An Analytic Solution for the Diffraction of Plane P Waves by a Cylindrical Inclusion in Half Space

2011 ◽  
Vol 255-260 ◽  
pp. 2520-2525
Author(s):  
Da Guang Li ◽  
Xue Ping Gao ◽  
Zhang Ying
Keyword(s):  
Half Space ◽  
Analytic Solution ◽  
Incident Angle ◽  
Surface Condition ◽  
Surface Displacement ◽  
Cylindrical Inclusion ◽  
Diffraction Effect ◽  
P Waves ◽  
Plane P Waves ◽  
The Impact

This paper presents an analytic solution for the diffraction of plane P waves by a cylindrical inclusion in half space by Fourier-Bessel wave function expansion method, in which the flat surface of half space is approximated by a large curved surface. The equation can be constructed by the continue boundary and the free surface condition. Based on parametric analysis, the impact of the inclusion on surface displacement amplitude is discussed. It is illustrated that there is large difference of the diffraction characteristics between the hard inclusion and soft inclusion. The displacement response depends strongly on the incident angle and frequency. The diffraction effect can be ignored with large embedded depth of the inclusion.

Diffraction of elastic waves by a fluid-filled crack in a fluid-saturated poroelastic half-space

2021 ◽  
Author(s):  
Zhongxian Liu ◽  
Jiaqiao Liu ◽  
Sibo Meng ◽  
Xiaojian Sun
Keyword(s):  
Half Space ◽  
Seismic Waves ◽  
Incident Angle ◽  
Excitation Frequency ◽  
Vertical Displacement ◽  
Crack Model ◽  
P Waves ◽  
Amplification Effect ◽  
Resonance Frequencies ◽  
Angle Crack

Summary An indirect boundary element method (IBEM) is developed to model the two-dimensional (2D) diffraction of seismic waves by a fluid-filled crack in a fluid-saturated poroelastic half-space, using Green's functions computed considering the distributed loads, flow, and fluid characteristics. The influence of the fluid-filled crack on the diffraction characteristics is investigated by analyzing key parameters, such as the excitation frequency, incident angle, crack width and depth, and medium porosity. The results for the fluid-filled crack model are compared to those for the fluid-free crack model under the same conditions. The numerical results demonstrate that the fluid-filled crack has a significant amplification effect on the surface displacements, and that the effect of the depth of the fluid-filled crack is more complex compared to the influence of other parameters. The resonance diffraction generates an amplification effect in the case of normally incident P waves. Furthermore, the horizontal and vertical displacement amplitudes reach 4.2 and 14.1, respectively. In the corresponding case of the fluid-free crack, the vertical displacement amplitude is only equal to 4.1, indicating the amplification effect of the fluid in the crack. Conversely, for normally incident SV waves at certain resonance frequencies, the displacement amplitudes above a fluid-filled crack may be lower than the displacement amplitudes observed in the corresponding case of a fluid-free crack.

Effects of Surface Elasticity on Scattering of P Waves by an Elastic Half-Plane with a Nanosized Semi-Cylindrical Inclusion

2013 ◽  
Vol 303-306 ◽  
pp. 2661-2666
Author(s):  
Zhi Ying Ou ◽  
Cheng Liu ◽  
Xiao Wei Liu
Keyword(s):  
Surface Energy ◽  
Half Plane ◽  
Surface Effect ◽  
Surface Elasticity ◽  
Expansion Method ◽  
Cylindrical Inclusion ◽  
P Waves ◽  
Wave Function Expansion Method ◽  
Plane P Waves ◽  
Incident Waves

The scattering of plane P waves by a nanosized semi-cylindrical inclusion embedded in an elastic half-plan has been studied in this paper. To account for the surface effect at nanoscale, the surface elasticity is also adopted. When the boundary condition at the straight edge of the half-plane is traction free, the analytical solutions of stress fields of the half plan with semi-cylindrical inclusion are expressed by employing a wave function expansion method. The results show that surface energy has a significant effect on the scattering of plane P waves as the radius of the semi-cylindrical inclusion shrinks to nanoscale. For incident waves with different frequencies, radius of semi-cylindrical inclusion, the effects of surface energy on the dynamic stress concentration near the semi-cylindrical inclusion are discussed in detail.

scholarly journals Scattering of Plane P1 Wave by an Inclusion in a Three-Dimension Poroelastic Half-Space

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Yanxi Zhao ◽  
Hai Zhang ◽  
Nan Xu ◽  
Youxin Wei ◽  
Zhongxian Liu
Keyword(s):  
Elastic Wave ◽  
Half Space ◽  
Coupling Effect ◽  
Incident Angle ◽  
Surface Displacement ◽  
Boundary Integral ◽  
Displacement Amplitude ◽  
Three Dimension ◽  
Dry Soil ◽  
Poroelastic Soil

