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1.
Closed-form expressions for the displacements and stresses at any point of either of two elastic half-spaces in welded contact caused by a dip-slip line source obtained earlier are integrated analytically to derive the elastic residual field due to a long dip-slip fault of finite width. The results are valid for an arbitrary dip of the fault. The variation of the displacement field with the distance from the fault as well as with the distance from the interface is studied numerically. It is found that the displacement field is heavily dependent on the dip angle. Contour maps showing the residual elastic field in the two half-spaces caused by a vertical dip-slip fault located in one of the half-spaces are also obtained. 相似文献
2.
The solution of static elastic deformation of a homogeneous, orthotropic elastic uniform half-space with rigid boundary due to a non-uniform slip along a vertical strike-slip fault of infinite length and finite width has been studied. The results obtained here are the generalisation of the results for an isotropic medium having rigid boundary in the sense that medium of the present work is orthotropic with rigid boundary which is more realistic than isotropic and the results for an isotropic case can be derived from our results. The variations of displacement with distance from the fault due to various slip profiles have been studied to examine the effect of anisotropy on the deformation. Numerically it has been found that for parabolic slip profile, the displacement in magnitude for isotropic elastic medium is greater than that for an orthotropic elastic half-space, but, in case of linear slip, the displacements in magnitude for an orthotropic medium is greater than that for the isotropic medium. 相似文献
3.
Closed form analytic expressions for displacement and stresses at any point of either of the two homogeneous, isotropic, perfectly
elastic half-spaces in welded contact due to very long strike-slip dislocations are obtained. Both cases of vertical and horizontal
strike-slip dislocations are discussed in detail. Variation of the displacement with horizontal distance from the fault and
with vertical distance from the interface for a vertical strike-slip fault is studied numerically. 相似文献
4.
The Biot linearized theory of fluid saturated porous materials is used to study the plane strain deformation of a two-phase
medium consisting of a homogeneous, isotropic, poroelastic half-space in welded contact with a homogeneous, isotropic, perfectly
elastic half-space caused by a two-dimensional source in the elastic half-space. The integral expressions for the displacements
and stresses in the two half-spaces in welded contact are obtained from the corresponding expressions for an unbounded elastic
medium by applying suitable boundary conditions at the interface. The case of a long dip-slip fault is discussed in detail.
The integrals for this source are solved analytically for two limiting cases: (i) undrained conditions in the high frequency
limit, and (ii) steady state drained conditions as the frequency approaches zero. It has been verified that the solution for
the drained case (ω → 0) coincides with the known elastic solution. The drained and undrained displacements and stresses are compared graphically.
Diffusion of the pore pressure with time is also studied. 相似文献
5.
Elastic closed-form solutions for the displacements and stresses in a transversely isotropic half-space subjected to various buried loading types are presented. The loading types include finite line loads and asymmetric loads (such as uniform and linearly varying rectangular loads, or trapezoidal loads). The planes of transverse isotropy are assumed to be parallel to its horizontal surface. These solutions are directly obtained from integrating the point load solutions in a transversely isotropic half-space, which were derived using the principle of superposition, Fourier and Hankel transformation techniques. The solutions for the displacements and stresses in transversely isotropic half-spaces subjected to linearly variable loads on a rectangular region are never mentioned in literature. These exact solutions indicate that the displacements and stresses are influenced by several factors, such as the buried depth, the loading types, and the degree and type of rock anisotropy. Two illustrative examples, a vertical uniform and a vertical linearly varying rectangular load acting on the surface of transversely isotropic rock masses, are presented to show the effect of various parameters on the vertical surface displacement and vertical stress. The results indicate that the displacement and stress distributions accounted for rock anisotropy are quite different for those calculated from isotropic solutions. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
6.
The solution of two-dimensional problem of an interface breaking long inclined dip-slip fault in two welded half-spaces is
well known. The purpose of this note is to obtain the corresponding solution for a blind fault. The solution is valid for
arbitrary values of the fault-depth and the dip angle. Graphs showing the variation of the displacement field with the distance
from the fault, for different values of fault depth and dip angle are presented. Contour maps showing the stress field around
a long dip-slip fault are also obtained 相似文献
7.
We rederive and present the complete closed-form solutions of the displacements and stresses subjected to a point load in a transversely isotropic elastic half-space. The half-space is bounded by a horizontal surface, and the plane of transverse isotropy of the medium is parallel to the horizontal surface. The solutions are obtained by superposing the solutions of two infinite spaces, one acting a point load in its interior and the other being free loading. The Fourier and Hankel transforms in a cylindrical co-ordinate system are employed for deriving the analytical solutions. These solutions are identical with the Mindlin and Boussinesq solutions if the half-space is homogeneous, linear elastic, and isotropic. Also, the Lekhnitskii solution for a transversely isotropic half-space subjected to a vertical point load on its horizontal surface is one of these solutions. Furthermore, an illustrative example is given to show the effect of degree of rock anisotropy on the vertical surface displacement and vertical stress that are induced by a single vertical concentrated force acting on the surface. The results indicate that the displacement and stress accounted for rock anisotropy are quite different for the displacement and stress calculated from isotropic solutions. © 1998 John Wiley & Sons, Ltd. 相似文献
8.
