Response of Shallow-Buried Circular Lining Tunnel to Incident PWave

2012 ◽  
Vol 160 ◽  
pp. 331-336 ◽  
Author(s):  
Y.S. Li ◽  
T.B. Li ◽  
X Zhang
Keyword(s):  
Half Space ◽  
Series Solution ◽  
Hoop Stress ◽  
Expansion Method ◽  
Typical Case ◽  
Dynamic Responses ◽  
Algebraic Equations ◽  
Circular Arc ◽  
Incident Plane ◽  
Incident Frequency

Taking the circular lining tunnel in half-space as prototype, this paper investigates the dynamic responses of this tunnel. A series solution for the scatting waves in half-space and the lining is derived by wave expansion method under the assumption of the large circular arc. And then, combining the boundary conditions, the tunnel dynamic response is shift to seeking the solution of series of algebraic equations. Finally, the effects of buried depth, lining rigidity and incident frequency upon the dynamic hoop stress in the inner lining surface caused by incident plane Pwave is quantitatively analyzed from the view of theory in a typical case.

The Scattering of SH-Wave Caused by Subsurface Circular Cavities in a Layered Half-Space

2011 ◽  
Vol 488-489 ◽  
pp. 226-229
Author(s):  
Dong Ni Chen ◽  
Hui Qi ◽  
Yong Shi
Keyword(s):  
Half Space ◽  
Elastic Layer ◽  
Complex Function ◽  
Expansion Method ◽  
Elastic Half Space ◽  
Wave Functions ◽  
Large Radius ◽  
Algebraic Equations ◽  
Sh Wave ◽  
Linear Algebraic Equations

The scattering of SH-wave caused by the subsurface circular cavities in an elastic half-space covered with an elastic layer was discussed, which was based on the complex function method ,wave functions expansion method and big circular arc postulation method in which the circular boundary of large radius was used to approximate straight boundary of surface elastic layer. By the theory of Helmholtz, the general solution of the Biot’s wave function was achieved. Utilizing the complex series expansion technology and the boundary conditions, we could transform the present problem into the problem in which we needed to solve the infinite linear algebraic equations with unknown coefficients in wave functions. Finally, the dynamic stress concentration factors around the circular cavities were discussed in numerical examples.

The Effect on Scattering of SH-Wave in a Layered Half-Space with the Subsurface Circular Cavities

2011 ◽  
Vol 194-196 ◽  
pp. 1908-1911
Author(s):  
Dong Ni Chen ◽  
Hui Qi ◽  
Yong Shi
Keyword(s):  
Half Space ◽  
Elastic Layer ◽  
Complex Function ◽  
Expansion Method ◽  
Elastic Half Space ◽  
Wave Functions ◽  
Large Radius ◽  
Algebraic Equations ◽  
Sh Wave ◽  
Linear Algebraic Equations

The scattering of SH-wave caused by the subsurface circular cavities in an elastic half-space covered with an elastic layer was discussed, which was based on the complex function method and wave functions expansion method. The solution of scattering of SH-wave was given by using circular boundary of large radius to approximate straight boundary of surface elastic layer. According to boundary conditions, we needed to solve the infinite linear algebraic equations with unknown coefficients in wave functions. Finally, the dynamic stress concentration factors around circular cavities were discussed in numerical examples.

scholarly journals A novel series method for fractional diffusion equation within Caputo fractional derivative

2016 ◽  
Vol 20 (suppl. 3) ◽  
pp. 695-699 ◽  
Author(s):  
Sheng-Ping Yan ◽  
Wei-Ping Zhong ◽  
Xiao-Jun Yang
Keyword(s):  
Diffusion Equation ◽  
Fractional Derivative ◽  
Caputo Fractional Derivative ◽  
Series Solution ◽  
Expansion Method ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Series Method ◽  
Time Fractional Diffusion Equation ◽  
Series Expansion Method

In this paper, we suggest the series expansion method for finding the series solution for the time-fractional diffusion equation involving Caputo fractional derivative.

scholarly journals The local fractional series expansion solution for local fractional Korteweg-de Vries equation

2016 ◽  
Vol 20 (suppl. 3) ◽  
pp. 863-866
Author(s):  
Wei Zhang ◽  
Kai-Li Xu ◽  
Yun Lei
Keyword(s):  
Series Expansion ◽  
Series Solution ◽  
Vries Equation ◽  
Expansion Method ◽  
De Vries ◽  
Series Expansion Method

In this paper, the local fractional series expansion method is used to find the series solution for the local fractional Korteweg-de Vries equation.

