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Combustion, Explosion, and Shock Waves, Vol. 40 , No. 6, pp. 674–678 , 2004

Craters of Large-Scale Surface Explosions

UDC 550.348+5512V. V. Adushkin

1

and B. D. Khristoforov

1

Translated from Fizika Goreniya i Vzryva , Vol. 40, No. 6, pp. 71–75, November–December, 2004.Original article submitted May 28, 2004.

Results of experimental studies of craters of chemical and nuclear surface explosions

with commensurable heights of the center of mass and TNT equivalents on soils of

different types are presented. Available databases were used, which are generally

utilized for predicting ecological consequences of natural and man-induced explosive

catastrophes, development of new methods of monitoring and identification of phe-

nomena under consideration, and their experimental and mathematical modeling.

Key words: explosion, explosion crater, databases, ecology.

INTRODUCTION

The year 2004 is the 100th anniversary of M. A. Sadovskii, an outstanding specialist in the field of explosion physics, who was the academic leader of manyprograms with the use of large-scale explosions [1]. Theresults of those studies are still important because of the natural and man-induced catastrophes, which havebecome more frequent [2]. Some results of investigat-ing parameters of craters formed by large-scale surfaceexplosions performed at different test sites, which were

based on available databases [3, 4], are described below.

CRATERS OF CHEMICAL

AND NUCLEAR EXPLOSIONS

The data on conditions of explosions of high explo-sives (HE) and crater sizes are summarized in Table 1.The database [3] contains geological sections under ex-plosion epicenters, obtained on the basis of geologicalresearch and seismic logging. Soil Nos. 1 and 2 aresoft soils with shallow and deep bedding of rocks andground water, respectively; soil No. 3 is weathered frac-

tured rock with a density of ≈2800 kg/m3

and witha velocity of longitudinal seismic waves of ≈3 km/sec;the velocity of sound in individual blocks being equalto ≈5.5 km/sec. In soil Nos. 2 and 3, the craters arenormally formed within the indicated layer of rocks.Craters of large-scale explosions in soil No. 1 usuallyinclude the bottom rock as well.

1Institute of Geosphere Dynamics, Russian Academyof Sciences, Moscow 119334; [email protected].

The geological sections under the epicenters of ex-plosion No. 4 with a mass of 1000 tons under permafrostconditions in soft soil No. 1 and explosion No. 6 with amass of 1152 tons in soft soil No. 2 with deep beddingof rocks and ground waters are described in Tables 2and 3. For conditions of explosion No. 6, the geologi-cal section to a depth of 350–400 m is a mixed bed of sediments followed by rocks. The sediments are alter-native strata of dense hardened clay, sand, sandstone,siltstone, and cretaceous mudstone.

Figures 1 and 2 show the photograph and the typi-

cal profile of the crater formed by a surface HE explosionwith a TNT equivalent q = 5000 tons. Figure 3 showsthe crater dimensions (volume V [m3], radius R [m],and depth H [m]) as functions of the parameter q in therange 1 q 5000 tons for HE explosions on soft (Nos.1 and 2) and firm (No. 3) soils (see Table 1). The valuesof H and V of explosion No. 3, which took place in thecrater of the previous explosion, are ignored. Statisti-cal processing of power lines of the trend yielded thefollowing empirical dependences of the crater volume,radius, and depth as functions of the TNT equivalentfor different soils.

— Soil Nos. 1 and 2:

V = 26.72q 0.999, r2 = 0.963;

R = 3.36q 0.336, r2 = 0.979;

H = 1.78q 0.316, r2 = 0.907;

674 0010-5082/04/4006-0674 c 2004 Springer Science + Business Media, Inc.

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Craters of Large-Scale Surface Explosions 675

