Strength and Deformation Properties of Granite, Basalt, Limestone, and Tuff at Various Loading Rates
C-l
MISCELLANEOUS PAPER C-69-1
STRENGTH AND DEFORMATION PROPERTIES OF GRANITE, BASALT, LIMESTONE AND TUFF AT VARIOUS LOADING RATES
by
R. L. Stowe
grew ¡01 I0S ÉBflns l
January 1969
Sponsored by
Defense Atomic Support Agency
Conducted by
U. S. Army Engineer Waterways Experiment Station CORPS OF ENGINEERS Vicksburg, Mississippi
THIS DOCUMENT HAS BEEN APPROVED FOR PUBLIC RELEASE AND SALE; ITS DISTRIBUTION IS UNLIMITED .'/<* • .'.¡f c -1 LIBRARY4
APR 15 1969
Bureau of Reclamation Denver, Colorado
Destroy this report v ¡1
The findings in this report are not to be construed as an official Department of the Army position, 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 RATES
by
R. L Stowe
January 1969
Sponsored by
Defense Atomic Support Agency
Conducted by
U. S. Army Engineer Waterways Experiment Station CORPS OF ENGINEERS Vicksburg, Mississippi
ARMY-MRC VICKSBURG. MISS.
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 EN DORSEMENT 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 basalt y indicated, 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------6
NOTATION------12
CONVERSION FACTORS, BRITISH TO METRIC UNITS OF MEASUREMENT...... l9
CHAPTER 1 INTRODUCTION------15
1.1 Background------15 1.2 Objective and Scope------16 1.3 Literature Survey------l8
CHAPTER 2 MATERIALS AND TEST METHODS------26
2.1 Rock Types------(26-' 2.2 Sample Preparation------28 2.3 Strain Gages------;----- 28 2.9- Nondestructive Test Methods------■------29 2.5 Destructive Test Methods------30
CHAPTER 3 PRESENTATION AND DISCUSSION OF RESULTS------38
3.1 Nondestructive Tests------39
3-2 Destructive Tests------9-2
CHAPTER 9 CONCLUSIONS AND RECOMMENDATIONS------...... 19-2
k.l Conclusions--- lU2 9.2 Recommendations 19-3
REFERENCES...... l99
TABLES
3.1 Test Results for Granite-- 59 3.2 Test Results for Basalt--- 6i 3.3 Test Results for Limestone-- 63 3.9- Test Results for Tuff----- 65
7 FIGURES
1.1 Effect of loading rate on ultimate compressive strength------23 1.2 Effect of time of loading on stress-strain diagram, compression------28 1.3 Effect of compressional stresses on the wave velocity in the axial and transverse directions under confining pressures------25 2.1 Triaxial chamber with transducers------36 2.2 200-kip dynamic loader------37 3.1 Photographs showing traces of compressional wave velocity for granite and basalt------67 3.2 Photographs showing traces of compressional wave velocity for limestone and tuff------68 3.3 Direct tensile stress versus axial strain, granite------69 3.8 Compressional wave velocity versus axial stress, tuff in unconfined compression------70 3.5 Compressional wave velocity versus deviator stress, tuff------71 3.6 Typical basalt shear breaks------72 3.7 Stress versus strain curves for granite Specimen G-2---- 73 3.8 Stress versus strain curves for granite Specimen G-10--- 78 3.9 Stress versus strain curves for granite Specimen G-15--- 75 3.10 Dynamic stress versus strain curves for granite (200-kip loader) Specimens G-ll and G-13------76 3.11 Stress versus strain curves for basalt Specimen B-l----- 77 3.12 Stress versus strain curves for basalt Specimen B-21---- 78 3.13 Stress versus strain curves for basalt Specimen B-22---- 79 3.l8 Stress versus strain curves for basalt Specimen B-29- — - 80 3.15 Stress versus strain curves for basalt Specimen B-20---- 8l 3.16 Stress versus strain curves for basalt Specimen B-9----- 82 3.17 Stress versus strain curves for basalt Specimen B-7----- 83 3.18 Stress versus strain curves for basalt Specimen B-3----- 88 3.19 Stress versus strain curves for basalt Specimen B-6----- 85 3.20 Stress versus strain curves for basalt Specimen B-15---- 86 3.21 Stress versus strain curves for basalt Specimen B-8----- 87 3.22 Stress versus strain curves for basalt Specimen B-ll---- 88 3-23 Dynamic stress versus strain curves for basalt (200-kip loader) Specimens B-10, B-l6, B-175 and B-l8------89 3.28 Stress versus strain curves for limestone Specimen L-2-- 90 3.25 Stress versus strain curves for limestone Specimen L-7-- 91 3.26 Stress versus strain curves for limestone Specimen L-8-- 92
8 Dynamic stress versus strain curves for limestone (200-kip loader) Specimens L-17> L-l8? and L-20------93 Stress versus strain curves for tuff Specimen T-7----- 94 Stress versus strain curves for tuff Specimen T-25----- 95 Stress versus strain curves for tuff Specimen T-26---- 96 Dynamic stress versus strain curves for tuff (drop tower) Specimens T-ll, T-2U? and T-27------97 Ultimate strength versus loading rate for basalt in unconfined compression------98 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------99 Loading rate versus total axial strain at failure for basalt------100 Loading rate versus total horizontal strain at failure for basalt------101 Loading rate versus modulus of elasticity for basalt- 102 Deviator stress versus strain curves for granite Specimen G-20------103 Deviator stress versus strain curves for granite Specimen G-7------104 Deviator stress versus strain curves for granite Specimen G-k------105 Deviator stress versus strain curves for basalt Specimen B-lU------io6 Deviator stress versus strain curves for basalt Specimen B-23------107 Deviator stress versus strain curves for basalt Specimen 2b------108 Deviator stress versus strain curves for basalt Specimen B-U------109 Deviator stress versus strain curves for basalt Specimen B-5------110 Deviator stress versus strain curves for basalt Specimen B-19------111 Deviator stress versus strain curves for basalt Specimen B-13------*------112 Deviator stress versus strain curves for basalt Specimen B-26------113 Deviator stress versus strain curves for basalt Specimen B-27------ll4 Deviator stress versus strain curves for basalt Specimen 28------115 Deviator stress versus strain curves for basalt Specimen 30------ll6 Deviator stress versus strain curves for basalt Specimen 31------117 Increase in deviator stress and axial strain with increase in loading rate at confining pressures av of 250, 1,000, and 5 >000 psi for basalt------118 Deviator stress versus strain curves for limestone Specimen L-U------119 Deviator stress versus strain curves for limestone Specimen L-7------120 Deviator stress versus strain curves for limestone Specimen L-12------121 Deviator stress versus strain curves for tuff Specimen T-21------122 Deviator stress versus strain curves for tuff Specimen T-20------123 Deviator stress versus strain curves for tuff Specimen T-]J+...... - ...... 