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By Jeff Jackson, Paul Axtell, David Graham

The Montana Department of Transportation recently awarded a contract to construct a replacement bridge across the Clark Fork River in Heron, MT. Both abutments and both intermediate bridge bents were to be founded on 6-ft and 8-ft diameter, permanently cased drilled shafts with rock sockets, respectively. Two drilled shafts per substructure location were designed for a total of eight drilled shafts. The original design included 6-ft diameter drilled shafts at the abutments but the Contractor elected to submit a Value Engineering proposal that increased them to 8-ft diameter. On the basis of the subsurface exploration program, extremely challenging subsurface conditions were known to exist, including the potential presence of large boulders within the predominantly sand and gravel soil matrix. The successful bidder elected to use an oscillator to install the permanent casing to the top of bedrock, while simultaneously removing the spoils from inside the casing with a clam-grab. On seven of the eight shafts, this approach worked well. Unfortunately, on one of the shafts, the casing met refusal on one or more boulders encountered in the predominantly sand and gravel soil overburden. Following several attempts, and despite several variations of approaches, it was determined that the casing could not be advanced beyond the obstruction without unacceptable risks to the pile-supported temporary work trestle (i.e., loss of soil and reduction in pile capacity for the foundations supporting the work trestle). To mitigate the problematic drilled shaft, a unique solution was designed and successfully constructed. The solution involved the construction of seven 16-in diameter micropiles constructed within the confines of the obstructed casing. The micropiles were drilled to bedrock through the sand, gravel, and boulders and include rock sockets to satisfy axial design requirements. The micropile casing thickness, grade and grout strength were designed to provide adequate flexural strength as well as to satisfy other design requirements. Upon completion of the micropile installation, the upper portion of the drilled shaft above the boulders and within the permanent casing was constructed as usual. This paper discusses the difficult subsurface conditions at the site, the drilled shaft construction difficulties, and the design and construction of the micropile solution.

Jan 1, 2018

By Robert B. Bittner

The new gated dam on the Monongahela River at Braddock, Pennsylvania, was built for the US Army Corps of Engineers using an innovative ?In-the-Wet? technology. A key feature of this technology involves construction of the foundations through the water and later mating the completed structure or a shell of the structure to the pre-installed foundation. This paper presents a description of the structure, its foundation, construction sequence and design details required to successfully implement this technology.

Jan 1, 2013

By Robert B. Bittner

The new gated dam on the Monongahela River at Braddock, Pennsylvania, was built for the US Army Corps of Engineers using an innovative "In-the-Wef' technology. A key feature of this technology involves construction of the foundations through the water and later mating the completed structure or a shell of the structure to the pre-installed foundation. This paper presents a description of the structure, its foundation, construction sequence and design details required to successfully Implement this technology.

May 11, 2007

By Paul J. Axtell

The design-build delivery system is being used to erect the landmark Christopher Bond Bridge as part of the kcICON project. The cable-stayed bridge is currently under construction and will span the Missouri River on I-29/35 in Kansas City, Missouri. The design-build process for the foundation work on this project has been successfully implemented as a result of cooperative efforts between the foundation designers and the constructors to develop a constructible design.

Jan 1, 2009

By Ivan Hee

The 2.5km long bridge over the Beauharnois Canal and St. Lawrence Seaway is a major structure in the new Autoroute 30 project near Montreal. Foundations for the bridge consist of footings on bedrock, driven piles, and drilled shafts. This paper describes the design, verification, and construction of 1.85m diameter drilled shafts socketed into very strong and abrasive dolomitic sandstone. Two loading tests on sacrificial, heavily-instrumented, 1.18m diameter test shafts using Osterberg load cells were performed, with telltales installed to monitor a possible rock cone failure mechanism. The loading tests resulted in a revision to the initial design and provided a greater understanding of the cone uplift mechanism in rock. Insights gained are discussed and economies of the load testing program presented. Construction methodologies are also presented.

Jan 1, 2011

The intent of this manual is to provide guidelines for inspectors of drilled shaft construction otherwise referred to as drilled piers, caissons or bored piles. It should also be helpful to train beginning geotechnical engineers with limited first hand experience or for geotechnical engineers who are training inspectors. It is expected that the general guidelines and procedures described here will be supplemented by local geotechnical engineers working in a particular region based on local practice and experience. Since drilled shaft construction procedures vary widely based on local geology and size of project, an all-inclusive manual is not considered practical. This manual focuses on traditional topside inspection for routine drilled shaft construction. Other inspection and evaluation methods that rely on electronic equipment are available, but these methods require extensive training and experience in the interpretation of results. These more sophisticated methods of drilled shaft inspection and evaluation are common in construction, but they are usually provided by specialty subconsultants. The subconsultant will typically submit a report for each shaft, which will be reviewed by the geotechnical engineer. Other manuals are available to describe the electronic methods of drilled shaft inspection.

