Green＇s functions for Blot＇s dynamic equation in the frequency domain can be a highly useful tool for the investigation of dynamic responses of a saturated porous medium. Its applications are found in soil dynamics,...Green＇s functions for Blot＇s dynamic equation in the frequency domain can be a highly useful tool for the investigation of dynamic responses of a saturated porous medium. Its applications are found in soil dynamics, seismology, earthquake engineering, rock mechanics, geophysics, and acoustics. However, the mathematical work for deriving it can be daunting. Green＇s functions have been presented utilizing an analogy between the dynamic thermoelasticity and the dynamic poroelasticity in the frequency domain using the u-p formulation. In this work, a special term ＂decoupling coefficient＂ for the decomposition of the fast and slow dilatational waves is proposed and expressed to present a new methodology for deriving the poroelastodynamic Green＇s functions. The correct- ness of the solution is demonstrated by numerically comparing the current solution with Cheng＇s previous solution. The separation of the two waves in the present methodology allows the more accurate evaluation of Green＇s functions, particularly the solution of the slow dilatational wave. This can be advantageous for the numerical implementation of the boundary element method （BEM） and other applications.展开更多
This article presents a case study concerning a seismic characterization project.Full-wave sonic logging was used to characterize the shallow compressional wave and shear wave velocity profiles in the site.Anomalous v...This article presents a case study concerning a seismic characterization project.Full-wave sonic logging was used to characterize the shallow compressional wave and shear wave velocity profiles in the site.Anomalous values of the Poisson’s ratio derived from the velocity profiles suggested that the boreholes might have traversed slow formations(i.e.with shear wave velocity smaller than the borehole fluid compressional wave velocity or“mud-wave speed”)and that conventional processing of the sonic logs might have misinterpreted the direct arrivals of fluid acoustic waves as arrivals caused by shear wave propagation in the rock.Consequently,the shear wave velocity profiles provided by the contractor were considered to be unreliable by the project team.To address these problems,a non-conventional determination of the shear wave velocity was implemented,based on the relationship between the Poisson’s ratio of the rock formation and the shape of the first train of sonic waves which arrived to the receivers in the sonic probe.The relationship was determined based on several hundreds of finite element simulations of the acoustic wave propagation in boreholes with the same diameter as used in the perforations.The present article describes how this non-conventional approach was developed and implemented to obtain the shear wave velocity profiles from the raw sonic logs.The approach allows an extension of the range of applicability of full-wave sonic logging to determination of shear wave velocity profiles in formations with low compressional wave velocities.The method could be used to obtain shear wave velocity profiles where compressional wave velocity is as low as slightly larger than the mud-wave speed.A sample sonic log in Log ASCII Standard(LAS)format is provided as supplementary material to this paper via Mendeley Data,together with the FORTRAN source code used to process the log following the approach described in this study.展开更多
Based on one type of practical Biot＇s equation and the dynamic-stiffness matrices ofa poroelastic soil layer and half-space, Green＇s functions were derived for unitformly distributed loads acting on an inclined line...Based on one type of practical Biot＇s equation and the dynamic-stiffness matrices ofa poroelastic soil layer and half-space, Green＇s functions were derived for unitformly distributed loads acting on an inclined line in a poroelastie layered site. This analysis overcomes significant problems in wave scattering due to local soil conditions and dynamic soil-structure interaction. The Green＇s functions can be reduced to the case of an elastic layered site developed by Wolf in 1985. Parametric studies are then carried out through two example problems.展开更多
