Fundamental solutions to Helmholtz's equation for inhomogeneous media by a first-order differential equation system

Helmholtz's equation with a variable wavenumber is solved for a point force through use of a first-order differential equation system approach. Since the system matrix in this formulation is non-constant, an eigensolution is no longer valid and recourse has to be made to approximate techniques such as series expansions and Picard iterations. These techniques can accommodate in principle any variation of the wavenumber with position and are applicable to scalar wave propagation in one, two and three dimensions, with the latter two cases requiring radial symmetry. As shown in the examples, good solution accuracy can be achieved in the near field region, irrespective of frequency, for the particular case examined, namely a wavenumber which increases (or decreases) as the square root of the radial distance from source to receiver. Finally, the resulting Green's functions can be used as kernels within the context of boundary element type solutions to study scalar wave scattering in inhomogeneous media.     

非均匀地基中倾斜桩基竖向承载特性模拟试验研究

群桩基础中设计的倾斜桩基以其横向阻抗能力强等优势在港口、码头以及桥梁基础中得到了较为广泛应用。随着山区及不均匀地基土地区高速公路等基础设施的建设,在滑坡、斜坡变形体和不均匀地基上设计倾斜群桩桥梁基础的情况将会越来越多。由于倾斜桩基受力状态的复杂性,目前倾斜桩基础设计仍参考竖向桩基承载力计算理论,凭借经验进行设计。对此人们虽然做了许多探索,但仍未形成完善的设计计算理论和标准。为此,结合厦深客运专线某特大桥桩基选型研究项目,利用相似材料物理模拟试验,就倾角为0°～12°周边斜桩的群桩基础竖向承载力进行了试验研究。结果表明,竖直桩基的荷载-沉降曲线呈缓变型,倾斜桩基则呈陡降型;就倾斜群桩基础竖向承载力而言,倾斜基桩的合理倾角为8°左右;竖直桩基中角桩轴力最大,边桩轴力次之,中桩轴力最小,倾斜桩基中的中桩轴力最大,角桩轴力次之,边桩轴力最小;倾斜桩基桩身弯矩分布形式与基桩的倾角有关,当倾角达到12°时,桩身将出现反向弯曲段。基桩倾角的不同是导致倾斜桩基和竖直桩基竖向承载特性显著不同的主要原因之一。     

A new approach for vertical impedance in radially inhomogeneous soil layer

In the past studies on pile vibrations, the soil around the pile is mainly regarded as homogeneous or multi‐layered piecewise homogeneous. However, under most engineering conditions, the surrounding soil becomes seriously disturbed due to construction effects. This may strengthen or weaken the shear modulus of the soil resulting in the soil becoming radially inhomogeneous. As a consequence of this, El Naggar extended Novak's plane‐strain model to account for the radial inhomogeneity by the use of multiple springs connected in series. Rather than using this approach, this paper proposes a new model which is thought to be theoretically more rigorous and one which may be described as complex stiffness transfer model. It is shown that the solution developed in this study agrees well with the more limited solutions of Novak and Dotson and Veletsos under several special conditions. Finally, the scope of application has been enlarged as a result of the generalizations made in the present model. Copyright © 2011 John Wiley & Sons, Ltd.     

饱和多孔介质中的非均匀平面波

讨论了两相饱和多孔介质中的非均匀平面波,在所采用的多孔介质模型中,利用了每种组分的微观密度保持不变而与体积分数相关的宏观密度是变化的假设。针对理想无粘流体充填的弹性多孔固体,深入讨论了两种非均匀平面波的传播特性以及质点运动的轨迹线。     

地震效应下三维非均质土坡稳定性极限分析

基于极限分析上限定理,采用拟动力法研究了地震效应下非均质土坡的三维稳定性,并通过重度加大法（GIM）推导出边坡安全系数的显式表达式。此外,采用遗传算法进行优化,将所得结果进行对比验证,详细分析了地震条件下相关参数对边坡稳定性的影响。分析结果表明：边坡高度一定时,宽高比、边坡倾角的增大以及土体内摩擦角、非均质系数的减小均会造成安全系数的降低;拟静力法获得的结果相比于拟动力法较大,两种方法结果的差值会随着水平地震系数、有效内摩擦角的增大而增大,随着边坡倾角的增大而减小;土体放大系数的增大会导致安全系数减小,而地震波周期及波速的变化几乎对安全系数没有影响;滑动面轨迹受水平地震系数的影响较大,而受非均质系数的影响相对较小。     

