具有双曲跳跃条件的裂隙岩石中一维弹性P波建模
Modeling 1-D elastic P-waves in a fractured rock with hyperbolic jump conditions
AI总结：
本文利用Bandis-Barton模型推导的非线性跳跃条件，通过理论分析和数值模拟研究裂隙岩石中弹性P波的传播，证明了初边值问题的适定性，并展示了接触非线性对波传播的影响。
摘要：
从理论和数值上研究了弹性波在裂隙岩石中的传播。在裂隙外部，压缩波的传播在一维线性弹性动力学的简单框架下描述。重点在于波与裂隙的相互作用：为此，使用从地球力学中经典使用的Bandis-Barton模型推导的非线性跳跃条件对裂隙的力学行为进行建模。证明了所得初边值问题的适定性。通过将时域有限差分方案与考虑跳跃条件的界面方法相结合进行数值模拟。数值实验显示了接触非线性的影响。产生的谐波可能提供评估裂隙力学性质的非破坏性手段。
英文摘要：
The propagation of elastic waves in a fractured rock is investigated, both theoretically and numerically. Outside the fractures, the propagation of compressional waves is described in the simple framework of one-dimensional linear elastodynamics. The focus here is on the interactions between the waves and fractures: for this purpose, the mechanical behavior of the fractures is modeled using nonlinear jump conditions deduced from the Bandis-Barton model classicaly used in geomechanics. Well-posedness of the initial-boundary value problem thus obtained is proved. Numerical modeling is performed by coupling a time-domain finite-difference scheme with an interface method accounting for the jump conditions. The numerical experiments show the effects of contact nonlinearities. The harmonics generated may provide a non-destructive means of evaluating the mechanical properties of fractures.
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