Plowshare Symposium (3d : 1964 : University of Cal.

Engineering with nuclear explosives; proceedings of the third Plowshare Symposium, April 21, 22, 23, 1964 online

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It is pertinent to describe the predictive pos-
sibilities of the proposed model of the gas accel-
eration phase of excavation (PUSH n). To do
this, PUSH II calculations have been performed
for a 0. 5-kt H. E. source emplaced at depth of
N x 7. 62 m, where 1 < N < 7. Estimates of
the apparent crater radius R have been prepared
as follows: (a) for N = 1, R c is approximated
as discussed in Section Vila, (b) for 2 < N < 5,
R C is well approximated by the projection of the
point of maximum curvature on the earth's free








H 50






I I I I \l I I I I I I I I I I


10 20 30 40 50 60 70 80 90 100

TIME 3.45 sec

Fig. 7. Calculated true crater for the Scooter event at 3. 45 seconds, prior
to collapse.

surface (at t^ plus a few seconds) along the sur-
face of stable repose to undisturbed ground level
(curve I in Fig. 10), and (c) for N > 5, it is very
likely that a quantitative collapse model is re-
quired before R c can be estimated well. The
above estimates of R c are shown in Fig. 10.
This figure also shows, for purposes of compar-
ison, the experimentally determined apparent
crater dimensions (Nordyke, 1961) for H. E.
sources in alluvium normalized to 1-kiloton yield.
It is evident that the R estimates prepared from
PUSH II are in reasonable agreement with exper-
iment for scaled depths of burial less than or
equal to 50 m.

The estimates of apparent crater depth for
shallow excavation, prepared in a manner dis-
cussed in Section Vila, are shown in Fig. V 10. A
comparison of these results with the observed
apparent crater depths suggests that for shallow
depths of burial, the PUSH II initial conditions
give a very reasonable estimate of apparent cra-
ter depth.

To date, the authors have not developed a
calculational model of the apparent crater config-
uration after collapse. The purpose of such a
model would be to estimate the final apparent
crater configuration from PUSH II mound condi-
tions at t plus several seconds. Such a collapse


I \ I I I I I I I I I I I I I I I I I

2O JO 40 SO bO 20

TIME 0.004 sec

90 100

10 20 10 40 SO 60 70 BO 40 1OO

TIME 0.014 sec

i I

I I I I I I I I I ! I I I I I I

20 SO 40 SO

TIME 0.024

I Xl 1 I I I 1 I I I I I I I

M 90 100 10 20 10 40 SO ii

i I

SO fcO 70

10 20

TIME 0.044 <-c

40 SO bO 70


Fig. 8. Calculated history of cavity, mound, and lip shallow burial.


I I I I \l I I I I I I I I I I I I I I

!0 10 )0 40 SO 60 70 80 90 100

TIME 1.061 st-c

20 30 40 50

TIME 1.561 i

40 50 60

TIME a. 061 sec

TIME 2.561 !

Fig. 9a. Calculated history of cavity, mound, and lip deep burial.

model is probably required before more refined
estimates of apparent crater radius and depth
become available.


This study has developed a simple, two-
dimensional, numerical-physical model of crater-
ing physics during the gas acceleration phase of
excavation for high- explosive sources in alluvium.
Further, the estimates of the apparent crater

radius and depth (for certain types of craters)
obtained from the model compare favorably to
the observed apparent crater dimensions. The
application of this model to deeper burial leads
to an upward-moving chimney of gas which at
late times radially accelerates the surface mate-
rial. This radial change in material motion re-
quired by the theory with deep burial suggests
that extrapolation of experimental crater dimen-
sion data to large scaled depths of burial (greater
than about 65 meters) is probably unreliable.



1. Butkovich, T. R. , "Calculation of the Shock Wave from an Underground Nuclear Explosion in Granite,"
Plowshare Symposium, April 1964.

