This dissertation has bean microfilmed exactly as received 68*8863
NOR M A N , Carl Edgar, 1931- MICRO FRACTURES IN BRITTLE ROCKS: THEIR RELATIONSHIP TO LARGER SCALE STRUCTURAL FEATURES AND EXISTING GROUND STRESSES. The Ohio State University, Ph.D., 1967 Geology
University Microfilms, Inc., Ann Arbor, Michigan MICROFRACTURES IN BRITTLE ROCKS: THEIR RELATIONSHIP TO LARGER SCALE STRUCTURAL FEATURES AND EXISTING GROUND STRESSES
DISSERTATION Presented in Partial Fulfillment of the Requirements for Degree Doctor of Philosophy In the Graduate School of The Ohio State University
By Carl Edgar Norman,, B.A.* M.Sc.
******
The Ohio State University 1967
Approved by
Advi«ers Department of Geology ACKNOWLEDGMENTS
The writer wishes to express sincere appreciation to Dr. H. J. Pincus who introduced him to the study of rock mechanics and provided guidance and stimulation of thought throughout the study. The Applied Physics Laboratory of the U. S. Bureau of Mines financed most of the field work by providing employment and field expenses during the summers of 1 9 6 3 1964; it also paid for the cost of the rock thin sections. Special thanks are due Dr. Leonard Obert of the U. S. Bureau of Mines who guided the in situ stress determination work and provided laboratory data on the physical properties of the rocks. The writer also wishes to acknowledge a National Science Foundation Graduate Fellowship which sponsored part of the research and field work. The writer expresses his indebtedness to Dr. Coiin Bull who served as adviser in the late stages of manu script preparation, to Mrs. Pat Price for her expert typing of the manuscript, and to his wife, Judith, for her patience, encouragement, and nontechnical advice.
ii VITA
February 1, 1931 B o m - Cokato, Minnesota 1957 ...... B.A., University of Minnesota, Minneapolis, Minnesota 195^1959 - • • Research and Teaching Assistant, Department of Geology, The Ohio State University, Columbus, Ohio
1959 ...... M.Sc., The Ohio State University, Columbus, Ohio 1959-1962 . . . Exploration Geologist, Humble Oil and Refining Company, Grand Rapids, Michigan; Durango, Colorado; and Mattoon, Illinois
1 9 6 2 -1 9 6 3 . . . Teaching Assistant, Department of Geology, The Ohio State University, Columbus, Jphio 1963-1964 . . . Geophysicist, Applied Physics (Summers) Research Lab, U. S. Bureau of Mines, College Park, Maryland 1963-1965 • • • National Science Foundation Graduate Fellow, Department of Geology, The Ohio State University, Columbus, Ohio 1965-1967 • • • Instructor, Department of Geology, University of Houston, Houston, Texas
PUBLICATIONS "Classification of the Limestones of the Type Cincinna- tian." (Abstract with M. P. Weiss): Geol. Soc. America Bull., v. 71, p. 2 0 2 8, i9 6 0
iii "The American Upper Ordovician Standard; II. Develop ment of Stratigraphic Classification of Ordovician Rocks in the Cincinnati Region." (with M. P. Weiss): Ohio Geol. Survey Info. Circ. No. 26, 14 p., i9 6 0 "The American Upper Ordovician Standard; IV. Classifi cation of the Limestones of the Type Cincinnatian." (with M. P. Weiss): Jour. Sed. Petrol., v. 30, p. 2 8 3- 2 9 6, i9 6 0 "The American Upper Ordovician Standard; VII. Stratig raphy and Petrology of the Cynthiana and Eden Forma tions of the Ohio Valley." (with M. P. Weiss, W. R. Edwards, and E. R. Sharp): Geol. Soc. America Special Paper 8l, 7 6 p., 1 9 6 5
FIELDS OF STUDY Major Field: Geology Studies in Geophysics: Professor Colin B. Bull Studies in Engineering Mechanics: Professors Edgar C. Clark and Samuel B. Folk Studies in Structural Geology and Engineering Geology: Professor Howard J. Plncus Studies in Stratigraphy: Professors Edmund M. Speiker, Malcolm P. Weiss, and Robert L. Bates Studies in Hydraulics: Professor George P. Hanna
iv TABLE OF CONTENTS Page ACKNOWLEDGMENTS . . ii VITA ...... ill LIST OF TABLES . . . vii LIST OF ILLUSTRATIONS viii INTRODUCTION .... 1 Chapter I. RATIONALE OF THE INVESTIGATION .... 7 Griffith Theory Influence of grain anisotropy on fracture orientation Microfractures and stress magnitudes Persistence of microfractures in time II. FIELD M E T H O D S ...... 17 Borehole deformation method Core deformation method Field procedure Photoelastic gages III. LABORATORY METHODS ...... 27 Compositional analysis Recording and error analysis of microfracture data Recording and error analysis of quartz c-axis data PetrofabrTc diagrams XV. MICROFRACTURES ...... 40 Definition Description Frequency of Occurrence Origin of microfractures In ex tension or shear Origin of microfractures during preparation of thin section Origin of microfractures during coring of rock Microfracture frequency according to grain size and composition in polymineralic rocks
v V. MICROFRACTURES, STRUCTURE, AND IN SITU STRESSES AT NORAD COC, C3I3TRADO SPRINGS, C O L O R A D O ...... 6 3 Geological setting Petrography In situ stress determinations Microfracture orientation data Open microfractures Filled and healed microfractures Summary of investigations at NORAD COC, Colorado VI. MICROFRACTURES, STRUCTURE, AND IN SITU STRESSES IN THE ATLANTA, SEMGIA, REGION ...... 102 Rock Chapel Mountain Petrography Structure Stress Determinations Microfractures Pine Mountain Petrography Structure Stress Determinations Microfracture s Arabia Mountain Petrography Structure Stress Determinations Microfractures Stone Mountain Petrography Structure Stress Determinations Microfractures Douglasville Petrography Structure Stress Determinations Microfractures Summary of investigations at At lanta, Georgia VII. CONCLUSION ...... 144 BIBLIOGRAPHY 149 LIST OP TABLES
1 Frequency of microfractures in four rock t y p e s ...... 48 2 Comparison of microfracture frequency with grain mineralogy ...... 6 0
3 Photoelastic strain gage data* NORAD COC, 1 C o l o r a d o ...... 78 4 Poisson probabilities of randomness in orientations of microfractures at NORAD COC, Colorado...... 8 8 5 Comparison of orientations of fluid in clusion planes, open microfractures, and common joints, NORAD COC, Colorado ...... 9 6
6 Calculated secondary principal stresses at Rock Chapel, Georgia...... 113
vii LIST OP ILLUSTRATIONS
Fluid inclusion planes transect two ad jacent grains without changing direction . Borehole deformation method of in situ stress determination ...... Core deformation method of in situ stress determination ...... Stress-relief drilling equipment ...... Photoelastic gage mounted on smoothed back of a 3-inch diameter hole ...... Borehole polariscope ...... Influence of thin section orientation on number of microfractures visible in thin section ...... Composite petrofabric diagram of data from two perpendicular sections, show ing areas to be contoured separately . . . Partially healed microfracture in a quartz grain ...... Microfracture filled with a material having high birefringence ...... Quartz grain with fluid inclusion plane Plagioclase grain showing open micro fractures transecting planes of fluid Inclusions...... Open microfracture transecting four quartz grains differing in crystal- lographic orientation ......
viii 14 Set of three parallel* open micro fractures in a quartz g r a i n ...... 46 15 Frequency of microfractures vs. princi pal strain magnitudes and differences . . 5 5
16 Microfracture frequency vs. grain size . . 57 17 Microfracture frequency per unit grain area vs. grain diameter ...... 5 8 18 Percent of total microfractures vs. percent total grain area in two rock s a m p l e s ...... 6 l 19 Plan and cross-sectional views of stress-relief holes at NORAD COC* Colorado...... 64 20 Cyclographic diagram of major dike and joint systems at NORAD COC* Colorado . 6 8 21 Stereonet plot of poles to joints* Chamber A* NORAD COC* Colorado...... 6 9 22 Equal area diagram of quartz c-axes* samples N2-4 and N5-4 72 23 Secondary principal stress directions and magnitudes at NORAD COC* Colorado . . 79 24 Microfracture filled sequentially with two secondary minerals ...... 84 25 Equal area diagrams of poles to filled* healed* and open microfractures* NORAD COC* C o l o r a d o ...... 93
2 6 Geologic map of the Atlanta* Georgia* r e g i o n ...... 103 27 Aplite vein concordant with foliation cut by later discordant v e i n ...... 1 0 7 28 Structure of the Lithonia gneiss* Consolidated Quarries* Rock Chapel* G e o r g i a ...... 108
ix 29 Equal area diagram of poles to foliae and concordant veins, Rock Chapel, Georgia ...... 30 Small valley developed along a natural fracture in Lithonia gneiss, Rock Chapel, Georgia ...... 31 Sheeting in Lithonia gneiss exposed in quarry at Rock Chapel, Georgia ...... Ill 32 Vertical, nearly planar fracture sur face induced in Lithonia gneiss by quarry operator ...... 33 Upwarped slab of rock on pavement sur face at Rock Chapel, Georgia ...... 117 34 En echelon array of vertical fractures Induced by detonation of explosives in vertical drill holes ...... 119 35 Orientations of open microfractures at Rock Chapel, Georgia ...... 36 Structure of the Lithonia gneiss, Pine Mountain, Georgia ...... 37 Orientation of open microfractures at Pine Mountain, Georgia ...... 38 Orientation of open microfractures at Arabia Mountain, Georgia ......
39 Orientation of open microfractures, Stone Mountain, Georgia ...... , . 134 4o Orientation of open microfractures, Douglasville, Georgia ......
Plate I Orientation of open microfractures at NORAD COC, Colorado Springs, Colorado ...... Back Binding
x INTRODUCTION
Deformation of the earth's crust throughout geologic time has produced a wide variety of structures in rocks that have long aroused the curiosity of geologists. A complete analysis of such structures normally progresses through three phases: the descriptive, kinematic, and dynamic phases (Goguel, 1952, p. 2). The descriptive phase includes both description and classification of structures, and it has reached a rather advanced stage. Kinematic analysis had its birth in Austria In the second decade of the present century. Due largely to the work of B. Sander and W. Schmidt (Sander, 1911), it has as its main thesis the concept that the fabric of a deformed body reflects the relative movements of its component parts during deformation. A study of rock fabrics presumably enables one to reconstruct the move ment of one component relative to any other. Such in terpretations are still In an early stage of development. A dynamic analysis is an attempt to reconstruct the forces that produced the movements responsible for rock fabrics. Only a small amount of progress has been made
1 in this very new phase of structural analysis. The orientation of principal stresses has been worked out for deformed samples of a few common minerals (Turner,
1953; Carter and Friedman, 19^5; Borg and Handin, 1 9 6 6;
Raleigh and Talbot, 1 9 6 7)* and methods for recognizing and measuring residual strains in rocks are being devel oped (Pincus, 1964; Friedman, 1 9 6 7). Within the past decade exciting new research in the field of rock mechanics has led to the development of several methods designed to determine existing stress fields in rock at depth. Data from these methods pro vide the geologist with an entirely new basis for dynamic structural interpretations. The present study relates the results of two of these methods applied in two localities to the microscopic, local, and regional geologic structure of the areas.
Purpose of Study
The primary purpose of the present study is to investigate the relationship, if any, of the orientation and frequency of microfractures in rock to principal stress directions as inferred from in situ strain measure ments. With one exception (Kehle, 1964), the existing methods of in situ stress determination cannot be used in drill holes more than a few tens of feet to a hundred 3 feet deep. The present study was initiated in the hope that the microfracture subfabric in cores from drill holes would yield at least directional Information on the stress field existing at depth. If such a relation ship can be demonstrated, the method would yield such information from holes thousands of feet deep, and at a very low cost. Attention is also directed to the correlation of microfracture orientations with the orientation of larger-scale local and regional structural features mapped in the field. A demonstrated correlation could establish a genetic relationship of these features in time and space. The study also provides an excellent test of re producibility of microfracture patterns over short dis tances. Thin sections were prepared from samples collect ed at each point where stress determinations were made, and this procedure provided microfracture data from sam ples spaced only a few feet apart.
Previous Studies
Recognition of naturally occurring microfractures in rock must date to the manufacture of the first thin section of rock by Alexander Bryson between 1051 and 4
1 8 5 8. Despite a common occurrence of microfractures in the more brittle rocks, such as quartzites, gneisses and granites, the results of only a few studies of micro fractures appear in the literature. The earliest investi gations were carried out by Europeans who published in German (Sander, 1930; Sahama, 1936; Wenk, 1943)* Fair- baira (1949> ch. 4, 11) summarizes some of the results of their work. In this country the most significant studies include, among others, Riley's (1947) correlation of the orientation patterns of microfractures and defor mation lamellae in the folded Baraboo Quartzite of Wis consin; Bonham's (1957) investigation of both micro fracture and macrofracture patterns in relation to the geometry of the Pico anticline-syncline structure in
California; Carter and Friedman's (1 9 6 5) dynamic analysis of the calcite and quartz fabrics of a calcareous sand stone from the Dry Creek Ridge anticline, Montana; and
Harper's (1 9 6 6) analysis of joint and microfracture patterns on the White River Arch, Glenwood Canyon, Colo rado. In somewhat more restricted studies Anderson (1945) compared the orientation of microfractures in a Cambrian vein quartz in Maryland to quartz crystallographic planes, and Naha (1959) related microfracture and deformation lamellae orientations in a highly contorted mica schist from India to the orientation of fold axes. Planes of fluid inclusions in quartz and feldspar apparently originate as microfractures, and in this connection the studies of Tuttle (1949) and Wise (1964) are important contributions to the literature of naturally occurring microfractures. There are many references to the occurrence of microfractures in experimentally deformed rocks, but a few studies are especially significant. The well-known investigations of Griggs, Handin and their colleagues
(i9 6 0) contain a large number of such references. In an extensive study of experimentally produced microfractures, Borg and Maxwell (1956) compared first the incidence of fracturing in deformed and undeformed specimens of un consolidated quartz sands and secondly related micro fracture orientations to the orientation of crystallo- graphic planes and known principal stress directions. Ingerson and Ramisch (1942) and Bloss (1957) investigated the relationship of fractures in crushed quartz grains to crystallographic directions. In a highly significant
recent experimental study, Friedman (1 9 6 3) demonstrated that microfracture orientations in an experimentally de formed calcite-cemented sandstone are essentially Inde pendent of grain mineralogy and orientation of quartz crystallographic planes. The present study draws heavily on these references In interpreting petrofabric diagrams. 6
A careful survey of earlier work has revealed no attempt by anyone to relate naturally occurring micro fractures to in situ stress determinations. This is not surprising considering the very short period of time methods for such determinations have been available. According to Merrill (1964,, p. 3^)? Lieurance (1932) made the first determination of in situ stress by drill ing a series of overlapping holes to isolate a four-foot square block of rock* into which reference pins had pre viously been driven. Since the early 1950’s several flatjack and overcoring methods have been developed (Merrill, 1964; Obert and Duvall, 19^7) and data are now being obtained in increasing numbers from the principal mining regions of the world. Although there are no published studies relating microfracture orientations and frequencies to such stress determinations, Helfrich (1 9 6 5)* in a study similar to this one, related the orientation of {0 0 l} mica cleavage planes to in situ stresses determined in a granite in northern Sweden by Hast (1958, Part 2). Helfrich suggests that the tectonic stresses that produced the rock fabric are still present and measurable as residual stresses. He implies that any deviation of measured principal ^ . strain directions from those inferred to have produced the fabric was caused by the influence of the underground opening on the residual stress field in the rock. RATIONALE OP THE INVESTIGATION
The microfracture subfabric was chosen for the pre sent study because it shows more promise of being an in dicator of the recent tectonic history of the rock, and possibly the present day stress field, than any other subfabric. The rationale for this lies in the Griffith theory of brittle failure (Griffith 1921, 1925) as dis cussed below. Other directional elements of the sub fabric, such as kink bands, deformation lamellae, and twin lamellae, have been studied in known stress fields and their angular relation to principal stress directions has been worked out (A good summary of the methods is presented by Friedman, 1964). However, most of these features appear only in strongly deformed rocks, and these constitute only a small percentage of the volume of near-surface rocks of the earth's crust. Microfrac- turing, on the other hand, is common not only in strongly deformed rocks, but also in rocks showing little or no macroscopic evidence of deformation. In fact, Borg et_ al. (i9 6 0, p. 1 6 93 1 7 2) found that the slightly deformed grains of an experimentally deformed quartz grain aggre gate showed a greater tendency toward preferred micro fracture orientations than those which were highly de formed. It is largely due to this experimental result that the writer chose to investigate the microfracture subfabric of rocks and relate it to in situ stress deter minations .
Griffith Theory
According to the Griffith theory, any brittle material originally contains randomly oriented flaws or cracks that may or may not be visible. When such a material is subjected to a load., stresses concentrate at the tips of favorably oriented cracks and cause them to grow. In this way loads much smaller than those predicted from chemical bond strengths cause failure of brittle materials. Furthermore, it can be shown that suitably oriented Griffith cracks will propagate under stresses that are macroscopically compressive, excluding the special case of hydrostatic compression, because shear stresses induce local tension along favorably oriented cracks (Griffith, 1925; Ode, i9 6 0). The rocks studied in greatest detail here, namely a granite and a gneiss, contain innumerable microscopic fractures and appear to approximate closely the ideal brittle material postulated by Griffith.