Jan 1, 2004

By Samer Rabab’ah, John C. Niedzielski, Jason Valeria

The PHX Sky Train is an automated people mover system located at Phoenix Sky Harbor International Airport. Phase II of the PHX Sky Train includes the design of over 150 drilled shafts for support of four guideway abutments, 75 guideway piers and three proposed stations. The soil conditions in this area generally consist of alluvial Sand, Gravel and Cobbles (locally known as SGC) deposited by the nearby Salt River. The foundation system will support relatively high axial loads, lateral loads and moments due to the height of the elevated guideway above the ground surface, where it needs to pass over roadways, parking lots, an existing terminal, and other buildings. Deep foundation design involves designing drilled shafts within the SGC deposits, some of which extend below the long-term groundwater table. Such extreme design loading conditions, together with difficult ground conditions at the site, result in several challenges for the design and construction of the deep foundation system for the project. This paper will present the results of a drilled shaft load test program implemented to provide site-specific measurement of the axial and lateral performance of the project drilled shafts. The load testing program consisted of a bi-directional load cell axial load test and a lateral load test performed on an instrumented test shaft 84 inches in diameter. The development and execution of the load test program and analysis of the test results are discussed. Comparisons were developed between predicted load capacities of drilled shafts using different design methodologies and the load capacity measured from the load tests. The load test results showed that underestimation of the capacity is evident using conventional methodologies. The load testing program was important for verifying the performance of the drilled shaft foundations on the project and was used to reduce the size of the drilled shafts. INTRODUCTION The PHX Sky Train is a five-mile long automated people mover system situated at-grade and on an elevated guideway which connects terminals, parking facilities, a rental car center and the Valley Metro Light Rail system in Phoenix. The purpose of this automated train system is to provide a secondary transportation system within the airport to relieve roadway congestion, minimize wait times and travel times for passengers and provide climate-controlled waiting areas. Phase 1 opened to the public on April 8, 2013. Phase 1A opened on December 8, 2014.

Jan 1, 2019

By J. A. Hayes

For over a decade the Osterberg Load Cell has been successfully used to determine the shear capacities of drilled shafts. Since the test method measures side shear directly, analytical complications due to the influence of end bearing resistance are removed. The data suggest that the side shear component of a drilled shaft's capacity is often more significant than end bearing. Given the interest in the use of side shear in drilled shaft design in compressible materials, it is important to examine factors that can influence capacity. We have found that some factors widely believed to influence capacity, such as slurry type, are not as important as commonly thought in most materials. Factors that are not usually considered as important, such as casing use, hoop spacing, concrete slump, concrete additives, spacers and rebar clear cover, seem to be more influential with respect to side shear capacity. For example, substantially lower than predicted shear resistance can occur when the rebar clear cover is small with respect to the cage diameter. We observe this most often in fine-grained cohesive soils. This effect can be exaggerated if the rebar cage has tight hoop spacing, if the concrete has low slump and if the hole is not straight. We have also noted that improper use of temporary casing can have a dramatic effect on side shear resistance. In some cases we have observed tested shear capacities reduced to less than 5% of either predicted or available shear values.

Jan 1, 2003

By J. B. Boisvert, D. S. Silva

"Drillhole placement involves benefits, costs, and constraints. Benefits are related to the drilling campaign value, which includes maximizing “indicated” and “measured” resources. Costs include drilling, rig movement, and access construction. Constraints include infeasible areas, maximum and minimum angles of drilling, maximum depth of drilling, and budget. Manually planning drillholes that meet these constraints is suboptimal. A framework for straight drillhole optimization that accounts for benefits, costs, and constraints is presented. The method aims to maximize the value of resources converted from “inferred” to indicated and measured. The framework is demonstrated for a Nevada gold deposit and outperforms manually selected drillholes.RÉSUMÉ Le choix de l’emplacement d’un trou de forage s’accompagne d’avantages, de coûts et de contraintes. Les avantages sont liés à la valeur d’une campagne de forage, qui comprend l’optimisation des ressources « indiquées » et « mesurées ». Les coûts englobent le forage, le déplacement de l’appareil de forage et la construction des routes d’accès. Quant aux contraintes, elles portent sur les zones impraticables, les angles maximums et minimums de forage, la profondeur maximale de forage ainsi que le budget. La planification manuelle des trous de forage répondant à ces contraintes est sous-optimale. Cet article présente un cadre relatif à l’optimisation des trous verticaux de forage tenant compte des avantages, des coûts et des contraintes. Cette méthode vise à optimiser la valeur des ressources converties de la phase « ressources présumées » à celle de « ressources indiquées et mesurées ». Ce cadre est appliqué à un gisement aurifère du Nevada et donne de meilleurs résultats que les trous de forage sélectionnés manuellement. INTRODUCTIONDetermining the optimum location of infill drilling has been studied because the high cost of drilling suggests that using fewer drillholes is preferred, and targeting locations of the deposit that are locally uncertain should result in better mine planning decisions and increased profit of the operation. Existing methods for optimizing drillhole locations consider minimizing the kriging variance (KV) as the objective and are mostly restricted to two dimensions (Soltani-Mohammadi & Hezarkhari, 2013a, b; Soltani- Mohammadi, Safa, & Mokhtari, 2016)."