2. Feigenbaum, S. A. and P. L. Wegkamp, Final Report, "Photographic Earth Motion Study Scooter
Event, " Edgerton, Germeshausen, and Grier, Inc., Report No. L-510, 1961.

3. Holloway, J. L. , "Smoothing and Filtering of Time Series and Space Fields," Advances in Geo-
physics, 4, pp. 351-388, 1958.

4. Holmboe, J. , et al. , (1964), "Dynamic Meteorology," John Wiley Co. , New York, N. Y. , p. 378.

5. Knox, J. B. and R. W. Terhune, "Cratering Physics Concepts Derived from an Analysis of Ground
Surface Motion," Lawrence Radiation Laboratory, Livermore, Rept. UCID-4664, 1963.

TIME i.Sfcl src

10 20 W

40 50 M> 70

TIME 4.061

HO '>0 100

10 ^0 JO 40 50

TIME 4.561 sec

70 SO ^0 100

Fig. 9b. Calculated history of cavity, mound, and lip- deep burial.


20 30 40 50 60 70

TIME 5.061 sec

i I i I \i I i I i I i I i I i I i I i

20 30 40 50 60 70

TIME 5.56) *ec

10 20 JO 40 50 60 70 80 90 100

TIME 6.061 ate

10 20 30 40 50 60 70

TIME 6.561 ec

Fig. 9c. Calculated history of cavity, mound, and lip deep burial.

6. Levine, J. , "Spherical Vortex Theory of Bubble- like Motion in Cumulus Clouds," J. Meteor., 10.
pp. 653-662, 1959.

7. Maenchen, G. and J. H. Nuckolls, "Calculation of Underground Explosions, " Lawrence Radiation
Laboratory, Livermore, Kept. UCRL-6438, Part II, p. Jl-6, 1961.

8. Malkus, J. S. and R. T. Williams, "On the Interaction Between Severe Storms and Large Cumulus
Clouds," Meteor. Monographs, _5, Wo. 27, pp. 59-64, 1963.

9. Nordyke, M. D. , "On Cratering. A Brief History, Analysis, and Theory of Cratering," Lawrence
Radiation Laboratory, Livermore, Rept. UCRL-6578, 1961.

10. Nuckolls, J. H. , "A Computer Calculation of Rainier (the First 100 Milliseconds)," Lawrence
Radiation Laboratory, Livermore, Rept. UCRL-5675, pp. 120-134, 1959.

11. Ferret, W. R. , A. J. Chabai, J. W. Reed, L. J. Vortman: "Project Scooter. " Final Report,
Sandia Laboratory, Albuquerque, New Mex. , p. 168, October 1963.


12. Priestley, C. H. B. , "Turbulent Transfer in the Lower Atmosphere," The University of Chicago
Press. , p. 130, 1959.

13. Rawson, D. E. , "Review and Summary of Some Project Gnome Results," Lawrence Radiation
Laboratory, Livermore, Rept. UCRL-7166, p. 17, 1962.






















Oj 10














DEPTH OF BURST (M/kt 1 / 3 ' 4 )

Fig. 10. PUSH II estimates of apparent crater radius and depth compared to experimental
results (H. E. sources in alluvium).


Computational Scheme

Given the following quantities at t


n n n n

W Gi' r Gi' P c' r ci' r c,0


n = 1 - t = t

n = n+l-t = t+At

i jjth mass element

> i > 4 > 6 > 90

~ ~ i

the calculation scheme is as follows:

n 3 [/ n\4 / nyll /[/ n\3 / n\_,
L ^ = ll( r Gi) -( r ci)J/[( r Gi) -( r ci)j l "' J

2. cm. = (r n f - (r n ) 3 " N * , :^"~'~ ~~~- ,

i \ Gi/ V ci/

/_n\3 / n\3

3. cm2. .. (r. ) -(r^J i = O,/

n/ n\2//_n\2
; i( r Gi)/( r i) i = ^

i/ n\2// n\2
( r Gi)/( r ci)


