Experiment using the HICell for stress measurements in a Utah coal mine

This thesis is concerned with the measurement of in situ stress state and the interpretation of data obtained from instruments such as the US Bureau of Mines borehole deformation gauge and the Australian Commonwealth Scientific and Industrial Research Organization Hollow Inclusion Stress Cell (HICell). Both are installed in long pilot holes and overcored to relieve the stress state. Gauges which are bonded to the end of a borehole such as the South African Council for Scientific and Industrial Research "doorstopper" are not considered. The data reduction formulas for calculating the stress state are based on a solution first obtained by Hiramatsu and Oka. Pariseau proposed an alternative solution in 1984. This alternative solution has since proved to be correct. The data reduction scheme for the HICell is not affected since both solutions are based on the same state of stress and strain. Data reduction is not affected for instruments which measure change in diameter of a borehole, but it is affected for those which measure axial displacement. The error due to the conventional formulas is dependent on the initial stress state. An experimental investigation of the correctness of these solutions was attempted under laboratory conditions. Also, the HICell was tested in a Utah coal mine for use as an absolute stress measurement instrument as well as a stress monitoring device.

AN EXPERIMENT USING THE HICELL FOR STRESS MEASUREMENTS IN A UTAH COAL MINE by Mark K. Larson A thesis submitted to the faculty of The University of Utah partial fulfillment of the requirements for the degree Master of Science Department of Mining Engineering University of Utah June 1987 in of • © Copyright © Mark K. Larson 1987 All Rights Reserved U N I V E R S I T Y U T A H SUPERVISORY COMMITTEE APPROVAL Mark K. Larson committee and majority to satisfactory. THE UN1VERSlTY OF UTAH GRADUATE SCHOOL COMl\fI1~TEE APPRC)V AL of a thesis submitted by This thesis has been read by each member of the following supervisory comnllttee aml by majoritv vote has been found be satisfactory. May 1, 1987 Chairman: William G. Pariseau May 1, 1987 v. J. Hucka May 1, 1987 ~K~._ Stephen R. Swanson THE UNIVERSITY OF UTAH GRADUATE SCHOOL FINAL READING APPROVAL T o o f T h e o f Mark K. Larson in j t s format, citations, figures, to May 1, 1987 Date William G. Pariseau Chairperson, Supervisory Committee Department M. K. McCarter Chairman / Dean B. Gale Dick To the Graduate Council of The University of Utah: I have read the dissertation of in its final form and have found that (1) its format. citations. and bibliographic style are consistent and acceptable; (2) its illustrative materials including figures. tables, and charts are in place; and (3) the final manuscript is satisfactory the Supervis­ory Committee and is ready for submission to the Graduate School. Dale 1987 Chairperson. Cammitt~ Approved for the Major Department I Approved for the Graduate Council Dean of The Graduate School ABSTRACT This thesis is concerned with the measurement of in situ stress state and the interpretation of data obtained from instruments such as the US Bureau of Mines borehole deformation gauge and the Australian Commonwealth Scientific and Industrial Research Organization Hollow Inclusion Stress Cell (HICell). Both are installed in long pilot holes and overcored to relieve the stress state. Gauges which are bonded to the end of a borehole such as the South African Council for Scientific and Industrial Research "doorstopper" are not considered. The data reduction formulas for calculating the stress state are based on a solution first obtained by Hiramatsu and Oka. Pariseau proposed an alternative solution in 1984. This alternative solution has since proved to be correct. The data reduction scheme for the HICell is not affected since both solutions are based on the same state of stress and strain. Data reduction is not affected for instruments which measure change in diameter of a borehole, but it is affected for those which measure axial displacement. The error due to the conven­tional formulas is dependent on the initial stress state. An experimental investigation of the correctness of these solutions was attempted under laboratory conditions. Also, the HICell was tested in a Utah coal mine for use as an absolute stress measurement instru­ment as well as a stress monitoring device. Hines 1S conven-tional 1n instru-ment IV. DATA REDUCTION THEORY 55 "Alternative" Solution 57 Theoretical Difference between "Conventional" and "Alternative" Solutions 58 Significance of the Solutions on Data Reduction 59 Instruments Which Measure Change in Borehole Diameter . . . . . 59 Instruments Which Measure Axial Displacement or Oblique Distances across the Borehole 60 Instruments Measuring Strain On or Near the Wall of the Borehole 61 Summary 62 V. EXPERIMENTAL INVESTIGATION OF THE DISPLACEMENT SOLUTIONS . . 63 Objective of Experimental Research 64 Approach 64 Apparatus . . . . . . •••• 70 Aluminum Model 70 Triaxial Loading Frame 74 Flat Jacks and Hydraulic System 79 Axial Displacement Measuring Device 81 Strain Gauges Procedure and Results Calibrations 88 Measurement of Material Properties of the Aluminum Model 104 Check of Uniformity of Load on the Model from Flat Jacks Confined in the Triaxial Frame 110 Calibration of Axial Displacement Measuring Device in Hole of Model 115 Measurement of Axial Displacement Under an Axial Shear Stress 125 Diagnostic Tests Evaluation of the Axial Displacement Measuring Device Evaluation of Loading of the Model 144 Summary 164 VI. CONCLUSIONS 165 REFERENCES 167 vi . . . . . . . . . . . Al ternat i ve" Sol ut ion • • • • • • • • • • • •••••••• . . . . . • • • • • • • • • • • • • • • On ••• • • • • • • • • . . . . . . . . . . . •••••••••••• •• •••• . . . • • • • • • • • • • • • • · . . . • • • • • • • ••••• • • • • • • • • • . . . . . . . . . Resul ts • • • • • • • Calibrations. • • • • ••• ••••••••••••••••••• • • • • ~alibration • • • • • • • • • • • • • • • • • • • • • • • . . . • • • • • • • • • • • • • • • • • •• · . . ••••••••• • • • • • · . . . . . . . . . . . • . . . . . . . . . . . . . . . . . . . . . . v}. S9 87 87 126 127 LIST OF TABLES 1. Secondary principal stresses and directions in the horizontal plane calculated from monitoring the USBM borehole deformation gauge . 52 2. Principal stresses and directions calculated from monitoring the HICell 53 3. Linear regression statistics of load cell calibration- half sensitivity 95 4. Linear regression statistics for load cell calibration- full sensitivity 98 5. Linear regression statistics for flat jack calibrations . . . 103 6. Linear regression statistics for LVDT calibrations 106 7. Measured material properties for cast aluminum . . . . . . . 109 8. Measured and calculated peak strains on the wall of the hole in the plate model for the uniaxial test . 134 9. Comparable measured strains in hole of aluminum model for uniaxial test in the configurations shown in Figures 38(a) and (b), and theoretical strains for uniaxial stress of -1500 psi 149 10. Measured versus calculated maximum strains on the wall of the hole for a uniaxial compression test 158 1n • • • • • · · · · · . . . . . · · • · cali brat ion-- . . · · · · · · · · · . . . calibration-- full sensitivity . . · · · · · . . . . . · · · · . . . s. Linear regression statistics for flat jack calibrations 6. Linear regression statistics for LVDT calibrations 7. Measured material properties for cast aluminum 8. Measured and calculated peak strains on the wall of the hole in the plate model for the uniaxial test • Compa:able •••••••• • . . 98 103 106 109 134 LIST OF FIGURES 1. General location of the Beaver Creek No.2 Mine 31 2. Test site in Section 22 at Beaver Creek No.2 Mine 33 3. Plot of strains measured during process of overcoring the first HICell 35 4. Plots of calibration of the USBM borehole deformation gauge (a) Component 1 (b) Component 2 (c) Component 3 37 5. Plot of displacements measured during process of overcoring the USBM borehole deformation gauge 40 6. Plot of changes in diameter of the pilot hole measured with USBM borehole deformation gauge during underground biaxial pressure test on 6-in. diameter core 41 7. Plot of results of uniaxial test on 5.72-in. diameter siltstone core 43 8. Sectioned siltstone core through pilot hole and HICell . . . 46 9. Plot of strains measured in a HICell during the underground monitoring period • 48 10. Plot of changes in diameter of the pilot hole measured with a USBM borehole deformation gauge during the underground monitoring period 51 11. Orientation of borehole with respect to Cartesian coordinate system; point Q defined by angle 0 56 12. Section of a medium with a circular hole subject to an axial shear stress in the hole coordinate system 65 13. State of pure shear in hole coordinate system obtained by application of normal stresses 66 14. Addition of desired stress state and biaxial stress state results in applied compressive stresses . . . . 68 ••••• • • • • • • • • • • • ••••••• ••••• •••••••••••• ~ HICel1 ••••••••••••• ••••• angfe e . . • • • • • • •••••• 15. Axial displacement profile of hole due to an axial shear stress state; Qi and are displaced to Qi' and Q2*- respectively 69 16. Proposed device for measuring relative axial displacement between two points diametrically opposite on the wall of the hole (a) Longitudinal view (b) Front view 71 17. Aluminum model 73 18. Triaxial frame 76 19. System of beams confines vertical load applied with flat jack 78 20. Sections showing flat jack construction near the edges (a) TT flat jack (b) WI flat jack 80 21. Axial displacement measuring device (a) One anchor (b) Two anchors 82 22. Installation clamp for aluminum stops 86 23. Plot of results for calibration of Enerpac Load Cell . . . . 89 24. Testing configurations in testing machine (a) Flat jack calibration (b) Measurement of material properties . . . . 91 25. Plot of results for calibration of testing machine load cell-half sensitivity 94 26. Plot of results for calibration of testing machine load cell-full sensitivity 97 27. Plot of results for linearity check of one of the pump and dial pressure indicator systems 100 28. Plot of results of calibration of one flat jack 102 29. Plot of results for calibration of an LVDT 105 30. Plot of results for measurement of material properties of the cast aluminum 108 31. Location of strain gauge rosettes on the outside surfaces of the aluminum model (a) Top view (b) Front view . . . . Ill ix Q1 Q2 Ql' Q2', • • • • • • • • • • • • • • • • • • • the hole (a) Longitudinal view (b) Front view • 71 17. Aluminum model 73 18. Triaxial frame 19. System of beams confines vertical load applied with flat jack • • • • • • • • • • • • •••• (b) Two anchors ••••••••••• . . . . . . . . 22. Installation clamp for aluminum stops • 23. Plot of results for calibration of Enerpac Load Cell 76 78 82 86 89 •••• cell--•• • • • • • • • • • • • • • • Jf cell--full • • • • • 28. 29. and dial pressure indicator systems • • • • • • • • • Plot of results of calibration of one flat jack Plot of results for calibration of an LVDT 30. Plot of results for measurement of material properties of 100 102 105 the cast aluminum • • • • • • • • • • • • • • • • • • • • 108 Vlew • • III lX 32. Plots of results for the check for uniformity of load by measuring vertical and horizontal strain on an outside surface of the aluminum model (a) Measured strains vs. average applied stress at locations 1, 2, and 3 (see Fig. 31) (b) Measured strains vs. average applied stress at locations 4, 5, and 6 (see Fig. 31) 112 33. Applied biaxial stress for calibrating the axial displacement measuring device in the hole of the model . . . 116 34. Configuration of axial displacement measuring device in the hole of the model for the purpose of calibration (a) Longitudinal view (b) Front view 118 35. Plot of results of calibration of axial displacement measuring device in the hole of the model using one anchor (a) Run 1 (b) Run 2 (c) Run 3 121 36. Plot of results of calibration of axial displacement measuring device in the hole of the model using two anchors (a) Run 1 (b) Run 2 124 37. Hole-in-plate aluminum model for performing diagnostic tests on the axial displacement measuring device 128 38. Plot of results of LVDT creep monitoring 130 39. Locations 1 and 2 of strain gauge rosettes in hole-in-plate model 131 40. Plot of ^results of measured strains on wall of the hole vs. average uniaxial stress applied to the hole-in-plate model 132 41. View of optimum orientation of axial displacement device in the hole of the plate with respect to the direction of the applied uniaxial stress 135 42. Sections showing diagnostic tests for axial displacement measuring device using short pins in the LVDTs (a) Stops glued to wall of hole opposite each other (b) Stops bonded to brass bar which is bonded to the outside surface of the plate (c) Stops bonded to brass bar which is bonded to the outside surface of the plate (includes use of long pin) 136 43. Sections showing diagnostic tests for axial displacement measuring device using long pins in the LVDTs (a) Stops bonded to brass bar which is bonded to the outside surface of the plate (b) Stops bonded to brass bar which is bonded to the outside surface of the plate . . . 137 x ••••••• •••••••••• ••••• •••••••••••• in-• • • • • . • . . . • • . . • • • • • . cesults • . . • . . • • • . . . . • . • • . . • • • . . . . • • • • • • • • • • • • • • • • 44. Plot of results of diagnostic tests for axial displacement measuring device using short pins in the LVDTs (a) Testing configuration in Figure 42(a) (b) Testing configuration in Figure 42(b) (c) Testing configuration in Figure 42(c) 139 45. Plot of results of diagnostic tests for axial displacement measuring device using long pins in the LVDTs (a) Testing configuration in Figure 43(a) (b) Testimg configuration in Figure 43(b) 143 46. Location of strain gauge rosettes in the hole of the model (a) Circumferential positions A, B, and C of a set of rosettes (b) Axial positions A and B of a set of three rosettes 145 47. Configuration for tests for evaluating deviation of the uniformity of load on the model due to nonparallel surfaces (a) Standard configuration (b) Model and adjacent hole access plate rotated 90° 148 48. Configuration for tests for evaluating deviation of the uniformity of loading of the model with a flat jack in the testing machine 150 49. Plot of results of measured strains on the inside of the hole of the aluminum block model when given a uniaxial stress with a flat jack confined in the testing machine (a) Strain gauges 1, 2, and 3 at position A (b) Strain gauges 4, 5, and 6 at position A (c) Strain gauges 7, 8, and 9 at* position A (d) Strain gauges 1 and 3 at position B (e) Strain gauges 4, 5, and 6 at position B (f) Strain gauges 7, 8, and 9 at position B 152 50. Measured strains versus calculated strains on the wall of the hole due to an applied uniaxial load (a) Calculated strains-plane stress (b) Calculated strains- plane strain 157 51. Plot of results of measured strains on the outside surfaces of the aluminum block model when given a uniaxial stress with a flat jack confined in the testing machine (a) Locations 1, 2, and 3 (see Fig. 31) (b) Locations 4, 5, and 6 (see Fig. 31) 160 52. Measured strain versus calculated strain on the outside face of the block due to an applied uniaxial load 161 xi • • • • • • • • • • • • • • •• • • • • • • • • • • • • • • • • • • • • • •• . . . . . . . . . . . 