C- lM ISCELLANEOUS PAPER C-69-1

STRENGTH AND DEFORMATION PROPERTIES OF GRANITE, BASALT, LIMESTONE

AND TUFF AT VARIOUS LOADING RATESby

R. L. Stowe

grew¡01 I0SÉBflnsl

January 1969

Sponsored by

Defense Atomic Support Agency

Conducted by

U. S. Army Engineer Waterways Experiment Station

C O R P S O F E N G IN E E R S

Vicksburg, Mississippi

THIS DOCUMENT HAS BEEN APPROVED FOR PUBLIC RELEASE AND SALE; ITS DISTRIBUTION IS UNLIMITED

.'/<* • .'.¡fLIBRARY4

APR 15 1969

Bureau of ReclamationDenver, Colorado

c-1

Destroy this report v¡1

The findings in this report are not to be construed as an o ff ic ia l Department of the Army posit ion, unless so

designated by other authorized documents.

vC*-/$ (K c\

' < y '

MISCELLANEOUS PAPER C-69-1

STRENGTH AND DEFORMATION PROPERTIES OF GRANITE, BASALT, LIMESTONE

AND TUFF AT VARIOUS LOADING RATESby

R. L Stowe

January 1969

Sponsored by

Defense Atomic Support Agency

Conducted by

U. S. Army Engineer Waterways Experiment Station

CORPS O F EN G IN EER SVicksburg, Mississippi

A R M Y -M R C V IC K S B U R G . M IS S .

THIS DOCUMENT HAS BEEN APPROVED FOR PUBLIC RELEASE AND SALE; ITS DISTRIBUTION IS UNLIMITED

THE CONTENTS OF THIS REPORT ARE NOT TO BE USED FOR ADVERTISING, PUBLICATION, OR PROMOTIONAL PURPOSES. CITATION OF TRADE NAMES DOES NOT CONSTITUTE AN OFFICIAL EN­DORSEMENT OR APPROVAL OF THE USE OF SUCH

COMMERCIAL PRODUCTS.

3

ABSTRACT

The objective of the work reported herein was to determine the

strength and stress-strain characteristics of rocks of four types

under various rates of loading. This was accomplished by conduct­

ing slow (specimens loaded at rates of less than 2,251 psi/sec) and

rapid (specimens loaded at rates greater than 2,251 psi/sec) uncon­

fined compression tests, tensile splitting tests, and triaxial com­

pression tests utilizing confining pressures ranging from 250 to

5,000 psi. Granite, basalt, limestone, and tuff from the Atomic

Energy Commission's Nevada Test Site, Mercury, Nevada, were used in

this program. Nondestructive tests such as specific gravity, poros­

ity, and compressional wave velocity were conducted on all specimens

to determine homogeneity of each rock. Results of nondestructive

tests indicated that the rock within each rock type was quite uni­

form. Results of the unconfined compressive strength tests on basaltyindicated, that as the loading rate was increased from 1 to 1.60 x 10

psi/sec, ultimate strength, total axial strain, and Young's modulus

of elasticity increased. Total diametral strain decreased as load­

ing rate was increased. Results of triaxial tests indicated that the

maximum deviator stress and total axial strain increased as the con­

fining pressure and loading rates were increased. Apparently, loading

rates from 1 to 2,250 psi/sec do not have a significant effect on the

angle of internal friction and cohesion of basalt at confining pres­

sures up to 5,000 psi. Compressional wave velocities recorded in the

direction of applied stress increased sharply within about one-half

of the maximum deviator stress and then generally remained constant

to failure. The difference in the unconfined compressive strength

between the slow and the rapid rates of loading for the rocks tested

varied considerably. The dynamic compressive strength factor for the

granite was less than 1; for the basalt, 1.35; for the limestone,

1.52; and for the tuff, 1.7 -« The compressional wave velocity of

rock is affected by increases in both the applied axial stress and

confining pressure. Velocities recorded in the direction of applied

stress increase sharply within about one-half of the maximum deviator

stress and then generally level off until failure.

\

5

PREFACE

The study reported herein was sponsored by the Defense Atomic

Support Agency and funded under the Nuclear Weapons Effects Research

Program Subtask 13.191A, "Rock Mechanics Research Relating to Deep

Underground Protective Construction."

The work was conducted during the period October 1965 through

October 1967 under the direction of Mr. Bryant Mather, Chief, Concrete

Division, U. S. Army Engineer Waterways Experiment Station (WES).

The investigation was conducted under the direct supervision of

Messrs. J. M. Polatty, Project Officer, W. 0. Tynes, and R. L. Stowe.

Messrs. J. L. Drake and J. R. Hossley of the Nuclear Weapons Effects

Division, WES, conducted the rapid loading tests. Mr. Stowe, who

was project leader, prepared this report.

Directors of WES during the conduct of this study and the prepa­

ration of this report were COL John R. Oswalt, Jr., CE, and

COL Levi A. Brown, CE. Technical Director was Mr. J. B. Tiffany.

6

CONTENTS

ABSTRACT---------------------------------------------- 9

PREFACE----------------------------------------------- 6NOTATION---- - ------------------ --------------------------------- 12

CONVERSION FACTORS, BRITISH TO METRIC UNITS OF MEASUREMENT...... l9

CHAPTER 1 INTRODUCTION---- ------------------------------------- 15

1.1 Background------------------------------------------------- 151.2 Objective and Scope--------------------------------------- 161.3 Literature Survey------------ l8

CHAPTER 2 MATERIALS AND TEST METHODS---------------------------- 26

2.1 Rock Types------------------------------------------------- (26-'2.2 Sample Preparation---------------------------------------- 282.3 Strain Gages----------------------------------------- ;----- 282.9- Nondestructive Test Methods-------■------------------------ 292.5 Destructive Test Methods--------------------------------- 30

CHAPTER 3 PRESENTATION AND DISCUSSION OF RESULTS-------------- - 38

3.1 Nondestructive Tests--------------------------------------- 393-2 Destructive Tests----------------------------------------- 9-2

CHAPTER 9 CONCLUSIONS AND RECOMMENDATIONS------------ - ................... 19-2k.l Conclusions---9.2 Recommendations

REFERENCES...... ...TABLES

3 . 1 Test Results for Granite--3.2 Test Results for Basalt---3. 3 Test Results for Limestone--3.9- Test Results for Tuff-----

lU219-3

l99

596i6365

7

FIGURES

1.1 Effect of loading rate on ultimate compressivestrength----------------------------------------------- 23

1.2 Effect of time of loading on stress-straindiagram, compression----------------------------------- 28

1.3 Effect of compressional stresses on the wave velocityin the axial and transverse directions under confining pressures---------------------------------------------- 25

2.1 Triaxial chamber with transducers---------------------- 362.2 200-kip dynamic loader--------------------------------- 373.1 Photographs showing traces of compressional wave

velocity for granite and basalt------------------------ 673.2 Photographs showing traces of compressional wave

velocity for limestone and tuff------------------------ 683.3 Direct tensile stress versus axial strain,

granite------------------------------------------------ 693.8 Compressional wave velocity versus axial stress, tuff

in unconfined compression------------------------------ 703.5 Compressional wave velocity versus deviator stress,

tuff--------------------------------------------------- 713.6 Typical basalt shear breaks--- ------------------------- 723.7 Stress versus strain curves for granite Specimen G-2---- 733.8 Stress versus strain curves for granite Specimen G-10--- 783.9 Stress versus strain curves for granite Specimen G-15--- 753.10 Dynamic stress versus strain curves for granite (200-kip

loader) Specimens G-ll and G-13------------------------ 763.11 Stress versus strain curves for basalt Specimen B-l----- 773.12 Stress versus strain curves for basalt Specimen B-21---- 783.13 Stress versus strain curves for basalt Specimen B-22---- 793.l8 Stress versus strain curves for basalt Specimen B-29- — - 803.15 Stress versus strain curves for basalt Specimen B-20---- 8l3.16 Stress versus strain curves for basalt Specimen B-9----- 823.17 Stress versus strain curves for basalt Specimen B-7----- 833.18 Stress versus strain curves for basalt Specimen B-3----- 883.19 Stress versus strain curves for basalt Specimen B-6----- 853.20 Stress versus strain curves for basalt Specimen B-15---- 863.21 Stress versus strain curves for basalt Specimen B-8----- 873.22 Stress versus strain curves for basalt Specimen B-ll---- 883-23 Dynamic stress versus strain curves for basalt (200-kip

loader) Specimens B-10, B-l6, B-175 and B-l8------------ 893.28 Stress versus strain curves for limestone Specimen L-2-- 903.25 Stress versus strain curves for limestone Specimen L-7-- 913.26 Stress versus strain curves for limestone Specimen L-8-- 92

8

93949596

97

98

99100101102

103

104

105

io6

107

108

109

110111112113

ll4

115

ll6

Dynamic stress versus strain curves for limestone(200-kip loader) Specimens L-17> L-l8? and L-20-------Stress versus strain curves for tuff Specimen T-7-----Stress versus strain curves for tuff Specimen T-25-----Stress versus strain curves for tuff Specimen T-26----Dynamic stress versus strain curves for tuff (droptower) Specimens T-ll, T-2U? and T-27-----------------Ultimate strength versus loading rate for basalt inunconfined compression------------------- --------------Ultimate strength versus total vertical strain at failure for basalt tested in unconfined compression atloading rates from 1 to 1.6 x 107 psi/sec-------------Loading rate versus total axial strain at failure forbasalt--------------------------------------------------Loading rate versus total horizontal strain at failure for basalt----------------------------------------------Loading rate versus modulus of elasticity for basalt- Deviator stress versus strain curves for graniteSpecimen G-20-----------------------------------------Deviator stress versus strain curves for graniteSpecimen G-7------------------------------------------Deviator stress versus strain curves for graniteSpecimen G-k------------------------------------------Deviator stress versus strain curves for basaltSpecimen B-lU--------------------- --------------------Deviator stress versus strain curves for basaltSpecimen B-23-----------------------------------------Deviator stress versus strain curves for basaltSpecimen 2b-------------------------------------------Deviator stress versus strain curves for basaltSpecimen B-U------------------------------------------Deviator stress versus strain curves for basaltSpecimen B-5------------------------------------------Deviator stress versus strain curves for basaltSpecimen B-19------------------------------------ -----Deviator stress versus strain curves for basaltSpecimen B-13--------*---------------------------------Deviator stress versus strain curves for basaltSpecimen B-26--------------------------------------- -Deviator stress versus strain curves for basaltSpecimen B-27-----------------------------------------Deviator stress versus strain curves for basalt Specimen 28-------------------------------------------Deviator stress versus strain curves for basalt Specimen 30-------------------------------------------

117

118

119

120

121122123

12k

125

126

127128

129

130

131

13213313U

135136

137

138139

Deviator stress versus strain curves for basaltSpecimen 31--------------------------------------------Increase in deviator stress and axial strain with increase in loading rate at confining pressures av of250, 1,000, and 5 >000 psi for basalt-------------------Deviator stress versus strain curves for limestoneSpecimen L-U-------------------------------------------Deviator stress versus strain curves for limestoneSpecimen L-7--------------- ----------------------------Deviator stress versus strain curves for limestoneSpecimen L-12----------------------------------------Deviator stress versus strain curves for tuff SpecimenT-21-------------------------------------------------Deviator stress versus strain curves for tuff SpecimenT-20----------------------------- -------------------Deviator stress versus strain curves for tuff SpecimenT-]J+........... ................................... - .................. ........................................Compressional wave velocity versus deviator stress forgranite------------------------------------------------Compressional wave velocity versus deviator stress forbasalt-------------------------------------------------Compressional wave velocity versus deviator stress forlimestone------ -----------------------------------------Mohr circles for granite-------------------------------Mohr circles for basalt tested at loading rate of1 psi/sec----------------------------------------------Mohr circles for basalt tested at loading rate of50 psi/sec----- ----------------------------------------Mohr circles for basalt tested at loading rate of500 psi/sec-------------------------------------- ------Mohr circles for basalt tested at loading rate of2,7^0 psi/sec------------------------------------------Mohr circles for limestone-----------------------------Mohr circles for tuff----------------------------------Average stress-strain curves for basalt at various rates of loading showing increase in ultimate strength andstrain at failure--------------------------------------Mohr envelope at various loading rates for basalt------Engineering classification for intact rock at a loadingrate of 50 psi/sec--------------------- ----------------Engineering classification for intact rock at a rapidloading rate of >50 psi/sec----------------------------Engineering classification for intact rock for basalt at loading rates from 1 to l6 X 10^ psi/sec------------

10

3.7*+ Relation of axial stress to lateral stress at failure intriaxial compression tests of rock cores--------------- l*+0

3.75 Relation of axial stress to lateral stress at failure in triaxial compression at different loading rates for basalt------------------------------------------------- 1*+1

11

NOTATION

A Area

c Cohesion or shearing stress

d Length of specimen, feet

E Young fs modulus of elasticity

E_j_ Tangent YoungTs modulus at one-half the ultimate compressive

strength

f ^ Dynamic compressive strength factor

G Specific gravity of solids sGq Bulk specific gravity

P Force

t Pulse traveltime5 milliseconds

T Shearing stress

u Pore pressure

V Velocity

Compressional wave velocity

Ae^ Change in axial strain

Aa Change in axial stress

e Axial strain aDiametral strain d

e Unit volumetric change ve Loading rate, psi/sec

12

(ji PoissonTs ratio

a Applied axial stress5 maximum deviator stress, or total

normal stress

aT Effective stresses

Major principal stress

Intermediate principal stress

Confining pressure3 lateral pressure, or minor principal

stress

ft Angle of internal friction

13

CONVERSION FACTORS, BRITISH TO METRIC UNITS OF MEASUREMENT

British units of measurement used in this report can be converted to metric units as follows.

Multiply By To Obtain

inches

feet

pounds

kips

pounds per square

2.54

0.30^8

0.45359237

453.59237

inch 0.070307

pounds per cubic foot

foot-pounds

feet per second

16.0185

0.138255

0.3048

centimeters

meters

kilograms

kilograms

kilograms per square centimeter

kilograms per cubic meter

meter-kilograms

meters per second

ib

CHAPTER 1

INTRODUCTION

1.1 BACKGROUND

There has been, and still is, a great need for information con­

cerning the strength and stress-strain characteristics of rock -under

various rates of loading e . This is particularly true for

protective-construction purposes. For design purposes, it is neces­

sary to know the mechanical properties of rock since they are used to

predict and control the behavior of the in situ rock mass. Past

studies of metals, concrete, and, to a small extent, rock have shown

considerable strength and deflection changes when the rate of loading

was increased.