Local inclusion topography has significant influence on seismic wave propagation, and the propagation characteristics of seismic waves in poroelastic soils are obviously different from those in single-phase media. Based on Biot’s theory, the scattering of plane P1 wave by inclusion in a three-dimensional poroelastic half-space is studied by using the indirect boundary element method (IBEM). The scattering field is constructed by introducing a virtual wave near the interface between inclusion and half-space and the surface of half-space, and the virtual wave density is obtained by establishing boundary integral equation based on the boundary conditions. The effects of the depth, geometric characteristics, boundary permeability, porosity, incident frequency, and incident angle of the inclusion on elastic wave scattering are systematically analyzed. The results show that due to the soil skeleton-pore water coupling effect, when the porosity is n = 0.3, the surface displacement amplitude of dry soil is larger than that of poroelastic soil. When the porosity is n = 0.36, the surface displacement amplitude of poroelastic soil is larger than that of dry soil. The surface displacement amplitude of poroelastic-drained condition is slightly larger than that of undrained condition. With the increase of inclusion depth, the scattering of elastic wave by inclusion decreases gradually. When P1 wave is incident, the surface displacement amplitude at the depth of H = 0.5 can be increased up to three times as much as that at the depth of H = 1.5. As the inclusion becomes narrower and flatter, the scattering of elastic waves by inclusion decreases gradually. When the ratio between height and length is S = 2/5, the surface displacement magnitude can reach up to 9.5.

scholarly journals Diffraction of plane P waves around an alluvial valley in poroelastic half-space

2010 ◽  
Vol 23 (1) ◽  
pp. 35-43 ◽  
Author(s):  
Zhongxian Liu ◽  
Jianwen Liang
Keyword(s):  
Half Space ◽  
Alluvial Valley ◽  
P Waves ◽  
Plane P Waves

scholarly journals Scattering of SH Waves by a Partially Debonded Cylindrical Inclusion in the Covering Layer

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Hui Qi ◽  
Yang Zhang ◽  
Fuqing Chu ◽  
Jing Guo
Keyword(s):  
Stress Concentration ◽  
Dynamic Stress ◽  
Complex Function ◽  
Surface Displacement ◽  
Expansion Method ◽  
Cylindrical Inclusion ◽  
Dynamic Stress Concentration ◽  
Sh Waves ◽  
Covering Layer ◽  
The Impact

This article presents analytical solutions to the problem of dynamic stress concentration and the surface displacement of a partially debonded cylindrical inclusion in the covering layer under the action of a steady-state horizontally polarized shear wave (SH wave); these solutions are using the complex function method and wave function expansion method. By applying the large-arc assumption method, the straight line boundary of the half-space covering layer is transformed into a curved boundary. The wave field of the debonded inclusion is constructed utilizing a Fourier series and boundary conditions of continuity. The impact of debonding upon the dynamic stress concentration and surface displacement around the cylindrical concrete or steel inclusion is analyzed through numerical examples of the SH waves that are incident at normal angles, from a harder medium to a softer medium and from a softer medium to a harder medium. The examples show that various factors (including the medium parameters of the soil layers and the inclusion, the frequency of the incident waves, and the debonding situations) jointly affect the dynamic stress concentration factor and the surface displacement around the structure.

scholarly journals Dynamic Response of Underground Circular Lining Tunnels Subjected to Incident P Waves

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Hua Xu ◽  
Tianbin Li ◽  
Jingsong Xu ◽  
Yingjun Wang
Keyword(s):  
Dynamic Response ◽  
Half Space ◽  
Structural Damage ◽  
Dynamic Stress ◽  
Elastic Half Space ◽  
Underground Structures ◽  
P Waves ◽  
Incident Plane ◽  
Plane P Waves ◽  
Rock Tunnels

Dynamic stress concentration in tunnels and underground structures during earthquakes often leads to serious structural damage. A series solution of wave equation for dynamic response of underground circular lining tunnels subjected to incident plane P waves is presented by Fourier-Bessel series expansion method in this paper. The deformation and stress fields of the whole medium of surrounding rock and tunnel were obtained by solving the equations of seismic wave propagation in an elastic half space. Based on the assumption of a large circular arc, a series of solutions for dynamic stress were deduced by using a wave function expansion approach for a circular lining tunnel in an elastic half space rock medium subjected to incident plane P waves. Then, the dynamic response of the circular lining tunnel was obtained by solving a series of algebraic equations after imposing its boundary conditions for displacement and stress of the circular lining tunnel. The effects of different factors on circular lining rock tunnels, including incident frequency, incident angle, buried depth, rock conditions, and lining stiffness, were derived and several application examples are presented. The results may provide a good reference for studies on the dynamic response and aseismic design of tunnels and underground structures.

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