900 ••••••••••• 1n • • • • • • • • • • • • • • • • a~ (f) • • • • strains--strains-- ••••••••••••••••••• • • • • Xl 53. Plot of results of measured strains on the wall of the hole in the aluminum block model and monitored during the same test as the measured strains plotted in Figures 51(a) and (b) 163 xii • • • • • • • • • • • • • • • • • • • • • • ACKNOWLEDGEMENTS The author would like to express his appreciation and gratitude to Dr. William G. Pariseau, who suggested this work, for his guidance, advice, and help in various aspects of this project. Thanks are also extended to Dr. V. J. Hucka and Dr. S. R. Swanson for their suggestions as members of the Supervisory Committee. Financial support for this work has been made available through Mineral Leasing, state of Utah. Support from the Department of Mining Engineering is also appreciated. Assistance in securing a field site from G. G. Ramos, of ARCO, is gratefully acknowledged. Ken Fleck and Mike Watson, of Beaver Creek Coal Company, assisted tremendously in obtaining field data. Finally, thanks must go to his fellow graduate students, especially Kevin Donovan, Fei Duan, Jeff Johnson, Hyunkoo Moon, and Chang-Ha Ryu, for their countless hours of participation in discussions, laboratory work, and field work. v. Hucks data • • CHAPTER 1 INTRODUCTION The measurement of the state of stress in rock masses has had much development in the past 30 years. The mining of new mineral properties proceeds deeper as time passes. Usually, an increase in ground control problems accompanies the trend of mining deeper deposits. Ground con­trol is a substantial expense to the mine operator. Overdesign of ground support systems is an unnecessary cost which makes some mining unfeasible. Underdesign means higher risk to men, equipment, and the whole mining operation. All coal mines in the state of Utah are underground operations. Mining operations proceed to deeper coal seams with time. Economic constraints motivate operators to restrict premining development to a minimum. As mining proceeds deeper and premining development is reduced, ground control problems may again increase. A fundamental part of any ground control program is a knowledge of the state of stress. Most coal operators make assumptions about the regional state of stress and the origin of the causing forces. Such assumptions usually lead to overdesign or underdesign of ground support systems. Knowledge of the stress state in coal mines from in situ measurements is sadly lacking. Measurement of the stress state is the only viable recourse. operat~ons 1S 1S 2 Two common instruments for stress measurements in situ are the U.S. Bureau of Mines (USBM) borehole deformation gauge and the Commonwealth Scientific and Industrial Research Organizations (CSIRO) Hollow Inclusion Stress Cell (HICell). Both instruments have been used exten­sively in "hard" rock mines. Their use in "soft" rock, which surrounds coal seams, is limited. Of particular interest is the HICell because of the quality of data and the ability to determine the stress state with measurements of strain in just one borehole. Since most stress measurement instruments require measurements to be taken in at least three nonparallel boreholes, the reduction in required boreholes for the HICell represents a substantial savings in drilling cost. Objectives The goals of this investigation are 1) to test the CSIRO HICell method for in situ stress measurements in a Utah coal mine and 2) to experimentally test an alternative solution for stress measure­ment data reduction. Approach A thorough review of the literature was the first step in the approach to the problem. Special attention was paid to 1) instruments and techniques for in situ stress measurements, 2) data reduction theory of these instruments, and 3) actual in situ stress measurements. u.s. USBM) CSIRO) exten-sively HICel1 'I 1n 1n measure-ment 3 Measurements of in situ stress in an underground coal mine using the HICell and the USBM borehole deformation gauge were carried out. Measurements with the latter served as a comparison to those with the former. Finally, an experimental investigation of the conventional and a new, alternative, data reduction theory was attempted. Historical Perspective The objectives and approach of this investigation remained essen­tially the same throughout this work, but the main emphasis changed. This historical perspective presents what was changed and why. Constraints of the mining company where the field testing was done did not allow enough time to work out the problems encountered and obtain meaningful data. However, many things were learned in the field about the performance of both instruments. In the literature review, data reduction theory for most instru- * ments was traced to a solution by Hiramatsu and Oka (1962a, 1962b) for the stresses about a long, cylindrical hole in an infinite, linear, elastic isotropic medium. A special case assumption in the derivation of this solution was discovered. The lack of meaningful data from the field work and the discovery of this possible error in the data reduction theory caused the emphasis of the work to shift to experimental testing of the alternative solu­tion, investigation of that solution's implications, and verification of that solution. The importance of such a solution for basic stress measurement data reduction theory was potentially very high and, in any case, unknown. 1n HICe11 attempted. essen-tia11y reV1ew, instru-ments was traced to a solution by Hiramatsu and Oka (1962a, 1962b) for the stresses about a long, cylindrical hole in an infinite, linear, elastic isotropic medium. A special case assumption in the derivation of this solution was discovered. The lack of meaningful data from the field work and the discovery of this possible error in the data reduction theory caused the emphasis of the work to shift to experimental testing of the alternative solu-tion, investigation of that solution's implications, and verification t of that solution. The importance of such a solution for basic stress measurement data reduction theory was potentially very high and, 1n any case, unknown. CHAPTER 2 LITERATURE REVIEW A knowledge of the premining state of stress is important in any ground control program. Measurement of the stress state has increased in importance in the last few decades. This review of the literature is divided into three categories: 1) instruments and techniques for in situ stress measurement, 2) data reduction theory, and 3) in situ stress measurements. A summary concludes this chapter. Instruments and Techniques for In Situ Stress Measurement Measurement of the state of stress in rock is accomplished by sev­eral different techniques. Alexander (1968) groups these methods into four categories: nondestructive, fracture, stress relief, and stress compensation. Nondestructive methods consist of measuring stress-de­pendent physical properties without altering the stress to be measured. Fracturing methods involve achieving a balance between applied pres­sures and pre-existing stresses. Stress relief methods involve measur­ing strain, displacement, or pressure due to relief of the stress state. Stress compensation involves stress relief followed by a restoration of stress by applying pressures until the measured quantity is at its initial reading. 1n 1n 1S 1) 1n Measuremen~ de­pendent 5 Nondestructive Methods These methods involve measuring some physical property such as wave velocity or rock resistivity. Enever (1970) states that these tech­niques have had limited success due to lack of knowledge between the measured quantities and the state of stress. Leeman (1964c) and Barnes (1967) have summarized these methods. Fracture Methods Hydraulic fracturing is a well-known method used in the oil industry to stimulate production from an oil-bearing formation. Fairhurst (1964) suggested the method for the primary purpose of in situ stress measurement. The method consists of sealing off an interval of a bore­hole with packers. Fluid is pumped into the interval until a maximum pressure is reached, at which time the wall of the hole fractures. This pressure is called the breakdown pressure. The crack is extended by pumping in more fluid. During this time the fluid pressure stabi­lizes to what is called the flowing pressure. When pumping is com­pleted, the pressure quickly stabilizes to the shut-in pressure. A borehole camera determines the fracture orientation. The orientation of the crack and the history of the fluid pressure at the bottom of the hole during the process enable one to determine the magnitude and orientation of the principal stresses, assuming one of them is the vertical direction. The method has the advantage that stresses can be determined at great depth from the borehole collar. The method measures only stresses directly. Also, it is a simple technique, which can be performed by unskilled workers. Fairhurst (1968) reports that disad- £never tech-niques known bearing bore-hole stabi-lizes com-pleted, quiCkly 6 vantages include the assumptions in the analysis of isotropy, of orientation of the borehole along a principal axis, of a circular smooth hole, and of elastic behavior of the rock. Also, it is diffi­cult to determine fluid pressure in the packed off interval at depth from usual hydraulic gauge readings at the surface. Other problems include the unknown tensile strengths of the rock in the axial and tangential directions, and laboratory tests show fracturing pressures much greater than those predicted by elastic theory and the measured tensile strength of the rock. Jaegar and Cook (1963) presented a method to determine the least principal stress using borehole jacks. The jacks are diametrically placed in a groove around a core stub. The arc of each jack covers 90 degrees. The rock around the ring is loaded to failure. The direction of the maximum principal stress is the fracture direction if it lies within the arc of the jacks. Stress Relief Methods Stress relief is accomplished by wholly or partially isolating some volume of rock from the influence of the surrounding rock. Merrill (1963) reported that this is done by drilling overlapping holes around the volume, by cutting the top of a pillar free from the roof, by removing rock from a slot, or by coring the rock by diamond core dril­ling. Hast (1958) was one of the early users of the overcoring method in the field. Leeman (1964a) described the overcoring or trepanning technique used to overcore an instrument bonded to the flat end of a borehole. Hooker and Bickel (1974) describe the overcoring technique and equipment in detail. 1n diffi-cult dril-ling. 7 Early instruments were designed to measure change in stress due to nearby excavation. These instruments were later adapted to measure absolute stress using stress relief techniques. Leeman (1964c) and Barnes (1967) described many of these early instruments. One class of those instruments is the borehole deformation strain cell. This kind of instrument measures the change in length of one or more diameters of a borehole. Among these cells are the Maihak strain cell, the CSIR strain cells Mark I and Mark II, the Sibek strain cell, the U.S. Bureau of Mines borehole deformation gauge, and the Griswold strain cells. These instruments, except the USBM borehole deformation gauge, are not commonly used at the present. Another class of early instrument described by Leeman (1964c) and Barnes (1967) is the borehole inclusion stressmeter. A borehole inclu­sion stressmeter is rigid and offers a relatively large resistance to deformation, and must be precalibrated. Changes of stress in the surrounding rock cause changes of stress and strain in the measuring component of the instrument. Stressmeters have to be prestressed in the borehole in order to be sensitive to tensile stress changes as well as compressive stress changes. Some of these instruments are Potts' stressmeter, May's stressmeter, the National Coal Board borehole plug gauge, Hast's stressmeter, and Salamon's strain cell. These instru­ments are not in common use at the present. Photoelastic techniques have been adapted to stress measurement in rock. A circular patch of photoelastic material with reflective backing can be bonded to a rock surface. Roberts and Hawkes (1963 and 8 1964) noted that results which are much easier to interpret are obtain­able if the circular patch is bonded to rock only at its perimeter. They also noted that a hole in the center of the patch produces a stress concentration that magnifies the measurable strain. Hawkes and Moxon (1965) described this photoelastic gauge and the technique for using it to make stress measurements. A photoelastic stressmeter was developed by Roberts, Hawkes, Williams, and Dhir (1964). The instrument includes a sheet of polaroid and a quarter wave plate sandwiched in between a plastic assembly and a cylindrical elastic inclusion made of a glass material possessing pho­toelastic properties. A light source is cast in the plastic assembly. A viewing device at the collar of the borehole contains the second polarizing filter and quarter wave plate. The instrument has the advantage that data reduction is only slightly dependent on the modulus of elasticity,of the rock if it is less that one-half of that of the inclusion (Roberts and Hawkes, 1964). Installation of the instrument is difficult, and unless a uniform thickness of cement is placed around the device, nonuniformity of fringe patterns results. Another disad­vantage is the necessity of an estimate of the ratio of major to minor principal stresses for data reduction. Another photoelastic method involves casting a photoelastic inclu­sion in a borehole and overcoring it. Riley, Goodman, and Nolting (1977) described this technique. The relieved core can be cut in transverse sections and the stress is analyzed. The method of measuring the change in length of diameters of a borehole upon stress relief is very popular. The U.S. Bureau of Mines uSing elasticity~of overcorlng 9 developed the single-component borehole deformation gauge described by Obert, Merrill, and Morgan (1962). A change in the borehole diameter is transmitted through a beryllium-copper cantilever. Four electrical resistance strain gauges are bonded to the cantilever and are connected as a complete wheatstone bridge. The signal from the strain gauges is proportional to changes in diameter. Merrill (1967) described a mod­ification of the instrument to facilitate the simultaneous measurement of borehole deformation along three diameters 60 degrees apart. Hooker, Aggson, and Bickel (1974) described improvements to the instru­ment which significantly improved its creep characteristics. Crouch and Fairhurst (1967) reported the development of a more sophisticated version of the U.S. Bureau of Mines borehole deformation gauge at the University of Minnesota. Crouch (1967) described the instrument in further detail. The four-component gauge makes measure­ments of diametral deformation at 45 degree intervals. There are two distinct advantages of this gauge over the U.S. Bureau of Mines gauge. First, the cantilevers of the U.S. Bureau of Mines gauge are pre-ten-sioned as the instrument is placed in the borehole, since the distance between the outside ends of the pistons is slightly greater than the borehole diameter. The corresponding distances of the four-component gauge is smaller than the borehole diameter. The instrument is first inserted into the borehole, and then the pistons are forced out against the wall of the hole when air pressure is applied to a pressure chamber and pressure pistons force the cantilevers to deflect. The second advantage is a built-in check of the measurements, since the sum of orthogonal deformations should be equal. component Hooker, Aggson, and Bickel (1974) described improvements to the instru­ment which significantly improved its creep characteristics. component diam~tral ten­sioned component gauge is smaller than the borehole diameter. The instrument is first inserted into the borehole, and then the pistons are forced out against the wall of the hole when alr pressure is applied to a pressure chamber and pressure pistons force the cantilevers to deflect. The second advantage is a built-in check of the measurements, since the sum of orthogonal deformations should be equal. 