There are two general approaches to the study of rock proper­

ties. The approach used for the work reported herein was one in

which intact specimens were extracted from the joint blocks and

tested in the laboratory. The results obtained are realized to be an

upper (or lower) limit of the in situ strength value that would apply

only if the in situ rock had no discontinuities. However, all rocks

possess various discontinuities, and a strength reduction factor must

be applied to modify appropriately the results obtained in the labora­

tory. It is understandable that the reduction factor is a function

of the kind, spacing, orientation, and physical character of the

15

natural discontinuities present. There is no reduction factor pre­

sented in this report.

The second approach to the study of rock properties is that of

field testing the rock in situ. In this testing environment, the

test area should be sufficiently large so that the effect of discon­

tinuities enters into the results. This type of testing is neces­

sarily large-scale and expensive. Because of the expense, quite

often only a few tests may be conducted, and the results may not be

statistically significant. This is a good reason for conducting

extensive laboratory testing in which the expense is low and the

number of tests large. However, efforts should be made to correlate

results of laboratory and in situ tests. If this is not done, the

laboratory test results could be meaningless.

1.2 OBJECTIVE AND SCOPE

The objective of the research reported herein was to determine,

under a wide range of loading rates, the strengths and stress-strain

properties of rock specimens belonging to four rock types. The

strength and stress-strain properties were determined in both an un-

confined state and a confined state under confining pressures up to

5,000 psi.^ A laboratory test was devised using a triaxial chamber

^ A table of factors for converting British units of measurement to

metric units is presented on page 12.

16

and sonic equipment in an effort to simulate the field in situ stress

conditions. This test will he discussed in detail later. The objec­

tive was accomplished by: (l) a literature survey that consisted of a

review of a collection of available experimental rock property data

from tests on rock and information regarding details of the particular

testing techniques used; and (2) a laboratory study that consisted of

nondestructive and destructive testing of four rocks from the Atomic

Energy Commission's Nevada Test Site (NTS) at Mercury., Nevada; the

rocks were granite from the Operation Flint Lock, Shot Pile Driver

Experiment, dense basalt from Buckboard Mesa, limestone from the Flat

Top Experiment, and tuff from the Red Hot-Deep Well Experiment. The

nondestructive tests run on all rocks consisted of bulk dry specific

gravity, specific gravity of solids, porosity, and compressional wave

velocity tests. The destructive tests consisted of tensile splitting 2strength, slow unconfined compressive strength, Young's modulus of

elasticity, Poisson's ratio, triaxial compressive strength, and3rapid unconfined compressive strength tests. A few direct tension

tests were rim on the granite only.

2 MSlow loading” in this report denotes that specimens were loaded

at rates less than 2,251 psi/sec.

,rRapid loading” denotes that specimens were loaded at rates

greater than 2,251 psi/sec.

17

During the literature survey, particular attention was given to

those articles and papers that pertained to the following: (l) the

effect of loading rate on stress-strain properties, strength, and

strain at failure; (2) the effect of confining pressure on stress-

strain properties, strength, and strain at failure; and (3) the

effect of confining pressures on the compressional wave velocity

of rock.

1 • 3 LITERATURE SURVEY

From the available literature, it is evident that not many pre­

vious investigators have been concerned with the effect of loading

rate on the stress-strain properties, strength, and strain at failure

of rock. The articles found concerning this effect (References 1

through 3) generally indicated that an increase in the loading rate

increased the ultimate unconfined compressive strength and increased

the Young*s modulus of elasticity (a stress-strain property). Data

from other tests with increased loading, such as impact and sonic

tests, show that the strength and YoungTs modulus of elasticity can in­

crease by as much as a factor of two (Reference k ) . Figure 1.1 is a

plot of stress rate versus ultimate strength that shows a considerable

increase in ultimate strength when the stress rate is increased from

10 to about 1011 psi/sec. The maximum stress rate used for the rapidn

testing reported herein was about 10 psi/sec. Figure 1.2 shows the

l8

dependence of the stress-strain curve on time of loading and shows a

decrease in strain at failure when the stress rate is increased

(Reference k ). Results of the research reported herein show that

this is not always true.

There were many articles found during the literature survey that

dealt with the effect of confining pressure on stress-strain proper­

ties , strength, and strain at failure for a wide range of rock

(References 5 through 15)«

References 5 and 6 present the works of some of the first inves­

tigators who attempted to determine the effect of confining pressure

on the strength of rock. These early investigators applied axial

loads to rock samples that were encased by a very tight-fitting steel

jacket. A drawback to this method of confining samples was that the

steel jacket restricted the lateral expansion of the rock, and a pres­

sure normal to the axis of loading was created at the rock-steel

boundary. The results of these investigations can be summarized by

stating that the ultimate strength and ductility of rock increase

with increased confinement (Reference 7)* However, due to the type

of constrainment of the samples, no exact relation between confining

pressure and increased strength could be established.

In 1911? the inherent inadequacies of steel-jacketed testing of

rock samples were recognized and worthwhile improvements were made,

both to the testing apparatus and the method of constraining the rock

19

(Reference 8) . From tests on marble and sandstone, a relation be­

tween confining pressure and rock strength was established. The re­

sults of these tests were presented in terms.of MohrTs circles, from

which it was concluded in Reference 8 that: (l) rock strength is

greatly increased by a lateral confining pressure, and (2) MohrTs

theory can be used to represent triaxial test data on rock. Since

the early 1900’s, investigators have made extensive refinements

both in testing apparatus and method of jacketing samples; however,

the conclusions drawn in Reference 8 remain basically unchanged. In

almost all the work referred to in References 5 through 15 ? it was

found that both axial and lateral strain increased with increasing

confining pressure on rock samples. The increase of compressive

strength caused by confining pressure is many times higher than that

caused by increased stress rates (Reference b ) .

Many investigators have been concerned with the effect of con­

fining pressures on the compressional wave and shear wave velocities

of various rocks (References l6 through 31)- Most of the early work

was conducted in the interest of geophysical problems in which the

interpretation of seismic velocities in petroleum exploration was most

important. However, in the late 1930’s, laboratory measurements were

made of elastic waves in rock (Reference l6). In the 1950’s, new

developments in pulse circuitry, fast-writing oscilloscopes, and other

electronic equipment were used to investigate wave velocities in rock

20

as well as in many other materials (References l8 through 2k).

One way to investigate wave velocities in rock as affected by

pressure is to record velocities in three different orientations at

right angles to one another. This adequately indicates the degree

and variations of anisotropy of the material. In some of the more

homogeneous rocks, the three velocities are within a few percentage

points of one another; this is true for equigranular rocks. In

schistose and bedded rocks, velocities can vary up to 25 percent,

depending on orientation. The greatest controlling variable of ve­

locity appears to be the density of the material (Reference 25). It

is stated in Reference 25 that, except for the most compact rocks,

little significance should be attached to the velocities for pres­

sures below 500 bars (7,250 psi); they are not reliably reproducible

to better than 10 percent.

The velocities recorded in the direction of applied stress for

almost all rocks increase toward failure and usually remain constant

at failure. Velocities recorded normal to the applied stress in most

rocks increase sharply, level off, and then decrease toward failure.

A logical reason for this is given in Reference 2 7. When a specimen

begins to fail, internal vertical cracking normally develops. Al­

though the velocities parallel to the load are not affected by the

cracks, the velocities normal to the cracks must travel around the

cracks and are, therefore, slower. Figure 1.3 shows the variation of

21

wave v e l o c i t i e s w ith s t r e s s in th e a x i a l and th e t r a n s v e r s e d i r e c ­

t io n s under v a r io u s c o n fin in g p r e s s u r e s .

In th e l i t e r a t u r e s e a r c h , a c o n s id e r a b le amount o f ro c k p ro p ­

e r t y d a ta was found co n ce rn in g a w ide ran g e o f p h y s ic a l p r o p e r t ie s o f

d i f f e r e n t ro c k t y p e s . A t a b u la t io n o f t h e s e p r o p e r t ie s has been com­

p i l e d and w i l l be p u b lis h e d s e p a r a t e ly from t h i s r e p o r t . The t a b u la ­

t io n c o n ta in s 58 d i f f e r e n t p h y s ic a l p r o p e r t ie s a lo n g w ith some r a t i o s

o f p h y s ic a l p r o p e r t ie s . T h is t a b le was co m p iled as a r e fe r e n c e

s o u rc e f o r th o s e w o rkin g in th e f i e l d o f ro c k m ech a n ics.

22

Str

ess

Rat

e, p

si/s

ec

20 30 40 50 60 70 80U ltim ate S trength , k ip s/sq in

F ig u re 1 .1 E f f e c t o f lo a d in g r a t e on u lt im a te co m p ressiv e s t r e n g th ( a f t e r R e fe re n c e l ) .

23

Stress, psi

ro4=-

Figure 1.2 Effect of time of loading on stress-strain diagram, compression (after Reference h ).

Dilatâtional Wave Velocity, f

t/sec

22,960

19,680

16,400 T7'Axial velo :ity (300-at a confining pressure)

Transverse velocity (300-atm confLning pressure)13,120

28.44 56.88 85.32 113.76 142.20Differential Stress, 10 psi

Figure 1.3 Effect of compressional stresses on the wave velocity in the axial and transverse directions under confining pressures.

CHAPTER 2

MATERIALS AND TEST METHODS

2.1 ROCK TYPES

The four rock types used in this program were to meet the fol­

lowing criteria: (l) they were to be taken from sites where weapons

tests had been performed or were to be performed, and (2) they were

to fit roughly into the strength classification system (Engineering

Classification of Intact Rock) developed at the University of Illi­

nois (Reference 32). The rocks are classified according to their un­

confined compressive strength into five groups. Group A is for very

high strength rocks, above 32,000 psi; Group B is for high strength

rocks, which range from, 16,000 to 32,000 psi; Group C is for medium

strength rocks, which range from 8,000 to 16,000 psi; Group D is for

low strength rocks, which range from U,000 to 8,000 psi; and Group E

is for very low strength rocks, which range from zero to U,000 psi.

Granodiorite (granite) from the Operation Flint Rock, Shot Pile

Driver Experiment at the NTS, taken from depths of 11.1 to 1,759-9

feet, was used for both Groups A and B. The unconfined compressive

strength of the rock varied from about 19^000 to 3^5000 psi; this

made it necessary to classify the rock under both Groups A and B.

The rock was a light gray, dense, coarse-grained, unweathered grano­

diorite. According to the classification system presented in

26

Reference 33> this rock is called a granodiorite or granite. The

rock will he referred to as a granite in this report. Plagioclase ■ feldspar having an average composition in the high oligoclase-low andesine range, orthoclase, and quartz were the most abundant con­

stituents. Biotite, some of which was in the process of altering to chlorite, was present in moderate amounts. Accessory minerals pres­ent in very minor amounts were sphene, an amphibole, an epidote-

group mineral, pyrite, and magnetite. Small patches of pyrite were disseminated throughout the rock and were present, along with quartz, in sealed fractures.

Dense basalt from Buckboard Mesa, NTS, taken from depths of 13.2 to 157.1 feet was used for Group B rocks. The rock was a light gray, dense, fine-grained, unweathered basalt or subandesite, and was com­posed of plagioclase feldspar, with lesser amounts of pyroxene, oli­vine, and magnetite.

Limestone from the Flat Top Experiment, NTS, taken from depths of 5-5 to 82.0 feet, was used for Group C rocks. The rock was a light olive-gray, dense, very fine-grained limestone containing some

stylolite seams. The seams were not planes of weakness within the rock but were areas of concentration of the relatively insoluble part of the limestone; X-ray diffraction analysis indicated that the

material was composed of clay mica (illite) and quartz. In thin

27

sections, the rock consisted of fine-grained calcite and coarser

dolomite. The rock contained 30 to kO percent dolomite, and was

tightly cemented.

Tuff from the Red Hot-Deep Well Experiment, NTS, taken from

depths of 0.0 to 76.0 feet, was used for Group E rocks. The rock

varied in color from a light greenish-yellow, to a brownish-red, to

a dark red. It was composed of volcanic ash and was fairly well

welded.

2.2 SAMPLE PREPARATION

The rock cores used for this program were NX (2-l/8-inch diam­

eter) in size. The cores were, cut to have a length-to-diameter

(l/d ) ratio equal to two using a diamond-blade, masonry-rock saw.

After the cores had been cut to proper size, the ends were surface

ground with a machine shop surface grinder. The core ends were then

hand lapped with No. 320 Carborundum abrasive to obtain plane' end

surfaces; the end surfaces were within 0.001 inch planeness, were

parallel to each other within 0.006 inch, and were perpendicular to

the sides within 0.5 degree.

2.3 STRAIN GAGES

The rock cores tested in unconfined and confined compression had

six 13/16-inch-long electrical-resistance strain gages bonded to the

core; three gages were placed vertically 120 degrees apart, and three

28

were placed horizontally 120 degrees apart. All gages were located

at the midpoint of the core, and had a resistance of 120.b +0.2 ohm,

and a gage factor of 2.01 0.01 percent.

2.b NONDESTRUCTIVE TEST METHODS

In order to obtain nearly homogeneous specimens for destructive

testing, a series of nondestructive tests was performed on all rock

cores. The tests included bulk specific gravities, specific gravi­

ties of solids, porosities, and compressional wave velocities. The

bulk specific gravity of a rock core is the ratio of the weight in air

of its volume of permeable material at a stated temperature to the

weight in air of an equal volume of distilled water at a stated tem­

perature. The specific gravities determined for the granite, basalt,

and limestone were ovendry determinations; the tuff specific gravity

was an as-received determination. The specific gravity of solids in

rock is the ratio of the weight in air of a given volume of solids

at a stated temperature to the weight in air of an equal volume of

distilled water at a stated temperature. The rock porosity value

was obtained by using the specific gravity values as follows:

— 2 X 100iUrS

where,

G is the specific gravity of solids, and sG is the bulk specific gravity.

