Correlation between stress and P-wave velocity in rock under uniaxial compression
MA Chi1, 2, WANG Peitao1, 2*, CHEN Ziming1, 2, HUANG Hao1, 2, ZHOU Baokun1, 2, MA Qiangying1, 2, CAI Meifeng1, 2
(1. Key Laboratory of Ministry of Education for Efficient Mining and Safety of Metal Mine, University of Science and Technology Beijing, Beijing 100083, China; 2. School of Resources and Safety Engineering, University of Science and Technology
Beijing, Beijing 100083, China)
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.
马 驰1，2，王培涛1，2*，陈子鸣1，2，黄 浩1，2，周宝坤1，2，马强英1，2，蔡美峰1，2. 单轴压缩条件下岩石纵波波速与应力相关性研究[J]. 岩石力学与工程学报, 2026, 45(8): 2354-2369.
MA Chi1, 2, WANG Peitao1, 2*, CHEN Ziming1, 2, HUANG Hao1, 2, ZHOU Baokun1, 2, MA Qiangying1, 2, CAI Meifeng1, 2. Correlation between stress and P-wave velocity in rock under uniaxial compression. , 2026, 45(8): 2354-2369.
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