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AD NUMBER
AD891964
NEW LIMITATION CHANGE
TOApproved for public release, distributionunlimited
FROMDistribution authorized to U.S. Gov't.agencies only; Test and Evaluation; 19 JAN1972. Other requests shall be referred toAir Force Weapons Lab., AFSC, KirtlandAFB, NM.
AUTHORITY
AFWL ltr, 6 Feb 1974
THIS PAGE IS UNCLASSIFIED
-IAFWL-TR-71-144 AFWL-TR-
-~iA :~~'71-144
I THE INFLUENCE OF SOIL AND ROCKPROPERTIES ON THE DIMENSIONS OF
EX PLOSIO N-PRODUCED CRATERS
Larry A. Dillon
Mai USAF
00 The Texas A&M Research Foundation
TECHNICAL REPORT NO. AFWL-TR-71-144
-' AIR FORCE WEAPONS LABORATORY
Distribution 'limited to U.S. Government agencies only becauseof test and evaluation (19 Jn 72). Other requests for this
~document must Be -referred to AFWL (0EV).
AFWL-TR-71-144
AIR FORCE WEAPONS LABORATORYAir Force Systems CommandKirtland Air Force Base
New Mexico 87117
When US Government drawings, specifications, or other data are used forany purpose other than a definitely related Government procurement operation,the Government thereby incurs no respnsibility nor any obligation whatsoever,and the !act that the Government may have formulated, furnished, or in any waysupplied the said drawings, specifications, or other data, is not to beregarded by implication or otherwise, as in any manner licensing the holderor any other person or corporation, or conveying any rights or permission tomanufacture, use, or sell any patented invention that may in any way berelated thereto.
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DO NOT RETURN THIS COPY. RETAIN OR DESTROY.
DDCDA
.....1IO ..........
'"'''~ ~ .......... L
............. ........ QDE 'i
DIST.
4E0
AFWL-TR-71-144
THE INFLUENCE OF SOIL AND ROCK PROPERTIES
ON THE DIMENSIONS OF EXPLOSION-PRODUCED CRATERS
Larry A. DillonMaj USAF
The Texas A&M Research Foundation
TECHNICAL REPORT NO. AFWL-TR-71-144
Distribution limited to U. S. Government agenciesonly because of test and evaluation (19 Jan 72).Other requests for this document must be referred
to AFWL (DEv)
_ _ _ __ __ __
6I• i F _
AFWL-TR-71-144
FOREWORD
This report was prepdred by the Texas A&M Research Foundation, CollegeStation, Texas, under Contract F29601-70-C-0032. This research was performedunder Program Element 61102H, Project 5710, Task SA102, and was funded by theDefense Nuclear Agency (DNA).
Inclusive dates of research were February 1970 through October 1971. Thereport was submitted 27 December 1971 by the Air Force Weapons LaboratoryProject Officer, Major Neal E. Lamping (DEV-G). The former project officerwas Captain Peter M. Terlecky.
This project was supervised by Dr. Louis J. Thompson whose help and encour-agement made it possible. Mr. Steve Clark provided invaluable research aid.Captain Paul Knott provided and modified the computer plotting program.
Appreciation is extended to Mr. Robert W. Henny, AFWL; Mr. Luke J. Vortman,Sandia Laboratories; Mr. Robert W. Terhune, Lawrence Radiation Laboratory; andto Lt Colonel Robert L. LaFranz and the many helpful people of the US ArmyEngineer Nuclear Cratering Group for providing data.
This technical report is the result of research performed at the GraduateCollege of Texas A&M Oniversity in partial fulfillment of the requirement forthe degree of Doctor of Philosophy in Civil Engineering for Major Larry A.Dillon.
This technical report has been reviewed and is approved.
NEAL E. LAMPINGMajor, USAFProject Officer
E ALD G. LEIGH WILLIAM B. LIDDICOETMajor, USAF Colonel, USAFChief, Facilities Survivability Chief, Civil Engineering ResearchBranch Division
ii
AFWL-TR-71-144
ABSTRACT
(Distribution Limitation Statement B)
\Analysis of data from published cratering experiments showsthe effect of soil and rock properties on the apparent dimensions
•: ~ of explosion produced crate. -More than 200 cratering testsnd relatedmtaterial properties were cataloged. The data con-
Isisted of 10 nuclear events whose yields varied from 0.42 to 1007 /kilotons and about 200 high explosive events whose yields variedfrom 1 to 1 million pounds of TNT. The different test sitesincluded materials for which the density ranged from 60 to 170pounds/cubic foot.
"- -By regression analysis, using bell shaped cu-ves,.predictionformulas were developed for the apparent crater radius, depth,and volume as a function of charge weight and depth of burst foreight different types of materials. The bell curves werenormalized using material properties and prediction equationswere generated using all the data. These general equations werethen studied to determine the specific effects of the materialproperties on resultant apparent crater dimensions.
S -Mterial properties are highly important in determining thesize of explosion-produced craters.cnd some of the more importantproperties are unit weight, degree ub satFration, she-aring s~i--..-taoce and seismic velocity. Previous investigators have beensomewhat negligent in measuring material properties for pastcratering experiments and no real data analysis can be made untilthe variables are either controlled or measured. Materialproperties which should be measured for future tests should atleast include the above properties and if possible the material'senergy dissipation and bulking characteristics. Better yet areasonably simple theory of cratering is needed which will betterdefine the material properties governing cratering mechanics.
iii/iv
Iij
-V -- - - _ _ _ __44- - - -NCONTENTS
Section
I INTRODUCTION ..... ..................... ...
II GENERAL CONCEPTS AND TERMINOLOGY............ 3
JI General Description of the Cratering Process 3Crater Terminology ...... ................ 5Cratering Mechanisms ..... ................ 7Effects of Depth of Burst ...... ............ 9
III REVIEW OF PREVIOUS CRATERING RESEARCH .......... ... 12
Nuclear Cratering Experience .... ........... 12High Explosive Cratering Experience ... ........ 12Symposiums Related to Cratering ............ ... 13Prediction Techniques and Scaling ... ......... 15Material Property Effects ... ............. ... 19
IV PURPOSE, SCOPE AND PROCEDURE ... ............ ... 21
V EXPERIMENTAL DATA ... ............... ..... 23
Data Acquisition ..... .. ................ 23Data Cataloging .... .................. ... 24Data Sorting ..... .. ................... 27
VI EMPIRICAL DATA ANALYSIS ..... ... ... .... 29
Regression Analysis .29Regression Approaches Considered'and'Tried" . . 31Regression Model Used ..... ............... 32Determination of Best Scaling Exponent ...... 34Equations and Data Plots for Specific Materials . 35Discussion of Approach Used .... ............ 38
VII MATERIAL EFFECTS ....... ................... 42
incorporation of Material Properties ....... .. 42Effects of Material Properties ... .......... 46
I Material Property Definition .... ........... 47Material Properties Used in This Research ..... 49Cratering Mechanics and Material Properties . . . . 54
V
4
<
gA~
CONTENTS (Continued)
Section PaeVIII CONCLUSIONS AND RECOMMENDATIONS .... ............ 56
APPENDIXES
I -CATALOGED CRATER DATA ..... .............. 61
Notations and Definitions. ......... .. 61Cataloged Crater Data .... ........ 65Cataloged Material Property Data ........ 65Notes ...... ...................... .65
II - THE COMPUTER PROGRAM ..... .............. 94
Description of the Program Elements.......... 94Typical Program .................... .. 96Sample Data Output ..... ............... 96
III - DATA AND PREDICTION CURVE PLOTS ............ 117
IV - GENERAL EQUATION COEFFICIENTS ............ 132
V - MATERIAL PROPERTY EFFECT PLOTS...... ... 139
REFERENCES ..... ....................... .147
vi
i "~
ILLUSTRATIONS
Figure Page
1 Cross Section of a Typical Crater ......... 4
2 Dimensional Data for Single Charge Crater . . . 8
3 Crater Profiles vs. Depth of Burst in Rock . 10
4 Estimated Relative Contribution of the VariousMechanisms to Apparent Crater Depth .l. .... 11
5 Crater Radius as a Function of Charge Depthfor Clay Shale....... . . .. .. . .. 118
6 6 Crater Depth as a Function of Charge Depth forClay Shale ....... ................ 118
7 Crater Volume as a Function of Charge Depth forClay Shale ...... .................. 119
8 Crater Radius as a Function of Charge Depth for, Desert Alluvium. ...................... 119
9 Crater Depth as a Function of Charge Depth for[(I Desert Alluvium ............. .l....9120
10 Crater Volume as a Function of Charge Depth forDesert Alluvium ..... ............... 120
11 Crater Radius as a Function of Charge Depth forSand. .. ........ ................ 121
12 Crater Depth as a Function of Charge Depth forSand ................ . .... 121
13 Crater Volume as a Function of Charge Depth forSand ....... .. .. .. .. ... ... 122
14 Crater Radius as a Function of Charge Depth forBasalt ....... .................... 122
15 Crater Depth as a Function of Charge Depth forBasalt ....... .................... 123
vii
'PI
ILLUSTRATIONS (Continued)
Figure Page
16 Crater Volume as a Function of Charge Depth forBasalt ....... .................... 123
17 Crater Radius as a Function of Charge Depth forAlluvium (Zulu Series) .... ............ 124
18 Crater Depth as a Function of Charge Depth forAlluvium (Zulu Series) .... ............ 124
19 Crater Volume as a Function of Charge Depth for
Alluvium (Zulu Series) .... ............ 125
20 Crater Radius as a Function of Charge Depth forVarious Rock ..... ................. 125
21 Crater Depth as a Function of Charge Depth for
Various Rock ..... ................. 126
22 Crater Volume as a Function of Charge Depth forVarious Rock ..... ................. 126
23 Crater Radius as a Function of Charge Depth forPlaya (Air Vent Series) ............ 127
24 Crater Depth as a Function of Charge Depth forPlaya (Air Vent Series) .... ............ 127
25 Crater Volume as a Function of Charge Depth forPlaya (Air Vent Series) .... ............ 128
26 Crater Radius as a Function of Charge Depth forPlaya (Toboggan Series) .... ............ 128
27 Crater Depth as a Function of Charge Depth forPlaya (Toboggan Series) .... ............ 129
28 Crater Volume as a Function of Charge Depth forPlaya (Toboggan Series) .... ............ 129
29 Crater Radius as a Function of Charge Depth forAll the Data ..... ................. 130
viii
ILLUSTRATIONS (Continued)
Figure Pae
30 Crater Depth as a Function of Charge Depth forAll the Data ...... ............... 130
31 Crater Volume as a Function of Charge Depth forL All the Data .. ....... .............. 131
32 Crater Volume as a Function of Charge Depth andPercent Saturation, S, for Specific Gravity =2.55 and Dry Unit Weight = 80 Pounds/CubicFoot ..... ..................... 140
33 Crater Volume as a Function of Dry Unit Weightand Percent Saturation, S, for Optimum ChargeDepth and Specific Gravity = 2.55 ....... 141
34 Crater Radius, Depth and Volume as a Functionof Percent Saturation for Optimum Charge Depth,Specific Gravity = 2.55 and Dry Unit Weight =
80 Pounds/Cubic Foot .... ............. 142
35 Crater Radius, Depth and Volume as a Functionof Percent Saturation for Optimum Charge Depth,Specific Gravity = 2.75 and Dry Unit Weight =160 Pounds/Cubic Foot .... ............ 143
36 Crater Radius, Depth and Volume as a Function~of Dry Unit Weight for Optimum Charge Depth,
Specific Gravity = 2.55 and Percent Saturation =
40 ....... ...................... 144
37 Crater Volume as a Function of Charge Depth andDry Unit Weight, Yd' Pounds/Cubic Foot, forSpecific Gravity = 2.65 and Percent Saturation =40 ........ .. ................. 145
38 Crater Volume as a Function of PercentSaturation and Dry Unit Weight, yd, Pounds/Cubic Foot, for Optimum Charge Depth andSpecific Gravity = 2.55 . ....... .. .. 146
ix
TABLES
Table Page
1 Equation Coefficients for Various Materials 36
2 Cataloged Crater Data ..... ............. 66
3 Cataloged Material Property Data ... ....... 74
4 General Equation Coefficients for Radius . . 133
5 General Equation Coefficients for Depth .... 135
6 General Equation Coefficients for Volume . 137
x
-"4NOTATION
The following symbols are used in this report:
Ai : coefficient of bell curve in coded form;
B. = coefficient of bell curve;
C, general coefficient;
D crater depth;
D = maximum depth of the apparent crater;
-- Dob : depth of burst;
Ev = vaporization energy;
Gs grain bulk specific gravity;
Hal : apparent crater- lip crest height;
La : linear apparent crater dimension
(radius, depth,or cube root of volume);
M = general material property;
R = crater radius;
Ra = radius of apparent crater;
Rm2 = multiple correlation coefficient
S = degree of saturation;
SGZ = surface ground zero;
TNT = the high explosive, trinitrotluene;
V crater volume;
Va volume of apparent crater;
W = weight of explosive;
xi
NOTATION (Continued
ZP = zero point-effective center of explosion energy;
c = seismic velocity;
exp = exponential (e);
g = acceleration due to gravity;
ln = natural logarithm;
m = the divisor portion of the scaling exponent, 1/m;
tan = tangent of the angle of shearing resistance;
x,y = rectangular Cartesian coordinates;
y = total unit weight;
Yd = dry unit weight;
p = mass unit weight.
xii
SECTION I
INTRODUCTION
Over the past several years, because of intensified studies
of possible engineering applications of nuclear energy, increased
attention has been devoted to the problem of cratering by explo-
sives. One of the most obvious peaceful applications of nuclear
explosives is that of earth excavation, as might be considered
for the construction of harbors, dams, or canals. Prediction
and design for survival of silo-launched missile systems has
also added urgency to these studies.
Although most investigators have recognized that the size
of a crater obtained from an explosive charge depends upon the
media in which it is detonated, properties describing the media
1, which relate to the dimensions of this crater are somewhat
obscure. The primary purpose of this investigation, then, was
to determine which engineering properties normally measured for
earth and rock materials could be related to the size of a
crater created by an explosive charge.
A large number of cratering experiments have been conducted
in various media (15,60,87). These experiments primarily
ii.
provided data on the effect of explosive energy and depth of
burst on crater dimensions. Although the experiments number
in the thousands and although engineering material properties
were measured for a good percentage of these experiments, very
little has been reported which relate these material properties
to the final crater geometry. Previous investigators seem to
have been of two minds: (1) Because material properties vary
greatly within one media in one location and because accurate
measurement of these properties is often difficult, the best
approaches are to ignore completely the material properties or
to over simplify and let the material be described by one
constant in a particular prediction relationship; and (2) be-
cause the cratering process is so complicated, extensive
measurement of material properties both in the field and in
the lab are required to describe the media to be subjected to
an explosive charge. It would appear that the better solution
lies somewhere between these two extremes.
I
I
SECTION II
GENERAL CONCEPTS AND TERMINOLOGY
This sectioq of the report presents basic concepts concern-
ing the parameters and mechanisms involved in the explosive
formulation of craters. The effect of explosive weight, depth
of burst and type of material are discussed. Ttrininology
generally associated with the cratering process is also presented.
General Description of the Cratering Process (63). When an
explosion occurs at or near the surface of a soil or rock-like
material, a crater is formed (see Fig. 1). The size of this
crater depends on at least four factors: (1) The energy re-
leased by the explosion; (2) the position of the explosive rela-
tive to- the surface; (3) the material type; and (4) gravitational
effects. The influence of the energy release is obvious, the
larger the charge, the larger the crater. When the charge is
on or above the ground surface, cratering effects are small.
As the charge is placed deeper in the ground, the size of the
crater increases, both in radius and depth, until a maximum is
reached after which the crater size will decrease with in-
creasing depth of burial. For deeply buried explosives, an
underground cavity is formed. Tile surface itself may be raised
and may eventually subside to form a depression crater. For
materials which bulk during the explosion process, there is a
region where rubble mounds will be formed. Mounding and
3!
LuI
z0N
z L
0
u<w
-- J-
LL.,
IVII
Lu-j
0 C0
0LL Lu
0, 0 0
C)
< Lu
0
-J U
zU <'C
Lu
< vi
Z u V)
<4
LLIL
0 V
1 .subsidence depend upon the material and depth of burst. The
larger the material's energy-dissipative properties, thesmaller the crater size will be. The size of the apparent crater
is affected by the amount of fall-back material, that is, the
material originally ejected which returns under gravity to
the crater zone.
U , Crater Terminology (22,27). A few basic terms and
i definitions are preBented to provide an acquaintance with
significant zones, dimensions and terminology used throughout
the report. Again referring to Fig. 1, the cross section of a
typical crater and the adjacent zones of disturbance are shown.
The apparent crater is defined as that portion of the
visible crater which is below the preshot ground surface. The
apparent crater would be the net design excavation for most
engineering applications.
The true crater is defined as the boundary (below preshot
ground level) between loose, broken, disarranged fall-back
materials and the underlying rupture zone material which has
been crushed and fractured, but has not experienced significant
displacement or disarrangement. The true crater boundary is
not a distinct surface of discontinuity, but rather a zone of
transition between the rupture zone and fall..back materials.The apparen,: lip is composed of two parts, the true lip,
which is formed by the upward displacement of the ground surface,
and the ejecta material deposited on the true lip.
5
The visible crater comprises the apparent crater and the
apparent lip.
The fall-back consists of natural materials which have
experienced significant disarrangement and displacement and
have come to rest within the true crater.
The ejecta consists of material thrown out above and
beyond the true crater.
The rupture zone is that zone extending from the true
crater boundary in which crushing and fracturing have occurred.
The plastic zone is that portion of the cratered medium
beyond the rupture zone in which permanent deformation has
occurred.
The elastic zone extends beyond the plastic zone and is
characterized by the absence of blast produced fissures,
cracks, or permanent displacement of material.
The optimum depth of burst is that depth for a specified
explosive charge which produces the largest crater. For any
one charge in any one medium, there may be three optimum depths
of burst depending upon whether the largest radius, depth, or
volume is desired.
A scaled dimension refers to a particular crater dimension
divided by the explosive weight of the charge to some power
(usually between 1/4 and 1/3). IF the proper exponent is
sele ted, scaling between different sized explosive charges for
a particular scaled depth of burst is then possible.
6
Crater dimensional data used in this report along with
accompanying symbols and definitions is given in Fig. 2. A
Ui detailed description of all pertinent single-charge crater
dimensional data can be found in reference 22.
Cratering Mechanisms (27,38,46). The primary mechanisms
or processes which produce craters in rock or soil may be
categorized as: (1) Vaporization and melting of the material
immediately surrounding the source of a nuclear explosion;
(2) crushing, compaction, fracturing, and plastic deformation
of the medium closely surrounding the explosive gas cavity;
(3) spalling of the surface; (4) acceleration of the fractured
material overlying the explosion by trapped gases; and (5) sub-
sidence and fall-back of the material as the explosive pressure
fgoes to zero and the force of gravity predominates.
The tremendous pressures resulting from an explosive
detonation (10-100 million atmospheres for a nuclear explosive)
generate a shock wave which propagates as a high-pressure
discontinuity. This high-pressure discontinuity, or shock front,
transfers energy to the medium, and in turn, alters the physical
characteristics of the medium. In the immediate vicinity of a
nuclear explosion, vaporization and melting of the material
occurs. The peak pressure in the shock wave diverges and energy
is expended in doing work on the medium. When the pressure
and shear stress levels exceed the dynamic crushing strength of
the material, work on the medium is manifested in crushing,
7U °hI2I'I V
---
1 4
=- I
J SG7--2 EJjT -- . _ _
H 1 4 6b" -b TRUE CRATER LIP (UPTHRUST)• , -.*.: .-- PRESHOT GROUND SURFACE
FALLBACK "-' : TRUE CRATER BOUNDARY
Ra - Radius of apparent crater measured at preshotground surface
Da - Maximum depth of apparent crater below preshotground surface
I Hal - Apparent crater lip crest height above preshotground surface
Va - Volume of apparent crater below preshot groundsurface
Dob - Depth of burst (distance to ZP from SGZ)
ZP - Zero Point-effective center of explosion energy
SGZ - Surface Ground Zero (poipt on surface verticallyabove ZP)
FIG. 2. DIMENSIONAL DATA FOR SINGLE CHARGE CRATER
8
heating, displacementand deformation of the material. When
the compressive and shear waves which propagate from the
detonation encounter the surface, a tensile wave and another
shear wave are reflected, and since the tensile strengths of
rock and soil are much less than their compressive strengths,
spalling of the surface occurs. Rock also tends to spall along
pre-existing fractures and planes of weakness. The first two
processes may be classified as short term mechanisms since
they last only a fraction of a second. Gas acceleration, on
the other hand, is a comparatively long-period process which
imparts motion to the material around the explosion by the
,adiabatic expansion of gases trapped in the cavity. Finally
the force of gravity pulls all the overlying fractured and
crushed material into the cavity and pulls all the loose
I material thrown into the air by spalling and gas acceleration
back into and around the crater. What remains is an apparent
crater underlayed with crushed and displaced material.