29

A through-sample method is used to measure compressional wave velocity. A transducer is coupled to each end of the sample by a film of silicone grease. The transducers used in this investigation were barium titanite with a lower resonant frequency of 1 Mc/sec. A pressure impulse is imparted to the sample from the expansion of a transducer caused by a step in voltage being applied to the trans­

ducer. The incidence of the transmitted pressure impulse on the re­ceiving transducer generates a voltage signal indicating this arrival. These signals are displayed on an oscilloscope and compared with a signal from a crystal-controlled, time-mark generator for determining the transit time through the sample. From this measurement of time and the known transmissive-path length, the compressional wave veloc­ity can be computed.

2.5 DESTRUCTIVE TEST METHODS

The slow tests consisted of tensile splitting, direct tensile, unconfined compressive strength, and triaxial compressive strength

tests using compressional wave velocity equipment. The tensile split­ting tests were conducted in accordance with Test Method CRD-C 77-6l of Reference 3^- The unconfined compressive strength tests were con­

ducted in accordance with Test Method CRD-C 19-65, except that the specimen ends had closer tolerances. Three specimens each of gran­ite, basalt, limestone, and tuff were loaded at a rate of 50 psi/sec.

30

Based on nondestructive and destructive test results, the basalt rock

was selected for extensive confined and unconfined compressive test­

ing; that is, loading rates of 1, 500, and 2,250 psi/sec for confined

tests and 1, 500, 2.00 X 10^, 3-00 X 10^, and 1 X 10^ psi/sec for un­

confined tests. The triaxial compressive strength tests were con­

ducted in accordance with Test Method CRD-C 93-6U, except that com-

pressional wave velocity equipment was used to determine the effect

of axial and lateral pressures on compressional wave velocities

through the long axes of the samples.

The principle of triaxial testing is summarized briefly as

follows. A cylindrical specimen encased in a flexible membrane is

placed in a triaxial chamber, subjected to a constant lateral fluid

pressure, then loaded axially to failure. The flexible membrane ex­

cludes the fluid from the specimen, thereby maintaining a constant

degree of saturation of the specimen during the test. At least three

specimens, each under a different lateral pressure, are tested to

failure to establish the relation between shear strength and normal

stress. During the application of axial load, the major principal

stress is equal to the applied axial stress cr( a = p/a ) where

P equals force and A equals area plus the lateral pressure .

The applied stress is termed the deviator stress. The intermediate

principal stress and the minor principal stress <j are assumed

to be identical and are equal to the lateral pressure used in the test.

31

Confining pressures of 250, 1,000, and 5^000 psi were selected as

reasonable pressures for the triaxial testing.

The method of using wave velocity apparatus in conjunction with

triaxial equipment is relatively new. Figure 2.1 is a sketch show­

ing the triaxial chamber and the accessories used inside the chamber

for velocity determinations. The measurement of velocity through the

rock sample is accomplished in a manner similar to the measurement

described for the unconfined samples. However, in the chamber it is

necessary to use end plates (housing the transducers) and bearing

plates, which allow for a size reduction to the NX size samples. In

this study, aluminum end plates and bearing plates were used because

the impedance of aluminum is closer to that of most dense rock than

any other material available. The traveltime through the end plates

and the bearing plates is accurately measured prior to testing; this

traveltime is the delay time that is subtracted from the traveltime

through the plates and rock sample. The equation V = •— was used tou

obtain the compressive velocity where V is the velocity, d is the

length of the specimen in feet, and t is the pulse traveltime

through the sample in milliseconds.

Commercially available barium titanite transducers were used

with no change except for light hand lapping of the flat surfaces

to ensure even contact. A light film of oil was applied to the

core end surfaces to fill any small irregularities that may have

32

been present on the specimen ends. The aluminum plates were the

wrought-type No. lU S-T having a yield strength in compression of

60,000 psi and a modulus of elasticity of 10.6 X 10^ psi. Connec­

tions between the transducers and the recording equipment were made

with coaxial cables; 50-ohm cables about 0.08 inch in diameter were

used.

A Hewlett-Packard 212-A square-wave voltage generator was

altered to produce a peak voltage of 200 volts. This was needed for

the longer transmission path. The oscilloscope used was a Tektronix,

Type 55I * dual beam, with a Tektronix 1121 amplifier. This system

was sufficient for detection of the low-level signals produced at the

receiving transducer over the increased transmission length. A Tek­

tronix 181 time-mark generator was used to measure pulse length.

The rapid tests were accomplished using two separate testing

apparatuses, a drop-tower facility and a hydraulic-operated 200-kip

loader. The drop-tower facility had a capability of 2,012 ft-lb of

energy, and consisted of a falling mass weighing 38U pounds guided by

two cylindrical steel columns. The mass was remotely triggered and

allowed to fall free from a predetermined height. Friction brakes

built into the falling mass prevented any rebound of the mass after

impact. A 200,000-pound-capacity SR k type load cell, two single­

sweep dual-beam oscilloscopes, and two Polariod cameras were used to

record the stress-strain traces. A 0.5-inch-thick piece of Celotex

33

was placed on top of the rock sample to mitigate the pulse. The tuff

rock was tested using the drop-tower apparatus.

The 200-kip loader consisted of a large hydraulic actuator and

a rigid support system as shown in Figure 2.2. The actuator is pres­

surized with a low-volume, high-pressure multiplier. The actuator

has three pressure chambers producing pressure above the piston,

below the piston, and between the rupture disks. The rupture disks

perform the task of a rapid-opening valve. The machine is pres­

surized by slow buildup of pressure above and below the piston while

a slight preload on the specimen is maintained. Concurrently, pressure

is built up in the volume between the two rupture disks; the pressure

between the rupture disks is maintained at exactly one-half the pres­

sure below the ram, thereby enabling half the total pressure below the

piston to be supported by the first rupture disk and the remaining

half of this total pressure to be supported by the second rupture disk.

When the machine is triggered, the rupture disks burst and move the

loading ram onto the specimen, which is positioned below the ram.

This loader is capable of applying a 200,000-pound force to a

rigid specimen with rise times of approximately 1.5 msec; longer

rise times can be created by placing a suitable orifice upstream

of the rupture disk assembly. The slowest loading rates obtained

to date have been about 2.0 X 10^ psi/sec. Total stroke of the

ram is k inches.

The load is measured above and below the test specimen by means

of strain-gage type load cells. Accelerations are measured above and

below the specimen by means of commercial-type accelerometers. The

outputs of all the sensing devices are recorded simultaneously on a

multichannel, magnetic tape recorder and later played back using a

light-beam galvanometer oscillograph.

35

Loading Head

Loading RamTransducer End PlateBearing Plate Sample

Bearing PlateEnd Plate TransducerBase PlateChamber Bearing Plate

Figure 2.1 Triaxial chamber with transducers.

36

_ PistonRupture Disk No. 1 Rupture Disk No. 2

Ram

Ram Load Cell

Specimen

Pedestal Load Cell

Pedestal

Lv-v~ i I— ConcreteFoundation

Figure 2.2 200-kip dynamic loader.

37

CHAPTER 3PRESEHTATION AMD DISCUSSION OF RESULTS

Visual appearance and physical test results, particularly the nondestructive results, indicated that within each rock type the rocks were reasonably uniform. The variations in test data within a rock type are best explained by (l) the slight change in mineral con­tent and inherent structure from one sample to the next; (2) the dif­

ference in specific gravities; (3 ) the difference in porosity; and

( h ) the chance for human error in sample preparation and in conducting the tests.

Due to the limited supply of granite rock cores, it was necessary to use cores from six different boreholes. The basalt cores were ob­tained from eight different boreholes; however, the depth interval from which they were taken was small. Based on a visual examination and an analysis of the nondestructive properties, the basalt cores were deemed very nearly the same. The limestone cores were taken from three separate boreholes, and the tuff cores were taken from one borehole.

Forty pieces of granite core were visually examined, and based on texture, presence or absence of fractures, gross grain size, and whether the cores were weathered or altered, 25 pieces were selected for nondestructive testing. Based on an analysis of the nondestructive

38

properties of the cores, 13 samples were used for destructive testing.

Thirty-nine basalt samples were selected for nondestructive testing,

from which 31 samples were selected for destructive testing. Twenty

samples of limestone were tested for nondestructive properties, from

which 12 were used for destructive testing. Thirty-one tuff samples

were tested for nondestructive properties, from which 12 samples were

used for destructive testing. Tables 3*1 through 3 -- list the nonde­

structive and destructive properties of the granite, basalt, lime­

stone, and tuff, respectively. A summary of the nondestructive physi­

cal properties is given in the following paragraphs.

3.1 NONDESTRUCTIVE TESTS

The range in bulk specific gravity, the difference between the

low and high specific gravity values, the average specific gravities,

and the density difference are given in the following tabulation for

the four :rock types tested. Similar data with regard to specific

Rock Type Range of Bulk Specific Gravity

Difference Average BulkSpecific Gravity

DensityDifference

Granite 2.66 to 2.71 0.05 2.69pcf3.11

Basalt 2.65 to 2.77 0.12 2.70 7.35

Limestone 2.68 to 2.72 0.0b 2.70 2.55

Tuff 1.89 to 1.98 0.09 1.92 5.73

39

gravity of solids are given below for the four rock types tested.

Rock Type Range ofSpecific Gravity of Solids

Difference Average Specific Gravity of Solids

DensityDifference

Granite 2.68 to 2 .71 0.03 2.69pcf

2.18

Basalt 2.81 to 2.81+ 0.03 2.83 1.68

Limestone 2.70 to 2.73 0.03 2.72 1-93

Tuff 2.33 to 2.1+9 0.16 2-39

Oo^03

The range in the calculated porosity for the granite was 0.10 to

0.75 percent or a difference of O .65 percent; the average porosity for

the 20 samples selected for destructive testing was 0.30 percent. The

range in the calculated porosity for the basalt was 3*07 to 5*37 per­

cent; the average porosity for the 16 samples selected for destructive

testing was 1+.60 percent. The range in the calculated porosity for

the limestone was 0.18 to O .85 percent; the average porosity for the

13 samples selected for destructive testing was 0.1+6 percent. The

range in the calculated porosity for the tuff was 15-90 to 23-30 per­

cent; the average porosity for the 12 samples selected for destructive

testing was 19-82 percent.

The compressional wave velocity was the only nondestructive phys­

ical property that varied greatly for the four rock types. The

1+0

following tabulation gives the range in velocity, the difference, and

the average velocity for those rock samples that were destructively

tested.

Rock Type Range in Compressional Wave Velocity

Difference Average Compressional Wave Velocity

ft /sec ft/sec ft /sec

Granite 17,^00 to 19,¥+0 2 , 0U0 18,¿+50

Basalt 15,270 to 17,760 2,^90 16,6 30

Limestone 19,885 to 22,320 2,^35 2 0 ,710

Tuff 6,597 to 8,810 2,213 7,890

The reproducibility of the compressional wave velocity through

the aluminum transducer holders and of the electronic components used

in conjunction with the transducers was checked and found to be very

good. The difference in the velocity, later referred to as the delay

velocity, of the aluminum holders for a series of nine readings was

less than one percent.

Prior to testing the cores for compressional wave velocities, a

granite and a basalt sample were tested for reproducibility of wave

velocities, A series of six velocities was recorded for each sample;

this was accomplished by placing the core between the transducers, re­

cording the velocity, and then removing the core. The difference in

the velocities for the granite was 2.6 percent and for the basalt was

3.0 percent. This difference is attributed to the fact that the first

signal arrival is not sharply defined on the oscilloscope trace. In

most cases? however, the signal was fairly sharp; Figures 3-1 and 3-2

are typical photographs of the wave velocity trace recorded for the

four rock types used in this work. The signal arrival for the tuff

samples was less distinct than that for the other three rock types.

3.2 DESTRUCTIVE TESTS

The average results of three tensile splitting tests for the four

rock types are given below.

Rock Type AverageTensileSplittingStrength

DirectTension

Range in Strength

Ratio of Compressive Strength to Tensile Strength at 50-psi/sec Loading Rate

psi psi psiGranite 1,700 1,700 380 12:1

Basalt 1,900 -- 300 13:1

Limestone 1,210 -- 390 9:1

Tuff 170 -- 120 10:1

Direct tension tests (pull tests) were conducted on the granite

in order to compare direct tension results with the results of the

tensile splitting test (see Figure 3-3 for stress-strain test results).

A comparison of the average strengths obtained from these two tests

shows that the average strengths are identical; however, the range of

individual data is greater for the tensile splitting test than for the

direct tension test. There is very little data from which to conclude

any distinct advantage of one method of tensile testing over the other

however? the test results indicate that the direct pull method is more

consistent. Logically, the direct method should give a truer tensile

strength because when the sample is pulled, it will fail along its

weakest plane, wherever that plane may be. In the tensile splitting

test, the plane selected for testing need not necessarily be the

weakest. The modulus of elasticity in tension is quite close to the

modulus calculated for specimens tested in unconfined compression.

There were three static unconfined compressive strength tests

conducted for each of the four rock types at a loading rate of

50 psi/sec. The basalt was then tested at 1, 500, 2.00 X 10^,

3.13 X id, 1.29 X 107, 1 .3^ x 107, and 1.60 X 107 psi/sec. A modulus

of elasticity E ’and a Poisson1 s ratio q were calculated for each

unconfined compression specimen tested. The modulus of elasticity is

A cta value calculated at one-half the ultimate strength, i.e., E = ,a,

where Act is the change in a,xial stress, and Ae is the change ^a,

axial strain. Poisson1 s ratio is also calculated at one-half the ulti

edmate strength, i.e., a = — , where e is the axial strain and en

r e a dais the diametral strain. The modulus of elasticity and PoissonTs

ratio calculated for the twelve unconfined compression tests are given in Tables 3«1 through 3«*+«

The modulus of elasticity values calculated for the static uncon­fined compression tests run on the granite rock compare quite closely with the in situ values reported in Reference 35. The work in Refer­

ence 35 was conducted on rock similar to that tested in this investi­gation. The average modulus values for Sites 1 and 2 of Reference 35

6 6were 8.91 X 10 and 9-73 X 10 psi, respectively. The average modulus for the granite cores tested during this project was 10.70 x 10^ psi.

The unit volumetric strain was also calculated for the unconfined compression and the triaxial compression tests reported herein. This value was plotted with the stress versus axial and diametral strain

curves to determine at what stress level the instantaneous rate of change of volumetric change is zero; the volumetric change is zero when the slope of the volumetric strain curve changes sign. Unit vol­umetric strain was also plotted to determine if it could be correlated with a significant change in compressional wave velocity on the devia­tor stress versus compressional wave velocity curve. It was felt that when the volumetric strain was constant, possibly indicating that in­ternal microcracks were closed, the compressional wave velocity might

be at its highest level. The results of this comparison will be given with the discussion of triaxial testing. According to the theory of elasticity, the unit volumetric change is given by:

44

(3.1), = 1 V E (<Ti + + a3)

where |i is the PoissonTs ratio and E is the modulus of elasticity-

taken at one-half the ultimate compressive strength.

