Theoretical study on the propagation characteristics of P-wave in oblique joints rock mass

HU Gang; SONG Baosen; FEI Honglu; BAO Shijie; GUO Jian

doi:10.11883/bzycj-2025-0146

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HU Gang, SONG Baosen, FEI Honglu, BAO Shijie, GUO Jian. Theoretical study on the propagation characteristics of P-wave in oblique joints rock mass[J]. Explosion And Shock Waves. doi: 10.11883/bzycj-2025-0146

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HU Gang, SONG Baosen, FEI Honglu, BAO Shijie, GUO Jian. Theoretical study on the propagation characteristics of P-wave in oblique joints rock mass[J]. Explosion And Shock Waves. doi: 10.11883/bzycj-2025-0146

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Theoretical study on the propagation characteristics of P-wave in oblique joints rock mass

doi: 10.11883/bzycj-2025-0146

1.
Institute of Blasting Technique, Liaoning Technical University, Fuxin 123000, Liaoning, China
2.
College of Mining Engineering, Heilongjiang University of Science and Technology, Harbin 150022, Heilongjiang, China

Received Date: 2025-05-20
Rev Recd Date: 2025-06-26

Available Online: 2025-07-02

Abstract

Abstract

In order to investigate the propagation characteristics of P-wave in nonlinear oblique joints rock mass, a comprehensive approach integrating theoretical analysis, comparative validation and numerical calculation was employed. Initially, the hyperbolic joint constitutive model featuring normal nonlinear deformation and tangential linear deformation was presented. Based on the interaction relationship between stress waves and a linear single joint, the propagation equation for P-wave incident on oblique joints was derived according to superposition principle. Then, by using the parameters of the incident P-wave and the conditions of jointed rock mass reported in literature, the transmission and reflection coefficients were calculated and found to be in close agreement, verifying the accuracy and feasibility of the theoretical model. Furthermore, the auxiliary function of δ function was selected as the incident P-wave to analyze the influence rule of waveform, duration and joint stiffness on the propagation characteristics of P-wave in oblique joints rock mass through parameter study. The results demonstrated that the phenomenon of amplitude reduction, amplitude-time delay and duration extension is pronounced when the auxiliary function of δ function incident on oblique joints, which can better reflect the abrupt change characteristics and nonlinear attenuation behavior of P-wave in a short time. The duration of the incident P-wave in oblique joints rock mass can significantly enhance the transmission performance of P-wave and slightly reduce the reflection characteristics of P-wave and S-wave. As the initial normal stiffness and the shear stiffness of joint increase, the reflection coefficient of S-wave decays in a concave surface shape, while the transmission coefficient of P-wave increases in a convex shape. The transmission performance of P-wave is closely related to the normal stiffness of joints, whereas the reflection characteristics of S-waves are significantly influenced by the second joint in the oblique joints. These research findings offer valuable insights into the mechanical properties and dynamic response of natural jointed rock mass.
- oblique joints rock mass,
- transmission and reflection coefficient,
- P-wave,
- duration,
- stiffness,
- the auxiliary function of δ function

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References(25)

