An efficient quasi-Newton approximation-based SORM to estimate the reliability of geotechnical problems

The first order reliability method (FORM) is efficient, but it has limited accuracy; the second order reliability method (SORM) provides greater accuracy, but with additional computational effort. In this study, a new method which integrates two quasi-Newton approximation algorithms is proposed to efficiently estimate the second order reliability of geotechnical problems with reasonable accuracy. In particular, the Hasofer–Lind–Rackwitz–Fiessler–Broyden–Fletcher–Goldfarb–Shanno (HLRF–BFGS) algorithm is applied to identify the design point on the limit state function (LSF), and consequently to compute the first order reliability index; whereas the Symmetric Rank-one (SR1) algorithm is nested within the HLRF–BFGS algorithm to compute good approximations, yet with a reduced computational effort, of the Hessian matrix required to compute second order reliabilities. Three typical geotechnical problems are employed to demonstrate the ability of the suggested procedure, and advantages of the proposed approach with respect to conventional alternatives are discussed. Results show that the proposed method is able to achieve the accuracy of conventional SORM, but with a reduced computational cost that is equal to the computational cost of HLRF–BFGS-based FORM.     

空间直角坐标和大地坐标的转换

目前国内在空间直角坐标和大地坐标转换公式使用问题上 ,还明显缺乏必要的统一性。针对这个问题 ,本文作者在全面分析和比较国内外现有各种转换方法的基础上 ,重点推荐和介绍根据 Bowring研究思路导出的转换公式 ,这组公式既简单又具有很高的计算精度 ,能够满足各个部门的使用要求     

Thermoelastic stress due to a rectangular heat source in a semi-infinite medium. Presentation of an analytical solution

The thermoelastic response due to a time-dependent rectangular heat source in a semi-infinite medium is analyzed. The problem originates from studies of nuclear waste repositories in rock. Canisters containing heat-emitting nuclear waste are deposited over a large rectangular area deep below the ground surface. The solution for a time-dependent heat source is obtained from the corresponding instantaneous heat source by superposition. The thermoelastic problem for the instantaneous rectangular heat source in a infinite surrounding is solved exactly. An important step is the introduction of so-called quadrantal heat sources. The solution for the rectangle is obtained from four quadrantal solutions. The solution for the quadrantal heat source depends on the three dimelasionless coordinates only. Time occurs in the scale factors only. The condition of zero normal and shear stresses at the ground surface is fulfilled by using a mirror heat source and a boundary solution. The boundary solution accounts for the residual normal stress at the ground surface. Using a Hertzian potential, a surprisingly simple solution is obtained. The final analytical solution is quite tractable considering the complexity of the initial problem. The solution may be used to test numerical models for coupled thermoelastic processes. It may also be used in more detailed numerical simulations of the process near the heat sources as boundary conditions to account for the three-dimensional global process.     

Isolation of plane shear wave using water saturated trench barrier

The article presents a theoretical investigation of the propagation of normally and obliquely incident plane shear waves past a rectangular trench filled up with water saturated soil sandwiched between anisotropic elastic media. The motivation for this work is due to the effectiveness of the isolation of waves by the in-filled rectangular trench. Unlike the most of the previous researchers, this model considers the soil–structure interaction effects and directly determines the influence of barrier in the form of in-filled trench on the mode of wave propagation. It is of interest to determine the reflection and transmission coefficients, and the energy partition distribution of shear waves in the in-filled rectangular trench showing the influence of barrier on the propagation of waves. An extensive parametric study through numerical computation is carried out to investigate the influence of the material properties of the in-filled trench and the amplitude ratios on shear waves. The in-filled trench barrier directly declines the intensity of waves significantly in such a way that the waves do not create any hazards to the nearby structures, if exists at all.     

Effects of backfill on seismic behavior of rectangular tanks

The reliability and/or stability of the lifeline structures against failure under seismic loads are of critical concern, and must be studied carefully. Therefore, the main objective of this paper is to demonstrate the commonly encountered backfill effects on the dynamic response of rectangular tanks. However, only the exterior wall of the tank which interacts with both the backfill and fluid is tackled, as each part of the structure shows considerable differences in terms of both the load bearing mechanisms and the geometrical and positional differences. Finite element analyses are employed, taking into consideration the fluid-wall-backfill interaction. The analyses are conducted to observe whether or not both backfill and wall behavior can be affected by variation of the internal friction angle. For that purpose, some comparisons are made on vertical displacements of the backfill, roof displacements, stress responses, etc., by means of internal friction angle variations of the backfill from 25° to 40°. Consequently, it is observed that the variations on maximum vertical displacements are affected considerably. In contrast, the maximum stress responses are affected partially. However, the inertial effects of the backfill show that pseudo-static approximations may be insufficient to understand the dynamic behavior of the backfill-wall-fluid system.     

卫星磁异常的理论模型

本文介绍了计算卫星磁异常理论模型的数学方法 ,即球谐分析方法、冠谐分析方法、矩谐分析方法和等效源方法 .根据相同的 MAGSAT资料 ,计算的卫星磁异常冠谐模型、矩谐模型和等效源模型都能很好地表示卫星磁异常的分布 .由于在整个研究区域 ( 1 0°N～60°N,70°E～ 1 40°E)都有卫星资料 ,所以这些理论模型没有所谓的“边界效应”.这一结论对计算地磁场的区域模型是很有意义的 .     

矩形含水层井流模型求解的软件实现

矩形含水层井流模型的求解过程比较繁琐,计算工作量较大,而且容易出错,而利用计算机编程技术可使求解变得极为简单、快捷,从而极大地提高工作效率。该文以矩形隔水边界承压井流模型为例,研究了实现软件求解该类问题的思路。     

典型矩形高层建筑风荷载与风振响应分析

对典型矩形高层建筑进行风洞试验,根据试验结果计算了各风向角下的等效静风荷载和风振响应,同时采用《建筑结构荷载规范》(GB50009-2012)计算方法对该建筑正交角度下的风荷载进行计算,结合风洞试验风荷载与规范计算结果,研究典型矩形高层建筑等效静风荷载和加速度响应分布规律。结果表明:结构基底风致响应最不利角度并非完全出现在正交角度,风洞试验楼层风荷载整体趋势与规范计算结果相同,数值上存在差异,宜以风洞试验结果为准,该结构的顶层加速度响应小于高规限值,舒适度满足要求。     

矩形大定源层状模型瞬变电磁响应计算

针对矩形大定源介绍了一种层状导电模型瞬变电磁响应的快速计算方法.其基本思想是,将大定源回线源用较少的有限大小方形回线叠加.在频率域,该叠加过程导出矩形大定源回线模型响应可以表示为一个标准的Hankel积分,叠加效应仅仅是相应Bessel函数的空间积分过程.瞬变电磁响应可以利用余弦变换由频率域响应获得.均匀半空间模型计算结果和解析解较为吻合,层状模型模拟结果符合物理规律,不同测点位置感应电动势的视电阻率具有很好的一致性.新方法误差只是来源于圆回线对小方形回线的等效误差.与均匀半空间解析结果比较,只用16个方形回线等效,相对误差就可以小于10^-3.