Recently McClintock and Walsh (1 9 6 2) extended the Griffith theory to include the closing of cracks and development of friction on crack surfaces in the region of compressional stress. Brace (i9 6 0) points out that this modification provides a failure condition nearly identical with the empirical Coulomb law observed for rocks in the region of compression. The modification therefore strengthens the applicability of Griffith theory to the failure of rocks. Although Griffith theory can predict the orienta tion of the crack most suitably positioned for propaga tion in a given stress field, it does not predict the direction the crack will follow as it grows, except in the obvious case of simple tension. Using a photoelas tic model of a Griffith material, Brace and Bombolakis
(1 9 6 3) show that in unconfined uniaxial compression a favorably oriented crack will grow out of its initial plane into an orientation parallel to the direction of compression where it ceases to propagate unless the applied compressive load is increased greatly. Rocks in situ, however, must be considered in a triaxial state of stress and prediction of crack paths in this general case is a much more complex, and as yet unsolved, problem. However, the cracks must follow a path influenced by the surrounding stress field, and a statistical analysis of microfracture patterns should provide a means for deter- 10 mining principal stress directions at the time the frac tures grew.
Influence of Crystal Anisotropy on Fracture Orientation
Intuitively one might expect that the orientation of anisotropic crystals in rocks would exert a strong influence on the direction taken by a growing micro fracture. A wealth of experimental and observational evidence suggests this is not the case, at least for the more common minerals. Individual quartz crystals show a slight tendency to fracture parallel to r{lOTn} and z {oiTl} (Griggs and Bell, 1938; Fairbaim, 1939; Inger- son and Ramisch, 1942; Borg and Maxwell, 1956; Bloss, 1957) but this tendency is greatly overshadowed by the consistent orientation of microfractures with respect to known prin ciple stress directions (Friedman, 1963; Borg et al., I960). The fact that naturally occurring microfractures are similarily independent of quartz £-axis orientations has been established by Sander (1930; in Fairbaim, 19^9j P*
68) and Anderson (1 9 4 5). Sander found a preferred orien tation of microfractures against a background of randomly oriented c-axes, whereas Anderson found randomly oriented fractures in a vein of preferentially oriented quartz grains. 11
There is also evidence that microfracture frequen cies and orientations are not influenced by mineralogy in polymineralic aggregates. In an experimentally de formed calcite-cemented sandstone Friedman (1963) found that the orientation and spacing of microfractures tend to be independent of the feldspar and quartz mineralogy of the detrital fraction. It is also significant that surfaces defined by fluid inclusions, interpreted as healed microfractures, extend across grains of different crystallographic orientation and of different mineralogy without changing direction (Bohm, 1 8 8 3; Hicks, l884j Tuttle, 1949). Figure 1 illustrates this phenomenon, which is common in granitic and gneissic rocks studied by the writer. Experimental evidence also shows that mineral grains, whether crystallographically isotropic or not, tend to fracture with respect to stresses across the boundary of the specimen rather than with respect to local stress concentrations at grain contacts (Borg et al., 19605
Friedman, 1 9 6 3, 1964). A conclusion reached by Griggs et al. (i9 6 0, p. 104) with regard to all fabrics produced in experimentally deformed rocks Is particularly appropri ate here: One simple law of sweeping consequences which has been abundantly tested In this and other experimental work concerns the symmetry of deformed fabrics. The geometric symmetry of 12
Figure 1. Photomicrograph of a fluid inclusion surface transecting two adjacent quartz grains differing in crystallographic orientation without changing direction. Sample N2-3, Pikes Peak Granite. Crossed polarizers.
the fabric in a strained crystalline aggregate is the same as that of the strain in the body. The unimportant role played by crystallographic orienta tion and mineralogy in the control of microfracture orientation in deformed rocks is, then, more than a mere assumption^ it is a conclusion deriving considerable support from experimental work. 13
Microfractures and Stress Magnitudes
Only a few experimental studies have yielded infor mation on the magnitudes of principal stresses and prin cipal stress differences required to produce micro- fracturing in various rocks under different conditions of load. Most experimental studies of fracture end with failure of the specimen, but microfracturing takes place under loads considerably less than that required to pro duce macroscopic failure. Bombolakis (1 9 6 3) investi gated the behavior of a "Griffith crack" in a photo elastic model and found that the crack would propagate in a direction dictated by the macroscopic stress field until it reached a stable orientation. Continued growth of the crack took place only when significantly larger loads were applied to the material.
Friedman (1 9 6 3) has obtained some experimental values of differential and confining pressure required to pro duce microfractures in a calcite-cemented sandstone. He observed first that uniform pressure (hydrostatic) alone does not cause fracturing. Then he varied confining pressure and axial loads on his samples and found that no microfractures appeared in a specimen subjected to a differential stress of ll6o bars at 1000 bars confining 14 pressure whereas fractures did appear when the differen tial stress was raised to 1 6 9 0 bars at 2 0 0 0 bars confining pressure. Working at much higher stress levels, Bridgman
(1 9 5 2, p. 1 0 8) produced tensional fractures in glass with a differential stress of 14,500 bars and a confining pressure of 2 5 ,2 0 0 bars. Many more tests of this type are needed to provide quantitative data on the loading conditions in compression necessary to produce microfractures in rock. Future re search should also consider the influence of temperature, pore pressure, and strain rate on the threshold level of microfracturing. However, the two studies cited above are most important because they prove that fractures form and propagate in stress fields that are macroscopically compressive, as predicted by the Griffith theory. The only restriction on microfracture development in brittle crustal or upper mantle rocks is that the ratio of differ ential to confining stress reach some critical value. Under conditions of uniaxial tension, microfractures form at much lower stress values. Applying the McClintock-
Walsh (1 9 6 2) modification of the Griffith theory, Brace (1964) found close correspondence between calculated and observed tensile strengths of marble, quartzite, granite, and diabase rocks. The tensile strengths Brace observed
ranged from about 5 0 to 400 bars, and microfracturing pre- 15 sumably would begin at somewhat smaller stresses. It appears likely that macroscopic tensile stresses large enough to cause microfracturing can occur at great depths in the earth's crust. Secor (1 9 6 5) combines Griffith and Mohr failure envelopes into a composite failure curve for crustal recks. Then assuming the pre sence of fluids under pressure in Griffith cracks, he derives expressions for the maximum depth at which ten sion can exist in the crust and tensional failure of crustal rocks can occur. Depending on the tensile strength of the rocks and the ratio of fluid pressure to overburden weight, the curves show that tensional fractures can form at depths of a few tens of thousands of feet.
Persistence of Microfractures in Time
If microfracture orientations are to be related to present-day principal stress directions we need to know something about their persistence in time. Many rock bodies have survived a number of tectonic events, each of which could have impressed its characteristic micro fracture pattern on the rocks. If each set of micro fractures remained intact indefinitely it would be ex tremely difficult, perhaps impossible, to recognize separate fracture patterns. However, there Is abundant evidence that natural processes do operate to seal the 16 tiny fractures. Healed microfractures are commonly ob served in thin sections of brittle rock, as are micro fractures filled with secondary minerals which have a ~ composition different from that of the fractured grain. To these should be added surfaces of fluid inclusions, which have been interpreted as microfractures that are healing in successive stages (Tuttle, 19^-9; Wise, 1964). At the present no quantitative statement about micro fracture longevity can be made. However, it is unlikely that such small fractures can remain open for long periods of geologic time. Water, at least in small amounts, is present in all rocks at all depths, and it can serve as a medium for migration of ions along fracture surfaces. The length of time required for a fracture to heal would depend on such factors as the spacing between fracture walls, rates of chemical activity, and so forth. At in creasing depths in the earth fractures should seal at faster rates because the space between fracture walls de creases as confining pressure increases, and most chemi cal reactions proceed at faster rates as temperature is increased. The procedure followed in the present study is to consider the open (unfilled, unhealed) microfractures as a discreet subfabric of the rock. In this way one can reasonably expect to find a distinct fracture pattern i that is related to some recent tectonic event. 17
FIELD METHODS
Field work was accomplished during the summer of 1 9 6 3 and the summer and fall of 1964 while the writer was a member of a U. S. Bureau of Mines team making in situ stress determinations through the use of stress relief techniques. Locations visited during the summer of
1 9 6 3 included mines at Iron Mountain, Viburnum, and Pea Ridge, Missouri; Hutchinson, Kansas; Moab, Utah; and the North American Air Defense (NORAD) Combat Operations Center (COC) at Colorado Springs, Colorado. Measurements were made in mines at Lyon Mountain, New York, and Bar berton, Ohio in the summer of 1964, and in rock quarries in the vicinity of Atlanta, Georgia In the fall of 1964. This report is primarily concerned with data gathered at the test sites in Colorado and Georgia because field and laboratory studies of the rocks at these localities yielded the best results. At each locality the writer collected oriented cores from the stress relief holes. Oriented thin sections were prepared from these at points ranging from 1 to 4 Inches distant from the points of strain measurement. Triaxial tests of the cores by the U. S. Bureau of Mines provided values for the elastic constants used in calcu lating stresses from measured strains. 18
To the extent that time permitted, the writer also recorded data on local macroscopic structural features for comparison with data from in situ stress determina tions and microscopic work. In situ determination of stress by relief techniques is accomplished by isolating a specimen of rock from its surrounding stress field and recording its response to the release of stress. Two fundamentally different methods were used in this project. Each is described in some detail below.
Borehole Deformation Method
The borehole deformation method, first developed by
Hast (1 9 5 8) from 195^ to 1958* consists of measuring diametral changes of a small diameter borehole that is overcored (trepanned). In 1958 and 1959 ihe U. S. Bureau of Mines developed a similar method (Merrill and Peterson,
1 9 6 1; Obert.et al., 1 9 6 2) that is used in this study. Briefly it consists of the following steps (figure 2): 1) An EX (1.5-inch diameter) hole is drilled horizontally
a distance of 10 to 30 feet. 2) A borehole deformation gage capable of measuring small changes in a single diameter of the EX hole is placed at a depth of about 6 inches in the hole and oriented 19
so that a diameter 3 0 degrees counterclockwise of horizontal is measured.
3) A 6 -inch diameter hole is drilled coaxially around the EX hole as diametral changes in the latter are recorded. Overcoring is stopped when further drilling produces no additional change in diameter of the EX hole. This occurs within an inch or two beyond the sensing element of the gage.
4) The gage is advanced 5 to 6 inches in the EX hole., oriented vertically, and again overcored. 5) Step 4) is repeated with the gage oriented 60 degrees counterclockwise of vertical. The three separate measurements, made over a dis tance of about 18 inches, are considered to be in the same plane for calculation purposes. These deformations are related to the biaxial stress field in a plane per pendicular to the axis of the hole by the following equa tions (Obert, 1 9 6 2, p. 52):
ai+ = H [ ( U1-U2)2+(U2-D3)S+( V U1>2]4 (2) where <7^ and are the greatest and least principal stresses in the plane perpendicular to the axis of the borehole; E is Young’s modulus of the rock; d is the 20 Borehole Deformation Gage A*6-inch / ~ ! diameter relief hole EX pilot hole / Steps 1 and 2 Step 3 Figure 2. Illustration of the borehole deformation method of in situ stress determination* diameter of the EX hole; U^* U2* and are borehole defor mations at 6 0 degree separations; and 9 is the angle be tween Cl^and Uj in a clockwise direction. (7 and E are given in psi* d in inches* and U in microinches per inch j/fin./in.)) The solution above is based on a theoretical solution for the deformation of a circular hole in an infinite* iso tropic* elastic plate. The result has been verified by laboratory experiments using rock models (Merrill and Peterson* 1961). Since three deformations are measured over a hole distance of 15 to 18 inches* the point of stress determination is taken at the position of U2. The borehole deformation gage has a strain sensitivity of 20 /din./in. If used in rock having a Young's modulus of ' £ 1 about 3X10 psi* it will have a range of about 29*000 psi 21 and a sensitivity of about 13 psi. It can be used in holes oriented vertically downward to those inclined up ward at an angle less than about 30 degrees. At the present time it has not been used in holes deeper than 1 0 0 feet, but its use is not limited to this depth. Core Deformation Method Field Procedure. The core deformation method of in situ stress determination is performed as follows (figure 3): 1) An NX (3-inch diameter) hole is drilled to the point at which a stress determination is desired. 2) The back of the hole is faced smooth with a diamond facing tool and washed clean. 3) The hole is dried with an electric drying pistol capable of delivering 25 cubic feet of air per minute at 80 degrees centigrade. 4) Epoxy cement is applied to the periphery of a photo elastic gage of 1 .2 5 to 2 .1 2 5 inches diameter and the gage is cemented to the smoothed back of the hole. The back of the gage is not coupled to rock. Strains in the rock are integrated across the diameter of the gage. 5) After the cement has set (12 hours in this investi gation) the gage is overcored with a thin-wall NX diamond coring bit to a depth of 4 to 5 inches. 21,3 ,3-inch diametei Photoelastic ,Stress relieved/ /.borehole ''Strain gage // v 'z. / / > x / Epoxy Cement Steps 1, 2, 3 Step 1; Step 5 Figure 3. Illustration of the core deformation method of in situ stress determination. 6 ) The core is broken from the hole and the strain pattern induced on the photoelastic gage is recorded by sketch. In horizontal holes flowage of unset cement provides a vertical reference mark on the core. Figure 4 is a photograph of the drilling equipment and * figure 5 shows an unrelieved photoelastic gage cemented on the smoothed back of a 6-inch deep NX'hole. No attempt was made in this study to use photoelastic gages in holes inclined downward. In order to obtain a satisfactory bond between gage and rock it is absolutely necessary to maintain a dry hole as the cement sets, a virtually insurmountable task in holes inclined downward. Hlgh-humidity cements and those which set under water were developed after the completion of the field work. These should be evaluated in future studies. 22 % Figure 4. Stress relief drilling equipment. Figure 5. Photoelastic gage mounted on the smoothed back of a 3-inch diameter hole. 23 Experience with field mounting of the gages showed that the best results could be obtained by using a 1 2- hour pre-pack epoxy cement. About 25 minutes after mixing it stiffens sufficiently to adhere in a thick fillet to the periphery of a gage as the gage is pushed to the back of the hole. Preset times of greater than about 45 minutes resulted in inadequate bonds. Immediately before overcoring, the gages are viewed with a borehole polarlscope to insure that no strains have developed in them (figure 6 ). Figure 6 . Borehole polariscope designed by Pincus (1 9 6 6, p. 8 9). The instrument is essentially a reflecting polariscope. It contains all the elements of a standard photoelastic bench and, in addition, a telemicroscope for im proved viewing of gages at remote distances. 24 In no instance were any such complicating initial strains recognized. The gages are then overcored and the core stub with attached gage is removed from the hole so that the strain patterns can be closely studied. It is essential that the patterns be recorded at the Immediate test site to avoid the effects of changes in temperature and humidity on the gages, should they be removed to different environ ment . Experience shows that normally the patterns are fully developed within 15 minutes after overcoring. The setting time of the cement and the distance at which the gages can be viewed in the borehole set a limit, as yet undetermined, on the depth at which reliable measurements can be made with photoelastic gages. In this study the most remote gage was mounted 1 0 9 inches from the collar of the hole; it Is doubtful with our methods that the limit can be extended to more than 20 feet. Photoelastic Gages. Two types of photoelastic strain gages were used in the field. Both consist of circular discs of a photoelastic plastic with a reflective backing, and both are mounted by peripheral bonding so that strains are Integrated over the entire area of the gage. A zero- order frozen ring gage developed by Pincus (196 6) is made 25 of a disc of plastic 2 .1 2 5 inches in diameter and 0 . 0 8 inches thick. It contains a centrally located "0"- order birefringent ring 0.75 inches in diameter. As the gage is strained in a uniaxial or biaxial stress field the ring deforms into an ellipse. Principal strain directions are given by the directions of the ellipse axes and strain magnitudes are obtained by measuring diametral changes and observing interference color changes of the frozen rings. Calibration tests by Pincus (1 9 6 6* p. 9 5) show that the gages clearly indicate strains as small as 24^tin./in. The other type of gage used in the study is avail able commercially (Budd Co.* 1 9 6 1). It consists of a photoelastic disc 1 .2 5 inches in diameter, 0 .1 2 5 inches thick, containing a central hole (figure 5). The gage contains concentric first and second order frozen bire fringent rings which deform into ellipses as the gage is strained. Displacements of the rings from reference circles scribed on the gages are measured and converted to strains through the use of calibration curves supplied by the manufacturer. The company claims that strains can be read to 40y«tin./in. and principal strain directions, which are coincident with the symmetry axes of the ellipses, can be read to within 5 degrees. Principal strains given by both types of gages can 26 be converted to stresses by use of Hooke's law as follows: °1 = -^ 2 ^ 1 + £2) ^ °2 = + where 0 ^ and CT^ are maximum and minimum principal stresses, and are maximum and minimum principal strains, E is Young's modulus for the rock, and jjl is Poisson's ratio for the rock. Both types of gages performed well in the field, but the thinner gages were more subject to failure of the cement bond than were the thicker ones. The difference in behavior can be attributed to the fact that thicker gages retain a thicker fillet of cement on their periph= eries and thus become more securely bonded to the struc tural member. LABORATORY METHODS Oriented thin sections were prepared from specimens collected in the field. The cores were sectioned so that the plane of each thin section was oriented perpendicular to the axis of the hole. Selected specimens were sectioned in three mutually perpendicular directions. Laboratory work on the thin sections and field data included the following: 1) Compositional analysis of representative specimens. 2) Recording of microfracture data from all specimens. 3) Recording of quartz c_-axis orientations in selected specimens. Construction and analysis of petrofabric diagrams of directional data obtained in the field and laboratory. Compositional Analysis Identification of mineral species was accomplished by the use of standard optical techniques. Grain per centages were obtained by visually estimating the area covered by each species in the thin section. 