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| UDEC simulation on cylindrical wave propagation through jointed rock masses |
| CHAI Shaobo，ZHAO Junhai，WANG Hao |
| (School of Civil Engineering，Chang?an University，Xi?an，Shaanxi 710064，China) |
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Abstract The cylindrical wave is one of the common wave types in rock mass blasting engineering and the cylindrical wave propagation is a great concern of rock mass excavation and underground structure safety. This paper presents a numerical study on cylindrical P-wave propagation across a jointed rock mass using UDEC. Firstly，a semicircular cylindrical cavity is established at the bottom of the model to simulate the cylindrical wave loading. Then，studies on cylindrical wave propagation across a rock mass without joint and with a single joint are conducted respectively. By compared with the theoretical results，UDEC is proved to be efficient to simulate cylindrical wave propagation across jointed rock mass. After that，parametric studies are carried out to investigate the influence of joint stiffness，the frequency of incident wave and the position of monitoring point on the transmission and reflection coefficients. The results show that the position of the monitoring point affects the transmission and reflection coefficients by influencing the geometric attenuation of the wave and changing the incident angle of the incident wave. Joint stiffness has a significant influence on the reflection coefficient within a certain range. The analysis of frequency effect verifies the characteristics of joint to filter high frequency waves. Finally，the character of cylindrical wave propagation across a set of joints is investigated. The results show that the transmission effect of the wave is corporately influenced by the joint spacing and the number of joints.
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| [1] PYRAK-NOLTE L J. The seismic response of fractures and the interrelations among fracture properties[J]. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts，Pergamon，1996，33(8)：787–802.
[2] SCHOENBERG M，MUIR F. A calculus for finely layered anisotropic media[J]. Geophysics，1989，54(5)：581–589.
[3] 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. Study on the interaction between stress waves and sliding rock interface[J]. Rock and Soil Mechanics，1996，17(3)：70–75.(in Chinese))
[4] COOK N G W. Natural joint in rock：mechanical，hydraulic and seismic behaviour and properties under normal stress[J]. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts，1992，29(3)：198–223.
[5] LI J C，MA G W，ZHAO J. An equivalent viscoelastic model for rock mass with parallel joints[J]. Journal of Geophysical Research：Solid Earth，2010，115(B3)：1–10.
[6] KOLSKY H. Stress waves in solids[M]. Oxford：Clarendon Press，1953：85–116.
[7] ZHU J B，ZHAO X B，LI J C，et al. Normally incident wave propagation across a joint set with the virtual wave source method[J]. Journal of Applied Geophysics，2011，73(3)：283–288.
[8] SCHOENBERG M. Elastic wave behavior across linear slip interfaces[J]. The Journal of the Acoustical Society of America，1980，68(5)：1 516–1 521.
[9] 赵 坚，蔡军刚，赵晓豹，等. 弹性纵波在具有非线性法向变形本构关系的节理处的传播特征[J]. 岩石力学与工程学报，2003，22(1)：9–17.(ZHAO Jian，CAI Jungang，ZHAO Xiaobao，et al. Transmission of elastic P-wave across single fracture with nonlinear normal deformation behavior[J]. Chinese Journal of Rock Mechanics and Engineering，2003，22(1)：9–17.(in Chinese))
[10] 王卫华，李夕兵，左宇军. 非线性法向变形节理对弹性纵波传播的影响[J]. 岩石力学与工程学报，2006，25(6)：1 218–1 225.(WANG Weihua，LI Xibing，ZUO Yujun. Effects of single joint with nonlinear normal deformation on P-wave propagation[J]. Chinese Journal of Rock Mechanics and Engineering，2006，25(6)：1 218–1 225.(in Chinese))
[11] 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.
[12] 俞 缙，宋博学，钱七虎. 节理岩体双重非线性弹性介质中的纵波传播特性[J]. 岩石力学与工程学报，2011，30(12)：2 463–2 473. (YU Jin，SONG Boxue，QIAN Qihu. Propagation of P-waves in dual nonlinear elastic medium for jointed rock mass[J]. Chinese Journal of Rock Mechanics and Engineering，2011，30(12)：2 463–2 473.(in Chinese))
[13] 刘婷婷，李建春，李海波，等. 应力波通过非线性平行节理的能量分析[J]. 岩石力学与工程学报，2013，32(8)：1 610–1 617.(LIU Tingting，LI Jianchun，LI Haibo，et al. Energy analysis of stress wave propagation across parallel nonlinear joints[J]. Chinese Journal of Rock Mechanics and Engineering，2013，32(8)：1 610–1 617.(in Chinese))
[14] 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，LI Jianchun，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))
[15] GHABOUSSI D，WILSON E L，ISENBERG J. Finite element for rock joints and interfaces[J]. Journal of the Soil Mechanics and Foundations Division，1973，99(10)：849–862.
[16] CROTTY J M，WARDLE L J. Boundary integral analysis of piecewise homogeneous media with structural discontinuities[J]. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts，1985，22(6)：419–427.
[17] DE BASABE J D，SEN M K，WHEELER M F. Seismic wave propagation in fractured media：a discontinuous Galerkin approach[J]. SEG Expanded Abstr，2011，30：2 921–2 924
[18] CUNDALL P A，STRACK O D L，AFFILIATIONS V. A discrete numerical model for granular assembles[J]. Géotechnique，1979，29(1)：47–65.
[19] 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)：4–8.(ZHAO Jian，CHEN Shougen，CAI Jungang，et al. Simulation of blast wave propagation in jointed rock mass using UDEC[J]. Journal of China University of Mining and Technology，2002，31(2)：4–8.(in Chinese))
[20] ZHAO X B，ZHAO J，CAI J G，et al. UDEC modeling on wave propagation across fractured rock masses[J]. Computers and Geotechnics，2008，35(1)：97–104.
[21] 杨风威，李海波，李建春，等. 斜入射线弹性节理应力波传播特征的数值模拟[J]. 岩土力学，2013，34(3)：901–907.(YANG Fengwei，LI Haibo，LI Jianchun，et al. Numerical simulation of transmission characteristics of oblique incidence of stress waves across linear elastic joints[J]. Rock and Soil Mechanics，2013，34(3)：901–907.(in Chinese))
[22] 杨善元. 岩石爆破动力学基础[M]. 北京：煤炭工业出版社，1993：136–149.(YANG Shanyuan. Dynamics base of rock blasting[M]. Beijing：China Coal Industry Publishing House，1991：136–149.(in Chinese))
[23] ZHAO J. Construction and utilization of rock caverns in Singapore. Part A：The Bukit Timah granite bedrock resource[J]. Tunnelling and Underground Space Technology，1996，11(1)：65–72.
[24] 王礼立，应力波基础[M]. 2版. 北京：国防工业出版社，2005：228–234.(WANG Lili. Foundation of stress waves[M]. 2nd ed. Beijing：National Defense Industry Press，2005：228–234.(in Chinese))
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2019, Vol. 38 