References

[1]	GOODMAN R E. Methods of geological engineering in discontinuous rock [J]. International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts, 1976, 13(10): 115. DOI: 10.1016/0148-9062(76)90566-0.
[2]	何满潮, 吕晓俭, 景海河. 深部工程围岩特性及非线性动态力学设计理念 [J]. 岩石力学与工程学报, 2002, 01(08): 1215–1224. DOI: 10.3321/j.issn:1000-6915.2002.08.022. HE M C, LV X J, JING H H. Characters of surrounding rockmass in deep engineering and its non-linear dynamic-mechanical design concept [J]. Chinese Journal of Rock Mechanics and Engineering, 2002, 01(08): 1215–1224. DOI: 10.3321/j.issn:1000-6915.2002.08.022.
[3]	谢和平, 高峰, 鞠杨, 等. 深地煤炭资源流态化开采理论与技术构想 [J]. 煤炭学报, 2017, 42(03): 547–556. DOI: 10.13225/j.cnki.jccs.2017.0299. XIE H P, GAO F, JU Y, et al. Theoretical and technological conception of the fluidization mining for deep coal resources [J]. Journal of China Coal Society, 2017, 42(03): 547–556. DOI: 10.13225/j.cnki.jccs.2017.0299.
[4]	ZHAO X B. Theoretical and numerical studies of wave attenuation across parallel fractures [D]. Singapore: Nanyang Technological University, 2004: 32–38.
[5]	宋彦琦, 李向上, 刘济琛, 等. 节理充填物厚度对运动裂纹扩展的影响 [J]. 爆炸与冲击, 2020, 40(08): 67–75. DOI: 10.11883/bzycj-2019-0358. SONG Y Q, LI X S, LIU J C, et al. Effects of joint filling thickness on creak propagation behaviors [J]. Explosion and Shock Waves, 2020, 40(08): 67–75. DOI: 10.11883/bzycj-2019-0358.
[6]	TANIMOTO C, KISHIDA K. Fundamental study on seismic wave propagating property through several kinds of rock joint under uniaxial stress [J]. Doboku Gakkai Ronbunshu, 1995, 1995(523): 49–58. DOI: 10.2208/jscej.1995.523_49.
[7]	李祥龙, 王建国, 张智宇, 等. 应变率及节理倾角对岩石模拟材料动力特性的影响 [J]. 爆炸与冲击, 2016, 36(04): 483–490. DOI: 10.11883/1001-1455(2016)04-0483-08. LI X L, WANG J G, ZHANG Z Y, et al. Experimental study for effects of strain rates and joint angles on dynamic responses of simulated rock materials [J]. Explosion and Shock Waves, 2016, 36(04): 483–490. DOI: 10.11883/1001-1455(2016)04-0483-08.
[8]	PYRAK‐NOLTE L J, MYER L R, COOK N G W. Transmission of seismic waves across single natural fractures [J]. Journal of Geophysical Research: Solid Earth, 1990, 95(B6): 8617–8638. DOI: 10.1029/jb095ib06p08617.
[9]	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. DOI: 10.1007/s00603-009-0062-0.
[10]	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(02): 133–140+236. DOI: 10.11776/cjam.29.02.B108. SONG L, YAN Y Z, HAN B X, 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(02): 133–140+236. DOI: 10.11776/cjam.29.02.B108.
[11]	俞缙, 钱七虎, 林从谋, 等. 纵波在改进的弹性非线性法向变形行为单节理处的传播特性研究 [J]. 岩土工程学报, 2009, 31(08): 1156–1164. DOI: 10.3321/j.issn:1000-4548.2009.08.002. YU J, QIAN Q H, LIN C M, et al. Transmission of elastic P-wave across one fracture with improved nonlinear normal deformation behaviors [J]. Chinese Journal of Geotechnical Engineering, 2009, 31(08): 1156–1164. DOI: 10.3321/j.issn:1000-4548.2009.08.002.
[12]	HILDYARD M W, YOUNG R P. Modelling seismic waves around underground openings in fractured rock [J]. The Mechanism of Induced Seismicity, 2002, 32(06): 247–276. DOI: 10.1007/978-3-0348-8179-1_12.