27 28 Recording and Error Analysis of Microfracture Data Orientation of microfractures was carried out on Leitz 5-axis and Zeiss 4-axis universal stages. Only two axes need be used, (inner vertical) and A 2 (N-S horizontal) or A^ (E-W horizontal). Because the largest number of fractures occurs in quartz and feldspar grains of about 1 .5 2 to I . 5 6 refractive index, hemispheres of index 1 .5 5 5 were used throughout the study. Microfractures, which will be described in deatil in a later section, were oriented parallel to the north- south crosshair by rotation on A^. The slide was then rotated on A 2 until the fracture appeared as a fine, distinct line. Rarely did a fracture deviate more than 3 degrees from a planar surface, so that approximation of plane orientations resulted in negligible errors of the type described by Tuttle (1949). Scale readings were recorded on a specially prepared form which provides col umns for additional items such as the stage coordinates and the mineralogy of the grain containing the fracture, the mineralogy of the fracture filling, if any, and the class of the microfracture. Replication of measurements showed a precision of 2 degrees for fracture strike and 3 degrees for fracture dip. The procedure followed in this study was to record 29 every microfracture or set of closely spaced microfrac tures appearing in a slide in traverses spaced 2 mm apart. The number of microfractures visible in a section depends on the magnification used* and the writer chose 50X as a standard because that gave 5 0 to 5 0 0 per thin section, a number normally regarded as sufficient for statistical analyses of this type. The diameter of the field of view was 1 . 8 mm so that adjacent edges of fields of view in the separate traverses were separated by 0.2 mm. Long fractures were measured and recorded in each field of view in which they appeared. There are several sources of error involved in ob taining valid quantitative representation of fractures lying in various positions within the slide. If the frac tures are preferentially oriented in one direction the angle at which the section is cut with respect to this direction will influence the count of fractures. Refer ring to figure 7 , the horizontal lines represent a set of preferentially oriented fractures and the inclined lines represent an edge view of a thin section. Let n be the total number of fractures“and 9 be the angle between the direction of preferred orientation and the plane of the thin section. Then the maximum number of fractures in tersected by a section of orientation 9 is: nQ oc n sin 9 (6 ) 30 Figure 7* Two-dimensional representation of the influence of thin section orientation on the number of microfractures that will appear in a given section if microfractures are pre ferentially oriented. Horizontal lines represent a set of preferentially oriented fractures. Inclined lines repre sent thin section orientations. The effect of this error can be decreased by recording data from two or more thin sections cut so that their planes intersect at a high angle. Petrofabric diagrams are then prepared for each set of data3 and the points for one section are rotated into the projection plane of the other. The two or more sets of data are then combined into a single petrofabric diagram. But even three mutually perpendicular sections will not insure a truly representative sample. Assume the hypothetical case of a sample containing n preferentially oriented fractures and n randomly oriented fractures, all of which transect the entire sample. A section cut parallel to the preferred direction would expose to view nearly n randomly oriented fractures (those parallel to the section cannot be seen) whereas two sections cut perpendicular to the plane of the first section and to each other would each expose nearly 2n fractures whose orientation in the domain would be properly represented, that is nearly n random and exactly n of the preferred orientation. A plot of these three sets of data com bined into a single diagram would consist of 5n (nearly) points, 3n of which represent the random set and 2n the preferred set. Sample bias has reduced the true abun dance of preferentially oriented fractures from 5 0 per cent of the sample to only 40 percent. The only way to avoid such a sample bias would be to record data from several sections cut in different directions. Prom the standpoint of time and tedium, few investigators may be willing to make such a sacrifice. The writer is not aware of any investigator who system atically combines data from more than three sections of different orientation; in fact he knows of only a few investigations where data from two or three mutually perpendicular sections have been combined. The irony of the situation is that the largest errors of this type arise where strong preferred orientations exist, and it is strong preferred orientations which one hopes to recognize. Part of the present study is an attempt to relate the orientation of open microfractures to directions of principal strain in rock cores, the strains being meas ured in a plane perpendicular to the axis of a borehole. For this special case of plane strain, fracture orienta tion data were obtained from single sections cut in the same plane in which the strain measurements were made. Where microfractuxe orientation data are compared with orientation data from other larger 3-dimensional struc tures, combined plots of data from two or more thin sec tions from planes intersecting at a high angle were used. Another source of error arises from the fact that tilts greater than 50 to 5 5 degrees are not mechanically possible on most universal stages, so that orientation of fractures lying within 35 to 40 degrees of the plane of the thin section cannot be measured. Furthermore, it becomes increasingly difficult to recognize fractures whose orientations approach the plane of the section and these tend to be eliminated from the fracture count. Plots of such data on an equal area net show a lessening of point density toward the center of the diagram (Borg et al., i9 6 0, p. 171). Errors due to these effects can 33 also be decreased by recording data from two or three perpendicular sections from a sample and rotating the data into a common reference plane. Frequent tilting on a horizontal axis as the slide is traversed will also aid in making visible and measurable those fractures lying near the plane of the section. It is important to recognize that any variation in strike of a fracture as viewed in a horizontal plane would be an equivalent variation of dip when the fracture is viewed in a vertical plane perpendicular to the strike direction. Where abrupt changes in strike occur over short distances in a thin section considerable error in dip measurement should be expected. Increased accuracy in dip measurements could be achieved through the use of sections thicker than standard size sections (0 .0 3 mm) so that the dip could be averaged over a greater distance. Harper (1 9 6 6), for example, worked with sections 0.06 mm thick. Sections of standard thickness were used through out this study. Even so, variations in dip of individual microfractures are probably small because in these sec tions abrupt changes in strike direction are rare, and variations in strike along a distance of 1 mm rarely exceed 2 degrees. Recording and Error Analysis of Quartz £-Axis Data Quartz c-axis orientations were measured on selected samples. Data were obtained on each grain larger than about 0 . 1 mm diameter that intersected the crosshairs on 1 mm traverses. Tilting of the thin section introduces errors due to refraction that increase with the tilt angle. However, the error correction (1.25 degrees for tilts of 45 degrees^ Turner and Weiss, 19^3> P- 205) is within the range of operator error so that this source can be ignored. The position of the axes plotted on equal area nets is considered accurate within 3 degrees. Petrofabric Diagrams All petrofabric data were plotted on transparent overlays to a 20 cm diameter equal area net. The ter minology used in this report follows that of Friedman (1964, p. 463): Partial diagram - illustrates data from one given field of observation. Composite diagram - contains data from more than one field of observation on the same sample. Synoptic diagram - shows data from a number of separate samples. The term combined diagram is used in this report for a 35 diagram illustrating data from two or more samples in the same field of observation. Although time can be saved by plotting data directly as the universal stage settings are obtained, this pro cedure was not followed because it was desired to record more data for each microfracture than could be conven iently color coded and plotted on a single diagram. Instead the data were first recorded on specially pre pared columnar forms, as described previously, and later plotted on transparent sheets overlying an equal area net. All the partial diagrams of poles to microfractures contain central "blind spots" due to the impossibility of measuring the orientation of fractures inclined less than about 40 degrees to the plane of the section. These blind areas do not seriously affect comparisons of micro fracture directions with the direction of principal stresses as determined in situ in this study because thin sections were cut in the same plane in which 2- dimensional in situ stresses were determined, namely the plane perpendicular to the axis of the stress relief hole. However, the blind spot must be eliminated when micro fracture data are to be compared with other three-dimen sional data. This is accomplished by preparing a com posite diagram. Data from a second thin section oriented 3 6 perpendicular to the first are rotated into the stereo- graphic projection plane of the first to fill its blind spot. The rotation procedure presents yet another problem - that of insuring that all areas of the composite diagram have equal opportunity for claiming points. There is danger that this goal will not be reached if one rotates all the points from the second section that fall in the blind area of the firsts because the second section may contain significantly more (or less) fractures than the first. Ingerson1s (Knopf and Ingerson, 1938* p. 233) method of determining the proper number to rotate is to plot points from the second section in the blind area of the first until the same number of points from each dia gram fall on the measurable area that is common to both. The resulting diagram is then contoured. Using Ingerson's method, the concentration of points in the blind area of the first diagram will depend partly on the number of points from the first section that fall in the area common to both sections on the composite diagram. There is no assurance that an identical com posite diagram would be obtained if the procedure were reversed and points from the first section were rotated into the projection plane of the second section. In this study the writer used a new procedure which gives the same composite diagram regardless of which 37 partial diagram is rotated. All points from a second section perpendicular to the first are rotated into the plane of the first. The resulting composite diagram then contains three separate areas, the two areas con taining points from each of the individual sections alone and an area containing points from both sections (Figure 8). Each area is contoured separately to allow for the fact that a single point in each area represents a different percentage because of the difference in total number of points available for each area. Con tours are then linked across adjacent areas. Composite diagrams made from three mutually per pendicular sections are prepared in the same way. These are more difficult to count out because the net then con tains four areas which must be contoured separately. If more than three partial diagrams differing in orientation are combined, it would be advisable to reduce the size of the counting circle to less than 1% of the area of the net because the diameter of a 1$ circle may exceed the width of large parts of the areas to be counted out separately. Points on the diagrams constructed in this study were counted out with a 1 percent ( 2 cm diameter) point counter on a 1 cm square grid according to the Schmidt method (Schmidt, 1925, p. 392-423). The zero contour T Area wit points from diagram A, only ' ' ‘ L L L Area with Area with points from Area with points points from diagrams from diagram B, only diagrams A and B A and B Area. rrrrr with points from diagram A, Figure 8 Composite diagram consisting of data from two perpendicular sections from the same sample, both of which contain cen tral blind spots of IiO degrees radius. Diagram B is rotat ed in to the reference plane of diagram A. line was generated by a compass; the remaining lines were first contoured mechanically and then smoothed. Accurate counting methods (Knopf and Ingerson, 1938, p. 249; Friedman, 1964, p. 465) were used to determine the posi tion of the maximum contour. MICROFRACTURES Definition In this study the term microfracture refers to any curved or planar microscopic surface in rock* excluding surfaces of distinct mineral cleavage, along which there has been an obvious total loss of cohesion. The defini tion differs from that of Friedman (19^3> p. 15) which restricts the term to: ...a fracture or fault within an individual detrital grain. The scale of the feature is determined by the grain size. The definition includes both intergranular and intragranular fractures and fractures occurring along grain boundaries. It does not include the planar frac- ture-like surfaces described from impactites (Carter, 1 9 6 5, p. 7 9 9), since these do not show an obvious total loss of cohesion. Surfaces of mineral cleavage are ex cluded from the definition because these are distinctive features that have long been studied, defined and dis cussed in great detail. Separate reference to mineral cleavage in fracture studies presents no great inconven ience. 40 41 Microfractures should not be confused with micro- joints (Wise* 1964, p. 2 8 7) which, according to defini tion, are macroscopic subparallel fractures spaced closer than 3 mm* In the present study directional data on mineral cleavages are not included with that on microfractures. Cleavage planes occur along directions of distinct weakness in a mineral, therefore their orientation is determined primarily by the structural orientation of the mineral and only secondarily by principal strain directions. Description Under the petrographic microscope microfractures are visible in both dark and bright field illumination. Phase contrast illumination enhances very thin fractures and those lying near the plane of the section. It is also useful in distinguishing healed microfractures from quartz deformation lamellae (Carter and Friedman, 1 9 6 5* p. 764). For routine work with microfractures the best results are obtained by viewing the sections between crossed polarizers. Three types of microfractures are distinguished in this study - open, healed and filled. Open microfractures 42 have no secondary mineral matter deposited along them. Healed microfractures are those that have been resealed by secondary growth of like mineral matter in optical continuity with the host grain (figure 9 )« In accord ance with the conclusions of Hicks (1884), Tuttle (1949) and Wise (1964), planes of fluid inclusions are regarded as healed microfractures. Pilled microfractures are those along which has grown an unlike secondary mineral (figure 1 0), or a like secondary mineral not in optical continuity with the host grain. Fracture fillings are rarely wide enough to permit positive identification of the fill material by optical means. In the present study low and high blrefringent minerals were found as fracture fillings. The NORAD granite samples showed these two types of fracture fill ings.plus fluid inclusion planes and open fractures, suggesting a deformational history of at least four events. Rocks from the Atlanta, Georgia, area contain only low birefringent material as fracture fillings. Fluid inclusion planes are present, some filled with liquid, but open microfractures are the most common planar feature. The age relations of the several frac ture systems are discussed in later sections that treat the geology of each region. The presence of healed microfractures and planes of Figure 9* Partially healed microfracture in a quartz grain. Upper left section of fracture remains open. Lithonia gneiss, sample AM-1. Crossed polarizers. Figure 10. Microfracture filled with a material having high birefringence (calcite?). Fracture cuts across three quartz grains of different crystallographic orientation. Pike's Peak granite, sample Nl-1. Crossed polarizers. fluid inclusions appear to exert an influence on the orientation of microfractures that form later. Open microfractures sometimes appear as continuations of fluid inclusion planes (figure 1 1)* and occasionally they occur within a healed fracture. Par more commonly* however* open microfractures intersect previously formed fractures and terminate there or continue across them (figure 1 2). Figure 11. Quartz grain containing a fluid inclusion plane (lower center) which continues as an open microfracture (upper center). Lithonia gneiss* sample AM-1. Crossed polarizers. 45 Figure 12. Plagioclase grain containing open micro fractures and planes of fluid inclusions. An open microfracture (lower center to upp&r right) cuts across three planes of fluid inclusions while another adjacent to it terminates at an inclusion plane. Pike's Peak granite, sample N2-2. Crossed polarizers. Most of the microfractures observed in this study are contained within a single grain. Some cross grain boundaries, and occasionally one is found that extends through three or more grains (figure 13)* Sets of parallel fractures are common (figure 14). 46 Figure 13- Open microfracture transects four quartz grains differing in crystallographic orien tation without changing its direction sig nificantly. Pike's Peak granite, sample N5-1. Crossed polarizers. Figure 14. A set of three parallel open microfractures in a quartz grain. Pike's Peak granite, sample Nl-4. Crossed polarizers. 