关于基质吸力及几个相关问题的一些思考

基质吸力是非饱和土力学中一个非常重要的概念,也是初学者学习中的一个难点,要把它理解透彻并不容易。本文从表面物理化学的基本公式,亦即Young-Laplace公式和Kelvin公式出发,对基质吸力概念和与基质吸力有关的若干问题进行了一些思考和初步探讨。研究表明,基质吸力的大小受土的孔径大小的影响;在环境条件下,基质吸力的大小受外界平衡相对深度的影响;土的孔径分布决定了土水特征曲线的特征。     

防护层中孔穴对轴向应力波的绕射屏蔽效应研究

随着新型武器的发展,在当今的人防工程中对防护层的功效要求越来越高。以工程抗爆设计为背景,主要研究了如何在防护层中利用空穴来绕射和屏蔽应力波的问题。经过大量计算发现,空穴的几何形状及尺寸效应等对其后方的应力波削减有显著影响。针对常见的方形和圆形空穴,提出了孔穴后方、位于其对称轴上点的轴向应力σy峰值削减因子DF的2个近似拟合式子。可分别用来估算在一定条件下孔穴后方特定位置处的削减因子,或用来计算所需空穴的尺寸,甚至可以推算为了达到某一削减效果而必须满足的最小安全距离等。其结果为在抗爆防震工程中智能的防护层的设计提供了一定理论依据。     

轻质土密度、强度与材料组成的关系研究

论述了轻质土试样的制备方法,对轻质土密度、无侧限抗压强度与材料组成之间的关系进行的研究表明：密度主要受到EPS颗粒添加量的影响;无侧限抗压强度主要受到水泥添加量、EPS颗粒添加量的影响。在此基础上给出了适合于工程应用的轻质土的配方公式。     

Ellipsoidal corrections to order e 2 of geopotential coefficients and Stokes’ formula

Assuming that the gravity anomaly and disturbing potential are given on a reference ellipsoid, the result of Sjöberg (1988, Bull Geod 62:93–101) is applied to derive the potential coefficients on the bounding sphere of the ellipsoid to order e ² (i.e. the square of the eccentricity of the ellipsoid). By adding the potential coefficients and continuing the potential downward to the reference ellipsoid, the spherical Stokes formula and its ellipsoidal correction are obtained. The correction is presented in terms of an integral over the unit sphere with the spherical approximation of geoidal height as the argument and only three well-known kernel functions, namely those of Stokes, Vening-Meinesz and the inverse Stokes, lending the correction to practical computations. Finally, the ellipsoidal correction is presented also in terms of spherical harmonic functions. The frequently applied and sometimes questioned approximation of the constant m, a convenient abbreviation in normal gravity field representations, by e ²/2, as introduced by Moritz, is also discussed. It is concluded that this approximation does not significantly affect the ellipsoidal corrections to potential coefficients and Stokes formula. However, whether this standard approach to correct the gravity anomaly agrees with the pure ellipsoidal solution to Stokes formula is still an open question.     

A computational scheme to model the geoid by the modified Stokes formula without gravity reductions

In a modern application of Stokes formula for geoid determination, regional terrestrial gravity is combined with long-wavelength gravity information supplied by an Earth gravity model. Usually, several corrections must be added to gravity to be consistent with Stokes formula. In contrast, here all such corrections are applied directly to the approximate geoid height determined from the surface gravity anomalies. In this way, a more efficient workload is obtained. As an example, in applications of the direct and first and second indirect topographic effects significant long-wavelength contributions must be considered, all of which are time consuming to compute. By adding all three effects to produce a combined geoid effect, these long-wavelength features largely cancel. The computational scheme, including two least squares modifications of Stokes formula, is outlined, and the specific advantages of this technique, compared to traditional gravity reduction prior to Stokes integration, are summarised in the conclusions and final remarks. AcknowledgementsThis paper was written whilst the author was a visiting scientist at Curtin University of Technology, Perth, Australia. The hospitality and fruitful discussions with Professor W. Featherstone and his colleagues are gratefully acknowledged.     