10 These two instruments have a particular disadvantage. Each instru­ment has a piston that has contact with the wall of the hole. Vibra­tions due to overcoring may cause slippage of the contact point. Another type of instrument measures strain on the flattened end of a borehole. Mohr (1956) was probably the first to report using strain gauges bonded to the flattened end of a borehole to measure the state of stress in rock. One instrument of this type that is commonly used is the 'doorstopper' strain cell developed by the Council for Scienti­fic and Industrial Research (CSIR) in South Africa, and was described by Leeman (1964c and 1969). The instrument consists of a rosette of three strain gauges bonded to an Araldite shim. The leads of the gauges are connected to a four-pin insulated connector plug. Rubber is cast with the shim and the plug in a mold to form the shape of a door­stopper. The rubber insulates the strain gauges and allows the use of the instrument"1 with either dry or wet drilling. Before installation, the end of the borehole must be ground smooth. Examination of the surface for joints and cracks can prevent installation in poor condi­tions . Pahl (1977) developed an instrument using inductive gauges as dis­placement sensing devices. The three sensing elements are oriented in orthogonal directions. Because of the insufficient number of measuring elements, measurements must be carried out in multiple nonparallel boreholes• Kanagawa and others (1986) have developed a new gauge recently. The instrument has five gauges protected by a rubber molding. The authors are not clear whether the gauges are strain gauges or displacement ~s doorstopper' ~s instrument 4 condi­tions. boreholes. 11 transducers. Four of the gauges are oriented in the radial direction at 45 degree intervals. The fifth gauge is oriented in the axial direction. The instrument is placed in a 56 mm diameter borehole, and the hole is filled with a cement paste. Sensitivity factors relate the difference between initial and final gauge readings to in situ stress. The previous instruments described have a disadvantage which some­times makes their use economically unfeasible. Measurements with the latter two gauges must be carried out in at least two nonparallel bore­holes. Measurements using any of the other previous three instruments must be carried out in at least three nonparallel drill holes. Some instruments allow the determination of the three-dimensional state of stress with a measurement in just one borehole. Leeman and Hayes (1966) proposed a technique for an instrument of this type. Leeman (1968) reported that laboratory results confirmed the validity of the technique. The method involves bonding three strain gauge rosettes to the cylindrical wall of the borehole. Leeman (1968 and 1969) described a tool and instrument based on this technique developed by the CSIR. Van Heerden (1976) described another model of this triax-ial gauge which uses four-gauge rosettes spaced at 120 degree intervals around the hole. The latter change was due to the results of a statis­tical analysis by Gray and Toews (1974), which showed that this rosette layout would make possible the determination of the stress tensor with greater accuracy than the old configuration. The new model did not allow measurement of strains during the overcoring operation. A disadvantage of this method is that strain readings can be taken only l. dimensional 1916) triax­ial gauge 1914), 12 before and after overcoring. Strain readings taken during the overcor­ing process would be useful in determining the quality of data from each gauge. Another disadvantage of this method is the problem of electrical shorting because of water. The mouth of the EX borehole must be plugged during overcoring in order to keep the hole dry. Water seepage may not be stopped completely, however, by plugging the bore­hole. Other versions of the technique of Leeman and Hayes (1966) have been described by Radmanovich and Friday (1968) and by Hiltscher, Martna, and Strindell (1979). Bonnechere (1969) described the "Universite de Liege" borehole deformation cell. The instrument measures the changes in length of three different diameters of the borehole due to stress relief using the same method described by Crouch and Fairhurst (1967) for their four-component borehole deformation gauge. In addition, the instrument also measures the relative axial displacement between the body of the cell and six points on the wall of the borehole using displacement transducers (DCDTs). The six points are three diametrically opposite pairs. Relative axial displacement is determined by the difference between axial displacement measurements of any two points. Instruments have been developed that have strain gauges embedded in a solid cylindrical epoxy probe, which is bonded to the wall of the borehole. Rocha and Silverio (1969) described the probe developed at the Laboratorio Nacional de Engenharia Civil (LNEC) in Portugal. Blackwood (1973) developed a cell similar to the LNEC instrument for overcor­lng l969) component DCDTs). ln LNEC) 13 use in coal. Blackwood and Enever (1973) described two early models. The disadvantage of the solid inclusion is the frequent failure of the rock-epoxy bond due to the high tensile stresses which develop during overcoring. Problems with the failure of the bond of a solid inclusion led to the development of the hollow inclusion probe. The LNEC version of the probe is described by Rocha, Silverio, Pedro, and Delgado (1974). The Commonwealth Scientific and Industrial Research Organization (CSIRO) in Australia developed a version named the Hollow Inclusion Stress Cell or HICell (Worotnicki and Walton, 1976). For the hollow probe, strain gauge rosettes are embedded in the walls of the hollow cylinder. The probes have the advantage of full moisture protection of the electron­ics and capabilities for monitoring during overcoring. A disadvantage is that relatively good ground conditions are required. « Stress Compensation Methods Panek (1961) described a stress compensation method using flat jacks developed by the U.S. Bureau of Mines. A series of overlapping holes is drilled to form four vertical slots. Two slots are in the same vertical plane. Strain gauges are cemented in each slot in the verti­cal direction. A slot is cut in the horizontal direction such that two of the strain gauges are within the zone of stress relief. A flat jack is cemented in the horizontal slot, and pressure is added until the strain gauge readings return to their prestressed values. The flat jack is sealed. The other slots are located away from the relieved zone of rock. They provide a reference of strains in case of mining induced stress changes. Panek and Stock (1964) discussed the method CSIRO) Stress Compensation Methods Panek (1961) described a stress compensation method using flat jacks developed by the U.S. Bureau of Mines. A series of overlapping holes is drilled to form four vertical slots. Two slots are in the same vertical plane. Strain gauges are cemented in each slot in the verti­cal direction. A slot is cut in the horizontal direction such that two of the strain gauges are within the zone of stress relief. A flat jack is cemented in the horizontal slot, and pressure is added until the strain gauge readings return to their prestressed values. The flat jack 1S sealed. The other slots are located away from the relieved zone of rock. They provide a reference of strains in case of m1n1ng induced stress changes. Panek and Stock (1964) discussed the method 14 and described a change in which small hydraulic cells installed in a drill hole are used instead of strain gauges. The advantage of this technique is that absolute rock pressure can be measured many times during a long period of time without installa­tion of more equipment. However, there is uncertainty of stress dis­tribution about an opening because of mining-induced fractures. The method used by Jaegar and Cook (1963) to determine a principal direction was already discussed. They also presented an extension of that method to determine the stress magnitudes which involves stress compensation. Two jacks, each covering a 90 degree arc, are placed diametrically opposite in the annular groove and given a pressure Pi. The jacks are overcored, and the change in Pi due to overcoring is noted. Four jacks, which also cover 90 degree arcs, are placed in the outer groove. Opposing pairs of the jacks have internal pressures increased to ?2 a n a ^2' t 0 restore the pressure in the inner jacks to Pi. The procedure is repeated with the inner jacks oriented 90 degrees to the original directions. Data Reduction Theory Theory for data reduction depends on the type of measurement method. For this section, theory in the literature is surveyed for nondestruc­tive methods, fracturing methods, stress relief methods, and stress compensation methods. Pl. PI 1S '2 and P2' to restore the pressure in the inner jacks to Pl. 15 Nondestructive Methods Leeman (1964b) summarized the theory of sonic and resistivity meth­ods. The principles of the methods are not clearly understood and have little chance of becoming viable stress measurement methods. Fracturing Methods The hydraulic fracturing theory for in situ stress measurement began when Hubbert and Willis (1957) showed that regional stress fields influence the orientation of a hydraulically induced fracture. That is, the hydraulic fractures propagate in the plane perpendicular to the least principal stress. Scheidegger (I960) used a spherical model to analyze the pressurized interval of the borehole. He modified the theory of Hubbert and Willis and calculated the regional stress state for several examples (1962). Kehle (1964) used a cylindrical cavity to model the borehole-fracturing operation. The model consists of a band of uniform hydrostatic pressure sandwiched between two bands of uniform shear stress in an infinite body. The principal stresses are assumed to be the vertical overburden stress and two horizontal stresses, which cause easily determined stress concentrations. Fairhurst (1964) was the first to propose using the hydraulic frac­turing method principally as a stress measuring technique. He summa­rized the theory of the method and investigated the theoretical effect of rock anisotropy on the stress distribution. His results show that anisotropy has a significant effect. Zoback and Haimson (1982) dis­cussed several complex problems encountered with the reduction of data. meth-ods. 1960) ~ l. fracturing • frac-turing summa-rized dis-cussed 16 Stress Relief Methods The photoelastic materials used in rock mechanics applications are analyzed with a circular polariscope. The theory of photoelasticity is well-known. Dally and Riley (1978) published a good review of photo­elastic theory. Hawkes (1968) described the theory and method for data reduction of photoelastic biaxial strain gauge data. He described the method of calculating the major and minor principal strain magnitudes by locating the point on the minor strain axis where the stress difference is inde­pendent of the strain ratio. A relationship between strain and fringe order is obtained to calculate the major principal strain. A strain ratio is determined to allow calculation of the minor principal strain. Hawkes and Fellers (1969) compared the theoretical distribution of stress in a photoelastic biaxial gauge with experimental results. They noted that the greatest principal stress can be related to fringe order by a sensitivity factor within some error. This sensitivity factor varies with the major/minor principal stress ratio. However, its application to all biaxial stress fields is within acceptable error limits. The theory of elasticity yields equations which relate the diameter change of a hole in an infinite media to the change in the applied stress (Timoshenko and Goodier 1951). Merrill and Peterson (1961) applied the theory to the deformation of a borehole in rock. They conducted a study in which rock models of three different rock types were subjected to a known applied stress. Deformations along various diameters were measured and compared with the theoretical deformation photoe1astic known. 1S 1n 1961) 17 assuming plane stress conditions and isotropy. They had good agree­ment. Deviations from theory could be explained by anisotropy of material properties of two of the rock types. Merrill and Peterson suggested that the method would be applicable for determining stress in situ if the plain strain assumption were used. Hiramatsu and Oka (1962a and 1962b) derived a solution for the components of displacement of a point in rock near a borehole due to relief of the stress state. They used the equations of equilibrium of stresses with boundary conditions to derive the equations. They assumed, however, that the components of stress, the radial and tangen­tial components of displacement, and the axial component of strain do not vary along the direction parallel with the axis of the hole. These assumptions collectively imply that all quantities are independent of z. It seems that these assumptions may force their solution to apply to only special stress case. The displacement solution of Hiramatsu and Oka is applicable to the data reduction schemes of the U.S. Bureau of Mines borehole deformation gauge and the University of Minnesota four-component borehole deforma­tion cell for diametral displacements. Bonnechere and Cornet (1977) list these equations as the basis of data reduction of the "Universite de Liege" borehole deformation cell, which measures axial and diametral displacements. The solution has been applied to any instrument using relative displacement of two points on the wall of a borehole due to stress relief to determine the stress tensor. Indeed, Hiramatsu and Oka (1968) suggested the measurement of relative displacement of two oblique points on the wall of a borehole as a stress measurement means. speciAl component 1977) 18 Also, Oka and Bain (1970) suggested using measurements of diametral and axial displacements to determine the stress tensor with measurements in one borehole. The equations which relate the strains on the wall of the borehole to relief of the in situ stress states can be obtained from the displacement equations of Hiramatsu and Oka by taking the appropriate derivatives. Hayes (1965) confirmed the displacement solution of Hira­matsu and Oka and applied the equations for strain on the wall of a borehole derived from that solution to a new technique for determining the preborehole stress state. Leeman and Hayes (1966) restated the theory of the method with a proposed instrument. Leeman (1968) tested the technique in the laboratory and underground. In the laboratory he used his instrument to bond the strain gauge rosettes to the wall of a hole in steel cubes, 12 inches along each length. The angle of the axis of the hdle varied from 0 to 30 degrees from horizontal in the seven steel blocks. The tests showed the theoretical basis to be valid. There is no mathematical relationship between the strains on the flat end of a borehole and the prehole state of stress. Leeman (1964b) experimentally determined a factor indicating stress concentration on