Nonstationary plane waves in media with bulk viscosity

The solution of the problem of propagation of a wave in soils is presented for the case when the wave is produced by the detonation of a spherical charge of some explosive material (EM). The solution is obtained on a computer by the method of characteristics. The soils are regarded as multicomponent media consisting of solid particles, water, and air in conformity with the model proposed in [1, 2]. The dependence of the pressure, velocity of the particles, and the density in the wave front on the distance is determined; the variation of these parameters with time at fixed points of the medium is also determined. The results are compared with the results of tests [1, 2]. Their close agreement for different contents of the components indicates the applicability of the multicomponent model to soils. The limits of applicability of the model are determined. The propagation of a plane wave under the same conditions was investigated in [3].

Spherical blast waves in multicomponent media

The problem of an explosion is considered on the basis of a model of a viscoplastic medium. It follows from the solution that the theoretical dependence of the cavity radius on the time coincides satisfactorily with the experimental data. The introduction of viscosity into the scheme of the motion leads to the appearance of the scaling effect. From an analysis of the stress field, a conclusion follows concerning the existence, even in the initial stage of motion, of intense tangential tensile stresses, which lead to the formation of a system of radial fissures, observed in the experiment.

Development of a camouflet cavity as a result of an explosion in soft ground

In [i, 2], a viscoplastic soil model was proposed. Below, on the basis of this model, the problem of the interaction of a plane one-dimensional wave and a fixed or displaceable barrier is solved using a computer and the method of characteristics. In [2, 3] the wavepropagation problem was solved on the basis of the same model. The results of blast-waveparameter measurements, indicating that the viscous and plastic properties of soils have an important effect on the wave-propagation characteristics, were presented in [2, 4-6].

Wave-barrier interaction in a viscoplastic medium

Questions of similarity and the scattering of waves in viscoplastic media

Models of elastoplastic media are applied to soils and rocks [1, 2]. In conformity with experimental data [3–5] a model of soils and rocks as a viscoplastic medium has been proposed [6]. Below we give a solution, based on this model, of the problem on the propagation of a plane one-dimensional wave. As the basis of computer programs we propose a finite-difference representation of the equations of motion of a continuous medium in Lagrange coordinates and the differential equations governing the behavior of the medium. A “direct calculation” procedure with pseudoviscosity is applied. It is shown that the damping of plane waves is connected with two energy-dissipating mechanisms, determined by the viscous and plastic properties of the medium. The washing out of a discontinuity can occur in the absence of a segment of the dynamical compression curve that is concave to the strain axis. Under certain conditions the maximum strain is attained during the phase of decreasing stress. These results agree with the experimental data [3].

G. M. Lyakhov

Papers

Calculation of viscous and plastic properties by the solution of wave problems