Effects of Depth of Burst. The part each of the above
mechanisms play in producing a crater is very strongly
dependent upon the scaled depth of burst of the explosion and
the medium in which the detonation occurs. Shown in Fig.
are typical crater cross sections in rock showing the effect
of depth of burst. As summarized by Nordyke (46), Fig. 4,
j the contribution of each of the mechanisms to apDarent
Icrater depth as a function of the charge depth of burst is shown.
-~1
U.j
I-I
U-
U-
C/)
.Pfl --0 U0
0
~ILI.l
71~
CL
TOTAL
LU GAS ACCELERATION
zLu
COMPACTION & SUBSIDENCE
CL
S PALL
DEPTH OF BURST
FIG. 4. ESTIMATED RELATIVE CONTRIBUTION OF THE VARIOUSMECHANISMS TO APPARENT CRATER DEPTH (FROM NORDYKE, 76)
I!
SECTION III
REVIEW OF PREVIOUS CRATERING RESEARCH
There have been thousands of cratering experiments and
hundreds of technical reports, articles,and b-ooks written as a
result of these experiments and associated phenomena. Over 300
of these publications were reviewed for this study. This
section presents a brief review of cratering experience and
analysis. A brief history of recent cratering research and
symposiums relating to that research is presented followed by
the various prediction techniques available and the information
found on the effects of material properties.
Nuclear Cratering Experience (13,45). There have been 10
nuclear detonations at the Nevada Test Site involving four
different geologic media in level terrain which resulted in the
creation of craters (or a mound as in the case of Sulky) which
are considered applicable to explosive excavation. These de-
tonations are listed as the first 10 events in Appendix I.
Yields for these events varied from 0.42 kiloton for Danny Boy
to 100 kilotons for Sedan (ono kiloton = 1,000 tons equivalent
weight of TNT).
High-Explosive Crate ring Experience. Good summaries of
past research in this area can be 'Found in references 46, 81
and 87. Lists for the majority of the experiments can be found
in references 15, 60 and 87. In all, these experiments number
12
in the thousands and involve more than 20 different soil and rock
materials. They range in yield from 1 gram to 1 million pounds
of TNT and include the full range of depths of burst. Con-
fl sidering each material, the largest number of these experiments
were performed in a lightly cemented sand-gravel mixture known
as desert alluvium. The number of experiments applicable
for this research was considerably less than the total number
available. For instance, original plans had included the
Dugway cratering series in limestone, granite,and sandstone (76).
Later review, however, determined that the crater dimensions
reported were not those for the apparent crater as had been
indicated by Vortman (87), but were mucked dimensions; i.e.,
all loose rubble in the crater was removed before crater dimen-
sions were measured. Crater dimensions for this series, there-
fore, lie somewhere between apparent and true crater definitions.
It was also necessary to eliminate hundreds of experiments
reported by Sager (60) because other than spherical charges were
used and because very few of the experimentors had reported
material properties. A good conclusion that can be made regarding
the various experiments and their data plots is that the data
are highly scattered because explosive experiments in natural
materials are difficult to control. The high-explosive experi-
ments used in this research are shown in Appendix I beginning
with event 9.
Symposiums Related to Cratering. The Plowshare Program
13
E63
4 L
(the peaceful uses of nuclear explosives) was formally estab-
lished in 1957 (30). At about the same time, the first con-
tained nuclear experiment, Ranierwas executed (31). Ranier
was a 1.7-kiloton explosion 900 feet below the surface. Be-
cause of the success of the Ranier event, numerous speculations
were made as to the uses of underground explosions. The gen-
eral range of ideas was first reported publicly in 1958 at
the Atoms for Peace Conference in Geneva. This later became
the First Plowshare Symposium. In 1959, the Second Plowshare
Symposium was held in San Francisco and initial presentations
on the uses of nuclear explosives for excavation and extrapo-
lation of chemical explosive data for possible nuclear explosive
application were presented (54).
In 1961, a Geophysical Laboratory - Lawrence Radiation
Cratering Symposium was held in Washington D.C. (44). This was
really the first somewhat all inclusive up-to-date presentation
relative to cratering data and phenomena. Scaling laws,
empirical analysis, theoretical calculations, nuclear cratering
to-date,and explosive craters in desert alluvium, tuff and
basalt were some of the more pertinent subjects presented.
Nordyke presented his preliminary theory for the mechanics of
crater formation; this theory is still being followed today.
In 1964, the Third Plowshare Symposium with its theme
"Engineering with Nuclear Explosives" was held at the University
of California, Davis Campus (74). Over 30 presentations were
14
made that offered an up-to-date picture for using nuclear
explosives for engineering purposes. By this time additional
nuclear cr.,tering data, including the 100-kiloton Sedan event,
were available. Knox and Terhune (32) presented results ob-
tained from using SOC, the two-dimensional computer model of
cratering physics during the gas acceleration phase. A good
portion of the data presented at the conference was later used
by Teller (70) to write the book The Constructive Uses of
Nuclear Weapons.
In January 1970, the most recent symposium, Engineering
with Nuclear Explosives, was held in Las Vegas, Nevada (55).
Over 100 presentations were made of which 17 were directly
related to excavation. Since a number of the presentations re-
late to this research, they are discussed in the next two sub-
sections.
Prediction Techniques and Scaling. To date therF are
basically two approaches being used for predicting crater
dimensions. The first involves computer calculations of the
mound and cavity growth used in conjunction with a free-fall,
throw out model which gives an estimate of the crater radius and
e ejecta boundary. The second basic approach uses empirical
scaling relationships. Another approach, although not so widely
used but which deserves mentioning, is a quasi-static approach
which considers cratering as an earth pressure problem.
SOC (spherical symmetry, one dimensional) and TENSOR
15
-'1
-: -
(cylindrical symmetry, two dimensional) computer codes numeri-
cally describe the propagation of a stress wave of arbitrary
amplitude through a medium (6,12,32,36,37,71). These codes are
hydrodynamic Lagrangian finite-difference approximations of the
equation of motion which describe the behavior of a medium
subjected to a stress tensor in one (SOC) and two (TENSOR)
space dimensions. The code calculations handle both the initial
shock wave phase, which creates spall velocities and thp ga3
acceleration phase. The end product of the TENSOR code cal-
culations is a chronological history of the cavity and mound
growth resulting from an underground explosive detonation. The
code calculations runs until the particle velocities ro longer
increase significantly from cycle to cycle. At this point, a
free-fall throw out model calculation is used to-determine the
mode of deposition of that material which has been' given suf-
ficient velocity to pass the original ground surface. The
ballistic trajectory of any given mass determines its final
position on the surface. The throw out model calculation
permits one to estimate crater radius and the maximum range to
which significant material is thrown by the detonation. An
estimate of the crater depth may also be made by considering
the stability of the cavity walls and the bulking characteristics
of the material which falls back into the crater opening. Since
these codes assume that the material behaves hydrodynamically
not only in the melted region but in the consolidated and
16
cracked regions of the media, extensive laboratory testing is
required to develop pressure-volume relationships for the
material involved. The big advantage to this method is that
it provides a visual graphical representation of the mound
and cavity growth and fall-back. The disadvantages are that
it requires an enormous amount of computer time to accomplish
the computation and it requires extensive material testing to
obtain, pressure-volume relationships, rigidity modulus, ten-
sile strength and distortional energy limits. Failure in the
material is assumed to occur either when the tensile strength
is exceeded or when maximum distortional strain energy is
reached.
The second crater geometry prediction approach involves
the use of scaling laws which relate crater dimensic. from
some reference yield to crater dimensions for any energy yield.
The preponderance of cratering resedrch (8,10,i,15,46,61,77,88)
has been concerned with or utilized this prediction approach.
This procedure in its simplest form is based on an empirical
determination of the scaling exponent, m, as a function of soil
type, using the assumed relationships
R cW; D = C2W V = C3 . ...... ()
where R, D and W are the radius, depth and volume, respecti,y,
' of the crater, C. are constants related to the soil type and1
depth of burst and W is the energy release. If a dimensional
17
H R
I_____ - __• , ,,
tii
analysis is made, it would appear that m should be 3 for radius
and depth and 1 for the volume if the effects of gravity and
Imaterial friction are omitted; however when gravity of the
material is considered, m becomes 4 for radius and depth and 4/3
for volume. The results of cratering experiments to date.
however, have led to the development of m = 3.4 for radius and
depth and m = 3.4/3 for volume. Although this relationship is
very simple, the only way Ci can be determined is by performing
a series of cratering experiments for the material in question.
There is considerable actual data scatter, however, compared
with the smooth curve this technique produces. The constants,
Ci., therefore,appear to be variables which depends on material
properties. At best, then, these relationship~s provide only a
very rough estimate of cratering dimensions since all material
properties are ignored.
A third mothod for predicting crater dinmensions considers
cratering as an earth pressure problem (42,78,79,80,81). This
method considers expansion of the explosive cavity to some
ultimate radius and pressure, at which time equilibrium is as-
sumed to exist, at least for a while. For the cratered medium,
it is assumed that a part of it, adjacent to the cavity,
behaves as a rigid plastic solid, defined by a Mohr's envelop for
the material. At a sufficient distance from the explosive
charge the medium is assumed to behave as a linearly deformable,
isotropic solid defined by a deformation modulus and a Poisson's
18
ratio. This method appears very reasonable, however it has
only been applied to very small scale laboratory experiments.
In addition, it does not consider surface spallation and does
not seem to apply for surface bursts.
f Material Property Effects. Although numerous observations
and studies of cratering for both conventional and nuclear
explosives have led to a fair understanding of the basic
processes and phenomena involved,the physical characteristics
of the cratering medium which significantly influence crater
sizes and shapes were found to be largely unknown.
Whitman (89) postulated that crater dimensions were
primarily related to soil type through the soil's shearing
resistance. His study developed trends between crater size
and soil strength for the weaker soils, but trends for the
stronger soils and rocks were quite obscure.
Based on limited data, Baker (1) was able to relate material
seismic velocity, angle of shearing resistance for sands, tensile
strength for rocks,and relative consistency of clay to a radius
modulus developed by Saxe (62) to relate a scaled normalized
radius and the scaled depth of burial.
Chabai (11) made a dimensional analysis of scaling
dimensions of craters and considered the following medium
properties as being sufficient to describe the phenomena of
cratering: density of undisturbed medium, yield strength of
the medium, a viscosity or dissipation variable of the medium
19
fl7
and the sonic velocity in the medium.
Westine (88) considered dimensional analysis and developed
the following relationship:
Ra/DOb = f{W7/ 24/(p7/ 24 gl/ 8 cl/ 3 Dob)] . . (2)
in which p = mass unit weight, g = acceleration due to gravity
and c = seismic velocity. Westine's plots of the data from
five different materials show some reduction of the data
scatter using his technique. The disadvantage in using this
approach is that it implicitly assumes that an increase in unit
weight and seismic velocity will result in a smaller crater
dimension.
Terhune (71) listed the following-.material parameters in
the order of their importance for determining the cratering
efficiency of the medium: (1) Water content; (2) shear
strength; (3) porosity (compactibility); and (4) compressibility.
He stressed the point that an increase in water content decreases
the compressibility, drastically reduces the shear strength and
provides an additional energy source in the form of a non-
condensable gas.
20
VA SECTION IV
PURPOSE, SCOPE,AND PROCEDURE
The purpose of this research was to evaluate the data from
published cratering experiments in an effort to show the effect
of soil and rock properties on crater dimensions in conjunction
Iwith the burial depth and energy of the explosive charge. A
secondary purpose was to show that no real analysis can ever
be made of cratering data untii crntrolled experiments dre con-
ducted or unless soil and rock property measurements are care-
fuily made throughout the material field.
Of the thousands of cratering experiments that have been
conducted, only a little more than 200 tests were selected for
analysis. The remaining tests did not meet the general criteria
established for this study. From the tests selected, those where
the charge was detonated above the surface or the depth of burial
was so great that a mound or slight depression developed, instead
of a crater, were not used in the analysis.
The procedure used to accomplish the research was
statistical analysis of data from existing cratering experiments.
This involved the following: cataloging all crater and related
material property data; selecting a proper regression model to
develop empirical equations for apparent crater radius, depth
and volume in terms of explosive weight and depth of burst for
specific materials; integration of the various material properties
21
into the model to develop the best equations for all the
materials combined; and analyzing the best equations to
determine the specific effect of the material properties used.
An inherent part of the procedure was the development and use
of computer o.rograms.
22
iii
SECTION V
EXPERIMENTAL DATA
This section presents the method and approach used to
acquire and catalog the experimental crater and associated
material property data necessary for this study. The cataloged
listing is referred to and discussed in some detail. Sorting
of the data to allow for better comparison and analysis is
briefly described.
Data Acquisition. Using the Corps of Engineers' "Com-
pendium of Crater Data" (60), Vortman's "Ten Years of High
Explosive Cratering Research at Sandia Laboratory" (8/), and
Circeo's "Nuclear Excavation: Review and Analysis" (13), as
guides to previously conducted experiments, the original source
documents were obtained and reviewed. This involved making
visits to Sandia Laboratory and Air Force Weapons Lab, Albuquerque,
*N.M. and to Lawrence Radiation Laboratory and U. S. Army Engineer
Nuclear Cratering Group, Livermore, California.
A review of the literature showed that there was a wide
variation in the experiments as well as a wide variation in the
parameters measured. The following criteria was established to
determine if a particular cratering experiment was to be
cataloged and used in this analysis:
1. The explosive charge had to be single and spherical
with a TNT equivalent weight of at least 1 pound.
23
,
Ii
2. The dimensions measured had to be for the apparent
crater.
3. The experimental terrain had to be reasonably level.
4. Sufficient material properties had to be measured or
it had to be possible to estimate -them with some
degree of confidence from other recorded data.
Although crater dimensions were obtained for the various
experiments with relative ease, soil and rock properties
presented a very perplexing problem. For a number of the
nuclear events, extensive soil borings and tests were reported.
In other cases, only one soil test pit and limited testing was
reported for a complete series of experiments. Somewhat
arbitrarily, but keeping in mind the cratering phenomenology
involved, those material properties which were thought to
effect crater geometry were selected to be cataloged.
Data Cataloging. By considering all the data required to
properly catalog each cratering event, formats and programs for
computer input and output were developed. Every effort was
made to keep the data for a particular cratering event to a
minimum but yet make the data as complete as possible. For
example, cataloging only the grain specific gravity, dry unit
weight and moisture content of the media for a particular event
allowed for computer calculation of various parameters such as
total unit weight, degree of saturation, porosity, percent
air, void ratio, etc. Data input to the computer was made to
24
serve a dual purpose. It was used to produce the cataloged
listing of crater data and as a basic data source for the
analysis.
The listing of all data cataloged for this research is
included in Appendix I. This appendix is divided into the
following four segments:
1. A list of all notation and definitions associated
with the cataloged data.
2. The computer output crater data list.
3. The two line computer listing of all the cataloged
material property data associated with the crater
data list.
4. The notes referred to in both the crater data and
material property data listings.
It was initially thought that there existed many more
measurements of cratering event material property data. In
the final analysis, sufficient data was just riot avail-
able to obtain measured values for each and every event or
in most cases even for a series of events. Estimated values
dominate the material property data section of the cataloged
data. To differentiate, estimated values are indicated by a
dollar sign in the data listing.
7 Viewing the crater data list, it can be seen that the
approximate energy of the nuclear explosive cratering events
was only estimated within 20 percent. This was due, apparently,
25
ih
to the unsureness of the amount of nuclear material which
actually participated in the reaction. As discussed by
Vortman (87) for most high explosive events, cast spherical
charges of TNT detonated at their centers were used for yields
of 1000 pounds or less. For charges larger than 1000 pounds,
cast blocks of TNT were stacked to approximate a sphere.
For certain experiments liquid nitromethane was used. The
liquid was placed in a spun aluminum sphere or in a mined
cavity lined with an impervious material. For a number of
the very small explosive tests, Military C-4 explosive was
used. Equivalent weight of TNT factors for these latter
explosives was based on the heat of detonation as reflected
in Cook (14). There is, however, some question as to whether
these equivalency factors are completely valid. There seems
to be an optimum rate of burning for an explosive for a
particular depth of burst in a particular material which will
produce the largest crater. It is felt, however, that the
equivalent weight of TNT shown in the crater data list for all
events except the nuclear tests is within five percent.
Depending on the method used by the original investigators
to measure crater dimensions, these dimensions are considered
accurate only to within five percent. Again as discussed by
Vortman (87), crater measurements have been determined using
various techniques. These techniques have consisted of almost
ever ything imaginable from conventional ground surveys to the
26
use of adjustable rods to aerial mapping. Lip heights and
slope angles shown in the listing (although not specifically
used in this research) were not reported by many of the
investigators. Values reported, in many cases, reflect values
measured from typical cross sections.
Material property values reported in the material property
data list reflect those which were either reported by the
investigator as an average for the experiment or series of
experiments, or where possible, taken from boring logs and
associated tests. In the latter case, a weighted average for
a particular material property was computed for the vertical
column in question. These weighted averages for the various
borings were then interpolated or extrapolated to obtain the
values reported for the explosive event location. Although
the material property data list contains predominately
estimated values, the majority of these estimated values were
extrapolated from experiments in like or similar materials.
It would have been advantageous to have been able to obtain
specific measured values for each event. Where measured,
material property values are considered accurate only to
within 10 percent. Where values are estimated, it is believed
that they are within 20 percent.
Data Sorting. To allow for better comparison and analysis
of the data cataloged, a computer subroutine was written and
used. This subroutine provided for sorting on any three
27
specified parameters at one time. The sorting scheme that
was found to be most useful aligned the data by type of
material, then by scaled depth of burst and lastly by explosive
weight.
28
SECTION VI
EMPIRICAL DATA ANALYSIS
This section describes the regression analysis technique
used to develop a functional relationship between crater dimen-
sions and explosive charge weight and depth of burst for a given
L soil or rock type. It also discusses the function constants
obtained, presents plots of the actual data and presents the
resultant regression curves to predict crater dimensions for
nine groupings of the data.
Regression Analysis (16,39). The data for this research
were analyzed and the prediction formulas for crater dimensions
were developed using applied regression analysis. First, the
dependent variable (the variable for which prediction was
desired) was selected and the independent variables (the
parameters thought to have some influence on the dependent
variable) were assumed. Next a form of the answer (the model)
was assumed and the data applied to the model to obtain its
coefficients. This was accomplished through the method of
least squares surface fitting, whereby the sum of squares of
the distances between the assumed surface and the actual data
points was minimized. If the sum of squares is a minimum and
the coefficients of the assumed model are determined, then this
is the best fitting surface for the model and data used. Lastly
through computation of a multiple correlation coefficient and
29
-I --- ----
t
by an examination of the least squares residuals the prediction
formula was evaluated.
Regression analysis has become a fairly common tool for
analyzing experimental data and developing function relation-
ships for that data. For this reason, it seems sufficient to
mention only that an enormous amount of mathematical computa-
tion, including the solution of a large number of simultaneous
equations, is required. Only through the use of a high-speed
computer is this possible.
The computer program used was specifically written for
this research. Although library regression analysis programs
were available, it was felt that these programs were too elabo-
rate and did not provide the flexibility needed for this
research. The computer program written was intended to be a very
flexible, minimum essential program that would adequately
accomplish the data cataloging and sorting, the least squares
surface fit and the evaluation of the fit. The multiple linear
regression portions of the program were written using statistics
books as guides (16,24). The matrix inversion, multiplication
and print subroutines were available from previous research (75)
and were modified for use here. As the research progressed,Inumerous changes, additions and deletions were made based on
Lthe scheme, procedure or purpose being tried at the moment.rThe program was originally written for the IBM 360/65 computer,
but was later revised for use on the CDC 6600. Appendix II
L 30
V
contains a brief description of the program and its essential
features along with a typical print-out of the essential
portions of the program and its output after being run on the
CDC 6600.