Approximate solutions to the half-space integral transport equation near a plane boundary

1980 ◽  
Vol 58 (9) ◽  
pp. 1291-1310 ◽  
Author(s):  
Michael S. Milgram
Keyword(s):  
Transport Equation ◽  
Half Space ◽  
Matrix Multiplication ◽  
Solution Space ◽  
Plane Geometry ◽  
Plane Boundary ◽  
Infinite Plane ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
Integral Transport

A set of functions spanning the solution space of the integral transport equation near a boundary in semi-infinite plane geometry is obtained and used to reduce the problem to that of a system of linear algebraic equations. Expressions for the boundary angular flux are obtained by matrix multiplication, and the theory is extended to adjacent half-space problems by matching the angular flux at the boundary. Thus a unified theory is obtained for well-behaved arbitrary sources in semi-infinite plane geometry. Numerical results are given for both Milne's problem and the problem of constant production in adjacent half-spaces, and albedo problems in semi-infinite geometry. The solutions for the flux density are best near the boundary, and for the angular flux are best for angles near the plane of the boundary; it is conjectured that the theory will prove most useful when extended to arrays of finite slabs.

Analysis of water wave interaction with a submerged quarter-circular breakwater using multipole method

2020 ◽  
Vol 234 (4) ◽  
pp. 846-860
Author(s):  
Ai-jun Li ◽  
Yong Liu ◽  
Zuo-rui Lyu
Keyword(s):  
Water Wave ◽  
Series Solution ◽  
Velocity Potential ◽  
Separation Of Variables ◽  
Wave Interaction ◽  
Wave Forces ◽  
Submerged Breakwater ◽  
Circular Arc ◽  
Internal Fluid ◽  
Multipole Expansion Method

This article studies water wave interaction with a submerged quarter-circular breakwater based on potential theory and multipole expansion method. The obliquely and normally incident waves are independently considered. The series solution of velocity potential in the external fluid domain is expressed through the multipole expansions, while the series solution of velocity potential in the quarter-circular internal fluid domain is obtained through the separation of variables. Then, the unknown coefficients in the series solutions are determined by matching the boundary conditions between external and internal fluid domains. The calculation methods for the reflection and transmission coefficients of the submerged quarter-circular breakwater as well as the horizontal and vertical wave forces on the breakwater are presented. The wave forces acting on the submerged breakwater with a seaside quarter-circular-arc and that with a leeside quarter-circular-arc are compared. The hydrodynamic quantities of the submerged quarter-circular breakwater are also compared with those of the submerged semi-circular breakwater. In addition, the effects of breakwater radius, incident frequency, and incident angle on the hydrodynamic quantities of the quarter-circular breakwater are clarified. Valuable results for practical engineering application are drawn.

Dynamic Response of Shallow Buried Tunnel Subjected to SH Wave

2010 ◽  
Vol 163-167 ◽  
pp. 4265-4268
Author(s):  
Zhi Gang Chen
Keyword(s):  
Stress Concentration ◽  
Half Space ◽  
Dynamic Stress ◽  
Complex Function ◽  
Least Square ◽  
Wave Number ◽  
Dynamic Stress Concentration ◽  
Algebraic Equations ◽  
Sh Wave ◽  
Scattering Wave

The dynamic stress concentration on quadratic and U-shaped cavities in half space, which are similar to the cross-section of the tunnels, is solved in this paper impacted by SH-wave. The analytical solution for the cavity in elastic half space is gained by the complex function method. In the complex plane, the scattering wave which satisfies the zero-stress condition at the horizontal surface can be constructed, the problem can be inverted into a set of algebraic equations to solve coefficients of the constructed scattering wave by least square method. For the earthquake-resistance researches, the numerical examples of the dynamic stress concentration around the quadratic and U-shaped cavities impacted by SH-wave are given. The influences of the dynamic stress concentration by the incident wave number and angle, the depth and shape of the cavity are discussed. It is showed that the interaction among the wave, the surface and the shallow buried tunnels should be cared in half space. In this situation, the dynamic stress concentration around the tunnel is greater obvious than the whole space.

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