25. In spite of certain difficulties that arise in the analysis of empirical relations and that are due to the absence of a physical model for the energy dissipation of the mechanical effect in rock, the parameters of the compressive waves may be predicted, on the basis of accumulated experience, with a precision sufficient for practical applications. (e) The seismic effect of an explosion 26. The seismic effect of an explosion is predicted by means of empirical relations. The conditions of an explosion are characterized by the energy, the depth at which the charge is placed, and the properties of the rock in which the charge is placed. The frequency-amplitude characteristics of the surface vibrations depend upon the geological structure along the propagation route of the seismic wave and upon the properties of the soil at the recording site. The large number of parameters which determine the seismic effect do not allow us to obtain simultaneously both a high precision and a sufficient universality of empirical formulae. 27. In essence, the seismic process of an explosion includes three independent problems: (1) the excitation of seismic waves due to the explosion; (2) the propagation of seismic waves in heterogenous media; (3) the effect of seismic vibrations upon the structures, including consideration of the properties of the foundation. 28. The first problem is actually reduced to a determination of the parameters for individual groups of waves in the immediate vicinity of the source (at distances on the order of the wave length), depending upon the conditions of the blast. A distinction should be made between deep explosions in which the fracture zone is separated from the free surface by a layer of undisturbed soil, and explosions close to the surface. In the case of deep explosions, the seismic wave is formed by a spherical compression wave and the equivalent source may be considered an expansion center. In explosions performed close to the surface, the source has a complex nature and this is evident in the redistribution of energy between individual wave groups. The experimental data available indicate that the force of gravity plays a considerable role in the process of formation of the seismic signal. The dependence of the seismic wave parameters upon the explosion energy does not, therefore, fit the frame of a simple geometric similitude. 29. The second problem consists in the finding of ways of accounting for the peculiarities of the geological structure along the propagation route of the seismic wave. The difficulties encountered are created by the fact that rocks under conditions of natural stratification present a rather heterogeneous medium, which differs considerably from an ideal elastic body. The nature of energy absorption of elastic waves in rock has still not been clarified, although this factor plays an essential role in the process of transformation of the seismic signal. 30. The third problem is connected with the establishing of the boundaries of the safety zone from the standpoint of ground shock. It has been determined in an experimental manner (applicable to rather small explosions) that the maximum amplitude of displacement of the surface is the critical parameter which determines the danger zone for seismic effects. This statement, in principle, was first formulated in the Soviet Union at the end of the 1930's and apparently has been generally accepted. It has been established that damage to low-rise buildings and other similar structures becomes apparent when the amplitude of the velocity reaches approximately 10 cm/sec. However, large nuclear explosions have demonstrated that this criterion is insufficient when the duration of the motion increases. 31. The seismic effect is an extremely important factor and determines in many cases both the possibility of conducting and the effectiveness of using underground nuclear explosions in previously developed industrial regions. Keeping in mind the modern level of scientific achievements, it is absolutely necessary to conduct special experimental explosions, striving to identify possible seismic situations in the areas of planned work using nuclear charges. In this manner, a substantially greater reliability of prediction of the seismic effect may be achieved. METHODS OF PREDICTION OF THE MECHANICAL EFFECT OF CRATERING EXPLOSIONS 32. The parameters of a cratering explosion, such as the dimensions of the apparent crater, the volume of the ground ejected, and its distribution over the surface, are determined by means of empirical formulae. The experience gained in using chemical cratering explosions has shown that the volume of the craters is proportional to the explosion energy. In accordance with the geometrical similitude law, the formula for calculating the charge has the following structure: k- the coefficient which considers the properties of the rock and the efficiency of the explosives. 33. Experimental investigations of chemical cratering explosions have established a series of rules: (a) The dimensions of the crater are determined by the magnitude of the kinetic energy of the ejected matter, which attains approximately 10 percent of the total energy of the explosion. (b) The development of the ejection in time has three stages: During the first stage, the motion of the medium is symmetrical, as it is in an underground explosion. The kinetic energy is transmitted by means of the compression wave, which simultaneously fractures the rock in the future crater. The symmetrical growth of the cavity practically ends at the conclusion of the first stage. During the second stage, the ejected rock noticeably increases its kinetic energy due to the plunger effect of gases in the cavity; this energy attains its maximum value when the top of the dome on the surface rises to a height equal to W. The dome of ground breaks up into individual pieces and the boundaries of the future crater begin to appear. The third stage is the trajectory of pieces in the gravity field. (c) The effect of the force of gravity upon the dimensions of the crater becomes noticeable as soon as the kinetic energy of the ejected rock and the work of lifting of the soil dome completed at the time of its destruction become commensurate. Due to this fact, the limit of applicability of geometrical similitude in computing the charges accompanied by ejections may be determined. It appears that in explosions of charges weighing 1,000 tons and more of TNT, the force of gravity plays a substantial role in the process of the formaion of the crater and should be considered as one of the determining parameers. Quite naturally, this critical value of the charge depends upon the properies of the rock and may be much smaller in explosions made in loose soil. 34. In the light of statements made above on the development of a cratering explosion, two peculiarities of a nuclear explosion, already mentioned, acquire he greatest importance: (1) The high initial energy concentration, thus stipulating the dependence of thermodynamic parameters of the explosion products upon rock properties; (2) The large scale of the explosions, thus excluding the application of the geometrical similitude law when predicting the mechanical effect. We may expect that the plunger effect of the gases in the second stage of crater development will (in the case of a nuclear explosion) depend to a considerable degree upon the moisture in the rock and upon the presence of minerals which discharge gaseous products during thermal decomposition. A large-scale explosion involves the manifestation of the role of the force of gravity as well as the necessity to consider the changes in the mechanical properties of rock with depth. Thus, for instance, the strength of the rock, the scale of heterogeneities, and the distribution of cracks may all change considerably, depending upon the depth; the methodology of their determination, even under conditions of natural stratification, has not yet been completely worked out. The peculiarities of a nuclear explosion given above, combined with all ensuing consequences, make us doubt that the method presently used in the nalysis of experimental data is sensible; this method aims at obtaining a ingle computation formula for the determination of the dimensions of the jection crater. 35. The theoretical computations of a cratering explosion present a picure of the lifting of the dome of ground which conforms with practice. Howver, the importance of these results should not be exaggerated, since the ondition of the medium and its behavior during large-scale deformations are ot quite known yet. This circumstance hampers the formulation of the condions which define the radius within whose limits the soil is ejected and preludes the computation of the dimensions of the apparent crater which is formed s a result of the failure of the slopes. Research is strongly recommended on modeling explosions which would larify the structure of the connections between the basic parameters of the rocess. A special installation simulating cratering explosions in loose soils has een designed at the Institute of Terrestrial Physics of the USSR Academy of ciences; this facility has provided us with very encouraging results, particurly, on the dependence of the crater radius upon the explosion energy. 36. The problems associated with seismic safety during cratering exploons are the same problems encountered during underground explosions, as we Ive already stated. It should be added that (for the most part) cratering exploons will be of the group type, which makes it necessary to study in great detail e problems of interference of waves excited by several or many sources. 37. In conclusion, we should emphasize once again that the unsolved probms listed above cannot raise any doubts as to the possibilities of an efficient e of nuclear explosions in industry and construction. |