In this paper, mantle circulation flow, continental drift, earthquake origin and other mechanical principles are examined as they apply to earthquake engineering, seismology and dynamics of fluid saturated porous medi...In this paper, mantle circulation flow, continental drift, earthquake origin and other mechanical principles are examined as they apply to earthquake engineering, seismology and dynamics of fluid saturated porous medium. The relationship of mantle flow to earthquakes is examined and clarified, and a new model, different from Haskell’s, is proposed for the earthquake mechanism. The proposed new model is based on the discovery that two pairs of jump stress and jump velocity will start to act from the fault plane. Records obtained directly from recent earthquakes nearby and right on the fault break show a very large velocity impulse, which verify, indirectly, the new mechanism proposed by the author. Further, at least two physical parameters that characterize the seismic intensity must be specified, because according to the discontinuous (jump) wave theory, at the earthquake source, the stress jump and the velocity jump of particle motion should act simultaneously when a sudden break occurs. The third key parameter is shown to be the break (fracture) propagation speed together with the break plane area. This parameter influences the form of the unloading time function at the source. The maximum seismic stress in and displacement of a building are estimated for two unfavorable combinations of the building and its base ground in terms of their relative rigidity. Finally, it is shown that Biot’s theory of wave propagation in fluid saturated porous media is valid only when fluid flow cannot occur.展开更多
A study of the dynamic interaction between foundation and the underlying soil has been presented in a recent paper based on the assumption of saturated ground and elastic circular plate excited by the axisymmetrical h...A study of the dynamic interaction between foundation and the underlying soil has been presented in a recent paper based on the assumption of saturated ground and elastic circular plate excited by the axisymmetrical harmonic source. However, the assumption may not always be valid. The work is extended to the case of a circular plate resting on transversely isotropic saturated soil and subjected to a non-axisymmetrical harmonic force. The analysis is based on the theory of elastic wave in transversely isotropic saturated poroelastic media established. By the technique of Fourier expansion and Hankel transform, the governing difference equations for transversely isotropic saturated soil are easily solved and the cooresponding Hankel transformed stress and displacement solutions are obtained. Then, under the contact conditions, the problem leads to a pair of dual integral equations which describe the mixed boundary-value problem. Furthermore, the dual integral equations can be reduced to the Fredholm integral equations of the second kind solved by numerical procedure. At the end, a numerical result is presented which indicates that on a certain frequency range, the displacement amplitude of the surface of the foundation increases with the increase of the frequency of the exciting force, and decreases in vibration form with the increase of the distance.展开更多
Numerical methods are developed to simulate the wave propagation in heterogeneous 2D fluid/poroelastic media.Wave propagation is described by the usual acoustics equations(in the fluid medium)and by the low-frequency ...Numerical methods are developed to simulate the wave propagation in heterogeneous 2D fluid/poroelastic media.Wave propagation is described by the usual acoustics equations(in the fluid medium)and by the low-frequency Biot’s equations(in the porous medium).Interface conditions are introduced to model various hydraulic contacts between the two media:open pores,sealed pores,and imperfect pores.Well-posedness of the initial-boundary value problem is proven.Cartesian grid numerical methods previously developed in porous heterogeneous media are adapted to the present context:a fourth-order ADER scheme with Strang splitting for timemarching;a space-time mesh-refinement to capture the slow compressional wave predicted by Biot’s theory;and an immersed interface method to discretize the interface conditions and to introduce a subcell resolution.Numerical experiments and comparisons with exact solutions are proposed for the three types of interface conditions,demonstrating the accuracy of the approach.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.51478435,11402150,and 11172268)
文摘Green＇s functions for Blot＇s dynamic equation in the frequency domain can be a highly useful tool for the investigation of dynamic responses of a saturated porous medium. Its applications are found in soil dynamics, seismology, earthquake engineering, rock mechanics, geophysics, and acoustics. However, the mathematical work for deriving it can be daunting. Green＇s functions have been presented utilizing an analogy between the dynamic thermoelasticity and the dynamic poroelasticity in the frequency domain using the u-p formulation. In this work, a special term ＂decoupling coefficient＂ for the decomposition of the fast and slow dilatational waves is proposed and expressed to present a new methodology for deriving the poroelastodynamic Green＇s functions. The correct- ness of the solution is demonstrated by numerically comparing the current solution with Cheng＇s previous solution. The separation of the two waves in the present methodology allows the more accurate evaluation of Green＇s functions, particularly the solution of the slow dilatational wave. This can be advantageous for the numerical implementation of the boundary element method （BEM） and other applications.
