P波在非线性交叉节理岩体中的传播特性研究
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摘要
岩体中的节理常会呈现交叉分布,使得应力波的传播极其复杂。通过理论和数值模拟方法对平面P波在具有非线性特性的交叉节理中的传播特性进行了研究。首先,采用时域递归分析法分析2条交叉节理之间多重反射波的传播过程,结合叠加原理建立了平面P波在2条交叉节理中的传播方程。其次,采用UDEC程序对2条交叉节理中的波传播进行了数值模拟,对比发现,理论结果与数值计算结果非常接近。然后,采用数值方法建立了平面P波在2组交叉节理中传播的计算模型。最后,对影响波传播的一些参数进行了分析。结果表明,节理刚度、节理分布以及入射波频率等都影响波的传播过程;交叉节理不同监测点处的透反射系数也不尽相同。提出的理论方法为分析应力波在交叉节理中的传播提供了新的思路,但该方法仍有很多局限,对于复杂工况,可以采用数值模拟方法。
The intersecting distribution of joints in rock mass makes the stress wave propagation complicated. In this paper,the propagation characteristics of stress P-waves across nonlinearly intersecting rock joints were studied by using theoretical analysis and numerical simulation. The propagation process of multiple reflected waves between two intersecting joints was analyzed using the time-domain recursive analysis method(TDRM) and the propagation equation was established combining the principle of superposition. The wave propagation process in two intersecting joints was simulated by UDEC. The comparison between the theoretical and numerical results shows that they are very close to each other. A numerical model was proposed for calculating the propagation of stress P-wave cross two sets of intersecting rock joints,and parameters studies were carried out. It is shown that the wave propagation is influenced by joint stiffness,joint distribution and incident wave frequency and that the transmission and reflection coefficients are different at different monitoring positions of intersecting joints. The theoretical method proposed in this paper,providing a new way for analyzing the propagation of stress waves in intersecting joints,still has some limitations. For complex conditions,the numerical simulation method can be adopted to study wave propagation across jointed rock mass.
The intersecting distribution of joints in rock mass makes the stress wave propagation complicated. In this paper,the propagation characteristics of stress P-waves across nonlinearly intersecting rock joints were studied by using theoretical analysis and numerical simulation. The propagation process of multiple reflected waves between two intersecting joints was analyzed using the time-domain recursive analysis method(TDRM) and the propagation equation was established combining the principle of superposition. The wave propagation process in two intersecting joints was simulated by UDEC. The comparison between the theoretical and numerical results shows that they are very close to each other. A numerical model was proposed for calculating the propagation of stress P-wave cross two sets of intersecting rock joints,and parameters studies were carried out. It is shown that the wave propagation is influenced by joint stiffness,joint distribution and incident wave frequency and that the transmission and reflection coefficients are different at different monitoring positions of intersecting joints. The theoretical method proposed in this paper,providing a new way for analyzing the propagation of stress waves in intersecting joints,still has some limitations. For complex conditions,the numerical simulation method can be adopted to study wave propagation across jointed rock mass.
