Diffraction of plane P waves by a canyon of arbitrary shape in poroelastic half-space (I): Formulation

2009

Earthq Sci

Self Cite

This paper investigates in detail the nature of diffraction of plane P waves around a canyon in poroelastic half-space, and studies the effects of incident frequency, drainage condition, porosity, etc, on the diffraction of waves. It is shown that the surface displacement amplitudes of the drained case are close to those of the undrained case, however, the surface displacement amplitudes of the dry case are very different from those of the saturated (either drained or undrained) cases. There are large phase shift between the dry case and the saturated cases, as well as slightly longer resultant wavelengths for the undrained case than those for the drained case and longer resultant wavelengths for the drained case than those for the dry case. For small porosity the surface displacement amplitudes for the saturated cases are almost identical to those for the dry case; while for large porosity, the effect of drainage condition becomes significant, and the surface displacement amplitudes for the undrained case are larger than those for the drained case. As the incident frequency increases, the effect of porosity becomes significant, and more significant for the undrained case than that for the drained case. As the porosity increases, the pore pressures increase significantly but their oscillations become smoother. As the incident frequency increases, the pore pressures become more complicated.

Section: Numerical Results and Discussionmentioning

confidence: 99%

Diffraction of plane P waves by a canyon of arbitrary shape in poroelastic half-space (II): Numerical results and discussion

Liang

2009

Earthq Sci

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“…In general, the calculation methods include the analytical method [6][7][8][9], finite element method [10][11][12], finite difference method [13][14][15], boundary element method [16][17][18][19], boundary integral equation method [20][21][22][23], etc. It is worth mentioning that all of these studies assumed that the lining and surrounding rock are completely bonded.…”

Section: Introductionmentioning

confidence: 99%

IBIEM Analysis of Dynamic Response of a Shallowly Buried Lined Tunnel Based on Viscous‐Slip Interface Model

Zhou

Liang

Advances in Civil Engineering

et al. 2019

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A viscous-slip interface model is proposed to simulate the contact state between a tunnel lining structure and the surrounding rock. The boundary integral equation method is adopted to solve the scattering of the plane SV wave by a tunnel lining in an elastic half-space. We place special emphasis on the dynamic stress concentration of the lining and the amplification effect on the surface displacement near the tunnel. Scattered waves in the lining and half-space are constructed using the fictitious wave sources close to the lining surfaces based on Green’s functions of cylindrical expansion and the shear wave source. The magnitudes of the fictitious wave sources are determined by viscous-slip boundary conditions, and then the total response is obtained by superposition of the free and scattered fields. The slip stiffness and viscosity coefficients at the lining-surrounding rock interface have a significant influence on the dynamic stress distribution and the nearby surface displacement response in the tunnel lining. Their influence is controlled by the incident wave frequency and angle. The hoop stress increases gradually in the inner wall of the lining as sliding stiffness increases under a low-frequency incident wave. In the high-frequency resonance frequency band, where incident wave frequency is consistent with the natural frequency of the soil column above the tunnel, the dynamic stress concentration effect is more significant when it is smaller. The dynamic stress concentration factor inside the lining decreases gradually as the viscosity coefficient increases. The spatial distribution and the displacement amplitudes of surface displacement near the tunnel change as incident wave frequency and angle increase. The effective dynamic analysis of the underground structure under an actual strong dynamic load should consider the slip effect at the lining-surrounding rock interface.

“…For poroelastic medium, Rajapakse and Senjuntichai developed the IBIEM to solve poroelastodynamic boundary value problems, in which the point force and fluid source solutions were used. Liang and Liu developed the poroelastodynamic MFS on the basis of the SWP fundamental solutions. The SWP‐MFS has been applied by Liang and Liu and Liu et al to solve problems of 2‐D scattering of seismic waves by a cavity or an alluvial valley in a poroelastic half‐plane.…”

Section: Introductionmentioning

confidence: 99%

“…The present paper is aimed at extending the 2‐D SWP‐MFS formulation of Liang and Liu to 3‐D and to implement it to 3‐D wave scattering and dynamic stress concentration problems. Particularly, cavity or poroelastic inclusions in infinite domain are examined.…”

Section: Introductionmentioning

confidence: 99%

The method of fundamental solution for 3‐D wave scattering in a fluid‐saturated poroelastic infinite domain

Num Anal Meth Geomechanics

Wang

Cheng

et al. 2018

Self Cite

By using a complete set of poroelastodynamic spherical wave potentials (SWPs) representing a fast compressional wave P I , a slow compressional wave P II , and a shear wave S with 3 vectorial potentials (not all are independent), a solution scheme based on the method of fundamental solution (MFS) is devised to solve 3-D wave scattering and dynamic stress concentration problems due to inhomogeneous inclusions and cavities embedded in an infinite poroelastic domain. The method is verified by comparing the result with the elastic analytical solution, which is a degenerated case, as well as with poroelastic solution obtained using other numerical methods. The accuracy and stability of the SWP-MFS are also demonstrated. The displacement, hoop stress, and fluid pore pressure around spherical cavity and poroelastic inclusion with permeable and impermeable boundary are investigated for incident plane P I and SV waves. The scattering characteristics are examined for a range of material properties, such as porosity and shear modulus contrast, over a range of frequency. Compared with other boundary-based numerical strategy, such as the boundary element method and the indirect boundary integral equation method, the current SWP-MFS is a meshless method that does not need elements to approximate the geometry and is free from the treatment of singularities. The SWP-MFS is a highly accurate and efficient solution methodology for wave scattering problems of arbitrary geometry, particularly when a part of the domain extends to infinity.