application, the behaviour of an excavation in a layered rock mass is examined. The displacement and stress fields given by smeared joint models based on the Cosserat continuum and the conventional anisotropic continuum approaches are compared with those obtained from the discrete joint model. The conventional anisotropic continuum model is found to break-down completely when the effective shear modulus in the direction parallel to layering is low in comparison to the shear modulus of the intact layer, whereas the Cosserat model is found to be capable of accurately reproducing complex load–deflection patterns irrespective of the differences in shear moduli. © 1998 John Wiley & Sons, Ltd.     

MODAL ANALYSIS OF SOFT-SOIL SITES INCLUDING RADIATION DAMPING

For the one-dimensional analysis of soft-soil layers on an elastic half-space, a general form of analytical solution is developed for converting radiation damping due to energy leaking back to the half-space into equivalent modal damping, allowing the modal analysis technique to be extended to a site where radiation damping has to be accounted for. Closed-form solutions for equivalent modal damping ratios and effective modal participation factors are developed for a single layer with a shear wave velocity distribution varying from constant to linearly increasing with depth. Compact and recursive forms of solutions for equivalent modal damping ratios are developed for a system with an arbitrary number of homogeneous layers on an elastic half-space. Comparisons with numerical solutions show that the modal solutions are accurate. The nominal frequency of a site, i.e. the inverse of four times the total shear wave travel time through the layers, is an important parameter for estimating the high mode frequencies. A parameter study shows that for the same impedance ratio of the bottom layer to the elastic half-space, a system of soil layers with an increasing soil rigidity with depth has, in general, larger peak modal amplifications at the ground surface than does a single homogeneous layer on an elastic half-space, while a system with a decreasing soil rigidity with depth has smaller modal peak amplifications. © 1997 by John Wiley & Sons, Ltd.     

任意刚性基础竖向动阻抗的简化计算

对于均质弹性半空间上的任意形状的刚性明置和埋置基础,其动刚度和阻尼系数的确定,已有很多这方面的研究。通常基础的任意形状用其外包的规则几何形状代替原有的不规则基础形状,以达到确定动刚度和阻尼系数的目的,而且这两个参数的确定仅仅是对单独刚性基础的,无法考虑相邻基础对其产生的影响。针对上述两方面不完善之处作了进一步探讨,引入相邻基础动力相互作用因子的概念,并利用地基为平面应变假定以求之。推荐的方法经验证,非常准确。     

地下结构抗震设计的改进等效反应加速度法

对地下结构横向抗震分析中的等效反应加速度法进行综合分析。结合算例,以动力时程法为基准,全面评价了等效反应加速度法的适用性;进而深入分析其误差来源,并做针对性改进优化,通过引入动力响应调整系数β,提出了一种改进等效反应加速度法;结合算例分析,评价了改进等效反应加速度法对不同工况的适用性。结果表明：等效反应加速度法计算所得结构内力及变形均偏小;且计算精度随地层剪切波速的增大整体呈上升趋势,但几乎不受结构埋深的影响;同时,明确了等效反应加速度法的误差源自于其忽略了地下结构对其周围土体动力响应的干扰作用,改进优化后提出了改进等效反应加速度法;相比现有等效反应加速度法,改进等效反应加速度法具有更广泛的适用性及更优的计算精度,可为地下结构抗震设计和分析提供新的计算方法。     

Effects of the improper modeling of viscous damping on the first-mode and higher-mode dominated responses of base-isolated buildings

In many finite element platforms, a classical global damping matrix based on the elastic stiffness of the system (including isolators) is usually developed as part of the solution to the equations of motion of base-isolated buildings. The conducted analytical and numerical investigations illustrate that this approach can lead to the introduction of unintended damping to the first and higher vibration modes and the spurious suppression of the respective structural responses. A similar shortcoming might be observed even when a nonclassical damping model (ie, an assembly of the superstructure and isolation system damping sub-matrices) is used. For example, the use of Rayleigh damping approach to develop the superstructure damping sub-matrix can lead to the undesired addition of damping to the isolated mode arising from the mass-proportional component of the superstructure damping. On the other hand, the improper use of nonclassical stiffness-proportional damping (eg, determining the proportional damping coefficient, β_k , based on the first mode) can result in assigning significant damping to the higher-modes and the unintended mitigation of the higher-mode responses. Results show that a nonclassical stiffness-proportional model in which β_k is determined based on the second modal period of a base-isolated building can reasonably specify the intended damping to the higher modes without imparting undesirable damping to the first mode. The nonclassical stiffness-proportional damping can be introduced to the numerical model through explicit viscous damper elements attached between adjacent floors. In structural analysis software such as SAP2000®, the desired nonclassical damping can be also modeled through specifying damping solely to the superstructure material.     

重复循环荷载作用下原状黄土动力特性试验研究

为探究重复循环荷载作用下含水率、固结压力对原状黄土动力特性、变形性状的影响规律,利用英国GDS双向动态三轴试验系统模拟交通荷载,对海东地区原状黄土进行动三轴试验研究。试验结果表明：单一重复循环动荷载作用下,在加载初期,海东地区原状黄土的轴向动应变随着循环次数的增大急剧增加,后期缓慢增加至趋于稳定,即发生应变硬化现象。在加载初期,含水率、固结压力对原状黄土的轴向动应变无明显影响,当循环次数N>400时,原状黄土的轴向动应变随含水率的升高而增加,随固结压力的增大而减小。动剪切模量随循环次数的增加出现先减小后增加再减小的变化,随含水率的升高有较大幅度的降低。动阻尼比随循环次数的增加先增加后减小,随含水率的升高而增大。表明海东地区原状黄土所具有的大孔隙架空结构使其在重复循环荷载作用下易发生振动变形。