UNCLASSIFIED

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.

This report is made available for study wiLih the understanding thatproprietary interests in and relating thereto will not be impaired. In caseof apparent conflict or any other questions between the Government's rightsand those of others, notify the Judge Advocate, Air Force Systems Command,Andrews Air Force Base, Washington, DC 20331.

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

W I WW 1 4

IL U. a i N aj I .0 0 1 - 4u a a a 0 a a a a a

I39LO I .4 in 1 N a N . . ._.3 I . " M M " i

La : I I

us. 4 0 a r 0 ao a t a a s

WZI

Et N P, a7 Pa ao a' a a a a a a a a a 0, a a a a

C C; . a , -0 u N N m al t m0 10 .4 Fo ' L~

t a 4 N P .4 y a .4 N N a V 0 UI S .4

4-,za~ ~~~~ ~~ W% a a a a . 0 a 4 a a aU% F

wZu. I 9 .3 a N a ) awa a US C .0 N a N F ' ) F N N .

CL~i. a a 0% f)N a I) N a 4 N F ' N N .0 40S m N4 .4 rv

I4 3t a a a a a aD us .0 04 0) %L W W ws 'D No4 .. a a a a N N t 4 C ) . 4 a

N4 N a a N N 4 N0 N0 . s U 4 . )a0 a4 .4 .4 4

L.3 0 to Us N a -t F) N4 20 . AU ' iS N 0

P- N m0 .4 m.

.PA 6i z W a a a a aJ a1 a a a a j a a a a a a a a 0 a a a

a a1 a a a a a0 a j a 1-- u00I a a: a I. a 4 a ao a a 0 o o o

x I . I a 40 U .4 N a m IA LA m m %0'% V% W W

04w~ ~ .0t . a N N N .* .) , I =0 Da ) z z z z

I-r W 1.- - -1. -9 p- p. -j s a j - a a i a i - - 1.06 I x ms co -9 us a 9 -9 - W4 W .9 .9 cJ -J .3 .3 3K 19 W. -4 .j

F) at 1 .0 0 I -I IN N 4 N 0 0 M 0 C O s 0 0 (7 o0 .0 0 .y, a,

z1 I N 4 5,I 1 0

: , .) .sa N.

IE I I 0 aL. . 0 . 0 4 4 .

01 W~ f 0. i n 4. 4 0 U 04 U 4 4 0 W W W W W W W W W1 0S0 ~ 4 0 5 2 2 2 O 0 C, 0 . ~0 0 0 .

t I a

01 .5 N 4 0 40 t 4 4 4 4 .1 0 . . 4 0

-.4 4 'y S o 'r VI 4 N I 0 0' I0 S0 SP N M I

LUZ I A u

U.S66

13Z!

atviw,

1! C! we: -0 . .C~ la CC

C- * a a av a I:, 9 a a a ua 0 a A

Ill I - I m a 0 ' 0 0 4 0 0 0' a) w. co

a a Cl a0 a a 0 ah " CO a, f4 IV "I . a

GOJ I

0 V% UN a a III a a 0 a t t Q aNO a

'cC e . I ':.9 9 . 4 . .9N . ') . 4

.9C .2 an N N % a, y 1 Il a a to a a,20

7F g~ a W% "s a, a a ON m a% m am a at a% a a C,L) I an am a a a a ai aO % V) a P73 N, a 0 C m~ P. e. a

4.4 1:C CJ C 4 0 ; I

N~ ~ ~ L a Q . 4 * I., U . a, U, in a a a12, .(A- . . t. N 0 . t 0 9 C . 9 s a a a ,. a

& W .4 .4 m m N ON a a 4 I) . . 0' N - j a Ncr- 4~ 4 =5 N4 N4 "4 N

e-l0 oC 1

.41 C : : : 1C!1 C!!.- xC z I w N o N u N o w - c N O w ' i N D N O 0

w.I

w< n 0 4 j ' aj a. j a u' * -j i CA -0 a a -.9 0 UC N .9 -0 -1 a a.4J .j NO NO NO NO NO N N 0 N N NO 'D N N %a 'D NO CA ao 10 NO 1 t'

co4I >

0 A P ~~ ' a a N j .9 i CA CA CA -8 CA a a j it. a CA a Cup 1n -0 1' a p, 4 -1 N1 .4 aj CA PC j' -1 -1 a a -j aj C. a' N jS...4K A 1 C.C. . . . . . .. . . . . . . . . . .

CCC.. 1~ 0 ON 0's 01 01 ar 01 .N . 0 I 0 Y .4 N Nj a C . . 4 a a i i TYu it i CS - (1 (L 0- 4- - I .. - 1 4 N- N

in =1 a a a) a) a) aL a a 0 C) 9-1 a) 0 o ua III A CA aO - in 1 4 CA IA an N 19.14 S . 0 a 0 PS - C , 0 Z a .4 a

0.C~~~4..s~ a a 0Na a a a p, a a a p~ . a u a .4 a Q4 kA~ mC

0 AIII a w m & w w NNN N N N 44 14 4 .4 .4 4 4 Q4

I i a a z a a = a a a wsa a a aa a a

52 a a aa a a a a ONa a a, a, a a , aN a ON a a aP.On tfi N N N N N N N N N N% UN UN N N UN N% N. . N 9 t U4y.443I

Wei~6-i4 I WI N F, 0 0% W N M 4 V ) f0

Wi) , N NY N N N Nf N2 N N N N N N N NI WX I.4 4

iit

6O- 1 0 a a D 0 Q 0 .0 a a a 0 0.

a a 0 a a a a

1 1 4 - a N 4 a a a 0 0 0)N a V 0 . N U .* 4-.

1L0I co 0.) co 0 0 N m 0 a a a m w t . ' N a u .

* a a 0 a a a a a a a a 0 a aD . aC . 0N N 0

200.UI~~ Wa at a 0 a a aN a a a a a N . a, V,. 0.a010uWI N % 4 N N4 N) 0. 0) 04 Nq40 2 a a 1 a N

wo aaa a aa a a ao a a a a" a a a a a a a a a ao a

Lo, a a :a a a a1 a a "D "n a, a .0 a a a 0 a9 a a a 10 24L. 1 0 0.) w. . .4 A . N a 14 U, a; 1; N, a a a, a a t; C-I I 14 0v 1Y cy a a j a Y a -4 -r - -0 - 4 N a % N w 0' o) 0 01

= W S .J r- 1 4 N 0 N . 0 .4 N .4 0) N r 4 % 0. U 0 4 N 14

0 to I

3c 2 1 ay a a a a a a a! a a10"' a' .4 a. 0m a a N 14 1 0. N a 4 0) 0 0 .

I00. 1M 4 N 4 .4 0 4 ..4 4 ~ .4 14 . .7 0 .4 .7 40% N M 4 M4 m.' m0j I- I4 n4 co N 0. 4 4 . '

C).

C~~ ~ ~ ~ ~ ~ c G ' . N . 4 4o0N a .0 0 4 4 0 a 0) co ao c4 IN I

a 0 1 N? Ni Nj .4 N N N N Ni .4 - .4 .4 j4 . 4 1 . 4 . 0 .. 0

I w

N w 40 N U, . 4 0 a4 Q4 0 N a0 a UN 0 0 0 N . 0m N0 %ma aC 0.4.. . . . . . . . . . . . . ...w 00. 4010 4 0 ' a 0 0 7 0 7 . 1 a 7 1 0 0 a U, .4 4

6 4 . . 4 4 . 1 ..4 ~.4 .4 .4 N M7 14 14 1 0 M 7 M t (p

a~ ~ I a a a a a a a a a a a a a a a z a

-j j j j a j j M - - - -S .4 'a -S a A aC a aC a Xa& I o a a a a a a a a a j a a % IDa a 0 a a a a a a a aD w aa a

a a3 aD a' a' a a a .a a o N o . o 0 a

U% 4) 0. 0.) 0. 1) UN

SNw 4 A

44. 40 0 0 0) 0 cm ) En 0 Em 0 cm 0A 0 0 a a

K~ ~~~~~~~~~~ 0 0 0 0 . 0 4 a a a a a a a a a a a K U

ON) I 0 .0 10 40 . 0 0 . 0 . . 4 . 0 . .0 0 .0 . .0 W= W0 40 40 0

* 1 1 1 1 1 1m 1 14 4 0 0 0 0 0 .0 0 a 0 0 0 0 0 0 0 N"0k I I I I I I D 0 " "I I4 1, w4 v4 v4 .4 . 4 . .4 0.4 .4 .4 0

I44. of I ) U) 1o co (a co U3 14 14 0 0 I Q 0 G C. I I I 1 0 0-1 N 1 4 1 4 0) 57 U U) 14 0.' u) 14 14 w4 1

w 1 t o c 0 04 0 ) 0 . mm7 0

ao ft. C3 0 C'f

tFIf ?I N s N 10 0 0 U% U% 0 M V % L N 0.7 I IA LA k 4- .0 VwoN w N 0.) .7 w4w40 0 O 0 0.7 1 N 0 0 .0 40 .4 . 0 0 ko 4) N

02 C 4 N M-f u% . 0 f, 0 C-. a a Y a a .0 C, a -a " a LM z 0

inK a N UN a a% U U 4) U% (40 10 10 ID 0 10 4D 0 a D a N0 N r U N K a

68

0 1S * I a a 1 al % 0 a a0 ao a a%= a a a a a a a 0 a 0 C, m a a a a

A I w a a a a a P o W a a, a a0 a a N a a, a % 93 a

o4w I I :Do 1 C N N m m4 r,a. I :) I , w FW I -j D a a) al aD a' aaaaa

.1 0 0 0 a a a" 1 t S U 0 . a . 0 . 1 a P .