文摘This article presents a case study concerning a seismic characterization project.Full-wave sonic logging was used to characterize the shallow compressional wave and shear wave velocity profiles in the site.Anomalous values of the Poisson’s ratio derived from the velocity profiles suggested that the boreholes might have traversed slow formations(i.e.with shear wave velocity smaller than the borehole fluid compressional wave velocity or“mud-wave speed”)and that conventional processing of the sonic logs might have misinterpreted the direct arrivals of fluid acoustic waves as arrivals caused by shear wave propagation in the rock.Consequently,the shear wave velocity profiles provided by the contractor were considered to be unreliable by the project team.To address these problems,a non-conventional determination of the shear wave velocity was implemented,based on the relationship between the Poisson’s ratio of the rock formation and the shape of the first train of sonic waves which arrived to the receivers in the sonic probe.The relationship was determined based on several hundreds of finite element simulations of the acoustic wave propagation in boreholes with the same diameter as used in the perforations.The present article describes how this non-conventional approach was developed and implemented to obtain the shear wave velocity profiles from the raw sonic logs.The approach allows an extension of the range of applicability of full-wave sonic logging to determination of shear wave velocity profiles in formations with low compressional wave velocities.The method could be used to obtain shear wave velocity profiles where compressional wave velocity is as low as slightly larger than the mud-wave speed.A sample sonic log in Log ASCII Standard(LAS)format is provided as supplementary material to this paper via Mendeley Data,together with the FORTRAN source code used to process the log following the approach described in this study.
基金National Natural Science Foundation of China Under Grant No.50378063
文摘Based on one type of practical Biot＇s equation and the dynamic-stiffness matrices ofa poroelastic soil layer and half-space, Green＇s functions were derived for unitformly distributed loads acting on an inclined line in a poroelastie layered site. This analysis overcomes significant problems in wave scattering due to local soil conditions and dynamic soil-structure interaction. The Green＇s functions can be reduced to the case of an elastic layered site developed by Wolf in 1985. Parametric studies are then carried out through two example problems.
文摘In this paper, mantle circulation flow, continental drift, earthquake origin and other mechanical principles are examined as they apply to earthquake engineering, seismology and dynamics of fluid saturated porous medium. The relationship of mantle flow to earthquakes is examined and clarified, and a new model, different from Haskell’s, is proposed for the earthquake mechanism. The proposed new model is based on the discovery that two pairs of jump stress and jump velocity will start to act from the fault plane. Records obtained directly from recent earthquakes nearby and right on the fault break show a very large velocity impulse, which verify, indirectly, the new mechanism proposed by the author. Further, at least two physical parameters that characterize the seismic intensity must be specified, because according to the discontinuous (jump) wave theory, at the earthquake source, the stress jump and the velocity jump of particle motion should act simultaneously when a sudden break occurs. The third key parameter is shown to be the break (fracture) propagation speed together with the break plane area. This parameter influences the form of the unloading time function at the source. The maximum seismic stress in and displacement of a building are estimated for two unfavorable combinations of the building and its base ground in terms of their relative rigidity. Finally, it is shown that Biot’s theory of wave propagation in fluid saturated porous media is valid only when fluid flow cannot occur.
文摘A study of the dynamic interaction between foundation and the underlying soil has been presented in a recent paper based on the assumption of saturated ground and elastic circular plate excited by the axisymmetrical harmonic source. However, the assumption may not always be valid. The work is extended to the case of a circular plate resting on transversely isotropic saturated soil and subjected to a non-axisymmetrical harmonic force. The analysis is based on the theory of elastic wave in transversely isotropic saturated poroelastic media established. By the technique of Fourier expansion and Hankel transform, the governing difference equations for transversely isotropic saturated soil are easily solved and the cooresponding Hankel transformed stress and displacement solutions are obtained. Then, under the contact conditions, the problem leads to a pair of dual integral equations which describe the mixed boundary-value problem. Furthermore, the dual integral equations can be reduced to the Fredholm integral equations of the second kind solved by numerical procedure. At the end, a numerical result is presented which indicates that on a certain frequency range, the displacement amplitude of the surface of the foundation increases with the increase of the frequency of the exciting force, and decreases in vibration form with the increase of the distance.
文摘Numerical methods are developed to simulate the wave propagation in heterogeneous 2D fluid/poroelastic media.Wave propagation is described by the usual acoustics equations(in the fluid medium)and by the low-frequency Biot’s equations(in the porous medium).Interface conditions are introduced to model various hydraulic contacts between the two media:open pores,sealed pores,and imperfect pores.Well-posedness of the initial-boundary value problem is proven.Cartesian grid numerical methods previously developed in porous heterogeneous media are adapted to the present context:a fourth-order ADER scheme with Strang splitting for timemarching;a space-time mesh-refinement to capture the slow compressional wave predicted by Biot’s theory;and an immersed interface method to discretize the interface conditions and to introduce a subcell resolution.Numerical experiments and comparisons with exact solutions are proposed for the three types of interface conditions,demonstrating the accuracy of the approach.