Regression Approaches Considered and Tried. The number
of regression approaches considered and tried was so numerous,
it is superfluous to list them all. At the beginning, regres-
sions of radius, depth, or volume as a linear function of depth
of burst, explosive weight and various material properties were
attempted. A second approach considered a linear crater dimen-
sion to be a function of various dimensionless parameters taken
from Chabai's work (11). An attempt was also made to consider
all material parameters which would refiect the amount of energy
being dissipated during the cratering process. A closely
related approach was to consider those material properties which
would relate to the mechanisms of compaction, subsidence, spall
and gas acceleration as proposed by Nordyke (46). In all of the
above cases, sufficient material properties were not available
to include all applicable terms thought to be important. An
attempt was made to use available and applicable material
parameters in a linear fit, but to no avail. When one considered
a second order regression model, the number of parameters to be
used suddenly becomes excessive for the data available and for
the basic research purpose.I Of special note was the attempt to use Westine's technique
31
(88). Regression using this approach produced a high multiple
correlation ratio. However, the residuals between the estimated
and actual values of the dependent variables were found to be
excessive. This was particularly true for the range of data
where Ra/Dob was lcss than 2.
Regression Model Used. After much deliberation and due
consideration of the literature reviewed, it was felt that the
better approach for the solution of crater dimensions for one
particular media was to consider a scaled linear crater dimen-
sion as a function of the scaled depth of burst. Although there
seemed to be some question as to the proper scaling to use, the
scaling exponent which appeared to most recently be used and
justified was 7/24. This figure is the average of conventional
cube root scaling (gravity effects excluded) and fourth root
scaling (gravity effects included). The scaling exponent
eventually used was 5/16 and resulted from a special study of
the data cataloged for this research. The next question which
arose was what model should be used for regression? After
studying plots of the scaled data and after considering what
happens to crater size as the depth of burst (or height of burst)
is varied from one extreme to the other it became obvious that a
curve reflecting the final dimension of a crater when plotted
as a function of depth of burst (and height of burst) should be
asymptotic at both extremes and reach its maximum value at the
optimum depth of burst. This suggested the bell shaped curve
32
I,
with its inherent advantages and disadvantages which will be
discussed later. Using this approach, the regression suddenly
improved for any one particular cratering media.
The general form of a bell curve is as follows:
y = B1 exp [B2 (x+B3)2 ] ...... (3)
That of the skewed bell curve used took the following form:
y = B exp [B2 (x+g(x+B42 (4)
1 ex 2 3 4 )
in which x = the scaled depth of burst (Dob/W 5/ 16) and where y
the scaled linear apparent crater dimension being considered:
(1) Radius (Ra/W 5/16 ); (2) depth (Da/W 5/16 ); or (3) cube root1/3 5/16,
of volume (Va /W ). A big advantage to these curves is that
B1 is the maximum height of the curve and it occurs along the
abscissa at -B3 for the standard curve and at -B4 for the
skewed form. In other words if y is equal to the scaled radius
for the first case, then the maximum scaled radius is BI, and
it occurs at an optimum scaled depth of burst of -B3 B2 sets
the rate of change of the slope away from the (B3 ,BI) point.
The (x+B3) term in the second case allows for skewing the
standard bell curve. As can be seen, this introduces a second
root to the equation. In the majority of surface fitting cases,
* this posed no problem since the second root and associated slope
change were outside the range of the data. Whare the data was
minimal and somewhat scattered, using the skewed bell curve
proved infeasible.
33
Since the above curves are not applicable to multiple
linear regression, they were used in the following coded forms.
For the standard bell curve:
In y = A1 + A2x+ A3 x2 . . .. . . . . . (5)
where A1 In B1 + B2 B32, A2 = 2B, B3 and A 3 B2 ; or con-
versely: B 1 exp (A1 - A22/4A3), B2 = A3 and B3 = A2/2A3.
For the skewed bell curve:
In y A1 + Ax+A3 x2 + A x3 . . . (6)
where A1 B i 1 + B2 B3 B4 2, A2 =2 B4 (2B3+B4) A3 82
(B3 2B 4) and A4 = 82; or conversely B2 = A4 , B4 : [A3/A4
(A32 /A 42_-3A 2/A 4)1/2]/3, R., = 3/A0 - 2B4 and B1 = exp(A1-B2
B3 B42)
' As can be seen for this later case, two sets of values for the
constants B42 B3 and B1 are obtained. Examination of the
numerical values ootained for a particular curve fit, however,
quickly show the cJresct .et to be used.
Determination of Best Scaling Exponent. ru, all the
initial surface fits made, 1/4, 7/24 and 1/3 were used as the
scaling exporents. For every set of data except one, 7/24 was
found to produce the best fit of the data. Where the data
consisted of a large amount of surface bursts, 1/3 was found
to produce the best fit. This suggested using a variable
exponent as a function of depth of burst. Numerous computer
runs were made attempting to use an exponent which was a
34
F
function of depth of birst or an initial scaled depth of burst.
Although a better fit was obtained for surface burst data, the
over-all fit was never as good as that obtained from just using
7/24. Vortman (84) showed that the scaling exponent for surface
bursts could vary from low of 0.23 for depth to 0.44 for radius
depending on the material in question.
A special computer run was made to vary the scaling
L exponent from a value of 0.29 to 0.35. It was found that a[ scaling exponent of 0.31 produced the best fits for radius and
cube root of volume while 0.32 produced the best fit for depth
(there was very little difference, however, between the fits
obtained from using 0.31 and 0.32). It was decided to use
5/16 (or 0.3125) as the scaling exponent for the remainder of
the research. This figure represents the average of the 7/24
and 1/3 figures which have been used so predominately by other
investigators.
Equations and Daca Plots for Specific Materials. Using
equations (3) and (4) as the regression models (the standard
bell curve and the skewed bell curve), the coefficients (B
values) were generated to obtain the best fit of the data to
rMDirically predict the scaled depth, radius or cube root of
volume. This was accomplished for each of eight groups ofmaterial (or experiment) data and in addition for all the data
combined. Linear dimensions used in these equations were in feet
while W was in pounds of TNT. Listed in Table 1 are the B values
135
I
4-)
-L.0 Oi3:0 0 C~ - O(0 ~ 0
a.
0 a
.)-- N~ N~ -Ca 00 - z Cr) S0 kto O N~ iO
0> S..-4-
0) 4-)LL- r- 00C to N~ Nl 0) mr
a) 00- Lr YU) -. Cr) 1.0 (.0 ~I-. CU totj ~
L '4-I I I I
-4 0LL V) m- OCOC Cr) 0in in to- 0 tD 0 'Or '
LU a2) N- CO N- co mr to - a- N N\ N~ (\ Cr) N-0) > m~
5-- -Ca cr, Cr) CO C; CO C
H a- N ' in) N-N 0~C COO a ) in -Il C) 0 ~ N l
LUj -O in M~ in 00 0 00 a) 00 t0 V 0 0o Lcoa)Ci C I) 'I I UI CI I D I
o a CO a- C), Ca in C0 N- in , cN C) N- l
0U n - i CO 1CJ 0y C 's CO r- O 0 - N- ::- 0~
__j ) co
C3 C~ \,- ~ ~ C
0S- .-(u V) Cr) Cr) Cr) C')
0o (a__ m _ _ _ (a_ co___0(a co_
a:
I *- 4-= >4-
4 >)(I rcI'o I'd Cl CLi
4..V) 0Aca
36
4-'
S r- C'i CY) cj co N.I r- LO CiY. i
0 +1 C'J C') C J 0 C4CO O in m r-. (\ C'J
0~ C C"j (Y C%.J N.) -T C.O Cnif ) CS~j CV)
04-
0
0 --i2
V) 0--* rD C'i COCJ () ~ 0 - r. o i:* D.ci .n L
ui M,~-*- C a Zj co o o CO C) co mt lf>-'W co~ Co C;o~ Q~O~ ~ 0, C W C
- u-I
Cz C C', C'cii 0- 0- P l . nC
C)co
tA 0 c;C<-C)0 C J ~ O ~ ' - ) C
> o
m - l > r k
0 -ca C) - C SJ I ' C n -o-C0 . tCJ - 0 C. 0
0t -o 0 000 00
I-. ci I I I I I I 37
obtained. The number of B values listed for a particular crater
dimension for a particular material reflects which equation
produced the best fit. Actual plots of the data used and the
resultant empirical curves obtained are included as Appendix
A study of these data plots reveals several interesting
facts. The smallest craters were produced in playa, the
lighter weight, weaker material; next came the rocks, alluvium
and sand; and lastly the largest craters were produced in the
clay shale. The exact order for the different materials changes
somewhat depending upon which crater dimension is being con-
sidered. A second important fact that can be noted is that in
almost every case, nuclear events produced smaller scaled
craters than their high-explosive counterparts in the sama
material. If attention is brought to bear on the surface burst
data for the Air Vent Series, which also included the two 20
ton Flat Top events, it becomes obvious that a larger scaling
factor would reduce the data scatter considerably. When this
fact is considered along with a close look at other surface
burst data, it would appear that surface and near surface bursts
should be studied separately and should possibly have been
eliminated from the data used in this research.
Discussion of Approach Used. S4nce a good portion of the
time spent on this research was in regression analysis, it seems
appropriatb to discuss this process and its applicability to
38
i
research of this type. In general, it is sufficient to say that
f . multiple regression analysis for such a complicated problem as
was encountered here is more of an art than a scientific
approach. For regression analysis to be of real benefit,
experience with its application and at least some knowledge of
how the dependent variable behaves as a function of the various
independent variables is hignly desired. Otherwise, it becomes
the problem instead of a tool to help solve the real problem.
Statistics books, in general, tend to oversimplify the process
(rightfully so if they are to teach the principles involved) but
the real world just does not seem to be composed of only one or
two independent variables. If a general series is assumed as
the regression model , a very few variables, applied to say
a fourth order fit, produces an excessive number of terms to be
evaluated. This number of terns can quickly exceed
the number of the observations or make it extremely difficult to
2obtain an accurate solution of the normal equations even using
the computer. It is only when the behavior can be simply
explained or when reasonably precise laws govern the behavior
that regression analysis can be used with the assurance of
gratifying resuls.
Even though the idea of using the bell curve as the
regression model was the key to any success achieved in this
research, it did not, of course, fit all the data well. Several
methods were tried in an attempt to skew this model to improve
39
the data fit, however each method had its inherent problems.
Although the method chosen works satisfactorily, it no longer
is a bell curve. It is asymptotic to the x-axis on only one
end. If this end falls toward the deeper depth of burst portion
of the graph then no real problem exists provided the "S"
portion of the curve does not situate itself in the middle of
the data as can be seen for the clay shale plots in Appendix
Il1. Extreme care, therefore, must be taken when using this
model to insure that the proper portion of the curve, did in
fact, fit the data points provided.
As can be noted from the results of the surface fits, the
standard bell curve fitted more of the data as well or better
than the skewed form. It also, in general, produced a better
fit for scaled radius data than it did for scaled depth and
scaled cube root of volume dpta. If the assumption is made
that the bell curve is truly representative of true crater
dimensions, then this fact makes sense. The apparent crater
radius is essentially equal to the true radius from depths of
burst ranging from zero to past optimum. It is only at the
deeper depths of burst that these two radii diverge. Of the
three crater dimensions, poorer fits were obtained for apparent
crater depth. Fall back is the important factor here, the
volume (and in turn the height) of the fall back being dependent
on bulking and other material characteristics. Judging from
the data scatter, material properties are very critical for this
40
V _L
Iparticular crater dimension. Judging also from the data plots,
I .e there exists a range of deep depths of burst in the explosion
process where the material either responds or does not respond
too well to being thrown out.
Obviously, from the above discussion, material properties
are important in determination of crater size. Their inclusion
into the bell curve prediction scheme is covered next.
41
SECTION VII
MATERIAL EFFECTS
This section describes the method used to incorporate soil
and rock properties into the bell curve regression models, the
resulting general equations obtained and the analysis of these
equations to determine specific material property effects. It
also includes a discussion of material properties in general
and of the material properties used in this research in partic-
ular. Lastly, it presents a brief discussion of the relation-
ship between material properties and cratering mechanics.
Incorporation of Material Properties. After normalizing
the crater dimensions and after determining that the bell curve
was an appropriate reqression model to use if material property
effects were ignored, it was surmised that the position of the
bell curve (i.e., the height, point of zero slope, etc.) was a
function of the media material properties. In other words, the
bell curve regression coefficients obtained for the various
materials are really a function of appropriate material prop-
erties. This led to regression analysis involving inclusion of
soil and rock properties.
Ideally, if sufficient data had been available at various
material property conditions, then each coefficient (B value) of
the bell curve could have been expressed as a function of these
conditions. However, to make full use of the data, it was
42
necessary to assume that the coefficients of the coded bell
curve, the A vialues, were functions of material properties. The
B values are, of course, related to the A values as described
by equations (5) and (6), but when the B values are shown in
terms of material parameters, the resulting equation is so
involved that it becomes meaningless. It was quickly determined
that the coded bell curve constants were not linear functions of
any one or more material properties. Reasonable regression began
to occur when second order and interaction terms were included.
This, however, reduced the number of material properties which
could be considered at one time without increasing the number of
parameters being used. Every effort was made throughout the
research to keep the number of parameters to 40 or less. In
the final analysis, the best prediction formulas were obtained
using either equation (5) or (6) and the following functional
relationships for their coefficients:
A1 = C1 2 y5/16 + C3 S + C4 M + C5 y 5/ 8 + C6 E (7a)
+ C M2 +C8 5/16 S + C9 y5/16 M + C10 SM
A2 = C11 + C12 Y 5/16 + + C 20 SM (7b)
A3 C2 1 +C22 5/16 + + C30 SM (7c)
A4 = C31 + C32 Y(5/16 + + C40 SM (7d)
in which y total unit weight of the material, in grams per
cubic centimeter; S degree of saturation, ranging from zero
43
to 1.0; Ev vaporization energy of the material, in thousands
of pounds per square inch per cubic inch (this factor is zero
for all except the nuclear events); and where M may equal any
one of the following: (1) Gs, the grain bulk specific gravity;
(2) tan , the material's shearing resistance; or (3) c , thei seismic velocity of the material, in feet per second.
Appendix IV coptains t e equation coefficients (C values)
for the various crater dimensions arid combinations of material
properties. Numerous computer runs were made to determine which
material properties correlated best with crater dimensions and
produced the best surface fit. As could be expected, those
material properties which were predominately measured values
correlated the best and these included the dry unit weight and A
moisture content and to a lesser degree the shearing resistance.
Dimensional analyses by Westine (88) and Saxe (61) suggested
the use of y5/16 and c' / 3 These scaled values produced better
regression than when their full values were used. Degree of
saturation, S, and specific gravity, G., were selected after
trying other related factors such as porosity, percent air and
void ratio. They appeared to correlate better and have a little
more meaning when considering their effect on crater dimensions.
The vaporization energy of the material, Ev, was used
primarily to differentiate between nuclear and high exDlosive
events. From actual experience (45) it was known that nuclear
events produced smaller craters than would be predicted by
44
scaling from high explosive cratering events. This fact became
evident when the nuclear events were analyzed with and without
the E v term as a parameter. To keep the number of parameters
to a minimum, Ev was used in place of the normally expected S2
term in the second order material property scheme utilized. The
S2 term was found to have the least effect of all the nine
material property terms on the scaled crater dimension.
Also Pn attempt was made to incorporate all the material
parameters used into one 40 parameter equation, by considering
the terms in previous surface fits which had the least effect
on the dependent variable. This attempt, however, did not
produce as good a surface fit as when only four materiel prop-
erties were used.
When this research was first undertaken, it was hoped that
crater dimensions for at ;east 90 percent of the events could
be predicted within ± 10 percent. After viewing the accuracy
of the basic cat3loged Jata, a goal of 80 percent of the events
to be predicted within ± 20 percent was established. This
second goal was more than met for radius and volume but not
quite met for predicting depth. The final figures obtained do
give, however, some indication as to the reliance of using
material properties to predict crater dimensions and provide
some validity to the assumption that investigation of the
general equations obtained would allow a determination of the
effect of soil and rock properties on crater dimensions.
45
JA
Although an attempt was made to go back over the data to try
and find specific explanations as to why specific events did
not predict well, very little success was obtained. In general,
it appeared that the accuracy of material property inputs was
the predominate reason. Not using a better scaling factor for
the surface bursts accounted for a small amount of discrepancy.
Even Palanquin (a nuclear test) (82) which did not produce the
crater expected and which in turn was blamed on a stemming
failure, predicted well. The general equations using y5/16 S
G and Ev predicted Palanquin's radius and volume only eight
and five percents higher respectively than those which occurred
and actually predicted the depth 5 percent lower than the
actual.
How well will the general equations obtained for the
various crater dimensions predict future events? Judging from
the data observed, there is an 85 percent chance of being within
± 15 percent for materials that fall within the range of the
ones used in this research and for a scaled depth of burst less
than 2.
Effects of Material Properties. After development of the
general equations for crater dimensions, parametric studies of
these equations were made to determine how crater geometry was
effected as the various material properties were varied over
their normally expected ranges. This was accomplished by
writing a second, but much smaller computer program, to vary
46
the parameters in the final prediction equations to determine
their effect on final crater geometry. Basically, this program
read in the constants obtained for the prediction equations,
varied the material parameters and scaled depth of burst within
their expected ranges and computed the estimated values for
scaled radius, depth, or cube root of volume. Since these
studies produced pages and pages of computer output, only
representative results are included here. These results are
graphically presented in Appendix V.
Material Property Definition. Because the results and
conclusions regarding the material properties used in this
research are presented next, it seems appropriate to discuss
just what is a "material property?" The term "material property"
appears to have many meanings. These meanings, as they apply
to engineering problems, can be catagorized into three areas:
(1) Basic, (2) material test,and (3) theoretical.
Basic or primitive material properties are those that
relate mass and volume. Examples for a single phase material
are: (1) Density, (2) specific volume and (3) specific gravity.
For a three phase material mixture, such as soil, where mineral
particles comprise the solid phase and where water and air
occupy the voids between the mineral particles, the basic
material properties relate not only mass to volume for each
phase but relate mass and/or volume of each phase to the total
volume or total mass. Examples of such basic properties are:
47
(1) Dry unit weight; (2) total unit weight; (3) saturated unit
weight; (4) moisture content; (5) void ratio; (6) porosity;
(7) percent saturation; and (3) percent air voids.
The second major category is material test properties.
They are defined operationally. The results of specified and
arbitrary tests yield these properties. Examples of such prop-
erties are: (1) Unconfined compressive strength; (2) Atterberg
limits for soils; (3) splitting tensile strength for rock; (4)
compressive strength of concrete at 28 days; and (5) Hveen
stability of bituminous concrete. Such tests as these are
usually standardized.
There may be some logic behina those test procedures that
in some way model a mechanics problem, but in essence these
test properties are empirical and arbitrary and may not relate
at all to the mechanical behavior of the material in other
situations. If they do, it is indeed fortunate and a tribute
to some investigator's intuitive insight into material behavior.
The third type of material properties depend on a theory
of material behavior that relates cause to effect. Usually the
cause is stress, or possibly temperature, and the effect, strain
or rate of strain. The coefficients in these theoretical
relationships are the constitutive constants that describe
idealized material behavior. The mathematical model used to
describe a material may be as complicated as necessary to cover
the range of interest of the material's behavior. Examples of
48
~t..
very simple constitutive equations are those for rigid bodies,
perfect fluids, linear elastic solids, perfect gases, and
linear viscous fluids. The constants in these equations are
called material properties. For example, in linear elastic
theory, there are two material properties: the two Lame'
constants. More complicated constitutive equations of nonlinear
form that relate the stress tensor to the strain tensor and
rate of strain tensor have been generated. In the case of
plasticity theory, the constants relate the various invariants
of the stress tensor at failure. In each of these cases, the
theory must exist before a material property is measured.
Without the theory, the property does not exist.
It would be ideal and very fortunate if valid relationships
existed between the various categories of material properties,
however, at best, we are fortunate that properties in one
category may be indicative of properties in another.
