静水沉降激波模型及其解答

Shockwave model and Lagrangian series solution of quiescent sedimentation

从混合物理论出发 ,建立了以土体颗粒体积含量为控制变量的土体静水沉降方程。该模型具有一阶非线性波动方程的形式 ,因此 ,可以将泥沙开始沉降的过程看作是一个出现激波的过程。在此基础上得到了某些特殊条件下的Lagrange级数解答。最后 ,通过尾矿沉降池实例分析 ,验证了所得解答的合理性和有效性。

Based on the mixture theory, a mathematical model for the sedimentation of soils in the steady water is established, depending on the volume fraction of the soils. The results show that the progress of the sedimentation of the soils is similar to the propagation of the shock wave, and thus the 'blow up' of the solution can be treated as the beginning of the sedimentation. Under certain initial conditions, the analytical solution is obtained by Lagrangian series method. Finally, the rationality and the validity of the solution achieved are shown by a case study.