47 Frequency of Occurrence Microfractures are abundant in many common rock types and rare in others. The number visible in thin section increases at a geometric rate with increasing magnification. Consequently, if one wishes to obtain meaningful comparisons of microfracture numbers in different samples, it is necessary to survey the rock sections under the same magnification. An enlarge ment of 50 diameters was used throughout the present study. This magnification provides a depth of field great enough to view the fracture through the entire thickness of a standard thin section (0 .0 3 mm), and, for most of the rocks studied here, it brought to view about 5 0 to 5 0 0 microfractures per thin section. Table 1 lists the rock types investigated in this study together with the average number of microfrac tures appearing in 6 0 0 square mm of thin section under a magnification of 50X. The average number is based on counts obtained from four to twelve thin sections per rock type. Individual counts are not absolute numbers of microfractures; sets of short, closely spaced fractures are counted as a single fracture, and long single fractures are counted once each time they appear in 2 mm traverses across the thin section. How ever, the counts are regarded valid for comparative TABLE 1 AVERAGE NUMBER OP MICROFRACTURES IN POUR ROCK TYPES ROCK TYPE LOCATION DEPTH BELOW AVERAGE GRAIN AV. NO. MICRO SURFACE (PEET) SIZE (mm) FRACTURES PER SAMPLE Granite Colo. Springs, Colo. 1375 + 25 2.5 235 Granite Gneiss Lithonia, Georgia 1.0 232 Andesite Porphyry Iron Mountain, Mo. 475 + 10 0.1 (Groundmass) 68 1.0 (Phenocrysts) Limestone Moab, Utah 2630 + 10 0.002 44 -pr 00 purposes because all were made by the same operator. The very small number of microfractures in finer grained rocks is striking. This observation is in agreement with the experimental result of Borg et al. (I960, p. 1 6 6-1 6 8). In samples of unconsolidated quartz grains they found that more fractures occur in samples of large grain size than those of small grain size. The opportunity for yielding along grain boundaries is greater in fine grained rocks, so that stresses may be relieved without fracturing of individual grains. In the case of limestones and marbles, experimental work shows that twin gliding of calcite is a much more im portant yield mechanism than fracture (Turner and Weiss, 19635 P. 3^6). Origin of Microfractures in Extension or Shear Microfractures may form as extension or shear frac tures, but it does not appear possible to determine with confidence the type of failure involved on the basis of features seen in thin sections. Actually some Investi gators now feel that shear fractures may simply be an en echelon array of tensional fractures. (Handin, per sonal communication). Macroscopic extension and shear failure surfaces can sometimes be distinguished in 50 experimentally deformed rock on the basis of features developed on or along the failure surface. Extension fractures are usually quite irregular whereas shear fractures are relatively straight and smooth with slickensides and comminuted material in evidence along the surface. In thin section most microfractures terminate within a single grain and show no evidence of relative movement between fracture walls. Such features do not constitute evidence for an origin in extension because release of shear stress along the fracture walls during shear failure would allow the walls to return to their original unstrained position. A system of en echelon fractures would imply failure due to shear in the en echelon zone, but in the writer’s experience distinct systems of this type are rarely encountered. A survey of the literature of naturally occurring microfractures shows that most authors interpret prin cipal stress directions such that the preferred direction of microfracturing turns out to be perpendicular to the least compressive stress (Carter and Friedman* 1965; Friedman’s 1964 interpretation of Riley’s 1947 data; Naha* 1959). Perhaps the reason for this is that exten- 51 slon fractures tend to form patterns far more clear cut than do shear fractures, as shown in studies of experi mentally deformed rock (Borg et al., 19^0* p. 172j Fried man, 1 9 6 3, p. 3^). Origin of Microfractures During Preparation of Thin Sections To the writer*s knowledge, there are no published accounts of the extent, if any, to which microfractures are produced during preparation of a thin section. A completely satisfactory answer to the question may always elude us because of the impossibility of produc ing by mechanical means a thin section under stress-free conditions. Some fracturing certainly does take place during the grinding and polishing operation. Experienced petrographers are well aware of the mosaic fracture patterns found only in quartz grains that have been thinned to a feather edge at the edges of a thin section. The fractures are actually imperfect rhombohedral cleav age of quartz, as can be demonstrated by a stereographic plot of the fractures and the quartz c-axis. Grinding and polishing are shear phenomena which 52 could produce shear fractures parallel to the plane of the section. However, since such fractures cannot be viewed under the microscope, their existence cannot be confirmed. Grinding could also induce tensile stresses in the plane of the section, and flexing of the section would produce tensile fractures oriented perpendicular to the plane of the section. In the present study it became apparent that signifi cantly larger numbers of microfractures are found approxi mately normal to the plane of the section than in other orientations, regardless of the direction a section is cut from a single sample (plots of poles to the micro fractures form a girdle which lies in the plane of the section). The same effect is noted in the published diagrams of many others. This leads one to suspect that a common process, preparation of the section, is pro ducing fractures of like orientation. However, fractures in this orientation are easier to recognize than those lying nearer the plane of the section, and the phenomenon may be due entirely to the viewing problem. Also, there is such a wide variation in the number of microfractures found in closely spaced samples of the same rock sectioned by a single operator that if some do form as the section is being prepared, quite likely it is a very small number. For example, the count of unfilled microfractures in one 53 sample (N2-1) is 20 whereas in another sample (N2-2) 25 inches from it the count is 246 (plate I). It is reassuring to note that microfracture orien tation data from previous studies are consistent with orientation data from larger scale features (Bonham* 1957; Carter and Friedman* 1965; Naha* 1959; Riley* 19^7; Harper* 1 9 6 6* among others). This result could not be possible* except fortuitously* if significantly large numbers of fractures were produced during prepara tion of the thin sections. It seems reasonable to conclude that if microfrac tures are produced during preparation of a thin section the number is probably too small to affect dynamic in terpretations of counts greater than about 100 micro fractures per section. Origin of Microfractures During Coring of Rock An equally important consideration is the extent to which microfractures form in a core of rock as stresses are relieved during an overcoring operation. Certainly where large strains or strain differences are measured in the core the likelihood of fracturing is increased. Figure 15 is a graph of strain magnitudes measured in cores plotted against counts of open microfractures from samples sectioned within a few inches of the point of 54 strain measurement. Strains were measured by means of the Budd Company Photostress Rosettes which were described earlier. All samples are granite obtained from nearly horizontal holes at a depth of 1 3 7 5 + 25 feet below the surface. Extension strains in the core after overcoring are positive. Although the accuracy of the strain measurements may be questionable, the precision is ex pected to be high because they were obtained from a single batch of gages used under constant environmental conditions. For this reason the data are considered valid for comparative purposes. Figure 15 shows that within the limits of strain measured in these cores there is no consistent correlation between the magnitude of principal strains or principal strain differences and the number of open microfractures. For example, the two samples having the largest and smallest number of micro fractures show very nearly the same magnitudes of princi pal strain and principal strain difference. The lack of correspondence between strain magnitude and microfracture frequency does not necessarily indicate that visible microfractures do not form as the cores are cut; it may simply indicate that under strains of the magnitude measured here so few form that they cannot be recognized against a background of pre-existing fractures. Micro fracture directional data from rocks near Atlanta, Georgia, give evidence of fracture formation due to stress relief 55 Strain Magnitude N*>-2 Nl-it NJ>-U Nl-1 Nl-3 Nl-2 (yu in./in*) -600 -800 lUO 160 180 200 220 Number of Microfractures Figure 15. Frequency of microfractures vs. magnitude of principal strains and principal strain difference. of the cores. The data are presented*later in this report. Microfracture Frequency According to Grain Size and Composition in Polymineralic Rocks A comparison of the amount of fracturing in rocks of different composition and grain size is presented in table 1 and in a short discussion earlier in this section. It is also interesting to compare the amount of .fracturing in various grain sizes and types within single rock 56 samples. To this end the writer surveyed two representa tive thin sections of rock and recorded the number of microfractures occurring in each of 100 grains encountered in random traverses of the section., together with the size and composition of each grain. Figure l6 shows plots of the number of microfractures against grain diameter for three mineral species in a granite (sample Nl-1) and three mineral species in a gneiss (sample RC-6l). It is obvious that the larger grains contain the most fractures* but it would be incorrect to conclude that large grains fracture in preference to small ones. On the contrary* fracture density is seen to increase with decreasing grain size when the number of fractures per unit cross-sectional grain area is plotted against grain diameter for the same samples (figure 17)- This result is similar to the experimental result of Borg et al. (i9 6 0* p. 1 6 6* 1 6 8) who found that the small grain size fraction of a single sample of unsorted* unconsoli dated quartz grains fractured to a greater extent than the large size fraction. Possibly their result would have been even more striking had they compared fracture density per unit grain area rather than number of frac tures per individual grain. It Is possible to construct a theoretical curve for the case where fractures cross grain boundaries and develop 57 Sample Nl-1 (Granite) Quarts Perthite-Kicroclinq Plagioclase 12 2 U 21* 8 16 16 * It * • * * * 8i 8 • {««# S * ^ • i *** ! » • # 4* • 0 jjiii* i > m ■■*■ .iJ . 0 0 1 . 0 2.0 "2T0 570 6 .0 Io & £ Sample RC-61 (Granite Gneiss) Quarts K-Feldspar Plagioclase £ 12 12 8 8 8 • h h 1 . 0 2.0 Grain Diameter (Millimeters) Figure 16. Plots of microfracture frequency vs. grain size for three mineral species in a granite and three mineral species in a gneiss. with respect to the rock as a whole. Here we would expect that a few of the very small grains would contain a single fracture and each of the larger grains would contain many fractures. Because of their small cross-sectional area, increasingly smaller grains cut by a fracture would show increasingly larger values of fractures per unit area. The converse would be true of increasingly larger grains. Figure Number of microfractures per ran2 of grain area 56 1*0 W 6 32 16 2 16 2 U U 8 h 8 17. Plots of microfracture frequency cross-sectional per frequency unit of microfracture Plots 17. Quartz urzPlagioclase Quartz rao ri 3 grain diameter. grain V3. of area Grain Diameter (Millimeters) Grain Diameter Sample RC-61 (Granite Gneiss) RC-61 Sample Sample Nl-1 (Granite) Sample Nl-1 Perth!te-Microcline 16 2 16 2 U 8 h 8 Plagioclase 1.0 Ym 10 2.0 58 59 Such a distribution would plot along a curve of the form y = ax" 2 (7) where is the number of microfractures per unit area of the grain, x is grain diameter, and a is a constant. Choosing larger values of a. shifts the curves upward and to the right, so that larger values of a correspond to samples with larger average grain size. The goodness of fit of these theoretical curves to the data plotted sug gests that fracturing in both these rocks is related to the rock as a whole and not to grains of a certain size range within the rock. The same data are used in table 2 to compare the relative amount of fracturing in different mineral spe cies for each of the two samples. Given in the first column is the percent of total area of the thin section occupied by each mineral species. The second column shows the percentage distribution of total fractures among the various mineral species. If one mineral fractures as readily as another, adjacent figures in the two columns should be about equal. For ease of visualization, these data are plotted in figure 18 and a theoretical curve is drawn to show where points from each sample would lie if fractures were equally distributed among the mineral species. For example, quartz accounts for 20 percent of 60 TABLE 2 COMPARISON OP MICROFRACTURE FREQUENCY WITH GRAIN MINERALOGY Mineral Percent of Percent of Percent of Percent of Total Area Fractures Total Area Fractures Quartz 20.4 2 1 .0 36.3 41.6 K-Feldspar 52.3 41.2 43.5 34.6 Plagioclase 27-3 37-8 2 0 .2 2 3 .8 the total area of the three mineral species mapped in sample Nl-1, therefore it should contain 20 percent of the total microfractures if all minerals show an equal tendency to fracture. The observed point lies only slightly above the theoretical curve, Indicating that quartz contains more than an average number of micro fractures in this sample. 6l Quartz K-Feldspar Plagioclase 60 O liO 20 2020 2 Vl '/ o 60 % Total Area Sample Nl-1 R* Sample RC-61 Theoretical Curve ------ Figure 18. Percent of total microfractures plotted against percent total area occuppied by each of three mineral species for two rock samples. In both samples K-feldspar (microcline, orthoclase, perthite) shows a lesser tendency to fracture than quartz or plagioclase, but the amount of fracturing in each mineral differs no more than about 10 percent from that expected if all mineral types fractured with equal ease. The results are in agreement with Short's (196 6, p. 1206) observation that the average number of fractures in quartz and feldspar grains of a granodiorite shocked in a nuclear explosion are comparable. They are also in accord with Friedman's (1 9 6 3) result that the spacing and orientation of microfractures in an experimentally deformed sandstone are independent of grain mineralogy. It appears that neither grain size nor mineralogy exert much control on fracture frequency in the rocks studied here. Rather the rocks tend to fracture with respect to the whole* not with respect to the units making up the whole. MICROFRACTURES, STRUCTURE, AND IN SITU STRESSES AT NORAD COC, COLORADO SPRINGS, COLORADO A U. S. Bureau of Mines field crew, of which the writer was a member, made in situ stress determinations at the site of the Combat Operations Center (COC) of the North American Air Defense Command (NORAD) during the summer of 1 9 6 3. The site is located in the SW^ of Section 13, T .1 5 S., R .6 7 W., El Paso County, Colo rado, about 5 miles south of Colorado Springs. The excavations are Inside Cheyenne Mountain at an elevation of about 7 1 0 0 feet, approximately 2 3 0 0 feet below and a few hundred feet east of the mountain1s 9 5 6 5-foot summit. These consist of a network of chambers intersecting orthogonally and oriented approximately N.70°¥. and N.20°E. The main chambers are 45 feet wide, 6 0 feet high and 5 8 8 feet long. Pillars between the chambers measure 100 by 125 feet. Figure 19 shows the location of the stress relief holes with respect to chamber geometry. Exploratory work at the site began in 1959 under 63 64 25 50 Ml—I 25 50 Cross - Sectional Views Inches Figure 19. Plan and cross-sectional views of stress relief holes at NORAD COC, Colorado. BDG»Borehole Deformation Gage; PSR* Photostress Rosette; n0"“0-order Fringe Gage. 65 contract with Parsons, Brinckerhoff-Ryan of Denver. During the summer of 1959 Dr. Lawrence Ogden mapped the surface geology and logged cores obtained from nine ex ploratory holes. Excavation began in 1 9 6 1 and reached completion in 1 9 6 3* Reports on the geological investi gations are contained in NORAD COC, Geological Addendum to Definitive Report published by Parsons, Brinckerhoff5 Quade and Douglas, New York, July i9 6 0. The local geological picture given below is derived from this report and from geological observations by the writer. Geological Setting Cheyenne Mountain consists of a mass of Precambrian granite (Pike’s Peak Formation) that has been thrust up ward and eastward over Cretaceous (Niobrara) shale to form a portion of the eastern edge of the Colorado Front Range. Overburden covers the fault line, but calcula tions based on data obtained from exploratory drill holes place the fault at the surface approximately 1 8 0 0 feet east of the chamber area at an elevation of about 7100 feet. The fault strikes approximately north-south and dips west about 40 degrees. No exploratory holes encountered the fault below the chamber area, but pro jection of the fault from shallower depths suggests it 66 passes at least 1 5 0 0 feet below the chamber floors. Ogden (i9 6 0, p. 3) estimates at least 6000 feet of throw and 5 0 0 0 feet of heave along the fault. Two basaltic dikes striking approximately north- south lie above the chamber area. Their thickness varies from about 20 to 40 feet. The upper dike dips about 25 degrees west, passing 3 5 0 to 450 feet above the chambers, and the lower dike dips about 15 degrees west, passing 275 to 350 feet above the chamber crown. The similarity in orientation of these and the major thrust fault sug gests that the dikes were intruded along shear fractures which developed concurrently with the thrust fault. Ogden’s preliminary study of the joints mapped at the surface and in exploratory holes in 195 9 led to the conclusion that the joints are not oriented in a regular pattern and that it would not be possible to predict the orientation of joints in the chamber area (i9 6 0 , p. 4). However, borehole camera studies of a single hole dis closed a conjugate system of joints striking N.4o°-6o°E. and N.10°-30°W. with dips of 60 to 90 degrees (Samuelson, i9 6 0 ) . These preferred orientations were confirmed when, after excavation began, it became apparent that two domi nant sets of nearly vertical joints intersected the chamber area, one oriented N.15°-20°W., and the other N.55°-70°E. (Dr. C. W. Livingston, personal communication). 67 Plans were altered to allow the chambers to follow approximately the bisectrices of the joint sets. Ex cavation also revealed the presence of a 1 0- to 1 5-foot thick basic dike in the chamber area. It strikes approxi mately N.40°E., dips about 70°NW., intersecting the chamber area approximately 1 2 5 feet southeast of the stress relief holes. Figure 20 is a cyclographic diagram of the major structural features described above. According to Anderson’s (1951) method of structural analysis, the principal stress directions at the time of failure were as follows: - horizontal, approximately N.90°E. 0C-, - horizontal, approximately N-S 0“^ - vertical Figure 21 is an equal area plot of poles to 64 joints that intersect the three walls of Chamber A in the vicinity of the stress relief holes. Care was taken to exclude all fresh fractures formed during blasting and excavation of the chamber. Chain-link netting covering the sides, back and crown of the chamber did not allow placement of the Brunton compass on the joint surfaces, and it disturbed the magnetic field near the surfaces. F^r these reasons measurements were made by sighting Figure 20. Lower hemisphere cyclographic diagram showing orientation of major dikes and joint systems at NORAD COC, Colorado. along joint surfaces at distances of 10 feet or more from them. The points are considered to he placed within an error range of + 5 degrees. A great circle plot of a small reverse fault intersecting Chamber A is also shov.Tt on the diagram. The point clusters show two sets of approximately 69 Kl Figure 21. Lower hemisphere stereonet plot of poles to 6U Joints intersecting Chamber A, NORAD COC, Colorado. Great circle shows orientation of small reverse fault inter secting the chamber. Short lines in center of diagram showstrikes of dominant joint sets. Arrows directed inward at periphery of diagram show interpreted direc tion of maximum compressive stress that produced the fault and joints. 70 vertical Joints striking about N.20°W. and N.65°E. These directions are in accord with those of the domi nant sets recognized by Livingston. Assuming both sets formed in the same local stress field, the maximum compressive stress (0 ^) was horizontal and oriented N.22°E., as shown by arrows on the diagram. The reverse fault indicates 0"^ was horizontal and oriented N.l4°E. Thus the two types of surfaces give the same orientation of CT^, within the limits of measurement error. The conjugate sets of Joints would place CT^ in a vertical position whereas the fault would require CT^ to be vertical. Assuming the fault and the Joints formed concurrently, this discrepancy may simply indicate that the magnitude of 0"^ was nearly that of C"2 so that locally the two may have exchanged positions. The considerable difference in orientation of principal stresses obtained for these smaller features and the orientation obtained for the large features (Figure 20) suggests the occurrence of two deformational events, the latter forming the fresh Joints. Petrography The main rock mass is a coarse-grained, pinkish-gray, biotite granite. Locally it is a quartz monzonite con sisting of about 35 percent microcline and orthoclase, 35 71 percent albite and oligoclase, 20 percent quartz, and 10 percent biotite. Monazite, apatite, zircon, chlorite, epidote, carbonate minerals, pyrite and magnetite occur as minor accessory minerals. The rock has no distinct megascopic structural characteristics. The average unconfined strength of the fresh rock, as determined by the Hock Mechanics Laboratory, Colorado School of Mines, is about 13,800 psi in compression and 1000 psi in tension. The conditions of the test are not stated in the report. Similar tests run by Obert (i9 6 0) on cores from the chamber area showed an average uncon fined compressive strength of 2 3 ,3 7 3 psi and an average flexural (tensile) strength of 2584 psi. These tests were performed according to ASTM tentative standards which require that a specimen with a width to height ratio of 1 .0 be loaded at a rate of 10 0 psi per second until failure occurs. Epis (i9 6 0) investigated the fabric of six samples of the NORAD granite. He found that 251 poles to {ooi} cleavage of biotite grains showed no preferred orienta tion. His synoptic diagram of 374 quartz c-axes orienta tions shows a rather diffuse girdle crossing the center of the net and trending N.26°E. Figure 22 is a synoptic diagram of 6 2 7 quartz c-axes in samples N2-4 and N5-4. Data from each sample have been rotated into a horizontal 72 N Figure 22. Lower hemisphere, equal area diagram of 627 quartz c-axes In samples N2-U and N^-U. Contours at 1%, 2%, and 1$ per l£ area. plane for ease of visualization. The diagram shows a poorly developed girdle trending about N.30°E., or in approximately the same direction as the one shown by Epis. The writer tested the distribution of his own orientation data for isotropism by means of the Poisson 73 Exponential Binomial Limit. A description of the pro cedure is given in the following section on microfrac tures. The results indicate that the probability of ob taining a 2 percent contour on this diagram, if the data are samples of an isotropic population, is 0 .0 2, or two chances in 1 0 0 , while the probability of obtaining a 3 percent contour is 0.00003. Statistically, then, the quartz c-axes do show a preferred orientation. However, the significance of a preferred orientation with regard to strength isotropy may not be great because quartz tends to fracture with respect to principal stress direc tions rather than with respect to crystallographic direc tions (Friedman, 19^3; Borg et al., i9 6 0). Ogden (i9 6 0, p. 13) studied strength data on individ ual samples of the NORAD rock and found that sample strengths showed no relation to the orientation of fabric elements, as determined by Epis, or the orientation of the samples with respect to geographic coordinates. He therefore concluded that fabric is of little importance in determining the strength of the rock. There is no known anisotropy of the rock with respect to elastic properties. No tests were performed specifi cally to identify anisotropy, but the absence of pre ferred orientation in the mica subfabric and the lack of consistent differences in strength of the rock with direction (Ogden* i9 6 0* p. 1 7* app. II) constitute nega tive evidence for isotropy. Inhomogeneity of the rock is evident from the wide variation in strength of closely spaced samples. Unconfined compressive strengths ob tained by the Colorado School of Mines Rock Mechanics Laboratory for 36 samples ranged from 3 8 5 8psi to 19*200 psi. If samples of only fresh, sound rock are considered the range is reduced from 8 2 5 2psi to 19*200 psi. Obert tested 23 samples from a 1 5 0-foot interval in a single core hole. He obtained unconfined compressive strengths ranging from 15*797 psi to 29*204 psi. In Situ Stress Determinations Strain measurements at N0RAD were accomplished through the use of the U.S.B.M. borehole deformation gage (Merrill and Peterson* 1961; Obert et al.