Jan 1, 2018

By Corry Goumans, Ron J. Elliot

This paper discusses the challenges encountered in drilling and blasting of a small diameter shaft underneath a parking garage in historic Gastown, Vancouver, BC. This project involved drilling in a restricted headroom area, blasting in a confined space environment, and excavating using a novel vacuum technique. The 1.2m x 1.2 m x 8.5m deep shaft was required for installation of a hydraulic piston for a show lift. The project called for very accurate drilling through inter-bedded sandstone and siltstone within the water table. Development of a unique blast design was required for blast vibration control on a historic structure located just 15.8 meters away. The shaft was successfully completed without damage to any of the surrounding structures.

Jan 1, 2004

The AusIMM/AMIC code for reporting Reserves seeks to improve the calibre of professional reporting on this subject. But have they gone far enough? Should the code appreciate that the degree of reliability of estimates required will vary with the type of mining planned? How does one "confirm continuity" as required by the code? The aim of optimum development drilling is to achieve appropriate ore zone definition for acceptable estimates of reserves and their economic extraction. Can this procedure be in conflict with the code? How does it affect finance decisions?

Jan 1, 1989

By H. C. H. Darley

The principal causes of unstable boreholes* have been known for many years. For example, in a paper published in 1938, Halbouty and Kaldenbachl listed nearly all the classes of troublesome shales that we know today. Much progress has been made since then, but we still have difficulty in identifying the cause of hole problems and consequently in selecting the right technique for combatting them. This subject was discussed at length by Kelly2 in a recent paper and much valuable information was provided. In the Shell Laboratory it was felt that there was a need for a better understanding of the basic mechanisms underlying the various forms of hole instability, and accordingly, a study was undertaken. This entailed reviewing the physics and chemistry of shales, developing tests for characterizing shales, and constructing a model to study borehole stability. Full simulation of underground conditions was not attempted; for example, we used reconstituted shale specimens, and often simple solutions or suspensions rather than practical drilling muds. Such procedures are necessary in order to establish mechanisms, but caution must be exercised in applying the results to the more complex conditions in the field. Part I — Compaction Swelling and Dispersion of Shales Compaction of Sediments Shales are formed by the compaction of sediments. Water is expressed as sediments are buried by subsequent layers, and the degree of compaction is proportional to the depth of burial, provided the water is able to escape easily to permeable formations. The younger sediments, when recovered at the surface, soften and disperse when mixed with water; the older shales have undergone diagenesis (alteration of the clay minerals, secondary cementation, etc.), and remain hard and unaffected by water. In this paper we shall apply the term "shale", as the drilling engineer does, to everything from clays, which are highly reactive to water, to completely lithified materials such as claystones and slates, which are completely inert. However, because these materials behave quite differently when encountered in the drilling well, it is desirable to develop a simple means of characterizing them. The feature that distinguishes the various shales is their dispersibility in water —soft clays disperse readily, harder shales disperse slowly when agitated, the lithified materials will not disperse at all unless milled. In the dispersibility test used in our study, a weighed amount of dry shale particles in the 12-to-100-mesh-size range was placed in a tube filled with distilled water and allowed to soak for 16 hours. The