引文
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[8]李新平,董千,刘婷婷,等.地应力下柱面应力波在节理岩体中传播规律研究[J].岩石力学与工程学报,2018,37(增1):3 121-3 130.(LI Ximping,DONG Qian,LIU Tingting,et al.Research on propagation law of cylindrical stress wave in jointed rock mass under in-situ stress[J].Chinese Journal of Rock Mechanics and Engineering,2018,37(Supp.1):3 121-3 130.(in Chinese))
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[10]柴少波,李建春,李海波.柱面波在节理岩体中的传播特性[J].岩石力学与工程学报,2014,33(3):523-530.(CHAI Shaobo,LIJianchun,LI Haibo.Propagation characteristics of cylindrical wave in joint rock masses[J].Chinese Journal of Rock Mechanics and Engineering,2014,33(3):523-530.(in Chinese))
[11]金解放,程昀,昌晓旭,等.轴向静载对红砂岩中应力波传播特性的影响试验研究[J].岩石力学与工程学报,2017,36(8):1 939-1 950.(JIN Jiefang,CHENG Yun,CHANG Xiaoxu,et al.Experimental study on stress wave propagation characteristics in red sandstone under axial static stress[J].Chinese Journal of Rock Mechanics and Engineering,2017,36(8):1 939-1 950.(in Chinese))
[12]李新平,董千,刘婷婷,等.不同地应力下爆炸应力波在节理岩体中传播规律模型试验研究[J].岩石力学与工程学报,2016,35(11):2 188-2 196.(LI Ximping,DONG Qian,LIU Tingting,et al.Model test on propagation of blasting stress wave in jointed rock mass under different in-situ stresses[J].Chinese Journal of Rock Mechanics and Engineering,2016,35(11):2 188-2 196.(in Chinese))
[13]LEMOS J V.A distinct element model for dynamic analysis of jointed rock with application to dam foundations and fault motion[Ph.D.Thesis][D].Minneapolis:University of Minnesota,1987:36-89.
[14]ZHAO X B,ZHAO J,CAI J G,et al.UDEC modelling on wave propagation across fractured rock masses[J].Computers and Geotechnics,2008,35(1):97-104.
[15]ZHU J B,DENG X F,ZHAO X B,et al.A numerical study on wave transmission across multiple intersecting joint sets in rock masses with UDEC[J].Rock Mechanics and Rock Engineering,2013,46(6):1 429-1 442.
[16]赵坚,陈寿根,蔡军刚,等.用UDEC模拟爆炸波在节理岩体中的传播[J].中国矿业大学学报,2002,31(2):111-115.(ZHAOJian,CHEN Shougen,CAI Jungang,et al.Simulating study on the wave propagation across jointed rock mass by using UDEC[J].Journal of China University of Mining and Technology,2002,31(2):111-115.(in Chinese))
[17]ZHAO J.Construction and utilization of rock caverns in Singapore,Part A:Bedrock resource of the Bukit Timah granite[J].Tunnelling and Underground Space Technology,1996,11(1):65-72.
[18]刘婷婷,李建春,李海波,等.非线性节理模型对应力波传播影响的数值分析[J].岩石力学与工程学报,2015,34(5):953-959.(LIUTingting,LI Jianchun,LI Haibo,et al.Numerical analysis for the effect of stress wave propagation through nonlinear joints[J].Chinese Journal of Rock Mechanics and Engineering,2015,34(5):953-959.(in Chinese))
[2]卢文波.应力波与可滑移岩石界面间的相互作用研究[J].岩土力学,1996,17(3):70-75.(LU Wenbo.A study on interaction between stress wave and slipping rock interface[J].Rock and Soil Mechanics,1996,17(3):70-75.(in Chinese))
[3]俞缙,关云飞,肖琳,等.弹性纵波在不同非线性法向变形行为节理处的传播[J].解放军理工大学学报:自然科学版,2007,8(6):589-594.(YU Jin,GUAN Yunfei,XIAO Lin,et al.Transmission of elastic P-wave across single fracture with different nonlinear normal deformation behaviors[J].Journal of PLA University of Science and Technology:Natural Science,2007,8(6):589-594.(in Chinese))
[4]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):1 316-1 321.(YUJin,ZHAO Xiaobao,ZHAO Weibing,et al.Improved nonlinear elastic constitutive model for normal deformation of rock fractures[J].Chinese Journal of Geotechnical Engineering,2008,30(9):1 316-1 321.(in Chinese))
[5]ZHAO J,CAI J G.Transmission of elastic P-wave across single fracture with a nonlinear normal deformation behavior[J].Rock Mechanics and Rock Engineering,2001,34(1):3-22.
[6]LI J C,MA G W.Analysis of blast wave interaction with a rock joint[J].Rock Mechanics and Rock Engineering,2010,43(6):777-787.
[7]Li J C,MA G W,ZHOU Y X.Analytical study of underground explosion induced ground surface motion[J].Rock Mechanics and Rock Engineering,2012,45(6):1 037-1 046.
