Wang Shuaifeng, Zhang Zixin, Huang Xin, Lei Qinghua
Department of Geotechnical Engineering, College of Civil Engineering, Tongji University, Shanghai, People's Republic of China.
Key Laboratory of Geotechnical and Underground Engineering, Ministry of Education, Tongji University, Shanghai, People's Republic of China.
Rock Mech Rock Eng. 2023;56(4):2717-2736. doi: 10.1007/s00603-022-03180-4. Epub 2022 Dec 19.
The arrival behavior of elastic waves in a naturally fractured rock is studied based on numerical simulations. We use the discrete fracture network method to represent the distribution of a natural fracture system and employ the displacement discontinuity method to compute the propagation of elastic waves across individual fractures. We analyze macroscopic wavefield arrival properties collectively arising from the interaction between elastic waves and numerous fractures in the system. We show that the dimensionless angular frequency = / exerts a fundamental control on the arrival behavior of a plane wave traveling through the fractured rock, where , , and are the angular frequency, seismic impedance, and fracture stiffness, respectively. An asynchronous arrival phenomenon of the wave energy occurs and becomes more significant with an increased . Two regimes are identified according to the two-branch dependency of the fractal dimension of the FFAW on , where the wave arrival behavior is within a non-fractal regime for smaller than the critical frequency ≈ 1.0, and enters the fractal regime for ≥ . The self-affine properties of the FFAW, i.e., the roughness exponent and the correlation length , both linearly decrease as a function of the exponent (with = 10 ) in the fractal regime. Early breakthrough of wave transport occurs in regions with relatively low fracture density, while late-time arrival happens in regions of high fracture density.
基于数值模拟研究了弹性波在天然裂隙岩石中的传播行为。我们使用离散裂隙网络方法来表示天然裂隙系统的分布，并采用位移不连续方法来计算弹性波在单个裂隙中的传播。我们分析了系统中弹性波与众多裂隙相互作用共同产生的宏观波场传播特性。结果表明，无量纲角频率 ω = ω /(Zκ) 对穿过裂隙岩石的平面波的传播行为具有根本性的控制作用，其中 ω、Z 和 κ 分别为角频率、地震阻抗和裂隙刚度。波能量出现异步到达现象，并且随着 ω 的增加变得更加显著。根据自由表面波（FFAW）的分形维数 D 对 ω 的双分支依赖性，确定了两种状态，其中当 ω 小于临界频率 ωc ≈ 1.0 时，波的传播行为处于非分形状态，而当 ω ≥ ωc 时进入分形状态。在分形状态下，FFAW 的自仿射特性，即粗糙度指数 α 和相关长度 ξ，都随指数 γ（γ = 10α）呈线性下降。波传播的早期突破发生在裂隙密度相对较低的区域，而晚期到达则发生在裂隙密度高的区域。
