Showing papers on "Discontinuity (geotechnical engineering) published in 1990"

Transmission of seismic waves across single natural fractures

Abstract: Fractures and other nonwelded contacts are important mechanical and hydrological features of rock masses. Their effects on seismic wave propagation can be modeled as a boundary condition in the seismic wave equation. Seismic stress is continuous across such a boundary, but seismic particle displacement and seismic particle velocity are not. The complete solutions for seismic wave reflection, conversion, and transmission across a displacement and velocity discontinuity between two half-spaces with different densities and elastic properties are derived for all angles of the incident wave. The ratio between the seismic stress across this boundary and the seismic particle displacement and velocity are described by a specific stiffness and a specific viscosity, respectively. A displacement discontinuity results in frequency-dependent reflection and transmission coefficients and a frequency-dependent group time delay. The velocity discontinuity results in frequency-independent coefficients and zero delay. Results of laboratory experiments on compressional and shear wave transmission across three different natural fractures in a quartz monzonite are described. Measurements were made at different effective stresses under dry and saturated conditions at room temperature. It is shown that the effect of these fractures on the spectral amplitudes for compressional and shear pulses transmitted across these fractures are described well by a displacement discontinuity for compressional pulses under dry and saturated conditions and by a combined displacement and velocity discontinuity for shear wave pulses under dry and saturated conditions. Values of specific stiffness and specific viscosity vary between fractures and increase with increasing effective stress, as does the static specific stiffness of these fractures. Changes in the spectral amplitudes of transmitted pulses are also analyzed in terms of attenuation using the seismic quality factor Q, which is found to be a function of frequency.

Anisotropy in seismic velocities and amplitudes from multiple parallel fractures

Abstract: Many rock structures include multiple, near-parallel, planar discontinuities such as bedding planes or joints. The effects of these nonwelded interfaces on seismic wave propagation are often analyzed using effective moduli, in terms of which seismic wave propagation is independent of frequency and without loss, unless the moduli include imaginary terms. An alternative approach is to treat these interfaces as a boundary condition in the seismic wave equation, across which seismic stress is continuous, but seismic particle displacements are discontinuous. The ratio of the stress to displacement is called the specific stiffness of the interface and characterizes the elastic properties of a fracture. For a completely elastic system this results in frequency-dependent reflection and transmission coefficients for each interface as well as a frequency-dependent group time delay. Using multiple, parallel displacement discontinuities and ignoring converted and reflected waves, expressions derived for transmitted wave amplitudes and group velocities show that these depend on frequency, angle of incidence, and polarization in the case of shear waves. Measurements on a laminated steel block show that shear pulses propagating parallel to the laminations and polarized parallel and perpendicular to the plane of the laminations both travel at the velocity for solid steel, although the spectra of these pulses differ considerably. However, the energy of the pulse polarized perpendicular to the laminations may propagate as an interface wave between each pair of laminations. Predictions of the displacement discontinuity model have features quite distinct from many crustal observations to date. We suggest that we are able to model dense populations of coplanar cracks that cannot be treated by effective moduli methods which require a dilute concentration of cracks.

Seismic imaging of upper-mantle structure with new evidence for a 520-km discontinuity

Abstract: Stacked images of long-period seismic data reveal many phases, some not previously observed, which are caused by reflections and conversions at discontinuities in the Earth's upper mantle. These images support the existence of discontinuities at 410, 520 and 660km depth, but no evidence is found for a significant interface at 220 km.

The mechanical behavior of silicon during small-scale indentation

Abstract: The mechanical behavior of crystalline silicon during small-scale indentation has been studied using a Nanoindenter Tests were performed on bothp-type andn-type materials in the (100), (110), and (111) orientations at peak loads ranging from 05 to 120 mN The indentation load-displacement curves exhibit two features which appear to be unique to silicon First, at large peak loads, a sharp discontinuity in displacement is observed as the indenter is unloaded Second, at small peak loads, a large, non-degenerative hysteresis is exhibited Possible mechanistic origins for the discontinuity and hysteresis are discussed

S‐P conversion from the transition zone beneath Tonga and the nature of the 670 km discontinuity

Abstract: SUMMARY Using more than 300 recordings of deep Tonga earthquakes from the Warramunga Seismic Array (central Australia), we have searched for short-period S-P conversions from the 670 km discontinuity arriving in the P-wave codas. The array seismograms were stacked and plotted in sections to optimize observation of S670P yielding the following results: For the northern part of Tonga (17.3°–18.4°S), S670P-phases are observed with apparent conversion depths between about 660 and 680 km. For the central part (20.2°–22.3°S), S670P is not clearly observed. For the southern part (23.1°–25.7°S), S670P is observed for conversion depths between about 660 and 700 km. Intermittent occurrence of S-P conversion may result from different characteristic source radiation patterns among the three sections. Overall uncertainties in conversion depths (resulting from unmodelled lateral velocity variations and hypocentral location errors) are perhaps a few tens of kilometres. The S-P rays must travel either within or very close to the subducted slab because of the source/receiver/slab-dip geometry, so we conclude that large (>50 km) deformations of the 670 km discontinuity do not occur beneath Tonga. Our observations appear to be inconsistent with a chemical discontinuity at 670 km, but are easily explained if the 670 km discontinuity is a strongly pressure-dependent and, perhaps, moderately endothermic phase change in both the slab and surrounding mantle.

