Non‐linear response analyses of rectangular rigid bodies subjected to horizontal and vertical ground motion

This investigation deals with non‐linear seismic responses of free‐standing rectangular rigid bodies on horizontally and vertically accelerating rigid foundations. The responses are classified into two initial responses and four subsequent responses, accordingly the equations of motion governing the liftoff, slip and liftoff–slip interaction motions and boundary conditions corresponding to commencement and termination of the motions are defined. The time histories of responses presented herein show that the body is sensitive to small changes in the friction coefficient and slenderness, and to the wave properties and intensity of ground motions. Systematic trends are observed: the bodies on the low‐grip foundation avoid overturning while they are allowed to slip regardless of details of ground motions; the long period earthquakes tend to make the body overturn and slip largely. In contrast, the timing when liftoff and slip commences and terminates and their directions do not directly correspond with intensity of ground motions. Moreover, the vertical ground motion adds irregularities on the responses, since it excites or damps the responses. It is concluded that governing equations of motion and boundary conditions in view of discontinuous non‐linear systems are necessary to analyse actual motions of the rectangular rigid bodies subjected to horizontal and vertical ground motion. Copyright © 2002 John Wiley & Sons, Ltd.     

岩石破坏非连续变形分析弹脆性本构模型的二次开发

岩石非连续变形分析方法DDARF成功实现了模拟岩体裂纹萌生、扩展、贯通、破碎的全过程,但算法只考虑了岩体的线弹性本构模型,没有分析岩体的非线性应力-应变关系。为更符合真实岩体工程,同时扩展岩石非线性本构模型的应用范围,分别采用摩尔-库仑强度准则和最大拉应力强度准则对岩体进行剪切和拉伸破坏判断;对理想弹脆性本构模型进行算法分析,并在VC++平台下程序实现;对“自定义”的岩体非连续变形分析方法弹脆性本构模型与室内单轴压缩试验进行比较分析;将岩体非连续变形分析方法弹脆性本构模型应用于大型地下洞室开挖,并与线弹性本构模型进行对比。结果表明,非连续变形分析方法中自定义岩体弹脆性本构模型是可行的,它能够反映岩体变形的非线性特征,与室内试验吻合度较好;非连续变形分析方法弹脆性本构模型应用于大型地下工程,能更安全且真实地分析洞室围岩的稳定性,进而更好地指导地下洞室的防护措施。     

西藏樟木后山危岩崩塌颗粒离散元数值分析

崩塌危岩是高陡岩质边坡浅表层破坏常见的动力地质灾害方式之一,它突发性强,随机性大,速度快,发生猛烈,一直是边坡工程勘察中的重点。对西藏樟木后山高陡边坡危岩进行了现场勘察,分析研究了危岩崩塌体的分布范围。利用PFC3D模拟了在降雨件下危岩崩塌危岩的运动轨迹、速度及不同摩擦系数崩塌体的堆积特征。计算分析结果表明,崩塌危岩运动路径受地形地貌影响较大,与地面发生碰撞,多次改变行进方向,简化二维计算可能得出错误结论;坡面摩擦系数影响崩塌危岩的堆积形态,摩擦系数越小,堆积体位置越远,运动状态易表现流态性状。坡面摩擦系数取1.2时,模拟结果与实际较为吻合;崩塌危岩主要危害的范围为陡崖下部武警二营至樟木沟口一带。利用PFC3D模拟危岩崩塌运动可以初步确定崩塌体三维堆积形态及影响范围,为防灾减灾工程设计提供有益参考。     

Site response analysis with two‐dimensional numerical discontinuous deformation analysis method

The capability of the numerical discontinuous deformation analysis (DDA) method to perform site response analysis is tested. We begin with modeling one‐dimensional shear wave propagation through a stack of horizontal layers and compare the obtained resonance frequency and amplification with results obtained with SHAKE. We use the algorithmic damping in DDA to condition the damping ratio in DDA by changing the time step size and use the same damping ratio in SHAKE to enable meaningful comparisons. We obtain a good agreement between DDA and SHAKE, even though DDA is used with first order approximation and with simply deformable blocks, proving that the original DDA formulation is suitable for modeling one‐dimensional wave propagation problems. The ability of DDA to simulate wave propagation through structures is tested by comparing the resonance frequency obtained for a multidrum column when modeling it with DDA and testing it in the field using geophysical site response survey. When the numerical control parameters are properly selected, we obtain a reasonable agreement between DDA and the site response experiment in the field. We find that the choice of the contact spring stiffness, or the numerical penalty parameter, is directly related to the obtained resonance frequency in DDA. The best agreement with the field experiment is obtained with a relatively soft contact spring stiffness of k = (1/25)(E × L) where E and L are the Young's modulus and mean diameter of the drums in the tested column. Copyright © 2013 John Wiley & Sons, Ltd.     

