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Summary. The symmetry relations between the reflection and transmission coefficients for plane elastic waves incident upon an arbitrary horizontally stratified medium are derived by a novel approach. Previous results, particularly for a single interface, are obtained as special cases of this treatment.
In addition, for perfectly elastic media, projection operators for travelling and evanescent waves are introduced and used to derive a number of new relationships between the reflection and transmission coefficients.  相似文献   

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Gaussian beams in anisotropic elastic media   总被引:2,自引:0,他引:2  
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Non-linear elastic behaviour of damaged rocks   总被引:1,自引:0,他引:1  
The pervasive damage of rocks by microcracks and voids strongly affects their macroscopic elastic properties. To evaluate the damage effects, we derive here the macroscopic stress-strain relations for a 3-D elastic solid with non-interacting cracks embedded inside a homogeneous matrix. The cracks considered are oriented either perpendicular to the maximum tension axis, or perpendicular to the maximum compression axis. In the first case they dilate during loading and in the second case they contract during loading. We derive a solution for the elastic energy of this rock following the self-consistent scheme of Budiansky & O'Connell (1976). The solution describes the stress-strain relations in terms of Λd and μd, which are the modified Lame constants, and an additional parameter Λ. The latter accounts for the non-linear behaviour of the solid and is related to crack density. The solution predicts a non-linear elastic rheology even for an infinitesimal strain of ɛ < 0.001, and abrupt change in the elastic moduli when the loading reverses from uniaxial compression to uniaxial tension.
We use the derived solution to analyse rock-mechanics experiments in which beams of Indiana limestone were deformed under four-point loading. This configuration provides simultaneously the apparent tensile and compressive moduli for small strains. The apparent moduli fit the effective elastic moduli calculated with the present damage model well, including the differences between tensile and compressive moduli.  相似文献   

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Freezing and thawing during the winter season change soil properties such as density. The density change in the particulate media influences soil stiffness. In addition, freezing of partially or fully saturated soils changes the soil matrix from a particulate media to a continuum. The goal of this study is to investigate the cyclic freezing and thawing effects on elastic waves. Sand-silt mixtures with 10% silt fraction in weight and 40% saturation are prepared. The sand-silt mixtures are placed in a nylon cell, onto which a pair of bender elements and a pair of piezoelectric disk elements are installed for the measurement of shear and compressional waves, respectively. The temperature of the mixtures decreases from 20°C to 10°C to freezing. The frozen sample is gradually thawed at room temperature (20°C). These freezing-thawing processes are repeated three times. The test result shows that the shear and compressional wave velocities significantly increase when the specimen is frozen. When the temperature is greater than 0°C, the elastic wave velocities are lower during thawing than during freezing due to soil structure change. This study demonstrates that soil structure change during the winter season may be effectively estimated from elastic waves.  相似文献   

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In 1976, the U.S. Congress enacted the Resource Conservation and Recovery Act (RCRA) to further address the problem of increasing industrial and municipal waste. The main objectives of RCRA were to responsibly manage hazardous and solid waste and to procure materials made from recovered wastes. To fulfill these objectives, four main programs of waste management were developed. These programs were defined under Subtitle C, the Hazardous Waste Program; Subtitle D, the Solid Waste Program; Subtitle I, the Underground Storage Tank Program; and Subtitle J, the Medical Waste Program. Subtitle D illustrates the solid waste dilemma occurring in the United States. Under this program, states are encouraged to develop and implement their own waste management plans. These plans include the promotion of recycling solid wastes and the closing and upgrading of all environmentally unsound dumps.Correspondence should be directed to Earle B. Amey, U.S. Geological Survey, National Center 983, Reston, Virginia 20192.  相似文献   

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Yet another elastic plane-wave, layer-matrix algorithm   总被引:1,自引:0,他引:1  
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