[8]李新平,董千,刘婷婷,等.地应力下柱面应力波在节理岩体中传播规律研究[J].岩石力学与工程学报,2018,37(增1):3 121-3 130.(LI Ximping,DONG Qian,LIU Tingting,et al.Research on propagation law of cylindrical stress wave in jointed rock mass under in-situ stress[J].Chinese Journal of Rock Mechanics and Engineering,2018,37(Supp.1):3 121-3 130.(in Chinese))
[9]宋林,邵珠山,吴敏哲,等.考虑剪切滑移效应时节理岩体中剪切S波的传播特性探析[J].西安建筑科技大学学报:自然科学版,2011,43(4):494-500.(SONG Lin,SHAO Zhushan,WU Minzhe,et al.Theoretical analysis on the propagation characteristic of S-wave across single fracture with consideration of shear slide behavior[J].Journal of Xi′an University of Architecture and Technology:Natural Science Edition,2011,43(4):494-500.(in Chinese))
[10]柴少波,李建春,李海波.柱面波在节理岩体中的传播特性[J].岩石力学与工程学报,2014,33(3):523-530.(CHAI Shaobo,LIJianchun,LI Haibo.Propagation characteristics of cylindrical wave in joint rock masses[J].Chinese Journal of Rock Mechanics and Engineering,2014,33(3):523-530.(in Chinese))
[11]金解放,程昀,昌晓旭,等.轴向静载对红砂岩中应力波传播特性的影响试验研究[J].岩石力学与工程学报,2017,36(8):1 939-1 950.(JIN Jiefang,CHENG Yun,CHANG Xiaoxu,et al.Experimental study on stress wave propagation characteristics in red sandstone under axial static stress[J].Chinese Journal of Rock Mechanics and Engineering,2017,36(8):1 939-1 950.(in Chinese))
[12]李新平,董千,刘婷婷,等.不同地应力下爆炸应力波在节理岩体中传播规律模型试验研究[J].岩石力学与工程学报,2016,35(11):2 188-2 196.(LI Ximping,DONG Qian,LIU Tingting,et al.Model test on propagation of blasting stress wave in jointed rock mass under different in-situ stresses[J].Chinese Journal of Rock Mechanics and Engineering,2016,35(11):2 188-2 196.(in Chinese))
[13]LEMOS J V.A distinct element model for dynamic analysis of jointed rock with application to dam foundations and fault motion[Ph.D.Thesis][D].Minneapolis:University of Minnesota,1987:36-89.
[14]ZHAO X B,ZHAO J,CAI J G,et al.UDEC modelling on wave propagation across fractured rock masses[J].Computers and Geotechnics,2008,35(1):97-104.
[15]ZHU J B,DENG X F,ZHAO X B,et al.A numerical study on wave transmission across multiple intersecting joint sets in rock masses with UDEC[J].Rock Mechanics and Rock Engineering,2013,46(6):1 429-1 442.
[16]赵坚,陈寿根,蔡军刚,等.用UDEC模拟爆炸波在节理岩体中的传播[J].中国矿业大学学报,2002,31(2):111-115.(ZHAOJian,CHEN Shougen,CAI Jungang,et al.Simulating study on the wave propagation across jointed rock mass by using UDEC[J].Journal of China University of Mining and Technology,2002,31(2):111-115.(in Chinese))
[17]ZHAO J.Construction and utilization of rock caverns in Singapore,Part A:Bedrock resource of the Bukit Timah granite[J].Tunnelling and Underground Space Technology,1996,11(1):65-72.
[18]刘婷婷,李建春,李海波,等.非线性节理模型对应力波传播影响的数值分析[J].岩石力学与工程学报,2015,34(5):953-959.(LIUTingting,LI Jianchun,LI Haibo,et al.Numerical analysis for the effect of stress wave propagation through nonlinear joints[J].Chinese Journal of Rock Mechanics and Engineering,2015,34(5):953-959.(in Chinese))