单轴压缩条件下岩石纵波波速与应力相关性研究

doi:10.3724/1000-6915.jrme.2025.0762

Abstract
Figure/Table
References (0)
Related Citation (15)

Download: PDF (3554 KB) HTML (1 KB)
Export: BibTeX | EndNote (RIS)

Abstract The wave velocity characteristics of rock materials comprehensively reflect their physical properties, macro- and microstructural features, and stress states, thereby providing a fundamental basis for identifying rock mass structures and mechanical behavior using acoustic techniques. To elucidate and quantitatively characterize the relationship between stress and wave velocity in rocks, this study integrates dynamic analysis of forced particle vibration with acoustoelastic theory to clarify the evolution mechanism of particle vibration characteristics under static loading. A functional model correlating rock stress and wave velocity is established by introducing the tangential elastic modulus and the dynamic elastic modulus as intermediate variables. This approach reveals the mechanism through which stress influences wave velocity and enables a quantitative description of wave velocity responses to changes in stress state. Theoretical derivations demonstrate that static force alters only the equilibrium position of particle oscillations within a material, without affecting the intrinsic vibration characteristics induced by acoustic excitation. Stress does not explicitly appear in the incremental vibration equation or the wave velocity formulation; rather, it indirectly influences wave velocity by modifying the material stiffness parameters. This characteristic constitutes a fundamental distinction between acoustic wave propagation in rocks and that in ideal isotropic materials. Experimental results indicate that, with increasing stress, rock wave velocity evolves through four distinct stages: an initial gradual increase, a rapid increase at intermediate stress levels, minor fluctuations prior to peak stress, and a rapid decrease post-failure. Within the linear elastic regime of the stress-strain response, the tangential elastic modulus varies synchronously with wave velocity and exhibits a strong linear correlation with the dynamic elastic modulus governing wave propagation. Based on the experimental results and critical stress points, a mathematical model describing the stress-wave velocity relationship is derived, clarifying the physical significance of the model parameters. In conjunction with existing studies, the applicability and limitations of the proposed model are further discussed. This study aims to reveal the microscopic driving mechanisms by which stress alters wave velocity, providing a quantifiable stress-wave velocity relationship for rock mechanics research and offering a scientific basis for stress state identification in rock engineering applications based on acoustic monitoring techniques.

Key words： rock mechanics wave velocity axial stress elastic modulus uniaxial compression stress measurement

	Service

	E-mail this article
	Add to my bookshelf
	Add to citation manager
	E-mail Alert
	RSS
	Articles by authors
	MA Chi1
	2
	WANG Peitao1
	2*
	CHEN Ziming1
	2
	HUANG Hao1
	2
	ZHOU Baokun1
	2
	MA Qiangying1
	2
	CAI Meifeng1
	2

Cite this article:

MA Chi1,2,WANG Peitao1, et al. Correlation between stress and P-wave velocity in rock under uniaxial compression[J]. , 2026, 45(8): 2354-2369.

URL:

https://rockmech.whrsm.ac.cn/EN/10.3724/1000-6915.jrme.2025.0762 OR https://rockmech.whrsm.ac.cn/EN/Y2026/V45/I8/2354