A hybridized displacement discontinuity and indirect boundary element method to model fracture propagation

Abstract: In mechanical modelling of fracture propagation, complications arise from the stress concentrations at the fracture tips and nonlinear responses caused by opening/closing of fractures, by nonlinear constitutive relations of fracture surfaces sliding on each other, and by fracture propagation. The hybridized Displacement Discontinuity and Indirect Boundary Element Method described in this paper avoids problems associated with other numerical methods when analyzing fracture propagation. The method, which includes analytical influence functions and thus makes numerical integration unnecessary, is described in the first part of this paper. In the second part a number of examples are given in which a variety of fracture propagation problems in two dimensions are modelled with the hybridized method. These examples include classical problems in which tension is applied to cracked plates but also others where shearing is applied. Comparisons with solutions obtained by other authors are shown to be satisfactory.

Effects of single fractures on seismic wave propagation

Abstract: Detection and characterization of fractures, joints and faults remains an important problem in mining and geotechnical engineering, as well as in petroleum reservoir engineering. A theoretical model has been developed which predicts the amplitude and group time delay of the transmitted, reflected, and converted waves resulting from a plane wave incident upon a single fracture. It is assumed that seismic stresses are continuous across the interface. Seismic particle displacements, however, are assumed to be discontinuous. For completely dry conditions, the magnitude of the displacement discontinuity is given by the ratio of the seismic stress to the stiffness, {kappa}, of the fracture. If a fluid is present in the fracture, we postulate that, in addition to the displacement discontinuity, a velocity discontinuity exists which is equal to the ratio of the seismic stress to specific viscosity, {eta}. The wave equation has been solved for two sets of boundary conditions, with each set incorporating both specific stiffness and specific viscosity. These boundary conditions have been designated as Kelvin and Maxwell models. 12 refs., 5 figs.

Tangential discontinuities and the optical analogy for stationary fields IV. High speed fluid sheets

Abstract: It was shown in the previous paper that a sufficiently strong pressure maximum applied to an equilibrium flux surface, by the fields on either side of the surface, produces a gap in the flux surface. The fields on either side make contact through the gap to produce a surface of tangential discontinuity (current sheet). It is shown in the present paper that there is a high speed sheet of fluid and field sliding over the surface of discontinuity when the applied pressure moves slowly across the flux surface. Conditions in the active X-ray corona of the sun suggest that such sheets are generally present, with velocities of the order of 102 km/sec, but with thicknesses too small to be observed. More substantial high speed sheets of fluid may occur in solar flares.

Analytical calculation of the impedance of a discontinuity

Abstract: In this paper we describe a powerful analytical approach to the study of the electromagnetic interaction between a bunch of particles and the discontinuities of the vacuum chamber. The method applied to a single discontinuity leads to an exact analytical solution allowing a deeper understanding of the radiation process via the investigation of the impedance behavior at any frequency and the role of the relativistic factor y.

Understanding the process of jointing in brittle rock masses

Abstract: Joints are the most ubiquitous structural discontinuity in the earth’s crust, occurring in a wide variety of rock types and tectonic environments, and they represent the most common result of brittle fracture of rock under natural conditions (Pollard and Aydin, 1989). As structural discontinuities, joints may significantly affect the stiffness, strength, and fluid transport properties of rock, and these effects are dependent on joint geometry. Thus, knowledge of the detailed geometric characteristics of joints is crucial for many engineering applications. At the present time such information is best obtained through direct geologic mapping, although borehole and geophysical techniques are making rapid progress toward the levels of resolution required to characterize joints in the subsurface.

A simple method of estimating rock mass porosity and permeability

Abstract: A simple method of estimating fracture porosity and permeability based on empirical relations between fracture aperture andJRC andJCS can be developed. This shows very close correlation with existing data, using simple discontinuity models. There is quite a good correlation between fracture porosity and permeability and depth for larger initial apertures.

