Double porosity modeling in elastic wave propagation for. As a result, the propagation velocities of waves in an elastic medium subjected to large. For inclusions with small aspect ratios almost flat cracks, all the models agree with. The elastic moduli for the homogeneous, anisotropic medium equivalent, in the long. This paper simulates wave propagation in an elastic medium containing elastic. Mie elastic scattering generated by cracks, journal of. Wave propagation in the presence of empty cracks in. Tadeu abstract the 3d wave propagation in solid media containing 2d cracks is modelled in the frequency domain by developing a traction boundary element method tbem. Love wave propagation in a nearsurface depthvarying distribution of cracks. Coupling the bemtbem and the mfs for the numerical simulation. The elastic inclusion, made of casting resin, is centered at 0.
The dissipation is assumed to be induced only by the multiple scattering between cracks, i. In the presence of aligned cracks as well as initial stress, an elastic medium behaves anisotropic to wave propagation. Dual simulations of fluid flow and seismic wave propagation in a. Crampin wave motion in anisotropic and cracked media equations 38. The reflected, transmitted and scattered waves are obtained by inversion of fourier transforms. It is well known that, in presence of multiple cracks, the coherent plane wave propagation in the damaged medium can be described by a complexvalued wavenumber k. In the case of a dimensionless empty crack, only a single line of boundary. Wave propagation in the presence of empty cracks in elastic. More recent work of propagation of elastic waves near cracks empty and fluidfilled, flat and very thin is given in mendes and tadeu 2006 and tadeu et al. The intention is to provide effective medium models for the calculation of elastic wave propagation with wavelengths greater than the dimensions of the cracks. At high frequencies, pressure release is so effective that it is as if the cracks were empty k 0. Highfrequency approximation of plane wave propagation in an. Love wave propagation in a nearsurface depthvarying. Detection and location of cracks using loss of reciprocity in ultrasonic waves propagation.
According to elastic wave theory, p wave velocity is a maximum, rayleigh wave velocity is a minimum, and s wave velocity is in between. The present study considers the propagation and attenua. The best way to look at medium wave frequencies as far as propagation issues, is to accept the fact that the majority of the time propagation is poor, especially past approximately 1050 miles, with occasional short lived good periods as far as 3100 miles. Wave propagation in the presence of empty cracks in an elastic medium 185 o xs, y s, z s. Seismic wave propagation in cracked porous media nasaads. Solutions for such problems involve a spatial fourier transform in thedirectioninwhichthegeometrydoesnotvary. The proposed formulation is developed in the frequency domain and handles the thinbody difficulty presented by the classical boundary element method bem. This article simulates the 3d wave propagation in a fluidfilled borehole, embedded in an elastic medium containing an empty crack, when excited by a sonic tool placed inside the borehole. Propagation and attenuation of elastic waves in a double. Crack effects on the propagation of elastic waves in structural elements 105 freund 8 made a detailed study of fracture dynamic problems, proposing solutions to different cases among which the case of cracks under stress waves is considered. From the physical point of view the question that arises is up to what degree a local perturbation in a medium modifies the scattered wavefield. Wave propagation in cracked elastic slabs and halfspace. Simulation of global seismic wave propagation through nonconforming curved finite.
The elastic wave equation derivation we can use our expression for the equation of motion and the relationship between stress and strain in an isotropic elastic medium to derive the elastic wave equation. An input routine rotates the elastic tensor into the desired configuration, leaving the main program inde pendent of direction of propagation and class of. Detection and location of cracks using loss of reciprocity. The scattering and diffraction of elastic waves by cracks or inclusions is an important engineering problem and has been investigated by numerous authors. Multiple scattering of elastic waves by subsurface. A nullthickness crack is embedded in the vicinity of this elastic inclusion. Scattering of elastic waves by a 2d crack using the. Until quite recently, the analysis of wave propagation in porous and. In the frequency domain, geometrical features of diffractors stamp a signature on reflected and diffracted wave fields. Wave propagation, elastic scattering, empty cracks, boundary element method, traction boundary element method, twoandahalfdimensional problem. Electromagnetic waves are waves which can travel through the vacuum of outer space. Propagation of a pulse in a layer with perfectly reflecting boundaries 39. Find materials for this course in the pages linked along the left.
