On the disturbance due to a spherical distortional pulse in an elastic medium

Summary Theoretical expressions are derived for the displacement, velocity and stress in the time domain induced by an axially symmetric shearing stress applied at the inner surface of a spherical cavity in a hornogeneous, isotropic, elastic medium of infinite extent. Theoretical seismograms are computed for a step source and for three sources with exponential decay in time. A satisfactory time-dependence of the source can be obtained by combining the step source with one or more exponentially decaying sources.     

Generation of SH-type waves due to shearing stress discontinuity in a sandy layer overlying an isotropic and inhomogeneous elastic half-space

The generation of SH-type waves due to sudden application of a stress discontinuity which moves after creation at the sandy layer of finite thickness overlying an isotropic and inhomogeneous elastic half-space is considered. The displacements are obtained in exact form by the method due to Cagniard modified by De Hoop. The numerical calculations are obtained. Two cases of shearing stress discontinuities are considered for different sandiness parameters. The graphs are drawn to show the effect of sandiness in the displacement components.     

断层错动引起的上覆土体破裂演化规律研究

断层引起的地面永久大变形是工程特别是生命线工程地震破坏的重要原因之一, 而研究断层错动下上覆土体变形和破裂的发展演化规律, 则是预测地面永久变形状态和分析断层危害性的基础． 本文采用有限元方法对垂直断层错动引起的上覆土体破裂演化规律进行了研究, 建立了垂直断层作用下上覆土体模拟的有限元模型, 对断层错动作用下上覆土体的破裂发展过程进行了模拟分析, 并分析了加载速率、 土体特性及断层倾角等参数对上覆土体的破裂演化发展过程的影响． 结果表明: ① 断层倾角越陡, 地表出现破裂时需要增加的垂直位移越大; ② 由于惯性力的影响, 断层加载速率对地表破裂所需施加位移和土层破裂角产生一定的影响; ③ 断层类型对土层地表破裂角与膨胀角、 摩擦角之间的关系有很大影响． 该分析结果可为新建工程的抗震设计和已建工程结构的抗震加固等工作提供依据．     

Poiseuille flow in a fluid overlying a highly porous material

This paper investigates the instability of Poiseuille flow in a fluid overlying a highly porous material. A two layer approach is adopted, where the Darcy–Brinkman equation is employed to describe the fluid flow in the porous medium, with a tangential stress jump boundary condition at the porous/fluid interface. The basic velocity profiles are continuous due to the interfacial boundary conditions. It is shown that for certain parameter ranges the neutral curves are no longer bimodal, such that the two modes of instability corresponding to the fluid and porous layers, respectively, are not distinct.     

Response analysis of buried pipelines crossing fault due to overlying soil rupture

A 3-D soil-pipe nonlinear finite element model with contact element is suggested and the influences of the rupture mode, thickness and rigidity of overlying soil on the response of buried pipeline are analyzed. The numerical results show that the soil rupture mode determines the location of the large deformation or failure of the pipeline, and the plastic deformation of the pipeline occurs at the zone where the plastic deformation or rupture of the overlying soil appears. When the fault dip angle on bedrock...     

Vibrations of the elastic half-space due to vertical surface loads

The displacements of the surface of the homogeneous elastic half-space subjected to a vertical concentrated load acting at the surface are calculated. The solution is shown to approach Lamb's simple formula for the far-field. The solution for the concentrated load can be used to calculate displacements due to distributed loads with high accuracy and economically. The results are applied to define the regions ‘near-field’ and ‘far-field’. Some near-field phenomena are described.     

Ground motion amplification due to elastic inclusions in a half-space

Scattering of plane harmonic SH, P, SV and Rayleigh waves by several inclusions of arbitrary shape, completely embedded into an elastic half-space, is considered. Perfect bonding between the half-space and the inclusions is assumed. The problem is investigated for linear, isotropic and homogeneous elastic materials. The displacement field is evaluated throughout the elastic medium so that the continuity conditions between the half-space and the inclusions are satisfied in mean-square sense. Numerical results of the surface displacement field are evaluated for single and two elliptic inclusions. The results show the following: (a) presence of a subsurface inhomogeneity may lead to large amplifications of the surface ground motion; (2) different surface displacement patterns emerge for different incident waves; (3) the presence of an additional inclusion may change significantly the surface displacement response of a single inclusion; (4) the surface motion extremes strongly depend upon (i) angle of incidence; (ii) frequency of incident field; (iii) embedment depth of the inclusions; (iv) separation distance between the inclusions; (v) material properties of the half-space and the inclusions; and (vi) location of observation point on the surface of the half-space.     

Displacement due to impulsive loadings on the surface of elastic half-space

Summary The displacement due to vertical impulsive load has been obtained by function theoretic method. Graphs have been drawn for horizontal as well as for vertical displacement. It has been shown thatPekeris's [12]²) method is easier to apply than that ofCagniard [2] for the same purpose.     

Disturbances due to time-dependent body forces in a non-isotropic elastic medium

Summary In this paper, the disturbances produced due to time-dependent body forces in an anisotropic elastic medium resting on a semi-infinite non-isotropic layer have been discussed.     

