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Gold Science and Technology ›› 2022, Vol. 30 ›› Issue (5): 691-703.doi: 10.11872/j.issn.1005-2518.2022.05.030

• Mining Technology and Mine Management • Previous Articles     Next Articles

Dynamic Stress Concentration Laws of Cylindrical Inclusion Under Incident Plane P Waves

Ming TAO1,2(),Jing YAO1,2,Xibing LI1,2   

  1. 1.School of Resources and Safety Engineering, Central South University, Changsha 410083, Hunan, China
    2.Hunan Key Laboratory of Resources Exploitation and Hazard Control for Deep Metal Mines, Changsha 410083, Hunan, China
  • Received:2022-02-21 Revised:2022-05-17 Online:2022-10-31 Published:2022-12-10

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Abstract:

The influences of blasting seismic waves on inclusion is crucial in the blasting excavation process. Part of the energy generated by blasting is used for the fragmentation of the rock mass，and the remaining part is propagated to a distance in the form of elastic waves.The scattering of stress waves at the structural discon-tinuity leads to the migration and accumulation of energy，resulting in local high energy and high stress，and then lead to rock failure.The plane P wave in the blasting seismic wave was taken as the research object and wave function expansion method was used to solve the scattering and dynamic stress concentration around the cylinder inclusion in the full plane under steady state linear elastic incident P wave.Under the cylindrical coor-dinate system，Bessel equation was obtained by separating variables from Helmholtz equation.Considering the simplicity of Bessel function in solving cylindrical boundary problem，the incident plane wave was expanded into the series of Bessel function，and the full wave function was obtained from the stress boundary condition of the cylindrical inclusion，then the response of the cylindrical inclusion subjected to the steady state linear elastic stationary incident P wave was obtained.Through the Fourier integral transformation of transient impact，the dynamic stress concentration of transient incident P wave around a cylindrical inclusion could be obtained.The effects of shear elastic modulus，Poisson’s ratio and wave number on the dynamic stress concentration factor were analyzed.The results show that the dynamic stress concentration factor reaches its maximum value when the wave number is 0.25，and the maximum value appears in the counterclockwise 90° and 270° directions of the inclusion.With the increase of wave number，tensile stress concentration occurs in the surrounding rock in the directions of 0° and 180°，which may lead to the failure of the surrounding rock. In addition，the finite element software LS-DYNA was used to establish a numerical model of wave incident rock mass with inclusions.The scattering and stress concentration of the transient wave at the inclusion were calculated，the pressure and effective stress chart around the inclusion and the rock mass failure were obtained.The distribution and numerical value of the stress concentration factor obtained by the simulation are very close to the numerical calculation，which proves the correctness of the numerical calculation.The results show that the larger the difference between the shear elastic modulus of the surrounding rock and the inclusion，the more obvious the dynamic stress concentration，and the larger the failure area of the surrounding rock is. The CSCM cap model material was used to establish a model，and the damage of surrounding rock under the action of transient wave incidence was obtained.The results show that the cracks appear in the counterclockwise 90° and 270° directions，that is，the position of the maximum value of the dynamic stress concentration factor.

Key words: stress wave, plane P wave, cylindrical inclusion, transient P wave scattering, dynamic stress concentration factor, wave number

CLC Number: 

  • TD313

Fig.1

Geometric model"

Fig.2

Stress diagram around the inclusion when the physical properties of the medium and inclusion are the same"

Fig.3

Relationship between hoop DSCF and wave number when the Poisson’s ratio is v1=0.25，v2=0.20"

Fig.4

Distribution of DSCF around the circular inclusion with different wave number"

Fig.5

Distribution of DSCF around the inclusion with different Poisson’s ratio combinations"

Fig.6

Ricker wavelet waveform with dominant frequency of 60π"

Fig.7

Hoop DSCF generated by the Ricker wavelet"

Fig.8

Transient hoop DSCF distribution around the circular inclusion at different times"

Fig.9

Radial DSCF generated by the Ricker wavelet"

Fig.10

Transient radial DSCF distribution around the circular inclusion at different times"

Fig.11

Numerical simulation model diagram"

Fig.12

Cloud diagram of pressure and effective stress"

Fig.13

Numerical simulation and theoretical calculation results of the DSCF distribution around the circular inclusion"

Fig.14

Damage around the circular inclusion"

Fig.15

Effect of Poisson’s ratio on DSCF under transient wave incidence"

Fig.16

Effect of shear modulus ratio on transient DSCF"

Fig.17

Point-line diagram of the variation of maximum and minimum of DSCF with wave number kD"