Jan 1, 1970

By J. L. LeBlanc, R. L. Lewis

This study presents an analysis of annular backpressure variations associated with controlled gas kicks and their pronounced effect on casing .strings and exposed under lying formations. A mathematical model describing the volumetric behavior of an extraneous gas as it is transported from reservoir to .surface conditions under changing temperatures and pressures has been programmed in a Kingston FORTRAN II language for digital computer analysis. The gases under investigation typify Gulf Coast reservoir gases within a 0.6 to 0.7 .specific gravity range. The program output has been substantiated by actual field cases. of gas kicks encountered in Gulf Coart we1l.s. The development of empirical equations for calculating suitable gamy deviation factors for unique temperatures and pressures was incorporated in the program to provide realistic solution.. An output listing of annular backpressures and corresponding equivalent fluid densities resulting at a predetermined critical depth (casing setting depth) and total depth for selected .stages of circulation is provided in a chronological .sequence. Additional information including reservoir pressure and temperature, kill rnrid density, produced gas or surface volume of the expanded gas intro vion, drill pipe and annular volumes can he obtained from the model. This paper illustrates that a precise knowledge of the volumetric behavior of extraneous gases in annular flow and its effect on equivalent fluid densities at a critical depth is significant and should receive .serious consideration in controlling threatened blowouts and in the design of drilling programs. Surface pressures in excess of formation limitations are a threat to zones of lost circula/ion and are potentially injurious to productive intervals. A knowledge of annular backpressure and equivalent fluid density profiles for probable gas kicks aids in a technological accomplishment of drilling programs and provides a .sale tolerance in the event a threatened blowout is encountered. Introduction Drilling operations are frequently interrupted when the drill bit penetrates permeable gas sands with reservoir CtfuJ manuscript was received in Society of Petroleum Engineers ofice Am. 1 1967. Revised manuscript received JuIy 7. 1968. Paper (SPE 1860) kae presented at SPE 42nd Annual Fall Meeting held in Houston. Tex., Oct 1-4, 1967. @ Copyright 1968 American Institute of Mining, Metallurgical, and Petroleum Engineem, Inc. pressures greater than that exerted by the drilling fluid. The differential pressures resulting permit an extraneous influx of gas into the wellbore. A suspension in drilling progress is necessary to restore fluid equilibrium throughout the system. Whether formation gas kicks originate unintentionally or by design, the prospect of a threatened or actual blowout exists and a method assuring a safe and effective well control procedure must be observed. A significant contribution to well control technology was advanced by Records et a1.l in 1962. Using the concept of transmitting a constant equivalent formation pressure at the point of intrusion, Records et al. introduced a calculation technique providing the annular backpressures encountered in a well control environment as a func tion of the volumetric behavior of a 0.6 specific gravity natural gas. In essence, the procedure outlined an annular backpressure schedule in terms of fluid volume circulated at different stages of a well control operation. A number of other publications2-' proposing various techniques for controlling gas intrusions in a wellbore achieve pressure control essentially through maintenance of a constant bottom-hole pressure by surface choke adjustments. The subsequent pressure effects induced in the annulus unfortunately receive little emphasis. Due to the tedious and repetitive nature of annular backpressure computations, a theoretical solution by digital computer is introduced for predicting annular backpressure and equivalent fluid density profiles associated with controlled gas kicks. We point out the effects of volumetric behavior of extraneous gases in annular flow and related field phenomena on equivalent fluid densities at a critical depth. The investigation indicated that equivalent fluid densities at a critical depth are of significance and should receive consideration in the control of threatened blowouts and in the design of drilling programs. Theoretical Considerations The mechanism of vertical gas flow through an annulus is governed by the PVT properties of the fluid, the pressure distribution within the system, the fluid flow rates and the geometry of flow. Due to the numerous variables involved in this type of problem, certain assumptions were imposed in deriving the mathematical model and in establishing the solutions. Two gases, characterized by specific gravities of 0.6 and 0.7, were selected to typify Gulf Coast reservoir fluids. The gas intrustion entered the wellbore as an immiscible 'References given at end of paper. JOURNAL OF PETROLEUM TECHNOLOGY