The tuff samples tested in unconfined compression at natural

water content had compressional wave velocities V recorded parallel

to the applied stress at various increments of applied stress. These

tests were conducted in order to compare the change in velocity in the

unconfined state with the change in velocity in the confined state,

i.e., in the triaxial compression test. Figure 3* - shows the change

in compressional wave velocity with a change in the axial stress for

the tuff samples, and Figure 3*5 shows the 'V data obtained from

triaxial testing. A comparison of Figures 3*^ and 3*5 shows that the

compressional wave velocity of tuff is affected more by combined

stresses and than by axial stress alone. The average initial

velocity for samples tested in unconfined compression (Figure 3*^) was

6 ,9 8 0 ft/sec, while the average velocity for these samples at failure

was 8,300 ft/sec. This was an increase due to axial loading of

1,320 ft/sec. The average initial velocity for samples tested under

combined stresses was 7>3^-0 ft/sec, while the average velocity at fail­

ure up to 1,500 psi, cj 5 was 9 A30 ft/sec. This was a 1,790-ft/sec

increase. The compressional wave velocity increased faster under com­

bined stresses than under axial stress only. This was due to the fact

^5

that a confining pressure tends to consolidate the specimen uniformly,

thereby closing internal cracks and causing V to increase morePsharply.

Generally the granite specimens tested in unconfined compression

at both slow and rapid rates of loading failed in shear; however, a

few failed by vertical splitting. Two basalt specimens tested at a

loading rate of 50 psi/sec failed on high-angle planes of approxir

mately 70 degrees, and one failed by vertical splitting.

The three limestone specimens failed by vertical splitting, while

the tuff specimens failed on planes approximately 65 degrees from the

horizontal. The high shear angle, approximately 65 degrees for the

granite and the basalt, was probably caused by localized stress con­

centrations within the constrained regions of the specimens. If the

specimen length-to-diameter ratio were increased from 2 to about 2.5,

then possibly the failure angle would develop in the specimen midsec­

tion outside the constrained regions. Typical basalt shear breaks are

shown in Figure 3-6.

Most of the available rock mechanics literature that was received

showed that brittle rock, such as granite and basalt, fails by verti­

cal splitting when tested in unconfined compression. This has been

the case at the WES laboratory in the past. However, it was found

that when the specimen ends of brittle rocks were surface ground, hand

lapped, and tested without a capping material, higher unconfined

k6

compressive strengths and pronounced shear failures were obtained.This was found to be true at various rates of loading when the samples were held within close tolerances; the ends were ground plane to 0.001 inch5 were perpendicular to the side of the specimen within

0.5 degrees? and were parallel to within 0.006 inch.

Figures 3*7 through 3*31 show the relation of stress to axial, diametral, and volumetric strains of rock specimens tested in uncon­fined compression. The slow stress-strain curves for the granite,

basalt, and limestone rocks behave elastically to failure, and the mode of failure is brittle. The rapid stress-strain curve for the

granite behaves elastically to about $ 0 percent of ultimate strength. The rapid stress-strain curves for the basalt behave elastically to about k-5 percent of ultimate strength, then behave plastically to failure. The rock is characterized by a slight ductile failure.The dynamic stress-strain curves for the limestone are highly irreg­ular; however, there is no clear explanation for this. Both the slow and rapid stress-strain curves for the tuff rock behave plastically, then elastically, and then plastically again towards failure; the mode of failure is ductile.

Results of the slow and the rapid unconfined compression tests show a significant difference in ultimate strength and total axial strain with the exception of the granite. The granite (Operation

Flint Lock, Shot Pile Driver, NTS) used for the unconfined compressive

strength tests was weaker than the same granite tested in the past at

the Concrete Division, WES, and at the Missouri River Division Labora­

tory, Omaha, Nebraska. Previous tests have shown that the slow com­pressive strength of the Pile Driver granite ranges from about 19,000 to about 31,000 psi, with an average of 25,000 psi (Reference 36). Evidently, the granite cores used for testing in this program were at the lower end of the strength range. The dynamic compressive strength factor f^ for granite was less than one.

Both strength and total axial strain at failure for the lime­stone and the tuff increased under rapid loading. The f ^ for the limestone was 1 .52, and the axial strain at failure under rapid loading was approximately 2.6 times greater than the strain under slow loading. The f^ for the tuff was I.7U, and the increase in axial strain at failure was about 2,267 M*in, or about 1.6 times greater under rapid loading. The tuff f^ appears to be quite high

compared with that of the other two rock types; however, additional rapid testing would have to be done to determine the validity of this factor.

As stated earlier, the basalt rock was selected for further con­

fined and unconfined compressive testing. Additional triaxial tests were run at loading rates of 1, 500, and 2,250 psi/sec, and addi­tional unconfined tests were run at loading rates of 1, 500, and 2.06 X lCr psi/sec. In summary, the loading rates for the basalt

rock ranged from 1 to 1.60 x 10 psi/sec. The average slow compres­

sive strength of the basalt was 21,460 psi, and the rapid compressive strength was 29,020 psi. This is an increase of 7*560 psi for a compressive strength factor f^ of 1.35* The difference between

the average rapid and the average slow axial strain at failure was

2?9 -0 |j,in/in, with the rapid strain being greater. Slow diamet­ral strain at failure was slightly greater than the rapid strain at

failure, i.e., l40 (jin/in greater. Figures 3*32 and 3«33 show the effects of increased rates of load on the unconfined compressive strength and total axial strain at failure of the basalt specimens.It can be seen from these graphs that loading rates up to 500 psi/sec do not have a pronounced effect on total axial strain and only a slight effect on the compressive strength. However, at higher rates of loading both strength and axial strain increase considerably. Figure 3*32 is a plot of the relation between loading rates and ulti­mate compressive strength. This plot definitely shows a considerable increase in strength with an increase in rate of loading. The curve of best fit for the data is very good for both ends of the curve;

however, the center portion of the curve could be improved consider-3 6ably if additional data were obtained between decades lCr and 10 .

The data were fitted with a least-squares polynomial curve fit pro­gram taken to the third order, GE program No. CD 225H6.004, with the

2 3form y .= a + bx + cx + dx .

7

Intuitively one might expect that total axial strain at failure

would decrease with an increase in rate of loading. This is graphi­

cally shown in Figure 1.1 for relatively low rates of loading. How­

ever 5 the test data presented herein show this not to be true at

faster loading rates. Reference 37 reports that similar results were

observed during testing of concrete cylinders utilizing stressing

rates ranging from 7*1 to 1.7 X 10^ psi/sec. Results of tests re­

ported in Reference 38 also indicated an increase in axial strain at

failure with an increase in stressing rates.

One explanation for the increase in rapid axial strain at failure

over slow axial strain at failure may be the fact that as the rock

begins to fail under dynamic loading, the rock midsection on which

the strain gages are bonded breaks away intact and continues to

strain. High-speed movies taken at WES of rock cores failing under

rapid loads show that the core fails in a cone break. This type

of break normally leaves the midsection intact after failure.

A curve of best fit for the strength-strain data shown in Fig­

ure 3-33 was judged to be in the form of a curvilinear equation of

form y = ax^ . The solution for the equation coefficients, a and b ,

and other pertinent statistical parameters was handled by a computer

program, OCE No. 0U-G1-Z5-002 (Reference 39)• This program uses the

method of least squares for a curvilinear regression to determine the

50

eq u ation c o e f f i c ie n t s o f th e l in e o f b e s t f i t fo r th e input d a ta .

F igu re 3.3k shows the r e la t io n o f lo ad in g r a te and t o t a l a x i a l

s t r a in a t f a i lu r e fo r b a s a l t . F igu re 3 .35 shows th a t with an in c re a se

in lo ad in g r a t e , the t o t a l d iam e tra l s t r a in a t f a i lu r e d e c re a se s

s l i g h t l y . F igu re 3*36 shows the r e la t io n o f lo ad in g r a te and modulus

o f e l a s t i c i t y taken a t o n e -h a lf the u ltim a te com pressive s tre n g th .

The v a r ia t io n in modulus a t a g iven lo ad in g r a t e i s q u ite w ide, and

a d d it io n a l d a ta should be developed to v e r i f y the in c re a se in modu­

lu s with in c re a se d r a t e s o f lo a d in g . Curves o f b e s t f i t were ob tain ed

by u sin g the p re v io u s ly mentioned OCE computer program . ^

F ig u re s 3 .37 through 3-58 show th e r e la t io n o f d e v ia to r s t r e s s

(o^ - cr^) to a x i a l , d ia m e tra l, and v o lu m etric s t r a i n s . F ig u re s 3 .5 9

through 3 .6 l and F igu re 3-5 g iv e r e s u l t s o f th e com pression al wave

v e lo c i t y t e s t s and show th e r e la t io n between wave v e lo c i t y and d e v i­

a to r s t r e s s . F ig u re s 3 .62 through 3 .68 are p lo t s o f Mohr c i r c l e s th a t

show the r e la t io n o f normal s t r e s s to sh e arin g s t r e s s ; th e an gle o f

in te r n a l f r i c t i o n and th e sh e arin g s t r e s s c are g iven fo r each

rock ty p e . These f ig u r e s a l s o show th e observed f a i lu r e p lan e in the

c o re . D ata from b a s a l t rock t e s t e d in t r i a x i a l com pression a t lo a d ­

in g r a t e s o f 1 , 50 , 500, and 2,250 p s i / s e c are in te r e s t in g in re g a rd

to th e lo a d in g r a t e s a t a s p e c i f i c co n fin in g p re ssu re o^ . F igu re

3.52 shows th a t a t o ^ 's o f 250 and 1 ,000 p s i th e maximum d e v ia to r

s t r e s s ct in c re a se d with in c re a se d lo ad in g r a t e except fo r the

51

specimens loaded at 50 psi/sec. At a of 5,000 psi, a in­

creased throughout the full range of loading rates used. Total axial

strain increased in all cases with an increase in loading rate at

each of the used except at a a 250 psi and a loading

rate of 50 psi/sec.

From the data presented for the unconfined compression tests

(Figure 3.69) and the above-described triaxial compression tests, it

is evident that at least the basalt rock behaves consistently under

various rates of loading, i.e., both strength and axial strain

increase.

The tuff rock was the only one tested that showed a decrease in

deviator stress with increased confining pressures. The rock was

tested at a natural moisture content of approximately 21 percent and

in the undrained state. The pore pressure buildup due to confining

pressure and axial loading probably caused the pore pressure to break

down some of the rock structure, thereby causing lower strengths at

increased confining pressure. This fact is cited a. number of times

in the literature that was reviewed. Should additional triaxial

testing be done, the effect of pore pressure should definitely be

accounted for in terms of effective stresses . a' = a - u , where ar=

effective stresses, a = applied axial stress, and u = pore pressure .

The results of the compressional wave velocity tests, which were

conducted along with the triaxial compression tests, agree quite well

52

w ith th e t e s t r e s u l t s found in th e l i t e r a t u r e s e a r c h . T here were

tw e lv e t e s t s ru n , and in a l l c a se s e x c e p t one th e co m p re ss io n a l wave

v e l o c i t y in c r e a s e d s h a r p ly when th e a x i a l s t r e s s was in c r e a s e d t o

about o n e - h a lf o f th e u lt im a te s t r e s s . The v e l o c i t i e s th en le v e le d

o f f u n t i l j u s t b e fo r e f a i l u r e ; a t f a i l u r e , th e y e i t h e r rem ained con­

s t a n t o r d e c re a s e d s l i g h t l y . V e l o c i t i e s a ls o in c r e a s e d w ith in ­

c r e a s e d c o n f in in g p r e s s u r e . The in c r e a s e s in v e l o c i t y from ze r o t o

maximum d e v ia t o r s t r e s s f o r th e ro c k s t e s t e d a r e g iv e n b e lo w :

Rock F a c to r by Which V e l o c i t i e s In c re a s e d a t C o n fin in g P r e s s u r e s

I n d ic a te d

250 500 1,000 1,500 ¿*,000 5,000

p s i p s i p s i p s i p s i p s i

G r a n ite 1.0 9 — 1 .1 0 — 1.0k —

B a s a lt 1 .0 3 — 1.0 6 — — 1.12

L im eston e 1.10 — 1.0U — — 1.10

T u f f — 1 .2 3 1.21 1 .2 7 — —

No d i s t i n c t c o r r e l a t i o n c o u ld be made betw een th e co m p re ss io n a l

wave v e l o c i t y v e r s u s d e v ia t o r s t r e s s and th e v o lu m e tr ic s t r a i n v e r s u s

d e v ia t o r s t r e s s c u r v e s . G e n e r a lly th o u g h , th e co m p re ss io n a l wave

v e l o c i t y cu rv e was a t a c o n s ta n t l e v e l , o r a t i t s h ig h e s t v a lu e when

th e v o lu m e tr ic cu rv e was e x p a n d in g , i . e . , j u s t a f t e r th e v o lu m e tr ic

change was c o n s t a n t .

53

For all practical purposes, the straight-line relation described

by Mohr’s criterion T = c + a tan ft where T is the shearing

stress, c is referred to as cohesion, o is normal stress on the

failure plane, and ft is the angle of internal friction, fits most

of the stress circles presented for the granite and basalt. A curvi­

linear analysis would best fit the stress circles presented for the

limestone rock. No envelope was drawn for the results of the tuff

rock due to the decrease in deviator stress with increased .

Nearly all the observed shear failure planes did approach those pre­

dicted from MohrTs criterion (ft = $0 - 2 a ). This can be seen in the

following tabulation.

