Analysis of a rigid footing lying on three-layered soil using the finite difference method

A numerical procedure is described for the analysis of the vertical deformation and the stress distribution of the strip footings on layered soil media. Three layers of soil with different stiffness are considered with the middle soil layer the thinnest and most stiff layer. The soil media is discretized and using the theory of elasticity, the governing differential equations are obtained in terms of vertical and horizontal displacements. These equations along with appropriate boundary and continuity conditions are solved by using the finite difference method. The vertical and horizontal displacements, strains and stresses are found at various nodes in the soil media. Parametric studies are carried out to study the effect of the placement depth of the middle soil layer, the relative ratios of the moduli of deformation of the soil layers on the vertical displacement of the footing and the vertical stress distribution. These studies reveal that the middle thin but very stiff layer acts like a plate and redistributes the stresses on the lower soft soil layer uniformly. The displacement on the top and bottom of the middle soil layer is almost the same showing that the compression of the middle layer is negligible as it is very stiff.     

Cyclicity in the Main and Upper Zones of the Bushveld Complex, South Africa: Crystallization from a Zoned Magma Sheet

The major element composition of plagioclase, pyroxene, olivine,and magnetite, and whole-rock ⁸⁷Sr/⁸⁶Sr data are presented forthe uppermost 2·1 km of the layered mafic rocks (upperMain Zone and Upper Zone) at Bierkraal in the western BushveldComplex. Initial ⁸⁷Sr/⁸⁶Sr ratios are near-constant (0·7073± 0·0001) for 24 samples and imply crystallizationfrom a homogeneous magma sheet without major magma rechargeor assimilation. The 2125 m thick section investigated in drillcore comprises 26 magnetitite and six nelsonite (magnetite–ilmenite–apatite)layers and changes up-section from gabbronorite (An₇₂ plagioclase;Mg# 74 clinopyroxene) to magnetite–ilmenite–apatite–fayaliteferrodiorite (An₄₃; Mg# 5 clinopyroxene; Fo₁ olivine). The overallfractionation trend is, however, interrupted by reversals characterizedby higher An% of plagioclase, higher Mg# of pyroxene and olivine,and higher V₂O₅ of magnetite. In the upper half of the successionthere is also the intermittent presence of cumulus olivine andapatite. These reversals in normal fractionation trends definethe bases of at least nine major cycles. We have calculateda plausible composition for the magma from which this entiresuccession formed. Forward fractional crystallization modelingof this composition predicts an initial increase in total iron,near-constant SiO₂ and an increasing density of the residualmagma before magnetite crystallizes. After magnetite beginsto crystallize the residual magma shows a near-constant totaliron, an increase in SiO₂ and decrease in density. We explainthe observed cyclicity by bottom crystallization. Initiallymagma stratification developed during crystallization of thebasal gabbronorites. Once magnetite began to crystallize, periodicdensity inversion led to mixing with the overlying magma layer,producing mineralogical breaks between fractionation cycles.The magnetitite and nelsonite layers mainly occur within fractionationcycles, not at their bases. In at least two cases, crystallizationof thick magnetitite layers may have lowered the density ofthe basal layer of melt dramatically, and triggered the proposeddensity inversion, resulting in close, but not perfect, coincidenceof mineralogical breaks and packages of magnetitite layers. KEY WORDS: layered intrusion; mineral chemistry; isotopes; magma; convection; differentiation     

滇西北地区富碱岩体(脉)地质学及岩石化学特征

喜山期富碱岩体广布于滇西北地区 ,通过对其地质学和岩石化学特征的研究 ,认为富碱岩体 (脉 )由正长 (斑 )岩、二长斑岩、花岗斑岩及相关的火山岩组成 ,具有多次活动的特征 ,并形成区内富有特色的岩浆岩系列 ;该系列岩浆岩以富碱高钾为突出特点 ,具有正常的岩浆演化趋势 ,不同岩带岩石地质学和岩石化学方面有区域性变化规律。     

软土地基沉降计算的误差分析

对引起路堤荷载下软土地基沉降从竖应力、固结沉降、瞬时沉降和后期沉降的计算四个方面,常见计算方法误差的诸多因素,从受力、沉降原理上进行了详细分析并提出一些建议,以使沉降更为接近实际.     

Three Alkali-Rich Intrusive Rock Belts Newly Discovered in the Mt. Kunlun-Mt. Altun Region, Xinjiang, China

The newly discovered three alkali-rich intrusive rock belts in the Mt. Kunlun Mt.Altun region of southern Xinjiang are the Lapeiquan-Yitunbulak alkali-rich intrusive rock belt,the Gez-Taxkorgan alkali-rich intrusive rock belt and the Beilisai-Abulash alkali-rich intrusive rock belt. The former two belts were formed during the Yanshanian period, and the third one was formed during the Himalayan period, which is the youngest alkali-rich intrusive rock belt in China. The discovery of the alkali-rich intrusive rock belts is of great significance in shedding light on the history of tectono-magmatic activities in this region.     