Material Properties Used in this Research. The best
regression equations were obtained as a result of using the
total unit weight, the percent saturation, the specific gravity
of the grains, the internal .,hearing resistance and the seismic
velocity. Although these pai-ameters may not really be the
properties governing material behavior during cratering, they
are at least indicators of the properties. None of these
parameters except the specific gravity remain constant durin;
the cratering process. They are all functions of the stress
49
.2
y
-1
(or strain) level and their initial values are not necessarily
indicative of their values during the actual explosive event.
However, when used in conjunction with one another and in
conjunction with the depth of burst, they provide some indication
of the governing material properties. It was interesting, how-
ever, to study tie effect these indicators did have on crater
dimensions.
At the optimum depth of burst for granular materials,
larger craters were produced at low and high degress of satu-
ration than were produced at the intermediate values (Figs. 32-
34). This was probably because granular materials
with low moisture contents have very little cohesion. However,
as the moisture content is increased, the material develops
some cohesion and therefore greater strength. Whitman (p0)
showed that cohesion due to pore water increased as the rate
of strain increased. The addition of water also increased the
weight of the material. When the degree of saturation starts
to approach 100 percent, the ability of the material to transmit
the shock wave markedly increases. In addition, the strength
of the material decreases consfderably as the pore water starts
to assume more and more of the pressare being exerted on the
mateial. For clay and rocks (Fig. 35), any increase in the
degree of saturation appeared to produce larger craters.
Additional moisture in these cases did not improve their
cohesion but only tended to increase their ability to transmit
50
___
the shock wave and to decrease their strength.
Now, if other than optimum depth of burst is considered,
the degree of saturation produced slightly different effects
(Fig. 32). For deep depths of burst, an increase in the degree
of saturation tends to always produce larger craters. For
surface bursts, the effect of the degree of saturation was
found to be the reverse of that determined for optimum depth
of burst. Low- and high-moisture contents produced smaller
craters, and there existed an optimum degree of saturation at
which the largest crater was obtained. Since compaction is the
predominate mechanism here, it follows that materials in this
region would behave essentially as they do in normal engineering
compaction problems.
Again, considering cratering events at or near optimum
depth of burst (Figs. 36 and 37), it was found that the smaller
craters resulted from low density and high density materials
and that there existed an optimum density at which the largest
crater resulted. This feature reflects again that better, prop-
erties are necessary to predict crater dimensions. If unit
mass, strength and the ability of the material to absorb the
shock wave are all considered together, then this phenomenon
seems plausible. Materials with low weight and strength appeav
to have high-energy absorption properties whereas dense, high-
strength materials do not. Somewhere in the middle, then,
there exists a material where these factors do not compliment
51
g --I
each other as much as they do for the two extremes. This density
Ifeature appears to hold true for all depths of bursts.
Because the effect of bulk grain specific gravity on crater
dimensions is not so meaningful in terms of its application to
the effects of material properties, it will only be discussed
briefly. A change in grain specific gravity affects the total
unit weight and degree of saturation and those were discussed
above.
Not so easily explained as the effect of density and deg.'ee
of saturation on cratering is the effect of the material's
internal shearing resistance, tan 4. It is very difficult to
determine what the actual ranges of tan are for a particular
soil density and degree of saturation. Every effort, then, was
made to stay within the area of the actual data to determine
the effect of tan p on crater dimensions. In general, it appeared
that as tan increased for soil materials at the lower degrees
of saturation and for the rocks, the size of the resultant
crater also increased. If high degrees of saturation are con-
sidered for the soils, then an increase in tan 4 decreases the
crater size. The only explanation that seems plausible for
these effects is to consider the ability of the paterial to
absorb energy in relation to tan p. Apparently the ability of
the material to absorb energy increases more with an increase
in internal shearing resistance than does the strength for the
lower degrees of saturation. At the high degrees of saturation,
52
,, , , , , , , , , ,,, ,,1, , , , ,
j }
however, the energy absorption value apparently levels off and
the strength increase is sufficient to produce smaller craters.
Because the parawetric study involving tan p appeared to be
somewhat meaningless unless values were considered in the same
area as the actual data, a parametric study was not performed
using the general equation which included seismic velocity.
Again it becomes extremely difficult to determine the range of
values in seismic velocity which would exist when the density
and degree of saturation are assumed. In addition, there were
fewer measured values for this -arameter and it was included in
the general equations with hesitancy. It was felt, however,
that even though the data were not the best and this variable
is stress dependent, it very likely would give some indication
of the material's ability to transmit the shock wave. A
cursory review of the data indicates that smaller craters
result when the seismic velocity is either low or high and that
there exists an optimum value where the largest crater will be
produced,
It becomes very difficult to sum up all the possibilities,
but in general it appears that for craters produced at or near
optimum depth of burst, there exists an optimum unit weight, an
optimum internal shearing resistance, an optimum seismic
velocity with the degree of saturation at zero percent where
the very largest craters will be produced for a particular
explosive energy source.
53
For practical considerations, it appears that the most
important of the material indicators used is the degree of
saturation (which is of course the result of water content).
This study should be helpful in determining whether the addition
of water to the medium will either enhance or decrease the size
of a crater being considered for the explosive charge weight
being used.
Cratering Mechanics and Material Properties. As a result
of this analysis of the effects of material properties on crater
L dimensions, it appears very likely that a reasonably simple
cratering theory should be possible. Hopefully the coefficients
(material properties) in this theoretical constitutive relation-
ship could be measured using simple laboratory or fieldI techniques. In any case it would appear that these cofficients
should in some way be related to the following material prop-
erties: (1) Energy dissipation; (2) total unit weight; (3) shear
strength; (4) volume change; and (5) moisture.
These five material properties should be measured over the
material field for each future test as a minimum material
property requirement. The energy dissipation constant should
account for the fact that smaller craters result in the light-
weight, weaker materials. Unit weight in conjunction with depth
of burst would give a measure of the total mass of the material
which must overcome gravity. The shear strength constant would
account for further energy dissipation. A volume change
54
constant would account for the change in density of the craterfall back wilich, in turn, effects the apparent crater depth and
volume, Last but not least is the moisture. Vaporiation of
moisture surrounding the explosive chargje enhances the gas
acceleratioi pI);e of cratering me~hanics. In addition,
moisture would modify the effects of all the other four
properties proposed.
55
SECTION VIII
CONCLUSIONS AND RECOMMENDATIONS
If explosives are to be used for excavation purposes, then
predictions of results must incorporate material properties.
This study has shown that soil and rock properties are important
in determining the size of explosion-produced craters and has
provided some insight as to their specific effects. It has
shown that previous investigators have been somewhat negligent
in measuring material properties fcr past cratering experiments
and that no real analysis of crater data can be made unless the
variables are either controlled or measured. This study also
has provided a means to predict crater dimensions for any
material provided certain soil and rock properties are measured
beforehand.
The final general equations obtained will predict the size
of 85 percent of the cratering events within ± 15 percent.
These equations predict apparent crater radius, depth, and volume
in terms of (1) depth of burst, (2) the explosive weight and
(3) the following material properties: total unit weight,
degree of saturation, grain specific gravity, internal shearing
resistance and seismic velocity. For nuclear explosions, the
vaporization energy of the material is also included. These
equations were developed from data which fell in the following
ranges: (1) Explosive charge weights from one pound to 100
56
kilotons; (2) materials in which the unit weight ranged from
60 to 170 pounds/cubic foot; and (3) charge depths from zero
to the point where no crater is produced.
It is not surprising that previous investigators have
concluded that the effect of material properties on crater
dimensions was somewhat obscure. This is particularly true if
only linear and simple curvilinear relationships are considered.
It is only when indicative soil and rock properties are con-
sidered in conjunction with one another for specific ranges of
depths of burst that they become meaningful.
Of the six material properties used in the general
equations, percent saturation and total unit weight appeared
to be the most important indicators of the effects of material
properties. This was due primarily because these two properties
were calculated from predominately measured values while those
for the other properties used were largely estimated. Prime
examples of these effects are as follows: (1) For surface
explosions, there exists an optimum percent saturation which
will produce the largest crater; (2) for soils and for the
explosive charge at optimum depth, zero moisture content pro-
duces the largest crater; in this case there is a least favor-
able percent saturation which will produce the smallest crater;
(3) for rock materials and for all materials at deep depths of
burst (at least twice the optimum), 100 percent saturation
results in the largest crater,and (4) in general, there exists
57
I=
an optimum unit weight which will produce the largest crater.
The bell curve provides a good model for predicting scaled
crater dimensions in terms of scaled depth of burst. Where
data indicate nonsymmetry, the skewed form of the bell curve
can be used, provided it is done cautiously. The inherent
advantage to the bell curve model is that the constants in this
model immediately provide the maximum value for the scaled
crater dimension under consideration and the optimum scaled
depth of burst at which it occurs. This feature makes it useful
for practical applications and allows quick comparisons between
rock and soil property conditions.
As a result of the knowledge gained in this research
effort, the following recommendations are made for future
cratering experiments and associated studies:
1. Sufficient material properties should be measured
for each and every cratering event. As a minimum,
unit weight, moisture content, grain specific
gravity, shearing resistance and seismic velocity
should be measured. In addition, some measure of
energy dissipation and material bulking would be
desirable.
2. A method needs to be developed to measure the
energy dissipation characteristics for soil and
rock in which cratering experiments have and will
be performed.
58
,, - , .. .4.. .F -
3. A method to measure and evaluate bulking or
compaction needs to be developed.
4. A series of laboratory type experiments to
cvnsider specifically the effects of percent
saturation on crater dimensions would be highly
desirable. As a minimum, five levels of the
degree of saturation for five levels of depth of
burst for a particular dry unit weight would
possibly suggest a more accruate relationship
between crater dimensions and this very important
material parameter.
This series could also be extended to include
a variation in the dry unit weight and the
inclusion of various types of materials.
5. For survival of silo-launched missile systems,
where the primary interest is in near surface
bursts, the surface burst data from this study
could be supplemented with additional data and a
regression analysis performed. This would allow
the scaling exponent, as well as the material
constant, to be a function of material properties.
Thus, a more accurate prediction of crater
dimensions could be obtained for this special case.
6. A simple theory of cratering should be developed
using the field equations of mechanics and a material
59
r0
constitutive equation with sufficient complexity
to account for soil or rock failure and energy
absorption. Such a constitutive equation should
also account for increase in strength as a function
of pressure and the thermodynamic properties.
6I
LI
. .. .
APPENDIX I
CATALOGED CRATER DATA
Notations and Definitions. The following notations and
abbreviations are used in the cataloged crater data and material
property data listings:
ALLUV - desert alluvium;
ATTBRG LIMITS - Atterberg limits (see also LL and
PI) relating to the water content at which
soil consistency changes from one state to
another, see Wu (91);
B - indicates that there is no value following even
though the computer printed zeros;
BULK FACTOR - bulking factor, a ratio of the unit
weight of the material in the crater fallback
to the preshot unit weight of the material.
Frandson (19) analyzed this value for severai
materials;
CH - inorganic clays of high plasticity;
CNF PRES, PSI - confining pressure at which the
confined compressive strength was obtained, in
pounds per square inch;
COHESION, PSI - cohesion of the material, in pounds
per square inch, based on Mohr-Coulomb failure
theory;
61
CONF COMP, PSI - confined compressive strength of
the material, in pounds per square inch, at
the particular confining pressure listed ir
the next column;
CORE RECOV, PRCT - the amount of core recovered
during coring operations, in percent; for rock
it indicates the material's soundness;
CU FT - cubic feet;
DRY UWT, LBS/CU FT - dry unit weight of the material
. in pounds per cubic foot;
ELEV, FT - elevation, in feet, which could have been
converted to atmospheric pressures which Herr
(25) showed to be important;
EQUIV WT, LBS-TNT - equivalent of the explosive
charge in pounds of trinitrotoluene;
EVT NO. - event number;
FLE STN, IN/IN - the strain at which failure occurred
in either the unconfined or confined compression
test, in inches per inch;
FPR MNT - Fort Peck Reservoir, Montana;
FT - feet;
KT - kiloton, one thousand tons equivalent weight
of TNT (trinitrotoluene);
LIP HT, FT - apparent crater lip height, in feet;
62
I
LL, PR CT - liquid limit (see ATTBRG LIMITS), in
percent; the water content of the soil which
differentiates between the plastic and liquid
consistencies of the soil;
LRL - Lawrence Radiation Laboratory, California;
MELT, MPSI/CIN - the energy required to melt the
j material, in thousands of pounds per square inch
per cubic inch;
ML - inorganic silts and very fine sands, silty or
clayey fine sands or clayey silts with slight
plasticity;
MOIST, PR CT - moisture content, expressed in per-
cent of the dry unit weight of the material;
MTCE - Multiple Threat Cratering Experiment;
NM - nitromethane;
NTS-A5 - Nevada Test Site Area 5;
NUC - nuclear;
PHI, DEG - the angle of internal shearing resistance,
in degrees ,based on Mohr-Coulomb failure theory;
PI, PR CT - plasticity index (see ATTBRG LIMITS), in
percent, the water content difference between the
liquid limit (LL) and the plastic limit; the
plastic limit being that water content of the soil
which differentiates between the semisolid and
and plastic consistencies of the soil;
63
POISN RATIO - Poisson's ratio, ratio of the horizontal
stress to the vertical stress, which resulted from
the theory of elasticity;
PRE-GDLA - Pre-Gondola;
REF NO. - reference number;
RMK, SEE NTE - remarks, see note;
SLP DEG - approximate angle the apparent crater slope
* makes with the horizontal preshot ground surface;
I SM - silty sands, sand-silt mixtures;
SP - poorly graded sands, gravelly sands, little or
* Ino fines;
SP GR - bulk specific gravity of soil or rock grains;
TNS - tons;
TNSLE-D, PSI - direct tensile strength of the material,
in pounds per square inch;
TNSLE-S, PSI - splitting tensile strength of the
material, in pounds per square inch;
UNC COMP, PSI - unconfined compressive strength of
the material, in pounds per square inch;
USCS CLASS - the "Unified Soil Classification System"
(73);
VAPOR, MPSI/CIN - the energy required to vaporize the
material, in thousands of pounds per square inch
per cubic inch;
64
WT-VOL - weight-volume;
YFC WSH - Yakima Firing Center, Washington;
$ - indicates the value following is an estimated
value.
Cataloged Crater Data. The crater data cataloged is
computer listed in Table 2.
Cataloged Material Property Data. The two line computer
listing of the cataloged material property data associated with
the cataloged crater data list is presented in Table 3.
Notes. The notes, referred to in either the catalog of
crater data or the catalog of associated material properties,
follow Table 3.
65
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'-C
X~ TIAPPENDIX II
THE COMPUTER PROGRAM
Description of the Program Elenents. Considerable time
and effort was expended in developing the program and its
formats. Therefore it seems appropriate to include it as an
appendix. A brief description of its essential features
follows.
Main Program. -This portion of the program is nothing more
than a calling program, i.e., it calls the various main sub-
routines to read, sort and print the data and to perform the
surface fit of selected data.
Subroutine REDATA. -This subroutine reads and stores all
crater and material property data into the computer data banks.
Six cards are read for each cratering event. in addition, any
note cards associated with an event are also read and stored.
Subroutine PRDATA and Related HEAD Subroutines. -This sub-
routine prints all crater and material property data along with
calling the related CDHEAD, MPHEAD1 and MPHEAD2 subroutines to
provide the necessary headings for the output data. This sub-
routine produces the cataloged data listing.
Subroutine SURFIT. -This subroutine is the main program
for the conduct of the least squares surface fit and analysis.
It primarily calls the various subroutines necessary to perform
the surface fit and analysis. It also specifies the dependent
94
variable (radius, depth or volume), the scaling exponent and
the number of independent variables to be used in the surface
fitting process. In addition, it calls for or specifies
printing of all pertinent matrices and coefficients.
Subroutine EQN. -This subroutine determines the type
regression and the independent variables to be used in the least
squares surface fit. It develops the vector of observations and
the matrix of measured independent variables and normalizes
these matrices to provide better matrix inversion and manipu-
lation.
Subroutine CORCO. -This subroutine develops a simple
4 correlation matrix between all the variables involved in the
surface fit; dependent as well as independent.
Subroutine COEFF.- This subroutine takes the vector of
observations and the matrix of measured independent variables
and generates the vector and x-coefficient matrices. These
latter matrices are, in essence, the normal equations which must
be solved simultaneously to obtain the regression coefficients.
Subroutine ABPRN. -This subroutine prints the coefficients
of the prediction equation. It also prints the decoded form of
these coefficients when the model used was either a three or
four parameter bell curve.
Subroutine PREDIC.- This subroutine calculates the
estimated value of the dependent variable for each observation
using the empirical equation generated and compares this value
95
N,
with the actual. It also calculates the multiple correlation
coefficient and standard deviation for all the data being
considered.
Subroutine MATINV. -This subroutine inverts the x-coeffi-
cient matrix to be used in solving the normal equations.
Subroutine MATPRN. -This subroutine prints a square matrix.
It is used to print the x-coefficient matrix as well as the unit
matrix which should result when the x-coefficient matrix and the
inverse of the x-coefficient matrix are multiplied together.
Subroutines SIMALT and MULT.- These subroutines multiply a
square matrix times a column matrix and a square matrix times
another square matrix respectively. They are used to multiply
the inverse of the x-coefficient matrix times the vector matrix
to obtain the coefficients of the curve fit and to multiply the
x-coefficient matrix times its inverse.
Typical Program.- A computer printout of the program as it
was run during the latter stages of the research follows.
Sample Data Output.- The computer output for a simple
regression analysis of scaled radius as a function of scaled
depth of burst and one material property, total unit weight,
using the skewed bell curve model follows the program.
96
PROGRAM hIAN(INPUT,DUTPUTtTAPE5:INPUT,TAPE6=OUTPUT,PUNCH,TAPE?=*PUNCH)
C MAIN PROGRAMC
CALL RE04TA (NOATA)CALL SURFITCHOATA)STOPENO
SUBROUT14c REBATA(NDATA)C THIS SUBROUTINE READS ALL CRATER AND MIATERIAL PkROPLRTY DATA FOR EACH4C CRATERING EVENT. SIX CARDS ARE READ FOR EACH EVENICITEM NO.) ALONGC WITH ANY RE41ARKS(NOTE) :ARDS. A BLANK CARD MUST BE INSERTED BETWEENC DATA CARDS AND NOTE CARDS AND AT THE END OF THE NOTE CARDS.