EI I NY t. l .

WI.JJ .4 US P1 U, N 0 'r.

C;I 4 N , N A

wK I US 4 a a 0 a 7 0a P0 0 .4 C . 0 N % N N 0 a a N .0

IN Ira a a a a a asN . S U 1 0 It 1 U 0 .0 a

CL I L N N U%. aQ0 N N N .Nmm

W.~. N) US VS P1 a a a 4 4 .4 f N 1 P 1 P0. ao I

C;z a; aaa; a a a0 a a 0 a .0 0 .0 a a a 11 ae a a0 a a a r

H1-N Ny r .7 .4 .4 .4 4co 1I- ~ I . .7 t7

CL~ I %a UN T 0 a C

* I OS a a .4 .4 .4 .44< -1 -.0 -1 N

1W I 41 11 '1 j -1 -1 Nj N -j Nj Nxc 1 0 W (4 ) 2 (A ) KL . CL r. IL (L 11 . (L (I x ZL a o Z 2 0. L

I - za .J x Z. Z. 1 - > >- D., >.N 3 - 7 . 3 - 7

1 I oo US US US US USD 0 0 0 0 t 0 0 D2 0 . 0 0 0. 0 . 0. 0 0. 01 0

1~ 0 0 1- 1- 0 0 0 0 0 10 0 10 0 10 0 ID 00 1 0 0* 21 f 2 z x31) 22K2KK3 2 K x

* I N N N .0 .0 0 . .0 .0 0 . .0 .0 0 10 .0 . 0 t 'A . .0 .0ZIW I r ce K y w rz K e 6- tK 0-. 4 . 4 . 4 4 . 4

.ILL. 1- 4-K N . Cl) . 14 4 (

6-I 1 ce 2 a I I) A I .0 U 4 CY w A4 U SNIN 12~a W U i U 4 .4 .4 Ni N1 P1 P 1 . 7 7 U S U

21 0 I a 0 US US US US 0 1.1 V) W IAS U) P1 W V.J W W .7P W ) US% U U)

1 .I.4 .4 1 _j J 4 _j _ .1 0 13 1 3 03 0. u3 Q1 Q3 Q3 %5 , 13 . 1 b 1 %3 03,- 0 0 0 0 a 0 a 0 za a a a a 0 0 0 13 0 13 0 0 13 0 0

1 I %D U3 %3 13 3 L S ao 'a a ao , ao to a 0 m D a a o a a) C a a' a0 W I I I I a I I 1 0 0 0 C, 0 0 to 0 0 0 aD 0 a 0 0 a aINC I U W U) W U). U) W ) N I- P . N I - 1. I I x2 w a~ m2 or

I I 0 0. 00 . 00

IWl N NS N N N N N

II-In NW 4 N 1 . S N 0Y m. z0 NA P1 17 U 0 a, 0m30 N C, 4 a a, a a a, m ay a a, a .

o W2 I 4 .

AF

I

In 0~~~ UN.w a. o4 1. a.t . a 0 ' 0 4 4 0

01 JW- I N N4 W4 N4 N4 .4 N4 m4 04 . 4 .SI Wo~ I

.~~ ~ N a a2 a a kA a a i0. U. U. a M 0 0 N 0 Q. a .

)IE w a- a Cya a In 4Y "' U, ) 00 In I4N-(4 In N N 1NIn 4 I

* I-

10.N. al M N a M N4. 4 4

(LU I C Ua a

44I

01. 4 C: N N t NL N N N IZ I, In In C:) Ln U:I I n n

I .1 a, J N aN . a a a 4 . . . 0 14 U

1 0 4 0 .I0 N .3 a c0 w 40

wI..l'- I 4 I

03I. I

_j.. 0w I

In 01 Io o t

0 II IIn m 0 . 4 . . 4 . n 9~ . .

u I I 0 a a 4 a 0, N, .7 I 7 I n a 0 a .1 .. .0a . a N a . a 4 0 .4 4 . N N N N N N N N N N N N

*0I I 1- 1- 1- 1.- 1-

I CL I a a a a a a a a a z z I a a a I I a a a a a a a a

4 'm .2 a a -a a a 1 a N 0 a 0 a a a a a a 4 4 a a a .0

0-I. 4, a' 4C "C a 4 a , a C a WC a a a a

S I I a af 1 a% a a$ 0% a3 a% 1. U% UN If% 9 m9 U A %A U In I n in 19) 10 99) 94) LM w9

ocZI 0 =0 0 : 0 0 a a a .4 14 04 04 04 04 4 . . . . .I -I a a a a a a

I1 I

z x z a at a ae w aw

Z 1 ow Z' Zl 1 ON Z & I x I . I S 1 I I n

1~~~~~~~~. 0 .) " .I 1 -

I~ Iz 0 C 0 .3 - , , r

In U' N m) w0 0 0' N , 0I-lIn m .I0 .2 40 . .0 4 N . 1 4 .4 .4 1 1 .4

I gO I W 0 W 13 . .9E . 4 E Z . aa

WEE .4 5 I I U 0 . .0 703 () 9 E E S S I S I 3

u4W4-* . .4 . 4 . 4 - 4 ..4 .4 .4 .4 .4 4 . . 44 4 - .4 4 4

44- W A0 I o M' .0 .4 N P' 0 M M4 M 4'o IA M40 . 4 0 4

z I o a. a, c N ' N 1.7 o N 4') 4 ' 4 4 N N ~ Q 44 N P v 4

*K z

w- I "j 0

WK I (L LL I f. .4 vi 14 .4 4I

WI 4o 0 0 0 0 0 N P. . . N a, 4 i 0 . 8 0 r N m 0

01.3- l& .4 N N N . 0 4 N ' N 0 0ND N N 4 N 0 N N .4 N N

u% I% 4= 0 MI

(A I I

00 co I0 0 ~ * . 0 N . 0

< C -1 0 D C D W C C D C D C 0 CD 1D 0D C D C m C '

< X. 1 4 .4 1 14 .4 ,4 . .4 .4 .4 . 14 .44 - -4 -4 -4 -4 . - 14 14

u'j 4-

I4-) I . .0 . 0 . 0 .0 . 0 . 0 . . . . '.t .Z .0 -1 -8 j0 j0 .0

m04~ 0 o- u) L w3 m. o- u, C) o o 'D ti 'o 0. .1 r 4 4 41 4 13

I o of a. U) 4 n o 0 0 Z 0 U UP w o W 0U) D 4 D m m z ) z Z) D m

omc o on x on on in o. in in% 4.) %In Lln i1 in')4,i 4) 4 4I l 4

NI J

f3 I _j 0 4 _j N 4 f _

4-I 4 N N t, 'D. .0 0 4 . ."

040W1~~ ~~ w o. o o o N o 4 . 4 N N 4)i .

forsS -) D -1 N -1 m 4 N N N-- - - - 4 4 4 4 4 4 440I4 n N = ND N = .(A 4 4 P4 4 .4 N N . . .4

w o LA % o u% u% m u m m % m 4% % 4 Lm N N o4W N N c N

I of 4

I4- I l -D 0' 0 14 N W) 41 0 0 N 0 0% 0 n4 N t kf) 4 . 01 0Q 4>o0 -t 4 1 4 % 0 h 0 % v. 0A 0n 0N IC. 0o 0D .0 .0 .0 .D 'D. 0 .0 . N N

71

V I W a 111 ' (Y' (P 0' a' a' 0' a' In C' In

III o 91 N4 II w)N U C ' i 0 N Q) Q) a) o) Q) z, o) o n) c) o) - o

a , In C' In G) In a) c ) r 0a ) G3 m W ) m o co

a Q I ) "o 4o A, qC) In C) to C) c) a, lo a, C) lo 4 oIN " N w t

zaOI~ 4 11) N N A) a5 w .2 1, a I, a 2 o ) Q o 0 4) w) o) a) a) a) Q

a-a

ar . I. a oo r) a' (. r.s r .4 w' a' C, a I N I.D

~~ a N .4U) . 4 ) N N . 2 U

a- a I. oo l mo a -NI

0ua a

o a

CW . a o

a NA

:o~ N 4 .4 NI N N n U N M4 M4 k0 1N 4 LA U) M0 N% LA 14

a. I .4 . .4 .4 z10- a l. S l .1 o I L 1

~0.e 'Uc .K A4 N . N 4 N N 4 N a .0 C ' N a a .C) m4 .4 . L

w w a -t .* 2 t 4 t I 1 . 71 c 7 r a 1 J 4 .