This work solves the case of a crack whose geometry does not change along one direction 2d while the source exhibits a 3d nature. Mie elastic scattering generated by cracks the response in the time domain does not seem to provide much information. Assessment of reinforced concrete surface breaking crack. The changes in the sonic surface wave velocity of concrete under stress were. In real life, the crack may be either empty or it may be.
Transverse and longitudinal wave propagation in an elastic. Wave propagation in the presence of empty cracks in an elastic medium. This volume contains a timely collection of research papers on the latest developments in the everincreasing use of elastic waves in a variety of contexts. Wave propagation in an elastic medium in the presence of distributed cracks is of interest in areas of engineering, rock mechanics and geophysics. Zongxian zhang, in rock fracture and blasting, 2016. For a general medium the stress in the medium depends in a complicated way on the deformation of the medium. Coupling the bemtbem and the mfs for the numerical. Request pdf from the authors highfrequency approximation of plane wave propagation in an elastic medium with periodic distribution of cracks in this work. Various numerical methods have been proposed to simulate the propagation of waves in elastic and acoustic media, since analytical solutions are only known for simple and regular g.
Elastic wave propagation in a layered medium youtube. We compare theories that predict elastic anisotropy due to the presence of filled or empty ellipsoidal inclusions with one another and with a theory that predicts. Read wave propagation across the imperfectly bonded interface between cracked elastic solid and porous solid saturated with two immiscible viscous fluids, international journal of solids and structures on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. Wave velocities in a prestressed anisotropic elastic medium. Elastic wave propagation and attenuation in a double. An example of a type of wave that is not a mechanical wave, that stands in contradistinction to a mechanical wave, is an electromagnetic wave such as a light wave since electromagnetic waves travel in a vacuum and are not dependent on any known elastic medium for their propagation. The model of interconnected cracks is based on a medium. Elastic wave propagation and attenuation in a doubleporosity dualpermeability medium j. The volume will be of interest to those who do theoretical studies of elastic wave propagation and to those who apply elastic waves whether in seismology, nondestructive testing, the fabrication of devices or underwater acoustics, etc.
This paper simulates wave propagation in an elastic medium containing elastic, fluid. Our tti acoustic wave equation is a fourthorder equation in time and space. They have used the indirect boundary element method ibem. In anisotropic media energy travels with group velocity along a ray at an angle to the propagation direction.
During january conditions have remained steady and february should remain the same with the solar flux mainly at 82. A theoretical model can also be useful for estimating the extent of fracturing in the context of oil extraction, or for analysing the seismic behaviour of rock layers. The hosting medium has density r and allows shear wave and compressional wave velocities of b and a. This paper simulates wave propagation in an elastic medium containing elastic, fluid, rigid, and empty heterogeneities, which may be thin. Abstract this paper proposes the use of a traction boundary element method tbem to evaluate 3d wave propagation in unbounded elastic media containing cracks whose geometry does not change along one direction.
Lecture notes wave propagation mechanical engineering. The paper presents a study of rayleigh waves propagation due to mountain of arbitrary shape and of width a. Wang this paper was prepared for submittal to the ned11 cook memorial conference berkeley, ca october 16l 7,1998 october 12,199s this is a preprint of a. Flow of fluids in many hydrocarbon reservoirs aquifers is enhanced by the presence of cracks and fractures. Study of lovetype wave propagation in an isotropic tri layers elastic medium overlying a semiinfinite elastic medium structure. A timedependent perturbation of an elastic medium e. Effective anisotropic elastic constants for wave propagation through cracked solids. Elastic wavefield evaluation in discontinuous poroelastic. Propagation of rayleigh waves through the surface of an elastic. Wave propagation in the presence of empty cracks in an elastic medium article in computational mechanics 383. This equation has fewer parameters than an elastic wave equation in tti media and yields an accurate description of p wave traveltimes and spreadingrelated attenuation. Citeseerx citation query propagation of elastic waves in. Seismology and the earths deep interior the elastic wave equation the elastic wave equationthe elastic wave equation elastic waves in infinite homogeneous isotropic media numerical simulations for simple sources plane wave propagation in infinite media frequency, wavenumber, wavelength conditions at material discontinuities snell. Propagation in a dielectric medium consider the propagation of an electromagnetic wave through a uniform dielectric medium of dielectric constant.