W i W Gi

n n n2/ n\2

W ci W Gi

n/ n\2 / n\2

3p (r . ) 3p (r^. )
_^n *c\ ci F a\ Gi /

6_^_" \s \ <^i. / a\ \ji / . ll

w. = - - g cos . - Kw. ; _

i p cm. p cm

i i

7. From derivatives of steps 4, 5, 6

.- n ^.n . n . n
W i' V W Gi' W ci

_n+l _n _n. ^n (At) 2 ^(At) 3 ^ (At) 4

8. r. = r. + w. At + w. N ' + w *-r*- + \v - 1 <

i i i i 2 6 24

9. n = n+l t = t + At


10. r- - - .

'^ =' ' '^ '

n 2 3



13 P D = p (y /v n V
c c , \ c , c /

14. W. n step 6 i = 0,

n n-1 / - n . n-l\ At

15. W. = W. +(w. + W ) - i = 0,

n n

16. w . , w_. step 4,5

ci Gi

17. Return to step 7.



Free-Surface Velocity at Time t

Consider a Cartesian coordinate system, origin at ground zero, with coordinate axes (x,y) shown
in Fig. B-l. In this appendix, the following notations and definitions are used:

V Q is the radial particle velocity associated with the compressional wave at the free surface
U. is the x-component of the free-surface velocity
V is the y-component of the free-surface velocity

X is the ratio of the compressional velocity to the shear velocity
6 is the angle of incidence of compressional wave

6 is the angle of reflection of shear wave


w is the peak radial spall velocity


W is yield of the explosive

D is depth of burial

a is an empirical constant

m is an empirical constant.

For an initial horizontal free surface, v is approximated by:

i A a o w

V :: 2 W s "\2 m

\ r


The x, y components of the surface velocity at t are:


U i = V

A 2 \ /B


A *V V , N

-T )sm 9 - r Tjcos (9
V p A i\P s >

7 A 2\ B 2 la \

(1 - jcos (9 -(-sin 6 }
\ A I P A IB sy
\ If 1 \T /

where, ( ) and! Jare found by simultaneous solution of






Fig. B-l. Geometrical definitions for prescription of free- surf ace velocity at t

(l - -r^Jcot 6 + -(cot 2 6 - l) =
\ V P V

P 2


+ 2 - cot
A l

= 0.

The angles 6 and 6 are related by:
P s


sin 6 = sin 9 .
s a p

Constants for the calculation of U., V. in alluvium are as follows:

a = 36. 58 m/sec,

m = 2.142,
f) = Ll



Joseph B. Knox was born in Pittsburgh, Pennsyl-
vania. From 1942 to 1946, he served as a meteorolo-
gist with the U.S. Army Air Force in the Mediterranean
Theater of Operation. He received his B.A. (1949),
M.A. (1950), and Ph.D. (1955) degrees from the
University of California at Los Angeles.

From 1955 to 1958, Dr. Knox served as Instruc-
tor and Assistant Professor in the Department of
Meteorology at UCLA. At the same time, he was
engaged as a consultant to the Rand Corporation in
connection with the prediction of radioactive fallout.
Since 1958, he has been associated with the Law-
rence Radiation Laboratory with primary interests in
dynamical wind prediction, numerical analysis,

fallout prediction, meteorological and hydrological
safety problems connected with the engineering
applications of nuclear explosives, and cratering
physics. Since October 1963, he has served as
Group Leader for the Plowshare Theoretical and
Computations Group.