a a C) I ) D m = m :) D) D) D C) ) Q. C. C) o. Q) C ) C C ) C ) C

a . . . . . .4 .4 . . .4 . . C) .) . C C) .) .) C ) C

I a .U a . 44 .

a- a zC

can 'D II

~.4a.W aCo. 4 4 . 2 .4 . .4 . 2 .2 ..5 -. .4 .4 . 4 . 4 4 L4 .

oa a- v- .-J w D To N T$ c - - a- - a- - a- -

I z zj j -j Zj 2j -j 2 -j=- a- a- a;= m Z) D m m m- a-I w- j a- a- a- a w u)

ae a o ' N Nn.N ' 3 >

aD -o 'ID 0. 0. 0 0 . . c C) C 0 13C ) ) Ca za 4) '1 -1 A5 N) j C5 N) C) ?v C) U) C) C ) C) C

C) C C) C) ) C C) C) )72

V a U-W

IIZ W I

CL S a a a a a a a a a a Q m a a a K 0 0 0'r

CDI to m 0 cc In 0 D o to 0 03 C C W 0 co to 0o 0) 0o 9D

*4 0. a a a =,a a a a a a a a a 0 a = aM a a

ma.~~~ . : : t gTa ~ ~C, . .0 .' C! C! 0 0 C C 0 C:0 0

aa w aN a0 2 a a 00 cy C N 0 -, a aIfp, .1 * 0 tv a2 a a N a, ro a It , . a C .

a 2. I 4M I N ) I . N t Cl 4 in N, NP N Q * N 0 0

L a 11 M N MIN N P- S NA N 0~4 p

I' I a a a ~ 4 . ~ - 4 p ti. Y I4 ?. p . r ID D .4 45a

.- w I*I I I

cy S 4 .0 40 no a 4a 44 4 Q a %o ty n! .0

I t0A .0 4 P) 0, a ( %0 on Q . e 4 r Fl In W 4 0 r U I, a

Ch. P. a ae aL a .0 m 4 m 0 N D N 0 0 .0 m0 N0 UN Q0 aa 0 0 0 a a0

ZI z I a 0 a a a . a a w a a w a a a 0 a a a a a a 4m a 'a a

0m. I n 4 U, 4 , 4 if 4 4 4 4 4 4 4 4 , UN m. m- U% p.n I w -w . -D p p. - . a p.

N4. IN a a IN a N4 a 0 a a a~

0 I1-1(A . CO . M 4 D 0 M .4 04 . . ID .0 It 0 0

fl I 'a 'D ' 'D 'D 'o . 'a 'o 'D P. P. P . P P . P . P. P 3 4 .5. I fin ul Ln ift LU LA LU In In LU mU LU LU .414 .14 .1 a .Q 4 LU 0 4 4 pw I N. W3 CY N f N Y %

ma T I .~ . . . C. C. C. . . . C. C. C. " . C. . a . . ..

I..0 .4 I 4 .- - 4 "1 1 4 1 4 1 4 . . . . 14 W a1,* a. aL N & ' 11 . a a 4 .a .4) Q. a am & (L

9P0 a Ce -t -t 4 Y 4 r 4 .4 .4 N N N N N N N N1 N1 N a1-.2 N- N N N 0 1 N ND N N N N0 N N N N N N N0 N0 N ND a a 1

73 zzz=0

1 1 C a: a

a as a a 'D A) .0 .0 Is 0 w T N .0 N N N NI 0'. a 1* N 0 &) 14 - 1 N N1 'A N a N 0 N DI ' CL 00 C a >(

I 4 A% N0 40 4 VI. Lo I~ . a p a .i a

I0 I

N N NNtI a a I aa . -

1w,~~ 11. . . .. I.. . . . . . .c

Z. w . zC~

Oz a 1. In, am a0 a. "a a aa~~I04S~c 0L 0. CD S N 4U'w C, Na

t 0 S a a1 C C 0 a C 0: C: C) C 0 0 0:

x j -. I .

L, * I ao NL at t. a 3

1,N ~ ~ ~ ~ .% aN at I a a ao aD C 0 0 aD an C o

w a' . -p " r C0 :A I U, " ' a 4 (Or J I a: N! a a a a a

0 6 a CD a a a 1 0' c Q .4 4 . 4

-J (A a ar a c a -M, '.. U i'

.3, 0 a . 4 '0 0 0' a A0 CD a a a a aA 44'. 'A4.0 a s

IO e z id a)( NA -a ' a a g .a a0 a a2 a, N N ) N

1S . . . . . . . . a i~ 0- 1 ab N 64 0 .4 co .4 I.

CD a N "5 10 #1 N N .TI I a V, 4N 0S.

N N 4A 1' 60 4 to LA Nh U'

< C I C0 1 a

a o . 4.0 P.' tA I IN ' () 4 a 554.-. a 0 LA &N 0 0 c I I L . a N U

w I ~ ). % 1. .4 04 w. 0I 0 04 50U. .o a

II t,C T02-1 LOD 0 M3. N' .3 2 , U% U, .1 . .2s U% N a a aI' 1S ltu . . .- 1 . . , I I (n a aD a N,

t4 S N 40 N P 4 .4 a .

jI 5m CA w. w. w w x x r

ION C, a 0.0 a Nw 1 1

N - .3 4 40 a, I

Sw S

I 4. c.0 ~ . 4

I- N N.S 1. .0 '. a% N, a 1 .4 .4 .KjIN N LA m. iS1-. a 0 .0I1 5 % I 0 4 tn 0 0 a - ', 0.Iaw S I 3 ~ 3 w w 13 1 51, S 0 0 0 4 - .3 . .

S-ea~~~~i,~ 0 -- Q .3 0 . 0 0 0 5 0 5 4 4 . 4.: . 4

05- 1 W0 a I-a z a w a 0 05 I WO. aIS 1 'a Z I X M -9 D w 0 z I I 'A . . . . . . . .

LI 5 100 0 3 4 0 ; a 0 .0 C 3 13 .7 1!I C I 1 .

I, w S . .. .4 4.-4.

,.-.sU IN NN U,7 U 0 N a a . ' 1 . . 0 U 0 N C a . '

74

I ,o: II 6 64 IA z a a, a a a aa.-

w I (4a- I

Of m 0 .4 .4 .4 .4 . 4 .of 14 .4 -, ~ 4 II U. I we Ia a D c D D C o c o 0 g

a.,2 za .

L t. ' I z I MI

1- aS 6 d3 -Il A N M V 4 A

P4 to to P4 4 14 64 vi 04 64 W4 p4 t. p4

XI 011 4I NIm raC 4 4 6- b4 #L I 1.4 a. is = 1 a.. g '#A I -me I .~- . . . .% . a C! a :

0 I a aD a j I a a a a am a-

I-s 4 1 4 1 4 1 14 14 4 14 CK K . I'Am0 I o a 4 a 4 .tA 0 %~ 4 'A 'A -Z .I I go CD ao a ao a a aD C 5 co

LM a al a a a a a a

F - I I Wo 14 14 14 14 14 In 4 1 4 a

C :) I1 2 4 S wm a a. a a. a

P.. M.aa -W0N N NY NY N N N N

1 z :... I " W Ito -ma I asa- a a a a a a a a a. a e

in 1 I I I w a a a a a a a a a a a

4-4 i a = CL-140 " 1s a 0! 14 C: C:14 1 14 14 1 1 4 40 Q 0 aaC;W- aIm)-o-I A4 a a a aC a 4 a . 4 .4 14 I4 I4 "4 14 1 14

< 1 0~ I a1 ta a a a a am a a aI to aI I Ua e p. .N I'. LA N- N ,,

za I 14 1~4 14 'A 14 6 4 14 taI~

aa 0s a C a a a aaa awI0-J .4 .4 (3 V) . 4 .1 .44I M 1) 14 14 vi 14 o4 .o~ o4 o4 z

*ce I. 14 141!w 1 4 4 a I a, a1 a, Ma a, a a, a, a, aI alca ~ ~ ~ ~ ~ ~a La a a a) a o a a a) ar aA a m & (4 10I~~~~~~~~~~~~ ea P (Laaaaaaaa

1-4a a1 a a aI ~a a a a a a n-

em a

*e I I

eva a m I f I I I I V) I Ia-o~ a 0.0 0. -0 - .- .- - .- . 0. - II

1w xi a a a w InCLa EI oI (

me a W J 1 5 0 %3 0 J 0 5 a 5 .5 .5 C3 0 a' 0IW a I ..a -4 z5 .j z. z5 2 x - C I~0 N N N N0 N0 N N N N N N

I (L 0 .4 .4 4 .4 .4 .4 .4 . 4 x 1 .4

m~~U ao K7 N aaa a a a wmwm- p4 7) ) 7 7) 4 7 7) 7) 4 1 >a e a; aIt a a a a

I~~~ .7 .7 I7 I7 .7 I7 . 7 . 7 . m a m . . 4 . 7 . 7 . 7

aw a aaa-............................