12k Compressional wave velocity versus deviator stress for granite------125 Compressional wave velocity versus deviator stress for basalt------126 Compressional wave velocity versus deviator stress for limestone------127 Mohr circles for granite------128 Mohr circles for basalt tested at loading rate of 1 psi/sec------129 Mohr circles for basalt tested at loading rate of 50 psi/sec------130 Mohr circles for basalt tested at loading rate of 500 psi/sec------131 Mohr circles for basalt tested at loading rate of 2,7^0 psi/sec------132 Mohr circles for limestone------133 Mohr circles for tuff------13U Average stress-strain curves for basalt at various rates of loading showing increase in ultimate strength and strain at failure------135 Mohr envelope at various loading rates for basalt------136 Engineering classification for intact rock at a loading rate of 50 psi/sec------137 Engineering classification for intact rock at a rapid loading rate of >50 psi/sec------138 Engineering classification for intact rock for basalt at loading rates from 1 to l6 X 10^ psi/sec------139
10 3.7*+ Relation of axial stress to lateral stress at failure in triaxial 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 s
Gq 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 a Diametral strain d
e Unit volumetric change v e 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 2.54 centimeters
feet 0.30^8 meters pounds 0.45359237 kilograms kips 453.59237 kilograms pounds per square inch 0.070307 kilograms per square centimeter pounds per cubic foot 16.0185 kilograms per cubic meter foot-pounds 0.138255 meter-kilograms feet per second 0.3048 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 2 strength, slow unconfined compressive strength, Young's modulus of elasticity, Poisson's ratio, triaxial compressive strength, and 3 rapid 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 1 0 11 psi/sec. The maximum stress rate used for the rapid n 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 27 . 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 velocities with stress in the axial and the transverse direc tions under various confining pressures.
In the literature search, a considerable amount of rock prop erty data was found concerning a wide range of physical properties of different rock types. A tabulation of these properties has been com piled and w ill be published separately from this report. The tabula tion contains 58 different physical properties along with some ratios of physical properties. This table was compiled as a reference source for those working in the field of rock mechanics.
22 gur 1 Effect of l ng rate o uli e cmprsi st h th g n e tr s e ressiv p com te a ltim u on e t a r g in d a lo f o t c e f f E .1 1 re u ig F er . ) l e c n re fe e R r e t f a (
Stress Rate, psi/sec 0 0 0 0 0 0 80 70 60 50 40 30 20 tmae tegh ki /q in s/sq ip k Strength, ate ltim U 23 4 ro =-
Stress, psi Figure 1.2 Effect of time of loading on stress-strain diagram, compression compression diagram, stress-strain on loading of time of Effect 1.2 Figure (after Reference (afterReference h ). Dilatâtional Wave Velocity, ft/sec 13,120 16,400 19,680 22,960 Figure 1.3 Effect of compressional stresses on the wave velocity in the axial axial the in velocity wave the on stresses compressional of Effect 1.3 Figure and transverse directions under confining pressures. confining under directions transverse and T7' 84 5.8 53 137 142.20 113.76 85.32 56.88 28.44 ifrnilSrs, 0 psi 10 Stress, Differential Axialvelo Transverse :ity(300-at eoiy ( velocity a confining 300-atm conf Lningpressu pressure) re) 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 pres ent 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 com posed of plagioclase feldspar, with lesser amounts of pyroxene, oli vine, 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 100i U r S where,
G is the specific gravity of solids, and s G 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 re ceiving 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 veloc ity 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 split ting 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 gran ite, 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 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 to u 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 Ram Transducer End Plate Bearing Plate Sample Bearing Plate End Plate Transducer Base Plate Chamber Bearing Plate Figure 2.1 Triaxial chamber with transducers. 36 _ Piston Rupture Disk No. 1 Rupture Disk No. 2 Ram Ram Load Cell Specimen Pedestal Load Cell Pedestal Concrete L v - v ~ i I— Foundation Figure 2.2 200-kip dynamic loader. 