* 1 9 6 2) and photoelastic gages designed by Pincus (1 9 6 6) and the Budd Company (1 9 6 1). Descriptions of the methods are given in an earlier section of this report. The measurements were made in July 1 9 6 3* more than two years before the first theory for a solution of all components of the ground stress tensor from borehole relief measurements was developed (Panek* 1 9 6 6; Gray and Toews* 1 9 6 7). Unfortunately the orientations of the 75 NORAD relief holes were not chosen in the most propitious mutual directions. For-this reason, together with others discussed below, the ground stress tensor cannot be solved from the data obtained. At best, one can hope to compare the results obtained for stresses in a plane perpendicular to the direction of the borehole. The plan at NORAD was to place gages of a single type in stress relief holes drilled into a body of essen tially uniform rock. Pairs of holes were to be closely spaced and nearly parallel in orientation so that each would interrupt approximately the same stress field (figure 1 9 )* In this way the two dimensional field cal culated from strains measured by each type of gage could be compared. The difference in stress concentration at the flattened end of a borehole where photoelastic gages are mounted and the concentration along the axis of the bore hole deformation gage pilot hole is taken into account by applying a stress concentration factor. No theoreti cal solution for stress concentration at the back of a borehole has been obtained, but Galle’s (1959) photo elastic analysis of stresses around the end of a borehole and Leeman's (1964) experimental work show that the principal stresses here are greater than the ground stresses by a factor of 1.53* In the case of the bore 76 hole deformation gage the equations relating diametral changes of the EX (1.5 in* diameter) pilot hole to in situ stresses (Merrill and Peterson* 1 9 6 1) give the magnitude of these stresses directly; no stress concentra tion factor need be applied. The disturbing influence of a hole in an elastic body on the pre-existing stress field is* according to Saint-Venant1s principle* negligible at distances which are large compared with the radius of the hole (Timoshenko and Goodier* 1951* p. 7 8). Generally the amount of dis turbance is considered insignificant at a distance of about 1.5 diameters from the edge of the hole. All strain measurements in the present study were made at distances greater than two diameters from an adjacent relief hole (figure 1 9)* None of the photoelastic patterns obtained at NORAD are perfectly symmetrical* but only two gages yielded distinctly asymmetrical patterns. The asymmetry is attributed to a change in direction of principal strains over the diameter of the gage (Budd Co.* 1 9 6 1* p. 11). Displacements of fringes on the gages were measured on all four semi-axes of the ellipse* and the two measure ments corresponding to one principal strain were then averaged. A more perplexing problem arose in two in stances where redundant strain measurements on a single gage did not agree. Measurements of the displacement of any visible fringe, first, second or higher order, should give the same (redundant) principal strain magnitude, but two gages from hole N1 did not perform in this way (see table 3). The differences in strain magnitude given by two fringes are too large (220 to 3 5 0y«in./in.) to be due to errors in measurement (+50ytd,n./in.) The cause of these errors is not known. Measurements of displacement of the first fringe are considered most accurate, and these were used to calculate the stresses shown in figure 2 3. Table 3 presents strain data obtained at the NORAD site through use of Budd Company photostress rosettes. The writer was not able to obtain strain magnitudes from any of the six "0"-order frozen ring gages installed at NORAD. Three of the gages, N2-3-. N2-4, and N5-3 separated from the core before their strain patterns could be recorded, and deformation of the central ring on the others was too slight to record. However, interference color bands inside the ring were sufficiently well developed to obtain secondary principal strain directions. Sub sequent experience with these gages in the laboratory led to excellent results, and the writer is confident the "Cf’-order gages will, when properly installed and interpreted, yield excellent results in the field as well. TABLE 3 PHOTOELASTIC STRAIN GAGE DATA, NORAD COC, COLORADO Gage Distance from Max. principal Min. principal No. collar (inches) strain (^cin,/in.) strain (^/cin./in.) Nl-1 35 2 8 0(-7 0 )b -550 Nl-2 57 130 -3 0 0 Nl-3 81 -l80 -790 Nl-4 94 400 (l8o)b -6 7 0 N5-2 48 0 -410 N5-4 106 150 -390 a Extensional strains in the core are taken as positive so that compressive in situ stresses will appear positive without a change in sign. b Values in parentheses are redundant strains obtained by measuring displacement of second order fringe on Photostress Rosettes. oo 79 Stress (psi) y 2000 [vertical Vertical 20 40 60 eo ICO tz.0 40 60 60 trv 120 so I BOO Vertical Vertical P% 3} H6>f soc 1300 DOC 6 00 1------— «----- 1---- -* - 4 . 3 0 O 40 60 80 ICO HO Distance from collar of hole (inches) Max* Principal Stress Min. Principal Stress Figure 23. Secondary principal stress magnitudes and directions at NORAD COC, Colorado. 8o Stresses calculated from the Budd gage data (equations 4 and 5) are given in figure 23 along with stresses cal culated from strains measured with the borehole deforma tion gage. Obert (personal communication) provided laboratory data on NORAD cores from which elastic con stants for the rock were determined. A stress concentration factor of 1.53 (p* 75) has been applied to the photoelastic data so that stress magnitudes obtained by the two methods can be compared directly. Compressive in situ stresses are taken as positive. Cross bars at top of each graph in figure 23 indicate directions of the principal stresses in a plane perpendicular to the axis of the borehole. These derive from the symmetry axes of photoelastic patterns and, in the case of the borehole deformation gage method, from equation 3 (p* 1 9)* Control points on the graph showing borehole deformation gage data are placed at the point where U2, the middle of the three gage readings required for a single stress determination, was measured. The graphs show a wide disparity in the magnitudes of principal stresses calculated from core deformations and those calculated from borehole deformations, all measured in closely spaced holes. In particular, the fluctuations of stress magnitude shown in holes instru mented with photoelastic gages seem unrealistically high. 81 Stresses calculated from borehole deformation gage measure ments, on the other hand, are realistically stable and in accordance with the expected increase in stress for short distances from the edge of the underground opening (Obert, 1 9 6 7, p. 218). It is not within the scope of the present report to investigate the causes of the discrepancies in stress magnitudes given by the two methods. Although no means for checking the accuracy of these results is available, the borehole deformation gage data are considered better. Future research should include laboratory cali bration of the photoelastic gages under conditions which simulate test conditions in the field. Preliminary In vestigations of this type have been undertaken by PIncus (1 9 6 6, p. 9 7} 2nd the writer. In contrast to the generally poor correlation of data on stress magnitudes, the two relief methods give closely comparable results on principal strain directions, as shown in figure 23. The fact that two types of photo elastic gages and the borehole deformation gage give nearly the same directions of strain as these change with depth in the hole attests to the reliability of the determined strain directions, and it speaks well for the methods. It should also be noted that the direction of maximum compressive strain, nearly vertical at all points of measurement, agrees with its expected orientation un 82 der a mountain which is free to expand laterally. These results make it possible to compare with confidence the directions of principal strains with microfracture orientation data. Microfracture Orientation Data Microfracture orientations at the NORAD site were obtained from 12 thin sections, four from each of the three stress relief holes in which photoelastic gages were used. The sections were obtained 1 to 4 inches from the point at which the gages were mounted. No sections were prepared from samples taken from hole N4 in which the borehole deformation gage was used. Figure 19 shows the location of the stress relief holes and the sample points. Most of the microfractures at NORAD are open (figure 1 3), but many are healed (figure 9) or filled with second ary minerals (figure 10). The filled zones are so narrow that positive identification of the secondary mineral by optical means is, in most cases, not possible. However, many of the fillings show the low birefringence and re fractive index characteristic of quartz whereas others have the strong birefringence and variable relief that distinguishes carbonate minerals. Slide N2-1 contains a thick filling in which calcite and oligoclase were 83 identified as secondary minerals. Planes of fluid inclusions, regarded as partially healed microfractures, are also common (figure 1). Many of the individual inclusions are so small (a few microns to a few tens of microns in diameter) that under low magnification the planes appear to be filled with an opaque material. Under magnifications of about 200 diameters their true fluid nature can be established. The writer recorded the type of material, if any, filling each microfracture counted and color-coded the fractures according to filling as each was plotted on an equal area net. Fractures containing each type of filling and those lacking a filling were then plotted on separate diagrams so that the orientation patterns of each could be compared with the others and with the orientation patterns of larger scale structural features. The relative ages of the different fracture systems can be established by cross-cutting relationships and the sequence of crystallization inward from the walls of wide fractures. Fluid inclusion planes are oldest, being cut by both types of filled fractures and by open fractures. Next youngest are the fractures filled with low birefringent material (quartz?, oligoclase?). These are cut by fractures filled with material of high bire fringence. The age relation between the secondary minerals 84 is further established in wide filled fractures where the low birefringent material invariably lines the fracture walls and encloses high birefringent material in the center of the filled zone (figure 24). Open fractures cut all the other types and therefore are youngest. Figure 24. Photomicrograph of a microfracture filled sequentially with two secondary minerals. Fracture walls were first lined with a low birefringent mineral (quartz?) and later by a mineral having high birefringence (calcite?). The cross-cutting and sequential relationships among the various types of fractures and fracture fillings suggest a deformational history of at least four events. 85 They also support an earlier supposition (p. 16) that open microfractures have a relatively short geologic history. There are, however, no means available for assigning absolute ages to the various microfracture systems. Open microfractures. Plate I (back binding) displays equal area net plots of open (unfilled, unhealed) micro fractures. The projection plane is perpendicular to the axis of the hole, and the reference hemisphere is convex toward the back of the hole. Arrows at the top of each diagram point to the upper side of the hole. Arrows directed toward the center of the diagram show the directions of maximum compressive stress determined in a plane perpendicular to the axis of the hole. Contours connect the loci of points where 1, 2, 3s and more than 5 percent of the total number of points on the dia gram occur within an area measuring 1 percent of the total area of the net. Distances between centers of the dia grams are scaled to distances between sample points in the individual holes. Lines in the center of the dia grams represent directions of preferred orientation of the microfractures as determined from diagram maxima. The direction of a line is chosen from the highest value contour, which, as seen from the explanation of the table, 86 is not always the highest value contour shown on the diagram. At the far right of the plate are three combined partial diagrams which summarize data from the four samples from each hole. A synoptic diagram containing data combined from holes N2 and N5 is shown in figure 25. The question arises as to whether or not the dia grams show random or preferred orientations. Pincus (1951, p. 101) used the Poisson Exponential Binomial Limit to test for departure of orientation data from an isotropic distribution. Friedman (1964, p. 468) has confirmed the Poisson approximation from tests of good ness of fit between the Poisson distribution and apparent ly random diagrams of fabric elements. According to this test the probability P^ of obtaining at least A points in any 1 percent area of an equal area diagram is given by: PA = S! e-m -mx (8) * x=A xl ' where m is the total number of points on the diagram divided by the number of 1 percent areas. A diagram con taining 100 points of all possible orientations would have an m value of 100/100 = 1.0. All the diagrams in plate I have central blind spots from 50 to 90 degrees 87 of tilt. Thus each diagram consists of only 6 7 usable 1 percent areas, and the m values are obtained by dividing the number of points on the diagram by 6 7 . The choice of the level of probability that is to be accepted as significant is left to the investigator. Spencer (1959» P* 478) used a probability of 0.01 or less. In the present study the writer evaluated from tables of cumulated terms of the Poisson function pre pared by Molina (1942). The results are shown in table 4. As an example, 211 microfractures are represented in diagram Nl-1. The highest contour shown on the diagram is 5 percent, which corresponds to concentrations of more than 10 points, or an A value of 11. The probability of such a concentration of points occurring in any one of the 6 7 available 1 percent areas is only 0.0004, or 4 chances in 10,000. The test indicates that all the diagrams are signifi cant departures from an isotropic distribution. Friedman (1964, p. 468) has pointed out that statisti cal significance does not necessarily imply geological significance. In the present case one might ask what con centrations of poles to microfractures are permissible for the sample to retain a random character. A random distribution in nature is not necessarily a statistically isotropic distribution. In addition to the purely mathe- 88 TABLE 4 POISSON PROBABILITIES OP RANDOMNESS IN THE ORIENTATION OP MICROFRACTURES AT NORAD COC3 COLORADO Orientation Highest Valued Probability of Diagram Contour Randomness Nl-1 5 0.0004 Nl-2 5 0 .0 0 0 2 Nl-3 5 0 .0 0 0 5 Nl-4 5 0 .0 0 2 0 N1 Comb. 4 < 0 .0 0 0 0 0 1 N2-1 20 0 .0 0 0 3 N2-2 5 0.0001 N2-3 5 0.0045 N2-4 5 0 .0 0 2 6 N2 Comb. 5 4 0.000001 N5-1 5 0 .0 0 5 9 N5-2 5 0.0034 N5-3 10 0 .0 0 0 0 8 N5-4 5 0 .0 0 0 6 N5 Comb. 5 <0.000001 89 matical statistical test used here, another could be devised by lumping specific fabric data from several geological environments into a single diagram and noting the concentrations that result. Comparison of orienta tion diagrams for the same specific fabric element with this ''standard random diagram" would provide a means for estimating the significance of various percentage con tours on the diagrams. Such a test will be possible for the microfracture subfabric when more data become avail able. The two tests will permit stronger statements as to the significance of point concentrations on the diagrams. Another point of view is expressed by Turner and Weiss (1 9 6 3, p. 5 8). They define a statistically random orientation as one that "...is expressed by a pattern in which there is no obvious tendency for reproducible local concentrations of plotted points." The term "local" is not defined. Perplexing results are obtained if one applies this definition to the diagrams in plate I. All four samples from hole N5 have closely similar diagrams even though the samples are spread over a lineal distance of 80 inches. Diagrams N2-3 and N2-4, from samples 8 inches apart, are very much alike, but they show little resemblance to other diagrams from similarly oriented samples only a few tens of inches away in the same hole and in hole Nl. In general, then the individual partial 90 diagrams do not show good reproducibility on this scale. The combined partial diagrams for holes N1 and N2 are closely similar, except for the fact that the maxi mum contours lie in opposite quadrants. The 10 degree difference in inclination between the holes which bear in the same compass direction, does not change the patterns appreciably. Both diagrams show girdle maxima patterns (dashed line) with girdle axes (G.A.) that are nearly coincident. These similarities indicate good reproduci bility of concentrations of microfractures on this larger scale. However the conclusion is tempered by the fact that the girdles are partly apparent due to the presence of a central blind spot in both diagrams. When principal strain directions in the relieved cores are compared with preferred directions of micro fractures in the same cores no consistent relationship appears. The principal strain direction does not deviate much from vertical at any sample point. However, micro fractures in hole N1 tend toward the vertical, while those in hole N5 are more nearly horizontal. The pre ferred directions in hole N2 vary between these extremes. Thus the most important result to be derived from plate I is that microfracture directions at the NORAD site could not be used to infer principal strain directions in the cores. 