COMMHON W(Z00,28),SNDTC200,4)tSITECZOO,?JDATE(200,21i*EMED(20Os,1EXTYPE(200)YEL(20,3)TNTdT(200!rgDDBC200)I'RAOIUS(200) DEPTHC200), VOL (200) ,tTL IPI200)t'RHICD(200),ELEVCZOO),CLASS(200,2)COMMON SPGR(200),UWT(23O),PMOIST(230),SPtEUC(20O),DITEN(200),'UCOMP(200) ,UCSTN(200) ,CCOMP(200) ,CONFP(200) ,C^CSTN(200) ,PHI(200)t#COHES(200),POI..(00,BULK(200),SECHOD(200),YOUNOD(2O0).'SHEMHD200),SELVEL(U.0I,SHEVOL(200I,ATTLL(200),'ATrPI(2001,CORE(200),EHELTc200),VAPOR(200),RNKMIP(200,2)COMMHON INO(200) ,NREF(2O) ,ISL(200) ,MREF(200)COMMON /NOTE/ NCARO(103) ,RNTE(100),TEXT(100?193I:0
4(DATE(IJIJ:I,2).(EMEO(I,J),J:l,2),EXTYPE(I),(YIELD(IJI,Ji3)1*TNrWT (I)IF(INO(I).EQ.0)GO TO 230
I'HT.IP(I) ,RHKCD(I)
'-SPGR(I),WC,5hsUWTI)t4(It6),pmoistCi)READ C5,40)W(lid),SPTENi(I),W(I,8),DITEN(I)tW(I,9),UCOMP(I),W(I,10),
READ(5,50)W(I, 14) ,PHI CI) ,W(1915) ,COHESC I) ,NCI,16) ,POISN(I),
#SHEMOOCI)
'W(I,24),ATTLLCI),W(I,23),ATTPICI),HCIv26),CORECI),W('i,2r),9EHELT(I)tW(1928),VAPORCI),CRMKMP(I,J),J:1,2)
10 FORHAT~iX, ?I'.6A'.,2A3 2A4,2X,3A4,A2,F13.2)20 FOR.MAT(5X, 3VF.2,F13.,Z,l3,A2,F6.ZA4)30 FOiRAT21X,2,z6.Ot8X,2A3, I',A2,F5.2!,A2,F6.1,A2,F5.1140 FOiRMATC5X,2(A2,F6.0) ,A2,F7.0,A2,F6.4,A2,F8.0,A2,F7.0,A2,F6.4)50 FDRMATCSX,42,F5.1,A2,FI.0.A2,F4.2,AZF'5.,3(A2tF9.0))60 FORHAT(5X,2CA2,F7.0),A2,?X,2(A2,F5.1) ,AZFL..0.A2.F6.0,A2,F?.0,A.,A
4 v3)
GO TO 100200 NOATA=I-I
J:0300 J=JI1
READ(5,70)N4CARD(J),RNTE(J),(TEXT(JK),<:i,i9)70 FORHAT(I1.F4.0*18A4,A3l
IFINCARD(J).NE.O)GO TO 300RETURN
'4'J
97
SUBROUTINE PROk\TA(NDAT43C THIS SUBROUTINE PRINTS ALL DATA READ INTO THE COMPUTER BY THE RECATA
COMMON t4200928)hSHOT(200,LdSIrE(2O0,2),DATE(200,2) .'EMEDC200,2),EXTYPE(200),YIELD(200,3),TtrwrcZ00),D0oc200),
*RAOIUS(U!00) DEPTH(200), VOL (200) ,HTLIP (200)t
*RMH(CO(200) ,ELEV(200) ,CLASS(200, 2)
f COMMON SOGR(200)tUWT(20O),PMOIST(20O),SPrEN(200),OITEN(2O0),
*UCOMP(200) .UCSTN(200) ,CCOMP(200) ,CONFP(2OC) ,CCSt'4(200) ,PHI (200)9'CO'ES(200)POISN(200),BULK(200),SECMOO(20hYOUMOD(200)t'SHEMOO(200),SEIVEL(200),SHEVOL(2O00)ATTLL (200),'ATTPI(200hoCDRE (200) ,EM1ELT (200) ,VAPOR(200) ,RMKMP(200, 2)COMMON INO(20O)tNREF(20O),ISL(200) ,MREF(200)COMMON /HOTE/ 4CARD(102),RNTE(100),TEXT2.0O,19)I1iJ
2.00 CALL COHEADNLINES:7
200 1:141bdRITE(6,1i )INO(IhtNREF(I), (SHor(i,J) ,J=1,'.),(SIrE(I,J) ,j:1,2),'(DATE(I,J) ,J:1,2),(EMEO(I,J) ,J=1,2) ,EXTYPECI) , YIELD(r.J) ,j:1,3),*TNTWT (I) ,O03 () IRAOIUS(I) DEPTH(t), VOL (II, 1(1, 1) ISL(I;,W1(I,2)1OHTLIP(I) ,RMKCD(I)IFCI.EQ.NOATA)GO ro 300HL INES=NLINES42IF(NLINES.EQ.59)GO 1*0 100GO TO 200
300 1=04.00 CALL MPHEOI
NLINES=8K=O
500 1=1+1
'(EMEDYJI ,J=1,2)t,(CLASS(IJ) ,J=1,2) ,MREF( I) ,W(I,9.) SPGR(I)t
'W(I,9),UCOHP(I),WCI,2.0,UCSTNCIhWCI,11),CCONP(I),W(1,12),*CONFP CI) ,W(I, 13),CCSrN( I)IF(I.EQ.NDTA)GO TO 550NLLNES=NLINES*2IF(NLINES.LT.30)GO TO 500
550 CALL MPHE02NLLNES:NLINES4IIll-K
560 1=1+1WRITE(6,301 INOCI) ,W(IL4.hPHL(I),W(I,15) ,COHES(IW(I, 16) ,POISN(I)
1,W(l,17)tBULKCl) ,W(1,13),SECMOO(I)tW(Il9) ,YOU.40D(I) ,WCI920)t*SHEMOD( I)tW( 1,21)tSET VEL ilhn( 1, WSE''J.'
W1(,24),ATTLL(l),W(1,25),ATTPI(I),W(1,26)vCORE(I),W(I#27)9EMELT(I),W(1,28),VAPOR(I),CRMKMP(I,J),J-'1,2)IF(I.EQ.NOArA)GO TO 603NLINES=NLINES42IF(NLINES.EQ.59)GO TO 4.00GO TO 56~1
00IF(NCARD(J*I).EQ.0)GO TO 700
620 14RITEC6,'.01NLLNE3=2
630 J:J~t
98
IF(NCAROfl).GT.L)Go To 650WRITE (6, 50)RNTEC , (rTExT U,I, K~i,19)NLINESNL'4ES*2GO TO 670
650 WRITE(6,60J (TEXT (JK) ,K:j,19)NLINES=NL14ES,1
670 IF(NCARD(Jfl).EQ.0)GO TO 700IF(NLINES.GE.60)GO TO 620GO TO 630
700 WRITE(6,tOINDATA10 FORMAT ('00,2146A4,2A3, 2At.ZXt3At,A2,F3.2,3F8.2,F13.2,A2,13,A2,F6
*.2tA4)L 20 FORHAT('0', 14,4A4,A2,F6. 0,2A4,2A3,I4,AZ,F5.ZA2,F6.1,A2,F5.1,2(A2,
*F6.0) ,A2,F7.0,A2,F6.c.,42,F8.0,A2,F?.0,A2,r 6.4)30 FORMAT('0#,I4,A2tF5.l,42,F7.09A2F,.2,A2,F5.2t3(A2,F9.0) ,2(A2,F?.0
.)2 (AZ ,F5. 1) ,A2, F4.0 2( A2,F7. 0) ,A'.,A3)40 FORMAT(*1',36X,'N 0 T E 5')50 FORMAT(*0',F..0, 18A'.,A3160 FORMAT( *v4X,18A4,A3)70 FORMAT(fif,wTHE NUMBER OF DATA ITEMS =*#15)
RETURNEND
SUBLROUTINE CDHEADC THIS SUBROUTINE PRINTS THE HEADINGS FOR THE CRATER DATA LIST~ING.
WRITE (6, 10)10 FO.RAT(#1#953X,'C R A T E R D A T A'//18X,'IDENTIFICATIONP,2.X,
**EXPLOSIVE OATA',dXvfDEPTH*,IOX,vAPPARENT CRATER DIMENSIONS*,7X,'*RMK*/2X,* -----------------------------------------
------------- 0: --------------------
WRITE (6,20)20 FOiRMAT( 0,0 EVT REF SERIES/SHOT',5Xt'SITE DATE MEDIUM TYPE
fYIELD',5X,'EQUIV WT alURST RA DIUS DEPTH*,5X,'VOLUME SLP#LIP NT SEE*/2X,ONO. NO.*,7X,'NAME*,14Xi*MO YR*,28X,'LDS-TNT*FT Fr FT*,7KP*CU FT DEG FT UTE*/2X,' ------- --
RETURNEND
99
TI
SUBROUTINE HPHEOIC THIS SUBROUTINE PRINTS THE HEADINGS FOR THE FIRST HALF OF THE MATERIALC PROPERTY LISTING
WRITE(6,30)30 FORHAT('I','3X,'H A r E R I A L P R 0 0 E R T Y 0 A T A//,
# /IOX,'SHOT IOENT.*,l4Xt*MATERIIAL*v6X,'W*r-VOL RELATIONSHIPS', 2X,'STREtJGTHS AND STRAINS#/2XP* ----------
------------------------------------
WRITE(6,O)40 FORMAT(
* f,* EVT SERIES/SHOTv,5X,*ELEV MEDIUM USCS REF SP GR
#D y UWT MOIST TNSLE-S TNSLE-D UNC GOMP FLE STN CONF COMP CNF PRE*S FLE SIN"f2X,'NO.*,7X,*NAME't9X,*FT',tI,*CLASS NO.',aX,*LB/CUFT0 PR CT PSI PSI*,6X,'PSI IN/IN PSI#,7Xt*SI INIIN*/
*2, --------------- --------------------------
--- 4 --- -------- ------- --------- -------- -----
REiURNENO
SUBROUTINE MPHED2
C THIS SUBROUTINE PRINTS THE HEADINGS FOR THE SECOND HALF OF THE MATERIALC PROPERTY DATA
WRITE(6,50)50 FORHAT(wO0*f 4/9X,*AI)(t STR-STNI PARAMETERS
**tl3X,*MOOULUS VALUES, LOX,OWAVE VELOCITIES't2X,'ATTORG LIMITS5X
, INTERNAL ENERGIES REMKS'/* ... ............................--------------------------------- -------------
*CORE ----------------------- '
WRITE(6,60160 FORMATI *,f EVI PHI COHESION POISN OULK SECANT YOUNGS*
t6Xt'SHE4R SEISMIC SHEAR LL PI',3X,'RECOV*'JXq*HELTf VAPOR SEE'/ NO. DEG PSI RATIO FACTOR PSI ',7X,f*PSI',8X,*PSI't7X,'FPS FPS*,4X,*PR CT PR CT *R Cl MPSI/CIN MP"SI/CIN NOIE /2X, ---.----------------------------------------
---------- #)
RETURNENO
100
SUBROUTINE SURFIT(ND)C THIS SUOROUTINE DOES A LEIST SQUARES SURFACE FIT FOR RADIUS* DEPTH, ANDC VOLUME OF THE APPARENT CRATER
DIMENSIONSEC (200) ,LX( 41hLY.1) ,AU( 200, 4OhCOL (2O) ,XMEANC(40),*VECT('.O),KKOEF(40,(401,KI((1600)si3(40),*HOLXK(409'.3),R(440,,),UMIAT(C,,'.),VAR(3)COMMON UUM(200,t8)tltO(200),IUUM(230*3)COMMON IAYC/ UAN(40),ANS(40),EXPOEQUIVALENCE (XKOEFtX()DATA BaCCDDEE,SMAL/(4HXKOF,4HPRtir,4tMUNlT,4HCORk,1.E-OQ6/DATA DVAR/6H4RADIUS,bH OEPTH.briVOLUME/
C M:1 FOR RADIUS, 2 FOR~ DEPTH, 3 FOR VOLUMEC L=1 FOR EXPO=0.250, 2 FOR 0.292, 3 FOP 0.3125, 4 FOR 0.333, 5 FOR VAR EXPO.C IKi FOR 3 PARAMETER, EQ3., 2 FOR 4 PARS., 3 AND 4 FOR 2 9AT. PROPS.,C 5 AND 6 FOR .5 MAT. P'zops., 7, 8, 9, AND 10 FJR 4. MAT. PROPS.
DO 900 1:1,3L=3DO 900 IK=.,10IF(KK.EQ.6.OR.K.EQ.7)GO TO 900CALL EQN(COLAU,NDN4P,LCNORM, XMEAN,R,SEC,KK,M4)
33 WRITE(69IIEXPOtOVAR(9)I FOIRMAT(*1',oEXPONENT=*,rb.4,* FOR *,A6lo EVALUATIC1N')CALL MATPRN(RtNPEE,CC)CALL COEFF(COL,AU,VECT,XKOEF,ND,NP;,M)WRITE (6,2)
e FORtiATC'lf/f PRESENT CONTENTS OF VECT HATRIXT11WRITE(6,5) (COL(IhvI=1,N0)
5 FORMAT(*'F12.4)CALL MATPRN(XKOEF#NP,OUtCOCDO 100 I:1,NP00 100 J=L,NPNOLXK(I,JD =XKOE;(19J)
100 CON4TINUECALL MATINV(XKsLx,L09NP,40,SiAL)CALL MULT (UMATiXKOEF, HOLXK,NP)CALL MArPRCUtMAT ,NPDU, CC)
150 CALL SIMALT(XKDEFVECTPAHSNP)WRITE (6,8)
d FORMAT(*1'/' NORM. COEFS. OF THE PREDICTION EQUATIO49'00 200 K(?I,NP
200 )RITE(69t3) KANS(K)10 FORMATC'0v NC', 12,*)=' ,F19.I0)
00 90 K=:1,NP90 UAN(K)=ANS(K)/XMEAN(K)'CNORM
CALL ADPR'4(UAtNNP,KK)CALL PREDIC(COL,AtJANS, INONDNPMCNORMSEC)
900 CONTINUERETURNEND
101
SUBROUTINE -QN(COLAUvNDNP, LtCNORMXMLAN9RsSECK<,H)C THIS SUOROUTINE DETERMINES THE TYPE REGRESSION AND VARIABLES TO BEC USED IN THE LEAST SQUARES SURFACE FIT AND DEVELOPS TH4E AU ARRAY
DIMENSION COL(N9),AU(ND,4O),XMEAN'(40hoRC40,40)REAL MEDDIMENSION MEOCZO0)hTYPE(6)oSEC(NO)DATA TYPEilk R9JH S?,5N 5,311 HM CISH CA4/COMMON W(20,28)tSHOT(200,4)*SIIEC2D002,OArE(200,21,
*EMEDI200,?) ,EXTYPEC200I ,YIELD(200,3)ttNTWTt2OOhDOOB(200)t*RAUOIUS(200OhDEPTH(C200) VOL (200) slTL IP(200) 9*RMa(CO(200) ,ELEV(200) ,CLASS(200,2)
COMMON SPGR(2OO),UWT(2301 PM IS T(200) SPFEN(200),0D1TEN (2001,UICOMP(200) ,UCSTN(2OO) ,CC.OHP(200) ,CONFP(200) ,CCSTN(200) ,PsIlc200)
*COHES(200) v PO ISN(200) ,BULKC200) ,SECMOB( 2U0) ,YOUMODC(200)*SHEHOD(200),SEIVEL(200ISHEVOL(200),ATTLL(2003,*ATTPI(2g0),CO'-E(200),EMELT(200),VAPOR(20J),RMKHiP(2Oo,2)COMMON INO(200hvNREF(200),15LC200) ,MREF(ZOO)COMMON /AYE/ UAN(40),ANS(40),EXPOCNORMH 0GO TO(30,3t,32,33,34)vL
30 EXPO~i./4.GO TO 40
31 EXPO:7./?4.GO TO 40
32 EX,'O=5./15.GO TO 40
33 EXPO=1./3.GO TO 40
34 EXPO=1.0h40 CONTiNUE
00 50 J= 1,NO43 WUW4T =((1.4PMOIST(J)/100.)'UWIT(JH/62.43
S HU T=WUNT ( E XPO)SIt;=I.O-(UWT(J)/62.43)' ((1.0/SPGR(J)) +PMOISTCJ)/100.)
VMOTST=PP4OIST(J)*UWf(J)/624J.P'ROS=SIGtVmOISTVOURA T=PROS/ (I 0-PR~S)DE5AT:vmotsr/P~osGO TO (210,220,230)tH
210 Y=iRADIUS(J) /TNTwtCj)wf(Expo)GO TO 250
220 Y:O)EPTMCJ) /TNTWT(J)'(EXPO)20GO TO 25020IF(VnL(J).LF.O.J) VOLWJ):.0
Y:V'JLCJ) ''C I./3.)/TNTWr (JI '*(EXPO)250 X= 008(J) /TNtNt(J)f4(EXPO)
1F(Y.LE.0.000)Y= .01
YY=ALOG( YIXX=ALOG(XO-1.0)COL (JI =YyCNORM=CNORM+COL(J)/NO
110 TO (ItO,120,130,135, 140,140,I60,15O, 150,160) ,K'
- AU(Jo 2)=X
NP=3
1 02
GO TO 50t20 AU(J,1)=COL(J)
- - AUCJ,2)=XAUCJ93)=X*<AU(J,4L=X*3NP=4GO TO 50
130 AU(J,L):1.0AA=SWUWT83=DESAT
AU(J,31=03
AU(J95) :80*?AU(J,6)=4A't3Cl
GO TO 180
AIJ(J,2) =SWwr
GO TO 180140 AU(J,L)=t.J
AA:SWUWTBB:OE SATCCzSPGR( J)AUCJ, 2)=AAAU(Jt3)=00AUC,4) CCAUCJ,5)=AA*02AU(J,6)=BBO*2AU(J,7) =CCIF2AU(J, 8)=AA'OflAU(J:9)=AA$CCAU(J, 10)=OO0CNMP=10GO TO 180
AA=SWUWTOB=OESATCC:=SPGR(J)PHE=PHI(J)/180.0*3.1.i593IF(KK(.EQ.9) CC:TANCPHE)
ALI(J,2) =AAAU CJ, 3) :9AU(J,4)=CCAL UJ, 5) =AA 1*2AUCJ,6)=VAPOR(J)AU(J,7)=CC*42AUCJ,8)=AA*9RAU(J, 9) :AA*%C
NNP=10180 tS=NHP~1
NP=NMP*300 300 M=,4S,NP
300 AU(J,tV4)=AU(Jt,419-NMPI*KIF(KK.EQ.3.OR.KK(.EQ.5)GO TO 47
103
IFIKK.EQ.I70O TO 47MS:NPiIMF=NP+NHP00 '400MM?1MS,MF
400 AU(JNt1) :U(J,MM-NP)fX '3NP=NP+NMP
4? AU)(J,I)=COL(J)50 SEC CJ)=D0D(J)/TNrwrT(J)'- (EXPO)55 00 60 K1I,NO
COL (K)=COL (/C.40RM60 CONTINUE
00 71 J~1,NPXMEAN(J) 3.000 70 I=1,NO
70 CONTINUE00 80 J=I,Np00 8c 11I,NaAU(IJ)=fUC:,J)/XMj-AN(J)
80 CONIINUECALL C0RG0(AU,R,N0,NP)00 85 K=1,ND
XME AN( 1) =1 . 3190 RETURN
END
SULJROUTINE C0RC0CXRvNONC)DI4ENSION X(NO,40)oR(40,40)DO too Izis.4G00 130 J=I,N:
100 RtI,j)=0.000 400 J:1,NCDO 400 I=JtNCTOPC=0. 0TOPI=0.0TOPJ=0.01OTI=0.3BOTJ=0.0DO 300 K:1,NDTOPC=TOPCt4(K,1)*Xi(KoJ)
TOI'J=YPJ.'K(K,J)dorIz9OTI*4(K,I)**2aoOVJ BOorJ' (K,J)*vz
300 CONTIVUER(Ij)=(TOPC-T0PI/NO'TOPJ)/ SQRT((I3OT1-TOPI/NO'T0PI) '(BOTJ-TOPJ/ND4**TOPJ))
400 CONTINUERETURNENO
104
SUOROTINEAOPR~jA~777KKDIESO jA(09(0942
00 200 K:2,NP200 WRITE(6,10) KUANP(K
GO TO (31013209 80098009 80098U0,v800, 800,9800,800) ,KK
8(2) mUAN(J)8(3S) UAN(?) / C2UAf4(3))4 WRITE (6,88)
88 iORtAT(*Df/f COEFFICIENTS OF THlE PREDICTION EQUATIONv)00 101 M4=1,NP
101 WR[TEC6,11) HMt,8(IIH)
GO TO 800320 8(2) =UAN(4.)
BFZUAN (3 )/UAN (4~)BP= ABS(DT)UNt.AOBP2.0-(3.0OUAN(2)/UANq(L))IF(UNRAO.GE.0.OiG0 r0 755WRITE(6909J) UNRAO
700 FORMAT(*9f,fUNRA:',F2j.10)UNRAO=0.*0
755 asQr= SQRT(UNRAD)04d1 =(OT48S))/3.004.(2)=:(Bl-BSQT)/3.000 900 JJ=1,2
813 0(4 )=84(JJ)812 0(4) :OT-(Z.0*0O4fl
8NEG= AtdS(3(d))0C1)= EXP(UA,4(1)- B(- l()dE*2WRITE (6,55
55 FORMAT(*O*/w COEFFICIENTS OF ITHE PREDICTION EQUATIOW"I00 191 MI=1,NP
191 4R;ITE(6,221 ?imN,3(MH.4)
900 CONTINUE800 RETURN
E NO
SULJROU11INE C^OEFF (tOLAU, VECrT XKOEF, NO,NP, N)C THIiS SUtTROUTINEr SENERATCS AND ASSEMOLLS THE VECT AND) Xl'EF MATRICIC5
DIMIENSION COL(NO),AUN,4,VECT(.o),XKOC' C40,4.9)ADA TA=NODO 10 I=1,NPVECT( I) =0.