the end of a borehole. The factor varied slightly for different mate­rials. Many investigations have been carried out to determine stress concentration factors. As many as three independent stress concentra­tions factors have been found for the case of isotropy. The assump­tions used in data reduction is that the normal stresses on the end of the borehole are related to linear combinations of the normal prehole 1n aX1S hOle 1n 1S 1964b) 1S 19 stresses, and that the shear stress on the end of the borehole is related linearly to the corresponding prehole shear stress. The strain measurements on the end of a borehole yield information on the prehole stress state in the plane parallel with the end of the borehole. Many investigations of these stress concentration factors have been con­ducted. Rahn (1984) summarized the methods and results of these investigations for the isotropic case. To determine the six independent components of the stress tensor, at least six independent measurements with an instrument are necessary. Leeman (1967) did an analysis of the "soft" borehole deformation gauge. He erroneously pointed out that four of the stress components could be obtained from measurements of the changes in length of four different diameters in the same borehole. The other two components of the stress tensor could be obtained with measurements in a second bore­hole that is riot parallel with the first. Moody (1968) pointed out in his discussion of Leeman's paper that only five such measurements from two boreholes are independent. In addition, only three such measure­ments from one borehole are independent. A measurement from a third borehole is necessary to determine all six components of the stress tensor. Panek (1966) described the application of the least squares statistical method for obtaining the average stress tensor from several measurements of the borehole deformation gauge. Gray and Toews (1967) discussed the question of the number of inde­pendent measurements with the CSIR's doorstopper. They concluded that only three measurements are independent for one borehole and five dot tpe 20 measurements are independent in two boreholes. A measurement from a borehole in a third direction is necessary. Amadei (1983) pointed out and discussed the cases where the aniso-tropy of the rock makes it possible to make six independent measure­ments in just two boreholes. Kanagawa and others (1986) explained that the strains measured with their instrument are converted to in situ stress by using strain sensi­tivity coefficients and the theory of elasticity. Their explanation of the data reduction scheme is vague. It is not clear whether the meas­urements are converted to strain or displacements. Also, it is not clear what assumptions were made concerning the effect of the glue inclusion on the reduction scheme. Hiramatsu and Oka (1968) discussed the measurement of strains on the wall of a borehole. They pointed out that six strain measurements at two locations*on the wall of a borehole are not enough to determine the complete stress tensor. A third location of measurement must be used, and the angle around the hole between any measurement sites must not be 180 degrees. Rocha and Silverio (1969) presented the data reduction theory for their LNEC solid inclusion cell. They superimposed solutions for deformations in a solid inclusion in a hole due to each stress compo­nent. Compatibility of displacements and axial strain across the rock-plastic interface are used for the solution for an axial normal stress. The solution for the effect of stresses in the plane perpendi­cular to the hole axis comes from Muskhelishvili (1953). The solution of strains in the inclusion due to axial shear stresses seems inade-measurements anlSO­tropy ln locations~on plastic Muskhelishvi1i inade- 21 quate because it is assumed that the inclusion does not hinder dis­placements on the hole boundary. Blackwood (1977) found the analysis of Rocha and Silverio to be inadequate and presented a new solution. Rocha, Silverio, Pedro, and Delgado (1974) developed a data reduc­tion scheme for the hollow inclusion type of cell. The strain gauges are not glued directly to the wall of the borehole. This means that the analysis of Leeman and Hayes is not applicable. Rocha and his colleagues developed expressions for strains in the plastic layer due to changes in the stress state of the surrounding rock, assuming that the plastic offers no resistance to displacement of the rock. For the axial normal stress and the two axial shear stress components, exact solutions were obtained. For the other stress components, numerical solutions were used. Worotnicki and Walton (1976) introduced the concept of "K factors" in the data reduction scheme of their gauge. They used Savin's (1961) solution for an elastic ring welded into a circular hole in a plate to develop expressions for two of the four K factors. Another K factor was estimated assuming continuity of gradients of deformations across the rock-plastic interface. The expression for the last K factor was based on a plane strain assumption in the rock-plastic composite. Duncan Fama and Pender (1980) developed an exact solution for strain at a point for the K factor that Worotnicki and Walton only estimated. Stress Compensation Methods Theory for these methods assumes that the rock's behavior is elastic and completely reversible (Alexander, 1968). It also assumes that the relieved stress is only normal to the cut slot. Shear stresses that 1S r~uction 1961) plastic plastic 22 may be relieved are neglected. The principal directions must be assumed or measured in order to overcome this difficulty. To obtain the stress tensor, measurements in planes perpendicular to the princi­pal directions must be carried out. In Situ Stress Measurements Many measurements have been carried out for determining in situ stress. The most popular instruments in the past have been the CSIR's doorstopper and the USBM's borehole deformation gauge. However, instruments that can measure the stress state in just one borehole are increasing in use. Since the stress state in situ at any point is unknown, complete verification of the stress measurements is impossible. However, the measured vertical stress can be compared with the theoretical vertical stress based on the weight of the overburden. This approach tacitly assumes that the vertical direction is a principal direction. The measurements of one instrument can be compared to measurements of other instruments at the same test site or at other sites nearby. Finally, several measurements of the same instrument can be compared for repro­ducibility. Stress measurements with the CSIR's doorstopper have been carried out by many investigators. Some of these are Leeman (1964a and 1964d), Bielenstein and Eisbacher (1970), Pallister, Gay, and Cook (1970), Gay (1979), and Beus and Chan (1980). Generally, the measured vertical stress component agreed with the theoretical overburden stress. Beus and Chan (1980) used the method in ground with extensive fracturing with good success. princi-pal 1n 1S • repro-ducibility. 23 The CSIR's triaxial strain cell has been used to determine the stress in situ by many investigators, also. Some of them are Leeman (1968), Herget (1973 and 1974), Gay (1975), and Van Heerden (1976). Tests have shown that results are consistent and are similar to meas­urements with other instruments. Herget (1974) reported stress meas­urements with the triaxial and doorstopper instruments. Results using the triaxial cell had better precision. Gay (1975) reported in situ stress measurements at several locations in South Africa using the CSIR's triaxial and doorstopper cells, photoelastic disc techniques, and a stressmeter developed by Hast. The results from all measurements were believable and showed good agreement between instruments. Ageton (1967) used the USBM's single-component borehole deformation gauge to measure the stress state in a zone 4000 feet below the surface in the Coeur d'Alene mining district in Idaho. Several measurements in two of the hoIfes were consistent. Only three readings were taken from the third hole. The four-component borehole deformation gauge was used by Le Francois (1970) to determine the stress state at a site in southern India. Test results of several measurements were uniform. The verti­cal component of stress was in agreement with the theoretical over­burden stress, and the horizontal stress was about twice the vertical stress. Stress measurements done with the USBM borehole deformation gauge are numerous. The instrument has been used extensively along with other instruments in order to compare measurements. Van Heerden and Grant (1967) reported a comparative study of results of in situ meas- photoe1astic component hol~s component 24 urements from the doorstopper and the borehole deformation gauge. The magnitudes of the principal stresses determined with the latter are consistently higher than those determined with the former. However, there is satisfactory agreement between results of the two methods. Similar stress magnitudes and orientations were obtained in situ when Rough and Lambert (1971) used the borehole deformation gauge and wire resistance strain gauges to measure the stress state. They had no success using photoelastic discs because of failure of the core to transmit tensile strains to the gauge. Lindner and Halpern (1978) compiled the results of stress measurements over a 20-year period in North America. The instruments or techniques used are the USBM's borehole deformation gauge, the CSIR's doorstopper, photoelastic strain gauge and electrical strain gauge techniques primarily on surface outcrops, and hydraulic fracturing techniques. The listing of these results and their locations is a tremendous aid for better understand­ing the in situ stresses in North America. Kanagawa and others (1986) used their gauge to measure the stress tensor at 23 sites throughout Japan. Results of the measurements show that the vertical stress component corresponds with the theoretical weight of the overburden. The measured maximum principal stress is usually horizontal. Successful measurements were effected in both hard and soft rock. Jalkanen (1982) used the CSIRO's HICell to measure the stress state in Upper Michigan. The strains are very consistent. The vertical stress component correlates very well with the calculated weight of the borehole' Wlre 1978) 1n th~ir 25 overburden. The horizontal components were roughly twice the vertical stress. Numerous comparisons of in situ measurements with the USBM borehole deformation gauge and the CSIRO's HICell have been done. Worotnicki and Walton (1976) reported good correlation between results of the two methods. The same investigators reported more results which were simi­lar between the gauges (1979). Denham (1979) reported a study of near-surface measurements with the two gauges with good agreement of horizontal stresses. Worotnicki and Denham (1976) summarized stress measurements at locations throughout Australia with several instruments and methods, including the doorstopper, flat jacks, the borehole defor­mation gauge, and the HICell. Results were similar and showed expected trends, but the flat jack method sometimes gave widely scattered results. Worotnicki and Walton (1983) had problems with core discing in attempting Itress measurements with the HICell and the borehole deformation gauge. Drilling at a 45 degree angle to the discing plane did not improve the problem sufficiently. Stress measurements using the hydraulic fracturing technique were carried out in Upper Michigan (Kim and Smith, 1980) and in Ontario (Haimson and Lee, 1980). Results showed good agreement with previous measurements in each region. Haimson (1978) described field results using the method at several sites in the United States and in Iceland. Depths ranged from near the surface to 5000 meters. The major princi­pal direction across the United States seemed to be uniform in a north­east direction. Stress measurements using both the HICell method and the hydraulic fracturing technique were carried out in Australia. S1m1- lar and methods, including the doorstopper, flat jacks, the borehole defor­mation gauge, and the HICell. Results were similar and showed expected trends, but the flat jack method sometimes gave widely scattered results. Worotnicki and Walton (1983) had problems with core discing in attempting Itress measurements with the HICell and the borehole deformation gauge. Drilling at a 45 degree angle to the discing plane did not improve the problem sufficiently. direction. Stress measurements using both the HICell method and 26 Enever and McKay (1980) report that the results of the two methods are comparable, except that the vertical component of stress differs. Pine, Ledingham, and Merrifield (1983) measured the stress state at a site in the United Kingdom using the hydraulic fracturing technique. Pine, Tunbridge, and Kwakwa (1983) reported overcoring tests at a nearby mine using the HICell and the USBM borehole deformation gauge. Agreement between results from the HICell and the borehole deformation gauge was satisfactory. The direction of the maximum horizontal stress from results of these two instruments compare well with that from the hydrofracturing test. The LNEC solid inclusion gauge was investigated in situ by its inventors. Rocha and Silverio (1969) reported that two test in the same borehole produced similar results except for the principal stress closest to the direction of the hole axis. They could not explain the difference. Binding failure was later found to be an inherent problem with the technique (Rocha, Silverio, Pedro, and Delgado, 1974). Blackwood's solid inclusion instrument was used to measure the stress state in coal (Blackwood, Hargraves, and McKay, 1976; Blackwood, 1982). In the first case study, the vertical stress was less than the expected weight of the overburden. This tends to confirm earlier tests in the same coal seam using flat jacks. The ratio of the measured major horizontal to vertical stress was much lower in the second case study than in the first. This was expected, given the geologic loca­tions . Led ingham, HICe11 B~nding glven loca-tions. 