37 CHAPTER 3 PRESEHTATION 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 con tent 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 ob tained 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 Difference Average Bulk Density Specific Gravity Specific Gravity Difference pcf Granite 2.66 to 2.71 0.05 2.69 3.11 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 of Difference Average Specific Density Specific Gravity Gravity of Solids Difference of Solids pcf Granite 2.68 to 2.71 0.03 2.69 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 3 0 O ^ o Tuff 2.33 to 2.1+9 0.16 2-39 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 Difference Average Compressional Wave Velocity 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 16,630 Limestone 19,885 to 22,320 2,^35 20,710 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 Average Direct Range in Ratio of Compressive Tensile Tension Strength Strength to Tensile Splitting Strength at 50-psi/sec Strength Loading Rate psi psi psi Granite 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 value calculated at one-half the ultimate strength, i.e., E = A ct , a, where Act is the change in a,xial stress, and Ae a, is the change ^ axial strain. Poisson1 s ratio is also calculated at one-half the ulti ed mate strength, i.e., a = — , where e is the axial strain and en r e a a d is 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 uncon fined 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 investi gation. The average modulus values for Sites 1 and 2 of Reference 35 6 6 were 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 vol umetric strain was also plotted to determine if it could be correlated with a significant change in compressional wave velocity on the devia tor stress versus compressional wave velocity curve. It was felt that when the volumetric strain was constant, possibly indicating that in ternal 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 , = 1 ( 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 6,980 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 A 3 0 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 more P sharply. 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 uncon fined 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 irreg ular; 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 com pressive 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 lime stone 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 addi tional 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 7 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 diamet ral 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 ulti mate 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 6 ably if additional data were obtained between decades lCr and 10 . The data were fitted with a least-squares polynomial curve fit pro gram taken to the third order, GE program No. CD 225H6.004, with the 2 3 form y .= a + bx + cx + dx . 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 equation coefficients of the line of best fit for the input data. F igu re 3.3k shows the relation of loading rate and total axial strain at failure for basalt. Figure 3.35 shows that with an increase in loading rate, the total diametral strain at failure decreases slightly. Figure 3*36 shows the relation of loading rate and modulus of elasticity taken at one-half the ultimate compressive strength. The variation in modulus at a given loading rate is quite wide, and additional data should be developed to verify the increase in modu lus with increased rates of loading. Curves of best fit were obtained by using the previously mentioned OCE computer program. ^ ^ Figures 3.37 through 3-58 show the relation of deviator stress (o^ - cr^) to axial, diametral, and volumetric strains. Figures 3.59 through 3.6l and Figure 3-5 give results of the compressional wave velocity tests and show the relation between wave velocity and devi ator stress. Figures 3.62 through 3.68 are plots of Mohr circles that show the relation of normal stress to shearing stress; the angle of internal friction and the shearing stress c are given for each rock type. These figures also show the observed failure plane in the core. Data from basalt rock tested in triaxial compression at load ing rates of 1, 50, 500, and 2,250 psi/sec are interesting in regard to the loading rates at a specific confining pressure o^ . Figure 3.52 shows that at o^'s of 250 and 1,000 psi the maximum deviator s t r e s s ct increased with increased loading rate except for 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 a r= 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 with the test results found in the literature search. There were twelve tests run, and in a ll cases except one the compressional wave velocity increased sharply when the axial stress was increased to about one-half of the ultimate stress. The velocities then leveled off until just before failure; at failure, they either remained con stant or decreased slightly. Velocities also increased with in creased confining pressure. The increases in velocity from zero to maximum deviator stress for the rocks tested are given below: Rock Factor by Which Velocities Increased at I n d ic a te d Confining Pressures 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 ra n ite 1.0 9 — 1 .1 0 — 1.0k — B a s a lt 1.0 3 — 1.0 6 — — 1.12 Lim estone 1.10 — 1.0U — — 1.10 T u ff — 1.2 3 1.21 1 .2 7 — — No distinct correlation could be made between the compressional wave velocity versus deviator stress and the volumetric strain versus deviator stress curves. Generally though, the compressional wave velocity curve was at a constant level, or at its highest value when the volumetric curve was expanding, i.e ., just after the volumetric change was constant. 