基于非均质边坡强度折减法的三维桥基边坡稳定性分析

基于场变量的强度折减法,以三维一般边坡和陡边坡作为算例模型,对非均质边坡的折减范围进行研究。研究中借鉴某学者研究成果,在ABAQUS中对岩体材料的抗剪强度参数( )和抗拉强度参数T同时进行强度折减,并结合目前边坡失稳判据存在的不足,提出采用坡体内关键部位特征点位移增量 与强度折减系数增量 之比值 和强度折减系数 关系曲线的突变点来确定边坡的临界失稳状态。结果表明,对于一般边坡,只有当黏聚力相差不大的情况下,对黏聚力较小土层实施局部折减才能得到合理的安全系数,对于坡体内存在岩质相差较大的边坡建议采用整体强度折减,相反对于高陡三维边坡而言对相对较软的岩体进行局部折减可以得出较为可信的结果。通过与传统特征点位移法判据相比较,验证了 法的实用性和合理性,同时基于该判据计算出桥基边坡运营期间的安全系数,可为岸坡治理提供理论依据。。     

Is the Stephani-Krasiński solution a viable model of the Universe?

We present a detailed study of the inhomogeneous Stephani-Krasinski solution with time-dependent curvature index. In general, the cosmological behaviour of the models depends on six arbitrary functions of time. Such models are termed ‘private universes’ and cannot be in accord with observation in the most general case. Two simple models with changing topology are considered as illustrating examples. In one of these models the pressure turns out to be negative and hence a violation of the weak energy condition in the singularity theorems is possible. A brief review of other inhomogeneous cosmologies is included for the sake of clarity. It is shown that the geodesic equation can be reduced to a complicated differential equation, which depends on the three arbitrary functions involved. Therefore, it is difficult to obtain explicit formulas for the various observational relations.     

吸收介质中的Maslov体波理论地震图

本文研究了横向非均匀吸收介质中的Maslov渐近理论地震图方法.对于如何提高计算精度及计算速度作了比较深入的探讨.本方法先计算远场格林函数,由褶积得到一般震源函数的弱吸收理论地震图.对于高Q引起的数值不稳定性,通过引入平滑函数得以解决.由此产生的新的被积函数具有非常好的收敛性,从而提高了计算精度及计算速度.以此理论编写的程序在模拟完全弹性介质以及一维吸收介质时与反射率法作了比较,并取得了令人满意的效果.对于二维横向非均匀吸收介质,计算方法与高斯光束方法作了对比,二者在主要特征上基本一致.数值对比中出现的一些差异也作了必要的讨论及说明.     

Electrical spectroscopy of porous rocks: a review—II. Experimental results and interpretation

In the frequency range from millihertz to hundreds of megahertz, many different physical and physico-chemical processes contribute to the electrical polarization of porous water-bearing rocks. This makes the interpretation of their electrical spectra a complicated problem and requires both elaborate theories and model experiments. At high frequencies, the Maxwell–Wagner–Bruggeman–Hanai (MWBH) theory of effective media, which takes into account only bulk properties, shape and partial volume of components, is very appropriate. At low frequencies, surface films, polarization of the electrical double layer (EDL) and clustering of conductive components can produce very strong polarization; corresponding theoretical models are considered in a companion paper ( Chelidze & Gueguen 1999 , hereafter referred to as Paper I). This paper is devoted to the review of experimental data and their comparison with theoretical models.
  Experiments on saturated mineral powders and rocks with various surface areas and surface chemistries confirm the existence of significant surface contributions to the electrical spectra of conductivity and polarization of water-bearing rocks and the dominance of this contribution over MWBH values at low frequencies. The effective dielectric constant of porous saturated rocks increases with the surface-to-volume ratio of the system and strongly depends on the surface charge ( ζ potential). At ζ potential, equal to zero, the low-frequency dielectric permittivity (DP) is minimal. The experimental data on relaxation times and the magnitude of the surface polarization of water-bearing porous systems can be satisfactorily explained by theories of film polarization, diffusional polarization generated by deformation of an 'open' electrical double layer (EDL) and percolation.