Jan 1, 1969

By P. F. Gnirk, J. B. Cheatham

The results of combined analytical and experimental studies involving simulated multiple bit-tooth penetration into mck are incorporated into a drilling rate equation for roller-cone bits assuming rather idealized downhole conditions. In particular, it is assumed that the rock behaves statically in a ductile fashion during bit-tooth penetration and that the rock chips are instantaneously removed from the bottom of the drill hole. The general analysis demonstrates an application of plasticity theory for the rock/bit-tooth interaction to the formulation of an upper limit on rotary drilling rate. INTRODUCTION Extensive experimentation involving single and indexed bit-tooth penetration into rock in a confining pressure environment has demonstrated that the chip formation process is of a ductile, or pseudoplastic, nature at sufficiently low differential pressures so as to be of interest in rotary drilling. Coincident with the experimentation, analytical consideration has been given to the theoretical problems of single and indexed bit-tooth penetration into rock. In general, the analyses have assumed that the rock behaves statically in a rigid-plastic fashion and obeys the Mohr-Coulomb yield criterion. The quantitative comparison between experimental and calculated values of bit-tooth load required for chip formation has been remarkably good for a variety of rocks commonly encountered in drilling and at simulated differential pressures as low as 500 to 1,000 psi. Results obtained recently for indexed bit-tooth penetration indicate that the work (or energy) required to produce a unit volume of rock chip can be minimized by a proper combination of bit-tooth spacing and bit-tooth load for a given rock type and differential pressure. By utilizing this information, it is possible to formulate a drilling rate equation, at least in a preliminary fashion, for a roller-cone bit performing under rather idealized downhole conditions. In particular, through the use of characteristic dimensionless quantities pertinent to a roller-cone bit and to indexed bit-tooth penetration, interrelationships among bit weight, rotary speed, rotary power, bit diameter, rock strength and bit-tooth shape and spacing can be explicitly expressed. In the formulation of the equations, however, it is assumed that the rock chips are instantaneously removed from the bottom of the drill hole and- that the rock behaves in a ductile manner during bit-tooth penetration. In addition, the effects of bit-tooth load application and penetration by a yawed tooth at an oblique angle are neglected. Although the analysis is presented in the light of some rather restrictive conditions, it does demonstrate a method of applying fundamental rock/bit-tooth interaction data, obtained by combining the results of analysis and experiment to the formulation of a drilling rate equation for rotary drilling. JNDEXED BIT-TOOTH/ROCK INTERACTION PREVIOUS RESULTS The mechanics of bit-tooth/rock interaction under simulated conditions of borehole environment have been extensively described in a number of papers.l-ll In particular, the effects of differential pressure, mechanical properties of rock, pore fluid, bit-tooth shape and spacing, rate of bit-tooth load application and dynamic filtration below the bit-tooth have been investigated experimentally. From a sequence of experiments.1-4 it was demonstrated that, for dry rock at atmospheric pore pressure, the mode of chip formation exhibits a transition, with increasing confining pressure, from predominantly brittle to predominantly ductile. This transition

Jan 1, 1970

By R. P. Harvey, J. E. Walstrom, A. A. Brown

In view of the large number of wells directionally drilled from offshore platforms and urban drillsites, greater interest is being focused on the directional survey and on the uncertainty inherent in calculating the position of the bottom of the hole, or other benchmarks in the wellbore. Of the two methods presented here for evaluating this uncertainty, the first is analytical and uses the principles of probability and statistics. The second method uses Monte Carlo simulation to generate a pattern of the scatter of possible bottom-hole locations. Both methods are based on a model for which the usual assumption is made that the curvilinear axis of the wellbore is adequately represented by a large number, M, of linear segments joined end to end from the top to the bottom of the hole and closely following the course of the hole. The errors due to this approximation are assumed to be negligible and are not studied here. One form of the model is to consider that for a given hole there exists a perfect set of data describing it, of the above form. Each linear segment has an angle of inclination with the vertical 7, in radians, an azimuthal angle from true north xi in radians, and a length Si, in feet. The subscript variable, i, extends from 1 to M. Each of the M linear segments representing the axis of the wellbore has three components in the X, Y, and Z directions. These components are calculated from the equations: The bottom-hole coordinates as determined from the reference set of data for the wellbore are given by the following for i = 1 to M: X=SX, Y = Sy, Z=SZ; . (2) A directional survey instrument, lowered into the wellbore to the M segments, or stations, measures the values of the 7; and the 3,. In general, because of errors from various sources, the resulting angular measurements will not be precisely equal to the 7" and xi. Random variables l, and Ai are therefore considered with associated probability density functions fi(li) and gi(Ai), respectively, which represent the distributions of potential survey measurements for this hole. Since it is assumed that the values Si are accurately measured they are treated deterministically. The random variables corresponding to the surveyed bottom-hole coordinates are given, for i = 1 to M, by:

Jan 1, 1970

By C. P. Besse, N. F. LeBlanc

Described in this paper are oceanographic data which should be considered by an offshore design engineer and methods for developing a design wave height from the oceanographic data. The selection of a design wave is predicated on contemplated waves which might affect the site throughout the life of the structure. Selection of a design wave height may be based on (1) arbitrarily established recurrence Frequencies of hurricanes affecting the structure (predicted wave heights are associated with the expected variations of forces resulting from these waves) and (2) a risk-type evaluation wherein all possible storms affecting the area are considered (anticipated wave heights are associated with both investment plus risk costs and expected variations of forces). It is shown how the following oceanographic predictions are integrated into design considerations: (1) a classification of storm intensity which considers all recorded storms which affected the design area, (2) the recurrence interval of storms of a given- intensity (this interval is dependent on the extent of the geographical area considered in the design problem) and (3) a forecast of all wave heights which might affect the area (geometry of a structure often necessitates consideration of waves from a multiplicity of directions). The authors believe that the described techniques can result in selecting an adequate and reasonable design wave. INTRODUCTION Since the inception of offshore operations in the Gulf of Mexico, engineers engaged in designing suuctural facilities have been plagued with the problem of selecting an adequate and reasonable design wave. In the development of any offshore structure it is mandatory that the engineer evaluate the ability of the structure to withstand the ocean waves to which it will be subjected. Selecting such design waves quite naturally necessitates a coalition of the oceanographer and the design engineer. The oceanographer must provide a detailed knowledge of scientific principles which govern the behavior of waters in the Gulf of Mexico. He should also have an adequate knowledge of the manner in which design waves are utilized by the engineer. Although the design engineer's primary responsibility is applying the oceanographer's specialized knowledge in the creation of real structures, it is important that he possess some knowledge of related oceanographic principles to reasonably evaluate and apply the recommendations of the oceanographer. In the Gulf of Mexico it is the hurricane wind waves which generally govern the design of an offshore facility. The oceanographer must therefore develop techniques for predicting the heights, periods and frequency of all hurricane waves which might affect a particular structure. From this mass of oceanographic data, the design engineer must select the design waves which will apply to his particular design. PAST STUDIES ON FREQUENCY AND AMPLITUDE OF HURRICANE WIND WAVES Past oceanographic studies on the frequency of hurricane wave heights in the Gulf of Mexico have been devoted largely to predicting the recurrence interval of hurricanes which will generate maximum significant waves of given heights. The maximum significant wave height is the average height of the highest one third of the waves in that portion of the storm producing maximum wave heights. Since these waves occur over a relatively small portion of the storm (Fig. 1) and since the paths of hurricanes vary considerably (Fig. 2), the recurrence frequency of such heights is largely a function of the extent of the geographical area considered. In establishing the frequency of maximum significant waves for the entire American Gulf coast, the major fully developed hurricanes which affected the coastline from BrOwnsville, Tex., to Key West, Fla., were considered (Fig. 2). These Storms were selected and described by C. L-

By J. A. Musselman, P. F. Gnirk

A study was made of indexed penetrations by a single dull bit tooth under statically applied loads into rock subjected to confining pressures from atmospheric to 5,000 p.si and atmospheric pore pressure. Experimental results obtained with a 45" wedge tooth over the above range of pressures are presented for two limestones and a sandstone, a variely of indexing distances and two degrees of tooth dullness. The optimum distance between successive bit-tooth penetrations required for maximum rock damage and chip formation decreases substantially with increa.sing confining pressure above the brittle-to-ductile transition pressure of a particular rock. However, the distance remains approximately constant for a variation in confining pressure below the transition pressure. At a given confining pressure, the bit-tooth force required lor chip formation is constant for indexing distances greater than optimum, but generally decreases linearly with decreasing indexing distance for distances less than optimum. The chip-formation force data obtained at confining pressures for which the chip-generation mechanism is macroscopic-ally of a pseudoplastic nature compare favorably with previous theoretical results for indexed dull hit-tooth penetrntion into an idealized, rigid, perfectly plastic rock. INTRODUCTION To study the cutting action of a roller-cone bit, the interaction of a penetrating bit tooth with craters formed in a rock surfacc by the passage of previous bit teeth must be considered. Current knowledge of the basic mechanics of bit tooth-rock intcract:on under simulated borehole environmental conditions has been extensively reviewed.',' Particularly of current interest are the effects of bit-tooth shape, distance between successive penetrations and differential pressure at the rock surface on the extent of the interaction. Pertinent to this paper are results of an experimental investigationb f the interaction between successive penetrations by sharp, wedge-shaped bit teeth. It was demonstrated that both bit-tooth angle and differential pressure influence the extent of rock damage between successive bit-tooth penetrations. Specifically, the optimum or minimum distance between successive penetrations required for maximum interact'on or chip generation tends to decrease with decreasing bit-tooth angle and increasing differential pressure. In addition, at differential pressures on the order of 2,000 psi for four va- rieties of limestones and sandstones, the macroscopic mechanism of chip formation exhibits a transition from brittle to ductile. In this paper, experimental consideration is given to successive or indexed penetrat ons by wedge-shaped bit teeth. Since pore pressure in a rock sample is maintained at atmospheric pressure, the differential pressure at the fluid-rock interface is equal to the confining pressure. The degrees of bit-tooth dullness include teeth with flat and round apexes (Fig. 1). Of primary concern in this paper are the bit-tooth forces required for chip formation, the macroscopic mechanism of chip formation and the minimum distance between successive penetrations, i.e., optimum indexing distance required for maximum rock damage, as functions of differential pressure. Of further interest is a comparison of actual bit-tooth chip formation forces at elevated differential pressures with calculated forces from previous theoretical results4 for indexed dull bit tooth penetration into a rigid-plastic rock. EXPERIMENTAL APPARATUS AND PROCEDURE The experimental apparatus consists of a pressure vessel equipped with a piston through the side of the vessel (Fig. 2). A single bit tooth inserted in the lower end of the piston is forced at a desired rate into the rock when the ram pressure chamber is pressurized. Electrical instrumentation incorporated into the apparatus yields a graphical plot of force on the piston as a function of bit-tooth penetration or displacement into the rock. Since the piston and ram assembly are in force equilibrium for a constant confining pressure in the main vessel, the fluid volume in the vessel remains constant during bit-tooth penetration. Hence, the force resisting penetration of the tooth is independent of the force exerted on either end of the as-

