Existing transversely isotropic poroelastodynamics solutions are limited to infinite domains and without experimental validation. Furthermore, there is a lack of analytical simulations for the elastic moduli dispersio...Existing transversely isotropic poroelastodynamics solutions are limited to infinite domains and without experimental validation. Furthermore, there is a lack of analytical simulations for the elastic moduli dispersion of fluid-saturated porous cylinders. To address these three limitations and investigate the mechanisms of moduli dispersion, we present the analytical solutions of the poromechanical responses and the elastic moduli dispersion of a transversely isotropic, fluid-saturated, finite porous cylinder subjected to a forced deformation test. Through an example, we demonstrate the effects of loading frequency, boundary conditions, and material's anisotropy, dimension, and permeability on the responses of pore pressure,force, displacement, and dynamic elastic moduli of the cylinder. The specimen's responses are significantly influenced by the frequency of the applied load, resulting in a drained state at low frequencies and an undrained state at high frequencies. At high frequencies, the sample behaves identically for an open or a closed lateral boundary, and permeability has insignificant effects. The dynamic elastic moduli are mainly controlled by the loading frequency and the ratio of the sample's radius to its height. Lastly,we show excellent matches between the newly derived analytical solution and laboratory measurements on one clay and two shale samples from Mont Terri.展开更多
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
文摘Existing transversely isotropic poroelastodynamics solutions are limited to infinite domains and without experimental validation. Furthermore, there is a lack of analytical simulations for the elastic moduli dispersion of fluid-saturated porous cylinders. To address these three limitations and investigate the mechanisms of moduli dispersion, we present the analytical solutions of the poromechanical responses and the elastic moduli dispersion of a transversely isotropic, fluid-saturated, finite porous cylinder subjected to a forced deformation test. Through an example, we demonstrate the effects of loading frequency, boundary conditions, and material's anisotropy, dimension, and permeability on the responses of pore pressure,force, displacement, and dynamic elastic moduli of the cylinder. The specimen's responses are significantly influenced by the frequency of the applied load, resulting in a drained state at low frequencies and an undrained state at high frequencies. At high frequencies, the sample behaves identically for an open or a closed lateral boundary, and permeability has insignificant effects. The dynamic elastic moduli are mainly controlled by the loading frequency and the ratio of the sample's radius to its height. Lastly,we show excellent matches between the newly derived analytical solution and laboratory measurements on one clay and two shale samples from Mont Terri.
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.