TABLE 1Parameters of Craters of Surface HE Explosions

No. TS q, ton S R, m H , m V , m3 No. TS q, ton S R, m H , m V , m3

5 2 5000 1 55 21.4 120,000 52 2 50 3 10.8 3.4 600

6 7 1152 2 34.2 12 23,500 56 2 20 1 7.5 4.5 380

7 2 1013 2 34.4 14 25,900 55 2 15 3 6.6 2.28 140

4 1 1000 1 26.7 16.5 — 16 3 12 1 8 — —

1 3 901 1 35 12 11,600 17 2 10 1 6.75 3.25 209

3 2 501 3 21 14.1 7791 18 2 10 1 7.53 3.5 308

2 2 500 3 20.9 7.9 5,540 19 2 10 1 7 4.75 304

27 2 500 3 22.5 7.5 6000 20 2 10 1 8.28 5.1 394

31 2 330 1 22.2 9.4 — 33 2 10 2 7.3 4 223

24 2 300 3 25.8 9.6 4470 34 2 10 2 8.8 4.4 —

12 2 280 2 26.7 14.1 13,100 35 2 10 2 7.35 4.53 —

22 2 250 1 19.3 8.5 5020 36 2 10 2 7.28 3.9 278

28 2 200 3 13.5 3.5 1250 37 2 10 2 7.02 3.03 218

30 2 155 1 17.2 8.9 — 38 2 10 2 7.3 3.2 203

29 2 150 2 21.3 10 6170 42 2 10 2 7 3.95 —

10 2 100 2 16.5 11 3150 43 2 10 3 6.85 3.25 190

11 2 100 2 17.5 10 3200 45 2 10 3 5.1 1.9 85.5

13 2 100 2 16.2 9 3565 46 7 10 2 6.8 2.5 173

14 2 100 2 17 10.8 4325 47 2 10 2 7 3.2 —

15 2 100 2 17.4 10.7 4430 51 2 10 3 4.9 — —

21 2 100 1 15.2 7.2 2140 58 2 10 1 7.25 4.28 —

23 2 100 1 18.2 7.6 4200 49 2 5 3 5 2.5 —

25 7 100 2 14.2 6.62 1820 40 2 1 2 3.4 1.55 —

26 2 100 2 15.2 7 2600 41 2 1 2 2.75 1.3 —

32 2 100 1 18 6.6 3 440 44 2 1 3 3 1.3 20.7

57 2 80 1 16 7.4 — 48 2 1 2 3.5 1.5 —

39 2 50 1 11.9 5.5 940 53 2 1 3 3.65 0.86 12

50 2 50 3 10 3.85 — 54 2 1 3 3 0.96 12.5

Notes. R, H , and V are the crater radius, depth, and volume, counted from the free surface; No. is thenumber of the explosion in the database [3], q is the TNT equivalent of the explosion, TS is the code of thetest site (2 and 7 refer to the Semipalatinsk test site), and S is the code of soil.

— Soil No. 3:

V = 16.40q 0.937, r2 = 0.973;

R = 2.76q 0.335, r2 = 0.958; (1)

H = 1.25q 0.305, r2 = 0.821;

— Soil Nos. 1, 2, and 3:

V = 19.37q 1.021, r2 = 0, 946;

R = 3.21q 0.336, r2 = 0.961;

H = 1.49q 0.332, r2 = 0.845.

Here r2 is a statistical function determining the reliabil-

ity of approximation of experimental data by empiricalformulas (if they coincide, r2 = 1). The data on craterdepth are in worst agreement with the trend lines. Theform of the formulas also depends on the range of q . Insoft soil Nos. 1 and 2, for 1 q 100 tons, we have

V = 18.86q 1.104, r2 = 0.95;

R = 3.20q 0.355, r2 = 0.973;

H = 1.55q 0.355, r2 = 0.893.

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676 Adushkin and Khristoforov

TABLE 2Geological Section under the Epicenter of Explosion No. 4 (see Table 1)

Depth, m Material Density, tons/m3 c, km/sec

0–2 Crumbly crushed stone 1.75 —

2–6 Pebbles with gravel 1.62 2.92

6–7 Pebbles with gravel 1.85 1.0–1.1

7–9 Clay sand with pebbles and gravel 1.9 3.27

9–13 Sand — —

Below 13 Clay sand with pebbles and gravel — —

Note. c is the velocity of longitudinal seismic waves.

TABLE 3Geological Section under the Epicenter of Explosion No. 6 (see Table 1)

Depth, m Material Density, tons/m3

c, km/sec

0–3 Sand; clay sand 1.6 0.2–0.4

3–20 Sandstone 1.7–1.8 0.7

20–50 Loamy soil; clay with sand inclusions 1.8–1.9 1.0–1.1

50–400 Clay; sandstone 1.9–2.0 2.0–2.1

Below 400 Slate — 4.5

Fig. 1. Photograph of the surface HE explosion with aTNT equivalent of 5000 tons.

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Craters of Large-Scale Surface Explosions 677

Fig. 2. Typical profile of the crater produced by thesurface HE explosion with a TNT equivalent of 5000 tons:the crater radius on the free surface is 55 m, the craterradius over the ejection is 70 m, the radius of soil ejectionis 360 m, the radius of scattering of rock fragments is1500 m, the crater depth from the free surface is 21.4 m,and the crater volume over the free surface is 120,000 m3;the charge is shown by the dashed curve.

The data of American researchers on contact ex-plosions (q = 1–18 tons) in soft soil of the Nevada testsite are described by the dependences [5]

V = 26q, R = 3.6q 1/3, H = 1.6q 1/3, (2)

which are similar to formulas (1).The empirical dependences of crater parameters as

functions of the TNT equivalent for 11 nuclear explo-sions and 53 chemical explosions performed at differ-ent sites of the Semipalatinsk test site are given be-low. Based on the data of [3, 4], nuclear explosions(Fig. 4) commensurable in terms of the height of thecenter of mass and TNT equivalents with HE explo-sions were chosen (a total of 32 surface explosions wereperformed).