[1] KAMALI-ASL A，BIJAY K C，GHAZANFARI E，et al. Alteration of ultrasonic signatures by stress-induced changes in hydro-mechanical properties of fractured rocks[J]. International Journal of Rock Mechanics and Mining Sciences，2021，142：104705.
[2] WANG P T，MA C，CAI M F. Relationships between rock ultrasonic properties with loading stresses and challenges in deep mining[J]. Journal of Central South University，2023，30(11)：3 737–3 762.
[3] YAGIZ S. P-wave velocity test for assessment of geotechnical properties of some rock materials[J]. Bulletin of Materials Science，2012，34(4)：947–953.
[4] BELTRAN F，YANEZ-GONZALEZ A，CRESPO M J. Indirect determination of shear wave velocity in slow formations using full-wave sonic logging technique[J]. Journal of Rock Mechanics and Geotechnical Engineering，2020，12(6)：1 226–1 233.
[5] 夏开宗，刘夏临，林英书，等. 基于岩体波速的地下洞室围岩损伤区岩体力学参数取值方法及工程应用[J]. 岩石力学与工程学报，2024，43(10)：2 414–2 429.(XIA Kaizong，LIU Xialin，LIN Yingshu，et al. A method for determining mechanical parameter values of rock mass in the damage zone of surrounding rocks of underground caverns based on wave velocities of rock mass and its engineering application[J]. Chinese Journal of Rock Mechanics and Engineering，2024，43(10)：2 414–2 429.(in Chinese))
[6] 齐勇攀，杨九鼎，李水平，等. 微动勘查技术在河南省嵩县九仗沟金成矿潜力调查中的应用[J]. 地球物理学进展，2025，40(4)：1 492–1 506.(QI Yongpan，YANG Jiuding，LI Shuiping，et al. Application of gold mineralization potential investigation of microtremor exploration technology in Jiuzhanggou area，Songxian County，Henan Province[J]. Progress in Geophysics，2025，40(4)：1 492–1 506.(in Chinese))
[7] NOURANI M H，MOGHADDER M T，SAFARI M. Classification and assessment of rock mass parameters in Choghart iron mine using P-wave velocity[J]. Journal of Rock Mechanics and Geotechnical Engineering，2017，9(2)：318–328.
[8] NAZAROVA L A，ZAKHAROV V N，SHKURATNIK V L，et al. Use of tomography in stress-strain analysis of coal-rock mass by solving boundary inverse problems[J]. Procedia Engineering，2017，191： 1 048–1 055.
[9] YANG J H，DAI J H，YAO C，et al. Estimation of rock mass properties in excavation damage zones of rock slopes based on the Hoek-Brown criterion and acoustic testing[J]. International Journal of Rock Mechanics and Mining Sciences，2020，126：104192.
[10] AMOS N，GENE S. Stress-induced velocity anisotropy in rock：An experimental study[J]. Journal of GeophysicalResearch.1969，74(27)：6 667–6 674.
[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] ZHANG L，ZHANG Z T，ZHANG R，et al. The ultrasonic P-wave velocity-stress relationship and energy evolution of sandstone under uniaxial loading-unloading conditions[J]. Advances in Materials Science and Engineering，2021，2021(1)：9921716.
[13] DONG L J，CHEN Y C，SUN D Y，et al. Implications for rock instability precursors and principal stress direction from rock acoustic experiments[J]. International Journal of Mining Science and Technology，2021，31(5)：789–798.
[14] 王贵宾，杨春和，郭印同，等. 川东北地区岩石纵波速度分布特征和影响因素的试验研究[J]. 岩石力学与工程学报，2011，30(增1)：2 834–2 842.(WANG Guibin，YANG Chunhe，GUO Yintong，et al. Experimental research on distribution characteristics and influential factors of P-wave velocity for rocks in northeast region of Sichuan Province[J]. Chinese Journal of Rock Mechanics and Engineering，2011，30(Supp.1)：2 834–2 842.(in Chinese))