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 - 2a). This can be seen in the following tabulation. Rock Loading Observed Predicted Envelope °3 Rate Failure Failure Angle Angle ft = 90 - 2a 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 Observed Predicted Envelope Rate ff3 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 0 psi/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 Spec Hole No. Depth Specific Poros Compres- Direct Tensile Slow Compression Rapid Compression imen Gravity ity sional Tension Splitting No. Wave Strength Unconfined Compressive Triaxial Compressive Strength with Unconfined Compressive Bulk Solids Velocity Strength Test Compressional Wave Velocity (V^) Strength Test Dry Loading Strength Y o u n g * s Pois Strength at Confining Young’s Pois Initial High Loading Strength Young * s Rate Modulus son* s Pressures of 25 0 , Modulus son * s V V Rate Modulus Ratio 1,000, and t,000 psi Ratio P P 250 1,000 it,000 feet pet ft/sec psi psi psi/sec psi_ 106 psi psi psi psi 106 psi ft/sec ft/sec psi/sec psi 106 psi G-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 — — — — — — — — 6 G-ll U-I5OI-UI I7O9.O to I7IO.7 2.70 2.70 0.11 19,220 — — — — — — — — — — — — 6.03 x 10 18,070 IO.5I G-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.t6 18,260 — — — — — — — — — -- — ------G- t 2 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 - H ole D epth S p e c i f i c P o r o s Com pres- T e n s ile Slow Compression Rapid Compression Mode o f :F a i lu r e men N o. G r a v it y i t y s i o n a l S p l i t t i n g No. Wave S t r e n g th Unconfined Compressive Triaxial Compressive Strength with Compressional Unconfined Compressive B u lk S o l id s V e l o c i t y Strength Test Wave Velocity (Vp) Strength Test D ry L o a d in g S t r e n g th Y ou n g' s P o is L o a d in g Strength at Confining Y ou n g ' s P o is I n i t i a l H ig h e s t L o a d in g S t r e n g th Y oung' s P o is R a te M odulus s o n 's R a te Pressures of 250, M odulus s o n 's V V R a te M odulus son ' s R a tio 1,000, and 5,000 psi R a tio P P R a tio 250 1,000 5,000 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 / se 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-1 138.2 to 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 from h o r iz o n t a l B-U DA-1 138.2 to 1U0.0 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 - -- - - Shear at 63 degrees from h o r iz 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 2.7k 2.83 3.11 1 7 ,7 6 0 - - - - - 5OO 2 5 ,6 2 0 -- - 1+.1+6 0.37 ------S h e ar a t 71 d e g r e e s from h o r iz o n t a l B-lk I 3 . 2 2 .6 8 2 .8 3 5 .2 6 17,650 - - - - - 1 21,21+0 -- - 5 .1 8 0.1+1 ------Vertical splitting 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 107 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 ------Shear at 63 degrees from h o r iz 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 .k3 ------Shear at 6l degrees from h o r iz o n t a l B- 2U C a le x - 2 .6 9 - ~ 1 6 ,1 0 0 - - - - - 1 - - 33,^ 30 1| .6-; 0 .2 2 ------Vertical splitting B-25 C a le x - 2 .6 8 - - 1 6 ,2 5 0 2 ,090 ------ B -26 C a le x - 2 .6 9 — 16,950 - - - - - 5OO - 31,290 - 3 -9^ . 0.27 ------S h e ar a t 75 d e g r e e s from h o r iz 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 ar a t 70 d e g r e e s from h o r iz o n t a l B-28 C a le x - 2 .7 0 - - 16 ,2 ^ 0 ------. 2, 7l+0 2 5 ,70 0 - - 1+.00' 0 .2 5 ------Vertical splitting 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 ar a t 7^+ d e g r e e s from h o r iz o n t a l 2 .7 0 1 6 ,8 9 0 2 ,2 5 0 5l+,000 B-31 C a le x ------5.O 3 0.15 ------S h e ar a t 72 d e g r e e s from h o r iz o n t a l A v e ra g e 2 .6 9 2 .8 3 1+.60 1 7 ,ll+ 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 Spec Hole Depth Specific Poros Compres Tensile Slow Compression Rapid Compression imen No. Gravity ity si onal Splitting No. Wave Strength Unconfined Compressive Triaxial Compressive Strength with Unconfined Compressive Bulk Solids Velocity Strength Test Compressional Wave Velocity U p ) Strength Test Dry Loading Strength Young's Pois Strength at Confining Young's Pois Initial Highest Loading Strength YoungT s Pois Rate Modulus son Ts Pressures of 2 5 0 , Modulus son^ V V Rate Modulus son's P P Ratio 1,000, and U,000 psi Ratio Ratio 250 1,000 U,000 feet pet ft/sec psi psi/sec psi 10^ psi psi psi psi 106 psi ft/sec ft/sec psi/sec psi 10i rß psi L-2 FT-1.3 5.5 to 6.5 2.68 2.70 0.81 19,890 -- 50 9,500 10. k2 0.19 ------ L-k FT-1 .1 12.1 to 12.8 2 .7 1 2.73 O.69 20,580 ------1 5 ,1^0 10.80 0.35 20,220 22,250 ------l -6 FT-1 68.0 2.72 2-73 0 I 3 20,990 ------— -- -- — ------ L-7 FT-1 69.O 2.72 2.73 olo 20,690 -- 50 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 -- 50 11,300 11.28 0.30 ------ L-10 — — 2.70 2.7 1 0.3 3 21,580 -- -- — ------— ------ L-12 FT-1 . 0 8 1 to 9.1 2.7 1 2.73 0.55 20,250 ------— -- -- 31,630 9.82 0 .3 2 19,880 21,930 — ------ L-13 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 2.71 2.7 3 0 -5-5 20,^90 1,100 ------— ------ L-15 FT-1 .3 5-5 to 6.5 2.70 2 .7 1 0.29 19,890 1,070 ------— ------ L-17 FT-1 18.6 2.70 2 .7 1 O l O 22,320 ------— -- 1.87 x 107 37,290 12.03 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 0.35 £ L-20 FT-1 27.8 2.7 1 2.72 0.18 21,150 -- -- — ------— — -- 1 I 9 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 Speci Hole No. Depth Specific Poros Natural Water Compres- Tensile Slow Compression Rapid Compression men Gravity ity Content sional Splitting No. Wave Strength Unconfined Compressive Triaxial Compressive Strength with Unconfined Compressive Bulk Solids Before After Velocity Strength Test Compressional Wave Velocity (7p) Strength Test Dry Test Test Loading Strength YoungT s Pois Strength at Confin YoungT s Pois In itial Highest Loading Strength Young' s P o i s Rate Modulus son^ ing Pressures of Modulus son's V Rate Modulus son Ts Patio 250, 1,000, and Ratio VP P P a t i o 1,500 psi 250 1,000 1,500 feet pet ft/sec psi psi/sec psi 10^ psi psi psi psi 101 rß 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 ------8.1+6 x 105 l+,230 0 .9 1 0.36 T -ll U12 GO 6ui+ 31.5 to 37.0 1.85 2.3!