10i CONTINUE00 30 11L,NP00 25 J=1,NOVECT CI) :VECT( I) +CJL(U) AU(J, I)
25 CONTINUE- VE0T(IJ=VECr(IfA0ATA
30 CONTINUE00 20 J=1,NP00 20 K=1,N?XKOEF(J,KI=0.0
20 CON TI NUE
105
-- -- ----
00 4.0 t=t,NP
DO '.0 Jzl,i~P
35 CONTINUEXKOEF(IJI:(KOEF(IJ)/ADATA
4.0 CONTINUE50 RETURN
ENO
SUBROUTINE PREOIC (COL ,AUANS, IEV oNO, NP, M, CNORt1,SEC)C TIS SUBRouriuzE OALCULAfES THE RAOIUS, DEPTH4, OR VOLUME USIN6 THECEMPIRICAL EQUAT ION G NERAIED AND COM9PARES THESE VALUES .4ITH THE ACTUAL.
DIMENSION IEV~t'),COL(D)AUINO,'.),ANS(NIP),)VAR(3),SEC(NO),PAR(2)DATA DVAR16HRAQIUS,6H OE-PTNivbHVOLU4E/WRITE(6,10)DVAR(M)
1G FORMATCI4 ,A46,0 PREOICfION AND EVALUATIONviWRI TE C6t231
20 FIMT411~"ROCE VALUE*,12X,fACTUAL VALUE*,12x,4 PERCENT*RROR*,12X, 'RESIDUAL4, 9XEVENT t;O.%96X,*SC ODO3~)CliEAN=0.0DO 90 'at,NO
90 CMEAN=CME4Nf EXP(COL(I'lCNORm)RTOP=0.0RBOT=0.0NLINES=000 200 1=1,40PREVAL =3.6~
00 100 J:I,NPPREVAL:PREYAL#-U(E.J)*ANS(J)
100 CONTINUEP RE VAL=PRE VAL'CN ORHAc r VAL=COL (I1) *C.OI1MPREVAL: EXP(PREVAL)ACTVAL: EXP(ACTVAL)
IF(CACTVAL, EQ.0 * ) AC IVAL=: .OE-3EiORSI/TAi10RES IO=PREVAL-ACTVAL
WPRITE (6,31)PRE VAL, ACT V4L ,ERROR ,-SIDIE V(I) , 3EC( )30 FOP(MAT(I- *,6X9Fll.6gdXtF17.6,15X,Fd.Zl6X,F17.6,gX,1I5,2x,F15.4.)
Rr0P:RT0~f PREVAL-CNORI '2RBOT=R8OT# (ACTVAL-C,4ORi)**?NLiNPS=NLINESflIF(NLINES.LT.50)GJ) 10 200
2:NL I fES=O
20 ONMTNUE UTCR~CE %921 TN.DVITO O
',F12.41'i
RETURNEND
106
SUBROUTINE MATINV (AtIROWeLCOLNPNOIMSNLST)DIMENSION A(1600),IROWC41) ,ICOL(4i)
* N=NP?PL=N+i GUNA 13600 5 I=1,N GUNA 137
FICOLI I) 1 GUNA 1385 IROW(II=I GUNA 139
00 75 ITER:1,N GUNA 14.0,IAXR: ITER GUNA 141?AAC~i C.UNA 142TE.1P= AOS(A(MAXR))LIg1ITC=NP1-ITER GUNA 144'00 15 I=IrER,N GUNA 14500 15 J=1,LIMlT: GuNA 146IJ:(J-1) 'WOIM4,I GUNA 147IF (TEMP-( ABSCA(IJ)))' 10,15915 GUNA 14dI:10 iAXR~I GUNA 149tAXC=J rUNA 150TEMP= ABS(4(IJ)) (,UNA 151
15 CON TINUVE (,UNA 152SMLST=-0.0 GUNA 153IF (TEIP-SfL3r) 20s2lo25 rtUNA 154
20 IROW(NP1)=ITER GUNA 155(RI TE (6, 203) ",UNA 156
200 FO.RNATU0',g*TIS IS A SINGULAR MATRIX ANO IT WILL NOT ltXVERT*)25 IF (MAXR-IrER) 30,40,33 rUNA 15930 00 35 J=1,N CUNA 160
tiAXRJ=(J-1)*N0I4+4AXR GUNA 161ITJ=(J-1) 'NOIM#ITER GUNA 162rEMP=A(MKRJ) qUNA 163A (MAXRJ):A (I TJ) GUNA 164.
35 A(ITJ)=TE4P GUNA 165ITEMP=lRO (IAXR) GUNA 166IROW(MAXR) :IR0W( irER) 'rUNA 167IROW( ITERI =I TEMP GUNA 168
4.0 IF (MAXC'-1J 45,55945 GUNA 169s4.5 00 50 119 GUNA 170
IMAXC=(MAXC-i) 'NLJI.'1+l IUNA 171TEmP:A( 1) tUNA 172AU[)=A(IMAXC) GUNA 173
50 A(IMAXC)=tEIP GUNA 17'.lTtMP:ICOL ('AX:) GUNA 1751^ OL(MAXC) :ICOL(l) GUNA 176ICJL(i)=IrEMP GUNA 177
55 TE IP=A(ITER) GUNA 178ITEMP=ICOL (1) r.UNA 17900 60 J=?,N GUNA 180ITJMI=(J-7^)"NOI?+IrER GUNA 181ITJ=CJ-1) 'NDIM+ITER GUNA 182A (I TJI) :A I TJ) / TcMP ';UNA 183
60 ICOL(J-L)=[I'0L(J) GUNA 18'.
ITN:(N-1I 'tJIM+I tER GUNA 185A( ITN):1.Oftr.N' GUNA 186IC3L(N) :ITEtP ';UNA 187
IF (I-IT! .R) 65915t65 GN 8
1.07
IJ314J-)NIMI G'JNA 193U' t(-1 NOIITE GUNA 193
70 CONT INUE GUNA 196INx(N-l)*XlIM#I GUNA 197ITNx(N-1I 'NOIM#ITER (GUNA 198
A(IN~u-(TENIP*A(ITN)) GUNA 19900 100TINUE N GUNA 20000 100 JIx,9N GUNA 202I0 6 (RWjl 8,8x8 GUNA 203I0 CONINUEJ-j 085 GUNA 203.
85 IF (1-J) 90,100,90 GUNA 20590 00 95 11,iN GUNA 206
LI' (I-1)*NAIM.L GUNA 207L~x(Ji)*HIM+LGUNA 208
TEAPmA (LI) GUNA 209A(L I)sA(LJ) GUNA 210
95 A(LJ)uTE1* GtJNA 211IROJW(J3 :IROW( I) GUNA 212
100 CONT INUE GUNA 21300 125 IstsN GUNA 21400 105 JVION GUNA 215IF (ICOL(JI-1) 105,110,105 GUNA 216
105 CON4TINUE~ GUNA 217i1 1 IF ([-4) 115,125,115 GUNA 218115 00 120 L'1,N GUNA 219
112 (1-I) N0IN~I GUNA 220JL' (L-1) 'NOI1.j GUNA 221TENlP2A IL) GUNA 222A(IL)xA(JLI GUNA 223
120 A(JL)zTEIP GUNA 224.ICOL(J) 'ICOL (II GUNA 225
125 CONTINUE GUNA 226IROW(NPi) '0 GUNA 227RETrURN GUNA 228ENO GUNA 229
SUaROUTIN( MArPRN CA ,NP, 8 v RITEDIMENSION AC'.0,'0)
5 FORMAT (90P//)10 FOAMAT(*'%11(ElZ.3))22 FOP(MA T t'i* , 24H~ PRESENT CONTENTS OF 9 44. t SUP 1277
12H H8TRIX ,.
0ATA YAZ/4HPRNT/IF I RITE .ME. YAZ I GO TO (20 SUP 1280WRITE (692?) 8 SUP 1285IF ( N.GT.11 )GO TO 6) SUP 128600 50 Is1,NpWRITE (6,19) (A(IJlJsivNP)
s0 CONTINUE SUP 1289GO TO 500 SUP 1290
60 NIa N/1i11-10
1 08
-------
00 200 K : 1 , NI , 11 SUP 1292
KK = K 10 SUP 129300 100 : 1 , N SUP 1294WRITE (6,10) 4 (1,J) , , K) 3UP 1295
100 CJNTINUE SUP 1296WRITE(6,5) SUP 129f
200 CONTINUE SUP 1299K=011I00 300 = , N SUP 1300
WRITE (6,13) A(IJl , J , N ISUP 1301300 CONTINUE SUP 1302600 ClNTINUE SUP 1304500 RETURN
EN0 SUP 1306
SUOROUTINE SIhALI (A,B,^,NP)OltiNSION A(40,'.) 0('.0),C(0)
N=NP00 200 1 . GUNA 124C([) : 0.0 vUNA 125
200 CON TINU GUNA 12600 500 1 : I , N GUNA 12700 40 J = N rUNA 128C(I) - C(1) A(I,J) * 00,) ,UNA 129
40u CONTINUE GUNA 130500 CONTINUC GUNA 131
RErURN GUNA 132ENO GUNA 133
SUJROUTINE MULT(A,,3,.,P)OIH ENSION A(40,40! ,8(40,40),L(40,40)
M=NPN=NP
00 100 I:ItK UAR 72300 200 J:I,t OUAR 724Q = 0.0 QUAR 12500 300 L=11 QUAR 726Q = + (ItL)*C(LoJ) QUAR 727
300 CONTINUE QUAR 721A(I,J) = Q QUAR 729
200 CONTINUE OUAR 730100 CONTINUE QUAR 131
RETURNENO
109
4
Pal1
l w "I p "I I
. A 17 N. 0 F 0
u. 11 10 11 "1 .1, 0 .1 0 -* 0 " 0
I I I I I>
N -r N N "1 0 %P
10 a, a, 0 .0 . 0 0
N1 U . N. 0' ' - 0
N2 N (V .. . 0 .4 .
z 0 0 a, 0 a N 0r
w 1 N1 CV N4 -0 0 N NN. OfN ~ 0F)0.4 ' 0 0 .
'0 N. 0' 0' 0' .4 0' 0
N N - . ~ .110
oaauaaa0 0 0 0 0
w. ui w. w w Li w4 W4 11 Li Li J4C, a , 10 C, 4 r 0 ) 0 W al -, In 1,a ') .0140 1 Nr Nl .l) I N 2 00
; 1) li Us i I p iLC, 10 t Z %D a a 0 62 ,
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0l 0 * t. W0 112 112 w1 .1 N1 w6 .
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LA UF .* 0 00 4N . .44444l4 444 .0" M041,42444400 .4 v Ci% = .-* .N 0N O
14 4
U, m U4.7 C' wNC0 to O0'OC aNOC'rN CNCUNU, 0 N- O N C.''UN . .000 t, .. COO
'~U. N ''CO 0 ' C0 00'4N4ON0NON C'0C.7 O '. C'0.4 0N 0
C ~ ~ ~ ~ ~ ~ ~ ~ - M N ON040 0 010N OC N '0 '0.4 ' 0 'COL pqU4'C'C. .0 U.0
.11
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Ua ... .44~ N w44 4 4 4 4 4 cyNNNc
i N 40 4 10NN NNNNN0 1 N Ca . 0 ty p N a r .b0 4D O CC UC . N N vi 0N aMJ U,. 10. NN0 0 1- N ,I Nc nNN m eJ o.
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116
IAPPENDIX III
DATA AND PREDICTION CURVE PLOTS
117
4.0
3.0.
eN.
cc1.0
-01:2 1:4 1.'6 1.8B 2.0 2.2 2.4 2.6 2.8o
FIG. 5. CRATER RADIUS AS A FUNCTION OF CHARGEDEPTH FOR CLAY SHALE
xcx
x
:I- x
f6 I-
4i .75
.25201.2 1.4 1.6 1.8 2. 2.2 ~2.4 2.6 2.8
0OB/14u5/ 16
FIG. 6. CRATER DEPTH AS A FUNCTION OF CHARGEDEPTH FOR CLAY SHALE
118
3.-0
2.5
1. 1.2.0.8 20 22 2. . .
-J/W*S1
FI.70RTRVLM SAFNTO FCAG
e.4 1. . B 202. . .
x
In 2.0 x
- I-
~ .0
1.4
a0 . . 1.5 2.0 ~.6 3.0 3.5 1.0 4.5 5DOB/W*5/1
FIG. 8. CRATER RADIUS AS A FUNCTION OF CHARGEDEPTH FOR DESERT ALLUVIUM
119
-x~
1.26 x X/ .x
Lo
x.75 x
-.0
-.0! .5 1.0 1.9 2.0 2.5 3.0 3 .5 4.0 4.s 5.
[JfB/Wwms/ 16
FIG. 9. CRATER DEPTH AS A FUNCTION OF CHARGEDEPTH FOR DESERT ALLUVIUM
2.4toxNx
InX
in e
1. 6 x
XN'xx x
1.2 x
K
.5 1.1. . . . . 4 0 4 5 !
FIG. 10. CRATER VOLUME AS A FUNCTION OF CHARGEDEPTH FOR DESERT ALLUVIUM
120
(0.6
x_.A /xIt 2.00
1%, x1 ].76
cc
1.25
1.0'.-. 6. 1 . 0 1 . 2 1 . 1 6 1 .B 2 .
DO B/ w wG/L6
FIG. 11. CRATER RADIUS AS A FUNCTION OF CHARGE
DEPTH FOR SAND
* 2.0
1.6
N..
IL
03x
.4 xx
-.0 ---------- 0 .2 .6 . 1 .0 1 .2 1 .4 1 6 1 .8 2 .
FIG. 12. CRATER DEPTH AS A FUNCTION OF CHARGEDEPTH FOR SAND
121
2- .60
e esx
I -.5D x
u 1.0is 1. 6 2
H 1..2
FIG. 13. CRATER VOLUME AS A FUNCTION OF CHARGEDEPTH FOR SAND
xx
1.25 K
.75
-.0 .25 50 .7S 1.00 1.25 1.503 1.75b~ 0 22
} OOB/Ww&/16
FIG. 14. CRATER RADIUS AS A FUNCTION OF CHARGEDEPTH FOR BASALT
J2
xx
IL-ILl
.4.
-.00 .25 -SO .79 1.00 4.2S .6 7S2.00 2.25
DOB/Wm*S/16
FIG. 15. CRATER DEPTH AS A FUNCTION OF CHARGEDEPTH FOR BASALT
1.70 x.
No
3c
K 1.26
1 .00
.75
-.00 .25 .50 .75 1.00 1.25 1-60 1.75 2.0 22
FIG. 16. CRATER VOLUME AS A FUNCTION OF CHARGEDEPTH FOR BASALT
123
e~0.
12.6
1o .4
X x
x
w 1.0.C3K
.4 .6 .8 1.0 1.2 1.4 1.6 1.8 2.0
FIG. 17. CRATER RDEPUS ASA FUNCTION OF CHARGEDEPTH FR ALLUVIUM (ZULU SERIES)
124
k~e 2, .....
1.8
[*x
x x
.5
cr,- . 6
0 .2 .46 .61 . 8 1. 1.2 1.4 1.6 1.8 1.0
r O/Wa~ws/16
FIG. 10. CRATER VOLIUE AS A FUNCTION OF CHARGEDEPTH FOR LLU IM(U RIES)
VT
L -
1.2
.~. 1.0
a-
.4
.2 4 6 .8 1.0 1.2 1.4 1.6 1.8 2.DOB/WuwS/16
FIG. 21. CRATER DEPTH AS A FUNCTION OF CHARGEDEPTH FOR VARIOUS ROCK
-e.O0 x
- 1.75o
1a
N.c
1.25
1 .00
,75
.0 .2 .4 .6 .8 1.0 1.2 1.4 1.6 1.8 2.
DOB/WmS/16
FIG. 22. CRATER VOLUME AS A FUNCTION OF CHARGEDEPTH FOR VARIOUS ROCK
126
LoCo xItL NN 1.4
crCC
-.0 .2 .4 .6 .8 1.0 1.2 1.4 1.6 1.8xv OB/Wmws/16
FIG. 23. ,CRATER RADIUS AS A FUNCTION OF CHARGE* DEPTH FOR PLAYA (AIR VENT SERIES) X
xx
.50
0O8/WwimS/16
FIG. 24. -CRATER-DEPTH AS A FUNCTION OF CHARGEDEPTH FOR PLAYA (AIR VENT SERIES)
127
x
i.e
1.2
.6
FIG. 25. CRATER VOLUME AS A FUNCTION OF CHARGL
1.6 DEPTH FOR PLAYA (AIR VENT SERIES)x
1.2
xx
C3I-
FIG. 26. CRATER RADIUS AS A FUNCTION OF CHARGEDEPTH FOR PLAYA (TOBOGGAN SERIES)
128
112
1.0
x
Lo X
CLu
[ .2
x
-.00 .25 .50 .75 1.00 1.25 1-50 1.7S 2..00 2.26
0B/4m5/ 1.6
FIG. 27. CRATER DEPTH AS A FUNCTION OF CHARGEDEPTH FOR PLAYA (TOBOGGAN SERIES)
m 1.6 1x 1.2
.4
-Do .25 -50 .7S 1.00 1.25 1.50 1.75 2.00 2.25
DOB/WmwS/16
FIG. 28. CRATER VOLUME AS A FUNCTION OF CHARGEDEPTH FOR PLAYA (TOBOGGAN SERIES)
129
4.0
Lo
rX X-. 0
.0 ~~ x 1. 15 2. X5 30 3S 40 4S 5
2.0 202 30 540455FFIG. 30. CRATER RDPTH AS A FUNCTION OF CHARGEFDEPTH FOR ALL THE DATA
e130
x
iiliEIxx xAeCo0
x 'x 2.0
Cx 1 x x t
x IX ^ft
I~~~ __________________
OO/ xM/1
FIG 31xRTRVLM SAFNTO FCAG
DEPT FO LTEDT
x
4x
131
1 APPENDIX IVGENERAL EQUATION COEFFICIENTS
132
TABLE 4. GENERAL EQUATION COEFFICIENTS FOR RADIUS.