91 Several attempts were made to find some explanation for the patterns by looking for trends within each of, and comparisons among, the following variables: a) Number of microfractures b) Magnitude of greatest and least principal strains and principal strain difference c) Distance of sample from collar of hole d) Angle between direction of maximum principal strain and preferred direction of microfractures e) Poisson probabilities of randomness Careful examination of each variable and compari sons among them failed to reveal any consistent trends or correlations. Although statistical measures indicate highly significant preferred orientations of the open microfractures, the writer is unable to identify any controlling factors from the data presented in plate I. The possibility exists that some microfractures did form or increase in size as the cores expanded, but not in numbers sufficient to be recognized over an established pattern of pre-existing microfractures. There is no evidence from the NORAD site to substantiate this claim, but, as will be seen later, field and laboratory data from the Georgia test sites, where significantly greater strains were measured, strongly suggest the possibility. Obert (1 9 6 7, p. 218) has drawn an "idealized measured stress distribution curve" based on a large number of stress determinations around underground openings. He finds that in situ stresses are lowest near the walls of the opening, rather than highest as predicted from elastic theory. This he attributes to a greater degree of fracturing, which relieves the stress, near the wall than at distances more remote from it. The present study did not reveal any differences in microfracture frequency with distance from the wall that would support this conclusion. Filled and healed microfractures. Synoptic petrofabric diagrams showing orientations of filled, healed, and open microfractures in NORAD rocks are shown in figure 25. Each diagram presents data obtained from a total of eight samples collected from holes N2 and N5. These data have been rotated into a horizontal reference plane, with the reference hemisphere convex downward, and combined. Be cause holes N2 and N5 are nearly orthogonal (actually 88 degrees apart), this procedure has eliminated the central blind spot inherent in diagrams constructed from fracture data obtained from parallel thin sections. Data from hole Nl, which is nearly parallel to hole N2 (figure 19), have been excluded to avoid over-representation of frac tures that are visible in this plane of sectioning. For 93 3 GA (C) i Figure 25 • Equal area diagrams of poles to filled, healed, and open microfractures* (a) 27U planes of fluid inclusions. Con tours at 2$, h*f and 6£ per 1$ area* (b) 115? microfractures filled with material of low birefringence. Contours at 2%, U % f and per l£ area, (c) U9 microfractures filled with material of high birefringence. Contours at h%, and 12^ per IjC area, (d) 107U open microfractures. Contours 1/, 2^ }&t and $% per 1# area. Arrows at top of diagrams point true north. 94 statistical purposes, each diagram contains three zones: a zone containing data from holes N2 and N5 combined, and two zones, each of which contains data from only one of the two holes (see figure 8 ). Each zone was contoured separately, after which the contours were linked across zonal boundaries. There is a close similarity among the patterns shown on the diagrams. The somewhat different character of diagram (c) probably can be attributed to the small num ber of control points (49) available for its construction. Crossed girdles appear fairly well developed on all the diagrams. Each girdle has two maxima, one of which is shared by its intersecting counterpart. The median position of each girdle is indicated by a dashed line. Crossed girdles occur only rarely in petrofabric diagrams (Turner and Weiss, 1 9 6 3, p. 5 8) and their appearance in each of these diagrams in nearly coincident positions strongly suggests a close relationship among fluid in clusions and filled and open microfractures. Cross cutting relationships among these features, as described in the preceding section, establish the fact that the fracture systems are separated in time. This fact dis allows any assumption that all fractures formed coevally and were filled during periods separated in time. 95 The close similarity of patterns of fractures which originated during different periods of earth history suggests that the earliest formed group (planes of fluid inclusions in this case) established directions of weak ness in the rocks and that these directions exerted a control on the orientation of all subsequent fracture systems. This general concept of tectonic heredity is not new. It dates at least to Ruedemann (1920) who com pared Precambrian trend lines with those present in younger rocks and found a close similarity between the two. More recently Wise (1964) studied microjoints and planes of fluid inclusions in the Precambrian basement rocks exposed in the Middle Rockies of Wyoming and Montana. He found a close correspondence between orientations of Laramide (late Cretaceous) microjoints and older fluid inclusion planes and concluded that microjoint orienta tions were controlled by pre-existing patterns of fluid inclusions. Microfracture data at NORAD point to a similar cause and effect relationship. Wise also studied orientations of common joints in the Middle Rockies. He found that these too tended to parallel the preferred orientations of fluid inclusion planes. It is interesting to make a similar comparison here. Table 5 lists the orientation of maxima of fluid inclusion planes, open microfractures and common joints TABLE 5 COMPARISON OP ORIENTATIONS OP FLUID INCLUSION PLANES, OPEN MICROFRACTURES, AND COMMON JOINTS, NORAD COC, COLORADO SPRINGS, COLORADO Maxima of 274 planes Maxima of 1074 open Maxima of 64 Maxima of 85 common of fluid inclusions in microfractures in common joints in joints above ground in Chamber A (fig. 26)____ Chamber A (fig. 26) Chamber A (fig. 21) chamber area(Ogden>1960) Strike Dip Strike Dip Strike Dip Strike Dip N82W 90 N75W 90 N65E 90 n 64e 74NW N32W 35NE N22W 30NE N20W 90 N28W 84NE n 44E 88nw n 42E 85NW vo cr\ 97 as measured in Chamber A at NORAD. Also listed are the maxima of common joints mapped by Ogden (1 9 6 0, figure 2) on the ground surface at the construction site. The maxima of common joints obtained by the writer from measurements within Chamber A are surprisingly close to those obtained by Ogden from measurements at the surface. However, these orientations do not compare well with the closely corresponding orientations of fluid inclusion planes and open microfractures. Thus the close relationship be tween orientations of smaller structural features does not carry over to the larger features, suggesting that features of each scale developed independently. Wise (1964, p. 295* 301) determined that the common Joints in his area of study formed after the microjoints, probably in the late Pleistocene or Recent. The age deter mination is based on the fact that the joints truncate against post-glacial sheeting. Such truncations were not observed in the present study, nor were they reported by Ogden. However, the writer favors a younger age for the common joints than any of the microfracture systems be cause their orientations do not correspond to the closely related orientations of fluid inclusion planes (which are certainly older) and all types of later-formed microfrac tures. A Pleistocene or Recent age for the common joints, following Wise, does not seem unreasonable. The reason why common joints developed independent of earlier formed planes of weakness while filled and open microfractures appear closely tied to such planes, is obscure. However, since nearly all the common joints lie within a few degrees of vertical they may be inter preted as extension fractures forming parallel to a ver tical maximum compressive stress, as indicated by the in situ stress determinations, and perpendicular to the directions of greatest lateral expansion, namely N.25°W* and N.65°E. Attempts could be made to infer principal stress directions from the microfracture plots, but it is doubt ful that such interpretations would be meaningful. First of all, which of the fracture systems represented by maxima on the diagrams developed simultaneously, if any, is not known. And if, say, three of the systems developed simultaneously, three distinct directions of fracture intersection would appear. Each of these directions defines the orientation of the intermediate principal stress, and knowing this and the acute angle of inter section of each combination of two planes, the corre sponding directions of the maximum and minimum principal stresses could be inferred. Thus three separate stress systems could be inferred. The number of uncertainties here is too great to make worthwhile such attempts at structural analysis of the systems. 99 Summary of Investigations At NORAD COC, Colorado The following is a summary of the results of the investigations at the NORAD COC site. In situ stress determinations were made in four nearly horizontal stress relief holes loacted in an underground chamber approximately 2500 feet below the summit of Cheyenne Mountain. Only two-dimensional strains in a plane normal to the axes of the holes were measured. No means are presently available for calculating all components of the ground stress tensor from these data. Reliable strain magnitudes were not achieved in three holes instrumented with photoelastic gages, but consistent and apparently reliable principal directions of plane strain were obtained. The results indicate that the existing principal compressive stress is oriented approximately vertical, in accordance with its expected position within a mountain free to expand laterally. There is no evidence of elastic anisotropy of the granite at NORAD, The usual assumption in elastic theory of parallel axes of stress and strain is regarded as valid for the rock. Fluid inclusion planes, open microfractures and filled microfractures in the NORAD rocks all show closely similar orientation patterns. Cross-cutting relationships 100 show that the three formed at different times. These relationships suggest that the earliest formed fractures, those which now exist as fluid inclusion planes, estab lished directions of weakness in the rocks that controlled the development of subsequent microfracture patterns. No means are available to determine the absolute dates of formation of the various microfracture systems. Open microfractures viewed in thin sections cut in a plane normal to the axis of a borehole show no consis tent relationship to the direction of the existing maxi mum compressive stress, as determined in situ in the same plane. Although the possibility of formation of micro fractures in the cores as these expand upon release from the in situ load cannot be excluded, microfracture orien tation patterns show no evidence of such a process oper ating. Close similarity between the synoptic diagram for open microfractures and diagrams of fractures formed earlier suggests an established background pattern of open microfractures which overshadows the pattern of any few microfractures formed under the small strains meas ured at NORAD. The same lack of a consistent relationship between principal strain directions and the preferred directions of open microfractures suggests that the determined 101 principal strain directions are not controlled by pre existing microfractures. If such a control had existed one would expect the cores to relax most freely in a direction normal to the preferred direction of pre-exist ing microfractures. Orientation maxima of open* filled, and healed micro fractures show no tendency to coincide with the maxima positions of common joints. Neither do these show any simple relationship to the orientations of other larger- scale structural features such as faults and dikes. The evidence suggests that these large-scale features developed independent of the smaller-scale features. The orientation of the local stress field during the Laramide deformation event can be established on the basis of the orientation of a major thrust surface and basic dikes lying above the chamber area. The maximum compres sive stress was horizontal, east-west, and the least principal stress was vertical. No attempt is made to infer paleostress directions from microfracture patterns. The patterns contain at least three maxima, and it is not known which, if any, formed simultaneously. Consequently, several possible stress distributions can be inferred and no criteria are available to make a reasoned choice among them. MICROFRACTURES, STRUCTURE AND IN SITU STRESSES IN THE ATLANTA, GEORGIA, REGION The region around Atlanta, Georgia, lies near the southern end of the Appalachian Piedmont Plateau which extends from Alabama to New York. It is underlain by igneous and metamorphic rocks, considered to be Pre cambrian in age, which have been intruded by late Paleo zoic granitic magmas and Triassic diabase dikes (figure 26). The rocks are exposed on gently undulating pave- ment-like surfaces. Numerous quarries in the area pro duce stone for use as poultry grit, road ballast, rip rap, dimension stone, and concrete aggregate. During the late 1950Ts U. S. Bureau of Mines per sonnel selected a site at Rock Chapel Mountain, about 18 miles east of Atlanta, to conduct blasting research. After detonation of explosives below the critical crater depth in vertical drill holes, the investigators ob served that vertical fractures induced by the blasts consistently followed a N.350 -6o°E. direction. In 1 9 6 2 Dow Chemical Company conducted similar experiments and obtained the same result. Although the rock at the test 102 LEGEND IGNEOUS ROCKS Biotife Ond~rrjsCOVita PROBABLY groatte LATE PALEOZOIC Porphyrific gronita Pari 10t'*S Porphyriticgronita gnsisa1 PROBABLY Gronile_j|o«i»» ro n i S T O N E MOUNTUNTA PRECAMBRIAN ATLANTA# f Augsn gnaias UGLASVILLE CHA PEL MOUNTAIN Hornbltnda ond diorita gronita METAMORPHOSED SEDIMENTARY ROCKS PROBABLY if? ;• •yr::"".: EARLY _ • t ^ •■«»#••##. B ravord sc Mat PALEOZOIC **••»»♦»■**•#.* I • » • I I 1 II • ■ I • * i • » • ► •I* Ashland schist PROBABLY m N"lil PRECAMBRIAN Q u o r tiits T att alts locations Biotue gneiss Seals, mllas and schist Faults not shown 103 Figure 26. Geologic map of the Atlanta, Georgia region# Arrongimsnt of units witMu (FTom Hooker and Duvall, 1966, p. 3) brockets doss nol indlcots chronologicol sequence 104 site is a biotite granite gneiss, the foliae are so con torted that, on the scale of the fractures produced, there are no obvious planes of weakness. This observa tion suggested to the investigators that the preferred fracture direction may be due to the existing stress field. Because tensile fractures tend to form parallel to the direction of maximum compressive stress, it was suspected that a large horizontal compressive stress existed in an approximately N.50°E. direction. In May and June 1964 U.S. Bureau of Mines personnel conducted a preliminary investigation to determine the state of stress in the rocks at the site of the experi mental blast holes. Encouraging results were obtained, and in October 1964 a field crew returned to extend the investigation to the surrounding region. At this time the writer accompanied the crew to investigate the drill sites, collect oriented samples for thin sectioning, and map in detail the geology of the Rock Chapel test area. The location of the initial test site and other test localities at Pine Mountain, Arabia Mountain, Stone Mountain and Douglasville are shown in figure 26. All stress determinations were made by means of the U.S.B.M. borehole deformation gage. With the exception of one horizontal hole drilled in a quarry wall at Rock Chapel, all borehole deformations were measured in vertical 105 holes ranging in depth from 0.5 to 28.7 feet. A report on the stress determinations in this area is given by- Hooker and Duvall (1 9 6 6). Herrmann (195^-) conducted a detailed investigation of the petrology and structure of the rocks in the Stone Mountain - Lithonia district. The writer prepared petrofabric diagrams of open microfracture orientations from oriented samples collected from each stress relief hole. Tests for isotropism of the orientation data by means of the Poisson Exponential Binomial Limit test establishes that the probability that the highest contour shown on each diagram would occur in a random sample is less than 0 .0 0 5- Rock Chapel Mountain Petrography. The Rock Chapel Mountain test site is located in and adjacent to a quarry operated by Consoli dated Quarries Division of the Georgia Marble Company. Situated 3 miles north of Lithonia, Georgia, near the small settlement of Rock Chapel, the quarry is the largest in the area. Exposed in the region is the Lithonia Gneiss, probab ly Precambrian in age. It is a gray-white granite gneiss, medium-grained, with highly contorted bands of biotite. Thin section analysis by the writer showed an average 106 composition of 3 5$ microcline, 3 0$ oligoclase, 2 5$ quartz, 5$ biotite and traces of muscovite, apatite and epidote. The grains are tightly interlocked along sinuous to suture d c ont ac t s. Fine-grained aplite dikes and thin veins of aplite and quartz are common features in the rock. Most of the thinner veins, 2 inches or less in thickness, are ptyg- matically folded parallel to the highly contorted banding, but some later veins cut across and sharply truncate the foliation (figure 2 7). The exposed rock is virtually unweathered. In many places completely fresh rock occurs only an inch or two beneath the pavement surfaces. Structure. Figure 28 is a structure map of the Lithonia gneiss in the Rock Chapel Mountain area. Over most of the area the foliation is so highly contorted that meas urement of its strike and dip would be meaningless. How ever, the writer recorded such measurements wherever the strike of the foliae remained essentially unchanged over a distance of a foot or more. Dip readings are difficult to obtain because the pavement surfaces are nearly flat and the rock is extremely resistant to the hammer. Con sequently many of the dip readings shown on the map have been determined from vertical faces only few inches deep. 107 Figure 27. Aplite vein dipping southwest (to the right), concordant with foliation, is cut by a later discordant vein dipping northeast. Vertical lines are old blast holes. Consolidated Quarries, Rock Chapel, Georgia. The most reliable orientations of foliation are those obtained in the blast holes, the locations of which coincide with map symbols for induced fractures. Figure 29 is an equal area plot of poles to the same foliae and aplite veins. Although the dips of these are quite variable, there is a distinct preference for n .30°-40°E. strike. Herrmann (195^* P* 100) found that aplite-filled shear zones in the quarry occur in EXPLANATION / Strike & dip of 'So aplite veins & . V Vertical aplite vein Iss SO / Strike & dip of 7 foliation m | ^ Approximate 1961* position of 8 ^ Vert, foliation ! quarry wall ^ Strike & dip of A / „ 70 .joints '♦-.Vertical joints \/ * X J Vert, fractures i ft «' f induced by blast ?SK \ 9 Location of stress $ ^ relief hole ? f S 0 500 iooo Solid lines separate rock Ilf t i 0 Pre-split line FEET outcrops from wooded areas Base map from Snellville, Ga. y| minute quadrangle (Geology by C. Norman) Figure 28. Structure of the Lithonia gneiss in the vicinity of Consolidated Quarries, Rock Chapel, Georgia. 901 109 N Figure 29 • Lower Hemisphere equal area diagram of poles to 102 foliae and aplite veins at Rock Chapel Mount ain test site. Arrow at top of diagram points true north. Contours at 2%t 1$, and per 1% area. major sets striking N.10°-30°E. and N.50°-70°W. With the exception of horizontal sheeting planes, joints are not a common feature in the Lithonia Gneiss. At Rock Chapel Mountain they are quite rare. One large fracture is located in the extreme northwestern portion of the outcrop east of the quarry (figure 30). It strikes 110 Figure 30. Small valley developed along a natural fracture in Lithonia gneiss, Rock Chapel, Georgia N.20°-32°E. and dips 85 degrees to the west. Most of the other joints shown on the map occur in small valleys at the edge of the dome-shaped outcrop area, and valley formation appears to be intimately associated with jointing in the rocks. Sheeting surfaces parallel to the topography are well developed in the quarry (figure 31)* The sheets increase in thickness from a few inches near the surface to 10 feet or more near the base of quarry walls 5 0 feet Figure 31. Sheeting in the Lithonia gneiss exposed on the southwest wall of quarry at Rock Chapel, Georgia. high. The ease with which the rock will sheet is a dis tinct advantage in quarrying dimension stone. Ledges of any desired thickness can be raised by a simple and inexpensive method. Holes 2.5 inches in diameter are drilled to the desired depth of about 8 feet. A teaspoon of blasting powder is placed at the bottom of the hole and connected to the surface with a fuse. The hole is backfilled with red clay. Quarry operators ignite the fuse in the spring of the year with the faith that as 112 the rock heats and expands during the summer, gas from burning powder also expands and generates horizontal fractures over an area of at least several tens to a few hundred square feet. After detonating the powder some operators force compressed air Into the hole to extend the fracture further. Straight, relatively smooth fractures can be pro duced with ease in most any direction in the Lithonia gneiss (figure 32). The directions of easiest breakage vary from quarry to quarry and are known from past ex perience. Fractures appear to form as readily across the foliation as parallel to it, but irregular breaks occur across veins of aplite, quartz or pegmatite (Herrmann, 1 9 5 4, p. 8 7). Figure 32. Vertical, nearly planar fracture surface in duced in the Lithonia gneiss by quarry oper ator at Arabia Mountain, Georgia. Short ver tical holes at top of lift are drilled to accomodate wedges. Bottom of lift is separa ted from underlying rock by an artificially induced horizontal fracture. 