应力波斜入射对岩体节理端部的影响
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摘要
岩体节理在受到应力波扰动时端部受力会发生不同程度的连续性变化,为具体分析这种动态变化与应力波入射角度之间的关系,引用岩石非线性法向本构关系与线性切向本构关系的组合模型以及相应的在P波斜入射节理的应力波传播方程,结合岩石断裂力学中Ⅰ、Ⅱ型裂纹尖端应力和位移场的相关理论,得出组合形式下的节理端部应力场和位移场随质点振速变化的计算公式。通过不同入射角的模拟脉冲信号作用对端部应力位移的变化分析:应力波斜入射节理导致节理端部上、下两侧应力与位移场非对称分布,随着入射波质点振速的增减变化,应力集中位置会出现变化;计算并整理模型中节理端部上、下两侧0.005 m位置的数据,节理法向刚度由入射波质点振速带来的变化直接影响到应力波的透射与反射,进而会导致端部的应力与位移出现滞后效应;节理端部横向位移值与入射角度并非单调变化,而竖向位移会随着入射角的增大呈现下降趋势。
When rock joints are disturbed by stress waves, the continuous stresses in joint ends change with various degrees of joints.To analyze the relationship between the dynamic change and the incident angle of stress wave, we introduce a combined model of the nonlinear normal normalised constitutive relation and the linear tangential constitutive relation of rock and the corresponding stress wave propagation equation of oblique incident joints in P wave oblique incidence joint. According to the theory of mode-I and mode-II crack-tip stress in fracture mechanics and the displacement field, a formula is obtained for calculating the stress field and displacement field with the change of the velocity of the joint in the combined form. This study investigates the effect of the simulated pulse signal with different incident angles on the simulation of stress and displacement at the end. Stress and displacement fields at the upper and lower ends of the joint present non-symmetric distribution under the oblique incidence of stress wave. With the increase and decrease of vibration velocity of the incident wave particle point, the position of the stress concentration changes. The data of 0.005 m position at the upper and lower sides of the joint end in the model are calculated, the change of joint normal stiffness bringing by the particle velocity of incident wave directly influences the transmission and reflection of stress wave, which leads to the lag of stress and displacement at the end of the joint. The lateral displacement and the incident angle do not change monotonically, but the vertical displacement decreases with the increase of incidence angle.
When rock joints are disturbed by stress waves, the continuous stresses in joint ends change with various degrees of joints.To analyze the relationship between the dynamic change and the incident angle of stress wave, we introduce a combined model of the nonlinear normal normalised constitutive relation and the linear tangential constitutive relation of rock and the corresponding stress wave propagation equation of oblique incident joints in P wave oblique incidence joint. According to the theory of mode-I and mode-II crack-tip stress in fracture mechanics and the displacement field, a formula is obtained for calculating the stress field and displacement field with the change of the velocity of the joint in the combined form. This study investigates the effect of the simulated pulse signal with different incident angles on the simulation of stress and displacement at the end. Stress and displacement fields at the upper and lower ends of the joint present non-symmetric distribution under the oblique incidence of stress wave. With the increase and decrease of vibration velocity of the incident wave particle point, the position of the stress concentration changes. The data of 0.005 m position at the upper and lower sides of the joint end in the model are calculated, the change of joint normal stiffness bringing by the particle velocity of incident wave directly influences the transmission and reflection of stress wave, which leads to the lag of stress and displacement at the end of the joint. The lateral displacement and the incident angle do not change monotonically, but the vertical displacement decreases with the increase of incidence angle.
引文
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[18]顾樵.数学物理方法[M].北京:科学出版社,2012.GU Qiao.Mathematical physical method[M].Beijing:Science Press,2012.
[19]张凤鹏,彭建宇,范光华,等.不同静应力和节理条件下岩体爆破破岩机制研究[J].岩土力学,2016,37(7):1839-1846+1913.ZHANG Feng-peng,PENG Jian-yu,FAN Guang-hua,et al.Mechanisms of blasting-induced rock fractures under different static stress and joint properties conditions[J].Rock and Soil Mechanics,2016,37(7):1839-1846+1913.
[2]CHE Ai-lan,YANG Hong-kai,WANG Bin,et al.Wave propagations through jointed rock masses and their effects on the stability of slopes[J].Engineering Geology,2016,201:45-56.
[3]HAMID REZA MOHAMMADI AZIZABADIA,HAMID MANSOURI,OLIVIER FOUCHé.Coupling of two methods,waveform superposition and numerical,to model blast vibration effect on slope stability in jointed rock masses[J].Computers and Geotechnics,2014,61:42-49.
[4]WANG Jin-an,WANG Yu-xi,CAO Qiu-ju,et al.Behavior of microcontacts in rock joints under direct shear creep loading[J].International Journal of Rock Mechanics&Mining Sciences,2015,78:217-229.