27 Summary Nondestructive methods and stress compensation methods for stress measurement have an uncertain future. For the former, a clear under­standing of all the factors that affect the techniques is not at hand. The accuracy of data of stress compensation methods is in doubt since shear stresses around the slot are also relieved. The application of the method near the surface of an opening in rock is also in doubt. The hydraulic fracturing method of stress measurement is a viable method for stress measurements at great depth, where assumptions for its data reduction theory are valid. The overcoring stress relief technique is well-established. Instru­ments which can measure the stress tensor in one borehole have great merit where good ground conditions exist. The borehole deformation gauge type of instrument still is a widely used technique as is the CSIR's doorstopper. The latter has a promising future because of the good results achieved in the past in poor ground conditions. The data reduction schemes of most of the instruments are based directly or indirectly on the solution by Hiramatsu and Oka (1962a and 1962b). Hiramatsu and Oka make a plane assumption in their analysis because of the existence of the hole. Their plane assumption is not only placed on the stress changes due to the inclusion of the hole, but also on the stress state that existed before the hole. The plane assumption indicates that the solution of Hiramatsu and Oka is a special case. An alternative solution was suggested by Pariseau (1984). An experimental test of the situation became an important part ~s ~s Instru-ments 1.S 28 of this thesis. The alternative solution has quite recently been proved correct (Pariseau, 1987). CHAPTER 3 STRESS MEASUREMENT FIELD WORK Stress measurements have not been commonplace in coal mines. As mining progresses to deeper seams and economic conditions force mining engineers to design more critically, stress measurement data become valuable. The advantages offered by the Commonwealth Scientific and Industrial Research Organization's (CSIRO) Hollow Inclusion Stress Cell (HICell) would be a great aid to the industry. The instrument was designed for absolute stress measurement by using the overcoring method of stress relief. The instrument has potential value as a stress change monitor in coal mines. It was determined to try the HICell in the field along with the US Bureau of Mines three-component borehole deformation gauge. The latter is a common instrument, and measurements from both instruments can provide a mutual check. Field work was conducted at the Beaver Creek Coal Company No.2 Mine, near Price, Utah. This chapter describes the field work and presents the results and conclusions. Objectives The purpose of the field work was to try out the HICell and USBM borehole deformation gauge in coal-measure rock and assess the feasi­bility of their use for coal mine operators. The emphasis of this assessment was originally to be absolute stress measurement, but when CSIRO) ~ component tryout measure feasi-bility 30 constraints of the company made it impossible to complete all of the desired testing, the main objective shifted to evaluating the HICell as a stress monitoring device in Utah coal mines. Field Work The mining company was short of man power and was operating in very tight economic conditions. Constraints allowed us to have an experienced driller for seven 10-hour shifts in a 2-week time period. This period of time was not sufficient to allow completion all the drilling required to complete the absolute stress measurement portion of the investigation. A HICell was installed in a borehole and moni­tored during almost 10 months while mining was retreating. The field testing will be described in three sections. First, the testing site is described. Second, the experience obtained overcoring the HICell and borehole deformation gauge will be briefly described. Third, the performance of the HICell during the period of monitoring will be discussed. It is assumed that the reader has some general knowledge about in situ stress measurements using the overcoring tech­nique and about the HICell. The overcoring technique is described by Hooker and Bickel (1974). The HICell technique is described by the field manual for the instrument, available from Geokon, in Lebanon, New Hampshire, and is also described by Worotnicki and Walton (1976) and by Jalkanen (1982). Site Description The Beaver Creek No.2 Mine is located near Helper, Utah. Figure 1 shows the general location of the mine. The coal seam lies under a m1n1ng lO-ln moni-tored 1n tech-nique 1S 1S State of Utah Beaver Creek Mine No.2 mine 12 miles from Highway 6 Helper US Highway 6 Price Figure 1. General location of the Beaver Creek No.2 Mine 31 32 relatively shallow cover of sedimentary rock. Immediately above the coal seam is a layer of sandstone about 1 ft in thickness. Above the sandstone is a layer of gray siltstone of unknown thickness. There are some vertical joints present, but they are generally spaced far enough apart that no problem should exist in intersecting major joints with a vertical drill hole. The greatest depth of overburden in the mine is about 750 ft. In order to get good resolution of strains from the HICell it was necessary to select a site in an area having nearly that much overburden. A test site was selected in Section 22. Figure 2 shows the layout of the area around the instrument site. The site is in a crosscut next to a virgin area. An igneous dike runs roughly parallel with the entries as shown in the figure. The width of the entries and crosscuts is roughly 20 ft. The seam thickness averages about 8 ft. Absolute Stress Measurement The testing plane called for installation of the instruments in the roof rock. It was known that coring in the coal seam was impossible due to the nature of the coal. Coring characteristics of the roof was unknown, but visual examination of the immediate roof gave reason to believe that coring would be successful. The testing plan called first for drilling a vertical hole up into the roof. In this hole an actual practice installation of the HICell would take place as soon as possible. Several measurements with the borehole deformation gauge would then be performed in the first bore­hole, and these measurements would indicate the extent of significant influence of the opening. As many as three more HICell installations 1S IS IS vlrg1n An about 8 ft. In 3333 t rue north v magnetic ....... ....... of measured horizontal principal stresses at test site Figure 2. Test site 1n Section 22 at Beaver Creek No.2 Mine 34 and overcorings would then take place. Finally, two more boreholes would be drilled at some degree to vertical into the roof. Installa­tion and overcoring of the borehole deformation gauge in these bore­holes beyond the influence of the opening would permit determination of all components of the state of stress to compare with that measured by the HICell. At about 12.5 ft up the vertical hole, the first HICell was installed. The piston which displaces the glue could not be fully depressed because of the glue viscosity, but it was estimated at the time that the piston had probably displaced enough glue to fully sur­round the rosettes embedded in the HICell. The drill was a TPT-65 post-mounted diamond drill. The recommended overcoring speed of the chuck is 120 rpm to minimize core breakage. The drill did not have the capability of such a slow speed. However, a core 16 in. inslength was obtained in that practice run, and most cores ranged from 12 to 16 in. in length. A Micromeasurements P-350A Strain Indicator, modified for use with an HICell, was used to read the strain gauges. The cycle of reading all nine strain gauges continued after the initial reading through the overcoring process and after the drilling had stopped until all read­ings had stabilized. Figure 3 is a plot of the gauge readings versus drilled inches along the core. Where there are no tick marks on the horizontal scale, it becomes a coarse, relative time scale. This is where no drilling took place, but readings still were taken. The drilling was forced to stop at one point in order to add another sec­tion of drill steel. The plot shows a discontinuity in the trend of overcorlng mounted in~length c • - I o 00 Q LU 00 < Ld O A + • X O V B GAUGE GAUGE GAUGE GAUGE GAUGE GAUGE GAUGE GAUGE GAUGE 1, AXIAL 2, CIRC. 3, 45 DEG. 4, 45 DEG. 5,135 DEG. 6, CIRC. 7, AXIAL 8, CIRC. 9, 45 DEG. 0 DRILLED INCHES ALONG CORE first HICell KEY 0 6 + x 0 5, 135 v ~ ~ • DEG . c• 120 '" 100 • I STOP C .- 80 FOR CENTER UNE (.0 DRILL OF" GAUGES 60 STEELS 0 ~ .. 40 -,,; DRIWNG «-Z 20 BEGINS ~ (/) 0 0w -20 a::: ~(/) -40 « w -60 DRIWNG ~ STOPS -80 5 10 15 20 Figure 3. Plot of strains measured during process of overcoring the fi r s t HI Ce 11 35 36 the readings at that point, but shows a continuation of the same trend afterward. A biaxial compression test was not performed in the field because an error in the preliminary starting of the EX hole made it impossible for the core to support the neoprene liner of the biaxial chamber around the its full circumference. Another HICell was installed at a hole depth of 13 ft-9.5 in. During the overcoring process, the core broke at the gauge site. The borehole deformation gauge was installed at a hole depth of 15 ft-1 in. during the last day that a driller was available. The instrument was calibrated underground in the mine environment. Figures 4(a), (b), and (c) are plots of the results of this calibration for each component. The results are linear. A plot of the overcoring data appears in Figure 5. The readings were not allowed to stabilize on completion of drilling because a surge in water pressure occurred, and the instrument*would have been damaged if the drilling water had been shut off. A biaxial pressure test was performed in the field on the core with the instrument in the EX hole. Figure 6 is a plot of the displacements versus biaxial pressure. Because the behavior of each component does not line up with each other, there may be a problem with either the calibration of the instrument, or with the contact of the component pistons with the wall of the hole. The behavior of the material seems to be nonlinear. In this case, the component 3 data should be used to determine Young's modulus because it is more likely that the pistons rather than those of components 1 and 2 were in contact with the wall of the hole during the test. A secant modulus of elasticity from 9.S IS l t) 1n S. instrument~would shut off. determine Young's modulus because it is more likely that the pistons rather than those of components 1 and 2 were 1n contact with the wall 37 Figure 4. Plots of calibration of the USBM borehole deformation gauge (a) Component 1 (b) Component 2 (c) Component 3 ~Component 38 -16 - - 2 4 - - 32 KEY o LOADING a UNLOADING I 1 1 i 1 1 i 1 1 i 1 1 I 1 1 i 1 1 i 1 • J i , , i . . i 3 STRAIN INDICATOR READING, 10~3 K / ia •? 1- 2 -16 - -24 - - 32 STRAIN INDICATOR READING, 10"3 in/in. (b) /; .~ '? -8 52 - -32 ~I@I-I",",",--,-"""''''''''.-''''''''''''''''''''-'''''''''''''' -24 -21 -18 -15 -12 -9 -6 -3 0 3 READING. 10-3 in/in. (a) .~ '? -8 52 -32 ..... oe-o~ ....................... --""-""""-'~ .................. -24 -21 -18 -15 -12 -9 -6 -3 0 3 READING. 10-3 39 KEY o LOADING a UNLOADING - 2 4 - - 32 C 9 - - 3 3 STRAIN INDICATOR READING, 10~3 in/in. c) LOADING to UNLOADNG .~ ot) -8 D I ~ ·i -16 ~ - 24 - -32 ......... -.-................................ --... ........... -24 -21 -18 -15 - 12 - 9 -6 -3 0 3 READING. 10-3 In. (d •- I o en < O < CJ O or m < LJ o COMPONENT 1 A COMPONENT 2 + COMPONENT 3 DRILL STOPS' 5 15 DRILLED INCHES ALONG CORE 40 KEY 0 .c-• l:. CCOOMMPPOONNEENNTT 23 ta 2200 ,0.... ... ... 2000 et: 1800 tJ 1600 ~ ~ 1400 0 1200 CENITR UNE Z OF" PISTONS - 1000 w '-' 800 Z <l: 600 UI 400 0w 200 :0::>:: 0 U') -200 <wl: 0 10 20 2 Figure 5. Plot of displacements measured during process of overcoring the USBM borehole deformation gauge 41 o COMPONENT 1 A COMPONENT 2 + COMPONENT 3 LOADING - UNLOADING MEASURED CHANGE IN DIAMETER, 10"6 In. 6. 6-0 .- (I) c.. ... U1 -200 ~ ~ -400 --1 « X « -600 C5 0 w -800 ~ « -1000 ~ 0 6 - KEY UNLOADING ,, , " , ," ,,' ~.---- .... , .. .... -j!' ,, , ,, , -, I ,, I I ,I I ,, , , , , , , .. " -3200 -2400 -1600 -800 0 10-6 in. Figure Plot of changes in diameter of the pilot hole measured with USBM borehole deformation gauge during underground biaxial pressure test on in. diameter core 42 component 3 using data points at biaxial loads of 0 and -600 psi was determined to be 0.270 x 10^ psi. Elastic properties were determined in a subsequent rough test in the laboratory on one of the cores. The specimen had an average diameter and length of 5.72 in. and 10.42 in., respectively. End parallelism was measured to be within 0.06 in. Four 0°-90° strain gauge rosettes were bonded at the axial midplane at 90° intervals. The strain gauges were monitored while a uniaxial load was applied to the specimen. The nonparallel ends caused eccentric load­ing, which fractured a chip from the edge of the top surface. This problem forced the use of a 2.50-in. diameter spherical seat and an 8- in. diameter plate of 2-in. thickness to distribute the load more evenly. The test was repeated. The results of this test are plotted in Figure 7. The results are nonlinear, and the loading was nonuni­form. The initial nonlinearity can be explained by the closing of cracks and microfractures. The mismatch of material properties along the interface of the specimen and the loading platen is also a possible explanation. Material properties were measured using the tangential slopes .of the axial gauges and lateral gauges of the linear portion of the curve greater in magnitude than -500 psi. The strain gauge read­ings were averaged to cancel any bending effects. Young's modulus and Poisson's ratio were measured to be 1.72 x 10^ psi, and 0.14, respec­tively. From this information, it was possible to calculate a secondary horizontal stress field, assuming that the measured displacements at the completion of drilling represented the end points of stress relief, and that the underground calibration of the components was accurate. 106 2.S0-mic~ofractures. pf pS1. read- 1ngs 106 KEY o POSITION 1, AXIAL GAUGE A POSITION 1, LATERAL GAUGE + POSITION 2, AXIAL GAUGE x POSITION 2, LATERAL GAUGE o POSITION 3, AXIAL GAUGE v POSITION 3, LATERAL GAUGE a POSITION 4, AXIAL GAUGE * POSITION 4, LATERAL GAUGE -1400 ' 1 1 ' 1 1 1 1 ' 1 1 1 ' 1 1 1 1 1 1 1 2000 10 6 5.72-diameter " 43 KEY ~ o \J ~ ~ .- 0 (/) n. ... -200 (f) (f) w 0:::: -400 I- (f) -600 >j 0 W --.J CL -800 CL <i w -1000 c..') « 0w:::: -1200 ~ -1400 ...................... .-.... ....... --.. ................................... ---. ................ - 2000 -1500 -1000 -500 0 MEASURED STRAIN, 10-6 in./in. Figure 7. Plot of results of uniaxial test on S.72-in. diameter siltstone core 44 It must be assumed that strain in the axial direction was negligible in order to have a determined system of equations (Obert and Duvall, 1967). The Young's modulus determined from the biaxial state of stress probably represents the in situ behavior of the core more accurately than the one determined from the laboratory uniaxial test. The secon­dary major principal stress was determined to be -60 psi (compression is negative) in the direction N 48° E with respect to true north, and the secondary minor principal stress is -140 psi with a bearing S 42° E. The magnitudes are consistent with gravity loading and the Poisson effect. In the laboratory, the core containing the first HICell was sec­tioned in the longitudinal direction. Figure 8 shows the sectioned core. Examination showed that there was no glue around the strain gauge rosettes. The glue was too viscous. Subsequent contact with personnel from the CSIRO produced a possible solution. A glue for temperature ranges between 4°C (39°F) and 15°C (59°F) is now available through Geokon (Lebanon, New Hampshire). Three successful field installations in underground environments below room temperature have occurred because the personnel involved were alerted to the glue vis­cosity problem (Johnson, 1986). Stress Change Monitoring During the last half of the last shift in which the driller was with us, he drilled an EX hole parallel with the first to a depth of approximately 11 ft. The centers of the two boreholes were 14.3 in. apart. Five days later the site was entered. In the first hole at a depth of 16 ft-5 in., another HICell was installed. The piston which In secon-dary compression sec-tioned ~ lSoC S9°VIS-cosity In. gure 8. Sectioned si Itstone core through pilot hole and HICell 45 Figure siltstone • - ( \ 47 forces the glue into the annulus between the rock and the instrument displaced farther compared to the first HICell installation, and there­fore, it is likely that the area of the strain gauges was bonded to the wall of the borehole. In the second drill hole at a depth of 10 ft-3.5 in., the borehole deformation gauge was installed. The purpose was to monitor the behavior of these two instruments as Section 22 was mined on retreat. Of interest were the stability of the instruments over time and their sensitivity to changes in stress caused by retreat mining. Changes in mine planning and scheduling delayed the passage of the pillar line by the instrument site, but selective mining of pillars was such that no pillars were mined within 350 ft of the instrument site. The monitoring data, then, are only an indication of the stability of the respective instruments over time. Figure 9 is a plot of the HICell strain readings over time. Also shown is the temperature history. The initial reading was taken within 30 minutes after installation. The scatter of the readings between day 0 and day 5 was due in part to relaxation of the instrument after stressing it in the installation process. The scatter was probably also due to shrinking of the glue during curing. Subsequent monitoring showed that the circumferential gauges had the highest compressive strain change of about -480 microstrain from day 5 to day 293. The axial gauges showed both tensile and compressive changes, but the changes were of low magnitude. The behavior of the 45°/135° gauges was variable, but generally, they were compressive and between the axial and circumferential gauges in magnitude. The glitch in the data UICel1 3.5 1n., m1n1ng. i~ UICel1 o KEY o A CIRC. + DEG. DEG. o DEG. CIRC, a * CIRC. • © ROCK TEMPERATURE TIME, days 0 50 DAY 0 AUGUST 1, 1984 igure c. 100 ".c" 50 to 0 I 0.