SH waves in a semi-infinite elastic space due to torsional disturbance

Summary The paper concerns the finding of displacement in a semi-infinite elastic space due to torsional disturbance produced by an expanding source. A formal solution has been derived by the integral transform technique and the modified Cagniard method in two different cases, viz. velocity of expansion is less than or greater than the velocity of shear waves in the medium.     

On two explosions in Danish waters in the autumn of 1946

Summary In ammunition sunk into the sea off the Danish coasts two large explosions occurred. Records of the resulting shocks were obtained at K?benhavn, Lund and G?ttingen. These are discussed and compared with those of some mine-explosions and of the earthquake of Oct. 31. 1930, 23h. Some macroseismic evidence is given and the methods available for the evaluation of the energy of the shocks are discussed.     

On the effect of discontinuity in boundary gradient or in material properties on propagation of elastic waves

Summary The effect of surface irregularities in the form of boundary discontinuous gradients has been studied. It has been shown that certain waves will be attenuated due to passage through such irregularities in internal structure.     

On stresses and displacements due to a moving line load over the plane boundary of a heterogeneous elastic half-space

Summary The problem of concentrated line load moving with supersonic speed along the boundary of an isotropic heterogeneous medium has been solved as a plane strain problem. The stresses and displacements in the heterogeneous case considered are found to decay exponentially with distance.     

The effect of clay distribution on the elastic properties of sandstones

The shape and location of clay within sandstones have a large impact on the P‐wave and S‐wave velocities of the rock. They also have a large effect on reservoir properties and the interpretation of those properties from seismic data and well logs. Numerical models of different distributions of clay – structural, laminar and dispersed clay – can lead to an understanding of these effects. Clay which is located between quartz grains, structural clay, will reduce the P‐wave and S‐wave velocities of the rock. If the clay particles become aligned or form layers, the velocities perpendicular to the alignment will be reduced further. S‐wave velocities decrease more rapidly than P‐wave velocities with increasing clay content, and therefore Poisson's ratios will increase as the velocities decrease. These effects are more pronounced for compacted sandstones. Small amounts of clay that are located in the pore space will have little effect on the P‐wave velocity due to the competing influence of the density effect and pore‐fluid stiffening. The S‐wave velocity will decrease due to the density effect and thus the Poisson's ratio will increase. When there is sufficient clay to bridge the gaps between the quartz grains, P‐wave and S‐wave velocities rise rapidly and the Poisson's ratios decrease. These effects are more pronounced for under‐compacted sandstones. These general results are only slightly modified when the intrinsic anisotropy of the clay material is taken into account. Numerical models indicate that there is a strong, nearly linear relationship between P‐wave and S‐wave velocity which is almost independent of clay distribution. S‐wave velocities can be predicted reasonably accurately from P‐wave velocities based on empirical relationships. However, this does not provide any connection between the elastic and petrophysical properties of the rocks. Numerical modelling offers this connection but requires the inclusion of clay distribution and anisotropy to provide a model that is consistent with both the elastic and petrophysical properties. If clay distribution is ignored, predicting porosities from P‐wave or S‐wave data, for example, can result in large errors. Estimation of the clay distribution from P‐wave and S‐wave velocities requires good estimates of the porosity and clay volume and verification from petrographic analyses of core or cuttings. For a real data example, numerical models of the elastic properties suggest the predominance of dispersed clay in a fluvial sand from matching P‐wave and S‐wave velocity well log data using log‐based estimates of the clay volume and porosity. This is consistent with an interpretation of other log data.     

Generation of rayleigh waves due to stress-discontinuity in a semi-infinite elastic medium

Summary In this paper, the displacements produced at the surface of a semi-infinite, clastic medium by the sudden creation and subsequent motion of discontinuities in the normal and tangential stresses have been obtained in the form of definite integrals byCagniard's method. Numerical values are given in a particular case.Published with the kind permission of the Director General, Geological Survey of India, Calcutta.     

The anomalous surface wave in uniaxially-stressed elastic material

Summary For a semi-infinite incompressible elastic medium which is subjected to a large primary extension (or compression) in a directionOX ₁ parallel to the free surfaceOX ₁ X ₂, the dispersion equation is derived for surface waves of small amplitude. It is shown in particular that in some cases for directions of propagation close toOX ₂, the surface waves exhibit novel features in that the displacement at the surface is almost parallel toOX ₁, that is, nearly transverse to the direction of wave-propagation.     

A note on permeability changes in geologic material due to stress

Summary Stress produces framatic changes in fluid permeability of geologic materials. An increase of nearly threefold occurred in granite at high stress, an increase of 20 percent in sandstone, and a hundredfold decrease in compacted sand. Permeability of sand and sandstone did not follow the effective stress law. Flow along joints was very sensitive to effected stress changes, a fourfold change being caused by as little as 1.0 MPa.     

Effect of couple-stresses in a semi-infinite elastic medium due to impulsive twist over the surface

Summary Displacement due to impulsive twist in a semi-infinite elastic medium is calculated in the light of Cosserats theory of couple stresses [1, 2]. Numerical results are obtained for a particular