Rock LoadingRate °3 Observed

FailureAngle

Predicted Failure Angle ft = 90 - 2a

Envelope

psi/sec psi degrees degrees degrees

Granite 50 250 52 72 5b

Granite 50 U ,000 50 72 5b

Basalt 1 1,000 6l 77 —

Basalt 1 5,000 — — —

Basalt 50 250 60 72 5^

Basalt 50 1,000 63 72 5b

Basalt 50 5,000 63 72 5b

Basalt 500 25O 71 70 50(Continued)

Rock Loading ff3 Observed Predicted EnvelopeRate Failure Failure Angle

Angle f = 90 - 2-Oi

psi/sec psi degrees degrees degrees

Basalt 500 1,000 75 70 50

Basalt 500 5,000 70 70 50

Basalt 2,250 1,000 lh 73 55

Basalt 2,250 5,000 72 73 55

Figure 3.70 shows Mohr (snvelopes for the basalt rock at loading

rates of 1, 50? 500? and 2,250 psi/sec. 1There is very little dif-

ference in / at the lower T s and at the higher T s with the

exception of the envelope developed from specimens loaded at a rate

of 50 psi/sec. The / T s of envelopes at the tangent point of the

1,000- and the 5?000-psi cr stress circles are presented below.

1,000-psi Circle 5,000-psi o’2 Circle

Loading Rate ? Loading Rate 0psi/sec degrees psi/sec degrees

1 -- 1 --

50 5^ 50 16

500 50 500 ^ 7

2,250 55 2,250 k6

55

The data on the previous page indicate that basalt under triaxial

stresses is not greatly affected by loading rates ranging from 1 to

2?250 psi/sec with regard to 0 , and that MohrTs criterion of

failure fits the basalt rock quite well. Generally, the observed

angles of failure do increase with increased rates of load at a given

confining pressure; however, the method of measuring these angles is

rather crude and not taken as very accurate. The cohesion values for

the loading rates used are presented below:

Loading Rate Cohesion (c)

psi/sec psi

1 —

50 3,800

500 3,900

2,250 3,700

Here again there is no clear indication that loading rates signifi­

cantly affect cohesion of basalt at rates up to 2,250 psi/sec.

Figures 3*71 through 3«73 are charts showing the engineering

classification for the intact rock specimens tested during the proj­

ect. This classification system is the one referred to earlier in

Reference 32. Generally, the data reported herein fell very close

to similar rock data plotted in Reference 32.

Figures 3*7- and 3*75 show the relation of axial stress to

56

lateral stress at failure in triaxial compression at various loading

rates for the rock tested during this program. The data shown in

Figure 3*3^ are consistent with data found in the literature search.

However5 there were no data found during the literature search on any

one rock that had been subjected to triaxial loading at different

loading rates. The results of this investigation show that as the

rate of loading is increased, for a set of confining pressures, a

straight-line equation exists; the samples tested at a loading rate

of 50 psi/sec are an exception to this statement.

57-58

TABLE 3 .1 TEST RESULTS FOR GRANITE

Spec­imenNo.

Hole No. Depth SpecificGravityBulk Solids Dry

Poros­ity

Compres-sionalWaveVelocity

DirectTension

TensileSplittingStrength

Slow Compression Rapid CompressionUnconfined Compressive Strength Test

Triaxial Compressive Strength with Compressional Wave Velocity (V )

Unconfined Compressive Strength Test

LoadingRate

Strength Y o u n g * s Modulus

Pois­son* s Ratio

Strength at Confining Pressures of 25 0, 1,000, and t,000 psi250 1,000 it,000

Young’sModulus

Pois­son * s Ratio

InitialVP

HighV

P

Loading Strength Rate

Young * s Modulus

feet pet ft/sec psi psi psi/sec psi_ 106 psi psi psi psi 106 psi ft/sec ft/sec psi/sec psi 106 psiG-l U-1501-U2 11.1 to 11.7 2.69 2.70 0 .3 3 18,8I+0 — 1,5 0 — — — — — — — — — — — --G-2 U-1501-U2 73.2 to 2.69 2.70 0 .3 3 18,590 — — 50 19,790 10.20 0.22 — — — — -- — — —G -h U-I5-I7 52.6 2 .7 1 2.71 0.10 18,820 — — -- — — — — 52,5^0 10.00 O.29 20,660 21,8t0 — —G-5 U-I5OI-UI 728.0 to 730.2 2.68 2.70 0.63 18,270 — 1,630 — — — — — — — — — -- — —g - 6 U-I5-27 121.0 2.69 2.70 O.29 18,550 1 ,770 — — — — — — — — — . -- — — —G-7 U-15E-01 9 9 . b 2.68 2.70 0 .6 3 18,000 — — — — — — — 29,320 11.30 0.22 18,000 19,9^0 —G-8 U-I5OI-UI 728.0 to 730.2 2.68 2.69 0 .3 3 17,500 1 ,770 — — — — — — — — — -- — — —G-IO U-I5OI-UI 728.0 to 730.2 2.68 2.69 0.29 19,230 — ~ 50 2 0,ltO II.60 0.22 — — — — — — — —G-ll U-I5OI-UI I7O9.O to I7IO.7 2.70 2.70 0.11 19,220 — — — — — — — — — — — — 66.03 x 10 18,070 IO.5IG-13 U-I5OI-UI 1709;o to 1710.7 2.66 2.68 0 .75 17,1+00 — — — -- — — — — — — — — 6.95 x 106 20,960 10 .03

G-15 U-I5OI-UI 1759.9 to 1760.9 2.70 2.71 0.11 19,M+o ~ — 50 22,290 IO.3O 0.22 — — — — — -- — --G-16 U-I5-27 178.0 2.68 2.69 0 .3 7 18,720 — 1,920 — — -- — — — — — — -- -- --G-17 U-15E-01 106.5 2.70 2.70 0.11 17,860 — — — — — — — — — — — -- — --G-18 U-I5OI-UI 1759.9 to 1760.9 2.70 2.71 0.11 18,380 — — — — — — — — — — -- — -- --G-19 U-1501-U1 — 2.69 2.69 0.22 18,660 — — — — — — -- — — — -- — -- --

G-20 U-I5OI-UI — 2.68 2.69 0 .7 7 18,250 — — — — — — 2t,120 — 10.70 O.25 18,250 20,050 — —

G-21 U-1501-U1 — 2.70 2.70 0 .0 3 18,270 — — — — — — — — — — -- — — --

G-22 U-I5-27 121.0 2.69 2.70 O.29 18,500 — — — — — — — __ -- — -- -- -- --

G-23 U-I5OI-UI — 2.68 2.69 o . t 6 18,260 — — — — — — — — — -- — -- -- --

G-2t U-1501-U1 — 2.68 2.69 0.37 18, 70 — — — — — — — — — — — — — —

Average 2.69 2.69 0.30 18, it 50 1 ,770 1,770 20,7t0 IO.7O 0.22 19,510 1 0 .27

59-60

TABLE 3.2 TEST RESULTS FOR BASALT

S p e c -menNo.

H oleN o.

D epth S p e c i f i cG r a v i t y

P o r o s ­i t y

C om pres-s i o n a lWaveV e l o c i t y

T e n s i leS p l i t t i n gS t r e n g t h

S lo w C o m p re ssio n R a p id C o m p re ssio n Mode o f :F a i lu r e

Unc o n f in e d C o m p re ss iv e S t r e n g t h T e s t

T r i a x i a l C o m p re ss iv e S t r e n g t h w it h C o m p re ss io n a l Wave V e l o c i t y (V p )

U n c o n fin e d C o m p re ssiv e S t r e n g t h T e s tB u lk

D ryS o l i d s

L o a d in gR a te

S t r e n g t h Y o u n g ' s M odulus

P o i s ­s o n 'sR a t io

L o a d in gR a te

S t r e n g t h a t C o n f in in g P r e s s u r e s o f 250, 1 ,0 0 0 , and 5 ,0 0 0 p s i

250 1 ,0 0 0 5 ,0 0 0

Y o u n g ' s M odulus

P o i s ­s o n 'sR a t io

I n i t i a lV

P

H ig h e s tV

P

L o a d in gR a te

S t r e n g t h Y ou ng' s M odulus

P o is ­son ' s R a t io

f e e t p e t f t / s e c p s i p s i / s e c p s i 10^ p s i p s i / s e c p s i p s i p s i 10^ p s i f t / s e c f t / s e c p s i / s e c p s i 10^ p s i

B - l DA-1 75.3 t o 76.5 2 .7O 2.83 15,61+0 - 1 21,370 1+ .66 0 .2 6 - - - - - - - - - - - - - - -

B-2 NCG-38 - 2 .6 8 2.83 5 .2 6 15,650 1 ,8 2 0 - - - - - - - - - - - - - - - - - - -

B-3 DA-1 1 3 8 .2 t o 1^ 0 .0 2.67 2 .8 2 5.35 16,350 - 500 2 1 ,8 1 0 1+.80 0 .2 9 - - - - - - - - - - - - S h e a r a t 60 d e g r e e s fro m h o r i z o n t a l

B-U DA-1 1 3 8 .2 t o 1U 0 .0 2.67 2 .8 2 5.35 16,370 - - - - - 50 30,000 - - b . 6 o 0 .2 2 16 ,0 6 0 1 6 ,5 1 0 - - - - - S h e a r a t 63 d e g r e e s fro m h o r i z o n t a l

B-5 NCG-^+2A 68.5 2 .6 6 2 .8 2 5.37 1 6 ,0 9 0 - - - - - 50 - 3 6 ,9 8 0 - 1+.90 0.17 16 ,0 2 0 17,130 - - - - - -

b -6 NCG- +5 73.9 2.73 2 . 81+ 3.^7 1 5 ,2 7 0 - 5OO 21,1+10 5-37 0 .3 2 - - - - - - - - - - - - -

B-7 C a le x - 2 .6 9 - - 16 , 1+30 - 5OO 2 2 ,3 1 0 1+.00 0 .2 5 - - - - - - - - - - - - - - -

B -8 C a le x - 2 .7 1 - 1 6 ,8 9 0 - - - - - - - - - - - - - - 2 .0 6 x 1 0 5 2l+,970 3.61 0.27 -

B-9 - 1 5 6 .8 2.73 2 . 81+ 3.59 1 5 ,6 7 0 - 50 2 2 , 7l+0 1+.17 0 .2 9 - - - - - - - - - - - - - -

B-10 - I 5 7 . I 2.73 2 . 81+ 3.59 16,1+90 - - - - - - - - - - - - - 3 .1 3 X i o 6 2 8 ,1 7 0 5.OO O.U5 -

B - l l C a le x 2 .7 0 - - 16,730 - - - - - - - - - - - - - 2 .0 6 x 10 5 2 7 ,5 2 0 3-^2 O .39 -

B-12 NOG-23 I+9.O 2 .7 ^ 2 .8 3 3.07 1 7 ,7 0 0 1,790 - - - - - - - - - - - - - - - - - - -

B-13 DA- 2 95.0 t o 9 6 .5 2 . 7 k 2.83 3.11 1 7 ,7 6 0 - - - - - 5OO 2 5 ,6 2 0 - - - 1+.1+6 0.37 - - - - - - - - S h e a r a t 71 d e g r e e s fro m h o r i z o n t a l

B - l k I 3 . 2 2 .6 8 2 .8 3 5 .2 6 17,650 - - - - - 1 21,21+0 - - - 5 .1 8 0.1+1 - - - - - - - - V e r t i c a l s p l i t t i n g

B-15 NCG-^+O 61.3 2 .6 8 2 .8 3 5 .2 6 1 5 ,U 6 o - - - - - - - - - - - - - - 2 .0 6 X 10 5 23,360 2 .7 1 O.35 -

B - l6 NCG-i+O 6 1 .3 2 .6 8 2 .8 3 5 .2 6 15,910 - - - - - - - - - - - - - 1 .6 0 x i o 7 3 2 ,1 2 0 ^.73 O .23 -

B-17 NCG-38 6 k . k 2 .6 9 2 .8 2 1+.61 17,550 - - - - - - - - - - - - - 1 .2 9 x i o 7 32,390 1+.68 0.. 20 -

B-18 NCG-38 6 k . h 2 .6 9 2 .8 2 1+.61 1 7 ,6 5 0 - - - - - - - - - - - - - 1.31+ x 10 7 3!+,580 6 .6 6 O.25 -

B-19 DA-2 6 7 .8 2 .6 8 2 .8 2 5 .2 0 1 7 ,3 6 0 - - - - - • 50 - - 1+6,280 6 .0 8 0 . l 6 1 6 ,6 7 0 18,750 - - - - - - S h e a r a t 63 d e g r e e s fro m h o r i z o n t a l

B-20 DA- 2 6 7 .8 2 .6 8 2 .8 2 5 . 21+ 17 ,200 - 50 20,730 1+.25 - - - - - - - - - - - - - - - -

B-21 C a le x - 2 .7 0 - - 16 ,8 0 0 - 1 2 2 ,5 8 0 1+.71 O.UU - - - - - - - - - - - - - - -

B-22 C a le x - 2 .7 0 - - - 1 6 ,8 5 0 - 1 1 8 ,9 2 0 3.^8 0 . 1+7 - - - - - - - - - - - - - - -

B-23 C a le x - 2 .7 0 - 1 6 ,5 0 0 - - - - - 1 - 2 7 ,8 8 0 - 4 .1 9 0 . k 3 - - - - - - - - S h e a r a t 6 l d e g r e e s fro m h o r i z o n t a l

B - 2U C a le x - 2 .6 9 - ~ 1 6 ,1 0 0 - - - - - 1 - - 3 3 ,^ 3 0 1| .6-; 0 .2 2 - - - - - - - V e r t i c a l s p l i t t i n g

B-25 C a le x - 2 .6 8 - - 1 6 ,2 5 0 2 ,0 9 0 - - - - - - - - - - - - - - - - - -

B-26 C a le x - 2 .6 9 — 16,950 - - - - - 5OO - 31,290 - 3 -9 . 0.27 - - - - - - S h e a r a t 75 d e g r e e s fro m h o r i z o n t a l

B-27 C a le x - 2 .7 1 - - 1 7 ,1 0 0 — - - - - - 5OO - - 1+9 ,13 0 k . k 2 0.31 - - - - - - - S h e a r a t 70 d e g r e e s fro m h o r i z o n t a l

B-28 C a le x - 2 .7 0 - - 16 ,2 ^ 0 - - - - - - . 2, 7l+0 2 5 ,7 0 0 - - 1+.00' 0 .2 5 - - - - - - - V e r t i c a l s p l i t t i n g

B-29 C a le x - - 2 .6 9 - 15,990 - 50 2 1 ,2 5 0 5 .0 0 0 .2 6 - - - - - - - - - - - - —

B-30 C a le x - 2 .7 2 - - 1 6 ,9 8 0 - - - - - 2 ,2 5 0 - - 3 5 ,0 1 0 - 1+.71 0 .2 5 . - - - - - - - S h e a r a t 7 + d e g r e e s fro m h o r i z o n t a l

B-31 C a le x - 2 .7 0 - - - 1 6 ,8 9 0 - - - - 2 ,2 5 0 - - 5l+,000 5.O 3 0.15 - - - - - - S h e a r a t 72 d e g r e e s fro m h o r i z o n t a l

A v e ra g e 2 .6 9 2 .8 3 1+.60 1 7 ,l l+ 0 1 ,9 0 0 21,1+60 0 .3 2 2 9 ,0 1 0 4.^0 O .3 I

L \ . i iQ

61-62

TABLE 3.3 TEST RESULTS FOR LIMESTONE

Spec­imenNo.