- -.. -50 Z -100 4: 0::: -150 I-Vl -200 0 w -250 0::: :J ... (J) -300 <! w -350 ~ -400 KEY 0 GAUGE 1, AXIAL 6. GAUGE 2, eiRe. GAUGE 3, 45 DEG. x GAUGE 4, 45 DEG. 0 GAUGE 5, 135 DEG. v GAUGE 6, eiRe. ~ GAUGE 7, AXIAL ~ GAUGE 8, eiRe. + GAUGE 9, 45 DEG. El I , , I , , , 0 50 100 150 200 100 150 200 TIME, days = 1984 48 250 300 250 300 Figure 9. Plot of strains measured in a HICell during the underground monitoring period 49 between days 124 and 132 was due to an electrical contact problem in the strain indicator switch unit. The second glitch at day 265 is thought to be due to workers pulling on the instrument's cable shortly before the readings were taken. The largest temperature difference during the time of monitoring was approximately -6°C (11°F) between day 0 and day 188. The thermal strains output for the circumferential and axial gauges were calculated to be 125 and 6 microstrain, respectively, using the equations of Walton and Worotnicki (1986). The siltstone coefficient of thermal expansion was assumed to be 10 microstrain/°C (5.5 microstrain/°F). Experimental results of Walton and Worotnicki (1986) show that the thermal strain output of the 45° and 135° gauges is roughly half that of the circumferential gauges. The sign of the thermal strains is tensile. Comparison of the trends in measured strain with the tempera­ture history shows that the trend of compressive strain was dampened during periods of falling temperature and accentuated during periods of rising temperature. The difference in circumferential strain from day 5 to day 293 was calculated to be 42 microstrain. Therefore the maxi­mum creep in the circumferential gauges was about -520 microstrain. The behavior of the instrument is consistent with the testing results of Walton and Worotnicki (1986). They left HICells in undis­turbed ground for 1.3 years in the temperature range of 20°C to 40°C (68°F to 104°F). All of their cells were heat cured at 50°C (122°F) to insure polymerization of the epoxy body of the shell. Their results show that the circumferential gauges had changed about -600 micro-strains in compression at about day 300. The axial gauges showed very microstrain/oC microstrain/oF). rlslng HICeils micro­strains 50 little change, and the 45°/135° gauges showed a compression with a magnitude about half of the circumferential gauges. Figure 10 is the plot of the results of monitoring the borehole deformation gauge. Day 6 readings are used as the initial readings due to the large change in readings between days 0 and 6. Table 1 lists the secondary principal stresses and directions calculated from these measurements, assuming material properties of 0.27 x 10^ psi for the Young's modulus and 0.14 for Poisson's ratio. Table 2 lists the calcu­lated principal stresses and directions from the HICell measurements. The near horizontal stresses calculated from the HICell measurements are generally greater than those calculated from the borehole deforma­tion gauge measurements. This results is probably due in part to the higher coefficient of thermal expansion of the epoxy shell of the HICell relative to the beryllium-copper cantilevers of the borehole deformation gauge. The horizontal principal directions generally are not in close agreement. The overburden stress was estimated to be -750 psi, assuming a vertical stress gradient of 1 psi/ft of depth. The largest calculated change of horizontal stress (-25 psi) is only 3% of the estimated over­burden stress. The stress changes are probably too small to be meas­ured accurately with the borehole deformation gauge. The erratic trends of the measured deformations was due mostly to a failure to fix the instrument properly in the hole. During the last month of observa­tion, the instrument slipped about 0.5 in. down the borehole. 106 calcu-lated HICe11 deforma-tion shel~ ~ over-burden meas-ured observa-tion, to I O I < X (J seZ nD - -200 - - CL 5 KEY o a + • ROCK TEMPERATURE « 1 1 u 0 30 60 90 i TIME, days 0 60 90 120 TIME, days DAY 0 = AUGUST 1, 1984 ure wi underground c 0- 100 a -100 -200 -300 .. -400 5 o COMPONENT 1 6 COMPONENT 2 COMPONENT 3 e o o 30 = 1984 120 51 Figure 10. Plot of changes in diameter of the pilot hole measured with a USBM borehole deformation gauge during the underground monitoring period 52 Table 1 Secondary principal stresses and directions in the horizontal plane calculated from monitoring the USBM borehole deformation gauge Day Secondary Principal Stress ( psi) Secondary Minor Principal Stress (psi) Secondary Major Principal Azimuth Secondary Minor Principal Azimuth 5 0 0 6 -1 -13 87° 357° 10 0 -19 95° 5° 14 -4 -23 92° 2° 19 -2 -23 89° 359° 27 -5 -22 90° 0° 57 -5 -25 83° 353° 76 -1 -19 82° 352° 117 -3 -21 79° 349° 124 5 -2 62° 332° 126 0 -16 77° 347° 132 -2 -23 80° 350° Note: Tension is positive. 1n " 352 0 -:-347 0 350 0 53 Table 2 Principal stresses and directions calculated from monitoring the HICell Princ. Princ. Day Stress Dip Azimth Day Stress Dip Azimth (psi) (psi) 6 0 0 0 10 5 -89° 238° 132 4 88° 54° -1 1° 295° -27 1° 166° -3 1° 206° -43 2° 256° 14 4 -84° 269° 167 10 86° 37° -2 5° 309° -24 2° 167° -6 4° 219° -46 3° 257° 19 2 -84° 256° 174 7 87° 28° -6 3° 316° -27 3° 168° -10 5° 226° -49 2° 258° 22 1 -86° 267° 188 7 86° 25° -8 * 3° 321° -28 4° 168° -13 4° 231° -50 3° 258° 27 0 -86° 267° 201 4 86° 43° -11 2° 326° -29 2° 164° -15 4° 236° -54 3° 254° 57 2 88° 35° 245 -10 86° 35° -19 1° 156° -42 3° 170° -26 2° 246° -71 3° 260° 76 5 88° 45° 257 -14 86° 27° -20 1° 156° -45 3° 171° -29 2° 246° -75 2° 261° 117 6 -86° 257° 265 -5 86° 30° -22 1° 334° -39 3° 172° -34 4° 244° -70 3° 262° 124 12 -84° 245° 280 -15 86° 18° -16 0° 333° -47 4° 171° -33 6° 243° -79 2° 261° 126 3 87° 52° 293 -18 83° 358° -27 1° 159° -51 7° 171° -42 3° 249° -83 1° 261° Note: Tension is positive. Dip is positive down HrCell Prine. Az irrith 890 880 2950 1660 2060 840 50 20 84 0 256 0 3 0 316 0 50 86 0 267 0 860 25 0 '" 321 ° 2310 860 267 0 2 0 40 236 0 3 0 86 0 156 0 2460 30 10 156 0 30 171 ° 246 0 261 ° 10 30 ISo 171 ° 60 IS 35So 171 ° ~s down. 54 Summary Although there were no successful HICell installations for measur­ing the absolute stress state, a problem with the glue viscosity at temperatures found in Utah coal mine environments was discovered. Consultation with CSIRO personnel brought to our knowledge an alterna­tive glue for use in that temperature range. That glue is available from Geokon in Lebanon, New Hampshire. The USBM borehole deformation gauge requires the drilling of at least three holes. This is a sub­stantial cost to the mine operator. Perhaps this instrument can be used in conjunction with the HICell to determine when the drilling has passed the influence of the opening. The HICell creep rates are in general agreement with the study of Walton and Worotnicki (1986). The HICell exhibited a maximum creep of about -480 microstrains in a circumferential gauge during approximately 290 days. The? net circumferential thermal strain during this time was calculated to be about 40 microstrain, and the creep was estimated to be about -520 microstrain. Such a rate of creep might be insignificant for a shorter period of time, but it would be significant if the modu­lus were greater in magnitude. The potential use of the HICell as a stress monitor is situation dependent. The stress change was too small to be accurately measured by the USBM borehole deformation gauge. The instrument was not adequately fixed in the borehole so that the measured deformations would be mean­ingful . S4 requ1res Th~ mean­ingful. CHAPTER 4 DATA REDUCTION THEORY The purpose of this chapter is to outline the theoretical basis for borehole stress measurements. In this regard the data reduction schemes of many in situ stress measuring instruments are based directly or indirectly on the solution by Hiramatsu and Oka (1962a, 1962b, 1968). The solution is for the displacement components of a point on the wall of a borehole or circular shaft due to relief of the prehole state of stress in the region surrounding the hole. Many instruments measure relative displacement-either diametric, axial, or oblique-of two points on the borehole wall. Others measure strains on the wall of the hole or ia some hollow, cylindrical medium bonded to the wall of the hole. Instruments which measure displacement use the Hiramatsu and Oka solution directly in their data reduction schemes. The Hiramatsu and Oka solution is based on assumptions that the rock is a homogeneous, isotropic, linear, elastic, infinite medium. The Hiramatsu and Oka solution describes the three displacement com­ponents in cylindrical coordinates. Given the coordinate system of Figure 11, the solution can be written 1+U u r ( ) {( O x ^ O y 0 aa^2 1-U ) [ - + r( )] + [( )cos20 + Tx v°sin20] E 2 r 1+U 2 lnthis displacement--either oblique--is com-ponents l+u Ox 0+ cry 0 a2 l-u Ox o_cry 0 Ur = (-) ( )[- r(-)] cos29 Txy °sin29] l+u 4a2 a4 vr * [r + (I-U)(-) - (-)] - (-)crz o} r r3 l+u 56 Q 8 S6 z Figure 11. Orientation of borehole with respect to Cartesian coordinate system; point Q defined by angle e 57 1+U O^+Oy0 2a2 a4 v Q = ( ) {[-( ) sin26 + Tx v°cos2e] [r + (l-2u)( ) + ~T] } 7 r rJ 1+U 2a2 w z = ( ) {(Tz x°cos© + T °sin0) [2r + ] E J r z • ( )[az°-ox°+ay°)]}. where the superscript , , 0 , , denotes the prehole stress components. In the review of the literature, it was pointed out that the solu­tion derived by Hiramatsu and Oka (1962a, 1962b, 1968) involves a planer assumption in the sense that derivatives with respect to z are zero with the exception of the displacement associated with the initial z-direction strain (a constant). "Alternative" Solution Assumptions for this solution are that the host medium or rock is homogeneous, isotropic, and linear-elastic, as before. It is also assumed that the prehole state of stress is uniform, as before. The necessary elements of theory are the stress-strain equations, the strain-displacement equations, the equations of equilibrium, the compa­tibility conditions, and the boundary conditions. The alternative solution (Pariseau, 1984, 1987) is: 1+U 0xO+ay° a2 U Ox°~°y u r = ( ) {( )[- + r( )] + [( )cos20 + Tx v°sin20] E 2 1+U y 4a2 a4 vr * [r + (1-U)( ) - Or-)] - ( )QZ° + z(Tz x°cos0 + Ty z°sin0)} r rJ 1+U 3 l+u Ox°+oyo 2a2 ve (-) ([ -( sin2e 'txy °cos2e] 2u)(-) (1) wz E 2 r l+2a2 + (-)[ Oz O_u( Ox o+oy O)]}. l+u 11011 denotes the prehole stress components. solu-tion 1S displacement compa-tibi1ity l+u Ox o+oy ° a2 1-u Ox o_oy ° = (-) ( )(- r(-)] cos29 Txy °sin29] r l+u 2 4a2 * [r l-u)(-) (---)OZO + TzxOcos9 + TyzOsin9)} l+u 58 1+U v 6 = t V + O y 0 2a2 a4 ( ) {[-( )sin20 + Tx v°cos20] [r + ( l - 2 u ) ( ) + ~ 7 ] y r rJ + z(-Tz x°sin0 + TyZ°cos0)} 1+U 2a4 w 7 = ( ) {(Tz x°cos0 + Ty z°sin0) [r + ] E J r ( Ma^-uCcV+Oy0)]}. 1+u J (2) Theoretical Difference between "Conventional" and "Alternative" Solutions The difference between the conventional and alternative solutions (Equations (1) and (2)) is in the z-direction shear stresses. In fact, as Pariseau (1987) shows, the difference is in the displacements asso­ciated with the initial stresses. The displacement changes due to the introduction of the pilot hole are the same in both solutions. The alternative solution initial displacements are > = (" w (") E a x 0 - u ( a y 0 + a z 0 ) (1+U) T x y ° ( l + u ) ay 0 - u ( a z 0 + a x °) tzx°(1+u) T y z ° ( l + u ) Tz x°(l+U) T y Z ° ( l + U ) a z 0 - u ( a x ° + a y 0 ) rx " \ For the conventional solution this part is w (-) E a x 0 - u ( a y ° + a z 0 ) Lxy '(1+U) T x y ° ( l + u ) ay 0 - u ( a z ° + a x °) 2 x z x ° ( l + u ) 2 T y z ° ( l + U ) a z 0 - u ( a x ° + a y 0 ) *4 y U A) vS Wz 1 +u Ox o+Oy ° 2a2 = (-) {[-( )sin2S + 1"xyOcos2S] [r + (1-2U)(-) E 2 r TzxOsinS TyzOCOSS)} l+u 2a2 = (-) {( 'tzx °cosS + 'tyz °sinS) [r + -] r z + (-) [oz O_U( Ox o+Oy O)]}. l+u 2» 1n asso-ciated ~f UO 1 Ox O-U( Oy o+oz 0) 'txy 0(1 +u) 1"zx °(1+x = (-) 1"xyO(1+U) OyO-U(Ozo+OXO) 1"yz °(1+u) y (3) 1"zx°(1+u) 1"yz °(1+u) Oz O-U( Ox o+Oy 0) z 1S UO Ox O-U( Oy o+oz 0) 1"xy°(1+u) 0 1 x VO = 'txy °(1+u) 0y O-U(oz o+OXO) 0 E y (4) WO 2 'tzx: ° (1 +u) 21"yz °(1+U) o Z O-U(.o x °+0y 0) z 59 An examination of the difference between Equations (3) and (4) shows that the conventional solution is a special case. Significance of the Solutions on Data Reduction The effect of the differences between the conventional and the alternative solutions on data reduction is not totally apparent. Whether these solutions show a difference in data reduction for various types of instruments is a question which must be addressed. Instruments Which Measure Change in Borehole Diameter According to the conventional equation, the change in diameter of a borehole during stress relief is a ur(0) - ur(&+90°) = (") {0*° [1 + 2(l-U2)cos29] E Oy° [1 - 2(l-U2cos2G] (5) + az ° [-u] + Tx y°[4(l-U2)sin26]}. The change in diameter of a borehole according to the alternative solution is a ur(6) - ur ( 9+90°) = ( - ) {Ox° [1 + 2(l-U2)E + Oy° [1 - 2(l-U2)cos29] Oz° [-u] o (6) Tx y 0[4(l-U2)sin26] + Ty z°[(z/a)(l+u) ( s i n 9 - s i n 9 )] + Tz x°[(z/a)(l+u)(cose-cose)]}. • (-) (OXO 2(1-U2)cos29] + ayO l-U2 )cos29] Oz ° [-U] + TxyO[4(1-u2)sin29]}. = (-) (OXO 1-U2)cos29] ayO l-U2 )cos2e] + Oz ° [-u] + TxyO[4(1-u2)sin2e] + Tyz O[(a)(1+U)(sin9-sin9)] + Tzxo[(z/a)(1+u)(cose-cose»)}. (6) 60 The data reduction equations are the same for the two solutions. Instruments Which Measure Axial Displacement or Oblique Distances across the Borehole If two points on the borehole wall separated by axial distance Az are spatially expressed by the same angle 0, then the change in axial distance between them is Az Aw (-) [az° - u(ax ° + a y ° ) ] (7) E according to both the conventional and the alternative solution. If the two points are also diametrically opposite, the expression for the relative axial displacement component using the conventional solution is 1+U * Aw = ( ) { 2[Tz x°cos0 + Ty z°sin0](4a) 3 Az ( )[az° - iXax0 <jy°)] } , l+u J and using the alternative solution it is 1+U Aw = ( ) { 2[Tz x°cos0 + Ty z°sin0](3a) E (9) Az + ( )[az° - uCcV + a . 0 ) ] }. 