Summary this paper evaluates the 3d wave propagation in an elastic slab containing cracks whose geometry does not change along the direction parallel to the forma tion surfaces. We demonstrate that the acoustic approximation allows the presence of shear waves in the solution. Wave propagation in the presence of empty cracks in an elastic medium web of science. There are reports on wave propagation in various types of media. Wave propagation wave speed rayleigh wave elastic medium rotation vector these keywords were added by machine and not by the authors. Explicit expressions, correct to lowest order in the ratio of the crack size to a wavelength, are derived here for the overall elastic parameters and the overall wave speeds and attenuation of elastic waves in cracked materials where the mean crack is circular, and the cracks. He considered that the medium which contains the semiin. Waves in a liquid layer lying on a homogeneous elastic halfspace 42. It is well known that, in presence of multiple cracks, the coherent plane wave propagation in the damaged medium can be.
Institute for earth sciences, department of geophysics, pb 80021, 3508 ta utrecht, the netherlands. Numerical computation of wave propagation in fractured. Propagation of inhomogeneous plane waves in dissipative. Furthermore, the simulation of wave propagation in the presence of very thin. Propagation of rayleigh waves through the surface of an elastic solid medium in the presence of a mountain rajesh kumar b.
The propagation of elastic waves in concrete medium could be more complicated compared to the 2d simulation. It uses a coupling formulation between the boundary element method bem the traction boundary element method tbem and the method of. Influence of the presence of lining materials in the acoustic behaviour of perforated. Its medium has a mass density of 1250 kgm 3, a dilatational wave speed of 2600 ms and a shear wave speed of 1100 ms. Effective medium theory predicts the overall wave speeds and attenuations of long.
Their presence causes reflections and scattering and makes the medium effectively anisotropic. These disturbances produce local changes in stress and strain. This work examines the antiplane strain elastodynamic problem for poroelastic geological media containing discontinuities in the form of cavities and cracks. Wave propagation in fractured rock in the course of seismic exploration is studied. Hence, the crustal rocks can, more closely, be modelled as anisotropic porous solids saturated with viscous fluid. To understand the propagation of elastic waves we need to describe kinematically the deformation of. Abstract this paper proposes the use of a traction boundary element method tbem to evaluate 3d wave propagation in unbounded elastic media containing cracks. Wave propagation around thin structures using the mfs. Wave propagation in the presence of empty cracks in elastic slabs tbem and mfs formulations article pdf available january 2007 with 21 reads how we measure reads. Problem formulation an unbounded homogeneous isotropic elastic medium, with no intrinsic attenuation, hosts a 2d. This paper proposes the use of a traction boundary element method tbem to evaluate 3d wave propagation in unbounded elastic media containing cracks whose geometry does not change along one direction. The same principle also has major advantages for numerical calculations.
The crack effect on wave propagation in the medium is taken into account by introducing cracks at the stage of grid generation with boundary conditions and conditions on the. Velocities of these waves are obtained from the roots of a cubic equation. Wave propagation in the presence of empty cracks in an elastic medium by p. Mechanical waves, unlike electromagnetic waves, require the presence of a material medium in order to transport their energy from one location to another. Coupling of the bem with the mfs for the numerical. General wave propagation and scattering problems for anisotropic media are discussed by stanke and kino, 18. Anisotropic parameters and pwave velocity for orthorhombic media. This process is experimental and the keywords may be updated as the learning algorithm improves.
The mechanical properties of materials with interconnected cracks. Propagation in anisotropic media linear anisotropic media d, e and k are in the same plane, orthogonal to b. Scattering of a compressional wave due to the presence of a rigid barrier in the surface of a. We compare theories that predict elastic anisotropy due to the presence of filled or empty ellipsoidal inclusions with one another and with a theory that predicts elastic anisotropy due to long compared to wavelength parallel joints or fractures. Crack effects on the propagation of elastic waves in. Hi glenn hauser, here is the february edition of the propagation report. Mfs to model the propagation of elastic waves around thin structures, like empty cracks or thin rigid screens, located in a homogeneous elastic medium. Feb 09, 2018 bdxc propagation report february 2011. Elastic anisotropy due to aligned cracks in porous rock. In the presence of aligned cracks, an elastic medium behaves anisotropic to wave propagation hudson 1980, 1981. In this paper, the traction boundary element method tbem and the method of fundamental solutions mfs, formulated in the frequency domain, are used to evaluate the 3d scattered wave field generated by 2d empty cracks embedded in an elastic slab and a halfspace. Reflection and refraction of plane waves at the boundary. Wave propagation in the presence of empty cracks in elastic slabs tbem and mfs formulations. Double porosity modeling in elastic wave propagation for reservoir characterization james g.