0 N a 0 0.3 CC: I. 8*0I~~~~ I a, al .4 - 4. - .4 (Y.~ 1 ' 0 ' 0' 0 ' 0 0' 0 M(C 0

to8 a CI

'L WI a.. I

It a C a a C. am a o- -10In I In In In In In a C C

12 a

*41 . ,C xC CC QC CC C- r- C- r- gn cu fu M0 UN2I,0U%

'A .1 .d . .4 .I a C .. 0 O , 0 C 0 a, 9 .

1- a a 'Z o 0 011 .11 0

08 I I IMP a a , a a ' 0 0

a a a. . a a a a a a a I aL a a0-1 a w4* 0 a aw a 0 a

re 18 o - La C! Ia Ca C: Ca 1: Ca C a Ca 2 0

.0 In .~ . . 64 Io, . . . I an a a In a5 a3 an ar aD D

to80 03 .- a a aI aIC, a a a1. 0 U. .. .. .. .

Kt I 0 zlu*4 U.-~~~~~~~~o I" 0I ai aIIj 0 1 01-4 a a a a 0 a aa

8*a C, a= a a a a a a 0

0. x C I , - -. -- -- Ca -zII

C aol24 a a a a a a a a a aw I A M._j IZ Ca CDa C 6 C 4 C a C I I

%A 64 . . a

In l IA %A M 0 UN 4) M 1% W a a a a a

IA 'A C a a a a

a a a0 a1 a a0 a0 a a

44 CaO Ca Ca Ca Ca Ca CA Ca In Ca al I a z48 IV a a. a. a I

*4 I4 (J I4 CA In V) V) *4 V) * v* In 0 a a a a a

>4 *4 M4 *4 * *4 * *4 * *4 .* I3 8 *0 0 0 *0 a a a a a a*41.4 IC .4 .4 .4 j -0 *0 -P a8

N ~ ~ ~ ~ l N N N .8 0 l . 4 C -Ca C a C4 to .4 4 4 C . 4 D I

a LL~C I 'A4

In In M In r t, aIS J J a a a a a

I~ DI

I 8 -I I It 81 I v 4 4

1 0. (. 0. 0. v. V 0 0. CA 0 0 4 1 .0.

7 7l Z 7 7 all: > I I I I a, a a a a"- " 4 O .

IC. a n a, aD N a a 0 a, a I a a . C18, I a a a .8 a a ~ 0 N N N N N N p4ii: w= I ) 4 4 4 4

8 8 C3'~76

'In,

I-2 a a a a a I z I-~

1 L,4L I 4 I4 w4 14 . 4 . . 8 . 0 0 0 0 0 0 0 0 0 0 m1

66. I 4 44 to 4. . .4 IA 64 4 4 0 z a % a a a a a 0 a a a az W v

xa a- aD a a a a a a a

0 6 40 90 44 W4 44 ID 90 44 4D GO 4406 Z

<~~ ~ ~ ~ IN0 C : 4

Z1 0.8 C6 a4 x u I 4 a aI-S 6 1- 0 0 0 It V I 0 0 W4 o co

CL 1 4 44 44 .4 . 4 . 4 4 . 4 0 " " 0 0 " 0 0 0 " "

M N N N N N N N N -e~ ~ ~~~ 1. a- a1 a a a .6 a a a. a a a a

I - . . . . . . .

.214 W .I a a a a a

0t 1D ED I t * ID * .

d.4 t . 06 a a a a a .60 2. 6-. 0. ..0* 0 a 0

86..4 cz 4 : 0: 1 N Iz ( M .

I 1 1 .4 . / . l . l 'A 'A 1 'A6CY) z Ia a a a a a a a a a a

a A a a a a a aIIJ .9 a3 V) IA a4 an a a a aI

11101,19~ ~ ~ ~ a, a al a1 a. a, a. a1 a1 a, 1.. . . . . . .. . . . . . .I u 0 0 0 0 MI I 0 0 0 0 MI

P) a) M a a a, a a a a 041 .4 4 4 14 4 . 4 4 4 4 4 a a a a

44 .4 .4 .4 44 .4 M4 .4 W444 4 % 6 4 6

aI a aA 1 a 0aa a

I w/ 1/ I .0 0 I: a I

0.~~' 0. .. .. .. .. 0 .I- IA IA ey IA UN 10 I./I 0 N

x 0.~go .j j . 2 . i .i j . 2 I 6 a a

664 .2 4 2 4 .4 .4 .4 . . . S O N N N N N N N7

I fI a a 40 A I0 1. C Q 3 0

o Ia.-

CL3 a a a '~ IW"4 L I CD CO M Co c an C C C C C I

* r I 0, 03

uz I

It S 1 .01 1 4 1 . 4 .3 W a) 4L a. C m a. a a, a, C

In In at C a a a a a C C ZI.S

X 2 SZ CL C0 .a . . . .4 .4 .4 . .

o1- 1 a" a' 4 4 4

LJI WIrg 0

- 1I I!C ! C1.I0~C I; W>- 0I I A I A U a a

'AW1 " 4 1 4 " .4 . .4 0 0" 0 m' III m' I m' c' U m' m'

i (10 01 0 3 0 Q 0 . ' :Ir Ca C C I

In a. CI

1. I~

In In 1-1 V, .

CY N N .N ,

ci' I*3IF- I a0 a Q 0 a 0 IA 1 IA I In IA% I . C . . 0 0 C00 1 .t .I ; I I I C C C a 4 0 14 m

0. WI r0 a~ 3e a0 a oa C Ia C

( ~ ~ ~ I~l A I A U It IA VA u' .0 .0 .0 .0 .

C) I~ J C) 0 a, C% CAA I A A I0 w4 - . .- I I 4 . . . . . . 4. . 44

<" 0 a .7 0 0 . 0 '7 I A I I 5IA I C C C I

< T10 1 IA IA A I II U. IA IA IAZ IA It' I: .1 C C 0 C

I N N N N N N N N N N Nj ~I0 I n CL I4 - . 4 . ,I . 4

* . 3; 1 4 .4 3 1 4 ko 10 34 4. 1. .4 M .I) I 0

w ~ ~ ~ ~ ~ ~ C 130. ( A00V n3IV L I 04 .0 .7 .7 .7 a0 Na . 0 4 . A . 4 * 44 1 1

110 01 0 0 0 .4 . 0 IA IA IA IA x3of II

OIUWI~ IA IA IA IA IIA I A IA I A 314 (4 4 I j -0 I a J I 3 1 -0 I n C. 3 ItWI1J I a -1 , C) C.- , -0 - C. _0 -. 0 - 100.1wWI 03 IA IA IA IA IA IA IA I I A A

I3 I -Y I I 1" I to

30 3 a a a a a eI ay I C I 4 C I I A l~

32 3 .4 .4 u v u. 4r 'r, 4 4 4 &i

UZ 0 N3 o M4 .4 14 .4 I4 I4 14 . to I

05 to a C . 4 0 N

IW I~I I 44

14100 3 . N 4 4 I .0 C; I l a, 3..)a~r * .4 n a '4 a I l 1A ). 0313

1-1(443~ * .7 4 4 ' 0 0 0 178

II(41 I

Il0 4.1 9 C0 0 I . N N 0 p

e.-Ka a a a a a *4 *4 . U. 2W-

a t 1 b 0 64 a - ae * * 6 e 6 - (1 Z 0 a m 0 , a 0 a

14 a a a a a a a 0 .a~1*4. coy a a a a 11 10.

.4 U N .4 M4 0 . Ia I L. CL I x( I C 6 C Q C L

(A 41 0-W "1_ a06 ae a a a a, a, a a Z

'r a Tr Q 0 . . .a . ..a a aC) I A I 4 * N a N a -

Ma O~ I.. Low a . . . a: C. C

< 0.1 a--

W-a CD m- 0 ar ac a a C3 m ao aD a

I C3 I a - .4QI

oLLJN oI o N N N N N N a, 0r a a

z a D cm. aD (D. D co a) o D a) aD a ao aIa. 1 * 6* 6* 6.4 V. .9 .* .4 .4 6 *m 0 o U 0 a -a 0 1

I4 &A 1 CL I4 t4 I .4 a a a1 a a a $ U, aoa a13a Z a > C.1

10 I4 *4 1 6* o* 6 *. a a a

w 110 I a aA a a D0 o4. 'D 'D ms(a a a 'D V% 4 I'DLO I,. .- Wl N: N! N! N N! N a

_j o c0 I Va2( ..4( 'AiiS I ai I a a a aa a a U

(rII Li I% an a% a% .1 a a a a C, a a c1*414 . .0 1 0 -.0 14a a a a a

0..l. 14 0: *4 VV N. CY ItV N* N* IA D

aZ a; W' '-.M ' tA 'U , 4 '0 '04 0 . .4 .4 ... .

- .I I I> D. >A >A >A >A . 4 . 4 I ao a co ao a a

(4IC. i J a a an 'A V, a a as a6 a0

1o a1414 10 .0 U 0 #A . . . . I. -. .