By G. J. Wilson

Difficulties experienced in correlating vertical and lateral locations of subsurface features that are encountered in directional wells prompted critical review of the tangential method of computing directional surveys. Inherent discrepancies were indicated to cause small incremental but significantly large cumulative errors in computed vertical depth and horizontal departure. A radius of curvature method, developed for planning and analyzing directional wells, was studied as a means of more accurately calculating survey data. Errors incurred in the tangential method were not present in the radius of curvature method. Conflicting assumptions in calculating dog-leg severity by the tangential method were resolved by a new procedure that was derived from the radius of curvature method. Results of the investigation showed the radius of curvature method to be an improved method for computing directional surveys. Introduction Many improvements in directional drilling tools and techniques have been made in the past 10 years,' but the method of computing survey data has remained virtually unchanged. While use of computers greatly aids the process of calculation' and eliminates many human errors, manual and computer calculations are still made with the assumption that the wellbore consists of straight-line segments. This paper points out discrepancies in the method and presents an improved method in which the wellbore is assumed to be curved. Tangential Method The method presently used to calculate vertical depth, horizontal departure and direction coordinates with measured values of well depth, inclination angle and direction angle is termed the tangential method. This term stems from performing calculations with a series of straight-line segments, with each segment assumed to be tangent to the wellbore at a corresponding survey point. A segment is defined by inclination and direction angles measured at only the lower or deeper end. Consequently, a discrepancy or error is introduced for each segment. Errors are not of extreme magnitude, but cumulatively are significant due to the need to define as accurately as possible the vertical and lateral location of subsurface features such as pay tops, fluid contacts and fault cuts encountered in expensive directional well bores. In Fig. 1, the curved-line segment ab represents a portion of the actual borehole as viewed in the vertical plane. Points a and b are survey stations and +, is the inclination angle at point b. The curved-line segment ab is assumed to be the straight-line segment arb of a length equal to ab and tangent at point b to the curved-line segment. Lengths a'c' and c'b are equal to a'b cos +, and a'b sin +,, respectively. Point a already has been fixed by calcillations performed with survey data obtained at point a, and calculated lengths m'c' and c'b are projected as lengths from point a, rather than from point a'. Point b1 is thus fixed and assumed to represent the actual point b. Calculated length ac" is shorter than actual length ac, and calculated length c"bl is longer than actual length cb. Since b1 is the point from which the next deeper segment will be projected, errors are cumulative. Cumulative error continues to increase as long as the inclination angle continues to increase. When the inclination angle decreases (Fig. 2), calculated length ac" is longer than actual length ac, and calculated length c"bl is shorter than actual length cb. These errors also are cumulative, but differences between calculated and actual lengths are opposite in mathematical sign to differences demonstrated in