Chen Tao， Hu Chao， Huang Wenhu，2006.Dynamic stress concentrations in a plate with cylindrical cavity by incident P wave ［J］.Earthquake Engineering and Engineering Dynamics，26（4）：32-36.
Chen Zhigang，2005.Scattering of SH-wave by a shallow buried elliptic cylindrical cavity and dynamic stress concentration ［J］.Journal of Jinan University（Natural Science），（3）：324-330.
Cui Z， Sheng Q， Leng X L，et al，2016.Control effect of a large geological discontinuity on the seismic response and stability of underground rock caverns：A case study of the Baihetan #1 surge chamber ［J］.Rock Mechanics and Engineering，49（6）：2099-2114.
Ghafarollahi A， Shodja H M，2018.Scattering of SH-waves by an elliptic cavity/crack beneath the interface between functionally graded and homogeneous half-spaces via multipole expansion method［J］.Journal of Sound and Vibration，435：372-389.
Li Z， Tao M， Du K，et al，2020. Dynamic stress state around shallow-buried cavity under transient P wave loads in different conditions［J］.Tunnelling and Underground Space Technology，97：1-12.
Liu Diankui， Tian Jiayong，1999.Scattering and dynamic stress concentration of SH-wave by interface cylindrical elastic inclusion ［J］.Explosion and Shock Waves，（2）：20-28.
Liu Zhongxian， Liang Jianwen， Li Fan，2012.Diffraction of plane SV waves by an inclusion in saturated poroelastic half-space ［J］.Chinese Quarterly of Mechanics，33（2）：256-268.
Lu Shiwei， Sun Jinshan， Liu Hongyu，et al，2021.Study on dynamic stress concentration of a pipeline under the cylindrical SH-waves ［J］.Engineering Blasting，27（4）：34-39.
Xiaotang Lü， Yang Zailin， Liu Diankui，2009.Antiplane reponse of multiple semi-cylindrical hills above a subsurface elastic cylindrical inclusion to incident SH waves［J］.World Earthquake Engineering，25（2）：114-119.
Nobes D C，2016. Ground penetrating radar response from voids： A demonstration using a simple model［C］//16th International Conference on Ground Penetrating Radar （GPR）.Hongkong：IEEE. DOI：10.1109/ICGPR.2016.7572511 .
doi: 10.1109/ICGPR.2016.7572511
Pao Y H， Mow C C， Achenbach J D，1973.Diffraction of elastic waves and dynamic stress concentrations［J］.Journal of Applied Mechanics，40（4）：213-219.
Ricker N H，1940. The form and nature of seismic waves and the structure of seismograms［J］. Geophysics，5（4）：348-366.
Tao M， Zhao R， Du K，et al，2020a.Dynamic stress concentration and failure characteristics around elliptical cavity subjected to impact loading［J］.International Journal of Solids and Structures，191/192：401-417. .
Tao M， Zhao H T， Li Z，et al，2020b.Analytical and numerical study of a circular cavity subjected to plane and cylindrical P-wave scattering ［J］.Tunnelling and Underground Space Technology，95：103143. .
Wang Z Z， Gao B， Jiang Y J，et al，2009.Investigation and assessment on mountain tunnels and geotechnical damage after the Wenchuan earthquake［J］.Science in China （Series E：Technological Sciences），52（2）：546-558.
Yang Zailin， Yan Peilei， Liu Diankui，2009.Scattering of SH-waves and ground motion by an elastic cylindrical inclusion and a crack in half space ［J］.Chinese Journal of Theoretical and Applied Mechanics，41（2）：229-235.
You Hongbing， Zhao Fengxin， Li Fangjie，2009.Scattering of P waves by a local nonhomogeneous body in a layered half-space ［J］.Rock and Soil Mechanics，30（10）：3133-3138.
Yuan Xiaoming，1996.The influence of the scattering from the plane of the circular inclusion under the ground surface on the ground motion ［J］.Chinese Journal of Geophysics，39（3）：373-381.
Zhang Yingying， Wang Yunzhuan， Shi Ying，et al，2017.Frequencies of the Ricker wavelet ［J］.Progress in Geophysics，32（5）：2162-2167.
Zhao Chunxiang， Qi Hui，2016.Dynamic effect of SH wave on interface circular cavity in half space［J］.Journal of Vibration and Shock，35（12）：132-135.
陈涛，胡超，黄文虎，2006. P波入射时含圆柱形空腔板弹性波散射与动应力集中 ［J］.地震工程与工程振动，26（4）：32-36.
陈志刚，2005.平面SH波在浅埋椭圆柱形孔洞上的散射与动应力集中 ［J］.暨南大学学报，（3）：324-330.
刘殿魁，田家勇，1999.SH波对界面圆柱形弹性夹杂散射及动应力集中［J］.爆炸与冲击，（2）：20-28.
刘中宪，梁建文，李帆，2012.流体饱和半空间中夹塞物对平面SV波的散射［J］.力学季刊，33（2）：256-268.
路世伟，孙金山，刘洪宇，等，2021.柱面SH波作用下管道的动应力集中研究 ［J］.工程爆破，27（4）：34-39.
吕晓棠，杨在林，刘殿魁，2009.SH波对浅埋圆柱形弹性夹杂附近多个半圆形凸起的散射［J］.世界地震工程，25（2）：114-119.
杨在林，闫培雷，刘殿魁，2009.SH波对浅埋弹性圆柱及裂纹的散射与地震动［J］.力学学报，41（2）：229-235.
尤红兵，赵凤新，李方杰，2009. 层状场地中局部不均体对平面P波的散射［J］. 岩土力学，30（10）：3133-3138.
袁晓铭，1996.地表下圆形夹塞区出平面散射对地面运动的影响［J］.地球物理学报，39（3）：373-381.
张莹莹，王云专，石颖，等，2017.雷克子波频率研究 ［J］.地球物理学进展，32（5）：2162-2167.
赵春香，齐辉，2016.SH波对半空间界面圆孔的动力效应［J］.振动与冲击，35（12）：132-135.
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