~ IO~ A I A I A a " .4 0 % 4 I NO ~ ~ ~ i a.u 0 1 I IA .0 N V (4%

~~ ~~0 .4 4 4. . 1 4 M. . . . .A .* *

Ie U, '4 0. a, aY aD fla a a CI aA 1 a a a a a

oa0 ~ ~ ~ ~ ~ ~ ~ Q W IA IA IA IA I A . 4 314 a a ,11 a3 IA IA 0A IA I a 4 0 0 N t1.1 a a a a1) II . . . . . . . . . *24 N 1- N0 Na N a 3 an aD c CI *0 I No No Nr N) ND NM l & 4 . 4 . 4 . 1 . 4I to I al N N N l .1 I I* I4 =4 =* :1 : 1 01 :7 0 0 6 U

a ~ ~ ~ ~ ~ C & o I, wm C j C

0' 12 a a, a) aa a a a a% aD a a0 aw4 I I ao a a1

allw~ K K K K V ~~ II aa a a9

F,1 ( 1 ( 4 ( ( 4 ( .3 U a -

I I- z--- -- M- - -- - -1 -- M .- .1 U 1 : : -

IZ V, 1 0 0 0 0 0 0 1 "1 ,I12 c) . . C .3 . c' Qt Ill z'N 2 L

mI s- a I a av v a 0 0 w 4 a .1*0 "I NM '.1 C0 M 0O 40 CD 0D 0 M r I . 4 * 4 .

I11 I It 0 0 t*- * 4 * 4 I zS 79 1 0 0 a ' . . 0 0 a 0 0 aIZ WI C.)5

ail I C 0 Q . 1 0 Q e.00.W9a 0 a K a ~ 0'

7 : 0 N N CY I4~ I

cr zZ1011~~~I a' CN 0 C' C - .C,~l . -7

C' -r4 NI N C 0 1 I

I: . 1s0

0 41. a. .. m. 01 a1 a 0 . C .

C!m 0. 1.39- C: a a ' a 3 a a C0*.) I Q . . . . . . . .

W0I I N) -0 N (.4 1)0 C) N ) a sJ IIV1 0- M a0 a a a 0 a t a a a aC'L Z . . . . . . ..Z 0 . . . . . . . . . . . . .

SIN NJI I .... C C; 0 a a a4- 05

I10. I a 1F- I' N C' a M a a

I ) 4 N N .a ) C a a -a a a) a a a 0 a . a a

8L 10 I I- 'Ar II ~~~ ~- w ) i1 01>- ul 0 a, aT 0 a aa a

C' 005C 00 C' aw a0 00 aw C' a aI a I C) ,~A ' .0 3 0 PI P N N ' C' C

0 aj a a, a, aD 0, N N a "it M a a 0 a a3 l.j'I . N .4 N W4 . N N NV I24 C) w ) a C) aP ) Q a . .

.4S~~L I I a a 0 a a a a a a C

C'IZ0-% Ir ai I a a L

101)~~ 1 . N .. . . . 2 N a a C

T7 10 .7 sl y 0 7 . 7 .7 .

804 a a a a a a a a a14 Um I 0 a a aa a a a

Cl > ,. 0 4C: 0 C! c . C C C' .s w a, a aA aUNaa a

w-C 1 N N N N 0 N N l N N N 90. 4 C . 1 a a ' 'l C

rx0 IIw

j I rZ j a a a a

J54tC'7S 01 0 0 0 0 w 0 :cs 0 7 .

Nr~J N~ Cr Cr Nr Nr Cr Nr Cr Cr Cr CW 0. A C . ~N C

11- 8*4 -A t

t I; 1 4f U% 4 0 4% P . 1 4 L A to *

1^ a a a , 0 C a a 3 0 C) V a av a a . .'

M jI C, C c Ix N z C' C' C) 0! a: C' II C. I 4 N 4 a, M 4 *4 L a P

I> I 4 4 C) .4 d3 N xD N 4 N WI W C) N A C' C' N I (A C) "1 C) MD MI 0 11 10 -T'a . ' ' ) C

I U. 4. C r 1 4 *4 cA I1 4.e * 4~a a )C 0 .4 21 I 3 0 . 34 4 a a a .1

W I I e 0 0 Nl 0 N M M Mt 7 LI aILI

S~..20 C, to Q44 . . 0 0 * 19-*41 00 0 0 (Y 0e k cm I -0 I M4 M. *4 "4 IA K4 *

OLn I I .7 I4 j w o 4 .0 a .3 .i .i .2.I5. x 13 41 CA 01 0 41 z C' C' C' w 0 I C ' C

I 1.1 ~~~0 0 3 0 ziI I I I C 542 . . . . . .IC 0 0a a 0 0 r Xr Cr Cr L 10 1 .0 t4 'A. 0 . C 3 N N .

I I 5e 0. 0. C. V) (A 0II I I. I I 4 55 us 11 *4 *4 Ct .! *!

1> 1 s1 7 0 10 M7 N Ne w N Ne N 900 1 1 ~ .7 l I N N N

SW T I I toLI

80

V4 V

*) I az 1 a a a a a aw~

1p ~ in w% in In i t% UN W% a a S 2 -*.W . P. a- t. a, P, a, a N m P. 0 1~nO . en e . n e. ) .0.

ne 1J. 011I ILF# W 1 3. 0

in # * ' A 64 n IA in in a 1 a a 0 Q a I

*.I 4L 1 0.- I N 0*1 i W1 10 10 R fl.41 N I* 04 Z I 4LI

o14 W 21 p- a, a a, a 42 a

z 0 I I- 1 .4 . . .1 .4 W4 ILj XI a a '

CD 4g *-S

wr V.. no iI O 0 C

-4 il O ox 42 14 14 . 4 . . 4~ 0 0 0 C. :0 .a : a r 1: I : t.

c I"i aw a a a a a W'

.Iw us". I a a0 en N 'o a a ah a a

.4.0.

eL4 I ini I aX aO a1, u " 0 4

inC I I "U5.xu I

,6 I I4 .4 .4 .: .4 C: %4 .4 .4 .

IA in U.% in U .I .1 1n en e 46.

mm N .. .4 .4 t

W1n. in iL IA En NIn e * 4 *

aj a a a a a aa

U N N N N N N N N N4 m OIL

, ; .4 4 .4 'AX4*O.4 .4 I4 a a a a a~ s a a a a

1 - 0 0 00n I . I 'll II 5C D~ .

aU~ p. p. p. p. W . p. p.W p. p.. p. 4 01 I 4 . 4 . 4 .4 .IWO .4 . 4 .4 . 4 . .

W4O in I Iz m I 1 I1 1 1 1 It .44 iC,P4 1 16 U 1 (.) 11 U 1 U 4 U Z Z Z

1 . U t 4 % 4 W W0 US W 5c2 N- NSin N N Na r I o o o45K L& N NI y N N

I 151 W W "- 4 4 4 I I a a a a

SO I1 N I M z M M U% 0 N 0 4 Ul P

51 , I I I I I I I I I all W.4 , 0I .4 4 .4 0 a a a a a aI OW IS U .4 .4 .4 .4 .4 .4 .4 .4 .I 3c 4 WI 045

S W I 1 0.. . . . . . .in.~ I4 I4 .4 .4 .4 4 .4 . 4 4 .

in WS W W lii

81 ~ ~ .

CA

I I U. C C C C r L C

C.IQ, s. II.,-ImuL. I m4 W4 M4 CD w4 M4 go m4 9 4 (l 2 C C C 0

LI % U 40 0 4 II- ,)I

v C IV Cy C C C C0 C C 4D -

Z I. UC ILI IL( 11 I21 0.1C

V)~C I w z

I W I -. . . I. . .l . . . . . . . . .0.

< Iz I IN IN NA Le U% UN UN " 11 j 1 0 z c M WW X I3 N N N N N N N N N .I-re 2 0 I .I (l

1- .. 411 LI 01 1: 0 C 1:0 0 C! C

I-00 I

I' C) C0 C1 U, U, m0 , III , N

w 0 I %l ~ ~ ~ 0 a) (3 C C 1 -

I. . -I i C C C' a C C C C C

aS CI 0.250 tI I E (A 1 C , " a 0a.1 I C C

:r o

zA I I I I 9.0

EL 2 I i d- CI

>~ ~~~~~ ID I D4 (4 I. . 4 9 4 ( 4 9 9 I S C C C C C 0 .

C C C C C Q C C

NI Cy N C C C C C N C CY Z1 0I

AI I0 m CA C* C C C C

i Ij -12 94 -0/ 4

IO I Q ( .4 (L a II L CL L 0. ) C C1 C ! C!

-j SL4I 4 .4 .42 4 4 - . 4 .wI- I .0 .0. C C C C 1

(-52( . . . . . . . . . . . . .C I t A V

of~ .4 .w Q 4 .o w4 44 44 .c. .

.: N N N P) N N N 0C

I 0.3 u3 5 CA w M C Ed Ct C C C. 1 C

41 I C C z CA C C0.I0 0 0 0 0 .0 0 C 0-I C C C C C

OI 0 9 a4 .4 0 .0 -j0 40 0 0

I ~ ~ ~ ~ ~ D I w 4 x ,1

I C 2 I C- C- C- C C C Cn C C6 C C

I I

820.