Anup Saha Santimoy Kundu Shishir Gupta Pramod Kumar Vaishnav 《Journal of Earth System Science》2016,125(4):885-895
The present paper is concerned with the propagation of torsional surface waves in an initially stressed anisotropic porous layer sandwiched between homogeneous and non-homogeneous half-space. We assume the quadratic inhomogeneity in rigidity and density in the lower half-space and irregularity is taken in the form of rectangle at the interface separating the layer from the lower half-space. The dispersion equation for torsional waves has been obtained in a closed form. Velocity equation is also obtained in the absence of irregularity. The study reveals that the presence of irregularity, initial stress, porosity, inhomogeneity and anisotropy factor in the dispersion equation approves the significant effect of these parameters in the propagation of torsional waves in porous medium. It has also been observed that for a uniform media, the velocity equation reduces to the classical result of Love wave. 相似文献
9.
Theoretical expressions for the surface displacement and shear stress caused by a long strike-slip dislocation in an elastic
layer overlying an elastic half-space are derived and the correspondence principle is used to obtain the quasi-static response
when the half-space is Maxwell-viscoelastic. Variation of the surface displacement and shear stress with horizontal distance
is studied for various times and vertical extents of the fault. It is seen that the quasi-static response differs significantly
from the corresponding elastic response. 相似文献
10.
The problem of the coseismic deformation of an earth model consisting of an elastic layer of uniform thickness overlying an
elastic half-space due to a very long tensile fault in the layer is solved analytically. Integral expressions for the surface
displacements are obtained for a vertical tensile fault and a horizontal tensile fault. The integrals involved are evaluated
approximately by using Sneddon’s method of replacing the integrand by a finite sum of exponential terms. Detailed numerical
results showing the variation of the displacements with epicentral distance for various source locations in the layer are
presented graphically. The displacement field in the layered half-space is compared with the corresponding field in a uniform
half-space to demonstrate the effect of the internal boundary. Relaxed rigidity method is used for computing the postseismic
deformation of an earth model consisting of an elastic layer of uniform thickness overlying a viscoelastic half-space. 相似文献
11.
The closed-form analytic expressions for the displacement and stresses at any point of an elastic layer lying over a base
due to a very long vertical strike-slip dislocation are obtained. The interface between the layer and the base is assumed
to be either ‘smooth-rigid’ or ‘rough-rigid’ or ‘welded’. The variations of displacement and stresses with the horizontal
distance from the fault for different types of coupling of the layer with the base have been studied. It is found that the
displacement for ‘welded interface’ lies between the displacements due to ‘smooth rigid’ and ‘rough-rigid’ interfaces for
different positions of the observer and different values of the ratio of rigidities of the layer and half-space. 相似文献
12.
The calculation of the deformation caused by shear and tensile faults is necessary for the investigation of seismic and volcanic
sources. The solution of the two-dimensional problem of a long inclined shear fault in two welded half-spaces is well known.
The purpose of this note is to present the corresponding solution for a tensile fault. Closed-form analytical expressions
for the Airy stress function for a tensile line source in two welded half-spaces are first obtained. These expressions are
then integrated analytically to derive the Airy stress function for a long tensile fault of arbitrary dip and finite width.
Closed-form analytical expressions for the displacements and stresses follow immediately from the Airy stress function. These
expressions are suitable for computing the displacement and stress fields around a long inclined tensile fault near an internal
boundary. 相似文献
13.
This paper treats the dynamic response of a multilayered transversely isotropic fluid saturated poroelastic half-space under surface time-harmonic traction. The governing system of partial differential equations is uncoupled with the use of a set of physically meaningful and complete potential functions that decompose different body waves in a saturated poroelastic transversely isotropic medium. After expressing the equations in the Hankel-Fourier domain, a proper algebraic factorization is applied to generate reflection and transmission matrices for decomposed waves. All responses including displacements, stresses, and pore fluid pressure for both general patch load and point load are presented in the form of semi-infinite line integrals. The verification of the method is confirmed with the degeneration of the solutions presented here to the existing solutions for dried both homogeneous and multilayered elastic half-spaces as well as poroelastic half-space. Selected numerical results are depicted to investigate the effects of layering and pore pressure on responses of a transversely isotropic poroelastic medium. The load distribution effects are studied by comparison of the patch and point load responses. Also, resonance notion and effective parameters on this phenomenon such as layering system and anisotropy contrast are discussed. Significant influence of materials and layering configuration on number and amplitude of resonances depicted through the numerical evaluation. 相似文献
14.
Analytical solution for the problem of a surface-breaking long strike-slip fault in an elastic layer overlying an elastic
half-space is well known. The purpose of this note is to obtain the corresponding solution for a blind fault. Since the solution
is valid for arbitrary values of the fault-depth and the dip angle, the effects of these two important fault parameters can
be studied numerically. The variation of the parallel displacement and shear stress with the distance from the fault is studied
numerically for different values of the fault-depth and dip angle. 相似文献
15.