113 Stress determination. Stress determinations were made at five localities in the Rock Chapel area. These are in dicated by number on figure 28 and the results are given in table 6 . TABLE 6 CALCULATED SECONDARY PRINCIPAL STRESSES AT ROCK CHAPEL, GEORGIA (from Hooker and Duvall, 196 6, p. 11) Location Number Depth (ft) O^(psi) 05>(psi) Direction of CT 1 3.3-4.2 1527 1138 N.42°E. 2 .5-1.5 1053 596 N.54°E. 2.1 -3 . 0 965 503 N .59 E . 3 23.5-24.5 1 8 0 6 1 0 8 0 N.50°E. 2 5.2-2 6 .2 1794 1 0 5 0 N .59 E . 4 25.7-28.7 3023 1390 N.5 6°E. 5 Vert.hole 10.7-11.5 1725 IO89 N.7 2°E. Horiz.hole 1 0 .0 1350 5 0 0 Horizontal Calculation of stresses from strain measurements requires a knowledge of E (Young’s modulus) of the rock. E can be obtained from curves of borehole deformation vs. applied pressure, which in turn are obtained from static triaxial tests on cores of rock taken from relief holes Obert, 1964): P A r 4ab APo E ' “ ( P C ? , a 7 ( 9 ) 114 where E = elastic modulus (psi) a = radius of axial hole in core (inches) b = outside radius of core (inches) Po = exterior radial pressure on core U = borehole deformation Separate determinations of E were obtained for each of the three borehole deformations measured in each test hole and the value of E used in the calculations is the arithmetic mean of these three values. The stress cal culations must be regarded as estimates because of un certainties in the true value of E. Hooker and Duvall (1 9 6 6 3 p. 1 7) found poor agreement between static deter minations of E as described above and dynamic values ob tained by laboratory and in situ methods. For example at site 2 (figure 2 8) static triaxial tests gave a secant modulus of 2 .1 5 x 10 psi whereas calculations based on travel time of shear waves generated by hammer blows at the site gave a dynamic value of 9*36 x 10^ psi. The static moduli were used in the calculations because these are obtained under conditions most nearly representing in situ test conditions. Although serious uncertainties remain regarding cal culated values of the absolute magnitudes of the secondary principal stresses, the ratio of maximum to minimum stress is large enough so that the directions of CT-^ given in table 6 can be regarded as reliable (Hooker and Duvall, 19663 p. 12). This statement is predicated on the assumption of elastic isotropy of the rock. 115 The horizontal stress relief hole drilled at loca tion 5 strikes N.65°W. Thus the secondary maximum com pressive stress, as listed in table 6 , is determined in a vertical plane striking N.25°E., which is 47 degrees from the N.72°E. direction of 0^ determined in a vertical hole at the same location. There is two-fold significance to results obtained in the horizontal hole. First, if the ground stresses were due only to the weight of overlying rock, the maximum compressive stress should be vertical and on the order of 50 to 6 0 psi (a one inch square prism of rock one foot long with a specific gravity of 2 . 3 weighs about one pound). The calculated value, 500 psi, is therefore about an order of magnitude greater than that expected. Secondly, assuming a Poisson’s ratio for the rock of about 0 .2 5 to 0 .3 5* the horizontal stress should be 2 5$ to 35$ that of the vertical stress, but the observed value is about 270$ of this component. These differences between calculated and observed values are much too high to attribute to errors in the measurement of strain and the modulus of elasticity. Consequently, the measurements by themselves strongly suggest the presence of large horizontal stresses in the rock at this site. Examination of table 6 reveals a tendency for stress magnitudes to increase sharply with depth. The maximum 116 compressive stress increases from an average of about 1 0 0 0 psi 1 foot below the surface to about 2 0 0 0 to 3 0 0 0 psi at 2 feet. These values are more than three orders of magni tude greater than expected. In addition to the results from the borehole relief methods, evidence of large in situ stresses near the sur face at Rock Chapel derives from both naturally and arti ficially fractured rock. On the pavement surface about 3 0 0 feet north and downslope from the north quarry face is an upwarped slab of rock approximately 4 inches thick, 15 feet long in direction N.17°E., and 6 feet wide (figure 33 and figure 28 at location of foliation symbol showing 75-90 degree dip). At the top center of the slab is a fracture running transverse to its long dimension. There are no blast holes in the immediate area and weathered edges on the block indicate that failure was initiated by natural causes unrelated to quarrying or experimental operations in the area. Buckling appears to be due to a residual compressive stress acting in a northeasterly direction along the long dimension of the block. About 350 feet northeast of site 2 (location A, figure 2 8) an experiment was conducted to determine the maximum hole spacing necessary to generate a continuous fracture using a given amount of explosives. Two rows of 2.5-inch diameter vertical holes were drilled, one on Figure 33. Upwarped slab of rock, approximately 4 inches thick, on pavement surface at Rock Chapel, Georgia. View is N.20 W. a line parallel to the mean direction of CT^, which is R.56°E., the average of directions obtained at sites 2, 3, and 4, and the other in a perpendicular direction. Centers of the holes were spaced 1.5 feet, 2 feet, 3 feet, 4 feet, etc., and equal amounts of explosives in each hole were detonated simultaneously. The separate rows (pre-split lines) were shot at different times. Some rather surprising results were obtained. First, no macroscopically visible fractures were generated from 118 any of the holes in the line perpendicular to the princi pal compressive stress direction. In the other line, vertical fractures were induced in every hole but no where was a continuous fracture generated between two holes. All fractures trend N.50°-51°E. and those from adjacent holes spaced 4 feet and less overlap forming an en echelon array (figure 34). Here as elsewhere in the Rock Chapel area there are no recognizable planes of weakness in the rock. The location of these pre-split lines is between sites 1 and 2 where the calculated maxi mum compressive stress directions are N.42°E. and N.57°E., respectively. It is not unreasonable, therefore, to expect a curving stress trajectory between sites 1 and 2 that would be oriented approximately parallel to the fractures induced in the pre-split line. A second pre-split line was run in direction N.53°E. at location B (figure 28). Here a continuous vertical fracture connects vertical holes, 2 . 5 inches in diameter, with centers spaced 18 inches. The fracture extends visibly 6 feet beyond the last hole at the northeast end of the line. Microfractures. The writer collected rock samples for microfracture analysis from locations A and B, figure 28. The samples were collected at the surface about midway 119 Figure 3^* En echelon array of vertical fractures in- cfuced by detonation of explosives in verti cal drill holes. Lithonia gneiss* Rock Chapel* Georgia. Line of drill holes trends N.56°E.; fractures trend N.50°-51°E. between drill holes in the pre-split lines at these localities. Collections were made after the holes had been shot. Cores from the stress relief holes* drilled four months before the writer visited the area, were not available to him. Petrofabric diagrams of the microfracture subfabric are shown in figure 35. Only open microfractures are represented. The data for each diagram were obtained from single thin sections oriented in a horizontal plane* Figure 3$* Lower hemisphere equal area plots of poles to open microfractures in samples RC-61 and RC-73j Rock Chapel Mountain, Georgia. Contours at l£, 33, and per 1?> area. Arrows at top of diagrams point true north. Lines in center of diagrams indicate directions of pre ferred orientation as established from diagram maxima. Inward-directed arrows show directions of maximum com pressive stress, determined in situ. Sample RC-61 represents 190 microfractures at site A and sample RC- 73 represents lf>0 microfractures at site B, causing a blind spot to appear in the center of the dia grams. Lines in the center of the section indicate pre ferred orientations of microfractures as established by the diagram maxima. The diagrams show good reproducibility over the 550- to 600-foot distance between sample points. They show a clear preference for microfracture strikes of about N.30°- 45°W. This direction Is approximately perpendicular to the maximum compressive stress calculated in the horizon- 121 tal plane, and it is about perpendicular to the strike of the blast-induced fractures in the pre-split lines. The microfracture subfabric, therefore, does not appear to derive directly from the in situ stress, and it cannot have an origin common with the blast induced fractures. Rather the patterns suggest that significant numbers of microfractures formed in tension as the rock relaxed upon release from high in situ stresses. A second possi bility is that fracturing occurred to relieve residual or "locked-in" strains in the rock when the dimensions of the sample were reduced to some small value during its preparation for thin sectioning. Further discussion of these possibilities is deferred to the section which follows the presentation of all data from the Atlanta area test sites. There appears to be no simple relationship between the conjugate shear zones striking N.10°-30°E. and N.50°- 70°W. reported by Herrmann (195^* P* 100) and the N.30°- 45°W. preferred direction of open microfractures. Assuming the shears are indeed conjugate, tensile fractures would be expected parallel to the acute bisectrix of the shears, that is approximately N.20°E. or possibly N.70°E. The N.30°-45°W. preferred orientation of microfractures does not approach these directions or the directions of the shears. Consequently, it seems likely that these tiny features did indeed develop independent of the larger features, and being unfilled, most certainly at a later time. Planes of fluid inclusions occur in some of the quartz grains, but not in sufficient number to merit statistical analysis. Pine Mountain Petrography. Pine Mountain is a nearly circular dome, 1 5 0 0 feet in diameter and 150 high located about 1 mile east of Lithonia, Georgia (figure 2 8). It consists of Lithonia gneiss in its typical medium-grained, banded, highly contorted form. Mineral species are the same and in approximately the same distribution as at Rock Chapel Mountain. Veins of aplite occur parallel to the banding. Structure. A structure map of the Lithonia gneiss at Pine Mountain (formerly called Little Stone Mountain) prepared by Herrmann (1954-, plate 4) Is shown in figure 3 6. It shows a principal set of shear zones striking about N.20°E. (Herrmann, 1954, p.106). These are healed fractures, often filled with aplite, that cut across the banding. Foliation of the gneiss is highly variable throughout the exposure. r i % P t N E MOUNTAIN L£6 END \ 6 »T IVwtTUftI ITMIDLS * _ ItRill Ml KllH llt H T I Figure 36. Structure of the Lithonia Gneiss, Pine Mountain,Georgia (eodifiod froa Herrraanrt, 195U, Plate U). 124 Stress determinations. A single stress determination was made at Pine Mountain. The relief hole was drilled in the Davidson Granite Company quarry on the north side of the dome at about the position of Herrmann's location 3 shown in figure 36 of this report. The foliation here tends to strike N.6o°-70°W. and dip northeasterly 30 to 60 degrees. The required three borehole deformations (equation 1 ) were measured over a distance of 0 . 5 to 1.5 feet below the surface. The calculated maximum and minimum principal stresses are, respectively, 1 1 1 1 psi in direction N.62°E. and 855 psi in the perpendicular direc tion (Hooker and Duvall, 1 9 6 6, p. 11). Microfractures. Three thin sections in three mutually perpendicular planes were prepared from a core removed from the stress relief hole at a depth of 14 inches below the surface. One section lies in a horizontal plane and the other two lie in vertical planes each striking parallel to one of the determined secondary principal stress direc tions, i.e. N.62°E. and N.28°W. Data from the two verti cal sections were rotated into the plane of the horizontal section. All the data were then combined to produce the petrofabric diagram shown in figure 37- Orientations of only open microfractures are represented. A distinct maximum in the center of the diagram corresponds to the N62E Figure 37. Lower Hemisphere, equal area plot of 732 poles to open microfractures at Pine fountain, Georgia. Contours at 1#> 355» and per 1$ area. Arrow at top of diagram points true north. Line in center of diagram indicates direction of preferred orientation of microfractures as established by diagram maxima. Inward-directed arrows show direction of secondary maximum principal stress, determined in situ. direction of sheeting in the rock, which is a pronounced feature of the Lithonia gneiss everywhere. A second maxi mum indicates a major set of vertical microfractures striking about N.30°W., approximately normal to the determined direction of the maximum compressive stress. This relationship is identical to that observed at the Rock Chapel site. The pattern can be explained as frac turing due to expansion of the rock in response to release of confining stress or release of residual or "locked-ln" stresses. The processes are discussed in a later section summarizing the results of the Atlanta work. Near the stress relief site are two sets of fractures induced during rasing of the ledge. One set strikes N.38°E. and dips 75 to 80 degrees southeast. The second set is nearly, vertical with a strike of about N.40°W. This corresponds closely with the orientation of the major set of vertical microfractures. The N.30°W. preferred direction for microfractures appears unrelated to the N.20°E. direction of shear zones at the test site. Arabia Mountain Two in situ stress determinations were made in vertical holes at the Arabia Mountain test site. These were drilled in the Coffey Quarry which is located about 2000 feet northwest of the 950 foot summit of Arabia Mountain. The quarry floor is at an elevation of about 840 feet. Petrography. Lithonia gneiss is produced in the Coffey quarry. It has an average composition of 35# quartz, 3 0# oligoclase, 2 5# microcline, 5# biotite, and small amounts of muscovite, epidote, apatite, and magnetite. Thin veins of aplite occur parallel to the banding. 127 Structure. Throughout the exposure biotite bands in the rock are highly contorted. At six localities where the bands maintained a uniform strike direction for a distance of 1 foot or more, the strike ranged from N.10°E. to N.26°E. and dips varied from 38°SE. through vertical to 40°NW. Herrmann (1954, p. 98) reports shear zones striking about N.20°E. in the same area. These are filled with veins of aplite and pegmatite. The writer recognized three large natural fractures in the quarry floor oriented as follows: Strike Dip N .68°E. 65°NW. N.57°E. 52°NW. N.64°E. 90° The largest of these, the N.64°E. fracture, can be traced for 60 feet. Its southeast wall is cut by five vertical fractures, 6 to 18 inches long, that strike N.26°E. Two of the same size and orientation cut the northeast wall, and all terminate against the main fracture. These are interpreted as tension fractures (pinnate tension joints of Hills, 1 9 6 3, p. 173) that formed as the southeast wall moved northeastward relative to the northwest wall (left- lateral movement). The quarry operator has found from experience that the rock fractures easiest along direction N.15°W* and N.42°E. Figure 32 shows the remarkably smooth N.15°W. 128 face that can be Induced by wedging the rock in shallow drill holes after the lift has been raised. Stress determinations. Borehole deformations in the in terval 0 . 5 to 1 .5 feet below the surface in the quarry floor gave a calculated secondary maximum compressive stress of 2210 psi in direction N.3^°E. The least princi pal stress was calculated to be 8 6 6 psi. A second stress relief hole drilled 1 .5 feet deep in a lift 8 feet thick showed no deformation in any of the three measurement directions, indicating that raising the lift had relieved the active stresses (Hooker and Duvall, 1966, p. 13)* The in situ stress here is approximately twice as great as that determined at comparable depths at Rock Chapel Mountain and Pine Mountain, but the secondary principal stress directions at all three localities are within 2 8 degrees of each other. Microfractures. Microfracture orientations were obtained from a single thin section cut in a horizontal plane from core removed from the relief hole at a depth of 2 1 inches. Figure 38 shows that open microfractures are preferen tially oriented in a vertical plane striking approximately N.45°W., which is nearly perpendicular to the calculated direction of the maximum compressive stress, in situ. N 129 Figure 33. Lower hemisphere, equal area plot of 286 open micro fractures at Arabia Mountain, Georgia. Contours at l£, and $% per area. Arrow at top of diagram points true north. Calculated direction of secondary maximum principal stress, in situ, is shown by in- ward-directed arrows. Line in center of diagram in dicates preferred direction of microfractures, as es tablished by diagram maxima. Since this relationship is the same as that observed at the Rock Chapel and Pine Mountain test sites, a similar origin for the microfractures is proposed. Figure 38 shows no set of open microfractures either parallel or perpendicular to the N.15°W. direction selected by the quarry operator to fracture the rock. The preferred set of microfractures is oriented nearly perpendicular to the N.42°E. direction of easy fracture.' This relationship is not in accord with that at Pine Mountain where the two occurred in parallel directions. 130 The N.45°W. direction of preferred microfracturing does not correspond or appear related in any simple way to the orientation of foliation (N.10°-26°E.) or shear zones (N.20°E.). Because the microfractures are unfilled they must be assigned to a deformational event later than that (or those) which produced the macroscopic structural features. In this light, an origin due to relaxation of in situ or residual stresses is certainly not inconsistent. Stone Mountain Petrography. Stone Mountain is an intrusive igneous body of granitic composition. Mica foliae within the rock body show it to have an asymmetrical shape In cross-section. Steeply inclined foliae dip westward on the west side of the exposed mass, pass through vertical, and dip gently eastward on the east side of the mountain (Herrmann, 195^, Plate 2). Although the rock is most frequently referred to as granite, its average mineralogic composition of 30# quartz, 31# oligoclase, 28# microcline, 1 0# muscovite, and 1.5# biotite places it In the quartz monzonite cate gory of most igneous rock classifications (Herrmann, 195^-> p. 8 3). The most frequently occurring grain sizes fall in the 0 . 5 to 2 . 0 mm range. The Intrusive character of the rock is indicated by 131 flow structure paralleling its contact with the Precam- brian Lithonia gneiss and other metamorphic rocks, its uniform grain size and mineralogic composition, and its occurrence in dikes at the edge of the intrusive mass. A tentative Permian age has been assigned to the intru sive event (Herrmann, 19f>4, P* 79)* Structure. The most pronounced structural feature of the Stone Mountain granite is flow foliation expressed by subparallel alignment of biotite and muscovite grains. The alignment tends to parallel the Intrusive contact. At the site of the stress relief hole on the southeast side of the mountain the foliation strikes N.42°E. and dips 50 to 6 0 degrees southeastward. Except for sheeting surfaces parallel to the topog raphy, joints are very rare in the Stone Mountain granite. Herrmann (1954, p. 60) found that a majority of 40 joints on the west side of the mountain were steeply dipping with a strike of about H.55°W. Grant (1 9 6 2, p. 8) reports a dominant joint direction of N.6o°W. and weaker sets striking N.25°W. and N.15°E. The writer found two 1/8-inch thick mineralized seams, each about 40 feet long, on the floor of the 0. A. King Quarry near the stress relief hole. The seams have strikes and dips of N.48°W; 132 63°NE. and N.3°W.; iL50W. Striae on the N.3°W. seam rake 50 degrees in that direction. Assuming the direction of smoothest feel on the surface of one block indicates the relative direction of movement of the adjacent block, a reverse fault is indicated. No reference points were found for determining the amount of displacement. There are no exposures of surfaces along the other seam. The southeast end of a diabase dike striking N.22°W. is exposed about 1600 feet in direction N.65°E. from the Stone Mountain test site. The dike has a thickness of about 1 0 feet, and it cuts diagonally across northeasterly striking foliation in this area. Stress determinations. Two stress determinations were made in a single vertical hole in the 0. A. King Quarry on the southeast side of Stone Mountain (Hooker and Duvall, 196 6, p. 11). The interval from 0.5 to 1.5 feet below the surface gave a calculated secondary maximum compressive stress of 1477 psi in direction N.12°E. The least com pressive stress was calculated to be 1075 psi. In the interval from 2 . 