I Le t6 II m- C

of~ ~~ -l Iac04

IL 0' 1I w

Hz I

64 j

I vK a) CD a0 OD 0 M0 CD a, CG q, a, 0 I

ly 0 'u I N' N I N. N g

Z 0 z z> w 0 0 0 0 U

I j1 I

< oz Il in 0 0 a a D 'o ' t4 o C a o 0 0

< N N N .4 - 4 N I

J I Wa I

ki -D0 10 0 0 0 :0t40

0Z 1 - r I I... I 6 U' 4 40 1 41 F) "1 U, "1 .1 U , 1ozIJ4 CL 1 00.1 xw4V -= IK' z I 0 1 0 11C

CIUl. tA 4 4 4 m P) m )6 x (nU I a ...4

-Q .4 w a a a 0 0 a

2e* 1 -I U, IN' U' kA U' U' u'. V U, U%Icn .4 .4 W4 .4 . - .4 - . 9

-0 -0I I 0 0mo.4 WI 6 *4 *4 1 In* * 4 *4 *

0.I0

t.)Ie. N N NY N N NV NJ NY N N fI 0.I 1Ic 1 I I'

I6100 1

I- cZI I41 (I 6 4 .

oxt I

1O 0 0. 0. M M CL a C4 0. C4 co I n I 8 ~ C ,

1 I 0. 43 Q. 0 0 0 0 0 0 0 0 w C i lJI tA 'A %

* ~ ~~~ 4A C4 0: 0. am 4 t, *4 * 4 * 4 * 4

61. 6 (13 0 4

E 1 4104.6'

1-6 t6 0 .0 U' a I ' C 13 4 1 1

a)46 (D ito CD ' 0 a co a4i) ito .1 11* 4 C:(A I I I I m I m m NOaI1.

'a

1 2 '0

0 ti

0l 0

0 0 0

(A2

26 1 I C, C

to0 a a o o . o . . . . . .

60 I 0 a 0 0 C' 0 0 i 12t1 F N N N NN83C

6*O P4 1 . I - K 1 0 F. ) F ) ) F ) N F

12 I A IA &A IA mA C 0 Q w .IwWI1142 "4 on1 eq 0 0. a a C K aa111I w a C C 4 ' .4 . - . WIV C : A f4A '0' (4 mA 0 Cl a C

I '. . . . . C . . C . C C CI 21 . 4 4 .4 4 N N N N N N1 4 04A 2A . IA 0 I

* .J .- .I .

ILL I x4 14 4 4 . 4 41 1 0 W U) C C C C C CO CD CI IWI ~~

Cc 1.1 > IL I

12 I

I 101 L O 1

< I :m , . . = a a 0 0 D f ( I CD CD CO CO CO CI . CD to1 CO 4n10 1~ IC w N 4 .Z wI a- N N~ . - 0 1 = 1(44

U% I. m. NI C; C C C; C C C C C 0~~II

-. ~ I C.a012 IA Co C0 C0 CI tDA I I A I

I t4 IIII I co .D Co Cn Co Co Co C Co Co CIC,I1 I C C C C C C 0 04 0 . 04 41 1 . C C C CIIA I a N4 II NI Nj N1 N -

I0 I,10fIX I w 1 CI

lo 1 ( 1 (A 4A 4A 4 0.. .

1('at40 ! C:.C WI m M I .N '4 *A '4 .4 .7 .4 .41 4 .4

_j~~~2( WI 4'Aw

120. IO IY Cy C C Cy CV C C C C C C .1 Q 02 1 I .4 44 14 .4 44 n 1 14 CLA C C C C

1(, I

b4-0 Q- m 4r .0 Ia ' '4 . C .4 . (4I% .4 4 4 '4 14 4 '4 1 .4 WI I 44 - -4 -4 14 44 -4 - 4 4I CCI

CA 41 .4 I w4 C Cv

-j I w w w w0 04 IA I A C I A > ~ I

I 04 04 4 0 0 4 0 4 0 40 0 1 6 0 0 0 m 0

a IA IA 0A IA IAt Z4 '4 .4 .4 .4 .

w 40 1 4 K - ;11Y Iz I ID 0 C1 CO C C4 C CJ I

I U I I . 0 '

wo ow a 0 0 0 C 0 'C 0. so 124*1 (4 C C 0 C ( 14 (4 14 (4 (4 104

CI.J x C C r I IS(OE ICWI 01 x ww I

VXW' w( I I% x I N N Em I I 4

IN 1 'A -41 1 f 0 I 0 0 Il 2 2 . . .I Z I 14 (4 (4 (4 (4 m0 m0 n 1 I C 4

gy ~ ~ W n m10 a"1 ~I>~ ~~~~ ~~ IQ0 .A I A ) C C C C W

I wXI 10 z-10101-

I I .4 4 4 44 .4 4 ' 44 4 .4 . C C I 4 4 14 4 1- 44 4 14 4 14 4

*er2 2 I C 4 0 L I 4 i4 4 .

to 0. a a a i Z

0gJ . L I

II .4.