HoleNo.

Depth SpecificGravity

Poros­ity

Compres­si onal WaveVelocity

TensileSplittingStrength

Slow Compression Rapid Compression

Unconfined Compressive Strength Test

Triaxial Compressive Strength with Compressional Wave Velocity Up)

Unconfined Compressive Strength TestBulk

DrySolids

LoadingRate

Strength Young's Modulus

Pois­son Ts Ratio

Strength at Confining Pressures of 2 5 0 , 1,000, and U,000 psi250 1,000 U,000

Young'sModulus

Pois­son^Ratio

InitialVP

HighestVP

LoadingRate

Strength YoungT s Modulus

Pois­son'sRatio

feet pet ft/sec psi psi/sec psi 10^ psi psi psi psi 106 psi ft/sec ft/sec psi/sec psi i rß10 psi

L- 2 FT-1 . 3 5.5 to 6.5 2.68 2.70 0.81 19,890 -- 5 0 9,500 10. k2 0.19 -- -- -- -- -- -- -- -- -- --

L-k FT-1 . 1 12.1 to 12.8 2 . 7 1 2 . 7 3 O.69 20,580 -- -- -- -- -- 1 5 ,1 ^ 0 10.80 0 . 3 5 20,220 22,250 -- -- -- --

l-6 FT- 1 68.0 2.72 2 - 7 3 0I3 20,990 -- -- -- -- -- — -- -- — -- -- -- -- --

L- 7 FT- 1 69.O 2.72 2 . 7 3 o lo 20,690 -- 5 0 1 2 , 7 5 0 12.00 0.29 -- 25,200 11.80 0.32 21,060 21,960 — -- -- --

l-8 FT- 1 82.0 2.70 2 . 7 1 0.22 20,760 -- 5 0 11,300 11.28 0.30 -- -- -- -- -- -- -- -- -- --

L- 1 0 — — 2.70 2 . 7 1 0 . 3 3 21,580 -- -- — -- -- -- -- -- -- -- -- — -- -- --

L- 1 2 FT-1 . 0 8 1 to 9.1 2 . 7 1 2 . 7 3 0 . 5 5 20,250 -- -- -- — -- -- 31,630 9.82 0 . 3 2 19,880 2 1 , 9 3 0 — -- -- --

L- 1 3 FT-1 . 0 13.6 to 1.8 2.68 2.70 O.85 1 9 , 7 0 0 l,k 6o -- -- -- -- -- -- -- -- -- — -- -- --

L-lU FT-1 . 1 8.0 to 8.8 2 . 7 1 2 . 7 3 0 -5-5 20,^90 1,100 -- -- -- -- -- — -- -- -- -- -- -- -- --

L- 1 5 FT-1 . 3 5-5 to 6.5 2.70 2 . 7 1 0.29 19,890 1,070 -- -- -- -- -- -- -- -- — -- -- -- -- --

L- 1 7 FT- 1 18.6 2.70 2 . 7 1 OlO 22,320 -- -- -- -- -- -- -- -- -- — -- 1.87 x 107 3 7 , 2 9 0 1 2 . 0 3 o.ko

L-l8 FT- 1 62.8 2 . 7 1 2.72 0.29 20,930 -- -- -- — -- -- — — -- -- 5.80 X 106 29,000 II.76 0.35L- 2 0 FT- 1 27.8 2 . 7 1 2.72 0.18 2 1 , 1 5 0 -- -- — -- -- -- -- — — --

£1I9 x 10 1 ^ , 9 3 0 7.61 0.U6

Average 2.70 2.72 0 1 6 20,710 1,210 11,180 11.23 0.26 27,070 1 0 1 6 olo

63-6b

TABLE 3.li- TEST RESULTS FOR TUFF

Speci­menNo.

Hole No. Depth SpecificGravity

Poros­ity

Natural Water Content

Compres-sionalWaveVelocity

TensileSplittingStrength

Slow Compression Rapid Compression

Unconfined Compressive Strength Test

Triaxial Compressive Strength with Compressional Wave Velocity (7p)

Unconfined Compressive Strength TestBulk

DrySolids Before

TestAfterTest

LoadingRate

Strength YoungT s Modulus

Pois­son^Patio

Strength at Confin­ing Pressures of 250, 1,000, and 1,500 psi

250 1,000 1,500

YoungT s Modulus

Pois­son'sRatio

In itia l

VP

HighestV

P

Loading Strength Rate

Young' s Modulus

Pois­son Ts Patio

feet pet ft/sec psi psi/sec psi 10 psi psi psi psi 1 rß10 psi ft/sec ft/sec psi/sec psi 106 psi

T-7 U12 GO 6ul+ 1 0 .0 to 1 2 .0 1-93 2-39 19.38 23.2 17-!+ 6,600 -- 50 1,560 0.k3 0.13 -- -- -- -- -- -- -- -- -- --

T -ll U12 GO 6ui+ 31.5 to 37.0 1.85 2.3!+ 21.77 22.1+ l 6 . 6 8,61+0 -- -- -- - - -- -- -- -- -- -- -- 8.1+6 x 105 l+,230 0 .9 1 0.36

T-13 U12 GO 6ui+ 31.5 to 37.0 1.92 2.1+1+ 2 1 .1 0 2 1 .0 17.1 7,190 210 -- -- -- -- -- -- -- -- --

T-ll+ U12 GO 6\Jb 1+1. b to 1+2.9 I.9I+ 2.35 17.60 19.7 15.7 8,810 -- — -- -- -- -- - 3,560 0.878 0.19 7,5 7 5 9,61+1+ -- -- -- --

T-15 U12 GO 6ul+ 1+1.1+ to 1+2.9 I.9I+ 2 .1+3 20.30 19-7 15.6 7 , 1+70 130 -- -- -- -- -- -- -- -- -- -- -- -- --

T-20 U12 GO 6uk 67.7 to 72.0 1.92 2.35 18.39 20.1+ 17.1 7,610 -- -- -- -- -- -- 3,610 0.333 0 .1 7 6 , 9 ^ 8 M 3 -- -- -- --

T-21 U12 GO 6ui+ 67.7 to 72.0 1.92 2.1+0 20.29 17.1 ll+.l 7,670 — -- - - - - -- U,910 - - 0.91+7 0.25 7 ,5 3 2 9 ,8 59 - - -- -- - -

T-23 U12 GO 6vb 67.7 to 72.0 I.98 2.35 15.90 21+.7 20.6 8,060 250 - - - - - - -- -- -- -- -- -- -- - - -- - -

T-21+ U12 GO 6ul+ 67.7 to 72.0 1.89 2.33 18.95 23.5 17.6 8,190 -- -- -- -- -- -- -- - - -- -- - - 1 . 6 8 x io5 1,850 0 .33 0.^2

T-25 U12 GO 6ul+ 67.7 to 72.0 1.91 2.1+9 23.30 20 .2 16.3 8,190 - - 50 .1,670 0 .7 7 0.2k -- -- -- -- -- -- - - -- - - - -

T-26 U12 GO 6ul+ 67.7 to 72.0 1.91 2.1+1+ 21.80 20 .2 16.5 8,000 — 50 1,680 0.1+0 0.19 -- -- -- -- -- -- -- - -- --

T-27 U12 GO 6uk 67.7 to 72.0 1.91 2.36 19.06 21.9 19.1 8,280 -- -- - - - - - - - - -- -- -- -- -- 3.11 x 105 2,1+90 0.1+1 0.^9

Average 1.92 2.39 19.82 21.1 16.9 7,891 197 1 , 61+0 0.53 0.19 2,860 0.55 0.1+2

65-66

b. Basalt.

Figure 3.1 Photographs showing traces of compressional wave velocity for granite and basalt. The top trace is the time-mark generator trace with one large division equal to 10 |isec. The bottom trace is the compressional wave velocity signal initiating at 1.5 time marks (zero time) and arriving ^1.5 |isec later.

67

a. Limestone.

b. Tuff.Figure 3.2 Photographs showing traces of compressional wave veloc­ity for limestone and tuff.

68

Tensll* 8trut| p*i

Strain, pin/in

Figure 3*3 Direct tensile stress versus axial strain, granite.

Compressional

Wave

Velocity, f

t/sec

Figure 3.h Compressional wave velocity versus axial stress, tuff in unconfined compression*

Comp

ress

iona

l Wa

ve V

eloc

ity,

ft/

sec

0 2 4 6Deviator Stress, 10 psi

Figure 3*5 Compressional wave velocity versus deviator stress, tuff.

Figure 3-6 Typical basalt shear breaks.

72

/

Y Diametral y^Axial 1 Volumetric

y Specim m No. G-20 Loadin1 Ultima r Modulu

0 Poisso

l Rate te strength s of elastic n* s ratio

50 psi/ 19,790

Ity 10.20 x 0.22

3ecpsi106 psi

1JOOO 2,000Strain, |iin/in

0 .1Strain, percent

Figure 3.7 Stress versus strain curves for granite Specimen G-2.

Stress, 1

0° psi

0 ipoo 2,000Strain, pin/in

Strain, percent

Figure 3.8 Stress versus strain curves for granite Specimen G-10.

Stress,

lCr

psi

0 .1 Strain, percent

Figure 3*9 Stress versus strain curves for granite Specimen G-15.

Dyna

mic

Stre

ss, 10

psi

205 G-13

/> G-ll

/

Specimen Ultimate M o d u l u s of No. Strength E l a sticity Rise Time Loadinig RateG-ll 18,070 psi 10.51x10^ psi 3.0 millisec 6.03x106 psi/sec G-13 20,960 psi 10.03x106 psi 3.0 millisec 6.95xl06 psi/sec

ip00 2p00 3,000Strain, p.in/in

Figure 3.10 Dynamic stress versus strain curves for granite (200-kip loader) Specimens G-ll and 0-13.

Str

ess

, lC

r p

si

Strain, Mdn/inExpansion*«— Strain, percent — ^Contraction

Figure 3.11 Stress versus strain curves for basalt Specimen B-l.

Stress,

10

psi

0 2,000 4,000Strain, l-iin/in

- 0.4 - 0.2 0 0.2Expansion <-- Strain, percent -- p Contraction

Figure 3.12 Stress versus strain curve for basalt Specimen B-21.

Stress, l

Cr psi

0.3 - 0.2 - 0.1 0 0.1Expansion Strain, percent — | Contraction

Figure 3.13 Stress versus strain curves for basalt Specimen B-22.

Stre

ss,

lCr

psi

2,000S tr a in , f i in / in

4,000 6,000

- . 1 0 .1 Expansion — Strain, percent— * Contraction

Figure 3.1 - Stress versus strain curves for basalt Specimen B-29.

20

15

10

5

2,000 4p00 6,000Strain, |~iin/in

Figure 3.15 Stress versus strain curves for basalt Specimen B-20.

Stress,

10

psi

Figure 3«l6 Stress versus strain curves for basalt Specimen B-9*

Stress,

10

psi

0 2,000Strain, pùn/in

4>000

- 0.2 - 0.1 0 0.1Expansion 1— Strain, percent Contraction

Figure 3.17 Stress versus strain curves for basalt Specimen B-7.

Stress,

10 psi

Expansion 4-- Strain, percent Contraction

Figure 3 . 1 8 Stress versus strain curves for basalt Specimen B - 3 .

Stre

ss,

10 -psi

Figure 3.19 Stress versus strain curves for basalt Specimen B-6.

Stress, 10^ psi

Figure 3.20 Stress versus strain curves for basalt Specimen B-15.

Stress,

lCr

psi

Figure 3*21 Stress versus strain curves for basalt Specimen B-8.

Stress,

lCr

psi

Figure 3.22 Stress versus strain curves for basalt Specimen B-ll.

Stress,

lCr

psi

Figure 3.23 Dynamic stress versus strain curves for basalt (200-kip loader) Specimens B-10, B-l6, 3-1..', and B-l8.

Stress 5

10 psi

Specimen No. L-2Loading Rj Ultimate Modulus o Poisson's

itestrength E elasticity ratio

50 psi/sec 9,500 psi 10.42 x 10 0.19

os CD H*

Diame-trai _ Axial3© Voltimetri

L0 400 800

Strain, pin/in0 0.4Strain, percent --► Contraction

Figure 3.21+ Stress versus strain curves for limestone Specimen L-2.

Stre

ss,

10

psi

SpecimenjLoadingUltimateModulus

No. L-7Ratestrength >f elasticit

50 psi/se 12,750 ps

r 12.0 x 10ci6 psi

Poisson* i ratio 0.29

Diametra1?>Axial )Volumetric

r r( >

o ip o oStrain, pin/in 0 0.4

Expansion#— Strain, percent— #• Contraction

Figure 3.25 Stress versus strain curves for limestone Specimen L-7.

Stress,

10 psi

0 400 800 1,200Strain, nin/in

0 0.04Strain, percent Contraction

Figure 3.26 Stress versus strain curves for limestone Specimen L-8.

Stress,

10 psi

0 ipoo 2,000 3,000Strain, nin/in

Figure 3-27 Dynamic stress versus strain curves for limestone (200-kip loader) Specimens L-17, L-l8, and L-20.

VO■P-

0 2p00 4,000Strain, lJtin/in

o a .2Strain, percent

Figure 3.28 Stress versus strain curves for tuff Specimen T-7.

20

15

10

5

0

Strain, percent -- 1 Contraction

Figure 3.29 Stress versus strain curves for tuff Specimen T-25.

Stress,

10 psi

0 2p00Strain, pin/in

4,000

0 0.1 0.2Strain, percent-- T Contraction

Figure 3.30 Stress versus strain curves for tuff Specimen T-26.

