基于球孔扩张理论和侧阻力退化效应的压桩力计算模拟

根据静压桩的贯入机制,将沉桩过程模拟为半无限土体中一系列球形孔的连续扩张,土体假定为Mohr-Coulomb材料。利用球孔扩张和源-源假设理论,并采用Boussinesq解进行地面应力的修正,在此基础上分别计算出桩侧极限摩阻力和桩端阻力。通过现场试验研究发现,沉桩过程中侧摩阻力退化效应带来的影响是明显的,提出了相应的侧阻力退化公式。在充分考虑以上因素的基础上推导出了静压桩压桩力的模拟计算公式。使用Matlab6.5软件进行理论计算,并与山西太原某试验进行对比分析,一定深度以下理论值与实测数据基本吻合,证明该计算模拟是可行的。     

非轴对称位移边界下球孔扩张挤土位移弹性解答

以现有半无限土体中球孔扩张挤土位移的解答为基础,分别对水平地表和非轴对称斜边两个位移边界进行应力修正,运用坐标转换法和叠加法的原理,改进现有的分析方法,得到较为简化的非轴对称位移边界下扩孔问题的解答,并对非轴对称斜边倾角以及球孔离斜边距离等因素对挤土位移的影响进行了分析。结果表明：倾斜边界条件的存在对球孔两侧的挤土位移有明显影响,且随着非轴对称边界倾角的增大,靠近倾斜边界侧的挤土位移也随之增大;球孔距自由边界的距离越大,自由边界对挤土位移的影响也越小。该解答对非轴对称边界条件下的静压沉桩以及相关扩孔问题的设计和施工具有一定的指导意义和实用价值。     

Band-limited functions on a bounded spherical domain: the Slepian problem on the sphere

The Slepian problem consists of determining a sequence of functions that constitute an orthonormal basis of a subset of ℝ (or ℝ²) concentrating the maximum information in the subspace of square integrable functions with a band-limited spectrum. The same problem can be stated and solved on the sphere. The relation between the new basis and the ordinary spherical harmonic basis can be explicitly written and numerically studied. The new base functions are orthogonal on both the subspace and the whole sphere. Numerical tests show the applicability of the Slepian approach with regard to solvability and stability in the case of polar data gaps, even in the presence of aliasing. This tool turns out to be a natural solution to the polar gap problem in satellite geodesy. It enables capture of the maximum amount of information from non-polar gravity field missions. Received: 10 June 1998 / Accepted: 20 May 1999     

Study of the crust and mantle using magnetic surveys by Magsat and other satellites

Among the first measurements made from near-Earth orbiting satellites were measurements of the magnetic field. The sources of that field lie both within the Earth, in its core and crust, and in the surrounding ionosphere and magnetosphere. This article summarizes some of the methodology and results for studies of the Earth’s mantle and crust. Mantle conductivity studies can be made either by studying signals impressed on the Earth from outside, e.g., the ionosphere or magnetosphere, or by studying signals originating in the core and transmitted through the mantle. Crustal field studies begin with a careful selection of the data and subsequent removal of core and external fields by some sort of filtering. Average maps from different local times sometimes differ, presumably due to the remaining presence of fields of external origin. Several techniques for further filtering are discussed. Where large-area aeromagnetic maps are available, crustal maps derived from satellite data can be compared with upward continued data. In general, the comparisons show agreement, with some differences, particularly in and near the auroral belts. The satellite data are further reduced by various methods of inverse and forward modelling, sometimes including reduction to the pole (RTP). These techniques are generally unstable at the equator. Common methods of stabilizing the inversions include principle components analysis and ridge regression. Because of the presence of the core field, the entire crustal contribution from the field is not known. Also, there is a basic nonuniqueness to the inverse solutions. Nevertheless, magnetizations that are interpretable can be derived.     

Efficiency of kriging estimation for square, triangular, and hexagonal grids

Although several researchers have pointed out some advantages and disadvantages of various soil sampling designs in the presence of spatial autocorrelation, a more detailed study is presented herein which examines the geometrical relationship of three sampling designs, namely the square, the equilateral triangle, and the regular hexagon. Both advantages and disadvantages exist in the use of these designs with respect to estimation of the semivariogram and their effect on the mean square error or variance of error. This research could be used to design optimal sampling strategies; it is based on the theory of regionalized variables, in which the intrinsic hypothesis is satisfied. Among alternative designs, an equilateral triangle design gives the most reliable estimate of the semivariogram. It also gives the minimum maximum mean square error of point estimation of the concentration over the other two designs for the same number of measurements when the nugget effect is small relative to the variance. If the nugget effect is large (.90 ² or more), and the linear sampling density is >0.85r where r is the range, the hexagonal design is best. This study computes and compares the maximum mean square error for each of these designs.     

对中国大陆区域地磁场提取的认识

本文从球谐函数理论的物理含义、中国地磁数据的分布情况及实际计算结果的分析,提出对当前用球谐函数拟合法提取中国大陆区域地磁异常的几点认识。     

基于能量耗散的球孔扩张理论解答

以空间准滑动面（SMP）准则为基础,推导了扩底桩扩孔压力的理论解。从能量耗散的角度分析球孔扩张的全过程,利用应力不变量推导了符合球孔扩张的屈服准则;化简微分方程得到了弹塑性区应力表达式,进而求出位移、应变表达式;分别利用体积守恒和能量守恒性推导出扩孔压力的表达式。该法考虑了塑性区弹性变形,并得到了扩孔压力p、塑性区半径R与扩孔半径a的关系。算例分析表明,该方法计算的扩孔压力与现场试验得出的结果较好地吻合,塑性区半径和扩孔压力均随扩孔半径的增加而增大,但增幅逐渐减小而趋于稳定值,剪胀角对塑性区半径和扩孔压力影响显著,随着剪胀角的增加,塑性区半径和扩孔压力明显增加。     

纯球坐标系内各项重力校正值计算方案和计算过程

在国内,首次阐述了"纯球坐标系内各项重力校正值的计算方案和计算过程".该计算方案有如下优点:①以观测点P为中心,以球面距离am=am-1+Δa·bm-1(m=2,3,...,M)为半径将计算区划分为M个环带,再以Δλ0为由P点出发射线的角度间隔将所有环带等分为N (整数)份的计算区划分方案是最严密拼接,因而校正值的计算精度相当高.②在地形复杂和相对高差大的情况下,通过减小Δa、b和Δλ0 数值,可进一步提高计算精度.③可以直接采用带有经、纬度坐标的高程数据,进行大面积测区的各项重力校正值计算,而不受6°带和标准图幅限制.     

Analysis of Error Caused by Replacing Spherical Shell with an Elastic Plate Model in Studying Bending Deformation of the Lithosphere

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Spectral and Multiscale Signal-to-Noise Thresholding of Spherical Vector Fields

The basic concepts of spectral and multiscale selective reconstruction of (geophysically relevant) vector fields on the sphere from error-affected data is outlined in detail. The reconstruction mechanism is formulated under the assumption that spectral as well as multiscale approximation is well-representable in terms of only a certain number of expansion coefficients at the various resolution levels. It is shown that spectral denoising by means of orthogonal expansions in terms of vector spherical harmonics reflects global a priori information of the noise (e.g., in form of a covariance tensor field), whereas multiscale signal-to-noise thresholding can be performed under locally dependent noise information within a multiresolution analysis in terms of spherical vector wavelets. An application of the multiscale formalism to Earth's magnetic field determination is presented.