1+U ' The general formula for the change in axial distance of any two points 1 and 2 on the wall of the hole is ~ e, b.z &i = (-) O'z ° u( O'x ° O'y ) ] ( 7 ) u , !J.w = (-) { 2( 't'zx °cose 't'yz °sine] (E !J.z + (-)[ O'zo _ u(ax ° + cry 0)] }, 1+u and using the alternative solution it IS l+u !J.w = (-) { 2['tzxocose + 'tyzOsine]Oa) E !J.z + (-)[ O'z ° - u( ax ° + cry 0)] }. l+u The general formula for the change In axial distance of any two points 1 and 2 on the wall of the hole IS (8) (9) 61 1+U Aw = < ~ ) { 2[Tz x°(cos92 " cosBi) + Ty 2 0(sin92 - sin0i)](4a) - sin0i)](3a) (11) z2-zi ( )[az° ax° ov°)] } 1+u 7 using the conventional solution, and 1+U Aw = C ~ ) ( 2[Tz x°(cos02 - cos0i) + Ty z°(sin02 z2-zi + ( )[az° u( ax° + aY°)] 1+u 7 using the alternative solution. The errors involved in using the conventional solution over the alternative solution depends on the stress state. The determination of the axial shear stresses is affected by 25%, but the affect of this error on the magnitude and directions of the principal stresses is dependent on the magnitudes of all components of the stress state. Instruments Measuring Strain On or Near the Wall of the Borehole The conventional and the alternative solutions are both based on the same state of stress and strain. The data reduction for instru­ments which measure strain on the wall of the borehole is not affected by the alternative solution. Also, the data reduction for hollow inclusion cells, such as the CSIRO's HICell is not affected for the same reason. (10) l+u = (---) ( TzxO(cOSe2 - COSel) TyzO(sine2 sinel)](4a) E Z 1 + (--) [OZO - u(Ox 0 + 0y 0)] l+u uS1ng the conventional solution, and l+u Aw = (---) { 2[TzxO(COSe2 - COSel) + TyzO(sine2 sinel)](3a) E z1 (--)[ oz ° - Ox ° 0y ° )] } l+u uS1ng 1S On instru-ments HrCell Summary The difference between the conventional solution and the alterna­tive solution for the displacement of a point due to relief of the stress state is in how each treats the prehole z-direction axial shear stress components. The conventional solution is a special case. The data reduction scheme of instruments that measures the change in diameter of a borehole due to stress relief is not changed by the alternative solution. The data reduction scheme of instruments which measure an axial component of displacement is affected by the alterna­tive solution. The error involved in using the conventional solution over the alternative solution is dependent on the stress state. Data reduction of strain measurements on the wall of the borehole or in a hollow inclusion bonded to the borehole wall are not affected by the alternative solution. 62 1n CHAPTER 5 EXPERIMENTAL INVESTIGATION OF THE DISPLACEMENT SOLUTIONS It was pointed out in Chapter 2 that the displacement solution derived by Hiramatsu and Oka (1962a, 1962b, 1968) was based on an assumption that there is no variation in the radial and circumferential displacements along the z-direction. In Chapter 3 the alternative solution shown does not make that restriction on the effect of the prehole stresses. It was also shown in Chapter 3 that the difference between the two solutions is a matter of simple shear deformation versus pure shear deformation in any plane parallel to the borehole axis. It may ^appear that the alternative solution would logically be correct, but the conventional solution has been accepted and used for data reduction purposes since 1962. To refute the conventional solu­tion without more proof would be quite bold. At the time of developing this thesis the hypothesis was that the alternative solution correctly describes the effect of stress relief on the displacement of any point on the wall of the borehole. A careful investigation would be useful in proving whether the hypothesis is correct. There were two ways to test the hypothesis. The displacements around a hole due to an axial shear stress component could be deter­mined using three-dimensional finite element or other numerical methods. The other choice was to make laboratory measurements of dis- 1S aX1S. appear dimensional 64 placements around the skin of a hole in a physical model. The labora­tory method was chosen for this investigation. Objective of Experimental Research The purpose of this investigation was to test experimentally the hypothesis that the alternative solution correctly describes the dis­placement components of some point on the wall of a borehole due to stress relief. Approach The differences between the conventional solution (Equations (1)) and the alternative solution (Equations (2)) involve the axial shear stress terms T v z ° and T z x ° . The approach was to 1) determine how to apply a pure axial shear stress to a medium, 2) determine which displacement component could be measured and how, * 3) design a method and equipment for applying a pure shear stress to the medium, and 4) perform the experiment. Figure 12 depicts a sectioned medium with a hole. The medium is subject to a pure axial shear stress. Applying a direct uniform shear stress to a medium would be difficult, if not impossible. Figure 13 shows how a pure shear stress in the hole coordinate system can be achieved by the application of (1) a uniform normal compressive stress, P, in a direction 45° from the hole axis, and (2) a uniform normal tensile stress equal in magnitude to the compressive stress in the direction perpendicular to the direction of the compressive stress. 1» 2» Tyz 0 Tzx o. 45 0 65 Txz L- i \\VA\ /A\X v\V// z \\Y7 ¥% x Figure 12. Section of a medium with a circular hole subject to an axial shear stress in the hole coordinate system Figure 13. State of pure shear in hole coordinate system obtained by application of normal stresses 66 p 67 Applying a uniform compressive load over a surface is physically possible in a laboratory, but applying a uniform tensile load is nearly impossible. The case of equal tensile and compressive stresses in perpendicular directions, as shown in Figure 13, produces the desired stress state. If a biaxial stress, P°, which is greater in magnitude than P, were added to that case, then the resulting normal stresses would be compressive, as shown in Figure 14. The difference between this case of superimposed stress states and the biaxial stress state, P°, is the desired stress state which results in a pure axial shear stress in the hole coordinate system. The next step is to determine what can be measured that will dis­tinguish which solution is correct. The strains on the wall of the hole in the medium are the same in both solutions. However, the dis­placements are not the same. Only the measurement of relative dis­placement is possible. In Chapter 3 it was pointed out that although an axial shear stress causes a radial displacement, there is no net change in any length of the diameter. The measurement of relative axial displacement of two diametrically opposite points is a possibil­ity. Figure 15 shows the section of an element with a hole. An axial shear stress is applied to the element. The figure indicates the axial displacement profile of all points around the skin of the hole mapped onto the section plane. The maximum displacement occurs at the top and bottom of the hole. In the horizontal plane-the plane that contains the hole axis and that is perpendicular to the plane of the paper-the axial displacement is equal to zero. The maximum displacement accord- pO, pO, correct.. plane--the paper--68 Figure 14. Addition of desired stress state and biaxial stress state results in applied compressive stresses. _p + po pO -p pO p + 69 zx Figure 15. Axial displacement profile of hole due to an axial shear stress state; Qi and Q2 are displaced to Qi' and Q2*» res­pectively TXz. ,. Ql Ql' :, ...• , . ,• . I. r TZX ..4 ,, • • ... . I ,, /1\\\ ./1\\\ Q2' Q2 of Ql Q2 Ql' Q2" res­pect i vel y 70 ing to the conventional solution is 33% higher than that calculated from the alternative solution. This difference appears to be high enough to allow a physical measurement to distinguish which solution is correct. Figure 16 shows how a device could be anchored in the hole in the plane of zero axial displacement. The device holds two linear variable differential transducers (LVDTs) which measure axial displacement between the device and two stops bonded diametrically opposite each other at the locations of maximum axial displacement. The device would limit errors due to anchorage in a plane of nonzero axial displacement and allow relative axial displacement measurements to two "points" on the wall of the hole. Apparatus The main piece of apparatus is the aluminum model of a borehole. A triaxial reaction frame confines the model and the loading apparatus. The model is loaded hydraulically with flat jacks. Measurements to be carried out are axial displacements inside the hole in the model and strains on the wall of the hole and on the outer surfaces of the model. Aluminum Model The physical model is a 12 by 12 by 12-in. cast T6061 aluminum block, shown in Figure 17. T6061 aluminum was selected because of its material properties. The block contains a 1.500 in. diameter hole. The axis of the hole intersects the edges of adjacent faces at their midpoints and parallels two of the outside faces. Cast material was selected in order to approximate a material which is ideally isotropic. In {LVDTs} ':! IS 1.S00 relative displacement I 71 - ( b) Figure 16. Proposed device for measuring relat i ve axial di splacement between two points diametrically opposite on the wall of the hole (a) Longitudinal view (b) Front view Figure 17. Aluminum model 72 74 The model was cut from 19.25-in. diameter 0-condition stock, which is untreated cast material. The material was heat treated to a T6 condi­tion to allow easier machining of the hole to the desired tolerance. The block size was selected to minimize finite size effects, and to lessen the chance of voids forming in the center of the block. Triaxial Loading Frame The loading frame was designed to provide the reaction for 288,000- lb loads in the three directions normal to the aluminum block model surfaces. Hole access was required for instrumentation when the block is positioned in the frame. Figure 18 shows the main part of the frame. It consists of a steel ring with an outer diameter of 24 in., a length of 12.5 in., and a thickness of 1.22 in. A nonshrink grout fills the space between the steel ring and the model space, allowing enough space to insert between the grout and the model two hole access plates on opposite sides and flat jacks along all four sides. The hole access plates are of T6061 aluminum of dimensions 1.75 by 12 by 12 in. A section was machined to form a cavity. The plate is placed against a block model surface that the hole intersects so that the cavity sur­rounds the hole and allows access to the hole in the model. This causes the applied stresses to be redistributed away from the thin collar areas. The ring was welded to a steel plate of dimensions 2.75 by 25 by 25 in. The plate provides a reaction surface for a vertical load, which is confined by a system of four beams and four long 1.50- in. diameter bolts, shown in Figure 19. In order that the hole is accessible while the aluminum model is in the frame cavity, the model is positioned so that the collar of the hole is located on an upper Q-condition In. in~ert causes the applied stresses to be redistributed away from the thin collar areas. The ring was welded to a steel plate of dimensions 2.75 by 25 by 25 in. The plate provides a reaction surface for a vertical load, which is confined by a system of four beams and four long 1.50- in. diameter bolts, shown in Figure 19. In order that the hole 1S accessible while the aluminum model is in the frame cavity, the model is positioned so that the collar of the hole is located on an upper Figure 18. Triaxial frame 7S 77 Figure 19. System of beams confines vertical load applied with flat jack 79 edge. Loading takes place in the directions normal to the faces that the hole intersects. A small frame work allows hoisting the model in and out of the reaction frame cavity. Flat Jacks and Hydraulic System The method of using flat jacks to apply a load has been well-devel­oped over the last 40 years. If confined to a small thickness, the device applies a uniformly distributed load. All flat jacks were made of stainless steel 304 and had two 0.125-in. diameter stainless steel tubes entering the flat jacks at adjacent corners. Two types of flat jacks were used in the tests. The first type, designated TT, consists of two stainless steel sheets 12 by 12 in. with 0.50-in. wide 16 gauge pieces sandwiched between the sheets at the edges. The sheets are welded to the spacer, shown in Figure 20(a). The outer sheets of four flat jacks (TT1^-TT4) were of 16 gauge material, and the corresponding sheets of two (TT5 and TT6) were of 20 gauge material. The second type, designated WI, has 18 gauge sheets of dimensions 12.13 by 12.13 in. Two sheets were welded together at the edges without the aid of spacers, shown in Figure 20(b). Four flat jacks (WI1-WI4) of the second type were manufactured. In case of pinhole leaks at the welds, it was usually possible to remedy the problem with additional welding if the fluid used in the flat jack was water. Hydraulic oil hand pumps and oil-water interface reservoirs were used to supply pressurized water to the flat jacks. 0.12S-in. O.SO-in. welded to the spacer, shown in Figure 20(a). The outer sheets of four flat jacks (TT~-TT4) were of 16 gauge material, and the corresponding sheets of two (TTS and TT6) were of 20 gauge material. The second type, designated WI, has 18 gauge sheets of dimensions 12.13 by 12.13 1n. Two sheets were welded together at the edges without the aid of spacers, shown in Figure 20(b). Four flat jacks (WII-WI4) of the second type were manufactured. water (a) (b) Figure 20. Sections showing flat jack construction near the edges (a) TT flat jack (b) WI flat jack 80 81 Axial Displacement Measuring Device Figure 21(a) depicts the axial displacement device, including two Linear Variable Differential Transformers (LVDT) and the brass holder. The LVDTs each have an electrical stroke of ±0.010 in. with a sensitiv­ity of 3.2 MV/0.001 in./V at 2.5 KHz. Two lengths of 1-72 threaded stock, 0.625 in. and 4.25 in., were available for the core. The holder was made of brass and has a removable handle for positioning in the hole in the model. It has the option of using one anchor, shown in Figure 21(a), for two anchors, shown in Figure 21(b). The pin surfaces which contact the surface of the hole were machined to match the con­tour of the hole in order to prevent damage to the wall of the hole. The LVDTs are clamped into the brass holder with set screws. The cores are each positioned on a 1-72 threaded pins and inserted into the LVDTs. Pins of two different lengths, 0.63 in. and 4.50 in., were used i for the tests. A system of nuts, washers and spring keeps the pin in contact with a stop that is bonded to the wall of the hole. The stops are bonded to the surface of the hole at the points of desired measurement. These stops were made of aluminum, and one edge was machined to match the curvature of the hole. An installation tool was manufactured to facilitate placement, orientation, and clamping of the stops in the hole to allow bonding. The tool, pistons, and stops are shown in Figure 22. The instrument is inserted in the hole and oriented to the desired position. The pistons are slowly released, pressing the stops, with glue covering its curved surface, against the surface of the hole. 2l(LVDT) O.OlO sensitiv-ity o.OOl V 2l(a}, con-tour for the tests. A system of nuts, washers and spring keeps the pin in contact with a stop that is bonded to the wall of the hole. The stops are bonded to the surface of the hole at the points of desired measurement. These stops were made of aluminum, and one edge was machined to match the curvature of the hole. An installation tool was manufactured to facilitate placement, orientation, and clamping