平面P波入射圆形夹塞动应力集中规律研究

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

在地下矿山的爆破开挖过程中,爆破地震波对夹塞周边围岩的稳定性具有重要的影响。为了研究平面P波作用下夹塞的动应力集中情况,以爆破地震波中的平面P波作为研究对象,利用波函数展开法以及Fourier积分得到了瞬态波入射夹塞的动应力集中因子的解析解。分析了围岩和夹塞的剪切弹性模量、泊松比及波数对动应力集中因子的影响。结果表明:低波数时瞬态波在夹塞周围产生更大的动应力集中因子。利用有限元软件LS-DYNA建立了波入射含夹塞岩体的数值模型,计算瞬态波在夹塞处的散射和应力集中,获得了夹塞周边的压力云图、有效应力云图以及破坏情况。研究结果验证了数值计算的正确性,并且得到破坏区域即为应力集中因子最大位置。

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 discontinuity 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 coordinate 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.