Seismic velocity in a medium containing oriented cracks transversely isotropic case. The equation of wave propagation in elastic solids are derived by using hookes law and newtons second law of motion. The mountain is present in the surface of an elastic solid medium. Elastic wavefield evaluation in discontinuous poroelastic media by bem.
Seismic wave propagation in cracked porous media eap british. In this paper, the wave propagation in a generalized thermo elastic plate embedded in an elastic medium winkler model is studied based on the lordschulman ls and greenlindsay gl generalized two dimensional theory of thermo elasticity. Wave propagation across the imperfectly bonded interface. Wave speeds and attenuation of elastic waves in material. Anisotropic parameters and p wave velocity for orthorhombic media.
Wave propagation in a prestressed anisotropic generalized. Nov 06, 20 informative video showcasing wave propagation in a slender rod. Fractures and cracks have a significant influence on the propagation of seismic waves. Seismic waves induce elastic deformation along the propagation path in the subsurface. Wave propagation in a generalized thermo elastic plate. Finite difference modeling of wave progpagation in.
Mathematical foundation of elastic wave propagation seg wiki. Elastic wave propagation in fractured media using the. Nondestructive investigation of stressinduced damage in concrete. Two displacement potential functions are introduced to uncouple the equations of motion. The deformation of the medium results from a displacement vector. Mie elastic scattering generated by cracks sciencedirect. We suggest that this is the reason why transonic rupture velocr,es are found in the numerical solutions of. The absence of point symmetry in pore distribution results in the anisotropy of general type with arbitrary symmetry. The idea that seismic waves can be used to identify the presence. It uses a coupling formulation between the boundary element method bemthe traction boundary element method tbem and the method of fundamental solutions mfs. The theoretical upper limit of crack speed in an elastic, isotropic, and homogeneous material is set at the rayleigh wave speed. The existence of three dilatational waves is explained through three scalar potentials satisfying wave equations. The empty crack may have any geometry and orientation and may even exhibit null thickness.
This study solves the mathematical model for the propagation of harmonic plane waves in a dissipative double porosity solid saturated by a viscous fluid. Pdf wave propagation in the presence of empty cracks in. These cracks could be detected by their effects on propagation of compressional and shear waves through the reservoir. Introduction various numerical methods have been proposed to simulate the propagation of waves in elastic and acoustic media, since analytical solutions are only known for simple and. The expression for the effective elastic constants of cracked material c. The anisotropic behaviour of crustal rocks due to the presence of cracks and fractures may beexplained through the anisotropic elastic constants crampin 1981. Jan 01, 2009 read mie elastic scattering generated by cracks, journal of applied geophysics on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. The gridcharacteristic method on hexahedral meshes is extended to the case of an elastic medium with empty and fluidsaturated cracks. The proposed formulation makes it possible to model thin bodies for. Study of lovetype wave propagation in an isotropic tri.
Wave propagation in the presence of empty cracks in an elastic medium 185 o x s, y s, z s. We shall begin with the stressstrain relation for elastic solids. Jan, 2015 elastic wave propagation in a layered medium ryan. Wave propagation in the presence of empty cracks in an. Schoenberg, schlumbergerdoll research, ridgefield, ct 068774108, usa. Propagation of elastic waves in layered media by finite difference methods 1968. We present a numerical approach to simulation of seismic waves in fractured media that does not require direct modelling of the fracture itself, but uses the concept of linear slip interfaces developed by. Interferometric modelling of wave propagation in inhomogeneous elastic media. The existence of connections between cracks, or of an equant. For example, the presence of microcracks generally results in a reduction in the.
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