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By Hassell E. Hunter

The Wyoming Mineral-Conoco Crownpoint Project represents the first time that big hole drilling has been exclusively used to develop totally a privately financed mine below a depth of 1000 feet. Three shafts, one ten feet in diameter and two six feet in diameter, were successfully drilled to depths of 2243', 2188' and 2188' respectively and cased with hydrostatic designed steel casing. The largest shaft is to be used to handle muck and water from station excavation and enlargement of the other two shafts. A reverse circulation system with potassium chloride base mud was used for drilling. The mud was cleaned by settling in steel lined tanks with assistance by cyclone type separators. Deviation was monitored by gyroscopic surveying at 30 foot intervals and did not exceed 16 inches off plumb. Casing was designed to withstand hydrostatic pressures with a 1.5 safety factor to the large shaft and 1.25 safety factor for the smaller shafts. All casing welds were x-ray tested prior to lowering the casing in the hole. Cementing the annular space completed the operation. The total time to mobilize, drill and move off the three shafts was 363 days. The drilling operation was completed ahead of schedule and under budget.

Jan 1, 1983

By Anil Bhandari

Using subsurface data collected at each drilled shaft location is an ideal approach for conducting drilled shaft design. However, conducting subsurface tests at each drilled shaft location and subsequently performing the drilled shaft design can be a daunting task for a noise barrier wall that is divided into six (6) sections and stretches for approximately four (4) miles. In addition, having individual drilled shaft designs complicates the construction process. Grouping the subsurface conditions into broad categories and performing the design for each of those categories is an attractive alternative to the design per boring approach. Currently there are no existing guidelines to aid a designer on grouping the subsurface conditions for the drilled shaft design for the noise barrier walls. Therefore, a method was developed based on the Standard Penetration Test (SPT) N values of the near surface soils to categorize the soil profiles into distinct categories. Since the soil engineering properties of the near surface soils are known to be critical for drilled shaft lateral capacity, these soils were emphasized in the methodology. This method was successfully implemented for the design of drilled shafts supporting the noise barrier walls along the I-20 in Columbia, SC. For this project, two distinct soil profiles, labeled as ?strong? and ?weak?, were used. An overview of the soil profile grouping methodology is presented as well as the vertical and lateral drilled shaft capacity analyses for this project for the two general soil profiles. The analyses indicated that the axial capacity governed the design in the ?weak? soil profile and the lateral capacity controlled the design in the ?strong? soil profile. However, this is not a generalization and whether the axial or the lateral capacity governs the design of drilled shaft depends on the soil profile and design loads. Nonetheless, our findings emphasize that both lateral and axial capacity should be checked for drilled shaft design even when the vertical load are minor.

Jan 1, 2011

By Riad Diab

In 2018 the Caisse de Dépôt et Placement du Québec (CDPQ) awarded a $6.3 billion (U.S. dollars) design-build contract to the Joint Venture (JV) team NouvLR for the design and construction of one of the largest automated transportation systems in the world, called the Réseau express métropolitain (REM). The REM project is a 67 km (41.6 mi) light rail system with 26 stations linking downtown, the airport and the greater Montreal area in Canada. Out of the 67 km (41.6 mi) network, over 25 km (15.5 mi) is being constructed on a 650- span elevated structure founded on single drilled shafts socketed into rock. Optimizing the design of the drilled shafts was one of the main objectives of the geotechnical team, as it would likely result in shorter shafts that help significantly reduce the project costs. As part of the optimization process, three static axial load tests and two fully instrumented lateral load tests were performed, during the preliminary design phase, on sacrificial shafts to simulate the ultimate load level and validate construction procedures.

May 1, 2022

By Abu B. Siddique, Anthony S. Crincoli

"The New Jersey Turnpike Section 2 widening program consisted of widening between Interchange 6 in Mansfield Township, Burlington County and Interchange 9 in East Brunswick Township, Middlesex County. To accommodate large volume of traffic the roadway was widened from 6 to 12 lanes with major modifications performed at four interchanges. The Section 2, NJTA Interchange 6 to 9 Widening Program is a 4.2-mile section of Turnpike roadway which included a total of 12 new or modified structures. In order to facilitate the construction process Section 2 was divided into three construction contract packages. This paper will cover the last and final Contract T869.120.203 which is 1.7 miles in length. The work generally consisted of eight new ramps connection to and from the toll plaza to the new inner and outer roadways. New mainline bridges were constructed over several ramps. A new bridge was constructed to take northbound outer lanes traffic over two ramps along with new mainline bridges over Black’s Creek, Georgetown Road, and Laurel Run. In addition, a new bridge was constructed to take a ramp over Laurel Run and the existing U-turn Bridge was replaced with a new one.For Contract T869.120.203 a total of 74 five-foot diameter drilled shafts has been constructed to support all pier foundations for bridges. Three drilled shafts were tested using Osterberg Load Cells to verify the estimated shaft resistance during design phase. One Osterberg Load Cell test was performed on a demonstration (sacrificial) shaft and the other two Osterberg Load Cell tests were performed on production shafts. This paper compares the estimated total, side and tip resistances with corresponding measured total, side and tip resistances and provided recommendations for future design purpose.INTRODUCTIONTo accommodate large volume of traffic the New Jersey Turnpike Authority (NJTA) decided to widen Section 2, which included Interchange 6 through Interchange 9. The Section 2, a 4.2-mile section of Turnpike roadway that was widened from 6 to 12 lanes with major modifications performed at four interchanges.The New Jersey Turnpike Authority (NJTA) procured AECOM to perform engineering services for the final design of Section 2, NJTA Interchange 6 to 9 Widening Program. Section 2 is a 4.2-mile section of Turnpike roadway that will widen from 6 to 12 lanes and will include a total of 12 new or modified structures. It encompasses modifications of the existing and the design of four new ramps at Interchange 7. The project also includes the modification of two local roads over the mainline, two local roads under the mainline, two maintenance U-turns, and retaining walls. In addition, the project consists of the design of noise walls, sign structures, storm water management basins and the more typical drainage, utilities, lighting, roadway, ROW, and signing and striping design."

Jan 1, 2015

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-