[15] FAN L F，SUN H Y. Seismic wave propagation through an in-situ stressed rock mass[J]. Journal of Applied Geophysics，2015，121：13–20.
[16] YANG S，DENG J H，ZHANG Z P，et al. Evaluating the degree of jointing in highly stressed rock masses：A simple wave velocity model and its application[J]. Tunnelling and Underground Space Technology，2026，167：107016.
[17] RACHED R M，GARCIA A V，SANTAMARINA J C. Long-wavelength propagation in fractured rock masses(3D stress field)[J]. Journal of Geophysical Research：Solid Earth，2022，127(9)：e2022JB024907.
[18] ZHOU K Y，MALKOWSKI P，DOU L M，et al. Using elastic wave velocity anomaly to predict rockburst hazard in coal mines[J]. Archives of Mining Sciences，2023，68(1)：141–164.
[19] 史謌，沈联蒂. 根据波速–压力关系评价岩石岩性、物性的实验研究[J]. 地球物理学报，1990，33(2)：212–219.(SHI Ge，SHEN Liandi. Evaluations of the lithological character and physical property of rocks from the relation between wave velocity and pressure：An experimental study[J]. Chinese Journal of Geophysics，1990，33(2)：212–219.(in Chinese))
[20] 张培森，赵成业，李腾辉，等. 红砂岩三轴加载过程中波速变化及能量演化规律试验研究[J]. 岩石力学与工程学报，2021，40(7)：1 369–1 382.(ZHANG Peisen，ZHAO Chengye，LI Tenghui，et al. Experimental study on wave velocity variation and energy evolution of red sandstone during triaxial loading process[J]. Chinese Journal of Rock Mechanics and Engineering，2021，40(7)：1 369–1 382.(in Chinese))
[21] GREENFIELD R J，GRAHAM E K. Application of a simple relation for describing wave velocity as a function of pressure in rocks containing microcracks[J]. Journal of Geophysical Research：Solid Earth，1996，101(B3)：5 643–5 652.
[22] HUANG X J，BURNS D R，TOKSOZ M N. The effect of stresses on the sound velocity in rocks：theory of acoustoelasticity and experimental measurements[R]. Cambridge，US：Massachusetts Institute of Technology，Earth Resources Laboratory，2001.
[23] FREUND D. Ultrasonic compressional and shear velocities in dry clastic rocks as a function of porosity，clay content，and confining pressure[J]. Geophysical Journal International，1992，108(1)：125–135.
[24] 陈祥，孙进忠，谭朝爽，等. 岩块波速–应力关系及其卸荷效应[J]. 岩土工程学报，2010，32(5)：757–761.(CHEN Xiang，SUN Jingzhong，TAN Chaoshuang，et al. Relation between P-wave velocity and stress of rock samples and their unloading effect[J]. Chinese Journal of Geotechnical Engineering，2010，32(5)：757–761.(in Chinese))
[25] WEPFER W W，CHRISTENSEN N I. A seismic velocity-confining pressure relation，with applications[J]. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts，1991，28(5)：451–456.
[26] HUANG X J，SINHA B K，TOKSOZ M N，et al. Formation stress estimation using standard acoustic logging[C]// SEG Technical Program Expanded Abstracts 1999. Houston：Society of Exploration Geophysicists，1999：53–56.
[27] 李杨，张超，宋卫东，等. 海底金矿岩石弹性纵波与孔隙率特性[J]. 中国矿业大学学报，2021，50(2)：239–247.(LI Yang，ZHANG Chao，SONG Weidong，et al. Elastic longitudinal wave and porosity of subsea gold deposits[J]. Journal of China University of Mining and Technology，2021，50(2)：239–247.(in Chinese))
[28] 田家勇，王恩福. 基于声弹理论的地应力超声测量方法[J]. 岩石力学与工程学报，2006，25(增2)：3 719–3 724.(TIAN Jiayong，WANG Enfu. Ultrasonic method for measuring in-situ stress based on acoustoelasticity theory[J]. Chinese Journal of Rock Mechanics and Engineering，2006，25(Supp.2)：3 719–3 724.(in Chinese))