Robert Terhune is a native of Seattle, Washing-
ton. He received the B.S. in Physics from San Diego
State College in 1961. He was employed as a physicist
by General Dynamics, San Diego, California, from
1961 to 1963. Since 1963 he has been employed as a
physicist at the Lawrence Radiation Laboratory,




W. C. Sherman, Jr.
W. E. Strohm, Jr.

U. S. Army Engineer Waterways Experiment Station
Vicksburg, Mississippi


The study of th engineering properties of
nuclear-explosion-produced craters has thus far
been limited primarily to the Sedan crater in desert
alluvium and the Danny Boy crater in basalt. Ex-
tensive preshot and postshot field and laboratory
investigations have been made to evaluate the preshot
engineering properties of the media and the changes
which occur in these properties as a result of the
explosions. In addition to changes in basic engi-
neering properties, such as density and shear strength,
large-scale effects such as strata distortion, displace-

ments, and fracturing in the cratered media have been
investigated. Results of the studies of the Sedan and
Danny Boy craters are presented. The nature and
characteristics of the fallback materials and dis-
turbed materials beyond the crater are presented.
Various engineeiing problems associated with the use
of explosion-produced craters are outlined and the
limitations imposed on the use of cratering for
excavations because of the scarcity of empirical
data are discussed.


The tremendous energy unleashed by nuclear
explosions provides an answer to man's continuous
quest for more practical and economical means of
accomplishing large-scale earthmoving projects.
Since nuclear excavations can be made for as
little as 1/10 to 1/20 the cost of conventional ex-
cavations, the benefit to large excavation and
earthmoving projects is obvious. In nuclear ex-
cavations , very large and very deep excavations
are dealt with for the reason that excavation costs
per unit volume are inversely proportional to the
yield of the device. No precedents exist to per-
mit a forecast of all the problems resulting from
the practically instantaneous removal of huge
quantities of material from great depths below
the ground surface; consequently, it is essential
to examine very closely the effects of, and engi-
neering problems attendant to , the initial experi-
ments involving the use of nuclear explosions in
moving earth.

For over a year , the U. S. Army Engineer
Waterways Experiment Station (WES) has been
conducting an investigation of the engineering
properties of nuclear craters, the objective being

to develop procedures for evaluating the stability
of slopes and the strength of foundation materials
adjacent to nuclear excavations for use in future
engineering projects. In addition, a theoretical
study is being made of the cratering mechanisms
affecting the engineering properties of crater
media. This paper outlines available information
on the engineer ing properties of materials adjacent
to nuclear craters and how these properties affect
the engineering utilization of these excavations and
adjacent materials.

General Plan

Because of the infinitely varied soil, rock, and
geologic conditions which may be encountered in
nature, it would be impossible to evaluate all the
possible changes in engineering properties of
material that might occur as a result of an explo-
sion-produced crater. Thus far, the investiga-
tions have been limited to relatively homogeneous
deposits. The basic approach to the problem is
twofold: First is the empirical approach in which
extensive preshot and postshot investigations are


samples. Geophysical logs similar to those made
in thepreshot borings were also made in the post-
shot borings and the results were compared.

The results of the postshot field mapping indi-
cated that the surface of the ejecta along the cra-
ter lip varied from 35 to 95 ft above the preshot
ground surface. The upward displacement of the
preshot ground surface varied from 2 to 17 ft.
Mapping and examination of the trenches indicated
that the ejecta consisted primarily of foldback ma-
terials. Foldback materials consist of relatively
undisturbed strata found in inverted order along
the edge of the crater. In the northeast quadrant,
where the ejecta thickness was greatest and a large
slide had occurred shortly after detonation , ejecta
consisted of slide blocks, relatively undisturbed
masses of material which are believed to have been
moved laterally from an initial position within the
cratered area by the blast. The ejecta investiga-
ted retained its original structure and stratifica-
tion, and results of field density tests in this ma-
terial indicated that the densities did not differ
significantly from the natural soil densities.

The fallback materials in the crater consisted
of loose, silty, sandy gravel with cobbles and boul-
ders , and the measured field densities near the
surface were as low as 70 Ib per cu ft, which is
near the minimum density on the basis of labora-
tory tests conducted. Measurements of the slope
angle of the fallback material indicated that the
slope had an average angle of repose of 35; which
agrees with the angle of internal friction deter-
mined in the laboratory on these materials in their
loosest state.