Analytical solution of boundary integral equations for 2-D steady linear wave problems

Based on the Fourier transform, the analytical solution of boundary integral equations formulated for the complex velocity of a 2-D steady linear surface flow is derived. It has been found that before the radiation condition is imposed, free waves appear both far upstream and downstream. In order to cancel the free waves in far upstream regions, the eigenso-lution of a specific eigenvalue, which satisfies the homogeneous boundary integral equation, is found and superposed to the analytical solution. An example, a submerged vortex, is used to demonstrate the derived analytical solution. Furthermore, an analytical approach to imposing the radiation condition in the numerical solution of boundary integral equations for 2-D steady linear wave problems is proposed.     

The analytical continuation bias in geoid determination using potential coefficients and terrestrial gravity data

One important application of an Earth Gravity Model (EGM) is to determine the geoid. Since an EGM is represented by an external-type series of spherical harmonics, a biased geoid model is obtained when the EGM is applied inside the masses in continental regions. In order to convert the downward-continued height anomaly to the corresponding geoid undulation, a correction has to be applied for the analytical continuation bias of the geoid height. This technique is here called the geoid bias method. A correction for the geoid bias can also be utilised when an EGM is combined with terrestrial gravity data, using the combined approach to topographic corrections. The geoid bias can be computed either by a strict integral formula, or by means of one or more terms in a binomial expansion. The accuracy of the lowest binomial terms is studied numerically. It is concluded that the first term (of power H²) can be used with high accuracy up to degree 360 everywhere on Earth. If very high mountains are disregarded, then the use of the H² term can be extended up to maximum degrees as high as 1800. It is also shown that the geoid bias method is practically equal to the technique applied by Rapp, which utilises the quasigeoid-to-geoid separation. Another objective is to carefully consider how the combined approach to topographic corrections should be interpreted. This includes investigations of how the above-mentioned H² term should be computed, as well as how it can be improved by a correction for the residual geoid bias. It is concluded that the computation of the combined topographic effect is efficient in the case that the residual geoid bias can be neglected, since the computation of the latter is very time consuming. It is nevertheless important to be able to compute the residual bias for individual stations. For reasonable maximum degrees, this can be used to check the quality of the H² approximation in different situations.Acknowledgement The author would like to thank Prof. L.E. Sjöberg for several ideas and for reading two draft versions of the paper. His support and constructive remarks have improved its quality considerably. The valuable suggestions from three unknown reviewers are also appreciated.     

A new strategy for the atmospheric gravity effect in gravimetric geoid determination

Prior to Stokes integration, the gravitational effect of atmospheric masses must be removed from the gravity anomaly g. One theory for the atmospheric gravity effect on the geoid is the well-known International Association of Geodesy approach in connection with Stokes integral formula. Another strategy is the use of a spherical harmonic representation of the topography, i.e. the use of a global topography computed from a set of spherical harmonics. The latter strategy is improved to account for local information. A new formula is derived by combining the local contribution of the atmospheric effect computed from a detailed digital terrain model and the global contribution computed from a spherical harmonic model of the topography. The new formula is tested over Iran and the results are compared with corresponding results from the old formula which only uses the global information. The results show significant differences. The differences between the two formulas reach 17 cm in a test area in Iran.     

Deduction and application of generalized Euler formula in topological relation of geographic information system (GIS)

Topological relation is one important characteris-tics of spatial data, and reflects the structural relation-ships among geographical objects, and is regarded as the core of spatial data processing[1,2]. Topological transformation has been widely used in diverse spatial studies, and in fact, the processing of geographical data is a kind of topological transformations[3]. There-fore, it is of significance to study the mathematical theory of generating and checking topological rela-tions in GIS…     

平原储灰库区地下潜水位影响评价模式探讨

以山东华能德州发电厂现役储灰库“灰水”对潜水位的影响和水量均衡原理 ,确定其对库区潜水位影响范围 ;对拟建储灰库区根据水文地质条件 ,采用非稳定流基本方程对库区潜水水位进行预测 ,得出平原储灰库区地下潜水位最大影响范围为 75 0m。