For nuclear explosions with a TNT equivalent q = 300–14,300 tons at heights of 0.5–2.1 m (H/q 1/3

= 0.02–0.2 m/tons1/3), we have

V = 0.449q 1.084, r2 = 0.808;

R = 0.707q 0.389, r2 = 0.855; (3)

H = 0.563q 0.327, r2 = 0.754;

for HE explosions with a TNT equivalent q = 1–5000 tons, we have

V = 18.57q 1.038, r2 = 0.946;

R = 3.17q 0.340, r2 = 0.961; (4)

H = 1.49q 0.331, r2 = 0.828.

DISCUSSION OF RESULTS

The approximation (r2) of the dependences of crater parameters on the TNT equivalent by power

Fig. 3. Crater volume, radius, and depth versus the TNTequivalent of surface explosions: on soft soil of type Nos. 1and 2 (a) and on firm soil of type No. 3.

functions is much less reliable in the case of nuclear ex-plosions than in chemical explosions. The coefficientsin expressions for the volume, radius, and depth fornuclear explosions are smaller than the coefficients forchemical explosions by a factor of 41, 4.5, and 2.7, re-spectively. As the normalized height of nuclear explo-sions H/q 1/3 decreases, the crater size increases andapproaches, with increasing charge depth, values typ-ical of HE explosions, yet remaining significantly lower.The dependence of the normalized volume of craters of the nuclear explosions on the TNT equivalent in therange −0.1 < H/q 1/3 < 2 (with q varied from 500 to1200 tons and with the values of H varied from theheight of 1.067 m to a depth of 20.4 m), which were ob-tained in tests at the Nevada test site, has the followingform [5]:

V /q = −5.53(H/q 1/3)2 + 39.83H/q 1/3 + 5.26. (5)

We have V /q = 5.26 m3/ton for H = 0 and V /q = 30.8 m3/ton for the half-embedded charge of castTNT [5].

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678 Adushkin and Khristoforov

Fig. 4. Crater volume, radius, and depth versus theTNT equivalent of nuclear surface explosions.

For the explosions considered, the dependences of crater parameters on the TNT equivalent obey the prin-ciple of geometric and energy similarity within the mea-surement error. The influence of the force of gravity,which can reduce the crater diameter because of thefallout of the ejected soil back and for which R ∼ q 1/3.4

according to [5] and R ∼ q 1/3.5 according to [6], was notobserved here.

The data obtained allow one to determine the in-fluence of the volume concentration of energy in thesource on the mechanical action and ecological conse-quences of the explosion and can be used in operationsassociated with safety of population and various objectswith allowance for the risk of natural and man-inducedcatastrophes, including determination of criteria, meth-ods, and systems of protection of potentially hazardousobjects.

CONCLUSIONS

1. A statistical analysis of experimental data onthe size of craters of chemical and nuclear surface explo-sions with commensurable heights of the center of massand TNT equivalents q = 1–5000 and 300–14,300 tons,respectively, has been performed.

2. It is shown that the coefficients in the depen-dences of the crater volume, radius, and depth on theTNT equivalent for nuclear explosions are smaller thanthose for chemical explosions by a factor of 41, 4.5, and2.7, respectively. The difference in the mechanical ac-tion of nuclear and chemical explosions decreases withincreasing depth of explosion.

3. The dependences of crater parameters on theTNT equivalent in large-scale surface explosions agreewith the principles of energy similarity and, within themeasurement error, are independent of the force of grav-ity.

This work was supported by the Russian Founda-tion for Basic Research (Grant No. 02-05-64134).

REFERENCES

1. M. A. Sadovskii, Geophysics and Physics of Explosion

[in Russian], Nauka, Moscow (1999).2. V. V. Adushkin, V. V. Garnov, and B. D. Khristoforov,

“Estimation of parameters of an emergency explosion

by comparisons with test explosions,” Bezopas. Trud.

Prom., No. 4, 28–32 (2001).3. V. V. Adushkin and B. D. Khristoforov, “Database on

nuclear and large-scale chemical explosions with ejection

into the atmosphere,” Registered Certificate No. 2863

dated December 12, 1997 (Registered as No. 0229703124

in the State Register); Database “Natural and man-

induced catastrophic phenomena such as explosions

with ejection of products into the atmosphere,” Reg-istered Certificate No. 7568 dated December 29, 2001

(Registered as No. 0220108099 in the State Register).4. V. N. Mikhailov, V. V. Adushkin, I. A. Andryushin, et

al. (eds.), Nuclear Tests in the USSR [in Russian], Vol. 2,

IzdAT, Moscow (1997), p. 320.5. L. J. Vortman, “Craters from surface explosions and

scaling laws,” J. Geophys. Res., 73, No. 14, 4621–4631

(1968).6. B. A. Ivanov, “The effect of gravity on crater formation:

thickness of ejecta and concentric basins,” in: Proc. Lu-

nar Sci. Conf. 7th (1976), pp. 2947–2965.

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