+ 21.77 22.1+ l 6 .6 8,61+0 ------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 75 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 9,859 ------ 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 ------1.68 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 ------ ------105 2,1+90 0.1+1 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 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 veloc ity for limestone and tuff. 68 Tensll* 8trut| p*i Figure Figure 3*3 tan pin/in Strain, iet esl srs ess xa sri, granite. strain, axial versus stress tensile Direct Figure Figure Compressional Wave Velocity, ft/sec 3.h opesoa ae eoiyvru ail tes tf i nofnd compression* unconfined in tuff stress, axial versus velocity wave Compressional Compressional Wave Velocity, ft/sec 2 6 4 2 0 Figure Figure 3*5 opesoa ae eoiyvru dvao srs, tuff. stress, deviator versus velocity wave Compressional eitrSrs, 0 psi Stress,Deviator 10 Figure 3-6 Typical basalt shear breaks. 72 / Y Diametral y^Axial 1 Volumetric y Specim m No. G-2 0 Loadin l Rate 50 psi/ 3ec 1 Ultima te strength 19,790 psi r Modulu s of elastic Ity 10.20 x 106 psi 0 Poisso n* s ratio 0.22 1JOOO 2,000 Strain, |iin/in 0 .1 Strain, percent Figure 3.7 Stress versus strain curves for granite Specimen G-2. Stress, 1 0 ° psi io 2,000 ipoo 0 Figure 3.8 Stress versus strain curves for granite Specimen G-10. Specimen granite for curves strain versus Stress 3.8 Figure Strain, pin/in tan percent Strain, Stress, lCr psi Figure Figure 3*9 Stress versus strain curves for granite Specimen Specimen granite for curves strain versus Stress 0 tan percent Strain, .1 G-15. iue .0 yai srs ess tan uvs o rnt (0-i odr Specimens loader) (200-kip granite for curves strain versus stress Dynamic 3.10 Figure G-ll and 0-13. and G-ll Dynamic Stress, 10 psi 20 / p0 2p00 ip00 of s u l u d o M e t a m i t l U n e m i c e p S G-ll -3 20,960 G-13 o Strength Elasticity t i c i t s a l E h t g n e r t S No. i s p ^ 0 1 x 1 5 . 0 1 i s p 0 7 0 , 8 1 / tan p.in/inStrain, p si si p 10.03x106 > G-ll i s p 5 G-13 3.0 e m i T e s i R 3.0 c e s i l l i m c e s i l l i m 3,000 6.03x106 6.95xl06 n i d a o L g ate t Ra ig c e s / i s p c e s / i s p Stress, lCr psi tan Mdn/in Strain, Figure 3.11 Stress versus strain curves for basalt Specimen B-l. Specimen basalt for curves strain versus Stress 3.11 Figure xaso*— tan pret—^Contraction — percent Strain, Expansion*«— Stress, 10 psi 0 Figure 3.12 Stress versus strain curve for basalt Specimen B-21. Specimen basalt for curve strain versus Stress 3.12 Figure Strain, l-iin/in 2,000 4,000 - 0.4 - Expansion < Expansion 0.2 -- Strain, percent percent Strain, 0 -- 0.2 p Contraction Stress, lCr psi Figure 3.13 Stress versus strain curves for basalt Specimen B-22. Specimen basalt for curves strain versus Stress 3.13 Figure 0.3 - 0.2 - xaso Sri, ecn | Contraction Strain, percent — Expansion 0.1 0 0.1 Stress, lCr psi Figure 3.1^- Stress versus strain curves for basalt Specimen B-29. Specimen basalt for curves strain versus Stress 3.1^- Figure tan, in/in fiin , Strain 2,000 xaso —Sri, ecn—* Contraction percent— Strain, — Expansion 4,000 -.1 0 6,000 .1 20 15 10 5 2,000 4p00 6,000 Strain, |~iin/in Figure 3.15 Stress versus strain curves for basalt Specimen B-20. Stress, 10 psi Figure Figure 3«l6 Stress versus strain curves for basalt Specimen Specimen basalt for curves strain versus Stress B-9* Stress, 10 psi 0 Figure 3.17 Stress versus strain curves for basalt Specimen B-7. Specimen basalt for curves strain versus Stress 3.17 Figure Strain, pùn/in 2,000 4>000 - 0.2 Expansion - 1 — Strain, percent — 0.1 0 Contraction 0.1 Stress, 10 psi Figure Figure 8 1 . 3 Stress versus strain curves for basalt Specimen Specimen basalt for curves strain versus Stress Expansion Expansion 4 -- Sri, ecn Contraction percent Strain, - B 3 . Stress, 10 -psi Figure 3.19 Stress versus strain curves for basalt Specimen Specimen basalt for curves strain versus Stress 3.19 Figure B-6. Stress, 10^ psi Figure 3.20 Stress versus strain curves for basalt Specimen B-15. Specimen forbasalt curves strain versus Stress 3.20 Figure Stress, lCr psi Figure 3*21 Stress versus strain curves for basalt Specimen B-8. Specimen basalt for curves strain versus Stress 3*21 Figure Stress, lCr psi Figure 3.22 Stress versus strain curves for basalt Specimen B-ll. Specimen basalt for curves strain versus Stress 3.22 Figure -0 B-l6, B-10, iue .3 yai tesvru sri uvs o aat 20kplae) Specimens loader) (200-kip forbasalt curves strain versus stress Dynamic 3.23 Figure Stress, lCr psi 3-1..', and B-l8. and Stress 5 1 0 psi 40 800 400 0 Figure 3.21+ Stress versus strain curves for limestone Specimen L-2. Specimen limestone for curves strain versus Stress 3.21+ Figure L tan pin/in Strain, Diame- trai © 3 _Axial 0.4 0 Strain, percent Loading Specimen Moduluso Ultimate Voltimetri Poisson's -- Contraction► R j E elasticity ite No.L-2 strength ratio 50 psi/sec 9,500 10.42x10 0.19 psi os CD H* Stress, 10 psi ipoo o r Figure 3.25 Stress versus strain curves for limestone Specimen L-7. Specimen limestone for curves strain versus Stress 3.25 Figure r Diametra tan pin/in Strain, 1 ? > Axial xaso# tan pret #• Strain, percent— Contraction Expansion#— ( 0.4 0 )Volumetric > Modulus Ultimate Poisson* Loading Specimenj Rate >f elasticit i strength No.L-7 ratio r 12,750ps 12.0 x10 50psi/se 0.29 i 6 psi c Stress, 10 psi 0 Figure 3.26 Stress versus strain curves for limestone Specimen L-8. Specimen limestone for curves strain versus Stress 3.26 Figure tan nin/inStrain, 400 800 1,200 0 tan percent Strain, 0.04 Contraction Stress, 10 psi Figure 3-27 Dynamic stress versus strain curves for limestone (200-kip loader) loader) (200-kip limestone for curves strain versus stress Dynamic 3-27 Figure Specimens L-17, L-l8, and L-20. and L-l8, L-17, Specimens ipoo 0 ,0 3,000 2,000 Strain, nin/in VO ■P- 0 2p00 4,000 Strain, lJtin/in o a .2 Strain, 