A comparison was made of the preshot and
postshot densities of the material below the pre-
shot ground surf ace based on the results of the ge-
ophysical Densilogs and also on the arithmetic av-
erage of densities of the undisturbed samples. No
evidence of a decrease in density which might ac-
count for the observed upward displacement of the
preshot ground surface was noted. On the con-
trary, the results indicated that, on the basis of
the Densilogs, the average dry density increased
after detonation about 11 to 12 Ib per cu ft at a dis-
tance of 600 to 600 ft from ground zero and in-
creased about 3 to 6 Ib per cu ft at a distance of
800 ft from ground zero. Although undisturbed
samples were not obtained from the preshot bor-
ing made 600 ft from ground zero, it is probable
that the preshot dry densities were equal to those
of samples from borings at 800 ft from ground

zero; on this basis, the weighted average dry den-
sity at a distance of about 600 to 660 ft was at the
most only several pounds per square foot greater
than the preshot density. Comparison of preshot
and postshot undisturbed sample densities at 800
ft from ground zero also indicated little or no in-
crease in density, which is not in accord with the
increase indicated by the Densilogs. It is consid-
ered that the undisturbed sample densities are
more reliable than the Densilog densities, since
Densilog results are affected by the degree of sat-
uration of the material forming the walls of the bor-
ings , and there probably were differences in this
respect between preshot borings and postshot bor-
ings. This is possible since postshot borings were
filled with drilling mud for a longer time prior to
logging than were the preshot borings.

The crater slopes above the upper limits of the
fallback materials include exposed portions of the
true crater surface and ejecta. The slopes in these
materials are extremely ragged, reflecting dis-
tortions caused by the explosive forces of the det-
onation and subsequent slumping of the crater walls
into the crater. The average slope of the surface
of these upper materials is about 38 , although in
many instances some of the strata are found stand-
ing at much steeper slopes for limited vertical dis-
tances. The angle of internal friction, <>' , of the
in-situ soils adjacent to the upper slopes was
found in laboratory tests to range between 40 and
48 , with an average value in the order of 43 . Ig-
noring any effects of cementation which may be
present, the factor of safety of these upper slopes
with respect to sliding is given by the expression:

Factor of Safety, FS =

tan 43

tangent 0'

tangent of slope angle

tan 38

This factor of safety indicates relatively stable
slopes, although environmental effects such as
weathering by wind and rain will have considerable
influence on the final slopes. Latent disturbance
beyond the crater walls which was not disclosed
by the subsurface explorations may also affect the
stability of the slopes. Available data indicate that
the upper slopes of the crater walls receded as
much as 12 ft in a 3-1/2-month period. This deg-
radation will continue, probably at a decreasing
rate as the slopes tend to flatten with time.


made of cratered media to evaluate fully the
changes resulting from a nuclear detonation. At
the present time WES has completed an investiga-
tion of the Sedan crater and has partially com-
pleted an investigation of the Danny Boy crater;
the results of these investigations will be de-
scribed subsequently. An important phase of this
work is to delineate and define those properties of
a deposit which are of interest from an engineer-
ing standpoint. Of particular importance are
those properties which affect the behavior and sta-
bility of large, jointed rock masses as nuclear
detonation would be most advantageous in excava-
ting rock. Current knowledge on this subject is
very meager, and, consequently, the study of the
stability of natural and cut slopes in rock is a ne-
cessary supplement to the field investigations of
nuclear craters in rock. The second approach,
which may be termed the "theoretical approach,"
involves the development of a suitable theory or
theories for predicting the changes that would
occur in media of various types and conditions
using data from models and field tests.