Dynamic

Stress,

10° psi

Figure 3.31 Dynamic stress versus strain curves for tuff (drop tower) Specimens T-ll, 1-2k, and 1-27.

UL

TIM

AT

E

ST

RE

NG

TH

, IO3

PS

I

Figure 3*32 Ultimate strength versus loading rate for basalt in unconfined compression.

Ultimate S

trength, 1

0 psi

Figure 3-33 Ultimate strength versus total vertical strain at failure for basalt tested in unconfined compression at loading rates from 1 to 1.6 x 107 psi/sec.

Figure 3*3 - Loading rate versus total axial strain at failure for basalt.

HOH

Figure 3.35 Loading rate versus total horizontal strain at failure for "basalt.

Youn

g1 s Mo

dulu

s of Elasticity, 1

0 psi

(unconfined

compression)

______ Q

Q Y = 4.15 + (0.0693) (*) —y

$

0--------—

O

______ O

— — — -....

C3S

0 —

0 0 0

^ NOTE : Modulus 0

is a tang< one-half 1

strength.j

: elasticity >nt value Ultimate

1 io i o 2 i o 3 io 4 i o 5 i o 6 107Loading Rate, psi/sec

Figure 3-36 Loading rate versus modulus of elasticity for basalt

Devi

ator

Stress, 1

0 psi

Strain, percent

Figure 3*37 Deviator stress versus strain curves for granite Specimen G-20.

Devi

ator

Stress, l

Cr p

si

30

20

Speciraen No, G - 7 : Loading I Confining Maximum d Maximum p

atepressure eviator stre rincipal str

50 psi/sec 1,000

ss 29,320 ass 30,320

psi psi psi '

Modulus 0 Poisson*s

f elasticity ratio

11.3 x 0.22

L0& psi

//C j Dian etral (? y / Axial VolumetricVV /

10

1P00 2p00Strain, pin/in

Figure 3.38 Deviator stress versus strain curves for granite Specimen G--7.

0 .1Strain, percent

Devi

ator

Stress, 1

0° p

siVi

//*/

i

Diametral ////////

/

A xial

/Volumetric

p'/ //

/// //

/Ì /

V/ ^ / ' J

’j :///"/

Spec in Load ir Confin Maxima Maxima Modulu

en No. G-4 g Rate Lng pressure n deviator s a principal 3 of elastic

50 psi/sec 4,0

:ress 52,5 stress 56,5 Lty 10.0 x

30 psi 0 psi ■0 psi L0 psi

1 / //_______

Poisso i's ratio 0 3

2,000 4,000Strain, pin/in

0 0.05 0.10 0.15Strain, percent

Figure 3.39 Deviator stress versus strain curves for granite Specimen G-U

20

15

10

5

0

Volumetric

Maximum Maximum Pri

Specimen Nd. B-14 Loading Ratfe Confining pressure

Delator Stress ncipal Stress

1 psi/sec 250 psi

21,240 psi 21,490 psi

Modulus of Poisson* s

ElasticityRatio

5.18 x 106 0.41

psi +

2,000Strain, pin/in

4,000

- 0.2 - 0.1 0Expansion Strain, percent ---1 Contraction

3. -0 Deviator stress versus strain curves for basalt Specimen B-lU.

Devi

ator

Str

ess,

lCr

psi

0 2,000 4,000 6,000Strain, j~iin/in

- 0.1 0 0.1Expansion* — Strain, percent ■ ■ 1 Contraction

Figure 3.kl Deviator stress versus strain curves for basalt Specimen B-23.

Devi

ator

Stress, 1

0° p

si

0 0.1 0.2 Expansion 4— Strain, percent — ► Contraction

Figure 3.^2 Deviator stress versus strain curves for basalt Specimen 2k.

Deviator Stress, 1

0° psi

0 2P00 4,000Strain, M-in/in

6,000

0 0.1 0.2Strain, percent

Figure 3. -3 Deviator stress versus strain curves for basalt Specimen B-^.

Devi

ator

Stress, 1

0J p

si

Strain, percent

Figure 3 . b k Deviator stress versus strain curves for basalt Specimen B-5.

Devi

ator

Stress, I

O0 p

si

0 2p00 4p00 6,000Strain, \ x l n / ± n

o o a 0.2Strain, percent

Figure 3.^5 Deviator stress versus strain curves for basalt Specimen B-19.

Devi

ator

Stress, 1

0° p

si

Expansion f Strain, percent ---^Contraction

Figure 3.^6 Deviator stress versus strain curves for basalt Specimen B-13.

Devi

ator S

tress, 1

0° psi

24

18

12

7_________

y

______ ^---

------

------

\ \ o

/ Diametral^ Axial

©

d

J >

& Specimen No Loading Rat! Confining f: Maximum Dev* Maximum Prij

. B-26aressure lator Stress icipal Stres

500 psi/se 1P00 psi

31,290 psi s 32,290 psi

: Volumetric

{/ Modulus of 1 Poisson's B

Elasticityatio

3.94 x 1 0 6

0.27?si f

0 2P00Strain 5 jiin/in

4,000

Expansion <

6000

Strain, percent ►Contraction

Figure 3. -7 Deviator stress versus strain curves for basalt Specimen B-26.

Devi

ator

Stress, 1

0J p

si

Figure 3.^8 Deviator stress versus strain curves for basalt Specimen B-27.

Devi

ator

Str

ess,

10° p

si

40

30

20

Specimen - Basalt 28 Loading Rate Confining Pressure Maximum Deviator Stress Maximum Principal Stresi

2,740 psi/se< 250 psi 25,700 psi

i 25,950 psiModulus of ] Poisson's R

Ilasticityitio

4,00 x 106 0.25

psi

.0

AA.. /

--------gCygS..

s * 'Diametral

O

O

® Axial

0 %/

A J ,/

t _________

..... G)

(

>^'1 < Volumetric

ii

10

2P00Strain, Mln/in

4,000 6,000

-o.i oExpansion f-- Strain, percent

0.1► Contraction

0.2

Figure 3.^9 Deviator stress versus strain curves for basalt Specimen 28.

Devi

ator S

tress, l

Cr p

si40

30

20

Specimen, Basalt 30 J Loading R$te %250 psi/sec Confining Pressure 1,000 psi Maximum Deviator Stress 35,01 Maximum Principal Stress 36,01

i-----------

.0 psi L0 psi

X )

Modulus o i Poisson’s_ - 0

o-

\ Elasticity/ Ratio

; 4.71 X 106 , 0.25

psi

.A Diametral : 0

Xs 'r-Y . .

0Axial

(VVolumetric \

x>

/)-- — -----

f ó

r -°i 0 7/ c10

4,000Strain, p-in/in

8,000 12,000

- 0.2 0Expansion 4-- Strain, percent

0.2» Contraction

Figure 3*50 Deviator stress versus strain curves for basalt Specimen 30.

Deviat

or S

tress, l

Cr p

si

60

45

30

15

-----------1-----------Specimen Basalt 31 Load Rate " 2,250 p Confining Pressure 5,000 Maximum Deviator Stress Maximum Principal Stres

ïi/secpsi54,000 psi

3 59.000 osiModulus of 1 Poisson's li

Elasticityatio

5.03 X IO6 0.15

)SÌ

%

á

DiametralAxial

Volli Vlet ne 0

— f

A _

CÏê

j

O à G>

\ (j

Gj

Strain, M-in/in4,000 8,000 120,000

Expansion < Strain,0.2

percent0.4

► Contraiti. on

Figure 3 .5I Deviator stress versus strain curves for basalt Specimen 31«

60

50

4 0

30

20

10

0 <

<73 = 2 50 PS 1

5 0 0 P S l / S E / P S U S E C - y

A - 5C/ I1 P S U S EC15 0 P S / /S E C

4 ,000 8 ,000 12,000 0 4 ,0 00 8 ,0 0 0 12,000 0A X IA L S TR A IN , JLLIN /IN

4 ,0 0 0 8 ,0 0 0 12,000

gure 3.52 Increase in deviator stress and axial strain with increase in loading rate confining pressures a ■ of 250, 1,000, and 5,000 psi for basalt.

Devi

ator

Stress, l

Cr p

siSpec iti Loadii Confin Maximui Maximui

len No. L-4 ig Rate Lng pressure i deviator st i principal

50 psi/secress 15, stress 15.

250 psi L40 psi 390 psi

Modulu Poisso

\ of elastici i's ratio

rr\

ty 10.8 x 0.35

106 psi

j Diametral

/Axial //Volumetric

/, 7V 1

0 500 ip00 1^00Strain, |iin/in

0 .04Strain, percent

Figure 3.53 Deviator stress versus strain curves for limestone Specimen L-U.

De viator Stress, lCr psi

0 ipOO 2p00Strain, nin/in

0 .04 .08Strain, percent

Figure 3.5 - Deviator stress versus strain curves for limestone Specimen L-7

Deviator Stress, 1

0° psi

0 lj600Strain, |iin/in 3,200 4,800

0 aStrain, percent

Figure 3.55 Deviator stress versus strain curves for limestone Specimen L-12.

Devi

ator

Str

ess,

10J p

si

0 lpoo 2,000 3,000 4,000Strain, M-in/in

5,000

0 0.1 0.2 Strain, percent

Figure 3.56 Deviator stress versus strain curves for tuff Specimen T-21

Devi

ator

Stress, 1

0 ps

i

Strain, percent

Figure 3«57 Deviator stress versus strain curves for tuff Specimen T-20.

Devi

ator

Stress, 1

0 psi

Figure 3.58 Deviator stress versus strain curves for tuff Specimen T-]J+.

Comp

ressional Wa

ve V

elocity, f

t/sec

Figure 3*59 Compressional wave velocity versus deviator stress for granite.

Compressional Wa

ve V

elocity, ft/sec

— ---------

— __________l- G ® —

© B-19

J---Gì

■>— -i— o-

-0 \B-5

(i) B-4Specimen No » Confinine Pressure

B-4B-5B-19

2501,0005 000

psipsipsi

10.000 30,000 50,000

Deviator Stress, psi

Figure 3.60 Compressional wave velocity versus deviator stress for basalt.

Compressional

Wave

Velocity, f

t/sec

0 10,000 20,000 30,000

Deviator Stress, psi

Figure 3«6l Compressional wave velocity versus deviator stress for limestone.

Shearing S

tress, p

si

Normal Stress, psi

Figure 3.62 Mohr circles for granite.

Shearing S

tress,

Figure 3.63 Mohr circles for basalt tested at loading rate of 1 psi/sec.

Shea

ring

Stress,

Figure 3.6 4 Mohr circles for basalt tested at loading rate of 50 psi/sec.

Shearing S

tress

Figure 3.65 Mohr circles for basalt tested at loading rate of 500 psi/sec.

Shearing S

tress, o

si

Figure 3.66 Mohr circles for basalt tested at loading rate of 2,7^0 psi/sec.

Shearing S

tress, p

si

Figure 3.67 Mohr circles for limestone.

Shea

ring S

tress, p

si

Figure 3.68 Mohr circles for tuff.

CjO\J1

Figure 3.69 Average stress-strain curves for basalt at various rates of loading showin increase in ultimate strength and strain at failure.

SH

EA

RIN

G S

TR

ES

S,

PS

I

0 10 ,000 20,000 30,000

N O R M A L S T R E S S , PSI

Figure 3*70 Mohr envelope at various loading rates for basalt.

136

YOU

NG

'S

MO

DU

LUS

«ooX

2U\

o

16 i-

N O T E : I E t = TANGENT M O D U L U S AT 5 0 % U L T IM A T E STREN G TH2 C L A S S I F Y ROCK A S B , B H , B L , E T C .

W

.5 -

.2 —

CDo

20

109876

8 16 32 P S I X 10°

EVERY LOW STRENGTH

DLOW

STRENGTH

cMEDIUM

STRENGTH

BHIGH

STRENGTH

AVERY HIGH

1 STRENGTH1 1 1 1 T~ 1 1 I 1 111 7~

I O GRAN ITE I A BA SA LT I □ L IM ESTO N E “ □ T U F F

A*/

/ \

□ □ D ;Y/

’

/ .// // “7

// /

A/ /. o -- 1 7 --

/ / A/ / Li--A

\? /c / D y

Z/

/<5A /

// /

'0*'

?j

>

____4// 1

/ /u / . J

'A /____ / □ / V P

/--/--- // /*

(VD/

□- T T__ /f zZ l . I N I . J_LL

5 6 7 8 9 1 0

_L _L20 30 40 50 60 P S I X 10-

75 125 250 500 1,000 2,000U N IA X IA L C O M P R E S S I V E S T R E N G T H y CTa ( ULT )

4,000 K G / C M 2

Figure 3.71 Engineering classification for intact rock at a loading rate of 50 psi/sec.

137

YO

UN

G'S

M

OD

UL

US

«ooN O T E : I E t = TANG ENT M O D U LU S AT 5 0 % U L T IM A T E STRENGTH

2 C L A S S IF Y ROCK AS B , B H , B L , E T C .

U N I A X I A L C O M P R E S S IV E S T R E N G T H f CTa ( U LT )

Fig-ore 3.72 Engineering classification for intact rock at a rapid loading rate of >50 psi/sec.

138

YOU

NG

'S

MO

DU

LUS

10oX

2U\o¥

16 |-

N O T E : I E t = TANGENT M O D U LU S AT 5 0 % U L T IM A T E STREN G TH

Ui

20

109876

5

4

.3

2 C L A S S I F Y ROCK A S B , B H , B L , ET C .

4 8 16 32 P S I X I0J

EVERY LOW STRENGTH ST

L■R

_D_.OVEN(

V3TH

IVST

IE■R

cDIUMENGTH

l-STR

BIIG »:e n <

Hj TH

VIS'

ERFR

YEh7—

\

H4G

IGH;t h

_________ 1______1____ 1___ 1___1__E 0 GRAN ITE- A BA SA LTI □ L IM ESTO N E- □ T U F F

* '7 “ j

0,./

/

Cl 0 7/

/ /7 /

j ? //

K 1. o . /

rA A/ /

u ^uA

* A7 A

A7

p / A

,>£

■ J/7

_ ^7 /

/ /'

o*?

4

>/

✓

/

j,/

& /

/ /

7 °/ OJ

1—1 7T—l/ 7/

r---- / A0°/

V*

/t

1V07 /

1 V/ t

/ □ l i l t . 1.1 13 4 5 6 7 8 9 10

_L

20 30 40 50 60 P S I X 10°

______ I_________ L_75 125 250 500 1,000 2,000

U N IA X IA L C O M P R E S S I V E S T R E N G T H ^ 0"a ( U L T )4 ,000 KG / C M '

Figure 3.73 Engineering classification for intact rock for basalt at loading rates from 1 to l6 x 10^ psi/sec.