[13]	杨仁树, 许鹏, 杨立云, 等. 节理岩体中爆炸应力波传播规律的研究 [J]. 金属矿山, 2016, 01(06): 49–54. DOI: 10.3969/j.issn.1001-1250.2016.06.009. YANG R S, XU P, YANG L Y, et al. Study of regularity of explosive stress wave propagation in jointed rock mass [J]. Metal Mine, 2016, 01(06): 49–54. DOI: 10.3969/j.issn.1001-1250.2016.06.009.
[14]	王卫华, 严哲, 姜海涛, 等. 不同形貌节理对应力波传播影响的数值模拟 [J]. 爆破, 2017, 34(02): 34–39. DOI: 10.3963/j.issn.1001-487X.2017.02.006. WANG W H, YAN Z, JIANG H T, et al. Numerical simulation on influence of different topography joints on stress wave propagation [J]. Blasting, 2017, 34(02): 34–39. DOI: 10.3963/j.issn.1001-487X.2017.02.006.
[15]	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): 2188–2196. DOI: 10.13722/j.cnki.jrme.2016.1004. LI X P, DONG Q, LIU T T, 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): 2188–2196. DOI: 10.13722/j.cnki.jrme.2016.1004.
[16]	ZHAO J, ZHAO X B, CAI J G. A further study of P-wave attenuation across parallel fractures with linear deformational behavior [J]. International Journal of Rock Mechanics and Mining Sciences, 2006, 43(5): 776–788. DOI: 10.1016/j.ijrmms.2005.12.007.
[17]	ZHAO X B, ZHAO J, CAI J G. P‐wave transmission across fractures with nonlinear deformational behavior [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2006, 30(11): 1097–1112. DOI: 10.1002/nag.515.
[18]	刘婷婷, 李新平, 李海波, 等. 应力波在充填节理岩体中传播规律的数值研究 [J]. 岩石力学与工程学报, 2016, 35(S2): 3552–3560. DOI: 10.13722/j.cnki.jrme.2016.0829. LIU T T, LI X P, LI H B, et al. Numerical study on stress wave propagation across filled joints [J]. Chinese Journal of Rock Mechanics and Engineering, 2016, 35(S2): 3552–3560. DOI: 10.13722/j.cnki.jrme.2016.0829.
[19]	张波, 李术才, 杨学英, 等. 含交叉裂隙节理岩体单轴压缩破坏机制研究 [J]. 岩土力学, 2014, 35(07): 1863–1870. DOI: 10.16285/j.rsm.2014.07.008. ZHANG B, LI S C, YANG X Y, et al. Uniaxial compression failure mechanism of jointed rock mass with cross-cracks [J]. Rock and Soil Mechanics, 2014, 35(07): 1863–1870. DOI: 10.16285/j.rsm.2014.07.008.
[20]	BANDIS S C, LUMSDEN A C, BARTON N R. Fundamentals of rock fracture deformation [J]. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts, 1983, 20(6): 249–268. DOI: 10.1016/0148-9062(84)91255-5.
[21]	BARTON N, BANDIS S, BAKHTAR K. Strength, deformation and conductivity coupling of rock joints [J]. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts, 1985, 22(3): 121–140. DOI: 10.1016/0148-9062(87)90610-3.
[22]	付宝连. 关于功的互等定理与叠加原理的等价性 [J]. 应用数学和力学, 1985, 6(09): 813–818. FU B L. On equivalents of the reciprocal theorem to superposition principles [J]. Applied Mathematics and Mechanics, 1985, 6(09): 813–818.
[23]	柴少波, 李建春, 赵均海, 等. P波在非线性交叉节理岩体中的传播特性研究 [J]. 岩石力学与工程学报, 2019, 38(06): 1149–1157. DOI: 10.13722/j.cnki.jrme.2018.1085. CHAI S B, LI J C, ZHAO J H, et al. Study on stress P-wave propagation across intersecting rock joints with nonlinear deformation [J]. Chinese Journal of Rock Mechanics and Engineering, 2019, 38(06): 1149–1157. DOI: 10.13722/j.cnki.jrme.2018.1085.
[24]	顾樵. 数学物理方法 [M]. 北京: 科学出版社, 2012: 47–52.
[25]	胡刚. 爆破载荷下岩体面内斜交节理端部的动力特性研究 [D]. 阜新: 辽宁工程技术大学, 2021: 23–36.