IL. a .a a, e a a a N aD a, a 1 0-a

I WIC viLL - t i vi I a34I

I4 0.P , zI Z , C L M aCKIZ I0U I >j 0e 0 a 0 Q

en. * t3 .3 a N a a a . a Z U,

x Wz~ N aeQ6 c a) a) a 0 am . (D at aDa9 1 IA a M a a Q .eU

Ul I 0 I Ice a a 0 a a a 0i a C.. .W'a

Q4InPI a a a 0 a a a a aI a a a a a a a s- a a a e a a 0 a

4 - IA I CY CN4 N4 .J NIUW N N N Cw~ w- a 0 CD a Q a a

< If I .0 .J

to to -I 0 o o.L1 o- a a aN 3 a a a a .1 I

I-

~~~ 0C I C 0 a a a a aI b-o I t% 4 ai a0 a, aY a . a I a a a

NN t, N

w- , a I4 ). I4 13 a4 a4 a 4 4 g 40 a o a o a * ao a a a a.......................................................

(Y N N a N aI N. a a N' IaI m 3 0. 13 Ns Nt . 3 N3 N 3 .3a a .4 a 4 4 .

.4~ ~~~ .4 toa . 4 .4 . ~.4) I4 I4 .4 I4 . 4 . 4 . 4 a t

4,~~~~ 0o., a) aILLJ ~ ~ ~ ~ ~ a) a a. aL a aL a. a. a. aL (

I-o~~~~~~~m~ a aCA a a a a a a a a a a a

a a aY a a a a a a a

w I Un0 0 0 0 0 0 0 W0 11W, r .1 I " I i i "

I- I0 "~ I

wI Pe I4. I-.ti~ , ~ 0 0 0 0 0 0 'A 0 0 a a a a a a a a a a a

z I Nt I U '4 .4 ..4 '4 .4 .4 .4 - -

'UW) I. zII a j a1 a a a i a i a a a a c- c

I L a a a a1 a a a a a WI

IC I Z1 1 43 14 4 4 3 . 3 .3 . 3

P-I I a F. a p85

Ila a a a a a a o a v ww6

6-24 0 w v 0 0 IA 0 v0 0 14aPa

IWz .e I ccI

a' z I a'L I

I. CL do .4 %a t4 %0 .D -D %0 it a4 1,-

LL, 6 I~ V,

6 Iw I a a, 1" 1 a a a a' 11 o*20 U

< .46 44

I0 L) 0' 'CID' -1 ;0; 1 :

4A 64 4..0 6. - CO O a O a D a D CD M. 0 a a M M

a w>4 0 a 44-4 I46 6i 44 .4 44 (A I4 4

0 aa. aaaa

I I. .a a a a a C. 40 2 a aI a Q44 a aa a a a a a a aU, -W 4.42.... ..... ... : ..... ........

CA4. C 6 CA (L C" .. .4 44 44 C. 440 C4 . r

j. .. W6 o .: .! I4 I4 N- 4A t4 .4 .4 .6

X,44 C.4 I6 of I a a a

40 La I- 0.6 I m 4 A %

0 aw a an a a 0 a a% a% LA kA LA 61 a

to4 6n I 4 I

06 I 44 44 t4 4* 44 44 4 4 4wl. * INNNNNNNNNNN .6

66) 6, Z.4Ij 6I 44 w4 W

~ 4 0 4 0 0 . 0 40 40 1 * 0 P m .w . P N w ' 0 z P.

.0 N a N 44 a 0 4 4 1 y a 6I

4 40 06 C I .4 .4 .4 .4 .4 .4 . .4

. 4

44 44 t4 . . 44

0 0 0 0 40 "0 4 0 40 40 CA 40 I444 cm ao'6. . . . . .. . .424 10

.0 4 .0 4 .0 .0 0 0 ~..3...0 6N N N N N NN N ~ NN N N N NsI64 w I46 6 ca I 4 . 4 . 4 4 4 4

6 686

IL 1 a6 a aA aA0 a a a 0 a eQUW

4 F. a 8 a N a N a Y a a Y a Y a I OLZ) N N N N N

a'Z I IM aii. x C3 co CL) a a a a as ~ a ao a am a) ao a ao

S- n 1 U 4 0, 1 N N N .1Iiw *f nI zi

a: a a a N N N NV N N Na a aaa a aI" s - aa a a a a a ,

--u - -' - - - - - - - - SCU

C.)s W ce

WI L 4- 4 w .o41VU£0j .45 Is I - a a a a a

CI IA a a a a a a a 0' 1

sI up a aI a

1 0 l , a a a a a a a a

(um4 .4 I1 U, 'D C, t1 a, i, c. 0 n1 .1

o a a J a a a a a a a a

cN N NY N N4 a a ( N N N4 m4 i = a : a a a In a o a In

I4 .4 .4 4 .c4 a 1 a4 a* a A a t4 a a0I N N N N N1 -Y r4 I4 .

4Ifl~~~~5 .4 a 4 .4 0 a .7 P1 N04W 5 CA . 4 . . 4 . 4a

OL -9 04 V) I4 &1 &4 m4 .4(L4 . s I a a - a a a 5

r .2 a a a a/ 0 a a a a a a l o

s-C N N N N i N N (7 N N N ~ ~ N N N N a a a a a a Paa a a a a j ' a a0 a -0 a W

45U n C. C. C. .C. C. . .C. C. C. . .

50 4 5D Zs a 1 N N N NN N N

SW I a~ a a- a I? .4 .4 .4 t4 t4 t4s ~ s a a a a5K~~ ~~~ 5 4 4 .4 44 4A . .a I......................

1 a a a 4 . 4 -14 ..4 5 0 N N N NX

i-s N .2 s-sOD ) DNn a w C's N N " C: alC

0 a aq aL 0 sr t l " PI a 4s

I' 5; 5 4 .4 w N N a a 1-sI

I - laI f -f wz 5

.4 . .4 487

12 I a aa a a a a a aj ay cIW

Is : 41 be 64 40 6 44 6. cc4 z9 A W I 0 - 4 1

I42. . .. . . . . I

I1V1 I N N Ny N N- Ny N N Ny C N -~ 140 09I4 I a 9 4 .9 . .8 .8 41 t 1 .6 4 I.1I1 .. I

I, 04 I0 M CD 0 CD M Go r C L

1 41 444 F i a z 1.

CA I WI c6 a a a ar a. a aIu = I 01

NO, -, : L, V, ma cc a aD 9 a ac ato a ,0

- ~ ~ V N Ne .4 o4. 4- 4Y4

t4 x- a W4 ay aIi a 0 a 0 0 a a a a a ao a a a

C) z, a a ay aY a4 a a C a a a

z Q, f 1 .1 -f j a r a a ao t D o c a) ao ao ao to aoat4 44 4 4 1 4 P

1444041 a a a a a a a a a a a

N N4 W . N N N N N N N N

c: Ii I i

a4I44 1 .4 5. 4 o 0 a a0 a c a a

.4 kA 0.1 I cmaI a a a a1 a a aT t a a az424 I0 D. I a a aI

LL) 1 I 14-4 a a a a a a a a - a atL.4 01 11 4 14 14 04 .4 a, m4 .4 .4 'A 0

W 1 4.1 01,1 44 P1 N ; 0' p09 ( ' 101 . 4 . .4 04 a4 a4 . 0

cr14 I . . .

4I I 1 U L4 19 a * p. N Il P LA0.4 14 .4 14 .4 1 a a .. a a a0 4

<4 Ie 1 a 0 a aI'~~- .4 * * 0 a. a aa

441 I N N 94 N CL. N N N NI NY N Z n 0.1 P 4 1 44 1 44 1 4 4 P 1

a1 I

I0Z L) IA 1 a. a. a. aL a. a

W I W I

~'4 I I 0 . 0 0 0. 0. 0. 0 0. 0 0. 1Q4m

'Al 0424 0 0 0 a,10.1 A" b-l WI m4 "4~ I) ci N

I- 14 I -41 I4 I -t

10 I Q4 04 to 4 c to . .0 (.) .9 L) Ce W 4 N NI4 1, 1 "4 .4 .4 UN m4 .D %a .4 aw a, I~ 0 N NI

I I 04 2 4 4 .4 4 .4 4 .4 4 14 14 1 -40~4 a 44 z

414i 4 I 4 .4 .4 .4 .4 4 N N4 04 1 01 0 at: a a a at"4 I N 01 a, m.. . .,.. . . . J. . 0

I J m1 4

I I

'm I 11 0 P1 N. P N N P1 N N N N 12144 IA 1.44.4

14410 I114444

I cc z Ty , a 0 I T N N N -vw~T I I

M 05* I OI

wU I 44 44 w m4 44 w4 44 co 44 cc cc co TI a a a aCD

11 0 U 0 % WI L)-~

EUJ ~ ~ ~ u W .7I .7 . 7 , .Il%Ifti-I N N Nyw C N N ~ 44

I0 w$ 121.~

1)~~d W -,1,(

0r I a' a' o a a 0 .~

oi u$1 1 .4 (A 1. a 0. a a dN I

WIa, I N N N N Ti a

a. a0 0. . . .r

CL Iw a 0. . . . . . . . . . .

A 40 4 4 M 4A %. "4 'A "4 -

~C 01n I .7 .t 7, aD an a a j0

CLWI Ia a a a a N N N

*z I 1. 'Aq 1 0 00 n L

G3 a r .cm a a a a a a a0 aD aD aaWU -C -i 7I A C; .7 V, 1. . a a it t 5

I : I t 1N IT Ii.I L N N N N N N N MI M I m4 4 4 4 4 14 1 4* 4 4

II Ir a aI 2I a a a a a a a

ti .4 4) 0. 0 . 7 ~ .

i~ In*~~~ >~ toaN 0D 44 0 0 0 a 0 0' . 4 I I - i . 4 4 4 4 - - -

It ~ ~ ~ ~ ~ wo -.C, 1 1 ** A 16 . . . .a a . .4 .

I U * .i I a 'A .7 ao a a a a -7 0 .4 IZ%. .4 . 0

~~4I~N .4 N 7 0 0 0 0 N .7 C I

.21 I a a a a a a a1 4 w4 IV 44 l1I a a a a a y

~0I& I . .7 .7 4 4 4 4 4 4 4 ~ a I a a a a a azIc IJ aN 554

II. .. .. .. .. .. a za a a a a a a 7 897

0 '.1 06 C. a 1 02 1 1 a ZI . . . . - . .1 . r .4

Sa- z I

a C, 0

SI. a I4 w4 4 4 4 . ~ V 4 VI r 0 0 0 0 0 C 0 C 0 m

*0~ NL I. . . . N I J-04~

a1, 5 .31 12 W0 C 2 X -f Z Z "1 2 a" C

LL *4, 14

In I U I I A IA I A I A I I) I ' Z P

w~~ or04ZS C... Ia I- z I j 4 a4 a C. a, a" lz