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 Figure 3.30 Stress versus strain curves for tuff Specimen T-26. Specimen tuff for curves strain versus Stress 3.30 Figure tan pin/inStrain, 2p00 4,000 0 tan percent Strain, 0.1 -- 0.2 Contraction T 1-2k, Figure 3.31 Dynamic stress versus strain curves for tuff (drop tower) Specimens T-ll, T-ll, Specimens tower) (drop tuff for curves strain versus stress Dynamic 3.31 Figure Dynamic Stress, 10° psi and and 1 - 27 . iue *2 liae tegh ess odn ae o bsl i nofnd compression. unconfined in basalt for rate loading versus strength Ultimate 3*32 Figure ULTIMATE STRENGTH, IO3 PSI 1.6 x 107 Figure Figure for basalt tested in unconfined compression at loading rates from 1 to 1 from rates loading at compression inunconfined tested basalt for Ultimate Strength, 10 psi 3-33 psi/sec. liae teghvru oa etcl tana failure at strain vertical total versus strength Ultimate Figure 3*3^- Loading rate versus total axial strain at failure for basalt. OH H Figure 3.35 Loading rate versus total horizontal strain at failure for "basalt. Young1 s Modulus of Elasticity, 10 psi (unconfined compression) 0 $ 0 1 o io io ------Figure 3-36 Loading rate versus modulus of elasticity forbasalt elasticity of modulus versus rate Loading 3-36 Figure - — ______Q ______2 io O O Q - — — — Loading Rate, psi/sec Rate, Loading 3 io Y Y = 4.15 = . . .. 4 io (0.0693) + — 0 5 (*) (*) io NOTE ^ 0 0 —y : Modulus Modulus : 6 10 one-half one-half strength.j tang< a is C3 0 1 Ultimate : >nt value S elasticity elasticity 7 Deviator Stress, 10 psi Figure Figure 3*37 Deviator stress versus strain curves for granite Specimen G-20. Specimen granite for curves strain versus stress Deviator tan percent Strain, Deviator Stress, lCr psi 10 20 30 iue .8 eitr tes ess tan uvs o gaie pcmn G--7. Specimen granite for curves strain versus stress Deviator 3.38 Figure V V Strain, pin/in j C / Dian etral ?y/ y (? 1P00 Axial Specirae n n No, : 7 - G 2p00 Modulus Maximum p Maximum Maximum d Maximum Confining Poisson*s Loading I Loading 0 rincipal str eviatorstre felasticity ate pressure ratio Volumetric Strain, percent 0 s 30,320 ass s 29,320 ss / 50psi/sec 0.22 11.3x 1,000 .1 / L0&psi psi psi psi ' Deviator Stress, 10° psi Figure Figure / 1 Ì Strain, pin/in / / / 3.39 3.39 p' ’j i J ' / ^ / / Diametral Deviator stress versus strain curves for granite Specimen Specimen granite for curves strain versus stress Deviator V i V / 2,000 / Strain, percent 00 01 0.15 0.10 0.05 0 / / ______/ / / / / :/ / / A A xial " / /////// / / 4,000 / Modulu Maxima Maxima Poisso Confin Load ir Spec in / /* Lngpressure i 3 of elastic aprincipal ndeviators g Rateg en No. G-4 Volumetric ' s ratio t 10.0x Lty tes 56,5 stress 52,5 :ress 50psi/sec 3 0 4,0 G-U ^■0psi ^0psi L0^psi 30psi 20 15 Volumetric 10 Specimen Nd. B-14 Loading Ratfe 1 psi/sec Confining pressure 250 psi Maximum Delator Stress 21,240 psi Maximum Pri ncipal Stress 21,490 psi 5 Modulus of Elasticity 5.18 x 106 psi + Poisson* s Ratio 0.41 0 2,000 4 ,000 Strain, pin/in - 0.2 - 0.1 0 Expansion Strain, percent ---1 Contraction 3.^-0 Deviator stress versus strain curves for basalt Specimen B-lU. Deviator Stress, lCr psi Figure Figure 0 3.kl Deviator stress versus strain curves for basalt Specimen B-23. Specimen forbasalt curves strain versus stress Deviator tan j~iin/in Strain, 2,000 4,000 xaso*— tan pret ■ ■ percent Strain, Expansion* — - 0.1 6,000 0 1 Contraction 0.1 Deviator Stress, 10° psi Figure 3.^2 Deviator stress versus strain curves for basalt Specimen Specimen basalt for curves strain versus stress Deviator 3.^2 Figure Expansion Expansion 4 Sri, ecn ► Contraction — percent Strain, — 0 0.1 0.2 0.2 2k. Deviator Stress, 10° psi Figure 3.^-3 Deviator stress versus strain curves for basalt Specimen B-^. Specimen forbasalt curves strain versus stress Deviator 3.^-3 Figure 0 0 tan percent Strain, 0.1 0.2 2P00 Strain, M-in/in 4,000 6,000 Deviator Stress, 10J psi Figure Figure tan percent Strain, 3.bk Deviator stress versus strain curves for basalt Specimen B-5. Specimen basalt for curves strain versus stress Deviator Deviator Stress, IO0 psi Figure 3.^5 Deviator stress versus strain curves for basalt Specimen B-19. Specimen forbasalt curves strain versus stress Deviator 3.^5 Figure oa 0.2 a o o 20 4p00 2p00 0 Strain, percent Strain, n ± / n l x \ 6,000 Deviator Stress, 10° psi Figure 3.^6 Deviator stress versus strain curves for basalt Specimen B-13. Specimen forbasalt curves strain versus stress Deviator 3.^6 Figure Expansion f Strain, percent percent Strain, f Expansion --- ^Contraction Deviator Stress, 10° psi 12 18 24 Figure 3.^-7 Deviator stress versus strain curves for basalt Specimen B-26. Specimen basalt for curves strain versus stress Deviator 3.^-7 Figure 2P00 0 {/ J > d / Strain 5 jiin/in Diametral ______7 & y ^ Axial ^ Maximum Prij Maximum Dev* Maximum Modulus of 1 of Modulus Loading Rat! Loading oso' B Poisson's Confining Confining Specimen No No Specimen ______4,000 f Expansion Expansion < : atio Elasticity Stres icipal Stress lator ressure a . B-26 ^ ------\ s 32,290 psis 32,290 0.27 31,290 psi 31,290 3.94x tan percent Strain, 500 psi/se 500 1P00 psi 1P00 \ 6 0 1 6000 ?si :Volumetric f ►Contraction © o Deviator Stress, 10J psi Figure Figure 3.^8 Deviator stress versus strain curves for basalt Specimen Specimen forbasalt curves strain versus stress Deviator B-27. Deviator Stress, 10 ° psi 40 20 10 30 t .. Figure 3.^9 Deviator stress versus strain curves for basalt Specimen 28. Specimen basalt for curves strain versus stress Deviator 3.^9 Figure / A A ______/ A A tan Mln/in Strain, , J ------) ' * s Diametral . . G ..... -gCygS.. 0 0 P 2 O Axial ® 4,000 O Expansion Expansion aiu rnia Stresi Principal Maximum Stress Deviator Maximum Modulus of ] of Modulus Rate Loading Confining Pressure Pressure Confining pcmn- aat 28 Basalt - Specimen oso' R Poisson's 0 f oi o -o.i -- itio Ilasticity Sri, percent Strain, . 