Towards to task about flat charge explosion in double-layer environment

Abstract

There is considered the problem of the explosion of a flat charge in two-layer medium, while the plane of the charge is close to the environment’s contact in a much more rigid half-space. Considered only the time interval in which there is a medium wave Riemann's load. An exact solution of a quasilinear wave equation with zero initial and inhomogeneous boundary conditions is obtained by the method of characteristics. The problem is reduced to a nonlinear integral-differential equation for the pressure acting on the half-contact. In general, non-linear models of physical environments found Lagrange coordinate place of origin of the shock wave from a simple load. Under the assumption that the behavior of the medium is described by the Prandtl model with rigid load, the contribution of wave loading and unloading in the value of the half-space contact’s displacement. If the numerical values of the parameters characteristic of the conditions of underground mining, the contribution of the wave load is approximately 6%, which makes it quite acceptable accuracy to solve more simple problem of the unloading wave impact. With the removal of the charge from the contact plane of the half-wave contribution to the load begins to increase. The proposed solution of a quasilinear wave equation different physical clarity, allowing, for example, is easy to solve the problem of wave loads in a heterogeneous environment of hardening.