[5]LI J C,WU W,LI H B,et al.A thin-layer interface model for wave propagation through filled rock joints[J].Journal of Applied Geophysics,2013,91:31-38.
[6]俞缙,赵晓豹,赵维炳,等.改进的岩石节理弹性非线性法向变形本构模型研究[J].岩土工程学报,2008,30(9):1316-1321.YU Jin,ZHAO Xiao-bao,ZHAO Wei-bing,et al.Improved nonlinear elastic constitutive model for normal deformation of rock fractures[J].Chinese Journal of Geotechnical Engineering,2008,30(9):1316-1321.
[7]石崇,徐卫亚,周家文,等.节理面非线性变形对SV波透反射性能影响[J].岩石力学与工程学报,2008,(增刊1):2661-2668.SHI Chong,XU Wei-ya,ZHOU Jia-wen,et al.Effect of nonlinear deformation at joint interface on transmission and reflection[J].Chinese Journal of Rock Mechanics and Engineering,2008,27(Supp.1):2661-2668.
[8]王观石,李长洪,陈保君,等.应力波在非线性结构面介质中的传播规律[J].岩土力学,2009,12:3747-3752.WANG Guan-shi,LI Chang-hong,CHEN Bao-jun,et al.Propagation law of stress wave in nonlinear structural surface medium[J].Rock and Soil Mechanics,2009,12:3747-3752.
[9]杨仁树,苏洪,龚悦,等.爆炸荷载下不对称Y型裂纹扩展规律的试验研究[J].岩土力学,2017,38(8):2175-2181.YANG Ren-shu,SU Hong,GONG Yue,et al.Study on the regularity of asymmetric Y-shaped cracks propagation under blast loading[J].Rock and Soil Mechanics,2017,38(8):2175-2181.
[10]刘婷婷,李建春,李海波,等.剪切速率对平直充填节理的剪切力学特性影响研究[J].岩土力学,2017,38(7):1967-1973.LIU Ting-ting,LI Jian-chun,LI Hai-bo,et al.Influence of shearing velocity on shear mechanical properties of planar filled joints[J].Rock and Soil Mechanics,2017,38(7):1967-1973.
[11]李业学,范建辉,李铮.岩体节理对应力波传播规律影响的研究进展[J].湖北文理学院学报,2015,36(11):10-14+22.LI Ye-xue,FAN Jian-hui,LI Zheng.Research progress of influence of rock jioint on propagation rule of stress wave[J].Journal of Hubei University of Arts and Science,2015,36(11):10-14+22.
[12]刘再华,解德,王元汉,等.工程断裂动力学[M].武汉:华中理工大学出版社,1996.LIU Zai-hua,XIE De,WANG Yuan-han,et al.Engineering fracture dynamic mechanics[M].Wuhan:Huazhong University of Science&Technology Press,1996.
[13]宋林,闫玉湛,韩八晓,等.非线性变形节理中纵波传播特性的理论研究[J].应用力学学报,2012,29(2):133-140+236.SONG Lin,YAN Yu-zhan,HAN Ba-xiao,et al.Theoretical research into the wave propagation of P-wave across rock joint with nonlinear deformation[J].Chinese Journal of Applied Mechanics,2012,29(2):133-140+236.
[14]BANDIS S C,LUMSDEN A C,BARTON N R.Fundamentals of rock joint deformation[J].International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts,1983,20(6):249-268.
[15]中国航空研究院.应力强度因子手册[M].北京:科学出版社,1981.China aviation academy.Stress intensity factor[M].Beijing:Science Press,1981.
[16]李世愚,和泰名,尹祥础,等.岩石断裂力学导论[M].合肥:中国科学技术大学出版社,2010.LI Shi-yu,HE Tai-ming,YIN Xiang-chu,et al.Introduction of rock fracture mechanics[M].Hefei:University of Science&Technology China Press,2010.
[17]程靳,赵树山.断裂力学[M].北京:科学出版社,2006.CHENG Jin,ZHAO Shu-shan.Rock fracture mechanics[M].Beijing:Science Press,2006.
[18]顾樵.数学物理方法[M].北京:科学出版社,2012.GU Qiao.Mathematical physical method[M].Beijing:Science Press,2012.
[19]张凤鹏,彭建宇,范光华,等.不同静应力和节理条件下岩体爆破破岩机制研究[J].岩土力学,2016,37(7):1839-1846+1913.ZHANG Feng-peng,PENG Jian-yu,FAN Guang-hua,et al.Mechanisms of blasting-induced rock fractures under different static stress and joint properties conditions[J].Rock and Soil Mechanics,2016,37(7):1839-1846+1913.