139

Figure 3.7^ Relation of axial stress to lateral stress at failure in triaxial compression tests of rock cores.

AX

IAL

ST

RE

SS

, 10

° P

SI

Figure 3.75 Relation of axial stress to lateral stress at failure in triaxial compression at different loading rates for basalt.

l4l

CHAPTER 1+

CONCLUSIONS AND RECOMMENDATIONS

4.1 CONCLUSIONS

On the basis of results obtained from the various slow and rapid

tests of rocks of four types, the following conclusions are drawn:

1. Nondestructive tests, such as specific gravity, porosity,

and compressional wave velocity tests, indicate that all rock speci­

mens within each type were uniform.

2. Results of unconfined compressive testing show that as the

rate of loading increases, the ultimate strength of the rock increases.

For the basalt rock, the total axial strain and the Young's modulus of

elasticity, as well as the ultimate compressive strength, increasen

at rates of loading from 1 to 1.60 x 10 psi/sec. However, the total

diametral strain decreased with increased rates of loading.

3. The difference in the unconfined compressive strength between

the slow and the rapid rates of loading for the rocks tested varied

considerably. The dynamic compressive strength factor f^ for the

granite was less than 1; for the basalt, 1.35; for the limestone,

1.52; and for the tuff, 1.74.

4. Results of triaxial compression tests on basalt show that

the maximum deviator stress - a ^ and total axial strain increase

as both confining pressure and loading rates increase. Loading rates

142

have a pronounced effect on maximum deviator stress with lateral pres­

sures up to 55OOO psi. Apparently, however, loading rates up to

2,250 psi/sec do not have a significant effect on the angle of inter­

nal friction ft and the cohesion c of basalt at confining pressures

up to 5^000 psi. Mohr!s theory of failure fits the basalt rock quite

well for 0 and cr used in this investigation.

5. The compressional wave velocity of rock is affected by in­

creases in both the applied axial stress and confining pressure. Ve­

locities recorded in the direction of applied stress increase sharply

within about one-half of the maximum deviator stress and then generally

level off until failure.

b.2 RECOMMENDATIONS

It is recommended that additional limestone and tuff rock be

tested under various loading rates to determine the validity of the

f^d presented in this report.

Based on information obtained from the literature search and on

the results of the triaxial tests reported herein, it is recommended

that the effects of pore pressure be taken into account if porous

rock with a high water content (such as tuff) is tested in the future

under triaxial conditions.

lbs

REFERENCES

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Stress Rate and Temperature on the Strength of Rocks"; Publisher

Unknown; Unclassified.

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Pile Driver"; Engineering Mechanics Division Specialty Conference

Proceedings, American Society of Civil Engineers, 12-lk October

1966 (abstract only); Unclassified.

3. H. C. Heard; "Effect of Large Changes in Strain Rate in the

Experimental Deformation of Yule Marble"; Journal of Geology, 1963>

Vol. 71? Pages 162-195; Unclassified.

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on the Strength and Elastic Properties of Rocks"; Quarterly of the

Colorado School of Mines, July 1959; Vol. 5 -? No. 3? Pages 3-31;

Unclassified.

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gation into the Flow of Marble"; Philosophical Transactions of the

Royal Society of London, 1901, Ser. A, Vol 1955 Pages 363-^d;

Unclassified.

6. J. Handin; "Strength and Plasticity"; Publication No. 99?

Ibk

1956; Pages 1-15; Shell Development Company Exploration and Produc­

tion Research; Unclassified.

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Sedimentary Rocks Under Confining Pressure; Tests at Room Temperature

on Dry Samples"; Bulletin of the American Association of Petroleum

Geologists, 1957j Vol. 1+1, No. 1, Pages 1-50; Unclassified.

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Zeilschrift des Vereines Deutscher Ingenieune, 19U , Vol. 55, No. 1+2,

Pages 17^+9-1757 (in German); Unclassified.

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Triaxial Stress"; Proceedings, Conference on Mechanical Properties of

Non-Metallic Brittle Materials, 1958, Page 106; Butterworth, London;

Unclassified.

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Triaxial Compression, and Its Application to Mine Roadways"; Inter­

national Journal Rock Mechanics Mining Sciences, 1966, Vol. 3;

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Pressure (l) Compression Tests on Dry Rock Sample"; Bulletin of the

Earthquake Research Institute, September 196I+, Vol. 1+2, Part 3,

Pages 1+91-51 -; Unclassified.

1 5

12. K. S. Lane and W. J. Heck; "Triaxial Testing for Strength

of Rock Joints"; Proceedings, Sixth Symposium on Rock Mechanics,196b, Pages 98-IO8; Missouri University, Rolla, Missouri; Unclassified.

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lb . M. S. Paterson; "Triaxial Testing of Materials at Pressures up to 10,000 kg./sq.cm. (150,000 lb./sq.in.)"; The Journal, Institu­tion of Engineers, Australia, January-February 196b, Vol. 36, No. 1-2,

Pages 23-29; Unclassified.

15. M. C. Redmond; "Laboratory Tests of Foundation Rock Cores,

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Unclassified.

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Rigidity of Rock"; Journal of Geology, 1938, Vol. b6, Pages 59-87 and

113-1^1; Unclassified.

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Pages 695-696; Unclassified.

1 b6

18. D. S. Hughes and H. J. Jones; n Variât ions of Elastic Moduli

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Geological Society of America, 1950, Vol. 6l, Pages 8U3-8 5 6;

Unclassified.

19. D. S. Hughes and H. J. Cross; ”Elastic Wave Velocities in Rocks at High Pressures and Temperatures”; Geophysics, 1951? Vol. l6, Wo. b, Pages 577-593; Unclassified.

20. D. S. Hughes and J. L. Kelly; "Variation of Elastic Wave

Velocity with Saturation in Sandstone”; Geophysics, 1952, Vol. 17,

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Experimental Investigation of Factors Affecting Elastic Wave Veloci­

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lb7

2b. M. P. Volarovich and D. B. Balashov; "Study of Velocities

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10 Kilobars", Part 1; Journal of Geophysical Research, April i960,

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10 Kilobars", Part 2; Journal of Geophysical Research, July 19 6 1,

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Rocks in the Process of Deformation and Fracture Under High Pressure"

Bulletin No. 32, March i960; Kyoto University, Disaster Prevention

Research Institute, Japan; Unclassified.

28. R. H. Bergman and R. A. Shahbender; "Effect of Statically

Applied Stresses on the Velocity of Propagation of Ultrasonic Waves”;

Journal of Applied Physics, 1958, Vol. 29, No. 12, Pages 1736-1738;

Unclassified.

29. G. Simmons; "Velocity of Compressional Waves in Various

Minerals at Pressures to 10 Kilobars"; Journal of Geophysical

Research, March I96U, Vol. 69? No. 6, Pages 1117-1121; Unclassified.

30. G. Baron, P. Habib, and P. Morlier; "Effect of Stresses

and Deformations on Velocity of Sound in Rock"; Fourth International

Conference on Strata Control and Rock Mechanics, U-8 May 196t;

Columbia University, New York; Unclassified.

31. J. S. Rinehart, J. Fortin, and L. Bürgin; "Propagation

Velocity of Longitudinal Waves in Rocks; Effect of State of

Stress, Stress Level of the Wave, Water Content, Porosity, Tem­

perature, Stratification and Texture"; Mining Engineering Series,

Rock Mechanics, Third Technical Session; Publishing Date Un­

known; Unclassified.

32. D. U. Deere and R. P. Miller; "Engineering Classification

and Index Properties for Intact Rock"; Technical Report No. AFWL-TR-

65- U 6, December 1966; University of Illinois, Urbana, Illinois;

Unclassified.

33- S. J. Shand;"Eruptive Rocks; Their Genesis, Composition,

Classification, and Their Relation to Ore-Deposits"; Third Edition,

19^7; John Wiley and Sons, Inc., New York; Unclassified.

3 -. U. S. Army Engineer Waterways Experiment Station, CE;

"Handbook for Concrete and Cement"; August 19 +9 ('with quarterly

supplements); Vicksburg, Mississippi; Unclassified.

35* L. Obert; "Static Stress Determinations"; Project 3-6, Operation Nougat, Shot Hard Hat, POR 1804, 12 April 1963; U. S.Bureau of Mines, College Park, Maryland; Unclassified.

36. R. L. Stowe; "Operation Flint Lock, Shot Pile Driver;Report 2, Physical Properties of Granodiorite from Operation Pile

Driver" (in preparation); U. S. Army Engineer Waterways Experiment Station, CE, Vicksburg, Mississippi; Unclassified.

37* B. L. Atchley and H. C. Furr; "Strength and Energy Absorp­tion Capabilities of Plain Concrete Under Dynamic and Static Load­ings"; American Concrete Institute, Proceedings, November 1967, Vol. 6k, No. 11, Pages 7^5-756; Unclassified.

38. D. Watstein; "Effect of Straining Rate on the Compressive Strength and Elastic Properties of Concrete"; American Concrete Institute, Proceedings, April 1953? Vol. k9, No. 8, Pages 729-7^; Unclassified.

39* D. L. Neumann and H. W. Heslin, Jr.; "A GE-225 Computer Program for Simple Linear and Curvilinear Regression Analyses (Method of Least Squares)"; Miscellaneous Paper No. 5-667, July 196 k; U. S. Army Engineer Waterways Experiment Station, CE, Vicksburg, Mississippi Unclassified.

150

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165-166

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U. S . Army E n g in e e r W aterw ays E xp erim en t S t a t io n V ic k s b u r g , M is s i s s i p p i

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3. R E P O R T T I T L E

STRENGTH AND DEFORMATION PROPERTIES OF GRANITE, BASALT, LIMESTONE, AND TUFF AT VARIOUS LOADING RATES

D E S C R I P T I V E N O T E S (T y p e o t re p o rt a n d in c lu s iv e d a te s )

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12. S P O N S O R I N G M I L I T A R Y A C T I V I T Y

D e fe n se A to m ic S u p p o rt A gen cy W ash in gto n , D. C.

The o b j e c t i v e o f th e work r e p o r te d h e r e in was t o d e te rm in e th e s t r e n g t h and s t r e s s - s t r a i n c h a r a c t e r i s t i c s o f ro c k s o f fo u r ty p e s u nder v a r io u s r a t e s o f lo a d in g . T h is was a cc o m p lish e d b y c o n d u c tin g s lo w (sp ecim en s lo a d e d a t r a t e s o f l e s s th a n 2 ,2 5 1 p s i/ s e c ) and r a p id (sp ecim en s lo a d e d a t r a t e s g r e a t e r th a n 2 ,2 5 1 p s i/ s e c ) u n c o n fin e d co m p ressio n t e s t s , t e n s i l e s p l i t t i n g t e s t s , and t r i a x i a l co m p ressio n t e s t s u t i l i z i n g c o n f in in g p r e s s u r e s ra n g in g from 250 t o 5,000 p s i . G r a n ite , b a s a l t , l im e s to n e , and t u f f from th e A to m ic E n erg y C om m ission ’ s Nevada T e s t S i t e , M ercu ry , N evad a, w ere u se d in t h i s p r o ­gram . N o n d e s tr u c t iv e t e s t s su ch as s p e c i f i c g r a v i t y , p o r o s i t y , and c o m p r e s s io n a l wave v e l o c i t y w ere co n d u cted on a l l sp ecim ens t o d e te rm in e h o m o gen eity o f each r o c k . Re­s u l t s o f n o n d e s t r u c t iv e t e s t s in d ic a t e d t h a t th e ro c k w it h in each r o c k ty p e was q u it e u n ifo rm . R e s u lts o f th e u n c o n fin e d co m p ressiv e s t r e n g t h t e s t s on b a s a l t in d ic a t e d t h a t as th e lo a d in g r a t e was in c r e a s e d from 1 t o 1 .6 0 x 107 p s i / s e c , u lt im a te s t r e n g t h , t o t a l a x i a l s t r a i n , and Y o u n g ’ s modulus o f e l a s t i c i t y in c r e a s e d . T o t a l d ia m e tr a l s t r a i n d e c r e a s e d as lo a d in g r a t e was in c r e a s e d . R e s u lts o f t r i a x i a l t e s t s in d ic a t e d t h a t th e maximum d e v ia t o r s t r e s s and t o t a l a x i a l s t r a i n in c r e a s e d as th e c o n f in in g p r e s s u r e and lo a d in g r a t e s w ere in c r e a s e d . A p p a r e n t ly , lo a d in g r a t e s from 1 t o 2 ,2 5 0 p s i / s e c do n o t h ave a s i g n i f i c a n t e f f e c t on th e a n g le o f i n t e r n a l f r i c t i o n and c o h e s io n o f b a s a l t a t c o n f in in g p r e s s u r e s up t o 5,000 p s i . C o m p re ss io n a l wave v e l o c i t i e s r e ­co rd ed in th e d i r e c t i o n o f a p p lie d s t r e s s in c r e a s e d s h a r p ly w it h in a b ou t o n e - h a lf o f th e maximum d e v ia t o r s t r e s s and th en g e n e r a l l y rem ain ed c o n s ta n t t o f a i l u r e . The d i f ­fe r e n c e in th e u n c o n fin e d c o m p re ssiv e s t r e n g t h b etw een th e s lo w and th e r a p id r a t e s o f lo a d in g f o r th e ro c k s t e s t e d v a r i e d c o n s id e r a b ly . The dynam ic c o m p re ssiv e s t r e n g t h

DD .1473 U n c l a s s i f i e dSecurity C la ss ific a tio n

UnclassifiedSecurity Classification

13. A B S T R A C T

factor for the granite was less than 1; for the basalt, 1.35; for the limestone, 1 .52; and for the tuff, 1.7^* The compressional wave velocity of rock is affected by in­creases in both the applied axial stress and confining pressure. Velocities recorded in the direction of applied stress increase sharply within about one-half of the maxi­mum deviator stress and then generally level off until failure.

1 4 .K E Y W O R D S

L I N K A L I N K B L I N K C

R O L E W T R O L E W T R O L E W T

GraniteBasaltLimestoneTuffRock properties

Unclassified Security Classification

168