Scattering and diffraction of plane P-waves in a 2-D elastic half-space II: shallow arbitrary shaped canyon

2017 ◽  
Vol 16 (3) ◽  
pp. 459-485 ◽  
Author(s):  
Heather P. Brandow ◽  
Vincent Lee
Keyword(s):  
Half Space ◽  
Elastic Half Space ◽  
P Waves ◽  
Plane P Waves

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.

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 Effects of a magnetic field and initial stress on reflection of SV-waves at a free surface with voids under gravity

2018 ◽  
Vol 27 (5-6) ◽  
Author(s):  
Augustine Igwebuike Anya ◽  
M.W. Akhtar ◽  
Syed Muhammad Abo-Dahab ◽  
Hajra Kaneez ◽  
Aftab Khan ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Free Surface ◽  
Magnetic Fields ◽  
Initial Stress ◽  
Half Space ◽  
Significant Role ◽  
Elastic Half Space ◽  
Wave Incident ◽  
P Waves

AbstractThe present study deals with the reflection of SV-waves at a free surface in the presence of magnetic field, initial stress, voids and gravity. When an SV-wave incident on the free surface of an elastic half space, two damped P-waves and an SV-wave are reflected. Among these waves, P-waves are only affected by magnetic fields whereas SV-waves are influenced by both, initial stress and magnetic fields. Effect of gravity is negligible whereas voids played a significant role. These observations can be helpful for seismology and earthquake sciences.

scholarly journals Weighted Residual Method for Diffraction of Plane P-Waves in a 2D Elastic Half-Space Revisited: On an Almost Circular Arbitrary-Shaped Canyon

2015 ◽  
Vol 2015 ◽  
pp. 1-21 ◽  
Author(s):  
Vincent W. Lee ◽  
Heather P. Brandow
Keyword(s):  
Half Space ◽  
Plane Waves ◽  
Classical Problem ◽  
Strong Motion ◽  
Elastic Half Space ◽  
Shear Stresses ◽  
Weighted Residual Method ◽  
P Waves ◽  
Closed Form Solutions ◽  
P And Sv Waves

Scattering and diffraction of elastic in-plane P- and SV-waves by a surface topography such as an elastic canyon at the surface of a half-space is a classical problem which has been studied by earthquake engineers and strong-motion seismologists for over forty years. The case of out-of-plane SH-waves on the same elastic canyon that is semicircular in shape on the half-space surface is the first such problem that was solved by analytic closed-form solutions over forty years ago by Trifunac. The corresponding case of in-plane P- and SV-waves on the same circular canyon is a much more complicated problem because the in-plane P- and SV-scattered-waves have different wave speeds and together they must have zero normal and shear stresses at the half-space surface. It is not until recently in 2014 that analytic solution for such problem is found by the author in the work of Lee and Liu. This paper uses the technique of Lee and Liu of defining these stress-free scattered waves to solve the problem of the scattering and diffraction of these in-plane waves on an on an almost-circular surface canyon that is arbitrary in shape.

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