Theoretical Studies

A theoretical study of cratering mechanisms
affecting the engineering properties of crater me-
dia is being conducted for WES by Dr. A. B. Vesic
of the Georgia Institute of Technology. 1 A pre-
liminary theory has been developed which enables
rational analysis of camouflets , subsidence cra-
ters, and the deep craters that are of primary in-
terest from an engineering standpoint. In this
theory, it is assumed that the material adjacent
to the cavity behaves as a rigid-plastic solid,
whose strength can be defined by a Mohr's enve-
lope. The theory indicates that the efficiency of
nuclear charges as compared with conventional
explosive charges of the same energy yield de-
pends on the properties of the crater media, as
well as on the depth of burst and the level of the
yield. Further extensions of the theory are now
being made to include such effects as soil dilat-
ancy, compression in the plastic zones, strain
hardening, etc. An analysis of all major crater-
ing investigations in the light of the new theory is
being conducted in connection with these problems.
Theoretical and experimental studies are also be-
ing conducted to gain information on excess pore
water stresses which might develop in the media
adjacent to the crater, as well as on volume and

structural changes such as fracturing and remold-
ing of various types of soils.

Sedan Event

The Sedan 100-kt subsurface shot on 6 July
1962 at the Nevada Test Site formed a crater ap-
proximately 320 ft deep and approximately 1200 ft
in diameter. Geologic and soils investigations
were made prior to the shot to determine the prop-
erties of the subsurface soils and to provide a
basis for estimating the changes in these proper-
ties resulting from the detonation. The locations
of preshot and postshot borings are shown in Fig.
1. The subsurface soils at the Sedan site are made
up of a series of alluvial beds, which consist pri-
marily of silty to sandy gravel (generally well
graded) to a depth of 1200 ft. All of the materials
exhibited some degree of cementation and, al-
though the degree varied widely, the strength of
the cementation was relatively weak in most cases.
The ground-water table at the site was about 1600
ft below ground surface and, consequently, had no
bearing on either the cratering mechanism or the
stability of the resultant slopes.

The preshot field investigation included two
undisturbed borings, U-l andU-2, to depths of
200 and 430 ft at distances of 800 and 400 ft, re-
spectively, from ground zero to obtain 6-in. -di-
ameter undisturbed samples, and two split-spoon
borings to depths of 200 and 300 ft at distances of
1100 and 600 ft, respectively, from ground zero.
The borings were made along aline bearing N 45
W from ground zero. Because of the presence of
large gravel sizes , penetration data from the split-
spoon borings were of little value. Drilling mud
had to be used in all borings and considerable dif-
ficulty was encountered in obtaining the undis-
turbed samples because of the gravel. Various
geophysical logs were made of each of the four
borings. Of the various logs (Densilog, Electro-
log, Focus Log, Gamma-ray/neutron, and Min-
ilog/caliper) , only the Densilog provided useful
information. Only about one month was available
for the preshot field work, and all desired work
was not accomplished; however, it is believed
that the initial subsurface conditions were reason-
ably well defined.

Laboratory testing of the preshot undisturbed
samples consisted of natural density and relative
density determinations; triaxial compression
shear strength tests; and classification tests, in-


eluding determinations of grain size, specific
gravity, and chemical constituents. Testing of
the undisturbed samples was extremely difficult
because of the gravelly nature of the material. In
general , the preishot investigations indicated that
the materials were relatively uniform in character
to the depths investigated (about 430 ft), except
that the upper 110 ft contained somewhat more silt
and less gravel than the underlying soils. In the
upper 110 ft the natural density increased with
depth from about 93 Ib per cu ft at a depth of 32 ft
to about 113 Ib per cu ft at a depth of about 110 ft;
otherwise , no important differences in soil prop-
erties were noted. Below a depth of about 110 ft,
the foundation soils were found to be at an average

Online LibraryPlowshare Symposium (3d : 1964 : University of CalEngineering with nuclear explosives; proceedings of the third Plowshare Symposium, April 21, 22, 23, 1964 → online text (page 9 of 36)