[29] 田家勇，胡莲莲. 岩石声弹性理论与应用的研究进展[J]. 地球物理学进展，2010，25(1)：162–168.(TIAN Jiayong，HU Lianlian. Review of the acoustoelaticity in rocks[J]. Progress in Geophysics，2010，25(1)：162–168.(in Chinese))
[30] 董陇军，闫先航，裴重伟，等. 岩体多源声学设备在地压与顶板灾害监测防控中的应用[J]. 金属矿山，2023，(5)：185–194.(DONG Longjun，YAN Xianhang，PEI Zhongwei，et al. Case study of rock mass multi-source acoustic equipment in monitoring and prevention of ground pressure and roof disaster[J]. Metal Mine，2023，(5)：185–194.(in Chinese))
[31] 中国石油天然气股份有限公司. 一种岩石地应力检测方法和系统：201410844721.0[P]. 2016–07–27.(PetroChina Company Limited. A rock in-situ stress detection method and system：201410844721.0[P]. 2016–07–27.(in Chinese))
[32] 中国石油大学(华东). 一种基于岩石波速各向异性确定地应力方向的测量装置及方法：201510620941.X[P]. 2015–12–09.(China University of Petroleum (East China). A measuring device and method for determining in-situ stress orientation based on the anisotropy of rock wave velocity：201510620941.X[P]. 2015–12–09.(in Chinese))
[33] 刘延柱，陈立群，陈文良. 振动力学[M]. 3版. 北京：高等教育出版社，2019：38–62.(LIU Yanzhu，CHEN Liqun，CHEN Wenliang. Vibrational Mechanics[M]. 3rd ed. Beijing：Higher Education Press，2019：38–62.(in Chinese))
[34] 唐杰. 各向异性岩石的静态模量与动态模量实验研究[J]. 岩石力学与工程学报，2014，33(增1)：3 185–3 191.(TANG Jie. Experimental study of static and dynamic moduli for anisotropic rock[J]. Chinese Journal of Rock Mechanics and Engineering，2014，33(Supp.1)：3 185–3 191.(in Chinese))
[35] 李新平，赵航，罗忆，等. 深部裂隙岩体中弹性波传播与衰减规律试验研究[J]. 岩石力学与工程学报，2015，34(11)：2 319–2 326.(LI Xinping，ZHAO Hang，LUO Yi，et al. Experimental study of propagation and attenuation of elastic wave in deep rock mass with joints[J]. Chinese Journal of Rock Mechanics and Engineering，2015，34(11)：2 319–2 326.(in Chinese))
[36] 郑贵平，赵兴东，刘建坡，等. 岩石加载过程声波波速变化规律实验研究[J]. 东北大学学报：自然科学版，2009，30(8)：1 197–1 200. (ZHENG Guiping，ZHAO Xingdong，LIU Jianpo，et al. Experimental study on change in acoustic wave velocity when rock is loading[J]. Journal of Northeastern University：Natural Science，2009，30(8)：1 197–1 200.(in Chinese))
[37] 郭印同，杨春和. 川东北砂岩单三轴压缩过程中应力-波速变化规律的试验研究[J]. 矿业研究与开发，2009，29(3)：17–20.(GUO Yintong，YANG Chunhe. Experimental study on the change law between stress and velocity of longitudinal wave for the sandstone from northeastern Sichuan in uniaxial and triaxial compression[J]. Mining Research and Development，2009，29(3)：17–20.(in Chinese))
[38] 程礼军，潘林华，张烨，等. 页岩三轴压缩条件下的纵横波速特征[J]. 断块油气田，2016，23(4)：465–469.(CHENG Lijun，PAN Linhua，ZHANG Ye，et al. Velocity characteristics of P-wave and S-wave for shale reservoir under tri-axial compression experiments[J]. Fault-Block Oil Gas Field，2016，23(4)：465–469.(in Chinese))
[39] ZHANG G K，LI H B，WANG M Y，et al. Crack initiation of granite under uniaxial compression tests：A comparison study[J]. Journal of Rock Mechanics and Geotechnical Engineering，2020，12(3)：656–666.
[40] 晏先震，白海波，翟明磊. 不同层理倾角页岩的超声波传播特性研究[J]. 地下空间与工程学报，2021，17(增2)：552–559.(YAN Xianzhen，BAI Haibo，ZHAI Minglei. Experimental study on ultrasonic characteristics of shale rock with different bedding angle under uniaxial loading[J]. Chinese Journal of Underground Space and Engineering，2021，17(Supp.2)：552–559.(in Chinese))
[41] HARRYPERSAD-DANIEL A M，BLAKE O O，RAMSOOK R. Determining the static Young?s modulus and Poisson?s ratio，and compressive strength of the friable Erin Formation rocks using P-wave velocity[J]. Journal of Applied Geophysics，2022，198：104557.