scholarly journals A Series Solution for 2D Scattering of Cylindrical SH-Waves by Surrounding Loose Rock Zone of Underground Tunnel Lining

2021 ◽  
Vol 9 ◽  
Author(s):  
Liguo Jin ◽  
Hongyang Sun ◽  
Shengnian Wang ◽  
Zhenghua Zhou
Keyword(s):  
Stress Concentration ◽  
Stress Concentration Factor ◽  
Concentration Factor ◽  
Series Solution ◽  
Dynamic Stress ◽  
Tunnel Lining ◽  
Dynamic Stress Concentration ◽  
Sh Wave ◽  
Wave Source ◽  
Loose Rock

This paper presents a closed-form series solution of cylindrical SH-wave scattering by the surrounding loose rock zone of underground tunnel lining in a uniform half-space based on the wave function expansion method and the mirror image method. The correctness of the series solution is verified through residual convergence and comparison with the published results. The influence of the frequency of the incident cylindrical SH-wave, the distance between the wave source and the lining, the lining buried depth, and the properties of the surrounding loose rock zone on the dynamic stress concentration of the tunnel lining is investigated. The results show that the incident wave with high frequency always makes the dynamic stress concentration of the tunnel lining obvious. With the increase of the distance between the wave source and the tunnel lining, the stress around the tunnel lining decreases, but the dynamic stress concentration factor around the tunnel lining does not decrease significantly but occasionally increases. The ground surface has a great influence on the stress concentration of the tunnel lining. The amplitude of the stress concentration factor of tunnel lining is highly related to the shear wave velocity of the surrounding loose rock zone. When the property of the surrounding rock (shear wave velocity) changes more, the amplitude of the stress concentration factor is larger, that is, the stress concentration is more significant.

Dynamic Stress Concentration of Circular Cavity and Double Linear Cracks in Elastic Medium

2009 ◽  
Vol 419-420 ◽  
pp. 825-828
Author(s):  
Xue Yi Zhang ◽  
Guang Ping Zou ◽  
Hong Liang Li
Keyword(s):  
Stress Concentration ◽  
Elastic Medium ◽  
Green's Function ◽  
Stress Concentration Factor ◽  
Concentration Factor ◽  
Dynamic Stress ◽  
Dynamic Stress Concentration ◽  
Circular Cavity ◽  
Sh Wave ◽  
Dynamic Stress Concentration Factor

Sacttering of SH-wave of combined deffectiveness which included single circular cavity and double linear cracks in elastic medium was investigated in detail. Analytic solution of this problem was obtained by Green’s Function method and idea of crack-division at actual position of crack at two times. There were two key steps of this method. First step was to employ a special Green’s Function which was a fundamental solution of displacement field for an elastic space with a cavity in it subjected to out-of-plane harmonic line source force at any point at first. The sceond step was crack-division which was artificially to produce a crack by apllying opposite shear stress caused by incident SH-wave. Distribution of dynamic stress concentration factor (DSCF) at edge of cavity was studied by numerical analysis. Distribution Curves of DSCF of three models were plotted by numerical method in polar coordinate system. Three models were one circular cavity and without crack, one circular cavity and single crack and single circular cavity double cracks. The results were compared and discussed in different incident angle of SH-wave.Conclusion was that the interaction among SH-wave, single cavity and double crack was obvious. Dynamic stress concentration factor varied with angle and distance between cavity and crack.

Scattering of Sh-Wave by Cylindrical Inclusion Near Interface in Bi-Material Half-Space

2011 ◽  
Vol 27 (1) ◽  
pp. 37-45 ◽  
Author(s):  
H. Qi ◽  
J. Yang ◽  
Y. Shi
Keyword(s):  
Stress Concentration ◽  
Half Space ◽  
Green's Function ◽  
Stress Concentration Factor ◽  
Concentration Factor ◽  
Dynamic Stress ◽  
Cylindrical Inclusion ◽  
Dynamic Stress Concentration ◽  
Sh Wave ◽  
Dynamic Stress Concentration Factor

ABSTRACTGreen's function and complex function methods are used here to investigate the problem of the scattering of SH-wave by a cylindrical inclusion near interface in bi-material half-space. Firstly, Green's function was constructed which was an essential solution of displacement field for an elastic right-angle space possessing a cylindrical inclusion while bearing out-of-plane harmonic line source load at any point of its vertical boundary. Secondly, the bi-material media was divided into two parts along the vertical interface using the idea of interface “conjunction”, then undetermined anti-plane forces were loaded at the linking sections respectively to satisfy continuity conditions, and a series of Fredholm integral equations of first kind for determining the unknown forces could be set up through continuity conditions on surface. Finally, some examples for dynamic stress concentration factor of the cylindrical elastic inclusion are given. Numerical results show that dynamic stress concentration factor is influenced by interfaces, free boundary and combination of different media parameters.

Dynamic Stress Concentration of Underground Lined Cavities in Different Distance under Incident Plane SV Wave

2012 ◽  
Vol 446-449 ◽  
pp. 2317-2320 ◽  
Author(s):  
Min Huang ◽  
Bing Yu Pan
Keyword(s):  
Stress Concentration ◽  
Stress Concentration Factor ◽  
Concentration Factor ◽  
Dynamic Stress ◽  
Expansion Method ◽  
Dynamic Stress Concentration ◽  
Dynamic Stress Concentration Factor ◽  
Incident Plane ◽  
Rigid Lining ◽  
Plane Sv Wave

A series solution for dynamic stress concentration of underground lined cavities in different distance under incident plane SV waves is given by wave function expansion method. The infinite series is cut and calculated under the required precision. The lining includes rigid lining, unlined cavities, flexible lining. The numerical results show that the distance between cavities has an important impact on the dynamic stress concentration factor and the interaction between two cavities greatly amplifies the dynamic stress concentration. With the distance increases the dynamic stress concentration factor turn smaller gradually and tend to the distribution case of one cavity; The rigidity of lining also has great effect on the dynamic stress concentration which is highest for the rigid lining, second for unlined cavities and is lowest for the flexible lining.

Sign in / Sign up

Export Citation Format

Share Document