Effect of the leakage of detonation products on the mechanical and elastic characteristics of a camouflet explosion

Abstract

In this paper we derive formulas enabling the calculation of the porosity of the material behind the front of the fracture wave, arising in the explosion, under very general assumptions about the behavior of the medium and the parameters characterizing it. The problem of expansion of a camouflet cavity and the emission of an elastic wave of the camoufiet discharge is solved. Based on model representations of the filtering of DP in the porous medium, forming behind the front of the fracture wave, it is shown that the leakage of PD strongly affects the mechanical and elastic characteristics of the eamouflet explosion. To describe the camouflet explosion we shall employ the well-known scheme based on the idea that the pores are selected instantaneously at the front of the fracture wave and that the plastic flow behind the front has a dilatant character [4, 5]. If the camouflet explosion is conducted in a porous medium, then the volume of the voids remaining behind the front of the fracture wave will be determined by the volumes of the cavities and not the completely closed pores. If the medium on the front of the fracture wave is pulverized, then the flow of the pulverized medium is accompanied by the diiatancy effect, which leads to loosening up of the medium and the formation of an additional pore space [4]. The detonation products can fill this pore space even at the cavity expansion stage, which causes the pressure in the cavity to drop and significantly reduces the mechanical effect of the explosion. The question of the calculation of the volume of the pore space of the medium after the explosion was discussed in [6, 7]. Using the results of [6], it is possible to calculate the volume of the unselected pores at the front of the fracture wave. A method for calculating the density of the medium after the explosion taking into account a dilatancy was proposed in [7], and the volume of the voids arising as a result of this effect was estimated; the latter estimate is valid if R >> a , where R is the radius of the fracture zone and a is the radius of the camouflet cavity. in this case it is necessary to have an expression for the volume of the pores that is valid for an arbitrary ratio of R and a, since gases can escape from the cavity at the starting stage of the explosion, when the condition R >> a does not hold. We assume that after the instantaneous detonation of the charge a fracture wave starts to propagate from the walls of the initial cavity. We assume that irreversible compaction of the medium and breaking up of the medium into separate blocks occur at the front of the fracture wave; the irreversible compaction is linked with the partial selection of pores. The remaining unselected porosity will not change in the subsequent post-front flow. We shall term this porosity intrablock porosity. The fractured material, consisting of separate blocks, whose density does not change, flows plastically. As a result of the dilatancy effect the medium is loosened up and an additional volume of voids forms. We shall term the porosity arising in this manner dilatant.