Using y5/16, S and Gs Using y5/16, S, Gs and'Ev
C( D= -31.8910003853 C( 1)F 4.7431667917
C(2)= 53,7596378609 C1 2)' -312.2659209015
) = -8.9711680343 C( 3)= 85.1020403634
C( 4) = .5549490163- C( 4)z 130.7525251740
C( 5)= -30.5239196038 C( 5)= 2,295385082
CC 6)= -3,3733199735 C( 6)= -.0000081432
CC 7)= -.9415056763 C( 7)= -52.375844279?F =): 14.0810150793 C( 8)= -12.4911945922
CC 9) = 5.093447123 G( 9)= 122.363631315'1C(1U) -1,9052946210 C(-10) -27. 8147 254654
S(11)= -61.0822676775 C(11)= -141.9455105232
C(12)= 10.5127003945 C(i2) 823.063152457513) -2.7082997779 CI3) -196.6141937964
S(14)= 41,4257955425 C(14): -251.5265120343
C 15)= 44,6352964490 C(15)= -153.2196787550(16)= 4.3584334973 0(16)= °0000127300kCC()= 1.7054916517 C(17)= 96.2318031404
0(i8)= -9.6728410805 C(18)= 126.6088317324
C(19)= -42.714063170- C(19)= -199.3081650435
C(20)= 3.8425311344 G(20)= 18.4750255695
G(2i)= 7L.0614236931 C(21)= l12.7398253173
0 (22)= -.8820397422 C(22)= -551.6962384152
G(23)= 1.7405271634 c(23)= 124.3090113793
C(24)= -53.1325358655 c(24)= 156.64858579700(25)= -30.3299093539 C(25)= 184.2976000120
C(26)= -1.4850841324 C(26)= -. 0000075941
C(27)= 4.110896013g C(27)= -48.5622042860
G(28) 5,4834047720 C(28)= -135.4315636625
G(29)= 26.7268983051 0(29)= 65.7358828227
0(30)= -2.6092817849 C(30)= 1=.98677267032 (31) 4 -13,479357255F
R = 95.9 C(32)= 112.24T8478970
63% within ± 10% C(33)= -24.0214629682
S8% within ± 20% C (34) = -38,98369980i5C(35)= -59,5632559447C(36)-= .0000004855C-(37): 7.3256515643C(38)= 39.1585126325C(39)= 5.2268297684C (40) = -8.6972701637~2
- R2 = 97.7
72% within - 10%[ 1 91% within 20%
133
I~"T
-- : - S
TABLE 4. -GENERAL EQUATION COEFFICIENTS FOR RADIUS (CONTINUED)
Using Y5/16, S, tan @ and Ev Using y Ss cI 3 and
CC 1) 18.8992452280 C( 1)= 29.3980672485
C( 2)= -31,8938433251 C( 2)= 17.2560192731.C( 3)= 20.3800253443 C( 3)= 10.0203963175
C( 4)= -8,3982809715 C( 4) = -4.4695237570C( 5)= 13.,2362688240 C( 5)= -33,2041384178
C 6)= -,0000027090 C( 6)= -,0000024075
C( 7)= C4473329001 C( 7)= -,0027363973
C( 8)= -17.5521678930 C( 8)= -6.6328662691 P
CC 9)- 6.8566842352 C( 9) = 3.6233822224 V
C(10)= 1.59463402214 C(10) - 1239487343
C(i)= -199.0532997153 C(il)= -122.33 73482461C(12)= 323.2985371951 C(12)= -7.4095270897
C(13)= -116,5369735224 C(13)= -46.8808333927
C(14)= 64.5695519242 C(14)= 14.6150371805
C(15)= -128.5006629243 C(15)= 89.2867812633
C(16)= -.0000105683 Ct16)= -.0000056701C(17)= -4.,0691506255 C(17)= .0232794163
C(8)= 94.5027765293 C(18)= 38.5678057694.C(19)= -51,7359125275 C(19) = -12,2559501815
C(20)= -1,0595754093 C(20)= .0819726642
C(21)= 225.6633484300 C(21)= 95.1305302502
C(22)= -361,8623322793 C(22)= 38.7459131353
C(23)= 125.7080514573 C(23)= 22 0664331670
C(24)= -76.6928891973 C(24)- - 23.1284346475C(25)= 140.4383152831 C(25)= -96.24551294465C(26)= 0000H76320 C(26)= ,0000127685C(27)= 2.5802223123 C(27)= -011490034:C(28)= -96.9396721804 C(28)= -13.6140033792C(29)= 66.088660412- C(29)= 10.8696441627
C(30)= -6.9956496680 Ck30)= .3975240262C(31)= -68.9475372935 C(31)= -24.6729413515C(32)= -0.548270723 C(32)= -13.6655896113
C(33)= -37.8928184431 C(33)= -. 8950301262C(34)= 24.912406273? C(34)= 3.5235047360C(35)= -41.8140082327 C(35)= 27.6217414053C(36)= -.0000078407 C(36) = -. 0000066210C(37)= -.3086871023 C(3l) -. 0011715210C(38)= 28.2818514475 C(38)= -2.1689813563
C(39)= -22.3678557147 C(39)= -2.8343303860C(40)= 3.8323586654 C(40)= .2215007433
R2 981 R2 97.7
75% within 1 20% 73% within ± 10%
94% within + 20% 95% within ± 20%
3L
I
TABLE 5. GENERAL EQUATION COEFFICIENTS FOR DEPTH
Using y5/16, Sand G Using y 5 S, G and Ev
C( l)= 5303958631782 C( l= -43.6 955-70 4 92 ZCl 2)= -127.9226404562 C( 2)= -263.0260424584CU 3)= 20*8301124395 C( 3)= 76.0756460915C( 4)= 17.9316706900 C( 4)= 143.4022465293C( 5) -48.4457154475 C( 5)= 14.6854054001C( 6)= -*5180822422 C( 6)= -.0000018621C( 7)= -24.731506505 C( 7)= -47.173097167C( 8) 15.87J9481683 C( 8)= "15.6964256283
C 9)= 91.6107413501 C( 9)= 90.9027550405C(10)= -15.2484978757 C(10)= -22.2985600530C( i) -4L.49. 1867152981 C(1t)= 87.o048968i84,C(12)= 368.5656181405 C(12)= 660.3121352892C(13)= -44.6720935833 C(13)= -126.3905248215C(14)= 166.2582151665 C(14)= -354.1566836962
C15)= 66.241I4675220 C(15)= -82.29504515i3C(16)= -3.7716040549 C(i6)= .0000200377C17)= 17.9221947624 C(17)= 112.9332700877C(18)= il.5629558875 CC 905.34757507C(I9)= -205.379462223B C(19)= -193.3862745515C(20)= 13.0681609205 C(20)= 8.2417379757C(21)= 254.9573454245 C(21)= -598.9320341567C(22)= -120. 7791721681 C(22)= -523.9584928841C(23)= 14.2414607555 C(23)= 41.3421692588C(24)= -134.8771751525 C(24)= 689.3555775099C(25)= -51.6017664322 C(25)= 107.4665743070C(26)= 1.9569970889 C(26)= -,0000353685C(27)= 2.9310692111, C(27)= -160o9998103999C(28)= -. 1726515931 C(28)= -93.9073485683C(29)= 94.4689354767 C(29)= 118.7384287103C(30)= -6.0438470627 C(30)= 25.6274231775
2 C (31) = 342.20231-9307Rm :93.6 C(32)- 175.6525289593
39% within - 10% C(33)= .338490797565% within - 20% C(34)= -340.15t5068641
C(35)= -53.7051347245C(36)= .0000i44485C(37)= 71.4063952381C(38)= 33.5127395672C(39)= -23.927364825?C(40)= -15.1138557381
R 96.0Rm =
47% within + 10%72% within t 20%
135
L'
i - L -7 "" -
s . . . . .. - -"... . . . . ... . .. .. . . . ...... .... . .. .. .
TABLE 5. GENERAL EQUATION COEFFICIENTS FOR DEPTH (CONTINUED)
[Ii_ Using y5/16, S. tan 4 and Ev Using y5/16, S, c1"3 and E
Cl i)= 17.1253607120 C( 1) 21;7086303701C( 2)= -37.3542155845 CC 2)= -42.8323530877C( 3)= 12.5105364460 C( 3): 14,6236850665C( 4)= 8.5029333445 C( 4) .1510212049CA 5)= 14.7403694965 C( 5)= 22.8611299503C( 6): .0000029697 C( 6)= .0000028219C( 7): -7.2-058081245 C( 7)= .0096628854CA 8)= -8,4253426900 CC 8): -14.1319628653C( 9)= 3.3999072147 C( 9)= -.4996236563C~iO)= -1.8629595715 C(10)= .2047476495C (1) -193.3918309651 C (11)= -85.5758975799C(12)= 330.9456858185 C(12)= 112.7124014233C(13) -97.2329269833 C(13)= -25.8712673551-(14)= 33.0550538845 C(14) = 2.6748938295C(15)= -134.3558827033 C(15)= -45.0963840333C(16)= -.0000253473 C(16)= -.0000128280C(17)= 4,4905080385 C(17)= -.0277178934c (-18) 72.4656077635 C(18)= 32.4942151045C (19)= -37.2785637467 C(19) -.9376620835C(20)= 7.6485959924 C(20)= -.7761191183C(21) 219,4717738692 C(21)= 90.0293948233 YC(22)= -361.0416787948 C(22)= -86,5807061315C(23)= 113.5789573079 C(23)= -16.6599345535C(24) = -63.5462262740 C(24)= -4.1166825850-C(25) = 144.1389355682 C(25)= 27.0640857132C(26) = .0000298469 C(26)= .0000219664C(27)= 2.6975157247 0 (27)= .0528352713C(28)= -83.6172087730 C(28)= 6.2005227223C(29)= 54.6615138674 C(29)= 1.3423129962C (30)= -12.3071777705 C(30)= .4649869039C(31)= -72.7217500183 C(31)= -31.6097537754C (32)= 1-162322451501 0(32)= 32,5439752743C(33)= -37.4935916521 C(33)= 11,47321207240(34)= 25.5528645197 C(34)= 1.1107085605b(35)= -45o3802628657 C(35)= -12.4902317355C(36)= -.0000108194 C(36)= -.0000104873C(37) = -1.332119417l C(37)= -.0264307464C(38)= 27.3519570403 C(38)= -8.2155628902C(39)= -21.34647891741 C(39)"-- -,0050793512C(40)= 4,9712599019 pC(40) -*0721852584Rm = 94.5 Rm 978
43% within ±1 0% 45% within 1 10%66% within ± 20% 72% within ± 20%
136
TABLE 6. GENERAL EQUATION COEFFICIENTS FOR VOLUME
Using y5 / 1 6 , S and Gs Using y S, Gs and Ev
C( 1)= -2A1752357205 C( 1)= -11.820 7236195C( 2)= 13.1141215646 C( 2)= -347.0492941075C( 3)= .5997600122 C( 3)= 97.9246661795C( 4) -3.6647026294 C( 4)= 156.8518890100C{ 5)= -30,4405669790 C( 5)= IU.557521057iC( 6)= -3.4757992071 C( 6) -*0000070363C( 7)= -3.8080378705 C( 7)= -58,4668518002-CC 8)= 14.9439527393 C( 8)= -16.1887586229CC 9)= 20.8239905855 C( 9)= 128.5893232243C(1o)= -5.9957649451 C(10)= -30.9888871631C(1i)= -215.7667550906 C(1)= -59.3569012349C(12)= 93.1623369373 C(12)= 875.9625480863C(13)= -16*50U8692970 C113) -209.5974746947C(14)= 118.9135549083 C(14)= -334,6553293740C(15)= 33.8867065685 C(15)= -147.6046367155C(i6)= 2.7663678702 C(16)= .0000132385C(17)= -6,3022t29785 C(i7)= i17.2272444493C(18)= 2,7930,3889' C(18)= 131.08L5866705C(19)= -67,2103550710 C(19)= -224.9307823733C(20)= 4.0009580139 C(20)= 21o5972214015C(21)= 146.5688958239 C(21)= -134.8691.756255C(22) -25.5385254205 C(22)= -617.5477326839C(23)= 6.38739296_27 C(23)= 122.2498533469C(24)= -98.0675342203 C(24) 372.8148507687C(25)= -30.2435268423 C(25)= 16-3.4194029422C(26)= -66234156121 C(26)= -.000011033C(27)= 9.8235554535 C(27)= -99.1900726417C(28)= 1.2453679293 C(28)= -133.4532348235C(29)= 37.1186765414 C(29)= 109.7545480(32C(30)= -'2.7689859994 C(30)= 13.5108852373
2 C(31)= 109.1642310421R= 94.7 C(32)= 152*11,33991992
59% within - I0% C(33)= -21.4879680004
84% within ± 20% C(34) -150.2371189017C(35)= -55.932223021tC(36)= .0000026885C(37)= 32.7649358627C(38)= 39.6790168769C(39)= -13.55,44018533
C(40)= -9. 817926960 9-
R= 97.2
65% within t 10%89% within ± 20%
137
_ _ - -- - - - -
TABLE 6. GENERAL EQUATION COEFFICIENTS FOR VOLUME (CONTINUED)
Using y S, tan * and Ev Using y5/16, S, cI13 and Ev
C( 1)= 22.3706247625 C( 1)= 20.4178474204CU 2)= -38.9723779360 C( 2)= b,721025911Ct 3)= 18.9610934544 C( 3)= 1119976882110C( 4)= -5.7817278439 C( 4)= -2.8361992670C( 5)= 15.6413196900 C( 5)= -17.5564771871CC 6)= -.0000019613 CC 6)= -.0000012370CC 7)= -1.4903246793 C( 7)= .0043463631
( ) -15.6027125598 C( 8)= -9.5472334444
CA 9)= 7.4617827703 C( 9)= 2.1i50419147C(iO)= .2976374547 C(10)= -.0237115983C (11)= -205.6266042500 Ci)= -88,7714888573C(12)= 332.7916277065 C(12)= -1.0129467374C(13) -107.5617213000 C(13)= -40.4930003277C(i4)= 65,3451232219 C(14)= 10.4469006002Ci5)= -131.09,6024125 C(15)= 56.239751972,C(16)= -,0000133719 C(16)= -,0000128355C( 17)= -2.7122525642 C(17)= -.0069710347C(18)= 85,1580280890 C(18)= 36.2108467755c41g)= -54.5527834882 C(19)= -8.0426022633C(20)= 2.9801404833 C(20)= -*1288631602C(21)= 224.1213882024 C(21)= 70.9874042555C(22)= -355.1369302715 C(22)= 39.8818213383C(23)= j15.568816362 C(23)= 5.8251333617C(24)= -82.6517911083 C(24)= -i0.3385864953C(25)= 136.3420036065 C(25)= -73.6285916503C(26)= ,0000208297 C(26)= .0000259077C(27)= 3.6172294425 C(27)= .0240818543C(28)= -87.3706458740 C(28)= -2.6011605493C(29)= 69.9345875052 C(29)= 7.5554455247C(30)= -10.0936503153 C(30)= -.2349178007C(31)= -68.0570038645 G(3i)= -20.25041i91554C(32)= 105.8756257875 C(32)= -13*2365012983C(33)= -35.1328556619 C(33)= 4.7647670677C(34)= 28.2071799715 C(34)= 2.9103610175C(35)= -39..6850247712 C(35)= 21,5041290069C(36)= -.000008705-2 C(36)= -,0000121125C(37) -.9340846773 C(37) -,0138504245C(38)= 25.7701411555' C(38)= -5.1011694772C(39)= -24.3306349045 C(39)= -1.950230715C(40)= 4.5780233701 C(40)= 1689371705
R2 =97.8R 96.9 m
66% within ± 10% 65% within ± 10%92% within ± 20% 93% within ± 20%
138H}
APPENDIX V
MATERIAL PROPERTY EFFECTS PLOTS
139
3.2 ~
2.8s = 2.55
S=0% y= 80 pcf
2.4-
a~ 2.0-
-o SS=60%-0
0.4
0-0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0
1"Scaled Depth of Burst, Dob/W 5 1
FIG. 32. CRATER VOLUME AS A FUNCTION OF CHARGE DEPTHAND PERCENT SATURATION, S, FOR SPECIFIC GRAVITY =2.55
AND DRY UNIT WEIGHT =80 POUNDS/CUBIC FOOT
F 140-
I
3.2 3. z !--S=0%S-- 00% -
2.8-
2.4 S
S=60%2.0
kS=40%
1 f.2
-- Dob = optimum0.84- Gs = 2.55
0.4-
0 I I i I60 80 100 120 140
Dry Unit Weight, Yd' Pounds/Cubic Foot
FIG. 33. CRATER VOLUME AS A FUNCTION OF DRY UNIT WEIGHTAND PERCENT SATURATION, S, FOR OPTIMUM CHARGE DEPTH
AND SPECIFIC GRAVITY = 2.55
141F I
[
F U
Dob = optimumGs = 2.55
3.0Yd = 80 pcf
I- 2.8
~2.4iaa11 ~ 2.0
r-, 1.6
1.2 riaa
0.4
0 - 10 20 40 60 80 100
Percent Saturation, S
FIG. 34. CRATER RADIUS, DEPTH AND VOLUME AS A FUNCTION OFPERCENT SATURATION FOR OPTI14UM CHARGE DEPTH, SPECIFIC
GRAVITY =2.55 AND DRY UNIT WEIGHT =80POUNDS/CUBIC FOOT
142
32
2.8-
2.4 Dob = optimum~G s = 2.75". 2.0- Yd = 160 pcf
0
Caa
0.4
0 I I I 1 J i
0 20 40 60 80 I00
Percent Saturation, S
FIG. 35. CRATER RADIUS, DEPTH AND VOLUME AS A FUNCTIONOF PERCENT SATURATION FOR OPTIMUM CHARGE DEPTH, SPECIFICGRAVITY = 2.75 AND DRY UNIT WEIGHT = 160 POUNDS/CUBIC FOOT
143
3.2-Dob = optimum
2.8 GS = 2.55ko S =40%
L =R
1 0o
.0-
F--
C.)
Q) 0.4-
60 80 100 120 140
Dry Unit Weight, d'Pounds/Cubic Foot
FIG. 36. CRATER RADIUS, DEPTH AND VOLUME AS A FUNCTIONOF DRY UNIT WEIGHT FOR OPTIMUM CHARGE DEPTH, SPECIFIC
GRAVITY =2.55 AND PERCENT SATURATION =40
C 4 144
2.8 G = 2.65
In S
S2.0
d10 0 pcf
y d 140 pcf
d f 160 pcf
0 0.4 0.8 1.4 1.6 2.0 2.4 2.8 3.2 3.6 4.0
Scaled Depth of Burst, Dob/W 5/16
FIG. 37. CRATER VOLUME AS A FUNCTION OF CHARGE DEPTHAND DRY UNIT WEIGHT, Yd, POUNDS/CUBIC FOOT, FORSPECIFIC GRAVITY =2.65 AND PERCENT SATURATION =40
145
I 32r Dob = optimum d14pc
2.8 Yd 1 pcf
I.00-
LIO
2.
Yd=8O pcf
0.8
U
0.4-
00 20 40 60 80 100
Percent Saturation,S
FIG. 38. CRATER VOLUME AS A FUNCTION OF PERCENT SATURATIONCHARGE DEPTH AND SPECIFIC GRAVITY =2.55
146
- -
REFERENCES
1. Baker, Warren J., "Effects of Soil and Rock Propertieson Explosion Crater Characteristics," Master of Sciencedissertation, Notre Dame, April 1962.
2. Banks, D.C., and Saucier, R.T., "Geology of BuckboardMesa, Nevada Test Site," Report PNE-5001P, U.S. ArmyEngineer Waterways Experiment Station, Vicksburg,Mississippi, July 1964.
3. Benfer, Richard H., Maj., "Project Pre-Schooner II,Apparent-Crater Studies," Report PNE-508, U.S. ArmyEngineer Nuclear Cratering Group, Livermore, California,May 1967.
4. Benfer, Richard H., "Variation of Project ZULU II CraterDimensions versus Medium Properties," NCG Technical Memo.66-18, U.S. Army Engineer Nuclear Cratering Group,UtTvTmore, California, October 1966.
5. Bening, Robert G., Maj., and Kurtz, Maurice K. Jr., Lt.Col., "The Formation of a Crater as Observed in a Seriesof Laboratory-Scale Cratering Experiments," Report PNE-5011, U.S. Army Engineer Nuclear Cratering Group,Evermore, California, October 1967.
6. Butkovich, Theordore R., "Calculation of the Shock WaveFrom an Underground Nuclear-Explosion in Granite," ThirdPlowshare Symposium on Engineering with Nuclear Explosives,Report TID 7695, Lawrence Radiation Laboratory, Livermore,California, April 1964.
7. Carlson, R.H., "Project Toboggan, High-Explosive DitchingFrom Linear Charges," Research Report SC-4483 (RR), SandiaCorp., Albuquerque, New Mexico, July 1961.
8. Carlson, R.H., (U) "Review of Test Results and PredictionMethods Associated .'ith Nuclear Craters and Their Related
4 Ejecta Distributions," Report No. D2-125706-1, The BoeingCo., Seattle, Washington, January 1968, (Secret-RD).
9. Carlson, R.H., and Jones, G.D., "Project MTCE, HighExplosive Cratering Studies in Hard Rock," Report D2-90704-1, The Boeing Co., Seattle, Washington, November1965.
147
Cf
- I
10. Chabai, A.J., (U) "Dimensional Analysis and Modeling ofCratering Explosions, Proceedings of the Symposium onNuclear Craters and Ejecta, Report TR-1001 (52855-40)-4,Aerospace Corp., Novemoer 1967, (U) pp. C-I-C-10, (Secret-RD).
11. Chabai, A.J., "Scaling Dimensions of Craters Produced byBuried Explosions," Research Report SC-RR-65-70, SandiaCorp., Albuquerque, New Mexico, February 1965.
12. Cherry, J.T., "Computer Calculations of Explosion-ProducedCraters," International Journal of Rock Mechanics andMineral Sciences, Vol. 4, 1967, pp. 1-22.
13. Circeo, L.J. Jr., "Nuclear Excavation: Review andAnalysis," Engineering Geology, 3, Elsevier PublishingCo., Amsterdam, Netherlands, June 1969, pp. 5-59.
14. Cook, Melvin A., The Science of High Explosives, ReinholdPublishing Corp., New York, 1958.
15. Dietz, John P., and Hayes, Dennis B., "Compilation ofCrater Data," Research Report SC-RR-65-220, Sandia Corp.,Albuquerque, New Mexico, July 1965.
