We consider the propagation of nonlinear plane waves in porous media within the framework of the Biot–Coussy biphasic mixture theory. The tortuosity effect is included in the model, and both constituents are assumed incompressible (Yeoh-type elastic skeleton, and saturating fluid). In this case, the linear dispersive waves governed by Biot’s theory are either of compression or shear-wave type, and nonlinear waves can be classified in a similar way. In the special case of a neo-Hookean skeleton, we derive the explicit expressions for the characteristic wave speeds, leading to the hyperbolicity condition. The sound speeds for a Yeoh skeleton are estimated using a perturbation approach. Then we arrive at the evolution equation for the amplitude of acceleration waves. In general, it is governed by a Bernoulli equation. With the present constitutive assumptions, we find that longitudinal jump amplitudes follow a nonlinear evolution, while transverse jump amplitudes evolve in an almost linearly degenerate fashion.

我们在 Biot-Coussy 双相混合理论的框架内考虑非线性平面波在多孔介质中的传播。模型中包含曲折效应，并且假设两个成分都是不可压缩的（Yeoh 型弹性骨架和饱和流体）。在这种情况下，Biot 理论支配的线性色散波是压缩波或剪切波类型，非线性波可以用类似的方式分类。在新胡克骨架的特殊情况下，我们推导出特征波速的显式表达式，导致双曲线条件。Yeoh 骨架的声速是使用扰动方法估计的。然后我们得到加速度波振幅的演化方程。通常，它由伯努利方程控制。