0 to 3*0 feet a maximum principal stress of 1 5 8 3 psi in direction N.9°E. and least principal stress of 1088 psi were calculated. These magnitudes are on the order of those calculated at the same depth at Rock Chapel, Pine Mountain, and Arabia Mountain. However, the direction 133 of the principal stresses has shifted northward about 25 to 50 degrees. Microfractures. Figure 39 is an equal area plot of poles to 228 open microfractures. The data were obtained from a single thin section cut in a horizontal plane from core removed from the stress relief hole 30 inches below the surface. Concentrations of microfractures are not as strong as those appearing in the diagrams for sites to the south at Rock Chapel,, Pine Mountain, and Arabia Moun tain, all of which are underlain by Lithonia gneiss. More importantly, the direction of preferred orientation, N.20°E., is nearly coincident with the determined direc tion of maximum compressive stress, in situ, not perpen dicular to it as at all other test sites in the Atlanta area, including the Douglasville site which will be dis cussed in the following section. Therefore the available evidence indicates that the relationship between secondary principal stress directions and open microfracture orien tations at the Stone Mountain site is anomalous. Here, as at all the other test sites, there appears to be no simple relationship between the N.20°E. pre ferred direction of microfracturing and the dominant direc tion of flow foliation (N.42°E.) or shear zones (N.3°W.; N.48°W.) described earlier. The microfractures apparently 134 N10E 4 T ~ Figure 39. Lower hemisphere, equal area plot of poles to 228 open microfractures, Stone Mountain, Georgia, Contours at l£, 3^j and per 1 % area. Inward-directed arro;*s show calculated direction of maximum principal stress in a horizontal plane. Diagram maxima indicate a pre ferred microfracture orientation of approximately N20E. are not related to the intrusion of the dike striking N.22°W., and their orientation does not correspond to either the major (N.60°W.) or secondary fN.25°W.) Joint systems reported by Grant (1 9 6 2, p. 8). Douglasville After the Bureau of Mines field crew had obtained remarkably consistent indications of stress magnitudes and directions at four localities east of Atlanta, a decision was made to extend the investigation into the outlying region so that the extent of these unusual conditions of in situ stress could be established. The Douglasville site (figure 2 6) is the only distant site investigated to date. Two stress determinations were made in a single vertical hole drilled 2 3 0 feet east of a quarry operated by Consolidated Quarries and located two miles west of Douglasville, Georgia. Petrography. The quarry at Douglasville is located in the Austell granite, which occurs in a 3-mile wide band 27 miles long in a N.35°E. direction between Carrollton and Austell, Georgia. The rock is shown as an augen gneiss, probably Precarabrian in age, on the Georgia State Geological Map (1939)* Crickmay (1952) describes it as consisting of "eyes'1 or phenocrysts of microcline, micro- perthite, albite, or quartz resulting from replacement. The writer analyzed a single thin section prepared from core taken from the stress relief hole and determined a composition of 3 5# quartz, 3 0# microcline, 25# oligoclase (An-j^), 5# biotite, 3# muscovite, and 2# perthite. All the quartz shows undulatory extinction. The rock consists mainly of grains 0.5 to 2.0 mm in diameter. Phenocrysts as large as 2 . 5 cm diameter occur in the quarry. Structure. The most conspicuous structural feature of 136 the Austell granite at the site of the stress relief hole is banding. The bands consist of sub-parallel grains of biotite and muscovite. Within a radius of 200 feet from the relief hole bands exposed on the nearly horizontal outcrop surface strike in the narrow range of N.40°E. to N.6o°E. A uniform northward dip of 4o degrees was ob served in the relief hole. No dip measurements were possible elsewhere in the vicinity of the test site and time limitations did not allow a close investigation of the rock exposed in the quarry. A 25-foot long fracture trending N.57°W. and dipping 85°SW. occurs on a sloping surface 400 feet southeast of the relief hole. There are no reference points available to establish whether or not movement has occurred along it. Stress determinations. Two stress determinations made at depths of 0 . 5 to 1 .5 and 2 . 0 to 3*0 feet be- .. the surface. A maximum secondary compressive stress of 455 psi in direction N.58°W. and a least compressive stress of 262 psi were calculated at the shallower depth (Hooker and Duvall* 1 9 6 6* p. 11). Corresponding values of 556 psi* N.52°W.* and 210 psi were obtained for the lower interval. These two sets of values show the same internal consistency obtained at Stone Mountain and the two loca- 137 tions at Rock Chapel Mountain where two determinations were made in single holes. However, the calculated stress magnitudes here, which are at least two orders of magnitude higher than would be expected if the in situ stress were due to the weight of overlying rock, are two to four times smaller than those obtained at the sites east of Atlanta. In addition the calculated secondary principal stress directions have shifted from the TJE-SW quadrant at all test sites east of Atlanta to the NW-SE quadrant here. Microfractures. The orientation of 205 open microfrac tures at the Douglasville test site is shown in figure 40. The data were obtained from one thin section lying in horizontal plane. The section was cut from core from the relief hole at a depth of 32 inches. This diagram shows more scatter of points than the diagrams prepared for the sites east of Atlanta, but significantly the same tendency toward an orthogonal relationship between open microfractures and direction of maximum compressive stress is apparent here. If, as proposed earlier, microfractur- ing is due to expansion of the sample upon relief from in situ stresses, the lower concentration of points here is explained by the lower magnitude of in situ stress. That is, "background" fractures tend to obscure the smaller 138 N Figure UO. Lower hemisphere, equal area plot of poles to 20$ open microfractures in the Austell granite near Douglasville, Georgia. Contours at 1$, 2%, 3$'t and h% per 1# area. Inward-directed arrows show direction of calculated maximum compressive stress in the horizontal plane. Dia gram maxima show a weak preference for nearly vertical microfractures striking approximately M20E. number of microfractures that form upon relief of in situ stresses. The N.20°E. preferred orientation of open microfrac tures does not appear related to the N.40°-60°E. range of strike for banding in the rock immediately surrounding the stress relief hole. Neither does the orientation correspond closely enough to that of the nearly vertical fracture southeast of the outcrop to postulate a common origin for the two features. It appears that here, as 139 at four of the five test sites east of Atlanta, open microfractures have an origin independent of all large scale structural features near the stress relief holes, but that they are related to existing ground stresses. — Summary of Investigations in the Atlanta Region Abnormally high ground stresses have been recognized in the near surface crystalline rocks exposed in the Stone Mountain region east of Atlanta. In situ stress determinations by means of the U. S. Bureau of Mines borehole deformation gage indicate the existence of com pressive stress magnitudes of about 1 0 0 0 to 3 0 0 0 psi acting in a northeasterly-southwesterly direction. Verti cal fractures induced by detonation of explosives in vertical drill holes also trend consistently in a north easterly direction. These corroborate the in situ data on principal stress directions. A third indication of large compressive stresses acting near the surface is an upwarped slab of rock, about 4 inches thick, which is elongate in a northeast-southwest direction and trans versely fractured at its apex along a perpendicular direc tion . Data from this study and previous investigations of the Atlanta region are not sufficient to establish the 140 origin of the recognized high stresses in the surface rocks. However, Triassic diabase dikes located just east of the Lithonia district strike nearly perpendicular (N.30°-40°W.) to the determined directions of maximum compressive stress (Herrmann* 195^* plate I). Injection of the dikes may have crowded the host rocks creating a high compressive stress which still exists today. None of the joints or blast-induced fractures at the test sites follow an obvious direction of weakness in the rock. Eight of the ten test sites in the Atlanta region are located in the Lithonia gneiss, which is characterized by foliae so sharply contorted that on the scale of joints and blast-induced fractures the rock appears homogeneous and isotropic. Banding is uniform over distances of a few feet to a few tens of feet in the Stone Mountain and Austell granites, but natural fractures in these rocks show no tendency to parallel the banding. Petrofabric diagrams of open microfractures show preferred orientations that do not coincide with, or show any obvious relationship to, larger scale structural features such as joints, healed or mineralized shear zones, foliation or other directional features of the igneous or metamorphic rocks at the test sites. However, at five of the six localities for which diagrams were prepared, the preferred direction of open microfractures occurs l4l nearly perpendicular to the determined direction of the in situ maximum compressive stress. This consistent relationship strongly suggests that the formation of microfractures derives either directly or indirectly from the in situ stress. Concerning the origin of the microfractures, there are at least two possibilities to consider. First, Hooker and Duvall (196 6, p. 14), after observing non linear elastic behavior of the rock sampled at all the Atlanta area test sites, followed Walsh’s (1 9 6 5) sug gestion that such non-linearity is due to the presence of cracks. They in turn suggested that release of crys talline rocks from high in situ stresses may contribute to the formation of such cracks. The preferred orienta tions of fresh microfractures at all but one of the At lanta area test sites are perfectly in accord with this postulated origin. Hooker and Duvall also obtained seismic velocity data on cores from the stress relief holes (1 9 6 6, p. 14, 1 5) that suggest microfractures formed in the cores upon release from in situ loads. They found that longitudinal velocities measured in situ are as much as 6 9 percent greater than longitudinal velocities in the same direc tion in the relieved core. When the cores were subjected to loads equal to the determined principal stress magni 142 tudes the longitudinal velocities increased 2 to 4-9 per cent over that in the unloaded core* but in no case did the velocities reach the magnitude of the in situ velocity. The rock appears to have suffered a permanent damage after its removal from the outcrop. It is suggested that this damage is development of microfractures. Seismic velocities in the unloaded samples were highest parallel to the direction of in six of ten cases. When loaded, seven of ten samples showed highest velocities parallel to the direction of (7-^. Four of five measurements of in situ velocity showed higher velocities In the 0^ direction than in the direction. Since microfractures are preferentially oriented parallel to 0^ higher seismic velocities would be expected in this direction than across the fractures. Closing of the fractures under load should effect an Increase in seismic velocity, but not necessarily great enough to regain the velocity before microfracture damage. The experimental results, therefore, are entirely in accord with the results expected from microfracturing in the samples due to their release from in situ loads. A second possibility, closely related to the first, is that significant numbers of microfractures form per pendicular to a principal residual stress direction as 143 the dimensions of a sample with "locked-in" stresses are reduced to some critical value. Friedman (196 6) recently developed an X-ray technique for determining residual stress magnitudes and directions in quartz-rich rocks through measurement of _d spacing in strained quartz crystals. He has recognized strains in excess of 4-00 x 10”-6 units in 2-inch diameter discs of rock 0.25 to 0.5 inches thick. However, he finds that relaxation of the strains extends to a depth of at least 0.01 to 0.02 mm. This allows the possibility that release of residual stress in the samples is accomplished by microfracturing as a dimension of the sample is reduced to some critical value between, say, 0.02 mm to 6.3 mm (0.25 in.). The mechanism could be one of stress concentration in the thin slice of rock along directions consistent with in situ and residual stress directions until the strength of the slice is ex ceeded and it fails in tension. The writer plans to test this hypothesis by thin-section analysis of the micro fracture subfabric of rocks in which high residual strains have been determined by the Friedman method. CONCLUSION Orientations of microfractures in granite and granite gneiss from seven test sites have been compared with the orientation of larger scale structural features in the rocks and with directions of plane principal stresses determined by in situ methods of the borehole relief type. Separate petrofabric diagrams of open, healed, and filled micro fractures show preferred orientations that do not show any simple relationship to the orientation of larger structural features such as faults, joints, dikes or banding in the rocks. The evidence suggests that microfractures have de veloped independent of large-scale structural features. Application of the Polsson Exponential Binomial Limit to test for randomness of three-dimensional plots of open microfractures indicates a preferred orientation of these fractures in all 18 samples included in the study. However, when these directions of preferred orientation are compared with directions of principal stresses, determined by in situ methods at each sample point, a consistent relationship between the two appears only where borehole principal strains on the order of 1 0 0 0 microinches per inch are recorded. At the NORAD COC site, diametral deformations of a single borehole at 39 points along its length were 144 145 measured by means of the U. S. B. M. borehole deformation gage. Measured strains ranged from 33 to 750 microinches per inch, with a mean value of 403. No consistent rela tion between directions of principal strain and preferred directions of microfractures in relieved core can be established at this site. In the vicinity of Atlanta, Georgia, a total of 27 deformations was measured in nine boreholes by means of the U. S. B. M. gage. Strains ranging from 102 to 2415 microinches per inch were recorded, the mean value being 1183 microinches per inch. At five of six of these localities, petrofabric diagrams of the open microfrac ture subfabric show that the preferred direction of micro fractures is perpendicular to the direction of maximum extensional strain in the stress-relieved rock. These results point up an inherent limitation of the use of open microfractures to infer in situ princi pal stress directions: A sufficiently large number of open microfractures, preferentially oriented in a plane perpendicular to the axis of greatest strain, must form so that this preferred orientation is not concealed by a pattern of pre-existing open microfractures. If the pre existing pattern is random, or if the number of fractures is small, then presumably smaller strains in the cores would produce enough fractures to give an interpretable 146 pattern. On the other hand, a large number of preferen tially oriented pre-existing fractures could completely overshadow those formed during stress-relief of the cores, even under conditions of high in situ stress. The most difficult condition to detect is that a pattern of pre-existing fractures is dominating the total pattern. In the case of the NORAD samples this condition can be recognized. The open microfractures form an orien tation pattern that is closely similar to the orientation patterns of fluid inclusion planes, filled and healed microfractures. Cross-cutting relationships show that all these fracture systems are separated in time, the open microfractures being latest. Thus at this locality the open fractures show a closer relationship to direc tional properties acquired by the rocks in remote geologic time than to directions of existing stress in these rocks, and this indicates that the dominant pattern was formed before the cores were stress-relieved. The rocks in the vicinity of Atlanta, Georgia, do contain planes of fluid inclusions, healed and filled microfractures, but not in numbers sufficient to analyze statistically from single thin sections. Their frequency of occurrence is one to two orders of magnitude less than in the NORAD rocks. Near absence of such fractures suggests that the open microfractures formed as the cores 147 expanded, without any control on the orientation being ex erted by pre-existing directions of weakness in the rocks. The consistent and logical relationship between pre ferred directions of open microfractures and directions of maximum principal strain in the Atlanta cores consti tutes strong evidence that under certain conditions the microfracture subfabric can be used to infer principal directions of in situ stress. The conditions are: a) The rock must yield by brittle fracture. b) Open microfractures existing before the rock is stress-relieved must be sufficiently few in number so that the pattern of fractures formed during stress-relief is not masked. Large numbers of planes of fluid inclusions, filled and healed microfractures in a rock should caution one to suspect the pattern of open microfractures has been influenced by both the directions of these and the directions of in situ stresses. A great many more measurements in the field and laboratory are needed to assess the significance of the results obtained in this study. The most important task which lies ahead is to obtain data from triaxial (0*-^>01j = ) or preferably polyaxial ((X^> 0*2 > 0*^) tests to determine threshold levels of strain in relieved cores at which microfractures form in sufficient number to analyze statistically. Such experiments must be conducted on brittle rocks having a wide range of elastic constants, 148 grain size, number of pre-existing defects, and so forth. The tests should duplicate as closely as possible the conditions of temperature, confining pressure, and fluid pressure at depths of interest in the earth’s crust. Incentive for continuing development of the petro- fabric method developed in this study is that it can be used to obtain Information on in situ stresses in holes several thousand feet deep. Thus it complements the in situ methods presently available, all of which are limited to hole depths of a few tens to a few hundred feet. An added advantage of the petrofabric method is that it requires no special equipment. The cost of a single stress determination is no greater than the cost of obtaining an oriented core and a thin section cut from it. BIBLIOGRAPHY Anderson, J. L., 19^-5, Deformation planes and crystallo- graphic directions in quartz: Geol. Soc. Am. Bull., v. 56, p. 409-430. Anderson, E. M., 1951, The dynamics of faulting and dyke formation with applications to Britain: Edinburgh, Oliver and Boyd, 206 p. Bloss, D. F., 1957, Anisotropy of fracture in quartz: Am. Jour, Sci., v. 255, P- 214-225. Boehm, A., 1 8 8 3, Uber die Gesteine des Wechsels: Tschermak min. u. petr. 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A. j i_ i i i i i i i DISTANCE OF SAMPLE FROM EXP1 SAMPLE UMBER H-1 Nl-2 Nl-3 N14 N1C0MB. N2-1 UMBER or OPEN 2II 230 216 1^7 80*t 20 RAD COC, COLORADO SPRINGS, COLORADO K1 COMBI i IQ COMBINED 75 80 u ill1**" COLLAR OF TEST HOLE (INCHES) PLANATIOH N5 COMB. N5-3 N5A H2 COMB. N5-1 N5-2 R2-1* 1C-2 *2-3 68 190 523 551 138 127 2L6 133 152 j i—i—i—i—1—*■ D 1ST MICE OF SAMPLE FROM COLLA1 expunat: Hl-lt HI COMB. H2-1 ®2"2 SAMPLE IWBER «Ml -1 N1-2 ^ 20 2W somber or m w 211 2^° WCR0FRACTUR8S . 2Q H I M W W W W lwW l”3” II $ PER 1 $ M E A 0 8 V 2? B 65 Hl-3 114 1(2 COMBINED 15 COMBINED , .8? ■I.75 I I I-L- 80 1 ‘ 1 JL- AR OF TEST HOLE (INCHES) LTIOH N5-3 N54 N5 COMB. N2 COMB. N5-1 N5-2 H2-3 N2-*+ 138 127 68 190 523 133 152 551 1,2,3,it,5 1,2,3,*+,5 1,2,3,>+,5 2,*t,6,8,10 1,2,3,*+,5 1,2,3,*+,5 it,5 1,2,3,*+,5 1,2,3,M 10 12 7 5 10 10 5 9