A fracture mechanical treatment of free edge stress singularities applied to a brazed ceramic)metal compound

Abstract: The theoretical fracture mechanical treatment of craek problems in regular stress fields is extended to account for singular stresses as occur in bi-material systems whenever a discontinuity in material properties and geometry exists. The singular stress fields are derived for arbitrary material combination and geometry and the global stress state as occurs in a real compound is obtained by Finite Element (FE) calculations. Then especially the mode I stress intensity factors are calculated for semi-elliptical surface cracks in the ceramic component of a brazed ceramic/metal joint. Critical crack sizes are determined for failure analysis of the compound.

Subcapsular zones of discontinuity in the human lens.

Abstract: Zones of discontinuity parallel to the lens surface can be seen in the normal lens on slitlamp examination. These zones have been suggested to be surfaces at which the refractive index changes from on

Analysis of circular and rectangular apertures in a circular waveguide

Abstract: An analysis is carried out to determine the discontinuity susceptibility of a circular or rectangular aperture in the transverse plane of a circular waveguide. A closed-form solution that shows good agreement with experimental results is derived. The results should have many applications in the design of circular waveguide components and cylindrical cavity-backed phased arrays. >

Device for making cast-in-situ piles using a continuous hollow auger

Abstract: A device for forming cast-in-situ piles in civil engineering work includes an auger which consists of a conventional lower part and an upper part comprising a hollow inner element and a removable outer element in the form of an auger having a longitudinal discontinuity which enables it to be fitted over the hollow inner element The hollow inner element may extend, fixedly, as an elongation of the lower part of the auger or be mounted telescopically in the latter

The Revival of Macrosociology: Methodological Issues of Discontinuity in Comparative- Historical Theory

Abstract: Three forms of discontinuity in social structure produce linked analogous problems about aggregates or wholes: discontinuity in units, discontinuity in time, and discontinuity in variables. Problems of macrotheory, of comparative-historical theory, and of levels of theory are analytically equivalent. Discontinuity in processes between different units produces macro-micro problems when processes involving individuals are different from processes involving larger aggregates. Discontinuity in time refers to the fact that in most dynamic processes, time does not appear homogeneous — if a process occurs in a century, that is not necessarily any reason to suppose that 1/100th of the process occurs in a year. Discontinuity in variables refers to the fact that all variables cannot operate coherently in the same explanatory system. These three discontinuities each produce problems of generalization and scope — problems getting from particular observed relationships to the underlying conditions and determinants of those relationships. For example, temporal discontinuity leads to problems of periodization and of stages. These problems are most visible in comparative-historical theory and they can only be resolved by comparative-historical data.

Structure of the contact discontinuity of nonstationary Mach reflections

Abstract: The structure of the contact discontinuity at the triple point of a pseudosteady Mach reflection was reconsidered, as it is known that in some cases the classical «three shock theory» fails to accurately predict the angles between the four discontinuities of the triple point. Based on experimental records, the slipstream was replaced by an angular mixing zone

Diffraction by a discontinuity in curvature including the effect of the creeping wave

Abstract: The existing geometrical theory of diffraction (GTD) solution for the diffraction by a discontinuity in curvature on a perfectly conducting cylindrical surface is uniformly extended in the region where the surface diffraction of the creeping wave launched by the discontinuity is involved. >

Surface Segmentation and Description

Abstract: As discussed previously, we have decided to use surface descriptions segmented at physical boundaries. In particular, we propose that the following surface points and lines are critical for a natural segmentation of the surface: Jump boundaries—where the surface undergoes a discontinuity; Creases—which corresponds to a surface orientation discontinuity.

Constraints on Moving Strong Discontinuity Surfaces in Dynamic Plane-Stress or Plane-Strain Deformations of Stable Elastic-Ideally Plastic Materials

Abstract: For dynamic deformations of compressible elastic-ideally plastic materials in the practically important cases of plane stress and plane strain, we investigate the possible existence of propagating surfaces of strong discontinuity within a small-displacement-gradient formulation

Effect of magnetic field on the sound velocity discontinuity near Tc in high Tc superconductors

Abstract: We have measured the velocity of sound in polycrystalline samples of Cu-oxide superconductors YBa2Cu3O7−δ (Lax−xSrx)2CuO4 (x = 0075) and (Nd1−xCex)2CuO4 (x = 0075), and observed a discontinuity near Tc in the sound velocity versus temperature curves except in (Nd1−xCex)2CuO4 The observed magnitude of the discontinuity was comparable to that expected from a thermodynamic estimation By applying a magnetic field the discontinuity became broad and its magnitude decreased, while the shift of the temperature position was much smaller than that of Tc(H) estimated from Hc2(T) versus T curves which were derived from the midpoint of the transition in the resistivity curves This behavior suggests that the “true” coherence length ξ(0) is much shorter than that derived from - d H c2 d T The effects of fluctuation and a large anisotropy of ξ(0) on the behaviour of the sound velocity discontinuity under magnetic fields are discussed