Subsoil structure and site effects: A comparison between results from SPAC and HVSR in sites of complex geology

We present the results of the analysis of array recorded microtremors at 14 sites, close to the edges of the Mygdonian basin in northern Greece (Euroseistest). These measurements were made in order to better constrain the geometry and velocity structure of the basin as the soil layers taper out close to rock outcrop, where geology is complex and we may expect significant changes of the subsoil structure over short distances. The data were analysed using the SPAC method and HVSR. The first interprets the measurements as Rayleigh waves (for the vertical component we analysed) and allows to invert a phase velocity dispersion curve from computed correlation coefficients. The second estimates a local transfer function directly, from ratios of Fourier amplitude spectra. A phase velocity dispersion curve could be derived for 12 of the 14 measurement sites, and at three of the sites no resonant frequency was observed in the HVSR. It is encouraging that we obtained good results at most of our sites, in spite of the lateral heterogeneity expected close to the edges of Euroseistest. Our results allow us to obtain shear wave velocity models at most of the measurement sites (12 out of 14). They are also useful to explore the relation between size of the array and wavelength range for which a dispersion curve may be estimated, which in our case has strong limitations. We identify the frequency of resonance of the sediments as a small loss of coherency in SPAC’s correlation coefficients. Finally, we also consider the applicability of the joint inversion of the resonance frequency determined using HVSR and the phase velocity dispersion curve obtained from SPAC.     

A method for stochastic seismic response analysis of non-classically damped structures

A method to calculate the stationary random response of a non-classically damped structure is proposed that features clearly-defined physical meaning and simple expression. The method is developed in the frequency domain, The expression of the proposed method consists of three terms, i.e., modal velocity response, modal displacement response, and coupled (between modal velocity and modal displacement response), Numerical results from the parametric study and three example structures reveal that the modal velocity response term and the coupled term are important to structural response estimates only for a dynamic system with a tuned mass damper. In typical cases, the modal displacement term can provide response estimates with satisfactory accuracy by itself, so that the modal velocity term and coupled term may be ignored without loss of accuracy, This is used to simplify the response computation of non-classically damped structures. For the white noise excitation, three modal correlation coefficients in closed form are derived. To consider the modal velocity response term and the coupled term, a simplified approximation based on white noise excitation is developed for the case when the modal velocity response is important to the structural responses. Numerical results show that the approximate expression based on white noise excitation can provide structural responses with satisfactory accuracy~     

养分含量对土壤冻融特征曲线的影响

土壤冻融特征曲线是反映土壤冻融过程中的水、热、盐迁移规律以及冻土强度、冻土的热性质的重要参数. 为了研究土壤冻融过程中土壤养分的迁移规律, 采用核磁共振法对加入不同浓度的硫酸铵溶液、磷酸二氢钾溶液和氯化钾溶液的土样的冻融特征曲线进行了测定和分析. 结果表明磷酸二氢钾溶液对土壤的冻融特征曲线影响不明显, 氯化钾溶液的影响最明显, 硫酸铵溶液的影响次之. 加入氯化钾溶液的部分试样, 以及加入硫酸铵溶液的部分试样的冻融特征曲线出现了二次突变点. 滞后现象普遍存在于各个试样的冻融特征曲线中, 滞后明显区间所处的温度范围随所加入的溶液浓度的增高而降低. 当加入试样的溶液浓度相同时, 加入氯化钾溶液的滞后明显区间所处的温度范围最低, 加入硫酸铵溶液的次之, 加入磷酸二氢钾溶液的最高.     

25℃时K2B4O7-H2O体系的离子相互作用模型研究

根据硼酸盐水溶液中硼浓度不同时硼物种之间形成多种聚合与解聚的平衡反应理论和光谱学研究结果,利用已有的该体系25℃等压实验数据,拟合获得了该体系的两个化学计量平衡常数、各种硼氧配阴离子单一的以及二离子和三离子之间的相互作用Pitzer参数,确定了该体系在不同总硼浓度范围内各种硼氧配阴离子的存在形式与定量分布,将所获得的离子相互作用模型计算出的渗透系数与实验值进行了比较,获得了令人满意的结果。     

非连续变形分析（DDA）线性方程组的高效求解算法

非连续变形分析(DDA)方法对大规模工程问题的数值模拟耗时太长,其中线性方程组求解耗时可占总计算时间的70%以上,因此,高效的线性方程组解法是重要研究课题。首先,阐述了适用于DDA方法的基于块的行压缩法和基于试验-误差迭代格式的非0位置记录;然后,针对DDA的子矩阵技术,将块雅可比迭代法 (BJ)、预处理的块共轭梯度法 (PCG,包括Jacobi-PCG、SSOR-PCG) 引入DDA方法,重点研究了线性方程组求解过程中的关键运算;最后,通过两个洞室开挖算例,分析了各线性方程组求解算法在DDA中的计算效率。研究表明：与迭代法相比,直解法无法满足大规模工程计算需要;BJ迭代法与块超松弛迭代法(BSOR)的效率差别不大,但明显不如PCG迭代法。因此,建议采用PCG迭代法求解DDA线性方程组,特别是SSOR-PCG值得推广;如果开展并行计算研究,Jacobi-PCG是较好的选择,当刚度矩阵惯性优势明显时,BJ迭代法同样有效。