W-S : W ua 5 ': C C : C C: 0 I.x- IoL j !O~ I N I . N N N N .

ol tA Um 1o 0 WC l Cl Cl CA VC CD WC 3 C D CD toSD

< o WZ Mea 00

z-~ I .4 I4 4 4 4 4 4 4 4 ~ 4 i otIC %4 aA IA I A I A I A I A I I 0 m 0 0 D 0 0 0

CD ON 0. 13 - 0 C C

I5. 'A 0 C C 4Io a a- cc.J11 0 c I o 0 ) a

401 t a 1 1 . -j O

>~ ~ I 44 4 4 4 44 .4 4 4 . Va . .4a 0 0 0 , 0 a

Sf3L I C0 vi a 0 a .3 a a a a C C1 a 1 0 4

55: OA .5 0 C ) " " % C 0C C C

S~~4 totobStU

Z 1 0 'A 4, U, 1 4 4 4 3 .3

4 u j xa a- LaI I C C 0 0 4 4 C 0 0 C 0

aj .1 SECO C0 C 0 C 4 0 C

5-4 It C SaU a

W ~ ~ ~ 1 100bS 4 . 0 c C' 10 10 wA 4 10 IA I 5 4 4 44 4 .0N 4 4N~aI S IA A I IA IA A I IA IA t) IA 10 1 0 C P 0 0

tom r: a aw a 0 C 0 C

I aWIz .4 .4 - .24

a b-a 4 IA IA IA II4 I A 4 . 4

x1~ I 3 -C N C .4 -W IA (D NC VD SD ID C D M C C

1a US -1 IA -C4 . 1 .Ne o o a4 a4 N 0

1~4 5. CC CL 0. CL CL M (9 C. 0L 0 C1-

211 I not I

I~~~a..I~~~ IA .4 IA 10 .4 % A . 4 .4 C 04 . " 4 5 - 4 4 4 4 I

SOZI a a C :j. IA I Sm I n M I

w a- US I .I Ia- I

ma a a a a a a a a a a w MS C 0: : C 0 ! C!

St S 0 C 0 0 0 Ca . t~b . . . . . . .a emo .4 .4 N4 I4 w N N N N

a-90

0 W ILaw

44 ) 4IZ 4 a a a a a a a 4ii

-ZI c a" a ae a a a ?WO. - C" 4 4470 4 -

I re- I C,* I4 - - - - - -

41 CL a a x a aD a. aL CI C 0 L a ID

.7 4 7. . .7 7 7. . * A :w :0 a au a a

$A~~~~ a Ua. a .. .. .a v1

Ni N N r. N N

4 4 I 4m - I 4 4 4 4 4 4

3 a a&.aa a

us e. 1 41 to7 0 tn co. co C3 .. o m a a)a a) a)

N ly fy w

4 1 -a ,I~ s - 4 >4 I4 "4 *. .4 .. .4 a ' a a

I w 64 64# ,4 a. 0, a x~ I a a aa

0 4 w 4 44 14

*, -) 4i 4 ; c; az a; ; a ; ag a: a I

>~~~24 I 4i 0 24

4.4-4 01 N0 40 1. .0 . 1. 40 a. a. a0 a C 4 I

tsar z 4 . 4 . 4 . I a a a a 0 . 0 a a . 0

- 4 5047 E4 .4 -1 -j 44 .4 .4 .4 .4 .4 -j-

co 0' 0' w' 0 4 0 ' 0 '

i-. 1s uD a, a1 47 a1 a 0 4

as fi 4. a Ma0 a (1 a. a. a G aj a C!0 : C :

0- a s= a Q a a I tA a .o a .44 .

4 ND N N N N N NN N N 4L

La4 1 04 15 1(

I M 44I 4 4 4 4 4 4 4 4 1

A41.0 0- . . .4 .4 - .4 .4 .

Ia 44*- 4 w W w w 0C

w4 UUx4 4 4C t 4 4 9 t- 4 44C;444 I 2 2 2 2 474

aIW I N4 N N N I 0 f.N G.4

~4.J4 4 491

x I i

ui V rc2 I C a a a lWI

a I a : 4D m '.. 0D co cD Zo .co

C IL I WjI ~.-

u . ue v, a a. a a a

ft I . a

x~ aj a m a

W I X I N5 N41 N a aW

o . 1 4 I a (D a a a a a

IN w 4. o . 4. 4 . 4 . 4wa- 4~~~~I 0 1I , L, 0 l D u

_j N N N 4 N I I a a a a .

C. 'A 4. 4 . 4 .I4-a a a a a a a a4O 1.40 o4 f4 .4 .4 .4 a .4 .1

< I -j.w . . .i.l.. . . .*u0.'l l al 15 05 o. 14 .4 I 1 4 j

I 4. >. 4. 4. U. 4

a1 al a a a

o-C of N N N N l N N N 0 aI x Q I I.1 (r a

k I . 4. o " " 4. . Ln 4.Iw~ .4 .4 . . .s* v,

WI j I1. Iw4 4I I1 I . b. w 0 b

-j I M 'At) 64 _j 14 . a .4 .

< ~ ~ ~ ~ .o a1 lo 'o l I o Ia~ N a a a a w N N I'. m . m%4s

%4r A a a a a . 1 0

1 1. 1 o5 45 .5 . 5 . 5 . ' 0 - I 5 . 5 . 5 . 5 .

L I 4.10x4xI~~~~~~ 0. 4. 4 . 4 0.41 14 4 4 . 4 .

ID011 1.4 M 0. 1.0 -I 0l 100 4 1

01.421 2o 21 2 -

t I .4 .4 tA 4% U. I W.a 4 4

4. 4 . 4

INPI ~ % al 44 . N .5 . 4Il a 41N a 5 .*~~~~0l~~~ N N NI . 1 0

2 41 Na No a.a *41 N 5

o 92 1o

z

IN0

.04

z w to - - 4I

Up 0 .

(If :) 0' tI

p: Up toUSt

0! z z w z z0z z z.0 * I InIn

to W re 0 x 4 . 0 4 -

. L. l W 0 0 - 0 0 3 (I M D m m a

to -9 -r -- 0, 4-. to t-o0 0 z 0 ) 0 0 V

0' 4 1- 0 4 * 0. <

to U. 1- -0 - -) 4 .0 jU po .1 ( 1 0 0 0 4- 4 0

j' z In In In lo .0 n 2 w t t .x .4 Z! US US N * 4 4 .4 N

US 0 >4 > " " S .0 N 4 ..

In 0 . to 4 4 _0 Ito . w ;' -4 , 4- 4- I - o

0 0 L co :, m ' =i W j ~ 0' 0' 0' > '

4 U N US 1,C 0 0 0 0 0 1) 0 0 -0l

2 0' ' -i. 0 0' ' 2 - i.

4-. 4 ~ US 0 0. 0 0 0 7 0 4 ~ 2 093

'-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 ,

w~ tj W~ U) .1 w 3o( w

(t ID 3 C D C)

0l 0 * t. W0 112 112 w1 .1 N1 w6 .

,I.') Y) -0 N N% .4, "I ") In" . a 4

* MI I r

w 2) 10 i .0 J wi U) IM Ili 1-i 4.4 1

0 0 w~ 1.0 10 C2 N1 'o P6 u0 us " J

Li Li i w 2' w .W , IA) ti L i w L IL Li

W 1 0 22' T 10 .0 I, n t, N0 :!

I. a w w 2w w ai 1 , w 4 .

.1 * 0 I I 4 I I I I7 ~ . LI *4) .i 4) ') '1 '1 r i L Li i 21 I. 1, '.

o 4 62 .0 a 0 2 . 2 0 '6 11 22 6O 0~J N . 7, 2 1 - .1 a N 2 6

Id Z

N 0

11

ui 44%

w4 CY Jn I7N I " "C IO Q O 0 o 1 .

31 7 C C t .oo~J. 7C~N % '.N OOrCI...OO

-j rm. UN ,- W", U,

cC.f1M 40UNM- co0. Nh N0 0 Q0 0 00g 0, .1i cor ic o bo a,00m0

4 9 11-t emm ,-

ft.

11

I Ll w

11. 1

-j * N a' m O (7 . 00 0a. .4 t, -a a- W) N 4 - 4 N !:y0c " .0 Nt. 0'. N, 0 N % No to0 a. 0 0 00.7 . C

11 t' 0 0 t4.7 m 'N*00OCCC.CC 0CCC )'0 :!0.4U'U 4

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

-h4C ]' Q4 nI %0 - DD1 nD1 3C 2 ~

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.

4j .J~A. .4 4~ .4 . .~l . 1

1144 I I Il l I I I I I I I

0

Of4. I NOOe., 7-0040N f 0..N VI n , N F a0% 7,'Ul D 'D OLf%. 0 VULfL.4.N.NO F, r d%

61 . t 1: 4. U%.. NNI I 11 I 1: 4 1 .4. . -" .* 4fN4... I IN

In r 10 NNI I 1 0 -1I C,

.J 41 n(A t 0 N J-0 4 . D N 40 N tN h-P %D0 V% . 0

%V ]OF% In -I.A M 'NJ " C NOYCNCC.N0 %474 0 C0 01 (),0r - - -

Na - - - -70 - -7 N' N N N' If. '0 N -. N N .4 N .0! IfNNI' 4-CN N f N N' N Nt - - t N

J.A4 D~0 f- N 0N P'aNP .0 =-I N 0 W4N tDDP'0P, 0 0'C0 0''0.04-94 I 01 t0 U -U D- 0 0 400 1 40 t , NM (,0M aO

C, -o0C .4~N4444444 N MN..4N 0NNNNNNNM N N4 NN(N.0C4N 00Z DIn0 t

C, 4 L% C C " . N %0 N.01 N 0% C0 N 04 01 "0. 4N0C 0M C'- W 44 .O N N Q'44 'ltP,1 0* , L n 0 - ,M r . Lh . 01 .44.41N''.P GI4'C C 0 90-00C

II -.. 44..005A A?'~4..d.4.....4 - - foo,.. . .f1150 00 .

C3 -4-.0 14 go1' 414 LA I N f, 0 C) n4 n~ j4. .- 7 .4) -, .4) M4441 1 'AU,

%A0 I 0N 1~0- -44 o .40 Q ID %o NO N 0c T 1441 w1'0 00

'4)

WU NNNN CN N N N 4 444-

-JM0 4 0 N 010 0D 0 0N On D 4tN 0 0ULnU%0 M 74 m0 r m 3 t Nm400l

Q m4DM0 a000~~ 47) O.4 m .4NaUF 1 0 0N?4)'4

0

LUI

N NN N~~1 0 4f 70 <44N 40 o . o- o 00 D t 0 V .0o0G'MI7W

4

0

to y0 0

LU Wis4

0 4N No ID"t2 '00'w cn:Nv 14 0 4 t 44 O 0M0 .44!o4Ott%4 )

-4-1 -4 N 4 4 -4 -4 N 4m N.W N W N U

0

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

I Ve..

~~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