16. Draper, N.R., and Smith, H., Applied Regression Analysis,John Wiley and Sons, Inc., New York, 1966.
17. Fisher, Paul R., Kley, Ronald J., Capt., and Jack, HaroldA., "Project Pre-Gondola I, Geologic Investigations andEngineering Properties of Craters," Report PNE-1103, U.S.Army Engineer Nuclear Cratering Group, Livermore,California, May 1969.
18. Flanagan, T.J., "Project Air Vent, Crater Studies," ReportSC-RR-64-1704, Sandia Corp., Albuquerque, New Mexico,April 1966.
19. Frandsen,-A.D., "Analysis and Re-evaluation of BulkingFactors," TM 70-1, U.S. Army Engineer Nuclear CrateringGroup, Lawrence Radiation Laboratory, Livermore,California, March 1970.
20. Frandsen, A.D., "Engineering Properties Investigations ofthe Cabriolet-Crater," Report PNE-957, U.S. Army EngineerNuclear Cratering Group, Livermore, California, March 1970.
21. Goode, T.B., end Mathews, A.L., "Operation Sun Beam, ShotJohnie Boy, Soils Survey, " Report POR-2285, U.S. ArmyEngineer Waterways Experiment Station, VTicksburg,Mississippi, May 1963.
22. Hansen, Spenst M., et. al., "Recommended Crater Nomen-clature," UCRL-7750, University of California, LawrenceRadiation Laboratory, Livermore, California, March 1964.
23. Harlan, R.W., Capt., "Project Pre-Gondola I, CraterStudies: Crater Measurements," Report PNE-1107, U.S. ArmyEngineer Nuclear Cratering Group, Livermore, California,December 1967.
24. Hemmerle, William J., Statistical Computations on a DigitalICompter Blaisdell Publishing Co., Waltham, Massachusetts,-1967
25. Herr, Robert W., "A Preliminary Look at Effects ofAtmospheric Pressure and Gravity on the Size of ExplosiveCraters," Langley Working Paper-790, NASA Langley Research
LCenter, Hampton, Virginia, August 1969.
26. Holzer, Fred, "Calculation of Seismic Source Mechanisms,"Report UCRL-12219, Lawrence Radiation Laboratory,Livermore, California, January 1965.
27. Hughes, Bernard C., Lt. Col., "Nuclear ConstructionEngineering Technology," NCG Technical Report No. 2, U.S.Army Engineer Nuclear Cratering Group, Livermore,California, September 1968.
28. Hughes, B.C., and Benfer, R.H., "Project ZULU, A One-Pound High Explosive Cratering Experiment in Scalped andRemoulded Desert Alluvium," NCG Technical Memo. 65-9,U.S. Army Engineer Nuclear Cratering Group, Livermore,California, October 1965.
29. Hunt, R.W., Bailey, D.M., and Carter, L.D., "PreshotGeological Engineering Investigations for ProjectCabriolet, Pahute Mesa, Nevada Test Site," Report PNE-966, U.S. Army Engineering Water.vays Expeliment Station,V'1cksburg, Mississippi, October 1968.
30. Johnson, Gerald W., et. al., "The Plowshare Program-Historyand Goals," Third Plowshare Symposium-on Engineering withNuclear Explosives , Report 1ID 7695,- Lawrence -RadiationLaboratory, Livermore, California, April 1964.
149
31. Johnson, Gerald W., et. al., "The Underground NuclearDetonation of September 19, 1957, Ranier, OperationPlumb-bob," Report UCRL 5124, University of CaliforniaRadiation Laboratory, Livermore, California, February1958.
32. Knox, J.B., and Terhune, R.W., "Calculation of Explosion-Produced Craters," Third Plowshare Symposium on Engineeringwith Nuclear Explosives, Report TID 7695, LawrenceRadiation Laboratory, Livermore, California, April 1964.
33. Lutton, R.J., et. al., "Project Pre-Schooner II, PreshotGeologic and Engineering Properties Investigations,"Report PNE-509, U.S. Army Engineer Waterways ExoerimentStation, Vicksburg, Mississippi, December 1967.
34. Lutton, R.6., and Girucky, F.E., "Project Sulky, Geologicand Engineering Properties Investigations," Report PNE-720, U.S. Army Engineer Waterways Experiment Station,Vicksburg, Mississippi, November 1966.
35. Lutton, R.J., Girucky, F.E., and Hunt, R.W., "ProjectPre-Schooner, Geologic and Engineering Properties Inves-tigations," Report PNE-505F, U.S. Army Engineer NuclearCratering Group, Livermore, California, April 1967.
36. Maenchen, George, and Nuckolls, John, "Calculation ofUnderground Explosions," Proceedings of the GeophysicalLaboratory - Lawrence Radiation Laboratory CrateringSyposium, Report UCRL-6438, Part i1, Lawrence RadiationLaboratory, Livermore, California, October 1961, pp.J-I-J-6.
37. Maenchen, G., and Sack, S., "The Tensor Code," ReportUCRL-7316, Lawrence Radiation Laboratory, Livermore,California, April 1963.
38. "Military Engineering with Nuclear Explosives," ReportDASA 1669, U.S. Army Engineer Nuclear Cratering Group,Livermore, California, June 1966.
39. Miller, Irwin, and Freund, John E., Probability andStatistics for Engineers, Prentice-Hall, Inc., EnglewoodC'iffs, New Jersey, 1965.
40. Murphey, Bryon F., "High Explosive Crater Studies: DesertAlluvium," Research Report SC-4611 (RR), Sandia Corp.,Albuquerque, New Mexico, May 1961.
150
I -
=i
....... ... ..... ... -T h_
41. -Murphey, Bryon F., "High Explosive Crater Studies: Tuff,"Research Report SC-4574 (RR), Sandia Corp., Albuquerque,New Mexico, April 1961.
42. Nelson, David L., lLt., and Taylor, T.S. III, Sp4,"Analysis of Vesic Crater Modeling Experiments," NCGTechnical Memo 68-14, U.S. Army Engineer Nuclear CrateringGroup, Livermore, Clifornia, November 1968.
43. Nordyke, M.D., "Nevada Test Site Nuclear Craters," Pro-ceedings of the Geophysical Laboratory - LawrenceRadiation Laboratory Cratering Symposium, Report UCRL-6438, Part I, Lawrence Radiation Laboratory, Livermore,Ca-Tfornai -October 1961, pp. F-I-F-14.
44. Nordyke, M.D., Editor, "Proceedings of the GeophysicalLaboratory - Lawrence Radiation Laboratory Cratering,Symposium," Report UCRL-6438, Parts I & II, LawrenceRadiation Laboratory, Livermore, Ca'fiTornia, October 1961.
45. Nordyke, M.D., "Cratering Experience with Chemical andNuclear Explosives," Third Plowshare Symposium onEngineering with Nuclear Explosives, Report TID 7695,Lawrence Radiation Laboratory, Li vermore, Cal ifornia,April 1964.
46. Nordyke, M.D., "On Cratering, A Brief History, Analysis,and Theory of Cratering," Report UCRL-6578, University ofCalifornia, Lawrence Radiation Laboratory, Livermore,California, August 1961.
47. Nordyke, M.D., and Williamson, M.M., "Project Sedan, TheSedan Event," Report PNE-242F, Lawrence Radiation Labo-ratory, Livermore, California, August 1965.
48. Nordyke, M.D., and Wray, W., "Cratering and RadioactivityResults from a Nuclear Cratering Detonation in Basalt,"Journal of Geophysical Research, Vol. 69, No. 4, February15, 196'4, pp. 675-1689.
49. Nugent, R.C., and Girucky, F.E., "Project Palanquin,Preshot Geologic and Engineering Properties Investi-gations," Report PNE-905, U.S. Army Engineer WaterwaysExperiment Station, VicTsburg, Mississippi, October 1968.
151
I. . . .
50. Nugent, R.C., and Banks, D.C., "Project Danny Boy, tEngineering - Geologic Investigations," Report PNE-5005,U.S. Army Engineer Nuclear Crdtering Group, Livermore,California, November 1966.
51. Nugent, R.C., and Banks, D.C., "Project Pre-Schooner,Preshot Investigations," Report PNE-505P, U.S. ArmyEngineer Nuclear Cratering Group, Livermore, California,September 1965.
52. Nugent, R.C., and Banks, D.C., "Project Sulky, PreshotGeologic Investigations," Report PNE-719P, U.S. ArmyEngineer Waterways Experiment Station, Vicksburg,Mississippi, July 1965.
53. Perret, William R., et. al., "Project Scooter," ResearchReport SC-4602 (RR), Sandia Corp., Albuquerque, NMexico, October 1963.
54. , Proceedings of the Second Plowshare Symposium,Report UCRL-5676, Lawrence Radiation Laboratory, Livermore,California, and AEC-San Francisco Operations Office, May1959.
55. __,Proceedings of the Sy/mposium on Engineering with
Nuclear Explosives, Report CONF-700101, Vols. 1 & 2, TheAmerican Nuclear Society, Las Vegas, Nevada, May 1970.
56. Ramspott, L.D., Stearns, R.T., and Meyer, G.L., "PreshotGeophysical Studies of Cabriolet Nuclear Crater Site,"Report PNE-953 (UCRL-50458), Lawrence Radiation Labo-ratory, Livermore, California, August 1969.
57. Rooke, A.D. Jr., "Project Pre-Buggy, Emplacement andFiring of High-Explosive Charges and Crater Measurements,"Report PNE-302, U.S. Army Engineer Nuclear Cratering Group,Livermore, California, February 1965.
58. Rooke, A.D. Jr., and Davis, L.R., "Ferris Wheel Series,Flat Top Event, Crater Measurements," Report POR-3008,U.S. Army Engineer Waterways Experiment Station, Vicksburg,I Mississippi, August 1966.i
59. Sachs, D.C., and Swift, L.M., "Small Explosion Tests,Project Mole," Report AFSWP-291, Vols. I & II, StanfordResearch Institute, Melo Park, California, December 1955.
152
I'
60. Sager, R.A., Denzel, C.W., and Tiffany, W.B., "Crateringfrom High Explosives, Compendium of Crater Data,"Technical Report No. 2-547, Report 1, U.S. Army EngineerWaterways Experiment Station, Vicksburg, Mississippi,May 1960.
61. Saxe, H.C., and DelManzo, D.D. Jr., "A Study of UndergroundExplosion and Cratering Phenomena in Desert Alluvium,"Proceedinqs of the Symposium on Engineering with NuclearExplosives, Report CONF-700101, Vols. I & 2, The AmericanNuclear Society, Las Vegas, Nevada, May 1970, pp. 1701-1725.
62. Saxe, Harry C., "Explosion Crater Prediction UtilizingCharacteristic Parameters," Rock Mechanics, C. Fairhurst,ed., Pergaman Press, New Yor-T9"63.
63. Sauer, F.M., Clark, G.B., and Anderson, D.C., "NuclearGeoplosives, Part Four-Empirical Analysis of Ground Motionand Cratering," Re ort DASA-1285 (IV), Stanford ResearchInstitute, Melo Park , CaliforniaMay 1964.
64. "Soil Data, Tonopah rest Site, Nevada," Woodward-Clyde-~Sherard and Associates, report to Sandia Corp., Denver,
Colorado, November 2.6, 1963.
65. Spruill, Joseph L., and Paul, Roger A., "Project Pre-Schooner, Crater Measurements," Report PNE-502F, U.S. ArmyEngineer Nuclear Cratering Group, Livermore, California,June 1965.
66. Spruill, Joseph L., and Videon, Fred F., "Project Pre-
Buggy II, Studies of the Pre-Buggy II Apparent Craters,"Report PNE-315F, U.S. Army Engineer Nuclear CrateringGroup, Livermore, California, June 1965.
67. Stearns, R.T., Meyer, G.L., and Hansen, S.M., "ProjectPalanquin, Preshot Geophysical Properties of PalanquinCrater Site," Report PNE-906, Lawrence Radiation Laboratory,Livermore, California, June 1968.
68. Stearns, R.T., and Rambo, J.T., "Project Pre-Gondola I,Preshot Geophysical Measurements," Report PNE-IIII, U.S.Army Engineer Nuclear Cratering Group, Livermore,CaliFornia, July 1967.
153
69. Strohm, W.E., Ferguson, J.S. Jr., and Krinitzsky, E.L.,"Project Sedan, Stability of Crater Slopes," Report PNE-234F, U.S. Army Engineer Waterways Experiment Station,Vicksburg, Mississippi, October 1964.
70. Teller, Edward, et. al., The Constructive uses of NuclearExplosives, McGraw-Hill .Book Co., New York, 1968.
71. Terhune, R.W., Stubbs, T.F., and Cherry, J.T., "NuclearCratering on a Digital Computer," Report UCRL-72032,Lawrence Radiation Laboratory, Livermore, Cal ifornia,February 1970.
72. Tewes, Howard A., "Results of the Schooner ExcavationExperiment," Report UCRL-71832, Lawrence RadiationLaboratory, Livermore, California, January 1970.
73. "The Unified Soil Classification System," Technical MemoNo. 3-357, U.S. Army Engineer Waterways Experiment Station,qicksburg, Mississippi, March 1953, (Rev. April 1960).
74. Third Plowshare Symposium on Engineering with NuclearExplosives, Report TID 7695, Lawrence Radiation Laboratory,Livermore, Cal ifornia, Apri 1964.
75. Thompson, L.J., et. al., "Earth Penetration and DynamicSoil Mechanics, The Effect of Soil Parameters on EarthPenetration of Projectiles," Project 596-1, report toSandia Laboratories, Texas A&M Researrh Foundation, CollegeStation, Texas, July 1969. _ _
76. "Underground Explosion Test Program, Sandstone," TechnicalReport No. 5, Vol. I, Engineering Research Associates,St. Pul, innesota, February 1953.
77. Vaile, R.B. Jr., "Pacific Craters and Scaling Laws,"Proceedings of the Geophysical Laboratory - Lawrence
ton Laboratory Cratering Symposium, Report UCRL-68, Part 1, Lawrence Radiation Laboratory, Livermore,California, October 1961, pp. E-l-E-36.
78. Vesic, A.S., "Cratering by Explosives as an Earth PressureProblem," Sixth International Conference on Soil Mechanicand Foundation Engineering, Vol. IT, Montreal, Canada,1965, pp. 427-431.
154
tI
L
79. Vesic, A.S., Boutwell, G.P. Jr., and Tai, Tein-Lie,"Engineering Properties of Nuclear Craters, TheoreticalStudies of Cratering Mechanisms Affecting the Stabilityof Cratered Slopes, Phase III," Technical Report No. 3-699,Report 6, U.S. Army Engineer Waterways Experiment Station,Vicksburg, Mississippi, March 1967.
80. Vesic, A.S., et. al., "Engineering Properties of NuclearCraters, Theoretical Studies of Cratering MechanismsAffecting the Stability of Cratered Slopes, Phase II,"Technical Report No. 3-699, Report 2, U.S. Army EngineerWaterways Experiment Staion, Vicksburg, Mississippi,October 1965.
81. Vesic, Aleksandar B., and Barksdale, Richard D.,"Theoretical Studies of Cratering Mechanics Affectingthe Stability of Cratered Slopes," Final report, ProjectNo. A-655, Engineering Experiment Station, GeorgiaInstitute of Technology, Atlanta, Georgia, September 1963.
82. Videon, F.F., "Project Palanquin, Studies of" ApparentCrater," Report PNE-904, U.S. Army Engineer NuclearCratering Group, Livermore, California, July 1966.
83. Videon, F.F., "Project Sulky, Crater Measurements," ReportPNE-713F, U.S. Army Engineer Nuclear Cratering Group,Livermore, California, October 1965.
84. Vortman, L.J., "Craters from Surface Explosions andScaling Laws" (Reprint), Sandia Laboratories, Albuquerque,New Mexico, July 1968.
85. Vortman, L.J., et. al., "Project Buckboard, 20-Ton and1/2-Ton High Explosive Cratering Experiments in BasaltRock," Report SC-4675 (RR), Sandia Corp., Albuquerque,New Mexico, August 1963.
86. Vortman, L.J., et. al., "Project Stagecoach, 20-Ton HECratering Experiments in Desert Alluvium," Report SC-4596 (RR), Sandia Corp., Albuquerque, New Mexico, March1960.
87. Vortman, L.J., "Ten Years of High Explosive CrateringResearch at Sandia Laboratory," Nuclear Applications &Technology, Vol. 7, September 1969, pp. 269-304.
88. Westine, P.S., "Explosive Cratering," Journal of Terra-mechanics, Vol. 7, No. 2, Pergamon Press, 1970, pp. 9-19.
155
I _ - -
89. Whitman, Robert V., "Soil Mechanics ConsiderationPertinent to Predicting the Immediate and Eventual Sizeof Explosion Craters," Report SC-4404 (RR), Sandia Corp.,Albuquerque, New Mexico, December 1959.
90. Whitman, Robert V., and Healy, Kent A., "The Response ofSoils to Dynamic Loadings, Report 9: Shearing Resistanceof Sands During Rapid Loadings," Research Report R-62-113,Massachusetts Institute of Technology, Cambridge,Massachusetts, May 1962.
9l. Wu, Tein Hsing, Soil Mechanics, Allyn and Bacon, Inc.,Boston, 1966.
156
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~~1I S . . - . . . : - . ,
-J UNCLASSI FIEDSecuityClsiiaon
DOCUMENT CONTROL DATA R & D(Security- elassiticaion of title, body -of abstract and indexIng annv to.ll must be ongehed kslen the .veli report s cIastie ,,_
I- ORIGINATING ACTIVITY (Co2porate StihOr) 2a. REPORT SCCJRITY CLASSIFICATION
-Texas AIM Research Foundation UNCLASSIFIEDlege Station, Texas 77843 b. GoP
-THE INFLU ENCE OF SOIL AND ROCK PROPERTIES ON THE PIMENSIONS OF J6XPLOSION-PRODUCED CRATERS.,
4. DESCRIPTIVE NOTES (Type of report and inclusive dates) 1?
,HORfS (First natme, middla initial, last ntn")
arry A.7Tilon Maj, USAF
Feb~970. TOTAL I166FII PAGES -0.NO O§1 RS
ir CONTRACT OR GRAN 09 RIGI NA R '_ REPO1 41 UMBLR[S)
/1 F2 5tl-g--(32 17FG7FW 71-144
571 ~___________Ob. O T HER R F.P 0R T N0I4S I (Any o thct numbers thatI may baa oSigned
this report)
10. DISTRIBUTION STATEMENT
* Distribution limited to US Government agencies only because of test and evaluation(19 Jan 72). Other requests for this document must be rtferred to AFWL (DEV).
II. SUPPLEMENTARY NOTES 12, SPONSORING MILITARY ACTIVITY
AFWL (DEV)Kirtland AFB, NM 87117
13,. ABSTRACT (Distribution Limitation Statement B)
Analysis of data from published cratering experiments shows the effect of soil androck properties on the apparent dimensions of explosion-produced craters. More than200 cratering tests and related material properties were cataloged. The data con-sisted of 10 nuclear events whose yields varied from 0.42 to 100 kilotons and about200 high explosive events whose yields varied from 1 to 1 million pounds of TNT. Thedifferent test sites included materials for which the density ranged from 60 to 170pounds/cubic foot. By regression analysis, using bell shaped curves, predictionformulas were developed for the apparent crater radius, depth, and volume as a func-tion of charge weight and depth of burst for eight different types of materials. Thebell curves were normalized using material properties and prediction equations weregenerated using all the data. These general equations were then studied to determinethe specific effects of the material properties on resultant apparent crater dimen-sions. Material properties are highly important in determining the size of explo-sion-produced craters and some of the more important properties are unit weight,degree of saturation, shearing resistance and seismic velocity. Previous investiga-tors have been somewhat negligent in measuring material properties for past crateringexperiments and no real data analysis can be made until the variables are eithercontrolled or measured. Material properties which should be measured for futuretests should at least include the above properties and if possible the material'senergy dissipation and bulking characteristics. Better yet a reasonably simpletheory of cratering is needed which will better define the material propertiesgoverning cratering mechanics.
DD FORMD I NOV ,- IUNCLASSIFIEDSecurity Classification
UNCLASSIFIEDSecurity Classificc^!on
14.'K fWPO LINK A LINK 11B IH7
ROLE WT R~OLE -WT ROLE WT
Civil engineeringCraters and crateringSoil mechanicsRock mechanicsExplosionsNuclear craters I1
UNLSSFESeuiy L9if.to
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