0 6,000 ( 1 '1 ^ < i 25,950 psi i 25,950 ,0x 106 x 4,00 250 psi psi 250 2,740 0.25 Volumetric 25,700 psi psi 25,700 psi/se< ► Contraction 0.1 > i i / psi % 0.2 Deviator Stress, lCr psi 10 20 40 30 i / -° r ó f Figure 3*50 Deviator stress versus strain curves for basalt Specimen 30. Specimen basalt for curves strain versus stress Deviator 3*50 Figure 07 0 Strain, p-in/in A Diametral 4,000 . . . x> Y - r ' s X 0 : Axial 0 ) X 8,000 Expansion 4 aiu eitr tes 35,01 Stress Deviator Maximum Modulus aiu rnia Srs 36,01 Principal Stress Maximum odn $e %250psi/sec R$teLoading Confining ^Pressure Poisson’s pcmn Bsl 3 J Specimen, 30 Basalt 0 - _ - -- o- 0.2 i o \ Strain, percent Ratio Elasticity/ 12,000 1,000 0 c ; 4.71 ,0.25 Volumetric psi X X / 106 » Contraction 0.2 (V \ L0psi .0psi i ) ------psi -- — ----- Deviator Stress, lCr psi 45 60 15 30 f — G> à ^ \ A _ Figure Figure (j á Strain, M-in/in O O 3 . 5 I Deviator stress versus strain curves for basalt Specimen 31« Specimen basalt for curves strain versus stress Deviator I Diametral CÏ 4,000 Axial 8,000 ------1 Modulusof Maximum DeviatorStress LoadRate MaximumPrincipal Stres ConfiningPressure Poisson's pcmn BasaltSpecimen31 Expansion < li 1 " atio Elasticity ------2,250 5,000 120,000 p 3 ïi/sec 59.000 osi psi 0.15 Strain, 5.03 54,000 psi X G j Volli IO percent 6 0.2 let )SÌ % ne ne j V ê ► Contraiti. on 0 0.4 60 <73 = 2 50 PS 1 50 4 0 30 A- 5C1 P S U S EC / I1 50 P S //S E C 5 0 0 P S l/S E / P S U S E C -y 20 10 0 < 4,000 8,000 12,000 0 4,000 8,000 12,000 0 4,000 8,000 12,000 AXIAL STRAIN, JLLIN/IN 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. Deviator Stress, lCr psi Figure 3.53 Deviator stress versus strain curves for limestone Specimen L-U. Specimen limestone for curves strain versus stress Deviator 3.53 Figure 50 p0 1^00 ip00 500 0 V /, Strain, |iin/in j Diametral /Axial .04 0 1 Strain, percent 7 Modulu Maximui Maximui Confin Poisso Loadii Spec iti / ig Rate len No.L-4 / i's ratio \ iprincipal ideviatorst Lngpressure ofelastici Volumetric rr\ tes 15. stress y 10.8x ty 15, ress 50psi/sec 0.35 390psi L40psi 250 psi 106 psi De viator Stress, lCr psi Figure 3.5^- Deviator stress versus strain curves for limestone Specimen L-7 Specimen limestone for curves strain versus stress Deviator 3.5^- Figure 0 ipOO ipOO 0 Strain, nin/in 2p00 0 tan percent Strain, .04 .08 Deviator Stress, 10° psi Figure Figure 0 3.55 Strain, |iin/in Deviator stress versus strain curves for limestone Specimen L-12. Specimen limestone for curves strain versus stress Deviator lj600 3,200 a 0 tan percent Strain, 4,800 Deviator Stress, 10J psi Figure 3.56 Deviator stress versus strain curves for tuff Specimen T-21 Specimen tuff for curves strain versus stress Deviator 3.56 Figure 0 lpoo ,0 300 4,000 3,000 2,000 tan M-in/inStrain, 5,000 0 tan percent Strain, 0.1 0.2 Deviator Stress, 10 psi Figure Figure 3«57 Deviator stress versus strain curves for tuff Specimen Specimen tuff for curves strain versus stress Deviator tan percent Strain, T-20. Deviator Stress, 10 psi Figure 3.58 Deviator stress versus strain curves for tuff Specimen T-]J+. Specimen tuff for curves strain versus stress Deviator 3.58 Figure Compressional Wave Velocity, ft/sec Figure Figure 3*59 opesoa aevlct ess eitr tes o granite. for stress deviator versus velocity wave Compressional Compressional Wave Velocity, ft/sec iue .0 opesoa aevlct ess eitrsrs for basalt. stress deviator versus velocity wave Compressional 3.60 Figure ■>— — — ------o- — 000 000 50,000 30,000 10.000 -i J ______--- Gì l -0 \ ( eitrSrs, psi Stress, Deviator i) B-4 ® G - — B-5 © Specimen No Specimen B-19 B-19 B-5 B-4 Confinine » 5^000 1,000 250 psi psi psi Pressure Compressional Wave Velocity, ft/sec iue «l opesoa aevlct ess eitrsrs fr limestone. for stress deviator versus velocity wave Compressional 3«6l Figure 0 10,000 eitrSrs, psiStress,Deviator 20,000 30,000 Shearing Stress, psi iue .2 or ice fr granite. for circles Mohr 3.62 Figure Normal Stress,Normal psi Shearing Stress, Figure 3.63 Mohr circles for basalt tested at loading rate of 1 psi/sec. 1 of rate loading at tested basalt for circles Mohr 3.63 Figure Shearing Stress, iue .^ Mh crls o aat etd t odn ae f 0 psi/sec. 50 of rate loading at tested basalt for circles Mohr 3.6^4 Figure Shearing Stress iue .5 or ice frbsl tse a laig ae f 0 psi/sec. 500 of rate loading at tested basalt for circles Mohr 3.65 Figure Shearing Stress, osi Figure Figure 3.66 or ice frbsl tse t odn ae f270 psi/sec. 2,7^0 of rate loading at tested basalt for circles Mohr Shearing Stress, psi iue .7 or ice fr limestone. for circles Mohr 3.67 Figure Shearing Stress, psi Figure 3.68 Mohr circles for tuff. for circles Mohr 3.68 Figure 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. rates for basalt. for rates Figure 3*70 Mohr envelope at various loading loading various at envelope Mohr 3*70 Figure SHEARING STRESS, PSI 0 10,000 RES PSI ESS, TR S L A M R O N 136 20,000 30,000 Figure 3.71 Engineering classificationforintactataloading rock Engineering 3.71Figure ae ofrate YOUNG'S MODULUS W .2 5 - .5 16i- «o — \ U 2 o o X CD 20 o 10 8 9 7 6 50 -- / ____ □ □“ A I O I I STRENGTH ATE ULTIM % 0 5 AT MODULUS TANGENT = t E I NOTE: 5 2 20 0 100 2,000 1,000 500 250 125 75 psi/sec. / --- / / □ TE TH G STREN VERY LOW LOW VERY T T - . / u z f l Z 1 1 T~ 1 1 1 1 ____ / CLASSI OK B, H BL, ETC. , L B BH, , B S A ROCK Y IF S S A L C 2 □ LIMESTONE LIMESTONE GRANITE GRANITE TUFF BASALT _L __ E 4 / / Z AXI COMPRESSI TRE H T G EN R ST E IV S S E R P M O C L IA X IA N U c 'A * / / \ / ? / _L ' / 1 / 0*' / o . STRENGTH / J LOW 5 / ? / / D V <5 678910 ( D A / 137 D V / j 8 P / STRENGTH MEDIUM > □ A .INI. / / c 1 1 1 I □ D / / / y 16 J_LL -- / STRENGTH / 111 / ; y 0 0 0 0 0PSI 10- IX S 60P 