Surface vibration due to a sequence of high speed moving harmonic rectangular loads

The transmission of vibrations over the surface of the ground, due to high-speed moving, vertical harmonic rectangular loads, is investigated theoretically. The problem is three-dimensional and the interior of the ground is modelled as an elastic half-space or a multilayered ground. The transformed solutions are obtained using the Fourier transform on the space variable. A new damping model in the spatial wavenumber domain, presented in Lefeuve-Mesgouez et al. [J. Sound. Vibr. 231 (2000) 1289] is used. Numerical results for the displacements on the surface are presented for loads moving with speeds up to and beyond the Rayleigh wave speed of the half-space.     

Inferring the relative measure of principal stress components

The phase velocity and the attenuation coefficient of compressional seismic waves, propagating in poroelastic, fluid-saturated, laminated sediments, are computed analytically from first principles. The wavefield is found to be strongly affected by the medium heterogeneity. Impedance fluctuations lead to poroelastic scattering; variations of the layer compressibilities cause inter-layer flow (a 1-D macroscopic local flow). These effects result in significant attenuation and dispersion of the seismic wavefield, even in the surface seismic frequency range, 10–100 Hz. The various attenuation mechanisms are found to be approximately additive, dominated by inter-layer flow at very low frequencies. Elastic scattering is important over a broad frequency range from seismic to sonic frequencies. Biot's global flow (the relative displacement of solid frame and fluid) contributes mainly in the range of ultrasonic frequencies. From the seismic frequency range up to ultrasonic frequencies, attenuation due to heterogeneity is strongly enhanced compared to homogeneous Biot models. Simple analytical expressions for the P -wave phase velocity and attenuation coefficient are presented as functions of frequency and of statistical medium parameters (correlation lengths, variances). These results automatically include different asymptotic approximations, such as poroelastic Backus averaging in the quasi-static and the no-flow limits, geometrical optics, and intermediate frequency ranges.     

P-SH conversions in a flat-layered medium with anisotropy of arbitrary orientation

P-SH conversion is commonly observed in teleseismic P waves, and is often attributed to dipping interfaces beneath the receiver. Our modelling suggests an alternative explanation in terms of flat-layered anisotropy. We use reflectivity techniques to compute three-component synthetic seismograms in a 1-D anisotropic layered medium. For each layer of the medium, we prescribe values of seismic velocities and hexagonally symmetric anisotropy about a common symmetry axis of arbitrary orientation. A compressional wave in an anisotropic velocity structure suffers conversion to both SV -and SH -polarized shear waves, unless the axis of symmetry is everywhere vertical or the wave travels parallel to all symmetry axes. The P-SV conversion forms the basis of the widely used 'receiver function' technique. The P-SH conversion occurs at interfaces where one or both layers are anisotropic. A tilted axis of symmetry and a dipping interface in isotropic media produce similar amplitudes of both direct ( P ) and converted ( Ps ) phases, leaving the backazimuth variation of the P-Ps delay as the main discriminant. Seismic anisotropy with a tilted symmetry axis leads to complex synthetic seismograms in velocity models composed of just a few flat homogeneous layers. It is possible therefore to model observations of P coda with prominent transverse components with relatively simple 1-D velocity structures. Successful retrieval of salient model characteristics appears possible using multiple realizations of a genetic-algorithm (GA) inversion of P coda from several backazimuths. Using GA inversion, we determine that six P coda recorded at station ARU in central Russia are consistent with models that possess strong (> 10 per cent) anisotropy in the top 5 km and between 30 and 43 km depth. The symmetry axes are tilted, and appear aligned with the seismic anisotropy orientation in the mantle under ARU suggested by SKS splitting.     

新疆乌伦古富碱侵入岩成因探讨

对沿乌伦古深断裂分布的钠闪石花岗岩、钾长花岗岩、闪长岩、碱性正长岩等富碱侵入体进行了较系统的岩石化学、微量元素、稀土元素地球化学及Ｏ、Ｐｂ、Ｓｒ、Ｎｄ同位素组成研究，确认它们为一类幔源重熔分异型富碱侵入岩类。在分析其物质来源、形成构造环境和成岩条件等特征基础上，用部分熔融、多阶段分离结晶和分离结晶－地壳混染等模型探讨了其成岩机理。     

铜陵地区中酸性侵入岩年代学研究

本文选择了铜陵地区主要岩石类型的代表性岩体中黑云母为测定对象，准确地测定了侵入岩的４０Ａｒ／３９Ａｒ同位素年龄。测定结果表明，区内侵入岩的年龄均小于１４０Ｍａ，属燕山晚期的产物，后期热事件为成矿时代，晚于岩浆侵入时代，在此基础上，分析了ＫＡｒ法、ＲｂＳｒ法同位素年龄产生偏差的原因