This paper deals with the propagation, reflection and transmission of shear waves in monoclinic media. The dispersion equation for a monoclinic layer overlying a monoclinic half-space has been obtained and curves are plotted. The amplitude ratios for both the reflected and transmitted waves due to reflection of shear waves at the interface of two monoclinic half-spaces have also been computed and the numerical results are presented graphically. The results are compared with the isotropic case. It has been observed that, in monoclinic media, the amplitude ratios for reflected and transmitted wave increases approximately by 25 and 50 per cent respectively, in comparison to the isotropic case. © 1997 John Wiley & Sons, Ltd. 相似文献
16.
In this paper, an integrated approach has been carried out with an intent to study the reflection and transmission phenomena of plane SH-type wave on a corrugated interface separating two magnetoelastic transversely isotropic half-space. Closed form expressions for reflection and transmission coefficients have been derived for both plane and corrugated surface. Rayleigh’s method of approximation have been incorporated to deduce equations for the first- and second-order approximation of corrugation. Analytical solutions for both the half-spaces have been worked out. All possible cases have been apprehended specially for anisotropic and an isotropic medium. The effects of magnetoelastic coupling parameter, angle at which the wave crosses the magnetic field, corrugation amplitude, frequency factor and wave number have been explained by collaborating with graphical analysis. 相似文献
17.
竖向圆形荷载作用下弹性半空间问题的位移和应力解是桩基分析的基础。利用Hankel积分变换,首先导出了弹性地基半空间位移与应力的积分形式的通解。通过适当地引入边界条件和界面位移和应力的连续条件,求得了内部作用竖向圆形荷载时弹性地基半空间位移与应力的积分形式解。在此基础上,给出了不同深度处荷载作用投影范围内竖向位移和竖向正应力的平均值。数值结果验证了解析解的正确性。 相似文献
18.
We present fully-discrete procedures for computing the impedance functions of rigid massless soil-structure interfaces that are embedded in arbitrarily heterogeneous half-spaces. The finite element method (FEM) is used for obtaining the wave responses of (visco-)elastic half-spaces truncated by Perfectly Matched Layers (PMLs), which provide the wave absorbing boundary conditions. The devised FEM-PML approach is verified in both time and frequency domains by using various benchmark solutions. Requirements on the prescribed input excitations for obtaining accurate impedances in the time domain as well as the relative computational cost of time- and frequency domain solutions are investigated. Accuracy of the implemented PMLs in extracting the impedance functions is also examined in comparison to Lysmer–Kuhlemeyer dashpots; and it was found that this simplified boundary treatment is generally inadequate. The utility of the proposed method is demonstrated by extracting the impedance matrix of rectangular and circular voids embedded in a linearly stiffening half-space. Impedance functions for such complex soil-structure systems are shown to be highly coupled and frequency-dependent due to wave reflections and interference caused by the soil heterogeneity and interface geometry. Fully discrete approaches, such as those proposed herein, are necessary to adequately capture these effects. 相似文献
19.
Guang Y. Sheu 《国际地质力学数值与分析法杂志》2004,28(5):437-463
Earlier solutions (Bull. Seismol. Soc. Amer. 1985; 75 :1135–1154; Bull. Seismol. Soc. Amer. 1992; 82 :1018–1040) of deformations caused by the movements of a shear or tensile fault in an isotropic half-space for finite rectangular sources of strain nucleus have been extended for a transversely isotropic half-space. Results of integrating previous solutions (Int. J. Numer. Anal. Meth. Geomech. 2001; 25 (10): 1175–1193) of deformations due to a shear or tensile fault in a transversely isotropic half-space for point sources of strain nucleus over the fault plane are presented. In addition, a boundary element (BEM) model (POLY3D:A three-dimensional, polygonal element, displacement discontinuity boundary element computer program with applications to fractures, faults, and cavities in the Earth's crust. M.S. Thesis, Stanford University, Department of Geology, 1993; 62) is given. Different from similar researches (e.g. Thomas), the Akaike's view on Bayesian statistics (Akaike Information Criterion Statistics. D. Reidel Publication: Dordrecht, 1986) is applied for inverting deformations due to a fault to obtain displacement discontinuities on the fault plane. An example is given for checking displacements predicted by proposed analytical expressions. Another example is generated for the use of proposed BEM model. It demonstrates the effectiveness of this model in exploring displacement behaviours of a fault. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
20.
Closed form analytical expressions of stresses and displacements at any field point due to a very long dip-slip fault of finite
width buried in a homogeneous, isotropic elastic half-space, are presented. Airy stress function is used to derive the expressions
of stresses and displacements which depend on the dip angle and depth of the upper edge of the fault. The effect of dip angle
and depth of the upper edge of the fault on stresses and displacements is studied numerically and the results obtained are
presented graphically. Contour maps for stresses and displacements are also presented. The results of Rani and Singh (1992b)
and Freund and Barnett (1976) have been reproduced. 相似文献