50 40 30 20 HIGH CTa ) ( ULT 1 Y 7 ^ / B A Li-- ^ / ’ -- / A A* 32 1 STRENGTH / VERY HIGH HIGH VERY / / / 7~ “7 A / ,0 KG/CM2 M C / G K 4,000 / . / \ SI 10° X IPS YOUNG'S MODULUS Fig-ore 3.72 Engineering classification for intact rock at a rapid rapid a at rock intact for classification Engineering 3.72 Fig-ore loading rate of of rate loading «o o OE I TNET OUU A 50% UTMT STRENGTH ULTIMATE % 0 5 AT MODULUS TANGENT = t E I NOTE: CLSIY OK S B, ETC. , L B BH, , B AS ROCK LASSIFY C 2 >50 U N IA X IA L C O M PR ESSIVE STRENGTH STRENGTH ESSIVE PR M O C L IA X IA N U psi/sec. 138 f CTa ) ( ULT YOUNG'S MODULUS Ui Figure Figure t odn rts rm1t l 1^ psi/sec. 10^ x l6 to 1 from rates loading at 16 10 - | \ 2 o U X o ¥ 20 10 .3 4 8 9 5 7 6 3.73 OE I TNET OUU A 50% ULI T STRENGTH ATE LTIM U % 0 5 AT MODULUS TANGENT = t E I NOTE: - I A - E ______5 2 20 0 100 2,000 1,000 500 250 125 75 □ □ 0 □ H T G N E R T S OW LO Y R E V / 1 ______CLASSI OK B, B, ETC. , L B BH, , B S A ROCK Y IF S S A L C 2 / r / Engineering classification for intact rock for basalt for rock intact for classification Engineering LIMESTONE GRANITE BASALT TUFF ---- □ / / ,> E 1 ____ / £ 7 AXI COMPRESSI TE H^ " ULT) T L (U 0"a ^ TH G STREN E IV S S E R P M O C L IA X IA N U A 1 ___ / t t 1 / OJ j, 4 3 1 ___ * & / / _L 1 __ ' ■ / J 4 * o o . o . / ST / T—l 1—1 V ■R 7 7 L 56789 1056789 .OV _D_ / ? EN( _ / 7 V ^ A 1 3T V 0 7 7 / 139 p H / / A V* 8 4 0° ST / IV > ■R IE 7 / ✓ ENGTH / DIUM c lilt ° 7 / / ? j 16 . 1.1 1 7 STR / / 0,. ______l- 0 0 0 0 0PSI 10° IX S 60P 50 40 30 20 : » IIG / K u ^ u n e A B A < j H u A A TH A / Cl I ______32 * r VI ' S' 1 “ 7 FR ER / 0 7 Y Eh — / 4G \ H / ,0 K CM' M /C KG 4,000 ; IGH / h t 7 L_ j I I0J X I S P Figure 3.7^ Relation of axial stress to lateral stress at failure in triaxial compression tests of rock cores. Figure 3.75 Relation of failurestresslateralstressaxial at Relationto 3.75 Figure incompression foratloadingtriaxialdifferentrates basalt. AXIAL STRESS, 10° PSI 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, increase n 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 1. A. Kuman, F. E. Hausser, and J. E. Dorr; f,The Effect of Stress Rate and Temperature on the Strength of Rocks"; Publisher Unknown; Unclassified. 2. R. L. Stowe; "Dynamic Properties of Granodiorite, Project 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. R. G. 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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 Absorp tion Capabilities of Plain Concrete Under Dynamic and Static Load ings"; 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 DISTRIBUTION LIST No. of Address______Copies Army Chief of Research and Development, Headquarters, 3 cop- Department of the Army ies of ATTN: Director of Army Technical Information Form Washington, D. C. 20310 1^-73 Chief of Research and Development, Department of the Army ATTN: Atomic Office 1 CRDES 1 Washington, D. C. 20310 Chief of Engineers, Department of the Army ATTN: ENGTE-E 1 ENGCW-E 1 ENGMC-E 1 ENGMC-M 1 Washington, D. C. 20315 Commanding General, U. S. Army Materiel Command 1 ATTN: AMCRD-DE-N Washington, D. C. 20310 Director of Civil Defense, Office of the Secretary of 2 the Army, ATTN: Mr. George Sisson (RE-ED) Washington, D. 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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 DESCRIPTIVE NOTES (Type ot report and inclusive dates) Final report 8- AUTHOR(S) (First name, middle initiai, last name) Richard L. Stowe 6. R E P O R T D A T E 7a. T O T A L NO. O F P A G E S 7b. NO. OF REFS January 1969 I 6 I 39 8«. CONTRACT OR GRANT NO. 9a. ORIGINATOR'S REPORT NUM%ER(S) Miscellaneous Paper C-69-l 6. p r o j e c t n o . UWER Subtask 13.191A Ob. OTHER REPORT NO(S) (Any other numbers that may be aeaidned this report) 10. DISTRIBUTION STATEMENT This document has been approved for public release and sale; its distribution is u n lim ite d . 11. SUPPLEMENTARY NOTES 12. SPONSORING MILITARY ACTIVITY Defense Atomic Support Agency Washington, D. C. 13. A B S T R A C T " ' 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 conducting slow (specimens loaded at rates of less than 2,251 psi/sec) and rapid (specimens loaded at rates greater than 2,251 psi/sec) unconfined compression tests, tensile splitting tests, and triaxial compression 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 pro gram. Nondestructive tests such as specific gravity, porosity, and compressional wave velocity were conducted on a ll specimens to determine homogeneity of each rock. Re sults of nondestructive tests indicated that the rock within each rock type was quite uniform. Results of the unconfined compressive strength tests on basalt indicated that as the loading rate was increased from 1 to 1.60 x 107 psi/sec, ultimate strength, total axial strain, and Young’s modulus of elasticity increased. Total diametral strain decreased as loading rate was increased. Results of triaxial tests indicated that the maximum deviator stress and total axial strain increased as the confining 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 pressures up to 5,000 psi. Compressional wave velocities re corded 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 dif ference in the unconfined compressive strength between the slow and the rapid rates of loading for the rocks tested varied considerably. The dynamic compressive strength DD .1473 Unclassified Security Classification Unclassified Security Classification 13. ABSTRACT 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 in creases 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 maxi mum deviator stress and then generally level off until failure. 14. LINK A LINK B LINK C KEY WORDS RO L E WT ROLE WT ROLE W T Granite Basalt Limestone Tuff Rock properties Unclassified Security Classification 168