Jan 1, 1969

By D. S. Rowley, F. C. Appl

Assuming that rock behavior, during cutting with a single diamond, may be approximated by that of a rigid, Coulomb, plastic material, a theory of single diamond cutting action has been developed. Using this theory, the stresses on the diamond cutting surface and the components of the cutting force have been determined. Theoretical results agree reasonably well with available experimental data. The theory of cutting of single diamonds may be used as the basis for subsequent study of the perfonnance of surface set diamond drill bits and other surface set diamond cutting tools. INTRODUCTION For more than twenty years, surface set diamond bits have been used successfully in the mining and petroleum industries to drill and core rock formations that range from medium hard to the hardest known formations. Most extremely hard rock formations cannot be economically drilled or cored by any other means. In view of the growing use and importance of surface set diamond drill bits, it is reasonable to study the way in which these tools cut, and the factors that influence wear of the diamonds. Such knowledge will contribute to better bit design and will improve operating procedures. To analyze the cutting performance of these tools it is appropriate to consider the way in which an individual diamond cuts. Once this is established, the over-all performance of the bits can be determined by considering the total effect of the individual diamonds. In recent years there has been a growing interest in rock mechanics and there now exist several publications dealing with the deformation and failure of rocks. Notable experimental work has been reported by Bredthauer,1 Handin and Hager,2, 3 and Gnirk and Cheatham.4 An extensive collection of data pertaining to rock properties at low confining pressures has been given by Wuerker.5 Cheatham and Gnirk have recently presented an excellent review of the state of knowledge regarding analytical and experimental rock deformation and failure.6 Generally rocks are extremely weak in uniaxial tension, and weak or only moderately strong in uniaxial compression. Both tensile failure and compressive failure are generally brittle in nature. This means that there is little or no deformation or "flow" of the material before shear or tensile fracture occurs. Thus, until fracture occurs, rock behaves very nearly like an elastic material in uniaxial stress. Significant changes in behavior of rock occur under conditions of triaxial compressive stress. There is generally a marked increase in compressive strength and in ductility. It has been demonstrated that the failure becomes plastic (in a macroscopic sense) at sufficiently high values of confining pressure. Sharp wedge chisel indentation studies conducted by Gnirk and Cheatham indicate that many rocks behave in a plastic manner at relatively low triaxial compressive stress states.4 If "failure" under triaxial compressive conditions is considered to be either complete rupture or macroscopic plastic flow, then the general failure characteristics of a rock can be reasonably well represented by the commonly known Mohr envelope. This certainly is not a perfect failure criterion (since the effect of the intermediate principal stress is neglected) but it has been found to be adequate for most engineering purposes. Mohr envelopes usually are constructed graphically using experimental triaxial test data. For purposes of analysis it is convenient to represent the envelope in equation form. Among the several approximate forms appearing in the literature, a parabolic form is suggested by Cheatham,7 and an exponential form is suggested by Paone and Tandanand.8 The exponential form has been adopted for this study, and based on published data, appropriate parameters have been established for 19 rock types. A typical plot of the data compared with the approximate envelope, and a summary of the rock properties and

Jan 1, 1969

By C. Dalton, H. L. McGill

The purpose of this study was to develop a method for predicting the time delay created by metering a fluid through an annular restriction with translational motion of the boundaries. This time delay is utilized to control the opening of valves in various down-hole oilfield tools and forms the basis for the "hydraulic jar". The hydraulic jar is used to give upward impact forces to tubing or other tools that become lodged down-hole. The design of these jars has primarily been by trial and error; varying the clearances, fluid viscosities and dimensions of the jar until a satisfactory time delay was achieved. Obviously, a better understanding of the fluid flow characteristics is required to produce designs that are satisfactory and to eliminate the trial-and-error approach. Previous studies of flow in annular spaces were based on constant length of the annular restriction. Any motion of the boundaries of the annular space was confined to a rotational motion, like that encountered in journal bearing design. Consideration of the effect of translational motion of one boundary with respect to the other was necessary in applying this previous work to a time delay device. A prediction method was developed that takes into account this relative translational motion. Equations were developed to predict the relative velocity, the flow rate, and the time delay in a concentric annular space. The effect of eccentricity also was included. Experimental data were obtained and closely correlated with the prediction method. This correlation is presented graphically in terms of predicted and actual relative velocities for various annular clearances and pressure drops. This extension provides design equations which predict the performance of the hydraulic jar, thereby eliminating trial-and-error solutions and reducing the development time required for satisfactory designs. INTRODUCTION The design of down-hole oilfield tools which use hydraulic delay systems based on flow through annular orifices with relative motion of the boundaries is usually a trial-and-error process. The annular clearances, fluid viscosities and dimensions of the mechanisms were varied until satisfactory delay times were obtained. The development of these tools has been expensive, and a better understanding of the characteristics of annular flow with relative motion of the boundaries could result in superior and less expensive designs. The purpose of this investigation was to provide a method of predicting the performance of down-hole tools which use annular flow and, in particular, the performance of a down-hole tool known as the "hydraulic jar". The hydraulic jar is used to free pipe, packers and other tools that become lodged down-hole. The jar, located in the tubing string between the surface and the object which is stuck, releases the object though the repeated application of upward impact blows. The jar is basically a slip joint that is restrained in a collapsed condition until the desired tubing tension has been developed. The slip joint is then released and accelerates rapidly until it shoulders, delivering an impact blow or jar to the object. The delay obtained by metering the fluid through the annulus formed by the jar valve and housing provides the time delay necessary to stretch and apply tension to the tubing or pipe. Fig. 1A gives a schematic diagram of the hydraulic jar and brief details of its operation. The metering of the hydraulic jar begins when the tension force being applied to the jar by the pipe creates a pressure differential across the valve that is approximately equal to the force divided by the displacement area of the valve. This pressure differential induces flow through the annular restriction formed between the valve and housing. The valve moves with respect to the housing as the

Jan 1, 1969