of the stops in the hole to allow bonding. The tool, pistons, and stops are shown in Figure 22. The instrument is inserted in the hole and oriented to the desired position. The pistons are slowly released, pressing the stops, with glue covering its curved surface, against the surface of the hole. Figure 21. Axial displacement measuring device (a) One anchor (b) Two anchors 82 Figure 22. Installation clamp for aluminum stops 85 • 87 Strain Gauges The strain gauges used in the investigation were of two types. For bonding in the hole of the model, a 0°-45°-90° stacked rosette of electrical resistance strain gauges, each with a length of 2 mm, was used. For bonding on the exterior surfaces of the model, a 0°-90° unstacked rosette of 0.250 in, length electrical resistance strain gauges was used. Bonding of the gauges in the hole is possible with a clamp manufac­tured specifically for this purpose. The rosette is positioned on a curved, padded surface attached to an installation piston with the electrical wires already soldered to the strain gauge leads. An Epoxy glue is applied over the rosette and bondable terminals. After inser­tion in the hole, a screw-action pushes the piston assembly so that the gauges are clamped against the surface of the hole. The strain gauges are monitored with two manual strain indicators. A 10-channel switch and balance box and a 9-channel switch box allow monitoring of several strain gauges without having to disconnect and reconnect electrical wires. Temperature compensation is accomplished by connecting in wheatstone-bridge fashion a strain gauge that is bonded to a cylindrical specimen of the cast aluminum. Procedure and Results The plan called for 1) doing preliminary calibrations of the equip­ment, 2) measuring material properties of the cast aluminum, 3) check­ing the uniformity of load on the aluminum block from a flat jack, 4) calibrating the LVDTs with the anchor/holder in the hole of the model, and 5) measuring axial displacement in the hole of the model due to an 90° in. In IS manufac-tured IS inser-tion ~ lO-g-l} equlp-ment, 3} check-ing 88 axial shear load. Other diagnostic tests may be necessary at some point. Calibrations Calibrations of the measuring equipment were carried out in order to measure loads, hydraulic pressure, and displacement effectively and accurately. Enerpac Load Cell Calibration of the Enerpac load cell was necessary because it is used as a standard in the Rock Mechanics Laboratory at the University of Utah to calibrate the testing machine load cell. The Enerpac load cell has a 200,000 lb capacity. A hydraulic dial gauge indicates the applied load* The Enerpac load cell was calibrated in a testing laboratory belonging to the Department of Mechanical Engineering at the University of Utah. A 100,000 lb capacity Olsen proving ring, which had been calibrated at a calibration standards laboratory, was used in the test. A large reaction frame restrained the load cell and the proving ring. Although loads in later testing exceeded this capacity, it was assumed that this calibration was applicable for loads above 100,000 lbs. The calibration plot of the testing machine load cell with the Enerpac load cell might give additional information about how good this assumption is. The results of the calibration are presented in Figure 23. The results are very linear. If a linear regression analysis were done on the loading portion of the data, excluding the 0 load point, the slope Ib load. tbe 1n ° l~' 89 9 0 8 0 * 70 I-o 9 6 0 - 5 0 - ^ 4 0 - 3 0 2 0 1 0 h o LOADING a UNLOADING 0 10 2 0 3 0 4 0 5 0 6 0 7 0 8 0 90 3 lbs Figure 23. Plot of results for calibration of Enerpac Load Cell KEY 0 II UNLOADING 90 80 0 (I) ~ 70 ", 0~ 60 .. 0 50 ~~ 40 8 30 ~ 20 « 10 0 o ~~~~----~--------~~--~ o ro ~ ~ ~ ~ ~ ~ M ~ ENERPAC LOAD CELL READING, 103 Ibs 90 of the least squares line is 1.016, the intercept on the Enerpac Reading axis is -5205, and the correlation coefficient is 1.00000. Testing Machine Load Cell The load cell in the testing machine was calibrated against the Enerpac load cell. It was used in subsequent tests for calibrations, determining material properties, etc. Strain gauges were bonded to the outer surface of the load cell in a wheatstone bridge configuration. The voltage output was monitored through a servo controller unit, which operated the testing machine. Calibration was done over two ranges. The first was 0 to 145,000 lbs with the servo output adjusted so that the sensitivity was reduced to half. The second was 0 to 40,000 lbs with the servo output set at full sensitivity. The reduction in sensitivity allowed the application of greater loads that were used subsequently when calibrating the flat jacks. Figure 24(a) demonstrates the layout of the load cells and platens in the testing machine for this test. The full-scale sen­sitivity setting was used when measuring the material properties of a cast aluminum cylinder. Figure 24(b) demonstrates the corresponding layout for this test. The tests were repeated three times for repro­ducibility. A plot of the results of one of the three calibration tests with the servo output set at half sensitivity is shown in Figure 25. The results of the other tests are similar. The results very closely approximate a straight line, and there seems to be only a slight variation in slope below a load of about 30,000 lbs. Table 3 lists the linear regression results. The average slope for both the loading and etc~. ° ~ jacKs. sen-sitivity repro-ducibility. Ibs. gure 24. Testing configurations in testing machine (a) Flat jack calibration (b) Measurement of material properties Figure 91 92 L 5~2 4 - U ) circular plate , ," circular plate ------~ __ P_ ____ ~-J (a) testing machine load cell steel plate hole access plates Enerpac load cell testing machine hydraulic ram 93 circular plate cast aluminum specimen testing machine load cell spherical seat testing machine hydraulic ram (b) circular plates (b) 93 testing machine hydraulic ram 94 £ h \- 60 h I-oA ULONKALEODYNIA DGNIG 0 1 2 3 4 5 6 7 8 Figure 25. Plot of results for calibration of testing machine load cell-half sensitivity KEY 0 LOADING ~ UNLOADING 150 1 I I I ' I I W ~ I£) - . en I£) :a 120 ~ 4J - I't') 0 4J ~ ~ I£) .. 90 I- - 0 I£J 4: ~ I£) 9 60 IJJ ~ - f3 I£) .. . ~ '!\ £) 30 4J - - 4: .. ID 4J 0 I I I I I I I 1 2 3 4 5 6 7 8 LOAD CELL READING, volts resul ts cal ibration cell--95 Table 3 Linear regression statistics for load cell calibration- half sensitivity Sequence y-Intercept Slope Correlation Number of (lbs) (lbs/volt) Coefficient Data Points Run 1 Loading 619 Unloading 2842 Loading & Unloading 1906 Run 2 Loading 1678 Unloading 3020 Loading & Unloading 2419 Run 3 Loading 1741 Unloading 3018 Loading & Unloading 2439 20,914 0.99985 14 20,955 0.99976 13 20,874 0.99937 27 20,920 0.99989 14 20,895 0.99979 20,882 0.99972 27 20,903 0.99991 20,864 0.99980 20,862 0.99976 Note: Data points at zero load are not used for the statistical calcu­lations. -.1 l calibration-- & Run2 "\ & & lbs!13 14 13 27 ca1cu-lations. 96 the unloading data points gives the constant for calibrations of flat jacks since the calibration constant was used for both loading and unloading curves. The average calibration constant of 20,873 lbs/volt was therefore selected. Only two calibration tests were performed with the servo output set at full-scale. The results of one set are plotted in Figure 26. The result of the other test is similar. The plots show that the data are very linear. Table 4 lists the linear regression results. Under the same reasoning as above, the calibration constant of 9482 lbs/volts was selected. The two calibration constants do not closely double each other. Examination of the testing layout for each test (Figures 24(a) and (b)) reveals one possible explanation. The loading of the load cell appears to be different between the two cases. Because of some plate bending, the layout in Figure 24(a) resulted in a greater load on the outside of the load cell where the strain gauges were bonded than did the layout in Figure 24(b). The initial nonlinearity of the calibration curve at half-sensitivity may indicate that the Enerpac load cell was not linear, and the load range may determine the calibration constant. The two testing ranges reflect the ranges of subsequent tests; therefore, the respective calibration constants were used. Pumps and Dial Pressure Indicators The purpose of this test was to determine the response of the hydraulic dial gauges and the hand pumps. It is not known if their response when used with the flat jacks was linear and reproducible. Each pump and dial gauge system was connected to a pressure transducer b» ·Figure linear, and the load range may determine the calibration constant. The two testing ranges reflect the ranges of subsequent tests; therefore, the respective calibration constants were used. 97 40 KEY o LOADING A UNLOADING • • i 1 1 i • i ^ ^ ^ ^ O . - - • - Q - • G • - J b_ J L_J i 30 20 10 h 0 ft 1 2 3 4 LOAD CELL READING, volts Figure 26. Plot of results for calibration of testing machine load cell-full sensitivity cell--full 98 Table 4 Linear regression statistics for load cell calibration- full sensitivity Sequence y-Intercept Slope Correlation Number of (lbs/volt) Coefficient Data Points Run 1 Loading -1039 9455 0.99927 Unloading -1127 9481 0.99956 6 Loading & Unloading -1082 9467 0.99939 13 Run 2 Loading -1087 9501 0.99925 7 Unloading -1188 9464 0.99957 6 Loading & Unloading -1160 9497 0.99934 13 Note: Data points at zero load are not used for the statistical calcu­lations. calibration-- & Urt10ading & (lbs) 7 calcu-lations. 99 to make the determination. The testing range was from 0 to 1500 psi in 100 psi increments. Tests were repeated three times for each of the three hydraulic systems. The results of the tests of the three respective hydraulic systems give information about system linearity. An example is plotted in Figure 27. The results show reproducibility and linearity. The linear regression correlation coefficients for all runs of each pump system are over 0.9999. Since the maximum range of the pressure transducer was 10,000 psi, there is some question about the linearity of the transducer in the pressure range of the test. However, the results of the test suggest that both the pump-dial gauge systems and the pressure transducer were linear in the 100 psi to 1500 psi range. Flat Jacks The loading system, including the hand pumps and dial gauges with the flat jacks, were calibrated using the electronic load cell in the testing machine. The flat jacks were calibrated individually or as a duo in parallel, according to their required use. The flat jack system was placed between a steel plate of 2.75 in. thickness and a series of two aluminum plates, each of 1.75 in. thickness. The testing machine reaction frame confined the flat jack system, the plates and the load cell, shown in Figure 24(a). The loading occurred by pumping fluid into the flat jack to expand it against the reaction system. The load cell voltage output and the hydraulic pressure dial reading were monitored during the test. The test range was 0 to 1500 psi in 100 psi increments. The test was repeated for each flat jack system. PSl ln dial l • 100 S \- \- 60 h h o LOADING A UNLOADING LU 0 psi Figure 27. Plot of results for linearity check of one of the pump and dial pressure indicator systems KEY 0 ~ 6 I I • I I U § 120 ~ ~ - ~ S!1 ~ a 0 90 ~ ~ S!1 - ffi ~ · u:::> ~ · Q 60 ~ ~ - (/") e ~ ~ ~ ~ " ~ ew:::: 30 ~ ~ - :(:/">) ( ~~ ~ ~ · ~ 4 ~ I L • L I J 0 R: 300 600 900 1200 1500 HYDRUAUC GAUGE READING, psi 101 Flat jack TT3 was filled with water and capped. It was not used to actively apply a force, but rather it provided a cushion-type surface to meet any irregularities in the grout surface of the triaxial frame. Flat jack TT3 was confined in series with flat jack TT2 during calibra­tion. Flat jacks TT1, TT2, TT4, and TT5 were calibrated individually in the large testing machine. Runs 1 and 2 for flat jack TT1 were performed with the testing machine's electric hydraulic pump turned off. Observation of the load cell output during the calibration revealed that there was some hydraulic oil leakage through the testing machine's servo valve. This caused the confinement for the flat jack to be, in effect, not as stiff. For this reason, flat jack TT1 was recalibrated with the electric hydraulic pump turned on so that the thickness of the expanded flat jack could be kept more constant. Runs 3 and 4 for flat jack TT3 were performed in this way as were all of the runs on the otner flat jacks. The results of all calibration runs are linear and reproducible. A plot of the results of one of these tests is found in Figure 28. The flat jacks WI1, WI2, WI3, and WI4 were all calibrated. Flat jacks WI2 and WI3 were required for testing in parallel-placed on opposite sides of the model, and both applying active loads. For this reason, the two were also calibrated in parallel. The results of these calibrations are quite linear, reproducible, and comparable between the systems. Table 5 lists the load-intercept, slope (calibration constant), and correlation coefficient of the linear regression line calculated for each run based on both loading and unloading data. The calibration ln ln TTl, TTS TTl 'to be, in effect, not as stiff. For this reason, flat jack TTl was reca1ibrated with the electric hydraulic pump turned on so that the thickness of the expanded flat jack could be kept more constant. Runs 3 and 4 for flat jack TT3 were performed in this way as were all of the runs on the other flat jacks. The results of all calibration runs are linear and reproducible. A plot of the results of one of these tests is found in Figure 28. parallel--S 102 o LOADING a UNLOADING 300 INTERNAL 103 Figure 28. Plot of results of calibration of one flat jack KEY 0 4 200 I • I I I 180 I- Jb (I) H .-0 160 - ~ - ~ 140 ~ 0 ~ - ~ fa --. 120 - a - ~ 100 ~ 9 I- ri - 80 ~ ~ - B " ~ ~ 60 ~ ~ - 40 I- ~ - ~ 20 I- ~ - 0 11'1 ~ I • r r I 0 600 900 1200 1500 IN I ERNAL FLAT JACK PRESSURE, 103 psi 103 Table 5 Linear regression statistics for flat jack calibrations Flat Jack Run No. Intercept (lbs) Slope (lbs/psi) Correlation Coefficient TT1 Run 1 Run 2 Run 3 Run 4 •2997 -2256 7902 8040 124.42 122.98 125.35 125.35 0.99962 0.99972 0.99972 0.99961 TT2 Run 1 Run 2 •3320 •3633 125.21 126.18 0.99986 0.99985 TT4 Run 1 Run 2 4615 3922 126.47 126.34 0.99942 0.99933 TT5 Run 1 Run 2 463 1398 127.51 126.61 0.99985 0.99984 WI1 Run 1 Run 2 6057 6042 131.97 132.26 0.99914 0.99901 WI2 and WI3 Run 1 Run 2 1493 1260 135.08 135.14 0.99800 0.99928 WI4 Run 1 -1757 135.22 0.99988 & TTl WIl • -2997 -2256 -3320 -3633 lbs! 104 constants of flat jacks of the same type are very similar, but the calibration constants of the WI flat jacks are higher than those of the TT flat jacks. Linear Variable Differential Transducers The LVDTs in the axial displacement measuring device were cali­brated with a 1-in. micrometer with a nonrotating spindle. Three LVDTs, designated 4, 5, and 6, were available for use. The LVDTs were calibrated only as their use required them. The output of the LVDT to be calibrated was monitored against displacement as measured with the micrometer. An aluminum frame held the micrometer and LVDT during the test. The range of the displacement during calibrations was 0.020 in. with increments of 0.001 in. Each calibration test was repeated twice for each LVDT. LVDTs 4 and 5 were calibrated with the short pins and the long pins. A plot of the results of one of these calibrations is in Figure 29. The results of all tests are quite linear and reproducible. Table 6 summarizes the results from linear regression calculations. Com­parison of the